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®ãŽããŽã®Lv.1ã¯åŸ®åãããããã¯æ²ç€ºããããšããããšã¯æãç«ããªã | ¬({C}{c} v {A}{c}) | fact1: ããããã®ã¿ã«ãã¿ã«ãLv.22ãæ²ç€ºããªããšããããã®ãŽããŽã®Lv.1ã¯åŸ®åããããããã¯æ²ç€ºããããããã¯ã©ã¡ããã fact2: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã埮åããªããšãããåçºããªãããšããããšã¯ç¢ºãã fact3: ãããªãããã®ã¢ã³ã¹ã¿ãŒãåçºããªããªãã°æ²ç€ºããªããŠãã®äžåŠæ€ããªã fact4: ãã®ãœããœã¡ã
Lv.50ã¯åçºããªã | fact1: ¬{A}{a} -> ({C}{c} v {A}{c}) fact2: (x): ¬{C}x -> ¬{B}x fact3: (x): ¬{B}x -> (¬{A}x & ¬{CP}x) fact4: ¬{B}{b} | [] | [] | ãã®ãŽããŽã®Lv.1ã¯åŠæ€ããªã | ¬{CP}{c} | [
"fact6 -> int1: ããä»®ã«ãã®ãŽããŽã®Lv.1ãåçºããªããšãããšæ²ç€ºããªããŠãã€åŠæ€ããªã; fact5 -> int2: ãã®ãŽããŽã®Lv.1ã¯åŸ®åããªããšããã°ãåçºããªãããšããããšã¯æ£ãã;"
] | 5 | 5 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®ã¿ã«ãã¿ã«ãLv.22ãæ²ç€ºããªããšããããã®ãŽããŽã®Lv.1ã¯åŸ®åããããããã¯æ²ç€ºããããããã¯ã©ã¡ããã fact2: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã埮åããªããšãããåçºããªãããšããããšã¯ç¢ºãã fact3: ãããªãããã®ã¢ã³ã¹ã¿ãŒãåçºããªããªãã°æ²ç€ºããªããŠãã®äžåŠæ€ããªã fact4: ãã®ãœããœã¡ã
Lv.50ã¯åçºããªã ; $hypothesis$ = ããã®ãŽããŽã®Lv.1ã¯åŸ®åãããããã¯æ²ç€ºããããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A}{a} -> ({C}{c} v {A}{c}) fact2: (x): ¬{C}x -> ¬{B}x fact3: (x): ¬{B}x -> (¬{A}x & ¬{CP}x) fact4: ¬{B}{b} ; $hypothesis$ = ¬({C}{c} v {A}{c}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãç²ãé£ããšããããšã¯çããªãããããã¯ç©æ²ãããšããããšã¯çããªããäž¡æ¹ã ããšããããšã¯åœã | ¬(¬{A} v ¬{B}) | fact1: åãå
¥ãé£ããšããããšã¯ç²ãé£ããšããããšã¯èµ·ããªããšããããšã«é»æ¢ããã fact2: ãå¯ããšããããšã¯èµ·ããªããŠå ããŠåãå
¥ãé£ããšããããšã¯èµ·ããªãããšããããšã¯ééãã§ãã fact3: åãå
¥ãé£ããšããããšã¯çããªããšããããšã¯ãå¯ããšããããšã¯èµ·ãããªãããã€åãå
¥ãé£ããšããããšã¯çºçããªãããšããããšãåŒãèµ·ãã fact4: åãå
¥ãé£ããšããããšã¯çããªããšããããšã¯ç©æ²ãããšããããšã¯èµ·ããªããšããããšã«ãããããã | fact1: ¬{A} -> ¬{C} fact2: ¬(¬{E} & ¬{C}) fact3: ¬{C} -> (¬{E} & ¬{C}) fact4: ¬{B} -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããç²ãé£ããšããããšã¯èµ·ããªãããããã¯ç©æ²ãããšããããšã¯çºçããªãããŸãã¯äž¡æ¹ã ; assump1 & fact1 & fact4 -> int1: åãå
¥ãé£ããšããããšã¯çããªã; int1 & fact3 -> int2: å¯ããšããããšã¯çããªããŠãã®äžåãå
¥ãé£ããšããããšã¯çããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: (¬{A} v ¬{B}); assump1 & fact1 & fact4 -> int1: ¬{C}; int1 & fact3 -> int2: (¬{E} & ¬{C}); int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: åãå
¥ãé£ããšããããšã¯ç²ãé£ããšããããšã¯èµ·ããªããšããããšã«é»æ¢ããã fact2: ãå¯ããšããããšã¯èµ·ããªããŠå ããŠåãå
¥ãé£ããšããããšã¯èµ·ããªãããšããããšã¯ééãã§ãã fact3: åãå
¥ãé£ããšããããšã¯çããªããšããããšã¯ãå¯ããšããããšã¯èµ·ãããªãããã€åãå
¥ãé£ããšããããšã¯çºçããªãããšããããšãåŒãèµ·ãã fact4: åãå
¥ãé£ããšããããšã¯çããªããšããããšã¯ç©æ²ãããšããããšã¯èµ·ããªããšããããšã«ãããããã ; $hypothesis$ = ãç²ãé£ããšããããšã¯çããªãããããã¯ç©æ²ãããšããããšã¯çããªããäž¡æ¹ã ããšããããšã¯åœã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããç²ãé£ããšããããšã¯èµ·ããªãããããã¯ç©æ²ãããšããããšã¯çºçããªãããŸãã¯äž¡æ¹ã ; assump1 & fact1 & fact4 -> int1: åãå
¥ãé£ããšããããšã¯çããªã; int1 & fact3 -> int2: å¯ããšããããšã¯çããªããŠãã®äžåãå
¥ãé£ããšããããšã¯çããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A} -> ¬{C} fact2: ¬(¬{E} & ¬{C}) fact3: ¬{C} -> (¬{E} & ¬{C}) fact4: ¬{B} -> ¬{C} ; $hypothesis$ = ¬(¬{A} v ¬{B}) ; $proof$ = | void -> assump1: (¬{A} v ¬{B}); assump1 & fact1 & fact4 -> int1: ¬{C}; int1 & fact3 -> int2: (¬{E} & ¬{C}); int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ãã·ãLv.44ã¯æã¡æã | {F}{c} | fact1: ãããã®ã·ãã·ãLv.44ãçãæ·±ããŠããŸãã«è³¢ããšãããšæã¡æããšããããšã¯ãªã fact2: ãã®ãŽã«ãŽã«Lv.4ã¯é ã fact3: ãããã®ã·ãã·ãªLv.76ãå²ãããšãããšãã®ã·ãã·ãLv.44ã¯çãæ·±ã fact4: ããä»®ã«ãã®ãŽã«ãŽã«Lv.4ãé ããšããããã®ã·ãã·ãªLv.76ã¯çæž©ãã fact5: ããã®ã·ãã·ãLv.44ã¯è³¢ãããšããããšã¯æ£ãã fact6: ããä»®ã«ãã®ã·ãã·ãªLv.76ã¯é ããããã«çæž©ãããšãããæã¡æããªã fact7: ããããã®ã·ãã·ãªLv.76ã¯çæž©ããããšããããšã¯äºå®ã ãšãããšããã¯å²ãã | fact1: ({D}{c} & {E}{c}) -> ¬{F}{c} fact2: {A}{a} fact3: {C}{b} -> {D}{c} fact4: {A}{a} -> {B}{b} fact5: {E}{c} fact6: ({A}{b} & {B}{b}) -> ¬{F}{b} fact7: {B}{b} -> {C}{b} | [
"fact4 & fact2 -> int1: ãã®ã·ãã·ãªLv.76ã¯çæž©ãã; int1 & fact7 -> int2: ããã®ã·ãã·ãªLv.76ã¯å²ããããšããããšã¯çå®ã ; int2 & fact3 -> int3: ãã®ã·ãã·ãLv.44ã¯çãæ·±ã; int3 & fact5 -> int4: ãã®ã·ãã·ãLv.44ã¯çãæ·±ãããããããã¯è³¢ã; int4 & fact1 -> hypothesis;"
] | [
"fact4 & fact2 -> int1: {B}{b}; int1 & fact7 -> int2: {C}{b}; int2 & fact3 -> int3: {D}{c}; int3 & fact5 -> int4: ({D}{c} & {E}{c}); int4 & fact1 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããã®ã·ãã·ãLv.44ãçãæ·±ããŠããŸãã«è³¢ããšãããšæã¡æããšããããšã¯ãªã fact2: ãã®ãŽã«ãŽã«Lv.4ã¯é ã fact3: ãããã®ã·ãã·ãªLv.76ãå²ãããšãããšãã®ã·ãã·ãLv.44ã¯çãæ·±ã fact4: ããä»®ã«ãã®ãŽã«ãŽã«Lv.4ãé ããšããããã®ã·ãã·ãªLv.76ã¯çæž©ãã fact5: ããã®ã·ãã·ãLv.44ã¯è³¢ãããšããããšã¯æ£ãã fact6: ããä»®ã«ãã®ã·ãã·ãªLv.76ã¯é ããããã«çæž©ãããšãããæã¡æããªã fact7: ããããã®ã·ãã·ãªLv.76ã¯çæž©ããããšããããšã¯äºå®ã ãšãããšããã¯å²ãã ; $hypothesis$ = ãã®ã·ãã·ãLv.44ã¯æã¡æã ; $proof$ = | fact4 & fact2 -> int1: ãã®ã·ãã·ãªLv.76ã¯çæž©ãã; int1 & fact7 -> int2: ããã®ã·ãã·ãªLv.76ã¯å²ããããšããããšã¯çå®ã ; int2 & fact3 -> int3: ãã®ã·ãã·ãLv.44ã¯çãæ·±ã; int3 & fact5 -> int4: ãã®ã·ãã·ãLv.44ã¯çãæ·±ãããããããã¯è³¢ã; int4 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({D}{c} & {E}{c}) -> ¬{F}{c} fact2: {A}{a} fact3: {C}{b} -> {D}{c} fact4: {A}{a} -> {B}{b} fact5: {E}{c} fact6: ({A}{b} & {B}{b}) -> ¬{F}{b} fact7: {B}{b} -> {C}{b} ; $hypothesis$ = {F}{c} ; $proof$ = | fact4 & fact2 -> int1: {B}{b}; int1 & fact7 -> int2: {C}{b}; int2 & fact3 -> int3: {D}{c}; int3 & fact5 -> int4: ({D}{c} & {E}{c}); int4 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸã«ããŸãLv.9ã¯æéåºæ¥ã | {A}{a} | fact1: ãããããšããã¢ã³ã¹ã¿ãŒã¯æ©ãèŸããŠåŸ¡è©³ããããšããããšã¯åœã§ãããšããã°ããã¯æ©ãèŸããªã fact2: ããã¯æ©ãèŸããŠåŸ¡è©³ãããšããã¢ã³ã¹ã¿ãŒã¯ãªã fact3: 圌ãããã¢ã³ã¹ã¿ãŒã¯æéåºæ¥ãªã | fact1: (x): ¬({D}x & {F}x) -> ¬{D}x fact2: (x): ¬({D}x & {F}x) fact3: (x): {C}x -> ¬{A}x | [] | [] | ãã®ãŸã«ããŸãLv.9ã¯æéåºæ¥ãªã | ¬{A}{a} | [
"fact5 -> int1: ä»®ã«ãã®ãŸã«ããŸãLv.9ã圌ããããªãã°ãã®ãŸã«ããŸãLv.9ã¯æéåºæ¥ãªã; fact6 -> int2: ä»®ã«ããã®ã¿ãã¿ã¡ãLv.79ã¯æ©ãèŸãããããããã¯åŸ¡è©³ããããšããããšã¯æãç«ã€ãšããããšã¯ãªããšããã°ãã®ã¿ãã¿ã¡ãLv.79ã¯æ©ãèŸããªã; fact4 -> int3: ããã®ã¿ãã¿ã¡ãLv.79ã¯æ©ãèŸããããã¯åŸ¡è©³ããããšããããšã¯æ¬åœã§ãªã; int2 & int3 -> int4: ãã®ã¿ãã¿ã¡ãLv.79ã¯æ©ãèŸããªã; int4 -> int5: ããããã¢ã³ã¹ã¿ãŒã¯æ©ãèŸããªã; int5 -> int6: ãã®ãã«ããã«ã
Lv.59ã¯æ©ãèŸããªã; int6 -> int7: ããã¢ã³ã¹ã¿ãŒã¯æ©ãèŸããªã;"
] | 7 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããããšããã¢ã³ã¹ã¿ãŒã¯æ©ãèŸããŠåŸ¡è©³ããããšããããšã¯åœã§ãããšããã°ããã¯æ©ãèŸããªã fact2: ããã¯æ©ãèŸããŠåŸ¡è©³ãããšããã¢ã³ã¹ã¿ãŒã¯ãªã fact3: 圌ãããã¢ã³ã¹ã¿ãŒã¯æéåºæ¥ãªã ; $hypothesis$ = ãã®ãŸã«ããŸãLv.9ã¯æéåºæ¥ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬({D}x & {F}x) -> ¬{D}x fact2: (x): ¬({D}x & {F}x) fact3: (x): {C}x -> ¬{A}x ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ãããèŠããšããããšãçºçãã | {A} | fact1: æŽãããŸãããšããããšã¯ãœããœã«ãLv.77äºä»¶ãåé¿ãã fact2: ããœããœã«ãLv.77äºä»¶ãçºçããããšããããšã¯æãç«ã€ fact3: ãœããœã«ãLv.77äºä»¶ã¯çããªããšããããšã¯èŠããšããããšãæŽãããŸãããšããããšããããã¯äž¡æ¹ãšãã«èµ·å ãã | fact1: {B} -> ¬{C} fact2: {C} fact3: ({A} v {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããèŠããšããããšãçºçãã; assump1 -> int1: èŠããšããããšãèµ·ããããããã¯æŽãããŸãããšããããšãèµ·ãã; int1 & fact3 -> int2: ãœããœã«ãLv.77äºä»¶ã¯èµ·ããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 3 | 5 | 3 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: æŽãããŸãããšããããšã¯ãœããœã«ãLv.77äºä»¶ãåé¿ãã fact2: ããœããœã«ãLv.77äºä»¶ãçºçããããšããããšã¯æãç«ã€ fact3: ãœããœã«ãLv.77äºä»¶ã¯çããªããšããããšã¯èŠããšããããšãæŽãããŸãããšããããšããããã¯äž¡æ¹ãšãã«èµ·å ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããèŠããšããããšãçºçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããèŠããšããããšãçºçãã; assump1 -> int1: èŠããšããããšãèµ·ããããããã¯æŽãããŸãããšããããšãèµ·ãã; int1 & fact3 -> int2: ãœããœã«ãLv.77äºä»¶ã¯èµ·ããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} -> ¬{C} fact2: {C} fact3: ({A} v {B}) -> ¬{C} ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãã¡ããã¡ãLv.2ã¯æ矩深ã | {E}{c} | fact1: ãã®ãŸã¡ããŸã®Lv.58ã¯ã¢ã¯ã»ã¹ãæã fact2: ä»®ã«ããã°ãããªãã¢ã³ã¹ã¿ãŒãèªã¿çµããªããšãããšãã®ãã¡ããã¡ãLv.2ã¯æ矩深ããªã fact3: ä»®ã«ãã®ãŸã¡ããŸã®Lv.58ãäŒèšããäžæ¹ã§è¶åºãããªããšãããšãã®ãŸã¡ããŸã®Lv.58ã¯ç±ã£ãœã fact4: ãããã®ãŸã¡ããŸã®Lv.58ãã¢ã¯ã»ã¹ãæããªãã°äŒèšãããå ããŠè¶åºãããªã | fact1: {A}{a} fact2: (x): (¬{D}x & ¬{C}x) -> ¬{E}{c} fact3: ({AA}{a} & ¬{AB}{a}) -> {B}{a} fact4: {A}{a} -> ({AA}{a} & ¬{AB}{a}) | [
"fact4 & fact1 -> int1: ãã®ãŸã¡ããŸã®Lv.58ã¯äŒèšãããã©è¶åºããããšããããšã¯ãªã; int1 & fact3 -> int2: ããã®ãŸã¡ããŸã®Lv.58ã¯ç±ã£ãœãããšããããšã¯æ¬åœã§ãã;"
] | [
"fact4 & fact1 -> int1: ({AA}{a} & ¬{AB}{a}); int1 & fact3 -> int2: {B}{a};"
] | null | null | [] | null | 5 | 5 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãŸã¡ããŸã®Lv.58ã¯ã¢ã¯ã»ã¹ãæã fact2: ä»®ã«ããã°ãããªãã¢ã³ã¹ã¿ãŒãèªã¿çµããªããšãããšãã®ãã¡ããã¡ãLv.2ã¯æ矩深ããªã fact3: ä»®ã«ãã®ãŸã¡ããŸã®Lv.58ãäŒèšããäžæ¹ã§è¶åºãããªããšãããšãã®ãŸã¡ããŸã®Lv.58ã¯ç±ã£ãœã fact4: ãããã®ãŸã¡ããŸã®Lv.58ãã¢ã¯ã»ã¹ãæããªãã°äŒèšãããå ããŠè¶åºãããªã ; $hypothesis$ = ãã®ãã¡ããã¡ãLv.2ã¯æ矩深ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} fact2: (x): (¬{D}x & ¬{C}x) -> ¬{E}{c} fact3: ({AA}{a} & ¬{AB}{a}) -> {B}{a} fact4: {A}{a} -> ({AA}{a} & ¬{AB}{a}) ; $hypothesis$ = {E}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãŸããŸãLv.98äºä»¶ã¯çããªã | ¬{C} | fact1: èŠåãé£ããšããããšã¯èãç¶ããããšã¯èµ·ããªããšããããšãåé¿ãã fact2: èãç¶ããããšã¯çããªã fact3: ãŸããŸãLv.98äºä»¶ã¯èŠåãé£ããšããããšã¯èµ·ãããªããšããããšã«åŒãèµ·ãããã fact4: ããªããLv.82äºä»¶ã¯ã·ã«ã
ã·ãLv.14äºä»¶ã«åž°çµãã | fact1: {A} -> {B} fact2: ¬{B} fact3: ¬{A} -> {C} fact4: {GQ} -> {BR} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããèŠåãé£ããšããããšãèµ·ãã; fact1 & assump1 -> int1: èãç¶ããããšãèµ·ãã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: èŠåãé£ããšããããšã¯çºçããªã; int3 & fact3 -> hypothesis;"
] | [
"void -> assump1: {A}; fact1 & assump1 -> int1: {B}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}; int3 & fact3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: èŠåãé£ããšããããšã¯èãç¶ããããšã¯èµ·ããªããšããããšãåé¿ãã fact2: èãç¶ããããšã¯çããªã fact3: ãŸããŸãLv.98äºä»¶ã¯èŠåãé£ããšããããšã¯èµ·ãããªããšããããšã«åŒãèµ·ãããã fact4: ããªããLv.82äºä»¶ã¯ã·ã«ã
ã·ãLv.14äºä»¶ã«åž°çµãã ; $hypothesis$ = ãŸããŸãLv.98äºä»¶ã¯çããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããèŠåãé£ããšããããšãèµ·ãã; fact1 & assump1 -> int1: èãç¶ããããšãèµ·ãã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: èŠåãé£ããšããããšã¯çºçããªã; int3 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} -> {B} fact2: ¬{B} fact3: ¬{A} -> {C} fact4: {GQ} -> {BR} ; $hypothesis$ = ¬{C} ; $proof$ = | void -> assump1: {A}; fact1 & assump1 -> int1: {B}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}; int3 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããŽããŽã®Lv.52äºä»¶ãèµ·ãã | {A} | fact1: ãŸã«ããŸãLv.33äºä»¶ãèµ·ãã fact2: ãŽããŽã«ã
Lv.58äºä»¶ãèµ·ãã fact3: ãŽããŽã®Lv.52äºä»¶ãšãŽããŽã«ã
Lv.58äºä»¶ãçºçããã¯ãŸã«ããŸãLv.33äºä»¶ãé»æ¢ãã | fact1: {C} fact2: {B} fact3: ({A} & {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããŽããŽã®Lv.52äºä»¶ãèµ·ãã; assump1 & fact2 -> int1: ãŽããŽã®Lv.52äºä»¶ãçºçããããã€ãŽããŽã«ã
Lv.58äºä»¶ãèµ·ãã; int1 & fact3 -> int2: ãŸã«ããŸãLv.33äºä»¶ã¯çºçããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact2 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãŸã«ããŸãLv.33äºä»¶ãèµ·ãã fact2: ãŽããŽã«ã
Lv.58äºä»¶ãèµ·ãã fact3: ãŽããŽã®Lv.52äºä»¶ãšãŽããŽã«ã
Lv.58äºä»¶ãçºçããã¯ãŸã«ããŸãLv.33äºä»¶ãé»æ¢ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããŽããŽã®Lv.52äºä»¶ãèµ·ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããŽããŽã®Lv.52äºä»¶ãèµ·ãã; assump1 & fact2 -> int1: ãŽããŽã®Lv.52äºä»¶ãçºçããããã€ãŽããŽã«ã
