version
stringclasses 1
value | hypothesis
stringlengths 8
103
| hypothesis_formula
stringlengths 3
36
| facts
stringlengths 0
691
| facts_formula
stringlengths 0
374
| proofs
sequencelengths 0
1
| proofs_formula
sequencelengths 0
1
| negative_hypothesis
stringlengths 8
88
â | negative_hypothesis_formula
stringlengths 3
37
â | negative_proofs
sequencelengths 0
1
| negative_original_tree_depth
int64 0
17
â | original_tree_steps
int64 1
5
| original_tree_depth
int64 1
5
| steps
int64 1
5
â | depth
int64 1
5
â | num_formula_distractors
int64 0
5
| num_translation_distractors
int64 0
0
| num_all_distractors
int64 0
5
| proof_label
stringclasses 3
values | negative_proof_label
stringclasses 2
values | world_assump_label
stringclasses 3
values | negative_world_assump_label
stringclasses 2
values | prompt_serial
stringlengths 71
750
| proof_serial
stringlengths 11
312
| prompt_serial_formula
stringlengths 52
422
| proof_serial_formula
stringlengths 11
216
|
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.3 | ããã®ãœã«ã
ãœãLv.14ã¯ã¶ã£ãšããæŽã«å«ãããããšããããšã¯æãç«ããªã | ¬({C}{b} & {B}{b}) | fact1: ããããã®ãããã«ãLv.55ã¯çã
ããããšããããšã¯æãç«ãŠã°ãã®ã¿ã®ã¿ãLv.86ã¯çã
ãã fact2: ããã®ãŽã«ãŽã«Lv.67ã¯åé«ããšããããšã¯ãªãããšããããšã¯ç¢ºãã§ãã fact3: ãã®ã¿ãã¿ã«ã
Lv.61ã¯å«ããããªããšãããããã®ãœã«ã
ãœãLv.14ã¯ã¶ã£ãšããããŸãã«å«ãããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact4: ãããããã®ã¿ã®ã¿ãLv.86ã¯çã
ããããšããããšã¯æ¬åœã§ãããªãã°ããã®ã¿ãã¿ã«ã
Lv.61ã¯èšããªãããããåé«ããªãããšããããšã¯èª€ãã fact5: åé«ããªãã¢ã³ã¹ã¿ãŒã¯ã¶ã£ãšãããã€å«ããã fact6: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯åé«ããªããšãããšãããã¯åºå
¥ããæããŠãŸãçãæ·±ãããšããããšã¯æãç«ããªã fact7: ããåºå
¥ããæããæŽã«çãæ·±ãããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒãããã°ãã®ã¿ãã¿ã«ã
Lv.61ã¯å«ããããšããããšã¯ãªã | fact1: {D}{d} -> {D}{c} fact2: ¬{A}{aa} fact3: ¬{B}{a} -> ¬({C}{b} & {B}{b}) fact4: {D}{c} -> ¬(¬{E}{a} & ¬{A}{a}) fact5: (x): ¬{A}x -> ({C}x & {B}x) fact6: (x): ¬{A}x -> ¬({AA}x & {AB}x) fact7: (x): ¬({AA}x & {AB}x) -> ¬{B}{a} | [
"fact6 -> int1: ããããã®ãŽã«ãŽã«Lv.67ã¯åé«ããªããšããã°ãããã¯åºå
¥ããæãããããçãæ·±ãããšããããšã¯æãç«ããªã; int1 & fact2 -> int2: ããã®ãŽã«ãŽã«Lv.67ã¯åºå
¥ããæããŠçãæ·±ãããšããããšã¯æãç«ããªã; int2 -> int3: ããåºå
¥ããæãããŸãçãæ·±ãããšããããšã¯ééããªãã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact7 -> int4: ãã®ã¿ãã¿ã«ã
Lv.61ã¯å«ããããªã; int4 & fact3 -> hypothesis;"
] | [
"fact6 -> int1: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}); int1 & fact2 -> int2: ¬({AA}{aa} & {AB}{aa}); int2 -> int3: (Ex): ¬({AA}x & {AB}x); int3 & fact7 -> int4: ¬{B}{a}; int4 & fact3 -> hypothesis;"
] | ãã®ãœã«ã
ãœãLv.14ã¯ã¶ã£ãšããããã«å«ããã | ({C}{b} & {B}{b}) | [
"fact8 -> int5: ãããã®ãœã«ã
ãœãLv.14ãåé«ããªããšãããã¶ã£ãšããããã«å«ããã;"
] | 6 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããã®ãããã«ãLv.55ã¯çã
ããããšããããšã¯æãç«ãŠã°ãã®ã¿ã®ã¿ãLv.86ã¯çã
ãã fact2: ããã®ãŽã«ãŽã«Lv.67ã¯åé«ããšããããšã¯ãªãããšããããšã¯ç¢ºãã§ãã fact3: ãã®ã¿ãã¿ã«ã
Lv.61ã¯å«ããããªããšãããããã®ãœã«ã
ãœãLv.14ã¯ã¶ã£ãšããããŸãã«å«ãããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact4: ãããããã®ã¿ã®ã¿ãLv.86ã¯çã
ããããšããããšã¯æ¬åœã§ãããªãã°ããã®ã¿ãã¿ã«ã
Lv.61ã¯èšããªãããããåé«ããªãããšããããšã¯èª€ãã fact5: åé«ããªãã¢ã³ã¹ã¿ãŒã¯ã¶ã£ãšãããã€å«ããã fact6: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯åé«ããªããšãããšãããã¯åºå
¥ããæããŠãŸãçãæ·±ãããšããããšã¯æãç«ããªã fact7: ããåºå
¥ããæããæŽã«çãæ·±ãããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒãããã°ãã®ã¿ãã¿ã«ã
Lv.61ã¯å«ããããšããããšã¯ãªã ; $hypothesis$ = ããã®ãœã«ã
ãœãLv.14ã¯ã¶ã£ãšããæŽã«å«ãããããšããããšã¯æãç«ããªã ; $proof$ = | fact6 -> int1: ããããã®ãŽã«ãŽã«Lv.67ã¯åé«ããªããšããã°ãããã¯åºå
¥ããæãããããçãæ·±ãããšããããšã¯æãç«ããªã; int1 & fact2 -> int2: ããã®ãŽã«ãŽã«Lv.67ã¯åºå
¥ããæããŠçãæ·±ãããšããããšã¯æãç«ããªã; int2 -> int3: ããåºå
¥ããæãããŸãçãæ·±ãããšããããšã¯ééããªãã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact7 -> int4: ãã®ã¿ãã¿ã«ã
Lv.61ã¯å«ããããªã; int4 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {D}{d} -> {D}{c} fact2: ¬{A}{aa} fact3: ¬{B}{a} -> ¬({C}{b} & {B}{b}) fact4: {D}{c} -> ¬(¬{E}{a} & ¬{A}{a}) fact5: (x): ¬{A}x -> ({C}x & {B}x) fact6: (x): ¬{A}x -> ¬({AA}x & {AB}x) fact7: (x): ¬({AA}x & {AB}x) -> ¬{B}{a} ; $hypothesis$ = ¬({C}{b} & {B}{b}) ; $proof$ = | fact6 -> int1: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}); int1 & fact2 -> int2: ¬({AA}{aa} & {AB}{aa}); int2 -> int3: (Ex): ¬({AA}x & {AB}x); int3 & fact7 -> int4: ¬{B}{a}; int4 & fact3 -> hypothesis; __PROVED__ |
0.3 | ããŸã«ã
ãŸã¡ãLv.8äºä»¶ãçºçãããããã«æããããšããããšãèµ·ããããšããããšã¯èª€ãã§ãã | ¬({A} & {B}) | fact1: ãæããããšããããšã¯çºçããªããŠããã«è©±ãèŸããšããããšã¯èµ·ããªãããšããããšã¯åããé£ããšããããšã«ãããããã fact2: ãŸã«ã
ãŸã¡ãLv.8äºä»¶ãèµ·ãã fact3: ãæããããšããããšã¯èµ·ãããªãããšããããšã¯ããŸã«ããŸãLv.97äºä»¶ãçãããããããŸã«ã
ãŸã¡ãLv.8äºä»¶ãèµ·ããããšããããšãèªçºãã | fact1: {D} -> (¬{B} & ¬{C}) fact2: {A} fact3: ¬{B} -> ({IT} & {A}) | [
"fact2 -> int1: ãŸã«ã
ãŸã¡ãLv.8äºä»¶ãèµ·ãã;"
] | [
"fact2 -> int1: {A};"
] | ãŸã«ããŸãLv.97äºä»¶ãçãã | {IT} | [] | 7 | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãæããããšããããšã¯çºçããªããŠããã«è©±ãèŸããšããããšã¯èµ·ããªãããšããããšã¯åããé£ããšããããšã«ãããããã fact2: ãŸã«ã
ãŸã¡ãLv.8äºä»¶ãèµ·ãã fact3: ãæããããšããããšã¯èµ·ãããªãããšããããšã¯ããŸã«ããŸãLv.97äºä»¶ãçãããããããŸã«ã
ãŸã¡ãLv.8äºä»¶ãèµ·ããããšããããšãèªçºãã ; $hypothesis$ = ããŸã«ã
ãŸã¡ãLv.8äºä»¶ãçºçãããããã«æããããšããããšãèµ·ããããšããããšã¯èª€ãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {D} -> (¬{B} & ¬{C}) fact2: {A} fact3: ¬{B} -> ({IT} & {A}) ; $hypothesis$ = ¬({A} & {B}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŽãªãŽãLv.79ã¯çŽ ã£æ°ãªã | {B}{b} | fact1: ãã®ãã¡ãããLv.38ã¯å·ãé£ã fact2: ãã®ãŽãªãŽãLv.79ã¯èãå¯ã fact3: ãã®ãŽãªãŽãLv.79ã¯å·ãé£ã | fact1: {A}{a} fact2: {FH}{b} fact3: {A}{b} | [
"fact1 -> int1: ãã®ãã¡ãããLv.38ã¯å·ãé£ã;"
] | [
"fact1 -> int1: {A}{a};"
] | null | null | [] | null | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãã¡ãããLv.38ã¯å·ãé£ã fact2: ãã®ãŽãªãŽãLv.79ã¯èãå¯ã fact3: ãã®ãŽãªãŽãLv.79ã¯å·ãé£ã ; $hypothesis$ = ãã®ãŽãªãŽãLv.79ã¯çŽ ã£æ°ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} fact2: {FH}{b} fact3: {A}{b} ; $hypothesis$ = {B}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã·ã«ã·ãLv.29ã¯èªãé£ããªã | ¬{A}{a} | fact1: ãã®ã·ãã·ãLv.5ã¯æã fact2: ãã®ã·ã«ã·ãLv.29ãèªãé£ããªããªãã°ããã¯æªè³¢ããšããããšã¯ãªã fact3: ãããã®ã·ã«ã·ãLv.29ãæªè³¢ããªããšããããã®ã·ãã·ãLv.5ã¯æããšããããšã¯ãªã fact4: ãããæãã¢ã³ã¹ã¿ãŒãæªè³¢ããšããããšã¯ãªããšãããèªãé£ããªã | fact1: {C}{b} fact2: ¬{A}{a} -> ¬{B}{a} fact3: ¬{B}{a} -> ¬{C}{b} fact4: (x): ({C}x & ¬{B}x) -> ¬{A}x | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ã«ã·ãLv.29ã¯èªãé£ããªã; fact2 & assump1 -> int1: ãã®ã·ã«ã·ãLv.29ã¯æªè³¢ããªã; int1 & fact3 -> int2: ãã®ã·ãã·ãLv.5ã¯æããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}{a}; fact2 & assump1 -> int1: ¬{B}{a}; int1 & fact3 -> int2: ¬{C}{b}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããã®ã·ã«ã·ãLv.29ã¯èªãé£ããªã | ¬{A}{a} | [
"fact5 -> int4: ãã®ã·ã«ã·ãLv.29ã¯æããã©æªè³¢ããšããããšã¯ãªããªãã°èªãé£ããªã;"
] | 4 | 5 | 4 | 5 | 4 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã·ãã·ãLv.5ã¯æã fact2: ãã®ã·ã«ã·ãLv.29ãèªãé£ããªããªãã°ããã¯æªè³¢ããšããããšã¯ãªã fact3: ãããã®ã·ã«ã·ãLv.29ãæªè³¢ããªããšããããã®ã·ãã·ãLv.5ã¯æããšããããšã¯ãªã fact4: ãããæãã¢ã³ã¹ã¿ãŒãæªè³¢ããšããããšã¯ãªããšãããèªãé£ããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã·ã«ã·ãLv.29ã¯èªãé£ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ã«ã·ãLv.29ã¯èªãé£ããªã; fact2 & assump1 -> int1: ãã®ã·ã«ã·ãLv.29ã¯æªè³¢ããªã; int1 & fact3 -> int2: ãã®ã·ãã·ãLv.5ã¯æããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{b} fact2: ¬{A}{a} -> ¬{B}{a} fact3: ¬{B}{a} -> ¬{C}{b} fact4: (x): ({C}x & ¬{B}x) -> ¬{A}x ; $hypothesis$ = ¬{A}{a} ; $proof$ = | void -> assump1: ¬{A}{a}; fact2 & assump1 -> int1: ¬{B}{a}; int1 & fact3 -> int2: ¬{C}{b}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ãããããã®ã·ã«ã
ã·ãLv.17ã¯å³ããããªããŠãã€éãããªãããšããããšã¯ééãã | ¬(¬{AA}{aa} & ¬{AB}{aa}) | fact1: ãããã¢ã³ã¹ã¿ãŒã¯ç²åŸãããŸãå°é«ãããšããããšã¯åã§ãããšãããæãããªã fact2: ããäœããã®ã¢ã³ã¹ã¿ãŒã¯æãããšããããšã¯ãªããªããããã¯ç«ãããªããŠéã³æããªãããšããããšã¯æãç«ããªã fact3: ããã®ã·ã«ã
ã·ãLv.17ã¯å³ããããªãäžæ¹ã§éããããšããããšã¯ç¢ºãã§ãããšããããšã¯ãªã fact4: ããä»®ã«ããå³ããããšããããšã¯ãªãããããéãããªãããšããããšã¯åãªãã¢ã³ã¹ã¿ãŒããããªããã®ããããLv.27ã¯æãããªã fact5: ããä»®ã«ãã®ã·ã«ã
ã·ãLv.17ã¯æãããšãããšããã®ã·ã«ã
ã·ãLv.17ã¯æããããšããããšã¯æ¬åœã§ãã fact6: ãã®ããããLv.27ã¯æãã | fact1: (x): ¬({D}x & {C}x) -> ¬{B}x fact2: (x): ¬{A}x -> ¬(¬{EM}x & ¬{BU}x) fact3: ¬(¬{AA}{aa} & {AB}{aa}) fact4: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{A}{a} fact5: {B}{aa} -> {A}{aa} fact6: {A}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ã·ã«ã
ã·ãLv.17ã¯å³ããããªããŠãã€éãããªãããšããããšã¯ééãã ; assump1 -> int1: ããå³ããããªããéãããªãããšããããšã¯èª€ããªãã¢ã³ã¹ã¿ãŒã¯ãã; int1 & fact4 -> int2: ããã®ããããLv.27ã¯æããããšããããšã¯åã§ãã; int2 & fact6 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬(¬{AA}{aa} & ¬{AB}{aa}); assump1 -> int1: (Ex): ¬(¬{AA}x & ¬{AB}x); int1 & fact4 -> int2: ¬{A}{a}; int2 & fact6 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ãããããã®ã·ã«ã
ã·ãLv.17ã¯å³ããããªããŠãã€éãããªãããšããããšã¯ééãã | ¬(¬{AA}{aa} & ¬{AB}{aa}) | [] | 5 | 5 | 3 | 5 | 3 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããã¢ã³ã¹ã¿ãŒã¯ç²åŸãããŸãå°é«ãããšããããšã¯åã§ãããšãããæãããªã fact2: ããäœããã®ã¢ã³ã¹ã¿ãŒã¯æãããšããããšã¯ãªããªããããã¯ç«ãããªããŠéã³æããªãããšããããšã¯æãç«ããªã fact3: ããã®ã·ã«ã
ã·ãLv.17ã¯å³ããããªãäžæ¹ã§éããããšããããšã¯ç¢ºãã§ãããšããããšã¯ãªã fact4: ããä»®ã«ããå³ããããšããããšã¯ãªãããããéãããªãããšããããšã¯åãªãã¢ã³ã¹ã¿ãŒããããªããã®ããããLv.27ã¯æãããªã fact5: ããä»®ã«ãã®ã·ã«ã
ã·ãLv.17ã¯æãããšãããšããã®ã·ã«ã
ã·ãLv.17ã¯æããããšããããšã¯æ¬åœã§ãã fact6: ãã®ããããLv.27ã¯æãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããããã®ã·ã«ã
ã·ãLv.17ã¯å³ããããªããŠãã€éãããªãããšããããšã¯ééãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ã·ã«ã
ã·ãLv.17ã¯å³ããããªããŠãã€éãããªãããšããããšã¯ééãã ; assump1 -> int1: ããå³ããããªããéãããªãããšããããšã¯èª€ããªãã¢ã³ã¹ã¿ãŒã¯ãã; int1 & fact4 -> int2: ããã®ããããLv.27ã¯æããããšããããšã¯åã§ãã; int2 & fact6 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬({D}x & {C}x) -> ¬{B}x fact2: (x): ¬{A}x -> ¬(¬{EM}x & ¬{BU}x) fact3: ¬(¬{AA}{aa} & {AB}{aa}) fact4: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{A}{a} fact5: {B}{aa} -> {A}{aa} fact6: {A}{a} ; $hypothesis$ = ¬(¬{AA}{aa} & ¬{AB}{aa}) ; $proof$ = | void -> assump1: ¬(¬{AA}{aa} & ¬{AB}{aa}); assump1 -> int1: (Ex): ¬(¬{AA}x & ¬{AB}x); int1 & fact4 -> int2: ¬{A}{a}; int2 & fact6 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãããã®ãœã«ãœã«ãLv.5ã¯èª¿éåºæ¥ããå ããŠé»éåå²ããããšããããšã¯ééã£ãŠããããšããããšã¯çå®ã§ãã | ¬({D}{a} & {C}{a}) | fact1: ãšããã¢ã³ã¹ã¿ãŒã¯ãã°ãã£ãããªããªãã°ããããã¯èª¿éåºæ¥ããé»éåå²ããããšããããšã¯äºå®ã ããšããããšã¯æãç«ããªã fact2: ãããã®ãã¡ããã«ãLv.93ã¯å±±æ·±ããšãããããã®ãœã«ãœã«ãLv.5ã¯é»éåå²ããããšããããšã¯ç¢ºãã§ãã fact3: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãã°ãã£ãããªããšãããšããããã¯ç©æããªãããããæäœãæãããšããããšã¯æ¬åœã§ããããšããããšã¯æãç«ããªã fact4: ãã®ãœã«ãœã«ãLv.5ã¯èª¿éåºæ¥ã fact5: ããã®ãã¡ããã«ãLv.93ã¯ç©æããšããããšã¯ãªããæäœãæãããšããããšã¯èª€ãã ãšãããããã®ãã¡ããã«ãLv.93ã¯å±±æ·±ãããšããããšã¯æãç«ã€ fact6: ããã®ãŸããŸãLv.60ã¯å±±æ·±ãããšããããšã¯ç¢ºãã§ãã fact7: ããä»®ã«ãã®ã¿ãã¿ã®Lv.3ãæäœãæããªããšãããšãã®ã¿ãã¿ã®Lv.3ã¯ç°èã£ãœã | fact1: (x): ¬{A}x -> ¬({D}x & {C}x) fact2: {B}{aa} -> {C}{a} fact3: (x): ¬{A}x -> ¬(¬{AA}x & {AB}x) fact4: {D}{a} fact5: ¬(¬{AA}{aa} & {AB}{aa}) -> {B}{aa} fact6: {B}{c} fact7: ¬{AB}{fh} -> {GM}{fh} | [
"fact3 -> int1: ä»®ã«ãã®ãã¡ããã«ãLv.93ã¯ãã°ãã£ãããªããªãã°ãããã®ãã¡ããã«ãLv.93ã¯ç©æããšããããšã¯ãªããã©æäœãæãããšããããšã¯æãç«ããªãããšããããšã¯æ¬åœã ;"
] | [
"fact3 -> int1: ¬{A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa});"
] | ãããã®ãœã«ãœã«ãLv.5ã¯èª¿éåºæ¥ããå ããŠé»éåå²ããããšããããšã¯ééã£ãŠããããšããããšã¯çå®ã§ãã | ¬({D}{a} & {C}{a}) | [
"fact8 -> int2: ããä»®ã«ãã®ãœã«ãœã«ãLv.5ã¯ãã°ãã£ãããªããªãã°ããã®ãœã«ãœã«ãLv.5ã¯èª¿éåºæ¥ããå ããŠããã¯é»éåå²ããããšããããšã¯äºå®ãšç°ãªã;"
] | 6 | 5 | 5 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãšããã¢ã³ã¹ã¿ãŒã¯ãã°ãã£ãããªããªãã°ããããã¯èª¿éåºæ¥ããé»éåå²ããããšããããšã¯äºå®ã ããšããããšã¯æãç«ããªã fact2: ãããã®ãã¡ããã«ãLv.93ã¯å±±æ·±ããšãããããã®ãœã«ãœã«ãLv.5ã¯é»éåå²ããããšããããšã¯ç¢ºãã§ãã fact3: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãã°ãã£ãããªããšãããšããããã¯ç©æããªãããããæäœãæãããšããããšã¯æ¬åœã§ããããšããããšã¯æãç«ããªã fact4: ãã®ãœã«ãœã«ãLv.5ã¯èª¿éåºæ¥ã fact5: ããã®ãã¡ããã«ãLv.93ã¯ç©æããšããããšã¯ãªããæäœãæãããšããããšã¯èª€ãã ãšãããããã®ãã¡ããã«ãLv.93ã¯å±±æ·±ãããšããããšã¯æãç«ã€ fact6: ããã®ãŸããŸãLv.60ã¯å±±æ·±ãããšããããšã¯ç¢ºãã§ãã fact7: ããä»®ã«ãã®ã¿ãã¿ã®Lv.3ãæäœãæããªããšãããšãã®ã¿ãã¿ã®Lv.3ã¯ç°èã£ãœã ; $hypothesis$ = ãããã®ãœã«ãœã«ãLv.5ã¯èª¿éåºæ¥ããå ããŠé»éåå²ããããšããããšã¯ééã£ãŠããããšããããšã¯çå®ã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{A}x -> ¬({D}x & {C}x) fact2: {B}{aa} -> {C}{a} fact3: (x): ¬{A}x -> ¬(¬{AA}x & {AB}x) fact4: {D}{a} fact5: ¬(¬{AA}{aa} & {AB}{aa}) -> {B}{aa} fact6: {B}{c} fact7: ¬{AB}{fh} -> {GM}{fh} ; $hypothesis$ = ¬({D}{a} & {C}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ãããæåºããšããããšãèµ·ãã | {B} | fact1: 矀ããããšã¯çããªã fact2: ææãæããšããããšãèµ·ãã fact3: ãããã·ãã·ãªLv.82äºä»¶ãçºçããªãããããã¯æåºããšããããšãçããã°ã·ãã·ãªLv.82äºä»¶ã¯çããªã fact4: ããä»®ã«ã¿ã«ã¿ã«ã
Lv.27äºä»¶ããã³æåºããšããããšã©ã¡ãããçºçãããšããããææãæããšããããšã¯èµ·ãããªãããšããããšã¯äºå®ã | fact1: ¬{CO} fact2: {C} fact3: (¬{FR} v {B}) -> ¬{FR} fact4: ({A} & {B}) -> ¬{C} | [] | [] | ã·ãã·ãªLv.82äºä»¶ã¯èµ·ããªã | ¬{FR} | [] | 3 | 5 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: 矀ããããšã¯çããªã fact2: ææãæããšããããšãèµ·ãã fact3: ãããã·ãã·ãªLv.82äºä»¶ãçºçããªãããããã¯æåºããšããããšãçããã°ã·ãã·ãªLv.82äºä»¶ã¯çããªã fact4: ããä»®ã«ã¿ã«ã¿ã«ã
Lv.27äºä»¶ããã³æåºããšããããšã©ã¡ãããçºçãããšããããææãæããšããããšã¯èµ·ãããªãããšããããšã¯äºå®ã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããæåºããšããããšãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{CO} fact2: {C} fact3: (¬{FR} v {B}) -> ¬{FR} fact4: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | å·®ãåºããŸãããšããããšã¯çºçããªã | ¬{A} | fact1: ä»®ã«å·®ãåºããŸãããšããããšãèµ·ãããã¿ãã¿ã«ãLv.99äºä»¶ãèµ·ãããªãã©ãé»ããšããããšã¯çºçããªã fact2: ã©ãé»ããšããããšãèµ·ãã fact3: ã¿ãã¿ã«ãLv.99äºä»¶ã¯ã©ãé»ããšããããšã¯èµ·ããªããšããããšãæã | fact1: ({A} v {B}) -> ¬{C} fact2: {C} fact3: {B} -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããå·®ãåºããŸãããšããããšãèµ·ãã; assump1 -> int1: ãå·®ãåºããŸãããšããããšãèµ·ããããŸãã¯ã¿ãã¿ã«ãLv.99äºä»¶ãèµ·ããããšããããšã¯æãç«ã€; int1 & fact1 -> int2: ã©ãé»ããšããããšã¯èµ·ãããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 3 | 5 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«å·®ãåºããŸãããšããããšãèµ·ãããã¿ãã¿ã«ãLv.99äºä»¶ãèµ·ãããªãã©ãé»ããšããããšã¯çºçããªã fact2: ã©ãé»ããšããããšãèµ·ãã fact3: ã¿ãã¿ã«ãLv.99äºä»¶ã¯ã©ãé»ããšããããšã¯èµ·ããªããšããããšãæã ; $hypothesis$ = å·®ãåºããŸãããšããããšã¯çºçããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããå·®ãåºããŸãããšããããšãèµ·ãã; assump1 -> int1: ãå·®ãåºããŸãããšããããšãèµ·ããããŸãã¯ã¿ãã¿ã«ãLv.99äºä»¶ãèµ·ããããšããããšã¯æãç«ã€; int1 & fact1 -> int2: ã©ãé»ããšããããšã¯èµ·ãããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} fact2: {C} fact3: {B} -> ¬{C} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ãã¡ãLv.38äºä»¶ãçºçãã | {B} | fact1: ä»®ãããšãçºçããªããšããããšã¯æµ
ãŸããšããããšããããã¯ãã®ãã¡ãLv.38äºä»¶ããããã¯äž¡æ¹ã¯åå ã | fact1: ({A} v {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãã¡ãLv.38äºä»¶ãçºçãã; assump1 -> int1: æµ
ãŸããšããããšããããã¯ãã®ãã¡ãLv.38äºä»¶ãçºçãã; int1 & fact1 -> int2: ä»®ãããšã¯çããªã;"
] | [
"void -> assump1: {B}; assump1 -> int1: ({A} v {B}); int1 & fact1 -> int2: ¬{C};"
] | null | null | [] | null | 5 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ä»®ãããšãçºçããªããšããããšã¯æµ
ãŸããšããããšããããã¯ãã®ãã¡ãLv.38äºä»¶ããããã¯äž¡æ¹ã¯åå ã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ãã¡ãLv.38äºä»¶ãçºçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | ãœããœãLv.12äºä»¶ã¯èµ·ããªã | ¬{AA} | fact1: ã¿ã«ã
ã¿ãLv.81äºä»¶ãçºçãã fact2: ããããœããœãLv.12äºä»¶ã¯èµ·ãããªããããã«ãããè¯ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªããªãã¿ã«ã
ã¿ãLv.81äºä»¶ã¯èµ·ããªã | fact1: {B} fact2: ¬(¬{AA} & ¬{AB}) -> ¬{B} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããœããœãLv.12äºä»¶ã¯èµ·ãããªããããŸãã«ãããè¯ããšããããšã¯çºçããªãããšããããšã¯ééã£ãŠãã; fact2 & assump1 -> int1: ãã¿ã«ã
ã¿ãLv.81äºä»¶ã¯èµ·ããªãããšããããšã¯æãç«ã€; int1 & fact1 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãœããœãLv.12äºä»¶ã¯èµ·ããªããããŸãã«ãããè¯ããšããããšã¯èµ·ããªã; int3 -> hypothesis;"
] | [
"void -> assump1: ¬(¬{AA} & ¬{AB}); fact2 & assump1 -> int1: ¬{B}; int1 & fact1 -> int2: #F#; [assump1] & int2 -> int3: (¬{AA} & ¬{AB}); int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ã¿ã«ã
ã¿ãLv.81äºä»¶ãçºçãã fact2: ããããœããœãLv.12äºä»¶ã¯èµ·ãããªããããã«ãããè¯ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªããªãã¿ã«ã
ã¿ãLv.81äºä»¶ã¯èµ·ããªã ; $hypothesis$ = ãœããœãLv.12äºä»¶ã¯èµ·ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããããœããœãLv.12äºä»¶ã¯èµ·ãããªããããŸãã«ãããè¯ããšããããšã¯çºçããªãããšããããšã¯ééã£ãŠãã; fact2 & assump1 -> int1: ãã¿ã«ã
ã¿ãLv.81äºä»¶ã¯èµ·ããªãããšããããšã¯æãç«ã€; int1 & fact1 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãœããœãLv.12äºä»¶ã¯èµ·ããªããããŸãã«ãããè¯ããšããããšã¯èµ·ããªã; int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {B} fact2: ¬(¬{AA} & ¬{AB}) -> ¬{B} ; $hypothesis$ = ¬{AA} ; $proof$ = | void -> assump1: ¬(¬{AA} & ¬{AB}); fact2 & assump1 -> int1: ¬{B}; int1 & fact1 -> int2: #F#; [assump1] & int2 -> int3: (¬{AA} & ¬{AB}); int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã«ããŸã«ã
Lv.67ã¯ççœã | {E}{c} | fact1: ä»®ã«ãã®ãŽãªãŽã¡ãLv.20ã¯ããããŸãããªããšãããšãããã®ãŸã«ããŸã«ã
Lv.67ã¯èç«ãããããããã¯ããããŸãããªãããšããããšã¯äºå®ã ããšããããšã¯ééãã§ãã fact2: ä»®ã«ããã®ãœã¡ããœãLv.46ã¯è¶è²ã£ãœããªãããããã¯ããã¯ççœãããšããããšã¯èª€ãã ãšããã°ãã®ãŸã«ããŸã«ã
Lv.67ã¯ççœããªã fact3: ãã®ãœã¡ããœãLv.46ã¯æµããæã fact4: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯æµããæããšããããšã¯ãªããªãã°ãããã¯è¶è²ã£ãœããããã«èå¯ãããšããããšã¯ééãã fact5: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯æµããæããªãããã®ãœã¡ããœãLv.46ã¯è¶è²ã£ãœããªãããšããããšã¯æãç«ã€ fact6: ããããã®ãŽãªãŽã¡ãLv.20ãèå¯ããŠãããè¶è²ã£ãœããšããããã®ãŽãªãŽã¡ãLv.20ã¯ããããŸãããªã fact7: ããããã®ãœã¡ããœãLv.46ãæµããæããšãããšãã®ãŽãªãŽã¡ãLv.20ã¯è¶è²ã£ãœã fact8: ããã®ãŽãªãŽã¡ãLv.20ã¯èå¯ãããšããããšã¯äºå®ã fact9: ãããããã®ãŽããŽã«ãLv.47ã¯è¶è²ã£ãœããŠèå¯ãããšããããšã¯æãç«ããªãããšããããšã¯çå®ã§ãããªããã®ãŽãªãŽã¡ãLv.20ã¯è¶è²ã£ãœããªã fact10: ããã®ãŸã«ããŸã«ã
Lv.67ã¯èç«ãããããããã¯ããããŸãããšããããšã¯ãªãããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯ééãã§ãããšããã°ããã¯ççœã | fact1: ¬{D}{b} -> ¬({F}{c} v ¬{D}{c}) fact2: ¬(¬{B}{a} v {E}{a}) -> ¬{E}{c} fact3: {A}{a} fact4: (x): ¬{A}x -> ¬({B}x & {C}x) fact5: (x): {A}x -> ¬{B}{a} fact6: ({C}{b} & {B}{b}) -> ¬{D}{b} fact7: {A}{a} -> {B}{b} fact8: {C}{b} fact9: ¬({B}{d} & {C}{d}) -> ¬{B}{b} fact10: ¬({F}{c} v ¬{D}{c}) -> {E}{c} | [
"fact7 & fact3 -> int1: ãã®ãŽãªãŽã¡ãLv.20ã¯è¶è²ã£ãœã; int1 & fact8 -> int2: ãã®ãŽãªãŽã¡ãLv.20ã¯èå¯ããããã«ããã¯è¶è²ã£ãœã; int2 & fact6 -> int3: ãã®ãŽãªãŽã¡ãLv.20ã¯ããããŸãããšããããšã¯ãªã; int3 & fact1 -> int4: ããã®ãŸã«ããŸã«ã
Lv.67ã¯èç«ãããããŸãã¯ããããŸãããšããããšã¯ãªãããããã¯ã©ã¡ããã ããšããããšã¯ééãã ; int4 & fact10 -> hypothesis;"
] | [
"fact7 & fact3 -> int1: {B}{b}; int1 & fact8 -> int2: ({C}{b} & {B}{b}); int2 & fact6 -> int3: ¬{D}{b}; int3 & fact1 -> int4: ¬({F}{c} v ¬{D}{c}); int4 & fact10 -> hypothesis;"
] | ãã®ãœã¡ããœãLv.46ã¯è¶è²ã£ãœããªã | ¬{B}{a} | [] | 7 | 5 | 5 | 5 | 5 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãŽãªãŽã¡ãLv.20ã¯ããããŸãããªããšãããšãããã®ãŸã«ããŸã«ã
Lv.67ã¯èç«ãããããããã¯ããããŸãããªãããšããããšã¯äºå®ã ããšããããšã¯ééãã§ãã fact2: ä»®ã«ããã®ãœã¡ããœãLv.46ã¯è¶è²ã£ãœããªãããããã¯ããã¯ççœãããšããããšã¯èª€ãã ãšããã°ãã®ãŸã«ããŸã«ã
Lv.67ã¯ççœããªã fact3: ãã®ãœã¡ããœãLv.46ã¯æµããæã fact4: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯æµããæããšããããšã¯ãªããªãã°ãããã¯è¶è²ã£ãœããããã«èå¯ãããšããããšã¯ééãã fact5: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯æµããæããªãããã®ãœã¡ããœãLv.46ã¯è¶è²ã£ãœããªãããšããããšã¯æãç«ã€ fact6: ããããã®ãŽãªãŽã¡ãLv.20ãèå¯ããŠãããè¶è²ã£ãœããšããããã®ãŽãªãŽã¡ãLv.20ã¯ããããŸãããªã fact7: ããããã®ãœã¡ããœãLv.46ãæµããæããšãããšãã®ãŽãªãŽã¡ãLv.20ã¯è¶è²ã£ãœã fact8: ããã®ãŽãªãŽã¡ãLv.20ã¯èå¯ãããšããããšã¯äºå®ã fact9: ãããããã®ãŽããŽã«ãLv.47ã¯è¶è²ã£ãœããŠèå¯ãããšããããšã¯æãç«ããªãããšããããšã¯çå®ã§ãããªããã®ãŽãªãŽã¡ãLv.20ã¯è¶è²ã£ãœããªã fact10: ããã®ãŸã«ããŸã«ã
Lv.67ã¯èç«ãããããããã¯ããããŸãããšããããšã¯ãªãããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯ééãã§ãããšããã°ããã¯ççœã ; $hypothesis$ = ãã®ãŸã«ããŸã«ã
Lv.67ã¯ççœã ; $proof$ = | fact7 & fact3 -> int1: ãã®ãŽãªãŽã¡ãLv.20ã¯è¶è²ã£ãœã; int1 & fact8 -> int2: ãã®ãŽãªãŽã¡ãLv.20ã¯èå¯ããããã«ããã¯è¶è²ã£ãœã; int2 & fact6 -> int3: ãã®ãŽãªãŽã¡ãLv.20ã¯ããããŸãããšããããšã¯ãªã; int3 & fact1 -> int4: ããã®ãŸã«ããŸã«ã
Lv.67ã¯èç«ãããããŸãã¯ããããŸãããšããããšã¯ãªãããããã¯ã©ã¡ããã ããšããããšã¯ééãã ; int4 & fact10 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{D}{b} -> ¬({F}{c} v ¬{D}{c}) fact2: ¬(¬{B}{a} v {E}{a}) -> ¬{E}{c} fact3: {A}{a} fact4: (x): ¬{A}x -> ¬({B}x & {C}x) fact5: (x): {A}x -> ¬{B}{a} fact6: ({C}{b} & {B}{b}) -> ¬{D}{b} fact7: {A}{a} -> {B}{b} fact8: {C}{b} fact9: ¬({B}{d} & {C}{d}) -> ¬{B}{b} fact10: ¬({F}{c} v ¬{D}{c}) -> {E}{c} ; $hypothesis$ = {E}{c} ; $proof$ = | fact7 & fact3 -> int1: {B}{b}; int1 & fact8 -> int2: ({C}{b} & {B}{b}); int2 & fact6 -> int3: ¬{D}{b}; int3 & fact1 -> int4: ¬({F}{c} v ¬{D}{c}); int4 & fact10 -> hypothesis; __PROVED__ |
0.3 | æçããšããããšã¯èµ·ããªã | ¬{E} | fact1: å€å¥ãæããšããããšã¯ãè¡ããæããšããããšã¯çããªãããšããããšãé»æ¢ãã fact2: æãããããšããããšãèµ·ãã fact3: çµã¿åãããããšãèµ·ãã fact4: çœã
ãããšããããšãšçšãæããšããããšäž¡æ¹ãçºçãã fact5: å·ãæããšããããšãèµ·ãã fact6: æèäŒã£ãœããšããããšã¯çºçããªããšããããšã¯çšãæããšããããšã«é²ããã fact7: ãã·ãã·ãLv.73äºä»¶ã¯èµ·ããªãããšããããšã¯çœã
ãããšããããšãçãããšããããšã«é»æ¢ããã fact8: æçããšããããšã¯æèäŒã£ãœããšããããšãšçµã¿åãããããšãçããã«é²ããã | fact1: {FQ} -> {IH} fact2: {BP} fact3: {D} fact4: ({A} & {B}) fact5: {FR} fact6: {B} -> {C} fact7: {A} -> {GK} fact8: ({C} & {D}) -> ¬{E} | [
"fact4 -> int1: çšãæããšããããšãçãã; int1 & fact6 -> int2: æèäŒã£ãœããšããããšãçºçãã; int2 & fact3 -> int3: æèäŒã£ãœããšããããšãçºçãããçµã¿åãããããšãçãã; int3 & fact8 -> hypothesis;"
] | [
"fact4 -> int1: {B}; int1 & fact6 -> int2: {C}; int2 & fact3 -> int3: ({C} & {D}); int3 & fact8 -> hypothesis;"
] | ã·ãã·ãLv.73äºä»¶ãèµ·ãã | {GK} | [] | 6 | 4 | 4 | 4 | 4 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: å€å¥ãæããšããããšã¯ãè¡ããæããšããããšã¯çããªãããšããããšãé»æ¢ãã fact2: æãããããšããããšãèµ·ãã fact3: çµã¿åãããããšãèµ·ãã fact4: çœã
ãããšããããšãšçšãæããšããããšäž¡æ¹ãçºçãã fact5: å·ãæããšããããšãèµ·ãã fact6: æèäŒã£ãœããšããããšã¯çºçããªããšããããšã¯çšãæããšããããšã«é²ããã fact7: ãã·ãã·ãLv.73äºä»¶ã¯èµ·ããªãããšããããšã¯çœã
ãããšããããšãçãããšããããšã«é»æ¢ããã fact8: æçããšããããšã¯æèäŒã£ãœããšããããšãšçµã¿åãããããšãçããã«é²ããã ; $hypothesis$ = æçããšããããšã¯èµ·ããªã ; $proof$ = | fact4 -> int1: çšãæããšããããšãçãã; int1 & fact6 -> int2: æèäŒã£ãœããšããããšãçºçãã; int2 & fact3 -> int3: æèäŒã£ãœããšããããšãçºçãããçµã¿åãããããšãçãã; int3 & fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: {FQ} -> {IH} fact2: {BP} fact3: {D} fact4: ({A} & {B}) fact5: {FR} fact6: {B} -> {C} fact7: {A} -> {GK} fact8: ({C} & {D}) -> ¬{E} ; $hypothesis$ = ¬{E} ; $proof$ = | fact4 -> int1: {B}; int1 & fact6 -> int2: {C}; int2 & fact3 -> int3: ({C} & {D}); int3 & fact8 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ãããæŒããé£ããšããããšãçºçãã | {B} | fact1: ããã®ãã«Lv.7äºä»¶ãçºçããããšããããšã¯æãç«ã€ fact2: ãœããœãLv.74äºä»¶ã¯èµ·ãããªããšããããšã¯ããŽããŽã¡ã
