premise
stringlengths 17
1.29k
| hypothesis
stringlengths 17
138
| label
stringclasses 3
values | proof
stringlengths 1
184k
| premise_tptp
stringlengths 61
1.7k
| hypothesis_tptp
stringlengths 55
400
| deberta_pred
stringclasses 3
values | deberta_pred_r1_label
stringclasses 3
values | deberta_pred_r2_label
stringclasses 3
values |
|---|---|---|---|---|---|---|---|---|
Charles, Evelyn, Karen are the only persons in the room.
'No one in the room who is not tall is not creative' if 'no one in the room who is quieter than Boyd does not like Jason'.
'Charles who does not own an Android phone, is not hated by Boyd' if 'Frank and Boyd like each other' and vice versa.
'Evelyn and Boyd hate each other' if 'Karen is the least tall in the room' and vice versa.
Charles is the tallest in the room.
Someone outside the room is hated by Boyd.
Evelyn is not quiet and likes Frank.
Evelyn is the quietest in the room.
Charles who does not own an Android phone, is not hated by Boyd.
Evelyn who is taller than Frank, is not tall.
Only one person in the room is hated by Frank.
Charles and Frank like each other.
Charles does not write poetry or is taller than Boyd or both. | Someone who is not quiet like someone who is not hated by Frank. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(susan_type, type, (
susan: $i)).
tff(john_type, type, (
john: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(1,plain,
((alice = fred) <=> (fred = alice)),
inference(commutativity,[status(thm)],[])).
tff(2,plain,
((fred = paul) <=> (paul = fred)),
inference(commutativity,[status(thm)],[])).
tff(3,assumption,(paul = |'mary'|), introduced(assumption)).
tff(4,plain,
(|'mary'| = paul),
inference(symmetry,[status(thm)],[3])).
tff(5,plain,
((fred = |'mary'|) <=> (fred = paul)),
inference(monotonicity,[status(thm)],[4])).
tff(6,plain,
((fred = |'mary'|) <=> (paul = fred)),
inference(transitivity,[status(thm)],[5, 2])).
tff(7,plain,
((paul = fred) <=> (fred = |'mary'|)),
inference(symmetry,[status(thm)],[6])).
tff(8,plain,
((~(paul = fred)) <=> (~(fred = |'mary'|))),
inference(monotonicity,[status(thm)],[7])).
tff(9,plain,
((~(paul = fred)) <=> (~(paul = fred))),
inference(rewrite,[status(thm)],[])).
tff(10,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//2457032324651689182200903.p','b14')).
tff(11,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[10])).
tff(12,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[11])).
tff(13,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[13])).
tff(15,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[17])).
tff(19,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[42])).
tff(44,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[43])).
tff(45,plain,
(~(paul = fred)),
inference(and_elim,[status(thm)],[44])).
tff(46,plain,
(~(paul = fred)),
inference(modus_ponens,[status(thm)],[45, 9])).
tff(47,plain,
(~(fred = |'mary'|)),
inference(modus_ponens,[status(thm)],[46, 8])).
tff(48,plain,
((fred = mary) <=> (mary = fred)),
inference(commutativity,[status(thm)],[])).
tff(49,assumption,(~(mary = |'paul'|)), introduced(assumption)).
tff(50,plain,
(^[X: $i] : refl(quieter(X, paul) <=> quieter(X, paul))),
inference(bind,[status(th)],[])).
tff(51,plain,
(![X: $i] : quieter(X, paul) <=> ![X: $i] : quieter(X, paul)),
inference(quant_intro,[status(thm)],[50])).
tff(52,plain,
(![X: $i] : quieter(X, paul) <=> ![X: $i] : quieter(X, paul)),
inference(rewrite,[status(thm)],[])).
tff(53,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((((~?[X: $i] : (room(X) => (quieter(susan, X) => (~like(lucy, X))))) => (~?[X: $i] : (room(X) => ((~tall(X)) => (~creative(X)))))) & ((like(alice, susan) & like(susan, alice)) <=> ((~preda(mary)) & (~hate(mary, susan))))) & (![X: $i] : taller(fred, X) <=> (hate(paul, susan) & hate(susan, paul)))) & ![X: $i] : taller(X, mary)) & ?[X: $i] : ((~room(X)) => hate(X, susan))) & ((~quiet(paul)) & like(alice, paul))) & ![X: $i] : quieter(X, paul)) & ((~preda(mary)) & (~hate(mary, susan)))) & (taller(alice, paul) & (~tall(paul)))) & (?[X: $i] : (room(X) & hate(X, alice)) & ![X: $i, Y: $i] : ((hate(X, alice) & hate(Y, alice)) => (X = Y)))) & (like(mary, alice) & like(alice, mary))) & ((~predb(mary)) | taller(susan, mary)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((~quiet(X)) & (~hate(Y, alice))) & like(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i] : ((~like(lucy, X)) | (~room(X)) | (~quieter(susan, X))) | (~?[X: $i] : (tall(X) | (~creative(X)) | (~room(X))))) & ((like(alice, susan) & like(susan, alice)) <=> ((~preda(mary)) & (~hate(mary, susan)))) & (![X: $i] : taller(fred, X) <=> (hate(paul, susan) & hate(susan, paul))) & ![X: $i] : taller(X, mary) & ?[X: $i] : (room(X) | hate(X, susan)) & (~quiet(paul)) & like(alice, paul) & ![X: $i] : quieter(X, paul) & (~preda(mary)) & (~hate(mary, susan)) & taller(alice, paul) & (~tall(paul)) & ?[X: $i] : (room(X) & hate(X, alice)) & ![X: $i, Y: $i] : ((~(hate(X, alice) & hate(Y, alice))) | (X = Y)) & like(mary, alice) & like(alice, mary) & ((~predb(mary)) | taller(susan, mary)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(54,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((((~?[X: $i] : (room(X) => (quieter(susan, X) => (~like(lucy, X))))) => (~?[X: $i] : (room(X) => ((~tall(X)) => (~creative(X)))))) & ((like(alice, susan) & like(susan, alice)) <=> ((~preda(mary)) & (~hate(mary, susan))))) & (![X: $i] : taller(fred, X) <=> (hate(paul, susan) & hate(susan, paul)))) & ![X: $i] : taller(X, mary)) & ?[X: $i] : ((~room(X)) => hate(X, susan))) & ((~quiet(paul)) & like(alice, paul))) & ![X: $i] : quieter(X, paul)) & ((~preda(mary)) & (~hate(mary, susan)))) & (taller(alice, paul) & (~tall(paul)))) & (?[X: $i] : (room(X) & hate(X, alice)) & ![X: $i, Y: $i] : ((hate(X, alice) & hate(Y, alice)) => (X = Y)))) & (like(mary, alice) & like(alice, mary))) & ((~predb(mary)) | taller(susan, mary)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((~quiet(X)) & (~hate(Y, alice))) & like(X, Y))))), file('/mnt/tmpfs//2457032324651689182200903.p','negated')).
tff(55,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i] : ((~like(lucy, X)) | (~room(X)) | (~quieter(susan, X))) | (~?[X: $i] : (tall(X) | (~creative(X)) | (~room(X))))) & ((like(alice, susan) & like(susan, alice)) <=> ((~preda(mary)) & (~hate(mary, susan)))) & (![X: $i] : taller(fred, X) <=> (hate(paul, susan) & hate(susan, paul))) & ![X: $i] : taller(X, mary) & ?[X: $i] : (room(X) | hate(X, susan)) & (~quiet(paul)) & like(alice, paul) & ![X: $i] : quieter(X, paul) & (~preda(mary)) & (~hate(mary, susan)) & taller(alice, paul) & (~tall(paul)) & ?[X: $i] : (room(X) & hate(X, alice)) & ![X: $i, Y: $i] : ((~(hate(X, alice) & hate(Y, alice))) | (X = Y)) & like(mary, alice) & like(alice, mary) & ((~predb(mary)) | taller(susan, mary)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))))),
inference(modus_ponens,[status(thm)],[54, 53])).
tff(56,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i] : ((~like(lucy, X)) | (~room(X)) | (~quieter(susan, X))) | (~?[X: $i] : (tall(X) | (~creative(X)) | (~room(X))))) & ((like(alice, susan) & like(susan, alice)) <=> ((~preda(mary)) & (~hate(mary, susan)))) & (![X: $i] : taller(fred, X) <=> (hate(paul, susan) & hate(susan, paul))) & ![X: $i] : taller(X, mary) & ?[X: $i] : (room(X) | hate(X, susan)) & (~quiet(paul)) & like(alice, paul) & ![X: $i] : quieter(X, paul) & (~preda(mary)) & (~hate(mary, susan)) & taller(alice, paul) & (~tall(paul)) & ?[X: $i] : (room(X) & hate(X, alice)) & ![X: $i, Y: $i] : ((~(hate(X, alice) & hate(Y, alice))) | (X = Y)) & like(mary, alice) & like(alice, mary) & ((~predb(mary)) | taller(susan, mary))),
inference(or_elim,[status(thm)],[55])).
tff(57,plain,
(![X: $i] : quieter(X, paul)),
inference(and_elim,[status(thm)],[56])).
tff(58,plain,
(![X: $i] : quieter(X, paul)),
inference(modus_ponens,[status(thm)],[57, 52])).
tff(59,plain,(
![X: $i] : quieter(X, paul)),
inference(skolemize,[status(sab)],[58])).
tff(60,plain,
(![X: $i] : quieter(X, paul)),
inference(modus_ponens,[status(thm)],[59, 51])).
tff(61,plain,
((~![X: $i] : quieter(X, paul)) | quieter(mary, paul)),
inference(quant_inst,[status(thm)],[])).
tff(62,plain,
(quieter(mary, paul)),
inference(unit_resolution,[status(thm)],[61, 60])).
tff(63,plain,
((~quiet(paul)) <=> (~quiet(paul))),
inference(rewrite,[status(thm)],[])).
tff(64,plain,
(~quiet(paul)),
inference(and_elim,[status(thm)],[56])).
tff(65,plain,
(~quiet(paul)),
inference(modus_ponens,[status(thm)],[64, 63])).
tff(66,plain,
((~(mary = paul)) <=> (~(mary = paul))),
inference(rewrite,[status(thm)],[])).
tff(67,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[44])).
tff(68,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[67])).
tff(69,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[68])).
tff(70,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[69])).
tff(71,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[70])).
tff(72,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[71])).
tff(73,plain,
(~(mary = paul)),
inference(and_elim,[status(thm)],[72])).
tff(74,plain,
(~(mary = paul)),
inference(modus_ponens,[status(thm)],[73, 66])).
tff(75,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y))) <=> ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y))))),
inference(bind,[status(th)],[])).
tff(76,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))),
inference(quant_intro,[status(thm)],[75])).
tff(77,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((quieter(X, Y) & quiet(X)) <=> (~((~quiet(X)) | (~quieter(X, Y))))), ((~(quieter(X, Y) & quiet(X))) <=> (~(~((~quiet(X)) | (~quieter(X, Y))))))), rewrite((~(~((~quiet(X)) | (~quieter(X, Y))))) <=> ((~quiet(X)) | (~quieter(X, Y)))), ((~(quieter(X, Y) & quiet(X))) <=> ((~quiet(X)) | (~quieter(X, Y))))), (((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) | quiet(Y) | ((~quiet(X)) | (~quieter(X, Y)))))), rewrite(((X = Y) | quiet(Y) | ((~quiet(X)) | (~quieter(X, Y)))) <=> ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))), (((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))))),
inference(bind,[status(th)],[])).
tff(78,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))),
inference(quant_intro,[status(thm)],[77])).
tff(79,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(rewrite,[status(thm)],[])).
tff(80,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((quieter(X, Y) & quiet(X)) => quiet(Y)) <=> (quiet(Y) | (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((~(X = Y)) => (quiet(Y) | (~(quieter(X, Y) & quiet(X))))))), rewrite(((~(X = Y)) => (quiet(Y) | (~(quieter(X, Y) & quiet(X))))) <=> ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))))),
inference(bind,[status(th)],[])).
tff(81,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(quant_intro,[status(thm)],[80])).
tff(82,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y)))), file('/mnt/tmpfs//2457032324651689182200903.p','b12')).
tff(83,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(modus_ponens,[status(thm)],[82, 81])).
tff(84,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(modus_ponens,[status(thm)],[83, 79])).
tff(85,plain,(
![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(skolemize,[status(sab)],[84])).
tff(86,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))),
inference(modus_ponens,[status(thm)],[85, 78])).
tff(87,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))),
inference(modus_ponens,[status(thm)],[86, 76])).
tff(88,plain,
(((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))) | ((mary = paul) | quiet(paul) | (~quiet(mary)) | (~quieter(mary, paul)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))) | (mary = paul) | quiet(paul) | (~quiet(mary)) | (~quieter(mary, paul)))),
inference(rewrite,[status(thm)],[])).
tff(89,plain,
((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))) | ((mary = paul) | quiet(paul) | (~quiet(mary)) | (~quieter(mary, paul)))),
inference(quant_inst,[status(thm)],[])).
tff(90,plain,
((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quiet(X)) | (~quieter(X, Y)))) | (mary = paul) | quiet(paul) | (~quiet(mary)) | (~quieter(mary, paul))),
inference(modus_ponens,[status(thm)],[89, 88])).
tff(91,plain,
(~quiet(mary)),
inference(unit_resolution,[status(thm)],[90, 87, 74, 65, 62])).
tff(92,assumption,(~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), introduced(assumption)).
tff(93,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | room(X!4)),
inference(tautology,[status(thm)],[])).
tff(94,plain,
(room(X!4)),
inference(unit_resolution,[status(thm)],[93, 92])).
tff(95,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(96,plain,
(~(X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[95, 92])).
tff(97,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(98,plain,
(~(X!4 = |'paul'|)),
inference(unit_resolution,[status(thm)],[97, 92])).
tff(99,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(100,plain,
(~(X!4 = |'fred'|)),
inference(unit_resolution,[status(thm)],[99, 92])).
tff(101,plain,
(^[X: $i] : refl(((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(102,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[101])).
tff(103,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(104,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[56])).
tff(105,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[104, 103])).
tff(106,plain,(
![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[105])).
tff(107,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[106, 102])).
tff(108,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(rewrite,[status(thm)],[])).
tff(109,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(quant_inst,[status(thm)],[])).
tff(110,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))),
inference(modus_ponens,[status(thm)],[109, 108])).
tff(111,plain,
($false),
inference(unit_resolution,[status(thm)],[110, 107, 100, 98, 96, 94])).
tff(112,plain,((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(lemma,lemma(discharge,[]))).
tff(113,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(114,plain,
(room(fred)),
inference(and_elim,[status(thm)],[56])).
tff(115,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[114, 113])).
tff(116,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(117,plain,
(room(paul)),
inference(and_elim,[status(thm)],[56])).
tff(118,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[117, 116])).
tff(119,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(120,plain,
(room(mary)),
inference(and_elim,[status(thm)],[56])).
tff(121,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[120, 119])).
tff(122,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | quiet(X) | hate(Y, alice))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | quiet(X) | hate(Y, alice)))),
inference(rewrite,[status(thm)],[])).
tff(123,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | quiet(X) | hate(Y, alice))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | quiet(X) | hate(Y, alice)))),
inference(rewrite,[status(thm)],[])).
tff(124,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)) <=> (~((~like(X, Y)) | quiet(X) | hate(Y, alice)))), ((~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))) <=> (~(~((~like(X, Y)) | quiet(X) | hate(Y, alice)))))), rewrite((~(~((~like(X, Y)) | quiet(X) | hate(Y, alice)))) <=> ((~like(X, Y)) | quiet(X) | hate(Y, alice))), ((~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))) <=> ((~like(X, Y)) | quiet(X) | hate(Y, alice))))),
inference(bind,[status(th)],[])).
tff(125,plain,
(![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))) <=> ![X: $i, Y: $i] : ((~like(X, Y)) | quiet(X) | hate(Y, alice))),
inference(quant_intro,[status(thm)],[124])).
tff(126,plain,
((~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(127,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | quiet(X) | hate(Y, alice)))),
inference(monotonicity,[status(thm)],[126, 125])).
tff(128,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | quiet(X) | hate(Y, alice)))),
inference(transitivity,[status(thm)],[127, 123])).
tff(129,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(130,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))))),
inference(monotonicity,[status(thm)],[126])).
tff(131,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))))),
inference(transitivity,[status(thm)],[130, 129])).
tff(132,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(133,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))))),
inference(monotonicity,[status(thm)],[132])).
tff(134,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(135,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))),
inference(or_elim,[status(thm)],[55])).
tff(136,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))),
inference(modus_ponens,[status(thm)],[135, 133])).
tff(137,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))),
inference(modus_ponens,[status(thm)],[136, 134])).
tff(138,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~quiet(X)) & (~hate(Y, alice)) & like(X, Y)))),
inference(modus_ponens,[status(thm)],[137, 133])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|)
(not (room X!4)))))
(a!6 (lambda ((X $i) (Y $i))
(let ((a!1 (and (not (quiet X)) (not (hate Y alice)) (like X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!7 (exists ((X $i) (Y $i))
(and (not (quiet X)) (not (hate Y alice)) (like X Y))))
(a!8 (forall ((X $i) (Y $i))
(let ((a!1 (and (not (quiet X)) (not (hate Y alice)) (like X Y))))
(not a!1)))))
(let ((a!9 (~ (not (and (room mary) (room paul) (room fred) a!4 a!7))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!8))))
(nnf-neg a!1
a!2
a!3
(sk (~ (not a!4) a!5))
(nnf-neg (proof-bind a!6) (~ (not a!7) a!8))
a!9)))
| room(charles)&room(evelyn)&room(karen)&(![X]:(room(X)=>(X='charles'|X='evelyn'|X='karen')))&
(((~?[X]:(room(X)=>(((quieter(boyd,X))=>(~like(jason,X))))))=>(~?[X]:(room(X)=>(((~tall(X))=>(~creative(X)))))))&
(((like(frank,boyd) & like(boyd,frank)))<=>((does_not_own_an_Android_phone(charles))&(~hate(charles,boyd))))&
((![X]:(taller(karen,X)))<=>((hate(evelyn,boyd) & hate(boyd,evelyn))))&
(![X]:(taller(X,charles)))&
(?[X]:(~room(X)=>(hate(X,boyd))))&
((~quiet(evelyn))&(like(frank,evelyn)))&
(![X]:(quieter(X,evelyn)))&
((does_not_own_an_Android_phone(charles))&(~hate(charles,boyd)))&
((taller(frank,evelyn))&(~tall(evelyn)))&
(((?[X]:(room(X)&hate(X,frank)))&(![X,Y]:((hate(X,frank)&hate(Y,frank))=>(X=Y)))))&
((like(charles,frank) & like(frank,charles)))&
(((does_not_write_poetry(charles))|(taller(boyd,charles))))) | room(charles)&room(evelyn)&room(karen)&(![X]:(room(X)=>(X='charles'|X='evelyn'|X='karen')))&
(?[X,Y]:((~quiet(X))&(~hate(Y,frank))&(like(X,Y)))) | neutral | neutral | entailment |
Janice, George are the only persons in the room. More than one person in the room is liked by Hector. | George is liked by Hector or likes Hector or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(tptp_fun_Y_0_type, type, (
tptp_fun_Y_0: $i)).
tff(mary_type, type, (
mary: $i)).
tff(1,assumption,(~like(paul, fred)), introduced(assumption)).
tff(2,assumption,(Y!0 = |'paul'|), introduced(assumption)).
tff(3,plain,
((X!1 = Y!0) <=> (X!1 = |'paul'|)),
inference(monotonicity,[status(thm)],[2])).
tff(4,plain,
((~(X!1 = Y!0)) <=> (~(X!1 = |'paul'|))),
inference(monotonicity,[status(thm)],[3])).
tff(5,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & like(X, fred) & like(Y, fred) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & like(X, fred) & like(Y, fred) & (~(X = Y)))),
inference(rewrite,[status(thm)],[])).
tff(6,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (like(X, fred) & like(Y, fred))) & (~(X = Y)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(paul, fred) | like(fred, paul))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & like(X, fred) & like(Y, fred) & (~(X = Y))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))))),
inference(rewrite,[status(thm)],[])).
tff(7,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (like(X, fred) & like(Y, fred))) & (~(X = Y)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(paul, fred) | like(fred, paul))))), file('/mnt/tmpfs//2890118946716251639587817.p','negated')).
tff(8,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & like(X, fred) & like(Y, fred) & (~(X = Y))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred))))),
inference(modus_ponens,[status(thm)],[7, 6])).
tff(9,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & like(X, fred) & like(Y, fred) & (~(X = Y)))),
inference(or_elim,[status(thm)],[8])).
tff(10,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & like(X, fred) & like(Y, fred) & (~(X = Y)))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & like(X, fred) & like(Y, fred) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[10, 5])).
tff(12,plain,(
room(X!1) & room(Y!0) & like(X!1, fred) & like(Y!0, fred) & (~(X!1 = Y!0))),
inference(skolemize,[status(sab)],[11])).
tff(13,plain,
(~(X!1 = Y!0)),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
(~(X!1 = |'paul'|)),
inference(modus_ponens,[status(thm)],[13, 4])).
tff(15,plain,
(room(X!1)),
inference(and_elim,[status(thm)],[12])).
tff(16,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(17,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[16])).
tff(18,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[9])).
tff(20,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[20])).
tff(22,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[21, 17])).
tff(23,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(quant_inst,[status(thm)],[])).
tff(25,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))),
inference(modus_ponens,[status(thm)],[24, 23])).
tff(26,plain,
((X!1 = |'paul'|) | (X!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[25, 22, 15])).
tff(27,plain,
(X!1 = |'mary'|),
inference(unit_resolution,[status(thm)],[26, 14])).
tff(28,plain,
(|'mary'| = X!1),
inference(symmetry,[status(thm)],[27])).
tff(29,plain,
(|'paul'| = Y!0),
inference(symmetry,[status(thm)],[2])).
tff(30,assumption,(paul = |'paul'|), introduced(assumption)).
tff(31,plain,
(paul = Y!0),
inference(transitivity,[status(thm)],[30, 29])).
tff(32,plain,
(like(paul, fred) <=> like(Y!0, fred)),
inference(monotonicity,[status(thm)],[31])).
tff(33,plain,
(like(Y!0, fred) <=> like(paul, fred)),
inference(symmetry,[status(thm)],[32])).
tff(34,plain,
(like(Y!0, fred)),
inference(and_elim,[status(thm)],[12])).
tff(35,plain,
(like(paul, fred)),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
($false),
inference(unit_resolution,[status(thm)],[1, 35])).
tff(37,plain,((~(paul = |'paul'|)) | like(paul, fred) | (~(Y!0 = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(38,plain,
(~(paul = |'paul'|)),
inference(unit_resolution,[status(thm)],[37, 2, 1])).
tff(39,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
(room(paul)),
inference(and_elim,[status(thm)],[9])).
tff(41,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[40, 39])).
tff(42,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
(((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul))) <=> ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)))),
inference(monotonicity,[status(thm)],[43])).
tff(45,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(transitivity,[status(thm)],[44, 42])).
tff(46,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))),
inference(quant_inst,[status(thm)],[])).
tff(47,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[46, 45])).
tff(48,plain,
((paul = |'paul'|) | (paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[47, 41, 22])).
tff(49,plain,
(paul = |'mary'|),
inference(unit_resolution,[status(thm)],[48, 38])).
tff(50,plain,
(paul = X!1),
inference(transitivity,[status(thm)],[49, 28])).
tff(51,plain,
(like(paul, fred) <=> like(X!1, fred)),
inference(monotonicity,[status(thm)],[50])).
tff(52,plain,
(like(X!1, fred) <=> like(paul, fred)),
inference(symmetry,[status(thm)],[51])).
tff(53,plain,
(like(X!1, fred)),
inference(and_elim,[status(thm)],[12])).
tff(54,plain,
(like(paul, fred)),
inference(modus_ponens,[status(thm)],[53, 52])).
tff(55,plain,
($false),
inference(unit_resolution,[status(thm)],[1, 54])).
tff(56,plain,((~(Y!0 = |'paul'|)) | like(paul, fred)), inference(lemma,lemma(discharge,[]))).
tff(57,plain,
(~(Y!0 = |'paul'|)),
inference(unit_resolution,[status(thm)],[56, 1])).
tff(58,plain,
(room(Y!0)),
inference(and_elim,[status(thm)],[12])).
tff(59,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0)))),
inference(rewrite,[status(thm)],[])).
tff(60,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0)))),
inference(quant_inst,[status(thm)],[])).
tff(61,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0))),
inference(modus_ponens,[status(thm)],[60, 59])).
tff(62,plain,
((Y!0 = |'paul'|) | (Y!0 = |'mary'|)),
inference(unit_resolution,[status(thm)],[61, 22, 58])).
tff(63,plain,
(Y!0 = |'mary'|),
inference(unit_resolution,[status(thm)],[62, 57])).
tff(64,plain,
((X!1 = Y!0) <=> (X!1 = |'mary'|)),
inference(monotonicity,[status(thm)],[63])).
tff(65,plain,
((~(X!1 = Y!0)) <=> (~(X!1 = |'mary'|))),
inference(monotonicity,[status(thm)],[64])).
tff(66,plain,
(~(X!1 = |'mary'|)),
inference(modus_ponens,[status(thm)],[13, 65])).
tff(67,plain,
(X!1 = |'paul'|),
inference(unit_resolution,[status(thm)],[26, 66])).
tff(68,plain,
(|'paul'| = X!1),
inference(symmetry,[status(thm)],[67])).
tff(69,plain,
(|'mary'| = Y!0),
inference(symmetry,[status(thm)],[63])).
tff(70,assumption,(paul = |'mary'|), introduced(assumption)).
tff(71,plain,
(paul = Y!0),
inference(transitivity,[status(thm)],[70, 69])).
tff(72,plain,
(like(paul, fred) <=> like(Y!0, fred)),
inference(monotonicity,[status(thm)],[71])).
tff(73,plain,
(like(Y!0, fred) <=> like(paul, fred)),
inference(symmetry,[status(thm)],[72])).
tff(74,plain,
(like(paul, fred)),
inference(modus_ponens,[status(thm)],[34, 73])).
tff(75,plain,
($false),
inference(unit_resolution,[status(thm)],[1, 74])).
tff(76,plain,((~(paul = |'mary'|)) | like(paul, fred)), inference(lemma,lemma(discharge,[]))).
tff(77,plain,
(~(paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[76, 1])).
tff(78,plain,
(paul = |'paul'|),
inference(unit_resolution,[status(thm)],[48, 77])).
tff(79,plain,
(paul = X!1),
inference(transitivity,[status(thm)],[78, 68])).
tff(80,plain,
(like(paul, fred) <=> like(X!1, fred)),
inference(monotonicity,[status(thm)],[79])).
tff(81,plain,
(like(X!1, fred) <=> like(paul, fred)),
inference(symmetry,[status(thm)],[80])).
tff(82,plain,
(like(paul, fred)),
inference(modus_ponens,[status(thm)],[53, 81])).
tff(83,plain,
($false),
inference(unit_resolution,[status(thm)],[1, 82])).
tff(84,plain,(like(paul, fred)), inference(lemma,lemma(discharge,[]))).
tff(85,plain,
((like(fred, paul) | like(paul, fred)) | (~like(paul, fred))),
inference(tautology,[status(thm)],[])).
tff(86,plain,
(like(fred, paul) | like(paul, fred)),
inference(unit_resolution,[status(thm)],[85, 84])).
tff(87,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(88,plain,
(room(mary)),
inference(and_elim,[status(thm)],[9])).
tff(89,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[88, 87])).
tff(90,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(like(fred, paul) | like(paul, fred)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(like(fred, paul) | like(paul, fred))))),
inference(rewrite,[status(thm)],[])).
tff(91,plain,
((~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))),
inference(rewrite,[status(thm)],[])).
tff(92,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(like(fred, paul) | like(paul, fred)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(like(fred, paul) | like(paul, fred))))),
inference(monotonicity,[status(thm)],[91])).
tff(93,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(like(fred, paul) | like(paul, fred)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(like(fred, paul) | like(paul, fred))))),
inference(transitivity,[status(thm)],[92, 90])).
tff(94,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))),
inference(rewrite,[status(thm)],[])).
tff(95,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred))))),
inference(monotonicity,[status(thm)],[94])).
tff(96,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred))))),
inference(rewrite,[status(thm)],[])).
tff(97,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))),
inference(or_elim,[status(thm)],[8])).
tff(98,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))),
inference(modus_ponens,[status(thm)],[97, 95])).
tff(99,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))),
inference(modus_ponens,[status(thm)],[98, 96])).
tff(100,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(fred, paul) | like(paul, fred)))),
inference(modus_ponens,[status(thm)],[99, 95])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!2 |'paul'|) (= X!2 |'mary'|) (not (room X!2)))))
(a!5 (~ (not (or (like fred paul) (like paul fred)))
(not (or (like fred paul) (like paul fred))))))
(let ((a!6 (not (and (room mary)
(room paul)
a!3
(or (like fred paul) (like paul fred)))))
(a!7 (or (not (room mary))
(not (room paul))
a!4
(not (or (like fred paul) (like paul fred))))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl a!5) (~ a!6 a!7))))
| room(janice)&room(george)&(![X]:(room(X)=>(X='janice'|X='george')))&
((?[X,Y]:(room(X)&room(Y)&(like(X,hector)&like(Y,hector))&(X!=Y)))) | room(janice)&room(george)&(![X]:(room(X)=>(X='janice'|X='george')))&
(((like(george,hector))|(like(hector,george)))) | entailment | entailment | entailment |
Doris, Todd, Milton, Velma are the only persons in the room.
Everyone outside the room who is a happy european is not happy, not rich, not quiet if everyone outside the room reads mystery novels.
If Velma is the least rich in the room then it is not the case that 'no one outside the room who is quieter than David is not happy'.
Milton and David hate each other.
Velma neither is not happy nor is not hated by Marie.
Milton is not a rich quiet happy tourist.
Milton who reads mystery novels, is a quiet european.
Only one person outside the room is a quiet tourist. | More than one person outside the room is not a rich happy quiet creative tourist. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(john_type, type, (
john: $i)).
tff(mary_type, type, (
mary: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(alice_type, type, (
alice: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(rich_type, type, (
rich: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(susan_type, type, (
susan: $i)).
tff(paul_type, type, (
paul: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(1,plain,
((john = mary) <=> (mary = john)),
inference(commutativity,[status(thm)],[])).
tff(2,plain,
((lucy = mary) <=> (mary = lucy)),
inference(commutativity,[status(thm)],[])).
tff(3,assumption,(~room(john)), introduced(assumption)).
tff(4,plain,
((lucy = fred) <=> (fred = lucy)),
inference(commutativity,[status(thm)],[])).
tff(5,assumption,(~(mary = |'paul'|)), introduced(assumption)).
tff(6,plain,
((lucy = alice) <=> (alice = lucy)),
inference(commutativity,[status(thm)],[])).
tff(7,assumption,(~(alice = |'mary'|)), introduced(assumption)).
tff(8,plain,
((alice = mary) <=> (mary = alice)),
inference(commutativity,[status(thm)],[])).
tff(9,plain,
((susan = alice) <=> (alice = susan)),
inference(commutativity,[status(thm)],[])).
tff(10,plain,
((fred = mary) <=> (mary = fred)),
inference(commutativity,[status(thm)],[])).
tff(11,assumption,(mary = |'mary'|), introduced(assumption)).
tff(12,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[11])).
tff(13,plain,
((fred = |'mary'|) <=> (fred = mary)),
inference(monotonicity,[status(thm)],[12])).
tff(14,plain,
((fred = |'mary'|) <=> (mary = fred)),
inference(transitivity,[status(thm)],[13, 10])).
tff(15,plain,
((mary = fred) <=> (fred = |'mary'|)),
inference(symmetry,[status(thm)],[14])).
tff(16,plain,
((~(mary = fred)) <=> (~(fred = |'mary'|))),
inference(monotonicity,[status(thm)],[15])).
tff(17,plain,
((~(mary = fred)) <=> (~(mary = fred))),
inference(rewrite,[status(thm)],[])).
tff(18,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//5173815561958952539467234.p','b14')).
tff(19,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[42])).
tff(44,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[43])).
tff(45,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[44])).
tff(46,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[45])).
tff(47,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[46])).
tff(48,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[47])).
tff(49,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[48])).
tff(50,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[49])).
tff(51,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[50])).
tff(52,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[51])).
tff(53,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[53])).
tff(55,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[55])).
tff(57,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[56])).
tff(58,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[57])).
tff(59,plain,
(~(mary = fred)),
inference(and_elim,[status(thm)],[58])).
tff(60,plain,
(~(mary = fred)),
inference(modus_ponens,[status(thm)],[59, 17])).
tff(61,plain,
(~(fred = |'mary'|)),
inference(modus_ponens,[status(thm)],[60, 16])).
tff(62,plain,
((susan = mary) <=> (mary = susan)),
inference(commutativity,[status(thm)],[])).
tff(63,plain,
((susan = |'mary'|) <=> (susan = mary)),
inference(monotonicity,[status(thm)],[12])).
tff(64,plain,
((susan = |'mary'|) <=> (mary = susan)),
inference(transitivity,[status(thm)],[63, 62])).
tff(65,plain,
((mary = susan) <=> (susan = |'mary'|)),
inference(symmetry,[status(thm)],[64])).
tff(66,plain,
((~(mary = susan)) <=> (~(susan = |'mary'|))),
inference(monotonicity,[status(thm)],[65])).
tff(67,plain,
((~(mary = susan)) <=> (~(mary = susan))),
inference(rewrite,[status(thm)],[])).
tff(68,plain,
(~(mary = susan)),
inference(and_elim,[status(thm)],[55])).
tff(69,plain,
(~(mary = susan)),
inference(modus_ponens,[status(thm)],[68, 67])).
tff(70,plain,
(~(susan = |'mary'|)),
inference(modus_ponens,[status(thm)],[69, 66])).
tff(71,plain,
((lucy = |'mary'|) <=> (lucy = mary)),
inference(monotonicity,[status(thm)],[12])).
tff(72,plain,
((lucy = |'mary'|) <=> (mary = lucy)),
inference(transitivity,[status(thm)],[71, 2])).
tff(73,plain,
((mary = lucy) <=> (lucy = |'mary'|)),
inference(symmetry,[status(thm)],[72])).
tff(74,plain,
((~(mary = lucy)) <=> (~(lucy = |'mary'|))),
inference(monotonicity,[status(thm)],[73])).
tff(75,plain,
((~(mary = lucy)) <=> (~(mary = lucy))),
inference(rewrite,[status(thm)],[])).
tff(76,plain,
(~(mary = lucy)),
inference(and_elim,[status(thm)],[54])).
tff(77,plain,
(~(mary = lucy)),
inference(modus_ponens,[status(thm)],[76, 75])).
tff(78,plain,
(~(lucy = |'mary'|)),
inference(modus_ponens,[status(thm)],[77, 74])).
tff(79,assumption,(~(lucy = |'mary'|)), introduced(assumption)).
tff(80,assumption,(alice = |'paul'|), introduced(assumption)).
tff(81,plain,
(|'paul'| = alice),
inference(symmetry,[status(thm)],[80])).
tff(82,plain,
((lucy = |'paul'|) <=> (lucy = alice)),
inference(monotonicity,[status(thm)],[81])).
tff(83,plain,
((lucy = |'paul'|) <=> (alice = lucy)),
inference(transitivity,[status(thm)],[82, 6])).
tff(84,plain,
((alice = lucy) <=> (lucy = |'paul'|)),
inference(symmetry,[status(thm)],[83])).
tff(85,plain,
((~(alice = lucy)) <=> (~(lucy = |'paul'|))),
inference(monotonicity,[status(thm)],[84])).
tff(86,plain,
((~(alice = lucy)) <=> (~(alice = lucy))),
inference(rewrite,[status(thm)],[])).
tff(87,plain,
(~(alice = lucy)),
inference(and_elim,[status(thm)],[36])).
tff(88,plain,
(~(alice = lucy)),
inference(modus_ponens,[status(thm)],[87, 86])).
tff(89,plain,
(~(lucy = |'paul'|)),
inference(modus_ponens,[status(thm)],[88, 85])).
tff(90,assumption,(~(fred = |'mary'|)), introduced(assumption)).
tff(91,plain,
((fred = |'paul'|) <=> (fred = alice)),
inference(monotonicity,[status(thm)],[81])).
tff(92,plain,
((fred = alice) <=> (fred = |'paul'|)),
inference(symmetry,[status(thm)],[91])).
tff(93,plain,
((~(fred = alice)) <=> (~(fred = |'paul'|))),
inference(monotonicity,[status(thm)],[92])).
tff(94,plain,
((~(fred = alice)) <=> (~(fred = alice))),
inference(rewrite,[status(thm)],[])).
tff(95,plain,
(~(fred = alice)),
inference(and_elim,[status(thm)],[45])).
tff(96,plain,
(~(fred = alice)),
inference(modus_ponens,[status(thm)],[95, 94])).
tff(97,plain,
(~(fred = |'paul'|)),
inference(modus_ponens,[status(thm)],[96, 93])).
tff(98,plain,
((|'alice'| = fred) <=> (fred = |'alice'|)),
inference(commutativity,[status(thm)],[])).
tff(99,plain,
((alice = fred) <=> (fred = alice)),
inference(commutativity,[status(thm)],[])).
tff(100,assumption,(paul = |'fred'|), introduced(assumption)).
tff(101,plain,
((john = fred) <=> (fred = john)),
inference(commutativity,[status(thm)],[])).
tff(102,assumption,(~(mary = |'alice'|)), introduced(assumption)).
tff(103,plain,
((|'fred'| = john) <=> (john = |'fred'|)),
inference(commutativity,[status(thm)],[])).
tff(104,plain,
((paul = john) <=> (|'fred'| = john)),
inference(monotonicity,[status(thm)],[100])).
tff(105,plain,
((paul = john) <=> (john = |'fred'|)),
inference(transitivity,[status(thm)],[104, 103])).
tff(106,plain,
((~(paul = john)) <=> (~(john = |'fred'|))),
inference(monotonicity,[status(thm)],[105])).
tff(107,plain,
((~(paul = john)) <=> (~(paul = john))),
inference(rewrite,[status(thm)],[])).
tff(108,plain,
(~(paul = john)),
inference(and_elim,[status(thm)],[50])).
tff(109,plain,
(~(paul = john)),
inference(modus_ponens,[status(thm)],[108, 107])).
tff(110,plain,
(~(john = |'fred'|)),
inference(modus_ponens,[status(thm)],[109, 106])).
tff(111,assumption,(~(alice = |'alice'|)), introduced(assumption)).
tff(112,plain,
((|'fred'| = fred) <=> (fred = |'fred'|)),
inference(commutativity,[status(thm)],[])).
tff(113,plain,
((paul = fred) <=> (|'fred'| = fred)),
inference(monotonicity,[status(thm)],[100])).
tff(114,plain,
((paul = fred) <=> (fred = |'fred'|)),
inference(transitivity,[status(thm)],[113, 112])).
tff(115,plain,
((~(paul = fred)) <=> (~(fred = |'fred'|))),
inference(monotonicity,[status(thm)],[114])).
tff(116,plain,
((~(paul = fred)) <=> (~(paul = fred))),
inference(rewrite,[status(thm)],[])).
tff(117,plain,
(~(paul = fred)),
inference(and_elim,[status(thm)],[52])).
tff(118,plain,
(~(paul = fred)),
inference(modus_ponens,[status(thm)],[117, 116])).
tff(119,plain,
(~(fred = |'fred'|)),
inference(modus_ponens,[status(thm)],[118, 115])).
tff(120,plain,
((alice = paul) <=> (paul = alice)),
inference(commutativity,[status(thm)],[])).
tff(121,plain,
(|'fred'| = paul),
inference(symmetry,[status(thm)],[100])).
tff(122,plain,
((alice = |'fred'|) <=> (alice = paul)),
inference(monotonicity,[status(thm)],[121])).
tff(123,plain,
((alice = |'fred'|) <=> (paul = alice)),
inference(transitivity,[status(thm)],[122, 120])).
tff(124,plain,
((paul = alice) <=> (alice = |'fred'|)),
inference(symmetry,[status(thm)],[123])).
tff(125,plain,
((~(paul = alice)) <=> (~(alice = |'fred'|))),
inference(monotonicity,[status(thm)],[124])).
tff(126,plain,
((~(paul = alice)) <=> (~(paul = alice))),
inference(rewrite,[status(thm)],[])).
tff(127,plain,
(~(paul = alice)),
inference(and_elim,[status(thm)],[51])).
tff(128,plain,
(~(paul = alice)),
inference(modus_ponens,[status(thm)],[127, 126])).
tff(129,plain,
(~(alice = |'fred'|)),
inference(modus_ponens,[status(thm)],[128, 125])).
tff(130,plain,
((susan = paul) <=> (paul = susan)),
inference(commutativity,[status(thm)],[])).
tff(131,plain,
((susan = |'fred'|) <=> (susan = paul)),
inference(monotonicity,[status(thm)],[121])).
tff(132,plain,
((susan = |'fred'|) <=> (paul = susan)),
inference(transitivity,[status(thm)],[131, 130])).
tff(133,plain,
((paul = susan) <=> (susan = |'fred'|)),
inference(symmetry,[status(thm)],[132])).
tff(134,plain,
((~(paul = susan)) <=> (~(susan = |'fred'|))),
inference(monotonicity,[status(thm)],[133])).
tff(135,plain,
((~(paul = susan)) <=> (~(paul = susan))),
inference(rewrite,[status(thm)],[])).
tff(136,plain,
(~(paul = susan)),
inference(and_elim,[status(thm)],[49])).
tff(137,plain,
(~(paul = susan)),
inference(modus_ponens,[status(thm)],[136, 135])).
tff(138,plain,
(~(susan = |'fred'|)),
inference(modus_ponens,[status(thm)],[137, 134])).
tff(139,plain,
((lucy = paul) <=> (paul = lucy)),
inference(commutativity,[status(thm)],[])).
tff(140,plain,
((lucy = |'fred'|) <=> (lucy = paul)),
inference(monotonicity,[status(thm)],[121])).
tff(141,plain,
((lucy = |'fred'|) <=> (paul = lucy)),
inference(transitivity,[status(thm)],[140, 139])).
tff(142,plain,
((paul = lucy) <=> (lucy = |'fred'|)),
inference(symmetry,[status(thm)],[141])).
tff(143,plain,
((~(paul = lucy)) <=> (~(lucy = |'fred'|))),
inference(monotonicity,[status(thm)],[142])).
tff(144,plain,
((~(paul = lucy)) <=> (~(paul = lucy))),
inference(rewrite,[status(thm)],[])).
tff(145,plain,
(~(paul = lucy)),
inference(and_elim,[status(thm)],[48])).
tff(146,plain,
(~(paul = lucy)),
inference(modus_ponens,[status(thm)],[145, 144])).
tff(147,plain,
(~(lucy = |'fred'|)),
inference(modus_ponens,[status(thm)],[146, 143])).
tff(148,plain,
((|'fred'| = susan) <=> (susan = |'fred'|)),
inference(commutativity,[status(thm)],[])).
tff(149,plain,
((|'fred'| = alice) <=> (alice = |'fred'|)),
inference(commutativity,[status(thm)],[])).
tff(150,plain,
((paul = alice) <=> (|'fred'| = alice)),
inference(monotonicity,[status(thm)],[100])).
tff(151,plain,
((paul = alice) <=> (alice = |'fred'|)),
inference(transitivity,[status(thm)],[150, 149])).
tff(152,plain,
((~(paul = alice)) <=> (~(alice = |'fred'|))),
inference(monotonicity,[status(thm)],[151])).
tff(153,plain,
(~(alice = |'fred'|)),
inference(modus_ponens,[status(thm)],[128, 152])).
tff(154,plain,
((mary = |'fred'|) <=> (mary = paul)),
inference(monotonicity,[status(thm)],[121])).
tff(155,plain,
((mary = paul) <=> (mary = |'fred'|)),
inference(symmetry,[status(thm)],[154])).
tff(156,plain,
((~(mary = paul)) <=> (~(mary = |'fred'|))),
inference(monotonicity,[status(thm)],[155])).
tff(157,plain,
((~(mary = paul)) <=> (~(mary = paul))),
inference(rewrite,[status(thm)],[])).
tff(158,plain,
(~(mary = paul)),
inference(and_elim,[status(thm)],[58])).
tff(159,plain,
(~(mary = paul)),
inference(modus_ponens,[status(thm)],[158, 157])).
tff(160,plain,
(~(mary = |'fred'|)),
inference(modus_ponens,[status(thm)],[159, 156])).
tff(161,assumption,(~(susan = |'mary'|)), introduced(assumption)).
tff(162,assumption,(~(mary = |'fred'|)), introduced(assumption)).
tff(163,assumption,(alice = |'mary'|), introduced(assumption)).
tff(164,plain,
(|'mary'| = alice),
inference(symmetry,[status(thm)],[163])).
tff(165,plain,
((mary = |'mary'|) <=> (mary = alice)),
inference(monotonicity,[status(thm)],[164])).
tff(166,plain,
((mary = alice) <=> (mary = |'mary'|)),
inference(symmetry,[status(thm)],[165])).
tff(167,plain,
((~(mary = alice)) <=> (~(mary = |'mary'|))),
inference(monotonicity,[status(thm)],[166])).
tff(168,plain,
((~(mary = alice)) <=> (~(mary = alice))),
inference(rewrite,[status(thm)],[])).
tff(169,plain,
(~(mary = alice)),
inference(and_elim,[status(thm)],[57])).
tff(170,plain,
(~(mary = alice)),
inference(modus_ponens,[status(thm)],[169, 168])).
tff(171,plain,
(~(mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[170, 167])).
tff(172,plain,
(^[X: $i] : refl(((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(173,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[172])).
tff(174,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(175,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((![X: $i] : ((~room(X)) => preda(X)) => ![X: $i] : ((~room(X)) => ((happy(X) & european(X)) => (((~happy(X)) & (~rich(X))) & (~quiet(X)))))) & (![X: $i] : richer(alice, X) => (~(~?[X: $i] : ((~room(X)) => (quieter(john, X) => (~happy(X)))))))) & (hate(fred, john) & hate(john, fred))) & (~((~happy(alice)) | (~hate(alice, lucy))))) & (~(((rich(fred) & quiet(fred)) & happy(fred)) & tourist(fred)))) & (preda(fred) & (quiet(fred) & european(fred)))) & (?[X: $i] : (((~room(X)) & quiet(X)) & tourist(X)) & ![X: $i, Y: $i] : ((((quiet(X) & tourist(X)) & quiet(Y)) & tourist(Y)) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~((((rich(X) & happy(X)) & quiet(X)) & creative(X)) & tourist(X))) & (~((((rich(Y) & happy(Y)) & quiet(Y)) & creative(Y)) & tourist(Y))))) & (~(X = Y)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((~![X: $i] : (preda(X) | room(X))) | ![X: $i] : (room(X) | ((~happy(X)) & (~rich(X)) & (~quiet(X))) | (~(happy(X) & european(X))))) & ((~![X: $i] : richer(alice, X)) | ?[X: $i] : (room(X) | (~happy(X)) | (~quieter(john, X)))) & hate(fred, john) & hate(john, fred) & (~((~happy(alice)) | (~hate(alice, lucy)))) & (~(rich(fred) & quiet(fred) & happy(fred) & tourist(fred))) & preda(fred) & quiet(fred) & european(fred) & ?[X: $i] : ((~room(X)) & quiet(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))))),
inference(rewrite,[status(thm)],[])).
tff(176,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((![X: $i] : ((~room(X)) => preda(X)) => ![X: $i] : ((~room(X)) => ((happy(X) & european(X)) => (((~happy(X)) & (~rich(X))) & (~quiet(X)))))) & (![X: $i] : richer(alice, X) => (~(~?[X: $i] : ((~room(X)) => (quieter(john, X) => (~happy(X)))))))) & (hate(fred, john) & hate(john, fred))) & (~((~happy(alice)) | (~hate(alice, lucy))))) & (~(((rich(fred) & quiet(fred)) & happy(fred)) & tourist(fred)))) & (preda(fred) & (quiet(fred) & european(fred)))) & (?[X: $i] : (((~room(X)) & quiet(X)) & tourist(X)) & ![X: $i, Y: $i] : ((((quiet(X) & tourist(X)) & quiet(Y)) & tourist(Y)) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~((((rich(X) & happy(X)) & quiet(X)) & creative(X)) & tourist(X))) & (~((((rich(Y) & happy(Y)) & quiet(Y)) & creative(Y)) & tourist(Y))))) & (~(X = Y)))))), file('/mnt/tmpfs//5173815561958952539467234.p','negated')).
tff(177,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((~![X: $i] : (preda(X) | room(X))) | ![X: $i] : (room(X) | ((~happy(X)) & (~rich(X)) & (~quiet(X))) | (~(happy(X) & european(X))))) & ((~![X: $i] : richer(alice, X)) | ?[X: $i] : (room(X) | (~happy(X)) | (~quieter(john, X)))) & hate(fred, john) & hate(john, fred) & (~((~happy(alice)) | (~hate(alice, lucy)))) & (~(rich(fred) & quiet(fred) & happy(fred) & tourist(fred))) & preda(fred) & quiet(fred) & european(fred) & ?[X: $i] : ((~room(X)) & quiet(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))))),
inference(modus_ponens,[status(thm)],[176, 175])).
tff(178,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((~![X: $i] : (preda(X) | room(X))) | ![X: $i] : (room(X) | ((~happy(X)) & (~rich(X)) & (~quiet(X))) | (~(happy(X) & european(X))))) & ((~![X: $i] : richer(alice, X)) | ?[X: $i] : (room(X) | (~happy(X)) | (~quieter(john, X)))) & hate(fred, john) & hate(john, fred) & (~((~happy(alice)) | (~hate(alice, lucy)))) & (~(rich(fred) & quiet(fred) & happy(fred) & tourist(fred))) & preda(fred) & quiet(fred) & european(fred) & ?[X: $i] : ((~room(X)) & quiet(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y))),
inference(or_elim,[status(thm)],[177])).
tff(179,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(and_elim,[status(thm)],[178])).
tff(180,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[179, 174])).
tff(181,plain,(
![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(skolemize,[status(sab)],[180])).
tff(182,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[181, 173])).
tff(183,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(184,plain,
(room(mary)),
inference(and_elim,[status(thm)],[178])).
tff(185,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[184, 183])).
tff(186,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'alice'|) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(mary)) | (mary = |'alice'|) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(187,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'alice'|) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(188,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(mary)) | (mary = |'alice'|) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[187, 186])).
tff(189,plain,
((mary = |'alice'|) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[188, 185, 182])).
tff(190,plain,
(mary = |'paul'|),
inference(unit_resolution,[status(thm)],[189, 171, 102, 162])).
tff(191,plain,
(|'paul'| = mary),
inference(symmetry,[status(thm)],[190])).
tff(192,plain,
((lucy = |'paul'|) <=> (lucy = mary)),
inference(monotonicity,[status(thm)],[191])).
tff(193,plain,
((lucy = |'paul'|) <=> (mary = lucy)),
inference(transitivity,[status(thm)],[192, 2])).
tff(194,plain,
((mary = lucy) <=> (lucy = |'paul'|)),
inference(symmetry,[status(thm)],[193])).
tff(195,plain,
((~(mary = lucy)) <=> (~(lucy = |'paul'|))),
inference(monotonicity,[status(thm)],[194])).
tff(196,plain,
(~(lucy = |'paul'|)),
inference(modus_ponens,[status(thm)],[77, 195])).
tff(197,assumption,(~(lucy = |'fred'|)), introduced(assumption)).
tff(198,plain,
((lucy = |'mary'|) <=> (lucy = alice)),
inference(monotonicity,[status(thm)],[164])).
tff(199,plain,
((lucy = |'mary'|) <=> (alice = lucy)),
inference(transitivity,[status(thm)],[198, 6])).
tff(200,plain,
((alice = lucy) <=> (lucy = |'mary'|)),
inference(symmetry,[status(thm)],[199])).
tff(201,plain,
((~(alice = lucy)) <=> (~(lucy = |'mary'|))),
inference(monotonicity,[status(thm)],[200])).
tff(202,plain,
(~(lucy = |'mary'|)),
inference(modus_ponens,[status(thm)],[88, 201])).
tff(203,plain,
((fred = |'mary'|) <=> (fred = alice)),
inference(monotonicity,[status(thm)],[164])).
tff(204,plain,
((fred = alice) <=> (fred = |'mary'|)),
inference(symmetry,[status(thm)],[203])).
tff(205,plain,
((~(fred = alice)) <=> (~(fred = |'mary'|))),
inference(monotonicity,[status(thm)],[204])).
tff(206,plain,
(~(fred = |'mary'|)),
inference(modus_ponens,[status(thm)],[96, 205])).
tff(207,assumption,(~(fred = |'fred'|)), introduced(assumption)).
tff(208,plain,
((fred = |'paul'|) <=> (fred = mary)),
inference(monotonicity,[status(thm)],[191])).
tff(209,plain,
((fred = |'paul'|) <=> (mary = fred)),
inference(transitivity,[status(thm)],[208, 10])).
tff(210,plain,
((mary = fred) <=> (fred = |'paul'|)),
inference(symmetry,[status(thm)],[209])).
tff(211,plain,
((~(mary = fred)) <=> (~(fred = |'paul'|))),
inference(monotonicity,[status(thm)],[210])).
tff(212,plain,
(~(fred = |'paul'|)),
inference(modus_ponens,[status(thm)],[60, 211])).
tff(213,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(214,plain,
(room(fred)),
inference(and_elim,[status(thm)],[178])).
tff(215,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[214, 213])).
tff(216,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(fred)) | (fred = |'alice'|) | (fred = |'fred'|) | (fred = |'paul'|) | (fred = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(fred)) | (fred = |'alice'|) | (fred = |'fred'|) | (fred = |'paul'|) | (fred = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(217,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(fred)) | (fred = |'alice'|) | (fred = |'fred'|) | (fred = |'paul'|) | (fred = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(218,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(fred)) | (fred = |'alice'|) | (fred = |'fred'|) | (fred = |'paul'|) | (fred = |'mary'|)),
inference(modus_ponens,[status(thm)],[217, 216])).
tff(219,plain,
((fred = |'alice'|) | (fred = |'fred'|) | (fred = |'paul'|) | (fred = |'mary'|)),
inference(unit_resolution,[status(thm)],[218, 215, 182])).
tff(220,plain,
(fred = |'alice'|),
inference(unit_resolution,[status(thm)],[219, 212, 207, 206])).
tff(221,plain,
(|'alice'| = fred),
inference(symmetry,[status(thm)],[220])).
tff(222,plain,
((lucy = |'alice'|) <=> (lucy = fred)),
inference(monotonicity,[status(thm)],[221])).
tff(223,plain,
((lucy = |'alice'|) <=> (fred = lucy)),
inference(transitivity,[status(thm)],[222, 4])).
tff(224,plain,
((fred = lucy) <=> (lucy = |'alice'|)),
inference(symmetry,[status(thm)],[223])).
tff(225,plain,
((~(fred = lucy)) <=> (~(lucy = |'alice'|))),
inference(monotonicity,[status(thm)],[224])).
tff(226,plain,
((~(fred = lucy)) <=> (~(fred = lucy))),
inference(rewrite,[status(thm)],[])).
tff(227,plain,
(~(fred = lucy)),
inference(and_elim,[status(thm)],[42])).
tff(228,plain,
(~(fred = lucy)),
inference(modus_ponens,[status(thm)],[227, 226])).
tff(229,plain,
(~(lucy = |'alice'|)),
inference(modus_ponens,[status(thm)],[228, 225])).
tff(230,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(lucy)) | (lucy = |'alice'|) | (lucy = |'fred'|) | (lucy = |'paul'|) | (lucy = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(lucy)) | (lucy = |'alice'|) | (lucy = |'fred'|) | (lucy = |'paul'|) | (lucy = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(231,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(lucy)) | (lucy = |'alice'|) | (lucy = |'fred'|) | (lucy = |'paul'|) | (lucy = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(232,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(lucy)) | (lucy = |'alice'|) | (lucy = |'fred'|) | (lucy = |'paul'|) | (lucy = |'mary'|)),
inference(modus_ponens,[status(thm)],[231, 230])).
tff(233,plain,
((~room(lucy)) | (lucy = |'alice'|) | (lucy = |'fred'|) | (lucy = |'paul'|) | (lucy = |'mary'|)),
inference(unit_resolution,[status(thm)],[232, 182])).
tff(234,plain,
(~room(lucy)),
inference(unit_resolution,[status(thm)],[233, 229, 202, 197, 196])).
tff(235,plain,
((susan = |'paul'|) <=> (susan = mary)),
inference(monotonicity,[status(thm)],[191])).
tff(236,plain,
((susan = |'paul'|) <=> (mary = susan)),
inference(transitivity,[status(thm)],[235, 62])).
tff(237,plain,
((mary = susan) <=> (susan = |'paul'|)),
inference(symmetry,[status(thm)],[236])).
tff(238,plain,
((~(mary = susan)) <=> (~(susan = |'paul'|))),
inference(monotonicity,[status(thm)],[237])).
tff(239,plain,
(~(susan = |'paul'|)),
inference(modus_ponens,[status(thm)],[69, 238])).
tff(240,assumption,(~(susan = |'fred'|)), introduced(assumption)).
tff(241,plain,
((|'alice'| = susan) <=> (susan = |'alice'|)),
inference(commutativity,[status(thm)],[])).
tff(242,plain,
((fred = susan) <=> (|'alice'| = susan)),
inference(monotonicity,[status(thm)],[220])).
tff(243,plain,
((fred = susan) <=> (susan = |'alice'|)),
inference(transitivity,[status(thm)],[242, 241])).
tff(244,plain,
((~(fred = susan)) <=> (~(susan = |'alice'|))),
inference(monotonicity,[status(thm)],[243])).
tff(245,plain,
((~(fred = susan)) <=> (~(fred = susan))),
inference(rewrite,[status(thm)],[])).
tff(246,plain,
(~(fred = susan)),
inference(and_elim,[status(thm)],[43])).
tff(247,plain,
(~(fred = susan)),
inference(modus_ponens,[status(thm)],[246, 245])).
tff(248,plain,
(~(susan = |'alice'|)),
inference(modus_ponens,[status(thm)],[247, 244])).
tff(249,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((susan = |'alice'|) | (~room(susan)) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (susan = |'alice'|) | (~room(susan)) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(250,plain,
(((~room(susan)) | (susan = |'alice'|) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|)) <=> ((susan = |'alice'|) | (~room(susan)) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(251,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(susan)) | (susan = |'alice'|) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((susan = |'alice'|) | (~room(susan)) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|)))),
inference(monotonicity,[status(thm)],[250])).
tff(252,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(susan)) | (susan = |'alice'|) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (susan = |'alice'|) | (~room(susan)) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|))),
inference(transitivity,[status(thm)],[251, 249])).
tff(253,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(susan)) | (susan = |'alice'|) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(254,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (susan = |'alice'|) | (~room(susan)) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|)),
inference(modus_ponens,[status(thm)],[253, 252])).
tff(255,plain,
((susan = |'alice'|) | (~room(susan)) | (susan = |'fred'|) | (susan = |'paul'|) | (susan = |'mary'|)),
inference(unit_resolution,[status(thm)],[254, 182])).
tff(256,plain,
(~room(susan)),
inference(unit_resolution,[status(thm)],[255, 248, 161, 240, 239])).
tff(257,assumption,(~((~quiet(john)) | (~tourist(john)) | (~rich(john)) | (~happy(john)) | (~creative(john)))), introduced(assumption)).
tff(258,assumption,(~((~creative(susan)) | (~rich(susan)) | (~quiet(susan)) | (~tourist(susan)) | (~happy(susan)))), introduced(assumption)).
tff(259,plain,
(((~creative(susan)) | (~rich(susan)) | (~quiet(susan)) | (~tourist(susan)) | (~happy(susan))) | quiet(susan)),
inference(tautology,[status(thm)],[])).
tff(260,plain,
(quiet(susan)),
inference(unit_resolution,[status(thm)],[259, 258])).
tff(261,plain,
(((~creative(susan)) | (~rich(susan)) | (~quiet(susan)) | (~tourist(susan)) | (~happy(susan))) | tourist(susan)),
inference(tautology,[status(thm)],[])).
tff(262,plain,
(tourist(susan)),
inference(unit_resolution,[status(thm)],[261, 258])).
tff(263,assumption,(tourist(susan)), introduced(assumption)).
tff(264,assumption,(quiet(susan)), introduced(assumption)).
tff(265,plain,
(((~quiet(john)) | (~tourist(john)) | (~rich(john)) | (~happy(john)) | (~creative(john))) | tourist(john)),
inference(tautology,[status(thm)],[])).
tff(266,plain,
(tourist(john)),
inference(unit_resolution,[status(thm)],[265, 257])).
tff(267,plain,
(((~quiet(john)) | (~tourist(john)) | (~rich(john)) | (~happy(john)) | (~creative(john))) | quiet(john)),
inference(tautology,[status(thm)],[])).
tff(268,plain,
(quiet(john)),
inference(unit_resolution,[status(thm)],[267, 257])).
tff(269,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))) <=> ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))))),
inference(bind,[status(th)],[])).
tff(270,plain,
(![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))),
inference(quant_intro,[status(thm)],[269])).
tff(271,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((quiet(X) & tourist(X) & quiet(Y) & tourist(Y)) <=> (~((~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))))), ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) <=> (~(~((~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))))))), rewrite((~(~((~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))))) <=> ((~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))), ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) <=> ((~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))))), (((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y)) <=> (((~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))) | (X = Y)))), rewrite((((~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X))) | (X = Y)) <=> ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))), (((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y)) <=> ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))))),
inference(bind,[status(th)],[])).
tff(272,plain,
(![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))),
inference(quant_intro,[status(thm)],[271])).
tff(273,plain,
(![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y))),
inference(rewrite,[status(thm)],[])).
tff(274,plain,
(![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y))),
inference(and_elim,[status(thm)],[178])).
tff(275,plain,
(![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y))),
inference(modus_ponens,[status(thm)],[274, 273])).
tff(276,plain,(
![X: $i, Y: $i] : ((~(quiet(X) & tourist(X) & quiet(Y) & tourist(Y))) | (X = Y))),
inference(skolemize,[status(sab)],[275])).
tff(277,plain,
(![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[276, 272])).
tff(278,plain,
(![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[277, 270])).
tff(279,plain,
((~(susan = john)) <=> (~(susan = john))),
inference(rewrite,[status(thm)],[])).
tff(280,plain,
(~(susan = john)),
inference(and_elim,[status(thm)],[25])).
tff(281,plain,
(~(susan = john)),
inference(modus_ponens,[status(thm)],[280, 279])).
tff(282,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))) | ((susan = john) | (~quiet(john)) | (~tourist(john)) | (~quiet(susan)) | (~tourist(susan)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))) | (susan = john) | (~quiet(john)) | (~tourist(john)) | (~quiet(susan)) | (~tourist(susan)))),
inference(rewrite,[status(thm)],[])).
tff(283,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))) | ((susan = john) | (~quiet(john)) | (~tourist(john)) | (~quiet(susan)) | (~tourist(susan)))),
inference(quant_inst,[status(thm)],[])).
tff(284,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~quiet(Y)) | (~tourist(Y)) | (~quiet(X)) | (~tourist(X)))) | (susan = john) | (~quiet(john)) | (~tourist(john)) | (~quiet(susan)) | (~tourist(susan))),
inference(modus_ponens,[status(thm)],[283, 282])).
tff(285,plain,
($false),
inference(unit_resolution,[status(thm)],[284, 281, 278, 268, 266, 264, 263])).
tff(286,plain,(((~quiet(john)) | (~tourist(john)) | (~rich(john)) | (~happy(john)) | (~creative(john))) | (~quiet(susan)) | (~tourist(susan))), inference(lemma,lemma(discharge,[]))).
tff(287,plain,
($false),
inference(unit_resolution,[status(thm)],[286, 262, 260, 257])).
tff(288,plain,(((~creative(susan)) | (~rich(susan)) | (~quiet(susan)) | (~tourist(susan)) | (~happy(susan))) | ((~quiet(john)) | (~tourist(john)) | (~rich(john)) | (~happy(john)) | (~creative(john)))), inference(lemma,lemma(discharge,[]))).
tff(289,plain,
((~creative(susan)) | (~rich(susan)) | (~quiet(susan)) | (~tourist(susan)) | (~happy(susan))),
inference(unit_resolution,[status(thm)],[288, 257])).
tff(290,assumption,(~room(lucy)), introduced(assumption)).
tff(291,assumption,(~room(susan)), introduced(assumption)).
tff(292,assumption,(~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))), introduced(assumption)).
tff(293,plain,
(((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)) | (~(X!4 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(294,plain,
(~(X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[293, 292])).
tff(295,plain,
(((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)) | (~(X!4 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(296,plain,
(~(X!4 = |'paul'|)),
inference(unit_resolution,[status(thm)],[295, 292])).
tff(297,plain,
(((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)) | (~(X!4 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(298,plain,
(~(X!4 = |'fred'|)),
inference(unit_resolution,[status(thm)],[297, 292])).
tff(299,plain,
(((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)) | (~(X!4 = |'alice'|))),
inference(tautology,[status(thm)],[])).
tff(300,plain,
(~(X!4 = |'alice'|)),
inference(unit_resolution,[status(thm)],[299, 292])).
tff(301,plain,
(((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)) | room(X!4)),
inference(tautology,[status(thm)],[])).
tff(302,plain,
(room(X!4)),
inference(unit_resolution,[status(thm)],[301, 292])).
tff(303,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(304,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(305,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)),
inference(modus_ponens,[status(thm)],[304, 303])).
tff(306,plain,
($false),
inference(unit_resolution,[status(thm)],[305, 182, 302, 300, 298, 296, 294])).
tff(307,plain,((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)), inference(lemma,lemma(discharge,[]))).
tff(308,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(309,plain,
(room(alice)),
inference(and_elim,[status(thm)],[178])).
tff(310,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[309, 308])).
tff(311,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(312,plain,
(room(paul)),
inference(and_elim,[status(thm)],[178])).
tff(313,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[312, 311])).
tff(314,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(315,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(316,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X)) <=> (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X))))), ((~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) <=> (~(~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X))))))), rewrite((~(~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X))))) <=> ((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))), ((~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) <=> ((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X))))), trans(monotonicity(rewrite((rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y)) <=> (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))), ((~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) <=> (~(~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))), rewrite((~(~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))) <=> ((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y)))), ((~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) <=> ((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))), (((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))) <=> ((~room(X)) & (~room(Y)) & ((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X))) & ((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))) & (~(X = Y))))), rewrite(((~room(X)) & (~room(Y)) & ((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X))) & ((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))) & (~(X = Y))) <=> (~((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))), (((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))) <=> (~((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y)))))))), ((~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))) <=> (~(~((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))))), rewrite((~(~((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))) <=> ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y)))))), ((~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))) <=> ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y)))))))),
inference(bind,[status(th)],[])).
tff(317,plain,
(![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))) <=> ![X: $i, Y: $i] : ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y)))))),
inference(quant_intro,[status(thm)],[316])).
tff(318,plain,
((~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) <=> (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(319,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))),
inference(monotonicity,[status(thm)],[318, 317])).
tff(320,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((X = Y) | room(Y) | room(X) | (~((~rich(X)) | (~quiet(X)) | (~tourist(X)) | (~happy(X)) | (~creative(X)))) | (~((~quiet(Y)) | (~rich(Y)) | (~happy(Y)) | (~tourist(Y)) | (~creative(Y))))))),
inference(transitivity,[status(thm)],[319, 315])).
tff(321,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))))),
inference(rewrite,[status(thm)],[])).
tff(322,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))))),
inference(monotonicity,[status(thm)],[318])).
tff(323,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!4)) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))))),
inference(transitivity,[status(thm)],[322, 321])).
tff(324,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))),
inference(rewrite,[status(thm)],[])).
tff(325,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))))),
inference(monotonicity,[status(thm)],[324])).
tff(326,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y)))))),
inference(rewrite,[status(thm)],[])).
tff(327,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))),
inference(or_elim,[status(thm)],[177])).
tff(328,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))),
inference(modus_ponens,[status(thm)],[327, 325])).
tff(329,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))),
inference(modus_ponens,[status(thm)],[328, 326])).
tff(330,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(rich(X) & happy(X) & quiet(X) & creative(X) & tourist(X))) & (~(rich(Y) & happy(Y) & quiet(Y) & creative(Y) & tourist(Y))) & (~(X = Y))))),
inference(modus_ponens,[status(thm)],[329, 325])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (not (room X))
(= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|))))
(a!6 (not (or (not (room X!4))
(= X!4 |'alice'|)
(= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|))))
(a!7 (lambda ((X $i) (Y $i))
(let ((a!1 (and (not (room X))
(not (room Y))
(not (and (rich X)
(happy X)
(quiet X)
(creative X)
(tourist X)))
(not (and (rich Y)
(happy Y)
(quiet Y)
(creative Y)
(tourist Y)))
(not (= X Y)))))
(refl (~ (not a!1) (not a!1))))))
(a!8 (exists ((X $i) (Y $i))
(and (not (room X))
(not (room Y))
(not (and (rich X)
(happy X)
(quiet X)
(creative X)
(tourist X)))
(not (and (rich Y)
(happy Y)
(quiet Y)
(creative Y)
(tourist Y)))
(not (= X Y)))))
(a!9 (forall ((X $i) (Y $i))
(let ((a!1 (and (not (room X))
(not (room Y))
(not (and (rich X)
(happy X)
(quiet X)
(creative X)
(tourist X)))
(not (and (rich Y)
(happy Y)
(quiet Y)
(creative Y)
(tourist Y)))
(not (= X Y)))))
(not a!1)))))
(let ((a!10 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
a!8))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
a!9))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
(nnf-neg (proof-bind a!7) (~ (not a!8) a!9))
a!10)))
| room(doris)&room(todd)&room(milton)&room(velma)&(![X]:(room(X)=>(X='doris'|X='todd'|X='milton'|X='velma')))&
(((![X]:(~room(X)=>(reads_mystery_novels(X))))=>(![X]:(~room(X)=>(((happy(X)&european(X))=>(~happy(X)&~rich(X)&~quiet(X)))))))&
((![X]:(richer(velma,X)))=>(~(~?[X]:(~room(X)=>(((quieter(david,X))=>(~happy(X))))))))&
((hate(milton,david) & hate(david,milton)))&
(~((~happy(velma))|(~hate(velma,marie))))&
(~(rich(milton)&quiet(milton)&happy(milton)&tourist(milton)))&
((reads_mystery_novels(milton))&(quiet(milton)&european(milton)))&
(((?[X]:(~room(X)&quiet(X)&tourist(X)))&(![X,Y]:((quiet(X)&tourist(X)&quiet(Y)&tourist(Y))=>(X=Y)))))) | room(doris)&room(todd)&room(milton)&room(velma)&(![X]:(room(X)=>(X='doris'|X='todd'|X='milton'|X='velma')))&
((?[X,Y]:(~room(X)&~room(Y)&(~(rich(X)&happy(X)&quiet(X)&creative(X)&tourist(X))&~(rich(Y)&happy(Y)&quiet(Y)&creative(Y)&tourist(Y)))&(X!=Y)))) | entailment | neutral | entailment |
Andrew, Nancy are the only persons in the room.
'Andrew and Nancy do not hate David' only if 'more than one person outside the room is hated by Daniel'.