Lv.58äºä»¶ãèµ·ãã; int1 & fact3 -> int2: ãŸã«ããŸãLv.33äºä»¶ã¯çºçããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C} fact2: {B} fact3: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: {A}; assump1 & fact2 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããŽã«ããŽã«ãLv.64äºä»¶ãèµ·ãã | {A} | fact1: æ¯èŠªããããšããããšã¯çºçããªã fact2: é»ããšããããšãèµ·ãã fact3: ããä»®ã«ãŽã«ããŽã«ãLv.64äºä»¶ããã³åãå§ããããšãçºçãããšãããé»ããšããããšã¯èµ·ãããªã | fact1: ¬{DG} fact2: {C} fact3: ({A} & {B}) -> ¬{C} | [] | [] | null | null | [] | null | 5 | 4 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: æ¯èŠªããããšããããšã¯çºçããªã fact2: é»ããšããããšãèµ·ãã fact3: ããä»®ã«ãŽã«ããŽã«ãLv.64äºä»¶ããã³åãå§ããããšãçºçãããšãããé»ããšããããšã¯èµ·ãããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããŽã«ããŽã«ãLv.64äºä»¶ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{DG} fact2: {C} fact3: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {A} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã®ããããLv.38ã¯æããããŠãŸãããã¯å£ãããªãããšããããšã¯èª€ãã§ããããšããããšã¯çå®ã | ¬({A}{a} & {B}{a}) | fact1: ãã®ãŽããŽãLv.63ã¯æããã fact2: ãããäœããã®ã¢ã³ã¹ã¿ãŒãåãæ±ãæãäžæ¹ã§ãããå£ãããªããšããããšã¯ãªããªãã°æããã fact3: ãã®ããããLv.38ã¯å£ãããªã fact4: ãã®ããããLv.38ã¯æããã | fact1: {A}{i} fact2: (x): ({C}x & ¬{B}x) -> {A}x fact3: {B}{a} fact4: {A}{a} | [
"fact4 -> int1: ãã®ããããLv.38ã¯æããã; int1 & fact3 -> hypothesis;"
] | [
"fact4 -> int1: {A}{a}; int1 & fact3 -> hypothesis;"
] | ããã®ãœããœãªLv.57ã¯æãããããšããããšã¯æãç«ã€ | {A}{da} | [
"fact5 -> int2: ãã®ãœããœãªLv.57ãåãæ±ãæãã¢ã³ã¹ã¿ãŒã§ãã£ãŠå ããŠå£ãããªããªããªãã°ãã®ãœããœãªLv.57ã¯æããã;"
] | 4 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŽããŽãLv.63ã¯æããã fact2: ãããäœããã®ã¢ã³ã¹ã¿ãŒãåãæ±ãæãäžæ¹ã§ãããå£ãããªããšããããšã¯ãªããªãã°æããã fact3: ãã®ããããLv.38ã¯å£ãããªã fact4: ãã®ããããLv.38ã¯æããã ; $hypothesis$ = ãããã®ããããLv.38ã¯æããããŠãŸãããã¯å£ãããªãããšããããšã¯èª€ãã§ããããšããããšã¯çå®ã ; $proof$ = | fact4 -> int1: ãã®ããããLv.38ã¯æããã; int1 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{i} fact2: (x): ({C}x & ¬{B}x) -> {A}x fact3: {B}{a} fact4: {A}{a} ; $hypothesis$ = ¬({A}{a} & {B}{a}) ; $proof$ = | fact4 -> int1: {A}{a}; int1 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ããããLv.82ã¯èœã¡æããæŽã«å
¥ãé£ãããšããããšã¯ç¢ºãã§ãªã | ¬({C}{c} & {D}{c}) | fact1: ãããããã¢ã³ã¹ã¿ãŒã¯åºæ¥é£ããªããèããããããã¯äž¡æ¹ãšãã ããšããããšã¯äºå®ãšç°ãªããšããã°ãèœã¡æããªãããšããããšã¯äºå®ã§ãã fact2: ããããé€éãããèŠãããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ããããLv.82ã¯èãã fact3: ä»®ã«ããã®ãœã«ãœãªLv.79ã¯åºæ¥é£ããªãããšããããšã¯æãç«ã€ãšããã°ããã®ã·ãã·ã¡ãLv.13ã¯é€éãããããã¯èŠãããšããããšã¯æãç«ããªã fact4: ãã®ãœã«ãœãªLv.79ã¯åºæ¥é£ããªã fact5: ããã®ããããLv.82ã¯å
¥ãé£ããšããããšã¯ãªãããšããããšã¯ééã£ãŠãã | fact1: (x): ¬(¬{A}x v {B}x) -> ¬{C}x fact2: (x): ¬({AA}x & {AB}x) -> {B}{c} fact3: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact4: ¬{A}{a} fact5: {D}{c} | [
"fact3 & fact4 -> int1: ããã®ã·ãã·ã¡ãLv.13ã¯é€éããããããèŠãããšããããšã¯æãç«ããªã; int1 -> int2: ããé€éãããèŠãããšããããšã¯æãç«ã€ãšããããšã¯ãªããã¢ã³ã¹ã¿ãŒã¯ãã; int2 & fact2 -> int3: ããã®ããããLv.82ã¯èããããšããããšã¯æãç«ã€;"
] | [
"fact3 & fact4 -> int1: ¬({AA}{b} & {AB}{b}); int1 -> int2: (Ex): ¬({AA}x & {AB}x); int2 & fact2 -> int3: {B}{c};"
] | ããã®ããããLv.82ã¯èœã¡æããæŽã«å
¥ãé£ãããšããããšã¯ç¢ºãã§ãªã | ¬({C}{c} & {D}{c}) | [
"fact6 -> int4: ããä»®ã«ãããã®ãœã«ãœãªLv.79ã¯åºæ¥é£ããšããããšã¯ãªãããŸãã¯èããããããã¯äž¡æ¹ã ããšããããšã¯æãç«ã€ããšããããšã¯æãç«ããªããšããã°ããã¯èœã¡æããªã;"
] | 5 | 5 | 5 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããããã¢ã³ã¹ã¿ãŒã¯åºæ¥é£ããªããèããããããã¯äž¡æ¹ãšãã ããšããããšã¯äºå®ãšç°ãªããšããã°ãèœã¡æããªãããšããããšã¯äºå®ã§ãã fact2: ããããé€éãããèŠãããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ããããLv.82ã¯èãã fact3: ä»®ã«ããã®ãœã«ãœãªLv.79ã¯åºæ¥é£ããªãããšããããšã¯æãç«ã€ãšããã°ããã®ã·ãã·ã¡ãLv.13ã¯é€éãããããã¯èŠãããšããããšã¯æãç«ããªã fact4: ãã®ãœã«ãœãªLv.79ã¯åºæ¥é£ããªã fact5: ããã®ããããLv.82ã¯å
¥ãé£ããšããããšã¯ãªãããšããããšã¯ééã£ãŠãã ; $hypothesis$ = ããã®ããããLv.82ã¯èœã¡æããæŽã«å
¥ãé£ãããšããããšã¯ç¢ºãã§ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬(¬{A}x v {B}x) -> ¬{C}x fact2: (x): ¬({AA}x & {AB}x) -> {B}{c} fact3: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact4: ¬{A}{a} fact5: {D}{c} ; $hypothesis$ = ¬({C}{c} & {D}{c}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ã«ãã·ãLv.72ã¯æãæããªããæŽã«åŸ¡åµ©ãŸãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬(¬{E}{a} & ¬{D}{a}) | fact1: ããä»®ã«ãã®ãœããœã¡ãLv.46ãé«ããŠããŸãã«æãé£ããªãã°ãã®ã·ã«ãã·ãLv.72ã¯åŸ¡åµ©ããšããããšã¯ãªã fact2: ããã®ãœããœã¡ãLv.46ã¯ã²ãããããšããããšã¯ç¢ºãã fact3: ã²ããããªãã¢ã³ã¹ã¿ãŒã¯åºããªããããŸãã«æãæããªã fact4: ãããšããã¢ã³ã¹ã¿ãŒã¯ã²ããããªãã°ãæãæããªãããã€åŸ¡åµ©ãŸãªãããšããããšã¯æãç«ããªã fact5: ã²ãããã¢ã³ã¹ã¿ãŒã¯æãé£ã fact6: ãã®ãœããœã¡ãLv.46ã¯é«ã fact7: ãã®ã·ã«ãã·ãLv.72ã¯æãæããªã | fact1: ({B}{aa} & {C}{aa}) -> ¬{D}{a} fact2: {A}{aa} fact3: (x): ¬{A}x -> (¬{BU}x & ¬{E}x) fact4: (x): {A}x -> ¬(¬{E}x & ¬{D}x) fact5: (x): {A}x -> {C}x fact6: {B}{aa} fact7: ¬{E}{a} | [
"fact5 -> int1: ä»®ã«ãã®ãœããœã¡ãLv.46ãã²ããããªããã®ãœããœã¡ãLv.46ã¯æãé£ã; int1 & fact2 -> int2: ãã®ãœããœã¡ãLv.46ã¯æãé£ã; int2 & fact6 -> int3: ãã®ãœããœã¡ãLv.46ã¯é«ããŠæãé£ã; int3 & fact1 -> int4: ãã®ã·ã«ãã·ãLv.72ã¯åŸ¡åµ©ãŸãªã; int4 & fact7 -> hypothesis;"
] | [
"fact5 -> int1: {A}{aa} -> {C}{aa}; int1 & fact2 -> int2: {C}{aa}; int2 & fact6 -> int3: ({B}{aa} & {C}{aa}); int3 & fact1 -> int4: ¬{D}{a}; int4 & fact7 -> hypothesis;"
] | ãã®ããããLv.13ã¯åºããšããããšã¯ãªããŠããã¯æãæããšããããšã¯ãªã | (¬{BU}{hp} & ¬{E}{hp}) | [
"fact8 -> int5: ããã®ããããLv.13ã¯ã²ãããããšããããšã¯åã ãšãããšãã®ããããLv.13ã¯åºããšããããšã¯ãªãããããæãæããªã;"
] | 6 | 5 | 5 | 5 | 5 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãœããœã¡ãLv.46ãé«ããŠããŸãã«æãé£ããªãã°ãã®ã·ã«ãã·ãLv.72ã¯åŸ¡åµ©ããšããããšã¯ãªã fact2: ããã®ãœããœã¡ãLv.46ã¯ã²ãããããšããããšã¯ç¢ºãã fact3: ã²ããããªãã¢ã³ã¹ã¿ãŒã¯åºããªããããŸãã«æãæããªã fact4: ãããšããã¢ã³ã¹ã¿ãŒã¯ã²ããããªãã°ãæãæããªãããã€åŸ¡åµ©ãŸãªãããšããããšã¯æãç«ããªã fact5: ã²ãããã¢ã³ã¹ã¿ãŒã¯æãé£ã fact6: ãã®ãœããœã¡ãLv.46ã¯é«ã fact7: ãã®ã·ã«ãã·ãLv.72ã¯æãæããªã ; $hypothesis$ = ããã®ã·ã«ãã·ãLv.72ã¯æãæããªããæŽã«åŸ¡åµ©ãŸãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact5 -> int1: ä»®ã«ãã®ãœããœã¡ãLv.46ãã²ããããªããã®ãœããœã¡ãLv.46ã¯æãé£ã; int1 & fact2 -> int2: ãã®ãœããœã¡ãLv.46ã¯æãé£ã; int2 & fact6 -> int3: ãã®ãœããœã¡ãLv.46ã¯é«ããŠæãé£ã; int3 & fact1 -> int4: ãã®ã·ã«ãã·ãLv.72ã¯åŸ¡åµ©ãŸãªã; int4 & fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({B}{aa} & {C}{aa}) -> ¬{D}{a} fact2: {A}{aa} fact3: (x): ¬{A}x -> (¬{BU}x & ¬{E}x) fact4: (x): {A}x -> ¬(¬{E}x & ¬{D}x) fact5: (x): {A}x -> {C}x fact6: {B}{aa} fact7: ¬{E}{a} ; $hypothesis$ = ¬(¬{E}{a} & ¬{D}{a}) ; $proof$ = | fact5 -> int1: {A}{aa} -> {C}{aa}; int1 & fact2 -> int2: {C}{aa}; int2 & fact6 -> int3: ({B}{aa} & {C}{aa}); int3 & fact1 -> int4: ¬{D}{a}; int4 & fact7 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãLv.2ã¯åãé£ããªã | ¬{A}{a} | fact1: ä»®ã«ãã®ãŸããŸãLv.2ãåãé£ããªãããã¯çžè«ãæã fact2: ãã®ãŸããŸãLv.2ã¯çžè«ãæããšããã°ããã®ãŽããŽãLv.75ã¯å¯ãŒãããšããããšã¯æãç«ã€ fact3: ãã®ãŽããŽãLv.75ã¯å¯ãŒããªã | fact1: {A}{a} -> {B}{a} fact2: {B}{a} -> {C}{b} fact3: ¬{C}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸããŸãLv.2ã¯åãé£ã; fact1 & assump1 -> int1: ãã®ãŸããŸãLv.2ã¯çžè«ãæã; int1 & fact2 -> int2: ãã®ãŽããŽãLv.75ã¯å¯ãŒã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{b}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ãã®ãŸããŸãLv.2ãåãé£ããªãããã¯çžè«ãæã fact2: ãã®ãŸããŸãLv.2ã¯çžè«ãæããšããã°ããã®ãŽããŽãLv.75ã¯å¯ãŒãããšããããšã¯æãç«ã€ fact3: ãã®ãŽããŽãLv.75ã¯å¯ãŒããªã ; $hypothesis$ = ãã®ãŸããŸãLv.2ã¯åãé£ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸããŸãLv.2ã¯åãé£ã; fact1 & assump1 -> int1: ãã®ãŸããŸãLv.2ã¯çžè«ãæã; int1 & fact2 -> int2: ãã®ãŽããŽãLv.75ã¯å¯ãŒã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} -> {B}{a} fact2: {B}{a} -> {C}{b} fact3: ¬{C}{b} ; $hypothesis$ = ¬{A}{a} ; $proof$ = | void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{b}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã«ã
ãŸã¡ã
Lv.59ã¯å€ã | {D}{b} | fact1: ããä»®ã«ãã®ãœããœã«Lv.60ãæãé£ããšãããããã¯çé
žã£ã±ãããããã¯ããã¯é¢ç®ç¡ã fact2: ãã®ãœããœã«Lv.60ã¯æãé£ãããããã¯ããã¯å€ããªã fact3: ãã®ãœããœã«Lv.60ã¯æãé£ã fact4: æãé£ãã¢ã³ã¹ã¿ãŒã¯çé
žã£ã±ãããŸãã¯é¢ç®ç¡ããšããããšã¯ãªã fact5: ãã®ãœã¡ããœã¡ãLv.83ãè¿ãããããšããããšã¯ãªããªããã®ãŸã«ã
ãŸã¡ã
Lv.59ã¯é£è¡æ©ããã fact6: ãããã®ãŸã«ã
ãŸã¡ã
Lv.59ãé£è¡æ©ããããšãããå€ã fact7: ãã®ãœããœã«Lv.60ã¯çé
žã£ã±ãããŸãã¯é¢ç®ç¡ã | fact1: {A}{aa} -> ({AA}{aa} v {AB}{aa}) fact2: ({A}{aa} v ¬{D}{aa}) fact3: {A}{aa} fact4: (x): {A}x -> ({AA}x v ¬{AB}x) fact5: ¬{B}{a} -> {C}{b} fact6: {C}{b} -> {D}{b} fact7: ({AA}{aa} v {AB}{aa}) | [
"fact4 -> int1: ããã®ãœããœã«Lv.60ã¯æãé£ãããšããããšã¯æãç«ã€ãšãããçé
žã£ã±ãããããã¯é¢ç®ç¡ããªã; int1 & fact3 -> int2: ãã®ãœããœã«Lv.60ã¯çé
žã£ã±ãããããã¯é¢ç®ç¡ããªãããŸãã¯ã©ã¡ããã ;"
] | [
"fact4 -> int1: {A}{aa} -> ({AA}{aa} v ¬{AB}{aa}); int1 & fact3 -> int2: ({AA}{aa} v ¬{AB}{aa});"
] | null | null | [] | null | 5 | 5 | null | null | 3 | 0 | 3 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããä»®ã«ãã®ãœããœã«Lv.60ãæãé£ããšãããããã¯çé
žã£ã±ãããããã¯ããã¯é¢ç®ç¡ã fact2: ãã®ãœããœã«Lv.60ã¯æãé£ãããããã¯ããã¯å€ããªã fact3: ãã®ãœããœã«Lv.60ã¯æãé£ã fact4: æãé£ãã¢ã³ã¹ã¿ãŒã¯çé
žã£ã±ãããŸãã¯é¢ç®ç¡ããšããããšã¯ãªã fact5: ãã®ãœã¡ããœã¡ãLv.83ãè¿ãããããšããããšã¯ãªããªããã®ãŸã«ã
ãŸã¡ã
Lv.59ã¯é£è¡æ©ããã fact6: ãããã®ãŸã«ã
ãŸã¡ã
Lv.59ãé£è¡æ©ããããšãããå€ã fact7: ãã®ãœããœã«Lv.60ã¯çé
žã£ã±ãããŸãã¯é¢ç®ç¡ã ; $hypothesis$ = ãã®ãŸã«ã
ãŸã¡ã
Lv.59ã¯å€ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{aa} -> ({AA}{aa} v {AB}{aa}) fact2: ({A}{aa} v ¬{D}{aa}) fact3: {A}{aa} fact4: (x): {A}x -> ({AA}x v ¬{AB}x) fact5: ¬{B}{a} -> {C}{b} fact6: {C}{b} -> {D}{b} fact7: ({AA}{aa} v {AB}{aa}) ; $hypothesis$ = {D}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãããã¡ãLv.65ã飲ã¿åºããªããã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ããªã | {A}{a} -> ¬{C}{c} | fact1: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ã fact2: ãããã®ãããã¡ãLv.65ã飲ã¿åºããªããã®ãŸããŸãLv.34ã¯ç©ºã
ãã fact3: ãã®ãŸããŸãLv.34ã空ã
ãããªããã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ããªã | fact1: {C}{c} fact2: {A}{a} -> {B}{b} fact3: {B}{b} -> ¬{C}{c} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãããã¡ãLv.65ã¯é£²ã¿åºã; fact2 & assump1 -> int1: ãã®ãŸããŸãLv.34ã¯ç©ºã
ãã; int1 & fact3 -> int2: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ããªã; [assump1] & int2 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{b}; int1 & fact3 -> int2: ¬{C}{c}; [assump1] & int2 -> hypothesis;"
] | null | null | [] | null | 4 | 3 | 4 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ã fact2: ãããã®ãããã¡ãLv.65ã飲ã¿åºããªããã®ãŸããŸãLv.34ã¯ç©ºã
ãã fact3: ãã®ãŸããŸãLv.34ã空ã
ãããªããã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ããªã ; $hypothesis$ = ãã®ãããã¡ãLv.65ã飲ã¿åºããªããã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãããã¡ãLv.65ã¯é£²ã¿åºã; fact2 & assump1 -> int1: ãã®ãŸããŸãLv.34ã¯ç©ºã
ãã; int1 & fact3 -> int2: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯åããé£ããªã; [assump1] & int2 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{c} fact2: {A}{a} -> {B}{b} fact3: {B}{b} -> ¬{C}{c} ; $hypothesis$ = {A}{a} -> ¬{C}{c} ; $proof$ = | void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{b}; int1 & fact3 -> int2: ¬{C}{c}; [assump1] & int2 -> hypothesis; __PROVED__ |
0.3 | ãéãŸãåºããªããªãã掻æ°ä»ããªããŠæ¬ãåãããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{A}x -> ¬(¬{AA}x & {AB}x) | fact1: ããä»®ã«ãã®ã¿ã«ãã¿ã®Lv.48ã¯éãŸãåºããªããªãããã®ã¿ã«ãã¿ã®Lv.48ã¯æŽ»æ°ä»ããªãããã©æ¬ãåãããšããããšã¯èª€ãã fact2: ãããã®ã¿ã«ãã¿ã®Lv.48ã¯éãŸãåºãã°ãããã¯æŽ»æ°ä»ããªããŠããŸãã«æ¬ãåãããšããããšã¯æãç«ããªã fact3: ãããããã¢ã³ã¹ã¿ãŒã¯éããªããšããã°ãå²ãæããªããŠèªç¶ãããããšããããšã¯åã fact4: ããããéãŸãåºããªããšãããšæŽ»æ°ä»ããªããŠæ¬ãåããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããä»®ã«ãã®ã¿ã«ãã¿ã®Lv.48ãéãŸãåºããªããšããããã®ã¿ã«ãã¿ã®Lv.48ã¯æŽ»æ°ä»ããªããæ¬ãåã fact6: ãããã®ã·ãã·ãªLv.70ã¯èŸããªããªãã°ããã®ã·ãã·ãªLv.70ã¯äžãæããªãã掻æ°ä»ããããšããããšã¯æãç«ããªã | fact1: ¬{A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact2: {A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact3: (x): ¬{GU}x -> ¬(¬{CO}x & {CQ}x) fact4: (Ex): ¬{A}x -> (¬{AA}x & {AB}x) fact5: ¬{A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact6: ¬{AQ}{gq} -> ¬(¬{HL}{gq} & {AA}{gq}) | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | ãããã®ãŸã«ããŸãLv.82ã¯éããªããªããããã¯å²ãæããªãããããèªç¶ãããããšããããšã¯èª€ã£ãŠãã | ¬{GU}{m} -> ¬(¬{CO}{m} & {CQ}{m}) | [
"fact7 -> hypothesis;"