Lv.59äºä»¶ããã³æ±ãé£ããšããããšäž¡æ¹ãšããçããããšããããšã«èªçºããã fact3: ããããŸããŸãLv.96äºä»¶ãšæŒããé£ããšããããšäž¡æ¹ãšããçºçãããšãããšãã®ãã«Lv.7äºä»¶ã¯èµ·ããªã fact4: ãŸããŸãLv.96äºä»¶ãçãã | fact1: {C} fact2: ({EC} & {AP}) -> ¬{IA} fact3: ({A} & {B}) -> ¬{C} fact4: {A} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããæŒããé£ããšããããšãçºçãã; fact4 & assump1 -> int1: ããŸããŸãLv.96äºä»¶ããã³æŒããé£ããšããããšã©ã¡ãããèµ·ããããšããããšã¯æãç«ã€; int1 & fact3 -> int2: ãã®ãã«Lv.7äºä»¶ã¯èµ·ããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; fact4 & assump1 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããã®ãã«Lv.7äºä»¶ãçºçããããšããããšã¯æãç«ã€ fact2: ãœããœãLv.74äºä»¶ã¯èµ·ãããªããšããããšã¯ããŽããŽã¡ã
Lv.59äºä»¶ããã³æ±ãé£ããšããããšäž¡æ¹ãšããçããããšããããšã«èªçºããã fact3: ããããŸããŸãLv.96äºä»¶ãšæŒããé£ããšããããšäž¡æ¹ãšããçºçãããšãããšãã®ãã«Lv.7äºä»¶ã¯èµ·ããªã fact4: ãŸããŸãLv.96äºä»¶ãçãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããæŒããé£ããšããããšãçºçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããæŒããé£ããšããããšãçºçãã; fact4 & assump1 -> int1: ããŸããŸãLv.96äºä»¶ããã³æŒããé£ããšããããšã©ã¡ãããèµ·ããããšããããšã¯æãç«ã€; int1 & fact3 -> int2: ãã®ãã«Lv.7äºä»¶ã¯èµ·ããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C} fact2: ({EC} & {AP}) -> ¬{IA} fact3: ({A} & {B}) -> ¬{C} fact4: {A} ; $hypothesis$ = {B} ; $proof$ = | void -> assump1: {B}; fact4 & assump1 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãä»®ã«ãã®ãŽã«ã
ãŽãLv.4ãå¿ããšããã°ãã®ãŽã«ã
ãŽãLv.4ã¯å¥³ã®åãããããšããããšã¯æãç«ããªã | ¬({A}{a} -> {C}{a}) | fact1: ä»®ã«ãã®ãŽã«ã
ãŽãLv.4ãå¿ããªãã°ãã®ãŽã«ã
ãŽãLv.4ã¯ãã£é
·ã fact2: ãããã®ãŽã«ã
ãŽãLv.4ãé»ããªããšããã°ããã¯æ°å¿ãããªãäžæ¹ã§ãã£é
·ã fact3: ããã¢ã³ã¹ã¿ãŒã¯æéè¯ããçŒãå§ãã fact4: ãã®ãŸããŸã®Lv.71ã¯ãã£é
·ã fact5: ãªãããã®ã¢ã³ã¹ã¿ãŒãå¿ããªããšããããã®ãŽã¡ããŽã¡ãLv.58ã¯å¥³ã®åããããå ããŠå¿ã fact6: æ°å¿ãããªãããããã¯å¿ããªãã¢ã³ã¹ã¿ãŒã¯å¿ããªã fact7: ä»®ã«ãã®ãŽã«ã
ãŽãLv.4ããã£é
·ããšãããšãã®ãŽã«ã
ãŽãLv.4ã¯å¥³ã®åããã | fact1: {A}{a} -> {B}{a} fact2: ¬{E}{a} -> (¬{D}{a} & {B}{a}) fact3: (Ex): ({G}x & {F}x) fact4: {B}{fu} fact5: (x): ¬{A}x -> ({C}{eh} & {A}{eh}) fact6: (x): (¬{D}x v ¬{A}x) -> ¬{A}x fact7: {B}{a} -> {C}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŽã«ã
ãŽãLv.4ã¯å¿ã; fact1 & assump1 -> int1: ãã®ãŽã«ã
ãŽãLv.4ã¯ãã£é
·ã; int1 & fact7 -> int2: ãã®ãŽã«ã
ãŽãLv.4ã¯å¥³ã®åããã; [assump1] & int2 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact7 -> int2: {C}{a}; [assump1] & int2 -> hypothesis;"
] | ãã®ãŽã¡ããŽã¡ãLv.58ã¯å¥³ã®åããã | {C}{eh} | [
"fact10 -> int3: ãããã®ãŽã«ã
ãŽãLv.4ãæ°å¿ãããªãããŸãã¯ãããå¿ããªããšããã°ããã¯å¿ããšããããšã¯ãªã;"
] | 8 | 4 | 3 | 4 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãŽã«ã
ãŽãLv.4ãå¿ããªãã°ãã®ãŽã«ã
ãŽãLv.4ã¯ãã£é
·ã fact2: ãããã®ãŽã«ã
ãŽãLv.4ãé»ããªããšããã°ããã¯æ°å¿ãããªãäžæ¹ã§ãã£é
·ã fact3: ããã¢ã³ã¹ã¿ãŒã¯æéè¯ããçŒãå§ãã fact4: ãã®ãŸããŸã®Lv.71ã¯ãã£é
·ã fact5: ãªãããã®ã¢ã³ã¹ã¿ãŒãå¿ããªããšããããã®ãŽã¡ããŽã¡ãLv.58ã¯å¥³ã®åããããå ããŠå¿ã fact6: æ°å¿ãããªãããããã¯å¿ããªãã¢ã³ã¹ã¿ãŒã¯å¿ããªã fact7: ä»®ã«ãã®ãŽã«ã
ãŽãLv.4ããã£é
·ããšãããšãã®ãŽã«ã
ãŽãLv.4ã¯å¥³ã®åããã ; $hypothesis$ = ãä»®ã«ãã®ãŽã«ã
ãŽãLv.4ãå¿ããšããã°ãã®ãŽã«ã
ãŽãLv.4ã¯å¥³ã®åãããããšããããšã¯æãç«ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŽã«ã
ãŽãLv.4ã¯å¿ã; fact1 & assump1 -> int1: ãã®ãŽã«ã
ãŽãLv.4ã¯ãã£é
·ã; int1 & fact7 -> int2: ãã®ãŽã«ã
ãŽãLv.4ã¯å¥³ã®åããã; [assump1] & int2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {B}{a} fact2: ¬{E}{a} -> (¬{D}{a} & {B}{a}) fact3: (Ex): ({G}x & {F}x) fact4: {B}{fu} fact5: (x): ¬{A}x -> ({C}{eh} & {A}{eh}) fact6: (x): (¬{D}x v ¬{A}x) -> ¬{A}x fact7: {B}{a} -> {C}{a} ; $hypothesis$ = ¬({A}{a} -> {C}{a}) ; $proof$ = | void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact7 -> int2: {C}{a}; [assump1] & int2 -> hypothesis; __DISPROVED__ |
0.3 | ããããé
ããªããªãæºéç¡ããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ééãã | ¬((Ex): ¬{B}x -> {C}x) | fact1: é
ãã¢ã³ã¹ã¿ãŒã¯æºéç¡ã fact2: ãªãããã®ã¢ã³ã¹ã¿ãŒãé
ããªããšãããæºéç¡ã | fact1: (x): {B}x -> {C}x fact2: (x): ¬{B}x -> {C}x | [
"fact2 -> int1: ããããã®ãœã¡ã
ãœã¡ã
Lv.29ãé
ããªããªãã°ãã®ãœã¡ã
ãœã¡ã
Lv.29ã¯æºéç¡ã; int1 -> hypothesis;"
] | [
"fact2 -> int1: ¬{B}{aa} -> {C}{aa}; int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: é
ãã¢ã³ã¹ã¿ãŒã¯æºéç¡ã fact2: ãªãããã®ã¢ã³ã¹ã¿ãŒãé
ããªããšãããæºéç¡ã ; $hypothesis$ = ããããé
ããªããªãæºéç¡ããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ééãã ; $proof$ = | fact2 -> int1: ããããã®ãœã¡ã
ãœã¡ã
Lv.29ãé
ããªããªãã°ãã®ãœã¡ã
ãœã¡ã
Lv.29ã¯æºéç¡ã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {B}x -> {C}x fact2: (x): ¬{B}x -> {C}x ; $hypothesis$ = ¬((Ex): ¬{B}x -> {C}x) ; $proof$ = | fact2 -> int1: ¬{B}{aa} -> {C}{aa}; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãLv.95ã¯ã€ã¹ãããŠå°œããé£ã | ({A}{a} & {C}{a}) | fact1: ãã®ãŸããŸãLv.95ã¯ã€ã¹ãããŠããã«åãé£ã fact2: ãã®ãŸããŸãLv.95ã¯åãé£ã fact3: ããã®ãŸããŸãLv.95ã¯å°œããé£ãããšããããšã¯æ¬åœã§ãã | fact1: ({A}{a} & {B}{a}) fact2: {B}{a} fact3: {C}{a} | [
"fact1 -> int1: ãã®ãŸããŸãLv.95ã¯ã€ã¹ãã; int1 & fact3 -> hypothesis;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact3 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãŸããŸãLv.95ã¯ã€ã¹ãããŠããã«åãé£ã fact2: ãã®ãŸããŸãLv.95ã¯åãé£ã fact3: ããã®ãŸããŸãLv.95ã¯å°œããé£ãããšããããšã¯æ¬åœã§ãã ; $hypothesis$ = ãã®ãŸããŸãLv.95ã¯ã€ã¹ãããŠå°œããé£ã ; $proof$ = | fact1 -> int1: ãã®ãŸããŸãLv.95ã¯ã€ã¹ãã; int1 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: {B}{a} fact3: {C}{a} ; $hypothesis$ = ({A}{a} & {C}{a}) ; $proof$ = | fact1 -> int1: {A}{a}; int1 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœããœã¡ãLv.82ã¯å£ç
©ããªã | ¬{A}{a} | fact1: ãšããã¢ã³ã¹ã¿ãŒãã°ãã€ãã°ç
ãã fact2: ãã®ãœããœã¡ãLv.82ãå£ç
©ããšããã°ãã®ãœããœã¡ãLv.82ã¯æãã¿ç¡ã fact3: ããããã®ãœããœã¡ãLv.82ãæãã¿ç¡ããªãã°ãã®ã¿ã«ã
ã¿ã«ãLv.27ã¯ã°ãã€ã fact4: ããã®ã¿ã«ã
ã¿ã«ãLv.27ã¯ã°ãã€ããªãããšããããšã¯çå®ã§ãã | fact1: (x): {C}x -> {IG}x fact2: {A}{a} -> {B}{a} fact3: {B}{a} -> {C}{b} fact4: ¬{C}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœã¡ãLv.82ã¯å£ç
©ã; fact2 & assump1 -> int1: ãã®ãœããœã¡ãLv.82ã¯æãã¿ç¡ã; int1 & fact3 -> int2: ãã®ã¿ã«ã
ã¿ã«ãLv.27ã¯ã°ãã€ã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{b}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ããä»®ã«ããã®ãœããœã¡ãLv.82ã¯ã°ãã€ãããšããããšã¯æãç«ãŠã°ãããã¯ç
ããããšããããšã¯æãç«ã€ | {C}{a} -> {IG}{a} | [
"fact5 -> hypothesis;"
] | 1 | 5 | 4 | 5 | 4 | 1 | 0 | 1 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãšããã¢ã³ã¹ã¿ãŒãã°ãã€ãã°ç
ãã fact2: ãã®ãœããœã¡ãLv.82ãå£ç
©ããšããã°ãã®ãœããœã¡ãLv.82ã¯æãã¿ç¡ã fact3: ããããã®ãœããœã¡ãLv.82ãæãã¿ç¡ããªãã°ãã®ã¿ã«ã
ã¿ã«ãLv.27ã¯ã°ãã€ã fact4: ããã®ã¿ã«ã
ã¿ã«ãLv.27ã¯ã°ãã€ããªãããšããããšã¯çå®ã§ãã ; $hypothesis$ = ãã®ãœããœã¡ãLv.82ã¯å£ç
©ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœã¡ãLv.82ã¯å£ç
©ã; fact2 & assump1 -> int1: ãã®ãœããœã¡ãLv.82ã¯æãã¿ç¡ã; int1 & fact3 -> int2: ãã®ã¿ã«ã
ã¿ã«ãLv.27ã¯ã°ãã€ã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {C}x -> {IG}x fact2: {A}{a} -> {B}{a} fact3: {B}{a} -> {C}{b} fact4: ¬{C}{b} ; $hypothesis$ = ¬{A}{a} ; $proof$ = | void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{b}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | åŸåŸ©ããããšã¯èµ·ãããªã | ¬{B} | fact1: éè¿ããšããããšãèµ·ãã fact2: ãœããœãLv.98äºä»¶ãçãã fact3: ãããœããœãLv.98äºä»¶ãçºçããããããéè¿ããšããããšã¯èµ·ãããªããªãã°åŸåŸ©ããããšãèµ·ãã fact4: ä»®ã«ã·ã«ã·ãªLv.9äºä»¶ãèµ·ãããšããã°ãœããœãLv.98äºä»¶ãèµ·ããããã©éè¿ããšããããšã¯çºçããªã fact5: ãããåŸåŸ©ããããšããã³ãã¡ããã«ãLv.72äºä»¶ã©ã¡ãããçºçããããšããããšã¯æãç«ããªããªãã°ãã¡ããã«ãLv.72äºä»¶ã¯èµ·ããªã fact6: ããœããœãLv.98äºä»¶ãèµ·ããããŸãåŸåŸ©ããããšãèµ·ããããšããããšã¯éè¿ããšããããšãåé¿ãã | fact1: {C} fact2: {A} fact3: ({A} & ¬{C}) -> {B} fact4: {D} -> ({A} & ¬{C}) fact5: ¬({B} & {I}) -> ¬{I} fact6: ({A} & {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããåŸåŸ©ããããšãçºçãã; fact2 & assump1 -> int1: ããœããœãLv.98äºä»¶ãèµ·ããããã®äžåŸåŸ©ããããšãèµ·ããããšããããšã¯æãç«ã€; int1 & fact6 -> int2: éè¿ããšããããšã¯èµ·ããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; fact2 & assump1 -> int1: ({A} & {B}); int1 & fact6 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ãã¡ããã«ãLv.72äºä»¶ã¯çããªã | ¬{I} | [] | 6 | 5 | 4 | 5 | 4 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: éè¿ããšããããšãèµ·ãã fact2: ãœããœãLv.98äºä»¶ãçãã fact3: ãããœããœãLv.98äºä»¶ãçºçããããããéè¿ããšããããšã¯èµ·ãããªããªãã°åŸåŸ©ããããšãèµ·ãã fact4: ä»®ã«ã·ã«ã·ãªLv.9äºä»¶ãèµ·ãããšããã°ãœããœãLv.98äºä»¶ãèµ·ããããã©éè¿ããšããããšã¯çºçããªã fact5: ãããåŸåŸ©ããããšããã³ãã¡ããã«ãLv.72äºä»¶ã©ã¡ãããçºçããããšããããšã¯æãç«ããªããªãã°ãã¡ããã«ãLv.72äºä»¶ã¯èµ·ããªã fact6: ããœããœãLv.98äºä»¶ãèµ·ããããŸãåŸåŸ©ããããšãèµ·ããããšããããšã¯éè¿ããšããããšãåé¿ãã ; $hypothesis$ = åŸåŸ©ããããšã¯èµ·ãããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããåŸåŸ©ããããšãçºçãã; fact2 & assump1 -> int1: ããœããœãLv.98äºä»¶ãèµ·ããããã®äžåŸåŸ©ããããšãèµ·ããããšããããšã¯æãç«ã€; int1 & fact6 -> int2: éè¿ããšããããšã¯èµ·ããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} fact2: {A} fact3: ({A} & ¬{C}) -> {B} fact4: {D} -> ({A} & ¬{C}) fact5: ¬({B} & {I}) -> ¬{I} fact6: ({A} & {B}) -> ¬{C} ; $hypothesis$ = ¬{B} ; $proof$ = | void -> assump1: {B}; fact2 & assump1 -> int1: ({A} & {B}); int1 & fact6 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã«ããŸãLv.71ã¯æ¬²æ·±ããªã | ¬{C}{b} | fact1: ãã®ããããLv.89ã¯è²·ãã fact2: ãã®ã·ãã·ã«ã
Lv.15ã¯éè²ãæããŠããŸãã«æ¬²æ·±ã fact3: ãã®ããããLv.89ã¯èº«è»œã fact4: ããä»®ã«ãã®ããããLv.89ã身軜ããªãã°ããã¯çã¿æããªãããããã²ããé·ã | fact1: {B}{a} fact2: ({HR}{bq} & {C}{bq}) fact3: {A}{a} fact4: {A}{a} -> (¬{AA}{a} & {AB}{a}) | [
"fact4 & fact3 -> int1: ãã®ããããLv.89ã¯çã¿æããªãããããã²ããé·ã; int1 -> int2: ãã®ããããLv.89ã¯ã²ããé·ã; int2 & fact1 -> int3: ãã®ããããLv.89ã¯ã²ããé·ããŠããã«è²·ãã; int3 -> int4: ããã¢ã³ã¹ã¿ãŒã¯ã²ããé·ããæŽã«è²·ãã;"
] | [
"fact4 & fact3 -> int1: (¬{AA}{a} & {AB}{a}); int1 -> int2: {AB}{a}; int2 & fact1 -> int3: ({AB}{a} & {B}{a}); int3 -> int4: (Ex): ({AB}x & {B}x);"
] | null | null | [] | null | 5 | 5 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ããããLv.89ã¯è²·ãã fact2: ãã®ã·ãã·ã«ã
Lv.15ã¯éè²ãæããŠããŸãã«æ¬²æ·±ã fact3: ãã®ããããLv.89ã¯èº«è»œã fact4: ããä»®ã«ãã®ããããLv.89ã身軜ããªãã°ããã¯çã¿æããªãããããã²ããé·ã ; $hypothesis$ = ãã®ãŸã«ããŸãLv.71ã¯æ¬²æ·±ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{a} fact2: ({HR}{bq} & {C}{bq}) fact3: {A}{a} fact4: {A}{a} -> (¬{AA}{a} & {AB}{a}) ; $hypothesis$ = ¬{C}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ããæãåºæ·±ããšããããšãèµ·ãããšãããšãŽãªãŽã«ãLv.2äºä»¶ã§ã¯ãªããŠã§ã£ãããšããããšãèµ·ãã | {A} -> (¬{C} & {E}) | fact1: ããèŠçŽãããšã¯çºçããªããšããã°èŠçŽãããšã§ã¯ãªãèªã¿å§ããããšãçãã fact2: ããŽãªãŽã«ãLv.2äºä»¶ã§ã¯ãªãã§ã£ãããšããããšãçããããšããããšã¯ãŽãªãŽã«ãLv.2äºä»¶ãçºçããªããšããããšã¯å¥æ©ã fact3: æã¡äžããæããšããããšãèµ·ãã fact4: ããŽãªãŽã«ãLv.2äºä»¶ã¯èµ·ãããªãããšããããšã¯ãæãåºæ·±ããšããããšããã³æã¡äžããæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã«åŒãèµ·ãããã fact5: éãé£ããšããããšã§ã¯ãªããŠéºã
ãããšããããšãèµ·ãã | fact1: ¬{FK} -> (¬{FK} & {EJ}) fact2: ¬{C} -> (¬{C} & {E}) fact3: {B} fact4: ({A} & {B}) -> ¬{C} fact5: (¬{GL} & {IR}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããæãåºæ·±ããšããããšãèµ·ãã; assump1 & fact3 -> int1: æãåºæ·±ããšããããšãçããããããæã¡äžããæããšããããšãèµ·ãã; int1 & fact4 -> int2: ãŽãªãŽã«ãLv.2äºä»¶ã¯çºçããªã; int2 & fact2 -> int3: ãŽãªãŽã«ãLv.2äºä»¶ã¯çºçããªããã§ã£ãããšããããšãèµ·ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact3 -> int1: ({A} & {B}); int1 & fact4 -> int2: ¬{C}; int2 & fact2 -> int3: (¬{C} & {E}); [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ããèŠçŽãããšã¯çºçããªããšããã°èŠçŽãããšã§ã¯ãªãèªã¿å§ããããšãçãã fact2: ããŽãªãŽã«ãLv.2äºä»¶ã§ã¯ãªãã§ã£ãããšããããšãçããããšããããšã¯ãŽãªãŽã«ãLv.2äºä»¶ãçºçããªããšããããšã¯å¥æ©ã fact3: æã¡äžããæããšããããšãèµ·ãã fact4: ããŽãªãŽã«ãLv.2äºä»¶ã¯èµ·ãããªãããšããããšã¯ãæãåºæ·±ããšããããšããã³æã¡äžããæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã«åŒãèµ·ãããã fact5: éãé£ããšããããšã§ã¯ãªããŠéºã
ãããšããããšãèµ·ãã ; $hypothesis$ = ããæãåºæ·±ããšããããšãèµ·ãããšãããšãŽãªãŽã«ãLv.2äºä»¶ã§ã¯ãªããŠã§ã£ãããšããããšãèµ·ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããæãåºæ·±ããšããããšãèµ·ãã; assump1 & fact3 -> int1: æãåºæ·±ããšããããšãçããããããæã¡äžããæããšããããšãèµ·ãã; int1 & fact4 -> int2: ãŽãªãŽã«ãLv.2äºä»¶ã¯çºçããªã; int2 & fact2 -> int3: ãŽãªãŽã«ãLv.2äºä»¶ã¯çºçããªããã§ã£ãããšããããšãèµ·ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{FK} -> (¬{FK} & {EJ}) fact2: ¬{C} -> (¬{C} & {E}) fact3: {B} fact4: ({A} & {B}) -> ¬{C} fact5: (¬{GL} & {IR}) ; $hypothesis$ = {A} -> (¬{C} & {E}) ; $proof$ = | void -> assump1: {A}; assump1 & fact3 -> int1: ({A} & {B}); int1 & fact4 -> int2: ¬{C}; int2 & fact2 -> int3: (¬{C} & {E}); [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã€ã£ãããšããããšã¯çããªã | ¬{A} | fact1: ãã€ã£ãããšããããšããã³ãœããœã«Lv.3äºä»¶ãèµ·ããã¯ã·ãã·ãLv.33äºä»¶ãé²ã fact2: ãœããœã«Lv.3äºä»¶ãèµ·ãã fact3: ã·ãã·ãLv.33äºä»¶ãèµ·ãã | fact1: ({A} & {B}) -> ¬{C} fact2: {B} fact3: {C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããã€ã£ãããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã; assump1 & fact2 -> int1: ãã€ã£ãããšããããšããã³ãœããœã«Lv.3äºä»¶ãçãã; int1 & fact1 -> int2: ã·ãã·ãLv.33äºä»¶ã¯çºçããªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact2 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã€ã£ãããšããããšããã³ãœããœã«Lv.3äºä»¶ãèµ·ããã¯ã·ãã·ãLv.33äºä»¶ãé²ã fact2: ãœããœã«Lv.3äºä»¶ãèµ·ãã fact3: ã·ãã·ãLv.33äºä»¶ãèµ·ãã ; $hypothesis$ = ãã€ã£ãããšããããšã¯çããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããããã€ã£ãããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã; assump1 & fact2 -> int1: ãã€ã£ãããšããããšããã³ãœããœã«Lv.3äºä»¶ãçãã; int1 & fact1 -> int2: ã·ãã·ãLv.33äºä»¶ã¯çºçããªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} & {B}) -> ¬{C} fact2: {B} fact3: {C} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; assump1 & fact2 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸããŸã¡ã
Lv.83ã¯ç°èèããªããŠãã€æ¬ã綎ãããªã | (¬{C}{a} & ¬{D}{a}) | fact1: åããŸãããªãã¢ã³ã¹ã¿ãŒã¯ããããããªããèãåãé£ããªããäž¡æ¹ã fact2: ãã®ãŸããŸã¡ã
Lv.83ã¯çŽèšŽããªã fact3: ãããã®ãŸããŸã¡ã
Lv.83ãèãåãé£ããšããããã®ãŽãªãŽã®Lv.85ã¯ããããã fact4: ãã®ãããã«ãLv.30ã¯ç°èèããªã fact5: ãªãããã®ã¢ã³ã¹ã¿ãŒãçŽèšŽããªããªãã°ç°èèããªã fact6: ä»®ã«ãã®ãŸããŸã¡ã
Lv.83ã¯èãåãé£ããªããšãããšãããã®ãŸããŸã¡ã
Lv.83ã¯ç°èèããªããããã¯æ¬ã綎ãããªãããšããããšã¯ééãã ããšããããšã¯åã ãšããããšã¯ãªã | fact1: (x): ¬{F}x -> (¬{B}x v ¬{A}x) fact2: ¬{E}{a} fact3: {A}{a} -> {B}{b} fact4: ¬{C}{ga} fact5: (x): ¬{E}x -> ¬{C}x fact6: ¬{A}{a} -> ¬(¬{C}{a} & ¬{D}{a}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸããŸã¡ã
Lv.83ã¯èãåãé£ã; fact3 & assump1 -> int1: ãã®ãŽãªãŽã®Lv.85ã¯ããããã;"
] | [
"void -> assump1: {A}{a}; fact3 & assump1 -> int1: {B}{b};"
] | ãã®ãŸããŸã¡ã
Lv.83ã¯ç°èèããªããŠãã€æ¬ã綎ãããªã | (¬{C}{a} & ¬{D}{a}) | [
"fact8 -> int2: ããä»®ã«ãã®ãŸããŸã¡ã
Lv.83ãçŽèšŽããªããšããã°ããã¯ç°èèããªã; int2 & fact7 -> int3: ãã®ãŸããŸã¡ã
Lv.83ã¯ç°èèããªã; fact9 -> int4: ãããã®ãŽãªãŽã®Lv.85ãåããŸãããªããªããã®ãŽãªãŽã®Lv.85ã¯ããããããªãããããã¯èãåãé£ããªãããããã¯äž¡æ¹ãšãã§ãã;"
] | 5 | 5 | 4 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: åããŸãããªãã¢ã³ã¹ã¿ãŒã¯ããããããªããèãåãé£ããªããäž¡æ¹ã fact2: ãã®ãŸããŸã¡ã
Lv.83ã¯çŽèšŽããªã fact3: ãããã®ãŸããŸã¡ã
Lv.83ãèãåãé£ããšããããã®ãŽãªãŽã®Lv.85ã¯ããããã fact4: ãã®ãããã«ãLv.30ã¯ç°èèããªã fact5: ãªãããã®ã¢ã³ã¹ã¿ãŒãçŽèšŽããªããªãã°ç°èèããªã fact6: ä»®ã«ãã®ãŸããŸã¡ã
Lv.83ã¯èãåãé£ããªããšãããšãããã®ãŸããŸã¡ã
Lv.83ã¯ç°èèããªããããã¯æ¬ã綎ãããªãããšããããšã¯ééãã ããšããããšã¯åã ãšããããšã¯ãªã ; $hypothesis$ = ãã®ãŸããŸã¡ã
Lv.83ã¯ç°èèããªããŠãã€æ¬ã綎ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{F}x -> (¬{B}x v ¬{A}x) fact2: ¬{E}{a} fact3: {A}{a} -> {B}{b} fact4: ¬{C}{ga} fact5: (x): ¬{E}x -> ¬{C}x fact6: ¬{A}{a} -> ¬(¬{C}{a} & ¬{D}{a}) ; $hypothesis$ = (¬{C}{a} & ¬{D}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã¿ãã¿ãLv.35ã¯èã£ãœããªããæãç¡ããªãããšããããšã¯æ£ãããªã | ¬(¬{A}{a} & ¬{C}{a}) | fact1: ãããã®ã¿ãã¿ãLv.35ãèã£ãœããªããšãããšããã¯èã£ãœããªããæãç¡ããªã fact2: ä»®ã«ãã®ã¿ãã¿ãLv.99ãçæ¯ããªããªããã®ã¿ãã¿ãLv.99ã¯çæ¯ããªãã瀌åæ£ãããªã fact3: ããããã®ã¿ãã¿ãLv.35ãèã£ãœããšããã°ãã®ã¿ãã¿ãLv.35ã¯ç¡ã£èŸã fact4: ãã®ã¿ãã¿ãLv.35ãèã£ãœããªããšãããšãã®ã¿ãã¿ãLv.35ã¯èã£ãœããªããŠãã€ããã¯ç±èŠãããªã fact5: ãã®ã¿ãã¿ãLv.35ã¯ç¡ã£èŸããªã fact6: ãã®ã¿ãã¿ãLv.35ã¯ã¡ã£ã¡ãã | fact1: ¬{A}{a} -> (¬{A}{a} & ¬{C}{a}) fact2: ¬{DC}{du} -> (¬{DC}{du} & ¬{HG}{du}) fact3: {A}{a} -> {B}{a} fact4: ¬{A}{a} -> (¬{A}{a} & ¬{EN}{a}) fact5: ¬{B}{a} fact6: {HM}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ãLv.35ã¯èã£ãœã; fact3 & assump1 -> int1: ãã®ã¿ãã¿ãLv.35ã¯ç¡ã£èŸã; int1 & fact5 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ã¿ãã¿ãLv.35ã¯èã£ãœããªã; int3 & fact1 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact3 & assump1 -> int1: {B}{a}; int1 & fact5 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}{a}; int3 & fact1 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããã®ã¿ãã¿ãLv.35ãèã£ãœããªããšãããšããã¯èã£ãœããªããæãç¡ããªã fact2: ä»®ã«ãã®ã¿ãã¿ãLv.99ãçæ¯ããªããªããã®ã¿ãã¿ãLv.99ã¯çæ¯ããªãã瀌åæ£ãããªã fact3: ããããã®ã¿ãã¿ãLv.35ãèã£ãœããšããã°ãã®ã¿ãã¿ãLv.35ã¯ç¡ã£èŸã fact4: ãã®ã¿ãã¿ãLv.35ãèã£ãœããªããšãããšãã®ã¿ãã¿ãLv.35ã¯èã£ãœããªããŠãã€ããã¯ç±èŠãããªã fact5: ãã®ã¿ãã¿ãLv.35ã¯ç¡ã£èŸããªã fact6: ãã®ã¿ãã¿ãLv.35ã¯ã¡ã£ã¡ãã ; $hypothesis$ = ããã®ã¿ãã¿ãLv.35ã¯èã£ãœããªããæãç¡ããªãããšããããšã¯æ£ãããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ãLv.35ã¯èã£ãœã; fact3 & assump1 -> int1: ãã®ã¿ãã¿ãLv.35ã¯ç¡ã£èŸã; int1 & fact5 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ã¿ãã¿ãLv.35ã¯èã£ãœããªã; int3 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A}{a} -> (¬{A}{a} & ¬{C}{a}) fact2: ¬{DC}{du} -> (¬{DC}{du} & ¬{HG}{du}) fact3: {A}{a} -> {B}{a} fact4: ¬{A}{a} -> (¬{A}{a} & ¬{EN}{a}) fact5: ¬{B}{a} fact6: {HM}{a} ; $hypothesis$ = ¬(¬{A}{a} & ¬{C}{a}) ; $proof$ = | void -> assump1: {A}{a}; fact3 & assump1 -> int1: {B}{a}; int1 & fact5 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}{a}; int3 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããããããåç¡ãããŸã埡ãã§ããããšããããšã¯æãç«ããªããªã埡å¿ãããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ééãã | ¬((Ex): ¬({AA}x & {AB}x) -> ¬{B}x) | fact1: ããããã®ãŸã®ãŸã«Lv.41ãåç¡ãããã®äžåŸ¡ãã§ããããšããããšã¯ç¢ºãã§ãªããªãã°åŸ¡å¿ãããªã | fact1: ¬({AA}{aa} & {AB}{aa}) -> ¬{B}{aa} | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 1 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããããã®ãŸã®ãŸã«Lv.41ãåç¡ãããã®äžåŸ¡ãã§ããããšããããšã¯ç¢ºãã§ãªããªãã°åŸ¡å¿ãããªã ; $hypothesis$ = ããããããåç¡ãããŸã埡ãã§ããããšããããšã¯æãç«ããªããªã埡å¿ãããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ééãã ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({AA}{aa} & {AB}{aa}) -> ¬{B}{aa} ; $hypothesis$ = ¬((Ex): ¬({AA}x & {AB}x) -> ¬{B}x) ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ã«ãã¿ã¡ãLv.37ã¯åãé£ã | {A}{a} | fact1: ããããã®ã¿ã«ãã¿ã¡ãLv.37ãå¡ãæããŠããŸãã«è¿·ä¿¡æ·±ããªããã®ãœã¡ã
ãœã«ãLv.70ã¯å
èŠãããªã fact2: ããã®ã¿ã«ãã¿ã¡ãLv.37ã¯ã©ãé»ããªãããã©æãæãããšããããšã¯èª€ã£ãŠãããšããã°ããã¯çãã fact3: ãããã¢ã³ã¹ã¿ãŒã¯å¡ãæããªããªããåãé£ãããã©å
èŠãããªãããšããããšã¯äºå®ãšç°ãªãããšããããšã¯çå®ã§ãã fact4: ãããã®ã¿ã«ãã¿ã¡ãLv.37ã埡é«ããšããã°ãã®ã¿ã«ãã¿ã¡ãLv.37ã¯å¡ãæã fact5: ãã®ã¿ã«ãã¿ã¡ãLv.37ã¯å
èŠãã fact6: ä»®ã«ããã®ã¿ã«ãã¿ã¡ãLv.37ã¯ã©ãé»ããšããããšã¯ãªãããããæµ
ãããšããããšã¯äºå®ãšç°ãªããšããããã®ã¿ã«ãã¿ã¡ãLv.37ã¯åãé£ã | fact1: ({C}{a} & {D}{a}) -> ¬{B}{fm} fact2: ¬(¬{AA}{a} & {G}{a}) -> {GK}{a} fact3: (x): ¬{C}x -> ¬({A}x & ¬{B}x) fact4: {F}{a} -> {C}{a} fact5: {B}{a} fact6: ¬(¬{AA}{a} & {AB}{a}) -> {A}{a} | [] | [] | ãã®ã¿ã«ãã¿ã¡ãLv.37ã¯åãé£ããªã | ¬{A}{a} | [
"fact7 -> int1: ããããã®ãŸããŸãLv.54ã¯å¡ãæããªããšãããšãããã¯åãé£ãããããå
èŠãããªãããšããããšã¯ééãã§ãã;"
] | 7 | 5 | 4 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®ã¿ã«ãã¿ã¡ãLv.37ãå¡ãæããŠããŸãã«è¿·ä¿¡æ·±ããªããã®ãœã¡ã
ãœã«ãLv.70ã¯å
èŠãããªã fact2: ããã®ã¿ã«ãã¿ã¡ãLv.37ã¯ã©ãé»ããªãããã©æãæãããšããããšã¯èª€ã£ãŠãããšããã°ããã¯çãã fact3: ãããã¢ã³ã¹ã¿ãŒã¯å¡ãæããªããªããåãé£ãããã©å
èŠãããªãããšããããšã¯äºå®ãšç°ãªãããšããããšã¯çå®ã§ãã fact4: ãããã®ã¿ã«ãã¿ã¡ãLv.37ã埡é«ããšããã°ãã®ã¿ã«ãã¿ã¡ãLv.37ã¯å¡ãæã fact5: ãã®ã¿ã«ãã¿ã¡ãLv.37ã¯å
èŠãã fact6: ä»®ã«ããã®ã¿ã«ãã¿ã¡ãLv.37ã¯ã©ãé»ããšããããšã¯ãªãããããæµ
ãããšããããšã¯äºå®ãšç°ãªããšããããã®ã¿ã«ãã¿ã¡ãLv.37ã¯åãé£ã ; $hypothesis$ = ãã®ã¿ã«ãã¿ã¡ãLv.37ã¯åãé£ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({C}{a} & {D}{a}) -> ¬{B}{fm} fact2: ¬(¬{AA}{a} & {G}{a}) -> {GK}{a} fact3: (x): ¬{C}x -> ¬({A}x & ¬{B}x) fact4: {F}{a} -> {C}{a} fact5: {B}{a} fact6: ¬(¬{AA}{a} & {AB}{a}) -> {A}{a} ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããLv.89äºä»¶ã¯èµ·ããªã | ¬{B} | fact1: å¿å°è¯ããšããããšãèµ·ãã fact2: å¿å°è¯ããšããããšãšããããLv.89äºä»¶ãèµ·ããã¯ãœããœãLv.50äºä»¶ãé»ã fact3: ãœããœãLv.50äºä»¶ãèµ·ãã | fact1: {A} fact2: ({A} & {B}) -> ¬{C} fact3: {C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããããLv.89äºä»¶ãèµ·ãã; fact1 & assump1 -> int1: å¿å°è¯ããšããããšãçãããããããLv.89äºä»¶ãèµ·ãã; int1 & fact2 -> int2: ãœããœãLv.50äºä»¶ã¯çããªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; fact1 & assump1 -> int1: ({A} & {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: å¿å°è¯ããšããããšãèµ·ãã fact2: å¿å°è¯ããšããããšãšããããLv.89äºä»¶ãèµ·ããã¯ãœããœãLv.50äºä»¶ãé»ã fact3: ãœããœãLv.50äºä»¶ãèµ·ãã ; $hypothesis$ = ããããLv.89äºä»¶ã¯èµ·ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããããããLv.89äºä»¶ãèµ·ãã; fact1 & assump1 -> int1: å¿å°è¯ããšããããšãçãããããããLv.89äºä»¶ãèµ·ãã; int1 & fact2 -> int2: ãœããœãLv.50äºä»¶ã¯çããªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} fact2: ({A} & {B}) -> ¬{C} fact3: {C} ; $hypothesis$ = ¬{B} ; $proof$ = | void -> assump1: {B}; fact1 & assump1 -> int1: ({A} & {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | äœããã®ã¢ã³ã¹ã¿ãŒã¯æ
ãšããããŠåãé£ã | (Ex): ({D}x & {C}x) | fact1: ããã®ã¿ãã¿ã«ãLv.60ã¯æ
ãšãããããšããããšã¯æãç«ã€ fact2: ã也ç
ããããããŸãã«èµ·ããé£ããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ã¿ãã¿ã«ãLv.60ã¯åãé£ã fact3: ããæ€ããããšããããšã¯äºå®ãªãã¢ã³ã¹ã¿ãŒã¯ãã fact4: ããããããã¢ã³ã¹ã¿ãŒã¯èµ·ããé£ãããšããããšã¯çå®ã§ãããšãããããã¯åã fact5: ãã®ããããLv.34ã¯ä¹Ÿç
ããã fact6: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ä¹Ÿç
ããã fact7: ãã®ããããLv.34ã¯èµ·ããé£ã fact8: ãã®ããããLv.34ã¯åŸ¡åŒãåãäžãããããã«ããã¯çéã»æéç®å
¥ãã fact9: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èª€ãç¡ã | fact1: {D}{b} fact2: (x): ({A}x & {B}x) -> {C}{b} fact3: (Ex): {EE}x fact4: (x): {B}x -> {BC}x fact5: {A}{a} fact6: (Ex): {A}x fact7: {B}{a} fact8: ({GL}{a} & {FS}{a}) fact9: (Ex): {GI}x | [
"fact5 & fact7 -> int1: ãã®ããããLv.34ã¯ä¹Ÿç
ãããããã€èµ·ããé£ã; int1 -> int2: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ä¹Ÿç
ãããããã€èµ·ããé£ã; int2 & fact2 -> int3: ãã®ã¿ãã¿ã«ãLv.60ã¯åãé£ã; int3 & fact1 -> int4: ãã®ã¿ãã¿ã«ãLv.60ã¯æ
ãšããããå ããŠããã¯åãé£ã; int4 -> hypothesis;"
] | [
"fact5 & fact7 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact2 -> int3: {C}{b}; int3 & fact1 -> int4: ({D}{b} & {C}{b}); int4 -> hypothesis;"
] | ãšããã¢ã³ã¹ã¿ãŒã¯éèããŠåã | (Ex): ({IE}x & {BC}x) | [
"fact10 -> int5: ä»®ã«ãã®ã¿ãã¿ã«ãLv.60ãèµ·ããé£ããšããããã®ã¿ãã¿ã«ãLv.60ã¯åã;"