If 'Andrew and Daniel hate each other' then 'Andrew is not a happy european or is a happy quiet creative tourist or both'.
'Nancy does not build model airplanes and is not hated by Daniel' if 'Nancy is the least quiet in the room'.
Everyone in the room who is not a happy quiet european does not hate Daniel.
Only one person in the room does not have a saltwater aquarium.
Andrew and Nancy are respectively creative and quiet.
Nancy and Andrew hate Daniel.
Andrew is hated by Daniel.
Nancy is the quietest in the room. | Andrew collects comic books or is a quiet creative tourist or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(predc_type, type, (
predc: $i > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(susan_type, type, (
susan: $i)).
tff(1,plain,
(^[X: $i] : refl(((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X))))) <=> ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X))))))),
inference(bind,[status(th)],[])).
tff(2,plain,
(![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X))))) <=> ![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))),
inference(quant_intro,[status(thm)],[1])).
tff(3,plain,
(^[X: $i] : rewrite(((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X))) <=> ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X))))))),
inference(bind,[status(th)],[])).
tff(4,plain,
(![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X))) <=> ![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))),
inference(quant_intro,[status(thm)],[3])).
tff(5,plain,
(![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X))) <=> ![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X)))),
inference(rewrite,[status(thm)],[])).
tff(6,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((~hate(susan, mary)) & (~hate(susan, paul))) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (hate(X, fred) & hate(Y, fred))) & (~(X = Y)))) & ((hate(mary, fred) & hate(fred, mary)) => ((~(happy(mary) & european(mary))) | (((happy(mary) & quiet(mary)) & creative(mary)) & tourist(mary))))) & (![X: $i] : quieter(paul, X) => ((~predb(paul)) & (~hate(paul, fred))))) & ![X: $i] : (room(X) => ((~((happy(X) & quiet(X)) & european(X))) => (~hate(fred, X))))) & (?[X: $i] : (room(X) & (~predc(X))) & ![X: $i, Y: $i] : (((~predc(X)) & (~predc(Y))) => (X = Y)))) & (creative(mary) & quiet(paul))) & (hate(fred, paul) & hate(fred, mary))) & hate(mary, fred)) & ![X: $i] : quieter(X, paul))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (preda(mary) | ((quiet(mary) & creative(mary)) & tourist(mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~hate(susan, mary)) & (~hate(susan, paul)))) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & hate(X, fred) & hate(Y, fred) & (~(X = Y)))) & ((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))) & ((~![X: $i] : quieter(paul, X)) | ((~predb(paul)) & (~hate(paul, fred)))) & ![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X))) & ?[X: $i] : (room(X) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & creative(mary) & quiet(paul) & hate(fred, paul) & hate(fred, mary) & hate(mary, fred) & ![X: $i] : quieter(X, paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(7,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((~hate(susan, mary)) & (~hate(susan, paul))) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (hate(X, fred) & hate(Y, fred))) & (~(X = Y)))) & ((hate(mary, fred) & hate(fred, mary)) => ((~(happy(mary) & european(mary))) | (((happy(mary) & quiet(mary)) & creative(mary)) & tourist(mary))))) & (![X: $i] : quieter(paul, X) => ((~predb(paul)) & (~hate(paul, fred))))) & ![X: $i] : (room(X) => ((~((happy(X) & quiet(X)) & european(X))) => (~hate(fred, X))))) & (?[X: $i] : (room(X) & (~predc(X))) & ![X: $i, Y: $i] : (((~predc(X)) & (~predc(Y))) => (X = Y)))) & (creative(mary) & quiet(paul))) & (hate(fred, paul) & hate(fred, mary))) & hate(mary, fred)) & ![X: $i] : quieter(X, paul))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (preda(mary) | ((quiet(mary) & creative(mary)) & tourist(mary)))))), file('/mnt/tmpfs//5621382790887112294862384.p','negated')).
tff(8,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~hate(susan, mary)) & (~hate(susan, paul)))) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & hate(X, fred) & hate(Y, fred) & (~(X = Y)))) & ((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))) & ((~![X: $i] : quieter(paul, X)) | ((~predb(paul)) & (~hate(paul, fred)))) & ![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X))) & ?[X: $i] : (room(X) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & creative(mary) & quiet(paul) & hate(fred, paul) & hate(fred, mary) & hate(mary, fred) & ![X: $i] : quieter(X, paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[7, 6])).
tff(9,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~hate(susan, mary)) & (~hate(susan, paul)))) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & hate(X, fred) & hate(Y, fred) & (~(X = Y)))) & ((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))) & ((~![X: $i] : quieter(paul, X)) | ((~predb(paul)) & (~hate(paul, fred)))) & ![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X))) & ?[X: $i] : (room(X) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & creative(mary) & quiet(paul) & hate(fred, paul) & hate(fred, mary) & hate(mary, fred) & ![X: $i] : quieter(X, paul)),
inference(or_elim,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X)))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X)))),
inference(modus_ponens,[status(thm)],[10, 5])).
tff(12,plain,(
![X: $i] : ((~room(X)) | (~hate(fred, X)) | (happy(X) & quiet(X) & european(X)))),
inference(skolemize,[status(sab)],[11])).
tff(13,plain,
(![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))),
inference(modus_ponens,[status(thm)],[12, 4])).
tff(14,plain,
(![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))),
inference(modus_ponens,[status(thm)],[13, 2])).
tff(15,plain,
(hate(fred, mary) <=> hate(fred, mary)),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(hate(fred, mary)),
inference(and_elim,[status(thm)],[9])).
tff(17,plain,
(hate(fred, mary)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(room(mary)),
inference(and_elim,[status(thm)],[9])).
tff(20,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(((~![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))) | ((~room(mary)) | (~hate(fred, mary)) | (~((~european(mary)) | (~happy(mary)) | (~quiet(mary)))))) <=> ((~![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))) | (~room(mary)) | (~hate(fred, mary)) | (~((~european(mary)) | (~happy(mary)) | (~quiet(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((~![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))) | ((~room(mary)) | (~hate(fred, mary)) | (~((~european(mary)) | (~happy(mary)) | (~quiet(mary)))))),
inference(quant_inst,[status(thm)],[])).
tff(23,plain,
((~![X: $i] : ((~room(X)) | (~hate(fred, X)) | (~((~european(X)) | (~happy(X)) | (~quiet(X)))))) | (~room(mary)) | (~hate(fred, mary)) | (~((~european(mary)) | (~happy(mary)) | (~quiet(mary))))),
inference(modus_ponens,[status(thm)],[22, 21])).
tff(24,plain,
(~((~european(mary)) | (~happy(mary)) | (~quiet(mary)))),
inference(unit_resolution,[status(thm)],[23, 20, 17, 14])).
tff(25,plain,
(((~european(mary)) | (~happy(mary)) | (~quiet(mary))) | quiet(mary)),
inference(tautology,[status(thm)],[])).
tff(26,plain,
(quiet(mary)),
inference(unit_resolution,[status(thm)],[25, 24])).
tff(27,plain,
(((~european(mary)) | (~happy(mary)) | (~quiet(mary))) | european(mary)),
inference(tautology,[status(thm)],[])).
tff(28,plain,
(european(mary)),
inference(unit_resolution,[status(thm)],[27, 24])).
tff(29,plain,
(hate(mary, fred) <=> hate(mary, fred)),
inference(rewrite,[status(thm)],[])).
tff(30,plain,
(hate(mary, fred)),
inference(and_elim,[status(thm)],[9])).
tff(31,plain,
(hate(mary, fred)),
inference(modus_ponens,[status(thm)],[30, 29])).
tff(32,plain,
(((~european(mary)) | (~happy(mary)) | (~quiet(mary))) | happy(mary)),
inference(tautology,[status(thm)],[])).
tff(33,plain,
(happy(mary)),
inference(unit_resolution,[status(thm)],[32, 24])).
tff(34,plain,
((((~happy(mary)) | (~european(mary))) | ((~hate(mary, fred)) | (~hate(fred, mary))) | (~((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))) <=> ((~happy(mary)) | (~european(mary)) | (~hate(mary, fred)) | (~hate(fred, mary)) | (~((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
((happy(mary) & quiet(mary) & creative(mary) & tourist(mary)) <=> (~((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
((~(~((~hate(mary, fred)) | (~hate(fred, mary))))) <=> ((~hate(mary, fred)) | (~hate(fred, mary)))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((hate(mary, fred) & hate(fred, mary)) <=> (~((~hate(mary, fred)) | (~hate(fred, mary))))),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
((~(hate(mary, fred) & hate(fred, mary))) <=> (~(~((~hate(mary, fred)) | (~hate(fred, mary)))))),
inference(monotonicity,[status(thm)],[37])).
tff(39,plain,
((~(hate(mary, fred) & hate(fred, mary))) <=> ((~hate(mary, fred)) | (~hate(fred, mary)))),
inference(transitivity,[status(thm)],[38, 36])).
tff(40,plain,
((~(~((~happy(mary)) | (~european(mary))))) <=> ((~happy(mary)) | (~european(mary)))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
((happy(mary) & european(mary)) <=> (~((~happy(mary)) | (~european(mary))))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
((~(happy(mary) & european(mary))) <=> (~(~((~happy(mary)) | (~european(mary)))))),
inference(monotonicity,[status(thm)],[41])).
tff(43,plain,
((~(happy(mary) & european(mary))) <=> ((~happy(mary)) | (~european(mary)))),
inference(transitivity,[status(thm)],[42, 40])).
tff(44,plain,
(((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))) <=> (((~happy(mary)) | (~european(mary))) | ((~hate(mary, fred)) | (~hate(fred, mary))) | (~((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(monotonicity,[status(thm)],[43, 39, 35])).
tff(45,plain,
(((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))) <=> ((~happy(mary)) | (~european(mary)) | (~hate(mary, fred)) | (~hate(fred, mary)) | (~((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(transitivity,[status(thm)],[44, 34])).
tff(46,plain,
(((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))) <=> ((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary)))),
inference(rewrite,[status(thm)],[])).
tff(47,plain,
((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))),
inference(and_elim,[status(thm)],[9])).
tff(48,plain,
((~(happy(mary) & european(mary))) | (~(hate(mary, fred) & hate(fred, mary))) | (happy(mary) & quiet(mary) & creative(mary) & tourist(mary))),
inference(modus_ponens,[status(thm)],[47, 46])).
tff(49,plain,
((~happy(mary)) | (~european(mary)) | (~hate(mary, fred)) | (~hate(fred, mary)) | (~((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(modus_ponens,[status(thm)],[48, 45])).
tff(50,plain,
(~((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(unit_resolution,[status(thm)],[49, 33, 31, 17, 28])).
tff(51,plain,
(((~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))) | tourist(mary)),
inference(tautology,[status(thm)],[])).
tff(52,plain,
(tourist(mary)),
inference(unit_resolution,[status(thm)],[51, 50])).
tff(53,plain,
(creative(mary) <=> creative(mary)),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(creative(mary)),
inference(and_elim,[status(thm)],[9])).
tff(55,plain,
(creative(mary)),
inference(modus_ponens,[status(thm)],[54, 53])).
tff(56,plain,
((~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))),
inference(tautology,[status(thm)],[])).
tff(57,plain,
((~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))) | (~quiet(mary)) | (~tourist(mary))),
inference(unit_resolution,[status(thm)],[56, 55])).
tff(58,plain,
(~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(unit_resolution,[status(thm)],[57, 52, 26])).
tff(59,plain,
((preda(mary) | (~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))) | ((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(tautology,[status(thm)],[])).
tff(60,plain,
(preda(mary) | (~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(unit_resolution,[status(thm)],[59, 58])).
tff(61,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(62,plain,
(room(paul)),
inference(and_elim,[status(thm)],[9])).
tff(63,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[62, 61])).
tff(64,plain,
(((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(65,plain,
(((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (quiet(mary) & creative(mary) & tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(66,plain,
((~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(67,plain,
(((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (quiet(mary) & creative(mary) & tourist(mary)))))),
inference(monotonicity,[status(thm)],[66])).
tff(68,plain,
(((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(preda(mary) | (quiet(mary) & creative(mary) & tourist(mary)))))),
inference(transitivity,[status(thm)],[67, 65])).
tff(69,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(70,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary)))))),
inference(monotonicity,[status(thm)],[69])).
tff(71,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(72,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))),
inference(or_elim,[status(thm)],[8])).
tff(73,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[72, 70])).
tff(74,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[73, 71])).
tff(75,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (preda(mary) | (quiet(mary) & creative(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[74, 70])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!4 |'paul'|) (= X!4 |'mary'|) (not (room X!4)))))
(a!5 (or (preda mary) (and (quiet mary) (creative mary) (tourist mary)))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 a!5))
(or (not (room mary)) (not (room paul)) a!4 (not a!5)))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (not a!5) (not a!5))) a!6)))
| room(andrew)&room(nancy)&(![X]:(room(X)=>(X='andrew'|X='nancy')))&
(((~hate(david,andrew)&~hate(david,nancy))=>((?[X,Y]:(~room(X)&~room(Y)&(hate(X,daniel)&hate(Y,daniel))&(X!=Y)))))&
(((hate(andrew,daniel) & hate(daniel,andrew)))=>(((~(happy(andrew)&european(andrew)))|(happy(andrew)&quiet(andrew)&creative(andrew)&tourist(andrew)))))&
((![X]:(quieter(nancy,X)))=>((does_not_build_model_airplanes(nancy))&(~hate(nancy,daniel))))&
(![X]:(room(X)=>(((~(happy(X)&quiet(X)&european(X)))=>(~hate(daniel,X))))))&
(((?[X]:(room(X)&does_not_have_a_saltwater_aquarium(X)))&(![X,Y]:((does_not_have_a_saltwater_aquarium(X)&does_not_have_a_saltwater_aquarium(Y))=>(X=Y)))))&
((creative(andrew))&(quiet(nancy)))&
(hate(daniel,nancy)&hate(daniel,andrew))&
(hate(andrew,daniel))&
(![X]:(quieter(X,nancy)))) | room(andrew)&room(nancy)&(![X]:(room(X)=>(X='andrew'|X='nancy')))&
(((collects_comic_books(andrew))|(quiet(andrew)&creative(andrew)&tourist(andrew)))) | neutral | neutral | neutral |
Laura, Christopher, Mark, Toni are the only persons in the room. If 'more than one person outside the room does not like Byron' then 'Laura either is not Christopher or likes Byron'. 'Someone who is not creative like someone who does not like Byron' if 'more than one person in the room is a rich quiet european' and vice versa. If 'no one in the room who likes Byron is not a quiet creative european' then 'Laura likes Byron and does not like Byron'. Mark and Laura are respectively rich and creative. Laura is not Mark or likes Byron or both. Mark is the least quiet in the room. More than one person in the room is not Mark. Mark is the least rich in the room. More than one person in the room is not liked by Byron. Byron is quieter than Mark. Laura neither is not liked by Byron nor does not like Byron. Laura likes Byron. | It is not the case that 'someone who is not a quiet person like someone who is not rich'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(rich_type, type, (
rich: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_Y_10_type, type, (
tptp_fun_Y_10: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(tptp_fun_X_11_type, type, (
tptp_fun_X_11: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_9_type, type, (
tptp_fun_X_9: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(mary_type, type, (
mary: $i)).
tff(susan_type, type, (
susan: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(paul_type, type, (
paul: $i)).
tff(1,assumption,(~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))), introduced(assumption)).
tff(2,plain,
(((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | room(X!9)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(room(X!9)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | (~(X!9 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(~(X!9 = |'mary'|)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
(((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | (~(X!9 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(~(X!9 = |'paul'|)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
(((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | (~(X!9 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(9,plain,
(~(X!9 = |'fred'|)),
inference(unit_resolution,[status(thm)],[8, 1])).
tff(10,plain,
(((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | (~(X!9 = |'alice'|))),
inference(tautology,[status(thm)],[])).
tff(11,plain,
(~(X!9 = |'alice'|)),
inference(unit_resolution,[status(thm)],[10, 1])).
tff(12,plain,
(^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(13,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[12])).
tff(14,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((((?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(susan, X)) & (~like(susan, Y)))) & (~(X = Y))) => (((~(mary = paul)) | like(susan, mary)) & (~((~(mary = paul)) | like(susan, mary))))) & (?[X: $i, Y: $i] : (((room(X) & room(Y)) & (((((rich(X) & quiet(X)) & european(X)) & rich(Y)) & quiet(Y)) & european(Y))) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (((~creative(X)) & (~like(susan, Y))) & like(X, Y)))) & ((~?[X: $i] : (room(X) => (like(susan, X) => (~((quiet(X) & creative(X)) & european(X)))))) => (like(susan, mary) & (~like(susan, mary))))) & (rich(fred) & creative(mary))) & ((~(mary = fred)) | like(susan, mary))) & ![X: $i] : quieter(fred, X)) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(X = fred)) & (~(Y = fred)))) & (~(X = Y)))) & ![X: $i] : richer(fred, X)) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~like(X, susan)) & (~like(Y, susan)))) & (~(X = Y)))) & quieter(fred, susan)) & (~((~like(mary, susan)) | (~like(susan, mary))))) & like(susan, mary))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~?[X: $i, Y: $i] : (((~(quiet(X) & person(X))) & (~rich(Y))) & like(X, Y)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(susan, X)) & (~like(susan, Y)) & (~(X = Y)))) & (?[X: $i, Y: $i] : (room(X) & room(Y) & rich(X) & quiet(X) & european(X) & rich(Y) & quiet(Y) & european(Y) & (~(X = Y))) <=> ?[X: $i, Y: $i] : ((~creative(X)) & (~like(susan, Y)) & like(X, Y))) & ?[X: $i] : ((~like(susan, X)) | (~room(X)) | (~(quiet(X) & creative(X) & european(X)))) & rich(fred) & creative(mary) & ((~(mary = fred)) | like(susan, mary)) & ![X: $i] : quieter(fred, X) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~like(X, susan)) & (~like(Y, susan)) & (~(X = Y))) & quieter(fred, susan) & (~((~like(mary, susan)) | (~like(susan, mary)))) & like(susan, mary))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))))),
inference(rewrite,[status(thm)],[])).
tff(16,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((((?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(susan, X)) & (~like(susan, Y)))) & (~(X = Y))) => (((~(mary = paul)) | like(susan, mary)) & (~((~(mary = paul)) | like(susan, mary))))) & (?[X: $i, Y: $i] : (((room(X) & room(Y)) & (((((rich(X) & quiet(X)) & european(X)) & rich(Y)) & quiet(Y)) & european(Y))) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (((~creative(X)) & (~like(susan, Y))) & like(X, Y)))) & ((~?[X: $i] : (room(X) => (like(susan, X) => (~((quiet(X) & creative(X)) & european(X)))))) => (like(susan, mary) & (~like(susan, mary))))) & (rich(fred) & creative(mary))) & ((~(mary = fred)) | like(susan, mary))) & ![X: $i] : quieter(fred, X)) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(X = fred)) & (~(Y = fred)))) & (~(X = Y)))) & ![X: $i] : richer(fred, X)) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~like(X, susan)) & (~like(Y, susan)))) & (~(X = Y)))) & quieter(fred, susan)) & (~((~like(mary, susan)) | (~like(susan, mary))))) & like(susan, mary))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~?[X: $i, Y: $i] : (((~(quiet(X) & person(X))) & (~rich(Y))) & like(X, Y)))))), file('/mnt/tmpfs//6593178791282250248881614.p','negated')).
tff(17,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(susan, X)) & (~like(susan, Y)) & (~(X = Y)))) & (?[X: $i, Y: $i] : (room(X) & room(Y) & rich(X) & quiet(X) & european(X) & rich(Y) & quiet(Y) & european(Y) & (~(X = Y))) <=> ?[X: $i, Y: $i] : ((~creative(X)) & (~like(susan, Y)) & like(X, Y))) & ?[X: $i] : ((~like(susan, X)) | (~room(X)) | (~(quiet(X) & creative(X) & european(X)))) & rich(fred) & creative(mary) & ((~(mary = fred)) | like(susan, mary)) & ![X: $i] : quieter(fred, X) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~like(X, susan)) & (~like(Y, susan)) & (~(X = Y))) & quieter(fred, susan) & (~((~like(mary, susan)) | (~like(susan, mary)))) & like(susan, mary))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y)))))),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(susan, X)) & (~like(susan, Y)) & (~(X = Y)))) & (?[X: $i, Y: $i] : (room(X) & room(Y) & rich(X) & quiet(X) & european(X) & rich(Y) & quiet(Y) & european(Y) & (~(X = Y))) <=> ?[X: $i, Y: $i] : ((~creative(X)) & (~like(susan, Y)) & like(X, Y))) & ?[X: $i] : ((~like(susan, X)) | (~room(X)) | (~(quiet(X) & creative(X) & european(X)))) & rich(fred) & creative(mary) & ((~(mary = fred)) | like(susan, mary)) & ![X: $i] : quieter(fred, X) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y))) & ![X: $i] : richer(fred, X) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~like(X, susan)) & (~like(Y, susan)) & (~(X = Y))) & quieter(fred, susan) & (~((~like(mary, susan)) | (~like(susan, mary)))) & like(susan, mary)),
inference(or_elim,[status(thm)],[17])).
tff(19,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[19, 14])).
tff(21,plain,(
![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[20])).
tff(22,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[21, 13])).
tff(23,plain,
(((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))),
inference(quant_inst,[status(thm)],[])).
tff(25,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))),
inference(modus_ponens,[status(thm)],[24, 23])).
tff(26,plain,
($false),
inference(unit_resolution,[status(thm)],[25, 22, 11, 9, 7, 5, 3])).
tff(27,plain,((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))), inference(lemma,lemma(discharge,[]))).
tff(28,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
(room(alice)),
inference(and_elim,[status(thm)],[18])).
tff(30,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[29, 28])).
tff(31,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(32,plain,
(room(fred)),
inference(and_elim,[status(thm)],[18])).
tff(33,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[32, 31])).
tff(34,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
(room(paul)),
inference(and_elim,[status(thm)],[18])).
tff(36,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
(room(mary)),
inference(and_elim,[status(thm)],[18])).
tff(39,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[38, 37])).
tff(40,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~(rich(Y!10) | (~((~quiet(X!11)) | (~person(X!11)))) | (~like(X!11, Y!10))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~(rich(Y!10) | (~((~quiet(X!11)) | (~person(X!11)))) | (~like(X!11, Y!10)))))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
((((~quiet(X!11)) | (~person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10)) <=> (~(rich(Y!10) | (~((~quiet(X!11)) | (~person(X!11)))) | (~like(X!11, Y!10))))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
((~(~((~quiet(X!11)) | (~person(X!11))))) <=> ((~quiet(X!11)) | (~person(X!11)))),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
((quiet(X!11) & person(X!11)) <=> (~((~quiet(X!11)) | (~person(X!11))))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
((~(quiet(X!11) & person(X!11))) <=> (~(~((~quiet(X!11)) | (~person(X!11)))))),
inference(monotonicity,[status(thm)],[43])).
tff(45,plain,
((~(quiet(X!11) & person(X!11))) <=> ((~quiet(X!11)) | (~person(X!11)))),
inference(transitivity,[status(thm)],[44, 42])).
tff(46,plain,
(((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10)) <=> (((~quiet(X!11)) | (~person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10))),
inference(monotonicity,[status(thm)],[45])).
tff(47,plain,
(((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10)) <=> (~(rich(Y!10) | (~((~quiet(X!11)) | (~person(X!11)))) | (~like(X!11, Y!10))))),
inference(transitivity,[status(thm)],[46, 41])).
tff(48,plain,
((~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) <=> (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~(rich(Y!10) | (~((~quiet(X!11)) | (~person(X!11)))) | (~like(X!11, Y!10)))))),
inference(monotonicity,[status(thm)],[48, 47])).
tff(50,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~(rich(Y!10) | (~((~quiet(X!11)) | (~person(X!11)))) | (~like(X!11, Y!10)))))),
inference(transitivity,[status(thm)],[49, 40])).
tff(51,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10)))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10)))),
inference(monotonicity,[status(thm)],[48])).
tff(53,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | ((~(quiet(X!11) & person(X!11))) & (~rich(Y!10)) & like(X!11, Y!10)))),
inference(transitivity,[status(thm)],[52, 51])).
tff(54,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(55,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y)))))),
inference(monotonicity,[status(thm)],[54])).
tff(56,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))),
inference(or_elim,[status(thm)],[17])).
tff(58,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))),
inference(modus_ponens,[status(thm)],[57, 55])).
tff(59,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))),
inference(modus_ponens,[status(thm)],[58, 56])).
tff(60,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~(quiet(X) & person(X))) & (~rich(Y)) & like(X, Y))))),
inference(modus_ponens,[status(thm)],[59, 55])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!9 |'alice'|)
(= X!9 |'fred'|)
(= X!9 |'paul'|)
(= X!9 |'mary'|)
(not (room X!9)))))
(a!7 (exists ((X $i) (Y $i))
(and (not (and (quiet X) (person X))) (not (rich Y)) (like X Y))))
(a!8 (and (not (and (quiet X!11) (person X!11)))
(not (rich Y!10))
(like X!11 Y!10))))
(let ((a!9 (nnf-neg (sk (~ a!7 a!8)) (~ (not (not a!7)) a!8)))
(a!10 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(not a!7)))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
a!8))))
(nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!9 a!10)))
| room(laura)&room(christopher)&room(mark)&room(toni)&(![X]:(room(X)=>(X='laura'|X='christopher'|X='mark'|X='toni')))&
((((?[X,Y]:(~room(X)&~room(Y)&(~like(byron,X)&~like(byron,Y))&(X!=Y))))=>((((laura!=christopher)|(like(byron,laura)))&(~((laura!=christopher)|(like(byron,laura)))))))&
(((?[X,Y]:(room(X)&room(Y)&(rich(X)&quiet(X)&european(X)&rich(Y)&quiet(Y)&european(Y))&(X!=Y))))<=>(?[X,Y]:((~creative(X))&(~like(byron,Y))&(like(X,Y)))))&
((~?[X]:(room(X)=>(((like(byron,X))=>(~(quiet(X)&creative(X)&european(X)))))))=>((like(byron,laura))&(~like(byron,laura))))&
((rich(mark))&(creative(laura)))&
(((laura!=mark)|(like(byron,laura))))&
(![X]:(quieter(mark,X)))&
((?[X,Y]:(room(X)&room(Y)&(X!=mark&Y!=mark)&(X!=Y))))&
(![X]:(richer(mark,X)))&
((?[X,Y]:(room(X)&room(Y)&(~like(X,byron)&~like(Y,byron))&(X!=Y))))&
(quieter(mark,byron))&
(~((~like(laura,byron))|(~like(byron,laura))))&
(like(byron,laura))) | room(laura)&room(christopher)&room(mark)&room(toni)&(![X]:(room(X)=>(X='laura'|X='christopher'|X='mark'|X='toni')))&
(~(?[X,Y]:((~(quiet(X)&person(X)))&(~rich(Y))&(like(X,Y))))) | entailment | entailment | entailment |
Daniel, Robert, Benjamin, James are the only persons in the room. “Robert and Benjamin are not Benjamin” only if “Robert is the quietest in the room”. Brandi is quieter than Benjamin. Everyone outside the room is not rich. Robert is the quietest in the room. Daniel neither is a quiet european nor builds model airplanes. Daniel and Benjamin are not a happy person. Benjamin neither builds model airplanes nor is not quiet. Benjamin is not a quiet tourist. It is not the case that 'everyone outside the room builds model airplanes'. | More than one person in the room is not a happy quiet person. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(happy_type, type, (
happy: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(rich_type, type, (
rich: $i > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(alice_type, type, (
alice: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(susan_type, type, (
susan: $i)).
tff(john_type, type, (
john: $i)).
tff(1,assumption,(~((~quiet(mary)) | (~happy(mary)) | (~person(mary)))), introduced(assumption)).
tff(2,plain,
(((~quiet(mary)) | (~happy(mary)) | (~person(mary))) | happy(mary)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(happy(mary)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~quiet(mary)) | (~happy(mary)) | (~person(mary))) | person(mary)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(person(mary)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
((~(~((~happy(mary)) | (~person(mary))))) <=> ((~happy(mary)) | (~person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
((happy(mary) & person(mary)) <=> (~((~happy(mary)) | (~person(mary))))),
inference(rewrite,[status(thm)],[])).
tff(8,plain,
((~(happy(mary) & person(mary))) <=> (~(~((~happy(mary)) | (~person(mary)))))),
inference(monotonicity,[status(thm)],[7])).
tff(9,plain,
((~(happy(mary) & person(mary))) <=> ((~happy(mary)) | (~person(mary)))),
inference(transitivity,[status(thm)],[8, 6])).
tff(10,plain,
((~(happy(mary) & person(mary))) <=> (~(happy(mary) & person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((~(paul = fred)) & (~(fred = fred))) => ![X: $i] : quieter(X, paul)) & quieter(fred, lucy)) & ![X: $i] : ((~room(X)) => (~rich(X)))) & ![X: $i] : quieter(X, paul)) & (~((quiet(mary) & european(mary)) | preda(mary)))) & ((~(happy(mary) & person(mary))) & (~(happy(fred) & person(fred))))) & (~(preda(fred) | (~quiet(fred))))) & (~(quiet(fred) & tourist(fred)))) & (~![X: $i] : ((~room(X)) => preda(X))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~((happy(X) & quiet(X)) & person(X))) & (~((happy(Y) & quiet(Y)) & person(Y))))) & (~(X = Y)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, lucy) & ![X: $i] : (room(X) | (~rich(X))) & ![X: $i] : quieter(X, paul) & (~((quiet(mary) & european(mary)) | preda(mary))) & (~(happy(mary) & person(mary))) & (~(happy(fred) & person(fred))) & (~(preda(fred) | (~quiet(fred)))) & (~(quiet(fred) & tourist(fred))) & (~![X: $i] : (room(X) | preda(X))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))))),
inference(rewrite,[status(thm)],[])).
tff(12,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((~(paul = fred)) & (~(fred = fred))) => ![X: $i] : quieter(X, paul)) & quieter(fred, lucy)) & ![X: $i] : ((~room(X)) => (~rich(X)))) & ![X: $i] : quieter(X, paul)) & (~((quiet(mary) & european(mary)) | preda(mary)))) & ((~(happy(mary) & person(mary))) & (~(happy(fred) & person(fred))))) & (~(preda(fred) | (~quiet(fred))))) & (~(quiet(fred) & tourist(fred)))) & (~![X: $i] : ((~room(X)) => preda(X))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~((happy(X) & quiet(X)) & person(X))) & (~((happy(Y) & quiet(Y)) & person(Y))))) & (~(X = Y)))))), file('/mnt/tmpfs//491741569972930525183641.p','negated')).
tff(13,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, lucy) & ![X: $i] : (room(X) | (~rich(X))) & ![X: $i] : quieter(X, paul) & (~((quiet(mary) & european(mary)) | preda(mary))) & (~(happy(mary) & person(mary))) & (~(happy(fred) & person(fred))) & (~(preda(fred) | (~quiet(fred)))) & (~(quiet(fred) & tourist(fred))) & (~![X: $i] : (room(X) | preda(X))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))))),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, lucy) & ![X: $i] : (room(X) | (~rich(X))) & ![X: $i] : quieter(X, paul) & (~((quiet(mary) & european(mary)) | preda(mary))) & (~(happy(mary) & person(mary))) & (~(happy(fred) & person(fred))) & (~(preda(fred) | (~quiet(fred)))) & (~(quiet(fred) & tourist(fred))) & (~![X: $i] : (room(X) | preda(X)))),
inference(or_elim,[status(thm)],[13])).
tff(15,plain,
(~(happy(mary) & person(mary))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(~(happy(mary) & person(mary))),
inference(modus_ponens,[status(thm)],[15, 10])).
tff(17,plain,
((~happy(mary)) | (~person(mary))),
inference(modus_ponens,[status(thm)],[16, 9])).
tff(18,plain,
($false),
inference(unit_resolution,[status(thm)],[17, 5, 3])).
tff(19,plain,((~quiet(mary)) | (~happy(mary)) | (~person(mary))), inference(lemma,lemma(discharge,[]))).
tff(20,assumption,(~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))), introduced(assumption)).
tff(21,plain,
(((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | room(X!1)),
inference(tautology,[status(thm)],[])).
tff(22,plain,
(room(X!1)),
inference(unit_resolution,[status(thm)],[21, 20])).
tff(23,plain,
(((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(24,plain,
(~(X!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[23, 20])).
tff(25,plain,
(((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(26,plain,
(~(X!1 = |'paul'|)),
inference(unit_resolution,[status(thm)],[25, 20])).
tff(27,plain,
(((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(28,plain,
(~(X!1 = |'fred'|)),
inference(unit_resolution,[status(thm)],[27, 20])).
tff(29,plain,
(((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'alice'|))),
inference(tautology,[status(thm)],[])).
tff(30,plain,
(~(X!1 = |'alice'|)),
inference(unit_resolution,[status(thm)],[29, 20])).
tff(31,plain,
(^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(32,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[31])).
tff(33,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[14])).
tff(35,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,(
![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[35])).
tff(37,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[36, 32])).
tff(38,plain,
(((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(rewrite,[status(thm)],[])).
tff(39,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(quant_inst,[status(thm)],[])).
tff(40,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))),
inference(modus_ponens,[status(thm)],[39, 38])).
tff(41,plain,
($false),
inference(unit_resolution,[status(thm)],[40, 37, 30, 28, 26, 24, 22])).
tff(42,plain,((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))), inference(lemma,lemma(discharge,[]))).
tff(43,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
(room(alice)),
inference(and_elim,[status(thm)],[14])).
tff(45,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[44, 43])).
tff(46,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(47,plain,
(room(fred)),
inference(and_elim,[status(thm)],[14])).
tff(48,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[47, 46])).
tff(49,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
(room(paul)),
inference(and_elim,[status(thm)],[14])).
tff(51,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[50, 49])).
tff(52,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(53,plain,
(room(mary)),
inference(and_elim,[status(thm)],[14])).
tff(54,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[53, 52])).
tff(55,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(56,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((happy(X) & quiet(X) & person(X)) <=> (~((~quiet(X)) | (~happy(X)) | (~person(X))))), ((~(happy(X) & quiet(X) & person(X))) <=> (~(~((~quiet(X)) | (~happy(X)) | (~person(X))))))), rewrite((~(~((~quiet(X)) | (~happy(X)) | (~person(X))))) <=> ((~quiet(X)) | (~happy(X)) | (~person(X)))), ((~(happy(X) & quiet(X) & person(X))) <=> ((~quiet(X)) | (~happy(X)) | (~person(X))))), trans(monotonicity(rewrite((happy(Y) & quiet(Y) & person(Y)) <=> (~((~happy(Y)) | (~quiet(Y)) | (~person(Y))))), ((~(happy(Y) & quiet(Y) & person(Y))) <=> (~(~((~happy(Y)) | (~quiet(Y)) | (~person(Y))))))), rewrite((~(~((~happy(Y)) | (~quiet(Y)) | (~person(Y))))) <=> ((~happy(Y)) | (~quiet(Y)) | (~person(Y)))), ((~(happy(Y) & quiet(Y) & person(Y))) <=> ((~happy(Y)) | (~quiet(Y)) | (~person(Y))))), ((room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))) <=> (room(X) & room(Y) & ((~quiet(X)) | (~happy(X)) | (~person(X))) & ((~happy(Y)) | (~quiet(Y)) | (~person(Y))) & (~(X = Y))))), rewrite((room(X) & room(Y) & ((~quiet(X)) | (~happy(X)) | (~person(X))) & ((~happy(Y)) | (~quiet(Y)) | (~person(Y))) & (~(X = Y))) <=> (~((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X))))), ((room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))) <=> (~((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X)))))), ((~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))) <=> (~(~((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X))))))), rewrite((~(~((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X))))) <=> ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X)))), ((~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))) <=> ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X)))))),
inference(bind,[status(th)],[])).
tff(58,plain,
(![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))) <=> ![X: $i, Y: $i] : ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X)))),
inference(quant_intro,[status(thm)],[57])).
tff(59,plain,
((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(60,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X))))),
inference(monotonicity,[status(thm)],[59, 58])).
tff(61,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((X = Y) | (~room(Y)) | (~((~quiet(X)) | (~happy(X)) | (~person(X)))) | (~((~happy(Y)) | (~quiet(Y)) | (~person(Y)))) | (~room(X))))),
inference(transitivity,[status(thm)],[60, 56])).
tff(62,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))))),
inference(rewrite,[status(thm)],[])).
tff(63,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))))),
inference(monotonicity,[status(thm)],[59])).
tff(64,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))))),
inference(transitivity,[status(thm)],[63, 62])).
tff(65,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))),
inference(rewrite,[status(thm)],[])).
tff(66,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))))),
inference(monotonicity,[status(thm)],[65])).
tff(67,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y)))))),
inference(rewrite,[status(thm)],[])).
tff(68,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))),
inference(or_elim,[status(thm)],[13])).
tff(69,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))),
inference(modus_ponens,[status(thm)],[68, 66])).
tff(70,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))),
inference(modus_ponens,[status(thm)],[69, 67])).
tff(71,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(happy(X) & quiet(X) & person(X))) & (~(happy(Y) & quiet(Y) & person(Y))) & (~(X = Y))))),
inference(modus_ponens,[status(thm)],[70, 66])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!1 |'alice'|)
(= X!1 |'fred'|)
(= X!1 |'paul'|)
(= X!1 |'mary'|)
(not (room X!1)))))
(a!7 (lambda ((X $i) (Y $i))
(let ((a!1 (and (room X)
(room Y)
(not (and (happy X) (quiet X) (person X)))
(not (and (happy Y) (quiet Y) (person Y)))
(not (= X Y)))))
(refl (~ (not a!1) (not a!1))))))
(a!8 (exists ((X $i) (Y $i))
(and (room X)
(room Y)
(not (and (happy X) (quiet X) (person X)))
(not (and (happy Y) (quiet Y) (person Y)))
(not (= X Y)))))
(a!9 (forall ((X $i) (Y $i))
(let ((a!1 (and (room X)
(room Y)
(not (and (happy X) (quiet X) (person X)))
(not (and (happy Y) (quiet Y) (person Y)))
(not (= X Y)))))
(not a!1)))))
(let ((a!10 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
a!8))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
a!9))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
(nnf-neg (proof-bind a!7) (~ (not a!8) a!9))
a!10)))
| room(daniel)&room(robert)&room(benjamin)&room(james)&(![X]:(room(X)=>(X='daniel'|X='robert'|X='benjamin'|X='james')))&
(((robert!=benjamin&benjamin!=benjamin)=>(![X]:(quieter(X,robert))))&
(quieter(benjamin,brandi))&
(![X]:(~room(X)=>(~rich(X))))&
(![X]:(quieter(X,robert)))&
(~((quiet(daniel)&european(daniel))|(builds_model_airplanes(daniel))))&
(~(happy(daniel)&person(daniel))&~(happy(benjamin)&person(benjamin)))&
(~((builds_model_airplanes(benjamin))|(~quiet(benjamin))))&
(~(quiet(benjamin)&tourist(benjamin)))&
(~(![X]:(~room(X)=>(builds_model_airplanes(X)))))) | room(daniel)&room(robert)&room(benjamin)&room(james)&(![X]:(room(X)=>(X='daniel'|X='robert'|X='benjamin'|X='james')))&
((?[X,Y]:(room(X)&room(Y)&(~(happy(X)&quiet(X)&person(X))&~(happy(Y)&quiet(Y)&person(Y)))&(X!=Y)))) | entailment | neutral | entailment |
Raymond is the only person in the room. 'It is not the case that 'Bradley is taller than Raymond'' if 'only one person outside the room is liked by Bradley' and vice versa. 'Raymond is a sibling of Bradley and is not tall' if 'Raymond is taller than Bradley or is not a quiet creative tourist or both' and vice versa. Raymond is a tall quiet tourist. Raymond is the least tall in the room. Raymond does not like Bradley. Raymond is the least quiet in the room. | Raymond is a quiet creative tall tourist or is liked by Jack or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(1,plain,
((~((tall(mary) | (~sibling(john, mary))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))) <=> (~((tall(mary) | (~sibling(john, mary))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
(((taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))) <=> (~(tall(mary) | (~sibling(john, mary))))) <=> (~((tall(mary) | (~sibling(john, mary))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(3,plain,
((sibling(john, mary) & (~tall(mary))) <=> (~(tall(mary) | (~sibling(john, mary))))),
inference(rewrite,[status(thm)],[])).
tff(4,plain,
((taller(john, mary) | ((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~(~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))) <=> ((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(rewrite,[status(thm)],[])).
tff(6,plain,
((quiet(mary) & creative(mary) & tourist(mary)) <=> (~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
((~(quiet(mary) & creative(mary) & tourist(mary))) <=> (~(~((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(monotonicity,[status(thm)],[6])).
tff(8,plain,
((~(quiet(mary) & creative(mary) & tourist(mary))) <=> ((~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(transitivity,[status(thm)],[7, 5])).
tff(9,plain,
((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (taller(john, mary) | ((~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(monotonicity,[status(thm)],[8])).
tff(10,plain,
((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(transitivity,[status(thm)],[9, 4])).
tff(11,plain,
(((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))) <=> ((taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))) <=> (~(tall(mary) | (~sibling(john, mary)))))),
inference(monotonicity,[status(thm)],[10, 3])).
tff(12,plain,
(((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))) <=> (~((tall(mary) | (~sibling(john, mary))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(transitivity,[status(thm)],[11, 2])).
tff(13,plain,
(((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))) <=> (~((tall(mary) | (~sibling(john, mary))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(transitivity,[status(thm)],[12, 1])).
tff(14,plain,
(((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))) <=> ((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary))))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((((?[X: $i] : ((~room(X)) & like(X, john)) & ![X: $i, Y: $i] : ((like(X, john) & like(Y, john)) => (X = Y))) <=> (~taller(mary, john))) & ((taller(john, mary) | (~((quiet(mary) & creative(mary)) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary))))) & ((tall(mary) & quiet(mary)) & tourist(mary))) & ![X: $i] : taller(mary, X)) & (~like(john, mary))) & ![X: $i] : quieter(mary, X))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((quiet(mary) & creative(mary)) & tall(mary)) & tourist(mary)) | like(mary, fred))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(taller(mary, john) <=> (?[X: $i] : ((~room(X)) & like(X, john)) & ![X: $i, Y: $i] : ((~(like(X, john) & like(Y, john))) | (X = Y))))) & ((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))) & tall(mary) & quiet(mary) & tourist(mary) & ![X: $i] : taller(mary, X) & (~like(john, mary)) & ![X: $i] : quieter(mary, X))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(16,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((((?[X: $i] : ((~room(X)) & like(X, john)) & ![X: $i, Y: $i] : ((like(X, john) & like(Y, john)) => (X = Y))) <=> (~taller(mary, john))) & ((taller(john, mary) | (~((quiet(mary) & creative(mary)) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary))))) & ((tall(mary) & quiet(mary)) & tourist(mary))) & ![X: $i] : taller(mary, X)) & (~like(john, mary))) & ![X: $i] : quieter(mary, X))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((quiet(mary) & creative(mary)) & tall(mary)) & tourist(mary)) | like(mary, fred))))), file('/mnt/tmpfs//4190469257015855953265067.p','negated')).
tff(17,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(taller(mary, john) <=> (?[X: $i] : ((~room(X)) & like(X, john)) & ![X: $i, Y: $i] : ((~(like(X, john) & like(Y, john))) | (X = Y))))) & ((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))) & tall(mary) & quiet(mary) & tourist(mary) & ![X: $i] : taller(mary, X) & (~like(john, mary)) & ![X: $i] : quieter(mary, X))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(taller(mary, john) <=> (?[X: $i] : ((~room(X)) & like(X, john)) & ![X: $i, Y: $i] : ((~(like(X, john) & like(Y, john))) | (X = Y))))) & ((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))) & tall(mary) & quiet(mary) & tourist(mary) & ![X: $i] : taller(mary, X) & (~like(john, mary)) & ![X: $i] : quieter(mary, X)),
inference(or_elim,[status(thm)],[17])).
tff(19,plain,
((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))),
inference(modus_ponens,[status(thm)],[19, 14])).
tff(21,plain,
((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))),
inference(modus_ponens,[status(thm)],[20, 14])).
tff(22,plain,
((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))),
inference(modus_ponens,[status(thm)],[21, 14])).
tff(23,plain,
((taller(john, mary) | (~(quiet(mary) & creative(mary) & tourist(mary)))) <=> (sibling(john, mary) & (~tall(mary)))),
inference(modus_ponens,[status(thm)],[22, 14])).
tff(24,plain,
(~((tall(mary) | (~sibling(john, mary))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(modus_ponens,[status(thm)],[23, 13])).
tff(25,plain,
(tall(mary) <=> tall(mary)),
inference(rewrite,[status(thm)],[])).
tff(26,plain,
(tall(mary)),
inference(and_elim,[status(thm)],[18])).
tff(27,plain,
(tall(mary)),
inference(modus_ponens,[status(thm)],[26, 25])).
tff(28,plain,
((tall(mary) | (~sibling(john, mary))) | (~tall(mary))),
inference(tautology,[status(thm)],[])).
tff(29,plain,
(tall(mary) | (~sibling(john, mary))),
inference(unit_resolution,[status(thm)],[28, 27])).
tff(30,plain,
(((tall(mary) | (~sibling(john, mary))) <=> (taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))) | (~(tall(mary) | (~sibling(john, mary)))) | (~(taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(tautology,[status(thm)],[])).
tff(31,plain,
(~(taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(unit_resolution,[status(thm)],[30, 29, 24])).
tff(32,plain,
((taller(john, mary) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))) | creative(mary)),
inference(tautology,[status(thm)],[])).
tff(33,plain,
(creative(mary)),
inference(unit_resolution,[status(thm)],[32, 31])).
tff(34,plain,
(tourist(mary) <=> tourist(mary)),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
(tourist(mary)),
inference(and_elim,[status(thm)],[18])).
tff(36,plain,
(tourist(mary)),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,
(quiet(mary) <=> quiet(mary)),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
(quiet(mary)),
inference(and_elim,[status(thm)],[18])).
tff(39,plain,
(quiet(mary)),
inference(modus_ponens,[status(thm)],[38, 37])).
tff(40,plain,
((~((~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))) | (~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))),
inference(tautology,[status(thm)],[])).
tff(41,plain,
((~((~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))) | (~creative(mary))),
inference(unit_resolution,[status(thm)],[40, 27, 39, 36])).
tff(42,plain,
(~((~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(unit_resolution,[status(thm)],[41, 33])).
tff(43,plain,
((like(mary, fred) | (~((~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))) | ((~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(tautology,[status(thm)],[])).
tff(44,plain,
(like(mary, fred) | (~((~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(unit_resolution,[status(thm)],[43, 42])).
tff(45,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(room(mary)),
inference(and_elim,[status(thm)],[18])).
tff(47,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[46, 45])).
tff(48,plain,
(((~room(mary)) | (~((~room(X!3)) | (X!3 = |'mary'|))) | (~(like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))) <=> ((~room(mary)) | (~((~room(X!3)) | (X!3 = |'mary'|))) | (~(like(mary, fred) | (~((~tall(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary)))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary)))))),
inference(monotonicity,[status(thm)],[49])).
tff(51,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))),
inference(or_elim,[status(thm)],[17])).
tff(53,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[52, 50])).
tff(54,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[53, 51])).
tff(55,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, fred) | (quiet(mary) & creative(mary) & tall(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[54, 50])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!3)) (= X!3 |'mary'|))))
(a!4 (or (like mary fred)
(and (quiet mary) (creative mary) (tall mary) (tourist mary)))))
(let ((a!5 (~ (not (and (room mary) a!2 a!4))
(or (not (room mary)) a!3 (not a!4)))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (not a!4) (not a!4))) a!5)))
| room(raymond)&(![X]:(room(X)=>(X='raymond')))&
(((((?[X]:(~room(X)&like(X,bradley)))&(![X,Y]:((like(X,bradley)&like(Y,bradley))=>(X=Y)))))<=>(~(taller(raymond,bradley))))&
((((taller(bradley,raymond))|(~(quiet(raymond)&creative(raymond)&tourist(raymond)))))<=>((sibling(bradley,raymond))&(~tall(raymond))))&
(tall(raymond)&quiet(raymond)&tourist(raymond))&
(![X]:(taller(raymond,X)))&
(~like(bradley,raymond))&
(![X]:(quieter(raymond,X)))) | room(raymond)&(![X]:(room(X)=>(X='raymond')))&
(((quiet(raymond)&creative(raymond)&tall(raymond)&tourist(raymond))|(like(raymond,jack)))) | neutral | neutral | neutral |
Chad, Billy, Berenice, Lisa are the only persons in the room.
'Chad and Billy are respectively quiet and happy' if 'someone outside the room is not allergic to anything' and vice versa.
'Everyone outside the room who is a coffee connoisseur does not practice yoga' if 'Lisa does practice yoga and is not liked by Jacob' and vice versa.
More than one person in the room is not quiet.
Someone in the room who is liked by Jacob is a quiet brave rich person.
Billy and Lisa like Jacob.
Someone who is not liked by Jacob is richer than someone who is not brave, not tall.
Only one person outside the room is a happy rich person.
Lisa likes Jacob or does not like Jacob or both.
Chad neither does not like Jacob nor is not liked by Jacob.
Billy is not quiet.
Someone outside the room is not allergic to anything.
Everyone outside the room likes Jacob. | It is not the case that 'Lisa is a rich tall brave happy person'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_8_type, type, (
tptp_fun_X_8: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(tptp_fun_X_7_type, type, (
tptp_fun_X_7: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(predc_type, type, (
predc: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(1,assumption,(X!7 = alice), introduced(assumption)).
tff(2,plain,
(room(X!7) <=> room(alice)),
inference(monotonicity,[status(thm)],[1])).
tff(3,plain,
(room(alice) <=> room(X!7)),
inference(symmetry,[status(thm)],[2])).
tff(4,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((((?[X: $i] : ((~room(X)) => (~predc(X))) <=> (quiet(mary) & happy(paul))) & ((predb(alice) & (~like(alice, susan))) <=> ![X: $i] : ((~room(X)) => (preda(X) => (~predb(X)))))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~quiet(X)) & (~quiet(Y)))) & (~(X = Y)))) & ?[X: $i] : (room(X) => (like(X, susan) => (((quiet(X) & brave(X)) & rich(X)) & person(X))))) & (like(susan, paul) & like(susan, alice))) & ?[X: $i, Y: $i] : (((~like(X, susan)) & ((~brave(Y)) & (~tall(Y)))) & richer(X, Y))) & (?[X: $i] : ((((~room(X)) & happy(X)) & rich(X)) & person(X)) & ![X: $i, Y: $i] : ((((((happy(X) & rich(X)) & person(X)) & happy(Y)) & rich(Y)) & person(Y)) => (X = Y)))) & (like(susan, alice) | (~like(susan, alice)))) & (~((~like(susan, mary)) | (~like(mary, susan))))) & (~quiet(paul))) & ?[X: $i] : ((~room(X)) => (~predc(X)))) & ![X: $i] : ((~room(X)) => like(susan, X)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((((rich(alice) & tall(alice)) & brave(alice)) & happy(alice)) & person(alice)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (room(X) | (~predc(X))) <=> (quiet(mary) & happy(paul))) & ((predb(alice) & (~like(alice, susan))) <=> ![X: $i] : (room(X) | (~predb(X)) | (~preda(X)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))) & ?[X: $i] : ((~room(X)) | (quiet(X) & brave(X) & rich(X) & person(X)) | (~like(X, susan))) & like(susan, paul) & like(susan, alice) & ?[X: $i, Y: $i] : ((~like(X, susan)) & (~brave(Y)) & (~tall(Y)) & richer(X, Y)) & ?[X: $i] : ((~room(X)) & happy(X) & rich(X) & person(X)) & ![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y)) & (~((~like(susan, mary)) | (~like(mary, susan)))) & (~quiet(paul)) & ?[X: $i] : (room(X) | (~predc(X))) & ![X: $i] : (room(X) | like(susan, X)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((((?[X: $i] : ((~room(X)) => (~predc(X))) <=> (quiet(mary) & happy(paul))) & ((predb(alice) & (~like(alice, susan))) <=> ![X: $i] : ((~room(X)) => (preda(X) => (~predb(X)))))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~quiet(X)) & (~quiet(Y)))) & (~(X = Y)))) & ?[X: $i] : (room(X) => (like(X, susan) => (((quiet(X) & brave(X)) & rich(X)) & person(X))))) & (like(susan, paul) & like(susan, alice))) & ?[X: $i, Y: $i] : (((~like(X, susan)) & ((~brave(Y)) & (~tall(Y)))) & richer(X, Y))) & (?[X: $i] : ((((~room(X)) & happy(X)) & rich(X)) & person(X)) & ![X: $i, Y: $i] : ((((((happy(X) & rich(X)) & person(X)) & happy(Y)) & rich(Y)) & person(Y)) => (X = Y)))) & (like(susan, alice) | (~like(susan, alice)))) & (~((~like(susan, mary)) | (~like(mary, susan))))) & (~quiet(paul))) & ?[X: $i] : ((~room(X)) => (~predc(X)))) & ![X: $i] : ((~room(X)) => like(susan, X)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((((rich(alice) & tall(alice)) & brave(alice)) & happy(alice)) & person(alice)))))), file('/mnt/tmpfs//3721914886515513327663205.p','negated')).
tff(7,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (room(X) | (~predc(X))) <=> (quiet(mary) & happy(paul))) & ((predb(alice) & (~like(alice, susan))) <=> ![X: $i] : (room(X) | (~predb(X)) | (~preda(X)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))) & ?[X: $i] : ((~room(X)) | (quiet(X) & brave(X) & rich(X) & person(X)) | (~like(X, susan))) & like(susan, paul) & like(susan, alice) & ?[X: $i, Y: $i] : ((~like(X, susan)) & (~brave(Y)) & (~tall(Y)) & richer(X, Y)) & ?[X: $i] : ((~room(X)) & happy(X) & rich(X) & person(X)) & ![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y)) & (~((~like(susan, mary)) | (~like(mary, susan)))) & (~quiet(paul)) & ?[X: $i] : (room(X) | (~predc(X))) & ![X: $i] : (room(X) | like(susan, X)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)))))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (room(X) | (~predc(X))) <=> (quiet(mary) & happy(paul))) & ((predb(alice) & (~like(alice, susan))) <=> ![X: $i] : (room(X) | (~predb(X)) | (~preda(X)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))) & ?[X: $i] : ((~room(X)) | (quiet(X) & brave(X) & rich(X) & person(X)) | (~like(X, susan))) & like(susan, paul) & like(susan, alice) & ?[X: $i, Y: $i] : ((~like(X, susan)) & (~brave(Y)) & (~tall(Y)) & richer(X, Y)) & ?[X: $i] : ((~room(X)) & happy(X) & rich(X) & person(X)) & ![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y)) & (~((~like(susan, mary)) | (~like(mary, susan)))) & (~quiet(paul)) & ?[X: $i] : (room(X) | (~predc(X))) & ![X: $i] : (room(X) | like(susan, X))),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(room(alice)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,
(room(X!7)),
inference(modus_ponens,[status(thm)],[10, 3])).
tff(12,plain,
(?[X: $i] : ((~room(X)) & happy(X) & rich(X) & person(X)) <=> ?[X: $i] : ((~room(X)) & happy(X) & rich(X) & person(X))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(?[X: $i] : ((~room(X)) & happy(X) & rich(X) & person(X))),
inference(and_elim,[status(thm)],[8])).
tff(14,plain,
(?[X: $i] : ((~room(X)) & happy(X) & rich(X) & person(X))),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,(
(~room(X!7)) & happy(X!7) & rich(X!7) & person(X!7)),
inference(skolemize,[status(sab)],[14])).
tff(16,plain,
(~room(X!7)),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
($false),
inference(unit_resolution,[status(thm)],[16, 11])).
tff(18,plain,(~(X!7 = alice)), inference(lemma,lemma(discharge,[]))).
tff(19,assumption,(~((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice)))), introduced(assumption)).
tff(20,plain,
(((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice))) | person(alice)),
inference(tautology,[status(thm)],[])).
tff(21,plain,
(person(alice)),
inference(unit_resolution,[status(thm)],[20, 19])).
tff(22,plain,
(((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice))) | happy(alice)),
inference(tautology,[status(thm)],[])).
tff(23,plain,
(happy(alice)),
inference(unit_resolution,[status(thm)],[22, 19])).
tff(24,plain,
(((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice))) | rich(alice)),
inference(tautology,[status(thm)],[])).
tff(25,plain,
(rich(alice)),
inference(unit_resolution,[status(thm)],[24, 19])).
tff(26,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))) <=> ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))))),
inference(bind,[status(th)],[])).
tff(27,plain,
(![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))),
inference(quant_intro,[status(thm)],[26])).
tff(28,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y)) <=> (~((~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))))), ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) <=> (~(~((~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))))))), rewrite((~(~((~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))))) <=> ((~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))), ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) <=> ((~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))))), (((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y)) <=> (((~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))) | (X = Y)))), rewrite((((~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y))) | (X = Y)) <=> ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))), (((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y)) <=> ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))))),
inference(bind,[status(th)],[])).
tff(29,plain,
(![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))),
inference(quant_intro,[status(thm)],[28])).
tff(30,plain,
(![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y))),
inference(and_elim,[status(thm)],[8])).
tff(32,plain,
(![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y))),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,(
![X: $i, Y: $i] : ((~(happy(X) & rich(X) & person(X) & happy(Y) & rich(Y) & person(Y))) | (X = Y))),
inference(skolemize,[status(sab)],[32])).
tff(34,plain,
(![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))),
inference(modus_ponens,[status(thm)],[33, 29])).
tff(35,plain,
(![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))),
inference(modus_ponens,[status(thm)],[34, 27])).
tff(36,plain,
(person(X!7)),
inference(and_elim,[status(thm)],[15])).
tff(37,plain,
(rich(X!7)),
inference(and_elim,[status(thm)],[15])).
tff(38,plain,
(happy(X!7)),
inference(and_elim,[status(thm)],[15])).
tff(39,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | ((~rich(alice)) | (~happy(alice)) | (~person(alice)) | (X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | (~rich(alice)) | (~happy(alice)) | (~person(alice)) | (X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
(((X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)) | (~happy(alice)) | (~rich(alice)) | (~person(alice))) <=> ((~rich(alice)) | (~happy(alice)) | (~person(alice)) | (X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | ((X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)) | (~happy(alice)) | (~rich(alice)) | (~person(alice)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | ((~rich(alice)) | (~happy(alice)) | (~person(alice)) | (X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7))))),
inference(monotonicity,[status(thm)],[40])).
tff(42,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | ((X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)) | (~happy(alice)) | (~rich(alice)) | (~person(alice)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | (~rich(alice)) | (~happy(alice)) | (~person(alice)) | (X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)))),
inference(transitivity,[status(thm)],[41, 39])).
tff(43,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | ((X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7)) | (~happy(alice)) | (~rich(alice)) | (~person(alice)))),
inference(quant_inst,[status(thm)],[])).
tff(44,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~rich(X)) | (~happy(X)) | (~person(X)) | (~happy(Y)) | (~rich(Y)) | (~person(Y)))) | (~rich(alice)) | (~happy(alice)) | (~person(alice)) | (X!7 = alice) | (~rich(X!7)) | (~happy(X!7)) | (~person(X!7))),
inference(modus_ponens,[status(thm)],[43, 42])).
tff(45,plain,
($false),
inference(unit_resolution,[status(thm)],[44, 38, 37, 36, 35, 25, 23, 21, 18])).
tff(46,plain,((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice))), inference(lemma,lemma(discharge,[]))).
tff(47,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(48,plain,
(room(fred)),
inference(and_elim,[status(thm)],[8])).
tff(49,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[48, 47])).
tff(50,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(51,plain,
(room(paul)),
inference(and_elim,[status(thm)],[8])).
tff(52,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[51, 50])).
tff(53,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(room(mary)),
inference(and_elim,[status(thm)],[8])).
tff(55,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[54, 53])).
tff(56,plain,
(((~((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))) | (~((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
((~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))) <=> (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(58,plain,
((rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)) <=> (~((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice))))),
inference(rewrite,[status(thm)],[])).
tff(59,plain,
(((rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|)))) <=> ((~((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))))),
inference(monotonicity,[status(thm)],[58, 57])).
tff(60,plain,
(((rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))) | (~((~rich(alice)) | (~tall(alice)) | (~brave(alice)) | (~happy(alice)) | (~person(alice)))))),
inference(transitivity,[status(thm)],[59, 56])).
tff(61,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))) | (rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))) <=> ((rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))))),
inference(rewrite,[status(thm)],[])).
tff(62,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))) | (rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))) | (rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)))),
inference(monotonicity,[status(thm)],[57])).
tff(63,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))) | (rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))) <=> ((rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!8)) | (X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|))))),
inference(transitivity,[status(thm)],[62, 61])).
tff(64,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))),
inference(rewrite,[status(thm)],[])).
tff(65,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)))))),
inference(monotonicity,[status(thm)],[64])).
tff(66,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(67,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))),
inference(or_elim,[status(thm)],[7])).
tff(68,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))),
inference(modus_ponens,[status(thm)],[67, 65])).
tff(69,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))),
inference(modus_ponens,[status(thm)],[68, 66])).
tff(70,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(rich(alice) & tall(alice) & brave(alice) & happy(alice) & person(alice))))),
inference(modus_ponens,[status(thm)],[69, 65])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (not (room X))
(= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|))))
(a!6 (not (or (not (room X!8))
(= X!8 |'alice'|)
(= X!8 |'fred'|)
(= X!8 |'paul'|)
(= X!8 |'mary'|))))
(a!7 (and (rich alice)
(tall alice)
(brave alice)
(happy alice)
(person alice))))
(let ((a!8 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(not a!7)))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
a!7))))
(nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!8)))
| room(chad)&room(billy)&room(berenice)&room(lisa)&(![X]:(room(X)=>(X='chad'|X='billy'|X='berenice'|X='lisa')))&
(((?[X]:(~room(X)=>(is_not_allergic_to_anything(X))))<=>((quiet(chad))&(happy(billy))))&
(((does_practice_yoga(lisa))&(~like(lisa,jacob)))<=>(![X]:(~room(X)=>(((is_a_coffee_connoisseur(X))=>(does_not_practice_yoga(X)))))))&
((?[X,Y]:(room(X)&room(Y)&(~quiet(X)&~quiet(Y))&(X!=Y))))&
(?[X]:(room(X)=>(((like(X,jacob))=>(quiet(X)&brave(X)&rich(X)&person(X))))))&
(like(jacob,billy)&like(jacob,lisa))&
(?[X,Y]:((~like(X,jacob))&(~brave(Y)&~tall(Y))&(richer(X,Y))))&
(((?[X]:(~room(X)&happy(X)&rich(X)&person(X)))&(![X,Y]:((happy(X)&rich(X)&person(X)&happy(Y)&rich(Y)&person(Y))=>(X=Y)))))&
(((like(jacob,lisa))|(~like(jacob,lisa))))&
(~((~like(jacob,chad))|(~like(chad,jacob))))&
(~quiet(billy))&
(?[X]:(~room(X)=>(is_not_allergic_to_anything(X))))&
(![X]:(~room(X)=>(like(jacob,X))))) | room(chad)&room(billy)&room(berenice)&room(lisa)&(![X]:(room(X)=>(X='chad'|X='billy'|X='berenice'|X='lisa')))&
(~(rich(lisa)&tall(lisa)&brave(lisa)&happy(lisa)&person(lisa))) | entailment | entailment | entailment |
Robbin is the only person in the room.
'Only one person outside the room is not rich, not happy, not quiet, not tall' only if 'Robbin neither likes Jeff nor is hated by Sandra'.
Robbin is the richest in the room.
Someone outside the room who practices urban gardening is richer than Jeff.
Robbin neither does not play the drums nor is not a quiet tourist. | Robbin neither is not a rich tall person nor is a quiet person. | contradiction | - | room(robbin)&(![X]:(room(X)=>(X='robbin')))&
(((((?[X]:(~room(X)&~rich(X)&~happy(X)&~quiet(X)&~tall(X)))&(![X,Y]:((~rich(X)&~happy(X)&~quiet(X)&~tall(X)&~rich(Y)&~happy(Y)&~quiet(Y)&~tall(Y))=>(X=Y)))))=>(~((like(jeff,robbin))|(hate(robbin,sandra)))))&
(![X]:(richer(X,robbin)))&
(?[X]:(~room(X)=>(((practices_urban_gardening(X))=>(richer(jeff,X))))))&
(~((does_not_play_the_drums(robbin))|(~(quiet(robbin)&tourist(robbin)))))) | room(robbin)&(![X]:(room(X)=>(X='robbin')))&
(~((~(rich(robbin)&tall(robbin)&person(robbin)))|(quiet(robbin)&person(robbin)))) | entailment | entailment | contradiction |
Stephanie, Carlos, Rosemary, Jenise are the only persons in the room.
"Only one person outside the room is not Rosemary" if "Carlos is not happy or enjoys kayaking or both".
"Someone outside the room who is not quiet likes Camille" unless "someone outside the room likes Camille".
Rosemary is not a creative happy quiet person or is not a brave person or both.
Stephanie neither is not happy, not creative nor does not enjoy kayaking.
Camille is taller than Stephanie.
Stephanie neither is not brave, not quiet, not happy nor is not hated by Camille.
Someone outside the room who is not hated by Camille is liked by Camille.
Carlos neither is a brave person nor is a creative person. | Carlos neither is not quiet, not happy nor is a creative quiet happy person. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(alice_type, type, (
alice: $i)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(john_type, type, (
john: $i)).
tff(1,assumption,(~((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul)))), introduced(assumption)).
tff(2,plain,
(((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul))) | person(paul)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(person(paul)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul))) | creative(paul)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(creative(paul)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
((~(~((~creative(paul)) | (~person(paul))))) <=> ((~creative(paul)) | (~person(paul)))),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
((creative(paul) & person(paul)) <=> (~((~creative(paul)) | (~person(paul))))),
inference(rewrite,[status(thm)],[])).
tff(8,plain,
((~(creative(paul) & person(paul))) <=> (~(~((~creative(paul)) | (~person(paul)))))),
inference(monotonicity,[status(thm)],[7])).
tff(9,plain,
((~(creative(paul) & person(paul))) <=> ((~creative(paul)) | (~person(paul)))),
inference(transitivity,[status(thm)],[8, 6])).
tff(10,plain,
((~(creative(paul) & person(paul))) <=> (~(creative(paul) & person(paul)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((~happy(paul)) | predb(paul)) => (?[X: $i] : ((~room(X)) & (~(X = fred))) & ![X: $i, Y: $i] : (((~(X = fred)) & (~(Y = fred))) => (X = Y)))) & ((~?[X: $i] : ((~room(X)) => like(susan, X))) => ?[X: $i] : ((~room(X)) => ((~quiet(X)) => like(susan, X))))) & ((~(((creative(fred) & happy(fred)) & quiet(fred)) & person(fred))) | (~(brave(fred) & person(fred))))) & (~(((~happy(mary)) & (~creative(mary))) | (~predb(mary))))) & taller(mary, susan)) & (~((((~brave(mary)) & (~quiet(mary))) & (~happy(mary))) | (~hate(mary, susan))))) & ?[X: $i] : ((~room(X)) => ((~hate(X, susan)) => like(X, susan)))) & (~((brave(paul) & person(paul)) | (creative(paul) & person(paul)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(((~quiet(paul)) & (~happy(paul))) | (((creative(paul) & quiet(paul)) & happy(paul)) & person(paul))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~happy(paul)) | predb(paul))) | (?[X: $i] : ((~room(X)) & (~(X = fred))) & ![X: $i, Y: $i] : ((~((~(X = fred)) & (~(Y = fred)))) | (X = Y)))) & (?[X: $i] : (room(X) | like(susan, X)) | ?[X: $i] : (quiet(X) | room(X) | like(susan, X))) & ((~(brave(fred) & person(fred))) | (~(creative(fred) & happy(fred) & quiet(fred) & person(fred)))) & (~(((~happy(mary)) & (~creative(mary))) | (~predb(mary)))) & taller(mary, susan) & (~((~hate(mary, susan)) | ((~brave(mary)) & (~quiet(mary)) & (~happy(mary))))) & ?[X: $i] : (room(X) | like(X, susan) | hate(X, susan)) & (~((brave(paul) & person(paul)) | (creative(paul) & person(paul)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))))),
inference(rewrite,[status(thm)],[])).
tff(12,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((~happy(paul)) | predb(paul)) => (?[X: $i] : ((~room(X)) & (~(X = fred))) & ![X: $i, Y: $i] : (((~(X = fred)) & (~(Y = fred))) => (X = Y)))) & ((~?[X: $i] : ((~room(X)) => like(susan, X))) => ?[X: $i] : ((~room(X)) => ((~quiet(X)) => like(susan, X))))) & ((~(((creative(fred) & happy(fred)) & quiet(fred)) & person(fred))) | (~(brave(fred) & person(fred))))) & (~(((~happy(mary)) & (~creative(mary))) | (~predb(mary))))) & taller(mary, susan)) & (~((((~brave(mary)) & (~quiet(mary))) & (~happy(mary))) | (~hate(mary, susan))))) & ?[X: $i] : ((~room(X)) => ((~hate(X, susan)) => like(X, susan)))) & (~((brave(paul) & person(paul)) | (creative(paul) & person(paul)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(((~quiet(paul)) & (~happy(paul))) | (((creative(paul) & quiet(paul)) & happy(paul)) & person(paul))))))), file('/mnt/tmpfs//5080462339923758923857440.p','negated')).
tff(13,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~happy(paul)) | predb(paul))) | (?[X: $i] : ((~room(X)) & (~(X = fred))) & ![X: $i, Y: $i] : ((~((~(X = fred)) & (~(Y = fred)))) | (X = Y)))) & (?[X: $i] : (room(X) | like(susan, X)) | ?[X: $i] : (quiet(X) | room(X) | like(susan, X))) & ((~(brave(fred) & person(fred))) | (~(creative(fred) & happy(fred) & quiet(fred) & person(fred)))) & (~(((~happy(mary)) & (~creative(mary))) | (~predb(mary)))) & taller(mary, susan) & (~((~hate(mary, susan)) | ((~brave(mary)) & (~quiet(mary)) & (~happy(mary))))) & ?[X: $i] : (room(X) | like(X, susan) | hate(X, susan)) & (~((brave(paul) & person(paul)) | (creative(paul) & person(paul)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul))))))),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~happy(paul)) | predb(paul))) | (?[X: $i] : ((~room(X)) & (~(X = fred))) & ![X: $i, Y: $i] : ((~((~(X = fred)) & (~(Y = fred)))) | (X = Y)))) & (?[X: $i] : (room(X) | like(susan, X)) | ?[X: $i] : (quiet(X) | room(X) | like(susan, X))) & ((~(brave(fred) & person(fred))) | (~(creative(fred) & happy(fred) & quiet(fred) & person(fred)))) & (~(((~happy(mary)) & (~creative(mary))) | (~predb(mary)))) & taller(mary, susan) & (~((~hate(mary, susan)) | ((~brave(mary)) & (~quiet(mary)) & (~happy(mary))))) & ?[X: $i] : (room(X) | like(X, susan) | hate(X, susan)) & (~((brave(paul) & person(paul)) | (creative(paul) & person(paul))))),
inference(or_elim,[status(thm)],[13])).
tff(15,plain,
(~((brave(paul) & person(paul)) | (creative(paul) & person(paul)))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(~(creative(paul) & person(paul))),
inference(or_elim,[status(thm)],[15])).
tff(17,plain,
(~(creative(paul) & person(paul))),
inference(modus_ponens,[status(thm)],[16, 10])).
tff(18,plain,
((~creative(paul)) | (~person(paul))),
inference(modus_ponens,[status(thm)],[17, 9])).
tff(19,plain,
($false),
inference(unit_resolution,[status(thm)],[18, 5, 3])).
tff(20,plain,((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul))), inference(lemma,lemma(discharge,[]))).
tff(21,assumption,(~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), introduced(assumption)).
tff(22,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | room(X!4)),
inference(tautology,[status(thm)],[])).
tff(23,plain,
(room(X!4)),
inference(unit_resolution,[status(thm)],[22, 21])).
tff(24,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(25,plain,
(~(X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[24, 21])).
tff(26,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(27,plain,
(~(X!4 = |'paul'|)),
inference(unit_resolution,[status(thm)],[26, 21])).
tff(28,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(29,plain,
(~(X!4 = |'fred'|)),
inference(unit_resolution,[status(thm)],[28, 21])).
tff(30,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'alice'|))),
inference(tautology,[status(thm)],[])).
tff(31,plain,
(~(X!4 = |'alice'|)),
inference(unit_resolution,[status(thm)],[30, 21])).
tff(32,plain,
(^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(33,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[32])).
tff(34,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[14])).
tff(36,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,(
![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[36])).
tff(38,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[37, 33])).
tff(39,plain,
(((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(quant_inst,[status(thm)],[])).
tff(41,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))),
inference(modus_ponens,[status(thm)],[40, 39])).
tff(42,plain,
($false),
inference(unit_resolution,[status(thm)],[41, 38, 31, 29, 27, 25, 23])).
tff(43,plain,((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(lemma,lemma(discharge,[]))).
tff(44,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(45,plain,
(room(alice)),
inference(and_elim,[status(thm)],[14])).
tff(46,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[45, 44])).
tff(47,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(48,plain,
(room(fred)),
inference(and_elim,[status(thm)],[14])).
tff(49,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[48, 47])).
tff(50,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(51,plain,
(room(paul)),
inference(and_elim,[status(thm)],[14])).
tff(52,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[51, 50])).
tff(53,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(room(mary)),
inference(and_elim,[status(thm)],[14])).
tff(55,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[54, 53])).
tff(56,plain,
(((~(happy(paul) | quiet(paul))) | (~((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(happy(paul) | quiet(paul))) | (~((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
((~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(58,plain,
((creative(paul) & quiet(paul) & happy(paul) & person(paul)) <=> (~((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul))))),
inference(rewrite,[status(thm)],[])).
tff(59,plain,
(((~quiet(paul)) & (~happy(paul))) <=> (~(happy(paul) | quiet(paul)))),
inference(rewrite,[status(thm)],[])).
tff(60,plain,
((((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~(happy(paul) | quiet(paul))) | (~((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(monotonicity,[status(thm)],[59, 58, 57])).
tff(61,plain,
((((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(happy(paul) | quiet(paul))) | (~((~happy(paul)) | (~quiet(paul)) | (~person(paul)) | (~creative(paul)))))),
inference(transitivity,[status(thm)],[60, 56])).
tff(62,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))) <=> (((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(rewrite,[status(thm)],[])).
tff(63,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul))))),
inference(monotonicity,[status(thm)],[57])).
tff(64,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))) <=> (((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(transitivity,[status(thm)],[63, 62])).
tff(65,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(66,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul))))))),
inference(monotonicity,[status(thm)],[65])).
tff(67,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul))))))),
inference(rewrite,[status(thm)],[])).
tff(68,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))),
inference(or_elim,[status(thm)],[13])).
tff(69,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[68, 66])).
tff(70,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[69, 67])).
tff(71,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~happy(paul))) | (creative(paul) & quiet(paul) & happy(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[70, 66])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!4 |'alice'|)
(= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|)
(not (room X!4)))))
(a!7 (or (and (not (quiet paul)) (not (happy paul)))
(and (creative paul) (quiet paul) (happy paul) (person paul)))))
(let ((a!8 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(not a!7)))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
a!7))))
(nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!8)))
| room(stephanie)&room(carlos)&room(rosemary)&room(jenise)&(![X]:(room(X)=>(X='stephanie'|X='carlos'|X='rosemary'|X='jenise')))&
(((((~happy(carlos))|(enjoys_kayaking(carlos))))=>(((?[X]:(~room(X)&X!=rosemary))&(![X,Y]:((X!=rosemary&Y!=rosemary)=>(X=Y))))))&
(~(?[X]:(~room(X)=>(like(camille,X))))=>(?[X]:(~room(X)=>(((~quiet(X))=>(like(camille,X)))))))&
(((~(creative(rosemary)&happy(rosemary)&quiet(rosemary)&person(rosemary)))|(~(brave(rosemary)&person(rosemary)))))&
(~((~happy(stephanie)&~creative(stephanie))|(does_not_enjoy_kayaking(stephanie))))&
(taller(stephanie,camille))&
(~((~brave(stephanie)&~quiet(stephanie)&~happy(stephanie))|(~hate(stephanie,camille))))&
(?[X]:(~room(X)=>(((~hate(X,camille))=>(like(X,camille))))))&
(~((brave(carlos)&person(carlos))|(creative(carlos)&person(carlos))))) | room(stephanie)&room(carlos)&room(rosemary)&room(jenise)&(![X]:(room(X)=>(X='stephanie'|X='carlos'|X='rosemary'|X='jenise')))&
(~((~quiet(carlos)&~happy(carlos))|(creative(carlos)&quiet(carlos)&happy(carlos)&person(carlos)))) | entailment | contradiction | entailment |
Carmen, Arlene are the only persons in the room.