] | 1 | 1 | 1 | 1 | 1 | 5 | 0 | 5 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ããä»®ã«ãã®ã¿ã«ãã¿ã®Lv.48ã¯éãŸãåºããªããªãããã®ã¿ã«ãã¿ã®Lv.48ã¯æŽ»æ°ä»ããªãããã©æ¬ãåãããšããããšã¯èª€ãã fact2: ãããã®ã¿ã«ãã¿ã®Lv.48ã¯éãŸãåºãã°ãããã¯æŽ»æ°ä»ããªããŠããŸãã«æ¬ãåãããšããããšã¯æãç«ããªã fact3: ãããããã¢ã³ã¹ã¿ãŒã¯éããªããšããã°ãå²ãæããªããŠèªç¶ãããããšããããšã¯åã fact4: ããããéãŸãåºããªããšãããšæŽ»æ°ä»ããªããŠæ¬ãåããã¢ã³ã¹ã¿ãŒã¯ãã fact5: ããä»®ã«ãã®ã¿ã«ãã¿ã®Lv.48ãéãŸãåºããªããšããããã®ã¿ã«ãã¿ã®Lv.48ã¯æŽ»æ°ä»ããªããæ¬ãåã fact6: ãããã®ã·ãã·ãªLv.70ã¯èŸããªããªãã°ããã®ã·ãã·ãªLv.70ã¯äžãæããªãã掻æ°ä»ããããšããããšã¯æãç«ããªã ; $hypothesis$ = ãéãŸãåºããªããªãã掻æ°ä»ããªããŠæ¬ãåãããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact2: {A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact3: (x): ¬{GU}x -> ¬(¬{CO}x & {CQ}x) fact4: (Ex): ¬{A}x -> (¬{AA}x & {AB}x) fact5: ¬{A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact6: ¬{AQ}{gq} -> ¬(¬{HL}{gq} & {AA}{gq}) ; $hypothesis$ = (Ex): ¬{A}x -> ¬(¬{AA}x & {AB}x) ; $proof$ = | fact1 -> hypothesis; __PROVED__ |
0.3 | ã¿ã¿ã£ã¡ããšããããšã¯çããªã | ¬{B} | fact1: è¡ããšããããšã¯ãã¿ã¿ã£ã¡ããšããããšãçããããšããããšãçãããã fact2: è¡ããšããããšãçãã | fact1: {A} -> {B} fact2: {A} | [
"fact2 -> int1: è¡ããšããããšãçãã; int1 & fact1 -> hypothesis;"
] | [
"fact2 -> int1: {A}; int1 & fact1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: è¡ããšããããšã¯ãã¿ã¿ã£ã¡ããšããããšãçããããšããããšãçãããã fact2: è¡ããšããããšãçãã ; $hypothesis$ = ã¿ã¿ã£ã¡ããšããããšã¯çããªã ; $proof$ = | fact2 -> int1: è¡ããšããããšãçãã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} -> {B} fact2: {A} ; $hypothesis$ = ¬{B} ; $proof$ = | fact2 -> int1: {A}; int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã ãããšããããšã¯ãã·ã«ã
ã·ãLv.32äºä»¶ã¯èµ·ããªãããšããããšãé²ãããšããããšã¯æãç«ããªã | ¬({A} -> {B}) | fact1: ãå€èª¿ããããšãçããã床ãé£ããšããããšãèµ·ããããšããããšã¯åã fact2: ããããå€èª¿ããããšãèµ·ããã床ãé£ããšããããšã¯çããªãããšããããšã¯åã§ãããªãã°ã·ã«ã
ã·ãLv.32äºä»¶ãçãã fact3: ããããŽããŽã«ãLv.64äºä»¶ãçºçãããªããå°è±¡æ·±ããšããããšãèµ·ããããšããããšã¯äºå®ã fact4: ãããã ãããšããããšãçããããšããããšã¯æ¬åœãªããå€èª¿ããããšãèµ·ãããããã«åºŠãé£ããšããããšãçããããšããããšã¯åœã§ãã fact5: ä»®ã«ã ãããšããããšã¯çããªããªãããŽã«ã
ãŽã«Lv.7äºä»¶ãçããããããæªããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact6: å¢ãé£ããšããããšã¯ã·ã«ã·ãLv.1äºä»¶ãçºçãããšããããšãçãããã | fact1: ¬({AA} & {AB}) fact2: ¬({AA} & ¬{AB}) -> {B} fact3: {EM} -> {EG} fact4: {A} -> ¬({AA} & {AB}) fact5: ¬{A} -> ¬({GJ} & ¬{DB}) fact6: {T} -> {E} | [] | [] | ããŽã«ã
ãŽã«Lv.7äºä»¶ãçããããã©æªããšããããšã¯èµ·ããªãããšããããšã¯åã | ¬({GJ} & ¬{DB}) | [] | 6 | 4 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãå€èª¿ããããšãçããã床ãé£ããšããããšãèµ·ããããšããããšã¯åã fact2: ããããå€èª¿ããããšãèµ·ããã床ãé£ããšããããšã¯çããªãããšããããšã¯åã§ãããªãã°ã·ã«ã
ã·ãLv.32äºä»¶ãçãã fact3: ããããŽããŽã«ãLv.64äºä»¶ãçºçãããªããå°è±¡æ·±ããšããããšãèµ·ããããšããããšã¯äºå®ã fact4: ãããã ãããšããããšãçããããšããããšã¯æ¬åœãªããå€èª¿ããããšãèµ·ãããããã«åºŠãé£ããšããããšãçããããšããããšã¯åœã§ãã fact5: ä»®ã«ã ãããšããããšã¯çããªããªãããŽã«ã
ãŽã«Lv.7äºä»¶ãçããããããæªããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact6: å¢ãé£ããšããããšã¯ã·ã«ã·ãLv.1äºä»¶ãçºçãããšããããšãçãããã ; $hypothesis$ = ãã ãããšããããšã¯ãã·ã«ã
ã·ãLv.32äºä»¶ã¯èµ·ããªãããšããããšãé²ãããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({AA} & {AB}) fact2: ¬({AA} & ¬{AB}) -> {B} fact3: {EM} -> {EG} fact4: {A} -> ¬({AA} & {AB}) fact5: ¬{A} -> ¬({GJ} & ¬{DB}) fact6: {T} -> {E} ; $hypothesis$ = ¬({A} -> {B}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããããã話ãé£ããŠããŸãã«ä»ãé£ããªããšããã°çŠãŸãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æ¬åœã | (Ex): ({AA}x & ¬{AB}x) -> {B}x | fact1: ããããã®ã·ã«ãã·ã«ãLv.16ã¯è©±ãé£ãäžæ¹ã§ä»ãé£ããªãããšããããšã¯çå®ãªããã®ã·ã«ãã·ã«ãLv.16ã¯çŠãŸãã | fact1: ({AA}{aa} & ¬{AB}{aa}) -> {B}{aa} | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 1 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ã·ã«ãã·ã«ãLv.16ã¯è©±ãé£ãäžæ¹ã§ä»ãé£ããªãããšããããšã¯çå®ãªããã®ã·ã«ãã·ã«ãLv.16ã¯çŠãŸãã ; $hypothesis$ = ããããã話ãé£ããŠããŸãã«ä»ãé£ããªããšããã°çŠãŸãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æ¬åœã ; $proof$ = | fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({AA}{aa} & ¬{AB}{aa}) -> {B}{aa} ; $hypothesis$ = (Ex): ({AA}x & ¬{AB}x) -> {B}x ; $proof$ = | fact1 -> hypothesis; __PROVED__ |
0.3 | ã·ãã·ãLv.78äºä»¶ãèµ·ããã骚ã£ãœããšããããšãèµ·ãã | ({A} & {B}) | fact1: ãã«ããã«ãLv.80äºä»¶ã¯èµ·ãããªããšããããšã¯ããããLv.98äºä»¶ãšãœããœã¡ã
Lv.26äºä»¶ãçããã®åå ãšãªã fact2: ããããã«ããã®Lv.50äºä»¶ã¯çºçããªããšããã°ãã·ãã·ãLv.78äºä»¶ãèµ·ããã骚ã£ãœããšããããšãçºçããããšããããšã¯æãç«ããªã fact3: ã·ãã·ãLv.78äºä»¶ãèµ·ãã fact4: ããããLv.98äºä»¶ã¯ããã«ããã®Lv.50äºä»¶ã§ã¯ãªãã·ãã·ã«ãLv.18äºä»¶ãèµ·ããããšããããšã«ç¹ãã fact5: ãã«ããã«ãLv.80äºä»¶ã¯ããŽããŽã¡ãLv.88äºä»¶ã¯çããªãããšããããšã«é²ããã fact6: 骚ã£ãœããšããããšãèµ·ãã | fact1: ¬{G} -> ({E} & {F}) fact2: ¬{C} -> ¬({A} & {B}) fact3: {A} fact4: {E} -> (¬{C} & {D}) fact5: ¬{H} -> ¬{G} fact6: {B} | [
"fact3 -> int1: ã·ãã·ãLv.78äºä»¶ãèµ·ãã; int1 & fact6 -> hypothesis;"
] | [
"fact3 -> int1: {A}; int1 & fact6 -> hypothesis;"
] | ãã·ãã·ãLv.78äºä»¶ãçããããŸã骚ã£ãœããšããããšãçºçããããšããããšã¯èª€ã£ãŠãã | ¬({A} & {B}) | [] | 9 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã«ããã«ãLv.80äºä»¶ã¯èµ·ãããªããšããããšã¯ããããLv.98äºä»¶ãšãœããœã¡ã
Lv.26äºä»¶ãçããã®åå ãšãªã fact2: ããããã«ããã®Lv.50äºä»¶ã¯çºçããªããšããã°ãã·ãã·ãLv.78äºä»¶ãèµ·ããã骚ã£ãœããšããããšãçºçããããšããããšã¯æãç«ããªã fact3: ã·ãã·ãLv.78äºä»¶ãèµ·ãã fact4: ããããLv.98äºä»¶ã¯ããã«ããã®Lv.50äºä»¶ã§ã¯ãªãã·ãã·ã«ãLv.18äºä»¶ãèµ·ããããšããããšã«ç¹ãã fact5: ãã«ããã«ãLv.80äºä»¶ã¯ããŽããŽã¡ãLv.88äºä»¶ã¯çããªãããšããããšã«é²ããã fact6: 骚ã£ãœããšããããšãèµ·ãã ; $hypothesis$ = ã·ãã·ãLv.78äºä»¶ãèµ·ããã骚ã£ãœããšããããšãèµ·ãã ; $proof$ = | fact3 -> int1: ã·ãã·ãLv.78äºä»¶ãèµ·ãã; int1 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{G} -> ({E} & {F}) fact2: ¬{C} -> ¬({A} & {B}) fact3: {A} fact4: {E} -> (¬{C} & {D}) fact5: ¬{H} -> ¬{G} fact6: {B} ; $hypothesis$ = ({A} & {B}) ; $proof$ = | fact3 -> int1: {A}; int1 & fact6 -> hypothesis; __PROVED__ |
0.3 | ããä»®ã«æž©ããšããããšã¯ãªããå¬ãããªãã°æãããããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ééãã§ãã | ¬((Ex): (¬{AA}x & {AB}x) -> {B}x) | fact1: ãããæž©ããŠããŸãã«å¬ãããšãããšæãããããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãããé²ãæããªãã¢ã³ã¹ã¿ãŒã絡ãŸããšããã°ããã¯éã
ãã fact3: æž©ããŠå¬ããã¢ã³ã¹ã¿ãŒã¯æãããã fact4: ããä»®ã«ãã®ãŸã«ãŸãLv.71ãæž©ããŠå ããŠå¬ãããšããããã®ãŸã«ãŸãLv.71ã¯æãããã fact5: ããããã®ãã¡ããã¡ã
Lv.83ãäºæž¬ãæããªãããã©ãããç©çããããªããã®ãã¡ããã¡ã
Lv.83ã¯å¬ãã | fact1: (Ex): ({AA}x & {AB}x) -> {B}x fact2: (x): (¬{HC}x & {CB}x) -> {BU}x fact3: (x): ({AA}x & {AB}x) -> {B}x fact4: ({AA}{aa} & {AB}{aa}) -> {B}{aa} fact5: (¬{DJ}{bo} & {EE}{bo}) -> {AB}{bo} | [] | [] | ãããä»®ã«é²ãæããªããã©çµ¡ãŸããšãããšãéã
ããããšããããšã¯æãç«ã€ãã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): (¬{HC}x & {CB}x) -> {BU}x | [
"fact6 -> int1: ãã®ãœã«ããœãLv.4ãé²ãæããšããããšã¯ãªãã絡ãŸãã°ãã®ãœã«ããœãLv.4ã¯éã
ãã; int1 -> hypothesis;"
] | 2 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | PROVED | UNKNOWN | PROVED | $facts$ = fact1: ãããæž©ããŠããŸãã«å¬ãããšãããšæãããããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãããé²ãæããªãã¢ã³ã¹ã¿ãŒã絡ãŸããšããã°ããã¯éã
ãã fact3: æž©ããŠå¬ããã¢ã³ã¹ã¿ãŒã¯æãããã fact4: ããä»®ã«ãã®ãŸã«ãŸãLv.71ãæž©ããŠå ããŠå¬ãããšããããã®ãŸã«ãŸãLv.71ã¯æãããã fact5: ããããã®ãã¡ããã¡ã
Lv.83ãäºæž¬ãæããªãããã©ãããç©çããããªããã®ãã¡ããã¡ã
Lv.83ã¯å¬ãã ; $hypothesis$ = ããä»®ã«æž©ããšããããšã¯ãªããå¬ãããªãã°æãããããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ééãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (Ex): ({AA}x & {AB}x) -> {B}x fact2: (x): (¬{HC}x & {CB}x) -> {BU}x fact3: (x): ({AA}x & {AB}x) -> {B}x fact4: ({AA}{aa} & {AB}{aa}) -> {B}{aa} fact5: (¬{DJ}{bo} & {EE}{bo}) -> {AB}{bo} ; $hypothesis$ = ¬((Ex): (¬{AA}x & {AB}x) -> {B}x) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãœã«ããœã«ãLv.90ã¯æããªã | ¬{B}{a} | fact1: ããããã®ãœã«ããœã«ãLv.90ãè¡æ£èããšããããã®ãœã«ããœã«ãLv.90ã¯æ©ããšããããšã¯ãªã fact2: ããä»®ã«ãã®ãœã«ããœã«ãLv.90ãè¡æ£èãããããã¯ããã¯æãããŸãã¯ã©ã¡ããã§ãããšãããšããã¯æ©ããšããããšã¯ãªã fact3: ãã®ãœã«ããœã«ãLv.90ã¯æ©ã | fact1: {A}{a} -> ¬{C}{a} fact2: ({A}{a} v {B}{a}) -> ¬{C}{a} fact3: {C}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã«ããœã«ãLv.90ã¯æã; assump1 -> int1: ãã®ãœã«ããœã«ãLv.90ã¯è¡æ£èãããããã¯ããã¯æã; int1 & fact2 -> int2: ãã®ãœã«ããœã«ãLv.90ã¯æ©ããšããããšã¯ãªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}{a}; assump1 -> int1: ({A}{a} v {B}{a}); int1 & fact2 -> int2: ¬{C}{a}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 3 | 5 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ãœã«ããœã«ãLv.90ãè¡æ£èããšããããã®ãœã«ããœã«ãLv.90ã¯æ©ããšããããšã¯ãªã fact2: ããä»®ã«ãã®ãœã«ããœã«ãLv.90ãè¡æ£èãããããã¯ããã¯æãããŸãã¯ã©ã¡ããã§ãããšãããšããã¯æ©ããšããããšã¯ãªã fact3: ãã®ãœã«ããœã«ãLv.90ã¯æ©ã ; $hypothesis$ = ãã®ãœã«ããœã«ãLv.90ã¯æããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã«ããœã«ãLv.90ã¯æã; assump1 -> int1: ãã®ãœã«ããœã«ãLv.90ã¯è¡æ£èãããããã¯ããã¯æã; int1 & fact2 -> int2: ãã®ãœã«ããœã«ãLv.90ã¯æ©ããšããããšã¯ãªã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} -> ¬{C}{a} fact2: ({A}{a} v {B}{a}) -> ¬{C}{a} fact3: {C}{a} ; $hypothesis$ = ¬{B}{a} ; $proof$ = | void -> assump1: {B}{a}; assump1 -> int1: ({A}{a} v {B}{a}); int1 & fact2 -> int2: ¬{C}{a}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | é£æ³ãæããšããããšã¯çããªã | ¬{B} | fact1: ä»®ã«é£æ³ãæããšããããšã¯èµ·ãããªããæšãŠé£ããšããããšã¯èµ·ããªããšãããšã¿ãã¿ã¡ãLv.20äºä»¶ãçºçãã fact2: 䌌ä»ãããããšããããšãçºçãã fact3: 䌌ä»ãããããšããããšã¯æšãŠé£ããšããããšãèµ·ãããšããããšãé£æ³ãæããšããããšã«é»æ¢ããã fact4: ã䌌ä»ãããããšããããšãçããããœã«ãœã¡ãLv.73äºä»¶ã¯èµ·ããªãããããã¯äž¡æ¹ã ããšããããšã¯æšãŠé£ããšããããšã¯èµ·ããªããšããããšã®ãã£ãããšãªã | fact1: (¬{B} v ¬{A}) -> {DU} fact2: {C} fact3: ({A} v {B}) -> ¬{C} fact4: ({C} v ¬{D}) -> ¬{A} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããé£æ³ãæããšããããšãèµ·ãã; assump1 -> int1: æšãŠé£ããšããããšãèµ·ããããããã¯é£æ³ãæããšããããšãçºçããããŸãã¯ã©ã¡ããã§ãã; int1 & fact3 -> int2: 䌌ä»ãããããšããããšã¯çããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; assump1 -> int1: ({A} v {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ã¿ãã¿ã¡ãLv.20äºä»¶ããŸãã¯ã·ã«ãã·ãLv.11äºä»¶ãçãã | ({DU} v {HG}) | [] | 7 | 5 | 3 | 5 | 3 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«é£æ³ãæããšããããšã¯èµ·ãããªããæšãŠé£ããšããããšã¯èµ·ããªããšãããšã¿ãã¿ã¡ãLv.20äºä»¶ãçºçãã fact2: 䌌ä»ãããããšããããšãçºçãã fact3: 䌌ä»ãããããšããããšã¯æšãŠé£ããšããããšãèµ·ãããšããããšãé£æ³ãæããšããããšã«é»æ¢ããã fact4: ã䌌ä»ãããããšããããšãçããããœã«ãœã¡ãLv.73äºä»¶ã¯èµ·ããªãããããã¯äž¡æ¹ã ããšããããšã¯æšãŠé£ããšããããšã¯èµ·ããªããšããããšã®ãã£ãããšãªã ; $hypothesis$ = é£æ³ãæããšããããšã¯çããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããé£æ³ãæããšããããšãèµ·ãã; assump1 -> int1: æšãŠé£ããšããããšãèµ·ããããããã¯é£æ³ãæããšããããšãçºçããããŸãã¯ã©ã¡ããã§ãã; int1 & fact3 -> int2: 䌌ä»ãããããšããããšã¯çããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: (¬{B} v ¬{A}) -> {DU} fact2: {C} fact3: ({A} v {B}) -> ¬{C} fact4: ({C} v ¬{D}) -> ¬{A} ; $hypothesis$ = ¬{B} ; $proof$ = | void -> assump1: {B}; assump1 -> int1: ({A} v {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | èœã¡é£ããšããããšããã³è²ã£ãœããšããããšãçºçãã | ({A} & {C}) | fact1: ãä»®ã«æããšããããšãçºçãããšãããšã¿ã«ã
ã¿ãLv.96äºä»¶ã¯èµ·ãããªããŠæŽã«é¿åããããšããããšã¯çããªãããšããããšã¯äºå®ã fact2: è²ã£ãœããšããããšãçãã fact3: ä»®ã«ãçãããšããããšã¯èµ·ããªãããã®äžé²ãæããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ããªããšãããšé©å¿ããããšãçãã fact4: é¿åããããšããããšã¯çºçããªã fact5: ããä»®ã«é¿åããããšããããšã¯çºçããªããªãã°ããœããœãLv.55äºä»¶ãçããªãããã®äžã¿ãã¿ã¡ãLv.28äºä»¶ã¯èµ·ãããªãããšããããšã¯æãç«ããªã fact6: èœã¡é£ããšããããšã¯çããªããšããããšã¯ã¿ã«ã
ã¿ãLv.96äºä»¶ãèµ·ãããšããããšã«é²ããã fact7: ããããœããœãLv.55äºä»¶ãèµ·ããªãããã€ã¿ãã¿ã¡ãLv.28äºä»¶ã¯çºçããªãããšããããšã¯ééãã ãšãããã¿ã«ã
ã¿ãLv.96äºä»¶ãçãã fact8: ã¿ã«ã
ã¿ãLv.96äºä»¶ã¯çããªããªãã°ãèœã¡é£ããšããããšãèµ·ãããããŸãã«è²ã£ãœããšããããšãèµ·ããããšããããšã¯åã | fact1: {E} -> (¬{B} & ¬{D}) fact2: {C} fact3: ¬(¬{GH} & ¬{U}) -> {II} fact4: ¬{D} fact5: ¬{D} -> ¬(¬{AA} & ¬{AB}) fact6: {B} -> {A} fact7: ¬(¬{AA} & ¬{AB}) -> {B} fact8: ¬{B} -> ¬({A} & {C}) | [
"fact4 & fact5 -> int1: ããœããœãLv.55äºä»¶ã¯èµ·ãããªããŠã¿ãã¿ã¡ãLv.28äºä»¶ã¯çºçããªãããšããããšã¯åã§ãã; fact7 & int1 -> int2: ã¿ã«ã