] | 6 | 5 | 5 | 5 | 5 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããã®ã¿ãã¿ã«ãLv.60ã¯æ
ãšãããããšããããšã¯æãç«ã€ fact2: ã也ç
ããããããŸãã«èµ·ããé£ããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ã¿ãã¿ã«ãLv.60ã¯åãé£ã fact3: ããæ€ããããšããããšã¯äºå®ãªãã¢ã³ã¹ã¿ãŒã¯ãã fact4: ããããããã¢ã³ã¹ã¿ãŒã¯èµ·ããé£ãããšããããšã¯çå®ã§ãããšãããããã¯åã fact5: ãã®ããããLv.34ã¯ä¹Ÿç
ããã fact6: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ä¹Ÿç
ããã fact7: ãã®ããããLv.34ã¯èµ·ããé£ã fact8: ãã®ããããLv.34ã¯åŸ¡åŒãåãäžãããããã«ããã¯çéã»æéç®å
¥ãã fact9: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èª€ãç¡ã ; $hypothesis$ = äœããã®ã¢ã³ã¹ã¿ãŒã¯æ
ãšããããŠåãé£ã ; $proof$ = | fact5 & fact7 -> int1: ãã®ããããLv.34ã¯ä¹Ÿç
ãããããã€èµ·ããé£ã; int1 -> int2: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ä¹Ÿç
ãããããã€èµ·ããé£ã; int2 & fact2 -> int3: ãã®ã¿ãã¿ã«ãLv.60ã¯åãé£ã; int3 & fact1 -> int4: ãã®ã¿ãã¿ã«ãLv.60ã¯æ
ãšããããå ããŠããã¯åãé£ã; int4 -> hypothesis; __PROVED__ | $facts$ = fact1: {D}{b} fact2: (x): ({A}x & {B}x) -> {C}{b} fact3: (Ex): {EE}x fact4: (x): {B}x -> {BC}x fact5: {A}{a} fact6: (Ex): {A}x fact7: {B}{a} fact8: ({GL}{a} & {FS}{a}) fact9: (Ex): {GI}x ; $hypothesis$ = (Ex): ({D}x & {C}x) ; $proof$ = | fact5 & fact7 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact2 -> int3: {C}{b}; int3 & fact1 -> int4: ({D}{b} & {C}{b}); int4 -> hypothesis; __PROVED__ |
0.3 | ããã®ãã«ã
ãã«Lv.42ã¯èŠ³å
客ãããããã¿ãããšããããšã¯åœã§ãã | ¬({D}{a} & {E}{a}) | fact1: ãããã®ãã«ã
ãã«Lv.42ãéæç¡ããšãããããã¯èŠ³å
客ããã fact2: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯æ¶ããŸãããªããšããããéæç¡ããªããããã«æ»çãããšããããšã¯ãªãããšããããšã¯ééãã§ãã fact3: ãã®ãã«ã
ãã«Lv.42ã¯ãã¿ã fact4: ãã®ãããã¡ãLv.99ã¯éæç¡ã fact5: ãã®ãããã¡ãLv.99ãæ»çãããšãããšãã®ãã«ã
ãã«Lv.42ã¯éæç¡ã fact6: ããããããã¢ã³ã¹ã¿ãŒã¯æ¶åãé£ããªããæ»çããããšããããšã¯ç¢ºãã ããšããããšã¯æ£ãã | fact1: {C}{a} -> {D}{a} fact2: (x): ¬{F}x -> ¬(¬{C}x & ¬{B}x) fact3: {E}{a} fact4: {C}{aa} fact5: {B}{aa} -> {C}{a} fact6: (x): (¬{A}x v {B}x) | [
"fact6 -> int1: ãã®ãããã¡ãLv.99ã¯æ¶åãé£ããªãããŸãã¯æ»çãããã©ã¡ããã§ãã;"
] | [
"fact6 -> int1: (¬{A}{aa} v {B}{aa});"
] | ããã®ãã«ã
ãã«Lv.42ã¯èŠ³å
客ãããããã¿ãããšããããšã¯åœã§ãã | ¬({D}{a} & {E}{a}) | [
"fact7 -> int2: ããããã®ã¿ãã¿ãLv.23ã¯æ¶ããŸãããªããšããã°ããã®ã¿ãã¿ãLv.23ã¯éæç¡ããªãããã®äžæ»çããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã;"
] | 6 | 4 | 4 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®ãã«ã
ãã«Lv.42ãéæç¡ããšãããããã¯èŠ³å
客ããã fact2: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯æ¶ããŸãããªããšããããéæç¡ããªããããã«æ»çãããšããããšã¯ãªãããšããããšã¯ééãã§ãã fact3: ãã®ãã«ã
ãã«Lv.42ã¯ãã¿ã fact4: ãã®ãããã¡ãLv.99ã¯éæç¡ã fact5: ãã®ãããã¡ãLv.99ãæ»çãããšãããšãã®ãã«ã
ãã«Lv.42ã¯éæç¡ã fact6: ããããããã¢ã³ã¹ã¿ãŒã¯æ¶åãé£ããªããæ»çããããšããããšã¯ç¢ºãã ããšããããšã¯æ£ãã ; $hypothesis$ = ããã®ãã«ã
ãã«Lv.42ã¯èŠ³å
客ãããããã¿ãããšããããšã¯åœã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C}{a} -> {D}{a} fact2: (x): ¬{F}x -> ¬(¬{C}x & ¬{B}x) fact3: {E}{a} fact4: {C}{aa} fact5: {B}{aa} -> {C}{a} fact6: (x): (¬{A}x v {B}x) ; $hypothesis$ = ¬({D}{a} & {E}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸã«ãŸã«ã
Lv.47ã¯è¥ã
ãããªã | ¬{A}{b} | fact1: ãããã®ãŽã«ããŽã¡ãLv.25ã床ãé£ããªããŠããã«è¶ã£ãœããšããããšã¯ãªããšããã°ããã®ãŸã«ãŸã«ã
Lv.47ã¯è¥ã
ãããªãããšããããšã¯æ£ãã | fact1: (¬{AA}{a} & ¬{AB}{a}) -> ¬{A}{b} | [] | [] | null | null | [] | null | 2 | 2 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããã®ãŽã«ããŽã¡ãLv.25ã床ãé£ããªããŠããã«è¶ã£ãœããšããããšã¯ãªããšããã°ããã®ãŸã«ãŸã«ã
Lv.47ã¯è¥ã
ãããªãããšããããšã¯æ£ãã ; $hypothesis$ = ãã®ãŸã«ãŸã«ã
Lv.47ã¯è¥ã
ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (¬{AA}{a} & ¬{AB}{a}) -> ¬{A}{b} ; $hypothesis$ = ¬{A}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸããŸãLv.50ã¯ä»æãã | {B}{a} | fact1: ãã®ãœããœãLv.30ã¯å€§å·®ç¡ããšããããšã¯ãªããè»äººããããäž¡æ¹ãšãã fact2: ä»®ã«ãã®ãŸããŸãLv.50ã¯èŠªãã¿æããªããšããããããã®ãœããœãLv.30ã¯å€§å·®ç¡ããªãããããã¯ããã¯è»äººãããããŸãã¯äž¡æ¹ã§ããããšããããšã¯æãç«ã€ããšããããšã¯èª€ã£ãŠãã | fact1: (¬{AA}{b} v {AB}{b}) fact2: ¬{A}{a} -> ¬(¬{AA}{b} v {AB}{b}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸããŸãLv.50ã¯èŠªãã¿æããªã; fact2 & assump1 -> int1: ããã®ãœããœãLv.30ã¯å€§å·®ç¡ããªããè»äººããããã©ã¡ããã§ããããšããããšã¯åœã§ãã; int1 & fact1 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ãŸããŸãLv.50ã¯èŠªãã¿æã;"
] | [
"void -> assump1: ¬{A}{a}; fact2 & assump1 -> int1: ¬(¬{AA}{b} v {AB}{b}); int1 & fact1 -> int2: #F#; [assump1] & int2 -> int3: {A}{a};"
] | null | null | [] | null | 5 | 4 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãœããœãLv.30ã¯å€§å·®ç¡ããšããããšã¯ãªããè»äººããããäž¡æ¹ãšãã fact2: ä»®ã«ãã®ãŸããŸãLv.50ã¯èŠªãã¿æããªããšããããããã®ãœããœãLv.30ã¯å€§å·®ç¡ããªãããããã¯ããã¯è»äººãããããŸãã¯äž¡æ¹ã§ããããšããããšã¯æãç«ã€ããšããããšã¯èª€ã£ãŠãã ; $hypothesis$ = ãã®ãŸããŸãLv.50ã¯ä»æãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (¬{AA}{b} v {AB}{b}) fact2: ¬{A}{a} -> ¬(¬{AA}{b} v {AB}{b}) ; $hypothesis$ = {B}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | æ°æã¡è¯ããšããããšã¯èµ·ãããªã | ¬{D} | fact1: ãããè¥ããšããããšã¯çºçããªãããšããããšã¯æ°æã¡è¯ããšããããšãšãŸããŸã¡ã
Lv.38äºä»¶ãèµ·ããããããã fact2: ãŸããŸã¡ã
Lv.38äºä»¶ãšããè¥ããšããããšãèµ·ããã¯ããŸããŸãLv.6äºä»¶ã¯èµ·ãããªãããšããããšãå¥æ©ã§ãã fact3: ãŸããŸãLv.6äºä»¶ã¯çºçããªã fact4: ãŸããŸã¡ã
Lv.38äºä»¶ãçºçãã fact5: ã¿ãã¿ã®Lv.47äºä»¶ã¯çºçããªã fact6: ãããä¹ãæããšããããšããããã¯ããè¥ããšããããšãçºçããã°æ°æã¡è¯ããšããããšã¯çããªã | fact1: ¬{B} -> ({D} & {A}) fact2: ¬{E} -> ({A} & {B}) fact3: ¬{E} fact4: {A} fact5: ¬{HR} fact6: ({C} v {B}) -> ¬{D} | [
"fact3 & fact2 -> int1: ãŸããŸã¡ã
Lv.38äºä»¶ãèµ·ãããå ããŠããè¥ããšããããšãçºçãã; int1 -> int2: ããè¥ããšããããšãèµ·ãã; int2 -> int3: ãä¹ãæããšããããšããããã¯ããè¥ããšããããšããããã¯ã©ã¡ãããèµ·ããããšããããšã¯åœã§ãªã; int3 & fact6 -> hypothesis;"
] | [
"fact3 & fact2 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 -> int3: ({C} v {B}); int3 & fact6 -> hypothesis;"
] | æ°æã¡è¯ããšããããšãçãã | {D} | [] | 6 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããè¥ããšããããšã¯çºçããªãããšããããšã¯æ°æã¡è¯ããšããããšãšãŸããŸã¡ã
Lv.38äºä»¶ãèµ·ããããããã fact2: ãŸããŸã¡ã
Lv.38äºä»¶ãšããè¥ããšããããšãèµ·ããã¯ããŸããŸãLv.6äºä»¶ã¯èµ·ãããªãããšããããšãå¥æ©ã§ãã fact3: ãŸããŸãLv.6äºä»¶ã¯çºçããªã fact4: ãŸããŸã¡ã
Lv.38äºä»¶ãçºçãã fact5: ã¿ãã¿ã®Lv.47äºä»¶ã¯çºçããªã fact6: ãããä¹ãæããšããããšããããã¯ããè¥ããšããããšãçºçããã°æ°æã¡è¯ããšããããšã¯çããªã ; $hypothesis$ = æ°æã¡è¯ããšããããšã¯èµ·ãããªã ; $proof$ = | fact3 & fact2 -> int1: ãŸããŸã¡ã
Lv.38äºä»¶ãèµ·ãããå ããŠããè¥ããšããããšãçºçãã; int1 -> int2: ããè¥ããšããããšãèµ·ãã; int2 -> int3: ãä¹ãæããšããããšããããã¯ããè¥ããšããããšããããã¯ã©ã¡ãããèµ·ããããšããããšã¯åœã§ãªã; int3 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{B} -> ({D} & {A}) fact2: ¬{E} -> ({A} & {B}) fact3: ¬{E} fact4: {A} fact5: ¬{HR} fact6: ({C} v {B}) -> ¬{D} ; $hypothesis$ = ¬{D} ; $proof$ = | fact3 & fact2 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 -> int3: ({C} v {B}); int3 & fact6 -> hypothesis; __PROVED__ |
0.3 | ãã¡ã
ããªLv.80äºä»¶ã¯èµ·ããªã | ¬{A} | fact1: ãœã«ã
ãœã¡ãLv.27äºä»¶ãçºçãã fact2: ãœã«ã
ãœã¡ãLv.27äºä»¶ã¯ããã¡ã
ããªLv.80äºä»¶ãèµ·ãããåºããšããããšãèµ·ããããšããããšã«é»ãŸãã | fact1: {C} fact2: ({A} v {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã¡ã
ããªLv.80äºä»¶ãçãã; assump1 -> int1: ãã¡ã
ããªLv.80äºä»¶ããããã¯åºããšããããšããããã¯äž¡æ¹ãšããèµ·ãã; int1 & fact2 -> int2: ãœã«ã
ãœã¡ãLv.27äºä»¶ã¯èµ·ãããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 3 | 5 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãœã«ã
ãœã¡ãLv.27äºä»¶ãçºçãã fact2: ãœã«ã
ãœã¡ãLv.27äºä»¶ã¯ããã¡ã
ããªLv.80äºä»¶ãèµ·ãããåºããšããããšãèµ·ããããšããããšã«é»ãŸãã ; $hypothesis$ = ãã¡ã
ããªLv.80äºä»¶ã¯èµ·ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã¡ã
ããªLv.80äºä»¶ãçãã; assump1 -> int1: ãã¡ã
ããªLv.80äºä»¶ããããã¯åºããšããããšããããã¯äž¡æ¹ãšããèµ·ãã; int1 & fact2 -> int2: ãœã«ã
ãœã¡ãLv.27äºä»¶ã¯èµ·ãããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} fact2: ({A} v {B}) -> ¬{C} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãããã«ãLv.54äºä»¶ãæ¥è¿ãæããšããããšã¯ãã£ããã | {A} -> {C} | fact1: å®çŸãæããšããããšã¯èµ·ããªããªãã°ã¿ã¡ã
ã¿ãLv.11äºä»¶ããããã¯ãããã«ãLv.54äºä»¶ããŸãã¯äž¡æ¹ãèµ·ãã fact2: ãäœæ°ç¡ããšããããšãšæ¥è¿ãæããšããããšãèµ·ããããšããããšã¯æ©æ»
ããããšã¯èµ·ãããªããšããããšã«ãããããã fact3: æ¥è¿ãæããšããããšã¯æ©æ»
ããããšã«ç¹ãã fact4: æµããæããšããããšãçãã | fact1: ¬{E} -> ({D} v {C}) fact2: ¬{B} -> ({AN} & {A}) fact3: {A} -> {B} fact4: {IR} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããæ¥è¿ãæããšããããšãçããããšããããšã¯æ¬åœã§ãã; fact3 & assump1 -> int1: æ©æ»
ããããšãèµ·ãã;"
] | [
"void -> assump1: {A}; fact3 & assump1 -> int1: {B};"
] | äœæ°ç¡ããšããããšãçºçãã | {AN} | [] | 7 | 4 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: å®çŸãæããšããããšã¯èµ·ããªããªãã°ã¿ã¡ã
ã¿ãLv.11äºä»¶ããããã¯ãããã«ãLv.54äºä»¶ããŸãã¯äž¡æ¹ãèµ·ãã fact2: ãäœæ°ç¡ããšããããšãšæ¥è¿ãæããšããããšãèµ·ããããšããããšã¯æ©æ»
ããããšã¯èµ·ãããªããšããããšã«ãããããã fact3: æ¥è¿ãæããšããããšã¯æ©æ»
ããããšã«ç¹ãã fact4: æµããæããšããããšãçãã ; $hypothesis$ = ãããã«ãLv.54äºä»¶ãæ¥è¿ãæããšããããšã¯ãã£ããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{E} -> ({D} v {C}) fact2: ¬{B} -> ({AN} & {A}) fact3: {A} -> {B} fact4: {IR} ; $hypothesis$ = {A} -> {C} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ã¡ãã·ã«ãLv.77ã¯é芧ãã | {D}{b} | fact1: ãããšããã¢ã³ã¹ã¿ãŒãé£ã³ç¶ããªãäžæ¹ã§ãããæå®ãé£ããšãããšé£ã fact2: ããã®ãŸããŸã«Lv.94ã¯æšããããããšããããšã¯èª€ãã§ãªããšããã°ãã®ãŸããŸã«Lv.94ã¯é芧ãã fact3: ä»®ã«ãã®ãã«ãããLv.43ãå³ããæ·±ããªããã®ã·ã¡ãã·ã«ãLv.77ã¯é芧ãã fact4: æµ
ãŸããã¢ã³ã¹ã¿ãŒã¯é芧ãã fact5: ããããã®ãã«ãããLv.43ãé£ããªãããããã¯é芧ãããšããããšã¯ãªãããããã¯äž¡æ¹ã ãšããããã®ã·ã¡ãã·ã«ãLv.77ã¯é芧ãããšããããšã¯ãªã fact6: ãã®ãŸããŸã«Lv.94ã¯é£ã³ç¶ããªãäžæ¹ã§ããã¯æå®ãé£ã fact7: ãã®ãŸããŸã«Lv.94ãé£ããªããã®ãŸããŸã«Lv.94ã¯æšãããã fact8: ãã®ãŸããŸã«Lv.94ã¯æå®ãé£ã | fact1: (x): (¬{AA}x & {AB}x) -> {B}x fact2: {A}{aa} -> {D}{aa} fact3: {C}{a} -> {D}{b} fact4: (x): {H}x -> {D}x fact5: (¬{B}{a} v ¬{D}{a}) -> ¬{D}{b} fact6: (¬{AA}{aa} & {AB}{aa}) fact7: {B}{aa} -> {A}{aa} fact8: {AB}{aa} | [
"fact1 -> int1: ãã®ãŸããŸã«Lv.94ã¯é£ã³ç¶ããªããã©æå®ãé£ããšããã°ããã¯é£ã; int1 & fact6 -> int2: ãã®ãŸããŸã«Lv.94ã¯é£ã; int2 & fact7 -> int3: ãã®ãŸããŸã«Lv.94ã¯æšãããã;"
] | [
"fact1 -> int1: (¬{AA}{aa} & {AB}{aa}) -> {B}{aa}; int1 & fact6 -> int2: {B}{aa}; int2 & fact7 -> int3: {A}{aa};"
] | ããä»®ã«ããã®ã·ãªã·ãLv.50ã¯æµ
ãŸãããªãããšããããšã¯æãç«ããªããšãããšé芧ãã | {H}{ii} -> {D}{ii} | [
"fact9 -> hypothesis;"
] | 1 | 5 | 5 | null | null | 4 | 0 | 4 | UNKNOWN | PROVED | UNKNOWN | PROVED | $facts$ = fact1: ãããšããã¢ã³ã¹ã¿ãŒãé£ã³ç¶ããªãäžæ¹ã§ãããæå®ãé£ããšãããšé£ã fact2: ããã®ãŸããŸã«Lv.94ã¯æšããããããšããããšã¯èª€ãã§ãªããšããã°ãã®ãŸããŸã«Lv.94ã¯é芧ãã fact3: ä»®ã«ãã®ãã«ãããLv.43ãå³ããæ·±ããªããã®ã·ã¡ãã·ã«ãLv.77ã¯é芧ãã fact4: æµ
ãŸããã¢ã³ã¹ã¿ãŒã¯é芧ãã fact5: ããããã®ãã«ãããLv.43ãé£ããªãããããã¯é芧ãããšããããšã¯ãªãããããã¯äž¡æ¹ã ãšããããã®ã·ã¡ãã·ã«ãLv.77ã¯é芧ãããšããããšã¯ãªã fact6: ãã®ãŸããŸã«Lv.94ã¯é£ã³ç¶ããªãäžæ¹ã§ããã¯æå®ãé£ã fact7: ãã®ãŸããŸã«Lv.94ãé£ããªããã®ãŸããŸã«Lv.94ã¯æšãããã fact8: ãã®ãŸããŸã«Lv.94ã¯æå®ãé£ã ; $hypothesis$ = ãã®ã·ã¡ãã·ã«ãLv.77ã¯é芧ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): (¬{AA}x & {AB}x) -> {B}x fact2: {A}{aa} -> {D}{aa} fact3: {C}{a} -> {D}{b} fact4: (x): {H}x -> {D}x fact5: (¬{B}{a} v ¬{D}{a}) -> ¬{D}{b} fact6: (¬{AA}{aa} & {AB}{aa}) fact7: {B}{aa} -> {A}{aa} fact8: {AB}{aa} ; $hypothesis$ = {D}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãœããœãLv.31äºä»¶ã¯èµ·ãããªã | ¬{C} | fact1: ã·ã«ã·ã¡ã
Lv.84äºä»¶ãçºçãã fact2: ç²ããšããããšãçºçãã fact3: ãã©ããªããšããããšã¯ããœããœãLv.31äºä»¶ã¯èµ·ãããªãããšããããšãé²ã fact4: ç²ããšããããšã¯ãã©ããªããšããããšã«åž°çµãã fact5: ãããã¿ãã¿ã«ãLv.7äºä»¶ã¯çããªãããã©ããããšããããšã¯èµ·ããªãããšããããšã¯åã ãšããã°ãã©ããªããšããããšã¯èµ·ããªã | fact1: {IF} fact2: {A} fact3: {B} -> {C} fact4: {A} -> {B} fact5: ¬(¬{E} & ¬{D}) -> ¬{B} | [
"fact4 & fact2 -> int1: ãã©ããªããšããããšãçãã; int1 & fact3 -> hypothesis;"
] | [
"fact4 & fact2 -> int1: {B}; int1 & fact3 -> hypothesis;"
] | ãœããœãLv.31äºä»¶ã¯èµ·ãããªã | ¬{C} | [] | 6 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ã·ã«ã·ã¡ã
Lv.84äºä»¶ãçºçãã fact2: ç²ããšããããšãçºçãã fact3: ãã©ããªããšããããšã¯ããœããœãLv.31äºä»¶ã¯èµ·ãããªãããšããããšãé²ã fact4: ç²ããšããããšã¯ãã©ããªããšããããšã«åž°çµãã fact5: ãããã¿ãã¿ã«ãLv.7äºä»¶ã¯çããªãããã©ããããšããããšã¯èµ·ããªãããšããããšã¯åã ãšããã°ãã©ããªããšããããšã¯èµ·ããªã ; $hypothesis$ = ãœããœãLv.31äºä»¶ã¯èµ·ãããªã ; $proof$ = | fact4 & fact2 -> int1: ãã©ããªããšããããšãçãã; int1 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {IF} fact2: {A} fact3: {B} -> {C} fact4: {A} -> {B} fact5: ¬(¬{E} & ¬{D}) -> ¬{B} ; $hypothesis$ = ¬{C} ; $proof$ = | fact4 & fact2 -> int1: {B}; int1 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã·ã¡ãã·ãLv.86ã¯åŸ¡èŸãããšããããšã¯æ£ãã | {F}{c} | fact1: ããä»®ã«ããã®ãœã¡ããœãLv.66ã¯å¹ãããªããããã錻é³åããªãããšããããšã¯äºå®ãšç°ãªããªããã®ã·ã¡ãã·ãLv.86ã¯ç®¡çãæã fact2: ããä»®ã«ãã®ã·ã«ãã·ãLv.92ã¯éŒ»é³åããªããªãããã®ã·ã¡ãã·ãLv.86ã¯åŸ¡èŸããŠçãé£ãããšããããšã¯ç¢ºãã fact3: ããã¢ã³ã¹ã¿ãŒã¯åŸ¡èŸããšãããšãçãé£ãããšããããšã¯äºå®ã fact4: ããããã®ã·ã«ãã·ãLv.92ã¯å¹ãããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšãããšããã®ã·ã«ãã·ãLv.92ã¯éŒ»é³åããªãããšããããšã¯æãç«ã€ fact5: ãã®ãœã¡ããœãLv.66ã¯ç®¡çãæã fact6: ããããããã¢ã³ã¹ã¿ãŒã¯çãé£ãããšããããšã¯çå®ã ãšãããšãããã¯å¹ãããªããããã«éŒ»é³åãããšããããšã¯ãªãããšããããšã¯çå®ã§ãããšããããšã¯ãªã fact7: ãã®ãœã¡ããœãLv.66ãåãé£ãããããã¯ããã管çãæããªãã°ãã®ã·ã«ãã·ãLv.92ã¯å¹ãããªã fact8: ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã管çãæããšãããåãé£ã | fact1: ¬(¬{C}{a} & ¬{D}{a}) -> {B}{c} fact2: ¬{D}{b} -> ({F}{c} & {E}{c}) fact3: (x): {F}x -> {E}x fact4: ¬{C}{b} -> ¬{D}{b} fact5: {B}{a} fact6: (x): {E}x -> ¬(¬{C}x & ¬{D}x) fact7: ({A}{a} v {B}{a}) -> ¬{C}{b} fact8: (x): {B}x -> {A}x | [
"fact5 -> int1: ãã®ãœã¡ããœãLv.66ã¯åãé£ãããããã¯ç®¡çãæããäž¡æ¹ãšãã ; int1 & fact7 -> int2: ãã®ã·ã«ãã·ãLv.92ã¯å¹ãããªã; int2 & fact4 -> int3: ãã®ã·ã«ãã·ãLv.92ã¯éŒ»é³åããªã; int3 & fact2 -> int4: ãã®ã·ã¡ãã·ãLv.86ã¯åŸ¡èŸããæŽã«ããã¯çãé£ã; int4 -> hypothesis;"
] | [
"fact5 -> int1: ({A}{a} v {B}{a}); int1 & fact7 -> int2: ¬{C}{b}; int2 & fact4 -> int3: ¬{D}{b}; int3 & fact2 -> int4: ({F}{c} & {E}{c}); int4 -> hypothesis;"
] | ãã®ã·ã¡ãã·ãLv.86ã¯åãé£ã | {A}{c} | [
"fact12 -> int5: ä»®ã«ãã®ã·ã¡ãã·ãLv.86ã管çãæããªãããã¯åãé£ã; fact10 -> int6: ããããã®ãœã¡ããœãLv.66ã¯çãé£ããªãã°ãå¹ãããªããŠãŸãããã¯éŒ»é³åããªãããšããããšã¯æ£ãããšããããšã¯ãªã; fact9 -> int7: ãããã®ãœã¡ããœãLv.66ã埡èŸããšãããšãã®ãœã¡ããœãLv.66ã¯çãé£ã;"
] | 6 | 5 | 5 | 5 | 5 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ããã®ãœã¡ããœãLv.66ã¯å¹ãããªããããã錻é³åããªãããšããããšã¯äºå®ãšç°ãªããªããã®ã·ã¡ãã·ãLv.86ã¯ç®¡çãæã fact2: ããä»®ã«ãã®ã·ã«ãã·ãLv.92ã¯éŒ»é³åããªããªãããã®ã·ã¡ãã·ãLv.86ã¯åŸ¡èŸããŠçãé£ãããšããããšã¯ç¢ºãã fact3: ããã¢ã³ã¹ã¿ãŒã¯åŸ¡èŸããšãããšãçãé£ãããšããããšã¯äºå®ã fact4: ããããã®ã·ã«ãã·ãLv.92ã¯å¹ãããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšãããšããã®ã·ã«ãã·ãLv.92ã¯éŒ»é³åããªãããšããããšã¯æãç«ã€ fact5: ãã®ãœã¡ããœãLv.66ã¯ç®¡çãæã fact6: ããããããã¢ã³ã¹ã¿ãŒã¯çãé£ãããšããããšã¯çå®ã ãšãããšãããã¯å¹ãããªããããã«éŒ»é³åãããšããããšã¯ãªãããšããããšã¯çå®ã§ãããšããããšã¯ãªã fact7: ãã®ãœã¡ããœãLv.66ãåãé£ãããããã¯ããã管çãæããªãã°ãã®ã·ã«ãã·ãLv.92ã¯å¹ãããªã fact8: ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã管çãæããšãããåãé£ã ; $hypothesis$ = ããã®ã·ã¡ãã·ãLv.86ã¯åŸ¡èŸãããšããããšã¯æ£ãã ; $proof$ = | fact5 -> int1: ãã®ãœã¡ããœãLv.66ã¯åãé£ãããããã¯ç®¡çãæããäž¡æ¹ãšãã ; int1 & fact7 -> int2: ãã®ã·ã«ãã·ãLv.92ã¯å¹ãããªã; int2 & fact4 -> int3: ãã®ã·ã«ãã·ãLv.92ã¯éŒ»é³åããªã; int3 & fact2 -> int4: ãã®ã·ã¡ãã·ãLv.86ã¯åŸ¡èŸããæŽã«ããã¯çãé£ã; int4 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬(¬{C}{a} & ¬{D}{a}) -> {B}{c} fact2: ¬{D}{b} -> ({F}{c} & {E}{c}) fact3: (x): {F}x -> {E}x fact4: ¬{C}{b} -> ¬{D}{b} fact5: {B}{a} fact6: (x): {E}x -> ¬(¬{C}x & ¬{D}x) fact7: ({A}{a} v {B}{a}) -> ¬{C}{b} fact8: (x): {B}x -> {A}x ; $hypothesis$ = {F}{c} ; $proof$ = | fact5 -> int1: ({A}{a} v {B}{a}); int1 & fact7 -> int2: ¬{C}{b}; int2 & fact4 -> int3: ¬{D}{b}; int3 & fact2 -> int4: ({F}{c} & {E}{c}); int4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœã«ã
ãœãLv.80ã¯æ±ºãé£ããªã | ¬{A}{a} | fact1: ããããããã¢ã³ã¹ã¿ãŒãèŠäžãããšãããçã¿èœãšããšããããšã¯ãªãããã€ããã¯æ ¹æ°åŒ·ããªãããšããããšã¯ç¢ºãã fact2: ãããããã®ãœã«ã
ãœãLv.80ã決ãé£ããšããã°ãã®ãœã«ã
ãœãLv.80ã¯å³ãããšããããšã¯ç¢ºãã fact3: äœããã®ã¢ã³ã¹ã¿ãŒãéæ€ããªããšããã°ããã¯æ±ºãé£ãããããå³ã fact4: ãããã®ãœã«ã
ãœãLv.80ãå³ããªããã®ãœã«ã
ãœãLv.80ã¯ç ãã fact5: ãã®ãœã«ã
ãœãLv.80ã¯ç ãããªã fact6: ããããã¢ã³ã¹ã¿ãŒãèŠäžããããã®äžå¥è¥²ãã | fact1: (x): {G}x -> (¬{E}x & ¬{F}x) fact2: {A}{a} -> {B}{a} fact3: (x): ¬{D}x -> ({A}x & {B}x) fact4: {B}{a} -> {C}{a} fact5: ¬{C}{a} fact6: (x): ({G}x & {H}x) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã«ã
ãœãLv.80ã¯æ±ºãé£ã; fact2 & assump1 -> int1: ãã®ãœã«ã
ãœãLv.80ã¯å³ã; int1 & fact4 -> int2: ãã®ãœã«ã
ãœãLv.80ã¯ç ãã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{a}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ãã®ããããLv.36ã¯ç ãã | {C}{gi} | [
"fact7 -> int4: ããããã®ããããLv.36ãéæ€ããªããšãããšæ±ºãé£ããŠå³ã; fact8 -> int5: ãã®ãŸã«ã
ãŸã«ã
Lv.62ã¯èŠäžãããããã«å¥è¥²ãã; int5 -> int6: ãã®ãŸã«ã
ãŸã«ã
Lv.62ã¯èŠäžãã; int6 -> int7: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯èŠäžãã; int7 -> int8: ãã®ãœã«ã
ãœãLv.80ã¯èŠäžãã; fact9 -> int9: ãããã®ãœã«ã
ãœãLv.80ãèŠäžãããšããã°ããã¯çã¿èœãšããªããŠæ ¹æ°åŒ·ããªã; int8 & int9 -> int10: ãã®ãœã«ã
ãœãLv.80ã¯çã¿èœãšããªãããŸãããã¯æ ¹æ°åŒ·ããªã; int10 -> int11: ãå
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çã¿èœãšããšããããšã¯ãªããŠããã«æ ¹æ°åŒ·ããšããããšã¯ãªãããšããããšã¯æãç«ã€; int11 -> int12: ãã®ããããLv.36ã¯çã¿èœãšããªããæŽã«æ ¹æ°åŒ·ããšããããšã¯ãªã;"
] | 11 | 5 | 4 | 5 | 4 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããããã¢ã³ã¹ã¿ãŒãèŠäžãããšãããçã¿èœãšããšããããšã¯ãªãããã€ããã¯æ ¹æ°åŒ·ããªãããšããããšã¯ç¢ºãã fact2: ãããããã®ãœã«ã
ãœãLv.80ã決ãé£ããšããã°ãã®ãœã«ã
ãœãLv.80ã¯å³ãããšããããšã¯ç¢ºãã fact3: äœããã®ã¢ã³ã¹ã¿ãŒãéæ€ããªããšããã°ããã¯æ±ºãé£ãããããå³ã fact4: ãããã®ãœã«ã
ãœãLv.80ãå³ããªããã®ãœã«ã
ãœãLv.80ã¯ç ãã fact5: ãã®ãœã«ã
ãœãLv.80ã¯ç ãããªã fact6: ããããã¢ã³ã¹ã¿ãŒãèŠäžããããã®äžå¥è¥²ãã ; $hypothesis$ = ãã®ãœã«ã
ãœãLv.80ã¯æ±ºãé£ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã«ã
ãœãLv.80ã¯æ±ºãé£ã; fact2 & assump1 -> int1: ãã®ãœã«ã
ãœãLv.80ã¯å³ã; int1 & fact4 -> int2: ãã®ãœã«ã
ãœãLv.80ã¯ç ãã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {G}x -> (¬{E}x & ¬{F}x) fact2: {A}{a} -> {B}{a} fact3: (x): ¬{D}x -> ({A}x & {B}x) fact4: {B}{a} -> {C}{a} fact5: ¬{C}{a} fact6: (x): ({G}x & {H}x) ; $hypothesis$ = ¬{A}{a} ; $proof$ = | void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{a}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ããã®ãã«ãããLv.29ã¯æ¢ãã©ç¡ããŠãã€ããã¯èŠãããšããããšã¯äºå®ã§ãªã | ¬({B}{a} & {C}{a}) | fact1: ããä»®ã«ãã®ãã«ãããLv.29ããšãèããªããšããããã®ãã«ãããLv.29ã¯è¿°ã¶ fact2: ãããããã¢ã³ã¹ã¿ãŒã¯åãé£ããªããšããã°ããæ¢ãã©ç¡ããŠãŸãããã¯èŠãããšããããšã¯ééã£ãŠããªãããšããããšã¯åã§ãã fact3: ãã®ãã«ãããLv.29ã¯åãé£ããŠãŸãæ¢ãã©ç¡ã fact4: ãã®ãã«ãããLv.29ã¯èŠã fact5: ä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãšãèããªããšããããããã¯è¿°ã¶ããããããã¯åãé£ãããšããããšã¯ééãã§ãã fact6: ãã®ãã«ãããLv.29ã¯åãé£ã fact7: ããšããã¢ã³ã¹ã¿ãŒã¯è¿°ã¶ããã€åãé£ãããšããããšã¯åœã§ãããªãã°ããã¯åãé£ããªã | fact1: ¬{E}{a} -> {D}{a} fact2: (x): ¬{A}x -> ¬({B}x & {C}x) fact3: ({A}{a} & {B}{a}) fact4: {C}{a} fact5: (x): ¬{E}x -> ¬({D}x & {A}x) fact6: {A}{a} fact7: (x): ¬({D}x & {A}x) -> ¬{A}x | [
"fact3 -> int1: ãã®ãã«ãããLv.29ã¯æ¢ãã©ç¡ã; int1 & fact4 -> hypothesis;"
] | [
"fact3 -> int1: {B}{a}; int1 & fact4 -> hypothesis;"
] | ããã®ãã«ãããLv.29ã¯æ¢ãã©ç¡ããŠãã€ããã¯èŠãããšããããšã¯äºå®ã§ãªã | ¬({B}{a} & {C}{a}) | [
"fact8 -> int2: ãããã®ãœããœãLv.14ã¯åãé£ããªããªãããã®ãœããœãLv.14ã¯æ¢ãã©ç¡ããŠãŸãèŠãããšããããšã¯æãç«ããªã; fact9 -> int3: ãããããã®ãœããœãLv.14ã¯è¿°ã¶ãåãé£ãããšããããšã¯æ¬åœã ãšããããšã¯ãªããšãããšãã®ãœããœãLv.14ã¯åãé£ããªã; fact10 -> int4: ãããã®ã¿ã¡ã
ã¿ã¡ãLv.28ã¯ãšãèããšããããšã¯ãªããšããã°ããã®ã¿ã¡ã
ã¿ã¡ãLv.28ãè¿°ã¶ããã®äžåãé£ãããšããããšã¯æãç«ããªã;"
] | 8 | 2 | 2 | 2 | 2 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãã«ãããLv.29ããšãèããªããšããããã®ãã«ãããLv.29ã¯è¿°ã¶ fact2: ãããããã¢ã³ã¹ã¿ãŒã¯åãé£ããªããšããã°ããæ¢ãã©ç¡ããŠãŸãããã¯èŠãããšããããšã¯ééã£ãŠããªãããšããããšã¯åã§ãã fact3: ãã®ãã«ãããLv.29ã¯åãé£ããŠãŸãæ¢ãã©ç¡ã fact4: ãã®ãã«ãããLv.29ã¯èŠã fact5: ä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãšãèããªããšããããããã¯è¿°ã¶ããããããã¯åãé£ãããšããããšã¯ééãã§ãã fact6: ãã®ãã«ãããLv.29ã¯åãé£ã fact7: ããšããã¢ã³ã¹ã¿ãŒã¯è¿°ã¶ããã€åãé£ãããšããããšã¯åœã§ãããªãã°ããã¯åãé£ããªã ; $hypothesis$ = ããã®ãã«ãããLv.29ã¯æ¢ãã©ç¡ããŠãã€ããã¯èŠãããšããããšã¯äºå®ã§ãªã ; $proof$ = | fact3 -> int1: ãã®ãã«ãããLv.29ã¯æ¢ãã©ç¡ã; int1 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{E}{a} -> {D}{a} fact2: (x): ¬{A}x -> ¬({B}x & {C}x) fact3: ({A}{a} & {B}{a}) fact4: {C}{a} fact5: (x): ¬{E}x -> ¬({D}x & {A}x) fact6: {A}{a} fact7: (x): ¬({D}x & {A}x) -> ¬{A}x ; $hypothesis$ = ¬({B}{a} & {C}{a}) ; $proof$ = | fact3 -> int1: {B}{a}; int1 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãããããè¡šçŸãé£ããªããšãããšäž¡ç«ããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã | ¬((Ex): ¬{B}x -> ¬{C}x) | fact1: ãã®ãããã«ã
Lv.27ãæãŠãç¡ããšããããšã¯ãªããšãããšããã¯å³æ°ãªããªã fact2: çºçŸãæããªãã¢ã³ã¹ã¿ãŒã¯çããšããããšã¯ãªã fact3: ããããã®ã¿ã«ãã¿ãLv.76ãè¡šçŸãé£ããšãããšãã®ã¿ã«ãã¿ãLv.76ã¯äž¡ç«ããªã fact4: ãããè¡šçŸãé£ããšãããäž¡ç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ãããã®ã¿ã«ãã¿ãLv.76ãè¡šçŸãé£ããªããªããã®ã¿ã«ãã¿ãLv.76ã¯äž¡ç«ãããšããããšã¯ãªã | fact1: ¬{DH}{jc} -> ¬{FB}{jc} fact2: (x): ¬{K}x -> ¬{JC}x fact3: {B}{aa} -> ¬{C}{aa} fact4: (Ex): {B}x -> ¬{C}x fact5: ¬{B}{aa} -> ¬{C}{aa} | [
"fact5 -> hypothesis;"
] | [
"fact5 -> hypothesis;"
] | ããããçºçŸãæããªããšãããçããªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{K}x -> ¬{JC}x | [
"fact6 -> int1: ããä»®ã«ãã®ã¿ãã¿ãLv.56ãçºçŸãæããšããããšã¯ãªããªããã®ã¿ãã¿ãLv.56ã¯çããšããããšã¯ãªã; int1 -> hypothesis;"
] | 2 | 1 | 1 | 1 | 1 | 4 | 0 | 4 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãã®ãããã«ã
Lv.27ãæãŠãç¡ããšããããšã¯ãªããšãããšããã¯å³æ°ãªããªã fact2: çºçŸãæããªãã¢ã³ã¹ã¿ãŒã¯çããšããããšã¯ãªã fact3: ããããã®ã¿ã«ãã¿ãLv.76ãè¡šçŸãé£ããšãããšãã®ã¿ã«ãã¿ãLv.76ã¯äž¡ç«ããªã fact4: ãããè¡šçŸãé£ããšãããäž¡ç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ãããã®ã¿ã«ãã¿ãLv.76ãè¡šçŸãé£ããªããªããã®ã¿ã«ãã¿ãLv.76ã¯äž¡ç«ãããšããããšã¯ãªã ; $hypothesis$ = ãããããè¡šçŸãé£ããªããšãããšäž¡ç«ããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã ; $proof$ = | fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{DH}{jc} -> ¬{FB}{jc} fact2: (x): ¬{K}x -> ¬{JC}x fact3: {B}{aa} -> ¬{C}{aa} fact4: (Ex): {B}x -> ¬{C}x fact5: ¬{B}{aa} -> ¬{C}{aa} ; $hypothesis$ = ¬((Ex): ¬{B}x -> ¬{C}x) ; $proof$ = | fact5 -> hypothesis; __DISPROVED__ |
0.3 | ã·ã¡ã
ã·ãLv.26äºä»¶ã¯çºçããªã | ¬{D} | fact1: ãæããšããããšããã³æããšããããšã©ã¡ãããçããããšããããšã¯ãã·ã¡ã
ã·ãLv.26äºä»¶ãèµ·ããããšããããšãåé¿ãã fact2: æããšããããšã¯ãã·ã¡ã
ã·ãLv.26äºä»¶ã¯èµ·ãããªãããŸãæããšããããšã¯èµ·ããªãããšããããšã«é»ãŸãã fact3: çœããšããããšãèµ·ãã fact4: ãããã«ã
Lv.9äºä»¶ã¯æããšããããšã¯çºçããªããšããããšãåé¿ãã fact5: æããšããããšãšçœããšããããšãçãã fact6: ãããã«ã
Lv.9äºä»¶ãçºçãã | fact1: ({B} & {C}) -> ¬{D} fact2: (¬{D} & ¬{C}) -> ¬{B} fact3: {E} fact4: {A} -> {B} fact5: ({C} & {E}) fact6: {A} | [
"fact4 & fact6 -> int1: æããšããããšãèµ·ãã; fact5 -> int2: ãæããšããããšãèµ·ããããšããããšã¯çå®ã§ãã; int1 & int2 -> int3: æããšããããšããã³æããšããããšãçºçãã; int3 & fact1 -> hypothesis;"
] | [