Carmen who is not a rich person, is not rich.
Carmen is the richest in the room.
Marilyn and Carmen like each other.
Carmen who is not liked by Owen, does not like Owen.
Marilyn and Owen like each other. | Someone who enjoys fishing like someone who is a rich tourist. | contradiction | - | room(carmen)&room(arlene)&(![X]:(room(X)=>(X='carmen'|X='arlene')))&
(((~(rich(carmen)&person(carmen)))&(~rich(carmen)))&
(![X]:(richer(X,carmen)))&
((like(marilyn,carmen) & like(carmen,marilyn)))&
((~like(carmen,owen))&(~like(owen,carmen)))&
((like(marilyn,owen) & like(owen,marilyn)))) | room(carmen)&room(arlene)&(![X]:(room(X)=>(X='carmen'|X='arlene')))&
(?[X,Y]:((enjoys_fishing(X))&(rich(Y)&tourist(Y))&(like(X,Y)))) | contradiction | neutral | contradiction |
Raymond, Jon, James, Loretta are the only persons in the room.
James and Jon are respectively tall and brave.
James neither does not hate Logan nor is not a brave person.
Jon and James are respectively quiet and brave.
James is the quietest in the room.
Logan is taller than Jon.
Logan and Jon hate each other.
Logan is a sibling of Raymond.
Someone in the room is not hated by Logan.
James is a sibling of Logan or is not tall, not brave, not quiet or both.
Logan is a sibling of James. | James is not a quiet brave person or likes Logan or both. | contradiction | - | room(raymond)&room(jon)&room(james)&room(loretta)&(![X]:(room(X)=>(X='raymond'|X='jon'|X='james'|X='loretta')))&
(((tall(james))&(brave(jon)))&
(~((~hate(logan,james))|(~(brave(james)&person(james)))))&
((quiet(jon))&(brave(james)))&
(![X]:(quieter(X,james)))&
(taller(jon,logan))&
((hate(logan,jon) & hate(jon,logan)))&
(sibling(raymond,logan))&
(?[X]:(room(X)=>(~hate(X,logan))))&
(((sibling(logan,james))|(~tall(james)&~brave(james)&~quiet(james))))&
(sibling(james,logan))) | room(raymond)&room(jon)&room(james)&room(loretta)&(![X]:(room(X)=>(X='raymond'|X='jon'|X='james'|X='loretta')))&
(((~(quiet(james)&brave(james)&person(james)))|(like(logan,james)))) | entailment | entailment | entailment |
Ruben, Audrea, Dorinda are the only persons in the room.
Someone who is a client of Krista like someone who is a happy person.
Audrea and Dorinda are taller than Virginia.
Ruben does not like Krista and is not a happy person.
Ruben is the tallest in the room.
It is not the case that 'Audrea neither is not a tall person nor is a client of Dorinda'.
Krista and Virginia like each other. | Audrea is a client of Krista or does not like Krista or both. | neutral | % SZS status Satisfiable
| room(ruben)&room(audrea)&room(dorinda)&(![X]:(room(X)=>(X='ruben'|X='audrea'|X='dorinda')))&
((?[X,Y]:((client(krista,X))&(happy(Y)&person(Y))&(like(X,Y))))&
(taller(virginia,audrea)&taller(virginia,dorinda))&
((~like(krista,ruben))&(~(happy(ruben)&person(ruben))))&
(![X]:(taller(X,ruben)))&
(~(~((~(tall(audrea)&person(audrea)))|(client(dorinda,audrea)))))&
((like(krista,virginia) & like(virginia,krista)))) | room(ruben)&room(audrea)&room(dorinda)&(![X]:(room(X)=>(X='ruben'|X='audrea'|X='dorinda')))&
(((client(krista,audrea))|(~like(krista,audrea)))) | entailment | entailment | entailment |
Billy, Rhonda are the only persons in the room.
“Billy is the least quiet in the room” only if “Rhonda and Billy like each other”.
“Rhonda is not liked by Linda” if “Billy and Linda like each other” and vice versa.
“It is not the case that 'Billy and Rhonda are not a brave tourist'” if “more than one person outside the room does not like Linda”.
Rhonda and Billy are respectively rich and tall.
It is not the case that 'someone who is not a rich quiet tall creative tourist is taller than someone who is a quiet rich tourist'.
Billy who is richer than Linda, is liked by Linda.
Someone outside the room who is not rich, not brave likes Linda.
Only one person outside the room is a rich tall tourist.
It is not the case that 'Billy and Rhonda are not a brave tourist'. | Billy is not a rich tourist or is a rich happy brave creative quiet tourist or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(paul_type, type, (
paul: $i)).
tff(tall_type, type, (
tall: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(1,assumption,(X!2 = mary), introduced(assumption)).
tff(2,plain,
(room(X!2) <=> room(mary)),
inference(monotonicity,[status(thm)],[1])).
tff(3,plain,
(room(mary) <=> room(X!2)),
inference(symmetry,[status(thm)],[2])).
tff(4,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((![X: $i] : quieter(mary, X) => (like(paul, mary) & like(mary, paul))) & ((like(mary, john) & like(john, mary)) <=> (~like(paul, john)))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(john, X)) & (~like(john, Y)))) & (~(X = Y))) => (~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))))) & (rich(paul) & tall(mary))) & (~?[X: $i, Y: $i] : (((~((((rich(X) & quiet(X)) & tall(X)) & creative(X)) & tourist(X))) & ((quiet(Y) & rich(Y)) & tourist(Y))) & taller(X, Y)))) & (richer(john, mary) & like(mary, john))) & ?[X: $i] : ((~room(X)) => (((~rich(X)) & (~brave(X))) => like(john, X)))) & (?[X: $i] : ((((~room(X)) & rich(X)) & tall(X)) & tourist(X)) & ![X: $i, Y: $i] : ((((((rich(X) & tall(X)) & tourist(X)) & rich(Y)) & tall(Y)) & tourist(Y)) => (X = Y)))) & (~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~(rich(mary) & tourist(mary))) | (((((rich(mary) & happy(mary)) & brave(mary)) & creative(mary)) & quiet(mary)) & tourist(mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : quieter(mary, X)) | (like(paul, mary) & like(mary, paul))) & (~(like(paul, john) <=> (like(mary, john) & like(john, mary)))) & ((~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))) | (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(john, X)) & (~like(john, Y)) & (~(X = Y))))) & rich(paul) & tall(mary) & (~?[X: $i, Y: $i] : ((~(rich(X) & quiet(X) & tall(X) & creative(X) & tourist(X))) & quiet(Y) & rich(Y) & tourist(Y) & taller(X, Y))) & richer(john, mary) & like(mary, john) & ?[X: $i] : (room(X) | like(john, X) | (~((~rich(X)) & (~brave(X))))) & ?[X: $i] : ((~room(X)) & rich(X) & tall(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y)) & (~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((![X: $i] : quieter(mary, X) => (like(paul, mary) & like(mary, paul))) & ((like(mary, john) & like(john, mary)) <=> (~like(paul, john)))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(john, X)) & (~like(john, Y)))) & (~(X = Y))) => (~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))))) & (rich(paul) & tall(mary))) & (~?[X: $i, Y: $i] : (((~((((rich(X) & quiet(X)) & tall(X)) & creative(X)) & tourist(X))) & ((quiet(Y) & rich(Y)) & tourist(Y))) & taller(X, Y)))) & (richer(john, mary) & like(mary, john))) & ?[X: $i] : ((~room(X)) => (((~rich(X)) & (~brave(X))) => like(john, X)))) & (?[X: $i] : ((((~room(X)) & rich(X)) & tall(X)) & tourist(X)) & ![X: $i, Y: $i] : ((((((rich(X) & tall(X)) & tourist(X)) & rich(Y)) & tall(Y)) & tourist(Y)) => (X = Y)))) & (~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~(rich(mary) & tourist(mary))) | (((((rich(mary) & happy(mary)) & brave(mary)) & creative(mary)) & quiet(mary)) & tourist(mary)))))), file('/mnt/tmpfs//5429521000825447809946509.p','negated')).
tff(7,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : quieter(mary, X)) | (like(paul, mary) & like(mary, paul))) & (~(like(paul, john) <=> (like(mary, john) & like(john, mary)))) & ((~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))) | (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(john, X)) & (~like(john, Y)) & (~(X = Y))))) & rich(paul) & tall(mary) & (~?[X: $i, Y: $i] : ((~(rich(X) & quiet(X) & tall(X) & creative(X) & tourist(X))) & quiet(Y) & rich(Y) & tourist(Y) & taller(X, Y))) & richer(john, mary) & like(mary, john) & ?[X: $i] : (room(X) | like(john, X) | (~((~rich(X)) & (~brave(X))))) & ?[X: $i] : ((~room(X)) & rich(X) & tall(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y)) & (~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : quieter(mary, X)) | (like(paul, mary) & like(mary, paul))) & (~(like(paul, john) <=> (like(mary, john) & like(john, mary)))) & ((~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul))))) | (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(john, X)) & (~like(john, Y)) & (~(X = Y))))) & rich(paul) & tall(mary) & (~?[X: $i, Y: $i] : ((~(rich(X) & quiet(X) & tall(X) & creative(X) & tourist(X))) & quiet(Y) & rich(Y) & tourist(Y) & taller(X, Y))) & richer(john, mary) & like(mary, john) & ?[X: $i] : (room(X) | like(john, X) | (~((~rich(X)) & (~brave(X))))) & ?[X: $i] : ((~room(X)) & rich(X) & tall(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y)) & (~((~(brave(mary) & tourist(mary))) & (~(brave(paul) & tourist(paul)))))),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(room(mary)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,
(room(X!2)),
inference(modus_ponens,[status(thm)],[10, 3])).
tff(12,plain,
(?[X: $i] : ((~room(X)) & rich(X) & tall(X) & tourist(X)) <=> ?[X: $i] : ((~room(X)) & rich(X) & tall(X) & tourist(X))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(?[X: $i] : ((~room(X)) & rich(X) & tall(X) & tourist(X))),
inference(and_elim,[status(thm)],[8])).
tff(14,plain,
(?[X: $i] : ((~room(X)) & rich(X) & tall(X) & tourist(X))),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,(
(~room(X!2)) & rich(X!2) & tall(X!2) & tourist(X!2)),
inference(skolemize,[status(sab)],[14])).
tff(16,plain,
(~room(X!2)),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
($false),
inference(unit_resolution,[status(thm)],[16, 11])).
tff(18,plain,(~(X!2 = mary)), inference(lemma,lemma(discharge,[]))).
tff(19,assumption,(~((~tourist(mary)) | (~rich(mary)) | (~((~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~happy(mary)) | (~creative(mary)) | (~quiet(mary)))))), introduced(assumption)).
tff(20,plain,
(((~tourist(mary)) | (~rich(mary)) | (~((~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~happy(mary)) | (~creative(mary)) | (~quiet(mary))))) | rich(mary)),
inference(tautology,[status(thm)],[])).
tff(21,plain,
(rich(mary)),
inference(unit_resolution,[status(thm)],[20, 19])).
tff(22,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))) <=> ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))))),
inference(bind,[status(th)],[])).
tff(23,plain,
(![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))),
inference(quant_intro,[status(thm)],[22])).
tff(24,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y)) <=> (~((~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))))), ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) <=> (~(~((~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))))))), rewrite((~(~((~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))))) <=> ((~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))), ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) <=> ((~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))))), (((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y)) <=> (((~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))) | (X = Y)))), rewrite((((~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y))) | (X = Y)) <=> ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))), (((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y)) <=> ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))))),
inference(bind,[status(th)],[])).
tff(25,plain,
(![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))),
inference(quant_intro,[status(thm)],[24])).
tff(26,plain,
(![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y))),
inference(rewrite,[status(thm)],[])).
tff(27,plain,
(![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y))),
inference(and_elim,[status(thm)],[8])).
tff(28,plain,
(![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y))),
inference(modus_ponens,[status(thm)],[27, 26])).
tff(29,plain,(
![X: $i, Y: $i] : ((~(rich(X) & tall(X) & tourist(X) & rich(Y) & tall(Y) & tourist(Y))) | (X = Y))),
inference(skolemize,[status(sab)],[28])).
tff(30,plain,
(![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))),
inference(modus_ponens,[status(thm)],[29, 25])).
tff(31,plain,
(![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))),
inference(modus_ponens,[status(thm)],[30, 23])).
tff(32,plain,
(tourist(X!2)),
inference(and_elim,[status(thm)],[15])).
tff(33,plain,
(tall(X!2)),
inference(and_elim,[status(thm)],[15])).
tff(34,plain,
(rich(X!2)),
inference(and_elim,[status(thm)],[15])).
tff(35,plain,
(tall(mary) <=> tall(mary)),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(tall(mary)),
inference(and_elim,[status(thm)],[8])).
tff(37,plain,
(tall(mary)),
inference(modus_ponens,[status(thm)],[36, 35])).
tff(38,plain,
(((~tourist(mary)) | (~rich(mary)) | (~((~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~happy(mary)) | (~creative(mary)) | (~quiet(mary))))) | tourist(mary)),
inference(tautology,[status(thm)],[])).
tff(39,plain,
(tourist(mary)),
inference(unit_resolution,[status(thm)],[38, 19])).
tff(40,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | ((~tourist(mary)) | (~rich(mary)) | (~tourist(X!2)) | (~rich(X!2)) | (~tall(X!2)) | (~tall(mary)) | (X!2 = mary))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | (~tourist(mary)) | (~rich(mary)) | (~tourist(X!2)) | (~rich(X!2)) | (~tall(X!2)) | (~tall(mary)) | (X!2 = mary))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(((X!2 = mary) | (~rich(mary)) | (~tourist(mary)) | (~rich(X!2)) | (~tall(X!2)) | (~tourist(X!2)) | (~tall(mary))) <=> ((~tourist(mary)) | (~rich(mary)) | (~tourist(X!2)) | (~rich(X!2)) | (~tall(X!2)) | (~tall(mary)) | (X!2 = mary))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | ((X!2 = mary) | (~rich(mary)) | (~tourist(mary)) | (~rich(X!2)) | (~tall(X!2)) | (~tourist(X!2)) | (~tall(mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | ((~tourist(mary)) | (~rich(mary)) | (~tourist(X!2)) | (~rich(X!2)) | (~tall(X!2)) | (~tall(mary)) | (X!2 = mary)))),
inference(monotonicity,[status(thm)],[41])).
tff(43,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | ((X!2 = mary) | (~rich(mary)) | (~tourist(mary)) | (~rich(X!2)) | (~tall(X!2)) | (~tourist(X!2)) | (~tall(mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | (~tourist(mary)) | (~rich(mary)) | (~tourist(X!2)) | (~rich(X!2)) | (~tall(X!2)) | (~tall(mary)) | (X!2 = mary))),
inference(transitivity,[status(thm)],[42, 40])).
tff(44,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | ((X!2 = mary) | (~rich(mary)) | (~tourist(mary)) | (~rich(X!2)) | (~tall(X!2)) | (~tourist(X!2)) | (~tall(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(45,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~rich(Y)) | (~tourist(Y)) | (~rich(X)) | (~tall(X)) | (~tourist(X)) | (~tall(Y)))) | (~tourist(mary)) | (~rich(mary)) | (~tourist(X!2)) | (~rich(X!2)) | (~tall(X!2)) | (~tall(mary)) | (X!2 = mary)),
inference(modus_ponens,[status(thm)],[44, 43])).
tff(46,plain,
($false),
inference(unit_resolution,[status(thm)],[45, 39, 37, 34, 33, 32, 31, 21, 18])).
tff(47,plain,((~tourist(mary)) | (~rich(mary)) | (~((~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~happy(mary)) | (~creative(mary)) | (~quiet(mary))))), inference(lemma,lemma(discharge,[]))).
tff(48,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
(room(paul)),
inference(and_elim,[status(thm)],[8])).
tff(50,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[49, 48])).
tff(51,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~tourist(mary)) | (~rich(mary)) | (~((~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~happy(mary)) | (~creative(mary)) | (~quiet(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
((~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))),
inference(rewrite,[status(thm)],[])).
tff(53,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary)))))),
inference(monotonicity,[status(thm)],[52])).
tff(54,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(55,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary)))))),
inference(monotonicity,[status(thm)],[54])).
tff(56,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))),
inference(or_elim,[status(thm)],[7])).
tff(58,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[57, 55])).
tff(59,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[58, 56])).
tff(60,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(rich(mary) & tourist(mary))) | (rich(mary) & happy(mary) & brave(mary) & creative(mary) & quiet(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[59, 55])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3)))))
(a!5 (or (not (and (rich mary) (tourist mary)))
(and (rich mary)
(happy mary)
(brave mary)
(creative mary)
(quiet mary)
(tourist mary)))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 a!5))
(or (not (room mary)) (not (room paul)) a!4 (not a!5)))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (not a!5) (not a!5))) a!6)))
| room(billy)&room(rhonda)&(![X]:(room(X)=>(X='billy'|X='rhonda')))&
(((![X]:(quieter(billy,X)))=>((like(rhonda,billy) & like(billy,rhonda))))&
(((like(billy,linda) & like(linda,billy)))<=>(~like(rhonda,linda)))&
(((?[X,Y]:(~room(X)&~room(Y)&(~like(linda,X)&~like(linda,Y))&(X!=Y))))=>(~(~(brave(billy)&tourist(billy))&~(brave(rhonda)&tourist(rhonda)))))&
((rich(rhonda))&(tall(billy)))&
(~(?[X,Y]:((~(rich(X)&quiet(X)&tall(X)&creative(X)&tourist(X)))&(quiet(Y)&rich(Y)&tourist(Y))&(taller(X,Y)))))&
((richer(linda,billy))&(like(billy,linda)))&
(?[X]:(~room(X)=>(((~rich(X)&~brave(X))=>(like(linda,X))))))&
(((?[X]:(~room(X)&rich(X)&tall(X)&tourist(X)))&(![X,Y]:((rich(X)&tall(X)&tourist(X)&rich(Y)&tall(Y)&tourist(Y))=>(X=Y)))))&
(~(~(brave(billy)&tourist(billy))&~(brave(rhonda)&tourist(rhonda))))) | room(billy)&room(rhonda)&(![X]:(room(X)=>(X='billy'|X='rhonda')))&
(((~(rich(billy)&tourist(billy)))|(rich(billy)&happy(billy)&brave(billy)&creative(billy)&quiet(billy)&tourist(billy)))) | entailment | entailment | contradiction |
Duane, Dan are the only persons in the room. Duane is the least rich in the room. Duane is not liked by Barbara and is a rich european. Duane is hated by Henry and is a rich european. Reatha is richer than Duane. Dan and Duane are respectively rich and happy. Dan who is liked by Reatha, is a happy european. Barbara is a client of Dan. | It is not the case that 'Dan is not a rich person and is hated by Barbara'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(paul_type, type, (
paul: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(mary_type, type, (
mary: $i)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(1,plain,
(european(paul) <=> european(paul)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((![X: $i] : richer(mary, X) & ((~like(mary, john)) & (rich(mary) & european(mary)))) & (hate(mary, lucy) & (rich(mary) & european(mary)))) & richer(mary, susan)) & (rich(paul) & happy(mary))) & (like(paul, susan) & (happy(paul) & european(paul)))) & client(paul, john))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((~(rich(paul) & person(paul))) & hate(paul, john)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : richer(mary, X) & (~like(mary, john)) & rich(mary) & european(mary) & hate(mary, lucy) & richer(mary, susan) & rich(paul) & happy(mary) & like(paul, susan) & happy(paul) & european(paul) & client(paul, john))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((![X: $i] : richer(mary, X) & ((~like(mary, john)) & (rich(mary) & european(mary)))) & (hate(mary, lucy) & (rich(mary) & european(mary)))) & richer(mary, susan)) & (rich(paul) & happy(mary))) & (like(paul, susan) & (happy(paul) & european(paul)))) & client(paul, john))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((~(rich(paul) & person(paul))) & hate(paul, john)))))), file('/mnt/tmpfs//890729243223234421725539.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : richer(mary, X) & (~like(mary, john)) & rich(mary) & european(mary) & hate(mary, lucy) & richer(mary, susan) & rich(paul) & happy(mary) & like(paul, susan) & happy(paul) & european(paul) & client(paul, john))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : richer(mary, X) & (~like(mary, john)) & rich(mary) & european(mary) & hate(mary, lucy) & richer(mary, susan) & rich(paul) & happy(mary) & like(paul, susan) & happy(paul) & european(paul) & client(paul, john)),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(european(paul)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(european(paul)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(^[X: $i] : refl((person(X) | (~european(X))) <=> (person(X) | (~european(X))))),
inference(bind,[status(th)],[])).
tff(9,plain,
(![X: $i] : (person(X) | (~european(X))) <=> ![X: $i] : (person(X) | (~european(X)))),
inference(quant_intro,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : (person(X) | (~european(X))) <=> ![X: $i] : (person(X) | (~european(X)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(^[X: $i] : rewrite((european(X) => person(X)) <=> (person(X) | (~european(X))))),
inference(bind,[status(th)],[])).
tff(12,plain,
(![X: $i] : (european(X) => person(X)) <=> ![X: $i] : (person(X) | (~european(X)))),
inference(quant_intro,[status(thm)],[11])).
tff(13,axiom,(![X: $i] : (european(X) => person(X))), file('/mnt/tmpfs//890729243223234421725539.p','b2')).
tff(14,plain,
(![X: $i] : (person(X) | (~european(X)))),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(![X: $i] : (person(X) | (~european(X)))),
inference(modus_ponens,[status(thm)],[14, 10])).
tff(16,plain,(
![X: $i] : (person(X) | (~european(X)))),
inference(skolemize,[status(sab)],[15])).
tff(17,plain,
(![X: $i] : (person(X) | (~european(X)))),
inference(modus_ponens,[status(thm)],[16, 9])).
tff(18,plain,
(((~![X: $i] : (person(X) | (~european(X)))) | (person(paul) | (~european(paul)))) <=> ((~![X: $i] : (person(X) | (~european(X)))) | person(paul) | (~european(paul)))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~![X: $i] : (person(X) | (~european(X)))) | (person(paul) | (~european(paul)))),
inference(quant_inst,[status(thm)],[])).
tff(20,plain,
((~![X: $i] : (person(X) | (~european(X)))) | person(paul) | (~european(paul))),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(person(paul)),
inference(unit_resolution,[status(thm)],[20, 17, 7])).
tff(22,plain,
(rich(paul) <=> rich(paul)),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
(rich(paul)),
inference(and_elim,[status(thm)],[5])).
tff(24,plain,
(rich(paul)),
inference(modus_ponens,[status(thm)],[23, 22])).
tff(25,plain,
((~((~rich(paul)) | (~person(paul)))) | (~rich(paul)) | (~person(paul))),
inference(tautology,[status(thm)],[])).
tff(26,plain,
((~((~rich(paul)) | (~person(paul)))) | (~person(paul))),
inference(unit_resolution,[status(thm)],[25, 24])).
tff(27,plain,
(~((~rich(paul)) | (~person(paul)))),
inference(unit_resolution,[status(thm)],[26, 21])).
tff(28,plain,
(((~((~rich(paul)) | (~person(paul)))) | (~hate(paul, john))) | ((~rich(paul)) | (~person(paul)))),
inference(tautology,[status(thm)],[])).
tff(29,plain,
((~((~rich(paul)) | (~person(paul)))) | (~hate(paul, john))),
inference(unit_resolution,[status(thm)],[28, 27])).
tff(30,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(32,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(35,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ((~(rich(paul) & person(paul))) & hate(paul, john))) <=> ((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~((~rich(paul)) | (~person(paul)))) | (~hate(paul, john)))))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ((~(rich(paul) & person(paul))) & hate(paul, john))) <=> ((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ((~(rich(paul) & person(paul))) & hate(paul, john)))),
inference(monotonicity,[status(thm)],[37])).
tff(39,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john)))))),
inference(monotonicity,[status(thm)],[39])).
tff(41,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john)))))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))),
inference(or_elim,[status(thm)],[4])).
tff(43,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))),
inference(modus_ponens,[status(thm)],[42, 40])).
tff(44,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))),
inference(modus_ponens,[status(thm)],[43, 41])).
tff(45,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(rich(paul) & person(paul))) & hate(paul, john))))),
inference(modus_ponens,[status(thm)],[44, 40])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0)))))
(a!5 (and (not (and (rich paul) (person paul))) (hate paul john))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 (not a!5)))
(or (not (room mary)) (not (room paul)) a!4 a!5))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ a!5 a!5)) a!6)))
| room(duane)&room(dan)&(![X]:(room(X)=>(X='duane'|X='dan')))&
((![X]:(richer(duane,X)))&
((~like(duane,barbara))&(rich(duane)&european(duane)))&
((hate(duane,henry))&(rich(duane)&european(duane)))&
(richer(duane,reatha))&
((rich(dan))&(happy(duane)))&
((like(dan,reatha))&(happy(dan)&european(dan)))&
(client(dan,barbara))) | room(duane)&room(dan)&(![X]:(room(X)=>(X='duane'|X='dan')))&
(~((~(rich(dan)&person(dan)))&(hate(dan,barbara)))) | entailment | entailment | neutral |
Carmen, Lucille, Marvin, Kari are the only persons in the room.
"Only one person outside the room likes Louis" if "someone outside the room likes Louis" and vice versa.
"It is not the case that 'Louis is taller than Carmen'" only if "Carmen and Louis like each other".
Marvin is the least tall in the room.
Marvin is liked by Louis.
Only one person outside the room is not liked by Louis. | It is not the case that 'Louis and Carmen like each other'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(mary_type, type, (
mary: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_5_type, type, (
tptp_fun_X_5: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(paul_type, type, (
paul: $i)).
tff(tptp_fun_Y_2_type, type, (
tptp_fun_Y_2: $i)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(1,assumption,(~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))), introduced(assumption)).
tff(2,plain,
(((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)) | (~(X!5 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(~(X!5 = |'mary'|)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)) | (~(X!5 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(~(X!5 = |'paul'|)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
(((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)) | (~(X!5 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(~(X!5 = |'fred'|)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
(((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)) | (~(X!5 = |'alice'|))),
inference(tautology,[status(thm)],[])).
tff(9,plain,
(~(X!5 = |'alice'|)),
inference(unit_resolution,[status(thm)],[8, 1])).
tff(10,plain,
(((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)) | room(X!5)),
inference(tautology,[status(thm)],[])).
tff(11,plain,
(room(X!5)),
inference(unit_resolution,[status(thm)],[10, 1])).
tff(12,plain,
(^[X: $i] : refl(((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(13,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[12])).
tff(14,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((?[X: $i] : ((~room(X)) => like(susan, X)) <=> (?[X: $i] : ((~room(X)) & like(susan, X)) & ![X: $i, Y: $i] : ((like(susan, X) & like(susan, Y)) => (X = Y)))) & ((~taller(mary, susan)) => (like(mary, susan) & like(susan, mary)))) & ![X: $i] : taller(fred, X)) & like(fred, susan)) & (?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : (((~like(X, susan)) & (~like(Y, susan))) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(like(susan, mary) & like(mary, susan)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (room(X) | like(susan, X)) <=> (?[X: $i] : ((~room(X)) & like(susan, X)) & ![X: $i, Y: $i] : ((~(like(susan, X) & like(susan, Y))) | (X = Y)))) & (taller(mary, susan) | (like(mary, susan) & like(susan, mary))) & ![X: $i] : taller(fred, X) & like(fred, susan) & ?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : ((~((~like(X, susan)) & (~like(Y, susan)))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))))),
inference(rewrite,[status(thm)],[])).
tff(16,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((?[X: $i] : ((~room(X)) => like(susan, X)) <=> (?[X: $i] : ((~room(X)) & like(susan, X)) & ![X: $i, Y: $i] : ((like(susan, X) & like(susan, Y)) => (X = Y)))) & ((~taller(mary, susan)) => (like(mary, susan) & like(susan, mary)))) & ![X: $i] : taller(fred, X)) & like(fred, susan)) & (?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : (((~like(X, susan)) & (~like(Y, susan))) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(like(susan, mary) & like(mary, susan)))))), file('/mnt/tmpfs//5303776073166695104678768.p','negated')).
tff(17,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (room(X) | like(susan, X)) <=> (?[X: $i] : ((~room(X)) & like(susan, X)) & ![X: $i, Y: $i] : ((~(like(susan, X) & like(susan, Y))) | (X = Y)))) & (taller(mary, susan) | (like(mary, susan) & like(susan, mary))) & ![X: $i] : taller(fred, X) & like(fred, susan) & ?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : ((~((~like(X, susan)) & (~like(Y, susan)))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan)))))),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (room(X) | like(susan, X)) <=> (?[X: $i] : ((~room(X)) & like(susan, X)) & ![X: $i, Y: $i] : ((~(like(susan, X) & like(susan, Y))) | (X = Y)))) & (taller(mary, susan) | (like(mary, susan) & like(susan, mary))) & ![X: $i] : taller(fred, X) & like(fred, susan) & ?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : ((~((~like(X, susan)) & (~like(Y, susan)))) | (X = Y))),
inference(or_elim,[status(thm)],[17])).
tff(19,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[19, 14])).
tff(21,plain,(
![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(skolemize,[status(sab)],[20])).
tff(22,plain,
(![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[21, 13])).
tff(23,plain,
(((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | ((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(25,plain,
((~![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) | (~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)),
inference(modus_ponens,[status(thm)],[24, 23])).
tff(26,plain,
($false),
inference(unit_resolution,[status(thm)],[25, 22, 11, 9, 7, 5, 3])).
tff(27,plain,((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)), inference(lemma,lemma(discharge,[]))).
tff(28,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
(room(alice)),
inference(and_elim,[status(thm)],[18])).
tff(30,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[29, 28])).
tff(31,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(32,plain,
(room(fred)),
inference(and_elim,[status(thm)],[18])).
tff(33,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[32, 31])).
tff(34,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
(room(paul)),
inference(and_elim,[status(thm)],[18])).
tff(36,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
(room(mary)),
inference(and_elim,[status(thm)],[18])).
tff(39,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[38, 37])).
tff(40,plain,
(((~((~like(mary, susan)) | (~like(susan, mary)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((~like(mary, susan)) | (~like(susan, mary)))))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
((~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) <=> (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
((like(susan, mary) & like(mary, susan)) <=> (~((~like(mary, susan)) | (~like(susan, mary))))),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
(((like(susan, mary) & like(mary, susan)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)))) <=> ((~((~like(mary, susan)) | (~like(susan, mary)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))))),
inference(monotonicity,[status(thm)],[42, 41])).
tff(44,plain,
(((like(susan, mary) & like(mary, susan)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((~like(mary, susan)) | (~like(susan, mary)))))),
inference(transitivity,[status(thm)],[43, 40])).
tff(45,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (like(susan, mary) & like(mary, susan))) <=> ((like(susan, mary) & like(mary, susan)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))))),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (like(susan, mary) & like(mary, susan))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (like(susan, mary) & like(mary, susan)))),
inference(monotonicity,[status(thm)],[41])).
tff(47,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (like(susan, mary) & like(mary, susan))) <=> ((like(susan, mary) & like(mary, susan)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((~room(X!5)) | (X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))))),
inference(transitivity,[status(thm)],[46, 45])).
tff(48,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan)))))),
inference(monotonicity,[status(thm)],[48])).
tff(50,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan)))))),
inference(rewrite,[status(thm)],[])).
tff(51,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))),
inference(or_elim,[status(thm)],[17])).
tff(52,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))),
inference(modus_ponens,[status(thm)],[51, 49])).
tff(53,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))),
inference(modus_ponens,[status(thm)],[52, 50])).
tff(54,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((~room(X)) | (X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (~(like(susan, mary) & like(mary, susan))))),
inference(modus_ponens,[status(thm)],[53, 49])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (not (room X))
(= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|))))
(a!6 (not (or (not (room X!5))
(= X!5 |'alice'|)
(= X!5 |'fred'|)
(= X!5 |'paul'|)
(= X!5 |'mary'|))))
(a!7 (refl (~ (and (like susan mary) (like mary susan))
(and (like susan mary) (like mary susan))))))
(let ((a!8 (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(not (and (like susan mary) (like mary susan))))))
(let ((a!9 (~ (not a!8)
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(and (like susan mary) (like mary susan))))))
(nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!9))))
| room(carmen)&room(lucille)&room(marvin)&room(kari)&(![X]:(room(X)=>(X='carmen'|X='lucille'|X='marvin'|X='kari')))&
(((?[X]:(~room(X)=>(like(louis,X))))<=>(((?[X]:(~room(X)&like(louis,X)))&(![X,Y]:((like(louis,X)&like(louis,Y))=>(X=Y))))))&
((~(taller(carmen,louis)))=>((like(carmen,louis) & like(louis,carmen))))&
(![X]:(taller(marvin,X)))&
(like(marvin,louis))&
(((?[X]:(~room(X)&~like(X,louis)))&(![X,Y]:((~like(X,louis)&~like(Y,louis))=>(X=Y)))))) | room(carmen)&room(lucille)&room(marvin)&room(kari)&(![X]:(room(X)=>(X='carmen'|X='lucille'|X='marvin'|X='kari')))&
(~((like(louis,carmen) & like(carmen,louis)))) | entailment | contradiction | contradiction |
Sherman, Deborah, Linda are the only persons in the room. Deborah and Sherman do not like Pedro. Everyone outside the room is not creative, not happy, not tall. Deborah neither is not a creative tourist nor is not liked by Karol. It is not the case that 'someone who likes Karol like someone who does not like Pedro'. Someone outside the room who is not liked by Pedro likes Pedro. Sherman is the least tall in the room. | Sherman who is a brave tall tourist, is taller than Pedro. | contradiction | - | room(sherman)&room(deborah)&room(linda)&(![X]:(room(X)=>(X='sherman'|X='deborah'|X='linda')))&
((~like(pedro,deborah)&~like(pedro,sherman))&
(![X]:(~room(X)=>(~creative(X)&~happy(X)&~tall(X))))&
(~((~(creative(deborah)&tourist(deborah)))|(~like(deborah,karol))))&
(~(?[X,Y]:((like(karol,X))&(~like(pedro,Y))&(like(X,Y)))))&
(?[X]:(~room(X)=>(((~like(X,pedro))=>(like(pedro,X))))))&
(![X]:(taller(sherman,X)))) | room(sherman)&room(deborah)&room(linda)&(![X]:(room(X)=>(X='sherman'|X='deborah'|X='linda')))&
((brave(sherman)&tall(sherman)&tourist(sherman))&(taller(pedro,sherman))) | contradiction | contradiction | contradiction |
Ida, Sheila, James are the only persons in the room. Only one of the following is true:. -Someone who has a fish tank is richer than someone who is not James. -James is the quietest in the room. | It is not the case that 'someone who is quieter than Marvel is richer than someone who is not Sheila'. | neutral | % SZS status Satisfiable
| room(ida)&room(sheila)&room(james)&(![X]:(room(X)=>(X='ida'|X='sheila'|X='james')))&
(((?[X,Y]:((has_a_fish_tank(X))&(Y!=james)&(richer(X,Y))))|(![X]:(quieter(X,james))))&~(?[X,Y]:((has_a_fish_tank(X))&(Y!=james)&(richer(X,Y)))&![X]:(quieter(X,james)))) | room(ida)&room(sheila)&room(james)&(![X]:(room(X)=>(X='ida'|X='sheila'|X='james')))&
(~(?[X,Y]:((quieter(marvel,X))&(Y!=sheila)&(richer(X,Y))))) | entailment | entailment | entailment |
Richard is the only person in the room. “Richard who collects antique clocks, is not tall” only if “someone outside the room who does not like Darwin enjoys stargazing”. Richard is the least quiet in the room. More than one person outside the room is not liked by Deanna. Richard is liked by Darwin or likes Darwin or both. It is not the case that 'Richard is the quietest in the room'. Darwin and Alberto like each other. | Richard is allergic to anything and is a tall rich creative quiet happy european. | neutral | % SZS status Satisfiable
| room(richard)&(![X]:(room(X)=>(X='richard')))&
((((collects_antique_clocks(richard))&(~tall(richard)))=>(?[X]:(~room(X)=>(((~like(darwin,X))=>(enjoys_stargazing(X)))))))&
(![X]:(quieter(richard,X)))&
((?[X,Y]:(~room(X)&~room(Y)&(~like(X,deanna)&~like(Y,deanna))&(X!=Y))))&
(((like(richard,darwin))|(like(darwin,richard))))&
(~(![X]:(quieter(X,richard))))&
((like(darwin,alberto) & like(alberto,darwin)))) | room(richard)&(![X]:(room(X)=>(X='richard')))&
((is_allergic_to_anything(richard))&(tall(richard)&rich(richard)&creative(richard)&quiet(richard)&happy(richard)&european(richard))) | contradiction | contradiction | contradiction |
Martha, Robert are the only persons in the room. "Martha hates Kara" if "Martha is the least quiet in the room". Martha neither is not hated by Kara nor hates Patricia. Robert is right-handed. Someone who is not hated by Janel hate someone who is not right-handed. Someone who is not a rich quiet tourist is quieter than someone who is a rich creative tourist. Only one person in the room is not quiet. Martha is hated by Kara or is not Robert or both. | Martha is a quiet tourist or is a client of Patricia or both. | neutral | % SZS status Satisfiable
| room(martha)&room(robert)&(![X]:(room(X)=>(X='martha'|X='robert')))&
(((![X]:(quieter(martha,X)))=>(hate(kara,martha)))&
(~((~hate(martha,kara))|(hate(patricia,martha))))&
(is_right-handed(robert))&
(?[X,Y]:((~hate(X,janel))&(is_not_right-handed(Y))&(hate(X,Y))))&
(?[X,Y]:((~(rich(X)&quiet(X)&tourist(X)))&(rich(Y)&creative(Y)&tourist(Y))&(quieter(X,Y))))&
(((?[X]:(room(X)&~quiet(X)))&(![X,Y]:((~quiet(X)&~quiet(Y))=>(X=Y)))))&
(((hate(martha,kara))|(martha!=robert)))) | room(martha)&room(robert)&(![X]:(room(X)=>(X='martha'|X='robert')))&
(((quiet(martha)&tourist(martha))|(client(patricia,martha)))) | contradiction | entailment | entailment |
Corey is the only person in the room.
'Corey neither does not hate Frank nor is not a quiet rich person' if 'Linda and Corey like each other'.
'Corey who does not practice kickboxing, is not a brave rich person' unless 'only one person in the room does not hate Linda'.
'Corey likes Frank' only if 'it is not the case that 'Corey is the tallest in the room''.
Corey does not practice kickboxing or is hated by Frank or both.
Corey neither does not hate Frank nor is not a quiet rich person.
Corey who is hated by Frank, is not happy.
Corey is the richest in the room.
Linda and Corey like each other. | It is not the case that 'Corey neither is not a rich brave happy person nor does not like Richard'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(1,plain,
((~happy(mary)) <=> (~happy(mary))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((((((like(paul, mary) & like(mary, paul)) => (~((~hate(john, mary)) | (~((quiet(mary) & rich(mary)) & person(mary)))))) & ((~(?[X: $i] : (room(X) & (~hate(paul, X))) & ![X: $i, Y: $i] : (((~hate(paul, X)) & (~hate(paul, Y))) => (X = Y)))) => ((~predb(mary)) & (~((brave(mary) & rich(mary)) & person(mary)))))) & (like(john, mary) => (~![X: $i] : taller(X, mary)))) & ((~predb(mary)) | hate(mary, john))) & (~((~hate(john, mary)) | (~((quiet(mary) & rich(mary)) & person(mary)))))) & (hate(mary, john) & (~happy(mary)))) & ![X: $i] : richer(X, mary)) & (like(paul, mary) & like(mary, paul)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~(~((~(((rich(mary) & brave(mary)) & happy(mary)) & person(mary))) | (~like(alice, mary)))))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~(like(paul, mary) & like(mary, paul))) | (~((~hate(john, mary)) | (~(quiet(mary) & rich(mary) & person(mary)))))) & ((?[X: $i] : (room(X) & (~hate(paul, X))) & ![X: $i, Y: $i] : ((~((~hate(paul, X)) & (~hate(paul, Y)))) | (X = Y))) | ((~predb(mary)) & (~(brave(mary) & rich(mary) & person(mary))))) & ((~like(john, mary)) | (~![X: $i] : taller(X, mary))) & ((~predb(mary)) | hate(mary, john)) & (~((~hate(john, mary)) | (~(quiet(mary) & rich(mary) & person(mary))))) & hate(mary, john) & (~happy(mary)) & ![X: $i] : richer(X, mary) & like(paul, mary) & like(mary, paul))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((((((like(paul, mary) & like(mary, paul)) => (~((~hate(john, mary)) | (~((quiet(mary) & rich(mary)) & person(mary)))))) & ((~(?[X: $i] : (room(X) & (~hate(paul, X))) & ![X: $i, Y: $i] : (((~hate(paul, X)) & (~hate(paul, Y))) => (X = Y)))) => ((~predb(mary)) & (~((brave(mary) & rich(mary)) & person(mary)))))) & (like(john, mary) => (~![X: $i] : taller(X, mary)))) & ((~predb(mary)) | hate(mary, john))) & (~((~hate(john, mary)) | (~((quiet(mary) & rich(mary)) & person(mary)))))) & (hate(mary, john) & (~happy(mary)))) & ![X: $i] : richer(X, mary)) & (like(paul, mary) & like(mary, paul)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~(~((~(((rich(mary) & brave(mary)) & happy(mary)) & person(mary))) | (~like(alice, mary)))))))), file('/mnt/tmpfs//1348724380035100597151354.p','negated')).
tff(4,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~(like(paul, mary) & like(mary, paul))) | (~((~hate(john, mary)) | (~(quiet(mary) & rich(mary) & person(mary)))))) & ((?[X: $i] : (room(X) & (~hate(paul, X))) & ![X: $i, Y: $i] : ((~((~hate(paul, X)) & (~hate(paul, Y)))) | (X = Y))) | ((~predb(mary)) & (~(brave(mary) & rich(mary) & person(mary))))) & ((~like(john, mary)) | (~![X: $i] : taller(X, mary))) & ((~predb(mary)) | hate(mary, john)) & (~((~hate(john, mary)) | (~(quiet(mary) & rich(mary) & person(mary))))) & hate(mary, john) & (~happy(mary)) & ![X: $i] : richer(X, mary) & like(paul, mary) & like(mary, paul))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary))))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~(like(paul, mary) & like(mary, paul))) | (~((~hate(john, mary)) | (~(quiet(mary) & rich(mary) & person(mary)))))) & ((?[X: $i] : (room(X) & (~hate(paul, X))) & ![X: $i, Y: $i] : ((~((~hate(paul, X)) & (~hate(paul, Y)))) | (X = Y))) | ((~predb(mary)) & (~(brave(mary) & rich(mary) & person(mary))))) & ((~like(john, mary)) | (~![X: $i] : taller(X, mary))) & ((~predb(mary)) | hate(mary, john)) & (~((~hate(john, mary)) | (~(quiet(mary) & rich(mary) & person(mary))))) & hate(mary, john) & (~happy(mary)) & ![X: $i] : richer(X, mary) & like(paul, mary) & like(mary, paul)),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~happy(mary)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(~happy(mary)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(((~happy(mary)) | (~like(alice, mary)) | (~rich(mary)) | (~person(mary)) | (~brave(mary))) | happy(mary)),
inference(tautology,[status(thm)],[])).
tff(9,plain,
((~happy(mary)) | (~like(alice, mary)) | (~rich(mary)) | (~person(mary)) | (~brave(mary))),
inference(unit_resolution,[status(thm)],[8, 7])).
tff(10,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(12,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[11, 10])).
tff(13,plain,
(((~room(mary)) | (~((~room(X!2)) | (X!2 = |'mary'|))) | (~((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))) <=> ((~room(mary)) | (~((~room(X!2)) | (X!2 = |'mary'|))) | (~((~happy(mary)) | (~like(alice, mary)) | (~rich(mary)) | (~person(mary)) | (~brave(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary))))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary))))))),
inference(monotonicity,[status(thm)],[14])).
tff(16,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(17,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))),
inference(or_elim,[status(thm)],[4])).
tff(18,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))),
inference(modus_ponens,[status(thm)],[17, 15])).
tff(19,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))),
inference(modus_ponens,[status(thm)],[18, 16])).
tff(20,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~like(alice, mary)) | (~(rich(mary) & brave(mary) & happy(mary) & person(mary)))))),
inference(modus_ponens,[status(thm)],[19, 15])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!2)) (= X!2 |'mary'|))))
(a!4 (or (not (like alice mary))
(not (and (rich mary) (brave mary) (happy mary) (person mary))))))
(let ((a!5 (~ (not (and (room mary) a!2 a!4))
(or (not (room mary)) a!3 (not a!4)))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (not a!4) (not a!4))) a!5)))
| room(corey)&(![X]:(room(X)=>(X='corey')))&
((((like(linda,corey) & like(corey,linda)))=>(~((~hate(frank,corey))|(~(quiet(corey)&rich(corey)&person(corey))))))&
(~(((?[X]:(room(X)&~hate(linda,X)))&(![X,Y]:((~hate(linda,X)&~hate(linda,Y))=>(X=Y)))))=>((does_not_practice_kickboxing(corey))&(~(brave(corey)&rich(corey)&person(corey)))))&
((like(frank,corey))=>(~(![X]:(taller(X,corey)))))&
(((does_not_practice_kickboxing(corey))|(hate(corey,frank))))&
(~((~hate(frank,corey))|(~(quiet(corey)&rich(corey)&person(corey)))))&
((hate(corey,frank))&(~happy(corey)))&
(![X]:(richer(X,corey)))&
((like(linda,corey) & like(corey,linda)))) | room(corey)&(![X]:(room(X)=>(X='corey')))&
(~(~((~(rich(corey)&brave(corey)&happy(corey)&person(corey)))|(~like(richard,corey))))) | entailment | neutral | entailment |
Lora, Ryan, Richard, Felix are the only persons in the room.
Only one person outside the room likes James.
Lora neither is right-handed nor is not happy.
Someone in the room who is not a happy creative european is hated by Anthony.
Only one person outside the room does not hate Anthony.
Anthony and Lora hate each other. | Ryan is not a creative person and does not hate Anthony. | contradiction | - | room(lora)&room(ryan)&room(richard)&room(felix)&(![X]:(room(X)=>(X='lora'|X='ryan'|X='richard'|X='felix')))&
((((?[X]:(~room(X)&like(james,X)))&(![X,Y]:((like(james,X)&like(james,Y))=>(X=Y)))))&
(~((is_right-handed(lora))|(~happy(lora))))&
(?[X]:(room(X)=>(((~(happy(X)&creative(X)&european(X)))=>(hate(X,anthony))))))&
(((?[X]:(~room(X)&~hate(anthony,X)))&(![X,Y]:((~hate(anthony,X)&~hate(anthony,Y))=>(X=Y)))))&
((hate(anthony,lora) & hate(lora,anthony)))) | room(lora)&room(ryan)&room(richard)&room(felix)&(![X]:(room(X)=>(X='lora'|X='ryan'|X='richard'|X='felix')))&
((~(creative(ryan)&person(ryan)))&(~hate(anthony,ryan))) | contradiction | neutral | contradiction |
Matthew, Paul, Roberta, Frieda are the only persons in the room. Paul is the least tall in the room. Only one person outside the room likes James. More than one person outside the room is not a rich person. Someone outside the room who is richer than James is not liked by James. It is not the case that 'Matthew is liked by James'. Someone who is not a brave tall rich person like someone who is taller than James. Someone who is richer than James like someone who is not a brave rich person. | Paul likes James or is not a rich tall person or both. | neutral | % SZS status Satisfiable
| room(matthew)&room(paul)&room(roberta)&room(frieda)&(![X]:(room(X)=>(X='matthew'|X='paul'|X='roberta'|X='frieda')))&
((![X]:(taller(paul,X)))&
(((?[X]:(~room(X)&like(james,X)))&(![X,Y]:((like(james,X)&like(james,Y))=>(X=Y)))))&
((?[X,Y]:(~room(X)&~room(Y)&(~(rich(X)&person(X))&~(rich(Y)&person(Y)))&(X!=Y))))&
(?[X]:(~room(X)=>(((richer(james,X))=>(~like(X,james))))))&
(~(like(matthew,james)))&
(?[X,Y]:((~(brave(X)&tall(X)&rich(X)&person(X)))&(taller(james,Y))&(like(X,Y))))&
(?[X,Y]:((richer(james,X))&(~(brave(Y)&rich(Y)&person(Y)))&(like(X,Y))))) | room(matthew)&room(paul)&room(roberta)&room(frieda)&(![X]:(room(X)=>(X='matthew'|X='paul'|X='roberta'|X='frieda')))&
(((like(james,paul))|(~(rich(paul)&tall(paul)&person(paul))))) | entailment | entailment | entailment |
Jesus is the only person in the room. Not all of the following is true:. -Jesus is the least rich in the room. -Jesus who is hated by Larry, does not hate Elizabeth. -Jesus does not hate Elizabeth and is not rich. | It is not the case that 'Jesus who hates Larry, is not rich'. | neutral | % SZS status Satisfiable
| room(jesus)&(![X]:(room(X)=>(X='jesus')))&
(~(![X]:(richer(jesus,X))&(hate(jesus,larry))&(~hate(elizabeth,jesus))&(~hate(elizabeth,jesus))&(~rich(jesus)))) | room(jesus)&(![X]:(room(X)=>(X='jesus')))&
(~((hate(larry,jesus))&(~rich(jesus)))) | entailment | entailment | entailment |
Nelly, Santiago are the only persons in the room.
'Santiago is the least tall in the room' if 'someone outside the room is a tall quiet person'.
'Santiago is a client of Perla and enjoys jogging' unless 'Dorothy is a client of Nelly'.
More than one person outside the room is not liked by Dorothy.
Nelly is a tall tourist and likes Dorothy.
Everyone outside the room who enjoys jogging is a tall person.
Nelly and Santiago are not liked by Gayle. | Santiago is not liked by Gayle or is a quiet tall person or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(tall_type, type, (
tall: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(mary_type, type, (
mary: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(1,plain,
((~like(paul, lucy)) <=> (~like(paul, lucy))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((?[X: $i] : ((~room(X)) => ((tall(X) & quiet(X)) & person(X))) => ![X: $i] : taller(paul, X)) & ((~client(mary, alice)) => (client(fred, paul) & predb(paul)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(X, alice)) & (~like(Y, alice)))) & (~(X = Y)))) & ((tall(mary) & tourist(mary)) & like(alice, mary))) & ![X: $i] : ((~room(X)) => (predb(X) => (tall(X) & person(X))))) & ((~like(mary, lucy)) & (~like(paul, lucy))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~like(paul, lucy)) | ((quiet(paul) & tall(paul)) & person(paul)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i] : (room(X) | (tall(X) & quiet(X) & person(X)))) | ![X: $i] : taller(paul, X)) & (client(mary, alice) | (client(fred, paul) & predb(paul))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(X, alice)) & (~like(Y, alice)) & (~(X = Y))) & tall(mary) & tourist(mary) & like(alice, mary) & ![X: $i] : (room(X) | (tall(X) & person(X)) | (~predb(X))) & (~like(mary, lucy)) & (~like(paul, lucy)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((?[X: $i] : ((~room(X)) => ((tall(X) & quiet(X)) & person(X))) => ![X: $i] : taller(paul, X)) & ((~client(mary, alice)) => (client(fred, paul) & predb(paul)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(X, alice)) & (~like(Y, alice)))) & (~(X = Y)))) & ((tall(mary) & tourist(mary)) & like(alice, mary))) & ![X: $i] : ((~room(X)) => (predb(X) => (tall(X) & person(X))))) & ((~like(mary, lucy)) & (~like(paul, lucy))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~like(paul, lucy)) | ((quiet(paul) & tall(paul)) & person(paul)))))), file('/mnt/tmpfs//7071539623690092817118119.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i] : (room(X) | (tall(X) & quiet(X) & person(X)))) | ![X: $i] : taller(paul, X)) & (client(mary, alice) | (client(fred, paul) & predb(paul))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(X, alice)) & (~like(Y, alice)) & (~(X = Y))) & tall(mary) & tourist(mary) & like(alice, mary) & ![X: $i] : (room(X) | (tall(X) & person(X)) | (~predb(X))) & (~like(mary, lucy)) & (~like(paul, lucy)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i] : (room(X) | (tall(X) & quiet(X) & person(X)))) | ![X: $i] : taller(paul, X)) & (client(mary, alice) | (client(fred, paul) & predb(paul))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(X, alice)) & (~like(Y, alice)) & (~(X = Y))) & tall(mary) & tourist(mary) & like(alice, mary) & ![X: $i] : (room(X) | (tall(X) & person(X)) | (~predb(X))) & (~like(mary, lucy)) & (~like(paul, lucy))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~like(paul, lucy)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(~like(paul, lucy)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(((~like(paul, lucy)) | (~((~quiet(paul)) | (~tall(paul)) | (~person(paul))))) | like(paul, lucy)),
inference(tautology,[status(thm)],[])).
tff(9,plain,
((~like(paul, lucy)) | (~((~quiet(paul)) | (~tall(paul)) | (~person(paul))))),
inference(unit_resolution,[status(thm)],[8, 7])).
tff(10,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(12,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[11, 10])).
tff(13,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(15,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[14, 13])).
tff(16,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (~((~quiet(paul)) | (~tall(paul)) | (~person(paul)))))))),
inference(rewrite,[status(thm)],[])).
tff(17,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
((~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul)))))),
inference(monotonicity,[status(thm)],[18])).
tff(20,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul)))))),
inference(transitivity,[status(thm)],[19, 17])).
tff(21,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul)))))),
inference(monotonicity,[status(thm)],[21])).
tff(23,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))),
inference(or_elim,[status(thm)],[4])).
tff(25,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))),
inference(modus_ponens,[status(thm)],[24, 22])).
tff(26,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))),
inference(modus_ponens,[status(thm)],[25, 23])).
tff(27,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, lucy)) | (quiet(paul) & tall(paul) & person(paul))))),
inference(modus_ponens,[status(thm)],[26, 22])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!2 |'paul'|) (= X!2 |'mary'|) (not (room X!2)))))
(a!5 (or (not (like paul lucy))
(and (quiet paul) (tall paul) (person paul)))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 a!5))
(or (not (room mary)) (not (room paul)) a!4 (not a!5)))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (not a!5) (not a!5))) a!6)))
| room(nelly)&room(santiago)&(![X]:(room(X)=>(X='nelly'|X='santiago')))&
(((?[X]:(~room(X)=>(tall(X)&quiet(X)&person(X))))=>(![X]:(taller(santiago,X))))&
(~(client(nelly,dorothy))=>((client(perla,santiago))&(enjoys_jogging(santiago))))&
((?[X,Y]:(~room(X)&~room(Y)&(~like(X,dorothy)&~like(Y,dorothy))&(X!=Y))))&
((tall(nelly)&tourist(nelly))&(like(dorothy,nelly)))&
(![X]:(~room(X)=>(((enjoys_jogging(X))=>(tall(X)&person(X))))))&
(~like(nelly,gayle)&~like(santiago,gayle))) | room(nelly)&room(santiago)&(![X]:(room(X)=>(X='nelly'|X='santiago')))&
(((~like(santiago,gayle))|(quiet(santiago)&tall(santiago)&person(santiago)))) | entailment | entailment | entailment |
Michael, Cecilia, Mark are the only persons in the room.
“Mark neither does not hate Julia nor hates Robert” if “Mark is the least rich in the room” and vice versa.
Only one person outside the room is hated by Julia.
Someone outside the room who does not like Robert is liked by Robert.
Mark is the least rich in the room.
Michael is not creative or is not a brave european or both.
Cecilia who does practice yoga, is not hated by David.
Julia is richer than Michael.
Cecilia and Robert like each other.
Michael and Mark are respectively rich and brave.
David is richer than Michael.
Cecilia is the richest in the room. | Someone who is not hated by Robert is richer than someone who does practice yoga. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(mary_type, type, (
mary: $i)).
tff(brave_type, type, (
brave: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(rich_type, type, (
rich: $i > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(susan_type, type, (
susan: $i)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(1,plain,
(like(paul, alice) <=> like(paul, alice)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((![X: $i] : richer(fred, X) <=> (~((~hate(lucy, fred)) | hate(alice, fred)))) & (?[X: $i] : ((~room(X)) & hate(X, lucy)) & ![X: $i, Y: $i] : ((hate(X, lucy) & hate(Y, lucy)) => (X = Y)))) & ?[X: $i] : ((~room(X)) => ((~like(alice, X)) => like(X, alice)))) & ![X: $i] : richer(fred, X)) & ((~creative(mary)) | (~(brave(mary) & european(mary))))) & (predb(paul) & (~hate(paul, john)))) & richer(mary, lucy)) & (like(paul, alice) & like(alice, paul))) & (rich(mary) & brave(fred))) & richer(mary, john)) & ![X: $i] : richer(X, paul))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((~hate(X, alice)) & predb(Y)) & richer(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~hate(lucy, fred)) | hate(alice, fred)) <=> ![X: $i] : richer(fred, X))) & ?[X: $i] : ((~room(X)) & hate(X, lucy)) & ![X: $i, Y: $i] : ((~(hate(X, lucy) & hate(Y, lucy))) | (X = Y)) & ?[X: $i] : (room(X) | like(X, alice) | like(alice, X)) & ![X: $i] : richer(fred, X) & ((~creative(mary)) | (~(brave(mary) & european(mary)))) & predb(paul) & (~hate(paul, john)) & richer(mary, lucy) & like(paul, alice) & like(alice, paul) & rich(mary) & brave(fred) & richer(mary, john) & ![X: $i] : richer(X, paul))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((![X: $i] : richer(fred, X) <=> (~((~hate(lucy, fred)) | hate(alice, fred)))) & (?[X: $i] : ((~room(X)) & hate(X, lucy)) & ![X: $i, Y: $i] : ((hate(X, lucy) & hate(Y, lucy)) => (X = Y)))) & ?[X: $i] : ((~room(X)) => ((~like(alice, X)) => like(X, alice)))) & ![X: $i] : richer(fred, X)) & ((~creative(mary)) | (~(brave(mary) & european(mary))))) & (predb(paul) & (~hate(paul, john)))) & richer(mary, lucy)) & (like(paul, alice) & like(alice, paul))) & (rich(mary) & brave(fred))) & richer(mary, john)) & ![X: $i] : richer(X, paul))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((~hate(X, alice)) & predb(Y)) & richer(X, Y))))), file('/mnt/tmpfs//8194486341890411435741140.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~hate(lucy, fred)) | hate(alice, fred)) <=> ![X: $i] : richer(fred, X))) & ?[X: $i] : ((~room(X)) & hate(X, lucy)) & ![X: $i, Y: $i] : ((~(hate(X, lucy) & hate(Y, lucy))) | (X = Y)) & ?[X: $i] : (room(X) | like(X, alice) | like(alice, X)) & ![X: $i] : richer(fred, X) & ((~creative(mary)) | (~(brave(mary) & european(mary)))) & predb(paul) & (~hate(paul, john)) & richer(mary, lucy) & like(paul, alice) & like(alice, paul) & rich(mary) & brave(fred) & richer(mary, john) & ![X: $i] : richer(X, paul))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~hate(lucy, fred)) | hate(alice, fred)) <=> ![X: $i] : richer(fred, X))) & ?[X: $i] : ((~room(X)) & hate(X, lucy)) & ![X: $i, Y: $i] : ((~(hate(X, lucy) & hate(Y, lucy))) | (X = Y)) & ?[X: $i] : (room(X) | like(X, alice) | like(alice, X)) & ![X: $i] : richer(fred, X) & ((~creative(mary)) | (~(brave(mary) & european(mary)))) & predb(paul) & (~hate(paul, john)) & richer(mary, lucy) & like(paul, alice) & like(alice, paul) & rich(mary) & brave(fred) & richer(mary, john) & ![X: $i] : richer(X, paul)),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(like(paul, alice)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(like(paul, alice)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
((~(paul = alice)) <=> (~(paul = alice))),
inference(rewrite,[status(thm)],[])).
tff(9,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//8194486341890411435741140.p','b14')).
tff(10,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[10])).
tff(12,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[11])).
tff(13,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[13])).
tff(15,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[17])).
tff(19,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
(~(paul = alice)),
inference(and_elim,[status(thm)],[42])).
tff(44,plain,
(~(paul = alice)),
inference(modus_ponens,[status(thm)],[43, 8])).
tff(45,plain,
(^[X: $i, Y: $i] : refl(((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y))))),
inference(bind,[status(th)],[])).
tff(46,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(quant_intro,[status(thm)],[45])).
tff(47,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(48,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite((like(X, Y) => (~hate(X, Y))) <=> ((~hate(X, Y)) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))))), rewrite(((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))))),
inference(bind,[status(th)],[])).
tff(49,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(quant_intro,[status(thm)],[48])).
tff(50,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y))))), file('/mnt/tmpfs//8194486341890411435741140.p','b0')).
tff(51,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[50, 49])).
tff(52,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[51, 47])).
tff(53,plain,(
![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(skolemize,[status(sab)],[52])).
tff(54,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[53, 46])).
tff(55,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((paul = alice) | (~hate(paul, alice)) | (~like(paul, alice)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (paul = alice) | (~hate(paul, alice)) | (~like(paul, alice)))),
inference(rewrite,[status(thm)],[])).
tff(56,plain,
(((~hate(paul, alice)) | (paul = alice) | (~like(paul, alice))) <=> ((paul = alice) | (~hate(paul, alice)) | (~like(paul, alice)))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(paul, alice)) | (paul = alice) | (~like(paul, alice)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((paul = alice) | (~hate(paul, alice)) | (~like(paul, alice))))),
inference(monotonicity,[status(thm)],[56])).
tff(58,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(paul, alice)) | (paul = alice) | (~like(paul, alice)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (paul = alice) | (~hate(paul, alice)) | (~like(paul, alice)))),
inference(transitivity,[status(thm)],[57, 55])).
tff(59,plain,
((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(paul, alice)) | (paul = alice) | (~like(paul, alice)))),
inference(quant_inst,[status(thm)],[])).
tff(60,plain,
((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (paul = alice) | (~hate(paul, alice)) | (~like(paul, alice))),
inference(modus_ponens,[status(thm)],[59, 58])).
tff(61,plain,
(~hate(paul, alice)),
inference(unit_resolution,[status(thm)],[60, 54, 44, 7])).
tff(62,assumption,(~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))), introduced(assumption)).
tff(63,plain,
(((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | room(X!3)),
inference(tautology,[status(thm)],[])).
tff(64,plain,
(room(X!3)),
inference(unit_resolution,[status(thm)],[63, 62])).
tff(65,plain,
(((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(66,plain,
(~(X!3 = |'mary'|)),
inference(unit_resolution,[status(thm)],[65, 62])).
tff(67,plain,
(((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(68,plain,
(~(X!3 = |'paul'|)),
inference(unit_resolution,[status(thm)],[67, 62])).
tff(69,plain,
(((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(70,plain,
(~(X!3 = |'fred'|)),
inference(unit_resolution,[status(thm)],[69, 62])).
tff(71,plain,
(^[X: $i] : refl(((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(72,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[71])).
tff(73,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(74,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[5])).
tff(75,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[74, 73])).
tff(76,plain,(
![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[75])).
tff(77,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[76, 72])).
tff(78,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))),
inference(rewrite,[status(thm)],[])).
tff(79,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))),
inference(quant_inst,[status(thm)],[])).
tff(80,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))),
inference(modus_ponens,[status(thm)],[79, 78])).
tff(81,plain,
($false),
inference(unit_resolution,[status(thm)],[80, 77, 70, 68, 66, 64])).
tff(82,plain,((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))), inference(lemma,lemma(discharge,[]))).
tff(83,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(84,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(85,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[84, 83])).
tff(86,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(87,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(88,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[87, 86])).
tff(89,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(90,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(91,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[90, 89])).
tff(92,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (hate(X, alice) | (~richer(X, Y)) | (~predb(Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (hate(X, alice) | (~richer(X, Y)) | (~predb(Y))))),
inference(rewrite,[status(thm)],[])).
tff(93,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (hate(X, alice) | (~richer(X, Y)) | (~predb(Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (hate(X, alice) | (~richer(X, Y)) | (~predb(Y))))),
inference(rewrite,[status(thm)],[])).
tff(94,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~hate(X, alice)) & predb(Y) & richer(X, Y)) <=> (~(hate(X, alice) | (~richer(X, Y)) | (~predb(Y))))), ((~((~hate(X, alice)) & predb(Y) & richer(X, Y))) <=> (~(~(hate(X, alice) | (~richer(X, Y)) | (~predb(Y))))))), rewrite((~(~(hate(X, alice) | (~richer(X, Y)) | (~predb(Y))))) <=> (hate(X, alice) | (~richer(X, Y)) | (~predb(Y)))), ((~((~hate(X, alice)) & predb(Y) & richer(X, Y))) <=> (hate(X, alice) | (~richer(X, Y)) | (~predb(Y)))))),
inference(bind,[status(th)],[])).
tff(95,plain,
(![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y))) <=> ![X: $i, Y: $i] : (hate(X, alice) | (~richer(X, Y)) | (~predb(Y)))),
inference(quant_intro,[status(thm)],[94])).
tff(96,plain,
((~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))),
inference(rewrite,[status(thm)],[])).
tff(97,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (hate(X, alice) | (~richer(X, Y)) | (~predb(Y))))),
inference(monotonicity,[status(thm)],[96, 95])).
tff(98,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (hate(X, alice) | (~richer(X, Y)) | (~predb(Y))))),
inference(transitivity,[status(thm)],[97, 93])).
tff(99,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(100,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y))))),
inference(monotonicity,[status(thm)],[96])).
tff(101,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~((~hate(X, alice)) & predb(Y) & richer(X, Y))))),
inference(transitivity,[status(thm)],[100, 99])).
tff(102,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(103,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y))))),
inference(monotonicity,[status(thm)],[102])).
tff(104,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(105,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))),
inference(or_elim,[status(thm)],[4])).
tff(106,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[105, 103])).
tff(107,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[106, 104])).
tff(108,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, alice)) & predb(Y) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[107, 103])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!3 |'fred'|)
(= X!3 |'paul'|)
(= X!3 |'mary'|)
(not (room X!3)))))
(a!6 (lambda ((X $i) (Y $i))
(let ((a!1 (and (not (hate X alice)) (predb Y) (richer X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!7 (exists ((X $i) (Y $i))
(and (not (hate X alice)) (predb Y) (richer X Y))))
(a!8 (forall ((X $i) (Y $i))
(let ((a!1 (and (not (hate X alice)) (predb Y) (richer X Y))))
(not a!1)))))
(let ((a!9 (~ (not (and (room mary) (room paul) (room fred) a!4 a!7))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!8))))
(nnf-neg a!1
a!2
a!3
(sk (~ (not a!4) a!5))
(nnf-neg (proof-bind a!6) (~ (not a!7) a!8))
a!9)))
| room(michael)&room(cecilia)&room(mark)&(![X]:(room(X)=>(X='michael'|X='cecilia'|X='mark')))&
(((![X]:(richer(mark,X)))<=>(~((~hate(julia,mark))|(hate(robert,mark)))))&
(((?[X]:(~room(X)&hate(X,julia)))&(![X,Y]:((hate(X,julia)&hate(Y,julia))=>(X=Y)))))&
(?[X]:(~room(X)=>(((~like(robert,X))=>(like(X,robert))))))&
(![X]:(richer(mark,X)))&
(((~creative(michael))|(~(brave(michael)&european(michael)))))&
((does_practice_yoga(cecilia))&(~hate(cecilia,david)))&
(richer(michael,julia))&
((like(cecilia,robert) & like(robert,cecilia)))&
((rich(michael))&(brave(mark)))&
(richer(michael,david))&
(![X]:(richer(X,cecilia)))) | room(michael)&room(cecilia)&room(mark)&(![X]:(room(X)=>(X='michael'|X='cecilia'|X='mark')))&
(?[X,Y]:((~hate(X,robert))&(does_practice_yoga(Y))&(richer(X,Y)))) | contradiction | entailment | neutral |
Glenn, Albert, Bessie, Julie are the only persons in the room.