ã¿ãLv.96äºä»¶ãèµ·ãã; int2 & fact6 -> int3: èœã¡é£ããšããããšãèµ·ãã; int3 & fact2 -> hypothesis;"
] | [
"fact4 & fact5 -> int1: ¬(¬{AA} & ¬{AB}); fact7 & int1 -> int2: {B}; int2 & fact6 -> int3: {A}; int3 & fact2 -> hypothesis;"
] | ãèœã¡é£ããšããããšããã³è²ã£ãœããšããããšãçããããšããããšã¯æãç«ããªã | ¬({A} & {C}) | [] | 7 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãä»®ã«æããšããããšãçºçãããšãããšã¿ã«ã
ã¿ãLv.96äºä»¶ã¯èµ·ãããªããŠæŽã«é¿åããããšããããšã¯çããªãããšããããšã¯äºå®ã fact2: è²ã£ãœããšããããšãçãã fact3: ä»®ã«ãçãããšããããšã¯èµ·ããªãããã®äžé²ãæããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ããªããšãããšé©å¿ããããšãçãã fact4: é¿åããããšããããšã¯çºçããªã fact5: ããä»®ã«é¿åããããšããããšã¯çºçããªããªãã°ããœããœãLv.55äºä»¶ãçããªãããã®äžã¿ãã¿ã¡ãLv.28äºä»¶ã¯èµ·ãããªãããšããããšã¯æãç«ããªã fact6: èœã¡é£ããšããããšã¯çããªããšããããšã¯ã¿ã«ã
ã¿ãLv.96äºä»¶ãèµ·ãããšããããšã«é²ããã fact7: ããããœããœãLv.55äºä»¶ãèµ·ããªãããã€ã¿ãã¿ã¡ãLv.28äºä»¶ã¯çºçããªãããšããããšã¯ééãã ãšãããã¿ã«ã
ã¿ãLv.96äºä»¶ãçãã fact8: ã¿ã«ã
ã¿ãLv.96äºä»¶ã¯çããªããªãã°ãèœã¡é£ããšããããšãèµ·ãããããŸãã«è²ã£ãœããšããããšãèµ·ããããšããããšã¯åã ; $hypothesis$ = èœã¡é£ããšããããšããã³è²ã£ãœããšããããšãçºçãã ; $proof$ = | fact4 & fact5 -> int1: ããœããœãLv.55äºä»¶ã¯èµ·ãããªããŠã¿ãã¿ã¡ãLv.28äºä»¶ã¯çºçããªãããšããããšã¯åã§ãã; fact7 & int1 -> int2: ã¿ã«ã
ã¿ãLv.96äºä»¶ãèµ·ãã; int2 & fact6 -> int3: èœã¡é£ããšããããšãèµ·ãã; int3 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {E} -> (¬{B} & ¬{D}) fact2: {C} fact3: ¬(¬{GH} & ¬{U}) -> {II} fact4: ¬{D} fact5: ¬{D} -> ¬(¬{AA} & ¬{AB}) fact6: {B} -> {A} fact7: ¬(¬{AA} & ¬{AB}) -> {B} fact8: ¬{B} -> ¬({A} & {C}) ; $hypothesis$ = ({A} & {C}) ; $proof$ = | fact4 & fact5 -> int1: ¬(¬{AA} & ¬{AB}); fact7 & int1 -> int2: {B}; int2 & fact6 -> int3: {A}; int3 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœããœãLv.71ã¯åŸ
ã¡é ãããªã | ¬{B}{a} | fact1: ãã®ãœããœãLv.71ã¯å¯æããã fact2: ãã®ãœããœãLv.71ãå¯æããããæŽã«ãããåŸ
ã¡é ãããªãã°ãã®ãŽã«ããŽã«ã
Lv.96ã¯ç¡ããªã fact3: ããä»®ã«ãã®ãŽã«ããŽã«ã
Lv.96ãåŸãããããªããšãããåºé£ããããã«å¯æããã fact4: ãã®ãŽã«ããŽã«ã
Lv.96ã¯ç¡ã | fact1: {A}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{b} fact3: ¬{D}{b} -> ({HF}{b} & {A}{b}) fact4: {C}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœãLv.71ã¯åŸ
ã¡é ãã; fact1 & assump1 -> int1: ãã®ãœããœãLv.71ã¯å¯æããããããã«åŸ
ã¡é ãã; int1 & fact2 -> int2: ãã®ãŽã«ããŽã«ã
Lv.96ã¯ç¡ããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}{a}; fact1 & assump1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{b}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ãã®ãŽã«ããŽã«ã
Lv.96ã¯åºé£ããããã«ããã¯æŽèšªãã | ({HF}{b} & {FG}{b}) | [] | 4 | 5 | 4 | 5 | 4 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãœããœãLv.71ã¯å¯æããã fact2: ãã®ãœããœãLv.71ãå¯æããããæŽã«ãããåŸ
ã¡é ãããªãã°ãã®ãŽã«ããŽã«ã
Lv.96ã¯ç¡ããªã fact3: ããä»®ã«ãã®ãŽã«ããŽã«ã
Lv.96ãåŸãããããªããšãããåºé£ããããã«å¯æããã fact4: ãã®ãŽã«ããŽã«ã
Lv.96ã¯ç¡ã ; $hypothesis$ = ãã®ãœããœãLv.71ã¯åŸ
ã¡é ãããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœãLv.71ã¯åŸ
ã¡é ãã; fact1 & assump1 -> int1: ãã®ãœããœãLv.71ã¯å¯æããããããã«åŸ
ã¡é ãã; int1 & fact2 -> int2: ãã®ãŽã«ããŽã«ã
Lv.96ã¯ç¡ããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{b} fact3: ¬{D}{b} -> ({HF}{b} & {A}{b}) fact4: {C}{b} ; $hypothesis$ = ¬{B}{a} ; $proof$ = | void -> assump1: {B}{a}; fact1 & assump1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{b}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœã«ããœã«Lv.58ã¯çœãããšããããšã¯ãªã | ¬{F}{b} | fact1: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯æããããªããšãããããã®ãœã«ããœã«Lv.58ã¯çœããªãããšããããšã¯ç¢ºãã fact2: ä»®ã«ãã®ãŸã¡ããŸã¡ã
Lv.92ãéãããªããå å·¥ããªããªããã®ãŸã¡ããŸã¡ã
Lv.92ã¯æããããªã fact3: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯éãããªã fact4: ããããã¢ã³ã¹ã¿ãŒã¯èšãé£ããŠããã«é£åããªã fact5: ããä»®ã«ãã®ãœã«ããœãLv.16ãèšãé£ãããã©é£åãããšããããšã¯ãªããªãã°ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯å å·¥ãããšããããšã¯ãªã | fact1: ¬{E}{a} -> ¬{F}{b} fact2: (¬{D}{a} & ¬{C}{a}) -> ¬{E}{a} fact3: ¬{D}{a} fact4: (x): ({A}x & ¬{B}x) fact5: ({A}{aa} & ¬{B}{aa}) -> ¬{C}{a} | [
"fact4 -> int1: ãã®ãœã«ããœãLv.16ã¯èšãé£ããã©ããã¯é£åããªã; int1 & fact5 -> int2: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯å å·¥ããªã; int2 & fact3 -> int3: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯éãããªããæŽã«å å·¥ããªã; int3 & fact2 -> int4: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯æããããªã; int4 & fact1 -> hypothesis;"
] | [
"fact4 -> int1: ({A}{aa} & ¬{B}{aa}); int1 & fact5 -> int2: ¬{C}{a}; int2 & fact3 -> int3: (¬{D}{a} & ¬{C}{a}); int3 & fact2 -> int4: ¬{E}{a}; int4 & fact1 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯æããããªããšãããããã®ãœã«ããœã«Lv.58ã¯çœããªãããšããããšã¯ç¢ºãã fact2: ä»®ã«ãã®ãŸã¡ããŸã¡ã
Lv.92ãéãããªããå å·¥ããªããªããã®ãŸã¡ããŸã¡ã
Lv.92ã¯æããããªã fact3: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯éãããªã fact4: ããããã¢ã³ã¹ã¿ãŒã¯èšãé£ããŠããã«é£åããªã fact5: ããä»®ã«ãã®ãœã«ããœãLv.16ãèšãé£ãããã©é£åãããšããããšã¯ãªããªãã°ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯å å·¥ãããšããããšã¯ãªã ; $hypothesis$ = ãã®ãœã«ããœã«Lv.58ã¯çœãããšããããšã¯ãªã ; $proof$ = | fact4 -> int1: ãã®ãœã«ããœãLv.16ã¯èšãé£ããã©ããã¯é£åããªã; int1 & fact5 -> int2: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯å å·¥ããªã; int2 & fact3 -> int3: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯éãããªããæŽã«å å·¥ããªã; int3 & fact2 -> int4: ãã®ãŸã¡ããŸã¡ã
Lv.92ã¯æããããªã; int4 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{E}{a} -> ¬{F}{b} fact2: (¬{D}{a} & ¬{C}{a}) -> ¬{E}{a} fact3: ¬{D}{a} fact4: (x): ({A}x & ¬{B}x) fact5: ({A}{aa} & ¬{B}{aa}) -> ¬{C}{a} ; $hypothesis$ = ¬{F}{b} ; $proof$ = | fact4 -> int1: ({A}{aa} & ¬{B}{aa}); int1 & fact5 -> int2: ¬{C}{a}; int2 & fact3 -> int3: (¬{D}{a} & ¬{C}{a}); int3 & fact2 -> int4: ¬{E}{a}; int4 & fact1 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããœã«ããœãLv.60äºä»¶ãçºçãã | {A} | fact1: ãããæªä¹±ããããšã¯èµ·ããªããšãããããœã«ããœãLv.60äºä»¶ãšã¿ã«ã
ã¿ãLv.20äºä»¶äž¡æ¹ãçºçããããšããããšã¯ç¢ºãã§ãã fact2: ãœããœãLv.97äºä»¶ãèµ·ãã fact3: æªä¹±ããããšãçãã fact4: ä»®ã«é€é¬Œã£ãœããšããããšãèµ·ãããšãããšãæªä¹±ããããšãèµ·ããããœããœãLv.97äºä»¶ã¯çããªãããšããããšã¯äºå®ãšç°ãªã fact5: ããœããœãLv.97äºä»¶ã¯çºçããªãããšããããšã¯ããœã«ããœãLv.60äºä»¶ãèµ·ããããã€æªä¹±ããããšãçããããšããããšã«ç±æ¥ãã | fact1: ¬{B} -> ({A} & {HM}) fact2: {C} fact3: {B} fact4: {D} -> ¬({B} & ¬{C}) fact5: ({A} & {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããœã«ããœãLv.60äºä»¶ãçºçãã; assump1 & fact3 -> int1: ãœã«ããœãLv.60äºä»¶ãšæªä¹±ããããšãèµ·ãã; int1 & fact5 -> int2: ããœããœãLv.97äºä»¶ãçããããšããããšã¯æãç«ããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact3 -> int1: ({A} & {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ã¿ã«ã
ã¿ãLv.20äºä»¶ãèµ·ãã | {HM} | [] | 7 | 5 | 4 | 5 | 4 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããæªä¹±ããããšã¯èµ·ããªããšãããããœã«ããœãLv.60äºä»¶ãšã¿ã«ã
ã¿ãLv.20äºä»¶äž¡æ¹ãçºçããããšããããšã¯ç¢ºãã§ãã fact2: ãœããœãLv.97äºä»¶ãèµ·ãã fact3: æªä¹±ããããšãçãã fact4: ä»®ã«é€é¬Œã£ãœããšããããšãèµ·ãããšãããšãæªä¹±ããããšãèµ·ããããœããœãLv.97äºä»¶ã¯çããªãããšããããšã¯äºå®ãšç°ãªã fact5: ããœããœãLv.97äºä»¶ã¯çºçããªãããšããããšã¯ããœã«ããœãLv.60äºä»¶ãèµ·ããããã€æªä¹±ããããšãçããããšããããšã«ç±æ¥ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããœã«ããœãLv.60äºä»¶ãçºçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããœã«ããœãLv.60äºä»¶ãçºçãã; assump1 & fact3 -> int1: ãœã«ããœãLv.60äºä»¶ãšæªä¹±ããããšãèµ·ãã; int1 & fact5 -> int2: ããœããœãLv.97äºä»¶ãçããããšããããšã¯æãç«ããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{B} -> ({A} & {HM}) fact2: {C} fact3: {B} fact4: {D} -> ¬({B} & ¬{C}) fact5: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: {A}; assump1 & fact3 -> int1: ({A} & {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãããã®ã¿ãã¿ãLv.73ã¯ç©ºã
ããããã©éããªãããšããããšã¯æ£ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({AA}{aa} & ¬{AB}{aa}) | fact1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯ããããŠããã¯æã¿éã fact2: ãã®ã¿ã¡ãã¿ã«ãLv.98ã¯æãæããããã空ã
ãããªã fact3: çãæããªãã¢ã³ã¹ã¿ãŒã¯ç©ºã
ãããã©éããªã fact4: çãæãã¢ã³ã¹ã¿ãŒã¯æµ
ãŸããããããéããªã fact5: ãã®ã¿ãã¿ãLv.73ãçãæããªããšããããã®ã¿ãã¿ãLv.73ã¯ç©ºã
ãã | fact1: (x): ({B}x & {C}x) fact2: ({CC}{ac} & ¬{AA}{ac}) fact3: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact4: (x): {A}x -> ({GE}x & ¬{AB}x) fact5: ¬{A}{aa} -> {AA}{aa} | [
"fact3 -> int1: ãã®ã¿ãã¿ãLv.73ãçãæããªããªãã°ç©ºã
ãããŠéããªã;"
] | [
"fact3 -> int1: ¬{A}{aa} -> ({AA}{aa} & ¬{AB}{aa});"
] | ãããã®ã¿ãã¿ãLv.73ã¯ç©ºã
ããããã©éããªãããšããããšã¯æ£ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({AA}{aa} & ¬{AB}{aa}) | [
"fact6 -> int2: ãã®ãŸã®ãŸãªLv.33ã¯ããããŠæã¿éã; int2 -> int3: ãã®ãŸã®ãŸãªLv.33ã¯ããã; int3 -> int4: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯ããã; int4 -> int5: ãã®ã¿ãã¿ã¡ãLv.15ã¯ããã;"
] | 7 | 2 | 2 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯ããããŠããã¯æã¿éã fact2: ãã®ã¿ã¡ãã¿ã«ãLv.98ã¯æãæããããã空ã
ãããªã fact3: çãæããªãã¢ã³ã¹ã¿ãŒã¯ç©ºã
ãããã©éããªã fact4: çãæãã¢ã³ã¹ã¿ãŒã¯æµ
ãŸããããããéããªã fact5: ãã®ã¿ãã¿ãLv.73ãçãæããªããšããããã®ã¿ãã¿ãLv.73ã¯ç©ºã
ãã ; $hypothesis$ = ãããã®ã¿ãã¿ãLv.73ã¯ç©ºã
ããããã©éããªãããšããããšã¯æ£ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ({B}x & {C}x) fact2: ({CC}{ac} & ¬{AA}{ac}) fact3: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact4: (x): {A}x -> ({GE}x & ¬{AB}x) fact5: ¬{A}{aa} -> {AA}{aa} ; $hypothesis$ = ¬({AA}{aa} & ¬{AB}{aa}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸããŸã®Lv.52ã¯æŒãæã | {D}{b} | fact1: è¡ãã¢ã³ã¹ã¿ãŒã¯ç®æã fact2: ä»®ã«ãã®ãŸããŸã®Lv.52ãç£èŠãæããšããã°æŒãæã fact3: äœããã®ã¢ã³ã¹ã¿ãŒãè¡ããšããã°æŒãæããªã fact4: ãããã®ã·ã®ã·ã«ã
Lv.50ãå
åãããšããããšã¯ãªããªãã°ãã®ã·ã®ã·ã«ã
Lv.50ã¯ãã€ç¡ãããããã¯ç£èŠãæãããŸãã¯ã©ã¡ããã fact5: ããã®ã·ã®ã·ã«ã
Lv.50ã¯ç®æãããšããããšã¯ç¢ºãã§ãããšãããšãã®ãŸããŸã®Lv.52ã¯ç£èŠãæã fact6: ããããã®ã·ãã·ã«ãLv.30ãæã¡åãããªããªããã®ã·ã®ã·ã«ã
Lv.50ã¯ç©ããšããããšã¯ãªãããã€å
åããªã fact7: ãã®ãŸããŸã®Lv.52ã¯ç®æã fact8: ãã®ãŸããŸã®Lv.52ã¯å®ã£ãœã | fact1: (x): {A}x -> {B}x fact2: {C}{b} -> {D}{b} fact3: (x): {A}x -> ¬{D}x fact4: ¬{F}{a} -> ({E}{a} v {C}{a}) fact5: {B}{a} -> {C}{b} fact6: ¬{H}{c} -> (¬{G}{a} & ¬{F}{a}) fact7: {B}{b} fact8: {CO}{b} | [
"fact1 -> int1: ä»®ã«ãã®ã·ã®ã·ã«ã
Lv.50ãè¡ããªãã°ããã¯ç®æã;"
] | [
"fact1 -> int1: {A}{a} -> {B}{a};"
] | ãã®ãŸããŸã®Lv.52ã¯æŒãæããªã | ¬{D}{b} | [
"fact11 -> int2: ãã®ãŸããŸã®Lv.52ãè¡ããšãããšæŒãæããªã;"
] | 6 | 4 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: è¡ãã¢ã³ã¹ã¿ãŒã¯ç®æã fact2: ä»®ã«ãã®ãŸããŸã®Lv.52ãç£èŠãæããšããã°æŒãæã fact3: äœããã®ã¢ã³ã¹ã¿ãŒãè¡ããšããã°æŒãæããªã fact4: ãããã®ã·ã®ã·ã«ã
Lv.50ãå
åãããšããããšã¯ãªããªãã°ãã®ã·ã®ã·ã«ã
Lv.50ã¯ãã€ç¡ãããããã¯ç£èŠãæãããŸãã¯ã©ã¡ããã fact5: ããã®ã·ã®ã·ã«ã
Lv.50ã¯ç®æãããšããããšã¯ç¢ºãã§ãããšãããšãã®ãŸããŸã®Lv.52ã¯ç£èŠãæã fact6: ããããã®ã·ãã·ã«ãLv.30ãæã¡åãããªããªããã®ã·ã®ã·ã«ã
Lv.50ã¯ç©ããšããããšã¯ãªãããã€å
åããªã fact7: ãã®ãŸããŸã®Lv.52ã¯ç®æã fact8: ãã®ãŸããŸã®Lv.52ã¯å®ã£ãœã ; $hypothesis$ = ãã®ãŸããŸã®Lv.52ã¯æŒãæã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): {A}x -> {B}x fact2: {C}{b} -> {D}{b} fact3: (x): {A}x -> ¬{D}x fact4: ¬{F}{a} -> ({E}{a} v {C}{a}) fact5: {B}{a} -> {C}{b} fact6: ¬{H}{c} -> (¬{G}{a} & ¬{F}{a}) fact7: {B}{b} fact8: {CO}{b} ; $hypothesis$ = {D}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã®ã¿ãLv.78ã¯é å ããããšããããšã¯ãªã | ¬{C}{b} | fact1: ä»®ã«ãã®ã¿ã®ã¿ãLv.78ãåããããšããã°ãã®ã¿ã®ã¿ãLv.78ã¯é å ããã fact2: ãã®ãŽã¡ã
ãŽã«ãLv.7ã¯ãã£ããŒã fact3: ãã£ããŒãã¢ã³ã¹ã¿ãŒã¯é å ãããªã fact4: ããä»®ã«ãã®ã¿ã®ã¿ãLv.78ãããŒãããªãããŸãã¯è奮ãæããªãããããã¯äž¡æ¹ã§ãããªããã®ã¿ã®ã¿ãLv.78ã¯ããŒãããªã fact5: ããŒãããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯è¥ããªããå ããŠãã¯ã€ãããŠã¹å
¥ãããªã fact6: è¥ããªãã¢ã³ã¹ã¿ãŒã¯ãã£ããŒãããŸãåããã fact7: ããããã®ãŽã¡ã
ãŽã«ãLv.7ã¯ãã£ããŒãããšããããšã¯äºå®ãªãã°ãã®ã¿ã®ã¿ãLv.78ã¯åããã | fact1: {B}{b} -> {C}{b} fact2: {A}{a} fact3: (x): {A}x -> ¬{C}x fact4: (¬{F}{b} v ¬{G}{b}) -> ¬{F}{b} fact5: (x): ¬{F}x -> (¬{D}x & ¬{E}x) fact6: (x): ¬{D}x -> ({A}x & {B}x) fact7: {A}{a} -> {B}{b} | [
"fact7 & fact2 -> int1: ãã®ã¿ã®ã¿ãLv.78ã¯åããã; int1 & fact1 -> hypothesis;"
] | [
"fact7 & fact2 -> int1: {B}{b}; int1 & fact1 -> hypothesis;"