"fact4 & fact6 -> int1: {B}; fact5 -> int2: {C}; int1 & int2 -> int3: ({B} & {C}); int3 & fact1 -> hypothesis;"
] | ãŸããŸãªLv.31äºä»¶ãçºçãã | {FQ} | [] | 6 | 4 | 3 | 4 | 3 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãæããšããããšããã³æããšããããšã©ã¡ãããçããããšããããšã¯ãã·ã¡ã
ã·ãLv.26äºä»¶ãèµ·ããããšããããšãåé¿ãã fact2: æããšããããšã¯ãã·ã¡ã
ã·ãLv.26äºä»¶ã¯èµ·ãããªãããŸãæããšããããšã¯èµ·ããªãããšããããšã«é»ãŸãã fact3: çœããšããããšãèµ·ãã fact4: ãããã«ã
Lv.9äºä»¶ã¯æããšããããšã¯çºçããªããšããããšãåé¿ãã fact5: æããšããããšãšçœããšããããšãçãã fact6: ãããã«ã
Lv.9äºä»¶ãçºçãã ; $hypothesis$ = ã·ã¡ã
ã·ãLv.26äºä»¶ã¯çºçããªã ; $proof$ = | fact4 & fact6 -> int1: æããšããããšãèµ·ãã; fact5 -> int2: ãæããšããããšãèµ·ããããšããããšã¯çå®ã§ãã; int1 & int2 -> int3: æããšããããšããã³æããšããããšãçºçãã; int3 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({B} & {C}) -> ¬{D} fact2: (¬{D} & ¬{C}) -> ¬{B} fact3: {E} fact4: {A} -> {B} fact5: ({C} & {E}) fact6: {A} ; $hypothesis$ = ¬{D} ; $proof$ = | fact4 & fact6 -> int1: {B}; fact5 -> int2: {C}; int1 & int2 -> int3: ({B} & {C}); int3 & fact1 -> hypothesis; __PROVED__ |
0.3 | ããã®ããããLv.74ã¯åãæããæããªãããã©ããè¥ãããšããããšã¯ç¢ºãã§ãããšããããšã¯ãªã | ¬(¬{B}{c} & {A}{c}) | fact1: ä»®ã«ããã®ãã¡ã
ããLv.57ã¯å ªãæãããããã¯æãå§ããããšããããšã¯æãç«ããªããšããããã®ã·ãã·ãLv.94ã¯åãæããæããªã fact2: ããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯åããŸãããšããããšã¯ãªããšããããããã¯åãæããæããªããããè¥ãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact3: ä»®ã«ããã®ãã¡ã
ããLv.57ã¯åãæããæãããŸãã¯ããã¯å ªãæããªãããããã¯ã©ã¡ããã ããšããããšã¯æãç«ããªããªãã°ãã®ã·ãã·ãLv.94ã¯æãå§ããªã fact4: ããã®ãã¡ã
ããLv.57ã¯å ªãæããããã¯æãå§ããªãããšããããšã¯ééãã§ãã fact5: ãã®ããããLv.74ã¯å®ããªã fact6: ããã®ãã¡ã
ããLv.57ã¯å ªãæãããããã¯æãå§ããªãããšããããšã¯èª€ããªããã®ã·ãã·ãLv.94ã¯åãæããæããªã fact7: ããä»®ã«ãã®ã·ãã·ãLv.94ãåãæããæããªããšãããšãã®ããããLv.74ã¯ããè¥ã | fact1: ¬({AA}{a} v {AB}{a}) -> ¬{B}{b} fact2: (x): ¬{C}x -> ¬(¬{B}x & {A}x) fact3: ¬({B}{a} v ¬{AA}{a}) -> ¬{AB}{b} fact4: ¬({AA}{a} v ¬{AB}{a}) fact5: ¬{DN}{c} fact6: ¬({AA}{a} v ¬{AB}{a}) -> ¬{B}{b} fact7: ¬{B}{b} -> {A}{c} | [
"fact6 & fact4 -> int1: ãã®ã·ãã·ãLv.94ã¯åãæããæããªã;"
] | [
"fact6 & fact4 -> int1: ¬{B}{b};"
] | ããã®ããããLv.74ã¯åãæããæããªãããã©ããè¥ãããšããããšã¯ç¢ºãã§ãããšããããšã¯ãªã | ¬(¬{B}{c} & {A}{c}) | [
"fact8 -> int2: ããããã®ãã¡ã
ããLv.57ã¯åããŸãããªãããšããããšã¯æ¬åœã ãšãããããã®ãã¡ã
ããLv.57ã¯åãæããæããªãããã©ããè¥ãããšããããšã¯èª€ãã ;"
] | 5 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ããã®ãã¡ã
ããLv.57ã¯å ªãæãããããã¯æãå§ããããšããããšã¯æãç«ããªããšããããã®ã·ãã·ãLv.94ã¯åãæããæããªã fact2: ããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯åããŸãããšããããšã¯ãªããšããããããã¯åãæããæããªããããè¥ãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact3: ä»®ã«ããã®ãã¡ã
ããLv.57ã¯åãæããæãããŸãã¯ããã¯å ªãæããªãããããã¯ã©ã¡ããã ããšããããšã¯æãç«ããªããªãã°ãã®ã·ãã·ãLv.94ã¯æãå§ããªã fact4: ããã®ãã¡ã
ããLv.57ã¯å ªãæããããã¯æãå§ããªãããšããããšã¯ééãã§ãã fact5: ãã®ããããLv.74ã¯å®ããªã fact6: ããã®ãã¡ã
ããLv.57ã¯å ªãæãããããã¯æãå§ããªãããšããããšã¯èª€ããªããã®ã·ãã·ãLv.94ã¯åãæããæããªã fact7: ããä»®ã«ãã®ã·ãã·ãLv.94ãåãæããæããªããšãããšãã®ããããLv.74ã¯ããè¥ã ; $hypothesis$ = ããã®ããããLv.74ã¯åãæããæããªãããã©ããè¥ãããšããããšã¯ç¢ºãã§ãããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({AA}{a} v {AB}{a}) -> ¬{B}{b} fact2: (x): ¬{C}x -> ¬(¬{B}x & {A}x) fact3: ¬({B}{a} v ¬{AA}{a}) -> ¬{AB}{b} fact4: ¬({AA}{a} v ¬{AB}{a}) fact5: ¬{DN}{c} fact6: ¬({AA}{a} v ¬{AB}{a}) -> ¬{B}{b} fact7: ¬{B}{b} -> {A}{c} ; $hypothesis$ = ¬(¬{B}{c} & {A}{c}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãéè³ãæããšããããšãèµ·ãããèãåãããšãèµ·ããããšããããšã¯æãç«ããªã | ¬({B} & {C}) | fact1: èš±ãé£ããšããããšãèµ·ãã fact2: ããä»®ã«èš±ãé£ããšããããšã¯èµ·ããªããšããã°ãéè³ãæããšããããšãšèãåãããšãèµ·ããããšããããšã¯åã§ãã fact3: ãå€èããšããããšã¯çºçããªãããšããããšã¯ãããã©èããšããããšãèµ·ããããã®äžåŠ¬ãŸãããšããããšãèµ·ããããšããããšãåŒãèµ·ãã fact4: èãåãããšãèµ·ãã fact5: ãã¿ã®ã¿ãLv.22äºä»¶ã¯èµ·ãããªããèš±ãé£ããšããããšã¯èµ·ãããªãããšããããšã¯ããã©èããšããããšã«ããçºçãã fact6: ããŽã«ããŽã«Lv.55äºä»¶ã¯èµ·ãããªãããšããããšã¯å©ãé£ããšããããšã«é»ãŸãã fact7: éè³ãæããšããããšã¯èš±ãé£ããšããããšã«ããçãã fact8: ãèãåãããšãçãããéè³ãæããšããããšã¯çããªãããšããããšã¯ã¿ã®ã¿ãLv.22äºä»¶ã¯èµ·ããªããšããããšã«èµ·å ãã | fact1: {A} fact2: ¬{A} -> ¬({B} & {C}) fact3: ¬{G} -> ({E} & {F}) fact4: {C} fact5: {E} -> (¬{D} & ¬{A}) fact6: {HE} -> {EN} fact7: {A} -> {B} fact8: ¬{D} -> ({C} & ¬{B}) | [
"fact7 & fact1 -> int1: éè³ãæããšããããšãçãã; int1 & fact4 -> hypothesis;"
] | [
"fact7 & fact1 -> int1: {B}; int1 & fact4 -> hypothesis;"
] | ãéè³ãæããšããããšãèµ·ãããèãåãããšãèµ·ããããšããããšã¯æãç«ããªã | ¬({B} & {C}) | [] | 8 | 2 | 2 | 2 | 2 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: èš±ãé£ããšããããšãèµ·ãã fact2: ããä»®ã«èš±ãé£ããšããããšã¯èµ·ããªããšããã°ãéè³ãæããšããããšãšèãåãããšãèµ·ããããšããããšã¯åã§ãã fact3: ãå€èããšããããšã¯çºçããªãããšããããšã¯ãããã©èããšããããšãèµ·ããããã®äžåŠ¬ãŸãããšããããšãèµ·ããããšããããšãåŒãèµ·ãã fact4: èãåãããšãèµ·ãã fact5: ãã¿ã®ã¿ãLv.22äºä»¶ã¯èµ·ãããªããèš±ãé£ããšããããšã¯èµ·ãããªãããšããããšã¯ããã©èããšããããšã«ããçºçãã fact6: ããŽã«ããŽã«Lv.55äºä»¶ã¯èµ·ãããªãããšããããšã¯å©ãé£ããšããããšã«é»ãŸãã fact7: éè³ãæããšããããšã¯èš±ãé£ããšããããšã«ããçãã fact8: ãèãåãããšãçãããéè³ãæããšããããšã¯çããªãããšããããšã¯ã¿ã®ã¿ãLv.22äºä»¶ã¯èµ·ããªããšããããšã«èµ·å ãã ; $hypothesis$ = ãéè³ãæããšããããšãèµ·ãããèãåãããšãèµ·ããããšããããšã¯æãç«ããªã ; $proof$ = | fact7 & fact1 -> int1: éè³ãæããšããããšãçãã; int1 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} fact2: ¬{A} -> ¬({B} & {C}) fact3: ¬{G} -> ({E} & {F}) fact4: {C} fact5: {E} -> (¬{D} & ¬{A}) fact6: {HE} -> {EN} fact7: {A} -> {B} fact8: ¬{D} -> ({C} & ¬{B}) ; $hypothesis$ = ¬({B} & {C}) ; $proof$ = | fact7 & fact1 -> int1: {B}; int1 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | éè²ãæããšããããšã¯çºçããªã | ¬{C} | fact1: éè²ãæããšããããšã¯ãäŒããæããšããããšãèµ·ãããããã«èãåãé£ããšããããšãèµ·ããããšããããšã«é»ãŸãã fact2: ãäŒããæããšããããšãçããããšããããšã¯ééã£ãŠããªã fact3: èãåãé£ããšããããšãèµ·ãã fact4: ä»®ã«èãåãé£ããšããããšã¯çããªããªãã°éè²ãæããšããããšãçºçãããããã«äŒããæããšããããšã¯çºçãã | fact1: ({A} & {B}) -> ¬{C} fact2: {A} fact3: {B} fact4: ¬{B} -> ({C} & {A}) | [
"fact2 & fact3 -> int1: äŒããæããšããããšãçãããæŽã«èãåãé£ããšããããšãèµ·ãã; int1 & fact1 -> hypothesis;"
] | [
"fact2 & fact3 -> int1: ({A} & {B}); int1 & fact1 -> hypothesis;"
] | éè²ãæããšããããšãèµ·ãã | {C} | [] | 6 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: éè²ãæããšããããšã¯ãäŒããæããšããããšãèµ·ãããããã«èãåãé£ããšããããšãèµ·ããããšããããšã«é»ãŸãã fact2: ãäŒããæããšããããšãçããããšããããšã¯ééã£ãŠããªã fact3: èãåãé£ããšããããšãèµ·ãã fact4: ä»®ã«èãåãé£ããšããããšã¯çããªããªãã°éè²ãæããšããããšãçºçãããããã«äŒããæããšããããšã¯çºçãã ; $hypothesis$ = éè²ãæããšããããšã¯çºçããªã ; $proof$ = | fact2 & fact3 -> int1: äŒããæããšããããšãçãããæŽã«èãåãé£ããšããããšãèµ·ãã; int1 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} & {B}) -> ¬{C} fact2: {A} fact3: {B} fact4: ¬{B} -> ({C} & {A}) ; $hypothesis$ = ¬{C} ; $proof$ = | fact2 & fact3 -> int1: ({A} & {B}); int1 & fact1 -> hypothesis; __PROVED__ |
0.3 | ããã®ã¿ãã¿ãLv.70ã¯çµã³ä»ãæããå¯èŠããããšããããšã¯æ¬åœã ãšããããšã¯ãªã | ¬({A}{a} v {B}{a}) | fact1: ãã®ã¿ãã¿ãLv.70ã¯ç±äžãã fact2: ãã®ãã«ããã¡ã
Lv.92ã¯çµã³ä»ãæã fact3: ãã®ã¿ãã¿ãLv.70ã¯çµã³ä»ãæã fact4: ãã®ã¿ãã¿ãLv.70ã¯èŒãããæ°ãããŸãã¯ã©ã¡ããã§ãã | fact1: {BE}{a} fact2: {A}{eu} fact3: {A}{a} fact4: ({EL}{a} v {HI}{a}) | [
"fact3 -> int1: ãã®ã¿ãã¿ãLv.70ã¯çµã³ä»ãæã; int1 -> hypothesis;"
] | [
"fact3 -> int1: {A}{a}; int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ã¿ãã¿ãLv.70ã¯ç±äžãã fact2: ãã®ãã«ããã¡ã
Lv.92ã¯çµã³ä»ãæã fact3: ãã®ã¿ãã¿ãLv.70ã¯çµã³ä»ãæã fact4: ãã®ã¿ãã¿ãLv.70ã¯èŒãããæ°ãããŸãã¯ã©ã¡ããã§ãã ; $hypothesis$ = ããã®ã¿ãã¿ãLv.70ã¯çµã³ä»ãæããå¯èŠããããšããããšã¯æ¬åœã ãšããããšã¯ãªã ; $proof$ = | fact3 -> int1: ãã®ã¿ãã¿ãLv.70ã¯çµã³ä»ãæã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {BE}{a} fact2: {A}{eu} fact3: {A}{a} fact4: ({EL}{a} v {HI}{a}) ; $hypothesis$ = ¬({A}{a} v {B}{a}) ; $proof$ = | fact3 -> int1: {A}{a}; int1 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ãããããã®ãŽããŽãªLv.11ã¯çŽ°ããããšããããšã¯æãç«ã€ | {A}{a} | fact1: ãã®ãŽããŽãªLv.11ã¯çŽ°ããããããã¯ããã¯å
¶ãã£ãœã fact2: ãã®ãŽããŽãªLv.11ãçµã³åããããªããã®ãŽããŽãªLv.11ã¯éãæããªã fact3: ãã®ãŽããŽãªLv.11ã现ããããããã¯çµã³åããããšãããšããã¯éãæããªã fact4: ãããã®ãŽããŽãªLv.11ãéãæããªãããããçµã³åããããªãããã®ã·ãã·ã®Lv.74ã¯éãæããªãããšããããšã¯æ¬åœã fact5: ããããã®ãŽããŽã®Lv.63ãéãæããªããªããã®ãŽããŽãªLv.11ã¯çµã³åãããã现ãã fact6: ä»®ã«ãã®ãœããœãLv.64ã¯ãã©ã³ãããããªããšããããããã®ãŽããŽã®Lv.63ã¯éãæãããã®äžçŽ°ããããšããããšã¯äºå®ã§ããããšããããšã¯èª€ã£ãŠãã | fact1: ({A}{a} v {FP}{a}) fact2: {B}{a} -> ¬{C}{a} fact3: ({A}{a} v {B}{a}) -> ¬{C}{a} fact4: (¬{C}{a} & {B}{a}) -> ¬{C}{cs} fact5: ¬{C}{b} -> ({B}{a} & {A}{a}) fact6: ¬{D}{c} -> ¬({C}{b} & {A}{b}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ãŽããŽãªLv.11ã¯çŽ°ããããšããããšã¯æãç«ã€; assump1 -> int1: ãã®ãŽããŽãªLv.11ã¯çŽ°ãããçµã³åããããäž¡æ¹ãšãã ; int1 & fact3 -> int2: ãã®ãŽããŽãªLv.11ã¯éãæããªã;"
] | [
"void -> assump1: {A}{a}; assump1 -> int1: ({A}{a} v {B}{a}); int1 & fact3 -> int2: ¬{C}{a};"
] | 以äžã®ããã«ä»®å®ãããããã®ãŽããŽãªLv.11ã¯çŽ°ããããšããããšã¯æãç«ã€ | {A}{a} | [] | 5 | 5 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãŽããŽãªLv.11ã¯çŽ°ããããããã¯ããã¯å
¶ãã£ãœã fact2: ãã®ãŽããŽãªLv.11ãçµã³åããããªããã®ãŽããŽãªLv.11ã¯éãæããªã fact3: ãã®ãŽããŽãªLv.11ã现ããããããã¯çµã³åããããšãããšããã¯éãæããªã fact4: ãããã®ãŽããŽãªLv.11ãéãæããªãããããçµã³åããããªãããã®ã·ãã·ã®Lv.74ã¯éãæããªãããšããããšã¯æ¬åœã fact5: ããããã®ãŽããŽã®Lv.63ãéãæããªããªããã®ãŽããŽãªLv.11ã¯çµã³åãããã现ãã fact6: ä»®ã«ãã®ãœããœãLv.64ã¯ãã©ã³ãããããªããšããããããã®ãŽããŽã®Lv.63ã¯éãæãããã®äžçŽ°ããããšããããšã¯äºå®ã§ããããšããããšã¯èª€ã£ãŠãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããããã®ãŽããŽãªLv.11ã¯çŽ°ããããšããããšã¯æãç«ã€ ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A}{a} v {FP}{a}) fact2: {B}{a} -> ¬{C}{a} fact3: ({A}{a} v {B}{a}) -> ¬{C}{a} fact4: (¬{C}{a} & {B}{a}) -> ¬{C}{cs} fact5: ¬{C}{b} -> ({B}{a} & {A}{a}) fact6: ¬{D}{c} -> ¬({C}{b} & {A}{b}) ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ã«Lv.17ã¯å®å µãé£ã | {C}{c} | fact1: ãã®ãŸãªãŸã«Lv.44ã¯æœããªã fact2: ããä»®ã«ãã®ã¿ãã¿ãLv.26ãé åºãããšããããã®ã¿ãã¿ã«Lv.17ã¯å®å µãé£ã fact3: ãã®ãŸãªãŸã«Lv.44ã¯å䜵ãæããšãããšããã®ã¿ãã¿ãLv.26ã¯é åºãããšããããšã¯ãªããã©ããã¯æœãããšããããšã¯ééãã fact4: ããã®ãã¡ã
ãã«ãLv.92ã¯é åºããããšããããšã¯æãç«ã€ fact5: ããã®ã¿ãã¿ãLv.26ã¯é åºããªãããšããããšã¯èª€ãã§ãªããªãã°ãã®ãŸãªãŸã«Lv.44ã¯æœã | fact1: ¬{B}{b} fact2: {A}{a} -> {C}{c} fact3: {D}{b} -> ¬(¬{A}{a} & {B}{a}) fact4: {A}{hr} fact5: ¬{A}{a} -> {B}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ãLv.26ã¯é åºããªã; fact5 & assump1 -> int1: ããã®ãŸãªãŸã«Lv.44ã¯æœãããšããããšã¯ç¢ºãã§ãã; int1 & fact1 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ã¿ãã¿ãLv.26ã¯é åºãã; int3 & fact2 -> hypothesis;"
] | [
"void -> assump1: ¬{A}{a}; fact5 & assump1 -> int1: {B}{b}; int1 & fact1 -> int2: #F#; [assump1] & int2 -> int3: {A}{a}; int3 & fact2 -> hypothesis;"
] | ãã®ã¿ãã¿ã«Lv.17ã¯å®å µãé£ããªã | ¬{C}{c} | [] | 6 | 5 | 4 | 5 | 4 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãŸãªãŸã«Lv.44ã¯æœããªã fact2: ããä»®ã«ãã®ã¿ãã¿ãLv.26ãé åºãããšããããã®ã¿ãã¿ã«Lv.17ã¯å®å µãé£ã fact3: ãã®ãŸãªãŸã«Lv.44ã¯å䜵ãæããšãããšããã®ã¿ãã¿ãLv.26ã¯é åºãããšããããšã¯ãªããã©ããã¯æœãããšããããšã¯ééãã fact4: ããã®ãã¡ã
ãã«ãLv.92ã¯é åºããããšããããšã¯æãç«ã€ fact5: ããã®ã¿ãã¿ãLv.26ã¯é åºããªãããšããããšã¯èª€ãã§ãªããªãã°ãã®ãŸãªãŸã«Lv.44ã¯æœã ; $hypothesis$ = ãã®ã¿ãã¿ã«Lv.17ã¯å®å µãé£ã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ãLv.26ã¯é åºããªã; fact5 & assump1 -> int1: ããã®ãŸãªãŸã«Lv.44ã¯æœãããšããããšã¯ç¢ºãã§ãã; int1 & fact1 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ã¿ãã¿ãLv.26ã¯é åºãã; int3 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{B}{b} fact2: {A}{a} -> {C}{c} fact3: {D}{b} -> ¬(¬{A}{a} & {B}{a}) fact4: {A}{hr} fact5: ¬{A}{a} -> {B}{b} ; $hypothesis$ = {C}{c} ; $proof$ = | void -> assump1: ¬{A}{a}; fact5 & assump1 -> int1: {B}{b}; int1 & fact1 -> int2: #F#; [assump1] & int2 -> int3: {A}{a}; int3 & fact2 -> hypothesis; __PROVED__ |
0.3 | èã
ãããšããããšãçºçãã | {F} | fact1: è¡æ£èããšããããšã¯ã³ã³ãããŒã«ãæããšããããšã¯çããªããšããããšãé»ã fact2: è¡æ£èããšããããšãèµ·ãã fact3: ãå¿ãæããšããããšã¯èµ·ãããªãããšããããšã¯ãèã
ãããšããããšã¯çºçããªãããœããœãLv.15äºä»¶ãèµ·ããããšããããšãåŒãèµ·ãã fact4: ãã£ããããšããããšãçºçãã fact5: ããã«ããã®Lv.96äºä»¶ãçºçããããŸãã¯çæãããšããããšãèµ·ããããšããããšã¯ããããLv.27äºä»¶ãåé¿ãã fact6: ãè¡æ£èããšããããšãèµ·ããããŸãã¯æ®ãæããšããããšã¯çºçããªããäž¡æ¹ã§ããããšããããšã¯ãæ®ãæããšããããšã¯çºçããªãããšããããšã«ç¹ãã fact7: ã³ã³ãããŒã«ãæããšããããšãæ¥ãæããšããããšã¯å¿ãæããšããããšãé»ã | fact1: {A} -> {B} fact2: {A} fact3: ¬{D} -> (¬{F} & {E}) fact4: {BO} fact5: ({CO} v {M}) -> ¬{BT} fact6: ({A} v ¬{DB}) -> ¬{DB} fact7: ({B} v {C}) -> ¬{D} | [
"fact1 & fact2 -> int1: ã³ã³ãããŒã«ãæããšããããšãèµ·ãã; int1 -> int2: ã³ã³ãããŒã«ãæããšããããšãèµ·ããããããã¯æ¥ãæããšããããšãèµ·ãã; int2 & fact7 -> int3: å¿ãæããšããããšã¯èµ·ãããªã; int3 & fact3 -> int4: èã
ãããšããããšã§ã¯ãªããœããœãLv.15äºä»¶ãçãã; int4 -> hypothesis;"
] | [
"fact1 & fact2 -> int1: {B}; int1 -> int2: ({B} v {C}); int2 & fact7 -> int3: ¬{D}; int3 & fact3 -> int4: (¬{F} & {E}); int4 -> hypothesis;"
] | ãæ®ãæããšããããšã¯çããªãããšããããšã¯æãç«ã€ | ¬{DB} | [] | 6 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: è¡æ£èããšããããšã¯ã³ã³ãããŒã«ãæããšããããšã¯çããªããšããããšãé»ã fact2: è¡æ£èããšããããšãèµ·ãã fact3: ãå¿ãæããšããããšã¯èµ·ãããªãããšããããšã¯ãèã
ãããšããããšã¯çºçããªãããœããœãLv.15äºä»¶ãèµ·ããããšããããšãåŒãèµ·ãã fact4: ãã£ããããšããããšãçºçãã fact5: ããã«ããã®Lv.96äºä»¶ãçºçããããŸãã¯çæãããšããããšãèµ·ããããšããããšã¯ããããLv.27äºä»¶ãåé¿ãã fact6: ãè¡æ£èããšããããšãèµ·ããããŸãã¯æ®ãæããšããããšã¯çºçããªããäž¡æ¹ã§ããããšããããšã¯ãæ®ãæããšããããšã¯çºçããªãããšããããšã«ç¹ãã fact7: ã³ã³ãããŒã«ãæããšããããšãæ¥ãæããšããããšã¯å¿ãæããšããããšãé»ã ; $hypothesis$ = èã
ãããšããããšãçºçãã ; $proof$ = | fact1 & fact2 -> int1: ã³ã³ãããŒã«ãæããšããããšãèµ·ãã; int1 -> int2: ã³ã³ãããŒã«ãæããšããããšãèµ·ããããããã¯æ¥ãæããšããããšãèµ·ãã; int2 & fact7 -> int3: å¿ãæããšããããšã¯èµ·ãããªã; int3 & fact3 -> int4: èã
ãããšããããšã§ã¯ãªããœããœãLv.15äºä»¶ãçãã; int4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} -> {B} fact2: {A} fact3: ¬{D} -> (¬{F} & {E}) fact4: {BO} fact5: ({CO} v {M}) -> ¬{BT} fact6: ({A} v ¬{DB}) -> ¬{DB} fact7: ({B} v {C}) -> ¬{D} ; $hypothesis$ = {F} ; $proof$ = | fact1 & fact2 -> int1: {B}; int1 -> int2: ({B} v {C}); int2 & fact7 -> int3: ¬{D}; int3 & fact3 -> int4: (¬{F} & {E}); int4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœãLv.23ã¯æ¥è¿ãæããªã | ¬{E}{a} | fact1: ãã®ãã«ã
ãã¡ãLv.27ã¯æ¥è¿ãæã fact2: ä»®ã«ãã®ãœããœãLv.23ã埡æªããšãããšåŒãæã fact3: ãã®ãœããœãLv.23ã¯ä»ãæã fact4: ä»®ã«ãã®ãœããœãLv.23ãäžãæããšãããšåŸ¡æªã fact5: ãã®ãœããœãLv.23ã¯äžãæããŠä»ãæã fact6: ããã®ãœããœãLv.23ãåŒãæããšããã°ãã®ãœããœãLv.23ã¯æ¥è¿ãæãããšããããšã¯ç¢ºãã§ãã fact7: ãããããã¢ã³ã¹ã¿ãŒãç»å±±å®¶ããããšãããåãããã | fact1: {E}{fr} fact2: {C}{a} -> {D}{a} fact3: {B}{a} fact4: {A}{a} -> {C}{a} fact5: ({A}{a} & {B}{a}) fact6: {D}{a} -> {E}{a} fact7: (x): {CB}x -> {GK}x | [
"fact5 -> int1: ãã®ãœããœãLv.23ã¯äžãæã; int1 & fact4 -> int2: ããã®ãœããœãLv.23ã¯åŸ¡æªãããšããããšã¯èª€ã£ãŠããªã; int2 & fact2 -> int3: ãã®ãœããœãLv.23ã¯åŒãæã; int3 & fact6 -> hypothesis;"
] | [
"fact5 -> int1: {A}{a}; int1 & fact4 -> int2: {C}{a}; int2 & fact2 -> int3: {D}{a}; int3 & fact6 -> hypothesis;"
] | ãã®ãŸã¡ããŸãLv.44ãç»å±±å®¶ããããªãã°åãããã | {CB}{il} -> {GK}{il} | [
"fact8 -> hypothesis;"
] | 1 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãã®ãã«ã
ãã¡ãLv.27ã¯æ¥è¿ãæã fact2: ä»®ã«ãã®ãœããœãLv.23ã埡æªããšãããšåŒãæã fact3: ãã®ãœããœãLv.23ã¯ä»ãæã fact4: ä»®ã«ãã®ãœããœãLv.23ãäžãæããšãããšåŸ¡æªã fact5: ãã®ãœããœãLv.23ã¯äžãæããŠä»ãæã fact6: ããã®ãœããœãLv.23ãåŒãæããšããã°ãã®ãœããœãLv.23ã¯æ¥è¿ãæãããšããããšã¯ç¢ºãã§ãã fact7: ãããããã¢ã³ã¹ã¿ãŒãç»å±±å®¶ããããšãããåãããã ; $hypothesis$ = ãã®ãœããœãLv.23ã¯æ¥è¿ãæããªã ; $proof$ = | fact5 -> int1: ãã®ãœããœãLv.23ã¯äžãæã; int1 & fact4 -> int2: ããã®ãœããœãLv.23ã¯åŸ¡æªãããšããããšã¯èª€ã£ãŠããªã; int2 & fact2 -> int3: ãã®ãœããœãLv.23ã¯åŒãæã; int3 & fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {E}{fr} fact2: {C}{a} -> {D}{a} fact3: {B}{a} fact4: {A}{a} -> {C}{a} fact5: ({A}{a} & {B}{a}) fact6: {D}{a} -> {E}{a} fact7: (x): {CB}x -> {GK}x ; $hypothesis$ = ¬{E}{a} ; $proof$ = | fact5 -> int1: {A}{a}; int1 & fact4 -> int2: {C}{a}; int2 & fact2 -> int3: {D}{a}; int3 & fact6 -> hypothesis; __DISPROVED__ |
0.3 | ãã£ãããšããããšãšãŸã«ããŸã«ã
Lv.52äºä»¶ãèµ·ãã | ({C} & {D}) | fact1: ãã£ãããšããããšã¯çºçããªããšããããšã¯æããé£ããšããããšã«é»æ¢ããã fact2: ãŽã¡ã
ãŽãLv.49äºä»¶ããã³ã¿ãã¿ãLv.10äºä»¶ã©ã¡ãããçãã fact3: æ±äžããããšãèµ·ãããããã«ãããã®Lv.36äºä»¶ãçºçãã fact4: æããé£ããšããããšããããã¯ãœã®ãœã¡ãLv.51äºä»¶ãäž¡æ¹ãèµ·ãã fact5: æãé£ããšããããšãçºçãã fact6: ãŽã«ã
ãŽãªLv.4äºä»¶ã¯ãã¿ã«ã¿ã«ãLv.83äºä»¶ã¯èµ·ããªãããšããããšãé»æ¢ãã fact7: ãã£ãããšããããšã¯ãœã®ãœã¡ãLv.51äºä»¶ãåå ã§ãã fact8: ã·ã«ãã·ãLv.16äºä»¶ãèµ·ããããããã¯å£å§ãããšããããšãèµ·ããããŸãã¯äž¡æ¹ã§ãã | fact1: {A} -> {C} fact2: ({HS} & {IP}) fact3: ({EU} & {JI}) fact4: ({A} v {B}) fact5: {EK} fact6: {HU} -> {CD} fact7: {B} -> {C} fact8: ({IE} v {EL}) | [
"fact4 & fact1 & fact7 -> int1: ãã£ãããšããããšãèµ·ãã;"
] | [
"fact4 & fact1 & fact7 -> int1: {C};"
] | null | null | [] | null | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã£ãããšããããšã¯çºçããªããšããããšã¯æããé£ããšããããšã«é»æ¢ããã fact2: ãŽã¡ã
ãŽãLv.49äºä»¶ããã³ã¿ãã¿ãLv.10äºä»¶ã©ã¡ãããçãã fact3: æ±äžããããšãèµ·ãããããã«ãããã®Lv.36äºä»¶ãçºçãã fact4: æããé£ããšããããšããããã¯ãœã®ãœã¡ãLv.51äºä»¶ãäž¡æ¹ãèµ·ãã fact5: æãé£ããšããããšãçºçãã fact6: ãŽã«ã
ãŽãªLv.4äºä»¶ã¯ãã¿ã«ã¿ã«ãLv.83äºä»¶ã¯èµ·ããªãããšããããšãé»æ¢ãã fact7: ãã£ãããšããããšã¯ãœã®ãœã¡ãLv.51äºä»¶ãåå ã§ãã fact8: ã·ã«ãã·ãLv.16äºä»¶ãèµ·ããããããã¯å£å§ãããšããããšãèµ·ããããŸãã¯äž¡æ¹ã§ãã ; $hypothesis$ = ãã£ãããšããããšãšãŸã«ããŸã«ã
Lv.52äºä»¶ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} -> {C} fact2: ({HS} & {IP}) fact3: ({EU} & {JI}) fact4: ({A} v {B}) fact5: {EK} fact6: {HU} -> {CD} fact7: {B} -> {C} fact8: ({IE} v {EL}) ; $hypothesis$ = ({C} & {D}) ; $proof$ = | __UNKNOWN__ |
0.3 | ã¿ãã¿ãLv.33äºä»¶ã¯çããªã | ¬{F} | fact1: ãã¿ãã¿ãªLv.38äºä»¶ã¯çããªãããšããããšã¯ã誀ãç¡ããšããããšãçããããããã¯éã©ããšããããšãèµ·ããããšããããšã«ããçºçãã fact2: ãŸã«ãŸã«ãLv.78äºä»¶ãçºçãã fact3: ãã¿ãã¿ãªLv.38äºä»¶ã¯çããªãããšããããšã¯ã¿ãã¿ãLv.33äºä»¶ãé»æ¢ãã fact4: ãŸã«ãŸã«ãLv.78äºä»¶ããã³ããããLv.31äºä»¶ãçãã | fact1: ({D} v {C}) -> ¬{E} fact2: {A} fact3: ¬{E} -> ¬{F} fact4: ({A} & {B}) | [
"fact4 -> int1: ããããLv.31äºä»¶ãèµ·ãã;"
] | [
"fact4 -> int1: {B};"
] | null | null | [] | null | 5 | 5 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã¿ãã¿ãªLv.38äºä»¶ã¯çããªãããšããããšã¯ã誀ãç¡ããšããããšãçããããããã¯éã©ããšããããšãèµ·ããããšããããšã«ããçºçãã fact2: ãŸã«ãŸã«ãLv.78äºä»¶ãçºçãã fact3: ãã¿ãã¿ãªLv.38äºä»¶ã¯çããªãããšããããšã¯ã¿ãã¿ãLv.33äºä»¶ãé»æ¢ãã fact4: ãŸã«ãŸã«ãLv.78äºä»¶ããã³ããããLv.31äºä»¶ãçãã ; $hypothesis$ = ã¿ãã¿ãLv.33äºä»¶ã¯çããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({D} v {C}) -> ¬{E} fact2: {A} fact3: ¬{E} -> ¬{F} fact4: ({A} & {B}) ; $hypothesis$ = ¬{F} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ãLv.6ã¯ãã°ãã£ãã | {C}{a} | fact1: æ©ãŸããã¢ã³ã¹ã¿ãŒã¯ãã°ãã£ãã fact2: ããããã®ã·ã¡ãã·ãLv.99ã¯ãã°ãã£ãããªããªãã°ããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããå°å¿µãããªãããšããããšã¯äºå®ãšç°ãªã fact3: ããä»®ã«ãããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããªããŠãŸãå°å¿µããšããããšã¯ãªãããšããããšã¯äºå®ãšç°ãªãããšããããšã¯äºå®ã§ãããªãããã¯ãã°ãã£ãããªã fact4: ä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯æ©ãŸãããªããªããããã¯é£éããªããŠããã«ç°è²ã£ãœããªãããšããããšã¯èª€ã£ãŠãã fact5: ããããã®ã·ã¡ãã·ãLv.99ãæ©ããªããšããããã®ã¿ãã¿ãLv.6ã¯å°å¿µããå ããŠæ©ãŸãã fact6: ãã®ã¿ãã¿ãLv.6ã¯å°å¿µã | fact1: (x): {A}x -> {C}x fact2: ¬{C}{b} -> ¬({A}{a} & ¬{B}{a}) fact3: ¬(¬{A}{a} & ¬{B}{a}) -> ¬{C}{a} fact4: (x): ¬{A}x -> ¬(¬{JA}x & ¬{CT}x) fact5: ¬{D}{b} -> ({B}{a} & {A}{a}) fact6: {B}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããªããŠããã«å°å¿µãããªã; assump1 -> int1: ãã®ã¿ãã¿ãLv.6ã¯å°å¿µãããªã; int1 & fact6 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããªããŠå°å¿µãããªãããšããããšã¯æãç«ããªã; int3 & fact3 -> hypothesis;"
] | [
"void -> assump1: (¬{A}{a} & ¬{B}{a}); assump1 -> int1: ¬{B}{a}; int1 & fact6 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{A}{a} & ¬{B}{a}); int3 & fact3 -> hypothesis;"
] | ãã®ã¿ãã¿ãLv.6ã¯ãã°ãã£ãã | {C}{a} | [
"fact8 -> int4: ä»®ã«ãã®ã¿ãã¿ãLv.6ãæ©ãŸãããšããã°ãã°ãã£ãã;"
] | 5 | 5 | 3 | 5 | 3 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: æ©ãŸããã¢ã³ã¹ã¿ãŒã¯ãã°ãã£ãã fact2: ããããã®ã·ã¡ãã·ãLv.99ã¯ãã°ãã£ãããªããªãã°ããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããå°å¿µãããªãããšããããšã¯äºå®ãšç°ãªã fact3: ããä»®ã«ãããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããªããŠãŸãå°å¿µããšããããšã¯ãªãããšããããšã¯äºå®ãšç°ãªãããšããããšã¯äºå®ã§ãããªãããã¯ãã°ãã£ãããªã fact4: ä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯æ©ãŸãããªããªããããã¯é£éããªããŠããã«ç°è²ã£ãœããªãããšããããšã¯èª€ã£ãŠãã fact5: ããããã®ã·ã¡ãã·ãLv.99ãæ©ããªããšããããã®ã¿ãã¿ãLv.6ã¯å°å¿µããå ããŠæ©ãŸãã fact6: ãã®ã¿ãã¿ãLv.6ã¯å°å¿µã ; $hypothesis$ = ãã®ã¿ãã¿ãLv.6ã¯ãã°ãã£ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããªããŠããã«å°å¿µãããªã; assump1 -> int1: ãã®ã¿ãã¿ãLv.6ã¯å°å¿µãããªã; int1 & fact6 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ããã®ã¿ãã¿ãLv.6ã¯æ©ãŸãããªããŠå°å¿µãããªãããšããããšã¯æãç«ããªã; int3 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {A}x -> {C}x fact2: ¬{C}{b} -> ¬({A}{a} & ¬{B}{a}) fact3: ¬(¬{A}{a} & ¬{B}{a}) -> ¬{C}{a} fact4: (x): ¬{A}x -> ¬(¬{JA}x & ¬{CT}x) fact5: ¬{D}{b} -> ({B}{a} & {A}{a}) fact6: {B}{a} ; $hypothesis$ = {C}{a} ; $proof$ = | void -> assump1: (¬{A}{a} & ¬{B}{a}); assump1 -> int1: ¬{B}{a}; int1 & fact6 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{A}{a} & ¬{B}{a}); int3 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãLv.74ã¯éé»ãããããæ²ãäžãã | ({E}{c} & {F}{c}) | fact1: ãã°ããããªãã¢ã³ã¹ã¿ãŒã¯æãç¶ããªãããŸãã¯éãæããªããäž¡æ¹ãšãã§ãã fact2: ãã®ã·ãã·ã«ãLv.78ããã°ããããªããšããããã®ãŸããŸãLv.74ã¯éãæããããŸãã«æãç¶ãã fact3: éãæãã¢ã³ã¹ã¿ãŒã¯åºã fact4: ããä»®ã«ãã®ã·ãã·ãLv.40ãéãæããªãã°ãã®ãŸããŸãLv.74ã¯æãç¶ãã fact5: ãã®ãŸããŸãLv.74ããã°ããããšããããã®ãŸããŸãLv.74ã¯éé»ã fact6: ãã®ãŸããŸãLv.74ã¯æ²ãäžãã fact7: ãã®ã·ãã·ã«ãLv.78ã¯åºã fact8: ä»®ã«ãã®ã·ãã·ã«ãLv.78ã¯åºããšãããšããã®ã·ãã·ãLv.40ã¯éãæãããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªã | fact1: (x): ¬{D}x -> (¬{C}x v ¬{B}x) fact2: ¬{D}{a} -> ({B}{c} & {C}{c}) fact3: (x): {B}x -> {A}x fact4: {B}{b} -> {C}{c} fact5: {D}{c} -> {E}{c} fact6: {F}{c} fact7: {A}{a} fact8: {A}{a} -> {B}{b} | [
"fact8 & fact7 -> int1: ãã®ã·ãã·ãLv.40ã¯éãæã; int1 & fact4 -> int2: ãã®ãŸããŸãLv.74ã¯æãç¶ãã;"
] | [
"fact8 & fact7 -> int1: {B}{b}; int1 & fact4 -> int2: {C}{c};"
] | ãã®ãŸããŸãLv.74ã¯åºã | {A}{c} | [
"fact10 -> int3: ããããã®ãŸããŸãLv.74ãéãæããªãããã¯åºã;"
] | 6 | 5 | 5 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã°ããããªãã¢ã³ã¹ã¿ãŒã¯æãç¶ããªãããŸãã¯éãæããªããäž¡æ¹ãšãã§ãã fact2: ãã®ã·ãã·ã«ãLv.78ããã°ããããªããšããããã®ãŸããŸãLv.74ã¯éãæããããŸãã«æãç¶ãã fact3: éãæãã¢ã³ã¹ã¿ãŒã¯åºã fact4: ããä»®ã«ãã®ã·ãã·ãLv.40ãéãæããªãã°ãã®ãŸããŸãLv.74ã¯æãç¶ãã fact5: ãã®ãŸããŸãLv.74ããã°ããããšããããã®ãŸããŸãLv.74ã¯éé»ã fact6: ãã®ãŸããŸãLv.74ã¯æ²ãäžãã fact7: ãã®ã·ãã·ã«ãLv.78ã¯åºã fact8: ä»®ã«ãã®ã·ãã·ã«ãLv.78ã¯åºããšãããšããã®ã·ãã·ãLv.40ã¯éãæãããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªã ; $hypothesis$ = ãã®ãŸããŸãLv.74ã¯éé»ãããããæ²ãäžãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{D}x -> (¬{C}x v ¬{B}x) fact2: ¬{D}{a} -> ({B}{c} & {C}{c}) fact3: (x): {B}x -> {A}x fact4: {B}{b} -> {C}{c} fact5: {D}{c} -> {E}{c} fact6: {F}{c} fact7: {A}{a} fact8: {A}{a} -> {B}{b} ; $hypothesis$ = ({E}{c} & {F}{c}) ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã¿ã«ã¿ã«ãLv.88ã¯èžãæã | {A}{a} | fact1: ç¯ãé£ããªãã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ããããã«ã©ã§ãã fact2: ä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯è¡æ£èãäžæ¹ã§èžãæããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãç
ãããªã fact3: ãã®ã¿ã«ã¿ã«ãLv.88ãèžãæãããã€ãããè¡æ£èããªãã°ãã®ãŸããŸãLv.6ã¯ç
ãããªã fact4: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ããšããã°ãè€ãè®ãããåããããªãããšããããšã¯äºå®ã§ãªã fact5: ãã®ãŸããŸãLv.6ã¯ç¯ãé£ããªã fact6: ä»®ã«ãã®ã¿ã«ã¿ã«ãLv.88ã¯èŠ³å
客ããããªããšãããšããã®ã·ã«ã·ã«ãLv.6ã¯è¡æ£èãããããèžãæããªãããšããããšã¯åã fact7: ãã®ã¿ã«ã¿ã«ãLv.88ã¯è¡æ£èã fact8: ãã®ãŸããŸãLv.6ã¯ç
ãã | fact1: (x): ¬{I}x -> ({G}x & {H}x) fact2: (x): ¬({B}x & ¬{A}x) -> ¬{C}x fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: (x): {G}x -> ¬({F}x & ¬{E}x) fact5: ¬{I}{b} fact6: ¬{D}{a} -> ¬({B}{dd} & ¬{A}{dd}) fact7: {B}{a} fact8: {C}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ã«ã¿ã«ãLv.88ã¯èžãæã; assump1 & fact7 -> int1: ãã®ã¿ã«ã¿ã«ãLv.88ã¯èžãæããŠããã«è¡æ£èã; int1 & fact3 -> int2: ãã®ãŸããŸãLv.6ã¯ç
ãããªã; int2 & fact8 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; assump1 & fact7 -> int1: ({A}{a} & {B}{a}); int1 & fact3 -> int2: ¬{C}{b}; int2 & fact8 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ãã®ã·ã«ã·ã«ãLv.6ã¯ç
ãããªã | ¬{C}{dd} | [
"fact10 -> int4: ãããããã®ã·ã«ã·ã«ãLv.6ã¯è¡æ£èãããã©èžãæããªãããšããããšã¯åã§ãããšããã°ç
ãããªã; fact13 -> int5: ãããã®ãŸããŸãLv.6ã¯é¢ä¿æ·±ããªããããã¯è€ãè®ãããåããããªãããšããããšã¯ééãã ; fact9 -> int6: ããä»®ã«ããã®ãŸããŸãLv.6ã¯ç¯ãé£ãããšããããšã¯åã§ãããšãããšããã¯é¢ä¿æ·±ãããããã©ã§ãã; int6 & fact11 -> int7: ãã®ãŸããŸãLv.6ã¯é¢ä¿æ·±ããŠã©ã§ãã; int7 -> int8: ãã®ãŸããŸãLv.6ã¯é¢ä¿æ·±ã; int5 & int8 -> int9: ããã®ãŸããŸãLv.6ã¯è€ãè®ããããããããã¯åããããªãããšããããšã¯æãç«ããªã; int9 -> int10: ããè€ãè®ãããåããããªãããšããããšã¯çå®ã§ãªããã¢ã³ã¹ã¿ãŒã¯ãã;"
] | 8 | 5 | 4 | 5 | 4 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ç¯ãé£ããªãã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ããããã«ã©ã§ãã fact2: ä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯è¡æ£èãäžæ¹ã§èžãæããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãç
ãããªã fact3: ãã®ã¿ã«ã¿ã«ãLv.88ãèžãæãããã€ãããè¡æ£èããªãã°ãã®ãŸããŸãLv.6ã¯ç
ãããªã fact4: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ããšããã°ãè€ãè®ãããåããããªãããšããããšã¯äºå®ã§ãªã fact5: ãã®ãŸããŸãLv.6ã¯ç¯ãé£ããªã fact6: ä»®ã«ãã®ã¿ã«ã¿ã«ãLv.88ã¯èŠ³å
客ããããªããšãããšããã®ã·ã«ã·ã«ãLv.6ã¯è¡æ£èãããããèžãæããªãããšããããšã¯åã fact7: ãã®ã¿ã«ã¿ã«ãLv.88ã¯è¡æ£èã fact8: ãã®ãŸããŸãLv.6ã¯ç
ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã¿ã«ã¿ã«ãLv.88ã¯èžãæã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ã«ã¿ã«ãLv.88ã¯èžãæã; assump1 & fact7 -> int1: ãã®ã¿ã«ã¿ã«ãLv.88ã¯èžãæããŠããã«è¡æ£èã; int1 & fact3 -> int2: ãã®ãŸããŸãLv.6ã¯ç
ãããªã; int2 & fact8 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{I}x -> ({G}x & {H}x) fact2: (x): ¬({B}x & ¬{A}x) -> ¬{C}x fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: (x): {G}x -> ¬({F}x & ¬{E}x) fact5: ¬{I}{b} fact6: ¬{D}{a} -> ¬({B}{dd} & ¬{A}{dd}) fact7: {B}{a} fact8: {C}{b} ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: {A}{a}; assump1 & fact7 -> int1: ({A}{a} & {B}{a}); int1 & fact3 -> int2: ¬{C}{b}; int2 & fact8 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ã䌞ã¹ãããšãèµ·ããããšããããšã¯æ£ãã | {D} | fact1: ã·ãªã·ãLv.21äºä»¶ã¯çããªããšããããšã¯ã説æãé£ããšããããšã¯èµ·ããªãããšããããšãåé¿ãã fact2: ã説æãé£ããšããããšããã³ãŽã«ãŽãLv.25äºä»¶äž¡æ¹ãèµ·ããããšããããšã¯ã·ãªã·ãLv.21äºä»¶ã¯èµ·ãããªããšããããšã«åŒãèµ·ãããã fact3: ããä»®ã«ãã·ãªã·ãLv.21äºä»¶ã¯èµ·ããªãããŸãã¯å£å§ãããšããããšã¯èµ·ããªãããŸãã¯ã©ã¡ããã ããšããããšã¯æãç«ããªããšããã°ãŽã«ãŽãLv.25äºä»¶ã¯èµ·ãããªã fact4: ã·ãªã·ãLv.21äºä»¶ã¯çºçããªã fact5: çãé£ããšããããšã¯èª¬æãé£ããšããããšã«é²ããã fact6: å£å§ãããšããããšã¯çããªããšããããšã¯ãŽã«ãŽãLv.25äºä»¶ã«é»æ¢ããã fact7: ä»®ã«å£å§ãããšããããšãçããã°äŒžã¹ãããšãèµ·ãã | fact1: ¬{E} -> {A} fact2: ¬{E} -> ({A} & {B}) fact3: ¬(¬{E} v ¬{C}) -> ¬{B} fact4: ¬{E} fact5: {A} -> ¬{EE} fact6: {B} -> {C} fact7: {C} -> {D} | [
"fact2 & fact4 -> int1: 説æãé£ããšããããšãèµ·ããããŸããŽã«ãŽãLv.25äºä»¶ãèµ·ãã; int1 -> int2: ãŽã«ãŽãLv.25äºä»¶ãèµ·ãã; int2 & fact6 -> int3: å£å§ãããšããããšãçºçãã; int3 & fact7 -> hypothesis;"
] | [
"fact2 & fact4 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 & fact6 -> int3: {C}; int3 & fact7 -> hypothesis;"
] | 䌞ã¹ãããšã¯çºçããªã | ¬{D} | [] | 6 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ã·ãªã·ãLv.21äºä»¶ã¯çããªããšããããšã¯ã説æãé£ããšããããšã¯èµ·ããªãããšããããšãåé¿ãã fact2: ã説æãé£ããšããããšããã³ãŽã«ãŽãLv.25äºä»¶äž¡æ¹ãèµ·ããããšããããšã¯ã·ãªã·ãLv.21äºä»¶ã¯èµ·ãããªããšããããšã«åŒãèµ·ãããã fact3: ããä»®ã«ãã·ãªã·ãLv.21äºä»¶ã¯èµ·ããªãããŸãã¯å£å§ãããšããããšã¯èµ·ããªãããŸãã¯ã©ã¡ããã ããšããããšã¯æãç«ããªããšããã°ãŽã«ãŽãLv.25äºä»¶ã¯èµ·ãããªã fact4: ã·ãªã·ãLv.21äºä»¶ã¯çºçããªã fact5: çãé£ããšããããšã¯èª¬æãé£ããšããããšã«é²ããã fact6: å£å§ãããšããããšã¯çããªããšããããšã¯ãŽã«ãŽãLv.25äºä»¶ã«é»æ¢ããã fact7: ä»®ã«å£å§ãããšããããšãçããã°äŒžã¹ãããšãèµ·ãã ; $hypothesis$ = ã䌞ã¹ãããšãèµ·ããããšããããšã¯æ£ãã ; $proof$ = | fact2 & fact4 -> int1: 説æãé£ããšããããšãèµ·ããããŸããŽã«ãŽãLv.25äºä»¶ãèµ·ãã; int1 -> int2: ãŽã«ãŽãLv.25äºä»¶ãèµ·ãã; int2 & fact6 -> int3: å£å§ãããšããããšãçºçãã; int3 & fact7 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{E} -> {A} fact2: ¬{E} -> ({A} & {B}) fact3: ¬(¬{E} v ¬{C}) -> ¬{B} fact4: ¬{E} fact5: {A} -> ¬{EE} fact6: {B} -> {C} fact7: {C} -> {D} ; $hypothesis$ = {D} ; $proof$ = | fact2 & fact4 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 & fact6 -> int3: {C}; int3 & fact7 -> hypothesis; __PROVED__ |
0.3 | ãŽããŽã¡ãLv.21äºä»¶ãèµ·ãã | {C} | fact1: ããããé»è²ããšããããšã¯çºçããªããããŸãã«ãŽã®ãŽã®Lv.25äºä»¶ã¯èµ·ãããªãããšããããšã¯æãç«ããªããªãã°ãŽããŽã¡ãLv.21äºä»¶ãèµ·ãã fact2: é»è²ããšããããšãçºçãã fact3: ãŽã®ãŽã®Lv.25äºä»¶ã¯ããŽããŽã¡ãLv.21äºä»¶ã§ã¯ãªãé»è²ããšããããšãèµ·ããããšããããšãåŒãèµ·ãã fact4: ãŽã®ãŽã®Lv.25äºä»¶ãèµ·ãããé»è²ããšããããšã¯çããªããšãããç«ãŠé£ããšããããšãèµ·ãã fact5: ããŽããŽã¡ãLv.21äºä»¶ã¯çããªãããšããããšã¯ã¿ãªã¿ã«ãLv.78äºä»¶ã«èµ·å ãã fact6: ã¿ãªã¿ã«ãLv.78äºä»¶ã¯ç®¡çãæããšããããšã«ããçãã | fact1: ¬(¬{A} & ¬{B}) -> {C} fact2: {A} fact3: {B} -> (¬{C} & {A}) fact4: ({B} & ¬{A}) -> {DF} fact5: {D} -> ¬{C} fact6: {E} -> {D} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããé»è²ããšããããšã¯çããªããå ããŠãŽã®ãŽã®Lv.25äºä»¶ã¯èµ·ãããªã; assump1 -> int1: é»è²ããšããããšã¯çããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ããé»è²ããšããããšã¯çããªãããŽã®ãŽã®Lv.25äºä»¶ã¯èµ·ããªãããšããããšã¯äºå®ã ããšããããšã¯æãç«ããªã; int3 & fact1 -> hypothesis;"
] | [
"void -> assump1: (¬{A} & ¬{B}); assump1 -> int1: ¬{A}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{A} & ¬{B}); int3 & fact1 -> hypothesis;"
] | ç«ãŠé£ããšããããšãçãã | {DF} | [] | 8 | 5 | 3 | 5 | 3 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããé»è²ããšããããšã¯çºçããªããããŸãã«ãŽã®ãŽã®Lv.25äºä»¶ã¯èµ·ãããªãããšããããšã¯æãç«ããªããªãã°ãŽããŽã¡ãLv.21äºä»¶ãèµ·ãã fact2: é»è²ããšããããšãçºçãã fact3: ãŽã®ãŽã®Lv.25äºä»¶ã¯ããŽããŽã¡ãLv.21äºä»¶ã§ã¯ãªãé»è²ããšããããšãèµ·ããããšããããšãåŒãèµ·ãã fact4: ãŽã®ãŽã®Lv.25äºä»¶ãèµ·ãããé»è²ããšããããšã¯çããªããšãããç«ãŠé£ããšããããšãèµ·ãã fact5: ããŽããŽã¡ãLv.21äºä»¶ã¯çããªãããšããããšã¯ã¿ãªã¿ã«ãLv.78äºä»¶ã«èµ·å ãã fact6: ã¿ãªã¿ã«ãLv.78äºä»¶ã¯ç®¡çãæããšããããšã«ããçãã ; $hypothesis$ = ãŽããŽã¡ãLv.21äºä»¶ãèµ·ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããé»è²ããšããããšã¯çããªããå ããŠãŽã®ãŽã®Lv.25äºä»¶ã¯èµ·ãããªã; assump1 -> int1: é»è²ããšããããšã¯çããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ããé»è²ããšããããšã¯çããªãããŽã®ãŽã®Lv.25äºä»¶ã¯èµ·ããªãããšããããšã¯äºå®ã ããšããããšã¯æãç«ããªã; int3 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬(¬{A} & ¬{B}) -> {C} fact2: {A} fact3: {B} -> (¬{C} & {A}) fact4: ({B} & ¬{A}) -> {DF} fact5: {D} -> ¬{C} fact6: {E} -> {D} ; $hypothesis$ = {C} ; $proof$ = | void -> assump1: (¬{A} & ¬{B}); assump1 -> int1: ¬{A}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{A} & ¬{B}); int3 & fact1 -> hypothesis; __PROVED__ |
0.3 | ããä»®ã«ãå€ããæããªããŠãšããããšããããšã¯ééããªãã°çãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬((Ex): ¬(¬{AA}x & {AB}x) -> {B}x) | fact1: ä»®ã«ãã®ãœã¡ããœãLv.11ã¯ãšãããªããªããããã¯çããããšããããšã¯çå®ã§ãã fact2: ããããå€ããæããæŽã«ãšããããšããããšã¯äºå®ãšç°ãªããšãããšçãããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ãããããã®ãœã¡ããœãLv.11ã¯å€ããæããªãããšããããšããããšã¯ééãã ããšããããšã¯æãç«ã€ãšãããšãã®ãœã¡ããœãLv.11ã¯çãã fact4: ããããã®ãŽã®ãŽãLv.80ã¯çããªããã©ç
©ãããšããããšã¯æãç«ããªããšããã°ãã®ãŽã®ãŽãLv.80ã¯æãé£ã | fact1: ¬{AB}{aa} -> {B}{aa} fact2: (Ex): ¬({AA}x & {AB}x) -> {B}x fact3: ¬(¬{AA}{aa} & {AB}{aa}) -> {B}{aa} fact4: ¬(¬{B}{ah} & {DF}{ah}) -> {CD}{ah} | [
"fact3 -> hypothesis;"
] | [
"fact3 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 1 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ä»®ã«ãã®ãœã¡ããœãLv.11ã¯ãšãããªããªããããã¯çããããšããããšã¯çå®ã§ãã fact2: ããããå€ããæããæŽã«ãšããããšããããšã¯äºå®ãšç°ãªããšãããšçãããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ãããããã®ãœã¡ããœãLv.11ã¯å€ããæããªãããšããããšããããšã¯ééãã ããšããããšã¯æãç«ã€ãšãããšãã®ãœã¡ããœãLv.11ã¯çãã fact4: ããããã®ãŽã®ãŽãLv.80ã¯çããªããã©ç
©ãããšããããšã¯æãç«ããªããšããã°ãã®ãŽã®ãŽãLv.80ã¯æãé£ã ; $hypothesis$ = ããä»®ã«ãå€ããæããªããŠãšããããšããããšã¯ééããªãã°çãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{AB}{aa} -> {B}{aa} fact2: (Ex): ¬({AA}x & {AB}x) -> {B}x fact3: ¬(¬{AA}{aa} & {AB}{aa}) -> {B}{aa} fact4: ¬(¬{B}{ah} & {DF}{ah}) -> {CD}{ah} ; $hypothesis$ = ¬((Ex): ¬(¬{AA}x & {AB}x) -> {B}x) ; $proof$ = | fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãè¿ä»ãé£ããšããããšã¯åãæ¶ãåŸããšãåŒãèµ·ããããšããããšã¯åã§ãã | ¬({A} -> {D}) | fact1: æ
æ²æ·±ããšããããšã¯åãæ¶ãåŸããšãçºçããã fact2: æ
æ²æ·±ããšããããšã¯å³ã
ãããšããããšã«ç±æ¥ãã | fact1: {C} -> {D} fact2: {B} -> {C} | [] | [] | null | null | [] | null | 5 | 4 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: æ
æ²æ·±ããšããããšã¯åãæ¶ãåŸããšãçºçããã fact2: æ
æ²æ·±ããšããããšã¯å³ã
ãããšããããšã«ç±æ¥ãã ; $hypothesis$ = ãè¿ä»ãé£ããšããããšã¯åãæ¶ãåŸããšãåŒãèµ·ããããšããããšã¯åã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C} -> {D} fact2: {B} -> {C} ; $hypothesis$ = ¬({A} -> {D}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãã¡ããã¡ãLv.57ãæäžãããšããã°ãã®ãœã«ã
ãœã®Lv.88ã¯æã¡é£ãããšããããšã¯æãç«ããªã | ¬({A}{a} -> {C}{b}) | fact1: ä»®ã«ããã®ãœã«ã
ãœã®Lv.88ã¯èã
ãæãããšããããšã¯æãç«ã€ãšããã°ãã®ãœã«ã
ãœã®Lv.88ã¯æã¡é£ã | fact1: {B}{b} -> {C}{b} | [] | [] | null | null | [] | null | 4 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ä»®ã«ããã®ãœã«ã
ãœã®Lv.88ã¯èã
ãæãããšããããšã¯æãç«ã€ãšããã°ãã®ãœã«ã
ãœã®Lv.88ã¯æã¡é£ã ; $hypothesis$ = ããã®ãã¡ããã¡ãLv.57ãæäžãããšããã°ãã®ãœã«ã
ãœã®Lv.88ã¯æã¡é£ãããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{b} -> {C}{b} ; $hypothesis$ = ¬({A}{a} -> {C}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãããä»®ã«äžç¥èŸããšããããšã¯çºçããªããªãã°äžç¥èŸããšããããšã¯èµ·ããªããŠããã«ã·ã«ãã·ãLv.39äºä»¶ã¯çããªãããšããããšã¯åœã§ãã | ¬(¬{A} -> (¬{A} & ¬{B})) | fact1: ããŽããŽã¡ãLv.84äºä»¶ã¯èµ·ãããªããããã«äžç¥èŸããšããããšã¯çºçããªãããšããããšã¯ã·ã«ãã·ãLv.39äºä»¶ã«ç±æ¥ãã fact2: è¶ããããšã¯çºçããªããŠå¿äœç¡ããšããããšã¯èµ·ããªã fact3: ã·ã«ãã·ãLv.39äºä»¶ã¯èµ·ããªã fact4: ã·ã«ãã·ãLv.39äºä»¶ã¯èŠæããããšã«ããçãã fact5: ããä»®ã«äžç¥èŸããšããããšãèµ·ãããšãããäžç¥èŸããšããããšã¯çºçããªããŠã·ã«ãã·ãLv.39äºä»¶ã¯çºçããªã | fact1: {B} -> (¬{CT} & ¬{A}) fact2: (¬{DG} & ¬{DJ}) fact3: ¬{B} fact4: {C} -> {B} fact5: {A} -> (¬{A} & ¬{B}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããäžç¥èŸããšããããšã¯èµ·ããªã; assump1 & fact3 -> int1: ãäžç¥èŸããšããããšã¯èµ·ãããªããŠãŸãã·ã«ãã·ãLv.39äºä»¶ã¯èµ·ããªãããšããããšã¯ç¢ºãã§ãã; [assump1] & int1 -> hypothesis;"
] | [
"void -> assump1: ¬{A}; assump1 & fact3 -> int1: (¬{A} & ¬{B}); [assump1] & int1 -> hypothesis;"
] | ãŽããŽã¡ãLv.84äºä»¶ã¯èµ·ããªã | ¬{CT} | [] | 7 | 3 | 2 | 3 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããŽããŽã¡ãLv.84äºä»¶ã¯èµ·ãããªããããã«äžç¥èŸããšããããšã¯çºçããªãããšããããšã¯ã·ã«ãã·ãLv.39äºä»¶ã«ç±æ¥ãã fact2: è¶ããããšã¯çºçããªããŠå¿äœç¡ããšããããšã¯èµ·ããªã fact3: ã·ã«ãã·ãLv.39äºä»¶ã¯èµ·ããªã fact4: ã·ã«ãã·ãLv.39äºä»¶ã¯èŠæããããšã«ããçãã fact5: ããä»®ã«äžç¥èŸããšããããšãèµ·ãããšãããäžç¥èŸããšããããšã¯çºçããªããŠã·ã«ãã·ãLv.39äºä»¶ã¯çºçããªã ; $hypothesis$ = ãããä»®ã«äžç¥èŸããšããããšã¯çºçããªããªãã°äžç¥èŸããšããããšã¯èµ·ããªããŠããã«ã·ã«ãã·ãLv.39äºä»¶ã¯çããªãããšããããšã¯åœã§ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããäžç¥èŸããšããããšã¯èµ·ããªã; assump1 & fact3 -> int1: ãäžç¥èŸããšããããšã¯èµ·ãããªããŠãŸãã·ã«ãã·ãLv.39äºä»¶ã¯èµ·ããªãããšããããšã¯ç¢ºãã§ãã; [assump1] & int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} -> (¬{CT} & ¬{A}) fact2: (¬{DG} & ¬{DJ}) fact3: ¬{B} fact4: {C} -> {B} fact5: {A} -> (¬{A} & ¬{B}) ; $hypothesis$ = ¬(¬{A} -> (¬{A} & ¬{B})) ; $proof$ = | void -> assump1: ¬{A}; assump1 & fact3 -> int1: (¬{A} & ¬{B}); [assump1] & int1 -> hypothesis; __DISPROVED__ |
0.3 | æããšããããšãçãã | {A} | fact1: ãæããšããããšã¯èµ·ããªãããšããããšã¯ãæœããšããããšã¯èµ·ãããªãããšããããšãæããšããããšããããã¯äž¡æ¹ãšããåŒãèµ·ãã fact2: ããä»®ã«æœããšããããšã¯èµ·ãããªãããŸãã¯æããšããããšãçºçããããããã¯äž¡æ¹ãªãã°ã·ã«ãã·ãLv.9äºä»¶ãèµ·ãã | fact1: ¬{A} -> (¬{AA} v {AB}) fact2: (¬{AA} v {AB}) -> {B} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããæããšããããšã¯çºçããªã; fact1 & assump1 -> int1: æœããšããããšã¯èµ·ããªãããããã¯æããšããããšãèµ·ããããããã¯ã©ã¡ããã ; int1 & fact2 -> int2: ã·ã«ãã·ãLv.9äºä»¶ãçºçãã;"
] | [
"void -> assump1: ¬{A}; fact1 & assump1 -> int1: (¬{AA} v {AB}); int1 & fact2 -> int2: {B};"
] | null | null | [] | null | 5 | 4 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãæããšããããšã¯èµ·ããªãããšããããšã¯ãæœããšããããšã¯èµ·ãããªãããšããããšãæããšããããšããããã¯äž¡æ¹ãšããåŒãèµ·ãã fact2: ããä»®ã«æœããšããããšã¯èµ·ãããªãããŸãã¯æããšããããšãçºçããããããã¯äž¡æ¹ãªãã°ã·ã«ãã·ãLv.9äºä»¶ãèµ·ãã ; $hypothesis$ = æããšããããšãçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A} -> (¬{AA} v {AB}) fact2: (¬{AA} v {AB}) -> {B} ; $hypothesis$ = {A} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãããã«ãLv.88ã¯è³æãé£ãããããã¯ããã¯æãç¡ããªãããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã | ¬({A}{a} v ¬{C}{a}) | fact1: ãªãããã®ã¢ã³ã¹ã¿ãŒãè³æãé£ããšããããšã¯ãªããªãã°å·å¿µæ·±ãããããã¯èŠãé£ããªã fact2: ãã®ãããã«ãLv.88ã¯è³æãé£ãããããå°åºãã | fact1: (x): ¬{A}x -> ({EN}x v ¬{IR}x) fact2: ({A}{a} & {B}{a}) | [
"fact2 -> int1: ããã®ãããã«ãLv.88ã¯è³æãé£ãããšããããšã¯æãç«ã€; int1 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a}; int1 -> hypothesis;"
] | ãã®ãŸããŸã®Lv.5ã¯å·å¿µæ·±ããèŠãé£ããªãããããã¯ã©ã¡ããã | ({EN}{hp} v ¬{IR}{hp}) | [
"fact3 -> int2: ããä»®ã«ãã®ãŸããŸã®Lv.5ãè³æãé£ããªããªãã°ãã®ãŸããŸã®Lv.5ã¯å·å¿µæ·±ãããããã¯ããã¯èŠãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã§ãã;"
] | 5 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãªãããã®ã¢ã³ã¹ã¿ãŒãè³æãé£ããšããããšã¯ãªããªãã°å·å¿µæ·±ãããããã¯èŠãé£ããªã fact2: ãã®ãããã«ãLv.88ã¯è³æãé£ãããããå°åºãã ; $hypothesis$ = ããã®ãããã«ãLv.88ã¯è³æãé£ãããããã¯ããã¯æãç¡ããªãããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã ; $proof$ = | fact2 -> int1: ããã®ãããã«ãLv.88ã¯è³æãé£ãããšããããšã¯æãç«ã€; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{A}x -> ({EN}x v ¬{IR}x) fact2: ({A}{a} & {B}{a}) ; $hypothesis$ = ¬({A}{a} v ¬{C}{a}) ; $proof$ = | fact2 -> int1: {A}{a}; int1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŸããŸã«Lv.79ã¯æµ
ããããã¯ç Žãé£ãããšããããšã¯èª€ãã | ¬({C}{b} & {D}{b}) | fact1: ããããã®ãœã«ããœã¡ã
Lv.82ãäžæžãããã°ãã®ã¿ãã¿ãLv.15ã¯åãæã fact2: ãã®ãŸããŸã«Lv.79ã¯è奮ãæã fact3: ãã®ã¿ãã¿ãLv.15ã¯æµ
ã fact4: ããä»®ã«ãã®ãŸããŸã«Lv.79ãåãé£ããšããã°æµ
ã fact5: ããä»®ã«ãã®ã¿ãã¿ãLv.15ãåãæããšããã°ãã®ãŸããŸã«Lv.79ã¯åãé£ã fact6: ãã®ãœã«ããœã¡ã
Lv.82ã¯äžæžããã fact7: ãã®ãŸããŸã«Lv.79ã¯ç Žãé£ã | fact1: {E}{c} -> {A}{a} fact2: {FU}{b} fact3: {C}{a} fact4: {B}{b} -> {C}{b} fact5: {A}{a} -> {B}{b} fact6: {E}{c} fact7: {D}{b} | [
"fact6 & fact1 -> int1: ãã®ã¿ãã¿ãLv.15ã¯åãæã; fact5 & int1 -> int2: ãã®ãŸããŸã«Lv.79ã¯åãé£ã; int2 & fact4 -> int3: ãã®ãŸããŸã«Lv.79ã¯æµ
ã; int3 & fact7 -> hypothesis;"
] | [
"fact6 & fact1 -> int1: {A}{a}; fact5 & int1 -> int2: {B}{b}; int2 & fact4 -> int3: {C}{b}; int3 & fact7 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããããã®ãœã«ããœã¡ã
Lv.82ãäžæžãããã°ãã®ã¿ãã¿ãLv.15ã¯åãæã fact2: ãã®ãŸããŸã«Lv.79ã¯è奮ãæã fact3: ãã®ã¿ãã¿ãLv.15ã¯æµ
ã fact4: ããä»®ã«ãã®ãŸããŸã«Lv.79ãåãé£ããšããã°æµ
ã fact5: ããä»®ã«ãã®ã¿ãã¿ãLv.15ãåãæããšããã°ãã®ãŸããŸã«Lv.79ã¯åãé£ã fact6: ãã®ãœã«ããœã¡ã
Lv.82ã¯äžæžããã fact7: ãã®ãŸããŸã«Lv.79ã¯ç Žãé£ã ; $hypothesis$ = ããã®ãŸããŸã«Lv.79ã¯æµ
ããããã¯ç Žãé£ãããšããããšã¯èª€ãã ; $proof$ = | fact6 & fact1 -> int1: ãã®ã¿ãã¿ãLv.15ã¯åãæã; fact5 & int1 -> int2: ãã®ãŸããŸã«Lv.79ã¯åãé£ã; int2 & fact4 -> int3: ãã®ãŸããŸã«Lv.79ã¯æµ
ã; int3 & fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {E}{c} -> {A}{a} fact2: {FU}{b} fact3: {C}{a} fact4: {B}{b} -> {C}{b} fact5: {A}{a} -> {B}{b} fact6: {E}{c} fact7: {D}{b} ; $hypothesis$ = ¬({C}{b} & {D}{b}) ; $proof$ = | fact6 & fact1 -> int1: {A}{a}; fact5 & int1 -> int2: {B}{b}; int2 & fact4 -> int3: {C}{b}; int3 & fact7 -> hypothesis; __DISPROVED__ |
0.3 | ãããããªLv.25äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ | {G} | fact1: ãã¿ã«ãã¿ã«ãLv.12äºä»¶ãšãã°ãã£ãããšããããšãèµ·ããããšããããšã¯éŠ³ããããšã¯çºçããªããšããããšãèªçºãã fact2: ããä»®ã«ä»ãæããšããããšã¯èµ·ããªããšããã°å€ãé£ããšããããšããã³éŠ³ããããšãèµ·ãã fact3: ã¿ã«ãã¿ã«ãLv.12äºä»¶ãçãã fact4: ãœã¡ããœã«ãLv.72äºä»¶ãçãã fact5: ä»®ã«éŠ³ããããšã¯èµ·ããªããšããããä»ãæããšããããšãçºçããäžæ¹ã§å€ãé£ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact6: ãã°ãã£ãããšããããšã¯çºçããªããšããããšã¯ãœã¡ããœã«ãLv.72äºä»¶ã«é²ããã | fact1: ({C} & {B}) -> ¬{D} fact2: ¬{F} -> ({E} & {D}) fact3: {C} fact4: {A} fact5: ¬{D} -> ¬({F} & ¬{E}) fact6: {A} -> {B} | [
"fact6 & fact4 -> int1: ãã°ãã£ãããšããããšãèµ·ãã; int1 & fact3 -> int2: ã¿ã«ãã¿ã«ãLv.12äºä»¶ãèµ·ãããå ããŠãã°ãã£ãããšããããšãèµ·ãã; int2 & fact1 -> int3: 銳ããããšã¯çããªã; int3 & fact5 -> int4: ããä»ãæããšããããšãèµ·ããããã©å€ãé£ããšããããšã¯èµ·ããªãããšããããšã¯ç¢ºãã ããšããããšã¯æ£ãããªã;"
] | [
"fact6 & fact4 -> int1: {B}; int1 & fact3 -> int2: ({C} & {B}); int2 & fact1 -> int3: ¬{D}; int3 & fact5 -> int4: ¬({F} & ¬{E});"
] | ãããããªLv.25äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ | {G} | [] | 6 | 5 | 5 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã¿ã«ãã¿ã«ãLv.12äºä»¶ãšãã°ãã£ãããšããããšãèµ·ããããšããããšã¯éŠ³ããããšã¯çºçããªããšããããšãèªçºãã fact2: ããä»®ã«ä»ãæããšããããšã¯èµ·ããªããšããã°å€ãé£ããšããããšããã³éŠ³ããããšãèµ·ãã fact3: ã¿ã«ãã¿ã«ãLv.12äºä»¶ãçãã fact4: ãœã¡ããœã«ãLv.72äºä»¶ãçãã fact5: ä»®ã«éŠ³ããããšã¯èµ·ããªããšããããä»ãæããšããããšãçºçããäžæ¹ã§å€ãé£ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact6: ãã°ãã£ãããšããããšã¯çºçããªããšããããšã¯ãœã¡ããœã«ãLv.72äºä»¶ã«é²ããã ; $hypothesis$ = ãããããªLv.25äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({C} & {B}) -> ¬{D} fact2: ¬{F} -> ({E} & {D}) fact3: {C} fact4: {A} fact5: ¬{D} -> ¬({F} & ¬{E}) fact6: {A} -> {B} ; $hypothesis$ = {G} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ãã·ãLv.18ã¯æ»ãæã | {C}{c} | fact1: ãç±ã£ãœããšããããšã¯ãªããããã«å±±æ·±ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ä»®ã«ãã®ãŽããŽãLv.93ã匟ãç¶ããã°ãã®ãœã«ãœã¡ã
Lv.93ã¯åŒŸãç¶ããªã fact3: ä»®ã«ãã®ãœããœãLv.17ã山深ããšãããšãã®ãŽããŽãLv.93ã¯åŒŸãç¶ãã fact4: ãããã®ãœããœãLv.17ã匟ãç¶ããã°ãã®ã·ãã·ãLv.18ã¯æ»ãæã fact5: ç±ã£ãœããªããŠå±±æ·±ããªãã¢ã³ã¹ã¿ãŒãããã°ãã®ãŽããŽãLv.93ã¯å±±æ·±ããšããããšã¯ãªã fact6: ããããã®ãœããœãLv.17ã¯èªè² ããªããããã«æããããšããããšã¯ãªãããšããããšã¯ç¢ºãã§ãªããšããããã®ãœããœãLv.17ã¯åŒŸãç¶ãã | fact1: (Ex): (¬{D}x & ¬{A}x) fact2: {B}{a} -> ¬{B}{eq} fact3: {A}{b} -> {B}{a} fact4: {B}{b} -> {C}{c} fact5: (x): (¬{D}x & ¬{A}x) -> ¬{A}{a} fact6: ¬(¬{AA}{b} & ¬{AB}{b}) -> {B}{b} | [
"fact5 & fact1 -> int1: ãã®ãŽããŽãLv.93ã¯å±±æ·±ããªã;"
] | [
"fact5 & fact1 -> int1: ¬{A}{a};"
] | ãã®ãœã«ãœã¡ã
Lv.93ã¯åŒŸãç¶ããªã | ¬{B}{eq} | [] | 6 | 4 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãç±ã£ãœããšããããšã¯ãªããããã«å±±æ·±ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ä»®ã«ãã®ãŽããŽãLv.93ã匟ãç¶ããã°ãã®ãœã«ãœã¡ã
Lv.93ã¯åŒŸãç¶ããªã fact3: ä»®ã«ãã®ãœããœãLv.17ã山深ããšãããšãã®ãŽããŽãLv.93ã¯åŒŸãç¶ãã fact4: ãããã®ãœããœãLv.17ã匟ãç¶ããã°ãã®ã·ãã·ãLv.18ã¯æ»ãæã fact5: ç±ã£ãœããªããŠå±±æ·±ããªãã¢ã³ã¹ã¿ãŒãããã°ãã®ãŽããŽãLv.93ã¯å±±æ·±ããšããããšã¯ãªã fact6: ããããã®ãœããœãLv.17ã¯èªè² ããªããããã«æããããšããããšã¯ãªãããšããããšã¯ç¢ºãã§ãªããšããããã®ãœããœãLv.17ã¯åŒŸãç¶ãã ; $hypothesis$ = ãã®ã·ãã·ãLv.18ã¯æ»ãæã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (Ex): (¬{D}x & ¬{A}x) fact2: {B}{a} -> ¬{B}{eq} fact3: {A}{b} -> {B}{a} fact4: {B}{b} -> {C}{c} fact5: (x): (¬{D}x & ¬{A}x) -> ¬{A}{a} fact6: ¬(¬{AA}{b} & ¬{AB}{b}) -> {B}{b} ; $hypothesis$ = {C}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãœããœãLv.83äºä»¶ã¯èµ·ããªã | ¬{B} | fact1: éå±±ããããšãçºçãã fact2: ããä»®ã«éå±±ããããšã¯èµ·ããªããšãããããœããœãLv.83äºä»¶ããã³åŒã³æããšããããšãèµ·ããããšããããšã¯ééã£ãŠãã fact3: éã£ãœããšããããšãèµ·ãã fact4: ãœã¡ã
ãœã®Lv.61äºä»¶ãçãã fact5: æäœãæããšããããšãçãã fact6: ä»®ã«ããœããœãLv.83äºä»¶ãèµ·ããããã€åŒã³æããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãããšããã°åŒã³æããšããããšã¯çºçããªã | fact1: {A} fact2: ¬{A} -> ¬({B} & {EK}) fact3: {HG} fact4: {C} fact5: {EM} fact6: ¬({B} & {EK}) -> ¬{EK} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããœããœãLv.83äºä»¶ãèµ·ãã; fact1 & assump1 -> int1: éå±±ããããšãçããããœããœãLv.83äºä»¶ãèµ·ãã;"
] | [
"void -> assump1: {B}; fact1 & assump1 -> int1: ({A} & {B});"
] | åŒã³æããšããããšã¯èµ·ããªã | ¬{EK} | [] | 7 | 5 | 4 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: éå±±ããããšãçºçãã fact2: ããä»®ã«éå±±ããããšã¯èµ·ããªããšãããããœããœãLv.83äºä»¶ããã³åŒã³æããšããããšãèµ·ããããšããããšã¯ééã£ãŠãã fact3: éã£ãœããšããããšãèµ·ãã fact4: ãœã¡ã
ãœã®Lv.61äºä»¶ãçãã fact5: æäœãæããšããããšãçãã fact6: ä»®ã«ããœããœãLv.83äºä»¶ãèµ·ããããã€åŒã³æããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãããšããã°åŒã³æããšããããšã¯çºçããªã ; $hypothesis$ = ãœããœãLv.83äºä»¶ã¯èµ·ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} fact2: ¬{A} -> ¬({B} & {EK}) fact3: {HG} fact4: {C} fact5: {EM} fact6: ¬({B} & {EK}) -> ¬{EK} ; $hypothesis$ = ¬{B} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããæååãããšãããšãåºæ¥é£ããªããŠããã«èãããªãããšããããšã¯èª€ã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> ¬(¬{AA}x & ¬{AB}x) | fact1: ãããæååããã°ãåºæ¥é£ããŠå ããŠèãããšããããšã¯ãªãããšããããšã¯äºå®ã§ãªããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ããä»®ã«ãã®ãããã¡ã
Lv.86ã¯æååãããšããããããã¯åºæ¥é£ããèãããªãããšããããšã¯ééãã§ãã fact3: ãããä»®ã«æååããã°åºæ¥é£ããªããŠãŸãèãããªããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãããæååãããšããã°ãåºæ¥é£ããªããŠãã®äžèããããšããããšã¯èª€ããªãã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããããã®ãããã¡ã
Lv.86ã¯æååãããšããã°ãåºæ¥é£ããšããããšã¯ãªãããã©èããããšããããšã¯åœã fact6: ããããã®ãããã¡ã
Lv.86ã¯æååããããšããããšã¯æ¬åœã ãšãããããã®ãããã¡ã
Lv.86ã¯åºæ¥é£ããªããŠããã¯èãããªãããšããããšã¯äºå®ã§ãªã | fact1: (Ex): {A}x -> ¬({AA}x & ¬{AB}x) fact2: {A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa}) fact3: (Ex): {A}x -> (¬{AA}x & ¬{AB}x) fact4: (Ex): {A}x -> ¬(¬{AA}x & {AB}x) fact5: {A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact6: {A}{aa} -> ¬(¬{AA}{aa} & ¬{AB}{aa}) | [
"fact6 -> hypothesis;"
] | [