Albert is the quietest in the room.
Albert is not hated by Mary or does not enjoy wildlife photography or both.
Julie and Glenn hate each other.
Glenn and Mary hate each other.
Albert is quieter than Mary.
Only one person outside the room does not hate Mary. | Albert hates Mary or enjoys wildlife photography or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(john_type, type, (
john: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(1,assumption,(X!0 = paul), introduced(assumption)).
tff(2,plain,
(room(X!0) <=> room(paul)),
inference(monotonicity,[status(thm)],[1])).
tff(3,plain,
(room(paul) <=> room(X!0)),
inference(symmetry,[status(thm)],[2])).
tff(4,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((![X: $i] : quieter(X, paul) & ((~hate(paul, john)) | (~predb(paul)))) & (hate(alice, mary) & hate(mary, alice))) & (hate(mary, john) & hate(john, mary))) & quieter(john, paul)) & (?[X: $i] : ((~room(X)) & (~hate(john, X))) & ![X: $i, Y: $i] : (((~hate(john, X)) & (~hate(john, Y))) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (hate(john, paul) | predb(paul))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : quieter(X, paul) & ((~hate(paul, john)) | (~predb(paul))) & hate(alice, mary) & hate(mary, alice) & hate(mary, john) & hate(john, mary) & quieter(john, paul) & ?[X: $i] : ((~room(X)) & (~hate(john, X))) & ![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((![X: $i] : quieter(X, paul) & ((~hate(paul, john)) | (~predb(paul)))) & (hate(alice, mary) & hate(mary, alice))) & (hate(mary, john) & hate(john, mary))) & quieter(john, paul)) & (?[X: $i] : ((~room(X)) & (~hate(john, X))) & ![X: $i, Y: $i] : (((~hate(john, X)) & (~hate(john, Y))) => (X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (hate(john, paul) | predb(paul))))), file('/mnt/tmpfs//6920551798442495957146197.p','negated')).
tff(7,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : quieter(X, paul) & ((~hate(paul, john)) | (~predb(paul))) & hate(alice, mary) & hate(mary, alice) & hate(mary, john) & hate(john, mary) & quieter(john, paul) & ?[X: $i] : ((~room(X)) & (~hate(john, X))) & ![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul))))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : quieter(X, paul) & ((~hate(paul, john)) | (~predb(paul))) & hate(alice, mary) & hate(mary, alice) & hate(mary, john) & hate(john, mary) & quieter(john, paul) & ?[X: $i] : ((~room(X)) & (~hate(john, X))) & ![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y))),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(room(paul)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,
(room(X!0)),
inference(modus_ponens,[status(thm)],[10, 3])).
tff(12,plain,
(?[X: $i] : ((~room(X)) & (~hate(john, X))) <=> ?[X: $i] : ((~room(X)) & (~hate(john, X)))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(?[X: $i] : ((~room(X)) & (~hate(john, X)))),
inference(and_elim,[status(thm)],[8])).
tff(14,plain,
(?[X: $i] : ((~room(X)) & (~hate(john, X)))),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,(
(~room(X!0)) & (~hate(john, X!0))),
inference(skolemize,[status(sab)],[14])).
tff(16,plain,
(~room(X!0)),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
($false),
inference(unit_resolution,[status(thm)],[16, 11])).
tff(18,plain,(~(X!0 = paul)), inference(lemma,lemma(discharge,[]))).
tff(19,assumption,(~hate(john, paul)), introduced(assumption)).
tff(20,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | hate(john, Y) | hate(john, X)) <=> ((X = Y) | hate(john, Y) | hate(john, X)))),
inference(bind,[status(th)],[])).
tff(21,plain,
(![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X)) <=> ![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))),
inference(quant_intro,[status(thm)],[20])).
tff(22,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~hate(john, X)) & (~hate(john, Y))) <=> (~(hate(john, Y) | hate(john, X)))), ((~((~hate(john, X)) & (~hate(john, Y)))) <=> (~(~(hate(john, Y) | hate(john, X)))))), rewrite((~(~(hate(john, Y) | hate(john, X)))) <=> (hate(john, Y) | hate(john, X))), ((~((~hate(john, X)) & (~hate(john, Y)))) <=> (hate(john, Y) | hate(john, X)))), (((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y)) <=> ((hate(john, Y) | hate(john, X)) | (X = Y)))), rewrite(((hate(john, Y) | hate(john, X)) | (X = Y)) <=> ((X = Y) | hate(john, Y) | hate(john, X))), (((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y)) <=> ((X = Y) | hate(john, Y) | hate(john, X))))),
inference(bind,[status(th)],[])).
tff(23,plain,
(![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))),
inference(quant_intro,[status(thm)],[22])).
tff(24,plain,
(![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y))),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y))),
inference(and_elim,[status(thm)],[8])).
tff(26,plain,
(![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y))),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,(
![X: $i, Y: $i] : ((~((~hate(john, X)) & (~hate(john, Y)))) | (X = Y))),
inference(skolemize,[status(sab)],[26])).
tff(28,plain,
(![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))),
inference(modus_ponens,[status(thm)],[27, 23])).
tff(29,plain,
(![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))),
inference(modus_ponens,[status(thm)],[28, 21])).
tff(30,plain,
(~hate(john, X!0)),
inference(and_elim,[status(thm)],[15])).
tff(31,plain,
(((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | (hate(john, paul) | hate(john, X!0) | (X!0 = paul))) <=> ((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | hate(john, paul) | hate(john, X!0) | (X!0 = paul))),
inference(rewrite,[status(thm)],[])).
tff(32,plain,
(((X!0 = paul) | hate(john, paul) | hate(john, X!0)) <=> (hate(john, paul) | hate(john, X!0) | (X!0 = paul))),
inference(rewrite,[status(thm)],[])).
tff(33,plain,
(((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | ((X!0 = paul) | hate(john, paul) | hate(john, X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | (hate(john, paul) | hate(john, X!0) | (X!0 = paul)))),
inference(monotonicity,[status(thm)],[32])).
tff(34,plain,
(((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | ((X!0 = paul) | hate(john, paul) | hate(john, X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | hate(john, paul) | hate(john, X!0) | (X!0 = paul))),
inference(transitivity,[status(thm)],[33, 31])).
tff(35,plain,
((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | ((X!0 = paul) | hate(john, paul) | hate(john, X!0))),
inference(quant_inst,[status(thm)],[])).
tff(36,plain,
((~![X: $i, Y: $i] : ((X = Y) | hate(john, Y) | hate(john, X))) | hate(john, paul) | hate(john, X!0) | (X!0 = paul)),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,
($false),
inference(unit_resolution,[status(thm)],[36, 30, 29, 19, 18])).
tff(38,plain,(hate(john, paul)), inference(lemma,lemma(discharge,[]))).
tff(39,plain,
((predb(paul) | hate(john, paul)) | (~hate(john, paul))),
inference(tautology,[status(thm)],[])).
tff(40,plain,
(predb(paul) | hate(john, paul)),
inference(unit_resolution,[status(thm)],[39, 38])).
tff(41,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(room(alice)),
inference(and_elim,[status(thm)],[8])).
tff(43,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[42, 41])).
tff(44,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(45,plain,
(room(fred)),
inference(and_elim,[status(thm)],[8])).
tff(46,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[45, 44])).
tff(47,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(48,plain,
(room(mary)),
inference(and_elim,[status(thm)],[8])).
tff(49,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[48, 47])).
tff(50,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | hate(john, paul)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | hate(john, paul))))),
inference(rewrite,[status(thm)],[])).
tff(51,plain,
((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | hate(john, paul)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | hate(john, paul))))),
inference(monotonicity,[status(thm)],[51])).
tff(53,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | hate(john, paul)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | hate(john, paul))))),
inference(transitivity,[status(thm)],[52, 50])).
tff(54,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))),
inference(rewrite,[status(thm)],[])).
tff(55,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul))))),
inference(monotonicity,[status(thm)],[54])).
tff(56,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))),
inference(or_elim,[status(thm)],[7])).
tff(58,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))),
inference(modus_ponens,[status(thm)],[57, 55])).
tff(59,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))),
inference(modus_ponens,[status(thm)],[58, 56])).
tff(60,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | hate(john, paul)))),
inference(modus_ponens,[status(thm)],[59, 55])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!1 |'alice'|)
(= X!1 |'fred'|)
(= X!1 |'paul'|)
(= X!1 |'mary'|)
(not (room X!1)))))
(a!7 (~ (not (or (predb paul) (hate john paul)))
(not (or (predb paul) (hate john paul))))))
(let ((a!8 (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(or (predb paul) (hate john paul)))))
(a!9 (or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(not (or (predb paul) (hate john paul))))))
(nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl a!7) (~ a!8 a!9))))
| room(glenn)&room(albert)&room(bessie)&room(julie)&(![X]:(room(X)=>(X='glenn'|X='albert'|X='bessie'|X='julie')))&
((![X]:(quieter(X,albert)))&
(((~hate(albert,mary))|(does_not_enjoy_wildlife_photography(albert))))&
((hate(julie,glenn) & hate(glenn,julie)))&
((hate(glenn,mary) & hate(mary,glenn)))&
(quieter(mary,albert))&
(((?[X]:(~room(X)&~hate(mary,X)))&(![X,Y]:((~hate(mary,X)&~hate(mary,Y))=>(X=Y)))))) | room(glenn)&room(albert)&room(bessie)&room(julie)&(![X]:(room(X)=>(X='glenn'|X='albert'|X='bessie'|X='julie')))&
(((hate(mary,albert))|(enjoys_wildlife_photography(albert)))) | contradiction | entailment | neutral |
Michael, Daniel, Dennis, Kaitlin are the only persons in the room. "Someone in the room who hates Lois is not Michael" unless "Kaitlin and Lois hate each other". Someone outside the room is not hated by Lois. Kaitlin is not happy or is liked by Lois or both. Kaitlin who is not Michael, is not an amateur astronomer. Kaitlin and Lois hate each other. Someone who is not happy hate someone who likes Lois. More than one person in the room is liked by Lois. | Dennis likes Lois or does not hate Lois or both. | neutral | % SZS status Satisfiable
| room(michael)&room(daniel)&room(dennis)&room(kaitlin)&(![X]:(room(X)=>(X='michael'|X='daniel'|X='dennis'|X='kaitlin')))&
((~((hate(kaitlin,lois) & hate(lois,kaitlin)))=>(?[X]:(room(X)=>(((hate(lois,X))=>(X!=michael))))))&
(?[X]:(~room(X)=>(~hate(X,lois))))&
(((~happy(kaitlin))|(like(kaitlin,lois))))&
((kaitlin!=michael)&(is_not_an_amateur_astronomer(kaitlin)))&
((hate(kaitlin,lois) & hate(lois,kaitlin)))&
(?[X,Y]:((~happy(X))&(like(lois,Y))&(hate(X,Y))))&
((?[X,Y]:(room(X)&room(Y)&(like(X,lois)&like(Y,lois))&(X!=Y))))) | room(michael)&room(daniel)&room(dennis)&room(kaitlin)&(![X]:(room(X)=>(X='michael'|X='daniel'|X='dennis'|X='kaitlin')))&
(((like(lois,dennis))|(~hate(lois,dennis)))) | entailment | entailment | entailment |
Tabitha is the only person in the room. “Tabitha is the least rich in the room” unless “only one person outside the room does not like Marlene”. Tabitha is a tall european. Marlene is richer than Tabitha. Everyone outside the room who is taller than Georgiana is not a drone photographer. Georgiana is richer than Tabitha. Only one person outside the room does not enjoy mountain biking. Tabitha is not liked by Georgiana or is a creative european or both. | Tabitha neither is taller than Reda nor is not a drone photographer. | neutral | % SZS status Satisfiable
| room(tabitha)&(![X]:(room(X)=>(X='tabitha')))&
((~(((?[X]:(~room(X)&~like(marlene,X)))&(![X,Y]:((~like(marlene,X)&~like(marlene,Y))=>(X=Y)))))=>(![X]:(richer(tabitha,X))))&
(tall(tabitha)&european(tabitha))&
(richer(tabitha,marlene))&
(![X]:(~room(X)=>(((taller(georgiana,X))=>(is_not_a_drone_photographer(X))))))&
(richer(tabitha,georgiana))&
(((?[X]:(~room(X)&does_not_enjoy_mountain_biking(X)))&(![X,Y]:((does_not_enjoy_mountain_biking(X)&does_not_enjoy_mountain_biking(Y))=>(X=Y)))))&
(((~like(tabitha,georgiana))|(creative(tabitha)&european(tabitha))))) | room(tabitha)&(![X]:(room(X)=>(X='tabitha')))&
(~((taller(reda,tabitha))|(is_not_a_drone_photographer(tabitha)))) | contradiction | contradiction | contradiction |
Willie is the only person in the room.
If Willie and Nancy hate each other then no one outside the room is not hated by Kelly.
Kelley is a sibling of Willie.
Willie neither is hated by Kelley nor is a creative brave tourist.
Willie does not hate Nancy or is not hated by Nancy or both.
Only one person outside the room is a sibling of Kelly.
Willie is quieter than Nancy. | Willie is a sibling of Kelley or is not a brave rich tall tourist or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(rich_type, type, (
rich: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(susan_type, type, (
susan: $i)).
tff(john_type, type, (
john: $i)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(1,plain,
((~(mary = lucy)) <=> (~(mary = lucy))),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//1344889762674577654575488.p','b14')).
tff(3,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[2])).
tff(4,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[3])).
tff(5,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[4])).
tff(6,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[6])).
tff(8,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[10])).
tff(12,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[11])).
tff(13,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[13])).
tff(15,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[17])).
tff(19,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
(~(mary = lucy)),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
(~(mary = lucy)),
inference(modus_ponens,[status(thm)],[39, 1])).
tff(41,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))))),
inference(bind,[status(th)],[])).
tff(42,plain,
(![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))),
inference(quant_intro,[status(thm)],[41])).
tff(43,plain,
(![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
(^[X: $i, Y: $i] : rewrite(((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X))) <=> ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))))),
inference(bind,[status(th)],[])).
tff(45,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))),
inference(quant_intro,[status(thm)],[44])).
tff(46,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X)))), file('/mnt/tmpfs//1344889762674577654575488.p','b4')).
tff(47,plain,
(![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))),
inference(modus_ponens,[status(thm)],[46, 45])).
tff(48,plain,
(![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))),
inference(modus_ponens,[status(thm)],[47, 43])).
tff(49,plain,(
![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))),
inference(skolemize,[status(sab)],[48])).
tff(50,plain,
(![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))),
inference(modus_ponens,[status(thm)],[49, 42])).
tff(51,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((mary = lucy) | (sibling(mary, lucy) <=> sibling(lucy, mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (mary = lucy) | (sibling(mary, lucy) <=> sibling(lucy, mary)))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((mary = lucy) | (sibling(mary, lucy) <=> sibling(lucy, mary)))),
inference(quant_inst,[status(thm)],[])).
tff(53,plain,
((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (mary = lucy) | (sibling(mary, lucy) <=> sibling(lucy, mary))),
inference(modus_ponens,[status(thm)],[52, 51])).
tff(54,plain,
(sibling(mary, lucy) <=> sibling(lucy, mary)),
inference(unit_resolution,[status(thm)],[53, 50, 40])).
tff(55,plain,
(sibling(mary, lucy) <=> sibling(mary, lucy)),
inference(rewrite,[status(thm)],[])).
tff(56,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((((hate(mary, paul) & hate(paul, mary)) => (~?[X: $i] : ((~room(X)) => (~hate(X, alice))))) & sibling(mary, lucy)) & (~(hate(mary, lucy) | ((creative(mary) & brave(mary)) & tourist(mary))))) & ((~hate(paul, mary)) | (~hate(mary, paul)))) & (?[X: $i] : ((~room(X)) & sibling(alice, X)) & ![X: $i, Y: $i] : ((sibling(alice, X) & sibling(alice, Y)) => (X = Y)))) & quieter(paul, mary))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (sibling(lucy, mary) | (~(((brave(mary) & rich(mary)) & tall(mary)) & tourist(mary))))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~(hate(mary, paul) & hate(paul, mary))) | (~?[X: $i] : (room(X) | (~hate(X, alice))))) & sibling(mary, lucy) & (~(hate(mary, lucy) | (creative(mary) & brave(mary) & tourist(mary)))) & ((~hate(paul, mary)) | (~hate(mary, paul))) & ?[X: $i] : ((~room(X)) & sibling(alice, X)) & ![X: $i, Y: $i] : ((~(sibling(alice, X) & sibling(alice, Y))) | (X = Y)) & quieter(paul, mary))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(57,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((((hate(mary, paul) & hate(paul, mary)) => (~?[X: $i] : ((~room(X)) => (~hate(X, alice))))) & sibling(mary, lucy)) & (~(hate(mary, lucy) | ((creative(mary) & brave(mary)) & tourist(mary))))) & ((~hate(paul, mary)) | (~hate(mary, paul)))) & (?[X: $i] : ((~room(X)) & sibling(alice, X)) & ![X: $i, Y: $i] : ((sibling(alice, X) & sibling(alice, Y)) => (X = Y)))) & quieter(paul, mary))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (sibling(lucy, mary) | (~(((brave(mary) & rich(mary)) & tall(mary)) & tourist(mary))))))), file('/mnt/tmpfs//1344889762674577654575488.p','negated')).
tff(58,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~(hate(mary, paul) & hate(paul, mary))) | (~?[X: $i] : (room(X) | (~hate(X, alice))))) & sibling(mary, lucy) & (~(hate(mary, lucy) | (creative(mary) & brave(mary) & tourist(mary)))) & ((~hate(paul, mary)) | (~hate(mary, paul))) & ?[X: $i] : ((~room(X)) & sibling(alice, X)) & ![X: $i, Y: $i] : ((~(sibling(alice, X) & sibling(alice, Y))) | (X = Y)) & quieter(paul, mary))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary))))))),
inference(modus_ponens,[status(thm)],[57, 56])).
tff(59,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~(hate(mary, paul) & hate(paul, mary))) | (~?[X: $i] : (room(X) | (~hate(X, alice))))) & sibling(mary, lucy) & (~(hate(mary, lucy) | (creative(mary) & brave(mary) & tourist(mary)))) & ((~hate(paul, mary)) | (~hate(mary, paul))) & ?[X: $i] : ((~room(X)) & sibling(alice, X)) & ![X: $i, Y: $i] : ((~(sibling(alice, X) & sibling(alice, Y))) | (X = Y)) & quieter(paul, mary)),
inference(or_elim,[status(thm)],[58])).
tff(60,plain,
(sibling(mary, lucy)),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
(sibling(mary, lucy)),
inference(modus_ponens,[status(thm)],[60, 55])).
tff(62,plain,
((~(sibling(mary, lucy) <=> sibling(lucy, mary))) | (~sibling(mary, lucy)) | sibling(lucy, mary)),
inference(tautology,[status(thm)],[])).
tff(63,plain,
((~(sibling(mary, lucy) <=> sibling(lucy, mary))) | sibling(lucy, mary)),
inference(unit_resolution,[status(thm)],[62, 61])).
tff(64,plain,
(sibling(lucy, mary)),
inference(unit_resolution,[status(thm)],[63, 54])).
tff(65,plain,
((sibling(lucy, mary) | (~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~tall(mary))) | (~sibling(lucy, mary))),
inference(tautology,[status(thm)],[])).
tff(66,plain,
(sibling(lucy, mary) | (~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~tall(mary))),
inference(unit_resolution,[status(thm)],[65, 64])).
tff(67,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(68,plain,
(room(mary)),
inference(and_elim,[status(thm)],[59])).
tff(69,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[68, 67])).
tff(70,plain,
(((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | (~(sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))) <=> ((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | (~(sibling(lucy, mary) | (~brave(mary)) | (~tourist(mary)) | (~rich(mary)) | (~tall(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(71,plain,
((~(sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary))))) <=> (~(sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(72,plain,
(((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | (~(sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))) <=> ((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | (~(sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary))))))),
inference(monotonicity,[status(thm)],[71])).
tff(73,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary))))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(74,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary))))))),
inference(monotonicity,[status(thm)],[73])).
tff(75,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(76,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))),
inference(or_elim,[status(thm)],[58])).
tff(77,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[76, 74])).
tff(78,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[77, 75])).
tff(79,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (sibling(lucy, mary) | (~(brave(mary) & rich(mary) & tall(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[78, 74])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!1)) (= X!1 |'mary'|))))
(a!4 (or (sibling lucy mary)
(not (and (brave mary) (rich mary) (tall mary) (tourist mary))))))
(let ((a!5 (~ (not (and (room mary) a!2 a!4))
(or (not (room mary)) a!3 (not a!4)))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (not a!4) (not a!4))) a!5)))
| room(willie)&(![X]:(room(X)=>(X='willie')))&
((((hate(willie,nancy) & hate(nancy,willie)))=>(~?[X]:(~room(X)=>(~hate(X,kelly)))))&
(sibling(willie,kelley))&
(~((hate(willie,kelley))|(creative(willie)&brave(willie)&tourist(willie))))&
(((~hate(nancy,willie))|(~hate(willie,nancy))))&
(((?[X]:(~room(X)&sibling(kelly,X)))&(![X,Y]:((sibling(kelly,X)&sibling(kelly,Y))=>(X=Y)))))&
(quieter(nancy,willie))) | room(willie)&(![X]:(room(X)=>(X='willie')))&
(((sibling(kelley,willie))|(~(brave(willie)&rich(willie)&tall(willie)&tourist(willie))))) | neutral | entailment | entailment |
Ernesto, Ruby, Stephanie, Joseph are the only persons in the room.
“Joseph who is taller than Tiffanie, is not hated by Tiffanie” only if “Ernesto is the least rich in the room”.
If “Ruby who is quieter than Tiffanie, does not enjoy cross-country skiing” then “it is not the case that 'someone outside the room is not tall'” otherwise “everyone outside the room is liked by Tiffanie”.
“Tiffanie is taller than Stephanie” only if “only one person outside the room is richer than Tiffanie”.
“Stephanie is the quietest in the room” only if “Ernesto hates Tiffanie”.
Only one person outside the room is not hated by Tiffanie.
Someone outside the room is taller than Tiffanie.
Tiffanie is richer than Stephanie.
Someone outside the room who is hated by Tiffanie enjoys cross-country skiing.
Stephanie is the quietest in the room.
It is not the case that 'it is not the case that 'Stephanie is the least tall in the room''. | Stephanie who is not liked by Tiffanie, is quieter than Tiffanie. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_5_type, type, (
tptp_fun_X_5: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(john_type, type, (
john: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(alice_type, type, (
alice: $i)).
tff(paul_type, type, (
paul: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(susan_type, type, (
susan: $i)).
tff(1,assumption,(~quieter(john, fred)), introduced(assumption)).
tff(2,plain,
(^[X: $i] : refl(quieter(X, fred) <=> quieter(X, fred))),
inference(bind,[status(th)],[])).
tff(3,plain,
(![X: $i] : quieter(X, fred) <=> ![X: $i] : quieter(X, fred)),
inference(quant_intro,[status(thm)],[2])).
tff(4,plain,
(![X: $i] : quieter(X, fred) <=> ![X: $i] : quieter(X, fred)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((taller(john, alice) & (~hate(alice, john))) => ![X: $i] : richer(mary, X)) & (((quieter(john, paul) & (~predb(paul))) => (~?[X: $i] : ((~room(X)) => (~tall(X))))) | ((~(quieter(john, paul) & (~predb(paul)))) => ![X: $i] : ((~room(X)) => like(X, john))))) & (taller(fred, john) => (?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((richer(john, X) & richer(john, Y)) => (X = Y))))) & (![X: $i] : quieter(X, fred) => hate(john, mary))) & (?[X: $i] : ((~room(X)) & (~hate(X, john))) & ![X: $i, Y: $i] : (((~hate(X, john)) & (~hate(Y, john))) => (X = Y)))) & ?[X: $i] : ((~room(X)) => taller(john, X))) & richer(fred, john)) & ?[X: $i] : ((~room(X)) => (hate(X, john) => predb(X)))) & ![X: $i] : quieter(X, fred)) & (~(~![X: $i] : taller(fred, X))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(fred, john)) & quieter(john, fred))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(taller(john, alice) & (~hate(alice, john)))) | ![X: $i] : richer(mary, X)) & ((~taller(fred, john)) | (?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((~(richer(john, X) & richer(john, Y))) | (X = Y)))) & ((~![X: $i] : quieter(X, fred)) | hate(john, mary)) & ?[X: $i] : ((~room(X)) & (~hate(X, john))) & ![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y)) & ?[X: $i] : (room(X) | taller(john, X)) & richer(fred, john) & ?[X: $i] : (room(X) | (~hate(X, john)) | predb(X)) & ![X: $i] : quieter(X, fred) & ![X: $i] : taller(fred, X))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((taller(john, alice) & (~hate(alice, john))) => ![X: $i] : richer(mary, X)) & (((quieter(john, paul) & (~predb(paul))) => (~?[X: $i] : ((~room(X)) => (~tall(X))))) | ((~(quieter(john, paul) & (~predb(paul)))) => ![X: $i] : ((~room(X)) => like(X, john))))) & (taller(fred, john) => (?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((richer(john, X) & richer(john, Y)) => (X = Y))))) & (![X: $i] : quieter(X, fred) => hate(john, mary))) & (?[X: $i] : ((~room(X)) & (~hate(X, john))) & ![X: $i, Y: $i] : (((~hate(X, john)) & (~hate(Y, john))) => (X = Y)))) & ?[X: $i] : ((~room(X)) => taller(john, X))) & richer(fred, john)) & ?[X: $i] : ((~room(X)) => (hate(X, john) => predb(X)))) & ![X: $i] : quieter(X, fred)) & (~(~![X: $i] : taller(fred, X))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(fred, john)) & quieter(john, fred))))), file('/mnt/tmpfs//2185362851710588708723215.p','negated')).
tff(7,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(taller(john, alice) & (~hate(alice, john)))) | ![X: $i] : richer(mary, X)) & ((~taller(fred, john)) | (?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((~(richer(john, X) & richer(john, Y))) | (X = Y)))) & ((~![X: $i] : quieter(X, fred)) | hate(john, mary)) & ?[X: $i] : ((~room(X)) & (~hate(X, john))) & ![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y)) & ?[X: $i] : (room(X) | taller(john, X)) & richer(fred, john) & ?[X: $i] : (room(X) | (~hate(X, john)) | predb(X)) & ![X: $i] : quieter(X, fred) & ![X: $i] : taller(fred, X))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred)))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(taller(john, alice) & (~hate(alice, john)))) | ![X: $i] : richer(mary, X)) & ((~taller(fred, john)) | (?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((~(richer(john, X) & richer(john, Y))) | (X = Y)))) & ((~![X: $i] : quieter(X, fred)) | hate(john, mary)) & ?[X: $i] : ((~room(X)) & (~hate(X, john))) & ![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y)) & ?[X: $i] : (room(X) | taller(john, X)) & richer(fred, john) & ?[X: $i] : (room(X) | (~hate(X, john)) | predb(X)) & ![X: $i] : quieter(X, fred) & ![X: $i] : taller(fred, X)),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(![X: $i] : quieter(X, fred)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : quieter(X, fred)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,(
![X: $i] : quieter(X, fred)),
inference(skolemize,[status(sab)],[10])).
tff(12,plain,
(![X: $i] : quieter(X, fred)),
inference(modus_ponens,[status(thm)],[11, 3])).
tff(13,plain,
((~![X: $i] : quieter(X, fred)) | quieter(john, fred)),
inference(quant_inst,[status(thm)],[])).
tff(14,plain,
($false),
inference(unit_resolution,[status(thm)],[13, 12, 1])).
tff(15,plain,(quieter(john, fred)), inference(lemma,lemma(discharge,[]))).
tff(16,assumption,(~hate(fred, john)), introduced(assumption)).
tff(17,assumption,(X!2 = fred), introduced(assumption)).
tff(18,plain,
(room(X!2) <=> room(fred)),
inference(monotonicity,[status(thm)],[17])).
tff(19,plain,
(room(fred) <=> room(X!2)),
inference(symmetry,[status(thm)],[18])).
tff(20,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(room(fred)),
inference(and_elim,[status(thm)],[8])).
tff(22,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[21, 20])).
tff(23,plain,
(room(X!2)),
inference(modus_ponens,[status(thm)],[22, 19])).
tff(24,plain,
(?[X: $i] : ((~room(X)) & (~hate(X, john))) <=> ?[X: $i] : ((~room(X)) & (~hate(X, john)))),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(?[X: $i] : ((~room(X)) & (~hate(X, john)))),
inference(and_elim,[status(thm)],[8])).
tff(26,plain,
(?[X: $i] : ((~room(X)) & (~hate(X, john)))),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,(
(~room(X!2)) & (~hate(X!2, john))),
inference(skolemize,[status(sab)],[26])).
tff(28,plain,
(~room(X!2)),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
($false),
inference(unit_resolution,[status(thm)],[28, 23])).
tff(30,plain,(~(X!2 = fred)), inference(lemma,lemma(discharge,[]))).
tff(31,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | hate(Y, john) | hate(X, john)) <=> ((X = Y) | hate(Y, john) | hate(X, john)))),
inference(bind,[status(th)],[])).
tff(32,plain,
(![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john)) <=> ![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))),
inference(quant_intro,[status(thm)],[31])).
tff(33,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~hate(X, john)) & (~hate(Y, john))) <=> (~(hate(Y, john) | hate(X, john)))), ((~((~hate(X, john)) & (~hate(Y, john)))) <=> (~(~(hate(Y, john) | hate(X, john)))))), rewrite((~(~(hate(Y, john) | hate(X, john)))) <=> (hate(Y, john) | hate(X, john))), ((~((~hate(X, john)) & (~hate(Y, john)))) <=> (hate(Y, john) | hate(X, john)))), (((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y)) <=> ((hate(Y, john) | hate(X, john)) | (X = Y)))), rewrite(((hate(Y, john) | hate(X, john)) | (X = Y)) <=> ((X = Y) | hate(Y, john) | hate(X, john))), (((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y)) <=> ((X = Y) | hate(Y, john) | hate(X, john))))),
inference(bind,[status(th)],[])).
tff(34,plain,
(![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))),
inference(quant_intro,[status(thm)],[33])).
tff(35,plain,
(![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y))),
inference(and_elim,[status(thm)],[8])).
tff(37,plain,
(![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y))),
inference(modus_ponens,[status(thm)],[36, 35])).
tff(38,plain,(
![X: $i, Y: $i] : ((~((~hate(X, john)) & (~hate(Y, john)))) | (X = Y))),
inference(skolemize,[status(sab)],[37])).
tff(39,plain,
(![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))),
inference(modus_ponens,[status(thm)],[38, 34])).
tff(40,plain,
(![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))),
inference(modus_ponens,[status(thm)],[39, 32])).
tff(41,plain,
(~hate(X!2, john)),
inference(and_elim,[status(thm)],[27])).
tff(42,plain,
(((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | (hate(X!2, john) | hate(fred, john) | (X!2 = fred))) <=> ((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | hate(X!2, john) | hate(fred, john) | (X!2 = fred))),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
(((X!2 = fred) | hate(fred, john) | hate(X!2, john)) <=> (hate(X!2, john) | hate(fred, john) | (X!2 = fred))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
(((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | ((X!2 = fred) | hate(fred, john) | hate(X!2, john))) <=> ((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | (hate(X!2, john) | hate(fred, john) | (X!2 = fred)))),
inference(monotonicity,[status(thm)],[43])).
tff(45,plain,
(((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | ((X!2 = fred) | hate(fred, john) | hate(X!2, john))) <=> ((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | hate(X!2, john) | hate(fred, john) | (X!2 = fred))),
inference(transitivity,[status(thm)],[44, 42])).
tff(46,plain,
((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | ((X!2 = fred) | hate(fred, john) | hate(X!2, john))),
inference(quant_inst,[status(thm)],[])).
tff(47,plain,
((~![X: $i, Y: $i] : ((X = Y) | hate(Y, john) | hate(X, john))) | hate(X!2, john) | hate(fred, john) | (X!2 = fred)),
inference(modus_ponens,[status(thm)],[46, 45])).
tff(48,plain,
($false),
inference(unit_resolution,[status(thm)],[47, 41, 40, 30, 16])).
tff(49,plain,(hate(fred, john)), inference(lemma,lemma(discharge,[]))).
tff(50,plain,
((~(fred = john)) <=> (~(fred = john))),
inference(rewrite,[status(thm)],[])).
tff(51,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//2185362851710588708723215.p','b14')).
tff(52,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[51])).
tff(53,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[53])).
tff(55,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[55])).
tff(57,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[56])).
tff(58,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[57])).
tff(59,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[58])).
tff(60,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[60])).
tff(62,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[61])).
tff(63,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[62])).
tff(64,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[63])).
tff(65,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[64])).
tff(66,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[65])).
tff(67,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[66])).
tff(68,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[67])).
tff(69,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[68])).
tff(70,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[69])).
tff(71,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[70])).
tff(72,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[71])).
tff(73,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[72])).
tff(74,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[73])).
tff(75,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[74])).
tff(76,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[75])).
tff(77,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[76])).
tff(78,plain,
(~(fred = john)),
inference(and_elim,[status(thm)],[77])).
tff(79,plain,
(~(fred = john)),
inference(modus_ponens,[status(thm)],[78, 50])).
tff(80,plain,
(^[X: $i, Y: $i] : refl(((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y))))),
inference(bind,[status(th)],[])).
tff(81,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(quant_intro,[status(thm)],[80])).
tff(82,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(83,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite((like(X, Y) => (~hate(X, Y))) <=> ((~hate(X, Y)) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))))), rewrite(((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))))),
inference(bind,[status(th)],[])).
tff(84,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(quant_intro,[status(thm)],[83])).
tff(85,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y))))), file('/mnt/tmpfs//2185362851710588708723215.p','b0')).
tff(86,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[85, 84])).
tff(87,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[86, 82])).
tff(88,plain,(
![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(skolemize,[status(sab)],[87])).
tff(89,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[88, 81])).
tff(90,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((fred = john) | (~like(fred, john)) | (~hate(fred, john)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (fred = john) | (~like(fred, john)) | (~hate(fred, john)))),
inference(rewrite,[status(thm)],[])).
tff(91,plain,
(((~hate(fred, john)) | (fred = john) | (~like(fred, john))) <=> ((fred = john) | (~like(fred, john)) | (~hate(fred, john)))),
inference(rewrite,[status(thm)],[])).
tff(92,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(fred, john)) | (fred = john) | (~like(fred, john)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((fred = john) | (~like(fred, john)) | (~hate(fred, john))))),
inference(monotonicity,[status(thm)],[91])).
tff(93,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(fred, john)) | (fred = john) | (~like(fred, john)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (fred = john) | (~like(fred, john)) | (~hate(fred, john)))),
inference(transitivity,[status(thm)],[92, 90])).
tff(94,plain,
((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(fred, john)) | (fred = john) | (~like(fred, john)))),
inference(quant_inst,[status(thm)],[])).
tff(95,plain,
((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (fred = john) | (~like(fred, john)) | (~hate(fred, john))),
inference(modus_ponens,[status(thm)],[94, 93])).
tff(96,plain,
(~like(fred, john)),
inference(unit_resolution,[status(thm)],[95, 89, 79, 49])).
tff(97,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(98,plain,
(room(alice)),
inference(and_elim,[status(thm)],[8])).
tff(99,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[98, 97])).
tff(100,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(101,plain,
(room(paul)),
inference(and_elim,[status(thm)],[8])).
tff(102,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[101, 100])).
tff(103,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(104,plain,
(room(mary)),
inference(and_elim,[status(thm)],[8])).
tff(105,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[104, 103])).
tff(106,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | like(fred, john) | (~quieter(john, fred))) <=> (like(fred, john) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~quieter(john, fred)))),
inference(rewrite,[status(thm)],[])).
tff(107,plain,
((~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) <=> (~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5))))),
inference(rewrite,[status(thm)],[])).
tff(108,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | like(fred, john) | (~quieter(john, fred))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | like(fred, john) | (~quieter(john, fred)))),
inference(monotonicity,[status(thm)],[107])).
tff(109,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | like(fred, john) | (~quieter(john, fred))) <=> (like(fred, john) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!5 = |'alice'|) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~quieter(john, fred)))),
inference(transitivity,[status(thm)],[108, 106])).
tff(110,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred)) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))),
inference(rewrite,[status(thm)],[])).
tff(111,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred)))),
inference(monotonicity,[status(thm)],[110])).
tff(112,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred)))),
inference(rewrite,[status(thm)],[])).
tff(113,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))),
inference(or_elim,[status(thm)],[7])).
tff(114,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))),
inference(modus_ponens,[status(thm)],[113, 111])).
tff(115,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))),
inference(modus_ponens,[status(thm)],[114, 112])).
tff(116,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(fred, john)) & quieter(john, fred))),
inference(modus_ponens,[status(thm)],[115, 111])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!5 |'alice'|)
(= X!5 |'fred'|)
(= X!5 |'paul'|)
(= X!5 |'mary'|)
(not (room X!5)))))
(a!7 (refl (~ (not (quieter john fred)) (not (quieter john fred))))))
(let ((a!8 (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(not (like fred john))
(quieter john fred)))))
(let ((a!9 (~ a!8
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(like fred john)
(not (quieter john fred))))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
(refl (~ (like fred john) (like fred john)))
a!7
a!9))))
| room(ernesto)&room(ruby)&room(stephanie)&room(joseph)&(![X]:(room(X)=>(X='ernesto'|X='ruby'|X='stephanie'|X='joseph')))&
((((taller(tiffanie,joseph))&(~hate(joseph,tiffanie)))=>(![X]:(richer(ernesto,X))))&
((((quieter(tiffanie,ruby))&(does_not_enjoy_cross-country_skiing(ruby)))=>(~(?[X]:(~room(X)=>(~tall(X))))))|((~((quieter(tiffanie,ruby))&(does_not_enjoy_cross-country_skiing(ruby))))=>(![X]:(~room(X)=>(like(X,tiffanie))))))&
((taller(stephanie,tiffanie))=>(((?[X]:(~room(X)&richer(tiffanie,X)))&(![X,Y]:((richer(tiffanie,X)&richer(tiffanie,Y))=>(X=Y))))))&
((![X]:(quieter(X,stephanie)))=>(hate(tiffanie,ernesto)))&
(((?[X]:(~room(X)&~hate(X,tiffanie)))&(![X,Y]:((~hate(X,tiffanie)&~hate(Y,tiffanie))=>(X=Y)))))&
(?[X]:(~room(X)=>(taller(tiffanie,X))))&
(richer(stephanie,tiffanie))&
(?[X]:(~room(X)=>(((hate(X,tiffanie))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(quieter(X,stephanie)))&
(~(~(![X]:(taller(stephanie,X)))))) | room(ernesto)&room(ruby)&room(stephanie)&room(joseph)&(![X]:(room(X)=>(X='ernesto'|X='ruby'|X='stephanie'|X='joseph')))&
((~like(stephanie,tiffanie))&(quieter(tiffanie,stephanie))) | neutral | contradiction | entailment |
David, Sharon are the only persons in the room. “Sharon and David are respectively quiet and rich” unless “Sharon is the richest in the room”. “Only one person in the room is not David” if “Elizabeth and Jacob hate each other” and vice versa. “Everyone outside the room who is not David is richer than Elizabeth” if “Sharon who is a quiet rich tourist, is not creative”. David is not hated by Elizabeth or does not enjoy mountain biking or both. David who is richer than Jacob, enjoys skydiving. Everyone in the room is hated by Elizabeth. Sharon is the quietest in the room. More than one person in the room is not a creative tourist. | David is not a happy quiet rich creative tourist. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_5_type, type, (
tptp_fun_X_5: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(tptp_fun_Y_3_type, type, (
tptp_fun_Y_3: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(1,assumption,(~((~rich(mary)) | (~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))), introduced(assumption)).
tff(2,plain,
(((~rich(mary)) | (~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))) | creative(mary)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(creative(mary)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~rich(mary)) | (~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))) | tourist(mary)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(tourist(mary)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,assumption,(mary = |'mary'|), introduced(assumption)).
tff(7,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[6])).
tff(8,assumption,(creative(mary)), introduced(assumption)).
tff(9,assumption,(tourist(mary)), introduced(assumption)).
tff(10,assumption,(~creative(Y!3)), introduced(assumption)).
tff(11,assumption,(X!4 = |'paul'|), introduced(assumption)).
tff(12,plain,
(|'paul'| = X!4),
inference(symmetry,[status(thm)],[11])).
tff(13,plain,
((|'paul'| = Y!3) <=> (Y!3 = |'paul'|)),
inference(commutativity,[status(thm)],[])).
tff(14,plain,
((X!4 = Y!3) <=> (|'paul'| = Y!3)),
inference(monotonicity,[status(thm)],[11])).
tff(15,plain,
((X!4 = Y!3) <=> (Y!3 = |'paul'|)),
inference(transitivity,[status(thm)],[14, 13])).
tff(16,plain,
((~(X!4 = Y!3)) <=> (~(Y!3 = |'paul'|))),
inference(monotonicity,[status(thm)],[15])).
tff(17,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & (~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))) & (~(X = Y)))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((~![X: $i] : richer(X, paul)) => (quiet(paul) & rich(mary))) & ((hate(susan, john) & hate(john, susan)) <=> (?[X: $i] : (room(X) & (~(X = mary))) & ![X: $i, Y: $i] : (((~(X = mary)) & (~(Y = mary))) => (X = Y))))) & ((((quiet(paul) & rich(paul)) & tourist(paul)) & (~creative(paul))) => ![X: $i] : ((~room(X)) => ((~(X = mary)) => richer(susan, X))))) & ((~hate(mary, susan)) | (~preda(mary)))) & (richer(john, mary) & predb(mary))) & ![X: $i] : (room(X) => hate(X, susan))) & ![X: $i] : quieter(X, paul)) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))))) & (~(X = Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((((happy(mary) & quiet(mary)) & rich(mary)) & creative(mary)) & tourist(mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : richer(X, paul) | (quiet(paul) & rich(mary))) & ((hate(susan, john) & hate(john, susan)) <=> (?[X: $i] : (room(X) & (~(X = mary))) & ![X: $i, Y: $i] : ((~((~(X = mary)) & (~(Y = mary)))) | (X = Y)))) & ((~(quiet(paul) & rich(paul) & tourist(paul) & (~creative(paul)))) | ![X: $i] : (room(X) | (X = mary) | richer(susan, X))) & ((~hate(mary, susan)) | (~preda(mary))) & richer(john, mary) & predb(mary) & ![X: $i] : ((~room(X)) | hate(X, susan)) & ![X: $i] : quieter(X, paul) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))) & (~(X = Y))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(19,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((~![X: $i] : richer(X, paul)) => (quiet(paul) & rich(mary))) & ((hate(susan, john) & hate(john, susan)) <=> (?[X: $i] : (room(X) & (~(X = mary))) & ![X: $i, Y: $i] : (((~(X = mary)) & (~(Y = mary))) => (X = Y))))) & ((((quiet(paul) & rich(paul)) & tourist(paul)) & (~creative(paul))) => ![X: $i] : ((~room(X)) => ((~(X = mary)) => richer(susan, X))))) & ((~hate(mary, susan)) | (~preda(mary)))) & (richer(john, mary) & predb(mary))) & ![X: $i] : (room(X) => hate(X, susan))) & ![X: $i] : quieter(X, paul)) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))))) & (~(X = Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((((happy(mary) & quiet(mary)) & rich(mary)) & creative(mary)) & tourist(mary)))))), file('/mnt/tmpfs//8220401575075607636389948.p','negated')).
tff(20,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : richer(X, paul) | (quiet(paul) & rich(mary))) & ((hate(susan, john) & hate(john, susan)) <=> (?[X: $i] : (room(X) & (~(X = mary))) & ![X: $i, Y: $i] : ((~((~(X = mary)) & (~(Y = mary)))) | (X = Y)))) & ((~(quiet(paul) & rich(paul) & tourist(paul) & (~creative(paul)))) | ![X: $i] : (room(X) | (X = mary) | richer(susan, X))) & ((~hate(mary, susan)) | (~preda(mary))) & richer(john, mary) & predb(mary) & ![X: $i] : ((~room(X)) | hate(X, susan)) & ![X: $i] : quieter(X, paul) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))) & (~(X = Y))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : richer(X, paul) | (quiet(paul) & rich(mary))) & ((hate(susan, john) & hate(john, susan)) <=> (?[X: $i] : (room(X) & (~(X = mary))) & ![X: $i, Y: $i] : ((~((~(X = mary)) & (~(Y = mary)))) | (X = Y)))) & ((~(quiet(paul) & rich(paul) & tourist(paul) & (~creative(paul)))) | ![X: $i] : (room(X) | (X = mary) | richer(susan, X))) & ((~hate(mary, susan)) | (~preda(mary))) & richer(john, mary) & predb(mary) & ![X: $i] : ((~room(X)) | hate(X, susan)) & ![X: $i] : quieter(X, paul) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))) & (~(X = Y)))),
inference(or_elim,[status(thm)],[20])).
tff(22,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & (~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))) & (~(X = Y)))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & (~(creative(X) & tourist(X))) & (~(creative(Y) & tourist(Y))) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[22, 17])).
tff(24,plain,(
room(X!4) & room(Y!3) & (~(creative(X!4) & tourist(X!4))) & (~(creative(Y!3) & tourist(Y!3))) & (~(X!4 = Y!3))),
inference(skolemize,[status(sab)],[23])).
tff(25,plain,
(~(X!4 = Y!3)),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
(~(Y!3 = |'paul'|)),
inference(modus_ponens,[status(thm)],[25, 16])).
tff(27,plain,
(room(Y!3)),
inference(and_elim,[status(thm)],[24])).
tff(28,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(29,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[28])).
tff(30,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[21])).
tff(32,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[32])).
tff(34,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[33, 29])).
tff(35,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!3 = |'paul'|) | (Y!3 = |'mary'|) | (~room(Y!3)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (Y!3 = |'paul'|) | (Y!3 = |'mary'|) | (~room(Y!3)))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!3 = |'paul'|) | (Y!3 = |'mary'|) | (~room(Y!3)))),
inference(quant_inst,[status(thm)],[])).
tff(37,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (Y!3 = |'paul'|) | (Y!3 = |'mary'|) | (~room(Y!3))),
inference(modus_ponens,[status(thm)],[36, 35])).
tff(38,plain,
((Y!3 = |'paul'|) | (Y!3 = |'mary'|)),
inference(unit_resolution,[status(thm)],[37, 34, 27])).
tff(39,plain,
(Y!3 = |'mary'|),
inference(unit_resolution,[status(thm)],[38, 26])).
tff(40,assumption,(Y!3 = |'mary'|), introduced(assumption)).
tff(41,plain,
(|'mary'| = Y!3),
inference(symmetry,[status(thm)],[40])).
tff(42,plain,
(mary = Y!3),
inference(transitivity,[status(thm)],[6, 41])).
tff(43,plain,
(creative(mary) <=> creative(Y!3)),
inference(monotonicity,[status(thm)],[42])).
tff(44,plain,
(creative(Y!3) <=> creative(mary)),
inference(symmetry,[status(thm)],[43])).
tff(45,plain,
((~creative(Y!3)) <=> (~creative(mary))),
inference(monotonicity,[status(thm)],[44])).
tff(46,plain,
(~creative(mary)),
inference(modus_ponens,[status(thm)],[10, 45])).
tff(47,plain,
($false),
inference(unit_resolution,[status(thm)],[8, 46])).
tff(48,plain,((~(mary = |'mary'|)) | (~creative(mary)) | creative(Y!3) | (~(Y!3 = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(49,plain,
(~(mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[48, 39, 10, 8])).
tff(50,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(51,plain,
(room(mary)),
inference(and_elim,[status(thm)],[21])).
tff(52,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[51, 50])).
tff(53,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary))) <=> ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(55,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)))),
inference(monotonicity,[status(thm)],[54])).
tff(56,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(transitivity,[status(thm)],[55, 53])).
tff(57,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(58,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[57, 56])).
tff(59,plain,
((mary = |'paul'|) | (mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[58, 52, 34])).
tff(60,plain,
(mary = |'paul'|),
inference(unit_resolution,[status(thm)],[59, 49])).
tff(61,plain,
(mary = X!4),
inference(transitivity,[status(thm)],[60, 12])).
tff(62,plain,
(tourist(mary) <=> tourist(X!4)),
inference(monotonicity,[status(thm)],[61])).
tff(63,plain,
(tourist(X!4) <=> tourist(mary)),
inference(symmetry,[status(thm)],[62])).
tff(64,plain,
((~tourist(X!4)) <=> (~tourist(mary))),
inference(monotonicity,[status(thm)],[63])).
tff(65,assumption,(~creative(X!4)), introduced(assumption)).
tff(66,assumption,(mary = |'paul'|), introduced(assumption)).
tff(67,plain,
(|'paul'| = mary),
inference(symmetry,[status(thm)],[66])).
tff(68,plain,
((|'mary'| = Y!3) <=> (Y!3 = |'mary'|)),
inference(commutativity,[status(thm)],[])).
tff(69,plain,
(X!4 = mary),
inference(transitivity,[status(thm)],[11, 67])).
tff(70,plain,
(creative(X!4) <=> creative(mary)),
inference(monotonicity,[status(thm)],[69])).
tff(71,plain,
(creative(mary) <=> creative(X!4)),
inference(symmetry,[status(thm)],[70])).
tff(72,plain,
(creative(X!4)),
inference(modus_ponens,[status(thm)],[8, 71])).
tff(73,plain,
($false),
inference(unit_resolution,[status(thm)],[65, 72])).
tff(74,plain,((~(X!4 = |'paul'|)) | creative(X!4) | (~creative(mary)) | (~(mary = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(75,plain,
(~(X!4 = |'paul'|)),
inference(unit_resolution,[status(thm)],[74, 66, 8, 65])).
tff(76,plain,
(room(X!4)),
inference(and_elim,[status(thm)],[24])).
tff(77,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(rewrite,[status(thm)],[])).
tff(78,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(quant_inst,[status(thm)],[])).
tff(79,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))),
inference(modus_ponens,[status(thm)],[78, 77])).
tff(80,plain,
((X!4 = |'paul'|) | (X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[79, 34, 76])).
tff(81,plain,
(X!4 = |'mary'|),
inference(unit_resolution,[status(thm)],[80, 75])).
tff(82,plain,
((X!4 = Y!3) <=> (|'mary'| = Y!3)),
inference(monotonicity,[status(thm)],[81])).
tff(83,plain,
((X!4 = Y!3) <=> (Y!3 = |'mary'|)),
inference(transitivity,[status(thm)],[82, 68])).
tff(84,plain,
((~(X!4 = Y!3)) <=> (~(Y!3 = |'mary'|))),
inference(monotonicity,[status(thm)],[83])).
tff(85,plain,
(~(Y!3 = |'mary'|)),
inference(modus_ponens,[status(thm)],[25, 84])).
tff(86,plain,
(Y!3 = |'paul'|),
inference(unit_resolution,[status(thm)],[38, 85])).
tff(87,plain,
(Y!3 = mary),
inference(transitivity,[status(thm)],[86, 67])).
tff(88,plain,
(creative(Y!3) <=> creative(mary)),
inference(monotonicity,[status(thm)],[87])).
tff(89,plain,
(creative(mary) <=> creative(Y!3)),
inference(symmetry,[status(thm)],[88])).
tff(90,plain,
(creative(Y!3)),
inference(modus_ponens,[status(thm)],[8, 89])).
tff(91,plain,
($false),
inference(unit_resolution,[status(thm)],[10, 90])).
tff(92,plain,((~(mary = |'paul'|)) | creative(Y!3) | (~creative(mary)) | creative(X!4)), inference(lemma,lemma(discharge,[]))).
tff(93,plain,
(~(mary = |'paul'|)),
inference(unit_resolution,[status(thm)],[92, 65, 8, 10])).
tff(94,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[59, 93])).
tff(95,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[94])).
tff(96,assumption,(X!4 = |'mary'|), introduced(assumption)).
tff(97,plain,
(X!4 = mary),
inference(transitivity,[status(thm)],[96, 7])).
tff(98,plain,
(creative(X!4) <=> creative(mary)),
inference(monotonicity,[status(thm)],[97])).
tff(99,plain,
(creative(mary) <=> creative(X!4)),
inference(symmetry,[status(thm)],[98])).
tff(100,plain,
(creative(X!4)),
inference(modus_ponens,[status(thm)],[8, 99])).
tff(101,plain,
($false),
inference(unit_resolution,[status(thm)],[65, 100])).
tff(102,plain,((~(X!4 = |'mary'|)) | creative(X!4) | (~creative(mary)) | (~(mary = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(103,plain,
(~(X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[102, 65, 8, 94])).
tff(104,plain,
(X!4 = |'paul'|),
inference(unit_resolution,[status(thm)],[80, 103])).
tff(105,plain,
((X!4 = Y!3) <=> (|'paul'| = Y!3)),
inference(monotonicity,[status(thm)],[104])).
tff(106,plain,
((X!4 = Y!3) <=> (Y!3 = |'paul'|)),
inference(transitivity,[status(thm)],[105, 13])).
tff(107,plain,
((~(X!4 = Y!3)) <=> (~(Y!3 = |'paul'|))),
inference(monotonicity,[status(thm)],[106])).
tff(108,plain,
(~(Y!3 = |'paul'|)),
inference(modus_ponens,[status(thm)],[25, 107])).
tff(109,plain,
(Y!3 = |'mary'|),
inference(unit_resolution,[status(thm)],[38, 108])).
tff(110,plain,
(Y!3 = mary),
inference(transitivity,[status(thm)],[109, 95])).
tff(111,plain,
(creative(Y!3) <=> creative(mary)),
inference(monotonicity,[status(thm)],[110])).
tff(112,plain,
(creative(mary) <=> creative(Y!3)),
inference(symmetry,[status(thm)],[111])).
tff(113,plain,
(creative(Y!3)),
inference(modus_ponens,[status(thm)],[8, 112])).
tff(114,plain,
($false),
inference(unit_resolution,[status(thm)],[10, 113])).
tff(115,plain,(creative(X!4) | creative(Y!3) | (~creative(mary))), inference(lemma,lemma(discharge,[]))).
tff(116,plain,
(creative(X!4)),
inference(unit_resolution,[status(thm)],[115, 10, 8])).
tff(117,plain,
((~(~((~creative(X!4)) | (~tourist(X!4))))) <=> ((~creative(X!4)) | (~tourist(X!4)))),
inference(rewrite,[status(thm)],[])).
tff(118,plain,
((creative(X!4) & tourist(X!4)) <=> (~((~creative(X!4)) | (~tourist(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(119,plain,
((~(creative(X!4) & tourist(X!4))) <=> (~(~((~creative(X!4)) | (~tourist(X!4)))))),
inference(monotonicity,[status(thm)],[118])).
tff(120,plain,
((~(creative(X!4) & tourist(X!4))) <=> ((~creative(X!4)) | (~tourist(X!4)))),
inference(transitivity,[status(thm)],[119, 117])).
tff(121,plain,
(~(creative(X!4) & tourist(X!4))),
inference(and_elim,[status(thm)],[24])).
tff(122,plain,
((~creative(X!4)) | (~tourist(X!4))),
inference(modus_ponens,[status(thm)],[121, 120])).
tff(123,plain,
(~tourist(X!4)),
inference(unit_resolution,[status(thm)],[122, 116])).
tff(124,plain,
(~tourist(mary)),
inference(modus_ponens,[status(thm)],[123, 64])).
tff(125,plain,
($false),
inference(unit_resolution,[status(thm)],[9, 124])).
tff(126,plain,((~(X!4 = |'paul'|)) | (~tourist(mary)) | creative(Y!3) | (~creative(mary))), inference(lemma,lemma(discharge,[]))).
tff(127,plain,
(~(X!4 = |'paul'|)),
inference(unit_resolution,[status(thm)],[126, 10, 9, 8])).
tff(128,plain,
(X!4 = |'mary'|),
inference(unit_resolution,[status(thm)],[80, 127])).
tff(129,plain,
(|'mary'| = X!4),
inference(symmetry,[status(thm)],[128])).
tff(130,plain,
((X!4 = Y!3) <=> (|'mary'| = Y!3)),
inference(monotonicity,[status(thm)],[128])).
tff(131,plain,
((X!4 = Y!3) <=> (Y!3 = |'mary'|)),
inference(transitivity,[status(thm)],[130, 68])).
tff(132,plain,
((~(X!4 = Y!3)) <=> (~(Y!3 = |'mary'|))),
inference(monotonicity,[status(thm)],[131])).
tff(133,plain,
(~(Y!3 = |'mary'|)),
inference(modus_ponens,[status(thm)],[25, 132])).
tff(134,plain,
(Y!3 = |'paul'|),
inference(unit_resolution,[status(thm)],[38, 133])).
tff(135,assumption,(Y!3 = |'paul'|), introduced(assumption)).
tff(136,plain,
(|'paul'| = Y!3),
inference(symmetry,[status(thm)],[135])).
tff(137,plain,
(mary = Y!3),
inference(transitivity,[status(thm)],[66, 136])).
tff(138,plain,
(creative(mary) <=> creative(Y!3)),
inference(monotonicity,[status(thm)],[137])).
tff(139,plain,
(creative(Y!3) <=> creative(mary)),
inference(symmetry,[status(thm)],[138])).
tff(140,plain,
((~creative(Y!3)) <=> (~creative(mary))),
inference(monotonicity,[status(thm)],[139])).
tff(141,plain,
(~creative(mary)),
inference(modus_ponens,[status(thm)],[10, 140])).
tff(142,plain,
($false),
inference(unit_resolution,[status(thm)],[8, 141])).
tff(143,plain,((~(mary = |'paul'|)) | (~creative(mary)) | creative(Y!3) | (~(Y!3 = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(144,plain,
(~(mary = |'paul'|)),
inference(unit_resolution,[status(thm)],[143, 10, 8, 134])).
tff(145,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[59, 144])).
tff(146,plain,
(mary = X!4),
inference(transitivity,[status(thm)],[145, 129])).
tff(147,plain,
(tourist(mary) <=> tourist(X!4)),
inference(monotonicity,[status(thm)],[146])).
tff(148,plain,
(tourist(X!4) <=> tourist(mary)),
inference(symmetry,[status(thm)],[147])).
tff(149,plain,
((~tourist(X!4)) <=> (~tourist(mary))),
inference(monotonicity,[status(thm)],[148])).
tff(150,plain,
(~tourist(mary)),
inference(modus_ponens,[status(thm)],[123, 149])).
tff(151,plain,
($false),
inference(unit_resolution,[status(thm)],[9, 150])).
tff(152,plain,(creative(Y!3) | (~tourist(mary)) | (~creative(mary))), inference(lemma,lemma(discharge,[]))).
tff(153,plain,
(creative(Y!3)),
inference(unit_resolution,[status(thm)],[152, 9, 8])).
tff(154,plain,
((~(~((~creative(Y!3)) | (~tourist(Y!3))))) <=> ((~creative(Y!3)) | (~tourist(Y!3)))),
inference(rewrite,[status(thm)],[])).
tff(155,plain,
((creative(Y!3) & tourist(Y!3)) <=> (~((~creative(Y!3)) | (~tourist(Y!3))))),
inference(rewrite,[status(thm)],[])).
tff(156,plain,
((~(creative(Y!3) & tourist(Y!3))) <=> (~(~((~creative(Y!3)) | (~tourist(Y!3)))))),
inference(monotonicity,[status(thm)],[155])).
tff(157,plain,
((~(creative(Y!3) & tourist(Y!3))) <=> ((~creative(Y!3)) | (~tourist(Y!3)))),
inference(transitivity,[status(thm)],[156, 154])).
tff(158,plain,
(~(creative(Y!3) & tourist(Y!3))),
inference(and_elim,[status(thm)],[24])).
tff(159,plain,
((~creative(Y!3)) | (~tourist(Y!3))),
inference(modus_ponens,[status(thm)],[158, 157])).
tff(160,plain,
(~tourist(Y!3)),
inference(unit_resolution,[status(thm)],[159, 153])).
tff(161,plain,
(Y!3 = mary),
inference(transitivity,[status(thm)],[40, 7])).
tff(162,plain,
(tourist(Y!3) <=> tourist(mary)),
inference(monotonicity,[status(thm)],[161])).
tff(163,plain,
(tourist(mary) <=> tourist(Y!3)),
inference(symmetry,[status(thm)],[162])).
tff(164,plain,
(tourist(Y!3)),
inference(modus_ponens,[status(thm)],[9, 163])).
tff(165,assumption,(~tourist(Y!3)), introduced(assumption)).
tff(166,plain,
($false),
inference(unit_resolution,[status(thm)],[165, 164])).
tff(167,plain,((~(Y!3 = |'mary'|)) | tourist(Y!3) | (~tourist(mary)) | (~(mary = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(168,plain,
(~(Y!3 = |'mary'|)),
inference(unit_resolution,[status(thm)],[167, 6, 9, 160])).
tff(169,plain,
(Y!3 = |'paul'|),
inference(unit_resolution,[status(thm)],[38, 168])).
tff(170,plain,
((X!4 = Y!3) <=> (X!4 = |'paul'|)),
inference(monotonicity,[status(thm)],[169])).
tff(171,plain,
((~(X!4 = Y!3)) <=> (~(X!4 = |'paul'|))),
inference(monotonicity,[status(thm)],[170])).
tff(172,plain,
(~(X!4 = |'paul'|)),
inference(modus_ponens,[status(thm)],[25, 171])).
tff(173,plain,
(X!4 = |'mary'|),
inference(unit_resolution,[status(thm)],[80, 172])).
tff(174,plain,
(X!4 = mary),
inference(transitivity,[status(thm)],[173, 7])).
tff(175,plain,
(tourist(X!4) <=> tourist(mary)),
inference(monotonicity,[status(thm)],[174])).
tff(176,plain,
(tourist(mary) <=> tourist(X!4)),
inference(symmetry,[status(thm)],[175])).
tff(177,plain,
(tourist(X!4)),
inference(modus_ponens,[status(thm)],[9, 176])).
tff(178,plain,
(creative(X!4)),
inference(unit_resolution,[status(thm)],[102, 173, 8, 6])).
tff(179,plain,
(~tourist(X!4)),
inference(unit_resolution,[status(thm)],[122, 178])).
tff(180,plain,
($false),
inference(unit_resolution,[status(thm)],[179, 177])).
tff(181,plain,((~(mary = |'mary'|)) | (~tourist(mary)) | (~creative(mary))), inference(lemma,lemma(discharge,[]))).
tff(182,plain,
(~(mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[181, 5, 3])).
tff(183,plain,
(mary = |'paul'|),
inference(unit_resolution,[status(thm)],[59, 182])).
tff(184,plain,
(|'paul'| = mary),
inference(symmetry,[status(thm)],[183])).
tff(185,plain,
(creative(Y!3)),
inference(unit_resolution,[status(thm)],[152, 5, 3])).
tff(186,plain,
(~tourist(Y!3)),
inference(unit_resolution,[status(thm)],[159, 185])).
tff(187,plain,
(Y!3 = mary),
inference(transitivity,[status(thm)],[135, 67])).
tff(188,plain,
(tourist(Y!3) <=> tourist(mary)),
inference(monotonicity,[status(thm)],[187])).
tff(189,plain,
(tourist(mary) <=> tourist(Y!3)),
inference(symmetry,[status(thm)],[188])).
tff(190,plain,
(tourist(Y!3)),
inference(modus_ponens,[status(thm)],[9, 189])).
tff(191,plain,
($false),
inference(unit_resolution,[status(thm)],[165, 190])).
tff(192,plain,((~(Y!3 = |'paul'|)) | tourist(Y!3) | (~tourist(mary)) | (~(mary = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(193,plain,
(~(Y!3 = |'paul'|)),
inference(unit_resolution,[status(thm)],[192, 186, 5, 183])).
tff(194,plain,
(Y!3 = |'mary'|),
inference(unit_resolution,[status(thm)],[38, 193])).
tff(195,plain,
((X!4 = Y!3) <=> (X!4 = |'mary'|)),
inference(monotonicity,[status(thm)],[194])).
tff(196,plain,
((~(X!4 = Y!3)) <=> (~(X!4 = |'mary'|))),
inference(monotonicity,[status(thm)],[195])).
tff(197,plain,
(~(X!4 = |'mary'|)),
inference(modus_ponens,[status(thm)],[25, 196])).
tff(198,plain,
(X!4 = |'paul'|),
inference(unit_resolution,[status(thm)],[80, 197])).
tff(199,plain,
(X!4 = mary),
inference(transitivity,[status(thm)],[198, 184])).
tff(200,plain,
(tourist(X!4) <=> tourist(mary)),
inference(monotonicity,[status(thm)],[199])).
tff(201,plain,
(tourist(mary) <=> tourist(X!4)),
inference(symmetry,[status(thm)],[200])).
tff(202,plain,
(tourist(X!4)),
inference(modus_ponens,[status(thm)],[5, 201])).
tff(203,plain,
(creative(X!4)),
inference(unit_resolution,[status(thm)],[74, 198, 3, 183])).
tff(204,plain,
(~tourist(X!4)),
inference(unit_resolution,[status(thm)],[122, 203])).
tff(205,plain,
($false),
inference(unit_resolution,[status(thm)],[204, 202])).
tff(206,plain,((~rich(mary)) | (~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary))), inference(lemma,lemma(discharge,[]))).
tff(207,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(208,plain,
(room(paul)),
inference(and_elim,[status(thm)],[21])).
tff(209,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[208, 207])).
tff(210,plain,
(((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))) <=> ((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~((~rich(mary)) | (~happy(mary)) | (~quiet(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(211,plain,
((~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) <=> (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5))))),
inference(rewrite,[status(thm)],[])).
tff(212,plain,
(((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))) <=> ((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary)))),
inference(monotonicity,[status(thm)],[211])).
tff(213,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(214,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary)))))),
inference(monotonicity,[status(thm)],[213])).
tff(215,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(216,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))),
inference(or_elim,[status(thm)],[20])).
tff(217,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[216, 214])).
tff(218,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[217, 215])).
tff(219,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(happy(mary) & quiet(mary) & rich(mary) & creative(mary) & tourist(mary))))),
inference(modus_ponens,[status(thm)],[218, 214])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!5 |'paul'|) (= X!5 |'mary'|) (not (room X!5)))))
(a!5 (and (happy mary)
(quiet mary)
(rich mary)
(creative mary)
(tourist mary))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 (not a!5)))
(or (not (room mary)) (not (room paul)) a!4 a!5))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ a!5 a!5)) a!6)))
| room(david)&room(sharon)&(![X]:(room(X)=>(X='david'|X='sharon')))&
((~(![X]:(richer(X,sharon)))=>((quiet(sharon))&(rich(david))))&
(((hate(elizabeth,jacob) & hate(jacob,elizabeth)))<=>(((?[X]:(room(X)&X!=david))&(![X,Y]:((X!=david&Y!=david)=>(X=Y))))))&
(((quiet(sharon)&rich(sharon)&tourist(sharon))&(~creative(sharon)))=>(![X]:(~room(X)=>(((X!=david)=>(richer(elizabeth,X)))))))&
(((~hate(david,elizabeth))|(does_not_enjoy_mountain_biking(david))))&
((richer(jacob,david))&(enjoys_skydiving(david)))&
(![X]:(room(X)=>(hate(X,elizabeth))))&
(![X]:(quieter(X,sharon)))&
((?[X,Y]:(room(X)&room(Y)&(~(creative(X)&tourist(X))&~(creative(Y)&tourist(Y)))&(X!=Y))))) | room(david)&room(sharon)&(![X]:(room(X)=>(X='david'|X='sharon')))&
(~(happy(david)&quiet(david)&rich(david)&creative(david)&tourist(david))) | contradiction | neutral | neutral |
Michael, Jason are the only persons in the room. "Lillian is quieter than Jason" unless "Jason is a quiet person and is liked by Lillian". If "Michael writes poetry or hates Lillian or both" then "someone outside the room is hated by Lillian" otherwise "Jason is the least tall in the room". More than one person outside the room likes Lillian. Someone outside the room is not a brave person. Everyone in the room hates Lillian. Michael and Jason are not hated by Lillian. | Jason neither is a quiet brave person nor hates Lillian. | contradiction | - | room(michael)&room(jason)&(![X]:(room(X)=>(X='michael'|X='jason')))&
((~((quiet(jason)&person(jason))&(like(jason,lillian)))=>(quieter(jason,lillian)))&
(((((writes_poetry(michael))|(hate(lillian,michael))))=>(?[X]:(~room(X)=>(hate(X,lillian)))))|((~(((writes_poetry(michael))|(hate(lillian,michael)))))=>(![X]:(taller(jason,X)))))&
((?[X,Y]:(~room(X)&~room(Y)&(like(lillian,X)&like(lillian,Y))&(X!=Y))))&
(?[X]:(~room(X)=>(~(brave(X)&person(X)))))&
(![X]:(room(X)=>(hate(lillian,X))))&
(~hate(michael,lillian)&~hate(jason,lillian))) | room(michael)&room(jason)&(![X]:(room(X)=>(X='michael'|X='jason')))&
(~((quiet(jason)&brave(jason)&person(jason))|(hate(lillian,jason)))) | entailment | neutral | contradiction |
Deborah, George, Carl are the only persons in the room.