] | ãã®ã¿ã®ã¿ãLv.78ã¯é å ããããšããããšã¯ãªã | ¬{C}{b} | [
"fact9 -> int2: ããããã®ã¿ã®ã¿ãLv.78ããã£ããŒããªãã°é å ãããªã; fact11 -> int3: ä»®ã«ãã®ã¿ã®ã¿ãLv.78ãè¥ããšããããšã¯ãªããšãããšãã®ã¿ã®ã¿ãLv.78ã¯ãã£ããŒããããã¯åããã; fact10 -> int4: ããããã®ã¿ã®ã¿ãLv.78ãããŒãããªããšãããšè¥ããªããŠãã¯ã€ãããŠã¹å
¥ããããšããããšã¯ãªã;"
] | 6 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ã¿ã®ã¿ãLv.78ãåããããšããã°ãã®ã¿ã®ã¿ãLv.78ã¯é å ããã fact2: ãã®ãŽã¡ã
ãŽã«ãLv.7ã¯ãã£ããŒã fact3: ãã£ããŒãã¢ã³ã¹ã¿ãŒã¯é å ãããªã fact4: ããä»®ã«ãã®ã¿ã®ã¿ãLv.78ãããŒãããªãããŸãã¯è奮ãæããªãããããã¯äž¡æ¹ã§ãããªããã®ã¿ã®ã¿ãLv.78ã¯ããŒãããªã fact5: ããŒãããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯è¥ããªããå ããŠãã¯ã€ãããŠã¹å
¥ãããªã fact6: è¥ããªãã¢ã³ã¹ã¿ãŒã¯ãã£ããŒãããŸãåããã fact7: ããããã®ãŽã¡ã
ãŽã«ãLv.7ã¯ãã£ããŒãããšããããšã¯äºå®ãªãã°ãã®ã¿ã®ã¿ãLv.78ã¯åããã ; $hypothesis$ = ãã®ã¿ã®ã¿ãLv.78ã¯é å ããããšããããšã¯ãªã ; $proof$ = | fact7 & fact2 -> int1: ãã®ã¿ã®ã¿ãLv.78ã¯åããã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{b} -> {C}{b} fact2: {A}{a} fact3: (x): {A}x -> ¬{C}x fact4: (¬{F}{b} v ¬{G}{b}) -> ¬{F}{b} fact5: (x): ¬{F}x -> (¬{D}x & ¬{E}x) fact6: (x): ¬{D}x -> ({A}x & {B}x) fact7: {A}{a} -> {B}{b} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | fact7 & fact2 -> int1: {B}{b}; int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | æ¯èŒãåŸãããšã¯èµ·ããªã | ¬{B} | fact1: å¯èŠãããšããããšãèµ·ãã fact2: çŸå³ãããšããããšãšæ¯èŒãåŸãããšãçºçããã¯ãå¯èŠãããšããããšã¯çºçããªãããšããããšãçãããã | fact1: {C} fact2: ({A} & {B}) -> ¬{C} | [] | [] | null | null | [] | null | 5 | 4 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: å¯èŠãããšããããšãèµ·ãã fact2: çŸå³ãããšããããšãšæ¯èŒãåŸãããšãçºçããã¯ãå¯èŠãããšããããšã¯çºçããªãããšããããšãçãããã ; $hypothesis$ = æ¯èŒãåŸãããšã¯èµ·ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C} fact2: ({A} & {B}) -> ¬{C} ; $hypothesis$ = ¬{B} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããŸãããšããããšãçãã | {D} | fact1: ãåãããšã¯çããªãããšããããšã¯ãã·ã¡ã
ã·ãLv.27äºä»¶ãçããããããåããèŸããšããããšãèµ·ããããšããããšãçãããã fact2: ãã究æããããšã¯çããªããšããã°ãåããèŸããšããããšã¯èµ·ããªãããããã·ã¡ã
ã·ãLv.27äºä»¶ãèµ·ããããšããããšã¯åœã fact3: 究æããããšã¯ããããŸãããšããããšã¯èµ·ãããªããšããããšãé»ã fact4: åããèŸããšããããšã¯ç©¶æããããšã®åå ãšãªã fact5: åãããšã¯èµ·ãããªã fact6: ã¿ãã¿ãLv.44äºä»¶ã¯ã究æããããšãèµ·ãããªããŠåãããšã¯çºçããããšããããšãæã | fact1: ¬{E} -> ({A} & {B}) fact2: ¬{C} -> ¬(¬{B} & {A}) fact3: {C} -> {D} fact4: {B} -> {C} fact5: ¬{E} fact6: {F} -> (¬{C} & {E}) | [
"fact5 & fact1 -> int1: ã·ã¡ã
ã·ãLv.27äºä»¶ãçºçãããåããèŸããšããããšãèµ·ãã; int1 -> int2: åããèŸããšããããšãèµ·ãã; int2 & fact4 -> int3: 究æããããšãèµ·ãã; int3 & fact3 -> hypothesis;"
] | [
"fact5 & fact1 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 & fact4 -> int3: {C}; int3 & fact3 -> hypothesis;"
] | ããããŸãããšããããšã¯èµ·ããªã | ¬{D} | [] | 7 | 4 | 4 | 4 | 4 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãåãããšã¯çããªãããšããããšã¯ãã·ã¡ã
ã·ãLv.27äºä»¶ãçããããããåããèŸããšããããšãèµ·ããããšããããšãçãããã fact2: ãã究æããããšã¯çããªããšããã°ãåããèŸããšããããšã¯èµ·ããªãããããã·ã¡ã
ã·ãLv.27äºä»¶ãèµ·ããããšããããšã¯åœã fact3: 究æããããšã¯ããããŸãããšããããšã¯èµ·ãããªããšããããšãé»ã fact4: åããèŸããšããããšã¯ç©¶æããããšã®åå ãšãªã fact5: åãããšã¯èµ·ãããªã fact6: ã¿ãã¿ãLv.44äºä»¶ã¯ã究æããããšãèµ·ãããªããŠåãããšã¯çºçããããšããããšãæã ; $hypothesis$ = ããããŸãããšããããšãçãã ; $proof$ = | fact5 & fact1 -> int1: ã·ã¡ã
ã·ãLv.27äºä»¶ãçºçãããåããèŸããšããããšãèµ·ãã; int1 -> int2: åããèŸããšããããšãèµ·ãã; int2 & fact4 -> int3: 究æããããšãèµ·ãã; int3 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{E} -> ({A} & {B}) fact2: ¬{C} -> ¬(¬{B} & {A}) fact3: {C} -> {D} fact4: {B} -> {C} fact5: ¬{E} fact6: {F} -> (¬{C} & {E}) ; $hypothesis$ = {D} ; $proof$ = | fact5 & fact1 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 & fact4 -> int3: {C}; int3 & fact3 -> hypothesis; __PROVED__ |
0.3 | æ³åãé£ããšããããšããã³æŽ»åãå§ããããšãèµ·ãã | ({F} & {E}) | fact1: ã¿ã¡ãã¿ãLv.23äºä»¶ã¯ãã«ãã«Lv.43äºä»¶ãçºçããã fact2: æ©ããšããããšãçãã fact3: ããä»®ã«ã¿ã«ã¿ãLv.87äºä»¶ãèµ·ãããšãããšã¿ãªã¿ã¡ãLv.34äºä»¶ãçºçãã fact4: èªã¿èŸããšããããšããããã¯ã¿ã¡ãã¿ãLv.23äºä»¶ããããã¯äž¡æ¹ãšããèµ·ãã fact5: èªã¿èŸããšããããšã¯ããã«ãã«Lv.43äºä»¶ã¯èµ·ããªãããšããããšãé»æ¢ãã fact6: æ³åãé£ããšããããšãçãã fact7: ããã«ãã«Lv.43äºä»¶ãçããããšããããšã¯ã·ãã·ãLv.28äºä»¶ãçãããšããããšãçãããã fact8: ã·ãã·ãLv.28äºä»¶ã掻åãå§ããããšã¯çºçããªããšããããšãåé¿ãã | fact1: {B} -> {C} fact2: {BI} fact3: {BJ} -> {AP} fact4: ({A} v {B}) fact5: {A} -> {C} fact6: {F} fact7: {C} -> {D} fact8: {D} -> {E} | [
"fact4 & fact5 & fact1 -> int1: ãã«ãã«Lv.43äºä»¶ãèµ·ãã; int1 & fact7 -> int2: ã·ãã·ãLv.28äºä»¶ãèµ·ãã; int2 & fact8 -> int3: 掻åãå§ããããšãçãã; int3 & fact6 -> hypothesis;"
] | [
"fact4 & fact5 & fact1 -> int1: {C}; int1 & fact7 -> int2: {D}; int2 & fact8 -> int3: {E}; int3 & fact6 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ã¿ã¡ãã¿ãLv.23äºä»¶ã¯ãã«ãã«Lv.43äºä»¶ãçºçããã fact2: æ©ããšããããšãçãã fact3: ããä»®ã«ã¿ã«ã¿ãLv.87äºä»¶ãèµ·ãããšãããšã¿ãªã¿ã¡ãLv.34äºä»¶ãçºçãã fact4: èªã¿èŸããšããããšããããã¯ã¿ã¡ãã¿ãLv.23äºä»¶ããããã¯äž¡æ¹ãšããèµ·ãã fact5: èªã¿èŸããšããããšã¯ããã«ãã«Lv.43äºä»¶ã¯èµ·ããªãããšããããšãé»æ¢ãã fact6: æ³åãé£ããšããããšãçãã fact7: ããã«ãã«Lv.43äºä»¶ãçããããšããããšã¯ã·ãã·ãLv.28äºä»¶ãçãããšããããšãçãããã fact8: ã·ãã·ãLv.28äºä»¶ã掻åãå§ããããšã¯çºçããªããšããããšãåé¿ãã ; $hypothesis$ = æ³åãé£ããšããããšããã³æŽ»åãå§ããããšãèµ·ãã ; $proof$ = | fact4 & fact5 & fact1 -> int1: ãã«ãã«Lv.43äºä»¶ãèµ·ãã; int1 & fact7 -> int2: ã·ãã·ãLv.28äºä»¶ãèµ·ãã; int2 & fact8 -> int3: 掻åãå§ããããšãçãã; int3 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: {B} -> {C} fact2: {BI} fact3: {BJ} -> {AP} fact4: ({A} v {B}) fact5: {A} -> {C} fact6: {F} fact7: {C} -> {D} fact8: {D} -> {E} ; $hypothesis$ = ({F} & {E}) ; $proof$ = | fact4 & fact5 & fact1 -> int1: {C}; int1 & fact7 -> int2: {D}; int2 & fact8 -> int3: {E}; int3 & fact6 -> hypothesis; __PROVED__ |
0.3 | ã¿ãã¿ã¡ãLv.0äºä»¶ã¯èµ·ããªã | ¬{A} | fact1: ã¿ãã¿ã¡ãLv.0äºä»¶ã¯èµ·ããªããšããããšã¯ã·ãã·ã«ã
Lv.99äºä»¶ã«é²ããã fact2: 移è¡ãæããšããããšã¯çºçããªããšããããšã¯ãã·ãã·ã«ã
Lv.99äºä»¶ãšé Œããããšããããšãèµ·ããããšããããšãèªçºãã fact3: ã¿ãã¿ã¡ãLv.0äºä»¶ãçããããããã¯ã·ãã·ã«ã
Lv.99äºä»¶ãèµ·ããã°é Œããããšããããšã¯çããªã fact4: ã·ãã·ã«ã
Lv.99äºä»¶ã¯ããã©ããããšããããšã¯èµ·ããªããŠã¿ãã¿ã¡ãLv.0äºä»¶ãèµ·ããããšããããšãèªçºãã fact5: ãè¡ããããšããããšãèµ·ãããå°æããšããããšã¯çºçããªãããšããããšã¯æãç«ããªããšãããšã移è¡ãæããšããããšã¯èµ·ãããªãããšããããšã¯æ¬åœã§ãã fact6: ãé Œããããšããããšãšã·ãã·ã«ã
Lv.99äºä»¶äž¡æ¹ãšããèµ·ããããšããããšã¯ç§»è¡ãæããšããããšã¯çºçããªããšããããšãå¥æ©ã§ãã | fact1: {B} -> {A} fact2: ¬{D} -> ({B} & {C}) fact3: ({A} v {B}) -> ¬{C} fact4: {B} -> (¬{CG} & {A}) fact5: ¬({F} v ¬{E}) -> ¬{D} fact6: ¬{D} -> ({C} & {B}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããã¿ãã¿ã¡ãLv.0äºä»¶ãçãã; assump1 -> int1: ã¿ãã¿ã¡ãLv.0äºä»¶ããããã¯ã·ãã·ã«ã
Lv.99äºä»¶ãèµ·ãã; int1 & fact3 -> int2: é Œããããšããããšã¯èµ·ããªã;"
] | [
"void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact3 -> int2: ¬{C};"
] | 以äžã®ããã«ä»®å®ãããã¿ãã¿ã¡ãLv.0äºä»¶ãçãã | {A} | [] | 7 | 5 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ã¿ãã¿ã¡ãLv.0äºä»¶ã¯èµ·ããªããšããããšã¯ã·ãã·ã«ã
Lv.99äºä»¶ã«é²ããã fact2: 移è¡ãæããšããããšã¯çºçããªããšããããšã¯ãã·ãã·ã«ã
Lv.99äºä»¶ãšé Œããããšããããšãèµ·ããããšããããšãèªçºãã fact3: ã¿ãã¿ã¡ãLv.0äºä»¶ãçããããããã¯ã·ãã·ã«ã
Lv.99äºä»¶ãèµ·ããã°é Œããããšããããšã¯çããªã fact4: ã·ãã·ã«ã
Lv.99äºä»¶ã¯ããã©ããããšããããšã¯èµ·ããªããŠã¿ãã¿ã¡ãLv.0äºä»¶ãèµ·ããããšããããšãèªçºãã fact5: ãè¡ããããšããããšãèµ·ãããå°æããšããããšã¯çºçããªãããšããããšã¯æãç«ããªããšãããšã移è¡ãæããšããããšã¯èµ·ãããªãããšããããšã¯æ¬åœã§ãã fact6: ãé Œããããšããããšãšã·ãã·ã«ã
Lv.99äºä»¶äž¡æ¹ãšããèµ·ããããšããããšã¯ç§»è¡ãæããšããããšã¯çºçããªããšããããšãå¥æ©ã§ãã ; $hypothesis$ = ã¿ãã¿ã¡ãLv.0äºä»¶ã¯èµ·ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B} -> {A} fact2: ¬{D} -> ({B} & {C}) fact3: ({A} v {B}) -> ¬{C} fact4: {B} -> (¬{CG} & {A}) fact5: ¬({F} v ¬{E}) -> ¬{D} fact6: ¬{D} -> ({C} & {B}) ; $hypothesis$ = ¬{A} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããå
¥ãèŸããªãã°çãŸãé£ããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> {C}x | fact1: ä»®ã«ãã®ãŽã¡ããŽãLv.67ãå
¥ãèŸããšããã°ãã®ãŽã¡ããŽãLv.67ã¯ççœã fact2: ãã®ãŽã¡ããŽãLv.67ãççœããšããã°ããã¯çãŸãé£ã | fact1: {A}{a} -> {B}{a} fact2: {B}{a} -> {C}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŽã¡ããŽãLv.67ã¯å
¥ãèŸã; fact1 & assump1 -> int1: ãã®ãŽã¡ããŽãLv.67ã¯ççœã; int1 & fact2 -> int2: ãã®ãŽã¡ããŽãLv.67ã¯çãŸãé£ã; [assump1] & int2 -> int3: ä»®ã«ããã®ãŽã¡ããŽãLv.67ã¯å
¥ãèŸãããšããããšã¯äºå®ã§ãããšããããã®ãŽã¡ããŽãLv.67ã¯çãŸãé£ã; int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{a}; [assump1] & int2 -> int3: {A}{a} -> {C}{a}; int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ãã®ãŽã¡ããŽãLv.67ãå
¥ãèŸããšããã°ãã®ãŽã¡ããŽãLv.67ã¯ççœã fact2: ãã®ãŽã¡ããŽãLv.67ãççœããšããã°ããã¯çãŸãé£ã ; $hypothesis$ = ããããå
¥ãèŸããªãã°çãŸãé£ããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŽã¡ããŽãLv.67ã¯å
¥ãèŸã; fact1 & assump1 -> int1: ãã®ãŽã¡ããŽãLv.67ã¯ççœã; int1 & fact2 -> int2: ãã®ãŽã¡ããŽãLv.67ã¯çãŸãé£ã; [assump1] & int2 -> int3: ä»®ã«ããã®ãŽã¡ããŽãLv.67ã¯å
¥ãèŸãããšããããšã¯äºå®ã§ãããšããããã®ãŽã¡ããŽãLv.67ã¯çãŸãé£ã; int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} -> {B}{a} fact2: {B}{a} -> {C}{a} ; $hypothesis$ = (Ex): {A}x -> {C}x ; $proof$ = | void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{a}; [assump1] & int2 -> int3: {A}{a} -> {C}{a}; int3 -> hypothesis; __PROVED__ |
0.3 | ãä»®ã«ããæããšããã°éæåãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> {C}x | fact1: ä»®ã«ãã®ããããLv.81ãåŸãããšããã°ããã¯éæåãã fact2: ãä»®ã«éæåãããªãåŸãããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ãã®ããããLv.81ãããæããªãåŸãã fact4: ããä»®ã«ãäœããã®ã¢ã³ã¹ã¿ãŒã¯çãæããªããé¢çœããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšãããçãæã fact5: ä»®ã«ãã®ãŽããŽãLv.74ã¯çãæããšããã°ããã®ããããLv.81ã¯ããããªãããã©ããã¯éæåããããšããããšã¯ç¢ºãã§ãããšããããšã¯ãªã fact6: ãããããšããã¢ã³ã¹ã¿ãŒã¯ããããªããéæåããããšããããšã¯æ¬åœã§ãªããªãéæåããªã | fact1: {B}{a} -> {C}{a} fact2: (Ex): {C}x -> {B}x fact3: {A}{a} -> {B}{a} fact4: (x): ¬(¬{E}x & ¬{F}x) -> {E}x fact5: {E}{b} -> ¬(¬{D}{a} & {C}{a}) fact6: (x): ¬(¬{D}x & {C}x) -> ¬{C}x | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ããããLv.81ã¯ããæãããšããããšã¯æ¬åœã§ãã; fact3 & assump1 -> int1: ãã®ããããLv.81ã¯åŸãã; int1 & fact1 -> int2: ãã®ããããLv.81ã¯éæåãã; [assump1] & int2 -> int3: ããä»®ã«ãã®ããããLv.81ãããæããªãã°ãã®ããããLv.81ã¯éæåãã; int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact3 & assump1 -> int1: {B}{a}; int1 & fact1 -> int2: {C}{a}; [assump1] & int2 -> int3: {A}{a} -> {C}{a}; int3 -> hypothesis;"
] | ãã®ãœããœãLv.9ã¯ããæã | {A}{e} | [
"fact9 -> int4: ããããã®ããããLv.81ã¯ããããªãããããéæåããããšããããšã¯åã§ãããšããããã®ããããLv.81ã¯éæåãããšããããšã¯ãªã; fact7 -> int5: ãããããã®ãŽããŽãLv.74ã¯çãæããªããŠããã«ããã¯é¢çœããªãããšããããšã¯ééãã ããšããããšã¯æãç«ã€ãªãããã¯çãæã;"
] | 7 | 5 | 4 | 5 | 4 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ããããLv.81ãåŸãããšããã°ããã¯éæåãã fact2: ãä»®ã«éæåãããªãåŸãããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ãã®ããããLv.81ãããæããªãåŸãã fact4: ããä»®ã«ãäœããã®ã¢ã³ã¹ã¿ãŒã¯çãæããªããé¢çœããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšãããçãæã fact5: ä»®ã«ãã®ãŽããŽãLv.74ã¯çãæããšããã°ããã®ããããLv.81ã¯ããããªãããã©ããã¯éæåããããšããããšã¯ç¢ºãã§ãããšããããšã¯ãªã fact6: ãããããšããã¢ã³ã¹ã¿ãŒã¯ããããªããéæåããããšããããšã¯æ¬åœã§ãªããªãéæåããªã ; $hypothesis$ = ãä»®ã«ããæããšããã°éæåãããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ããããLv.81ã¯ããæãããšããããšã¯æ¬åœã§ãã; fact3 & assump1 -> int1: ãã®ããããLv.81ã¯åŸãã; int1 & fact1 -> int2: ãã®ããããLv.81ã¯éæåãã; [assump1] & int2 -> int3: ããä»®ã«ãã®ããããLv.81ãããæããªãã°ãã®ããããLv.81ã¯éæåãã; int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{a} -> {C}{a} fact2: (Ex): {C}x -> {B}x fact3: {A}{a} -> {B}{a} fact4: (x): ¬(¬{E}x & ¬{F}x) -> {E}x fact5: {E}{b} -> ¬(¬{D}{a} & {C}{a}) fact6: (x): ¬(¬{D}x & {C}x) -> ¬{C}x ; $hypothesis$ = (Ex): {A}x -> {C}x ; $proof$ = | void -> assump1: {A}{a}; fact3 & assump1 -> int1: {B}{a}; int1 & fact1 -> int2: {C}{a}; [assump1] & int2 -> int3: {A}{a} -> {C}{a}; int3 -> hypothesis; __PROVED__ |