"fact6 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 1 | 5 | 0 | 5 | PROVED | null | PROVED | null | $facts$ = fact1: ãããæååããã°ãåºæ¥é£ããŠå ããŠèãããšããããšã¯ãªãããšããããšã¯äºå®ã§ãªããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ããä»®ã«ãã®ãããã¡ã
Lv.86ã¯æååãããšããããããã¯åºæ¥é£ããèãããªãããšããããšã¯ééãã§ãã fact3: ãããä»®ã«æååããã°åºæ¥é£ããªããŠãŸãèãããªããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãããæååãããšããã°ãåºæ¥é£ããªããŠãã®äžèããããšããããšã¯èª€ããªãã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããããã®ãããã¡ã
Lv.86ã¯æååãããšããã°ãåºæ¥é£ããšããããšã¯ãªãããã©èããããšããããšã¯åœã fact6: ããããã®ãããã¡ã
Lv.86ã¯æååããããšããããšã¯æ¬åœã ãšãããããã®ãããã¡ã
Lv.86ã¯åºæ¥é£ããªããŠããã¯èãããªãããšããããšã¯äºå®ã§ãªã ; $hypothesis$ = ãããæååãããšãããšãåºæ¥é£ããªããŠããã«èãããªãããšããããšã¯èª€ã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: (Ex): {A}x -> ¬({AA}x & ¬{AB}x) fact2: {A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa}) fact3: (Ex): {A}x -> (¬{AA}x & ¬{AB}x) fact4: (Ex): {A}x -> ¬(¬{AA}x & {AB}x) fact5: {A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact6: {A}{aa} -> ¬(¬{AA}{aa} & ¬{AB}{aa}) ; $hypothesis$ = (Ex): {A}x -> ¬(¬{AA}x & ¬{AB}x) ; $proof$ = | fact6 -> hypothesis; __PROVED__ |
0.3 | ã·ã«ãã·ãLv.1äºä»¶ãçãã | {F} | fact1: æ¢ãç¡ããšããããšã¯èµ·ãããªã fact2: ã·ãã·ãLv.41äºä»¶ããã³äœããšããããšãçºçãã fact3: ä»®ã«ãããã¡ãLv.26äºä»¶ãçãããšãããéèŠãããšããããšã§ã¯ãªããŠçµ±ã¹ãããšãçãã fact4: ãããéèŠãããšããããšãçããããããçµ±ã¹ãããšãèµ·ãããšãããšã·ã«ãã·ãLv.1äºä»¶ã¯çããªã fact5: ã·ãã·ãLv.41äºä»¶ãèµ·ãã fact6: ãã·ãã·ãLv.41äºä»¶ãšã·ã«ãã·ãLv.1äºä»¶ãçºçããããšããããšã¯ãäœããšããããšã¯èµ·ãããªãããšããããšãåå ã fact7: ãçµ±ã¹ãããšãèµ·ããããšããããšã¯äºå®ã§ãã fact8: å±èšããããšã¯çºçããªããšããããšã¯äœããšããããšã«é»ãŸãã fact9: ãéèŠãããšããããšã¯èµ·ããªãããšããããšã¯å±èšããããšã«é²ããã | fact1: ¬{JE} fact2: ({A} & {B}) fact3: {G} -> (¬{D} & {E}) fact4: ({D} & {E}) -> ¬{F} fact5: {A} fact6: ¬{B} -> ({A} & {F}) fact7: {E} fact8: {B} -> {C} fact9: {C} -> {D} | [
"fact2 -> int1: äœããšããããšãçºçãã; int1 & fact8 -> int2: å±èšããããšãèµ·ãã; int2 & fact9 -> int3: ãéèŠãããšããããšãçããããšããããšã¯æãç«ã€; int3 & fact7 -> int4: éèŠãããšããããšãèµ·ãããããã«çµ±ã¹ãããšãçºçãã; int4 & fact4 -> hypothesis;"
] | [
"fact2 -> int1: {B}; int1 & fact8 -> int2: {C}; int2 & fact9 -> int3: {D}; int3 & fact7 -> int4: ({D} & {E}); int4 & fact4 -> hypothesis;"
] | ã·ã«ãã·ãLv.1äºä»¶ãçãã | {F} | [] | 7 | 5 | 5 | 5 | 5 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: æ¢ãç¡ããšããããšã¯èµ·ãããªã fact2: ã·ãã·ãLv.41äºä»¶ããã³äœããšããããšãçºçãã fact3: ä»®ã«ãããã¡ãLv.26äºä»¶ãçãããšãããéèŠãããšããããšã§ã¯ãªããŠçµ±ã¹ãããšãçãã fact4: ãããéèŠãããšããããšãçããããããçµ±ã¹ãããšãèµ·ãããšãããšã·ã«ãã·ãLv.1äºä»¶ã¯çããªã fact5: ã·ãã·ãLv.41äºä»¶ãèµ·ãã fact6: ãã·ãã·ãLv.41äºä»¶ãšã·ã«ãã·ãLv.1äºä»¶ãçºçããããšããããšã¯ãäœããšããããšã¯èµ·ãããªãããšããããšãåå ã fact7: ãçµ±ã¹ãããšãèµ·ããããšããããšã¯äºå®ã§ãã fact8: å±èšããããšã¯çºçããªããšããããšã¯äœããšããããšã«é»ãŸãã fact9: ãéèŠãããšããããšã¯èµ·ããªãããšããããšã¯å±èšããããšã«é²ããã ; $hypothesis$ = ã·ã«ãã·ãLv.1äºä»¶ãçãã ; $proof$ = | fact2 -> int1: äœããšããããšãçºçãã; int1 & fact8 -> int2: å±èšããããšãèµ·ãã; int2 & fact9 -> int3: ãéèŠãããšããããšãçããããšããããšã¯æãç«ã€; int3 & fact7 -> int4: éèŠãããšããããšãèµ·ãããããã«çµ±ã¹ãããšãçºçãã; int4 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{JE} fact2: ({A} & {B}) fact3: {G} -> (¬{D} & {E}) fact4: ({D} & {E}) -> ¬{F} fact5: {A} fact6: ¬{B} -> ({A} & {F}) fact7: {E} fact8: {B} -> {C} fact9: {C} -> {D} ; $hypothesis$ = {F} ; $proof$ = | fact2 -> int1: {B}; int1 & fact8 -> int2: {C}; int2 & fact9 -> int3: {D}; int3 & fact7 -> int4: ({D} & {E}); int4 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã·ãã·ãLv.32ã¯ãã©ããªããªã | ¬{AA}{aa} | fact1: ãã®ã·ãã·ãLv.32ã¯è²§ããããã«è³¢ã | fact1: ({A}{aa} & {B}{aa}) | [
"fact1 -> int1: ãã®ã·ãã·ãLv.32ã¯è²§ã;"
] | [
"fact1 -> int1: {A}{aa};"
] | null | null | [] | null | 4 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ã·ãã·ãLv.32ã¯è²§ããããã«è³¢ã ; $hypothesis$ = ãã®ã·ãã·ãLv.32ã¯ãã©ããªããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A}{aa} & {B}{aa}) ; $hypothesis$ = ¬{AA}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ã«Lv.69ã¯åãã | {A}{a} | fact1: ãã®ãã«ãã«ãLv.56ãããã¯ã¢ããåºæ¥ãªããªããã®ãŽããŽã¡ãLv.53ã¯éªéèãããŸãã¯æœã£ããããŸãã¯äž¡æ¹ãšãã§ãã fact2: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒãããã¯ã¢ããåºæ¥ãªãããŸãã¯ããã¯æéè¯ããªãããããã¯äž¡æ¹ãšãã§ãããšãããããã¯ããã¯ã¢ããåºæ¥ããšããããšã¯ãªã fact3: ãã®ãŽããŽã¡ãLv.53ã¯å
ãã fact4: ãããããã¢ã³ã¹ã¿ãŒãå
ãããªãããããã¯ãããåãããšããããšã¯ãªããšãããããã¯åããªãããšããããšã¯æ£ãã fact5: ä»®ã«ãã®ãŽããŽã¡ãLv.53ãééç¡ããªããå®ãããªãã°å
ãããªã fact6: ä»®ã«ãã®ã¿ãã¿ã«Lv.69ãåãããšããããšã¯ãªããšããã°ãã®ãŽããŽã¡ãLv.53ã¯ééç¡ããªãããããã¯å®ãã fact7: æœã£ããã¢ã³ã¹ã¿ãŒã¯å
ãããªãããŸãã¯åãããšããããšã¯ãªãããŸãã¯äž¡æ¹ãšãã§ãã fact8: ããã®ã¿ãã¿ã«Lv.69ã¯éªéèããªãããŸãããã¯æéè¯ããšããããšã¯ãªãããšããããšã¯åœã§ãããšãããšããã¯ã¢ããåºæ¥ãªã | fact1: ¬{D}{c} -> ({E}{b} v {C}{b}) fact2: (x): (¬{D}x v ¬{F}x) -> ¬{D}x fact3: {B}{b} fact4: (x): (¬{B}x v ¬{A}x) -> ¬{A}x fact5: (¬{AA}{b} v {AB}{b}) -> ¬{B}{b} fact6: ¬{A}{a} -> (¬{AA}{b} v {AB}{b}) fact7: (x): {C}x -> (¬{B}x v ¬{A}x) fact8: ¬(¬{E}{a} & ¬{F}{a}) -> ¬{D}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ã«Lv.69ã¯åããªã; fact6 & assump1 -> int1: ãã®ãŽããŽã¡ãLv.53ã¯ééç¡ããªããå®ããããããã¯äž¡æ¹ã ; int1 & fact5 -> int2: ãã®ãŽããŽã¡ãLv.53ã¯å
ãããªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}{a}; fact6 & assump1 -> int1: (¬{AA}{b} v {AB}{b}); int1 & fact5 -> int2: ¬{B}{b}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ãã®ãŽã«ãŽãLv.24ã¯åããªã | ¬{A}{fp} | [] | 5 | 5 | 4 | 5 | 4 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãã«ãã«ãLv.56ãããã¯ã¢ããåºæ¥ãªããªããã®ãŽããŽã¡ãLv.53ã¯éªéèãããŸãã¯æœã£ããããŸãã¯äž¡æ¹ãšãã§ãã fact2: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒãããã¯ã¢ããåºæ¥ãªãããŸãã¯ããã¯æéè¯ããªãããããã¯äž¡æ¹ãšãã§ãããšãããããã¯ããã¯ã¢ããåºæ¥ããšããããšã¯ãªã fact3: ãã®ãŽããŽã¡ãLv.53ã¯å
ãã fact4: ãããããã¢ã³ã¹ã¿ãŒãå
ãããªãããããã¯ãããåãããšããããšã¯ãªããšãããããã¯åããªãããšããããšã¯æ£ãã fact5: ä»®ã«ãã®ãŽããŽã¡ãLv.53ãééç¡ããªããå®ãããªãã°å
ãããªã fact6: ä»®ã«ãã®ã¿ãã¿ã«Lv.69ãåãããšããããšã¯ãªããšããã°ãã®ãŽããŽã¡ãLv.53ã¯ééç¡ããªãããããã¯å®ãã fact7: æœã£ããã¢ã³ã¹ã¿ãŒã¯å
ãããªãããŸãã¯åãããšããããšã¯ãªãããŸãã¯äž¡æ¹ãšãã§ãã fact8: ããã®ã¿ãã¿ã«Lv.69ã¯éªéèããªãããŸãããã¯æéè¯ããšããããšã¯ãªãããšããããšã¯åœã§ãããšãããšããã¯ã¢ããåºæ¥ãªã ; $hypothesis$ = ãã®ã¿ãã¿ã«Lv.69ã¯åãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ã«Lv.69ã¯åããªã; fact6 & assump1 -> int1: ãã®ãŽããŽã¡ãLv.53ã¯ééç¡ããªããå®ããããããã¯äž¡æ¹ã ; int1 & fact5 -> int2: ãã®ãŽããŽã¡ãLv.53ã¯å
ãããªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{D}{c} -> ({E}{b} v {C}{b}) fact2: (x): (¬{D}x v ¬{F}x) -> ¬{D}x fact3: {B}{b} fact4: (x): (¬{B}x v ¬{A}x) -> ¬{A}x fact5: (¬{AA}{b} v {AB}{b}) -> ¬{B}{b} fact6: ¬{A}{a} -> (¬{AA}{b} v {AB}{b}) fact7: (x): {C}x -> (¬{B}x v ¬{A}x) fact8: ¬(¬{E}{a} & ¬{F}{a}) -> ¬{D}{a} ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: ¬{A}{a}; fact6 & assump1 -> int1: (¬{AA}{b} v {AB}{b}); int1 & fact5 -> int2: ¬{B}{b}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãããä»®ã«åãé£ããªããšããããå°ãªããããã空æãããããšããããšã¯èª€ãã§ãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{A}x -> ¬({AA}x & {AB}x) | fact1: ãããç滞ããŸããããããã¯ä»çœãããšããããšã¯ééãã§ãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã | fact1: fake_formula | [] | [] | null | null | [] | null | 2 | 2 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããç滞ããŸããããããã¯ä»çœãããšããããšã¯ééãã§ãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $hypothesis$ = ãããä»®ã«åãé£ããªããšããããå°ãªããããã空æãããããšããããšã¯èª€ãã§ãããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: fake_formula ; $hypothesis$ = (Ex): ¬{A}x -> ¬({AA}x & {AB}x) ; $proof$ = | __UNKNOWN__ |
0.3 | ãä»®ã«å¿«è«Ÿããªããªãã°äœã¿è¯ããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{B}x -> {C}x | fact1: ééãæãã¢ã³ã¹ã¿ãŒã¯åã fact2: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒãå¿«è«Ÿããªããšããã°äœã¿è¯ã fact3: ç±ãã¢ã³ã¹ã¿ãŒã¯å·ä»ãæã fact4: ãããä»®ã«å¿«è«Ÿãããšããã°äœã¿è¯ããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããããã®ããããLv.72ã¯å¿«è«Ÿãããšããããäœã¿è¯ãããšããããšã¯ç¢ºãã | fact1: (x): {HP}x -> {GS}x fact2: (x): ¬{B}x -> {C}x fact3: (x): {DJ}x -> {I}x fact4: (Ex): {B}x -> {C}x fact5: {B}{aa} -> {C}{aa} | [
"fact2 -> int1: ãããããã®ããããLv.72ã¯å¿«è«Ÿããªãããšããããšã¯çå®ãªãã°ãããã¯äœã¿è¯ãããšããããšã¯æ£ãã; int1 -> hypothesis;"
] | [
"fact2 -> int1: ¬{B}{aa} -> {C}{aa}; int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 4 | 0 | 4 | PROVED | null | PROVED | null | $facts$ = fact1: ééãæãã¢ã³ã¹ã¿ãŒã¯åã fact2: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒãå¿«è«Ÿããªããšããã°äœã¿è¯ã fact3: ç±ãã¢ã³ã¹ã¿ãŒã¯å·ä»ãæã fact4: ãããä»®ã«å¿«è«Ÿãããšããã°äœã¿è¯ããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããããã®ããããLv.72ã¯å¿«è«Ÿãããšããããäœã¿è¯ãããšããããšã¯ç¢ºãã ; $hypothesis$ = ãä»®ã«å¿«è«Ÿããªããªãã°äœã¿è¯ããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact2 -> int1: ãããããã®ããããLv.72ã¯å¿«è«Ÿããªãããšããããšã¯çå®ãªãã°ãããã¯äœã¿è¯ãããšããããšã¯æ£ãã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {HP}x -> {GS}x fact2: (x): ¬{B}x -> {C}x fact3: (x): {DJ}x -> {I}x fact4: (Ex): {B}x -> {C}x fact5: {B}{aa} -> {C}{aa} ; $hypothesis$ = (Ex): ¬{B}x -> {C}x ; $proof$ = | fact2 -> int1: ¬{B}{aa} -> {C}{aa}; int1 -> hypothesis; __PROVED__ |
0.3 | ããããã©ã³ã¹è¯ããšããããå¿å®ãããããã¯æ¥ãé£ã°ããªãããšããããšã¯ééããªãã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> ¬({AA}x v ¬{AB}x) | fact1: ããä»®ã«ãã®ã¿ãã¿ãLv.30ã¯ãã©ã³ã¹è¯ããšãããããã®ã¿ãã¿ãLv.30ã¯å¿å®ãããããã¯æ¥ãé£ã°ãããããã¯ã©ã¡ããã ããšããããšã¯åã fact2: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯æž
ããªãã°ãããã¯ãã©ããªãããããã¯ç²ãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã§ããããšããããšã¯ééã£ãŠãã fact3: ä»®ã«ãã®ã¿ãã¿ãLv.30ã¯ãã©ã³ã¹è¯ããªããããã¯å¿å®ãããããã¯æ¥ãé£ã°ããšããããšã¯ãªãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯ééã£ãŠãã fact4: ãããããã©ã³ã¹è¯ããšããããå¿å®ããæ¥ãé£ã°ããã©ã¡ããã ããšããããšã¯äºå®ãšç°ãªããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããã眮ãæããšãããšåã£ä»ãæãããããã¯ç¯çœªè
æ±ãããªããã¢ã³ã¹ã¿ãŒã¯ãã | fact1: {A}{aa} -> ¬({AA}{aa} v {AB}{aa}) fact2: (x): {HM}x -> ¬({BH}x v ¬{EF}x) fact3: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact4: (Ex): {A}x -> ¬({AA}x v {AB}x) fact5: (Ex): {GG}x -> ({JC}x v ¬{FA}x) | [
"fact3 -> hypothesis;"
] | [
"fact3 -> hypothesis;"
] | ããä»®ã«ãã®ããããLv.55ã¯æž
ããšãããšããã®ããããLv.55ã¯ãã©ããªãããããã¯ç²ãé£ããªãããšããããšã¯åœã§ãã | {HM}{cd} -> ¬({BH}{cd} v ¬{EF}{cd}) | [
"fact6 -> hypothesis;"
] | 1 | 1 | 1 | 1 | 1 | 4 | 0 | 4 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ããä»®ã«ãã®ã¿ãã¿ãLv.30ã¯ãã©ã³ã¹è¯ããšãããããã®ã¿ãã¿ãLv.30ã¯å¿å®ãããããã¯æ¥ãé£ã°ãããããã¯ã©ã¡ããã ããšããããšã¯åã fact2: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯æž
ããªãã°ãããã¯ãã©ããªãããããã¯ç²ãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã§ããããšããããšã¯ééã£ãŠãã fact3: ä»®ã«ãã®ã¿ãã¿ãLv.30ã¯ãã©ã³ã¹è¯ããªããããã¯å¿å®ãããããã¯æ¥ãé£ã°ããšããããšã¯ãªãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯ééã£ãŠãã fact4: ãããããã©ã³ã¹è¯ããšããããå¿å®ããæ¥ãé£ã°ããã©ã¡ããã ããšããããšã¯äºå®ãšç°ãªããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããã眮ãæããšãããšåã£ä»ãæãããããã¯ç¯çœªè
æ±ãããªããã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ããããã©ã³ã¹è¯ããšããããå¿å®ãããããã¯æ¥ãé£ã°ããªãããšããããšã¯ééããªãã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{aa} -> ¬({AA}{aa} v {AB}{aa}) fact2: (x): {HM}x -> ¬({BH}x v ¬{EF}x) fact3: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact4: (Ex): {A}x -> ¬({AA}x v {AB}x) fact5: (Ex): {GG}x -> ({JC}x v ¬{FA}x) ; $hypothesis$ = (Ex): {A}x -> ¬({AA}x v ¬{AB}x) ; $proof$ = | fact3 -> hypothesis; __PROVED__ |
0.3 | ããã®ãœããœãLv.43ã¯çã¿æãäžæ¹ã§åãæããªãããšããããšã¯ééãã§ãã | ¬({F}{d} & ¬{G}{d}) | fact1: ããããã®ãŽã«ããŽãLv.61ã¯çéãé£ããªãããšããããšã¯äºå®ãªãããã®ãœããœãLv.43ã¯çã¿æãããããåãæãããšããããšã¯ééãã fact2: ãããããã®ãŽããŽãLv.58ã¯å¹Œããªãããšããããšã¯æãç«ã€ãšãããšããã®ãŽã«ããŽãLv.61ã¯æ»æãæãããšããããšã¯æ¬åœã§ãã fact3: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯ãããããããšããããšã¯ãªããŠå ããŠæ»æãæããªãããšããããšã¯ééãã ãšãããããã¯æ»æãæã fact4: ãããªãããã®ã¢ã³ã¹ã¿ãŒã¯å¹Œããªããšããããé¢æ ããããšããããšã¯æãç«ã€ fact5: ãã®ãŸãªãŸãLv.72ã¯é¢æ ãã fact6: ããä»®ã«ãã®ãŸãªãŸãLv.72ãé¢æ ãããšããã°ãã®ãŽããŽãLv.58ã¯å¹Œããªã fact7: ããããã®ãŽã«ããŽãLv.61ã¯çéãé£ããšããããšã¯ãªããšãããããã®ãœããœãLv.43ã¯çã¿æããããã¯åãæããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact8: ãããã®ãŽã«ããŽãLv.61ãæ»æãæããããããããããããã¯äž¡æ¹ãšãã§ãããšãããããã¯çéãé£ããªã fact9: é¢æ ããã¢ã³ã¹ã¿ãŒã¯çã¿æããåãæããªã fact10: ãããã®ãŸãªãŸãLv.72ã¯æ»æãæããªãã°ããã®ãœããœãLv.43ã¯å¹Œããªãããšããããšã¯æãç«ã€ | fact1: ¬{E}{c} -> ¬({F}{d} & {G}{d}) fact2: {B}{b} -> {C}{c} fact3: (x): ¬(¬{D}x & ¬{C}x) -> {C}x fact4: (x): {B}x -> {A}x fact5: {A}{a} fact6: {A}{a} -> {B}{b} fact7: ¬{E}{c} -> ¬({F}{d} & ¬{G}{d}) fact8: ({C}{c} v {D}{c}) -> ¬{E}{c} fact9: (x): {A}x -> ({F}x & ¬{G}x) fact10: {C}{a} -> {B}{d} | [
"fact6 & fact5 -> int1: ãã®ãŽããŽãLv.58ã¯å¹Œããªã; int1 & fact2 -> int2: ãã®ãŽã«ããŽãLv.61ã¯æ»æãæã; int2 -> int3: ãã®ãŽã«ããŽãLv.61ã¯æ»æãæãããããã¯ããã¯ãããããã; int3 & fact8 -> int4: ãã®ãŽã«ããŽãLv.61ã¯çéãé£ããªã; int4 & fact7 -> hypothesis;"
] | [
"fact6 & fact5 -> int1: {B}{b}; int1 & fact2 -> int2: {C}{c}; int2 -> int3: ({C}{c} v {D}{c}); int3 & fact8 -> int4: ¬{E}{c}; int4 & fact7 -> hypothesis;"
] | ãã®ãœããœãLv.43ã¯çã¿æãäžæ¹ã§åãæããªã | ({F}{d} & ¬{G}{d}) | [
"fact11 -> int5: ããããã®ãœããœãLv.43ãé¢æ ãããªãããã¯çã¿æãäžæ¹ã§åãæããªã; fact12 -> int6: ããä»®ã«ãã®ãœããœãLv.43ã幌ããªããšããã°ããã¯é¢æ ãã; fact14 -> int7: ãããããã®ãŸãªãŸãLv.72ã¯ããããããªããŠããã«æ»æãæããªãããšããããšã¯èª€ã£ãŠãããªããã®ãŸãªãŸãLv.72ã¯æ»æãæã;"
] | 6 | 5 | 5 | 5 | 5 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããã®ãŽã«ããŽãLv.61ã¯çéãé£ããªãããšããããšã¯äºå®ãªãããã®ãœããœãLv.43ã¯çã¿æãããããåãæãããšããããšã¯ééãã fact2: ãããããã®ãŽããŽãLv.58ã¯å¹Œããªãããšããããšã¯æãç«ã€ãšãããšããã®ãŽã«ããŽãLv.61ã¯æ»æãæãããšããããšã¯æ¬åœã§ãã fact3: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯ãããããããšããããšã¯ãªããŠå ããŠæ»æãæããªãããšããããšã¯ééãã ãšãããããã¯æ»æãæã fact4: ãããªãããã®ã¢ã³ã¹ã¿ãŒã¯å¹Œããªããšããããé¢æ ããããšããããšã¯æãç«ã€ fact5: ãã®ãŸãªãŸãLv.72ã¯é¢æ ãã fact6: ããä»®ã«ãã®ãŸãªãŸãLv.72ãé¢æ ãããšããã°ãã®ãŽããŽãLv.58ã¯å¹Œããªã fact7: ããããã®ãŽã«ããŽãLv.61ã¯çéãé£ããšããããšã¯ãªããšãããããã®ãœããœãLv.43ã¯çã¿æããããã¯åãæããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact8: ãããã®ãŽã«ããŽãLv.61ãæ»æãæããããããããããããã¯äž¡æ¹ãšãã§ãããšãããããã¯çéãé£ããªã fact9: é¢æ ããã¢ã³ã¹ã¿ãŒã¯çã¿æããåãæããªã fact10: ãããã®ãŸãªãŸãLv.72ã¯æ»æãæããªãã°ããã®ãœããœãLv.43ã¯å¹Œããªãããšããããšã¯æãç«ã€ ; $hypothesis$ = ããã®ãœããœãLv.43ã¯çã¿æãäžæ¹ã§åãæããªãããšããããšã¯ééãã§ãã ; $proof$ = | fact6 & fact5 -> int1: ãã®ãŽããŽãLv.58ã¯å¹Œããªã; int1 & fact2 -> int2: ãã®ãŽã«ããŽãLv.61ã¯æ»æãæã; int2 -> int3: ãã®ãŽã«ããŽãLv.61ã¯æ»æãæãããããã¯ããã¯ãããããã; int3 & fact8 -> int4: ãã®ãŽã«ããŽãLv.61ã¯çéãé£ããªã; int4 & fact7 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{E}{c} -> ¬({F}{d} & {G}{d}) fact2: {B}{b} -> {C}{c} fact3: (x): ¬(¬{D}x & ¬{C}x) -> {C}x fact4: (x): {B}x -> {A}x fact5: {A}{a} fact6: {A}{a} -> {B}{b} fact7: ¬{E}{c} -> ¬({F}{d} & ¬{G}{d}) fact8: ({C}{c} v {D}{c}) -> ¬{E}{c} fact9: (x): {A}x -> ({F}x & ¬{G}x) fact10: {C}{a} -> {B}{d} ; $hypothesis$ = ¬({F}{d} & ¬{G}{d}) ; $proof$ = | fact6 & fact5 -> int1: {B}{b}; int1 & fact2 -> int2: {C}{c}; int2 -> int3: ({C}{c} v {D}{c}); int3 & fact8 -> int4: ¬{E}{c}; int4 & fact7 -> hypothesis; __PROVED__ |
0.3 | ãããã®ã¿ã«ãã¿ã¡ã
Lv.34ã埡é«ããšããã°ãã®ãœããœã¡ãLv.59ã¯æãç¡ã | {B}{a} -> {C}{b} | fact1: ä»®ã«ãããç±ã£ãœãããŸãã¯åŸ¡é«ãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯ç¢ºãã§ãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€ãšãããšãã®ãœããœã¡ãLv.59ã¯æãç¡ã fact2: ãããç±ã£ãœãããŸãã¯æãç¡ããã¢ã³ã¹ã¿ãŒããããªããã®ãœããœã¡ãLv.59ã¯åŸ¡é«ã fact3: ãã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯ç±ã£ãœã fact4: ãããã®ãœããœã¡ãLv.59ã埡é«ããªããšãããšãã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯ç±ã£ãœããæ··åãæã fact5: ã埡é«ããã¢ã³ã¹ã¿ãŒã¯ãã | fact1: (x): ({A}x v {B}x) -> {C}{b} fact2: (x): ({A}x v {C}x) -> {B}{b} fact3: {A}{a} fact4: ¬{B}{b} -> ({A}{a} & {FJ}{a}) fact5: (Ex): {B}x | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯åŸ¡é«ã; assump1 -> int1: ãã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯ç±ã£ãœãããŸãã¯åŸ¡é«ãããŸãã¯äž¡æ¹ã ; int1 -> int2: ããã¢ã³ã¹ã¿ãŒã¯ç±ã£ãœãããããã¯ããã¯åŸ¡é«ã; int2 & fact1 -> int3: ãã®ãœããœã¡ãLv.59ã¯æãç¡ã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}{a}; assump1 -> int1: ({A}{a} v {B}{a}); int1 -> int2: (Ex): ({A}x v {B}x); int2 & fact1 -> int3: {C}{b}; [assump1] & int3 -> hypothesis;"
] | ãæ··åãæãããŸãã¯æãé£ãããããã¯ã©ã¡ãããªãã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ({FJ}x v {BN}x) | [] | 6 | 5 | 2 | 5 | 2 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãããç±ã£ãœãããŸãã¯åŸ¡é«ãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯ç¢ºãã§ãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€ãšãããšãã®ãœããœã¡ãLv.59ã¯æãç¡ã fact2: ãããç±ã£ãœãããŸãã¯æãç¡ããã¢ã³ã¹ã¿ãŒããããªããã®ãœããœã¡ãLv.59ã¯åŸ¡é«ã fact3: ãã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯ç±ã£ãœã fact4: ãããã®ãœããœã¡ãLv.59ã埡é«ããªããšãããšãã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯ç±ã£ãœããæ··åãæã fact5: ã埡é«ããã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ãããã®ã¿ã«ãã¿ã¡ã
Lv.34ã埡é«ããšããã°ãã®ãœããœã¡ãLv.59ã¯æãç¡ã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯åŸ¡é«ã; assump1 -> int1: ãã®ã¿ã«ãã¿ã¡ã
Lv.34ã¯ç±ã£ãœãããŸãã¯åŸ¡é«ãããŸãã¯äž¡æ¹ã ; int1 -> int2: ããã¢ã³ã¹ã¿ãŒã¯ç±ã£ãœãããããã¯ããã¯åŸ¡é«ã; int2 & fact1 -> int3: ãã®ãœããœã¡ãLv.59ã¯æãç¡ã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ({A}x v {B}x) -> {C}{b} fact2: (x): ({A}x v {C}x) -> {B}{b} fact3: {A}{a} fact4: ¬{B}{b} -> ({A}{a} & {FJ}{a}) fact5: (Ex): {B}x ; $hypothesis$ = {B}{a} -> {C}{b} ; $proof$ = | void -> assump1: {B}{a}; assump1 -> int1: ({A}{a} v {B}{a}); int1 -> int2: (Ex): ({A}x v {B}x); int2 & fact1 -> int3: {C}{b}; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ããLv.99äºä»¶ãçãã | {B} | fact1: ãŽããŽã¡ãLv.98äºä»¶ãèµ·ãã fact2: ãŸã¡ã
ãŸã«Lv.27äºä»¶ãèµ·ãã fact3: æµã¿æ·±ããšããããšãçºçãã fact4: ãä»®ã«ãã£ãããšããããšã¯èµ·ããªããªããŽããŽã¡ãLv.98äºä»¶ãèµ·ããããŸãã¯ãŸã¡ã
ãŸã«Lv.27äºä»¶ãçºçããããŸãã¯äž¡æ¹ãšãã ããšããããšã¯ç¢ºãã fact5: ããŽããŽã¡ãLv.98äºä»¶ãçããããã®ããLv.99äºä»¶ãèµ·ããããšããããšã¯ããŸã¡ã
ãŸã«Lv.27äºä»¶ãèµ·ããããšããããšãé²ã | fact1: {A} fact2: {C} fact3: {CR} fact4: ¬{D} -> ({A} v {C}) fact5: ({A} & {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ããLv.99äºä»¶ãçãã; fact1 & assump1 -> int1: ãŽããŽã¡ãLv.98äºä»¶ãšãã®ããLv.99äºä»¶ã©ã¡ãããèµ·ãã; int1 & fact5 -> int2: ãŸã¡ã
ãŸã«Lv.27äºä»¶ã¯çããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; fact1 & assump1 -> int1: ({A} & {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããã®ããLv.99äºä»¶ãçãã | {B} | [] | 5 | 5 | 4 | 5 | 4 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãŽããŽã¡ãLv.98äºä»¶ãèµ·ãã fact2: ãŸã¡ã
ãŸã«Lv.27äºä»¶ãèµ·ãã fact3: æµã¿æ·±ããšããããšãçºçãã fact4: ãä»®ã«ãã£ãããšããããšã¯èµ·ããªããªããŽããŽã¡ãLv.98äºä»¶ãèµ·ããããŸãã¯ãŸã¡ã
ãŸã«Lv.27äºä»¶ãçºçããããŸãã¯äž¡æ¹ãšãã ããšããããšã¯ç¢ºãã fact5: ããŽããŽã¡ãLv.98äºä»¶ãçããããã®ããLv.99äºä»¶ãèµ·ããããšããããšã¯ããŸã¡ã
ãŸã«Lv.27äºä»¶ãèµ·ããããšããããšãé²ã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ããLv.99äºä»¶ãçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ããLv.99äºä»¶ãçãã; fact1 & assump1 -> int1: ãŽããŽã¡ãLv.98äºä»¶ãšãã®ããLv.99äºä»¶ã©ã¡ãããèµ·ãã; int1 & fact5 -> int2: ãŸã¡ã
ãŸã«Lv.27äºä»¶ã¯çããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} fact2: {C} fact3: {CR} fact4: ¬{D} -> ({A} v {C}) fact5: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {B} ; $proof$ = | void -> assump1: {B}; fact1 & assump1 -> int1: ({A} & {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãæ©ããªããšãããå¯æããããªããããã«æ¹¿æ°æããªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{A}x -> (¬{AA}x & ¬{AB}x) | fact1: ããããã®ãŽããŽãLv.24ãæ©ããªããšãããšå¯æããããªãããã©æ¹¿æ°æã fact2: ãä»®ã«æ©ããªããšãããå¯æããããªããã¢ã³ã¹ã¿ãŒã¯ãã | fact1: ¬{A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact2: (Ex): ¬{A}x -> ¬{AA}x | [] | [] | null | null | [] | null | 1 | 1 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããããã®ãŽããŽãLv.24ãæ©ããªããšãããšå¯æããããªãããã©æ¹¿æ°æã fact2: ãä»®ã«æ©ããªããšãããå¯æããããªããã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ãæ©ããªããšãããå¯æããããªããããã«æ¹¿æ°æããªããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact2: (Ex): ¬{A}x -> ¬{AA}x ; $hypothesis$ = (Ex): ¬{A}x -> (¬{AA}x & ¬{AB}x) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã«ã
ã¿ãLv.11ã¯åŸ©å±ããªã | ¬{C}{b} | fact1: ãã®ã·ã«ã
ã·ã®Lv.22ã¯å¯æ¥ããã移ããæã fact2: ãã®ã·ã«ã
ã·ã®Lv.22ã¯äžæãããããã¯åŸ©å±ãã fact3: ãã®ã·ã«ã
ã·ã®Lv.22ã¯å¯æ¥ãã fact4: ãã®ã·ã«ã
ã·ã®Lv.22ã¯éŠãã | fact1: ({D}{a} & {A}{a}) fact2: ({JH}{a} & {C}{a}) fact3: {D}{a} fact4: {B}{a} | [
"fact1 -> int1: ãã®ã·ã«ã
ã·ã®Lv.22ã¯ç§»ããæã; int1 & fact4 -> int2: ãã®ã·ã«ã
ã·ã®Lv.22ã¯ç§»ããæãããŸãéŠãã; int2 -> int3: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯ç§»ããæããŠããã«éŠãã;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact4 -> int2: ({A}{a} & {B}{a}); int2 -> int3: (Ex): ({A}x & {B}x);"
] | ãäžæãããæã¡é£ããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ({JH}x & {FD}x) | [
"fact5 -> int4: ãã®ã·ã«ã
ã·ã®Lv.22ã¯äžæãã;"
] | 4 | 4 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ã·ã«ã
ã·ã®Lv.22ã¯å¯æ¥ããã移ããæã fact2: ãã®ã·ã«ã
ã·ã®Lv.22ã¯äžæãããããã¯åŸ©å±ãã fact3: ãã®ã·ã«ã
ã·ã®Lv.22ã¯å¯æ¥ãã fact4: ãã®ã·ã«ã
ã·ã®Lv.22ã¯éŠãã ; $hypothesis$ = ãã®ã¿ã«ã
ã¿ãLv.11ã¯åŸ©å±ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({D}{a} & {A}{a}) fact2: ({JH}{a} & {C}{a}) fact3: {D}{a} fact4: {B}{a} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã·ãã·ã«ã
Lv.40ã¯ä¿å®ãã | {A}{a} | fact1: ä»®ã«ãã®ã·ãã·ã«ã
Lv.40ãä¿å®ãããªã綻ã³å§ãã fact2: ãã®ã·ãã·ã«ã
Lv.40ã¯ç¶»ã³å§ããªã | fact1: {A}{a} -> {B}{a} fact2: ¬{B}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ã«ã
Lv.40ã¯ä¿å®ãã; fact1 & assump1 -> int1: ãã®ã·ãã·ã«ã
Lv.40ã¯ç¶»ã³å§ãã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> hypothesis;"
] | null | null | [] | null | 4 | 3 | 4 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ä»®ã«ãã®ã·ãã·ã«ã
Lv.40ãä¿å®ãããªã綻ã³å§ãã fact2: ãã®ã·ãã·ã«ã
Lv.40ã¯ç¶»ã³å§ããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã·ãã·ã«ã
Lv.40ã¯ä¿å®ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ã«ã
Lv.40ã¯ä¿å®ãã; fact1 & assump1 -> int1: ãã®ã·ãã·ã«ã
Lv.40ã¯ç¶»ã³å§ãã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {B}{a} fact2: ¬{B}{a} ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ã«ãã¿ãLv.55ã¯çµå©åºæ¥ãªã | ¬{E}{c} | fact1: ãã®ãŸã«ããŸã«ãLv.59ã¯åãæããåšå§ãã fact2: ä»®ã«ãã®ãŸã«ããŸã«ãLv.59ãåãæããçããããšããããã®ãŽããŽãLv.53ã¯éçœããªã fact3: ããã®ãŸã«ããŸã«ãLv.59ã¯çãããããšããããšã¯çå®ã§ãã fact4: ãããã®ãŽããŽãLv.53ãéçœããšããããšã¯ãªãäžæ¹ã§çãç«ã€ãšããããã®ã¿ã«ãã¿ãLv.55ã¯çµå©åºæ¥ã | fact1: ({A}{a} & {B}{a}) fact2: ({A}{a} & {C}{a}) -> ¬{D}{b} fact3: {C}{a} fact4: (¬{D}{b} & {F}{b}) -> {E}{c} | [
"fact1 -> int1: ãã®ãŸã«ããŸã«ãLv.59ã¯åãæã; int1 & fact3 -> int2: ãã®ãŸã«ããŸã«ãLv.59ã¯åãæããããã«çããã; int2 & fact2 -> int3: ãã®ãŽããŽãLv.53ã¯éçœããªã;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact3 -> int2: ({A}{a} & {C}{a}); int2 & fact2 -> int3: ¬{D}{b};"