Someone who is not tall, not happy, not brave is taller than someone who is not a brave tall happy tourist.
Deborah who is liked by Marilyn, is not a tall tourist.
George who is not liked by Jacqueline, is hated by Martin.
George is the least tall in the room.
Everyone in the room who is not a tall tourist is a sibling of Martin. | It is not the case that 'Deborah either is a tall happy brave rich tourist or hates Marilyn'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(mary_type, type, (
mary: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(1,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((?[X: $i, Y: $i] : (((((~tall(X)) & (~happy(X))) & (~brave(X))) & (~(((brave(Y) & tall(Y)) & happy(Y)) & tourist(Y)))) & taller(X, Y)) & (like(mary, lucy) & (~(tall(mary) & tourist(mary))))) & ((~like(paul, alice)) & hate(paul, john))) & ![X: $i] : taller(paul, X)) & ![X: $i] : (room(X) => ((~(tall(X) & tourist(X))) => sibling(john, X))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~((((((tall(mary) & happy(mary)) & brave(mary)) & rich(mary)) & tourist(mary)) | hate(lucy, mary)) & (~(((((tall(mary) & happy(mary)) & brave(mary)) & rich(mary)) & tourist(mary)) | hate(lucy, mary)))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~happy(X)) & (~brave(X)) & (~(brave(Y) & tall(Y) & happy(Y) & tourist(Y))) & taller(X, Y)) & like(mary, lucy) & (~(tall(mary) & tourist(mary))) & (~like(paul, alice)) & hate(paul, john) & ![X: $i] : taller(paul, X) & ![X: $i] : (sibling(john, X) | (tall(X) & tourist(X)) | (~room(X))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((?[X: $i, Y: $i] : (((((~tall(X)) & (~happy(X))) & (~brave(X))) & (~(((brave(Y) & tall(Y)) & happy(Y)) & tourist(Y)))) & taller(X, Y)) & (like(mary, lucy) & (~(tall(mary) & tourist(mary))))) & ((~like(paul, alice)) & hate(paul, john))) & ![X: $i] : taller(paul, X)) & ![X: $i] : (room(X) => ((~(tall(X) & tourist(X))) => sibling(john, X))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~((((((tall(mary) & happy(mary)) & brave(mary)) & rich(mary)) & tourist(mary)) | hate(lucy, mary)) & (~(((((tall(mary) & happy(mary)) & brave(mary)) & rich(mary)) & tourist(mary)) | hate(lucy, mary)))))))), file('/mnt/tmpfs//3550456762701603261470268.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~happy(X)) & (~brave(X)) & (~(brave(Y) & tall(Y) & happy(Y) & tourist(Y))) & taller(X, Y)) & like(mary, lucy) & (~(tall(mary) & tourist(mary))) & (~like(paul, alice)) & hate(paul, john) & ![X: $i] : taller(paul, X) & ![X: $i] : (sibling(john, X) | (tall(X) & tourist(X)) | (~room(X))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~happy(X)) & (~brave(X)) & (~(brave(Y) & tall(Y) & happy(Y) & tourist(Y))) & taller(X, Y)) & like(mary, lucy) & (~(tall(mary) & tourist(mary))) & (~like(paul, alice)) & hate(paul, john) & ![X: $i] : taller(paul, X) & ![X: $i] : (sibling(john, X) | (tall(X) & tourist(X)) | (~room(X)))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(10,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(13,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))),
inference(monotonicity,[status(thm)],[15])).
tff(17,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))),
inference(transitivity,[status(thm)],[16, 14])).
tff(18,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(monotonicity,[status(thm)],[18])).
tff(20,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(or_elim,[status(thm)],[4])).
tff(22,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[21, 19])).
tff(23,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[22, 20])).
tff(24,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[23, 19])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!2 |'fred'|)
(= X!2 |'paul'|)
(= X!2 |'mary'|)
(not (room X!2))))))
(let ((a!6 (~ (not (and (room mary) (room paul) (room fred) a!4))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5))))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) a!6)))
| room(deborah)&room(george)&room(carl)&(![X]:(room(X)=>(X='deborah'|X='george'|X='carl')))&
((?[X,Y]:((~tall(X)&~happy(X)&~brave(X))&(~(brave(Y)&tall(Y)&happy(Y)&tourist(Y)))&(taller(X,Y))))&
((like(deborah,marilyn))&(~(tall(deborah)&tourist(deborah))))&
((~like(george,jacqueline))&(hate(george,martin)))&
(![X]:(taller(george,X)))&
(![X]:(room(X)=>(((~(tall(X)&tourist(X)))=>(sibling(martin,X))))))) | room(deborah)&room(george)&room(carl)&(![X]:(room(X)=>(X='deborah'|X='george'|X='carl')))&
(~((((tall(deborah)&happy(deborah)&brave(deborah)&rich(deborah)&tourist(deborah))|(hate(marilyn,deborah)))&(~((tall(deborah)&happy(deborah)&brave(deborah)&rich(deborah)&tourist(deborah))|(hate(marilyn,deborah))))))) | contradiction | entailment | entailment |
Diana, Carol are the only persons in the room.
If 'only one person outside the room is liked by Jacqueline' then 'Carol and Diana are not liked by Rubye' otherwise 'someone outside the room who is a quiet brave person does not like Rubye'.
'Diana and Carol are not quiet' only if 'Diana is a creative person or does not like Rubye or both'.
If 'Carol and Diana like each other' then 'someone who is not a quiet creative person is quieter than someone who is a quiet person' otherwise 'Carol does not enjoy windsurfing and is not liked by Rubye'.
More than one person outside the room plays a musical instrument.
Carol and Diana like each other.
More than one person outside the room is liked by Rubye.
Carol neither is not liked by Rubye nor does not play a musical instrument.
Diana neither does not like Rubye nor enjoys windsurfing.
Diana is the least quiet in the room.
Carol collects antique jewelry and plays a musical instrument.
Diana is a creative person or does not like Rubye or both. | Diana likes Rubye or is not a quiet brave creative person or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(brave_type, type, (
brave: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(1,plain,
(like(lucy, mary) <=> like(lucy, mary)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((((?[X: $i] : ((~room(X)) & like(X, alice)) & ![X: $i, Y: $i] : ((like(X, alice) & like(Y, alice)) => (X = Y))) => ((~like(paul, lucy)) & (~like(mary, lucy)))) | ((~(?[X: $i] : ((~room(X)) & like(X, alice)) & ![X: $i, Y: $i] : ((like(X, alice) & like(Y, alice)) => (X = Y)))) => ?[X: $i] : ((~room(X)) => (((quiet(X) & brave(X)) & person(X)) => (~like(lucy, X)))))) & (((~quiet(mary)) & (~quiet(paul))) => ((creative(mary) & person(mary)) | (~like(lucy, mary))))) & (((like(paul, mary) & like(mary, paul)) => ?[X: $i, Y: $i] : (((~((quiet(X) & creative(X)) & person(X))) & (quiet(Y) & person(Y))) & quieter(X, Y))) | ((~(like(paul, mary) & like(mary, paul))) => ((~predc(paul)) & (~like(paul, lucy)))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (predb(X) & predb(Y))) & (~(X = Y)))) & (like(paul, mary) & like(mary, paul))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (like(X, lucy) & like(Y, lucy))) & (~(X = Y)))) & (~((~like(paul, lucy)) | (~predb(paul))))) & (~((~like(lucy, mary)) | predc(mary)))) & ![X: $i] : quieter(mary, X)) & (preda(paul) & predb(paul))) & ((creative(mary) & person(mary)) | (~like(lucy, mary))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(lucy, mary) | (~(((quiet(mary) & brave(mary)) & creative(mary)) & person(mary))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((creative(mary) & person(mary)) | (~like(lucy, mary)) | (~((~quiet(mary)) & (~quiet(paul))))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & predb(X) & predb(Y) & (~(X = Y))) & like(paul, mary) & like(mary, paul) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(X, lucy) & like(Y, lucy) & (~(X = Y))) & (~((~like(paul, lucy)) | (~predb(paul)))) & (~((~like(lucy, mary)) | predc(mary))) & ![X: $i] : quieter(mary, X) & preda(paul) & predb(paul) & ((creative(mary) & person(mary)) | (~like(lucy, mary))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((((?[X: $i] : ((~room(X)) & like(X, alice)) & ![X: $i, Y: $i] : ((like(X, alice) & like(Y, alice)) => (X = Y))) => ((~like(paul, lucy)) & (~like(mary, lucy)))) | ((~(?[X: $i] : ((~room(X)) & like(X, alice)) & ![X: $i, Y: $i] : ((like(X, alice) & like(Y, alice)) => (X = Y)))) => ?[X: $i] : ((~room(X)) => (((quiet(X) & brave(X)) & person(X)) => (~like(lucy, X)))))) & (((~quiet(mary)) & (~quiet(paul))) => ((creative(mary) & person(mary)) | (~like(lucy, mary))))) & (((like(paul, mary) & like(mary, paul)) => ?[X: $i, Y: $i] : (((~((quiet(X) & creative(X)) & person(X))) & (quiet(Y) & person(Y))) & quieter(X, Y))) | ((~(like(paul, mary) & like(mary, paul))) => ((~predc(paul)) & (~like(paul, lucy)))))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (predb(X) & predb(Y))) & (~(X = Y)))) & (like(paul, mary) & like(mary, paul))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (like(X, lucy) & like(Y, lucy))) & (~(X = Y)))) & (~((~like(paul, lucy)) | (~predb(paul))))) & (~((~like(lucy, mary)) | predc(mary)))) & ![X: $i] : quieter(mary, X)) & (preda(paul) & predb(paul))) & ((creative(mary) & person(mary)) | (~like(lucy, mary))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(lucy, mary) | (~(((quiet(mary) & brave(mary)) & creative(mary)) & person(mary))))))), file('/mnt/tmpfs//901537138767112121113886.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((creative(mary) & person(mary)) | (~like(lucy, mary)) | (~((~quiet(mary)) & (~quiet(paul))))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & predb(X) & predb(Y) & (~(X = Y))) & like(paul, mary) & like(mary, paul) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(X, lucy) & like(Y, lucy) & (~(X = Y))) & (~((~like(paul, lucy)) | (~predb(paul)))) & (~((~like(lucy, mary)) | predc(mary))) & ![X: $i] : quieter(mary, X) & preda(paul) & predb(paul) & ((creative(mary) & person(mary)) | (~like(lucy, mary))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary))))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((creative(mary) & person(mary)) | (~like(lucy, mary)) | (~((~quiet(mary)) & (~quiet(paul))))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & predb(X) & predb(Y) & (~(X = Y))) & like(paul, mary) & like(mary, paul) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & like(X, lucy) & like(Y, lucy) & (~(X = Y))) & (~((~like(paul, lucy)) | (~predb(paul)))) & (~((~like(lucy, mary)) | predc(mary))) & ![X: $i] : quieter(mary, X) & preda(paul) & predb(paul) & ((creative(mary) & person(mary)) | (~like(lucy, mary)))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~((~like(lucy, mary)) | predc(mary))),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(like(lucy, mary)),
inference(or_elim,[status(thm)],[6])).
tff(8,plain,
(like(lucy, mary)),
inference(modus_ponens,[status(thm)],[7, 1])).
tff(9,plain,
(((~quiet(mary)) | like(lucy, mary) | (~creative(mary)) | (~person(mary)) | (~brave(mary))) | (~like(lucy, mary))),
inference(tautology,[status(thm)],[])).
tff(10,plain,
((~quiet(mary)) | like(lucy, mary) | (~creative(mary)) | (~person(mary)) | (~brave(mary))),
inference(unit_resolution,[status(thm)],[9, 8])).
tff(11,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(13,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(16,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[15, 14])).
tff(17,plain,
(((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~quiet(mary)) | like(lucy, mary) | (~creative(mary)) | (~person(mary)) | (~brave(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
((~(like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary))))) <=> (~(like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
(((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary))))))),
inference(monotonicity,[status(thm)],[19, 18])).
tff(21,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary))))))),
inference(monotonicity,[status(thm)],[21])).
tff(23,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))),
inference(or_elim,[status(thm)],[4])).
tff(25,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))),
inference(modus_ponens,[status(thm)],[24, 22])).
tff(26,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))),
inference(modus_ponens,[status(thm)],[25, 23])).
tff(27,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(lucy, mary) | (~(quiet(mary) & brave(mary) & creative(mary) & person(mary)))))),
inference(modus_ponens,[status(thm)],[26, 22])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!4 |'paul'|) (= X!4 |'mary'|) (not (room X!4)))))
(a!5 (or (like lucy mary)
(not (and (quiet mary)
(brave mary)
(creative mary)
(person mary))))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 a!5))
(or (not (room mary)) (not (room paul)) a!4 (not a!5)))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (not a!5) (not a!5))) a!6)))
| room(diana)&room(carol)&(![X]:(room(X)=>(X='diana'|X='carol')))&
((((((?[X]:(~room(X)&like(X,jacqueline)))&(![X,Y]:((like(X,jacqueline)&like(Y,jacqueline))=>(X=Y)))))=>(~like(carol,rubye)&~like(diana,rubye)))|((~(((?[X]:(~room(X)&like(X,jacqueline)))&(![X,Y]:((like(X,jacqueline)&like(Y,jacqueline))=>(X=Y))))))=>(?[X]:(~room(X)=>(((quiet(X)&brave(X)&person(X))=>(~like(rubye,X))))))))&
((~quiet(diana)&~quiet(carol))=>(((creative(diana)&person(diana))|(~like(rubye,diana)))))&
((((like(carol,diana) & like(diana,carol)))=>(?[X,Y]:((~(quiet(X)&creative(X)&person(X)))&(quiet(Y)&person(Y))&(quieter(X,Y)))))|((~((like(carol,diana) & like(diana,carol))))=>((does_not_enjoy_windsurfing(carol))&(~like(carol,rubye)))))&
((?[X,Y]:(~room(X)&~room(Y)&(plays_a_musical_instrument(X)&plays_a_musical_instrument(Y))&(X!=Y))))&
((like(carol,diana) & like(diana,carol)))&
((?[X,Y]:(~room(X)&~room(Y)&(like(X,rubye)&like(Y,rubye))&(X!=Y))))&
(~((~like(carol,rubye))|(does_not_play_a_musical_instrument(carol))))&
(~((~like(rubye,diana))|(enjoys_windsurfing(diana))))&
(![X]:(quieter(diana,X)))&
((collects_antique_jewelry(carol))&(plays_a_musical_instrument(carol)))&
(((creative(diana)&person(diana))|(~like(rubye,diana))))) | room(diana)&room(carol)&(![X]:(room(X)=>(X='diana'|X='carol')))&
(((like(rubye,diana))|(~(quiet(diana)&brave(diana)&creative(diana)&person(diana))))) | entailment | entailment | entailment |
Mina, Matthew are the only persons in the room. If “Mina collects foreign coins” then “Matthew either is richer than Johnnie or is not liked by Raquel”. Only one person outside the room is not a quiet brave rich tourist. Everyone in the room does not collect foreign coins. Mina is the least quiet in the room. | Someone who is liked by Johnnie is richer than someone who is not quiet. | contradiction | - | room(mina)&room(matthew)&(![X]:(room(X)=>(X='mina'|X='matthew')))&
(((collects_foreign_coins(mina))=>((((richer(johnnie,matthew))|(~like(matthew,raquel)))&(~((richer(johnnie,matthew))|(~like(matthew,raquel)))))))&
(((?[X]:(~room(X)&~(quiet(X)&brave(X)&rich(X)&tourist(X))))&(![X,Y]:((~(quiet(X)&brave(X)&rich(X)&tourist(X))&~(quiet(Y)&brave(Y)&rich(Y)&tourist(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(does_not_collect_foreign_coins(X))))&
(![X]:(quieter(mina,X)))) | room(mina)&room(matthew)&(![X]:(room(X)=>(X='mina'|X='matthew')))&
(?[X,Y]:((like(X,johnnie))&(~quiet(Y))&(richer(X,Y)))) | contradiction | neutral | neutral |
Ronald, Carl, Thomas are the only persons in the room.
Thomas is not creative and is hated by Phillip unless Thomas is the quietest in the room.
Thomas does not collect vintage vinyl records.
Thomas is the quietest in the room.
Someone who does not hate Mary hate someone who is a tall happy european. | It is not the case that 'Thomas either is not a quiet creative person or hates Phillip'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(john_type, type, (
john: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(1,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((~![X: $i] : quieter(X, fred)) => ((~creative(fred)) & hate(fred, lucy))) & (~predc(fred))) & ![X: $i] : quieter(X, fred)) & ?[X: $i, Y: $i] : (((~hate(john, X)) & ((tall(Y) & happy(Y)) & european(Y))) & hate(X, Y)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(((~((quiet(fred) & creative(fred)) & person(fred))) | hate(lucy, fred)) & (~((~((quiet(fred) & creative(fred)) & person(fred))) | hate(lucy, fred)))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : quieter(X, fred) | ((~creative(fred)) & hate(fred, lucy))) & (~predc(fred)) & ![X: $i] : quieter(X, fred) & ?[X: $i, Y: $i] : ((~hate(john, X)) & tall(Y) & happy(Y) & european(Y) & hate(X, Y)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((~![X: $i] : quieter(X, fred)) => ((~creative(fred)) & hate(fred, lucy))) & (~predc(fred))) & ![X: $i] : quieter(X, fred)) & ?[X: $i, Y: $i] : (((~hate(john, X)) & ((tall(Y) & happy(Y)) & european(Y))) & hate(X, Y)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(((~((quiet(fred) & creative(fred)) & person(fred))) | hate(lucy, fred)) & (~((~((quiet(fred) & creative(fred)) & person(fred))) | hate(lucy, fred)))))))), file('/mnt/tmpfs//4919968428517810720795099.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : quieter(X, fred) | ((~creative(fred)) & hate(fred, lucy))) & (~predc(fred)) & ![X: $i] : quieter(X, fred) & ?[X: $i, Y: $i] : ((~hate(john, X)) & tall(Y) & happy(Y) & european(Y) & hate(X, Y)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : quieter(X, fred) | ((~creative(fred)) & hate(fred, lucy))) & (~predc(fred)) & ![X: $i] : quieter(X, fred) & ?[X: $i, Y: $i] : ((~hate(john, X)) & tall(Y) & happy(Y) & european(Y) & hate(X, Y))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(10,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(13,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))),
inference(monotonicity,[status(thm)],[15])).
tff(17,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))),
inference(transitivity,[status(thm)],[16, 14])).
tff(18,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(monotonicity,[status(thm)],[18])).
tff(20,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(or_elim,[status(thm)],[4])).
tff(22,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[21, 19])).
tff(23,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[22, 20])).
tff(24,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[23, 19])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!2 |'fred'|)
(= X!2 |'paul'|)
(= X!2 |'mary'|)
(not (room X!2))))))
(let ((a!6 (~ (not (and (room mary) (room paul) (room fred) a!4))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5))))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) a!6)))
| room(ronald)&room(carl)&room(thomas)&(![X]:(room(X)=>(X='ronald'|X='carl'|X='thomas')))&
((~(![X]:(quieter(X,thomas)))=>((~creative(thomas))&(hate(thomas,phillip))))&
(does_not_collect_vintage_vinyl_records(thomas))&
(![X]:(quieter(X,thomas)))&
(?[X,Y]:((~hate(mary,X))&(tall(Y)&happy(Y)&european(Y))&(hate(X,Y))))) | room(ronald)&room(carl)&room(thomas)&(![X]:(room(X)=>(X='ronald'|X='carl'|X='thomas')))&
(~((((~(quiet(thomas)&creative(thomas)&person(thomas)))|(hate(phillip,thomas)))&(~((~(quiet(thomas)&creative(thomas)&person(thomas)))|(hate(phillip,thomas))))))) | entailment | entailment | entailment |
Kenneth, Arthur are the only persons in the room.
Kenneth is the least rich in the room if Kenneth is a brave tourist and vice versa.
Kenneth is the least rich in the room if no one outside the room who is not liked by John is not Kenneth and vice versa.
It is not the case that 'no one outside the room is a client of Charlotte'.
Everyone outside the room is a sibling of Armand.
It is not the case that 'Kenneth either is hated by Charlotte or hates Charlotte'.
Kenneth is not happy.
Kenneth is a sibling of John.
Someone outside the room is a brave happy person.
Kenneth is the richest in the room. | Arthur neither is a sibling of Armand nor is not a creative quiet person. | neutral | % SZS status Satisfiable
| room(kenneth)&room(arthur)&(![X]:(room(X)=>(X='kenneth'|X='arthur')))&
(((brave(kenneth)&tourist(kenneth))<=>(![X]:(richer(kenneth,X))))&
((~?[X]:(~room(X)=>(((~like(X,john))=>(X!=kenneth)))))<=>(![X]:(richer(kenneth,X))))&
(~(~?[X]:(~room(X)=>(client(charlotte,X)))))&
(![X]:(~room(X)=>(sibling(armand,X))))&
(~((((hate(kenneth,charlotte))|(hate(charlotte,kenneth)))&(~((hate(kenneth,charlotte))|(hate(charlotte,kenneth)))))))&
(~happy(kenneth))&
(sibling(john,kenneth))&
(?[X]:(~room(X)=>(brave(X)&happy(X)&person(X))))&
(![X]:(richer(X,kenneth)))) | room(kenneth)&room(arthur)&(![X]:(room(X)=>(X='kenneth'|X='arthur')))&
(~((sibling(armand,arthur))|(~(creative(arthur)&quiet(arthur)&person(arthur))))) | contradiction | contradiction | contradiction |
Thomas is the only person in the room. 'Robert is a sibling of Thomas' if 'someone outside the room who is not liked by Joseph is a happy tourist'. 'No one outside the room who is not Thomas is not quiet, not brave' unless 'Thomas who is a brave quiet tall tourist, is not a creative tourist'. 'Thomas is the least tall in the room' unless 'Thomas neither does not like Judy nor watches fantasy movies'. Only one person outside the room likes Charles. Thomas who is a brave quiet tall tourist, is not a creative tourist. Someone who likes Charles like someone who is a client of Joseph. Only one person outside the room does not have a tattoo. Thomas neither does not have a tattoo nor is liked by Robert. | Thomas is liked by Joseph or is a brave quiet person or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(predc_type, type, (
predc: $i > $o)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(john_type, type, (
john: $i)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(1,plain,
(tourist(mary) <=> tourist(mary)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((((?[X: $i] : ((~room(X)) => ((~like(X, alice)) => (happy(X) & tourist(X)))) => sibling(mary, paul)) & ((~((((brave(mary) & quiet(mary)) & tall(mary)) & tourist(mary)) & (~(creative(mary) & tourist(mary))))) => (~?[X: $i] : ((~room(X)) => ((~(X = mary)) => ((~quiet(X)) & (~brave(X)))))))) & ((~(~((~like(john, mary)) | predb(mary)))) => ![X: $i] : taller(mary, X))) & (?[X: $i] : ((~room(X)) & like(fred, X)) & ![X: $i, Y: $i] : ((like(fred, X) & like(fred, Y)) => (X = Y)))) & ((((brave(mary) & quiet(mary)) & tall(mary)) & tourist(mary)) & (~(creative(mary) & tourist(mary))))) & ?[X: $i, Y: $i] : ((like(fred, X) & client(alice, Y)) & like(X, Y))) & (?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : (((~predc(X)) & (~predc(Y))) => (X = Y)))) & (~((~predc(mary)) | like(mary, paul))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (like(mary, alice) | ((brave(mary) & quiet(mary)) & person(mary)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~?[X: $i] : (room(X) | (happy(X) & tourist(X)) | like(X, alice))) | sibling(mary, paul)) & ((brave(mary) & quiet(mary) & tall(mary) & tourist(mary) & (~(creative(mary) & tourist(mary)))) | (~?[X: $i] : (room(X) | ((~quiet(X)) & (~brave(X))) | (X = mary)))) & ((~((~like(john, mary)) | predb(mary))) | ![X: $i] : taller(mary, X)) & ?[X: $i] : ((~room(X)) & like(fred, X)) & ![X: $i, Y: $i] : ((~(like(fred, X) & like(fred, Y))) | (X = Y)) & brave(mary) & quiet(mary) & tall(mary) & tourist(mary) & (~(creative(mary) & tourist(mary))) & ?[X: $i, Y: $i] : (like(fred, X) & client(alice, Y) & like(X, Y)) & ?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & (~((~predc(mary)) | like(mary, paul))))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((((?[X: $i] : ((~room(X)) => ((~like(X, alice)) => (happy(X) & tourist(X)))) => sibling(mary, paul)) & ((~((((brave(mary) & quiet(mary)) & tall(mary)) & tourist(mary)) & (~(creative(mary) & tourist(mary))))) => (~?[X: $i] : ((~room(X)) => ((~(X = mary)) => ((~quiet(X)) & (~brave(X)))))))) & ((~(~((~like(john, mary)) | predb(mary)))) => ![X: $i] : taller(mary, X))) & (?[X: $i] : ((~room(X)) & like(fred, X)) & ![X: $i, Y: $i] : ((like(fred, X) & like(fred, Y)) => (X = Y)))) & ((((brave(mary) & quiet(mary)) & tall(mary)) & tourist(mary)) & (~(creative(mary) & tourist(mary))))) & ?[X: $i, Y: $i] : ((like(fred, X) & client(alice, Y)) & like(X, Y))) & (?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : (((~predc(X)) & (~predc(Y))) => (X = Y)))) & (~((~predc(mary)) | like(mary, paul))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (like(mary, alice) | ((brave(mary) & quiet(mary)) & person(mary)))))), file('/mnt/tmpfs//7108341839985969790592386.p','negated')).
tff(4,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~?[X: $i] : (room(X) | (happy(X) & tourist(X)) | like(X, alice))) | sibling(mary, paul)) & ((brave(mary) & quiet(mary) & tall(mary) & tourist(mary) & (~(creative(mary) & tourist(mary)))) | (~?[X: $i] : (room(X) | ((~quiet(X)) & (~brave(X))) | (X = mary)))) & ((~((~like(john, mary)) | predb(mary))) | ![X: $i] : taller(mary, X)) & ?[X: $i] : ((~room(X)) & like(fred, X)) & ![X: $i, Y: $i] : ((~(like(fred, X) & like(fred, Y))) | (X = Y)) & brave(mary) & quiet(mary) & tall(mary) & tourist(mary) & (~(creative(mary) & tourist(mary))) & ?[X: $i, Y: $i] : (like(fred, X) & client(alice, Y) & like(X, Y)) & ?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & (~((~predc(mary)) | like(mary, paul))))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~?[X: $i] : (room(X) | (happy(X) & tourist(X)) | like(X, alice))) | sibling(mary, paul)) & ((brave(mary) & quiet(mary) & tall(mary) & tourist(mary) & (~(creative(mary) & tourist(mary)))) | (~?[X: $i] : (room(X) | ((~quiet(X)) & (~brave(X))) | (X = mary)))) & ((~((~like(john, mary)) | predb(mary))) | ![X: $i] : taller(mary, X)) & ?[X: $i] : ((~room(X)) & like(fred, X)) & ![X: $i, Y: $i] : ((~(like(fred, X) & like(fred, Y))) | (X = Y)) & brave(mary) & quiet(mary) & tall(mary) & tourist(mary) & (~(creative(mary) & tourist(mary))) & ?[X: $i, Y: $i] : (like(fred, X) & client(alice, Y) & like(X, Y)) & ?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & (~((~predc(mary)) | like(mary, paul)))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(tourist(mary)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(tourist(mary)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(^[X: $i] : refl((person(X) | (~tourist(X))) <=> (person(X) | (~tourist(X))))),
inference(bind,[status(th)],[])).
tff(9,plain,
(![X: $i] : (person(X) | (~tourist(X))) <=> ![X: $i] : (person(X) | (~tourist(X)))),
inference(quant_intro,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : (person(X) | (~tourist(X))) <=> ![X: $i] : (person(X) | (~tourist(X)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(^[X: $i] : rewrite((tourist(X) => person(X)) <=> (person(X) | (~tourist(X))))),
inference(bind,[status(th)],[])).
tff(12,plain,
(![X: $i] : (tourist(X) => person(X)) <=> ![X: $i] : (person(X) | (~tourist(X)))),
inference(quant_intro,[status(thm)],[11])).
tff(13,axiom,(![X: $i] : (tourist(X) => person(X))), file('/mnt/tmpfs//7108341839985969790592386.p','b3')).
tff(14,plain,
(![X: $i] : (person(X) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(![X: $i] : (person(X) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[14, 10])).
tff(16,plain,(
![X: $i] : (person(X) | (~tourist(X)))),
inference(skolemize,[status(sab)],[15])).
tff(17,plain,
(![X: $i] : (person(X) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[16, 9])).
tff(18,plain,
(((~![X: $i] : (person(X) | (~tourist(X)))) | (person(mary) | (~tourist(mary)))) <=> ((~![X: $i] : (person(X) | (~tourist(X)))) | person(mary) | (~tourist(mary)))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~![X: $i] : (person(X) | (~tourist(X)))) | (person(mary) | (~tourist(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(20,plain,
((~![X: $i] : (person(X) | (~tourist(X)))) | person(mary) | (~tourist(mary))),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(person(mary)),
inference(unit_resolution,[status(thm)],[20, 17, 7])).
tff(22,plain,
(quiet(mary) <=> quiet(mary)),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
(quiet(mary)),
inference(and_elim,[status(thm)],[5])).
tff(24,plain,
(quiet(mary)),
inference(modus_ponens,[status(thm)],[23, 22])).
tff(25,plain,
(brave(mary) <=> brave(mary)),
inference(rewrite,[status(thm)],[])).
tff(26,plain,
(brave(mary)),
inference(and_elim,[status(thm)],[5])).
tff(27,plain,
(brave(mary)),
inference(modus_ponens,[status(thm)],[26, 25])).
tff(28,plain,
((~((~brave(mary)) | (~quiet(mary)) | (~person(mary)))) | (~brave(mary)) | (~quiet(mary)) | (~person(mary))),
inference(tautology,[status(thm)],[])).
tff(29,plain,
((~((~brave(mary)) | (~quiet(mary)) | (~person(mary)))) | (~person(mary))),
inference(unit_resolution,[status(thm)],[28, 27, 24])).
tff(30,plain,
(~((~brave(mary)) | (~quiet(mary)) | (~person(mary)))),
inference(unit_resolution,[status(thm)],[29, 21])).
tff(31,plain,
((like(mary, alice) | (~((~brave(mary)) | (~quiet(mary)) | (~person(mary))))) | ((~brave(mary)) | (~quiet(mary)) | (~person(mary)))),
inference(tautology,[status(thm)],[])).
tff(32,plain,
(like(mary, alice) | (~((~brave(mary)) | (~quiet(mary)) | (~person(mary))))),
inference(unit_resolution,[status(thm)],[31, 30])).
tff(33,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(35,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
(((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | (~(like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))) <=> ((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | (~(like(mary, alice) | (~((~brave(mary)) | (~quiet(mary)) | (~person(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary)))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary)))))),
inference(monotonicity,[status(thm)],[37])).
tff(39,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))),
inference(or_elim,[status(thm)],[4])).
tff(41,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))),
inference(modus_ponens,[status(thm)],[40, 38])).
tff(42,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))),
inference(modus_ponens,[status(thm)],[41, 39])).
tff(43,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (like(mary, alice) | (brave(mary) & quiet(mary) & person(mary))))),
inference(modus_ponens,[status(thm)],[42, 38])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!4)) (= X!4 |'mary'|))))
(a!4 (or (like mary alice) (and (brave mary) (quiet mary) (person mary)))))
(let ((a!5 (~ (not (and (room mary) a!2 a!4))
(or (not (room mary)) a!3 (not a!4)))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (not a!4) (not a!4))) a!5)))
| room(thomas)&(![X]:(room(X)=>(X='thomas')))&
(((?[X]:(~room(X)=>(((~like(X,joseph))=>(happy(X)&tourist(X))))))=>(sibling(thomas,robert)))&
(~((brave(thomas)&quiet(thomas)&tall(thomas)&tourist(thomas))&(~(creative(thomas)&tourist(thomas))))=>(~?[X]:(~room(X)=>(((X!=thomas)=>(~quiet(X)&~brave(X)))))))&
(~(~((~like(judy,thomas))|(watches_fantasy_movies(thomas))))=>(![X]:(taller(thomas,X))))&
(((?[X]:(~room(X)&like(charles,X)))&(![X,Y]:((like(charles,X)&like(charles,Y))=>(X=Y)))))&
((brave(thomas)&quiet(thomas)&tall(thomas)&tourist(thomas))&(~(creative(thomas)&tourist(thomas))))&
(?[X,Y]:((like(charles,X))&(client(joseph,Y))&(like(X,Y))))&
(((?[X]:(~room(X)&does_not_have_a_tattoo(X)))&(![X,Y]:((does_not_have_a_tattoo(X)&does_not_have_a_tattoo(Y))=>(X=Y)))))&
(~((does_not_have_a_tattoo(thomas))|(like(thomas,robert))))) | room(thomas)&(![X]:(room(X)=>(X='thomas')))&
(((like(thomas,joseph))|(brave(thomas)&quiet(thomas)&person(thomas)))) | entailment | entailment | neutral |
Michael, Edith are the only persons in the room.
“Michael has a piercing” only if “Michael who is not hated by Patricia, hates Sadie”.
“Michael who is a brave person, is hated by Patricia” if “it is not the case that 'someone outside the room who collect rare sneakers is quieter than Patricia'”.
If “Michael is hated by Sadie or is not hated by Sadie or both” then “Michael is the least quiet in the room” otherwise “Michael and Edith are respectively quiet and brave”.
“Michael either is not a happy person or is not Edith” if “Edith either is not hated by Sadie or is not Michael” and vice versa.
“Sadie is taller than Edith” unless “Sadie is quieter than Michael”.
Michael is the least quiet in the room.
Only one person in the room collect rare sneakers.
Michael is the least quiet in the room.
Michael is not Edith and enjoys logic puzzles.
Sadie is a sibling of Michael.
Michael hates Patricia.
Michael is hated by Patricia or is not a happy quiet person or both. | Michael has a piercing or is not a brave rich happy quiet european or both. | neutral | % SZS status Satisfiable
| room(michael)&room(edith)&(![X]:(room(X)=>(X='michael'|X='edith')))&
(((has_a_piercing(michael))=>((~hate(michael,patricia))&(hate(sadie,michael))))&
((~(?[X]:(~room(X)=>(((collect_rare_sneakers(X))=>(quieter(patricia,X)))))))=>((brave(michael)&person(michael))&(hate(michael,patricia))))&
(((((hate(michael,sadie))|(~hate(michael,sadie))))=>(![X]:(quieter(michael,X))))|((~(((hate(michael,sadie))|(~hate(michael,sadie)))))=>((quiet(michael))&(brave(edith)))))&
(((((~hate(edith,sadie))|(edith!=michael))&(~((~hate(edith,sadie))|(edith!=michael)))))<=>((((~(happy(michael)&person(michael)))|(michael!=edith))&(~((~(happy(michael)&person(michael)))|(michael!=edith))))))&
(~(quieter(michael,sadie))=>(taller(edith,sadie)))&
(![X]:(quieter(michael,X)))&
(((?[X]:(room(X)&collect_rare_sneakers(X)))&(![X,Y]:((collect_rare_sneakers(X)&collect_rare_sneakers(Y))=>(X=Y)))))&
(![X]:(quieter(michael,X)))&
((michael!=edith)&(enjoys_logic_puzzles(michael)))&
(sibling(michael,sadie))&
(hate(patricia,michael))&
(((hate(michael,patricia))|(~(happy(michael)&quiet(michael)&person(michael)))))) | room(michael)&room(edith)&(![X]:(room(X)=>(X='michael'|X='edith')))&
(((has_a_piercing(michael))|(~(brave(michael)&rich(michael)&happy(michael)&quiet(michael)&european(michael))))) | neutral | entailment | entailment |
Joel is the only person in the room.
Joel who is taller than Bertha, does not hate Frank unless Joel who is not hated by Steven, likes Steven.
Joel is the least tall in the room.
Someone outside the room who hates Bertha does not have completed a triathlon.
Joel neither likes Bertha nor is not happy, not tall. | Joel is not hated by Steven or is not liked by Bertha or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(alice_type, type, (
alice: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(john_type, type, (
john: $i)).
tff(susan_type, type, (
susan: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(1,plain,
(^[X: $i] : refl(((~room(X)) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(2,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[1])).
tff(3,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(4,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((~((~hate(mary, fred)) & like(fred, mary))) => (taller(paul, mary) & (~hate(alice, mary)))) & ![X: $i] : taller(mary, X)) & ?[X: $i] : ((~room(X)) => (hate(paul, X) => (~preda(X))))) & (~(like(paul, mary) | ((~happy(mary)) & (~tall(mary))))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(mary, fred)) | (~like(mary, paul)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))) & ![X: $i] : taller(mary, X) & ?[X: $i] : (room(X) | (~preda(X)) | (~hate(paul, X))) & (~(like(paul, mary) | ((~happy(mary)) & (~tall(mary))))))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))))),
inference(rewrite,[status(thm)],[])).
tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((~((~hate(mary, fred)) & like(fred, mary))) => (taller(paul, mary) & (~hate(alice, mary)))) & ![X: $i] : taller(mary, X)) & ?[X: $i] : ((~room(X)) => (hate(paul, X) => (~preda(X))))) & (~(like(paul, mary) | ((~happy(mary)) & (~tall(mary))))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(mary, fred)) | (~like(mary, paul)))))), file('/mnt/tmpfs//6252740944665899065618349.p','negated')).
tff(6,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))) & ![X: $i] : taller(mary, X) & ?[X: $i] : (room(X) | (~preda(X)) | (~hate(paul, X))) & (~(like(paul, mary) | ((~happy(mary)) & (~tall(mary))))))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul)))))),
inference(modus_ponens,[status(thm)],[5, 4])).
tff(7,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))) & ![X: $i] : taller(mary, X) & ?[X: $i] : (room(X) | (~preda(X)) | (~hate(paul, X))) & (~(like(paul, mary) | ((~happy(mary)) & (~tall(mary)))))),
inference(or_elim,[status(thm)],[6])).
tff(8,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[8, 3])).
tff(10,plain,(
![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(skolemize,[status(sab)],[9])).
tff(11,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[10, 2])).
tff(12,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(room(mary)),
inference(and_elim,[status(thm)],[7])).
tff(14,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(17,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[17, 14, 11])).
tff(19,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[18])).
tff(20,plain,
(taller(paul, |'mary'|) <=> taller(paul, mary)),
inference(monotonicity,[status(thm)],[19])).
tff(21,plain,
((~taller(paul, |'mary'|)) <=> (~taller(paul, mary))),
inference(monotonicity,[status(thm)],[20])).
tff(22,plain,
((paul = mary) <=> (mary = paul)),
inference(commutativity,[status(thm)],[])).
tff(23,plain,
((paul = |'mary'|) <=> (paul = mary)),
inference(monotonicity,[status(thm)],[19])).
tff(24,plain,
((paul = |'mary'|) <=> (mary = paul)),
inference(transitivity,[status(thm)],[23, 22])).
tff(25,plain,
((mary = paul) <=> (paul = |'mary'|)),
inference(symmetry,[status(thm)],[24])).
tff(26,plain,
((~(mary = paul)) <=> (~(paul = |'mary'|))),
inference(monotonicity,[status(thm)],[25])).
tff(27,plain,
((~(mary = paul)) <=> (~(mary = paul))),
inference(rewrite,[status(thm)],[])).
tff(28,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//6252740944665899065618349.p','b14')).
tff(29,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[42])).
tff(44,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[43])).
tff(45,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[44])).
tff(46,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[45])).
tff(47,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[46])).
tff(48,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[47])).
tff(49,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[48])).
tff(50,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[49])).
tff(51,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[50])).
tff(52,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[51])).
tff(53,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[53])).
tff(55,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[55])).
tff(57,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[56])).
tff(58,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[57])).
tff(59,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[58])).
tff(60,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[60])).
tff(62,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[61])).
tff(63,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[62])).
tff(64,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[63])).
tff(65,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[64])).
tff(66,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[65])).
tff(67,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[66])).
tff(68,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[67])).
tff(69,plain,
(~(mary = paul)),
inference(and_elim,[status(thm)],[68])).
tff(70,plain,
(~(mary = paul)),
inference(modus_ponens,[status(thm)],[69, 27])).
tff(71,plain,
(~(paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[70, 26])).
tff(72,plain,
(taller(mary, paul) <=> taller(|'mary'|, paul)),
inference(monotonicity,[status(thm)],[18])).
tff(73,plain,
(taller(|'mary'|, paul) <=> taller(mary, paul)),
inference(symmetry,[status(thm)],[72])).
tff(74,plain,
((~taller(|'mary'|, paul)) <=> (~taller(mary, paul))),
inference(monotonicity,[status(thm)],[73])).
tff(75,assumption,(~taller(|'mary'|, paul)), introduced(assumption)).
tff(76,plain,
(~taller(mary, paul)),
inference(modus_ponens,[status(thm)],[75, 74])).
tff(77,plain,
(^[X: $i] : refl(taller(mary, X) <=> taller(mary, X))),
inference(bind,[status(th)],[])).
tff(78,plain,
(![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)),
inference(quant_intro,[status(thm)],[77])).
tff(79,plain,
(![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)),
inference(rewrite,[status(thm)],[])).
tff(80,plain,
(![X: $i] : taller(mary, X)),
inference(and_elim,[status(thm)],[7])).
tff(81,plain,
(![X: $i] : taller(mary, X)),
inference(modus_ponens,[status(thm)],[80, 79])).
tff(82,plain,(
![X: $i] : taller(mary, X)),
inference(skolemize,[status(sab)],[81])).
tff(83,plain,
(![X: $i] : taller(mary, X)),
inference(modus_ponens,[status(thm)],[82, 78])).
tff(84,plain,
((~![X: $i] : taller(mary, X)) | taller(mary, paul)),
inference(quant_inst,[status(thm)],[])).
tff(85,plain,
(taller(mary, paul)),
inference(unit_resolution,[status(thm)],[84, 83])).
tff(86,plain,
($false),
inference(unit_resolution,[status(thm)],[85, 76])).
tff(87,plain,(taller(|'mary'|, paul)), inference(lemma,lemma(discharge,[]))).
tff(88,plain,
(![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(89,plain,
(![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(90,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite((taller(X, Y) => (~taller(Y, X))) <=> ((~taller(Y, X)) | (~taller(X, Y)))), (((~(X = Y)) => (taller(X, Y) => (~taller(Y, X)))) <=> ((~(X = Y)) => ((~taller(Y, X)) | (~taller(X, Y)))))), rewrite(((~(X = Y)) => ((~taller(Y, X)) | (~taller(X, Y)))) <=> ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))), (((~(X = Y)) => (taller(X, Y) => (~taller(Y, X)))) <=> ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))))),
inference(bind,[status(th)],[])).
tff(91,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => (taller(X, Y) => (~taller(Y, X)))) <=> ![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))),
inference(quant_intro,[status(thm)],[90])).
tff(92,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (taller(X, Y) => (~taller(Y, X))))), file('/mnt/tmpfs//6252740944665899065618349.p','b10')).
tff(93,plain,
(![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))),
inference(modus_ponens,[status(thm)],[92, 91])).
tff(94,plain,
(![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))),
inference(modus_ponens,[status(thm)],[93, 89])).
tff(95,plain,(
![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))),
inference(skolemize,[status(sab)],[94])).
tff(96,plain,
(![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))),
inference(modus_ponens,[status(thm)],[95, 88])).
tff(97,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | ((~taller(|'mary'|, paul)) | (paul = |'mary'|) | (~taller(paul, |'mary'|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | (~taller(|'mary'|, paul)) | (paul = |'mary'|) | (~taller(paul, |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(98,plain,
(((paul = |'mary'|) | (~taller(|'mary'|, paul)) | (~taller(paul, |'mary'|))) <=> ((~taller(|'mary'|, paul)) | (paul = |'mary'|) | (~taller(paul, |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(99,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | ((paul = |'mary'|) | (~taller(|'mary'|, paul)) | (~taller(paul, |'mary'|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | ((~taller(|'mary'|, paul)) | (paul = |'mary'|) | (~taller(paul, |'mary'|))))),
inference(monotonicity,[status(thm)],[98])).
tff(100,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | ((paul = |'mary'|) | (~taller(|'mary'|, paul)) | (~taller(paul, |'mary'|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | (~taller(|'mary'|, paul)) | (paul = |'mary'|) | (~taller(paul, |'mary'|)))),
inference(transitivity,[status(thm)],[99, 97])).
tff(101,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | ((paul = |'mary'|) | (~taller(|'mary'|, paul)) | (~taller(paul, |'mary'|)))),
inference(quant_inst,[status(thm)],[])).
tff(102,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~taller(Y, X)) | (~taller(X, Y)))) | (~taller(|'mary'|, paul)) | (paul = |'mary'|) | (~taller(paul, |'mary'|))),
inference(modus_ponens,[status(thm)],[101, 100])).
tff(103,plain,
((~taller(|'mary'|, paul)) | (paul = |'mary'|) | (~taller(paul, |'mary'|))),
inference(unit_resolution,[status(thm)],[102, 96])).
tff(104,plain,
(~taller(paul, |'mary'|)),
inference(unit_resolution,[status(thm)],[103, 87, 71])).
tff(105,plain,
(~taller(paul, mary)),
inference(modus_ponens,[status(thm)],[104, 21])).
tff(106,plain,
(((~taller(paul, mary)) | hate(alice, mary)) | taller(paul, mary)),
inference(tautology,[status(thm)],[])).
tff(107,plain,
((~taller(paul, mary)) | hate(alice, mary)),
inference(unit_resolution,[status(thm)],[106, 105])).
tff(108,plain,
(((~(hate(mary, fred) | (~like(fred, mary)))) | (~((~taller(paul, mary)) | hate(alice, mary)))) <=> ((~(hate(mary, fred) | (~like(fred, mary)))) | (~((~taller(paul, mary)) | hate(alice, mary))))),
inference(rewrite,[status(thm)],[])).
tff(109,plain,
((taller(paul, mary) & (~hate(alice, mary))) <=> (~((~taller(paul, mary)) | hate(alice, mary)))),
inference(rewrite,[status(thm)],[])).
tff(110,plain,
(((~hate(mary, fred)) & like(fred, mary)) <=> (~(hate(mary, fred) | (~like(fred, mary))))),
inference(rewrite,[status(thm)],[])).
tff(111,plain,
((((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))) <=> ((~(hate(mary, fred) | (~like(fred, mary)))) | (~((~taller(paul, mary)) | hate(alice, mary))))),
inference(monotonicity,[status(thm)],[110, 109])).
tff(112,plain,
((((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))) <=> ((~(hate(mary, fred) | (~like(fred, mary)))) | (~((~taller(paul, mary)) | hate(alice, mary))))),
inference(transitivity,[status(thm)],[111, 108])).
tff(113,plain,
((((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))) <=> (((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary))))),
inference(rewrite,[status(thm)],[])).
tff(114,plain,
(((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))),
inference(and_elim,[status(thm)],[7])).
tff(115,plain,
(((~hate(mary, fred)) & like(fred, mary)) | (taller(paul, mary) & (~hate(alice, mary)))),
inference(modus_ponens,[status(thm)],[114, 113])).
tff(116,plain,
((~(hate(mary, fred) | (~like(fred, mary)))) | (~((~taller(paul, mary)) | hate(alice, mary)))),
inference(modus_ponens,[status(thm)],[115, 112])).
tff(117,plain,
(~(hate(mary, fred) | (~like(fred, mary)))),
inference(unit_resolution,[status(thm)],[116, 107])).
tff(118,plain,
((hate(mary, fred) | (~like(fred, mary))) | (~hate(mary, fred))),
inference(tautology,[status(thm)],[])).
tff(119,plain,
(~hate(mary, fred)),
inference(unit_resolution,[status(thm)],[118, 117])).
tff(120,plain,
(((~hate(mary, fred)) | (~like(mary, paul))) | hate(mary, fred)),
inference(tautology,[status(thm)],[])).
tff(121,plain,
((~hate(mary, fred)) | (~like(mary, paul))),
inference(unit_resolution,[status(thm)],[120, 119])).
tff(122,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul)))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))),
inference(rewrite,[status(thm)],[])).
tff(123,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul)))))),
inference(monotonicity,[status(thm)],[122])).
tff(124,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul)))))),
inference(rewrite,[status(thm)],[])).
tff(125,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))),
inference(or_elim,[status(thm)],[6])).
tff(126,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))),
inference(modus_ponens,[status(thm)],[125, 123])).
tff(127,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))),
inference(modus_ponens,[status(thm)],[126, 124])).
tff(128,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, fred)) | (~like(mary, paul))))),
inference(modus_ponens,[status(thm)],[127, 123])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!1)) (= X!1 |'mary'|))))
(a!4 (not (or (not (hate mary fred)) (not (like mary paul))))))
(let ((a!5 (and (room mary)
a!2
(or (not (hate mary fred)) (not (like mary paul))))))
(let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 a!4))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!6))))
| room(joel)&(![X]:(room(X)=>(X='joel')))&
((~((~hate(joel,steven))&(like(steven,joel)))=>((taller(bertha,joel))&(~hate(frank,joel))))&
(![X]:(taller(joel,X)))&
(?[X]:(~room(X)=>(((hate(bertha,X))=>(does_not_have_completed_a_triathlon(X))))))&
(~((like(bertha,joel))|(~happy(joel)&~tall(joel))))) | room(joel)&(![X]:(room(X)=>(X='joel')))&
(((~hate(joel,steven))|(~like(joel,bertha)))) | entailment | entailment | neutral |
Jason, Miguel, Brenda are the only persons in the room.
If 'no one outside the room enjoys landscape photography' then 'everyone outside the room is not a brave european'.
'Jason is the tallest in the room' only if 'someone who is hated by Minda like someone who hates Minda'.
Brenda is a quiet tall happy tourist and does not hate Whitney.
Miguel neither is not liked by Whitney nor is not a happy european.
Only one person outside the room enjoys kayaking.
Brenda hates Minda and is not Miguel.
Miguel neither is a brave european nor does not enjoy landscape photography.
Minda is taller than Miguel.
Brenda hates Minda. | Brenda is a quiet person or is a tall quiet brave tourist or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_5_type, type, (
tptp_fun_X_5: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(brave_type, type, (
brave: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(paul_type, type, (
paul: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(mary_type, type, (
mary: $i)).
tff(1,plain,
(tourist(fred) <=> tourist(fred)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((~?[X: $i] : ((~room(X)) => predb(X))) => ![X: $i] : ((~room(X)) => (~(brave(X) & european(X))))) & (![X: $i] : taller(X, mary) => ?[X: $i, Y: $i] : ((hate(X, lucy) & hate(lucy, Y)) & like(X, Y)))) & ((((quiet(fred) & tall(fred)) & happy(fred)) & tourist(fred)) & (~hate(susan, fred)))) & (~((~like(paul, susan)) | (~(happy(paul) & european(paul)))))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y)))) & (hate(lucy, fred) & (~(fred = paul)))) & (~((brave(paul) & european(paul)) | (~predb(paul))))) & taller(paul, lucy)) & hate(lucy, fred))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((quiet(fred) & person(fred)) | (((tall(fred) & quiet(fred)) & brave(fred)) & tourist(fred)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (predb(X) | room(X)) | ![X: $i] : (room(X) | (~(brave(X) & european(X))))) & ((~![X: $i] : taller(X, mary)) | ?[X: $i, Y: $i] : (hate(X, lucy) & hate(lucy, Y) & like(X, Y))) & quiet(fred) & tall(fred) & happy(fred) & tourist(fred) & (~hate(susan, fred)) & (~((~like(paul, susan)) | (~(happy(paul) & european(paul))))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & hate(lucy, fred) & (~(fred = paul)) & (~((brave(paul) & european(paul)) | (~predb(paul)))) & taller(paul, lucy))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((~?[X: $i] : ((~room(X)) => predb(X))) => ![X: $i] : ((~room(X)) => (~(brave(X) & european(X))))) & (![X: $i] : taller(X, mary) => ?[X: $i, Y: $i] : ((hate(X, lucy) & hate(lucy, Y)) & like(X, Y)))) & ((((quiet(fred) & tall(fred)) & happy(fred)) & tourist(fred)) & (~hate(susan, fred)))) & (~((~like(paul, susan)) | (~(happy(paul) & european(paul)))))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y)))) & (hate(lucy, fred) & (~(fred = paul)))) & (~((brave(paul) & european(paul)) | (~predb(paul))))) & taller(paul, lucy)) & hate(lucy, fred))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((quiet(fred) & person(fred)) | (((tall(fred) & quiet(fred)) & brave(fred)) & tourist(fred)))))), file('/mnt/tmpfs//7414844477210273605288842.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (predb(X) | room(X)) | ![X: $i] : (room(X) | (~(brave(X) & european(X))))) & ((~![X: $i] : taller(X, mary)) | ?[X: $i, Y: $i] : (hate(X, lucy) & hate(lucy, Y) & like(X, Y))) & quiet(fred) & tall(fred) & happy(fred) & tourist(fred) & (~hate(susan, fred)) & (~((~like(paul, susan)) | (~(happy(paul) & european(paul))))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & hate(lucy, fred) & (~(fred = paul)) & (~((brave(paul) & european(paul)) | (~predb(paul)))) & taller(paul, lucy))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & (?[X: $i] : (predb(X) | room(X)) | ![X: $i] : (room(X) | (~(brave(X) & european(X))))) & ((~![X: $i] : taller(X, mary)) | ?[X: $i, Y: $i] : (hate(X, lucy) & hate(lucy, Y) & like(X, Y))) & quiet(fred) & tall(fred) & happy(fred) & tourist(fred) & (~hate(susan, fred)) & (~((~like(paul, susan)) | (~(happy(paul) & european(paul))))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & hate(lucy, fred) & (~(fred = paul)) & (~((brave(paul) & european(paul)) | (~predb(paul)))) & taller(paul, lucy)),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(tourist(fred)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(tourist(fred)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(^[X: $i] : refl((person(X) | (~tourist(X))) <=> (person(X) | (~tourist(X))))),
inference(bind,[status(th)],[])).
tff(9,plain,
(![X: $i] : (person(X) | (~tourist(X))) <=> ![X: $i] : (person(X) | (~tourist(X)))),
inference(quant_intro,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : (person(X) | (~tourist(X))) <=> ![X: $i] : (person(X) | (~tourist(X)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(^[X: $i] : rewrite((tourist(X) => person(X)) <=> (person(X) | (~tourist(X))))),
inference(bind,[status(th)],[])).
tff(12,plain,
(![X: $i] : (tourist(X) => person(X)) <=> ![X: $i] : (person(X) | (~tourist(X)))),
inference(quant_intro,[status(thm)],[11])).
tff(13,axiom,(![X: $i] : (tourist(X) => person(X))), file('/mnt/tmpfs//7414844477210273605288842.p','b3')).
tff(14,plain,
(![X: $i] : (person(X) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(![X: $i] : (person(X) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[14, 10])).
tff(16,plain,(
![X: $i] : (person(X) | (~tourist(X)))),
inference(skolemize,[status(sab)],[15])).
tff(17,plain,
(![X: $i] : (person(X) | (~tourist(X)))),
inference(modus_ponens,[status(thm)],[16, 9])).
tff(18,plain,
(((~![X: $i] : (person(X) | (~tourist(X)))) | (person(fred) | (~tourist(fred)))) <=> ((~![X: $i] : (person(X) | (~tourist(X)))) | person(fred) | (~tourist(fred)))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~![X: $i] : (person(X) | (~tourist(X)))) | (person(fred) | (~tourist(fred)))),
inference(quant_inst,[status(thm)],[])).
tff(20,plain,
((~![X: $i] : (person(X) | (~tourist(X)))) | person(fred) | (~tourist(fred))),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(person(fred)),
inference(unit_resolution,[status(thm)],[20, 17, 7])).
tff(22,plain,
(quiet(fred) <=> quiet(fred)),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
(quiet(fred)),
inference(and_elim,[status(thm)],[5])).
tff(24,plain,
(quiet(fred)),
inference(modus_ponens,[status(thm)],[23, 22])).
tff(25,plain,
((~((~quiet(fred)) | (~person(fred)))) | (~quiet(fred)) | (~person(fred))),
inference(tautology,[status(thm)],[])).
tff(26,plain,
((~((~quiet(fred)) | (~person(fred)))) | (~person(fred))),
inference(unit_resolution,[status(thm)],[25, 24])).
tff(27,plain,
(~((~quiet(fred)) | (~person(fred)))),
inference(unit_resolution,[status(thm)],[26, 21])).
tff(28,plain,
(((~((~quiet(fred)) | (~person(fred)))) | (~((~quiet(fred)) | (~tall(fred)) | (~brave(fred)) | (~tourist(fred))))) | ((~quiet(fred)) | (~person(fred)))),
inference(tautology,[status(thm)],[])).
tff(29,plain,
((~((~quiet(fred)) | (~person(fred)))) | (~((~quiet(fred)) | (~tall(fred)) | (~brave(fred)) | (~tourist(fred))))),
inference(unit_resolution,[status(thm)],[28, 27])).
tff(30,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(32,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(35,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(38,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[37, 36])).
tff(39,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((~((~quiet(fred)) | (~person(fred)))) | (~((~quiet(fred)) | (~tall(fred)) | (~brave(fred)) | (~tourist(fred))))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((~((~quiet(fred)) | (~person(fred)))) | (~((~quiet(fred)) | (~tall(fred)) | (~brave(fred)) | (~tourist(fred)))))))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))) <=> (~((~((~quiet(fred)) | (~person(fred)))) | (~((~quiet(fred)) | (~tall(fred)) | (~brave(fred)) | (~tourist(fred))))))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
((~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) <=> (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((~((~quiet(fred)) | (~person(fred)))) | (~((~quiet(fred)) | (~tall(fred)) | (~brave(fred)) | (~tourist(fred)))))))),
inference(monotonicity,[status(thm)],[41, 40])).
tff(43,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((~((~quiet(fred)) | (~person(fred)))) | (~((~quiet(fred)) | (~tall(fred)) | (~brave(fred)) | (~tourist(fred)))))))),
inference(transitivity,[status(thm)],[42, 39])).
tff(44,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))))),
inference(rewrite,[status(thm)],[])).
tff(45,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))))),
inference(monotonicity,[status(thm)],[41])).
tff(46,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((~room(X!5)) | (X!5 = |'fred'|) | (X!5 = |'paul'|) | (X!5 = |'mary'|))) | (~((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))))),
inference(transitivity,[status(thm)],[45, 44])).
tff(47,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))),
inference(rewrite,[status(thm)],[])).
tff(48,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))))),
inference(monotonicity,[status(thm)],[47])).
tff(49,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred)))))),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))),
inference(or_elim,[status(thm)],[4])).
tff(51,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))),
inference(modus_ponens,[status(thm)],[50, 48])).
tff(52,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))),
inference(modus_ponens,[status(thm)],[51, 49])).
tff(53,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((~room(X)) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|)) & ((quiet(fred) & person(fred)) | (tall(fred) & quiet(fred) & brave(fred) & tourist(fred))))),
inference(modus_ponens,[status(thm)],[52, 48])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (not (room X)) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|))))
(a!5 (not (or (not (room X!5))
(= X!5 |'fred'|)
(= X!5 |'paul'|)
(= X!5 |'mary'|))))
(a!6 (or (and (quiet fred) (person fred))
(and (tall fred) (quiet fred) (brave fred) (tourist fred)))))
(let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 a!6))
(or (not (room mary))
(not (room paul))
(not (room fred))
a!5
(not a!6)))))
(nnf-neg a!1
a!2
a!3
(sk (~ (not a!4) a!5))
(refl (~ (not a!6) (not a!6)))
a!7)))
| room(jason)&room(miguel)&room(brenda)&(![X]:(room(X)=>(X='jason'|X='miguel'|X='brenda')))&
(((~?[X]:(~room(X)=>(enjoys_landscape_photography(X))))=>(![X]:(~room(X)=>(~(brave(X)&european(X))))))&
((![X]:(taller(X,jason)))=>(?[X,Y]:((hate(X,minda))&(hate(minda,Y))&(like(X,Y)))))&
((quiet(brenda)&tall(brenda)&happy(brenda)&tourist(brenda))&(~hate(whitney,brenda)))&
(~((~like(miguel,whitney))|(~(happy(miguel)&european(miguel)))))&
(((?[X]:(~room(X)&enjoys_kayaking(X)))&(![X,Y]:((enjoys_kayaking(X)&enjoys_kayaking(Y))=>(X=Y)))))&
((hate(minda,brenda))&(brenda!=miguel))&
(~((brave(miguel)&european(miguel))|(does_not_enjoy_landscape_photography(miguel))))&
(taller(miguel,minda))&
(hate(minda,brenda))) | room(jason)&room(miguel)&room(brenda)&(![X]:(room(X)=>(X='jason'|X='miguel'|X='brenda')))&
(((quiet(brenda)&person(brenda))|(tall(brenda)&quiet(brenda)&brave(brenda)&tourist(brenda)))) | entailment | entailment | entailment |
Pamela, George are the only persons in the room.
"Pamela is the least quiet in the room" if "Lance is quieter than George" and vice versa.
If "Pamela and George are hated by John" then "George hates Lance or is taller than Lance or both".
"George neither is a happy quiet tourist nor is not liked by John" if "John is a sibling of George" and vice versa.
"Pamela is the quietest in the room" if "Pamela is the least tall in the room".
"Pamela is not George or does not hate John or both" only if "someone in the room who is quieter than Lance likes John".
If "Pamela who does not hate John, is liked by John" then "it is not the case that 'Pamela is the least rich in the room'".
"Only one person in the room is not a tall tourist" unless "only one person in the room does not like Lance".
Pamela is the least tall in the room.
George neither is a happy quiet tourist nor is not liked by John.
John is a sibling of Pamela.
John is a sibling of George. | Pamela is liked by Lance or is quieter than Anthony or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_6_type, type, (
tptp_fun_X_6: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(alice_type, type, (
alice: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(paul_type, type, (
paul: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(1,assumption,(~quieter(alice, mary)), introduced(assumption)).
tff(2,plain,
(^[X: $i] : refl(taller(mary, X) <=> taller(mary, X))),
inference(bind,[status(th)],[])).
tff(3,plain,
(![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)),
inference(quant_intro,[status(thm)],[2])).
tff(4,plain,
(![X: $i] : taller(mary, X) <=> ![X: $i] : taller(mary, X)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((quieter(paul, susan) <=> ![X: $i] : quieter(mary, X)) & ((hate(mary, lucy) & hate(paul, lucy)) => (hate(susan, paul) | taller(susan, paul)))) & (sibling(paul, lucy) <=> (~(((happy(paul) & quiet(paul)) & tourist(paul)) | (~like(paul, lucy)))))) & (![X: $i] : taller(mary, X) => ![X: $i] : quieter(X, mary))) & (((~(mary = paul)) | (~hate(lucy, mary))) => ?[X: $i] : (room(X) => (quieter(susan, X) => like(lucy, X))))) & (((~hate(lucy, mary)) & like(mary, lucy)) => (~![X: $i] : richer(mary, X)))) & ((~(?[X: $i] : (room(X) & (~like(susan, X))) & ![X: $i, Y: $i] : (((~like(susan, X)) & (~like(susan, Y))) => (X = Y)))) => (?[X: $i] : (room(X) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y))))) & ![X: $i] : taller(mary, X)) & (~(((happy(paul) & quiet(paul)) & tourist(paul)) | (~like(paul, lucy))))) & sibling(mary, lucy)) & sibling(paul, lucy))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(mary, susan) | quieter(alice, mary))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(paul, susan) <=> ![X: $i] : quieter(mary, X)) & (hate(susan, paul) | taller(susan, paul) | (~(hate(mary, lucy) & hate(paul, lucy)))) & (~(((~like(paul, lucy)) | (happy(paul) & quiet(paul) & tourist(paul))) <=> sibling(paul, lucy))) & ((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)) & ((~((~(mary = paul)) | (~hate(lucy, mary)))) | ?[X: $i] : (like(lucy, X) | (~room(X)) | (~quieter(susan, X)))) & ((~![X: $i] : richer(mary, X)) | (~((~hate(lucy, mary)) & like(mary, lucy)))) & ((?[X: $i] : (room(X) & (~like(susan, X))) & ![X: $i, Y: $i] : ((~((~like(susan, X)) & (~like(susan, Y)))) | (X = Y))) | (?[X: $i] : (room(X) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y)))) & ![X: $i] : taller(mary, X) & (~((~like(paul, lucy)) | (happy(paul) & quiet(paul) & tourist(paul)))) & sibling(mary, lucy) & sibling(paul, lucy))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(mary, susan) | quieter(alice, mary)))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((quieter(paul, susan) <=> ![X: $i] : quieter(mary, X)) & ((hate(mary, lucy) & hate(paul, lucy)) => (hate(susan, paul) | taller(susan, paul)))) & (sibling(paul, lucy) <=> (~(((happy(paul) & quiet(paul)) & tourist(paul)) | (~like(paul, lucy)))))) & (![X: $i] : taller(mary, X) => ![X: $i] : quieter(X, mary))) & (((~(mary = paul)) | (~hate(lucy, mary))) => ?[X: $i] : (room(X) => (quieter(susan, X) => like(lucy, X))))) & (((~hate(lucy, mary)) & like(mary, lucy)) => (~![X: $i] : richer(mary, X)))) & ((~(?[X: $i] : (room(X) & (~like(susan, X))) & ![X: $i, Y: $i] : (((~like(susan, X)) & (~like(susan, Y))) => (X = Y)))) => (?[X: $i] : (room(X) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y))))) & ![X: $i] : taller(mary, X)) & (~(((happy(paul) & quiet(paul)) & tourist(paul)) | (~like(paul, lucy))))) & sibling(mary, lucy)) & sibling(paul, lucy))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(mary, susan) | quieter(alice, mary))))), file('/mnt/tmpfs//899232389276469481996709.p','negated')).
tff(7,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(paul, susan) <=> ![X: $i] : quieter(mary, X)) & (hate(susan, paul) | taller(susan, paul) | (~(hate(mary, lucy) & hate(paul, lucy)))) & (~(((~like(paul, lucy)) | (happy(paul) & quiet(paul) & tourist(paul))) <=> sibling(paul, lucy))) & ((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)) & ((~((~(mary = paul)) | (~hate(lucy, mary)))) | ?[X: $i] : (like(lucy, X) | (~room(X)) | (~quieter(susan, X)))) & ((~![X: $i] : richer(mary, X)) | (~((~hate(lucy, mary)) & like(mary, lucy)))) & ((?[X: $i] : (room(X) & (~like(susan, X))) & ![X: $i, Y: $i] : ((~((~like(susan, X)) & (~like(susan, Y)))) | (X = Y))) | (?[X: $i] : (room(X) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y)))) & ![X: $i] : taller(mary, X) & (~((~like(paul, lucy)) | (happy(paul) & quiet(paul) & tourist(paul)))) & sibling(mary, lucy) & sibling(paul, lucy))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (like(mary, susan) | quieter(alice, mary))))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(paul, susan) <=> ![X: $i] : quieter(mary, X)) & (hate(susan, paul) | taller(susan, paul) | (~(hate(mary, lucy) & hate(paul, lucy)))) & (~(((~like(paul, lucy)) | (happy(paul) & quiet(paul) & tourist(paul))) <=> sibling(paul, lucy))) & ((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)) & ((~((~(mary = paul)) | (~hate(lucy, mary)))) | ?[X: $i] : (like(lucy, X) | (~room(X)) | (~quieter(susan, X)))) & ((~![X: $i] : richer(mary, X)) | (~((~hate(lucy, mary)) & like(mary, lucy)))) & ((?[X: $i] : (room(X) & (~like(susan, X))) & ![X: $i, Y: $i] : ((~((~like(susan, X)) & (~like(susan, Y)))) | (X = Y))) | (?[X: $i] : (room(X) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y)))) & ![X: $i] : taller(mary, X) & (~((~like(paul, lucy)) | (happy(paul) & quiet(paul) & tourist(paul)))) & sibling(mary, lucy) & sibling(paul, lucy)),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(![X: $i] : taller(mary, X)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : taller(mary, X)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,(
![X: $i] : taller(mary, X)),
inference(skolemize,[status(sab)],[10])).
tff(12,plain,
(![X: $i] : taller(mary, X)),
inference(modus_ponens,[status(thm)],[11, 3])).
tff(13,assumption,(~taller(mary, X!1)), introduced(assumption)).
tff(14,plain,
((~![X: $i] : taller(mary, X)) | taller(mary, X!1)),
inference(quant_inst,[status(thm)],[])).
tff(15,plain,
($false),
inference(unit_resolution,[status(thm)],[14, 13, 12])).
tff(16,plain,(taller(mary, X!1)), inference(lemma,lemma(discharge,[]))).
tff(17,plain,
(((~taller(mary, X!1)) | ![X: $i] : quieter(X, mary)) <=> ((~taller(mary, X!1)) | ![X: $i] : quieter(X, mary))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
(((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)) <=> ((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)),
inference(and_elim,[status(thm)],[8])).
tff(20,plain,
((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)),
inference(modus_ponens,[status(thm)],[20, 18])).
tff(22,plain,
((~![X: $i] : taller(mary, X)) | ![X: $i] : quieter(X, mary)),
inference(modus_ponens,[status(thm)],[21, 18])).
| room(pamela)&room(george)&(![X]:(room(X)=>(X='pamela'|X='george')))&
(((quieter(george,lance))<=>(![X]:(quieter(pamela,X))))&
((hate(pamela,john)&hate(george,john))=>(((hate(lance,george))|(taller(lance,george)))))&
((sibling(george,john))<=>(~((happy(george)&quiet(george)&tourist(george))|(~like(george,john)))))&
((![X]:(taller(pamela,X)))=>(![X]:(quieter(X,pamela))))&
((((pamela!=george)|(~hate(john,pamela))))=>(?[X]:(room(X)=>(((quieter(lance,X))=>(like(john,X)))))))&
(((~hate(john,pamela))&(like(pamela,john)))=>(~(![X]:(richer(pamela,X)))))&
(~(((?[X]:(room(X)&~like(lance,X)))&(![X,Y]:((~like(lance,X)&~like(lance,Y))=>(X=Y)))))=>(((?[X]:(room(X)&~(tall(X)&tourist(X))))&(![X,Y]:((~(tall(X)&tourist(X))&~(tall(Y)&tourist(Y)))=>(X=Y))))))&
(![X]:(taller(pamela,X)))&
(~((happy(george)&quiet(george)&tourist(george))|(~like(george,john))))&
(sibling(pamela,john))&
(sibling(george,john))) | room(pamela)&room(george)&(![X]:(room(X)=>(X='pamela'|X='george')))&
(((like(pamela,lance))|(quieter(anthony,pamela)))) | neutral | neutral | neutral |
Michael is the only person in the room.
If “someone who is not brave like someone who is not Michael” then “someone who is not Michael like someone who likes Dorothy”.
Someone who is not brave like someone who is not Michael.
Michael is the least quiet in the room.
Someone outside the room does not like Lana.
More than one person outside the room is not brave.