0.3 | æå³ãããšããããšã¯çºçããªã | ¬{A} | fact1: æå³ãããšããããšããããã¯åžåãæããšããããšãçãããšãããšæãåºæ·±ããšããããšã¯çããªã fact2: ãæå³ãããšããããšã¯çããªãããšããããšã¯åžåãæããšããããšã«é»æ¢ããã fact3: ãããæžã蟌ãããšã¯èµ·ãããªããšããã°æãåºæ·±ããšããããšãèµ·ããããããåžåãæããšããããšãèµ·ãã fact4: æãåºæ·±ããšããããšãèµ·ãã | fact1: ({A} v {B}) -> ¬{C} fact2: {B} -> {A} fact3: ¬{D} -> ({C} & {B}) fact4: {C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããæå³ãããšããããšãçºçãã; assump1 -> int1: æå³ãããšããããšãçãããåžåãæããšããããšãçºçããããããã¯äž¡æ¹ãšãã§ãã; int1 & fact1 -> int2: æãåºæ·±ããšããããšã¯èµ·ãããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ãããæå³ãããšããããšãçºçãã | {A} | [] | 7 | 5 | 3 | 5 | 3 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: æå³ãããšããããšããããã¯åžåãæããšããããšãçãããšãããšæãåºæ·±ããšããããšã¯çããªã fact2: ãæå³ãããšããããšã¯çããªãããšããããšã¯åžåãæããšããããšã«é»æ¢ããã fact3: ãããæžã蟌ãããšã¯èµ·ãããªããšããã°æãåºæ·±ããšããããšãèµ·ããããããåžåãæããšããããšãèµ·ãã fact4: æãåºæ·±ããšããããšãèµ·ãã ; $hypothesis$ = æå³ãããšããããšã¯çºçããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããæå³ãããšããããšãçºçãã; assump1 -> int1: æå³ãããšããããšãçãããåžåãæããšããããšãçºçããããããã¯äž¡æ¹ãšãã§ãã; int1 & fact1 -> int2: æãåºæ·±ããšããããšã¯èµ·ãããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} fact2: {B} -> {A} fact3: ¬{D} -> ({C} & {B}) fact4: {C} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãéãé£ããšããããšãèµ·ããããšããããšã¯æãç«ã€ | {A} | fact1: è¶è²ã£ãœããšããããšãçºçãã fact2: ãéãé£ããšããããšã¯çããªãããšããããšã¯ãè¶è²ã£ãœããšããããšã¯çããªããŠéããšããããšãçããããšããããšããããã fact3: éããšããããšã¯éãé£ããšããããšã¯èµ·ãããªããšããããšã«èµ·å ãã fact4: ãã«ã
ãã«Lv.52äºä»¶ãèµ·ãã fact5: éããšããããšãèµ·ãã fact6: ã¿ã¡ãã¿ãLv.79äºä»¶ã¯èµ·ãããªãããã©ãœããœãLv.83äºä»¶ãèµ·ãã | fact1: {AA} fact2: ¬{A} -> (¬{AA} & {AB}) fact3: ¬{A} -> {AB} fact4: {BT} fact5: {AB} fact6: (¬{FT} & {HF}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããéãé£ããšããããšã¯èµ·ãããªã; fact2 & assump1 -> int1: è¶è²ã£ãœããšããããšã¯çããªãããã©éããšããããšãçºçãã; int1 -> int2: è¶è²ã£ãœããšããããšã¯çããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}; fact2 & assump1 -> int1: (¬{AA} & {AB}); int1 -> int2: ¬{AA}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 4 | 0 | 4 | PROVED | null | PROVED | null | $facts$ = fact1: è¶è²ã£ãœããšããããšãçºçãã fact2: ãéãé£ããšããããšã¯çããªãããšããããšã¯ãè¶è²ã£ãœããšããããšã¯çããªããŠéããšããããšãçããããšããããšããããã fact3: éããšããããšã¯éãé£ããšããããšã¯èµ·ãããªããšããããšã«èµ·å ãã fact4: ãã«ã
ãã«Lv.52äºä»¶ãèµ·ãã fact5: éããšããããšãèµ·ãã fact6: ã¿ã¡ãã¿ãLv.79äºä»¶ã¯èµ·ãããªãããã©ãœããœãLv.83äºä»¶ãèµ·ãã ; $hypothesis$ = ãéãé£ããšããããšãèµ·ããããšããããšã¯æãç«ã€ ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããéãé£ããšããããšã¯èµ·ãããªã; fact2 & assump1 -> int1: è¶è²ã£ãœããšããããšã¯çããªãããã©éããšããããšãçºçãã; int1 -> int2: è¶è²ã£ãœããšããããšã¯çããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {AA} fact2: ¬{A} -> (¬{AA} & {AB}) fact3: ¬{A} -> {AB} fact4: {BT} fact5: {AB} fact6: (¬{FT} & {HF}) ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: ¬{A}; fact2 & assump1 -> int1: (¬{AA} & {AB}); int1 -> int2: ¬{AA}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãæ匷ããšããããšã¯çºçããªãããã©å·ãæããšããããšãçºçããããšããããšã¯èª€ãã | ¬(¬{E} & {D}) | fact1: ãåæ°ãªããšããããšã¯èµ·ãããªãããšããããšã¯ãœãªãœãLv.77äºä»¶ãèªçºãã fact2: ä»®ã«åããããšããããšãèµ·ããã°æ匷ããšããããšã§ã¯ãªããŠå·ãæããšããããšãçãã fact3: åããããšããããšã¯äŸæ ããããšã«ããçãã fact4: åæ°ãªããšããããšã¯èµ·ããªã | fact1: ¬{F} -> {A} fact2: {C} -> (¬{E} & {D}) fact3: {B} -> {C} fact4: ¬{F} | [] | [] | null | null | [] | null | 4 | 4 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãåæ°ãªããšããããšã¯èµ·ãããªãããšããããšã¯ãœãªãœãLv.77äºä»¶ãèªçºãã fact2: ä»®ã«åããããšããããšãèµ·ããã°æ匷ããšããããšã§ã¯ãªããŠå·ãæããšããããšãçãã fact3: åããããšããããšã¯äŸæ ããããšã«ããçãã fact4: åæ°ãªããšããããšã¯èµ·ããªã ; $hypothesis$ = ãæ匷ããšããããšã¯çºçããªãããã©å·ãæããšããããšãçºçããããšããããšã¯èª€ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{F} -> {A} fact2: {C} -> (¬{E} & {D}) fact3: {B} -> {C} fact4: ¬{F} ; $hypothesis$ = ¬(¬{E} & {D}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãé倪ããªããªããè·³æ¢ããªããå ããŠãããŸãªãããšããããšã¯èª€ããªãã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{A}x -> ¬(¬{AA}x & ¬{AB}x) | fact1: ãããããªãããã®ã¢ã³ã¹ã¿ãŒã¯çãèŸããªãããšããããšã¯äºå®ã ãšãããšãæ ãããªããããŸãã«åŸ¡å¿ãããªãããšããããšã¯ééã£ãŠãã fact2: ããä»®ã«ãã®ã·ã«ãã·ãªLv.8ã¯é倪ããšããããšã¯ãªããªãã°ããã®ã·ã«ãã·ãªLv.8ã¯è·³æ¢ããªãããããŸãªãããšããããšã¯æãç«ããªã | fact1: (x): ¬{II}x -> ¬(¬{AR}x & ¬{U}x) fact2: ¬{A}{aa} -> ¬(¬{AA}{aa} & ¬{AB}{aa}) | [
"fact2 -> hypothesis;"
] | [
"fact2 -> hypothesis;"
] | ããä»®ã«ãã®ãŸããŸãLv.87ã¯çãèŸããªããšããã°ãæ ãããªããŠãŸã埡å¿ãããªãããšããããšã¯ééãã§ãã | ¬{II}{au} -> ¬(¬{AR}{au} & ¬{U}{au}) | [
"fact3 -> hypothesis;"
] | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãããããªãããã®ã¢ã³ã¹ã¿ãŒã¯çãèŸããªãããšããããšã¯äºå®ã ãšãããšãæ ãããªããããŸãã«åŸ¡å¿ãããªãããšããããšã¯ééã£ãŠãã fact2: ããä»®ã«ãã®ã·ã«ãã·ãªLv.8ã¯é倪ããšããããšã¯ãªããªãã°ããã®ã·ã«ãã·ãªLv.8ã¯è·³æ¢ããªãããããŸãªãããšããããšã¯æãç«ããªã ; $hypothesis$ = ãé倪ããªããªããè·³æ¢ããªããå ããŠãããŸãªãããšããããšã¯èª€ããªãã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬{II}x -> ¬(¬{AR}x & ¬{U}x) fact2: ¬{A}{aa} -> ¬(¬{AA}{aa} & ¬{AB}{aa}) ; $hypothesis$ = (Ex): ¬{A}x -> ¬(¬{AA}x & ¬{AB}x) ; $proof$ = | fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ãã·ã«Lv.69ã¯çœªæ·±ã | {A}{a} | fact1: ãã®ã·ãã·ã«Lv.69ã¯çœªæ·±ããªããšããããçã
ãããªããåããæããªãããšããããšã¯æãç«ããªã fact2: ãã®ã·ãã·ã«Lv.69ã¯è§£ãæã fact3: ä»®ã«ããã®ã·ãã·ã«Lv.69ã¯çã
ãããªããŠãã€åããæããªãããšããããšã¯åã ãšããã°è§£ãæããªã | fact1: ¬{A}{a} -> ¬(¬{AA}{a} & ¬{AB}{a}) fact2: {B}{a} fact3: ¬(¬{AA}{a} & ¬{AB}{a}) -> ¬{B}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ã«Lv.69ã¯çœªæ·±ããªã; fact1 & assump1 -> int1: ããã®ã·ãã·ã«Lv.69ã¯çã
ãããšããããšã¯ãªããŠæŽã«åããæããªãããšããããšã¯æãç«ããªã; int1 & fact3 -> int2: ãã®ã·ãã·ã«Lv.69ã¯è§£ãæããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}{a}; fact1 & assump1 -> int1: ¬(¬{AA}{a} & ¬{AB}{a}); int1 & fact3 -> int2: ¬{B}{a}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ã·ãã·ã«Lv.69ã¯çœªæ·±ããªããšããããçã
ãããªããåããæããªãããšããããšã¯æãç«ããªã fact2: ãã®ã·ãã·ã«Lv.69ã¯è§£ãæã fact3: ä»®ã«ããã®ã·ãã·ã«Lv.69ã¯çã
ãããªããŠãã€åããæããªãããšããããšã¯åã ãšããã°è§£ãæããªã ; $hypothesis$ = ãã®ã·ãã·ã«Lv.69ã¯çœªæ·±ã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ã«Lv.69ã¯çœªæ·±ããªã; fact1 & assump1 -> int1: ããã®ã·ãã·ã«Lv.69ã¯çã
ãããšããããšã¯ãªããŠæŽã«åããæããªãããšããããšã¯æãç«ããªã; int1 & fact3 -> int2: ãã®ã·ãã·ã«Lv.69ã¯è§£ãæããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A}{a} -> ¬(¬{AA}{a} & ¬{AB}{a}) fact2: {B}{a} fact3: ¬(¬{AA}{a} & ¬{AB}{a}) -> ¬{B}{a} ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: ¬{A}{a}; fact1 & assump1 -> int1: ¬(¬{AA}{a} & ¬{AB}{a}); int1 & fact3 -> int2: ¬{B}{a}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽã¡ããŽã«Lv.31ã¯å€åãæããªã | ¬{C}{b} | fact1: ããããã®ãœã«ããœã«ãLv.91ãæ¯äŸæ¡åãããšãããšãã®ãŽã¡ããŽã«Lv.31ã¯çµ¶äº€ãã fact2: ãã®ãœã«ããœã«ãLv.91ã¯çŸããããã¯æ¶ååžåããæã fact3: ããããã¢ã³ã¹ã¿ãŒã¯ãªã¹ãã©ããªã fact4: ãã®ãœã«ããœã«ãLv.91ã¯çµ¶äº€ãã fact5: ä»®ã«ãã®ãœã«ããœã«ãLv.91ã絶亀ããã°ãã®ãŽã¡ããŽã«Lv.31ã¯çµ¶äº€ãã fact6: ãã®ãœã«ããœã«ãLv.91ã¯æ¯äŸæ¡åãã fact7: ãã®ãœããœãLv.24ã¯å€åãæã | fact1: {A}{a} -> {B}{b} fact2: ({BJ}{a} & {IU}{a}) fact3: (x): ¬{F}x fact4: {B}{a} fact5: {B}{a} -> {B}{b} fact6: {A}{a} fact7: {C}{cs} | [
"fact6 & fact4 -> int1: ããã®ãœã«ããœã«ãLv.91ã¯æ¯äŸæ¡åãããæŽã«çµ¶äº€ããããšããããšã¯äºå®ã§ãã;"
] | [
"fact6 & fact4 -> int1: ({A}{a} & {B}{a});"
] | ãã®ãŽã¡ããŽã«Lv.31ã¯çµ¶äº€ãã | {B}{b} | [
"fact9 -> int2: ãã®ãŸã¡ããŸã¡ã
Lv.56ã¯ãªã¹ãã©ããªã;"
] | 8 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®ãœã«ããœã«ãLv.91ãæ¯äŸæ¡åãããšãããšãã®ãŽã¡ããŽã«Lv.31ã¯çµ¶äº€ãã fact2: ãã®ãœã«ããœã«ãLv.91ã¯çŸããããã¯æ¶ååžåããæã fact3: ããããã¢ã³ã¹ã¿ãŒã¯ãªã¹ãã©ããªã fact4: ãã®ãœã«ããœã«ãLv.91ã¯çµ¶äº€ãã fact5: ä»®ã«ãã®ãœã«ããœã«ãLv.91ã絶亀ããã°ãã®ãŽã¡ããŽã«Lv.31ã¯çµ¶äº€ãã fact6: ãã®ãœã«ããœã«ãLv.91ã¯æ¯äŸæ¡åãã fact7: ãã®ãœããœãLv.24ã¯å€åãæã ; $hypothesis$ = ãã®ãŽã¡ããŽã«Lv.31ã¯å€åãæããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} -> {B}{b} fact2: ({BJ}{a} & {IU}{a}) fact3: (x): ¬{F}x fact4: {B}{a} fact5: {B}{a} -> {B}{b} fact6: {A}{a} fact7: {C}{cs} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ãã·ãLv.3ã¯æ«æããããæ°ä»ãé£ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({G}{e} v ¬{F}{e}) | fact1: ãã®ã·ãã·ãLv.3ã¯æ«æãããããŸãã¯æ°ä»ãé£ããäž¡æ¹ãšãã§ãã fact2: ãã®ãŸã¡ããŸãªLv.12ã浞è»ãããšããããã®ãŽããŽã«ãLv.54ã¯ã€ããªã fact3: ãããã®ãŽããŽã«ãLv.54ãè©Šã¿ãããã€ã€ããªããšãããšãã®ãŸããŸã¡ãLv.73ã¯è²ãŠæããªã fact4: ãããã®ã¿ãªã¿ãLv.59ãé¥å¹ãããšããã°ãã®ãŸã¡ããŸãªLv.12ã¯æµžè»ãã fact5: ãã®ãŽããŽã«ãLv.54ã¯è©Šã¿ã fact6: ãã®ã¿ãªã¿ãLv.59ã¯é¥å¹ãã fact7: ããä»®ã«ãã®ãŸããŸã¡ãLv.73ãè²ãŠæããªããªãã°ãã®ã·ãã·ãLv.3ã¯æ«æããããæ°ä»ãé£ããªã fact8: ãããã浞è»ããªãããŸãã¯ã€ããªããªãããããã¯äž¡æ¹ã§ããããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒããããšããããã®ã·ãã·ãLv.3ã¯é¥å¹ããªã | fact1: ({G}{e} v {F}{e}) fact2: {B}{b} -> {C}{c} fact3: ({D}{c} & {C}{c}) -> ¬{E}{d} fact4: {A}{a} -> {B}{b} fact5: {D}{c} fact6: {A}{a} fact7: ¬{E}{d} -> ({G}{e} v ¬{F}{e}) fact8: (x): ¬(¬{B}x v ¬{C}x) -> ¬{A}{e} | [
"fact4 & fact6 -> int1: ãã®ãŸã¡ããŸãªLv.12ã¯æµžè»ãã; int1 & fact2 -> int2: ããã®ãŽããŽã«ãLv.54ã¯ã€ããªãããšããããšã¯æ¬åœã§ãã; int2 & fact5 -> int3: ãã®ãŽããŽã«ãLv.54ã¯è©Šã¿ããããã«ã€ããªã; int3 & fact3 -> int4: ãã®ãŸããŸã¡ãLv.73ã¯è²ãŠæããªã; int4 & fact7 -> hypothesis;"
] | [
"fact4 & fact6 -> int1: {B}{b}; int1 & fact2 -> int2: {C}{c}; int2 & fact5 -> int3: ({D}{c} & {C}{c}); int3 & fact3 -> int4: ¬{E}{d}; int4 & fact7 -> hypothesis;"
] | ããã®ã·ãã·ãLv.3ã¯æ«æããããæ°ä»ãé£ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({G}{e} v ¬{F}{e}) | [] | 7 | 5 | 5 | 5 | 5 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã·ãã·ãLv.3ã¯æ«æãããããŸãã¯æ°ä»ãé£ããäž¡æ¹ãšãã§ãã fact2: ãã®ãŸã¡ããŸãªLv.12ã浞è»ãããšããããã®ãŽããŽã«ãLv.54ã¯ã€ããªã fact3: ãããã®ãŽããŽã«ãLv.54ãè©Šã¿ãããã€ã€ããªããšãããšãã®ãŸããŸã¡ãLv.73ã¯è²ãŠæããªã fact4: ãããã®ã¿ãªã¿ãLv.59ãé¥å¹ãããšããã°ãã®ãŸã¡ããŸãªLv.12ã¯æµžè»ãã fact5: ãã®ãŽããŽã«ãLv.54ã¯è©Šã¿ã fact6: ãã®ã¿ãªã¿ãLv.59ã¯é¥å¹ãã fact7: ããä»®ã«ãã®ãŸããŸã¡ãLv.73ãè²ãŠæããªããªãã°ãã®ã·ãã·ãLv.3ã¯æ«æããããæ°ä»ãé£ããªã fact8: ãããã浞è»ããªãããŸãã¯ã€ããªããªãããããã¯äž¡æ¹ã§ããããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒããããšããããã®ã·ãã·ãLv.3ã¯é¥å¹ããªã ; $hypothesis$ = ããã®ã·ãã·ãLv.3ã¯æ«æããããæ°ä»ãé£ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact4 & fact6 -> int1: ãã®ãŸã¡ããŸãªLv.12ã¯æµžè»ãã; int1 & fact2 -> int2: ããã®ãŽããŽã«ãLv.54ã¯ã€ããªãããšããããšã¯æ¬åœã§ãã; int2 & fact5 -> int3: ãã®ãŽããŽã«ãLv.54ã¯è©Šã¿ããããã«ã€ããªã; int3 & fact3 -> int4: ãã®ãŸããŸã¡ãLv.73ã¯è²ãŠæããªã; int4 & fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({G}{e} v {F}{e}) fact2: {B}{b} -> {C}{c} fact3: ({D}{c} & {C}{c}) -> ¬{E}{d} fact4: {A}{a} -> {B}{b} fact5: {D}{c} fact6: {A}{a} fact7: ¬{E}{d} -> ({G}{e} v ¬{F}{e}) fact8: (x): ¬(¬{B}x v ¬{C}x) -> ¬{A}{e} ; $hypothesis$ = ¬({G}{e} v ¬{F}{e}) ; $proof$ = | fact4 & fact6 -> int1: {B}{b}; int1 & fact2 -> int2: {C}{c}; int2 & fact5 -> int3: ({D}{c} & {C}{c}); int3 & fact3 -> int4: ¬{E}{d}; int4 & fact7 -> hypothesis; __DISPROVED__ |
0.3 | ãŸã«ããŸãLv.17äºä»¶ã¯çºçããªã | ¬{C} | fact1: ãŸã«ããŸãªLv.93äºä»¶ããŸã«ããŸãLv.17äºä»¶ã¯èµ·ãããªããšããããšãé²ã fact2: çŽåŸãé£ããšããããšã¯ããŸããŸã«Lv.43äºä»¶ãçããªããŠãã®äžã¿ãªã¿ãLv.81äºä»¶ã¯çããªãããšããããšã«ç¹ãã fact3: ããŸã«ããŸãªLv.93äºä»¶ã§ã¯ãªããŠåŒŸãæããšããããšãçºçããããšããããšã¯ãŸããŸã«Lv.43äºä»¶ã¯èµ·ããªããšããããšã«åŒãèµ·ãããã fact4: ãœããœã®Lv.67äºä»¶ãèµ·ãã fact5: ãœããœã®Lv.67äºä»¶ã¯ããŸã«ããŸãªLv.93äºä»¶ã¯çºçããªãããšããããšãé»æ¢ãã | fact1: {B} -> {C} fact2: {G} -> (¬{E} & ¬{F}) fact3: ¬{E} -> (¬{B} & {D}) fact4: {A} fact5: {A} -> {B} | [
"fact5 & fact4 -> int1: ãŸã«ããŸãªLv.93äºä»¶ãçºçãã; int1 & fact1 -> hypothesis;"
] | [
"fact5 & fact4 -> int1: {B}; int1 & fact1 -> hypothesis;"