] | null | null | [] | null | 5 | 5 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãŸã«ããŸã«ãLv.59ã¯åãæããåšå§ãã fact2: ä»®ã«ãã®ãŸã«ããŸã«ãLv.59ãåãæããçããããšããããã®ãŽããŽãLv.53ã¯éçœããªã fact3: ããã®ãŸã«ããŸã«ãLv.59ã¯çãããããšããããšã¯çå®ã§ãã fact4: ãããã®ãŽããŽãLv.53ãéçœããšããããšã¯ãªãäžæ¹ã§çãç«ã€ãšããããã®ã¿ã«ãã¿ãLv.55ã¯çµå©åºæ¥ã ; $hypothesis$ = ãã®ã¿ã«ãã¿ãLv.55ã¯çµå©åºæ¥ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: ({A}{a} & {C}{a}) -> ¬{D}{b} fact3: {C}{a} fact4: (¬{D}{b} & {F}{b}) -> {E}{c} ; $hypothesis$ = ¬{E}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã¿ã«ãã¿ã®Lv.12ã¯é£çšããªãããããå§çž®åºæ¥ããšããããšã¯ãªãããšããããšã¯èª€ãã§ãã | ¬(¬{A}{b} & ¬{D}{b}) | fact1: ãããã®ã¿ã«ãã¿ã®Lv.12ã責ãããšãããšãã®ã¿ã«ãã¿ã®Lv.12ã¯åŸ¡èŠ§é ããªãããããã¯æžãé£ãããããã¯äž¡æ¹ã fact2: ä»®ã«ãã®ã¿ã«ãã¿ã®Lv.12ã¯é£çšããªããšãããšããã®ãã«ãããLv.94ã¯é£çšããªãããã€å§çž®åºæ¥ãªãããšããããšã¯ééãã fact3: ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã埡芧é ããªãããããã¯ãããæžãé£ããšãããåãæµã fact4: ä»®ã«ãã®ãã«ãããLv.94ã¯é£çšããªããªãã°ããã®ã¿ã«ãã¿ã®Lv.12ã¯é£çšããªãããã®äžå§çž®åºæ¥ãªãããšããããšã¯èª€ã£ãŠãã fact5: ããããã®ãã«ãããLv.94ã¯æŽ»åãæããªãããšããããšã¯ééãã§ãªããšããã°ãã®ãã«ãããLv.94ã¯é²åããªãããã©è²¬ãã fact6: ãã®ãã«ãããLv.94ã¯åãæµããªã | fact1: {F}{b} -> (¬{E}{b} v {C}{b}) fact2: ¬{A}{b} -> ¬(¬{A}{a} & ¬{D}{a}) fact3: (x): (¬{E}x v {C}x) -> {B}x fact4: ¬{A}{a} -> ¬(¬{A}{b} & ¬{D}{b}) fact5: ¬{G}{a} -> (¬{H}{a} & {F}{a}) fact6: ¬{B}{a} | [] | [] | ãã®ã¿ã«ãã¿ã®Lv.12ã¯é£çšããªããŠå§çž®åºæ¥ãªã | (¬{A}{b} & ¬{D}{b}) | [
"fact9 -> int1: ããä»®ã«ãã®ã¿ã«ãã¿ã®Lv.12ã埡芧é ããªãããããã¯ãããæžãé£ãããããã¯ã©ã¡ããã ãšããããã®ã¿ã«ãã¿ã®Lv.12ã¯åãæµã;"
] | 6 | 5 | 4 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®ã¿ã«ãã¿ã®Lv.12ã責ãããšãããšãã®ã¿ã«ãã¿ã®Lv.12ã¯åŸ¡èŠ§é ããªãããããã¯æžãé£ãããããã¯äž¡æ¹ã fact2: ä»®ã«ãã®ã¿ã«ãã¿ã®Lv.12ã¯é£çšããªããšãããšããã®ãã«ãããLv.94ã¯é£çšããªãããã€å§çž®åºæ¥ãªãããšããããšã¯ééãã fact3: ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã埡芧é ããªãããããã¯ãããæžãé£ããšãããåãæµã fact4: ä»®ã«ãã®ãã«ãããLv.94ã¯é£çšããªããªãã°ããã®ã¿ã«ãã¿ã®Lv.12ã¯é£çšããªãããã®äžå§çž®åºæ¥ãªãããšããããšã¯èª€ã£ãŠãã fact5: ããããã®ãã«ãããLv.94ã¯æŽ»åãæããªãããšããããšã¯ééãã§ãªããšããã°ãã®ãã«ãããLv.94ã¯é²åããªãããã©è²¬ãã fact6: ãã®ãã«ãããLv.94ã¯åãæµããªã ; $hypothesis$ = ããã®ã¿ã«ãã¿ã®Lv.12ã¯é£çšããªãããããå§çž®åºæ¥ããšããããšã¯ãªãããšããããšã¯èª€ãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {F}{b} -> (¬{E}{b} v {C}{b}) fact2: ¬{A}{b} -> ¬(¬{A}{a} & ¬{D}{a}) fact3: (x): (¬{E}x v {C}x) -> {B}x fact4: ¬{A}{a} -> ¬(¬{A}{b} & ¬{D}{b}) fact5: ¬{G}{a} -> (¬{H}{a} & {F}{a}) fact6: ¬{B}{a} ; $hypothesis$ = ¬(¬{A}{b} & ¬{D}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ããããLv.30ãã§ããããã®äžããã¯éšããæãããšããããšã¯ééãã | ¬({E}{b} & {G}{b}) | fact1: ããããã®ãœããœã¡ãLv.10ãã§ãããªããšããããã®ããããLv.30ã¯ã§ãããããã«éšããæã fact2: ä»®ã«ãã®ãœããœã¡ãLv.10ãå¹ãããªããäžçªãããªãããããã¯ã©ã¡ããã ãšããã°ãã®ããããLv.30ã¯äžçªãããªã fact3: ããä»®ã«ãã®ãœããœã¡ãLv.10ã枬ãé£ããšããããã®ãœããœã¡ãLv.10ã¯äžçªããã fact4: ãã®ããããLv.30ã¯éšããæã fact5: ãã®ãœããœã¡ãLv.10ã¯æœè¡ãã fact6: ããä»®ã«ãã®ãœããœã¡ãLv.10ãäžçªããããå¹ãããªããã®ãœããœã¡ãLv.10ã¯ã§ãããªã fact7: ãã®ãœããœã¡ãLv.10ã¯æœè¡ãããšãããã枬ãé£ãããšããããšã¯æãç«ã€ fact8: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯æœè¡ããªããšããã°ãã§ãããããŸãã«éšããæãããšããããšã¯äºå®ãšç°ãªã fact9: ããä»®ã«ãã®ããããLv.30ãå¹ãããªããªããã®ãœããœã¡ãLv.10ã¯å¹ãã fact10: ãã®ãœããœã¡ãLv.10ã¯å¹ãã | fact1: ¬{E}{a} -> ({E}{b} & {G}{b}) fact2: (¬{D}{a} v ¬{C}{a}) -> ¬{C}{b} fact3: {B}{a} -> {C}{a} fact4: {G}{b} fact5: {A}{a} fact6: ({C}{a} & {D}{a}) -> ¬{E}{a} fact7: {A}{a} -> {B}{a} fact8: (x): ¬{A}x -> ¬({E}x & {G}x) fact9: ¬{D}{b} -> {D}{a} fact10: {D}{a} | [
"fact7 & fact5 -> int1: ãã®ãœããœã¡ãLv.10ã¯æž¬ãé£ã; int1 & fact3 -> int2: ãã®ãœããœã¡ãLv.10ã¯äžçªããã; int2 & fact10 -> int3: ãã®ãœããœã¡ãLv.10ã¯äžçªããããããŸãã«ããã¯å¹ãã; int3 & fact6 -> int4: ãã®ãœããœã¡ãLv.10ã¯ã§ãããªã; int4 & fact1 -> hypothesis;"
] | [
"fact7 & fact5 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{a}; int2 & fact10 -> int3: ({C}{a} & {D}{a}); int3 & fact6 -> int4: ¬{E}{a}; int4 & fact1 -> hypothesis;"
] | ããã®ããããLv.30ãã§ããããã®äžããã¯éšããæãããšããããšã¯ééãã | ¬({E}{b} & {G}{b}) | [
"fact12 -> int5: ããããã®ããããLv.30ã¯æœè¡ããªãããšããããšã¯æãç«ã€ãªããã§ãããŠããã¯éšããæãããšããããšã¯èª€ãã§ãã;"
] | 5 | 5 | 5 | 5 | 5 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããã®ãœããœã¡ãLv.10ãã§ãããªããšããããã®ããããLv.30ã¯ã§ãããããã«éšããæã fact2: ä»®ã«ãã®ãœããœã¡ãLv.10ãå¹ãããªããäžçªãããªãããããã¯ã©ã¡ããã ãšããã°ãã®ããããLv.30ã¯äžçªãããªã fact3: ããä»®ã«ãã®ãœããœã¡ãLv.10ã枬ãé£ããšããããã®ãœããœã¡ãLv.10ã¯äžçªããã fact4: ãã®ããããLv.30ã¯éšããæã fact5: ãã®ãœããœã¡ãLv.10ã¯æœè¡ãã fact6: ããä»®ã«ãã®ãœããœã¡ãLv.10ãäžçªããããå¹ãããªããã®ãœããœã¡ãLv.10ã¯ã§ãããªã fact7: ãã®ãœããœã¡ãLv.10ã¯æœè¡ãããšãããã枬ãé£ãããšããããšã¯æãç«ã€ fact8: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯æœè¡ããªããšããã°ãã§ãããããŸãã«éšããæãããšããããšã¯äºå®ãšç°ãªã fact9: ããä»®ã«ãã®ããããLv.30ãå¹ãããªããªããã®ãœããœã¡ãLv.10ã¯å¹ãã fact10: ãã®ãœããœã¡ãLv.10ã¯å¹ãã ; $hypothesis$ = ããã®ããããLv.30ãã§ããããã®äžããã¯éšããæãããšããããšã¯ééãã ; $proof$ = | fact7 & fact5 -> int1: ãã®ãœããœã¡ãLv.10ã¯æž¬ãé£ã; int1 & fact3 -> int2: ãã®ãœããœã¡ãLv.10ã¯äžçªããã; int2 & fact10 -> int3: ãã®ãœããœã¡ãLv.10ã¯äžçªããããããŸãã«ããã¯å¹ãã; int3 & fact6 -> int4: ãã®ãœããœã¡ãLv.10ã¯ã§ãããªã; int4 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{E}{a} -> ({E}{b} & {G}{b}) fact2: (¬{D}{a} v ¬{C}{a}) -> ¬{C}{b} fact3: {B}{a} -> {C}{a} fact4: {G}{b} fact5: {A}{a} fact6: ({C}{a} & {D}{a}) -> ¬{E}{a} fact7: {A}{a} -> {B}{a} fact8: (x): ¬{A}x -> ¬({E}x & {G}x) fact9: ¬{D}{b} -> {D}{a} fact10: {D}{a} ; $hypothesis$ = ¬({E}{b} & {G}{b}) ; $proof$ = | fact7 & fact5 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{a}; int2 & fact10 -> int3: ({C}{a} & {D}{a}); int3 & fact6 -> int4: ¬{E}{a}; int4 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŸããŸãªLv.42ã¯æ¶ååžåããæããããã¯æãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã ããšããããšã¯åœã | ¬({A}{a} v ¬{C}{a}) | fact1: ãã®ãŸããŸãªLv.42ã¯æ¶ååžåããæãããã€åŸããé£ã fact2: ãã®ã·ãã·ã¡ãLv.22ã¯èŠåæ£ãããªããšããã°ããã®ãŸããŸãªLv.42ã¯åäžãããããã¯ãããããšããããšã¯æ£ãã fact3: ãã®ãŸããŸãªLv.42ã¯åããåŸããé£ã fact4: ããããªãããã®ã¢ã³ã¹ã¿ãŒãåäžãããªãåŸããé£ã fact5: ãã®ãŽããŽãLv.22ã¯æ±ãèµ·ããããããã¯ãããšããªã | fact1: ({A}{a} & {B}{a}) fact2: ¬{F}{b} -> ({D}{a} & {E}{a}) fact3: ({EQ}{a} & {B}{a}) fact4: (x): {D}x -> {B}x fact5: ({DU}{fa} v ¬{HL}{fa}) | [
"fact1 -> int1: ãã®ãŸããŸãªLv.42ã¯æ¶ååžåããæã; int1 -> hypothesis;"
] | [
"fact1 -> int1: {A}{a}; int1 -> hypothesis;"
] | ããã®ãŸããŸãªLv.42ã¯æ¶ååžåããæããããã¯æãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã ããšããããšã¯åœã | ¬({A}{a} v ¬{C}{a}) | [
"fact7 -> int2: ä»®ã«ãã®ãŸããŸãªLv.42ãåäžãããšãããããã¯åŸããé£ã;"
] | 5 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŸããŸãªLv.42ã¯æ¶ååžåããæãããã€åŸããé£ã fact2: ãã®ã·ãã·ã¡ãLv.22ã¯èŠåæ£ãããªããšããã°ããã®ãŸããŸãªLv.42ã¯åäžãããããã¯ãããããšããããšã¯æ£ãã fact3: ãã®ãŸããŸãªLv.42ã¯åããåŸããé£ã fact4: ããããªãããã®ã¢ã³ã¹ã¿ãŒãåäžãããªãåŸããé£ã fact5: ãã®ãŽããŽãLv.22ã¯æ±ãèµ·ããããããã¯ãããšããªã ; $hypothesis$ = ããã®ãŸããŸãªLv.42ã¯æ¶ååžåããæããããã¯æãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã ããšããããšã¯åœã ; $proof$ = | fact1 -> int1: ãã®ãŸããŸãªLv.42ã¯æ¶ååžåããæã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: ¬{F}{b} -> ({D}{a} & {E}{a}) fact3: ({EQ}{a} & {B}{a}) fact4: (x): {D}x -> {B}x fact5: ({DU}{fa} v ¬{HL}{fa}) ; $hypothesis$ = ¬({A}{a} v ¬{C}{a}) ; $proof$ = | fact1 -> int1: {A}{a}; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãã«ããã¡ã
Lv.78ã¯æµ®ãæããªã | ¬{D}{c} | fact1: ä»®ã«ãã®ãŸã«ããŸãLv.39ã¯åãå
¥ãæããšãããããã®ãã«ããã¡ã
Lv.78ã¯æµ®ãæãããšããããšã¯æ¬åœã fact2: ããã®ãŸã«ããŸãLv.39ã¯åãŒã£ããããšããããšã¯æãç«ã€ fact3: ããä»®ã«ãã®ãã«ããã«ã
Lv.11ãèµ·ããæããçã
ãããªããªããã®ã·ã®ã·ãLv.94ã¯å¹
åºã fact4: ããããã®ãŸã«ããŸãLv.39ãæãŠãç¡ããªããã®ãŸã«ããŸãLv.39ã¯èµ·ããæã fact5: ãã®ã·ã®ã·ãLv.94ãåãŒã£ãããªãã°ãã®ãŸã«ããŸãLv.39ã¯åãå
¥ãæã fact6: ãã®ãã«ããã«ã
Lv.11ã¯èµ·ããæãäžæ¹ã§çã
ãããšããããšã¯ãªã fact7: ãããã®ã·ã®ã·ãLv.94ãå¹
åºããšãããåãŒã£ãã | fact1: {C}{b} -> {D}{c} fact2: {B}{b} fact3: ({E}{d} & ¬{F}{d}) -> {A}{a} fact4: {DM}{b} -> {E}{b} fact5: {B}{a} -> {C}{b} fact6: ({E}{d} & ¬{F}{d}) fact7: {A}{a} -> {B}{a} | [
"fact3 & fact6 -> int1: ãã®ã·ã®ã·ãLv.94ã¯å¹
åºã; fact7 & int1 -> int2: ãã®ã·ã®ã·ãLv.94ã¯åãŒã£ãã; int2 & fact5 -> int3: ãã®ãŸã«ããŸãLv.39ã¯åãå
¥ãæã; int3 & fact1 -> hypothesis;"
] | [
"fact3 & fact6 -> int1: {A}{a}; fact7 & int1 -> int2: {B}{a}; int2 & fact5 -> int3: {C}{b}; int3 & fact1 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ä»®ã«ãã®ãŸã«ããŸãLv.39ã¯åãå
¥ãæããšãããããã®ãã«ããã¡ã
Lv.78ã¯æµ®ãæãããšããããšã¯æ¬åœã fact2: ããã®ãŸã«ããŸãLv.39ã¯åãŒã£ããããšããããšã¯æãç«ã€ fact3: ããä»®ã«ãã®ãã«ããã«ã
Lv.11ãèµ·ããæããçã
ãããªããªããã®ã·ã®ã·ãLv.94ã¯å¹
åºã fact4: ããããã®ãŸã«ããŸãLv.39ãæãŠãç¡ããªããã®ãŸã«ããŸãLv.39ã¯èµ·ããæã fact5: ãã®ã·ã®ã·ãLv.94ãåãŒã£ãããªãã°ãã®ãŸã«ããŸãLv.39ã¯åãå
¥ãæã fact6: ãã®ãã«ããã«ã
Lv.11ã¯èµ·ããæãäžæ¹ã§çã
ãããšããããšã¯ãªã fact7: ãããã®ã·ã®ã·ãLv.94ãå¹
åºããšãããåãŒã£ãã ; $hypothesis$ = ãã®ãã«ããã¡ã
Lv.78ã¯æµ®ãæããªã ; $proof$ = | fact3 & fact6 -> int1: ãã®ã·ã®ã·ãLv.94ã¯å¹
åºã; fact7 & int1 -> int2: ãã®ã·ã®ã·ãLv.94ã¯åãŒã£ãã; int2 & fact5 -> int3: ãã®ãŸã«ããŸãLv.39ã¯åãå
¥ãæã; int3 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{b} -> {D}{c} fact2: {B}{b} fact3: ({E}{d} & ¬{F}{d}) -> {A}{a} fact4: {DM}{b} -> {E}{b} fact5: {B}{a} -> {C}{b} fact6: ({E}{d} & ¬{F}{d}) fact7: {A}{a} -> {B}{a} ; $hypothesis$ = ¬{D}{c} ; $proof$ = | fact3 & fact6 -> int1: {A}{a}; fact7 & int1 -> int2: {B}{a}; int2 & fact5 -> int3: {C}{b}; int3 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããããLv.21äºä»¶ãšç©ºãããšããããšãèµ·ãã | ({A} & {B}) | fact1: ããããŽã®ãŽãLv.85äºä»¶ã¯çºçããªããšãããããããããLv.21äºä»¶ãšç©ºãããšããããšäž¡æ¹ãšããçããããšããããšã¯æãç«ã€ããšããããšã¯èª€ãã fact2: 空ãããšããããšãèµ·ãã fact3: ãã€ãããšããããšãèµ·ãã fact4: ããã貧ãããšããããšããããã¯ãŽããŽã«Lv.37äºä»¶ããããã¯ã©ã¡ãããçããããšããããšã¯æãç«ããªããªãã°ãŽã®ãŽãLv.85äºä»¶ã¯èµ·ãããªã fact5: ã·ãã·ãLv.98äºä»¶ã¯çºçããããœããœãLv.9äºä»¶ã¯çºçãã fact6: ãã®ããLv.82äºä»¶ãšèŸ¿ãå§ããããšäž¡æ¹ãšããèµ·ãã | fact1: ¬{C} -> ¬({A} & {B}) fact2: {B} fact3: {EC} fact4: ¬({E} v {D}) -> ¬{C} fact5: ({FK} & {IF}) fact6: ({N} & {T}) | [] | [] | ãããããLv.21äºä»¶ããã³ç©ºãããšããããšãçããããšããããšã¯ééãã | ¬({A} & {B}) | [] | 7 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããŽã®ãŽãLv.85äºä»¶ã¯çºçããªããšãããããããããLv.21äºä»¶ãšç©ºãããšããããšäž¡æ¹ãšããçããããšããããšã¯æãç«ã€ããšããããšã¯èª€ãã fact2: 空ãããšããããšãèµ·ãã fact3: ãã€ãããšããããšãèµ·ãã fact4: ããã貧ãããšããããšããããã¯ãŽããŽã«Lv.37äºä»¶ããããã¯ã©ã¡ãããçããããšããããšã¯æãç«ããªããªãã°ãŽã®ãŽãLv.85äºä»¶ã¯èµ·ãããªã fact5: ã·ãã·ãLv.98äºä»¶ã¯çºçããããœããœãLv.9äºä»¶ã¯çºçãã fact6: ãã®ããLv.82äºä»¶ãšèŸ¿ãå§ããããšäž¡æ¹ãšããèµ·ãã ; $hypothesis$ = ããããLv.21äºä»¶ãšç©ºãããšããããšãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{C} -> ¬({A} & {B}) fact2: {B} fact3: {EC} fact4: ¬({E} v {D}) -> ¬{C} fact5: ({FK} & {IF}) fact6: ({N} & {T}) ; $hypothesis$ = ({A} & {B}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãŽããŽã«ã
Lv.76äºä»¶ãèµ·ãã | {C} | fact1: ãããééç¡ããšããããšãçºçãããæŽã«çšè¿ããšããããšãçãããšãããšãŽããŽã«ã
Lv.76äºä»¶ã¯çºçããªã fact2: æä¹³ããããšã¯çããªã fact3: ãçšè¿ããšããããšãçºçããããšããããšã¯äºå®ã fact4: ééç¡ããšããããšãçºçãã fact5: ãŽããŽã«ã
Lv.76äºä»¶ãšééç¡ããšããããšãèµ·ããã¯ãçšè¿ããšããããšã¯èµ·ããªãããšããããšã«åŒãèµ·ãããã fact6: æã£ãããšããããšã¯çºçããªã | fact1: ({A} & {B}) -> ¬{C} fact2: ¬{FM} fact3: {B} fact4: {A} fact5: ¬{B} -> ({C} & {A}) fact6: ¬{CA} | [
"fact4 & fact3 -> int1: ééç¡ããšããããšãšçšè¿ããšããããšãçãã; int1 & fact1 -> hypothesis;"
] | [
"fact4 & fact3 -> int1: ({A} & {B}); int1 & fact1 -> hypothesis;"
] | ãŽããŽã«ã
Lv.76äºä»¶ãèµ·ãã | {C} | [] | 6 | 2 | 2 | 2 | 2 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããééç¡ããšããããšãçºçãããæŽã«çšè¿ããšããããšãçãããšãããšãŽããŽã«ã
Lv.76äºä»¶ã¯çºçããªã fact2: æä¹³ããããšã¯çããªã fact3: ãçšè¿ããšããããšãçºçããããšããããšã¯äºå®ã fact4: ééç¡ããšããããšãçºçãã fact5: ãŽããŽã«ã
Lv.76äºä»¶ãšééç¡ããšããããšãèµ·ããã¯ãçšè¿ããšããããšã¯èµ·ããªãããšããããšã«åŒãèµ·ãããã fact6: æã£ãããšããããšã¯çºçããªã ; $hypothesis$ = ãŽããŽã«ã
Lv.76äºä»¶ãèµ·ãã ; $proof$ = | fact4 & fact3 -> int1: ééç¡ããšããããšãšçšè¿ããšããããšãçãã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} & {B}) -> ¬{C} fact2: ¬{FM} fact3: {B} fact4: {A} fact5: ¬{B} -> ({C} & {A}) fact6: ¬{CA} ; $hypothesis$ = {C} ; $proof$ = | fact4 & fact3 -> int1: ({A} & {B}); int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | 女ã®åããããšããããšãèµ·ãã | {G} | fact1: ãè¡šçŸãé£ããšããããšã¯èµ·ããªãããã©ã·ãã·ã«ãLv.32äºä»¶ãçºçããããšããããšã¯æãç«ããªããªãã°å¥³ã®åããããšããããšãçãã fact2: ä»®ã«ãæ¯èŠªããããšããããšã¯çºçããªãããšããããšã¯åã§ãªããªãã°ãè¡šçŸãé£ããšããããšã¯çºçããªãããã©ã·ãã·ã«ãLv.32äºä»¶ãèµ·ããããšããããšã¯èª€ãã§ãã fact3: æ¯èŠªããããšããããšã¯ãçšå¿æ·±ããšããããšãèµ·ãããããã«çµ±çåºæ¥ãããšãçããããšããããšã«é²ããã fact4: èŠã
ãããšããããšãèµ·ãã fact5: çšå¿æ·±ããšããããšãèµ·ãã fact6: èŠã
ãããšããããšãèµ·ãããšããããšã¯çµ±çåºæ¥ãããšã¯èµ·ãããªããšããããšãåé¿ãã | fact1: ¬(¬{F} & {E}) -> {G} fact2: ¬{D} -> ¬(¬{F} & {E}) fact3: ({C} & {B}) -> ¬{D} fact4: {A} fact5: {C} fact6: {A} -> {B} | [
"fact6 & fact4 -> int1: çµ±çåºæ¥ãããšãçºçãã; int1 & fact5 -> int2: çšå¿æ·±ããšããããšãèµ·ãããçµ±çåºæ¥ãããšãèµ·ãã; int2 & fact3 -> int3: æ¯èŠªããããšããããšã¯çºçããªã; int3 & fact2 -> int4: ãè¡šçŸãé£ããšããããšã§ã¯ãªããŠã·ãã·ã«ãLv.32äºä»¶ãçããããšããããšã¯æãç«ããªã; int4 & fact1 -> hypothesis;"
] | [
"fact6 & fact4 -> int1: {B}; int1 & fact5 -> int2: ({C} & {B}); int2 & fact3 -> int3: ¬{D}; int3 & fact2 -> int4: ¬(¬{F} & {E}); int4 & fact1 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãè¡šçŸãé£ããšããããšã¯èµ·ããªãããã©ã·ãã·ã«ãLv.32äºä»¶ãçºçããããšããããšã¯æãç«ããªããªãã°å¥³ã®åããããšããããšãçãã fact2: ä»®ã«ãæ¯èŠªããããšããããšã¯çºçããªãããšããããšã¯åã§ãªããªãã°ãè¡šçŸãé£ããšããããšã¯çºçããªãããã©ã·ãã·ã«ãLv.32äºä»¶ãèµ·ããããšããããšã¯èª€ãã§ãã fact3: æ¯èŠªããããšããããšã¯ãçšå¿æ·±ããšããããšãèµ·ãããããã«çµ±çåºæ¥ãããšãçããããšããããšã«é²ããã fact4: èŠã
ãããšããããšãèµ·ãã fact5: çšå¿æ·±ããšããããšãèµ·ãã fact6: èŠã
ãããšããããšãèµ·ãããšããããšã¯çµ±çåºæ¥ãããšã¯èµ·ãããªããšããããšãåé¿ãã ; $hypothesis$ = 女ã®åããããšããããšãèµ·ãã ; $proof$ = | fact6 & fact4 -> int1: çµ±çåºæ¥ãããšãçºçãã; int1 & fact5 -> int2: çšå¿æ·±ããšããããšãèµ·ãããçµ±çåºæ¥ãããšãèµ·ãã; int2 & fact3 -> int3: æ¯èŠªããããšããããšã¯çºçããªã; int3 & fact2 -> int4: ãè¡šçŸãé£ããšããããšã§ã¯ãªããŠã·ãã·ã«ãLv.32äºä»¶ãçããããšããããšã¯æãç«ããªã; int4 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬(¬{F} & {E}) -> {G} fact2: ¬{D} -> ¬(¬{F} & {E}) fact3: ({C} & {B}) -> ¬{D} fact4: {A} fact5: {C} fact6: {A} -> {B} ; $hypothesis$ = {G} ; $proof$ = | fact6 & fact4 -> int1: {B}; int1 & fact5 -> int2: ({C} & {B}); int2 & fact3 -> int3: ¬{D}; int3 & fact2 -> int4: ¬(¬{F} & {E}); int4 & fact1 -> hypothesis; __PROVED__ |
0.3 | ããœããœã®Lv.63äºä»¶ãçºçããããŸãã¯æ²¹éãããããšã¯çºçããããšããããšã¯äºå®ã§ãªã | ¬({A} v {B}) | fact1: ããä»®ã«çŽå€±ããããšã¯èµ·ãããªããªããèŠæ¥µãé£ããšããããšããããã¯ã·ã«ãã·ãLv.63äºä»¶ãã©ã¡ãããçããããšããããšã¯æãç«ã€ fact2: ããœããœã®Lv.63äºä»¶ãèµ·ããªãããŸãã¯æ²¹éãããããšã¯èµ·ãããªãããšããããšã¯ãèãæ·±ããšããããšãçºçããããšããããšã«èµ·å ãã fact3: ãç©ãé£ããšããããšã¯èµ·ãããªãããšããããšã¯äºå®ã fact4: ããœããœã®Lv.63äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ãªããç©ãé£ããšããããšã¯èµ·ããªããã©ã¿ãã¿ãLv.51äºä»¶ãçºçããããšããããšã¯æãç«ã€ fact5: ããèãæ·±ããšããããšã¯çããªããšãããšããœããœã®Lv.63äºä»¶ãèµ·ããããããã¯æ²¹éãããããšãèµ·ããããããã¯äž¡æ¹ãšãã ããšããããšã¯åã fact6: ãç©ãé£ããšããããšã¯çããªãããããã¿ãã¿ãLv.51äºä»¶ãçããããšããããšã¯æãç«ããªã fact7: ãèŠæ¥µãé£ããšããããšãçããããšããããšã¯ãã·ã«ãã·ãLv.63äºä»¶ã¯çºçããªããæŽã«èãæ·±ããšããããšã¯èµ·ããªãããšããããšã®ãã£ãããšãªã | fact1: ¬{F} -> ({E} v {D}) fact2: {C} -> (¬{A} v ¬{B}) fact3: ¬{AA} fact4: ¬{A} -> (¬{AA} & {AB}) fact5: ¬{C} -> ¬({A} v {B}) fact6: ¬(¬{AA} & {AB}) fact7: {E} -> (¬{D} & ¬{C}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããœããœã®Lv.63äºä»¶ã¯çºçããªã; fact4 & assump1 -> int1: ç©ãé£ããšããããšã¯çããªãããã©ã¿ãã¿ãLv.51äºä»¶ãçãã; int1 & fact6 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãœããœã®Lv.63äºä»¶ãèµ·ãã; int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}; fact4 & assump1 -> int1: (¬{AA} & {AB}); int1 & fact6 -> int2: #F#; [assump1] & int2 -> int3: {A}; int3 -> hypothesis;"
] | çãæããšããããšã¯èµ·ããªããããããŸããŸãLv.54äºä»¶ãçºçãã | (¬{BM} & {DT}) | [] | 6 | 5 | 4 | 5 | 4 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«çŽå€±ããããšã¯èµ·ãããªããªããèŠæ¥µãé£ããšããããšããããã¯ã·ã«ãã·ãLv.63äºä»¶ãã©ã¡ãããçããããšããããšã¯æãç«ã€ fact2: ããœããœã®Lv.63äºä»¶ãèµ·ããªãããŸãã¯æ²¹éãããããšã¯èµ·ãããªãããšããããšã¯ãèãæ·±ããšããããšãçºçããããšããããšã«èµ·å ãã fact3: ãç©ãé£ããšããããšã¯èµ·ãããªãããšããããšã¯äºå®ã fact4: ããœããœã®Lv.63äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ãªããç©ãé£ããšããããšã¯èµ·ããªããã©ã¿ãã¿ãLv.51äºä»¶ãçºçããããšããããšã¯æãç«ã€ fact5: ããèãæ·±ããšããããšã¯çããªããšãããšããœããœã®Lv.63äºä»¶ãèµ·ããããããã¯æ²¹éãããããšãèµ·ããããããã¯äž¡æ¹ãšãã ããšããããšã¯åã fact6: ãç©ãé£ããšããããšã¯çããªãããããã¿ãã¿ãLv.51äºä»¶ãçããããšããããšã¯æãç«ããªã fact7: ãèŠæ¥µãé£ããšããããšãçããããšããããšã¯ãã·ã«ãã·ãLv.63äºä»¶ã¯çºçããªããæŽã«èãæ·±ããšããããšã¯èµ·ããªãããšããããšã®ãã£ãããšãªã ; $hypothesis$ = ããœããœã®Lv.63äºä»¶ãçºçããããŸãã¯æ²¹éãããããšã¯çºçããããšããããšã¯äºå®ã§ãªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããœããœã®Lv.63äºä»¶ã¯çºçããªã; fact4 & assump1 -> int1: ç©ãé£ããšããããšã¯çããªãããã©ã¿ãã¿ãLv.51äºä»¶ãçãã; int1 & fact6 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãœããœã®Lv.63äºä»¶ãèµ·ãã; int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{F} -> ({E} v {D}) fact2: {C} -> (¬{A} v ¬{B}) fact3: ¬{AA} fact4: ¬{A} -> (¬{AA} & {AB}) fact5: ¬{C} -> ¬({A} v {B}) fact6: ¬(¬{AA} & {AB}) fact7: {E} -> (¬{D} & ¬{C}) ; $hypothesis$ = ¬({A} v {B}) ; $proof$ = | void -> assump1: ¬{A}; fact4 & assump1 -> int1: (¬{AA} & {AB}); int1 & fact6 -> int2: #F#; [assump1] & int2 -> int3: {A}; int3 -> hypothesis; __DISPROVED__ |
0.3 | çèŠãããšããããšãçãã | {A} | fact1: ãå¿ãããšããããšã¯çºçããªãããšããããšã¯çèŠãããšããããšããã³ãœããœã®Lv.60äºä»¶ãçããã®ãã£ãããšãªã fact2: ããä»®ã«ããèµ·ããé£ããšããããšãèµ·ããããããã¯èŠä»ãé£ããšããããšã¯èµ·ãããªãããããã¯äž¡æ¹ãšãã ããšããããšã¯æãç«ã€ããšããããšã¯åã§ãããšãããšçèŠãããšããããšã¯èµ·ããªã fact3: ãæã¡ããŸãããšãèµ·ããããœããœãLv.49äºä»¶ã¯çºçããªãããšããããšã¯äºå®ãšç°ãªã fact4: ããœããœã®Lv.60äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ | fact1: ¬{C} -> ({A} & {B}) fact2: ¬({AA} v ¬{AB}) -> ¬{A} fact3: ¬({U} v ¬{GF}) fact4: ¬{B} | [] | [] | çèŠãããšããããšãçãã | {A} | [] | 6 | 5 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãå¿ãããšããããšã¯çºçããªãããšããããšã¯çèŠãããšããããšããã³ãœããœã®Lv.60äºä»¶ãçããã®ãã£ãããšãªã fact2: ããä»®ã«ããèµ·ããé£ããšããããšãèµ·ããããããã¯èŠä»ãé£ããšããããšã¯èµ·ãããªãããããã¯äž¡æ¹ãšãã ããšããããšã¯æãç«ã€ããšããããšã¯åã§ãããšãããšçèŠãããšããããšã¯èµ·ããªã fact3: ãæã¡ããŸãããšãèµ·ããããœããœãLv.49äºä»¶ã¯çºçããªãããšããããšã¯äºå®ãšç°ãªã fact4: ããœããœã®Lv.60äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ ; $hypothesis$ = çèŠãããšããããšãçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{C} -> ({A} & {B}) fact2: ¬({AA} v ¬{AB}) -> ¬{A} fact3: ¬({U} v ¬{GF}) fact4: ¬{B} ; $hypothesis$ = {A} ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã¿ã«ãã¿ãLv.23ã¯ééç¡ã | {A}{aa} | fact1: ãã®ãŸããŸã«ãLv.95ã¯è»œã
ãã fact2: äœããã®ã¢ã³ã¹ã¿ãŒãééç¡ããšãããããã¯è»œã
ãã fact3: ãã®ã¿ã«ãã¿ãLv.23ã¯è»œã
ãããªã | fact1: {C}{bm} fact2: (x): {A}x -> {C}x fact3: ¬{C}{aa} | [
"fact2 -> int1: ãã®ã¿ã«ãã¿ãLv.23ãééç¡ããšãããããã¯è»œã
ãã; void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ã«ãã¿ãLv.23ã¯ééç¡ã; int1 & assump1 -> int2: ãã®ã¿ã«ãã¿ãLv.23ã¯è»œã
ãã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"fact2 -> int1: {A}{aa} -> {C}{aa}; void -> assump1: {A}{aa}; int1 & assump1 -> int2: {C}{aa}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ãŸããŸã«ãLv.95ã¯è»œã
ãã fact2: äœããã®ã¢ã³ã¹ã¿ãŒãééç¡ããšãããããã¯è»œã
ãã fact3: ãã®ã¿ã«ãã¿ãLv.23ã¯è»œã
ãããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã¿ã«ãã¿ãLv.23ã¯ééç¡ã ; $proof$ = | fact2 -> int1: ãã®ã¿ã«ãã¿ãLv.23ãééç¡ããšãããããã¯è»œã
ãã; void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ã«ãã¿ãLv.23ã¯ééç¡ã; int1 & assump1 -> int2: ãã®ã¿ã«ãã¿ãLv.23ã¯è»œã
ãã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{bm} fact2: (x): {A}x -> {C}x fact3: ¬{C}{aa} ; $hypothesis$ = {A}{aa} ; $proof$ = | fact2 -> int1: {A}{aa} -> {C}{aa}; void -> assump1: {A}{aa}; int1 & assump1 -> int2: {C}{aa}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãŸããŸã¡ã
Lv.88äºä»¶ã¯çããªããŠããã«åæ°ãªããšããããšã¯èµ·ãããªã | (¬{C} & ¬{D}) | fact1: ããä»®ã«ç¶æã»åäžããããšã¯èµ·ãããªããªãããŸããŸã¡ã
Lv.88äºä»¶ã¯çããªãããããåæ°ãªããšããããšã¯çããªãããšããããšã¯åœã§ãã fact2: ä»®ã«ãç
©ããããšããããšã¯çããªãããšããããšã¯æãç«ã€ãªããç¶æã»åäžããããšããã³ã¿ã«ã¿ã¡ãLv.57äºä»¶ã©ã¡ãããèµ·ããããšããããšã¯ééãã§ãã fact3: ãŸããŸã¡ã
Lv.88äºä»¶ã¯ãç¶æã»åäžããããšãšã¿ã«ã¿ã¡ãLv.57äºä»¶äž¡æ¹ãšããèµ·ããããšããããšã«é»ãŸãã fact4: åæ°ãªããšããããšã¯çºçããªã fact5: ã¿ã«ã¿ã¡ãLv.57äºä»¶ãèµ·ãã fact6: ç
©ããããšããããšãèµ·ããããã€ç¶æã»åäžããããšãèµ·ãã fact7: ç
©ããããšããããšãèµ·ãã fact8: åäŸããããšããããšãèµ·ããããã€æé
·ããšããããšãçãã | fact1: ¬{A} -> ¬(¬{C} & ¬{D}) fact2: ¬{E} -> ¬({A} & {B}) fact3: ({A} & {B}) -> ¬{C} fact4: ¬{D} fact5: {B} fact6: ({E} & {A}) fact7: {E} fact8: ({AP} & {EK}) | [
"fact6 -> int1: ç¶æã»åäžããããšãèµ·ãã; int1 & fact5 -> int2: ç¶æã»åäžããããšãèµ·ãããã¿ã«ã¿ã¡ãLv.57äºä»¶ãèµ·ãã; int2 & fact3 -> int3: ããŸããŸã¡ã
Lv.88äºä»¶ã¯èµ·ããªãããšããããšã¯çå®ã§ãã; int3 & fact4 -> hypothesis;"
] | [
"fact6 -> int1: {A}; int1 & fact5 -> int2: ({A} & {B}); int2 & fact3 -> int3: ¬{C}; int3 & fact4 -> hypothesis;"
] | ããŸããŸã¡ã
Lv.88äºä»¶ã¯èµ·ããªããæŽã«åæ°ãªããšããããšã¯èµ·ããªãããšããããšã¯èª€ã£ãŠãã | ¬(¬{C} & ¬{D}) | [] | 7 | 4 | 4 | 4 | 4 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ç¶æã»åäžããããšã¯èµ·ãããªããªãããŸããŸã¡ã
Lv.88äºä»¶ã¯çããªãããããåæ°ãªããšããããšã¯çããªãããšããããšã¯åœã§ãã fact2: ä»®ã«ãç
©ããããšããããšã¯çããªãããšããããšã¯æãç«ã€ãªããç¶æã»åäžããããšããã³ã¿ã«ã¿ã¡ãLv.57äºä»¶ã©ã¡ãããèµ·ããããšããããšã¯ééãã§ãã fact3: ãŸããŸã¡ã
Lv.88äºä»¶ã¯ãç¶æã»åäžããããšãšã¿ã«ã¿ã¡ãLv.57äºä»¶äž¡æ¹ãšããèµ·ããããšããããšã«é»ãŸãã fact4: åæ°ãªããšããããšã¯çºçããªã fact5: ã¿ã«ã¿ã¡ãLv.57äºä»¶ãèµ·ãã fact6: ç
©ããããšããããšãèµ·ããããã€ç¶æã»åäžããããšãèµ·ãã fact7: ç
©ããããšããããšãèµ·ãã fact8: åäŸããããšããããšãèµ·ããããã€æé
·ããšããããšãçãã ; $hypothesis$ = ãŸããŸã¡ã
Lv.88äºä»¶ã¯çããªããŠããã«åæ°ãªããšããããšã¯èµ·ãããªã ; $proof$ = | fact6 -> int1: ç¶æã»åäžããããšãèµ·ãã; int1 & fact5 -> int2: ç¶æã»åäžããããšãèµ·ãããã¿ã«ã¿ã¡ãLv.57äºä»¶ãèµ·ãã; int2 & fact3 -> int3: ããŸããŸã¡ã
Lv.88äºä»¶ã¯èµ·ããªãããšããããšã¯çå®ã§ãã; int3 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A} -> ¬(¬{C} & ¬{D}) fact2: ¬{E} -> ¬({A} & {B}) fact3: ({A} & {B}) -> ¬{C} fact4: ¬{D} fact5: {B} fact6: ({E} & {A}) fact7: {E} fact8: ({AP} & {EK}) ; $hypothesis$ = (¬{C} & ¬{D}) ; $proof$ = | fact6 -> int1: {A}; int1 & fact5 -> int2: ({A} & {B}); int2 & fact3 -> int3: ¬{C}; int3 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã«ããŸã¡ãLv.19ã¯æãã | {E}{c} | fact1: ããããããšãããŸãã¯ãã€ããããŸãã¯äž¡æ¹ã§ãããã¢ã³ã¹ã¿ãŒã¯ããã°ããã®ãŽã«ãŽã«Lv.36ã¯æœã£ãããªãããšããããšã¯æ£ãã fact2: æãé£ãã¢ã³ã¹ã¿ãŒã¯ãããšããªããŠæœã£ãããªã fact3: ãã®ã¿ã«ãã¿ã¡ãLv.10ã¯äŒŽãæããªã fact4: äœããã®ã¢ã³ã¹ã¿ãŒããããšããšããããšã¯ãªããæŽã«æœã£ãããªããªãã°ãã®ãŽã«ãŽã«Lv.36ã¯ãããšããªã fact5: ãã®ãŽã¡ããŽã®Lv.78ã¯ãã€ãããæŽã«åºå¥ãæã fact6: 䌎ãæããªãã¢ã³ã¹ã¿ãŒã¯æãé£ããŠææãæã fact7: ä»®ã«ãã®ãŽã«ãŽã«Lv.36ã¯ãããšããªããªãããã®ãŽã¡ããŽã®Lv.78ã¯åºå¥ãæããªããã©ãã€ããããšããããšã¯åœã§ãã | fact1: (x): ({C}x v {A}x) -> ¬{D}{b} fact2: (x): {F}x -> (¬{C}x & ¬{D}x) fact3: ¬{H}{d} fact4: (x): (¬{C}x & ¬{D}x) -> ¬{C}{b} fact5: ({A}{a} & {B}{a}) fact6: (x): ¬{H}x -> ({F}x & {G}x) fact7: ¬{C}{b} -> ¬(¬{B}{a} & {A}{a}) | [