Only one person outside the room reads mystery novels. | It is not the case that 'Michael either is not a brave european or likes Lana'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_8_type, type, (
tptp_fun_X_8: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(1,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((?[X: $i, Y: $i] : (((~brave(X)) & (~(Y = mary))) & like(X, Y)) => ?[X: $i, Y: $i] : (((~(X = mary)) & like(alice, Y)) & like(X, Y))) & ?[X: $i, Y: $i] : (((~brave(X)) & (~(Y = mary))) & like(X, Y))) & ![X: $i] : quieter(mary, X)) & ?[X: $i] : ((~room(X)) => (~like(john, X)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~brave(X)) & (~brave(Y)))) & (~(X = Y)))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~(((~(brave(mary) & european(mary))) | like(john, mary)) & (~((~(brave(mary) & european(mary))) | like(john, mary)))))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~?[X: $i, Y: $i] : ((~brave(X)) & (~(Y = mary)) & like(X, Y))) | ?[X: $i, Y: $i] : ((~(X = mary)) & like(alice, Y) & like(X, Y))) & ?[X: $i, Y: $i] : ((~brave(X)) & (~(Y = mary)) & like(X, Y)) & ![X: $i] : quieter(mary, X) & ?[X: $i] : (room(X) | (~like(john, X))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~brave(X)) & (~brave(Y)) & (~(X = Y))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((?[X: $i, Y: $i] : (((~brave(X)) & (~(Y = mary))) & like(X, Y)) => ?[X: $i, Y: $i] : (((~(X = mary)) & like(alice, Y)) & like(X, Y))) & ?[X: $i, Y: $i] : (((~brave(X)) & (~(Y = mary))) & like(X, Y))) & ![X: $i] : quieter(mary, X)) & ?[X: $i] : ((~room(X)) => (~like(john, X)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~brave(X)) & (~brave(Y)))) & (~(X = Y)))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~(((~(brave(mary) & european(mary))) | like(john, mary)) & (~((~(brave(mary) & european(mary))) | like(john, mary)))))))), file('/mnt/tmpfs//2875259434303584920175130.p','negated')).
tff(4,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~?[X: $i, Y: $i] : ((~brave(X)) & (~(Y = mary)) & like(X, Y))) | ?[X: $i, Y: $i] : ((~(X = mary)) & like(alice, Y) & like(X, Y))) & ?[X: $i, Y: $i] : ((~brave(X)) & (~(Y = mary)) & like(X, Y)) & ![X: $i] : quieter(mary, X) & ?[X: $i] : (room(X) | (~like(john, X))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~brave(X)) & (~brave(Y)) & (~(X = Y))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~?[X: $i, Y: $i] : ((~brave(X)) & (~(Y = mary)) & like(X, Y))) | ?[X: $i, Y: $i] : ((~(X = mary)) & like(alice, Y) & like(X, Y))) & ?[X: $i, Y: $i] : ((~brave(X)) & (~(Y = mary)) & like(X, Y)) & ![X: $i] : quieter(mary, X) & ?[X: $i] : (room(X) | (~like(john, X))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~brave(X)) & (~brave(Y)) & (~(X = Y))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))))),
inference(monotonicity,[status(thm)],[8])).
tff(10,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))),
inference(or_elim,[status(thm)],[4])).
tff(12,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))),
inference(modus_ponens,[status(thm)],[11, 9])).
tff(13,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))),
inference(modus_ponens,[status(thm)],[12, 10])).
tff(14,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))),
inference(modus_ponens,[status(thm)],[13, 9])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!8)) (= X!8 |'mary'|)))))
(let ((a!4 (~ (not (and (room mary) a!2)) (or (not (room mary)) a!3))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4)))
| room(michael)&(![X]:(room(X)=>(X='michael')))&
(((?[X,Y]:((~brave(X))&(Y!=michael)&(like(X,Y))))=>(?[X,Y]:((X!=michael)&(like(dorothy,Y))&(like(X,Y)))))&
(?[X,Y]:((~brave(X))&(Y!=michael)&(like(X,Y))))&
(![X]:(quieter(michael,X)))&
(?[X]:(~room(X)=>(~like(lana,X))))&
((?[X,Y]:(~room(X)&~room(Y)&(~brave(X)&~brave(Y))&(X!=Y))))&
(((?[X]:(~room(X)&reads_mystery_novels(X)))&(![X,Y]:((reads_mystery_novels(X)&reads_mystery_novels(Y))=>(X=Y)))))) | room(michael)&(![X]:(room(X)=>(X='michael')))&
(~((((~(brave(michael)&european(michael)))|(like(lana,michael)))&(~((~(brave(michael)&european(michael)))|(like(lana,michael))))))) | entailment | entailment | entailment |
Ryan, Gordon, Erik are the only persons in the room. If 'John is quieter than Erik' then 'only one person outside the room is quieter than Norman'. Only one person outside the room is quieter than Norman. Norman is quieter than Erik. | It is not the case that 'Ryan is quieter than Norman and is not hated by Norman'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(mary_type, type, (
mary: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(fred_type, type, (
fred: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(paul_type, type, (
paul: $i)).
tff(1,assumption,(mary = X!0), introduced(assumption)).
tff(2,plain,
(room(mary) <=> room(X!0)),
inference(monotonicity,[status(thm)],[1])).
tff(3,plain,
(room(X!0) <=> room(mary)),
inference(symmetry,[status(thm)],[2])).
tff(4,plain,
((~room(X!0)) <=> (~room(mary))),
inference(monotonicity,[status(thm)],[3])).
tff(5,plain,
(?[X: $i] : ((~room(X)) & quieter(susan, X)) <=> ?[X: $i] : ((~room(X)) & quieter(susan, X))),
inference(rewrite,[status(thm)],[])).
tff(6,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((quieter(fred, lucy) => (?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((quieter(susan, X) & quieter(susan, Y)) => (X = Y)))) & (?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((quieter(susan, X) & quieter(susan, Y)) => (X = Y)))) & quieter(fred, susan))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(quieter(susan, mary) & (~hate(mary, susan))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quieter(fred, lucy)) | (?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)))) & ?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)) & quieter(fred, susan))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))))),
inference(rewrite,[status(thm)],[])).
tff(7,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((quieter(fred, lucy) => (?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((quieter(susan, X) & quieter(susan, Y)) => (X = Y)))) & (?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((quieter(susan, X) & quieter(susan, Y)) => (X = Y)))) & quieter(fred, susan))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(quieter(susan, mary) & (~hate(mary, susan))))))), file('/mnt/tmpfs//355113475726240872635415.p','negated')).
tff(8,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quieter(fred, lucy)) | (?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)))) & ?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)) & quieter(fred, susan))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan))))))),
inference(modus_ponens,[status(thm)],[7, 6])).
tff(9,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quieter(fred, lucy)) | (?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)))) & ?[X: $i] : ((~room(X)) & quieter(susan, X)) & ![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)) & quieter(fred, susan)),
inference(or_elim,[status(thm)],[8])).
tff(10,plain,
(?[X: $i] : ((~room(X)) & quieter(susan, X))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(?[X: $i] : ((~room(X)) & quieter(susan, X))),
inference(modus_ponens,[status(thm)],[10, 5])).
tff(12,plain,(
(~room(X!0)) & quieter(susan, X!0)),
inference(skolemize,[status(sab)],[11])).
tff(13,plain,
(~room(X!0)),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
(~room(mary)),
inference(modus_ponens,[status(thm)],[13, 4])).
tff(15,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(room(mary)),
inference(and_elim,[status(thm)],[9])).
tff(17,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
($false),
inference(unit_resolution,[status(thm)],[17, 14])).
tff(19,plain,(~(mary = X!0)), inference(lemma,lemma(discharge,[]))).
tff(20,assumption,(quieter(susan, mary)), introduced(assumption)).
tff(21,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y))) <=> ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y))))),
inference(bind,[status(th)],[])).
tff(22,plain,
(![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))),
inference(quant_intro,[status(thm)],[21])).
tff(23,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((quieter(susan, X) & quieter(susan, Y)) <=> (~((~quieter(susan, X)) | (~quieter(susan, Y))))), ((~(quieter(susan, X) & quieter(susan, Y))) <=> (~(~((~quieter(susan, X)) | (~quieter(susan, Y))))))), rewrite((~(~((~quieter(susan, X)) | (~quieter(susan, Y))))) <=> ((~quieter(susan, X)) | (~quieter(susan, Y)))), ((~(quieter(susan, X) & quieter(susan, Y))) <=> ((~quieter(susan, X)) | (~quieter(susan, Y))))), (((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)) <=> (((~quieter(susan, X)) | (~quieter(susan, Y))) | (X = Y)))), rewrite((((~quieter(susan, X)) | (~quieter(susan, Y))) | (X = Y)) <=> ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))), (((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)) <=> ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))))),
inference(bind,[status(th)],[])).
tff(24,plain,
(![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))),
inference(quant_intro,[status(thm)],[23])).
tff(25,plain,
(![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y))),
inference(rewrite,[status(thm)],[])).
tff(26,plain,
(![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y))),
inference(and_elim,[status(thm)],[9])).
tff(27,plain,
(![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y))),
inference(modus_ponens,[status(thm)],[26, 25])).
tff(28,plain,(
![X: $i, Y: $i] : ((~(quieter(susan, X) & quieter(susan, Y))) | (X = Y))),
inference(skolemize,[status(sab)],[27])).
tff(29,plain,
(![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))),
inference(modus_ponens,[status(thm)],[28, 24])).
tff(30,plain,
(![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))),
inference(modus_ponens,[status(thm)],[29, 22])).
tff(31,plain,
(quieter(susan, X!0)),
inference(and_elim,[status(thm)],[12])).
tff(32,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | ((~quieter(susan, mary)) | (~quieter(susan, X!0)) | (mary = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | (~quieter(susan, mary)) | (~quieter(susan, X!0)) | (mary = X!0))),
inference(rewrite,[status(thm)],[])).
tff(33,plain,
(((mary = X!0) | (~quieter(susan, mary)) | (~quieter(susan, X!0))) <=> ((~quieter(susan, mary)) | (~quieter(susan, X!0)) | (mary = X!0))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | ((mary = X!0) | (~quieter(susan, mary)) | (~quieter(susan, X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | ((~quieter(susan, mary)) | (~quieter(susan, X!0)) | (mary = X!0)))),
inference(monotonicity,[status(thm)],[33])).
tff(35,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | ((mary = X!0) | (~quieter(susan, mary)) | (~quieter(susan, X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | (~quieter(susan, mary)) | (~quieter(susan, X!0)) | (mary = X!0))),
inference(transitivity,[status(thm)],[34, 32])).
tff(36,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | ((mary = X!0) | (~quieter(susan, mary)) | (~quieter(susan, X!0)))),
inference(quant_inst,[status(thm)],[])).
tff(37,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~quieter(susan, X)) | (~quieter(susan, Y)))) | (~quieter(susan, mary)) | (~quieter(susan, X!0)) | (mary = X!0)),
inference(modus_ponens,[status(thm)],[36, 35])).
tff(38,plain,
($false),
inference(unit_resolution,[status(thm)],[37, 31, 30, 20, 19])).
tff(39,plain,(~quieter(susan, mary)), inference(lemma,lemma(discharge,[]))).
tff(40,plain,
(((~quieter(susan, mary)) | hate(mary, susan)) | quieter(susan, mary)),
inference(tautology,[status(thm)],[])).
tff(41,plain,
((~quieter(susan, mary)) | hate(mary, susan)),
inference(unit_resolution,[status(thm)],[40, 39])).
tff(42,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
(room(fred)),
inference(and_elim,[status(thm)],[9])).
tff(44,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[43, 42])).
tff(45,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(room(paul)),
inference(and_elim,[status(thm)],[9])).
tff(47,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[46, 45])).
tff(48,plain,
(((~((~quieter(susan, mary)) | hate(mary, susan))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~((~quieter(susan, mary)) | hate(mary, susan))))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
((~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
((quieter(susan, mary) & (~hate(mary, susan))) <=> (~((~quieter(susan, mary)) | hate(mary, susan)))),
inference(rewrite,[status(thm)],[])).
tff(51,plain,
(((quieter(susan, mary) & (~hate(mary, susan))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> ((~((~quieter(susan, mary)) | hate(mary, susan))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))),
inference(monotonicity,[status(thm)],[50, 49])).
tff(52,plain,
(((quieter(susan, mary) & (~hate(mary, susan))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~((~quieter(susan, mary)) | hate(mary, susan))))),
inference(transitivity,[status(thm)],[51, 48])).
tff(53,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (quieter(susan, mary) & (~hate(mary, susan)))) <=> ((quieter(susan, mary) & (~hate(mary, susan))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (quieter(susan, mary) & (~hate(mary, susan)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (quieter(susan, mary) & (~hate(mary, susan))))),
inference(monotonicity,[status(thm)],[49])).
tff(55,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (quieter(susan, mary) & (~hate(mary, susan)))) <=> ((quieter(susan, mary) & (~hate(mary, susan))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))),
inference(transitivity,[status(thm)],[54, 53])).
tff(56,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan))))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan))))))),
inference(monotonicity,[status(thm)],[56])).
tff(58,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan))))))),
inference(rewrite,[status(thm)],[])).
tff(59,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))),
inference(or_elim,[status(thm)],[8])).
tff(60,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))),
inference(modus_ponens,[status(thm)],[59, 57])).
tff(61,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))),
inference(modus_ponens,[status(thm)],[60, 58])).
tff(62,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(quieter(susan, mary) & (~hate(mary, susan)))))),
inference(modus_ponens,[status(thm)],[61, 57])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!1 |'fred'|)
(= X!1 |'paul'|)
(= X!1 |'mary'|)
(not (room X!1)))))
(a!6 (~ (and (quieter susan mary) (not (hate mary susan)))
(and (quieter susan mary) (not (hate mary susan)))))
(a!7 (not (and (quieter susan mary) (not (hate mary susan))))))
(let ((a!8 (or (not (room mary))
(not (room paul))
(not (room fred))
a!5
(and (quieter susan mary) (not (hate mary susan))))))
(let ((a!9 (~ (not (and (room mary) (room paul) (room fred) a!4 a!7)) a!8)))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl a!6) a!9))))
| room(ryan)&room(gordon)&room(erik)&(![X]:(room(X)=>(X='ryan'|X='gordon'|X='erik')))&
(((quieter(erik,john))=>(((?[X]:(~room(X)&quieter(norman,X)))&(![X,Y]:((quieter(norman,X)&quieter(norman,Y))=>(X=Y))))))&
(((?[X]:(~room(X)&quieter(norman,X)))&(![X,Y]:((quieter(norman,X)&quieter(norman,Y))=>(X=Y)))))&
(quieter(erik,norman))) | room(ryan)&room(gordon)&room(erik)&(![X]:(room(X)=>(X='ryan'|X='gordon'|X='erik')))&
(~((quieter(norman,ryan))&(~hate(ryan,norman)))) | entailment | neutral | neutral |
Minnie and Gregory like each other. Gregory who does not have scuba dived, is not liked by Walter. Gregory is liked by Walter or is not liked by Walter or both. | It is not the case that 'Minnie and Walter like each other'. | neutral | % SZS status Satisfiable
| room(gregory)&(![X]:(room(X)=>(X='gregory')))&
(((like(minnie,gregory) & like(gregory,minnie)))&
((does_not_have_scuba_dived(gregory))&(~like(gregory,walter)))&
(((like(gregory,walter))|(~like(gregory,walter))))) | room(gregory)&(![X]:(room(X)=>(X='gregory')))&
(~((like(minnie,walter) & like(walter,minnie)))) | contradiction | entailment | contradiction |
Lauren, Ronald are the only persons in the room.
'Someone who is hated by Norma is taller than someone who does not own a smart tv' if 'Norma is taller than Ronald'.
Lauren does not hate Norma and does not hate Linda.
Lauren is the least tall in the room.
Only one person outside the room is hated by Norma.
Lauren and Ronald are brave tourist. | Lauren neither is hated by Norma nor is not brave. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(brave_type, type, (
brave: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(1,assumption,(~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))), introduced(assumption)).
tff(2,plain,
(((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | room(X!3)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(room(X!3)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(~(X!3 = |'mary'|)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
(((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(~(X!3 = |'paul'|)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(9,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((taller(paul, fred) => ?[X: $i, Y: $i] : ((hate(X, fred) & (~predb(Y))) & taller(X, Y))) & ((~hate(fred, mary)) & (~hate(john, mary)))) & ![X: $i] : taller(mary, X)) & (?[X: $i] : ((~room(X)) & hate(X, fred)) & ![X: $i, Y: $i] : ((hate(X, fred) & hate(Y, fred)) => (X = Y)))) & (((brave(mary) & tourist(mary)) & brave(paul)) & tourist(paul)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(hate(mary, fred) | (~brave(mary))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~taller(paul, fred)) | ?[X: $i, Y: $i] : (hate(X, fred) & (~predb(Y)) & taller(X, Y))) & (~hate(fred, mary)) & (~hate(john, mary)) & ![X: $i] : taller(mary, X) & ?[X: $i] : ((~room(X)) & hate(X, fred)) & ![X: $i, Y: $i] : ((~(hate(X, fred) & hate(Y, fred))) | (X = Y)) & brave(mary) & tourist(mary) & brave(paul) & tourist(paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(12,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((taller(paul, fred) => ?[X: $i, Y: $i] : ((hate(X, fred) & (~predb(Y))) & taller(X, Y))) & ((~hate(fred, mary)) & (~hate(john, mary)))) & ![X: $i] : taller(mary, X)) & (?[X: $i] : ((~room(X)) & hate(X, fred)) & ![X: $i, Y: $i] : ((hate(X, fred) & hate(Y, fred)) => (X = Y)))) & (((brave(mary) & tourist(mary)) & brave(paul)) & tourist(paul)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(hate(mary, fred) | (~brave(mary))))))), file('/mnt/tmpfs//326616177405843049743037.p','negated')).
tff(13,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~taller(paul, fred)) | ?[X: $i, Y: $i] : (hate(X, fred) & (~predb(Y)) & taller(X, Y))) & (~hate(fred, mary)) & (~hate(john, mary)) & ![X: $i] : taller(mary, X) & ?[X: $i] : ((~room(X)) & hate(X, fred)) & ![X: $i, Y: $i] : ((~(hate(X, fred) & hate(Y, fred))) | (X = Y)) & brave(mary) & tourist(mary) & brave(paul) & tourist(paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary))))))),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~taller(paul, fred)) | ?[X: $i, Y: $i] : (hate(X, fred) & (~predb(Y)) & taller(X, Y))) & (~hate(fred, mary)) & (~hate(john, mary)) & ![X: $i] : taller(mary, X) & ?[X: $i] : ((~room(X)) & hate(X, fred)) & ![X: $i, Y: $i] : ((~(hate(X, fred) & hate(Y, fred))) | (X = Y)) & brave(mary) & tourist(mary) & brave(paul) & tourist(paul)),
inference(or_elim,[status(thm)],[13])).
tff(15,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[15, 10])).
tff(17,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[16])).
tff(18,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[17, 9])).
tff(19,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))),
inference(quant_inst,[status(thm)],[])).
tff(21,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))),
inference(modus_ponens,[status(thm)],[20, 19])).
tff(22,plain,
($false),
inference(unit_resolution,[status(thm)],[21, 18, 7, 5, 3])).
tff(23,plain,((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))), inference(lemma,lemma(discharge,[]))).
tff(24,plain,
(brave(mary) <=> brave(mary)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(brave(mary)),
inference(and_elim,[status(thm)],[14])).
tff(26,plain,
(brave(mary)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
(room(paul)),
inference(and_elim,[status(thm)],[14])).
tff(29,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(room(mary)),
inference(and_elim,[status(thm)],[14])).
tff(32,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (hate(mary, fred) | (~brave(mary)))) <=> (hate(mary, fred) | (~brave(mary)) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
((hate(mary, fred) | (~brave(mary))) <=> (hate(mary, fred) | (~brave(mary)))),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
((~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (hate(mary, fred) | (~brave(mary)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (hate(mary, fred) | (~brave(mary))))),
inference(monotonicity,[status(thm)],[35, 34])).
tff(37,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (hate(mary, fred) | (~brave(mary)))) <=> (hate(mary, fred) | (~brave(mary)) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))),
inference(transitivity,[status(thm)],[36, 33])).
tff(38,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(39,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary))))))),
inference(monotonicity,[status(thm)],[38])).
tff(40,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))),
inference(or_elim,[status(thm)],[13])).
tff(42,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))),
inference(modus_ponens,[status(thm)],[41, 39])).
tff(43,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))),
inference(modus_ponens,[status(thm)],[42, 40])).
tff(44,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, fred) | (~brave(mary)))))),
inference(modus_ponens,[status(thm)],[43, 39])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3)))))
(a!5 (~ (or (hate mary fred) (not (brave mary)))
(or (hate mary fred) (not (brave mary)))))
(a!6 (not (or (hate mary fred) (not (brave mary))))))
(let ((a!7 (or (not (room mary))
(not (room paul))
a!4
(or (hate mary fred) (not (brave mary))))))
(let ((a!8 (~ (not (and (room mary) (room paul) a!3 a!6)) a!7)))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl a!5) a!8))))
| room(lauren)&room(ronald)&(![X]:(room(X)=>(X='lauren'|X='ronald')))&
(((taller(ronald,norma))=>(?[X,Y]:((hate(X,norma))&(does_not_own_a_smart_tv(Y))&(taller(X,Y)))))&
((~hate(norma,lauren))&(~hate(linda,lauren)))&
(![X]:(taller(lauren,X)))&
(((?[X]:(~room(X)&hate(X,norma)))&(![X,Y]:((hate(X,norma)&hate(Y,norma))=>(X=Y)))))&
(brave(lauren)&tourist(lauren)&brave(ronald)&tourist(ronald))) | room(lauren)&room(ronald)&(![X]:(room(X)=>(X='lauren'|X='ronald')))&
(~((hate(lauren,norma))|(~brave(lauren)))) | entailment | contradiction | entailment |
Not all of the following are true:.
-Jacob who is not Frank, is not a wine connoisseur.
-Frank is a wine connoisseur and is not hated by Caitlin.
-Frank neither is hated by Jamel nor is a quiet person. | Frank who is hated by Jamel, is hated by Caitlin. | neutral | % SZS status Satisfiable
| room(frank)&room(jacob)&(![X]:(room(X)=>(X='frank'|X='jacob')))&
(~((jacob!=frank)&(is_not_a_wine_connoisseur(jacob))&(is_a_wine_connoisseur(frank))&(~hate(frank,caitlin))&~((hate(frank,jamel))|(quiet(frank)&person(frank))))) | room(frank)&room(jacob)&(![X]:(room(X)=>(X='frank'|X='jacob')))&
((hate(frank,jamel))&(hate(frank,caitlin))) | contradiction | contradiction | contradiction |
Guy, Carl are the only persons in the room.
Carl and Guy hate each other.
Everyone outside the room is not Carl.
More than one person in the room is not hated by Venessa.
Guy hates Venessa.
Guy and Carl are respectively happy and brave.
Guy is the tallest in the room. | Guy neither is not hated by Venessa nor practices digital art. | contradiction | - | room(guy)&room(carl)&(![X]:(room(X)=>(X='guy'|X='carl')))&
(((hate(carl,guy) & hate(guy,carl)))&
(![X]:(~room(X)=>(X!=carl)))&
((?[X,Y]:(room(X)&room(Y)&(~hate(X,venessa)&~hate(Y,venessa))&(X!=Y))))&
(hate(venessa,guy))&
((happy(guy))&(brave(carl)))&
(![X]:(taller(X,guy)))) | room(guy)&room(carl)&(![X]:(room(X)=>(X='guy'|X='carl')))&
(~((~hate(guy,venessa))|(practices_digital_art(guy)))) | neutral | neutral | neutral |
David, Tiffany are the only persons in the room.
“David is the least rich in the room” if “David is not liked by Jessica” and vice versa.
David is the least rich in the room.
Jessica is richer than David.
David is the least rich in the room. | David enjoys fishing and is liked by Jessica. | contradiction | - | room(david)&room(tiffany)&(![X]:(room(X)=>(X='david'|X='tiffany')))&
(((~like(david,jessica))<=>(![X]:(richer(david,X))))&
(![X]:(richer(david,X)))&
(richer(david,jessica))&
(![X]:(richer(david,X)))) | room(david)&room(tiffany)&(![X]:(room(X)=>(X='david'|X='tiffany')))&
((enjoys_fishing(david))&(like(david,jessica))) | neutral | neutral | neutral |
Caroline, Joe, Frank, Dwayne are the only persons in the room.
Caroline is not hated by Herbert or does not hate Jose or both.
Someone in the room who is a tall happy person is a brave european.
Caroline neither likes Lynnette nor does not collect comic books.
Caroline neither is a client of Herbert nor is a client of Lynnette.
Joe who does not like Herbert, is not hated by Lynnette.
Only one person outside the room does not collect comic books.
Joe is the tallest in the room.
Joe is liked by Lynnette or is not a creative tall person or both. | Joe neither is a tall quiet rich brave creative european nor is a client of Lynnette. | neutral | % SZS status Satisfiable
| room(caroline)&room(joe)&room(frank)&room(dwayne)&(![X]:(room(X)=>(X='caroline'|X='joe'|X='frank'|X='dwayne')))&
((((~hate(caroline,herbert))|(~hate(jose,caroline))))&
(?[X]:(room(X)=>(((tall(X)&happy(X)&person(X))=>(brave(X)&european(X))))))&
(~((like(lynnette,caroline))|(does_not_collect_comic_books(caroline))))&
(~((client(herbert,caroline))|(client(lynnette,caroline))))&
((~like(herbert,joe))&(~hate(joe,lynnette)))&
(((?[X]:(~room(X)&does_not_collect_comic_books(X)))&(![X,Y]:((does_not_collect_comic_books(X)&does_not_collect_comic_books(Y))=>(X=Y)))))&
(![X]:(taller(X,joe)))&
(((like(joe,lynnette))|(~(creative(joe)&tall(joe)&person(joe)))))) | room(caroline)&room(joe)&room(frank)&room(dwayne)&(![X]:(room(X)=>(X='caroline'|X='joe'|X='frank'|X='dwayne')))&
(~((tall(joe)&quiet(joe)&rich(joe)&brave(joe)&creative(joe)&european(joe))|(client(lynnette,joe)))) | neutral | entailment | contradiction |
If Justin is a sibling of Sharon then Darla who does not hate Justin, enjoys photography.
Sharon and Darla are respectively happy and tall.
Sharon neither is a client of Justin nor is not tall. | Sharon is not a tall rich european or does not hate Justin or both. | neutral | % SZS status Satisfiable
| room(darla)&room(sharon)&(![X]:(room(X)=>(X='darla'|X='sharon')))&
(((sibling(sharon,justin))=>((~hate(justin,darla))&(enjoys_photography(darla))))&
((happy(sharon))&(tall(darla)))&
(~((client(justin,sharon))|(~tall(sharon))))) | room(darla)&room(sharon)&(![X]:(room(X)=>(X='darla'|X='sharon')))&
(((~(tall(sharon)&rich(sharon)&european(sharon)))|(~hate(justin,sharon)))) | neutral | entailment | entailment |
At least one of the following is true:.
-Carol either is not quiet, not tall or makes homemade pastries.
-Dorothy neither is a happy tourist nor is hated by Erin. | Dorothy is not a tall tourist or is not happy or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(tall_type, type, (
tall: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(predc_type, type, (
predc: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(1,assumption,(~((~happy(alice)) | (~tourist(alice)) | (~tall(alice)))), introduced(assumption)).
tff(2,plain,
(((~happy(alice)) | (~tourist(alice)) | (~tall(alice))) | happy(alice)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(happy(alice)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~happy(alice)) | (~tourist(alice)) | (~tall(alice))) | tourist(alice)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(tourist(alice)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
((~(~((~happy(alice)) | (~tourist(alice))))) <=> ((~happy(alice)) | (~tourist(alice)))),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
((happy(alice) & tourist(alice)) <=> (~((~happy(alice)) | (~tourist(alice))))),
inference(rewrite,[status(thm)],[])).
tff(8,plain,
((~(happy(alice) & tourist(alice))) <=> (~(~((~happy(alice)) | (~tourist(alice)))))),
inference(monotonicity,[status(thm)],[7])).
tff(9,plain,
((~(happy(alice) & tourist(alice))) <=> ((~happy(alice)) | (~tourist(alice)))),
inference(transitivity,[status(thm)],[8, 6])).
tff(10,plain,
((~(happy(alice) & tourist(alice))) <=> (~(happy(alice) & tourist(alice)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((~quiet(paul)) & (~tall(paul))) | predc(paul)) & (~(((~quiet(paul)) & (~tall(paul))) | predc(paul)))) | (~((happy(alice) & tourist(alice)) | hate(alice, lucy))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((happy(alice) & tourist(alice)) | hate(alice, lucy))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))))),
inference(rewrite,[status(thm)],[])).
tff(12,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((~quiet(paul)) & (~tall(paul))) | predc(paul)) & (~(((~quiet(paul)) & (~tall(paul))) | predc(paul)))) | (~((happy(alice) & tourist(alice)) | hate(alice, lucy))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice)))))), file('/mnt/tmpfs//6116816420740681223430367.p','negated')).
tff(13,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((happy(alice) & tourist(alice)) | hate(alice, lucy))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice)))))),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((happy(alice) & tourist(alice)) | hate(alice, lucy)))),
inference(or_elim,[status(thm)],[13])).
tff(15,plain,
(~((happy(alice) & tourist(alice)) | hate(alice, lucy))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(~(happy(alice) & tourist(alice))),
inference(or_elim,[status(thm)],[15])).
tff(17,plain,
(~(happy(alice) & tourist(alice))),
inference(modus_ponens,[status(thm)],[16, 10])).
tff(18,plain,
((~happy(alice)) | (~tourist(alice))),
inference(modus_ponens,[status(thm)],[17, 9])).
tff(19,plain,
($false),
inference(unit_resolution,[status(thm)],[18, 5, 3])).
tff(20,plain,((~happy(alice)) | (~tourist(alice)) | (~tall(alice))), inference(lemma,lemma(discharge,[]))).
tff(21,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
(room(alice)),
inference(and_elim,[status(thm)],[14])).
tff(23,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[22, 21])).
tff(24,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(room(fred)),
inference(and_elim,[status(thm)],[14])).
tff(26,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
(room(paul)),
inference(and_elim,[status(thm)],[14])).
tff(29,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(room(mary)),
inference(and_elim,[status(thm)],[14])).
tff(32,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~happy(alice)) | (~tourist(alice)) | (~tall(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~happy(alice)) | (~tourist(alice)) | (~tall(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
((~((~(tall(alice) & tourist(alice))) | (~happy(alice)))) <=> (~((~happy(alice)) | (~tourist(alice)) | (~tall(alice))))),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
((~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~happy(alice)) | (~tourist(alice)) | (~tall(alice)))))),
inference(monotonicity,[status(thm)],[35, 34])).
tff(37,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~happy(alice)) | (~tourist(alice)) | (~tall(alice)))))),
inference(transitivity,[status(thm)],[36, 33])).
tff(38,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(39,plain,
(((~(tall(alice) & tourist(alice))) | (~happy(alice))) <=> ((~(tall(alice) & tourist(alice))) | (~happy(alice)))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((~((~(tall(alice) & tourist(alice))) | (~happy(alice)))) <=> (~((~(tall(alice) & tourist(alice))) | (~happy(alice))))),
inference(monotonicity,[status(thm)],[39])).
tff(41,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice)))))),
inference(monotonicity,[status(thm)],[35, 40])).
tff(42,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~happy(alice)))))),
inference(transitivity,[status(thm)],[41, 38])).
tff(43,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice)))))),
inference(monotonicity,[status(thm)],[43])).
tff(45,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))),
inference(or_elim,[status(thm)],[13])).
tff(47,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))),
inference(modus_ponens,[status(thm)],[46, 44])).
tff(48,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))),
inference(modus_ponens,[status(thm)],[47, 45])).
tff(49,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~happy(alice))))),
inference(modus_ponens,[status(thm)],[48, 44])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!0 |'alice'|)
(= X!0 |'fred'|)
(= X!0 |'paul'|)
(= X!0 |'mary'|)
(not (room X!0)))))
(a!7 (or (not (and (tall alice) (tourist alice))) (not (happy alice)))))
(let ((a!8 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
a!7))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(not a!7)))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
(refl (~ (not a!7) (not a!7)))
a!8)))
| room(willie)&room(carol)&room(george)&room(dorothy)&(![X]:(room(X)=>(X='willie'|X='carol'|X='george'|X='dorothy')))&
((((((~quiet(carol)&~tall(carol))|(makes_homemade_pastries(carol)))&(~((~quiet(carol)&~tall(carol))|(makes_homemade_pastries(carol))))))|
(~((happy(dorothy)&tourist(dorothy))|(hate(dorothy,erin)))))) | room(willie)&room(carol)&room(george)&room(dorothy)&(![X]:(room(X)=>(X='willie'|X='carol'|X='george'|X='dorothy')))&
(((~(tall(dorothy)&tourist(dorothy)))|(~happy(dorothy)))) | entailment | neutral | entailment |
Stephen, Tammy, Jessie, Amy are the only persons in the room.
'Tammy is the tallest in the room' only if 'someone who is a quiet creative tall brave person is a sibling of someone who is not a tall creative person'.
Stephen and Tammy are hated by Christopher.
Stephen is the least quiet in the room.
Tammy is the tallest in the room.
Jessie is not tall and is taller than Christopher.
Tammy is the tallest in the room.
Amy is the quietest in the room.
Tammy is not Amy and does not like Christopher. | Stephen neither is liked by Christopher nor is not quiet, not rich, not brave, not tall. | neutral | % SZS status Satisfiable
| room(stephen)&room(tammy)&room(jessie)&room(amy)&(![X]:(room(X)=>(X='stephen'|X='tammy'|X='jessie'|X='amy')))&
(((![X]:(taller(X,tammy)))=>(?[X,Y]:((quiet(X)&creative(X)&tall(X)&brave(X)&person(X))&(~(tall(Y)&creative(Y)&person(Y)))&(sibling(X,Y)))))&
(hate(stephen,christopher)&hate(tammy,christopher))&
(![X]:(quieter(stephen,X)))&
(![X]:(taller(X,tammy)))&
((~tall(jessie))&(taller(christopher,jessie)))&
(![X]:(taller(X,tammy)))&
(![X]:(quieter(X,amy)))&
((tammy!=amy)&(~like(christopher,tammy)))) | room(stephen)&room(tammy)&room(jessie)&room(amy)&(![X]:(room(X)=>(X='stephen'|X='tammy'|X='jessie'|X='amy')))&
(~((like(stephen,christopher))|(~quiet(stephen)&~rich(stephen)&~brave(stephen)&~tall(stephen)))) | entailment | contradiction | entailment |
Stephanie, Robert, Shirley are the only persons in the room.
'Stephanie neither is hated by James nor is richer than Myra' if 'Myra and Stephanie like each other'.
'Stephanie neither collects antique jewelry nor is a rich european' if 'more than one person in the room is not quiet' and vice versa.
Stephanie is the quietest in the room.
Only one person outside the room is not liked by Myra.
More than one person in the room is not quiet.
James is richer than Stephanie.
Someone who is richer than James is quieter than someone who is liked by Myra.
Someone who is richer than James like someone who is not a rich european.
More than one person in the room is not a brave quiet rich european. | Shirley is not a creative rich quiet person or does not collect luxury watches or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(quiet_type, type, (
quiet: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(mary_type, type, (
mary: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_Y_0_type, type, (
tptp_fun_Y_0: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_9_type, type, (
tptp_fun_X_9: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(alice_type, type, (
alice: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(1,assumption,(~(mary = |'paul'|)), introduced(assumption)).
tff(2,assumption,(~(Y!0 = |'paul'|)), introduced(assumption)).
tff(3,assumption,(fred = |'mary'|), introduced(assumption)).
tff(4,plain,
(|'mary'| = fred),
inference(symmetry,[status(thm)],[3])).
tff(5,assumption,(Y!0 = |'mary'|), introduced(assumption)).
tff(6,plain,
(Y!0 = fred),
inference(transitivity,[status(thm)],[5, 4])).
tff(7,plain,
(quiet(Y!0) <=> quiet(fred)),
inference(monotonicity,[status(thm)],[6])).
tff(8,plain,
(quiet(fred) <=> quiet(Y!0)),
inference(symmetry,[status(thm)],[7])).
tff(9,assumption,(~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))), introduced(assumption)).
tff(10,plain,
(((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | room(X!9)),
inference(tautology,[status(thm)],[])).
tff(11,plain,
(room(X!9)),
inference(unit_resolution,[status(thm)],[10, 9])).
tff(12,plain,
(((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | (~(X!9 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(13,plain,
(~(X!9 = |'mary'|)),
inference(unit_resolution,[status(thm)],[12, 9])).
tff(14,plain,
(((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | (~(X!9 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(15,plain,
(~(X!9 = |'paul'|)),
inference(unit_resolution,[status(thm)],[14, 9])).
tff(16,plain,
(((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))) | (~(X!9 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(17,plain,
(~(X!9 = |'fred'|)),
inference(unit_resolution,[status(thm)],[16, 9])).
tff(18,plain,
(^[X: $i] : refl(((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(19,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[18])).
tff(20,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((like(susan, mary) & like(mary, susan)) => (~(hate(mary, john) | richer(susan, mary)))) & (?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~quiet(X)) & (~quiet(Y)))) & (~(X = Y))) <=> (~(predb(mary) | (rich(mary) & european(mary)))))) & ![X: $i] : quieter(X, mary)) & (?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : (((~like(X, susan)) & (~like(Y, susan))) => (X = Y)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~quiet(X)) & (~quiet(Y)))) & (~(X = Y)))) & richer(mary, john)) & ?[X: $i, Y: $i] : ((richer(john, X) & like(Y, susan)) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((richer(john, X) & (~(rich(Y) & european(Y)))) & like(X, Y))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(((brave(X) & quiet(X)) & rich(X)) & european(X))) & (~(((brave(Y) & quiet(Y)) & rich(Y)) & european(Y))))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~(((creative(fred) & rich(fred)) & quiet(fred)) & person(fred))) | (~preda(fred)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(like(susan, mary) & like(mary, susan))) | (~(hate(mary, john) | richer(susan, mary)))) & (~((predb(mary) | (rich(mary) & european(mary))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))))) & ![X: $i] : quieter(X, mary) & ?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : ((~((~like(X, susan)) & (~like(Y, susan)))) | (X = Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))) & richer(mary, john) & ?[X: $i, Y: $i] : (richer(john, X) & like(Y, susan) & quieter(X, Y)) & ?[X: $i, Y: $i] : (richer(john, X) & (~(rich(Y) & european(Y))) & like(X, Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(brave(X) & quiet(X) & rich(X) & european(X))) & (~(brave(Y) & quiet(Y) & rich(Y) & european(Y))) & (~(X = Y))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))))),
inference(rewrite,[status(thm)],[])).
tff(22,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((like(susan, mary) & like(mary, susan)) => (~(hate(mary, john) | richer(susan, mary)))) & (?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~quiet(X)) & (~quiet(Y)))) & (~(X = Y))) <=> (~(predb(mary) | (rich(mary) & european(mary)))))) & ![X: $i] : quieter(X, mary)) & (?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : (((~like(X, susan)) & (~like(Y, susan))) => (X = Y)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~quiet(X)) & (~quiet(Y)))) & (~(X = Y)))) & richer(mary, john)) & ?[X: $i, Y: $i] : ((richer(john, X) & like(Y, susan)) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((richer(john, X) & (~(rich(Y) & european(Y)))) & like(X, Y))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(((brave(X) & quiet(X)) & rich(X)) & european(X))) & (~(((brave(Y) & quiet(Y)) & rich(Y)) & european(Y))))) & (~(X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~(((creative(fred) & rich(fred)) & quiet(fred)) & person(fred))) | (~preda(fred)))))), file('/mnt/tmpfs//5805677639004063544639899.p','negated')).
tff(23,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(like(susan, mary) & like(mary, susan))) | (~(hate(mary, john) | richer(susan, mary)))) & (~((predb(mary) | (rich(mary) & european(mary))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))))) & ![X: $i] : quieter(X, mary) & ?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : ((~((~like(X, susan)) & (~like(Y, susan)))) | (X = Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))) & richer(mary, john) & ?[X: $i, Y: $i] : (richer(john, X) & like(Y, susan) & quieter(X, Y)) & ?[X: $i, Y: $i] : (richer(john, X) & (~(rich(Y) & european(Y))) & like(X, Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(brave(X) & quiet(X) & rich(X) & european(X))) & (~(brave(Y) & quiet(Y) & rich(Y) & european(Y))) & (~(X = Y))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))))),
inference(modus_ponens,[status(thm)],[22, 21])).
tff(24,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(like(susan, mary) & like(mary, susan))) | (~(hate(mary, john) | richer(susan, mary)))) & (~((predb(mary) | (rich(mary) & european(mary))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))))) & ![X: $i] : quieter(X, mary) & ?[X: $i] : ((~room(X)) & (~like(X, susan))) & ![X: $i, Y: $i] : ((~((~like(X, susan)) & (~like(Y, susan)))) | (X = Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~quiet(X)) & (~quiet(Y)) & (~(X = Y))) & richer(mary, john) & ?[X: $i, Y: $i] : (richer(john, X) & like(Y, susan) & quieter(X, Y)) & ?[X: $i, Y: $i] : (richer(john, X) & (~(rich(Y) & european(Y))) & like(X, Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(brave(X) & quiet(X) & rich(X) & european(X))) & (~(brave(Y) & quiet(Y) & rich(Y) & european(Y))) & (~(X = Y)))),
inference(or_elim,[status(thm)],[23])).
tff(25,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[25, 20])).
tff(27,plain,(
![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[26])).
tff(28,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[27, 19])).
tff(29,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))),
inference(rewrite,[status(thm)],[])).
tff(30,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))),
inference(quant_inst,[status(thm)],[])).
tff(31,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))),
inference(modus_ponens,[status(thm)],[30, 29])).
tff(32,plain,
($false),
inference(unit_resolution,[status(thm)],[31, 28, 17, 15, 13, 11])).
tff(33,plain,((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))), inference(lemma,lemma(discharge,[]))).
tff(34,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
(room(fred)),
inference(and_elim,[status(thm)],[24])).
tff(36,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
(room(paul)),
inference(and_elim,[status(thm)],[24])).
tff(39,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[38, 37])).
tff(40,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(room(mary)),
inference(and_elim,[status(thm)],[24])).
tff(42,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[41, 40])).
tff(43,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~creative(fred)) | (~rich(fred)) | (~quiet(fred)) | (~person(fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~creative(fred)) | (~rich(fred)) | (~quiet(fred)) | (~person(fred)))))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
((~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))) <=> (~((~preda(fred)) | (~creative(fred)) | (~rich(fred)) | (~quiet(fred)) | (~person(fred))))),
inference(rewrite,[status(thm)],[])).
tff(45,plain,
((~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) <=> (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))))),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~creative(fred)) | (~rich(fred)) | (~quiet(fred)) | (~person(fred)))))),
inference(monotonicity,[status(thm)],[45, 44])).
tff(47,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~creative(fred)) | (~rich(fred)) | (~quiet(fred)) | (~person(fred)))))),
inference(transitivity,[status(thm)],[46, 43])).
tff(48,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))))),
inference(monotonicity,[status(thm)],[45])).
tff(50,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))))),
inference(transitivity,[status(thm)],[49, 48])).
tff(51,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))))),
inference(monotonicity,[status(thm)],[51])).
tff(53,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred))))))),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))),
inference(or_elim,[status(thm)],[23])).
tff(55,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))),
inference(modus_ponens,[status(thm)],[54, 52])).
tff(56,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))),
inference(modus_ponens,[status(thm)],[55, 53])).
tff(57,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~preda(fred)) | (~(creative(fred) & rich(fred) & quiet(fred) & person(fred)))))),
inference(modus_ponens,[status(thm)],[56, 52])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!9 |'fred'|)
(= X!9 |'paul'|)
(= X!9 |'mary'|)
(not (room X!9)))))
(a!6 (or (not (preda fred))
(not (and (creative fred) (rich fred) (quiet fred) (person fred))))))
(let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 a!6))
(or (not (room mary))
(not (room paul))
(not (room fred))
a!5
(not a!6)))))
(nnf-neg a!1
a!2
a!3
(sk (~ (not a!4) a!5))
(refl (~ (not a!6) (not a!6)))
a!7)))
| room(stephanie)&room(robert)&room(shirley)&(![X]:(room(X)=>(X='stephanie'|X='robert'|X='shirley')))&
((((like(myra,stephanie) & like(stephanie,myra)))=>(~((hate(stephanie,james))|(richer(myra,stephanie)))))&
(((?[X,Y]:(room(X)&room(Y)&(~quiet(X)&~quiet(Y))&(X!=Y))))<=>(~((collects_antique_jewelry(stephanie))|(rich(stephanie)&european(stephanie)))))&
(![X]:(quieter(X,stephanie)))&
(((?[X]:(~room(X)&~like(X,myra)))&(![X,Y]:((~like(X,myra)&~like(Y,myra))=>(X=Y)))))&
((?[X,Y]:(room(X)&room(Y)&(~quiet(X)&~quiet(Y))&(X!=Y))))&
(richer(stephanie,james))&
(?[X,Y]:((richer(james,X))&(like(Y,myra))&(quieter(X,Y))))&
(?[X,Y]:((richer(james,X))&(~(rich(Y)&european(Y)))&(like(X,Y))))&
((?[X,Y]:(room(X)&room(Y)&(~(brave(X)&quiet(X)&rich(X)&european(X))&~(brave(Y)&quiet(Y)&rich(Y)&european(Y)))&(X!=Y))))) | room(stephanie)&room(robert)&room(shirley)&(![X]:(room(X)=>(X='stephanie'|X='robert'|X='shirley')))&
(((~(creative(shirley)&rich(shirley)&quiet(shirley)&person(shirley)))|(does_not_collect_luxury_watches(shirley)))) | neutral | neutral | entailment |
William and Janet are liked by April. | Janet likes April. | neutral | % SZS status Satisfiable
| room(janet)&room(william)&(![X]:(room(X)=>(X='janet'|X='william')))&
(like(william,april)&like(janet,april)) | room(janet)&room(william)&(![X]:(room(X)=>(X='janet'|X='william')))&
(like(april,janet)) | contradiction | neutral | neutral |
Leslie, Janet, Rita, Will are the only persons in the room.
“Leslie and Janet do not hate Kenneth” if “Janet who is not hated by Mary, is right-handed”.
Janet is the least tall in the room.
Janet who is not hated by Mary, is right-handed. | Rita is not right-handed and hates Kenneth. | neutral | % SZS status Satisfiable
| room(leslie)&room(janet)&room(rita)&room(will)&(![X]:(room(X)=>(X='leslie'|X='janet'|X='rita'|X='will')))&
((((~hate(janet,mary))&(is_right-handed(janet)))=>(~hate(kenneth,leslie)&~hate(kenneth,janet)))&
(![X]:(taller(janet,X)))&
((~hate(janet,mary))&(is_right-handed(janet)))) | room(leslie)&room(janet)&room(rita)&room(will)&(![X]:(room(X)=>(X='leslie'|X='janet'|X='rita'|X='will')))&
((is_not_right-handed(rita))&(hate(kenneth,rita))) | neutral | contradiction | neutral |
Ruth, Jessie, Kurt are the only persons in the room.
Kurt who is not Ruth, is liked by Dora.
Ruth is not a happy rich person and is not liked by Justin.
Everyone outside the room who is richer than Justin likes Justin. | Jessie is a happy rich person or is richer than Justin or both. | neutral | % SZS status Satisfiable
| room(ruth)&room(jessie)&room(kurt)&(![X]:(room(X)=>(X='ruth'|X='jessie'|X='kurt')))&
(((kurt!=ruth)&(like(kurt,dora)))&
((~(happy(ruth)&rich(ruth)&person(ruth)))&(~like(ruth,justin)))&
(![X]:(~room(X)=>(((richer(justin,X))=>(like(justin,X))))))) | room(ruth)&room(jessie)&room(kurt)&(![X]:(room(X)=>(X='ruth'|X='jessie'|X='kurt')))&
(((happy(jessie)&rich(jessie)&person(jessie))|(richer(justin,jessie)))) | contradiction | entailment | entailment |
Delores, Joyce, Jerry, Floyd are the only persons in the room. 'Delores who likes Brian, is not a creative brave quiet european' if 'everyone outside the room does not hate Brian'. 'Delores collects first edition books and is not a quiet european' if 'no one outside the room is a brave european'. Someone outside the room collects first edition books. Delores is not quiet, not rich, not brave. Delores neither is not hated by James nor does not collect rare sneakers. Joyce hates Brian or is a tall european or both. | Joyce is a tall happy quiet brave person. | neutral | % SZS status Satisfiable
| room(delores)&room(joyce)&room(jerry)&room(floyd)&(![X]:(room(X)=>(X='delores'|X='joyce'|X='jerry'|X='floyd')))&
(((![X]:(~room(X)=>(~hate(brian,X))))=>((like(brian,delores))&(~(creative(delores)&brave(delores)&quiet(delores)&european(delores)))))&
((~?[X]:(~room(X)=>(brave(X)&european(X))))=>((collects_first_edition_books(delores))&(~(quiet(delores)&european(delores)))))&
(?[X]:(~room(X)=>(collects_first_edition_books(X))))&
(~quiet(delores)&~rich(delores)&~brave(delores))&
(~((~hate(delores,james))|(does_not_collect_rare_sneakers(delores))))&
(((hate(brian,joyce))|(tall(joyce)&european(joyce))))) | room(delores)&room(joyce)&room(jerry)&room(floyd)&(![X]:(room(X)=>(X='delores'|X='joyce'|X='jerry'|X='floyd')))&
(tall(joyce)&happy(joyce)&quiet(joyce)&brave(joyce)&person(joyce)) | contradiction | contradiction | contradiction |
Rodney, Sharon are the only persons in the room.
Steve and Sharon hate each other.
It is not the case that 'Sharon neither is not hated by Kevin nor is not liked by Kevin'.
Someone outside the room who is hated by Kevin does not build model airplanes.
Only one person outside the room is a tall brave european.
Rodney is the tallest in the room.
Sharon is taller than Steve.
It is not the case that 'Sharon is the least tall in the room'.
Someone in the room collects modern art. | Rodney is a tall brave european and works on fridays. | contradiction | - | room(rodney)&room(sharon)&(![X]:(room(X)=>(X='rodney'|X='sharon')))&
(((hate(steve,sharon) & hate(sharon,steve)))&
(~(~((~hate(sharon,kevin))|(~like(sharon,kevin)))))&
(?[X]:(~room(X)=>(((hate(X,kevin))=>(does_not_build_model_airplanes(X))))))&
(((?[X]:(~room(X)&tall(X)&brave(X)&european(X)))&(![X,Y]:((tall(X)&brave(X)&european(X)&tall(Y)&brave(Y)&european(Y))=>(X=Y)))))&
(![X]:(taller(X,rodney)))&
(taller(steve,sharon))&
(~(![X]:(taller(sharon,X))))&
(?[X]:(room(X)=>(collects_modern_art(X))))) | room(rodney)&room(sharon)&(![X]:(room(X)=>(X='rodney'|X='sharon')))&
((tall(rodney)&brave(rodney)&european(rodney))&(works_on_fridays(rodney))) | neutral | neutral | contradiction |
Edna, Carlos, Madeline, Leonard are the only persons in the room. If no one in the room who is a client of Catherine is not hated by Catherine then Catherine is quieter than Carlos. If Carlos and Edna are not a tall creative tourist then it is not the case that 'Edna and Catherine hate each other'. Carlos hates Catherine or is not happy, not tall or both. Carlos and Edna are not a tall creative tourist. Edna who hates Catherine, makes homemade pastries. Carlos is the tallest in the room. | Edna who is not a brave creative tall tourist, is not hated by Catherine. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(tall_type, type, (
tall: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(1,assumption,(~((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary)))), introduced(assumption)).
tff(2,plain,
(((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary))) | tourist(mary)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(tourist(mary)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary))) | creative(mary)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(creative(mary)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
(((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary))) | tall(mary)),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(tall(mary)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
((~(~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))) <=> ((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
((tall(mary) & creative(mary) & tourist(mary)) <=> (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(10,plain,
((~(tall(mary) & creative(mary) & tourist(mary))) <=> (~(~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(monotonicity,[status(thm)],[9])).
tff(11,plain,
((~(tall(mary) & creative(mary) & tourist(mary))) <=> ((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))),
inference(transitivity,[status(thm)],[10, 8])).
tff(12,plain,
((~(tall(mary) & creative(mary) & tourist(mary))) <=> (~(tall(mary) & creative(mary) & tourist(mary)))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~?[X: $i] : (room(X) => (client(john, X) => (~hate(X, john))))) => quieter(paul, john)) & (((~((tall(paul) & creative(paul)) & tourist(paul))) & (~((tall(mary) & creative(mary)) & tourist(mary)))) => (~(hate(mary, john) & hate(john, mary))))) & (hate(john, paul) | ((~happy(paul)) & (~tall(paul))))) & ((~((tall(paul) & creative(paul)) & tourist(paul))) & (~((tall(mary) & creative(mary)) & tourist(mary))))) & (hate(john, mary) & preda(mary))) & ![X: $i] : taller(X, paul))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~(((brave(mary) & creative(mary)) & tall(mary)) & tourist(mary))) & (~hate(mary, john)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(paul, john) | ?[X: $i] : ((~hate(X, john)) | (~room(X)) | (~client(john, X)))) & ((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))) & (hate(john, paul) | ((~happy(paul)) & (~tall(paul)))) & (~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary))) & hate(john, mary) & preda(mary) & ![X: $i] : taller(X, paul))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))))),
inference(rewrite,[status(thm)],[])).
tff(14,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~?[X: $i] : (room(X) => (client(john, X) => (~hate(X, john))))) => quieter(paul, john)) & (((~((tall(paul) & creative(paul)) & tourist(paul))) & (~((tall(mary) & creative(mary)) & tourist(mary)))) => (~(hate(mary, john) & hate(john, mary))))) & (hate(john, paul) | ((~happy(paul)) & (~tall(paul))))) & ((~((tall(paul) & creative(paul)) & tourist(paul))) & (~((tall(mary) & creative(mary)) & tourist(mary))))) & (hate(john, mary) & preda(mary))) & ![X: $i] : taller(X, paul))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~(((brave(mary) & creative(mary)) & tall(mary)) & tourist(mary))) & (~hate(mary, john)))))), file('/mnt/tmpfs//535586968609496806482839.p','negated')).
tff(15,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(paul, john) | ?[X: $i] : ((~hate(X, john)) | (~room(X)) | (~client(john, X)))) & ((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))) & (hate(john, paul) | ((~happy(paul)) & (~tall(paul)))) & (~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary))) & hate(john, mary) & preda(mary) & ![X: $i] : taller(X, paul))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john))))),
inference(modus_ponens,[status(thm)],[14, 13])).
tff(16,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(paul, john) | ?[X: $i] : ((~hate(X, john)) | (~room(X)) | (~client(john, X)))) & ((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))) & (hate(john, paul) | ((~happy(paul)) & (~tall(paul)))) & (~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary))) & hate(john, mary) & preda(mary) & ![X: $i] : taller(X, paul)),
inference(or_elim,[status(thm)],[15])).
tff(17,plain,
(~(tall(mary) & creative(mary) & tourist(mary))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
(~(tall(mary) & creative(mary) & tourist(mary))),
inference(modus_ponens,[status(thm)],[17, 12])).
tff(19,plain,
((~tall(mary)) | (~creative(mary)) | (~tourist(mary))),
inference(modus_ponens,[status(thm)],[18, 11])).
tff(20,plain,
($false),
inference(unit_resolution,[status(thm)],[19, 7, 5, 3])).
tff(21,plain,((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary))), inference(lemma,lemma(discharge,[]))).
tff(22,assumption,(~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))), introduced(assumption)).
tff(23,plain,
(((~tall(paul)) | (~creative(paul)) | (~tourist(paul))) | tourist(paul)),
inference(tautology,[status(thm)],[])).
tff(24,plain,
(tourist(paul)),
inference(unit_resolution,[status(thm)],[23, 22])).
tff(25,plain,
(((~tall(paul)) | (~creative(paul)) | (~tourist(paul))) | tall(paul)),
inference(tautology,[status(thm)],[])).
tff(26,plain,
(tall(paul)),
inference(unit_resolution,[status(thm)],[25, 22])).
tff(27,plain,
(((~tall(paul)) | (~creative(paul)) | (~tourist(paul))) | creative(paul)),
inference(tautology,[status(thm)],[])).
tff(28,plain,
(creative(paul)),
inference(unit_resolution,[status(thm)],[27, 22])).
tff(29,plain,
((~(~((~tall(paul)) | (~creative(paul)) | (~tourist(paul))))) <=> ((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))),
inference(rewrite,[status(thm)],[])).
tff(30,plain,
((tall(paul) & creative(paul) & tourist(paul)) <=> (~((~tall(paul)) | (~creative(paul)) | (~tourist(paul))))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
((~(tall(paul) & creative(paul) & tourist(paul))) <=> (~(~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))))),
inference(monotonicity,[status(thm)],[30])).
tff(32,plain,
((~(tall(paul) & creative(paul) & tourist(paul))) <=> ((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))),
inference(transitivity,[status(thm)],[31, 29])).
tff(33,plain,
((~(tall(paul) & creative(paul) & tourist(paul))) <=> (~(tall(paul) & creative(paul) & tourist(paul)))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(~(tall(paul) & creative(paul) & tourist(paul))),
inference(and_elim,[status(thm)],[16])).
tff(35,plain,
(~(tall(paul) & creative(paul) & tourist(paul))),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
((~tall(paul)) | (~creative(paul)) | (~tourist(paul))),
inference(modus_ponens,[status(thm)],[35, 32])).
tff(37,plain,
($false),
inference(unit_resolution,[status(thm)],[36, 28, 26, 24])).
tff(38,plain,((~tall(paul)) | (~creative(paul)) | (~tourist(paul))), inference(lemma,lemma(discharge,[]))).
tff(39,assumption,(~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))), introduced(assumption)).
tff(40,plain,
(((~tall(mary)) | (~creative(mary)) | (~tourist(mary))) | tourist(mary)),
inference(tautology,[status(thm)],[])).
tff(41,plain,
(tourist(mary)),
inference(unit_resolution,[status(thm)],[40, 39])).
tff(42,plain,
(((~tall(mary)) | (~creative(mary)) | (~tourist(mary))) | tall(mary)),
inference(tautology,[status(thm)],[])).
tff(43,plain,
(tall(mary)),
inference(unit_resolution,[status(thm)],[42, 39])).
tff(44,plain,
(((~tall(mary)) | (~creative(mary)) | (~tourist(mary))) | creative(mary)),
inference(tautology,[status(thm)],[])).
tff(45,plain,
(creative(mary)),
inference(unit_resolution,[status(thm)],[44, 39])).
tff(46,plain,
($false),
inference(unit_resolution,[status(thm)],[19, 45, 43, 41])).
tff(47,plain,((~tall(mary)) | (~creative(mary)) | (~tourist(mary))), inference(lemma,lemma(discharge,[]))).
tff(48,plain,
(hate(john, mary) <=> hate(john, mary)),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
(hate(john, mary)),
inference(and_elim,[status(thm)],[16])).
tff(50,plain,
(hate(john, mary)),
inference(modus_ponens,[status(thm)],[49, 48])).
tff(51,plain,
((((~hate(mary, john)) | (~hate(john, mary))) | ((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))))) <=> ((~hate(mary, john)) | (~hate(john, mary)) | (~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
((~(~((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))))) <=> ((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(53,plain,
((((~tall(paul)) | (~creative(paul)) | (~tourist(paul))) & ((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))) <=> (~((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))) <=> (((~tall(paul)) | (~creative(paul)) | (~tourist(paul))) & ((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(monotonicity,[status(thm)],[32, 11])).
tff(55,plain,
(((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))) <=> (~((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))))),
inference(transitivity,[status(thm)],[54, 53])).
tff(56,plain,
((~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary))))) <=> (~(~((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))))))),
inference(monotonicity,[status(thm)],[55])).
tff(57,plain,
((~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary))))) <=> ((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(transitivity,[status(thm)],[56, 52])).
tff(58,plain,
((~(~((~hate(mary, john)) | (~hate(john, mary))))) <=> ((~hate(mary, john)) | (~hate(john, mary)))),
inference(rewrite,[status(thm)],[])).
tff(59,plain,
((hate(mary, john) & hate(john, mary)) <=> (~((~hate(mary, john)) | (~hate(john, mary))))),
inference(rewrite,[status(thm)],[])).
tff(60,plain,
((~(hate(mary, john) & hate(john, mary))) <=> (~(~((~hate(mary, john)) | (~hate(john, mary)))))),
inference(monotonicity,[status(thm)],[59])).
tff(61,plain,
((~(hate(mary, john) & hate(john, mary))) <=> ((~hate(mary, john)) | (~hate(john, mary)))),
inference(transitivity,[status(thm)],[60, 58])).
tff(62,plain,
(((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))) <=> (((~hate(mary, john)) | (~hate(john, mary))) | ((~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))))),
inference(monotonicity,[status(thm)],[61, 57])).
tff(63,plain,
(((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))) <=> ((~hate(mary, john)) | (~hate(john, mary)) | (~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary)))))),
inference(transitivity,[status(thm)],[62, 51])).
tff(64,plain,
(((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))) <=> ((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(65,plain,
((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))),
inference(and_elim,[status(thm)],[16])).
tff(66,plain,
((~(hate(mary, john) & hate(john, mary))) | (~((~(tall(paul) & creative(paul) & tourist(paul))) & (~(tall(mary) & creative(mary) & tourist(mary)))))),
inference(modus_ponens,[status(thm)],[65, 64])).
tff(67,plain,
((~hate(mary, john)) | (~hate(john, mary)) | (~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(modus_ponens,[status(thm)],[66, 63])).
tff(68,plain,
((~hate(mary, john)) | (~((~tall(paul)) | (~creative(paul)) | (~tourist(paul)))) | (~((~tall(mary)) | (~creative(mary)) | (~tourist(mary))))),
inference(unit_resolution,[status(thm)],[67, 50])).
tff(69,plain,
(~hate(mary, john)),
inference(unit_resolution,[status(thm)],[68, 47, 38])).
tff(70,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(71,plain,
(room(alice)),
inference(and_elim,[status(thm)],[16])).
tff(72,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[71, 70])).
tff(73,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(74,plain,
(room(fred)),
inference(and_elim,[status(thm)],[16])).
tff(75,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[74, 73])).
tff(76,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(77,plain,
(room(paul)),
inference(and_elim,[status(thm)],[16])).
tff(78,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[77, 76])).
tff(79,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(80,plain,
(room(mary)),
inference(and_elim,[status(thm)],[16])).
tff(81,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[80, 79])).
tff(82,plain,
((hate(mary, john) | (~((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> (hate(mary, john) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(83,plain,
((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(84,plain,
((brave(mary) & creative(mary) & tall(mary) & tourist(mary)) <=> (~((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary))))),
inference(rewrite,[status(thm)],[])).
tff(85,plain,
((hate(mary, john) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> (hate(mary, john) | (~((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))),
inference(monotonicity,[status(thm)],[84, 83])).
tff(86,plain,
((hate(mary, john) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> (hate(mary, john) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~((~brave(mary)) | (~creative(mary)) | (~tall(mary)) | (~tourist(mary)))))),
inference(transitivity,[status(thm)],[85, 82])).
tff(87,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | hate(mary, john)) <=> (hate(mary, john) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))),
inference(rewrite,[status(thm)],[])).
tff(88,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | hate(mary, john)) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | hate(mary, john))),
inference(monotonicity,[status(thm)],[83])).
tff(89,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | hate(mary, john)) <=> (hate(mary, john) | (brave(mary) & creative(mary) & tall(mary) & tourist(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))),
inference(transitivity,[status(thm)],[88, 87])).
tff(90,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))),
inference(rewrite,[status(thm)],[])).
tff(91,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john))))),
inference(monotonicity,[status(thm)],[90])).
tff(92,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john))))),
inference(rewrite,[status(thm)],[])).
tff(93,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))),
inference(or_elim,[status(thm)],[15])).
tff(94,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))),
inference(modus_ponens,[status(thm)],[93, 91])).
tff(95,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))),
inference(modus_ponens,[status(thm)],[94, 92])).
tff(96,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(mary) & creative(mary) & tall(mary) & tourist(mary))) & (~hate(mary, john)))),
inference(modus_ponens,[status(thm)],[95, 91])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!1 |'alice'|)
(= X!1 |'fred'|)
(= X!1 |'paul'|)
(= X!1 |'mary'|)
(not (room X!1)))))
(a!7 (refl (~ (and (brave mary)
(creative mary)
(tall mary)
(tourist mary))
(and (brave mary)
(creative mary)
(tall mary)
(tourist mary))))))
(let ((a!8 (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(not (and (brave mary)
(creative mary)
(tall mary)
(tourist mary)))
(not (hate mary john)))))
(let ((a!9 (~ (not a!8)
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(and (brave mary) (creative mary) (tall mary) (tourist mary))
(hate mary john)))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
a!7
(refl (~ (hate mary john) (hate mary john)))
a!9))))
| room(edna)&room(carlos)&room(madeline)&room(leonard)&(![X]:(room(X)=>(X='edna'|X='carlos'|X='madeline'|X='leonard')))&
(((~?[X]:(room(X)=>(((client(catherine,X))=>(~hate(X,catherine))))))=>(quieter(carlos,catherine)))&
((~(tall(carlos)&creative(carlos)&tourist(carlos))&~(tall(edna)&creative(edna)&tourist(edna)))=>(~((hate(edna,catherine) & hate(catherine,edna)))))&
(((hate(catherine,carlos))|(~happy(carlos)&~tall(carlos))))&
(~(tall(carlos)&creative(carlos)&tourist(carlos))&~(tall(edna)&creative(edna)&tourist(edna)))&
((hate(catherine,edna))&(makes_homemade_pastries(edna)))&
(![X]:(taller(X,carlos)))) | room(edna)&room(carlos)&room(madeline)&room(leonard)&(![X]:(room(X)=>(X='edna'|X='carlos'|X='madeline'|X='leonard')))&
((~(brave(edna)&creative(edna)&tall(edna)&tourist(edna)))&(~hate(edna,catherine))) | neutral | contradiction | contradiction |
If 'Kenneth is richer than Betty' then 'Betty collects action figures or is richer than Kenneth or both'.
Kenneth is richer than Betty.
Sharon and Kenneth like each other. | Betty neither does not collect action figures nor is richer than Kenneth. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(mary_type, type, (
mary: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(predc_type, type, (
predc: $i > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(susan_type, type, (
susan: $i)).
tff(john_type, type, (
john: $i)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(1,plain,
(richer(mary, lucy) <=> richer(mary, lucy)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((richer(mary, lucy) => (predc(mary) | richer(lucy, mary))) & richer(mary, lucy)) & (like(paul, lucy) & like(lucy, paul)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((~predc(mary)) | richer(lucy, mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))) & richer(mary, lucy) & like(paul, lucy) & like(lucy, paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((richer(mary, lucy) => (predc(mary) | richer(lucy, mary))) & richer(mary, lucy)) & (like(paul, lucy) & like(lucy, paul)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((~predc(mary)) | richer(lucy, mary)))))), file('/mnt/tmpfs//8289623707661099813265802.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))) & richer(mary, lucy) & like(paul, lucy) & like(lucy, paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))) & richer(mary, lucy) & like(paul, lucy) & like(lucy, paul)),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(richer(mary, lucy)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(richer(mary, lucy)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,assumption,(~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))), introduced(assumption)).
tff(9,plain,
(((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | room(X!0)),
inference(tautology,[status(thm)],[])).
tff(10,plain,
(room(X!0)),
inference(unit_resolution,[status(thm)],[9, 8])).
tff(11,plain,
(((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(12,plain,
(~(X!0 = |'mary'|)),
inference(unit_resolution,[status(thm)],[11, 8])).
tff(13,plain,
(((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(14,plain,
(~(X!0 = |'paul'|)),
inference(unit_resolution,[status(thm)],[13, 8])).
tff(15,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(16,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[15])).
tff(17,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[5])).
tff(19,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[18, 17])).
tff(20,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[19])).
tff(21,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[20, 16])).
tff(22,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))),
inference(quant_inst,[status(thm)],[])).
tff(24,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))),
inference(modus_ponens,[status(thm)],[23, 22])).
tff(25,plain,
($false),
inference(unit_resolution,[status(thm)],[24, 21, 14, 12, 10])).
tff(26,plain,((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))), inference(lemma,lemma(discharge,[]))).
tff(27,assumption,(~richer(lucy, mary)), introduced(assumption)).
tff(28,plain,
((predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))) <=> (predc(mary) | richer(lucy, mary) | (~richer(mary, lucy)))),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
(predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))),
inference(and_elim,[status(thm)],[5])).
tff(30,plain,
(predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))),
inference(modus_ponens,[status(thm)],[29, 28])).
tff(31,plain,
(predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))),
inference(modus_ponens,[status(thm)],[30, 28])).
tff(32,plain,
(predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))),
inference(modus_ponens,[status(thm)],[31, 28])).
tff(33,plain,
(predc(mary) | richer(lucy, mary) | (~richer(mary, lucy))),
inference(modus_ponens,[status(thm)],[32, 28])).
tff(34,plain,
(predc(mary) | richer(lucy, mary)),
inference(unit_resolution,[status(thm)],[33, 7])).
tff(35,plain,
(predc(mary)),
inference(unit_resolution,[status(thm)],[34, 27])).
tff(36,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(38,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[37, 36])).
tff(39,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(41,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[40, 39])).
tff(42,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ((~predc(mary)) | richer(lucy, mary))) <=> (richer(lucy, mary) | (~predc(mary)) | (~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
((~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ((~predc(mary)) | richer(lucy, mary))) <=> ((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ((~predc(mary)) | richer(lucy, mary)))),
inference(monotonicity,[status(thm)],[43])).
tff(45,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ((~predc(mary)) | richer(lucy, mary))) <=> (richer(lucy, mary) | (~predc(mary)) | (~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))),
inference(transitivity,[status(thm)],[44, 42])).
tff(46,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))),
inference(rewrite,[status(thm)],[])).
tff(47,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary)))))),
inference(monotonicity,[status(thm)],[46])).
tff(48,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary)))))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))),
inference(or_elim,[status(thm)],[4])).
tff(50,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))),
inference(modus_ponens,[status(thm)],[49, 47])).
tff(51,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))),
inference(modus_ponens,[status(thm)],[50, 48])).
tff(52,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~predc(mary)) | richer(lucy, mary))))),
inference(modus_ponens,[status(thm)],[51, 47])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0)))))
(a!5 (~ (or (not (predc mary)) (richer lucy mary))
(or (not (predc mary)) (richer lucy mary))))
(a!6 (not (or (not (predc mary)) (richer lucy mary)))))
(let ((a!7 (or (not (room mary))
(not (room paul))
a!4
(or (not (predc mary)) (richer lucy mary)))))
(let ((a!8 (~ (not (and (room mary) (room paul) a!3 a!6)) a!7)))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl a!5) a!8))))
| room(betty)&room(sharon)&(![X]:(room(X)=>(X='betty'|X='sharon')))&
(((richer(betty,kenneth))=>(((collects_action_figures(betty))|(richer(kenneth,betty)))))&
(richer(betty,kenneth))&
((like(sharon,kenneth) & like(kenneth,sharon)))) | room(betty)&room(sharon)&(![X]:(room(X)=>(X='betty'|X='sharon')))&
(~((does_not_collect_action_figures(betty))|(richer(kenneth,betty)))) | neutral | contradiction | contradiction |
None of the following is true:.