] | ãŸã«ããŸãLv.17äºä»¶ã¯çºçããªã | ¬{C} | [] | 7 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãŸã«ããŸãªLv.93äºä»¶ããŸã«ããŸãLv.17äºä»¶ã¯èµ·ãããªããšããããšãé²ã fact2: çŽåŸãé£ããšããããšã¯ããŸããŸã«Lv.43äºä»¶ãçããªããŠãã®äžã¿ãªã¿ãLv.81äºä»¶ã¯çããªãããšããããšã«ç¹ãã fact3: ããŸã«ããŸãªLv.93äºä»¶ã§ã¯ãªããŠåŒŸãæããšããããšãçºçããããšããããšã¯ãŸããŸã«Lv.43äºä»¶ã¯èµ·ããªããšããããšã«åŒãèµ·ãããã fact4: ãœããœã®Lv.67äºä»¶ãèµ·ãã fact5: ãœããœã®Lv.67äºä»¶ã¯ããŸã«ããŸãªLv.93äºä»¶ã¯çºçããªãããšããããšãé»æ¢ãã ; $hypothesis$ = ãŸã«ããŸãLv.17äºä»¶ã¯çºçããªã ; $proof$ = | fact5 & fact4 -> int1: ãŸã«ããŸãªLv.93äºä»¶ãçºçãã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} -> {C} fact2: {G} -> (¬{E} & ¬{F}) fact3: ¬{E} -> (¬{B} & {D}) fact4: {A} fact5: {A} -> {B} ; $hypothesis$ = ¬{C} ; $proof$ = | fact5 & fact4 -> int1: {B}; int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããåããèŸãã人éèããªãããããã¯äž¡æ¹ãšããªãã°å«å³ã£ãœããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã | ¬((Ex): ({AA}x v ¬{AB}x) -> {B}x) | fact1: ãããã®ã¿ãªã¿ã¡ã
Lv.34ã人éèããªããšããããã®ã¿ãªã¿ã¡ã
Lv.34ã¯å«å³ã£ãœã fact2: ãããç»çãããšããã°å€åãæããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãæºãŸãæãããŸãã¯ããã¯æ²ãããªãããŸãã¯äž¡æ¹ã§ãããšãããããã¯èŠªã | fact1: ¬{AB}{aa} -> {B}{aa} fact2: (Ex): {HL}x -> {BF}x fact3: (x): ({HR}x v ¬{BI}x) -> {BE}x | [] | [] | ããæºãŸãæããæ²ãããªããšããã芪ããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯çå®ã | (Ex): ({HR}x v ¬{BI}x) -> {BE}x | [
"fact4 -> int1: ãã®ãŽã«ããŽã«Lv.48ãæºãŸãæããæ²ãããªããªãã°ãã®ãŽã«ããŽã«Lv.48ã¯èŠªã; int1 -> hypothesis;"
] | 2 | 1 | 1 | null | null | 3 | 0 | 3 | UNKNOWN | PROVED | UNKNOWN | PROVED | $facts$ = fact1: ãããã®ã¿ãªã¿ã¡ã
Lv.34ã人éèããªããšããããã®ã¿ãªã¿ã¡ã
Lv.34ã¯å«å³ã£ãœã fact2: ãããç»çãããšããã°å€åãæããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãæºãŸãæãããŸãã¯ããã¯æ²ãããªãããŸãã¯äž¡æ¹ã§ãããšãããããã¯èŠªã ; $hypothesis$ = ããåããèŸãã人éèããªãããããã¯äž¡æ¹ãšããªãã°å«å³ã£ãœããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{AB}{aa} -> {B}{aa} fact2: (Ex): {HL}x -> {BF}x fact3: (x): ({HR}x v ¬{BI}x) -> {BE}x ; $hypothesis$ = ¬((Ex): ({AA}x v ¬{AB}x) -> {B}x) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ã¡ã
Lv.52ã¯ã³ã³ãããŒã«ãæããªã | ¬{E}{c} | fact1: ããããã®ã¿ã¡ã
ã¿ãLv.72ãåãåºãæããªãã°ãã®ãŽã¡ããŽã«ãLv.87ã¯éèŠãã fact2: ãããšããã¢ã³ã¹ã¿ãŒãããã¡ãªããŠæŽã«éèŠãããšããããã®ã¿ãã¿ã¡ã
Lv.52ã¯ã³ã³ãããŒã«ãæã fact3: ãéèŠãããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ããã®ãŽã¡ããŽã«ãLv.87ã¯ããã¡ãªãããšããããšã¯çå®ã§ãã fact5: ãã®ã¿ã¡ã
ã¿ãLv.72ã¯ç¢ºãããã fact6: ããã¢ã³ã¹ã¿ãŒã¯ç¢ºãããã | fact1: {A}{a} -> {C}{b} fact2: (x): ({D}x & {C}x) -> {E}{c} fact3: (Ex): {C}x fact4: {D}{b} fact5: {B}{a} fact6: (Ex): {B}x | [] | [] | null | null | [] | null | 5 | 5 | null | null | 3 | 0 | 3 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããããã®ã¿ã¡ã
ã¿ãLv.72ãåãåºãæããªãã°ãã®ãŽã¡ããŽã«ãLv.87ã¯éèŠãã fact2: ãããšããã¢ã³ã¹ã¿ãŒãããã¡ãªããŠæŽã«éèŠãããšããããã®ã¿ãã¿ã¡ã
Lv.52ã¯ã³ã³ãããŒã«ãæã fact3: ãéèŠãããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ããã®ãŽã¡ããŽã«ãLv.87ã¯ããã¡ãªãããšããããšã¯çå®ã§ãã fact5: ãã®ã¿ã¡ã
ã¿ãLv.72ã¯ç¢ºãããã fact6: ããã¢ã³ã¹ã¿ãŒã¯ç¢ºãããã ; $hypothesis$ = ãã®ã¿ãã¿ã¡ã
Lv.52ã¯ã³ã³ãããŒã«ãæããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} -> {C}{b} fact2: (x): ({D}x & {C}x) -> {E}{c} fact3: (Ex): {C}x fact4: {D}{b} fact5: {B}{a} fact6: (Ex): {B}x ; $hypothesis$ = ¬{E}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã·ã«ãã·ãLv.22äºä»¶ãšã¿ãã¿ãªLv.21äºä»¶äž¡æ¹ãšããçããããšããããšã¯èª€ãã§ãã | ¬({A} & {B}) | fact1: ãã¿ãã¿ã¡ãLv.7äºä»¶ããã³ã¿ã¡ãã¿ãLv.25äºä»¶ã©ã¡ãããçããããšããããšã¯äºå®ãšç°ãªã fact2: ã¿ãã¿ãªLv.21äºä»¶ãçºçãã fact3: ãã¿ãã¿ã¡ãLv.7äºä»¶ã§ã¯ãªãã¿ã¡ãã¿ãLv.25äºä»¶ãçºçããããšããããšã¯äºå®ãšç°ãªã fact4: ãã¿ãã¿ã¡ãLv.7äºä»¶ãçºçããªããã©ã¿ã¡ãã¿ãLv.25äºä»¶ã¯çºçããããšããããšã¯ãã·ã«ãã·ãLv.22äºä»¶ã¯èµ·ããªãããšããããšãå¥æ©ã§ãã | fact1: ¬({AA} & {AB}) fact2: {B} fact3: ¬(¬{AA} & {AB}) fact4: ¬{A} -> (¬{AA} & {AB}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããã·ã«ãã·ãLv.22äºä»¶ã¯èµ·ããªã; fact4 & assump1 -> int1: ã¿ãã¿ã¡ãLv.7äºä»¶ã§ã¯ãªãã¿ã¡ãã¿ãLv.25äºä»¶ãèµ·ãã; int1 & fact3 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã·ã«ãã·ãLv.22äºä»¶ã¯çããªãããšããããšã¯åã ; int3 & fact2 -> hypothesis;"
] | [
"void -> assump1: ¬{A}; fact4 & assump1 -> int1: (¬{AA} & {AB}); int1 & fact3 -> int2: #F#; [assump1] & int2 -> int3: {A}; int3 & fact2 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã¿ãã¿ã¡ãLv.7äºä»¶ããã³ã¿ã¡ãã¿ãLv.25äºä»¶ã©ã¡ãããçããããšããããšã¯äºå®ãšç°ãªã fact2: ã¿ãã¿ãªLv.21äºä»¶ãçºçãã fact3: ãã¿ãã¿ã¡ãLv.7äºä»¶ã§ã¯ãªãã¿ã¡ãã¿ãLv.25äºä»¶ãçºçããããšããããšã¯äºå®ãšç°ãªã fact4: ãã¿ãã¿ã¡ãLv.7äºä»¶ãçºçããªããã©ã¿ã¡ãã¿ãLv.25äºä»¶ã¯çºçããããšããããšã¯ãã·ã«ãã·ãLv.22äºä»¶ã¯èµ·ããªãããšããããšãå¥æ©ã§ãã ; $hypothesis$ = ãã·ã«ãã·ãLv.22äºä»¶ãšã¿ãã¿ãªLv.21äºä»¶äž¡æ¹ãšããçããããšããããšã¯èª€ãã§ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããã·ã«ãã·ãLv.22äºä»¶ã¯èµ·ããªã; fact4 & assump1 -> int1: ã¿ãã¿ã¡ãLv.7äºä»¶ã§ã¯ãªãã¿ã¡ãã¿ãLv.25äºä»¶ãèµ·ãã; int1 & fact3 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã·ã«ãã·ãLv.22äºä»¶ã¯çããªãããšããããšã¯åã ; int3 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({AA} & {AB}) fact2: {B} fact3: ¬(¬{AA} & {AB}) fact4: ¬{A} -> (¬{AA} & {AB}) ; $hypothesis$ = ¬({A} & {B}) ; $proof$ = | void -> assump1: ¬{A}; fact4 & assump1 -> int1: (¬{AA} & {AB}); int1 & fact3 -> int2: #F#; [assump1] & int2 -> int3: {A}; int3 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãã¡ããã®Lv.11ã¯éãé£ããšããããšã¯ãªã | ¬{A}{a} | fact1: ãã®ãœããœãLv.32ã¯éãé£ã fact2: ãªãããã®ã¢ã³ã¹ã¿ãŒãä»°è¥ããªããšãããããã¯æå³ãããªãããããã¯éãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã§ãã | fact1: {A}{fo} fact2: (x): ¬{B}x -> (¬{C}x v ¬{A}x) | [] | [] | ãã®ãã¡ããã®Lv.11ã¯éãé£ããšããããšã¯ãªã | ¬{A}{a} | [
"fact3 -> int1: ãããã®ãŸããŸã¡ãLv.77ãä»°è¥ãããšããããšã¯ãªããšããããã®ãŸããŸã¡ãLv.77ã¯æå³ãããªãããããã¯éãé£ããšããããšã¯ãªããäž¡æ¹ã§ãã;"
] | 5 | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãœããœãLv.32ã¯éãé£ã fact2: ãªãããã®ã¢ã³ã¹ã¿ãŒãä»°è¥ããªããšãããããã¯æå³ãããªãããããã¯éãé£ããšããããšã¯ãªãããããã¯ã©ã¡ããã§ãã ; $hypothesis$ = ãã®ãã¡ããã®Lv.11ã¯éãé£ããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{fo} fact2: (x): ¬{B}x -> (¬{C}x v ¬{A}x) ; $hypothesis$ = ¬{A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãœãªãœãLv.37ã¯èã | {C}{b} | fact1: ãçéãé£ããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãèããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ããä»®ã«çéãé£ãã¢ã³ã¹ã¿ãŒãããªã¢ããªãŒåãããšãããšãã®ãœãªãœãLv.37ã¯èããªã fact4: èãããã®äžçéãé£ãã¢ã³ã¹ã¿ãŒã¯ãã fact5: ãã®ã·ã«ãã·ãLv.42ã¯çéãé£ã fact6: ãã®ã·ã«ãã·ãLv.42ã¯ããªã¢ããªãŒåãããæŽã«ãŸã©ãã£ããã fact7: ããããã®ã·ã«ãã·ãLv.42ã¯ããªã¢ããªãŒåãããããããŸã©ãã£ãããããªããšãããšãã®ãœãªãœãLv.37ã¯ãŸã©ãã£ãããããªã | fact1: (Ex): {A}x fact2: (Ex): {C}x fact3: (x): ({A}x & {B}x) -> ¬{C}{b} fact4: (Ex): ({C}x & {A}x) fact5: {A}{a} fact6: ({B}{a} & {D}{a}) fact7: ({B}{a} & ¬{D}{a}) -> ¬{D}{b} | [
"fact6 -> int1: ãã®ã·ã«ãã·ãLv.42ã¯ããªã¢ããªãŒåãã; fact5 & int1 -> int2: ãã®ã·ã«ãã·ãLv.42ã¯çéãé£ããŠããªã¢ããªãŒåãã; int2 -> int3: çéãé£ãã¢ã³ã¹ã¿ãŒã§ãã£ãŠããªã¢ããªãŒåããã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact3 -> hypothesis;"
] | [
"fact6 -> int1: {B}{a}; fact5 & int1 -> int2: ({A}{a} & {B}{a}); int2 -> int3: (Ex): ({A}x & {B}x); int3 & fact3 -> hypothesis;"
] | ããã®ãœãªãœãLv.37ã¯ãŸã©ãã£ãããããªãããšããããšã¯èª€ãã§ãããšããããšã¯ãªã | ¬{D}{b} | [] | 5 | 4 | 4 | 4 | 4 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãçéãé£ããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãèããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ããä»®ã«çéãé£ãã¢ã³ã¹ã¿ãŒãããªã¢ããªãŒåãããšãããšãã®ãœãªãœãLv.37ã¯èããªã fact4: èãããã®äžçéãé£ãã¢ã³ã¹ã¿ãŒã¯ãã fact5: ãã®ã·ã«ãã·ãLv.42ã¯çéãé£ã fact6: ãã®ã·ã«ãã·ãLv.42ã¯ããªã¢ããªãŒåãããæŽã«ãŸã©ãã£ããã fact7: ããããã®ã·ã«ãã·ãLv.42ã¯ããªã¢ããªãŒåãããããããŸã©ãã£ãããããªããšãããšãã®ãœãªãœãLv.37ã¯ãŸã©ãã£ãããããªã ; $hypothesis$ = ãã®ãœãªãœãLv.37ã¯èã ; $proof$ = | fact6 -> int1: ãã®ã·ã«ãã·ãLv.42ã¯ããªã¢ããªãŒåãã; fact5 & int1 -> int2: ãã®ã·ã«ãã·ãLv.42ã¯çéãé£ããŠããªã¢ããªãŒåãã; int2 -> int3: çéãé£ãã¢ã³ã¹ã¿ãŒã§ãã£ãŠããªã¢ããªãŒåããã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (Ex): {A}x fact2: (Ex): {C}x fact3: (x): ({A}x & {B}x) -> ¬{C}{b} fact4: (Ex): ({C}x & {A}x) fact5: {A}{a} fact6: ({B}{a} & {D}{a}) fact7: ({B}{a} & ¬{D}{a}) -> ¬{D}{b} ; $hypothesis$ = {C}{b} ; $proof$ = | fact6 -> int1: {B}{a}; fact5 & int1 -> int2: ({A}{a} & {B}{a}); int2 -> int3: (Ex): ({A}x & {B}x); int3 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãŽã«ã
ãŽãªLv.50äºä»¶ã¯çºçããªã | ¬{C} | fact1: ä»®ã«ã埡èŸããšããããšããã³æ§ç¯ãããšäž¡æ¹ãšããèµ·ããããšããããšã¯åã ãšããã°ãœããœã¡ã
Lv.68äºä»¶ã¯çºçããªã fact2: ãããçãããŸãããšããããšãçãããå°æ±ããšããããšã¯çããªããªãçå
ããããšã¯çããªã fact3: ãæšããšããããšãšãœããœã¡ãLv.8äºä»¶äž¡æ¹ãšããèµ·ããããšããããšã¯ééããªããŸããŸã®Lv.72äºä»¶ã¯èµ·ããªã fact4: èŠé£ããšããããšãèµ·ãã fact5: ãŸããŸã®Lv.72äºä»¶ã¯èµ·ããªããšãããçãããŸãããšããããšãèµ·ããããããå°æ±ããšããããšã¯èµ·ãããªã fact6: ããä»®ã«ãœããœã¡ã
Lv.68äºä»¶ã¯èµ·ãããªããšããã°ãæšããšããããšãèµ·ãããå ããŠãœããœã¡ãLv.8äºä»¶ãçºçããããšããããšã¯åœã§ãã fact7: ããèŠé£ããšããããšããããã¯çå
ããããšãçãããšãããããŽã«ã
ãŽãªLv.50äºä»¶ã¯çããªãããšããããšã¯ç¢ºãã | fact1: ¬({K} & {J}) -> ¬{I} fact2: ({E} & ¬{D}) -> ¬{B} fact3: ¬({H} & {G}) -> ¬{F} fact4: {A} fact5: ¬{F} -> ({E} & ¬{D}) fact6: ¬{I} -> ¬({H} & {G}) fact7: ({A} v {B}) -> ¬{C} | [
"fact4 -> int1: èŠé£ããšããããšããããã¯çå
ããããšãçºçãã; int1 & fact7 -> hypothesis;"
] | [
"fact4 -> int1: ({A} v {B}); int1 & fact7 -> hypothesis;"
] | ãŽã«ã
ãŽãªLv.50äºä»¶ãçºçãã | {C} | [] | 10 | 2 | 2 | 2 | 2 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ã埡èŸããšããããšããã³æ§ç¯ãããšäž¡æ¹ãšããèµ·ããããšããããšã¯åã ãšããã°ãœããœã¡ã
Lv.68äºä»¶ã¯çºçããªã fact2: ãããçãããŸãããšããããšãçãããå°æ±ããšããããšã¯çããªããªãçå
ããããšã¯çããªã fact3: ãæšããšããããšãšãœããœã¡ãLv.8äºä»¶äž¡æ¹ãšããèµ·ããããšããããšã¯ééããªããŸããŸã®Lv.72äºä»¶ã¯èµ·ããªã fact4: èŠé£ããšããããšãèµ·ãã fact5: ãŸããŸã®Lv.72äºä»¶ã¯èµ·ããªããšãããçãããŸãããšããããšãèµ·ããããããå°æ±ããšããããšã¯èµ·ãããªã fact6: ããä»®ã«ãœããœã¡ã
Lv.68äºä»¶ã¯èµ·ãããªããšããã°ãæšããšããããšãèµ·ãããå ããŠãœããœã¡ãLv.8äºä»¶ãçºçããããšããããšã¯åœã§ãã fact7: ããèŠé£ããšããããšããããã¯çå
ããããšãçãããšãããããŽã«ã
ãŽãªLv.50äºä»¶ã¯çããªãããšããããšã¯ç¢ºãã ; $hypothesis$ = ãŽã«ã
ãŽãªLv.50äºä»¶ã¯çºçããªã ; $proof$ = | fact4 -> int1: èŠé£ããšããããšããããã¯çå
ããããšãçºçãã; int1 & fact7 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({K} & {J}) -> ¬{I} fact2: ({E} & ¬{D}) -> ¬{B} fact3: ¬({H} & {G}) -> ¬{F} fact4: {A} fact5: ¬{F} -> ({E} & ¬{D}) fact6: ¬{I} -> ¬({H} & {G}) fact7: ({A} v {B}) -> ¬{C} ; $hypothesis$ = ¬{C} ; $proof$ = | fact4 -> int1: ({A} v {B}); int1 & fact7 -> hypothesis; __PROVED__ |
0.3 | ãããããéŠãããªããªã絶ãéç¡ããªããŠçããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã | ¬((Ex): ¬{A}x -> (¬{AA}x & ¬{AB}x)) | fact1: ããããã®ã·ãã·ã«Lv.49ãéŠãããªããªããã®ã·ãã·ã«Lv.49ã¯çµ¶ãéç¡ããã©çããªãããšããããšã¯äºå®ã fact2: ããããä»®ã«ãéŠãããªãããšããããšã¯æãç«ã€ãšããã°çµ¶ãéç¡ããªããŠãããçããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯çå®ã | fact1: ¬{A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) fact2: (Ex): ¬{A}x -> (¬{AA}x & {AB}x) | [] | [] | null | null | [] | null | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããããã®ã·ãã·ã«Lv.49ãéŠãããªããªããã®ã·ãã·ã«Lv.49ã¯çµ¶ãéç¡ããã©çããªãããšããããšã¯äºå®ã fact2: ããããä»®ã«ãéŠãããªãããšããããšã¯æãç«ã€ãšããã°çµ¶ãéç¡ããªããŠãããçããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯çå®ã ; $hypothesis$ = ãããããéŠãããªããªã絶ãéç¡ããªããŠçããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) fact2: (Ex): ¬{A}x -> (¬{AA}x & {AB}x) ; $hypothesis$ = ¬((Ex): ¬{A}x -> (¬{AA}x & ¬{AB}x)) ; $proof$ = | __UNKNOWN__ |
0.3 | å·çããããšãçºçãã | {B} | fact1: ãŽã«ããŽãLv.43äºä»¶ã¯èµ·ããªããšããããšã¯ãœã«ã
ãœãLv.95äºä»¶ã«é»æ¢ããã fact2: èŠãããšããããšãèµ·ãã fact3: åãæããšããããšã¯çŽ°ãããšããããšã¯èµ·ããªããšããããšãé»æ¢ãã fact4: å·çããããšã¯èŠãããšããããšã«ããçãã fact5: ãã¡ããã«Lv.98äºä»¶ãèµ·ãã fact6: å°é£ãããšããããšãèµ·ãã fact7: åã¡æããšããããšãçºçãã | fact1: {EM} -> {GH} fact2: {A} fact3: {AJ} -> {EU} fact4: {A} -> {B} fact5: {P} fact6: {GE} fact7: {FC} | [
"fact2 -> int1: èŠãããšããããšãèµ·ãã; int1 & fact4 -> hypothesis;"
] | [
"fact2 -> int1: {A}; int1 & fact4 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 5 | 0 | 5 | PROVED | null | PROVED | null | $facts$ = fact1: ãŽã«ããŽãLv.43äºä»¶ã¯èµ·ããªããšããããšã¯ãœã«ã