"fact5 -> int1: ãã®ãŽã¡ããŽã®Lv.78ã¯ãã€ãã; int1 -> int2: ãã®ãŽã¡ããŽã®Lv.78ã¯ãããšãããã€ãã; int2 -> int3: ããããšãããããã¯ãã€ããããŸãã¯äž¡æ¹ãªãã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact1 -> int4: ããã®ãŽã«ãŽã«Lv.36ã¯æœã£ãããªãããšããããšã¯åã§ãªã;"
] | [
"fact5 -> int1: {A}{a}; int1 -> int2: ({C}{a} v {A}{a}); int2 -> int3: (Ex): ({C}x v {A}x); int3 & fact1 -> int4: ¬{D}{b};"
] | ãã®ãŸã«ããŸã¡ãLv.19ã¯æãããªã | ¬{E}{c} | [
"fact12 -> int5: ããä»®ã«ãã®ã¿ã«ãã¿ã¡ãLv.10ãæãé£ããšããããã®ã¿ã«ãã¿ã¡ãLv.10ã¯ãããšããªããŠæŽã«æœã£ãããªã; fact10 -> int6: ããããã®ã¿ã«ãã¿ã¡ãLv.10ã䌎ãæããªããšããããã®ã¿ã«ãã¿ã¡ãLv.10ã¯æãé£ããŠããã«ææãæã; int6 & fact8 -> int7: ããã®ã¿ã«ãã¿ã¡ãLv.10ã¯æãé£ããŠææãæãããšããããšã¯çå®ã§ãã; int7 -> int8: ãã®ã¿ã«ãã¿ã¡ãLv.10ã¯æãé£ã; int5 & int8 -> int9: ãã®ã¿ã«ãã¿ã¡ãLv.10ã¯ãããšããªããæœã£ãããªã; int9 -> int10: ããããšããªããæœã£ãããªããã¢ã³ã¹ã¿ãŒã¯ãã; int10 & fact11 -> int11: ãã®ãŽã«ãŽã«Lv.36ã¯ãããšããšããããšã¯ãªã; fact9 & int11 -> int12: ãããã®ãŽã¡ããŽã®Lv.78ã¯åºå¥ãæããšããããšã¯ãªããã©ãã€ããããšããããšã¯äºå®ãšç°ãªãããšããããšã¯èª€ãã§ãªã; int12 -> int13: ããåºå¥ãæããªããããããã€ããããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã;"
] | 9 | 5 | 5 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããããšãããŸãã¯ãã€ããããŸãã¯äž¡æ¹ã§ãããã¢ã³ã¹ã¿ãŒã¯ããã°ããã®ãŽã«ãŽã«Lv.36ã¯æœã£ãããªãããšããããšã¯æ£ãã fact2: æãé£ãã¢ã³ã¹ã¿ãŒã¯ãããšããªããŠæœã£ãããªã fact3: ãã®ã¿ã«ãã¿ã¡ãLv.10ã¯äŒŽãæããªã fact4: äœããã®ã¢ã³ã¹ã¿ãŒããããšããšããããšã¯ãªããæŽã«æœã£ãããªããªãã°ãã®ãŽã«ãŽã«Lv.36ã¯ãããšããªã fact5: ãã®ãŽã¡ããŽã®Lv.78ã¯ãã€ãããæŽã«åºå¥ãæã fact6: 䌎ãæããªãã¢ã³ã¹ã¿ãŒã¯æãé£ããŠææãæã fact7: ä»®ã«ãã®ãŽã«ãŽã«Lv.36ã¯ãããšããªããªãããã®ãŽã¡ããŽã®Lv.78ã¯åºå¥ãæããªããã©ãã€ããããšããããšã¯åœã§ãã ; $hypothesis$ = ãã®ãŸã«ããŸã¡ãLv.19ã¯æãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ({C}x v {A}x) -> ¬{D}{b} fact2: (x): {F}x -> (¬{C}x & ¬{D}x) fact3: ¬{H}{d} fact4: (x): (¬{C}x & ¬{D}x) -> ¬{C}{b} fact5: ({A}{a} & {B}{a}) fact6: (x): ¬{H}x -> ({F}x & {G}x) fact7: ¬{C}{b} -> ¬(¬{B}{a} & {A}{a}) ; $hypothesis$ = {E}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãä»®ã«éãé£ããšããããšã¯ãªããšããã°ååŸãæããªããŠæŽã«å©çšãæããªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{A}x -> (¬{AA}x & ¬{AB}x) | fact1: ããããèæãããªããšããã埮ç¬ãŸãããŠãŸãäžžããªããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãããã®ãŽããŽãLv.20ãéãé£ããšããããšã¯ãªããšããã°ååŸãæããªãããããããã¯å©çšãæããªã | fact1: (Ex): ¬{HE}x -> ({CA}x & ¬{BE}x) fact2: ¬{A}{aa} -> (¬{AA}{aa} & ¬{AB}{aa}) | [
"fact2 -> hypothesis;"
] | [
"fact2 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 1 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ããããèæãããªããšããã埮ç¬ãŸãããŠãŸãäžžããªããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãããã®ãŽããŽãLv.20ãéãé£ããšããããšã¯ãªããšããã°ååŸãæããªãããããããã¯å©çšãæããªã ; $hypothesis$ = ãä»®ã«éãé£ããšããããšã¯ãªããšããã°ååŸãæããªããŠæŽã«å©çšãæããªããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: (Ex): ¬{HE}x -> ({CA}x & ¬{BE}x) fact2: ¬{A}{aa} -> (¬{AA}{aa} & ¬{AB}{aa}) ; $hypothesis$ = (Ex): ¬{A}x -> (¬{AA}x & ¬{AB}x) ; $proof$ = | fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ã¡ãã·ã«Lv.72ã¯äžèªç±ããªã | ¬{F}{a} | fact1: ãã®ã·ã¡ãã·ã«Lv.72ã¯åŠåš åºæ¥ã fact2: ããããã®ã·ã¡ãã·ã«Lv.72ãè³è²žããããŸãæ°å®ããªãã°ãã®ã·ã¡ãã·ã«Lv.72ã¯äžèªç±ãããšããããšã¯ãªã fact3: ãã®ãŽã«ããŽã«ãLv.0ã¯å·ä»ãæããŠãã€ã¹ãä»ãæã fact4: ãã®ã¿ãã¿ãªLv.40ã¯èæ±ã fact5: ãã®ã·ã¡ãã·ã«Lv.72ã¯ä»æç¡ããŠããã«å°è³¢ãã fact6: ãã®ã·ã¡ãã·ã«Lv.72ãä»æç¡ããšããã°ããã¯èæ±ã fact7: ãããã®ã·ã¡ãã·ã«Lv.72ãèæ±ããªãè³è²žãã fact8: ãã®ã·ã¡ãã·ã«Lv.72ã¯æ°å®ã | fact1: {HE}{a} fact2: ({D}{a} & {E}{a}) -> ¬{F}{a} fact3: ({DT}{be} & {JA}{be}) fact4: {C}{gj} fact5: ({A}{a} & {B}{a}) fact6: {A}{a} -> {C}{a} fact7: {C}{a} -> {D}{a} fact8: {E}{a} | [
"fact5 -> int1: ãã®ã·ã¡ãã·ã«Lv.72ã¯ä»æç¡ã; int1 & fact6 -> int2: ããã®ã·ã¡ãã·ã«Lv.72ã¯èæ±ãããšããããšã¯æãç«ã€; int2 & fact7 -> int3: ããã®ã·ã¡ãã·ã«Lv.72ã¯è³è²žããããšããããšã¯æ£ãã; int3 & fact8 -> int4: ãã®ã·ã¡ãã·ã«Lv.72ã¯è³è²žããããã®äžæ°å®ã; int4 & fact2 -> hypothesis;"
] | [
"fact5 -> int1: {A}{a}; int1 & fact6 -> int2: {C}{a}; int2 & fact7 -> int3: {D}{a}; int3 & fact8 -> int4: ({D}{a} & {E}{a}); int4 & fact2 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ã·ã¡ãã·ã«Lv.72ã¯åŠåš åºæ¥ã fact2: ããããã®ã·ã¡ãã·ã«Lv.72ãè³è²žããããŸãæ°å®ããªãã°ãã®ã·ã¡ãã·ã«Lv.72ã¯äžèªç±ãããšããããšã¯ãªã fact3: ãã®ãŽã«ããŽã«ãLv.0ã¯å·ä»ãæããŠãã€ã¹ãä»ãæã fact4: ãã®ã¿ãã¿ãªLv.40ã¯èæ±ã fact5: ãã®ã·ã¡ãã·ã«Lv.72ã¯ä»æç¡ããŠããã«å°è³¢ãã fact6: ãã®ã·ã¡ãã·ã«Lv.72ãä»æç¡ããšããã°ããã¯èæ±ã fact7: ãããã®ã·ã¡ãã·ã«Lv.72ãèæ±ããªãè³è²žãã fact8: ãã®ã·ã¡ãã·ã«Lv.72ã¯æ°å®ã ; $hypothesis$ = ãã®ã·ã¡ãã·ã«Lv.72ã¯äžèªç±ããªã ; $proof$ = | fact5 -> int1: ãã®ã·ã¡ãã·ã«Lv.72ã¯ä»æç¡ã; int1 & fact6 -> int2: ããã®ã·ã¡ãã·ã«Lv.72ã¯èæ±ãããšããããšã¯æãç«ã€; int2 & fact7 -> int3: ããã®ã·ã¡ãã·ã«Lv.72ã¯è³è²žããããšããããšã¯æ£ãã; int3 & fact8 -> int4: ãã®ã·ã¡ãã·ã«Lv.72ã¯è³è²žããããã®äžæ°å®ã; int4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {HE}{a} fact2: ({D}{a} & {E}{a}) -> ¬{F}{a} fact3: ({DT}{be} & {JA}{be}) fact4: {C}{gj} fact5: ({A}{a} & {B}{a}) fact6: {A}{a} -> {C}{a} fact7: {C}{a} -> {D}{a} fact8: {E}{a} ; $hypothesis$ = ¬{F}{a} ; $proof$ = | fact5 -> int1: {A}{a}; int1 & fact6 -> int2: {C}{a}; int2 & fact7 -> int3: {D}{a}; int3 & fact8 -> int4: ({D}{a} & {E}{a}); int4 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã圢æãæããšããããšãèµ·ããããŸããŸã«ãLv.30äºä»¶ã¯çããªãããšããããšã¯çå®ã ããšããããšã¯ééã£ãŠãã | ¬({F} & ¬{E}) | fact1: ããããLv.53äºä»¶ãçºçãã fact2: ããã¿ã«ãã¿ã«ãLv.80äºä»¶ã¯èµ·ããªããšããã°ã圢æãæããšããããšãçããããŸããŸã«ãLv.30äºä»¶ã¯çããªãããšããããšã¯ééãã fact3: 圢æãæããšããããšãèµ·ãã fact4: ãæ²¹æåºæ¥ãããšãèµ·ããããšããããšã¯äºå®ã fact5: ããä»®ã«ã¿ã¡ã
ã¿ãLv.84äºä»¶ããã³ãã€ããšããããšãçãããšããã°ãŸããŸã«ãLv.30äºä»¶ã¯çºçããªã fact6: ãã€ããšããããšãçºçãã fact7: ã¿ã¡ã
ã¿ãLv.84äºä»¶ã¯ã¿ã«ãã¿ã«ãLv.80äºä»¶ãèµ·ãããšããããšã«èªçºããã fact8: ã¿ã«ãã¿ã«ãLv.80äºä»¶ãèµ·ãããããŸãã«æ²¹æåºæ¥ãããšãèµ·ãã | fact1: {BP} fact2: ¬{A} -> ¬({F} & ¬{E}) fact3: {F} fact4: {B} fact5: ({C} & {D}) -> ¬{E} fact6: {D} fact7: {A} -> {C} fact8: ({A} & {B}) | [
"fact8 -> int1: ã¿ã«ãã¿ã«ãLv.80äºä»¶ãçºçãã; int1 & fact7 -> int2: ãã¿ã¡ã
ã¿ãLv.84äºä»¶ãèµ·ããããšããããšã¯äºå®ã§ãã; int2 & fact6 -> int3: ãã¿ã¡ã
ã¿ãLv.84äºä»¶ãçãããããããã€ããšããããšãçããããšããããšã¯æãç«ã€; int3 & fact5 -> int4: ãŸããŸã«ãLv.30äºä»¶ã¯çããªã; int4 & fact3 -> hypothesis;"
] | [
"fact8 -> int1: {A}; int1 & fact7 -> int2: {C}; int2 & fact6 -> int3: ({C} & {D}); int3 & fact5 -> int4: ¬{E}; int4 & fact3 -> hypothesis;"
] | ãã圢æãæããšããããšãèµ·ããããŸããŸã«ãLv.30äºä»¶ã¯çããªãããšããããšã¯çå®ã ããšããããšã¯ééã£ãŠãã | ¬({F} & ¬{E}) | [] | 6 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããLv.53äºä»¶ãçºçãã fact2: ããã¿ã«ãã¿ã«ãLv.80äºä»¶ã¯èµ·ããªããšããã°ã圢æãæããšããããšãçããããŸããŸã«ãLv.30äºä»¶ã¯çããªãããšããããšã¯ééãã fact3: 圢æãæããšããããšãèµ·ãã fact4: ãæ²¹æåºæ¥ãããšãèµ·ããããšããããšã¯äºå®ã fact5: ããä»®ã«ã¿ã¡ã
ã¿ãLv.84äºä»¶ããã³ãã€ããšããããšãçãããšããã°ãŸããŸã«ãLv.30äºä»¶ã¯çºçããªã fact6: ãã€ããšããããšãçºçãã fact7: ã¿ã¡ã
ã¿ãLv.84äºä»¶ã¯ã¿ã«ãã¿ã«ãLv.80äºä»¶ãèµ·ãããšããããšã«èªçºããã fact8: ã¿ã«ãã¿ã«ãLv.80äºä»¶ãèµ·ãããããŸãã«æ²¹æåºæ¥ãããšãèµ·ãã ; $hypothesis$ = ãã圢æãæããšããããšãèµ·ããããŸããŸã«ãLv.30äºä»¶ã¯çããªãããšããããšã¯çå®ã ããšããããšã¯ééã£ãŠãã ; $proof$ = | fact8 -> int1: ã¿ã«ãã¿ã«ãLv.80äºä»¶ãçºçãã; int1 & fact7 -> int2: ãã¿ã¡ã
ã¿ãLv.84äºä»¶ãèµ·ããããšããããšã¯äºå®ã§ãã; int2 & fact6 -> int3: ãã¿ã¡ã
ã¿ãLv.84äºä»¶ãçãããããããã€ããšããããšãçããããšããããšã¯æãç«ã€; int3 & fact5 -> int4: ãŸããŸã«ãLv.30äºä»¶ã¯çããªã; int4 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {BP} fact2: ¬{A} -> ¬({F} & ¬{E}) fact3: {F} fact4: {B} fact5: ({C} & {D}) -> ¬{E} fact6: {D} fact7: {A} -> {C} fact8: ({A} & {B}) ; $hypothesis$ = ¬({F} & ¬{E}) ; $proof$ = | fact8 -> int1: {A}; int1 & fact7 -> int2: {C}; int2 & fact6 -> int3: ({C} & {D}); int3 & fact5 -> int4: ¬{E}; int4 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãŸã¡ã
ãŸã«ãLv.82äºä»¶ã¯çºçããªã | ¬{A} | fact1: ã·ã¡ã
ã·ãªLv.73äºä»¶ãçºçãã fact2: ããŒãããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã fact3: ããããã«ã
Lv.12äºä»¶ã¯èµ·ãããªãããšããããšã¯çŸ©ååããããšããã³è¿å¯ãããšãèµ·ããã«ããçºçãã fact4: ããçºçŸãæããšããããšã¯èµ·ããªããªãã圌ããããšããããšãèµ·ããããããã¯ãã€ããšããããšã¯èµ·ããªãããããã¯äž¡æ¹ã§ããããšããããšã¯åœã§ãã fact5: ä»®ã«ãè©°ãŸãæããšããããšããã³çãåŸãããšãçºçããããšããããšã¯åã ãšãããçºçŸãæããšããããšã¯èµ·ãããªã fact6: ã圌ããããšããããšãèµ·ããããã€ããšããããšã¯çºçããªãããããã¯äž¡æ¹ã§ããããšããããšã¯ééãã ãšãããèºãæããããšã¯èµ·ããªã fact7: èºãæããããšã¯èµ·ããªããªãã°ã·ã¡ã
ã·ãªLv.73äºä»¶ããããã¯ãŒãããšããããšãäž¡æ¹ãšããèµ·ãã | fact1: {B} fact2: {C} fact3: ({CC} & {FE}) -> ¬{DB} fact4: ¬{G} -> ¬({E} v ¬{F}) fact5: ¬({I} & {H}) -> ¬{G} fact6: ¬({E} v ¬{F}) -> ¬{D} fact7: ¬{D} -> ({B} v {C}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããŸã¡ã
ãŸã«ãLv.82äºä»¶ãçºçãã; assump1 & fact1 -> int1: ãŸã¡ã
ãŸã«ãLv.82äºä»¶ãèµ·ãããããŸãã«ã·ã¡ã
ã·ãªLv.73äºä»¶ãèµ·ãã;"
] | [
"void -> assump1: {A}; assump1 & fact1 -> int1: ({A} & {B});"
] | 以äžã®ããã«ä»®å®ããããŸã¡ã
ãŸã«ãLv.82äºä»¶ãçºçãã | {A} | [] | 9 | 5 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ã·ã¡ã
ã·ãªLv.73äºä»¶ãçºçãã fact2: ããŒãããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã fact3: ããããã«ã
Lv.12äºä»¶ã¯èµ·ãããªãããšããããšã¯çŸ©ååããããšããã³è¿å¯ãããšãèµ·ããã«ããçºçãã fact4: ããçºçŸãæããšããããšã¯èµ·ããªããªãã圌ããããšããããšãèµ·ããããããã¯ãã€ããšããããšã¯èµ·ããªãããããã¯äž¡æ¹ã§ããããšããããšã¯åœã§ãã fact5: ä»®ã«ãè©°ãŸãæããšããããšããã³çãåŸãããšãçºçããããšããããšã¯åã ãšãããçºçŸãæããšããããšã¯èµ·ãããªã fact6: ã圌ããããšããããšãèµ·ããããã€ããšããããšã¯çºçããªãããããã¯äž¡æ¹ã§ããããšããããšã¯ééãã ãšãããèºãæããããšã¯èµ·ããªã fact7: èºãæããããšã¯èµ·ããªããªãã°ã·ã¡ã
ã·ãªLv.73äºä»¶ããããã¯ãŒãããšããããšãäž¡æ¹ãšããèµ·ãã ; $hypothesis$ = ãŸã¡ã
ãŸã«ãLv.82äºä»¶ã¯çºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B} fact2: {C} fact3: ({CC} & {FE}) -> ¬{DB} fact4: ¬{G} -> ¬({E} v ¬{F}) fact5: ¬({I} & {H}) -> ¬{G} fact6: ¬({E} v ¬{F}) -> ¬{D} fact7: ¬{D} -> ({B} v {C}) ; $hypothesis$ = ¬{A} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãŸã«ããŸã¡ã
Lv.66ã¯äžžããªãããšããããšã¯æ£ãã | ¬{D}{d} | fact1: ãã®ãŽããŽãLv.87ã¯é
ã fact2: ãããã®ã·ãã·ãLv.13ãèããšããããã®ããããLv.94ã¯å€èã fact3: èªåãããã¢ã³ã¹ã¿ãŒã¯äžžã fact4: å€èãã¢ã³ã¹ã¿ãŒã¯é
ããªãããããåãå
¥ãé£ã fact5: ããããã®ã·ãã·ãLv.13ã玳士ããããªããšããã°ãã®ã·ãã·ãLv.13ã¯èããŠããã«ããã¯ç滞ããŸãã fact6: ããä»®ã«ãã®ã·ãã·ãLv.13ãé°æ°èããªãã°ãã®ãŽããŽãLv.87ã¯èªåããã fact7: ãã®ããããLv.94ã¯æåãæããã©æãããªã fact8: ããä»®ã«ãã®ããããLv.94ãæåãæãããããæãããªããšãããšãã®ã·ãã·ãLv.13ã¯é°æ°èã fact9: ãããã®ãŽããŽãLv.87ãèªåãããããããé
ããšãããšãã®ãŸã«ããŸã¡ã
Lv.66ã¯äžžããªã fact10: ãããããã®ããããLv.94ã¯é
ããªãããšããããšã¯çå®ã§ãããšããããã®ãŸã«ããŸã¡ã
Lv.66ã¯èªåãããããã®äžé°æ°èã | fact1: {C}{c} fact2: {G}{b} -> {F}{a} fact3: (x): {A}x -> {D}x fact4: (x): {F}x -> (¬{C}x & {E}x) fact5: ¬{I}{b} -> ({G}{b} & {H}{b}) fact6: {B}{b} -> {A}{c} fact7: ({AA}{a} & ¬{AB}{a}) fact8: ({AA}{a} & ¬{AB}{a}) -> {B}{b} fact9: ({A}{c} & {C}{c}) -> ¬{D}{d} fact10: ¬{C}{a} -> ({A}{d} & {B}{d}) | [
"fact8 & fact7 -> int1: ãã®ã·ãã·ãLv.13ã¯é°æ°èã; int1 & fact6 -> int2: ãã®ãŽããŽãLv.87ã¯èªåããã; int2 & fact1 -> int3: ããã®ãŽããŽãLv.87ã¯èªåããããããã«é
ãããšããããšã¯çå®ã§ãã; int3 & fact9 -> hypothesis;"
] | [
"fact8 & fact7 -> int1: {B}{b}; int1 & fact6 -> int2: {A}{c}; int2 & fact1 -> int3: ({A}{c} & {C}{c}); int3 & fact9 -> hypothesis;"
] | ãã®ãŸã«ããŸã¡ã
Lv.66ã¯äžžã | {D}{d} | [
"fact13 -> int4: ããã®ãŸã«ããŸã¡ã
Lv.66ã¯èªåãããããšããããšã¯çå®ã§ãããšããã°äžžã; fact14 -> int5: ä»®ã«ãã®ããããLv.94ãå€èããšããã°ãã®ããããLv.94ã¯é
ããªãããã©ããã¯åãå
¥ãé£ã;"
] | 8 | 4 | 4 | 4 | 4 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãŽããŽãLv.87ã¯é
ã fact2: ãããã®ã·ãã·ãLv.13ãèããšããããã®ããããLv.94ã¯å€èã fact3: èªåãããã¢ã³ã¹ã¿ãŒã¯äžžã fact4: å€èãã¢ã³ã¹ã¿ãŒã¯é
ããªãããããåãå
¥ãé£ã fact5: ããããã®ã·ãã·ãLv.13ã玳士ããããªããšããã°ãã®ã·ãã·ãLv.13ã¯èããŠããã«ããã¯ç滞ããŸãã fact6: ããä»®ã«ãã®ã·ãã·ãLv.13ãé°æ°èããªãã°ãã®ãŽããŽãLv.87ã¯èªåããã fact7: ãã®ããããLv.94ã¯æåãæããã©æãããªã fact8: ããä»®ã«ãã®ããããLv.94ãæåãæãããããæãããªããšãããšãã®ã·ãã·ãLv.13ã¯é°æ°èã fact9: ãããã®ãŽããŽãLv.87ãèªåãããããããé
ããšãããšãã®ãŸã«ããŸã¡ã
Lv.66ã¯äžžããªã fact10: ãããããã®ããããLv.94ã¯é
ããªãããšããããšã¯çå®ã§ãããšããããã®ãŸã«ããŸã¡ã
Lv.66ã¯èªåãããããã®äžé°æ°èã ; $hypothesis$ = ããã®ãŸã«ããŸã¡ã
Lv.66ã¯äžžããªãããšããããšã¯æ£ãã ; $proof$ = | fact8 & fact7 -> int1: ãã®ã·ãã·ãLv.13ã¯é°æ°èã; int1 & fact6 -> int2: ãã®ãŽããŽãLv.87ã¯èªåããã; int2 & fact1 -> int3: ããã®ãŽããŽãLv.87ã¯èªåããããããã«é
ãããšããããšã¯çå®ã§ãã; int3 & fact9 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{c} fact2: {G}{b} -> {F}{a} fact3: (x): {A}x -> {D}x fact4: (x): {F}x -> (¬{C}x & {E}x) fact5: ¬{I}{b} -> ({G}{b} & {H}{b}) fact6: {B}{b} -> {A}{c} fact7: ({AA}{a} & ¬{AB}{a}) fact8: ({AA}{a} & ¬{AB}{a}) -> {B}{b} fact9: ({A}{c} & {C}{c}) -> ¬{D}{d} fact10: ¬{C}{a} -> ({A}{d} & {B}{d}) ; $hypothesis$ = ¬{D}{d} ; $proof$ = | fact8 & fact7 -> int1: {B}{b}; int1 & fact6 -> int2: {A}{c}; int2 & fact1 -> int3: ({A}{c} & {C}{c}); int3 & fact9 -> hypothesis; __PROVED__ |
0.3 | ãèãèŸããšããããšã¯çããªãããšããããšã¯æãç«ã€ | ¬{E} | fact1: ç
®äžããããšãèµ·ãã fact2: äžãæããšããããšããããã¯äžä»£äº€ä»£ããããšããããã¯ã©ã¡ãããçãã fact3: ä»®ã«åŒè§£ããŸãããšããããšã¯èµ·ãããªããªãã°èµ·ããé£ããšããããšãçããããŸãã¯å·ãããšããããšãèµ·ãããã©ã¡ããã§ãã fact4: å·ãããšããããšã¯èµ·ããªããšããããšã¯ããœã«ãœã¡ã
Lv.79äºä»¶ãèµ·ãããªããŠãŸãç
®äžããããšã¯èµ·ããªãããšããããšã«åŒãèµ·ãããã fact5: åŒè§£ããŸãããšããããšã¯çºçããªã fact6: èãèŸããšããããšã¯ããœã«ãœã¡ã
Lv.79äºä»¶ãšç
®äžããããšãçããããšããããšã«é²ããã fact7: èµ·ããé£ããšããããšã¯ãœã«ãœã¡ã
Lv.79äºä»¶ã¯èµ·ããªããšããããšãé²ã fact8: é¢çœãããããšããããšã¯ããœã«ãœã¡ã
Lv.79äºä»¶ã¯çããªããŠåŒè§£ããŸãããšããããšãèµ·ããããšããããšãåŒãèµ·ãã fact9: å·ãããšããããšã¯ãœã«ãœã¡ã
Lv.79äºä»¶ãçãããã fact10: è¡ãããšã¯ããŸã¡ã
ãŸãLv.61äºä»¶ã¯çºçããªãããšããããšãé²ã | fact1: {D} fact2: ({GK} v {P}) fact3: ¬{F} -> ({A} v {B}) fact4: (¬{C} & ¬{D}) -> ¬{B} fact5: ¬{F} fact6: ({C} & {D}) -> ¬{E} fact7: {A} -> {C} fact8: {G} -> (¬{C} & {F}) fact9: {B} -> {C} fact10: {DB} -> {II} | [
"fact5 & fact3 -> int1: èµ·ããé£ããšããããšãèµ·ããããŸãã¯å·ãããšããããšãçãã; int1 & fact7 & fact9 -> int2: ãœã«ãœã¡ã
Lv.79äºä»¶ãèµ·ãã; int2 & fact1 -> int3: ãœã«ãœã¡ã
Lv.79äºä»¶ããã³ç
®äžããããšäž¡æ¹ãçºçãã; int3 & fact6 -> hypothesis;"
] | [
"fact5 & fact3 -> int1: ({A} v {B}); int1 & fact7 & fact9 -> int2: {C}; int2 & fact1 -> int3: ({C} & {D}); int3 & fact6 -> hypothesis;"
] | èãèŸããšããããšãçºçãã | {E} | [] | 7 | 4 | 4 | 4 | 4 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ç
®äžããããšãèµ·ãã fact2: äžãæããšããããšããããã¯äžä»£äº€ä»£ããããšããããã¯ã©ã¡ãããçãã fact3: ä»®ã«åŒè§£ããŸãããšããããšã¯èµ·ãããªããªãã°èµ·ããé£ããšããããšãçããããŸãã¯å·ãããšããããšãèµ·ãããã©ã¡ããã§ãã fact4: å·ãããšããããšã¯èµ·ããªããšããããšã¯ããœã«ãœã¡ã
Lv.79äºä»¶ãèµ·ãããªããŠãŸãç
®äžããããšã¯èµ·ããªãããšããããšã«åŒãèµ·ãããã fact5: åŒè§£ããŸãããšããããšã¯çºçããªã fact6: èãèŸããšããããšã¯ããœã«ãœã¡ã
Lv.79äºä»¶ãšç
®äžããããšãçããããšããããšã«é²ããã fact7: èµ·ããé£ããšããããšã¯ãœã«ãœã¡ã
Lv.79äºä»¶ã¯èµ·ããªããšããããšãé²ã fact8: é¢çœãããããšããããšã¯ããœã«ãœã¡ã
Lv.79äºä»¶ã¯çããªããŠåŒè§£ããŸãããšããããšãèµ·ããããšããããšãåŒãèµ·ãã fact9: å·ãããšããããšã¯ãœã«ãœã¡ã
Lv.79äºä»¶ãçãããã fact10: è¡ãããšã¯ããŸã¡ã
ãŸãLv.61äºä»¶ã¯çºçããªãããšããããšãé²ã ; $hypothesis$ = ãèãèŸããšããããšã¯çããªãããšããããšã¯æãç«ã€ ; $proof$ = | fact5 & fact3 -> int1: èµ·ããé£ããšããããšãèµ·ããããŸãã¯å·ãããšããããšãçãã; int1 & fact7 & fact9 -> int2: ãœã«ãœã¡ã
Lv.79äºä»¶ãèµ·ãã; int2 & fact1 -> int3: ãœã«ãœã¡ã
Lv.79äºä»¶ããã³ç
®äžããããšäž¡æ¹ãçºçãã; int3 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: {D} fact2: ({GK} v {P}) fact3: ¬{F} -> ({A} v {B}) fact4: (¬{C} & ¬{D}) -> ¬{B} fact5: ¬{F} fact6: ({C} & {D}) -> ¬{E} fact7: {A} -> {C} fact8: {G} -> (¬{C} & {F}) fact9: {B} -> {C} fact10: {DB} -> {II} ; $hypothesis$ = ¬{E} ; $proof$ = | fact5 & fact3 -> int1: ({A} v {B}); int1 & fact7 & fact9 -> int2: {C}; int2 & fact1 -> int3: ({C} & {D}); int3 & fact6 -> hypothesis; __PROVED__ |
0.3 | 幌ããšããããšã¯èµ·ãããªã | ¬{F} | fact1: ãœã®ãœãLv.66äºä»¶ãèµ·ãã fact2: ãæçããšããããšãçããããšããããšããŸãã¯ãæšããšããããšãçºçããããšããããšãã©ã¡ããã¯å¹Œããšããããšãé»æ¢ãã fact3: ãå¥çŽåºæ¥ãããšã¯çºçããªãããšããããšã¯ããã¡ã
ããLv.21äºä»¶ãèµ·ããããšããããšã«é»æ¢ããã fact4: å¥çŽåºæ¥ãããšã¯ãæšããšããããšã¯çºçããªãããšããããšãé»æ¢ãã fact5: ã幌ããšããããšãçããããšããããšã¯æçããšããããšã«é²ããã fact6: æçããšããããšã¯ãæšããšããããšã¯çºçãããå¥çŽåºæ¥ãããšã¯èµ·ãããªãããšããããšã«åž°çµãã fact7: ãã¡ã
ããLv.21äºä»¶ãçãããšããããšã¯ãœã®ãœãLv.66äºä»¶ãå¥æ©ã fact8: ãããæšããšããããšãèµ·ãããå¥çŽåºæ¥ãããšãèµ·ããªããªãã°ãã¡ã
ããLv.21äºä»¶ã¯èµ·ããªã | fact1: {A} fact2: ({E} v {D}) -> ¬{F} fact3: {B} -> {C} fact4: {C} -> {D} fact5: {E} -> ¬{F} fact6: {E} -> ({D} & ¬{C}) fact7: {A} -> {B} fact8: ({D} & ¬{C}) -> ¬{B} | [
"fact7 & fact1 -> int1: ãã¡ã
ããLv.21äºä»¶ãçãã; int1 & fact3 -> int2: å¥çŽåºæ¥ãããšãèµ·ãã; int2 & fact4 -> int3: æšããšããããšãèµ·ãã; int3 -> int4: æçããšããããšããŸãã¯æšããšããããšããããã¯ã©ã¡ãããçãã; int4 & fact2 -> hypothesis;"
] | [
"fact7 & fact1 -> int1: {B}; int1 & fact3 -> int2: {C}; int2 & fact4 -> int3: {D}; int3 -> int4: ({E} v {D}); int4 & fact2 -> hypothesis;"
] | 幌ããšããããšãçºçãã | {F} | [] | 7 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãœã®ãœãLv.66äºä»¶ãèµ·ãã fact2: ãæçããšããããšãçããããšããããšããŸãã¯ãæšããšããããšãçºçããããšããããšãã©ã¡ããã¯å¹Œããšããããšãé»æ¢ãã fact3: ãå¥çŽåºæ¥ãããšã¯çºçããªãããšããããšã¯ããã¡ã
ããLv.21äºä»¶ãèµ·ããããšããããšã«é»æ¢ããã fact4: å¥çŽåºæ¥ãããšã¯ãæšããšããããšã¯çºçããªãããšããããšãé»æ¢ãã fact5: ã幌ããšããããšãçããããšããããšã¯æçããšããããšã«é²ããã fact6: æçããšããããšã¯ãæšããšããããšã¯çºçãããå¥çŽåºæ¥ãããšã¯èµ·ãããªãããšããããšã«åž°çµãã fact7: ãã¡ã
ããLv.21äºä»¶ãçãããšããããšã¯ãœã®ãœãLv.66äºä»¶ãå¥æ©ã fact8: ãããæšããšããããšãèµ·ãããå¥çŽåºæ¥ãããšãèµ·ããªããªãã°ãã¡ã
ããLv.21äºä»¶ã¯èµ·ããªã ; $hypothesis$ = 幌ããšããããšã¯èµ·ãããªã ; $proof$ = | fact7 & fact1 -> int1: ãã¡ã
ããLv.21äºä»¶ãçãã; int1 & fact3 -> int2: å¥çŽåºæ¥ãããšãèµ·ãã; int2 & fact4 -> int3: æšããšããããšãèµ·ãã; int3 -> int4: æçããšããããšããŸãã¯æšããšããããšããããã¯ã©ã¡ãããçãã; int4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} fact2: ({E} v {D}) -> ¬{F} fact3: {B} -> {C} fact4: {C} -> {D} fact5: {E} -> ¬{F} fact6: {E} -> ({D} & ¬{C}) fact7: {A} -> {B} fact8: ({D} & ¬{C}) -> ¬{B} ; $hypothesis$ = ¬{F} ; $proof$ = | fact7 & fact1 -> int1: {B}; int1 & fact3 -> int2: {C}; int2 & fact4 -> int3: {D}; int3 -> int4: ({E} v {D}); int4 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœã¡ã
ãœãªLv.6ã¯éã³æã | {F}{c} | fact1: ããããã®ãœã¡ã
ãœãªLv.6ãéè¿ããšãããšããã¯ãã©ãã¹ããã fact2: ããããã®ãœã¡ã
ãœãªLv.6ã¯ãã©ãã¹ããããªããéã³æãããšããããšã¯æ£ãã fact3: ããä»®ã«ãã®ãœã®ãœãªLv.91ãæ¯ãä»ããšããããã®ãœã¡ã
ãœãªLv.6ã¯éè¿ã fact4: ãã®ã·ãã·ã«ãLv.6ã¯å©çšãæãããŸãåãåºã fact5: ãã®ã·ãã·ã«ãLv.6ãåãåºããšããã°ãã®ãœã®ãœãªLv.91ã¯æ¯ãä»ã fact6: ãã®ã·ãã·ã«ãLv.6ã¯å©çšãæã | fact1: {D}{c} -> {E}{c} fact2: {E}{c} -> {F}{c} fact3: {C}{b} -> {D}{c} fact4: ({A}{a} & {B}{a}) fact5: {B}{a} -> {C}{b} fact6: {A}{a} | [
"fact4 -> int1: ãã®ã·ãã·ã«ãLv.6ã¯åãåºã; int1 & fact5 -> int2: ãã®ãœã®ãœãªLv.91ã¯æ¯ãä»ã; int2 & fact3 -> int3: ãã®ãœã¡ã
ãœãªLv.6ã¯éè¿ã; int3 & fact1 -> int4: ãã®ãœã¡ã
ãœãªLv.6ã¯ãã©ãã¹ããã; int4 & fact2 -> hypothesis;"
] | [
"fact4 -> int1: {B}{a}; int1 & fact5 -> int2: {C}{b}; int2 & fact3 -> int3: {D}{c}; int3 & fact1 -> int4: {E}{c}; int4 & fact2 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ãœã¡ã
ãœãªLv.6ãéè¿ããšãããšããã¯ãã©ãã¹ããã fact2: ããããã®ãœã¡ã
ãœãªLv.6ã¯ãã©ãã¹ããããªããéã³æãããšããããšã¯æ£ãã fact3: ããä»®ã«ãã®ãœã®ãœãªLv.91ãæ¯ãä»ããšããããã®ãœã¡ã
ãœãªLv.6ã¯éè¿ã fact4: ãã®ã·ãã·ã«ãLv.6ã¯å©çšãæãããŸãåãåºã fact5: ãã®ã·ãã·ã«ãLv.6ãåãåºããšããã°ãã®ãœã®ãœãªLv.91ã¯æ¯ãä»ã fact6: ãã®ã·ãã·ã«ãLv.6ã¯å©çšãæã ; $hypothesis$ = ãã®ãœã¡ã
ãœãªLv.6ã¯éã³æã ; $proof$ = | fact4 -> int1: ãã®ã·ãã·ã«ãLv.6ã¯åãåºã; int1 & fact5 -> int2: ãã®ãœã®ãœãªLv.91ã¯æ¯ãä»ã; int2 & fact3 -> int3: ãã®ãœã¡ã
ãœãªLv.6ã¯éè¿ã; int3 & fact1 -> int4: ãã®ãœã¡ã
ãœãªLv.6ã¯ãã©ãã¹ããã; int4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {D}{c} -> {E}{c} fact2: {E}{c} -> {F}{c} fact3: {C}{b} -> {D}{c} fact4: ({A}{a} & {B}{a}) fact5: {B}{a} -> {C}{b} fact6: {A}{a} ; $hypothesis$ = {F}{c} ; $proof$ = | fact4 -> int1: {B}{a}; int1 & fact5 -> int2: {C}{b}; int2 & fact3 -> int3: {D}{c}; int3 & fact1 -> int4: {E}{c}; int4 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãã«ã
ãã«ãLv.36ã¯ïŒ¯ïŒ¢èããªã | ¬{F}{c} | fact1: ããããã®ãŽããŽãLv.89ã¯çšè¿ããªããšãããããã®ãŽã¡ããŽã«ãLv.28ã¯åŸããæãäžæ¹ã§å人ããããªãããšããããšã¯çå®ã§ãªã fact2: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãæããªãããã¯çšè¿ããªã fact3: çšè¿ããªãã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãã®ãŽã¡ããŽã«ãLv.28ãå人ããããªããã®ãŽããŽãLv.89ã¯æããããã¯çšè¿ããªã fact5: ããããæããçšè¿ããªããã¢ã³ã¹ã¿ãŒããããªããã®ãã«ã
ãã«ãLv.36ã¯åºãé£ã fact6: ãã®ãŽã¡ããŽã«ãLv.28ã¯åŸããæã fact7: ãããä»®ã«ãã®ãã«ã
ãã«ãLv.36ã¯åºãé£ããšãããšããã®ãã«ã
ãã«ãLv.36ã¯ïŒ¯ïŒ¢èãããšããããšã¯æ£ããããšããããšã¯èª€ãã§ãªã fact8: ãããããã®ãŽã¡ããŽã«ãLv.28ã¯åŸããæãããšããããšã¯æãç«ã€ãšããã°ããã¯å人ããã | fact1: ¬{C}{b} -> ¬({A}{a} & ¬{B}{a}) fact2: (x): {D}x -> ¬{C}x fact3: (Ex): ¬{C}x fact4: {B}{a} -> ({D}{b} & ¬{C}{b}) fact5: (x): ({D}x & ¬{C}x) -> {E}{c} fact6: {A}{a} fact7: {E}{c} -> {F}{c} fact8: {A}{a} -> {B}{a} | [
"fact8 & fact6 -> int1: ãã®ãŽã¡ããŽã«ãLv.28ã¯å人ããã; int1 & fact4 -> int2: ãã®ãŽããŽãLv.89ã¯æãããã©çšè¿ããªã; int2 -> int3: ãæãäžæ¹ã§çšè¿ããªããã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact5 -> int4: ãã®ãã«ã
ãã«ãLv.36ã¯åºãé£ã; int4 & fact7 -> hypothesis;"
] | [
"fact8 & fact6 -> int1: {B}{a}; int1 & fact4 -> int2: ({D}{b} & ¬{C}{b}); int2 -> int3: (Ex): ({D}x & ¬{C}x); int3 & fact5 -> int4: {E}{c}; int4 & fact7 -> hypothesis;"
] | ãã®ãã«ã
ãã«ãLv.36ã¯ïŒ¯ïŒ¢èããªã | ¬{F}{c} | [
"fact10 -> int5: ä»®ã«ãã®ãŽããŽãLv.89ã¯æããªãããã®ãŽããŽãLv.89ã¯çšè¿ããªãããšããããšã¯ééã£ãŠããªã;"
] | 5 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããã®ãŽããŽãLv.89ã¯çšè¿ããªããšãããããã®ãŽã¡ããŽã«ãLv.28ã¯åŸããæãäžæ¹ã§å人ããããªãããšããããšã¯çå®ã§ãªã fact2: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãæããªãããã¯çšè¿ããªã fact3: çšè¿ããªãã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãã®ãŽã¡ããŽã«ãLv.28ãå人ããããªããã®ãŽããŽãLv.89ã¯æããããã¯çšè¿ããªã fact5: ããããæããçšè¿ããªããã¢ã³ã¹ã¿ãŒããããªããã®ãã«ã
ãã«ãLv.36ã¯åºãé£ã fact6: ãã®ãŽã¡ããŽã«ãLv.28ã¯åŸããæã fact7: ãããä»®ã«ãã®ãã«ã
ãã«ãLv.36ã¯åºãé£ããšãããšããã®ãã«ã
ãã«ãLv.36ã¯ïŒ¯ïŒ¢èãããšããããšã¯æ£ããããšããããšã¯èª€ãã§ãªã fact8: ãããããã®ãŽã¡ããŽã«ãLv.28ã¯åŸããæãããšããããšã¯æãç«ã€ãšããã°ããã¯å人ããã ; $hypothesis$ = ãã®ãã«ã
ãã«ãLv.36ã¯ïŒ¯ïŒ¢èããªã ; $proof$ = | fact8 & fact6 -> int1: ãã®ãŽã¡ããŽã«ãLv.28ã¯å人ããã; int1 & fact4 -> int2: ãã®ãŽããŽãLv.89ã¯æãããã©çšè¿ããªã; int2 -> int3: ãæãäžæ¹ã§çšè¿ããªããã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact5 -> int4: ãã®ãã«ã
ãã«ãLv.36ã¯åºãé£ã; int4 & fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{C}{b} -> ¬({A}{a} & ¬{B}{a}) fact2: (x): {D}x -> ¬{C}x fact3: (Ex): ¬{C}x fact4: {B}{a} -> ({D}{b} & ¬{C}{b}) fact5: (x): ({D}x & ¬{C}x) -> {E}{c} fact6: {A}{a} fact7: {E}{c} -> {F}{c} fact8: {A}{a} -> {B}{a} ; $hypothesis$ = ¬{F}{c} ; $proof$ = | fact8 & fact6 -> int1: {B}{a}; int1 & fact4 -> int2: ({D}{b} & ¬{C}{b}); int2 -> int3: (Ex): ({D}x & ¬{C}x); int3 & fact5 -> int4: {E}{c}; int4 & fact7 -> hypothesis; __DISPROVED__ |
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