-Nathan is not liked by Anthony or does not like Anthony or both.
-Nathan either does not enjoy spelunking or is not liked by Anthony. | Anthony and Nathan like each other. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(susan_type, type, (
susan: $i)).
tff(paul_type, type, (
paul: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(1,plain,
(like(susan, mary) <=> like(susan, mary)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((~like(mary, susan)) | (~like(susan, mary))) | (((~preda(mary)) | (~like(mary, susan))) & (~((~preda(mary)) | (~like(mary, susan)))))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(susan, mary) & like(mary, susan))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~like(mary, susan)) | (~like(susan, mary)))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((~like(mary, susan)) | (~like(susan, mary))) | (((~preda(mary)) | (~like(mary, susan))) & (~((~preda(mary)) | (~like(mary, susan)))))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(susan, mary) & like(mary, susan))))), file('/mnt/tmpfs//7840199516688146450388042.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~like(mary, susan)) | (~like(susan, mary)))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan)))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~like(mary, susan)) | (~like(susan, mary))))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~((~like(mary, susan)) | (~like(susan, mary)))),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(like(susan, mary)),
inference(or_elim,[status(thm)],[6])).
tff(8,plain,
(like(susan, mary)),
inference(modus_ponens,[status(thm)],[7, 1])).
tff(9,plain,
(like(mary, susan) <=> like(mary, susan)),
inference(rewrite,[status(thm)],[])).
tff(10,plain,
(like(mary, susan)),
inference(or_elim,[status(thm)],[6])).
tff(11,plain,
(like(mary, susan)),
inference(modus_ponens,[status(thm)],[10, 9])).
tff(12,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(14,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(17,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~like(susan, mary)) | (~like(mary, susan))) <=> ((~like(mary, susan)) | (~like(susan, mary)) | (~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~like(susan, mary)) | (~like(mary, susan))) <=> ((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~like(susan, mary)) | (~like(mary, susan)))),
inference(monotonicity,[status(thm)],[19])).
tff(21,plain,
(((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~like(susan, mary)) | (~like(mary, susan))) <=> ((~like(mary, susan)) | (~like(susan, mary)) | (~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))),
inference(transitivity,[status(thm)],[20, 18])).
tff(22,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan)) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan)))),
inference(monotonicity,[status(thm)],[22])).
tff(24,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan)))),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))),
inference(or_elim,[status(thm)],[4])).
tff(26,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))),
inference(modus_ponens,[status(thm)],[25, 23])).
tff(27,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))),
inference(modus_ponens,[status(thm)],[26, 24])).
tff(28,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(susan, mary) & like(mary, susan))),
inference(modus_ponens,[status(thm)],[27, 23])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0)))))
(a!5 (refl (~ (not (like susan mary)) (not (like susan mary)))))
(a!6 (refl (~ (not (like mary susan)) (not (like mary susan))))))
(let ((a!7 (~ (not (and (room mary)
(room paul)
a!3
(like susan mary)
(like mary susan)))
(or (not (room mary))
(not (room paul))
a!4
(not (like susan mary))
(not (like mary susan))))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5 a!6 a!7)))
| room(nathan)&room(william)&(![X]:(room(X)=>(X='nathan'|X='william')))&
(~((((~like(nathan,anthony))|(~like(anthony,nathan))))|((((does_not_enjoy_spelunking(nathan))|(~like(nathan,anthony)))&(~((does_not_enjoy_spelunking(nathan))|(~like(nathan,anthony)))))))) | room(nathan)&room(william)&(![X]:(room(X)=>(X='nathan'|X='william')))&
((like(anthony,nathan) & like(nathan,anthony))) | contradiction | neutral | contradiction |
Nancy, Roger, Frank are the only persons in the room.
“More than one person outside the room is not Roger” if “Roger either is a tall tourist or is not a rich tourist”.
“Heather is a sibling of Roger” if “Roger is a brave tourist” and vice versa.
“Roger is the least tall in the room” if “Roger either is not hated by Heather or is not hated by David” and vice versa.
Heather and David hate each other.
Roger neither is hated by David nor practices urban gardening.
Roger neither is a rich brave tall creative tourist nor is not hated by Heather.
Heather is a client of Roger.
Roger is a brave tourist. | Someone who is a brave tourist hate someone who does not like David. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(alice_type, type, (
alice: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(brave_type, type, (
brave: $i > $o)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(mary_type, type, (
mary: $i)).
tff(john_type, type, (
john: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(1,plain,
(hate(alice, susan) <=> hate(alice, susan)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((tall(paul) & tourist(paul)) | (~(rich(paul) & tourist(paul)))) & (~((tall(paul) & tourist(paul)) | (~(rich(paul) & tourist(paul)))))) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = paul)) & (~(Y = paul)))) & (~(X = Y)))) & ((brave(paul) & tourist(paul)) <=> sibling(paul, susan))) & ((((~hate(paul, susan)) | (~hate(paul, alice))) & (~((~hate(paul, susan)) | (~hate(paul, alice))))) <=> ![X: $i] : taller(paul, X))) & (hate(susan, alice) & hate(alice, susan))) & (~(hate(paul, alice) | predc(paul)))) & (~(((((rich(paul) & brave(paul)) & tall(paul)) & creative(paul)) & tourist(paul)) | (~hate(paul, susan))))) & client(paul, susan)) & (brave(paul) & tourist(paul)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((brave(X) & tourist(X)) & (~like(alice, Y))) & hate(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((brave(paul) & tourist(paul)) <=> sibling(paul, susan)) & (~![X: $i] : taller(paul, X)) & hate(susan, alice) & hate(alice, susan) & (~(hate(paul, alice) | predc(paul))) & (~((~hate(paul, susan)) | (rich(paul) & brave(paul) & tall(paul) & creative(paul) & tourist(paul)))) & client(paul, susan) & brave(paul) & tourist(paul))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((tall(paul) & tourist(paul)) | (~(rich(paul) & tourist(paul)))) & (~((tall(paul) & tourist(paul)) | (~(rich(paul) & tourist(paul)))))) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = paul)) & (~(Y = paul)))) & (~(X = Y)))) & ((brave(paul) & tourist(paul)) <=> sibling(paul, susan))) & ((((~hate(paul, susan)) | (~hate(paul, alice))) & (~((~hate(paul, susan)) | (~hate(paul, alice))))) <=> ![X: $i] : taller(paul, X))) & (hate(susan, alice) & hate(alice, susan))) & (~(hate(paul, alice) | predc(paul)))) & (~(((((rich(paul) & brave(paul)) & tall(paul)) & creative(paul)) & tourist(paul)) | (~hate(paul, susan))))) & client(paul, susan)) & (brave(paul) & tourist(paul)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((brave(X) & tourist(X)) & (~like(alice, Y))) & hate(X, Y))))), file('/mnt/tmpfs//7184807268001402352967404.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((brave(paul) & tourist(paul)) <=> sibling(paul, susan)) & (~![X: $i] : taller(paul, X)) & hate(susan, alice) & hate(alice, susan) & (~(hate(paul, alice) | predc(paul))) & (~((~hate(paul, susan)) | (rich(paul) & brave(paul) & tall(paul) & creative(paul) & tourist(paul)))) & client(paul, susan) & brave(paul) & tourist(paul))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((brave(paul) & tourist(paul)) <=> sibling(paul, susan)) & (~![X: $i] : taller(paul, X)) & hate(susan, alice) & hate(alice, susan) & (~(hate(paul, alice) | predc(paul))) & (~((~hate(paul, susan)) | (rich(paul) & brave(paul) & tall(paul) & creative(paul) & tourist(paul)))) & client(paul, susan) & brave(paul) & tourist(paul)),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(hate(alice, susan)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(hate(alice, susan)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
((~(alice = susan)) <=> (~(alice = susan))),
inference(rewrite,[status(thm)],[])).
tff(9,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//7184807268001402352967404.p','b14')).
tff(10,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[10])).
tff(12,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[11])).
tff(13,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[13])).
tff(15,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[17])).
tff(19,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(~(alice = susan)),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
(~(alice = susan)),
inference(modus_ponens,[status(thm)],[29, 8])).
tff(31,plain,
(^[X: $i, Y: $i] : refl(((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y))))),
inference(bind,[status(th)],[])).
tff(32,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(quant_intro,[status(thm)],[31])).
tff(33,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite((like(X, Y) => (~hate(X, Y))) <=> ((~hate(X, Y)) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))))), rewrite(((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))))),
inference(bind,[status(th)],[])).
tff(35,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(quant_intro,[status(thm)],[34])).
tff(36,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y))))), file('/mnt/tmpfs//7184807268001402352967404.p','b0')).
tff(37,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[36, 35])).
tff(38,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[37, 33])).
tff(39,plain,(
![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(skolemize,[status(sab)],[38])).
tff(40,plain,
(![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))),
inference(modus_ponens,[status(thm)],[39, 32])).
tff(41,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((alice = susan) | (~hate(alice, susan)) | (~like(alice, susan)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (alice = susan) | (~hate(alice, susan)) | (~like(alice, susan)))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(((~hate(alice, susan)) | (alice = susan) | (~like(alice, susan))) <=> ((alice = susan) | (~hate(alice, susan)) | (~like(alice, susan)))),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(alice, susan)) | (alice = susan) | (~like(alice, susan)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((alice = susan) | (~hate(alice, susan)) | (~like(alice, susan))))),
inference(monotonicity,[status(thm)],[42])).
tff(44,plain,
(((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(alice, susan)) | (alice = susan) | (~like(alice, susan)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (alice = susan) | (~hate(alice, susan)) | (~like(alice, susan)))),
inference(transitivity,[status(thm)],[43, 41])).
tff(45,plain,
((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(alice, susan)) | (alice = susan) | (~like(alice, susan)))),
inference(quant_inst,[status(thm)],[])).
tff(46,plain,
((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (alice = susan) | (~hate(alice, susan)) | (~like(alice, susan))),
inference(modus_ponens,[status(thm)],[45, 44])).
tff(47,plain,
(~like(alice, susan)),
inference(unit_resolution,[status(thm)],[46, 40, 30, 7])).
tff(48,assumption,(~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))), introduced(assumption)).
tff(49,plain,
(((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | room(X!1)),
inference(tautology,[status(thm)],[])).
tff(50,plain,
(room(X!1)),
inference(unit_resolution,[status(thm)],[49, 48])).
tff(51,plain,
(((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(52,plain,
(~(X!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[51, 48])).
tff(53,plain,
(((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(54,plain,
(~(X!1 = |'paul'|)),
inference(unit_resolution,[status(thm)],[53, 48])).
tff(55,plain,
(((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(56,plain,
(~(X!1 = |'fred'|)),
inference(unit_resolution,[status(thm)],[55, 48])).
tff(57,plain,
(^[X: $i] : refl(((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(58,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[57])).
tff(59,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(60,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[5])).
tff(61,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[60, 59])).
tff(62,plain,(
![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[61])).
tff(63,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[62, 58])).
tff(64,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(rewrite,[status(thm)],[])).
tff(65,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(quant_inst,[status(thm)],[])).
tff(66,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))),
inference(modus_ponens,[status(thm)],[65, 64])).
tff(67,plain,
($false),
inference(unit_resolution,[status(thm)],[66, 63, 56, 54, 52, 50])).
tff(68,plain,((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))), inference(lemma,lemma(discharge,[]))).
tff(69,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(70,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(71,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[70, 69])).
tff(72,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(73,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(74,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[73, 72])).
tff(75,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(76,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(77,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[76, 75])).
tff(78,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X))))),
inference(rewrite,[status(thm)],[])).
tff(79,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X))))),
inference(rewrite,[status(thm)],[])).
tff(80,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite((brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)) <=> (~((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X))))), ((~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))) <=> (~(~((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X))))))), rewrite((~(~((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X))))) <=> ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X)))), ((~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))) <=> ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X)))))),
inference(bind,[status(th)],[])).
tff(81,plain,
(![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X)))),
inference(quant_intro,[status(thm)],[80])).
tff(82,plain,
((~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(83,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X))))),
inference(monotonicity,[status(thm)],[82, 81])).
tff(84,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : ((~hate(X, Y)) | like(alice, Y) | (~brave(X)) | (~tourist(X))))),
inference(transitivity,[status(thm)],[83, 79])).
tff(85,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(86,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))))),
inference(monotonicity,[status(thm)],[82])).
tff(87,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))))),
inference(transitivity,[status(thm)],[86, 85])).
tff(88,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(89,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))))),
inference(monotonicity,[status(thm)],[88])).
tff(90,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(91,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))),
inference(or_elim,[status(thm)],[4])).
tff(92,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))),
inference(modus_ponens,[status(thm)],[91, 89])).
tff(93,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))),
inference(modus_ponens,[status(thm)],[92, 90])).
tff(94,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~like(alice, Y)) & hate(X, Y)))),
inference(modus_ponens,[status(thm)],[93, 89])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!1 |'fred'|)
(= X!1 |'paul'|)
(= X!1 |'mary'|)
(not (room X!1)))))
(a!6 (lambda ((X $i) (Y $i))
(let ((a!1 (and (brave X)
(tourist X)
(not (like alice Y))
(hate X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!7 (exists ((X $i) (Y $i))
(and (brave X) (tourist X) (not (like alice Y)) (hate X Y))))
(a!8 (forall ((X $i) (Y $i))
(let ((a!1 (and (brave X)
(tourist X)
(not (like alice Y))
(hate X Y))))
(not a!1)))))
(let ((a!9 (~ (not (and (room mary) (room paul) (room fred) a!4 a!7))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!8))))
(nnf-neg a!1
a!2
a!3
(sk (~ (not a!4) a!5))
(nnf-neg (proof-bind a!6) (~ (not a!7) a!8))
a!9)))
| room(nancy)&room(roger)&room(frank)&(![X]:(room(X)=>(X='nancy'|X='roger'|X='frank')))&
((((((tall(roger)&tourist(roger))|(~(rich(roger)&tourist(roger))))&(~((tall(roger)&tourist(roger))|(~(rich(roger)&tourist(roger)))))))=>((?[X,Y]:(~room(X)&~room(Y)&(X!=roger&Y!=roger)&(X!=Y)))))&
((brave(roger)&tourist(roger))<=>(sibling(roger,heather)))&
(((((~hate(roger,heather))|(~hate(roger,david)))&(~((~hate(roger,heather))|(~hate(roger,david))))))<=>(![X]:(taller(roger,X))))&
((hate(heather,david) & hate(david,heather)))&
(~((hate(roger,david))|(practices_urban_gardening(roger))))&
(~((rich(roger)&brave(roger)&tall(roger)&creative(roger)&tourist(roger))|(~hate(roger,heather))))&
(client(roger,heather))&
(brave(roger)&tourist(roger))) | room(nancy)&room(roger)&room(frank)&(![X]:(room(X)=>(X='nancy'|X='roger'|X='frank')))&
(?[X,Y]:((brave(X)&tourist(X))&(~like(david,Y))&(hate(X,Y)))) | entailment | neutral | neutral |
Peter, Michael are the only persons in the room.
"Michael who does not can play the harmonica, does not enjoy spelunking" if "Peter is the least tall in the room".
"No one outside the room does not can play the harmonica" if "Michael is not brave or does not hate Howard or both" and vice versa.
If "James is quieter than Peter" then "Peter is not creative" otherwise "Michael does not enjoy spelunking".
Only one person outside the room does not hate Charles.
Someone outside the room who does not can play the harmonica does not hate James. | Michael who is hated by Charles, is not brave, not creative. | contradiction | - | room(peter)&room(michael)&(![X]:(room(X)=>(X='peter'|X='michael')))&
(((![X]:(taller(peter,X)))=>((does_not_can_play_the_harmonica(michael))&(does_not_enjoy_spelunking(michael))))&
((((~brave(michael))|(~hate(howard,michael))))<=>(~?[X]:(~room(X)=>(does_not_can_play_the_harmonica(X)))))&
(((quieter(peter,james))=>(~creative(peter)))|((~(quieter(peter,james)))=>(does_not_enjoy_spelunking(michael))))&
(((?[X]:(~room(X)&~hate(charles,X)))&(![X,Y]:((~hate(charles,X)&~hate(charles,Y))=>(X=Y)))))&
(?[X]:(~room(X)=>(((does_not_can_play_the_harmonica(X))=>(~hate(james,X))))))) | room(peter)&room(michael)&(![X]:(room(X)=>(X='peter'|X='michael')))&
((hate(michael,charles))&(~brave(michael)&~creative(michael))) | neutral | neutral | neutral |
Sheila is the only person in the room.
"Sheila either does not practice graffiti art or practices graffiti art" only if "someone who is a quiet tourist is quieter than someone who does not practice graffiti art".
If "Sheila who does not hate Dallas, is a rich tourist" then "Renee and Sheila hate each other" otherwise "Sheila and Dallas hate each other".
Someone who is a quiet tourist is quieter than someone who does not practice graffiti art.
Renee is a sibling of Sheila.
Sheila who is hated by Frank, is hated by Renee.
Everyone outside the room who is not rich is not quiet.
Only one person outside the room is not a quiet happy european.
Sheila does not hate Frank or is a creative rich happy european or both. | Sheila is not rich or is not a creative quiet person or both. | neutral | % SZS status Satisfiable
| room(sheila)&(![X]:(room(X)=>(X='sheila')))&
((((((does_not_practice_graffiti_art(sheila))|(practices_graffiti_art(sheila)))&(~((does_not_practice_graffiti_art(sheila))|(practices_graffiti_art(sheila))))))=>(?[X,Y]:((quiet(X)&tourist(X))&(does_not_practice_graffiti_art(Y))&(quieter(X,Y)))))&
((((~hate(dallas,sheila))&(rich(sheila)&tourist(sheila)))=>((hate(renee,sheila) & hate(sheila,renee))))|((~((~hate(dallas,sheila))&(rich(sheila)&tourist(sheila))))=>((hate(sheila,dallas) & hate(dallas,sheila)))))&
(?[X,Y]:((quiet(X)&tourist(X))&(does_not_practice_graffiti_art(Y))&(quieter(X,Y))))&
(sibling(sheila,renee))&
((hate(sheila,frank))&(hate(sheila,renee)))&
(![X]:(~room(X)=>(((~rich(X))=>(~quiet(X))))))&
(((?[X]:(~room(X)&~(quiet(X)&happy(X)&european(X))))&(![X,Y]:((~(quiet(X)&happy(X)&european(X))&~(quiet(Y)&happy(Y)&european(Y)))=>(X=Y)))))&
(((~hate(frank,sheila))|(creative(sheila)&rich(sheila)&happy(sheila)&european(sheila))))) | room(sheila)&(![X]:(room(X)=>(X='sheila')))&
(((~rich(sheila))|(~(creative(sheila)&quiet(sheila)&person(sheila))))) | contradiction | entailment | contradiction |
James, Kristen, Bernice are the only persons in the room.
If 'someone outside the room is not hated by Marshall' then 'it is not the case that 'only one person outside the room hates Marshall'' otherwise 'James neither is a happy tourist nor is not quiet, not rich, not creative'.
'Only one person outside the room is a creative tourist' unless 'Bernice and Marshall hate each other'.
'Someone who does not hate Marshall hate someone who is not Bernice' only if 'James hates Marshall'.
Bernice and James are not hated by Marshall.
James is the least quiet in the room.
Someone who is not James is quieter than someone who is not quiet.
Someone who hates Marshall is a sibling of someone who is a brave rich tourist.
Only one person outside the room does not enjoy macrame.
James and Bernice are respectively happy and brave. | Kristen and Bernice are not a creative happy rich brave quiet tourist. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(paul_type, type, (
paul: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun_X_6_type, type, (
tptp_fun_X_6: $i)).
tff(1,assumption,(X!0 = paul), introduced(assumption)).
tff(2,plain,
(room(X!0) <=> room(paul)),
inference(monotonicity,[status(thm)],[1])).
tff(3,plain,
(room(paul) <=> room(X!0)),
inference(symmetry,[status(thm)],[2])).
tff(4,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((?[X: $i] : ((~room(X)) => (~hate(X, alice))) => (~(?[X: $i] : ((~room(X)) & hate(alice, X)) & ![X: $i, Y: $i] : ((hate(alice, X) & hate(alice, Y)) => (X = Y))))) | ((~?[X: $i] : ((~room(X)) => (~hate(X, alice)))) => (~((happy(mary) & tourist(mary)) | (((~quiet(mary)) & (~rich(mary))) & (~creative(mary))))))) & ((~(hate(fred, alice) & hate(alice, fred))) => (?[X: $i] : (((~room(X)) & creative(X)) & tourist(X)) & ![X: $i, Y: $i] : ((((creative(X) & tourist(X)) & creative(Y)) & tourist(Y)) => (X = Y))))) & (?[X: $i, Y: $i] : (((~hate(alice, X)) & (~(Y = fred))) & hate(X, Y)) => hate(alice, mary))) & ((~hate(fred, alice)) & (~hate(mary, alice)))) & ![X: $i] : quieter(mary, X)) & ?[X: $i, Y: $i] : (((~(X = mary)) & (~quiet(Y))) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((hate(alice, X) & ((brave(Y) & rich(Y)) & tourist(Y))) & sibling(X, Y))) & (?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : (((~predb(X)) & (~predb(Y))) => (X = Y)))) & (happy(mary) & brave(fred)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~(((((creative(paul) & happy(paul)) & rich(paul)) & brave(paul)) & quiet(paul)) & tourist(paul))) & (~(((((creative(fred) & happy(fred)) & rich(fred)) & brave(fred)) & quiet(fred)) & tourist(fred))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))) & ((~?[X: $i, Y: $i] : ((~hate(alice, X)) & (~(Y = fred)) & hate(X, Y))) | hate(alice, mary)) & (~hate(fred, alice)) & (~hate(mary, alice)) & ![X: $i] : quieter(mary, X) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~quiet(Y)) & quieter(X, Y)) & ?[X: $i, Y: $i] : (hate(alice, X) & brave(Y) & rich(Y) & tourist(Y) & sibling(X, Y)) & ?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : ((~((~predb(X)) & (~predb(Y)))) | (X = Y)) & happy(mary) & brave(fred))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((?[X: $i] : ((~room(X)) => (~hate(X, alice))) => (~(?[X: $i] : ((~room(X)) & hate(alice, X)) & ![X: $i, Y: $i] : ((hate(alice, X) & hate(alice, Y)) => (X = Y))))) | ((~?[X: $i] : ((~room(X)) => (~hate(X, alice)))) => (~((happy(mary) & tourist(mary)) | (((~quiet(mary)) & (~rich(mary))) & (~creative(mary))))))) & ((~(hate(fred, alice) & hate(alice, fred))) => (?[X: $i] : (((~room(X)) & creative(X)) & tourist(X)) & ![X: $i, Y: $i] : ((((creative(X) & tourist(X)) & creative(Y)) & tourist(Y)) => (X = Y))))) & (?[X: $i, Y: $i] : (((~hate(alice, X)) & (~(Y = fred))) & hate(X, Y)) => hate(alice, mary))) & ((~hate(fred, alice)) & (~hate(mary, alice)))) & ![X: $i] : quieter(mary, X)) & ?[X: $i, Y: $i] : (((~(X = mary)) & (~quiet(Y))) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((hate(alice, X) & ((brave(Y) & rich(Y)) & tourist(Y))) & sibling(X, Y))) & (?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : (((~predb(X)) & (~predb(Y))) => (X = Y)))) & (happy(mary) & brave(fred)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~(((((creative(paul) & happy(paul)) & rich(paul)) & brave(paul)) & quiet(paul)) & tourist(paul))) & (~(((((creative(fred) & happy(fred)) & rich(fred)) & brave(fred)) & quiet(fred)) & tourist(fred))))))), file('/mnt/tmpfs//8174667396750592479317994.p','negated')).
tff(7,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))) & ((~?[X: $i, Y: $i] : ((~hate(alice, X)) & (~(Y = fred)) & hate(X, Y))) | hate(alice, mary)) & (~hate(fred, alice)) & (~hate(mary, alice)) & ![X: $i] : quieter(mary, X) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~quiet(Y)) & quieter(X, Y)) & ?[X: $i, Y: $i] : (hate(alice, X) & brave(Y) & rich(Y) & tourist(Y) & sibling(X, Y)) & ?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : ((~((~predb(X)) & (~predb(Y)))) | (X = Y)) & happy(mary) & brave(fred))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)))))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))) & ((~?[X: $i, Y: $i] : ((~hate(alice, X)) & (~(Y = fred)) & hate(X, Y))) | hate(alice, mary)) & (~hate(fred, alice)) & (~hate(mary, alice)) & ![X: $i] : quieter(mary, X) & ?[X: $i, Y: $i] : ((~(X = mary)) & (~quiet(Y)) & quieter(X, Y)) & ?[X: $i, Y: $i] : (hate(alice, X) & brave(Y) & rich(Y) & tourist(Y) & sibling(X, Y)) & ?[X: $i] : ((~room(X)) & (~predb(X))) & ![X: $i, Y: $i] : ((~((~predb(X)) & (~predb(Y)))) | (X = Y)) & happy(mary) & brave(fred)),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(room(paul)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,
(room(X!0)),
inference(modus_ponens,[status(thm)],[10, 3])).
tff(12,plain,
((~hate(fred, alice)) <=> (~hate(fred, alice))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(~hate(fred, alice)),
inference(and_elim,[status(thm)],[8])).
tff(14,plain,
(~hate(fred, alice)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(((~hate(fred, alice)) | (~hate(alice, fred))) | hate(fred, alice)),
inference(tautology,[status(thm)],[])).
tff(16,plain,
((~hate(fred, alice)) | (~hate(alice, fred))),
inference(unit_resolution,[status(thm)],[15, 14])).
tff(17,plain,
(((~((~hate(fred, alice)) | (~hate(alice, fred)))) | (~(room(X!0) | (~creative(X!0)) | (~tourist(X!0)) | (~![X: $i, Y: $i] : ((X = Y) | (~tourist(Y)) | (~creative(X)) | (~tourist(X)) | (~creative(Y))))))) <=> ((~((~hate(fred, alice)) | (~hate(alice, fred)))) | (~(room(X!0) | (~creative(X!0)) | (~tourist(X!0)) | (~![X: $i, Y: $i] : ((X = Y) | (~tourist(Y)) | (~creative(X)) | (~tourist(X)) | (~creative(Y)))))))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
(((hate(fred, alice) & hate(alice, fred)) | ((~room(X!0)) & creative(X!0) & tourist(X!0) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))) <=> ((~((~hate(fred, alice)) | (~hate(alice, fred)))) | (~(room(X!0) | (~creative(X!0)) | (~tourist(X!0)) | (~![X: $i, Y: $i] : ((X = Y) | (~tourist(Y)) | (~creative(X)) | (~tourist(X)) | (~creative(Y)))))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(((hate(fred, alice) & hate(alice, fred)) | (((~room(X!0)) & creative(X!0) & tourist(X!0)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))) <=> ((hate(fred, alice) & hate(alice, fred)) | ((~room(X!0)) & creative(X!0) & tourist(X!0) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y))))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
((?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y))) <=> (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))) <=> ((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y))))),
inference(monotonicity,[status(thm)],[20])).
tff(22,plain,
(((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))) <=> ((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y))))),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))),
inference(and_elim,[status(thm)],[8])).
tff(24,plain,
((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))),
inference(modus_ponens,[status(thm)],[23, 21])).
tff(25,plain,
((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))),
inference(modus_ponens,[status(thm)],[24, 22])).
tff(26,plain,
((hate(fred, alice) & hate(alice, fred)) | (?[X: $i] : ((~room(X)) & creative(X) & tourist(X)) & ![X: $i, Y: $i] : ((~(creative(X) & tourist(X) & creative(Y) & tourist(Y))) | (X = Y)))),
inference(modus_ponens,[status(thm)],[25, 21])).
| room(james)&room(kristen)&room(bernice)&(![X]:(room(X)=>(X='james'|X='kristen'|X='bernice')))&
((((?[X]:(~room(X)=>(~hate(X,marshall))))=>(~(((?[X]:(~room(X)&hate(marshall,X)))&(![X,Y]:((hate(marshall,X)&hate(marshall,Y))=>(X=Y)))))))|((~(?[X]:(~room(X)=>(~hate(X,marshall)))))=>(~((happy(james)&tourist(james))|(~quiet(james)&~rich(james)&~creative(james))))))&
(~((hate(bernice,marshall) & hate(marshall,bernice)))=>(((?[X]:(~room(X)&creative(X)&tourist(X)))&(![X,Y]:((creative(X)&tourist(X)&creative(Y)&tourist(Y))=>(X=Y))))))&
((?[X,Y]:((~hate(marshall,X))&(Y!=bernice)&(hate(X,Y))))=>(hate(marshall,james)))&
(~hate(bernice,marshall)&~hate(james,marshall))&
(![X]:(quieter(james,X)))&
(?[X,Y]:((X!=james)&(~quiet(Y))&(quieter(X,Y))))&
(?[X,Y]:((hate(marshall,X))&(brave(Y)&rich(Y)&tourist(Y))&(sibling(X,Y))))&
(((?[X]:(~room(X)&does_not_enjoy_macrame(X)))&(![X,Y]:((does_not_enjoy_macrame(X)&does_not_enjoy_macrame(Y))=>(X=Y)))))&
((happy(james))&(brave(bernice)))) | room(james)&room(kristen)&room(bernice)&(![X]:(room(X)=>(X='james'|X='kristen'|X='bernice')))&
(~(creative(kristen)&happy(kristen)&rich(kristen)&brave(kristen)&quiet(kristen)&tourist(kristen))&~(creative(bernice)&happy(bernice)&rich(bernice)&brave(bernice)&quiet(bernice)&tourist(bernice))) | neutral | neutral | neutral |
William, Joan are the only persons in the room. 'Only one person outside the room is not a tall tourist' only if 'William is a client of Edward or does not like Joseph or both'. Only one person outside the room is not a tall tourist. Only one person outside the room is not a tall tourist. Edward is a client of Joan. William who is a tall tourist, is liked by Joseph. Joan likes Jimmy. | Someone who likes Jimmy is a client of someone who is not Joan. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(alice_type, type, (
alice: $i)).
tff(mary_type, type, (
mary: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(john_type, type, (
john: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(susan_type, type, (
susan: $i)).
tff(1,assumption,(~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))), introduced(assumption)).
tff(2,plain,
(((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | room(X!3)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(room(X!3)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(~(X!3 = |'mary'|)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
(((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(~(X!3 = |'paul'|)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(9,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y))) => (client(john, mary) | (~like(alice, mary)))) & (?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y)))) & (?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y)))) & client(paul, john)) & ((tall(mary) & tourist(mary)) & like(mary, alice))) & like(fred, paul))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : ((like(fred, X) & (~(Y = paul))) & client(X, Y))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (client(john, mary) | (~like(alice, mary)) | (~(?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y))))) & ?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y)) & client(paul, john) & tall(mary) & tourist(mary) & like(mary, alice) & like(fred, paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(12,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y))) => (client(john, mary) | (~like(alice, mary)))) & (?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y)))) & (?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : (((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y)))) => (X = Y)))) & client(paul, john)) & ((tall(mary) & tourist(mary)) & like(mary, alice))) & like(fred, paul))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : ((like(fred, X) & (~(Y = paul))) & client(X, Y))))), file('/mnt/tmpfs//695929346084095589933116.p','negated')).
tff(13,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (client(john, mary) | (~like(alice, mary)) | (~(?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y))))) & ?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y)) & client(paul, john) & tall(mary) & tourist(mary) & like(mary, alice) & like(fred, paul))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y))))),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (client(john, mary) | (~like(alice, mary)) | (~(?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y))))) & ?[X: $i] : ((~room(X)) & (~(tall(X) & tourist(X)))) & ![X: $i, Y: $i] : ((~((~(tall(X) & tourist(X))) & (~(tall(Y) & tourist(Y))))) | (X = Y)) & client(paul, john) & tall(mary) & tourist(mary) & like(mary, alice) & like(fred, paul)),
inference(or_elim,[status(thm)],[13])).
tff(15,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[15, 10])).
tff(17,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[16])).
tff(18,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[17, 9])).
tff(19,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))),
inference(quant_inst,[status(thm)],[])).
tff(21,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))),
inference(modus_ponens,[status(thm)],[20, 19])).
tff(22,plain,
($false),
inference(unit_resolution,[status(thm)],[21, 18, 7, 5, 3])).
tff(23,plain,((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))), inference(lemma,lemma(discharge,[]))).
tff(24,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(room(paul)),
inference(and_elim,[status(thm)],[14])).
tff(26,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
(room(mary)),
inference(and_elim,[status(thm)],[14])).
tff(29,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : ((Y = paul) | (~like(fred, X)) | (~client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : ((Y = paul) | (~like(fred, X)) | (~client(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~(like(fred, X) & (~(Y = paul)) & client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : ((Y = paul) | (~like(fred, X)) | (~client(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(32,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~(like(fred, X) & (~(Y = paul)) & client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | ![X: $i, Y: $i] : (~(like(fred, X) & (~(Y = paul)) & client(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(33,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y))))),
inference(monotonicity,[status(thm)],[33])).
tff(35,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))),
inference(or_elim,[status(thm)],[13])).
tff(37,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))),
inference(modus_ponens,[status(thm)],[36, 34])).
tff(38,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))),
inference(modus_ponens,[status(thm)],[37, 35])).
tff(39,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~(Y = paul)) & client(X, Y)))),
inference(modus_ponens,[status(thm)],[38, 34])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3)))))
(a!5 (lambda ((X $i) (Y $i))
(let ((a!1 (and (like fred X) (not (= Y paul)) (client X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!6 (exists ((X $i) (Y $i))
(and (like fred X) (not (= Y paul)) (client X Y))))
(a!7 (forall ((X $i) (Y $i))
(let ((a!1 (and (like fred X) (not (= Y paul)) (client X Y))))
(not a!1)))))
(let ((a!8 (~ (not (and (room mary) (room paul) a!3 a!6))
(or (not (room mary)) (not (room paul)) a!4 a!7))))
(nnf-neg a!1
a!2
(sk (~ (not a!3) a!4))
(nnf-neg (proof-bind a!5) (~ (not a!6) a!7))
a!8)))
| room(william)&room(joan)&(![X]:(room(X)=>(X='william'|X='joan')))&
(((((?[X]:(~room(X)&~(tall(X)&tourist(X))))&(![X,Y]:((~(tall(X)&tourist(X))&~(tall(Y)&tourist(Y)))=>(X=Y)))))=>(((client(edward,william))|(~like(joseph,william)))))&
(((?[X]:(~room(X)&~(tall(X)&tourist(X))))&(![X,Y]:((~(tall(X)&tourist(X))&~(tall(Y)&tourist(Y)))=>(X=Y)))))&
(((?[X]:(~room(X)&~(tall(X)&tourist(X))))&(![X,Y]:((~(tall(X)&tourist(X))&~(tall(Y)&tourist(Y)))=>(X=Y)))))&
(client(joan,edward))&
((tall(william)&tourist(william))&(like(william,joseph)))&
(like(jimmy,joan))) | room(william)&room(joan)&(![X]:(room(X)=>(X='william'|X='joan')))&
(?[X,Y]:((like(jimmy,X))&(Y!=joan)&(client(X,Y)))) | contradiction | neutral | contradiction |
Corey, Michael, Zachary are the only persons in the room. At least one of the following is true:. -Shirley is a client of Zachary. -Corey is the least rich in the room. -Michael is not creative or hates Shirley or both. | Michael is not hated by Jeff or is not a creative person or both. | neutral | % SZS status Satisfiable
| room(corey)&room(michael)&room(zachary)&(![X]:(room(X)=>(X='corey'|X='michael'|X='zachary')))&
(((client(zachary,shirley))|
(![X]:(richer(corey,X)))|
(((~creative(michael))|(hate(shirley,michael)))))) | room(corey)&room(michael)&room(zachary)&(![X]:(room(X)=>(X='corey'|X='michael'|X='zachary')))&
(((~hate(michael,jeff))|(~(creative(michael)&person(michael))))) | neutral | neutral | entailment |
Dawn is the only person in the room.
Dawn is the least rich in the room only if Geraldine and Suzanne like each other.
Everyone outside the room does not enjoy stand-up paddleboarding only if Geraldine is a sibling of Dawn.
Only one person outside the room likes Suzanne only if Dawn either does not enjoy stand-up paddleboarding or is not liked by Geraldine.
Someone who is a sibling of Michael is richer than someone who does not enjoy stand-up paddleboarding.
Dawn is the least rich in the room.
Someone who is not liked by Geraldine is taller than someone who is a tall person.
Someone who enjoys stand-up paddleboarding is taller than someone who is liked by Geraldine.
It is not the case that 'Dawn likes Michael or is liked by Irene or both'.
Dawn is the least tall in the room.
Someone who is not Dawn like someone who does not enjoy stand-up paddleboarding.
Dawn and Geraldine like each other. | Dawn who is taller than Geraldine, likes Stephen. | contradiction | - | room(dawn)&(![X]:(room(X)=>(X='dawn')))&
(((![X]:(richer(dawn,X)))=>((like(geraldine,suzanne) & like(suzanne,geraldine))))&
((![X]:(~room(X)=>(does_not_enjoy_stand-up_paddleboarding(X))))=>(sibling(dawn,geraldine)))&
((((?[X]:(~room(X)&like(suzanne,X)))&(![X,Y]:((like(suzanne,X)&like(suzanne,Y))=>(X=Y)))))=>((((does_not_enjoy_stand-up_paddleboarding(dawn))|(~like(dawn,geraldine)))&(~((does_not_enjoy_stand-up_paddleboarding(dawn))|(~like(dawn,geraldine)))))))&
(?[X,Y]:((sibling(michael,X))&(does_not_enjoy_stand-up_paddleboarding(Y))&(richer(X,Y))))&
(![X]:(richer(dawn,X)))&
(?[X,Y]:((~like(X,geraldine))&(tall(Y)&person(Y))&(taller(X,Y))))&
(?[X,Y]:((enjoys_stand-up_paddleboarding(X))&(like(Y,geraldine))&(taller(X,Y))))&
(~(((like(michael,dawn))|(like(dawn,irene)))))&
(![X]:(taller(dawn,X)))&
(?[X,Y]:((X!=dawn)&(does_not_enjoy_stand-up_paddleboarding(Y))&(like(X,Y))))&
((like(dawn,geraldine) & like(geraldine,dawn)))) | room(dawn)&(![X]:(room(X)=>(X='dawn')))&
((taller(geraldine,dawn))&(like(stephen,dawn))) | neutral | neutral | contradiction |
Only one of the following is true:.
-Matthew is not tall.
-It is not the case that 'Matthew is a rich tall european'. | Matthew is a rich european. | contradiction | - | room(david)&room(matthew)&(![X]:(room(X)=>(X='david'|X='matthew')))&
(((~tall(matthew))|(~(rich(matthew)&tall(matthew)&european(matthew))))&~(~tall(matthew)&~(rich(matthew)&tall(matthew)&european(matthew)))) | room(david)&room(matthew)&(![X]:(room(X)=>(X='david'|X='matthew')))&
(rich(matthew)&european(matthew)) | contradiction | neutral | neutral |
Alma, Michael, Daniel, Mark are the only persons in the room. Alma is the tallest in the room. More than one person outside the room is not quiet, not happy. Mark is the quietest in the room. Alma is the richest in the room. Mark likes James. | Mark is quieter than James or is not a quiet creative tall european or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(tall_type, type, (
tall: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(1,assumption,(~quieter(john, alice)), introduced(assumption)).
tff(2,plain,
(^[X: $i] : refl(quieter(X, alice) <=> quieter(X, alice))),
inference(bind,[status(th)],[])).
tff(3,plain,
(![X: $i] : quieter(X, alice) <=> ![X: $i] : quieter(X, alice)),
inference(quant_intro,[status(thm)],[2])).
tff(4,plain,
(![X: $i] : quieter(X, alice) <=> ![X: $i] : quieter(X, alice)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((((~quiet(X)) & (~happy(X))) & (~quiet(Y))) & (~happy(Y)))) & (~(X = Y)))) & ![X: $i] : quieter(X, alice)) & ![X: $i] : richer(X, mary)) & like(john, alice))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (quieter(john, alice) | (~(((quiet(alice) & creative(alice)) & tall(alice)) & european(alice))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~quiet(X)) & (~happy(X)) & (~quiet(Y)) & (~happy(Y)) & (~(X = Y))) & ![X: $i] : quieter(X, alice) & ![X: $i] : richer(X, mary) & like(john, alice))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((((~quiet(X)) & (~happy(X))) & (~quiet(Y))) & (~happy(Y)))) & (~(X = Y)))) & ![X: $i] : quieter(X, alice)) & ![X: $i] : richer(X, mary)) & like(john, alice))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (quieter(john, alice) | (~(((quiet(alice) & creative(alice)) & tall(alice)) & european(alice))))))), file('/mnt/tmpfs//551953660095719269468249.p','negated')).
tff(7,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~quiet(X)) & (~happy(X)) & (~quiet(Y)) & (~happy(Y)) & (~(X = Y))) & ![X: $i] : quieter(X, alice) & ![X: $i] : richer(X, mary) & like(john, alice))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~quiet(X)) & (~happy(X)) & (~quiet(Y)) & (~happy(Y)) & (~(X = Y))) & ![X: $i] : quieter(X, alice) & ![X: $i] : richer(X, mary) & like(john, alice)),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(![X: $i] : quieter(X, alice)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : quieter(X, alice)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,(
![X: $i] : quieter(X, alice)),
inference(skolemize,[status(sab)],[10])).
tff(12,plain,
(![X: $i] : quieter(X, alice)),
inference(modus_ponens,[status(thm)],[11, 3])).
tff(13,plain,
((~![X: $i] : quieter(X, alice)) | quieter(john, alice)),
inference(quant_inst,[status(thm)],[])).
tff(14,plain,
($false),
inference(unit_resolution,[status(thm)],[13, 12, 1])).
tff(15,plain,(quieter(john, alice)), inference(lemma,lemma(discharge,[]))).
tff(16,plain,
((quieter(john, alice) | (~quiet(alice)) | (~creative(alice)) | (~tall(alice)) | (~european(alice))) | (~quieter(john, alice))),
inference(tautology,[status(thm)],[])).
tff(17,plain,
(quieter(john, alice) | (~quiet(alice)) | (~creative(alice)) | (~tall(alice)) | (~european(alice))),
inference(unit_resolution,[status(thm)],[16, 15])).
tff(18,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(room(alice)),
inference(and_elim,[status(thm)],[8])).
tff(20,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
(room(fred)),
inference(and_elim,[status(thm)],[8])).
tff(23,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[22, 21])).
tff(24,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(room(paul)),
inference(and_elim,[status(thm)],[8])).
tff(26,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
(room(mary)),
inference(and_elim,[status(thm)],[8])).
tff(29,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~quiet(alice)) | (~creative(alice)) | (~tall(alice)) | (~european(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~quiet(alice)) | (~creative(alice)) | (~tall(alice)) | (~european(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
((~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))) <=> (~(quieter(john, alice) | (~quiet(alice)) | (~creative(alice)) | (~tall(alice)) | (~european(alice))))),
inference(rewrite,[status(thm)],[])).
tff(32,plain,
((~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))),
inference(rewrite,[status(thm)],[])).
tff(33,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~quiet(alice)) | (~creative(alice)) | (~tall(alice)) | (~european(alice)))))),
inference(monotonicity,[status(thm)],[32, 31])).
tff(34,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~quiet(alice)) | (~creative(alice)) | (~tall(alice)) | (~european(alice)))))),
inference(transitivity,[status(thm)],[33, 30])).
tff(35,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
((~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))) <=> (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))))),
inference(monotonicity,[status(thm)],[32, 36])).
tff(38,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))))),
inference(transitivity,[status(thm)],[37, 35])).
tff(39,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))))),
inference(monotonicity,[status(thm)],[39])).
tff(41,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice))))))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))),
inference(or_elim,[status(thm)],[7])).
tff(43,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))),
inference(modus_ponens,[status(thm)],[42, 40])).
tff(44,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))),
inference(modus_ponens,[status(thm)],[43, 41])).
tff(45,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, alice) | (~(quiet(alice) & creative(alice) & tall(alice) & european(alice)))))),
inference(modus_ponens,[status(thm)],[44, 40])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!2 |'alice'|)
(= X!2 |'fred'|)
(= X!2 |'paul'|)
(= X!2 |'mary'|)
(not (room X!2)))))
(a!7 (or (quieter john alice)
(not (and (quiet alice)
(creative alice)
(tall alice)
(european alice))))))
(let ((a!8 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
a!7))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(not a!7)))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
(refl (~ (not a!7) (not a!7)))
a!8)))
| room(alma)&room(michael)&room(daniel)&room(mark)&(![X]:(room(X)=>(X='alma'|X='michael'|X='daniel'|X='mark')))&
((![X]:(taller(X,alma)))&
((?[X,Y]:(~room(X)&~room(Y)&(~quiet(X)&~happy(X)&~quiet(Y)&~happy(Y))&(X!=Y))))&
(![X]:(quieter(X,mark)))&
(![X]:(richer(X,alma)))&
(like(james,mark))) | room(alma)&room(michael)&room(daniel)&room(mark)&(![X]:(room(X)=>(X='alma'|X='michael'|X='daniel'|X='mark')))&
(((quieter(james,mark))|(~(quiet(mark)&creative(mark)&tall(mark)&european(mark))))) | neutral | entailment | entailment |
Raymond, Ryan, Melonie are the only persons in the room.
It is not the case that 'only one person outside the room is richer than Herbert'.
Herbert is richer than Raymond.
Ryan is the least tall in the room.
Ryan is not Melonie or is richer than Herbert or both.
Melonie and Ryan are not creative. | Melonie and Ryan are respectively creative and rich. | contradiction | - | room(raymond)&room(ryan)&room(melonie)&(![X]:(room(X)=>(X='raymond'|X='ryan'|X='melonie')))&
((~(((?[X]:(~room(X)&richer(herbert,X)))&(![X,Y]:((richer(herbert,X)&richer(herbert,Y))=>(X=Y))))))&
(richer(raymond,herbert))&
(![X]:(taller(ryan,X)))&
(((ryan!=melonie)|(richer(herbert,ryan))))&
(~creative(melonie)&~creative(ryan))) | room(raymond)&room(ryan)&room(melonie)&(![X]:(room(X)=>(X='raymond'|X='ryan'|X='melonie')))&
((creative(melonie))&(rich(ryan))) | contradiction | contradiction | contradiction |
Nikki is the only person in the room. Nikki neither is not rich nor is not liked by Kelly only if Nikki who is not rich, is a sibling of Tammi. Only one person outside the room is not a rich person. Nikki who is a client of John, does not like John. | Nikki is not liked by Kelly and is a client of John. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(rich_type, type, (
rich: $i > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(mary_type, type, (
mary: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(alice_type, type, (
alice: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(1,plain,
(^[X: $i] : refl(((~room(X)) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(2,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[1])).
tff(3,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(4,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((~((~rich(mary)) | (~like(mary, alice)))) => ((~rich(mary)) & sibling(fred, mary))) & (?[X: $i] : ((~room(X)) & (~(rich(X) & person(X)))) & ![X: $i, Y: $i] : (((~(rich(X) & person(X))) & (~(rich(Y) & person(Y)))) => (X = Y)))) & (client(lucy, mary) & (~like(lucy, mary))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~like(mary, alice)) & client(lucy, mary))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~rich(mary)) | (~like(mary, alice)) | ((~rich(mary)) & sibling(fred, mary))) & ?[X: $i] : ((~room(X)) & (~(rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & person(X))) & (~(rich(Y) & person(Y))))) | (X = Y)) & client(lucy, mary) & (~like(lucy, mary)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))))),
inference(rewrite,[status(thm)],[])).
tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((~((~rich(mary)) | (~like(mary, alice)))) => ((~rich(mary)) & sibling(fred, mary))) & (?[X: $i] : ((~room(X)) & (~(rich(X) & person(X)))) & ![X: $i, Y: $i] : (((~(rich(X) & person(X))) & (~(rich(Y) & person(Y)))) => (X = Y)))) & (client(lucy, mary) & (~like(lucy, mary))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~like(mary, alice)) & client(lucy, mary))))), file('/mnt/tmpfs//1780014541841700636214182.p','negated')).
tff(6,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~rich(mary)) | (~like(mary, alice)) | ((~rich(mary)) & sibling(fred, mary))) & ?[X: $i] : ((~room(X)) & (~(rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & person(X))) & (~(rich(Y) & person(Y))))) | (X = Y)) & client(lucy, mary) & (~like(lucy, mary)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary)))),
inference(modus_ponens,[status(thm)],[5, 4])).
tff(7,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~rich(mary)) | (~like(mary, alice)) | ((~rich(mary)) & sibling(fred, mary))) & ?[X: $i] : ((~room(X)) & (~(rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & person(X))) & (~(rich(Y) & person(Y))))) | (X = Y)) & client(lucy, mary) & (~like(lucy, mary))),
inference(or_elim,[status(thm)],[6])).
tff(8,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[8, 3])).
tff(10,plain,(
![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(skolemize,[status(sab)],[9])).
tff(11,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[10, 2])).
tff(12,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(room(mary)),
inference(and_elim,[status(thm)],[7])).
tff(14,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(17,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[17, 14, 11])).
tff(19,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[18])).
tff(20,plain,
(rich(|'mary'|) <=> rich(mary)),
inference(monotonicity,[status(thm)],[19])).
tff(21,plain,
(rich(mary) <=> rich(|'mary'|)),
inference(symmetry,[status(thm)],[20])).
tff(22,plain,
((~rich(mary)) <=> (~rich(|'mary'|))),
inference(monotonicity,[status(thm)],[21])).
tff(23,assumption,(~((~room(X!1)) | (X!1 = |'mary'|))), introduced(assumption)).
tff(24,plain,
(((~room(X!1)) | (X!1 = |'mary'|)) | (~(X!1 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(25,plain,
(~(X!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[24, 23])).
tff(26,plain,
(((~room(X!1)) | (X!1 = |'mary'|)) | room(X!1)),
inference(tautology,[status(thm)],[])).
tff(27,plain,
(room(X!1)),
inference(unit_resolution,[status(thm)],[26, 23])).
tff(28,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!1)) | (X!1 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!1)) | (X!1 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!1)) | (X!1 = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(30,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!1)) | (X!1 = |'mary'|)),
inference(modus_ponens,[status(thm)],[29, 28])).
tff(31,plain,
($false),
inference(unit_resolution,[status(thm)],[30, 11, 27, 25])).
tff(32,plain,((~room(X!1)) | (X!1 = |'mary'|)), inference(lemma,lemma(discharge,[]))).
tff(33,plain,
(client(lucy, mary) <=> client(lucy, mary)),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(client(lucy, mary)),
inference(and_elim,[status(thm)],[7])).
tff(35,plain,
(client(lucy, mary)),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
(((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | like(mary, alice) | (~client(lucy, mary))) <=> (like(mary, alice) | (~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | (~client(lucy, mary)))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary)) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary)))),
inference(monotonicity,[status(thm)],[37])).
tff(39,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary)))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))),
inference(or_elim,[status(thm)],[6])).
tff(41,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))),
inference(modus_ponens,[status(thm)],[40, 38])).
tff(42,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))),
inference(modus_ponens,[status(thm)],[41, 39])).
tff(43,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~like(mary, alice)) & client(lucy, mary))),
inference(modus_ponens,[status(thm)],[42, 38])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!1)) (= X!1 |'mary'|))))
(a!4 (refl (~ (not (client lucy mary)) (not (client lucy mary))))))
(let ((a!5 (not (and (room mary) a!2 (not (like mary alice)) (client lucy mary)))))
(let ((a!6 (~ a!5
(or (not (room mary))
a!3
(like mary alice)
(not (client lucy mary))))))
(nnf-neg a!1
(sk (~ (not a!2) a!3))
(refl (~ (like mary alice) (like mary alice)))
a!4
a!6))))
| room(nikki)&(![X]:(room(X)=>(X='nikki')))&
(((~((~rich(nikki))|(~like(nikki,kelly))))=>((~rich(nikki))&(sibling(tammi,nikki))))&
(((?[X]:(~room(X)&~(rich(X)&person(X))))&(![X,Y]:((~(rich(X)&person(X))&~(rich(Y)&person(Y)))=>(X=Y)))))&
((client(john,nikki))&(~like(john,nikki)))) | room(nikki)&(![X]:(room(X)=>(X='nikki')))&
((~like(nikki,kelly))&(client(john,nikki))) | contradiction | contradiction | contradiction |
Not all of the following are true:.
-It is not the case that 'Robert either is not liked by Lois or is a sibling of Maryann'.
-Robert and Lois hate each other.
-Myra and Maryann hate each other. | It is not the case that 'Myra is a sibling of Lois and is hated by Lois'. | neutral | % SZS status Satisfiable
| room(deborah)&room(robert)&room(myra)&room(esther)&(![X]:(room(X)=>(X='deborah'|X='robert'|X='myra'|X='esther')))&
(~(~((((~like(robert,lois))|(sibling(maryann,robert)))&(~((~like(robert,lois))|(sibling(maryann,robert))))))&(hate(robert,lois) & hate(lois,robert))&(hate(myra,maryann) & hate(maryann,myra)))) | room(deborah)&room(robert)&room(myra)&room(esther)&(![X]:(room(X)=>(X='deborah'|X='robert'|X='myra'|X='esther')))&
(~((sibling(lois,myra))&(hate(myra,lois)))) | entailment | entailment | neutral |
Donna, Andrew, Linda, Leroy are the only persons in the room.
"Donna who is not a scotch connoisseur, likes Max" if "someone who does not like Max like someone who is not a creative rich tourist".
If "no one outside the room who is not Leroy is not hated by Max" then "Leroy is the quietest in the room".
"Donna is the richest in the room" only if "only one person outside the room is quieter than Max".
If "more than one person outside the room is not Leroy" then "Leroy neither is quieter than Max nor is hated by Max".
It is not the case that 'Leroy is the least quiet in the room'.
Leroy who is not quiet, is not a creative european.
Everyone outside the room who likes Max is not rich, not creative.
Leroy is the richest in the room.
Only one person outside the room is quieter than Max.
Leroy neither is quieter than Max nor is hated by Max. | Someone who is not hated by Max is richer than someone who is not a brave quiet tourist. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(quiet_type, type, (
quiet: $i > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(alice_type, type, (
alice: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(brave_type, type, (
brave: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(1,assumption,(alice = |'paul'|), introduced(assumption)).
tff(2,plain,
(hate(alice, lucy) <=> hate(|'paul'|, lucy)),
inference(monotonicity,[status(thm)],[1])).
tff(3,plain,
(hate(|'paul'|, lucy) <=> hate(alice, lucy)),
inference(symmetry,[status(thm)],[2])).
tff(4,plain,
(^[X: $i] : refl(richer(X, alice) <=> richer(X, alice))),
inference(bind,[status(th)],[])).
tff(5,plain,
(![X: $i] : richer(X, alice) <=> ![X: $i] : richer(X, alice)),
inference(quant_intro,[status(thm)],[4])).
tff(6,plain,
(![X: $i] : richer(X, alice) <=> ![X: $i] : richer(X, alice)),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((?[X: $i, Y: $i] : (((~like(lucy, X)) & (~((creative(Y) & rich(Y)) & tourist(Y)))) & like(X, Y)) => ((~preda(mary)) & like(lucy, mary))) & ((~?[X: $i] : ((~room(X)) => ((~(X = alice)) => (~hate(X, lucy))))) => ![X: $i] : quieter(X, alice))) & (![X: $i] : richer(X, mary) => (?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((quieter(lucy, X) & quieter(lucy, Y)) => (X = Y))))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = alice)) & (~(Y = alice)))) & (~(X = Y))) => (~(quieter(lucy, alice) | hate(alice, lucy))))) & (~![X: $i] : quieter(alice, X))) & ((~quiet(alice)) & (~(creative(alice) & european(alice))))) & ![X: $i] : ((~room(X)) => (like(lucy, X) => ((~rich(X)) & (~creative(X)))))) & ![X: $i] : richer(X, alice)) & (?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((quieter(lucy, X) & quieter(lucy, Y)) => (X = Y)))) & (~(quieter(lucy, alice) | hate(alice, lucy))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((~hate(X, lucy)) & (~((brave(Y) & quiet(Y)) & tourist(Y)))) & richer(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~like(lucy, X)) & (~(creative(Y) & rich(Y) & tourist(Y))) & like(X, Y))) | ((~preda(mary)) & like(lucy, mary))) & (![X: $i] : quieter(X, alice) | ?[X: $i] : (room(X) | (~hate(X, lucy)) | (X = alice))) & ((~![X: $i] : richer(X, mary)) | (?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((~(quieter(lucy, X) & quieter(lucy, Y))) | (X = Y)))) & ((~(hate(alice, lucy) | quieter(lucy, alice))) | (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) & (~![X: $i] : quieter(alice, X)) & (~quiet(alice)) & (~(creative(alice) & european(alice))) & ![X: $i] : (room(X) | ((~rich(X)) & (~creative(X))) | (~like(lucy, X))) & ![X: $i] : richer(X, alice) & ?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((~(quieter(lucy, X) & quieter(lucy, Y))) | (X = Y)) & (~(hate(alice, lucy) | quieter(lucy, alice))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(8,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((?[X: $i, Y: $i] : (((~like(lucy, X)) & (~((creative(Y) & rich(Y)) & tourist(Y)))) & like(X, Y)) => ((~preda(mary)) & like(lucy, mary))) & ((~?[X: $i] : ((~room(X)) => ((~(X = alice)) => (~hate(X, lucy))))) => ![X: $i] : quieter(X, alice))) & (![X: $i] : richer(X, mary) => (?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((quieter(lucy, X) & quieter(lucy, Y)) => (X = Y))))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = alice)) & (~(Y = alice)))) & (~(X = Y))) => (~(quieter(lucy, alice) | hate(alice, lucy))))) & (~![X: $i] : quieter(alice, X))) & ((~quiet(alice)) & (~(creative(alice) & european(alice))))) & ![X: $i] : ((~room(X)) => (like(lucy, X) => ((~rich(X)) & (~creative(X)))))) & ![X: $i] : richer(X, alice)) & (?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((quieter(lucy, X) & quieter(lucy, Y)) => (X = Y)))) & (~(quieter(lucy, alice) | hate(alice, lucy))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((~hate(X, lucy)) & (~((brave(Y) & quiet(Y)) & tourist(Y)))) & richer(X, Y))))), file('/mnt/tmpfs//584390516026060674087926.p','negated')).
tff(9,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~like(lucy, X)) & (~(creative(Y) & rich(Y) & tourist(Y))) & like(X, Y))) | ((~preda(mary)) & like(lucy, mary))) & (![X: $i] : quieter(X, alice) | ?[X: $i] : (room(X) | (~hate(X, lucy)) | (X = alice))) & ((~![X: $i] : richer(X, mary)) | (?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((~(quieter(lucy, X) & quieter(lucy, Y))) | (X = Y)))) & ((~(hate(alice, lucy) | quieter(lucy, alice))) | (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) & (~![X: $i] : quieter(alice, X)) & (~quiet(alice)) & (~(creative(alice) & european(alice))) & ![X: $i] : (room(X) | ((~rich(X)) & (~creative(X))) | (~like(lucy, X))) & ![X: $i] : richer(X, alice) & ?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((~(quieter(lucy, X) & quieter(lucy, Y))) | (X = Y)) & (~(hate(alice, lucy) | quieter(lucy, alice))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))))),
inference(modus_ponens,[status(thm)],[8, 7])).
tff(10,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~like(lucy, X)) & (~(creative(Y) & rich(Y) & tourist(Y))) & like(X, Y))) | ((~preda(mary)) & like(lucy, mary))) & (![X: $i] : quieter(X, alice) | ?[X: $i] : (room(X) | (~hate(X, lucy)) | (X = alice))) & ((~![X: $i] : richer(X, mary)) | (?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((~(quieter(lucy, X) & quieter(lucy, Y))) | (X = Y)))) & ((~(hate(alice, lucy) | quieter(lucy, alice))) | (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) & (~![X: $i] : quieter(alice, X)) & (~quiet(alice)) & (~(creative(alice) & european(alice))) & ![X: $i] : (room(X) | ((~rich(X)) & (~creative(X))) | (~like(lucy, X))) & ![X: $i] : richer(X, alice) & ?[X: $i] : ((~room(X)) & quieter(lucy, X)) & ![X: $i, Y: $i] : ((~(quieter(lucy, X) & quieter(lucy, Y))) | (X = Y)) & (~(hate(alice, lucy) | quieter(lucy, alice)))),
inference(or_elim,[status(thm)],[9])).
tff(11,plain,
(![X: $i] : richer(X, alice)),
inference(and_elim,[status(thm)],[10])).
tff(12,plain,
(![X: $i] : richer(X, alice)),
inference(modus_ponens,[status(thm)],[11, 6])).
tff(13,plain,(
![X: $i] : richer(X, alice)),
inference(skolemize,[status(sab)],[12])).
tff(14,plain,
(![X: $i] : richer(X, alice)),
inference(modus_ponens,[status(thm)],[13, 5])).
tff(15,plain,
((~![X: $i] : richer(X, alice)) | richer(|'paul'|, alice)),
inference(quant_inst,[status(thm)],[])).
tff(16,plain,
(richer(|'paul'|, alice)),
inference(unit_resolution,[status(thm)],[15, 14])).
tff(17,plain,
((~quiet(alice)) <=> (~quiet(alice))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
(~quiet(alice)),
inference(and_elim,[status(thm)],[10])).
tff(19,plain,
(~quiet(alice)),
inference(modus_ponens,[status(thm)],[18, 17])).
tff(20,plain,
(((~brave(alice)) | (~quiet(alice)) | (~tourist(alice))) | quiet(alice)),
inference(tautology,[status(thm)],[])).
tff(21,plain,
((~brave(alice)) | (~quiet(alice)) | (~tourist(alice))),
inference(unit_resolution,[status(thm)],[20, 19])).
tff(22,assumption,(~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), introduced(assumption)).
tff(23,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | room(X!4)),
inference(tautology,[status(thm)],[])).
tff(24,plain,
(room(X!4)),
inference(unit_resolution,[status(thm)],[23, 22])).
tff(25,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(26,plain,
(~(X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[25, 22])).
tff(27,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(28,plain,
(~(X!4 = |'paul'|)),
inference(unit_resolution,[status(thm)],[27, 22])).
tff(29,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(30,plain,
(~(X!4 = |'fred'|)),
inference(unit_resolution,[status(thm)],[29, 22])).
tff(31,plain,
(((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'alice'|))),
inference(tautology,[status(thm)],[])).
tff(32,plain,
(~(X!4 = |'alice'|)),
inference(unit_resolution,[status(thm)],[31, 22])).
tff(33,plain,
(^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(34,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[33])).
tff(35,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[10])).
tff(37,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[36, 35])).
tff(38,plain,(
![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[37])).
tff(39,plain,
(![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[38, 34])).
tff(40,plain,
(((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(quant_inst,[status(thm)],[])).
tff(42,plain,
((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))),
inference(modus_ponens,[status(thm)],[41, 40])).
tff(43,plain,
($false),
inference(unit_resolution,[status(thm)],[42, 39, 32, 30, 28, 26, 24])).
tff(44,plain,((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(lemma,lemma(discharge,[]))).
tff(45,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(room(alice)),
inference(and_elim,[status(thm)],[10])).
tff(47,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[46, 45])).
tff(48,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
(room(fred)),
inference(and_elim,[status(thm)],[10])).
tff(50,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[49, 48])).
tff(51,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
(room(paul)),
inference(and_elim,[status(thm)],[10])).
tff(53,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[52, 51])).
tff(54,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(55,plain,
(room(mary)),
inference(and_elim,[status(thm)],[10])).
tff(56,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[55, 54])).
tff(57,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(58,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(59,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((brave(Y) & quiet(Y) & tourist(Y)) <=> (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))), ((~(brave(Y) & quiet(Y) & tourist(Y))) <=> (~(~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))), rewrite((~(~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))) <=> ((~brave(Y)) | (~quiet(Y)) | (~tourist(Y)))), ((~(brave(Y) & quiet(Y) & tourist(Y))) <=> ((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))), (((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)) <=> ((~hate(X, lucy)) & ((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))) & richer(X, Y)))), rewrite(((~hate(X, lucy)) & ((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))) & richer(X, Y)) <=> (~(hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))), (((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)) <=> (~(hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y)))))))), ((~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))) <=> (~(~(hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))))), rewrite((~(~(hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))) <=> (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y)))))), ((~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))) <=> (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y)))))))),
inference(bind,[status(th)],[])).
tff(60,plain,
(![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))) <=> ![X: $i, Y: $i] : (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y)))))),
inference(quant_intro,[status(thm)],[59])).
tff(61,plain,
((~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(62,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))),
inference(monotonicity,[status(thm)],[61, 60])).
tff(63,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(X, lucy) | (~richer(X, Y)) | (~((~brave(Y)) | (~quiet(Y)) | (~tourist(Y))))))),
inference(transitivity,[status(thm)],[62, 58])).
tff(64,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(65,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))))),
inference(monotonicity,[status(thm)],[61])).
tff(66,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))))),
inference(transitivity,[status(thm)],[65, 64])).
tff(67,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(68,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))))),
inference(monotonicity,[status(thm)],[67])).
tff(69,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(70,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))),
inference(or_elim,[status(thm)],[9])).
tff(71,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[70, 68])).
tff(72,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[71, 69])).
tff(73,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(X, lucy)) & (~(brave(Y) & quiet(Y) & tourist(Y))) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[72, 68])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!4 |'alice'|)
(= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|)
(not (room X!4)))))
(a!7 (lambda ((X $i) (Y $i))
(let ((a!1 (and (not (hate X lucy))
(not (and (brave Y) (quiet Y) (tourist Y)))
(richer X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!8 (exists ((X $i) (Y $i))
(and (not (hate X lucy))
(not (and (brave Y) (quiet Y) (tourist Y)))
(richer X Y))))
(a!9 (forall ((X $i) (Y $i))
(let ((a!1 (and (not (hate X lucy))
(not (and (brave Y) (quiet Y) (tourist Y)))
(richer X Y))))
(not a!1)))))
(let ((a!10 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
a!8))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
a!9))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
(nnf-neg (proof-bind a!7) (~ (not a!8) a!9))
a!10)))
| room(donna)&room(andrew)&room(linda)&room(leroy)&(![X]:(room(X)=>(X='donna'|X='andrew'|X='linda'|X='leroy')))&
(((?[X,Y]:((~like(max,X))&(~(creative(Y)&rich(Y)&tourist(Y)))&(like(X,Y))))=>((is_not_a_scotch_connoisseur(donna))&(like(max,donna))))&
((~?[X]:(~room(X)=>(((X!=leroy)=>(~hate(X,max))))))=>(![X]:(quieter(X,leroy))))&
((![X]:(richer(X,donna)))=>(((?[X]:(~room(X)&quieter(max,X)))&(![X,Y]:((quieter(max,X)&quieter(max,Y))=>(X=Y))))))&
(((?[X,Y]:(~room(X)&~room(Y)&(X!=leroy&Y!=leroy)&(X!=Y))))=>(~((quieter(max,leroy))|(hate(leroy,max)))))&
(~(![X]:(quieter(leroy,X))))&
((~quiet(leroy))&(~(creative(leroy)&european(leroy))))&
(![X]:(~room(X)=>(((like(max,X))=>(~rich(X)&~creative(X))))))&
(![X]:(richer(X,leroy)))&
(((?[X]:(~room(X)&quieter(max,X)))&(![X,Y]:((quieter(max,X)&quieter(max,Y))=>(X=Y)))))&
(~((quieter(max,leroy))|(hate(leroy,max))))) | room(donna)&room(andrew)&room(linda)&room(leroy)&(![X]:(room(X)=>(X='donna'|X='andrew'|X='linda'|X='leroy')))&
(?[X,Y]:((~hate(X,max))&(~(brave(Y)&quiet(Y)&tourist(Y)))&(richer(X,Y)))) | entailment | neutral | entailment |
Russell, Ricky are the only persons in the room.
Only one person outside the room is not a rich tourist.
Russell is the tallest in the room.
Someone outside the room is a wine connoisseur.
Robert and Kimberly hate each other.
More than one person outside the room is not a happy european.
Ricky is not rich or is not a tall rich happy tourist or both.
More than one person outside the room is not Ricky.
Only one person outside the room is quieter than Robert.
Only one person outside the room is a rich european. | Russell is not hated by Robert and is not a quiet person. | neutral | % SZS status Satisfiable
| room(russell)&room(ricky)&(![X]:(room(X)=>(X='russell'|X='ricky')))&
((((?[X]:(~room(X)&~(rich(X)&tourist(X))))&(![X,Y]:((~(rich(X)&tourist(X))&~(rich(Y)&tourist(Y)))=>(X=Y)))))&
(![X]:(taller(X,russell)))&
(?[X]:(~room(X)=>(is_a_wine_connoisseur(X))))&
((hate(robert,kimberly) & hate(kimberly,robert)))&
((?[X,Y]:(~room(X)&~room(Y)&(~(happy(X)&european(X))&~(happy(Y)&european(Y)))&(X!=Y))))&
(((~rich(ricky))|(~(tall(ricky)&rich(ricky)&happy(ricky)&tourist(ricky)))))&
((?[X,Y]:(~room(X)&~room(Y)&(X!=ricky&Y!=ricky)&(X!=Y))))&
(((?[X]:(~room(X)&quieter(robert,X)))&(![X,Y]:((quieter(robert,X)&quieter(robert,Y))=>(X=Y)))))&
(((?[X]:(~room(X)&rich(X)&european(X)))&(![X,Y]:((rich(X)&european(X)&rich(Y)&european(Y))=>(X=Y)))))) | room(russell)&room(ricky)&(![X]:(room(X)=>(X='russell'|X='ricky')))&
((~hate(russell,robert))&(~(quiet(russell)&person(russell)))) | neutral | contradiction | contradiction |
Adolph is the only person in the room.
Adolph and Ericka like each other.
Adolph does enjoy trail running and is a happy european.
Adolph who is not a happy tourist, is not quiet.
Adolph is the quietest in the room.
Everyone outside the room is not a quiet happy european. | Adolph does not build model airplanes or is quieter than Ericka or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(paul_type, type, (
paul: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(1,assumption,(~quieter(paul, mary)), introduced(assumption)).
tff(2,plain,
(^[X: $i] : refl(quieter(X, mary) <=> quieter(X, mary))),
inference(bind,[status(th)],[])).
tff(3,plain,
(![X: $i] : quieter(X, mary) <=> ![X: $i] : quieter(X, mary)),
inference(quant_intro,[status(thm)],[2])).
tff(4,plain,
(![X: $i] : quieter(X, mary) <=> ![X: $i] : quieter(X, mary)),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((like(mary, paul) & like(paul, mary)) & (predc(mary) & (happy(mary) & european(mary)))) & ((~(happy(mary) & tourist(mary))) & (~quiet(mary)))) & ![X: $i] : quieter(X, mary)) & ![X: $i] : ((~room(X)) => (~((quiet(X) & happy(X)) & european(X)))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~preda(mary)) | quieter(paul, mary))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & like(mary, paul) & like(paul, mary) & predc(mary) & happy(mary) & european(mary) & (~(happy(mary) & tourist(mary))) & (~quiet(mary)) & ![X: $i] : quieter(X, mary) & ![X: $i] : (room(X) | (~(quiet(X) & happy(X) & european(X)))))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))))),
inference(rewrite,[status(thm)],[])).
tff(6,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((like(mary, paul) & like(paul, mary)) & (predc(mary) & (happy(mary) & european(mary)))) & ((~(happy(mary) & tourist(mary))) & (~quiet(mary)))) & ![X: $i] : quieter(X, mary)) & ![X: $i] : ((~room(X)) => (~((quiet(X) & happy(X)) & european(X)))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~preda(mary)) | quieter(paul, mary))))), file('/mnt/tmpfs//6093125497634725603401114.p','negated')).
tff(7,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & like(mary, paul) & like(paul, mary) & predc(mary) & happy(mary) & european(mary) & (~(happy(mary) & tourist(mary))) & (~quiet(mary)) & ![X: $i] : quieter(X, mary) & ![X: $i] : (room(X) | (~(quiet(X) & happy(X) & european(X)))))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary))))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & like(mary, paul) & like(paul, mary) & predc(mary) & happy(mary) & european(mary) & (~(happy(mary) & tourist(mary))) & (~quiet(mary)) & ![X: $i] : quieter(X, mary) & ![X: $i] : (room(X) | (~(quiet(X) & happy(X) & european(X))))),
inference(or_elim,[status(thm)],[7])).
tff(9,plain,
(![X: $i] : quieter(X, mary)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(![X: $i] : quieter(X, mary)),
inference(modus_ponens,[status(thm)],[9, 4])).
tff(11,plain,(
![X: $i] : quieter(X, mary)),
inference(skolemize,[status(sab)],[10])).
tff(12,plain,
(![X: $i] : quieter(X, mary)),
inference(modus_ponens,[status(thm)],[11, 3])).
tff(13,plain,
((~![X: $i] : quieter(X, mary)) | quieter(paul, mary)),
inference(quant_inst,[status(thm)],[])).
tff(14,plain,
($false),
inference(unit_resolution,[status(thm)],[13, 12, 1])).
tff(15,plain,(quieter(paul, mary)), inference(lemma,lemma(discharge,[]))).
tff(16,plain,
(((~preda(mary)) | quieter(paul, mary)) | (~quieter(paul, mary))),
inference(tautology,[status(thm)],[])).
tff(17,plain,
((~preda(mary)) | quieter(paul, mary)),
inference(unit_resolution,[status(thm)],[16, 15])).
tff(18,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(room(mary)),
inference(and_elim,[status(thm)],[8])).
tff(20,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(((~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))) | (~((~preda(mary)) | quieter(paul, mary)))) <=> ((~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))) | (~((~preda(mary)) | quieter(paul, mary))))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary))))),
inference(monotonicity,[status(thm)],[22])).
tff(24,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary))))),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))),
inference(or_elim,[status(thm)],[7])).
tff(26,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))),
inference(modus_ponens,[status(thm)],[25, 23])).
tff(27,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))),
inference(modus_ponens,[status(thm)],[26, 24])).
tff(28,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~preda(mary)) | quieter(paul, mary)))),
inference(modus_ponens,[status(thm)],[27, 23])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!0)) (= X!0 |'mary'|))))
(a!4 (not (or (not (preda mary)) (quieter paul mary)))))
(let ((a!5 (and (room mary) a!2 (or (not (preda mary)) (quieter paul mary)))))
(let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 a!4))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!6))))
| room(adolph)&(![X]:(room(X)=>(X='adolph')))&
(((like(adolph,ericka) & like(ericka,adolph)))&
((does_enjoy_trail_running(adolph))&(happy(adolph)&european(adolph)))&
((~(happy(adolph)&tourist(adolph)))&(~quiet(adolph)))&
(![X]:(quieter(X,adolph)))&
(![X]:(~room(X)=>(~(quiet(X)&happy(X)&european(X)))))) | room(adolph)&(![X]:(room(X)=>(X='adolph')))&
(((does_not_build_model_airplanes(adolph))|(quieter(ericka,adolph)))) | contradiction | neutral | entailment |
George, Mark, Calvin are the only persons in the room.
At least one of the following is true:.
-George and Mark are not rich.
-Someone outside the room enjoys stand-up paddleboarding.
-George is the richest in the room. | Calvin who is not rich, is richer than Mary. | neutral | % SZS status Satisfiable
| room(george)&room(mark)&room(calvin)&(![X]:(room(X)=>(X='george'|X='mark'|X='calvin')))&
(((~rich(george)&~rich(mark))|
(?[X]:(~room(X)=>(enjoys_stand-up_paddleboarding(X))))|
(![X]:(richer(X,george))))) | room(george)&room(mark)&room(calvin)&(![X]:(room(X)=>(X='george'|X='mark'|X='calvin')))&
((~rich(calvin))&(richer(mary,calvin))) | neutral | neutral | contradiction |
Troy, Glenda are the only persons in the room. Troy who hates Steven, does not read mystery novels. Only one person outside the room is not a tall quiet person. Someone outside the room who is not hated by Mary is not a happy quiet tourist. Troy is the least quiet in the room. Rick and Troy like each other. It is not the case that 'someone who is not liked by Rick hate someone who is liked by Mary'. | Troy who is quieter than Steven, does not like Rick. | contradiction | - | room(troy)&room(glenda)&(![X]:(room(X)=>(X='troy'|X='glenda')))&
(((hate(steven,troy))&(does_not_read_mystery_novels(troy)))&
(((?[X]:(~room(X)&~(tall(X)&quiet(X)&person(X))))&(![X,Y]:((~(tall(X)&quiet(X)&person(X))&~(tall(Y)&quiet(Y)&person(Y)))=>(X=Y)))))&
(?[X]:(~room(X)=>(((~hate(X,mary))=>(~(happy(X)&quiet(X)&tourist(X)))))))&
(![X]:(quieter(troy,X)))&
((like(rick,troy) & like(troy,rick)))&
(~(?[X,Y]:((~like(X,rick))&(like(Y,mary))&(hate(X,Y)))))) | room(troy)&room(glenda)&(![X]:(room(X)=>(X='troy'|X='glenda')))&
((quieter(steven,troy))&(~like(rick,troy))) | contradiction | contradiction | contradiction |
George is the only person in the room. “George is the least quiet in the room” only if “George neither hates Denise nor hates Carlos”. George neither is not hated by Robert nor is a rich european. Only one person outside the room does not hate Carlos. George is a client of Denise and is not quiet. Denise and George hate each other. | George is quieter than Conrad and hates Conrad. | neutral | % SZS status Satisfiable
| room(george)&(![X]:(room(X)=>(X='george')))&
(((![X]:(quieter(george,X)))=>(~((hate(denise,george))|(hate(carlos,george)))))&
(~((~hate(george,robert))|(rich(george)&european(george))))&
(((?[X]:(~room(X)&~hate(carlos,X)))&(![X,Y]:((~hate(carlos,X)&~hate(carlos,Y))=>(X=Y)))))&
((client(denise,george))&(~quiet(george)))&
((hate(denise,george) & hate(george,denise)))) | room(george)&(![X]:(room(X)=>(X='george')))&
((quieter(conrad,george))&(hate(conrad,george))) | contradiction | contradiction | contradiction |
Nancy, Jerry, Val are the only persons in the room.
If “Val and Jerry are respectively rich and brave” then “more than one person outside the room is not a quiet rich tourist” otherwise “someone outside the room who is not a brave tourist can play the piano”.
“Only one person outside the room is not tall” if “Nancy is the least quiet in the room” and vice versa.
Fred is a sibling of Val.
Jerry and Nancy do not like Jose.
Val is liked by Fred and does not like Jose.
Val does not like Ashley. | It is not the case that 'Nancy either is not liked by Jose or is not a quiet brave creative rich tourist'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(susan_type, type, (
susan: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(mary_type, type, (
mary: $i)).
tff(paul_type, type, (
paul: $i)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(1,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((rich(fred) & brave(paul)) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~((quiet(X) & rich(X)) & tourist(X))) & (~((quiet(Y) & rich(Y)) & tourist(Y))))) & (~(X = Y)))) | ((~(rich(fred) & brave(paul))) => ?[X: $i] : ((~room(X)) => ((~(brave(X) & tourist(X))) => preda(X))))) & (![X: $i] : quieter(mary, X) <=> (?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : (((~tall(X)) & (~tall(Y))) => (X = Y))))) & sibling(fred, lucy)) & ((~like(susan, paul)) & (~like(susan, mary)))) & (like(fred, lucy) & (~like(susan, fred)))) & (~like(john, fred)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(((~like(mary, susan)) | (~((((quiet(mary) & brave(mary)) & creative(mary)) & rich(mary)) & tourist(mary)))) & (~((~like(mary, susan)) | (~((((quiet(mary) & brave(mary)) & creative(mary)) & rich(mary)) & tourist(mary)))))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : quieter(mary, X) <=> (?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)))) & sibling(fred, lucy) & (~like(susan, paul)) & (~like(susan, mary)) & like(fred, lucy) & (~like(susan, fred)) & (~like(john, fred)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((rich(fred) & brave(paul)) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~((quiet(X) & rich(X)) & tourist(X))) & (~((quiet(Y) & rich(Y)) & tourist(Y))))) & (~(X = Y)))) | ((~(rich(fred) & brave(paul))) => ?[X: $i] : ((~room(X)) => ((~(brave(X) & tourist(X))) => preda(X))))) & (![X: $i] : quieter(mary, X) <=> (?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : (((~tall(X)) & (~tall(Y))) => (X = Y))))) & sibling(fred, lucy)) & ((~like(susan, paul)) & (~like(susan, mary)))) & (like(fred, lucy) & (~like(susan, fred)))) & (~like(john, fred)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(((~like(mary, susan)) | (~((((quiet(mary) & brave(mary)) & creative(mary)) & rich(mary)) & tourist(mary)))) & (~((~like(mary, susan)) | (~((((quiet(mary) & brave(mary)) & creative(mary)) & rich(mary)) & tourist(mary)))))))))), file('/mnt/tmpfs//1285577431293731584286361.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : quieter(mary, X) <=> (?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)))) & sibling(fred, lucy) & (~like(susan, paul)) & (~like(susan, mary)) & like(fred, lucy) & (~like(susan, fred)) & (~like(john, fred)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : quieter(mary, X) <=> (?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)))) & sibling(fred, lucy) & (~like(susan, paul)) & (~like(susan, mary)) & like(fred, lucy) & (~like(susan, fred)) & (~like(john, fred))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(10,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(13,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(paul)) | (~room(mary)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(monotonicity,[status(thm)],[15])).
tff(17,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(paul)) | (~room(mary)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(transitivity,[status(thm)],[16, 14])).
tff(18,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(monotonicity,[status(thm)],[18])).
tff(20,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(or_elim,[status(thm)],[4])).
tff(22,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[21, 19])).
tff(23,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[22, 20])).
tff(24,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[23, 19])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|)
(not (room X!4))))))
(let ((a!6 (~ (not (and (room mary) (room paul) (room fred) a!4))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5))))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) a!6)))
| room(nancy)&room(jerry)&room(val)&(![X]:(room(X)=>(X='nancy'|X='jerry'|X='val')))&
(((((rich(val))&(brave(jerry)))=>((?[X,Y]:(~room(X)&~room(Y)&(~(quiet(X)&rich(X)&tourist(X))&~(quiet(Y)&rich(Y)&tourist(Y)))&(X!=Y)))))|((~((rich(val))&(brave(jerry))))=>(?[X]:(~room(X)=>(((~(brave(X)&tourist(X)))=>(can_play_the_piano(X))))))))&
((![X]:(quieter(nancy,X)))<=>(((?[X]:(~room(X)&~tall(X)))&(![X,Y]:((~tall(X)&~tall(Y))=>(X=Y))))))&
(sibling(val,fred))&
(~like(jose,jerry)&~like(jose,nancy))&
((like(val,fred))&(~like(jose,val)))&
(~like(ashley,val))) | room(nancy)&room(jerry)&room(val)&(![X]:(room(X)=>(X='nancy'|X='jerry'|X='val')))&
(~((((~like(nancy,jose))|(~(quiet(nancy)&brave(nancy)&creative(nancy)&rich(nancy)&tourist(nancy))))&(~((~like(nancy,jose))|(~(quiet(nancy)&brave(nancy)&creative(nancy)&rich(nancy)&tourist(nancy)))))))) | entailment | entailment | entailment |
Lillie, William are the only persons in the room. "Someone who is liked by Gwendolyn like someone who likes Gene" unless "no one in the room who is not happy does not like Gwendolyn". Lillie is the richest in the room. William is not rich or is a happy person or both. William and Son like each other. | Lillie neither does not hate Gwendolyn nor is a rich person. | neutral | % SZS status Satisfiable
| room(lillie)&room(william)&(![X]:(room(X)=>(X='lillie'|X='william')))&
((~(~?[X]:(room(X)=>(((~happy(X))=>(~like(gwendolyn,X))))))=>(?[X,Y]:((like(X,gwendolyn))&(like(gene,Y))&(like(X,Y)))))&
(![X]:(richer(X,lillie)))&
(((~rich(william))|(happy(william)&person(william))))&
((like(william,son) & like(son,william)))) | room(lillie)&room(william)&(![X]:(room(X)=>(X='lillie'|X='william')))&
(~((~hate(gwendolyn,lillie))|(rich(lillie)&person(lillie)))) | contradiction | contradiction | contradiction |
David, Jose, Venice are the only persons in the room.
It is not the case that 'someone who is not liked by Heather is quieter than someone who is liked by Larry'.
Jose does not like Larry and does not like Heather.
Everyone in the room does not like Larry.
Larry is quieter than Jose. | Venice does not like Larry or is not hated by Heather or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(fred_type, type, (
fred: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(1,plain,
(^[X: $i] : refl(((~room(X)) | (~like(john, X))) <=> ((~room(X)) | (~like(john, X))))),
inference(bind,[status(th)],[])).
tff(2,plain,
(![X: $i] : ((~room(X)) | (~like(john, X))) <=> ![X: $i] : ((~room(X)) | (~like(john, X)))),
inference(quant_intro,[status(thm)],[1])).
tff(3,plain,
(![X: $i] : ((~room(X)) | (~like(john, X))) <=> ![X: $i] : ((~room(X)) | (~like(john, X)))),
inference(rewrite,[status(thm)],[])).
tff(4,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((~?[X: $i, Y: $i] : (((~like(X, lucy)) & like(Y, john)) & quieter(X, Y))) & ((~like(john, paul)) & (~like(lucy, paul)))) & ![X: $i] : (room(X) => (~like(john, X)))) & quieter(paul, john))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~like(john, fred)) | (~hate(fred, lucy)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~like(X, lucy)) & like(Y, john) & quieter(X, Y))) & (~like(john, paul)) & (~like(lucy, paul)) & ![X: $i] : ((~room(X)) | (~like(john, X))) & quieter(paul, john))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))))),
inference(rewrite,[status(thm)],[])).
tff(5,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((~?[X: $i, Y: $i] : (((~like(X, lucy)) & like(Y, john)) & quieter(X, Y))) & ((~like(john, paul)) & (~like(lucy, paul)))) & ![X: $i] : (room(X) => (~like(john, X)))) & quieter(paul, john))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~like(john, fred)) | (~hate(fred, lucy)))))), file('/mnt/tmpfs//7869122158147669970616317.p','negated')).
tff(6,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~like(X, lucy)) & like(Y, john) & quieter(X, Y))) & (~like(john, paul)) & (~like(lucy, paul)) & ![X: $i] : ((~room(X)) | (~like(john, X))) & quieter(paul, john))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy)))))),
inference(modus_ponens,[status(thm)],[5, 4])).
tff(7,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~?[X: $i, Y: $i] : ((~like(X, lucy)) & like(Y, john) & quieter(X, Y))) & (~like(john, paul)) & (~like(lucy, paul)) & ![X: $i] : ((~room(X)) | (~like(john, X))) & quieter(paul, john)),
inference(or_elim,[status(thm)],[6])).
tff(8,plain,
(![X: $i] : ((~room(X)) | (~like(john, X)))),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(![X: $i] : ((~room(X)) | (~like(john, X)))),
inference(modus_ponens,[status(thm)],[8, 3])).
tff(10,plain,(
![X: $i] : ((~room(X)) | (~like(john, X)))),
inference(skolemize,[status(sab)],[9])).
tff(11,plain,
(![X: $i] : ((~room(X)) | (~like(john, X)))),
inference(modus_ponens,[status(thm)],[10, 2])).
tff(12,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(room(fred)),
inference(and_elim,[status(thm)],[7])).
tff(14,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(((~![X: $i] : ((~room(X)) | (~like(john, X)))) | ((~room(fred)) | (~like(john, fred)))) <=> ((~![X: $i] : ((~room(X)) | (~like(john, X)))) | (~room(fred)) | (~like(john, fred)))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
((~![X: $i] : ((~room(X)) | (~like(john, X)))) | ((~room(fred)) | (~like(john, fred)))),
inference(quant_inst,[status(thm)],[])).
tff(17,plain,
((~![X: $i] : ((~room(X)) | (~like(john, X)))) | (~room(fred)) | (~like(john, fred))),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(~like(john, fred)),
inference(unit_resolution,[status(thm)],[17, 14, 11])).
tff(19,plain,
(((~like(john, fred)) | (~hate(fred, lucy))) | like(john, fred)),
inference(tautology,[status(thm)],[])).
tff(20,plain,
((~like(john, fred)) | (~hate(fred, lucy))),
inference(unit_resolution,[status(thm)],[19, 18])).
tff(21,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
(room(paul)),
inference(and_elim,[status(thm)],[7])).
tff(23,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[22, 21])).
tff(24,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(room(mary)),
inference(and_elim,[status(thm)],[7])).
tff(26,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~like(john, fred)) | (~hate(fred, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~like(john, fred)) | (~hate(fred, lucy)))))),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
(((~like(john, fred)) | (~hate(fred, lucy))) <=> ((~like(john, fred)) | (~hate(fred, lucy)))),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
((~((~like(john, fred)) | (~hate(fred, lucy)))) <=> (~((~like(john, fred)) | (~hate(fred, lucy))))),
inference(monotonicity,[status(thm)],[28])).
tff(30,plain,
((~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~like(john, fred)) | (~hate(fred, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~like(john, fred)) | (~hate(fred, lucy)))))),
inference(monotonicity,[status(thm)],[30, 29])).
tff(32,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~like(john, fred)) | (~hate(fred, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~like(john, fred)) | (~hate(fred, lucy)))))),
inference(transitivity,[status(thm)],[31, 27])).
tff(33,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy)))))),
inference(monotonicity,[status(thm)],[33])).
tff(35,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy)))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))),
inference(or_elim,[status(thm)],[6])).
tff(37,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))),
inference(modus_ponens,[status(thm)],[36, 34])).
tff(38,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))),
inference(modus_ponens,[status(thm)],[37, 35])).
tff(39,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(john, fred)) | (~hate(fred, lucy))))),
inference(modus_ponens,[status(thm)],[38, 34])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!0 |'fred'|)
(= X!0 |'paul'|)
(= X!0 |'mary'|)
(not (room X!0)))))
(a!6 (not (or (not (like john fred)) (not (hate fred lucy))))))
(let ((a!7 (and (room mary)
(room paul)
(room fred)
a!4
(or (not (like john fred)) (not (hate fred lucy))))))
(let ((a!8 (~ (not a!7)
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!6))))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ a!6 a!6)) a!8))))
| room(david)&room(jose)&room(venice)&(![X]:(room(X)=>(X='david'|X='jose'|X='venice')))&
((~(?[X,Y]:((~like(X,heather))&(like(Y,larry))&(quieter(X,Y)))))&
((~like(larry,jose))&(~like(heather,jose)))&
(![X]:(room(X)=>(~like(larry,X))))&
(quieter(jose,larry))) | room(david)&room(jose)&room(venice)&(![X]:(room(X)=>(X='david'|X='jose'|X='venice')))&
(((~like(larry,venice))|(~hate(venice,heather)))) | contradiction | entailment | neutral |
Walter, Jerry are the only persons in the room. Jerry is the quietest in the room if only one person in the room is not liked by Myra and vice versa. If Walter is a client of Myra and is hated by Monte then Jeremy is a client of Walter. More than one person in the room is not happy, not quiet only if Myra and Walter like each other. If Myra is a client of Jerry then it is not the case that 'Monte is a client of Jerry'. Someone in the room who is not liked by Monte hates Monte. Walter does not like Jeremy and is not quiet. Walter and Myra like each other. Walter and Jeremy hate each other. Everyone in the room is a client of Google. Jerry neither does not hate Jeremy nor is hated by Jeremy. Jerry neither hates Monte nor is a client of Jeremy. | Walter is not quiet or is a client of Monte or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_5_type, type, (
tptp_fun_X_5: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(fred_type, type, (
fred: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(susan_type, type, (
susan: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(1,plain,
((~quiet(mary)) <=> (~quiet(mary))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((((((((?[X: $i] : (room(X) & (~like(X, alice))) & ![X: $i, Y: $i] : (((~like(X, alice)) & (~like(Y, alice))) => (X = Y))) <=> ![X: $i] : quieter(X, paul)) & ((client(alice, mary) & hate(mary, fred)) => client(mary, susan))) & (?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((((~happy(X)) & (~quiet(X))) & (~happy(Y))) & (~quiet(Y)))) & (~(X = Y))) => (like(alice, mary) & like(mary, alice)))) & (client(paul, alice) => (~client(paul, fred)))) & ?[X: $i] : (room(X) => ((~like(X, fred)) => hate(fred, X)))) & ((~like(susan, mary)) & (~quiet(mary)))) & (like(mary, alice) & like(alice, mary))) & (hate(mary, susan) & hate(susan, mary))) & ![X: $i] : (room(X) => predb(X))) & (~((~hate(susan, paul)) | hate(paul, susan)))) & (~(hate(fred, paul) | client(susan, paul))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~quiet(mary)) | client(fred, mary))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((?[X: $i] : (room(X) & (~like(X, alice))) & ![X: $i, Y: $i] : ((~((~like(X, alice)) & (~like(Y, alice)))) | (X = Y))) <=> ![X: $i] : quieter(X, paul)) & ((~(client(alice, mary) & hate(mary, fred))) | client(mary, susan)) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & (~happy(X)) & (~quiet(X)) & (~happy(Y)) & (~quiet(Y)) & (~(X = Y)))) | (like(alice, mary) & like(mary, alice))) & ((~client(paul, alice)) | (~client(paul, fred))) & ?[X: $i] : (hate(fred, X) | like(X, fred) | (~room(X))) & (~like(susan, mary)) & (~quiet(mary)) & like(mary, alice) & like(alice, mary) & hate(mary, susan) & hate(susan, mary) & ![X: $i] : (predb(X) | (~room(X))) & (~((~hate(susan, paul)) | hate(paul, susan))) & (~(hate(fred, paul) | client(susan, paul))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((((((((?[X: $i] : (room(X) & (~like(X, alice))) & ![X: $i, Y: $i] : (((~like(X, alice)) & (~like(Y, alice))) => (X = Y))) <=> ![X: $i] : quieter(X, paul)) & ((client(alice, mary) & hate(mary, fred)) => client(mary, susan))) & (?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((((~happy(X)) & (~quiet(X))) & (~happy(Y))) & (~quiet(Y)))) & (~(X = Y))) => (like(alice, mary) & like(mary, alice)))) & (client(paul, alice) => (~client(paul, fred)))) & ?[X: $i] : (room(X) => ((~like(X, fred)) => hate(fred, X)))) & ((~like(susan, mary)) & (~quiet(mary)))) & (like(mary, alice) & like(alice, mary))) & (hate(mary, susan) & hate(susan, mary))) & ![X: $i] : (room(X) => predb(X))) & (~((~hate(susan, paul)) | hate(paul, susan)))) & (~(hate(fred, paul) | client(susan, paul))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~quiet(mary)) | client(fred, mary))))), file('/mnt/tmpfs//432277498604013084513482.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((?[X: $i] : (room(X) & (~like(X, alice))) & ![X: $i, Y: $i] : ((~((~like(X, alice)) & (~like(Y, alice)))) | (X = Y))) <=> ![X: $i] : quieter(X, paul)) & ((~(client(alice, mary) & hate(mary, fred))) | client(mary, susan)) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & (~happy(X)) & (~quiet(X)) & (~happy(Y)) & (~quiet(Y)) & (~(X = Y)))) | (like(alice, mary) & like(mary, alice))) & ((~client(paul, alice)) | (~client(paul, fred))) & ?[X: $i] : (hate(fred, X) | like(X, fred) | (~room(X))) & (~like(susan, mary)) & (~quiet(mary)) & like(mary, alice) & like(alice, mary) & hate(mary, susan) & hate(susan, mary) & ![X: $i] : (predb(X) | (~room(X))) & (~((~hate(susan, paul)) | hate(paul, susan))) & (~(hate(fred, paul) | client(susan, paul))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((?[X: $i] : (room(X) & (~like(X, alice))) & ![X: $i, Y: $i] : ((~((~like(X, alice)) & (~like(Y, alice)))) | (X = Y))) <=> ![X: $i] : quieter(X, paul)) & ((~(client(alice, mary) & hate(mary, fred))) | client(mary, susan)) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & (~happy(X)) & (~quiet(X)) & (~happy(Y)) & (~quiet(Y)) & (~(X = Y)))) | (like(alice, mary) & like(mary, alice))) & ((~client(paul, alice)) | (~client(paul, fred))) & ?[X: $i] : (hate(fred, X) | like(X, fred) | (~room(X))) & (~like(susan, mary)) & (~quiet(mary)) & like(mary, alice) & like(alice, mary) & hate(mary, susan) & hate(susan, mary) & ![X: $i] : (predb(X) | (~room(X))) & (~((~hate(susan, paul)) | hate(paul, susan))) & (~(hate(fred, paul) | client(susan, paul)))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~quiet(mary)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(~quiet(mary)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(((~quiet(mary)) | client(fred, mary)) | quiet(mary)),
inference(tautology,[status(thm)],[])).
tff(9,plain,
((~quiet(mary)) | client(fred, mary)),
inference(unit_resolution,[status(thm)],[8, 7])).
tff(10,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(12,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[11, 10])).
tff(13,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(15,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[14, 13])).
tff(16,plain,
(((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~((~quiet(mary)) | client(fred, mary)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~((~quiet(mary)) | client(fred, mary))))),
inference(rewrite,[status(thm)],[])).
tff(17,plain,
((~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) <=> (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5))))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
(((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~((~quiet(mary)) | client(fred, mary)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~((~quiet(mary)) | client(fred, mary))))),
inference(monotonicity,[status(thm)],[17])).
tff(19,plain,
(((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~((~quiet(mary)) | client(fred, mary)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!5 = |'paul'|) | (X!5 = |'mary'|) | (~room(X!5)))) | (~((~quiet(mary)) | client(fred, mary))))),
inference(transitivity,[status(thm)],[18, 16])).
tff(20,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary))))),
inference(monotonicity,[status(thm)],[20])).
tff(22,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary))))),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))),
inference(or_elim,[status(thm)],[4])).
tff(24,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))),
inference(modus_ponens,[status(thm)],[23, 21])).
tff(25,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))),
inference(modus_ponens,[status(thm)],[24, 22])).
tff(26,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~quiet(mary)) | client(fred, mary)))),
inference(modus_ponens,[status(thm)],[25, 21])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!5 |'paul'|) (= X!5 |'mary'|) (not (room X!5)))))
(a!5 (not (or (not (quiet mary)) (client fred mary)))))
(let ((a!6 (and (room mary)
(room paul)
a!3
(or (not (quiet mary)) (client fred mary)))))
(let ((a!7 (~ (not a!6) (or (not (room mary)) (not (room paul)) a!4 a!5))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ a!5 a!5)) a!7))))
| room(walter)&room(jerry)&(![X]:(room(X)=>(X='walter'|X='jerry')))&
(((((?[X]:(room(X)&~like(X,myra)))&(![X,Y]:((~like(X,myra)&~like(Y,myra))=>(X=Y)))))<=>(![X]:(quieter(X,jerry))))&
(((client(myra,walter))&(hate(walter,monte)))=>(client(walter,jeremy)))&
(((?[X,Y]:(room(X)&room(Y)&(~happy(X)&~quiet(X)&~happy(Y)&~quiet(Y))&(X!=Y))))=>((like(myra,walter) & like(walter,myra))))&
((client(jerry,myra))=>(~(client(jerry,monte))))&
(?[X]:(room(X)=>(((~like(X,monte))=>(hate(monte,X))))))&
((~like(jeremy,walter))&(~quiet(walter)))&
((like(walter,myra) & like(myra,walter)))&
((hate(walter,jeremy) & hate(jeremy,walter)))&
(![X]:(room(X)=>(is_a_client_of_Google(X))))&
(~((~hate(jeremy,jerry))|(hate(jerry,jeremy))))&
(~((hate(monte,jerry))|(client(jeremy,jerry))))) | room(walter)&room(jerry)&(![X]:(room(X)=>(X='walter'|X='jerry')))&
(((~quiet(walter))|(client(monte,walter)))) | entailment | entailment | entailment |
Jasmin, Paula, Garry, Melissa are the only persons in the room.
Melissa is the least tall in the room only if Paula likes Lisa and is a tall tourist.
More than one person outside the room is a client of Lisa.
Melissa is the least tall in the room. | Melissa and Paula are tall tourist. | neutral | % SZS status Satisfiable
| room(jasmin)&room(paulaa)&room(garry)&room(melissa)&(![X]:(room(X)=>(X='jasmin'|X='paulaa'|X='garry'|X='melissa')))&
(((![X]:(taller(melissa,X)))=>((like(lisa,paulaa))&(tall(paulaa)&tourist(paulaa))))&
((?[X,Y]:(~room(X)&~room(Y)&(client(lisa,X)&client(lisa,Y))&(X!=Y))))&
(![X]:(taller(melissa,X)))) | room(jasmin)&room(paulaa)&room(garry)&room(melissa)&(![X]:(room(X)=>(X='jasmin'|X='paulaa'|X='garry'|X='melissa')))&
(tall(melissa)&tourist(melissa)&tall(paulaa)&tourist(paulaa)) | entailment | contradiction | contradiction |
Sharon, William, Anne, Jim are the only persons in the room.
If 'Anne and William are liked by Eileen' then 'Eileen is quieter than Jim'.
'Someone outside the room who is a quiet european owns a telescope' if 'Jim is a quiet happy tourist and is not liked by Eileen' and vice versa.
'Jim neither does not like Eileen nor is a client of Eileen' if 'only one person outside the room is quieter than Eileen'.
Someone outside the room who is a quiet european owns a telescope.
Anne does not own a telescope.
Only one person outside the room likes Eileen.
Someone outside the room who is a quiet european owns a telescope.
Jim is the least quiet in the room.
Everyone outside the room who is not happy is liked by Eileen. | Someone who is not a creative quiet tourist is quieter than someone who is not creative, not quiet, not happy. | contradiction | - | room(sharon)&room(william)&room(anne)&room(jim)&(![X]:(room(X)=>(X='sharon'|X='william'|X='anne'|X='jim')))&
(((like(anne,eileen)&like(william,eileen))=>(quieter(jim,eileen)))&
(((quiet(jim)&happy(jim)&tourist(jim))&(~like(jim,eileen)))<=>(?[X]:(~room(X)=>(((quiet(X)&european(X))=>(owns_a_telescope(X)))))))&
((((?[X]:(~room(X)&quieter(eileen,X)))&(![X,Y]:((quieter(eileen,X)&quieter(eileen,Y))=>(X=Y)))))=>(~((~like(eileen,jim))|(client(eileen,jim)))))&
(?[X]:(~room(X)=>(((quiet(X)&european(X))=>(owns_a_telescope(X))))))&
(does_not_own_a_telescope(anne))&
(((?[X]:(~room(X)&like(eileen,X)))&(![X,Y]:((like(eileen,X)&like(eileen,Y))=>(X=Y)))))&
(?[X]:(~room(X)=>(((quiet(X)&european(X))=>(owns_a_telescope(X))))))&
(![X]:(quieter(jim,X)))&
(![X]:(~room(X)=>(((~happy(X))=>(like(X,eileen))))))) | room(sharon)&room(william)&room(anne)&room(jim)&(![X]:(room(X)=>(X='sharon'|X='william'|X='anne'|X='jim')))&
(?[X,Y]:((~(creative(X)&quiet(X)&tourist(X)))&(~creative(Y)&~quiet(Y)&~happy(Y))&(quieter(X,Y)))) | neutral | neutral | neutral |
Sharon, Ruben, Richard are the only persons in the room. If "Ruben neither is quieter than Nicolas nor is not quiet, not tall" then "someone who is not a happy person hate someone who is not a quiet person" otherwise "someone who hates Barbara hate someone who enjoys cycling". Ruben neither is hated by Nicolas nor is not a quiet tourist. Someone who hates Barbara hate someone who enjoys cycling. Someone who is not a happy person hate someone who is not a quiet person. Richard is a happy tall quiet person or is not Sharon or both. Ruben and Richard are respectively happy and tall. Barbara is taller than Ruben. | Ruben neither is not a happy tourist nor is not tall, not quiet. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tall_type, type, (
tall: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(1,plain,
(quiet(paul) <=> quiet(paul)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((~(quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))))) => ?[X: $i, Y: $i] : (((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y)))) & hate(X, Y))) | ((~(~(quieter(john, paul) | ((~quiet(paul)) & (~tall(paul)))))) => ?[X: $i, Y: $i] : ((hate(alice, X) & preda(Y)) & hate(X, Y)))) & (~(hate(paul, john) | (~(quiet(paul) & tourist(paul)))))) & ?[X: $i, Y: $i] : ((hate(alice, X) & preda(Y)) & hate(X, Y))) & ?[X: $i, Y: $i] : (((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y)))) & hate(X, Y))) & ((((happy(fred) & tall(fred)) & quiet(fred)) & person(fred)) | (~(fred = mary)))) & (happy(paul) & tall(fred))) & taller(paul, alice))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul)))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))) | (~(quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))))) | ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y))) & hate(X, Y)) | ?[X: $i, Y: $i] : (hate(alice, X) & preda(Y) & hate(X, Y))) & (~(hate(paul, john) | (~(quiet(paul) & tourist(paul))))) & ?[X: $i, Y: $i] : (hate(alice, X) & preda(Y) & hate(X, Y)) & ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y))) & hate(X, Y)) & ((~(fred = mary)) | (happy(fred) & tall(fred) & quiet(fred) & person(fred))) & happy(paul) & tall(fred) & taller(paul, alice))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((~(quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))))) => ?[X: $i, Y: $i] : (((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y)))) & hate(X, Y))) | ((~(~(quieter(john, paul) | ((~quiet(paul)) & (~tall(paul)))))) => ?[X: $i, Y: $i] : ((hate(alice, X) & preda(Y)) & hate(X, Y)))) & (~(hate(paul, john) | (~(quiet(paul) & tourist(paul)))))) & ?[X: $i, Y: $i] : ((hate(alice, X) & preda(Y)) & hate(X, Y))) & ?[X: $i, Y: $i] : (((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y)))) & hate(X, Y))) & ((((happy(fred) & tall(fred)) & quiet(fred)) & person(fred)) | (~(fred = mary)))) & (happy(paul) & tall(fred))) & taller(paul, alice))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul)))))))), file('/mnt/tmpfs//3325026412341183652816424.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))) | (~(quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))))) | ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y))) & hate(X, Y)) | ?[X: $i, Y: $i] : (hate(alice, X) & preda(Y) & hate(X, Y))) & (~(hate(paul, john) | (~(quiet(paul) & tourist(paul))))) & ?[X: $i, Y: $i] : (hate(alice, X) & preda(Y) & hate(X, Y)) & ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y))) & hate(X, Y)) & ((~(fred = mary)) | (happy(fred) & tall(fred) & quiet(fred) & person(fred))) & happy(paul) & tall(fred) & taller(paul, alice))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul)))))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))) | (~(quieter(john, paul) | ((~quiet(paul)) & (~tall(paul))))) | ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y))) & hate(X, Y)) | ?[X: $i, Y: $i] : (hate(alice, X) & preda(Y) & hate(X, Y))) & (~(hate(paul, john) | (~(quiet(paul) & tourist(paul))))) & ?[X: $i, Y: $i] : (hate(alice, X) & preda(Y) & hate(X, Y)) & ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~(quiet(Y) & person(Y))) & hate(X, Y)) & ((~(fred = mary)) | (happy(fred) & tall(fred) & quiet(fred) & person(fred))) & happy(paul) & tall(fred) & taller(paul, alice)),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~(hate(paul, john) | (~(quiet(paul) & tourist(paul))))),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(quiet(paul) & tourist(paul)),
inference(or_elim,[status(thm)],[6])).
tff(8,plain,
(quiet(paul)),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(quiet(paul)),
inference(modus_ponens,[status(thm)],[8, 1])).
tff(10,plain,
((quiet(paul) | tall(paul)) | (~quiet(paul))),
inference(tautology,[status(thm)],[])).
tff(11,plain,
(quiet(paul) | tall(paul)),
inference(unit_resolution,[status(thm)],[10, 9])).
tff(12,plain,
(happy(paul) <=> happy(paul)),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(happy(paul)),
inference(and_elim,[status(thm)],[5])).
tff(14,plain,
(happy(paul)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(tourist(paul) <=> tourist(paul)),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(tourist(paul)),
inference(and_elim,[status(thm)],[7])).
tff(17,plain,
(tourist(paul)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(20,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(23,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[22, 21])).
tff(24,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(26,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
((((~happy(paul)) | (~tourist(paul))) | (~(quiet(paul) | tall(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~happy(paul)) | (~tourist(paul)) | (~(quiet(paul) | tall(paul))))),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
((~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
(((~tall(paul)) & (~quiet(paul))) <=> (~(quiet(paul) | tall(paul)))),
inference(rewrite,[status(thm)],[])).
tff(30,plain,
((~(~((~happy(paul)) | (~tourist(paul))))) <=> ((~happy(paul)) | (~tourist(paul)))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
((happy(paul) & tourist(paul)) <=> (~((~happy(paul)) | (~tourist(paul))))),
inference(rewrite,[status(thm)],[])).
tff(32,plain,
((~(happy(paul) & tourist(paul))) <=> (~(~((~happy(paul)) | (~tourist(paul)))))),
inference(monotonicity,[status(thm)],[31])).
tff(33,plain,
((~(happy(paul) & tourist(paul))) <=> ((~happy(paul)) | (~tourist(paul)))),
inference(transitivity,[status(thm)],[32, 30])).
tff(34,plain,
(((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> (((~happy(paul)) | (~tourist(paul))) | (~(quiet(paul) | tall(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(monotonicity,[status(thm)],[33, 29, 28])).
tff(35,plain,
(((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~happy(paul)) | (~tourist(paul)) | (~(quiet(paul) | tall(paul))))),
inference(transitivity,[status(thm)],[34, 27])).
tff(36,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))) <=> ((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul)))))),
inference(monotonicity,[status(thm)],[28])).
tff(38,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))) <=> ((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))),
inference(transitivity,[status(thm)],[37, 36])).
tff(39,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul)))))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul)))))))),
inference(monotonicity,[status(thm)],[39])).
tff(41,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul)))))))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))),
inference(or_elim,[status(thm)],[4])).
tff(43,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))),
inference(modus_ponens,[status(thm)],[42, 40])).
tff(44,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))),
inference(modus_ponens,[status(thm)],[43, 41])).
tff(45,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(happy(paul) & tourist(paul))) | ((~tall(paul)) & (~quiet(paul))))))),
inference(modus_ponens,[status(thm)],[44, 40])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|)
(not (room X!4)))))
(a!6 (or (not (and (happy paul) (tourist paul)))
(and (not (tall paul)) (not (quiet paul))))))
(let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 (not a!6)))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!6))))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ a!6 a!6)) a!7)))
| room(sharon)&room(ruben)&room(richard)&(![X]:(room(X)=>(X='sharon'|X='ruben'|X='richard')))&
((((~((quieter(nicolas,ruben))|(~quiet(ruben)&~tall(ruben))))=>(?[X,Y]:((~(happy(X)&person(X)))&(~(quiet(Y)&person(Y)))&(hate(X,Y)))))|((~(~((quieter(nicolas,ruben))|(~quiet(ruben)&~tall(ruben)))))=>(?[X,Y]:((hate(barbara,X))&(enjoys_cycling(Y))&(hate(X,Y))))))&
(~((hate(ruben,nicolas))|(~(quiet(ruben)&tourist(ruben)))))&
(?[X,Y]:((hate(barbara,X))&(enjoys_cycling(Y))&(hate(X,Y))))&
(?[X,Y]:((~(happy(X)&person(X)))&(~(quiet(Y)&person(Y)))&(hate(X,Y))))&
(((happy(richard)&tall(richard)&quiet(richard)&person(richard))|(richard!=sharon)))&
((happy(ruben))&(tall(richard)))&
(taller(ruben,barbara))) | room(sharon)&room(ruben)&room(richard)&(![X]:(room(X)=>(X='sharon'|X='ruben'|X='richard')))&
(~((~(happy(ruben)&tourist(ruben)))|(~tall(ruben)&~quiet(ruben)))) | entailment | contradiction | contradiction |
Michael, Aura are the only persons in the room.
“Everyone outside the room does not hate Norma” only if “only one person outside the room does not hate Norma”.
More than one person outside the room is not a happy person.
Only one person outside the room does not hate Norma.
Only one person outside the room is not liked by Norma. | Michael is not liked by Norma and is a happy creative person. | contradiction | - | room(michael)&room(aura)&(![X]:(room(X)=>(X='michael'|X='aura')))&
(((![X]:(~room(X)=>(~hate(norma,X))))=>(((?[X]:(~room(X)&~hate(norma,X)))&(![X,Y]:((~hate(norma,X)&~hate(norma,Y))=>(X=Y))))))&
((?[X,Y]:(~room(X)&~room(Y)&(~(happy(X)&person(X))&~(happy(Y)&person(Y)))&(X!=Y))))&
(((?[X]:(~room(X)&~hate(norma,X)))&(![X,Y]:((~hate(norma,X)&~hate(norma,Y))=>(X=Y)))))&
(((?[X]:(~room(X)&~like(X,norma)))&(![X,Y]:((~like(X,norma)&~like(Y,norma))=>(X=Y)))))) | room(michael)&room(aura)&(![X]:(room(X)=>(X='michael'|X='aura')))&
((~like(michael,norma))&(happy(michael)&creative(michael)&person(michael))) | neutral | neutral | contradiction |
Ruth, William, Gladys, Thomas are the only persons in the room. Someone who is not Gladys like someone who is not a creative tourist. Only one person in the room does not like Maynard. Gladys who does not hate Maynard, does not like Maynard. It is not the case that 'William likes Maynard and does not know morse code'. More than one person outside the room is hated by Maynard. | William neither does not hate Maynard nor is not creative. | contradiction | - | room(ruth)&room(william)&room(gladys)&room(thomas)&(![X]:(room(X)=>(X='ruth'|X='william'|X='gladys'|X='thomas')))&
((?[X,Y]:((X!=gladys)&(~(creative(Y)&tourist(Y)))&(like(X,Y))))&
(((?[X]:(room(X)&~like(maynard,X)))&(![X,Y]:((~like(maynard,X)&~like(maynard,Y))=>(X=Y)))))&
((~hate(maynard,gladys))&(~like(maynard,gladys)))&
(~((like(maynard,william))&(does_not_know_morse_code(william))))&
((?[X,Y]:(~room(X)&~room(Y)&(hate(X,maynard)&hate(Y,maynard))&(X!=Y))))) | room(ruth)&room(william)&room(gladys)&room(thomas)&(![X]:(room(X)=>(X='ruth'|X='william'|X='gladys'|X='thomas')))&
(~((~hate(maynard,william))|(~creative(william)))) | contradiction | contradiction | neutral |
At most one of the following is true:. -Erin is richer than Tonya and is not a rich person. -Alton who is a rich person, enjoys fishing. | Alton is the least rich in the room. | neutral | % SZS status Satisfiable
| room(erin)&room(robert)&room(andy)&room(alton)&(![X]:(room(X)=>(X='erin'|X='robert'|X='andy'|X='alton')))&
(~((richer(tonya,erin))&(~(rich(erin)&person(erin)))&(rich(alton)&person(alton))&(enjoys_fishing(alton)))) | room(erin)&room(robert)&room(andy)&room(alton)&(![X]:(room(X)=>(X='erin'|X='robert'|X='andy'|X='alton')))&
(![X]:(richer(alton,X))) | contradiction | neutral | contradiction |
Michael, Jodi, Otis, Angela are the only persons in the room. At least one of the following is true:. -Someone who does not like Linda like someone who is not Otis. -More than one person outside the room does not like Linda. | Otis does not like Linda or is not Michael or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(john_type, type, (
john: $i)).
tff(mary_type, type, (
mary: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(paul_type, type, (
paul: $i)).
tff(susan_type, type, (
susan: $i)).
tff(alice_type, type, (
alice: $i)).
tff(1,plain,
((~(fred = mary)) <=> (~(fred = mary))),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//9131379067848230603417448.p','b14')).
tff(3,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[2])).
tff(4,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[3])).
tff(5,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[4])).
tff(6,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[6])).
tff(8,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[10])).
tff(12,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[11])).
tff(13,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[13])).
tff(15,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[17])).
tff(19,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
(~(fred = mary)),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
(~(fred = mary)),
inference(modus_ponens,[status(thm)],[32, 1])).
tff(34,plain,
(((~(fred = mary)) | (~like(john, fred))) | (fred = mary)),
inference(tautology,[status(thm)],[])).
tff(35,plain,
((~(fred = mary)) | (~like(john, fred))),
inference(unit_resolution,[status(thm)],[34, 33])).
tff(36,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (?[X: $i, Y: $i] : (((~like(john, X)) & (~(Y = fred))) & like(X, Y)) | ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(john, X)) & (~like(john, Y)))) & (~(X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(john, fred)) | (~(fred = mary)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~like(john, X)) & (~(Y = fred)) & like(X, Y)) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(john, X)) & (~like(john, Y)) & (~(X = Y)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))))),
inference(rewrite,[status(thm)],[])).
tff(38,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (?[X: $i, Y: $i] : (((~like(john, X)) & (~(Y = fred))) & like(X, Y)) | ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~like(john, X)) & (~like(john, Y)))) & (~(X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(john, fred)) | (~(fred = mary)))))), file('/mnt/tmpfs//9131379067848230603417448.p','negated')).
tff(39,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~like(john, X)) & (~(Y = fred)) & like(X, Y)) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(john, X)) & (~like(john, Y)) & (~(X = Y)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred)))))),
inference(modus_ponens,[status(thm)],[38, 37])).
tff(40,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~like(john, X)) & (~(Y = fred)) & like(X, Y)) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~like(john, X)) & (~like(john, Y)) & (~(X = Y))))),
inference(or_elim,[status(thm)],[39])).
tff(41,plain,
(room(alice)),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[41, 36])).
tff(43,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
(room(fred)),
inference(and_elim,[status(thm)],[40])).
tff(45,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[44, 43])).
tff(46,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(47,plain,
(room(paul)),
inference(and_elim,[status(thm)],[40])).
tff(48,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[47, 46])).
tff(49,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
(room(mary)),
inference(and_elim,[status(thm)],[40])).
tff(51,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[50, 49])).
tff(52,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~(fred = mary)) | (~like(john, fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~(fred = mary)) | (~like(john, fred)))))),
inference(rewrite,[status(thm)],[])).
tff(53,plain,
((~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~(fred = mary)) | (~like(john, fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~(fred = mary)) | (~like(john, fred)))))),
inference(monotonicity,[status(thm)],[53])).
tff(55,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~(fred = mary)) | (~like(john, fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~(fred = mary)) | (~like(john, fred)))))),
inference(transitivity,[status(thm)],[54, 52])).
tff(56,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))),
inference(rewrite,[status(thm)],[])).
tff(57,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred)))))),
inference(monotonicity,[status(thm)],[56])).
tff(58,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred)))))),
inference(rewrite,[status(thm)],[])).
tff(59,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))),
inference(or_elim,[status(thm)],[39])).
tff(60,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))),
inference(modus_ponens,[status(thm)],[59, 57])).
tff(61,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))),
inference(modus_ponens,[status(thm)],[60, 58])).
tff(62,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(fred = mary)) | (~like(john, fred))))),
inference(modus_ponens,[status(thm)],[61, 57])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!4 |'alice'|)
(= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|)
(not (room X!4)))))
(a!7 (not (or (not (= fred mary)) (not (like john fred))))))
(let ((a!8 (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(or (not (= fred mary)) (not (like john fred))))))
(let ((a!9 (~ (not a!8)
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
a!7))))
(nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!9))))
| room(michael)&room(jodi)&room(otis)&room(angela)&(![X]:(room(X)=>(X='michael'|X='jodi'|X='otis'|X='angela')))&
(((?[X,Y]:((~like(linda,X))&(Y!=otis)&(like(X,Y))))|
((?[X,Y]:(~room(X)&~room(Y)&(~like(linda,X)&~like(linda,Y))&(X!=Y)))))) | room(michael)&room(jodi)&room(otis)&room(angela)&(![X]:(room(X)=>(X='michael'|X='jodi'|X='otis'|X='angela')))&
(((~like(linda,otis))|(otis!=michael))) | entailment | neutral | entailment |
Michael, George are the only persons in the room.
“George is the quietest in the room” if “someone who does not like Susie like someone who is not liked by Bobbie” and vice versa.
Michael who is a quiet european, is a tea enthusiast.
It is not the case that 'Bobbie is quieter than Michael'.
Susie is quieter than George. | Michael is not a quiet european or is quieter than Anthony or both. | neutral | % SZS status Satisfiable
| room(michael)&room(george)&(![X]:(room(X)=>(X='michael'|X='george')))&
(((?[X,Y]:((~like(susie,X))&(~like(Y,bobbie))&(like(X,Y))))<=>(![X]:(quieter(X,george))))&
((quiet(michael)&european(michael))&(is_a_tea_enthusiast(michael)))&
(~(quieter(michael,bobbie)))&
(quieter(george,susie))) | room(michael)&room(george)&(![X]:(room(X)=>(X='michael'|X='george')))&
(((~(quiet(michael)&european(michael)))|(quieter(anthony,michael)))) | contradiction | entailment | contradiction |
Donna is the only person in the room. If 'Donna neither enjoys pottery nor is not happy, not rich' then 'Donna enjoys pottery and is not quiet'. Everyone outside the room is not liked by Allison. Someone who is not liked by Allison is taller than someone who is a rich tourist. | Donna neither is hated by Allison nor is a happy rich creative tourist. | neutral | % SZS status Satisfiable
| room(donna)&(![X]:(room(X)=>(X='donna')))&
(((~((enjoys_pottery(donna))|(~happy(donna)&~rich(donna))))=>((enjoys_pottery(donna))&(~quiet(donna))))&
(![X]:(~room(X)=>(~like(X,allison))))&
(?[X,Y]:((~like(X,allison))&(rich(Y)&tourist(Y))&(taller(X,Y))))) | room(donna)&(![X]:(room(X)=>(X='donna')))&
(~((hate(donna,allison))|(happy(donna)&rich(donna)&creative(donna)&tourist(donna)))) | neutral | contradiction | contradiction |
Tonya, Melissa, Willard are the only persons in the room.
“Melissa hates Kathy and is not liked by James” unless “James is quieter than Tonya”.
“Melissa is the least quiet in the room” unless “everyone in the room who is quieter than James is hated by Kathy”.
Tonya is a sibling of Kathy and does not own a telescope.
More than one person outside the room owns a telescope.
Someone who is quieter than James hate someone who is not brave.
Tonya and Melissa are respectively quiet and creative.
Melissa does not own a telescope.
More than one person in the room does not hate James.
Melissa hates Kathy and is not liked by James.
Tonya is the quietest in the room. | Melissa is a brave quiet creative happy tourist and does not like Kathy. | neutral | % SZS status Satisfiable
| room(tonya)&room(melissa)&room(willard)&(![X]:(room(X)=>(X='tonya'|X='melissa'|X='willard')))&
((~(quieter(tonya,james))=>((hate(kathy,melissa))&(~like(melissa,james))))&
(~(![X]:(room(X)=>(((quieter(james,X))=>(hate(X,kathy))))))=>(![X]:(quieter(melissa,X))))&
((sibling(kathy,tonya))&(does_not_own_a_telescope(tonya)))&
((?[X,Y]:(~room(X)&~room(Y)&(owns_a_telescope(X)&owns_a_telescope(Y))&(X!=Y))))&
(?[X,Y]:((quieter(james,X))&(~brave(Y))&(hate(X,Y))))&
((quiet(tonya))&(creative(melissa)))&
(does_not_own_a_telescope(melissa))&
((?[X,Y]:(room(X)&room(Y)&(~hate(james,X)&~hate(james,Y))&(X!=Y))))&
((hate(kathy,melissa))&(~like(melissa,james)))&
(![X]:(quieter(X,tonya)))) | room(tonya)&room(melissa)&room(willard)&(![X]:(room(X)=>(X='tonya'|X='melissa'|X='willard')))&
((brave(melissa)&quiet(melissa)&creative(melissa)&happy(melissa)&tourist(melissa))&(~like(kathy,melissa))) | neutral | contradiction | entailment |
Gregory, Bethany, Courtney are the only persons in the room.
"Sandra is a sibling of Bethany" if "Courtney is the richest in the room" and vice versa.
If "Courtney and Bethany are respectively quiet and creative" then "Courtney neither is a quiet european nor is quieter than Miranda".
If "someone outside the room who is not quiet hates Tom" then "only one person outside the room is not a rich creative quiet person".
"Bethany is a creative quiet person" only if "Bethany and Gregory are hated by Sandra".
Miranda is a sibling of Courtney.
Courtney and Bethany are not a rich quiet european.
Someone who is hated by Tom hate someone who does not hate Sandra.
Someone who is not a creative person is a client of someone who is not Bethany.
Everyone outside the room hates Tom.
It is not the case that 'Courtney is quieter than Miranda'.
Everyone outside the room is a sibling of Miranda. | Courtney neither is a quiet person nor does not hate Francine. | contradiction | - | room(gregory)&room(bethany)&room(courtney)&(![X]:(room(X)=>(X='gregory'|X='bethany'|X='courtney')))&
(((![X]:(richer(X,courtney)))<=>(sibling(bethany,sandra)))&
(((quiet(courtney))&(creative(bethany)))=>(~((quiet(courtney)&european(courtney))|(quieter(miranda,courtney)))))&
((?[X]:(~room(X)=>(((~quiet(X))=>(hate(tom,X))))))=>(((?[X]:(~room(X)&~(rich(X)&creative(X)&quiet(X)&person(X))))&(![X,Y]:((~(rich(X)&creative(X)&quiet(X)&person(X))&~(rich(Y)&creative(Y)&quiet(Y)&person(Y)))=>(X=Y))))))&
((creative(bethany)&quiet(bethany)&person(bethany))=>(hate(bethany,sandra)&hate(gregory,sandra)))&
(sibling(courtney,miranda))&
(~(rich(courtney)&quiet(courtney)&european(courtney))&~(rich(bethany)&quiet(bethany)&european(bethany)))&
(?[X,Y]:((hate(X,tom))&(~hate(sandra,Y))&(hate(X,Y))))&
(?[X,Y]:((~(creative(X)&person(X)))&(Y!=bethany)&(client(X,Y))))&
(![X]:(~room(X)=>(hate(tom,X))))&
(~(quieter(miranda,courtney)))&
(![X]:(~room(X)=>(sibling(miranda,X))))) | room(gregory)&room(bethany)&room(courtney)&(![X]:(room(X)=>(X='gregory'|X='bethany'|X='courtney')))&
(~((quiet(courtney)&person(courtney))|(~hate(francine,courtney)))) | neutral | neutral | neutral |
Gabriel, Jason are the only persons in the room.
"Everyone outside the room does not enjoy rooftop gardening" if "Jason and Gabriel do not like John" and vice versa.
"Jason either is not a client of Google or is not liked by Linda" unless "more than one person in the room does not like John".
It is not the case that 'Jason is not a quiet creative rich european or is not a client of Google or both'.
Gabriel who is a rich quiet tall european, is a tall rich creative european.
More than one person in the room does not like John.
It is not the case that 'Linda is taller than Jason'.
Gabriel is the quietest in the room.
Everyone in the room who likes Linda is not a tall european.
Gabriel is not liked by Linda or is richer than Linda or both. | Jason who is a rich person, is a rich creative quiet person. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(susan_type, type, (
susan: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(1,plain,
(european(paul) <=> european(paul)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((~like(lucy, paul)) & (~like(lucy, mary))) <=> ![X: $i] : ((~room(X)) => (~preda(X)))) & ((~?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~like(lucy, X)) & (~like(lucy, Y)))) & (~(X = Y)))) => (((~predc(paul)) | (~like(paul, susan))) & (~((~predc(paul)) | (~like(paul, susan))))))) & (~((~(((quiet(paul) & creative(paul)) & rich(paul)) & european(paul))) | (~predc(paul))))) & ((((rich(mary) & quiet(mary)) & tall(mary)) & european(mary)) & (((tall(mary) & rich(mary)) & creative(mary)) & european(mary)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~like(lucy, X)) & (~like(lucy, Y)))) & (~(X = Y)))) & (~taller(paul, susan))) & ![X: $i] : quieter(X, mary)) & ![X: $i] : (room(X) => (like(susan, X) => (~(tall(X) & european(X)))))) & ((~like(mary, susan)) | richer(susan, mary)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((rich(paul) & person(paul)) & (((rich(paul) & creative(paul)) & quiet(paul)) & person(paul)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (((~like(lucy, paul)) & (~like(lucy, mary))) <=> ![X: $i] : (room(X) | (~preda(X)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~like(lucy, X)) & (~like(lucy, Y)) & (~(X = Y))) & (~((~predc(paul)) | (~(quiet(paul) & creative(paul) & rich(paul) & european(paul))))) & rich(mary) & quiet(mary) & tall(mary) & european(mary) & creative(mary) & (~taller(paul, susan)) & ![X: $i] : quieter(X, mary) & ![X: $i] : ((~room(X)) | (~(tall(X) & european(X))) | (~like(susan, X))) & ((~like(mary, susan)) | richer(susan, mary)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((~like(lucy, paul)) & (~like(lucy, mary))) <=> ![X: $i] : ((~room(X)) => (~preda(X)))) & ((~?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~like(lucy, X)) & (~like(lucy, Y)))) & (~(X = Y)))) => (((~predc(paul)) | (~like(paul, susan))) & (~((~predc(paul)) | (~like(paul, susan))))))) & (~((~(((quiet(paul) & creative(paul)) & rich(paul)) & european(paul))) | (~predc(paul))))) & ((((rich(mary) & quiet(mary)) & tall(mary)) & european(mary)) & (((tall(mary) & rich(mary)) & creative(mary)) & european(mary)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~like(lucy, X)) & (~like(lucy, Y)))) & (~(X = Y)))) & (~taller(paul, susan))) & ![X: $i] : quieter(X, mary)) & ![X: $i] : (room(X) => (like(susan, X) => (~(tall(X) & european(X)))))) & ((~like(mary, susan)) | richer(susan, mary)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((rich(paul) & person(paul)) & (((rich(paul) & creative(paul)) & quiet(paul)) & person(paul)))))), file('/mnt/tmpfs//3916528604416107732413559.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (((~like(lucy, paul)) & (~like(lucy, mary))) <=> ![X: $i] : (room(X) | (~preda(X)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~like(lucy, X)) & (~like(lucy, Y)) & (~(X = Y))) & (~((~predc(paul)) | (~(quiet(paul) & creative(paul) & rich(paul) & european(paul))))) & rich(mary) & quiet(mary) & tall(mary) & european(mary) & creative(mary) & (~taller(paul, susan)) & ![X: $i] : quieter(X, mary) & ![X: $i] : ((~room(X)) | (~(tall(X) & european(X))) | (~like(susan, X))) & ((~like(mary, susan)) | richer(susan, mary)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul)))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (((~like(lucy, paul)) & (~like(lucy, mary))) <=> ![X: $i] : (room(X) | (~preda(X)))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~like(lucy, X)) & (~like(lucy, Y)) & (~(X = Y))) & (~((~predc(paul)) | (~(quiet(paul) & creative(paul) & rich(paul) & european(paul))))) & rich(mary) & quiet(mary) & tall(mary) & european(mary) & creative(mary) & (~taller(paul, susan)) & ![X: $i] : quieter(X, mary) & ![X: $i] : ((~room(X)) | (~(tall(X) & european(X))) | (~like(susan, X))) & ((~like(mary, susan)) | richer(susan, mary))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~((~predc(paul)) | (~(quiet(paul) & creative(paul) & rich(paul) & european(paul))))),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(quiet(paul) & creative(paul) & rich(paul) & european(paul)),
inference(or_elim,[status(thm)],[6])).
tff(8,plain,
(european(paul)),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(european(paul)),
inference(modus_ponens,[status(thm)],[8, 1])).
tff(10,plain,
(^[X: $i] : refl((person(X) | (~european(X))) <=> (person(X) | (~european(X))))),
inference(bind,[status(th)],[])).
tff(11,plain,
(![X: $i] : (person(X) | (~european(X))) <=> ![X: $i] : (person(X) | (~european(X)))),
inference(quant_intro,[status(thm)],[10])).
tff(12,plain,
(![X: $i] : (person(X) | (~european(X))) <=> ![X: $i] : (person(X) | (~european(X)))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(^[X: $i] : rewrite((european(X) => person(X)) <=> (person(X) | (~european(X))))),
inference(bind,[status(th)],[])).
tff(14,plain,
(![X: $i] : (european(X) => person(X)) <=> ![X: $i] : (person(X) | (~european(X)))),
inference(quant_intro,[status(thm)],[13])).
tff(15,axiom,(![X: $i] : (european(X) => person(X))), file('/mnt/tmpfs//3916528604416107732413559.p','b2')).
tff(16,plain,
(![X: $i] : (person(X) | (~european(X)))),
inference(modus_ponens,[status(thm)],[15, 14])).
tff(17,plain,
(![X: $i] : (person(X) | (~european(X)))),
inference(modus_ponens,[status(thm)],[16, 12])).
tff(18,plain,(
![X: $i] : (person(X) | (~european(X)))),
inference(skolemize,[status(sab)],[17])).
tff(19,plain,
(![X: $i] : (person(X) | (~european(X)))),
inference(modus_ponens,[status(thm)],[18, 11])).
tff(20,plain,
(((~![X: $i] : (person(X) | (~european(X)))) | (person(paul) | (~european(paul)))) <=> ((~![X: $i] : (person(X) | (~european(X)))) | person(paul) | (~european(paul)))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
((~![X: $i] : (person(X) | (~european(X)))) | (person(paul) | (~european(paul)))),
inference(quant_inst,[status(thm)],[])).
tff(22,plain,
((~![X: $i] : (person(X) | (~european(X)))) | person(paul) | (~european(paul))),
inference(modus_ponens,[status(thm)],[21, 20])).
tff(23,plain,
(person(paul)),
inference(unit_resolution,[status(thm)],[22, 19, 9])).
tff(24,plain,
(rich(paul) <=> rich(paul)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(rich(paul)),
inference(and_elim,[status(thm)],[7])).
tff(26,plain,
(rich(paul)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
(creative(paul) <=> creative(paul)),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
(creative(paul)),
inference(and_elim,[status(thm)],[7])).
tff(29,plain,
(creative(paul)),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,
(quiet(paul) <=> quiet(paul)),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(quiet(paul)),
inference(and_elim,[status(thm)],[7])).
tff(32,plain,
(quiet(paul)),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(35,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(38,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[37, 36])).
tff(39,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~rich(paul)) | (~person(paul)) | (~creative(paul)) | (~quiet(paul))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~rich(paul)) | (~person(paul)) | (~creative(paul)) | (~quiet(paul)))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~rich(paul)) | (~person(paul)) | (~creative(paul)) | (~quiet(paul))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~rich(paul)) | (~person(paul)) | (~creative(paul)) | (~quiet(paul)))),
inference(monotonicity,[status(thm)],[40])).
tff(42,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~rich(paul)) | (~person(paul)) | (~creative(paul)) | (~quiet(paul))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~rich(paul)) | (~person(paul)) | (~creative(paul)) | (~quiet(paul)))),
inference(transitivity,[status(thm)],[41, 39])).
tff(43,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul)) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul)))),
inference(monotonicity,[status(thm)],[43])).
tff(45,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul)))),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))),
inference(or_elim,[status(thm)],[4])).
tff(47,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))),
inference(modus_ponens,[status(thm)],[46, 44])).
tff(48,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))),
inference(modus_ponens,[status(thm)],[47, 45])).
tff(49,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & rich(paul) & person(paul) & creative(paul) & quiet(paul))),
inference(modus_ponens,[status(thm)],[48, 44])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3)))))
(a!5 (refl (~ (not (rich paul)) (not (rich paul)))))
(a!6 (refl (~ (not (person paul)) (not (person paul)))))
(a!7 (refl (~ (not (creative paul)) (not (creative paul)))))
(a!8 (refl (~ (not (quiet paul)) (not (quiet paul))))))
(let ((a!9 (~ (not (and (room mary)
(room paul)
a!3
(rich paul)
(person paul)
(creative paul)
(quiet paul)))
(or (not (room mary))
(not (room paul))
a!4
(not (rich paul))
(not (person paul))
(not (creative paul))
(not (quiet paul))))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5 a!6 a!7 a!8 a!9)))
| room(gabriel)&room(jason)&(![X]:(room(X)=>(X='gabriel'|X='jason')))&
(((~like(john,jason)&~like(john,gabriel))<=>(![X]:(~room(X)=>(does_not_enjoy_rooftop_gardening(X)))))&
(~((?[X,Y]:(room(X)&room(Y)&(~like(john,X)&~like(john,Y))&(X!=Y))))=>((((is_not_a_client_of_Google(jason))|(~like(jason,linda)))&(~((is_not_a_client_of_Google(jason))|(~like(jason,linda)))))))&
(~(((~(quiet(jason)&creative(jason)&rich(jason)&european(jason)))|(is_not_a_client_of_Google(jason)))))&
((rich(gabriel)&quiet(gabriel)&tall(gabriel)&european(gabriel))&(tall(gabriel)&rich(gabriel)&creative(gabriel)&european(gabriel)))&
((?[X,Y]:(room(X)&room(Y)&(~like(john,X)&~like(john,Y))&(X!=Y))))&
(~(taller(jason,linda)))&
(![X]:(quieter(X,gabriel)))&
(![X]:(room(X)=>(((like(linda,X))=>(~(tall(X)&european(X)))))))&
(((~like(gabriel,linda))|(richer(linda,gabriel))))) | room(gabriel)&room(jason)&(![X]:(room(X)=>(X='gabriel'|X='jason')))&
((rich(jason)&person(jason))&(rich(jason)&creative(jason)&quiet(jason)&person(jason))) | entailment | neutral | neutral |
Stephen, Dale, Zachary are the only persons in the room. More than one person in the room likes Randy. Someone outside the room who is not Stephen likes Joseph. Someone who is not a creative quiet rich person is a client of someone who does not enjoy cross-country skiing. Someone who likes Joseph like someone who is liked by Joseph. Only one person outside the room is not a quiet tourist. Someone who is not a creative quiet person like someone who is richer than Joseph. Only one person outside the room is a rich quiet tourist. Someone who is a sibling of Joseph is a client of someone who does not enjoy cross-country skiing. Stephen is the least rich in the room. | Zachary is a rich european and is a sibling of Roger. | contradiction | - | room(stephen)&room(dale)&room(zachary)&(![X]:(room(X)=>(X='stephen'|X='dale'|X='zachary')))&
(((?[X,Y]:(room(X)&room(Y)&(like(randy,X)&like(randy,Y))&(X!=Y))))&
(?[X]:(~room(X)=>(((X!=stephen)=>(like(joseph,X))))))&
(?[X,Y]:((~(creative(X)&quiet(X)&rich(X)&person(X)))&(does_not_enjoy_cross-country_skiing(Y))&(client(X,Y))))&
(?[X,Y]:((like(joseph,X))&(like(Y,joseph))&(like(X,Y))))&
(((?[X]:(~room(X)&~(quiet(X)&tourist(X))))&(![X,Y]:((~(quiet(X)&tourist(X))&~(quiet(Y)&tourist(Y)))=>(X=Y)))))&
(?[X,Y]:((~(creative(X)&quiet(X)&person(X)))&(richer(joseph,Y))&(like(X,Y))))&
(((?[X]:(~room(X)&rich(X)&quiet(X)&tourist(X)))&(![X,Y]:((rich(X)&quiet(X)&tourist(X)&rich(Y)&quiet(Y)&tourist(Y))=>(X=Y)))))&
(?[X,Y]:((sibling(joseph,X))&(does_not_enjoy_cross-country_skiing(Y))&(client(X,Y))))&
(![X]:(richer(stephen,X)))) | room(stephen)&room(dale)&room(zachary)&(![X]:(room(X)=>(X='stephen'|X='dale'|X='zachary')))&
((rich(zachary)&european(zachary))&(sibling(roger,zachary))) | neutral | neutral | neutral |
Matthew, Jerry, Efrain are the only persons in the room. More than one person outside the room hates John. Matthew is quieter than John and is not liked by John. | Matthew neither is not hated by John nor is quieter than John. | contradiction | - | room(matthew)&room(jerry)&room(efrain)&(![X]:(room(X)=>(X='matthew'|X='jerry'|X='efrain')))&
(((?[X,Y]:(~room(X)&~room(Y)&(hate(john,X)&hate(john,Y))&(X!=Y))))&
((quieter(john,matthew))&(~like(matthew,john)))) | room(matthew)&room(jerry)&room(efrain)&(![X]:(room(X)=>(X='matthew'|X='jerry'|X='efrain')))&
(~((~hate(matthew,john))|(quieter(john,matthew)))) | contradiction | contradiction | contradiction |
Mark, Domingo, Ellen are the only persons in the room.
If John and Gayle like each other then Ellen is a client of Gayle and is not rich, not creative otherwise Ellen either does not use an ios phone or is not a creative quiet person.
John is a client of Ellen.
John and Gayle like each other.
Someone who is a client of John is a client of someone who is a rich person. | Ellen is not liked by Gayle or is not quiet, not rich or both. | neutral | % SZS status Satisfiable
| room(mark)&room(domingo)&room(ellen)&(![X]:(room(X)=>(X='mark'|X='domingo'|X='ellen')))&
(((((like(john,gayle) & like(gayle,john)))=>((client(gayle,ellen))&(~rich(ellen)&~creative(ellen))))|((~((like(john,gayle) & like(gayle,john))))=>((((does_not_use_an_ios_phone(ellen))|(~(creative(ellen)&quiet(ellen)&person(ellen))))&(~((does_not_use_an_ios_phone(ellen))|(~(creative(ellen)&quiet(ellen)&person(ellen)))))))))&
(client(ellen,john))&
((like(john,gayle) & like(gayle,john)))&
(?[X,Y]:((client(john,X))&(rich(Y)&person(Y))&(client(X,Y))))) | room(mark)&room(domingo)&room(ellen)&(![X]:(room(X)=>(X='mark'|X='domingo'|X='ellen')))&
(((~like(ellen,gayle))|(~quiet(ellen)&~rich(ellen)))) | entailment | entailment | entailment |