ãœãLv.95äºä»¶ã«é»æ¢ããã fact2: èŠãããšããããšãèµ·ãã fact3: åãæããšããããšã¯çŽ°ãããšããããšã¯èµ·ããªããšããããšãé»æ¢ãã fact4: å·çããããšã¯èŠãããšããããšã«ããçãã fact5: ãã¡ããã«Lv.98äºä»¶ãèµ·ãã fact6: å°é£ãããšããããšãèµ·ãã fact7: åã¡æããšããããšãçºçãã ; $hypothesis$ = å·çããããšãçºçãã ; $proof$ = | fact2 -> int1: èŠãããšããããšãèµ·ãã; int1 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {EM} -> {GH} fact2: {A} fact3: {AJ} -> {EU} fact4: {A} -> {B} fact5: {P} fact6: {GE} fact7: {FC} ; $hypothesis$ = {B} ; $proof$ = | fact2 -> int1: {A}; int1 & fact4 -> hypothesis; __PROVED__ |
0.3 | ããã®ããããLv.10ã¯ãã£ããªããªãäžæ¹ã§èæãããšããããšã¯åã | ¬(¬{E}{c} & {C}{c}) | fact1: ããä»®ã«ãã®ããããLv.18ãã³ã³ãã€ã«åºæ¥ãã°ãã®ããããLv.18ã¯ä¹ãæã fact2: ãã®ããããLv.18ã¯ã³ã³ãã€ã«åºæ¥ã fact3: ãããããã®ããããLv.18ãä¹ãæããããŸãã«ç«ã¡å
¥ããªããã®ãœããœãLv.81ã¯èæããšããããšã¯ãªãããšããããšã¯ç¢ºãã fact4: ãã®ãœããœã¡ãLv.99ã¯ç«ã¡å
¥ã fact5: ããã®ããããLv.18ã¯ç«ã¡å
¥ãããšããããšã¯ééãã§ãªã | fact1: {D}{a} -> {A}{a} fact2: {D}{a} fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: {B}{io} fact5: {B}{a} | [
"fact2 & fact1 -> int1: ããã®ããããLv.18ã¯ä¹ãæãããšããããšã¯æ¬åœã ; int1 & fact5 -> int2: ãã®ããããLv.18ã¯ä¹ãæããç«ã¡å
¥ã; int2 & fact3 -> int3: ãã®ãœããœãLv.81ã¯èæããªã;"
] | [
"fact2 & fact1 -> int1: {A}{a}; int1 & fact5 -> int2: ({A}{a} & {B}{a}); int2 & fact3 -> int3: ¬{C}{b};"
] | null | null | [] | null | 4 | 4 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããä»®ã«ãã®ããããLv.18ãã³ã³ãã€ã«åºæ¥ãã°ãã®ããããLv.18ã¯ä¹ãæã fact2: ãã®ããããLv.18ã¯ã³ã³ãã€ã«åºæ¥ã fact3: ãããããã®ããããLv.18ãä¹ãæããããŸãã«ç«ã¡å
¥ããªããã®ãœããœãLv.81ã¯èæããšããããšã¯ãªãããšããããšã¯ç¢ºãã fact4: ãã®ãœããœã¡ãLv.99ã¯ç«ã¡å
¥ã fact5: ããã®ããããLv.18ã¯ç«ã¡å
¥ãããšããããšã¯ééãã§ãªã ; $hypothesis$ = ããã®ããããLv.10ã¯ãã£ããªããªãäžæ¹ã§èæãããšããããšã¯åã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {D}{a} -> {A}{a} fact2: {D}{a} fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: {B}{io} fact5: {B}{a} ; $hypothesis$ = ¬(¬{E}{c} & {C}{c}) ; $proof$ = | __UNKNOWN__ |
0.3 | èãæããšããããšã¯çããªã | ¬{D} | fact1: ããããLv.12äºä»¶ã¯ãŸããŸã«ãLv.75äºä»¶ã®ãã£ãããšãªã fact2: ããŸããŸã«ãLv.75äºä»¶ã¯çºçããªãããšããããšã¯ã¿ãã¿ã«Lv.9äºä»¶ãçãããšããããšã«é»ãŸãã fact3: ããããLv.12äºä»¶ããããã¯ã¿ãã¿ã«Lv.9äºä»¶ãçãã fact4: èãæããšããããšã¯èµ·ãããªããšããããšã¯ãŸããŸã«ãLv.75äºä»¶ã«é²ããã | fact1: {A} -> {C} fact2: {B} -> {C} fact3: ({A} v {B}) fact4: {C} -> {D} | [
"fact3 & fact1 & fact2 -> int1: ãŸããŸã«ãLv.75äºä»¶ãèµ·ãã; int1 & fact4 -> hypothesis;"
] | [
"fact3 & fact1 & fact2 -> int1: {C}; int1 & fact4 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããããLv.12äºä»¶ã¯ãŸããŸã«ãLv.75äºä»¶ã®ãã£ãããšãªã fact2: ããŸããŸã«ãLv.75äºä»¶ã¯çºçããªãããšããããšã¯ã¿ãã¿ã«Lv.9äºä»¶ãçãããšããããšã«é»ãŸãã fact3: ããããLv.12äºä»¶ããããã¯ã¿ãã¿ã«Lv.9äºä»¶ãçãã fact4: èãæããšããããšã¯èµ·ãããªããšããããšã¯ãŸããŸã«ãLv.75äºä»¶ã«é²ããã ; $hypothesis$ = èãæããšããããšã¯çããªã ; $proof$ = | fact3 & fact1 & fact2 -> int1: ãŸããŸã«ãLv.75äºä»¶ãèµ·ãã; int1 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} -> {C} fact2: {B} -> {C} fact3: ({A} v {B}) fact4: {C} -> {D} ; $hypothesis$ = ¬{D} ; $proof$ = | fact3 & fact1 & fact2 -> int1: {C}; int1 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | é
ãæããšããããšã¯çºçããªãããã©ãŸã¡ããŸãLv.87äºä»¶ãèµ·ãã | (¬{E} & {F}) | fact1: ãã¡ã
ããLv.32äºä»¶ããã³ãœããœãLv.15äºä»¶ã©ã¡ãããçãã fact2: ãŸã¡ããŸãLv.87äºä»¶ãèµ·ãã fact3: ã·ãã·ãLv.49äºä»¶ãšè²å¥œããšããããšã©ã¡ãããèµ·ãã fact4: ãŸã«ã
ãŸãLv.45äºä»¶ã¯èµ·ããªããšããããšã¯ãã¡ã
ããLv.32äºä»¶ã«é»æ¢ããã fact5: ãŸã«ã
ãŸãLv.45äºä»¶ãšéãé£ããšããããšãçããã¯ãé
ãæããšããããšãèµ·ããããšããããšãåé¿ãã fact6: éãé£ããšããããšãçºçãã fact7: ãœããœãLv.15äºä»¶ãèµ·ãã | fact1: ({A} & {B}) fact2: {F} fact3: ({IG} & {FS}) fact4: {A} -> {C} fact5: ({C} & {D}) -> ¬{E} fact6: {D} fact7: {B} | [
"fact1 -> int1: ãã¡ã
ããLv.32äºä»¶ãèµ·ãã; int1 & fact4 -> int2: ãŸã«ã
ãŸãLv.45äºä»¶ãèµ·ãã; int2 & fact6 -> int3: ãŸã«ã
ãŸãLv.45äºä»¶ãçãããããã«éãé£ããšããããšãèµ·ãã; int3 & fact5 -> int4: é
ãæããšããããšã¯èµ·ããªã; int4 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: {A}; int1 & fact4 -> int2: {C}; int2 & fact6 -> int3: ({C} & {D}); int3 & fact5 -> int4: ¬{E}; int4 & fact2 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãã¡ã
ããLv.32äºä»¶ããã³ãœããœãLv.15äºä»¶ã©ã¡ãããçãã fact2: ãŸã¡ããŸãLv.87äºä»¶ãèµ·ãã fact3: ã·ãã·ãLv.49äºä»¶ãšè²å¥œããšããããšã©ã¡ãããèµ·ãã fact4: ãŸã«ã
ãŸãLv.45äºä»¶ã¯èµ·ããªããšããããšã¯ãã¡ã
ããLv.32äºä»¶ã«é»æ¢ããã fact5: ãŸã«ã
ãŸãLv.45äºä»¶ãšéãé£ããšããããšãçããã¯ãé
ãæããšããããšãèµ·ããããšããããšãåé¿ãã fact6: éãé£ããšããããšãçºçãã fact7: ãœããœãLv.15äºä»¶ãèµ·ãã ; $hypothesis$ = é
ãæããšããããšã¯çºçããªãããã©ãŸã¡ããŸãLv.87äºä»¶ãèµ·ãã ; $proof$ = | fact1 -> int1: ãã¡ã
ããLv.32äºä»¶ãèµ·ãã; int1 & fact4 -> int2: ãŸã«ã
ãŸãLv.45äºä»¶ãèµ·ãã; int2 & fact6 -> int3: ãŸã«ã
ãŸãLv.45äºä»¶ãçãããããã«éãé£ããšããããšãèµ·ãã; int3 & fact5 -> int4: é
ãæããšããããšã¯èµ·ããªã; int4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} & {B}) fact2: {F} fact3: ({IG} & {FS}) fact4: {A} -> {C} fact5: ({C} & {D}) -> ¬{E} fact6: {D} fact7: {B} ; $hypothesis$ = (¬{E} & {F}) ; $proof$ = | fact1 -> int1: {A}; int1 & fact4 -> int2: {C}; int2 & fact6 -> int3: ({C} & {D}); int3 & fact5 -> int4: ¬{E}; int4 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ã®ã·ãªLv.37ã¯å¹Œã | {C}{b} | fact1: ä»®ã«ãã®ãŽã®ãŽãLv.92ã幌ããšãããšãã®ã·ã®ã·ãªLv.37ã¯è»¢èœãã fact2: ããããã®ãŽã®ãŽãLv.92ãããŒã¹ããããšããã°ãã®ã·ã®ã·ãªLv.37ã¯å¹Œã fact3: ãã®ãŽã®ãŽãLv.92ã¯ããŒã¹ãããã転èœãã fact4: ãšããã¢ã³ã¹ã¿ãŒã幌ããªããªãã°ããŒã¹ãããããã€ããã¯è»¢èœãã fact5: ãã®ãŽã®ãŽãLv.92ã¯è»¢èœãã | fact1: {C}{a} -> {B}{b} fact2: {A}{a} -> {C}{b} fact3: ({A}{a} & {B}{a}) fact4: (x): ¬{C}x -> ({A}x & {B}x) fact5: {B}{a} | [
"fact3 -> int1: ãã®ãŽã®ãŽãLv.92ã¯ããŒã¹ããã; int1 & fact2 -> hypothesis;"
] | [
"fact3 -> int1: {A}{a}; int1 & fact2 -> hypothesis;"
] | ãã®ãã«ãããLv.30ã¯ããŒã¹ããã | {A}{bn} | [
"fact6 -> int2: ä»®ã«ãã®ãã«ãããLv.30ã幌ããªããšãããšããã¯ããŒã¹ãããã転èœãã;"
] | 5 | 2 | 2 | 2 | 2 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãŽã®ãŽãLv.92ã幌ããšãããšãã®ã·ã®ã·ãªLv.37ã¯è»¢èœãã fact2: ããããã®ãŽã®ãŽãLv.92ãããŒã¹ããããšããã°ãã®ã·ã®ã·ãªLv.37ã¯å¹Œã fact3: ãã®ãŽã®ãŽãLv.92ã¯ããŒã¹ãããã転èœãã fact4: ãšããã¢ã³ã¹ã¿ãŒã幌ããªããªãã°ããŒã¹ãããããã€ããã¯è»¢èœãã fact5: ãã®ãŽã®ãŽãLv.92ã¯è»¢èœãã ; $hypothesis$ = ãã®ã·ã®ã·ãªLv.37ã¯å¹Œã ; $proof$ = | fact3 -> int1: ãã®ãŽã®ãŽãLv.92ã¯ããŒã¹ããã; int1 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{a} -> {B}{b} fact2: {A}{a} -> {C}{b} fact3: ({A}{a} & {B}{a}) fact4: (x): ¬{C}x -> ({A}x & {B}x) fact5: {B}{a} ; $hypothesis$ = {C}{b} ; $proof$ = | fact3 -> int1: {A}{a}; int1 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãŸã¡ã
ãŸã«ãLv.80äºä»¶ã¯èµ·ãããªã | ¬{E} | fact1: ç²ãæããšããããšããã³ã¿ãã¿ãLv.85äºä»¶ãèµ·ããã¯ãŸã¡ã
ãŸã«ãLv.80äºä»¶ã¯èµ·ãããªããšããããšã«åž°çµãã fact2: ãããããLv.31äºä»¶ã¯çºçããªãããšããããšã¯ãŸããŸã«ãLv.9äºä»¶ã«é»æ¢ããã fact3: ã¿ãã¿ã«ã
Lv.36äºä»¶ãèµ·ãã fact4: ã·ãã·ã¡ãLv.81äºä»¶ãçºçãã fact5: ãã«ã
ããLv.3äºä»¶ã¯çºçããªã fact6: çŸã
ãããšããããšãšããããLv.12äºä»¶ãèµ·ãã fact7: ãœã®ãœã«ã
Lv.44äºä»¶ã¯ãç²ãæããšããããšã¯èµ·ãããªãããšããããšãé²ã fact8: ãœã«ã
ãœã«ãLv.11äºä»¶ãšãœã®ãœã«ã
Lv.44äºä»¶äž¡æ¹ãšããçºçãã | fact1: ({C} & {D}) -> ¬{E} fact2: {DO} -> {FP} fact3: {DK} fact4: {DT} fact5: ¬{L} fact6: ({IH} & {BM}) fact7: {B} -> {C} fact8: ({A} & {B}) | [
"fact8 -> int1: ãœã®ãœã«ã
Lv.44äºä»¶ãèµ·ãã; int1 & fact7 -> int2: ç²ãæããšããããšãèµ·ãã;"
] | [
"fact8 -> int1: {B}; int1 & fact7 -> int2: {C};"
] | null | null | [] | null | 4 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ç²ãæããšããããšããã³ã¿ãã¿ãLv.85äºä»¶ãèµ·ããã¯ãŸã¡ã
ãŸã«ãLv.80äºä»¶ã¯èµ·ãããªããšããããšã«åž°çµãã fact2: ãããããLv.31äºä»¶ã¯çºçããªãããšããããšã¯ãŸããŸã«ãLv.9äºä»¶ã«é»æ¢ããã fact3: ã¿ãã¿ã«ã
Lv.36äºä»¶ãèµ·ãã fact4: ã·ãã·ã¡ãLv.81äºä»¶ãçºçãã fact5: ãã«ã
ããLv.3äºä»¶ã¯çºçããªã fact6: çŸã
ãããšããããšãšããããLv.12äºä»¶ãèµ·ãã fact7: ãœã®ãœã«ã
Lv.44äºä»¶ã¯ãç²ãæããšããããšã¯èµ·ãããªãããšããããšãé²ã fact8: ãœã«ã
ãœã«ãLv.11äºä»¶ãšãœã®ãœã«ã
Lv.44äºä»¶äž¡æ¹ãšããçºçãã ; $hypothesis$ = ãŸã¡ã
ãŸã«ãLv.80äºä»¶ã¯èµ·ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({C} & {D}) -> ¬{E} fact2: {DO} -> {FP} fact3: {DK} fact4: {DT} fact5: ¬{L} fact6: ({IH} & {BM}) fact7: {B} -> {C} fact8: ({A} & {B}) ; $hypothesis$ = ¬{E} ; $proof$ = | __UNKNOWN__ |
0.3 | çãåãããšãèµ·ããããããã«ãLv.44äºä»¶ãèµ·ãã | ({B} v {C}) | fact1: ã·ãã·ã«ãLv.4äºä»¶ããã³çãåãããšãçãã fact2: ãããã·ãã·ã«ãLv.4äºä»¶ã¯çºçããªããšããããçãåãããšããããã¯ãããã«ãLv.44äºä»¶ãã©ã¡ãããçããããšããããšã¯ééã£ãŠãã | fact1: ({A} & {B}) fact2: ¬{A} -> ¬({B} v {C}) | [
"fact1 -> int1: çãåãããšãèµ·ãã; int1 -> hypothesis;"
] | [
"fact1 -> int1: {B}; int1 -> hypothesis;"
] | ãçãåãããšãèµ·ããããããã¯ãããã«ãLv.44äºä»¶ãçããããŸãã¯ã©ã¡ããã§ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({B} v {C}) | [] | 6 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ã·ãã·ã«ãLv.4äºä»¶ããã³çãåãããšãçãã fact2: ãããã·ãã·ã«ãLv.4äºä»¶ã¯çºçããªããšããããçãåãããšããããã¯ãããã«ãLv.44äºä»¶ãã©ã¡ãããçããããšããããšã¯ééã£ãŠãã ; $hypothesis$ = çãåãããšãèµ·ããããããã«ãLv.44äºä»¶ãèµ·ãã ; $proof$ = | fact1 -> int1: çãåãããšãèµ·ãã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} & {B}) fact2: ¬{A} -> ¬({B} v {C}) ; $hypothesis$ = ({B} v {C}) ; $proof$ = | fact1 -> int1: {B}; int1 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœããœã«ãLv.34ã¯æšããã | {A}{a} | fact1: ä»®ã«ããã®ãœããœã«ãLv.34ã¯èãããªããã©æ©ãæãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšããã°ãã®ãœããœã«ãLv.34ã¯æšããããªã fact2: ãã®ã·ã¡ãã·ã¡ãLv.2ã¯ããã fact3: ä»®ã«ããã®ãœããœã«ãLv.34ã¯åããäžæ¹ã§ããã¯ããããªãããšããããšã¯ééãã ãšããããã®ãœã¡ã
ãœã¡ã
Lv.33ã¯æšããããªã fact4: ãã®ãœããœã«ãLv.34ã¯èãããªãããããæ©ãæããšãããšãã®ã·ã¡ãã·ã¡ãLv.2ã¯ããããªã | fact1: ¬(¬{AA}{a} & {AB}{a}) -> ¬{A}{a} fact2: {B}{b} fact3: ¬({C}{a} & ¬{B}{a}) -> ¬{A}{gd} fact4: (¬{AA}{a} & {AB}{a}) -> ¬{B}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœã«ãLv.34ã¯èãããªãäžæ¹ã§æ©ãæã; fact4 & assump1 -> int1: ãã®ã·ã¡ãã·ã¡ãLv.2ã¯ããããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ããã®ãœããœã«ãLv.34ã¯èãããšããããšã¯ãªããã©ããã¯æ©ãæãããšããããšã¯äºå®ã§ãªã; int3 & fact1 -> hypothesis;"
] | [
"void -> assump1: (¬{AA}{a} & {AB}{a}); fact4 & assump1 -> int1: ¬{B}{b}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{AA}{a} & {AB}{a}); int3 & fact1 -> hypothesis;"
] | ãã®ãœã¡ã
ãœã¡ã
Lv.33ã¯æšããããªã | ¬{A}{gd} | [] | 6 | 5 | 4 | 5 | 4 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ããã®ãœããœã«ãLv.34ã¯èãããªããã©æ©ãæãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšããã°ãã®ãœããœã«ãLv.34ã¯æšããããªã fact2: ãã®ã·ã¡ãã·ã¡ãLv.2ã¯ããã fact3: ä»®ã«ããã®ãœããœã«ãLv.34ã¯åããäžæ¹ã§ããã¯ããããªãããšããããšã¯ééãã ãšããããã®ãœã¡ã
ãœã¡ã
Lv.33ã¯æšããããªã fact4: ãã®ãœããœã«ãLv.34ã¯èãããªãããããæ©ãæããšãããšãã®ã·ã¡ãã·ã¡ãLv.2ã¯ããããªã ; $hypothesis$ = ãã®ãœããœã«ãLv.34ã¯æšããã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœã«ãLv.34ã¯èãããªãäžæ¹ã§æ©ãæã; fact4 & assump1 -> int1: ãã®ã·ã¡ãã·ã¡ãLv.2ã¯ããããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ããã®ãœããœã«ãLv.34ã¯èãããšããããšã¯ãªããã©ããã¯æ©ãæãããšããããšã¯äºå®ã§ãªã; int3 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬(¬{AA}{a} & {AB}{a}) -> ¬{A}{a} fact2: {B}{b} fact3: ¬({C}{a} & ¬{B}{a}) -> ¬{A}{gd} fact4: (¬{AA}{a} & {AB}{a}) -> ¬{B}{b} ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: (¬{AA}{a} & {AB}{a}); fact4 & assump1 -> int1: ¬{B}{b}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{AA}{a} & {AB}{a}); int3 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãœããœãLv.23ã¯çãæããŠæŽã«ããã¯æç»ããããšããããšã¯äºå®ã§ãªã | ¬({D}{aa} & {C}{aa}) | fact1: ããã®ãœããœãLv.23ã¯ç¡ããªããéªéèããªãããšããããšã¯åã fact2: ãã®ãœãªãœãLv.73ã¯éªéèã fact3: ããããã®ãœããœãLv.23ã¯ç· ãã£ãœãããšããããšã¯äºå®ã§ãããªãæç»ãã fact4: ãã®ãœããœãLv.23ã¯çãæã fact5: ä»®ã«ããã®ãœããœãLv.23ã¯å±±æ·±ãããšããããšã¯äºå®ãªããã®ãœããœãLv.23ã¯ç· ãã£ãœã fact6: ããã®ã¿ã®ã¿ãªLv.83ã¯å±±æ·±ããªãäžæ¹ã§æç»ããããšããããšã¯åœã§ãããšããããã®ãŽã¡ããŽãLv.20ã¯æç»ããªã fact7: ããããã®ãŽã¡ããŽãLv.20ãèãåãé£ããšãããšãã®ã¿ãã¿ã«ã
Lv.0ã¯èãåãé£ã | fact1: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact2: {AB}{fb} fact3: {A}{aa} -> {C}{aa} fact4: {D}{aa} fact5: {B}{aa} -> {A}{aa} fact6: ¬(¬{B}{b} & {C}{b}) -> ¬{C}{a} fact7: {GH}{a} -> {GH}{di} | [] | [] | ãã®ã¿ãã¿ã«ã
Lv.0ã¯é
ãæããŠèãåãé£ã | ({BK}{di} & {GH}{di}) | [] | 4 | 5 | 5 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã®ãœããœãLv.23ã¯ç¡ããªããéªéèããªãããšããããšã¯åã fact2: ãã®ãœãªãœãLv.73ã¯éªéèã fact3: ããããã®ãœããœãLv.23ã¯ç· ãã£ãœãããšããããšã¯äºå®ã§ãããªãæç»ãã fact4: ãã®ãœããœãLv.23ã¯çãæã fact5: ä»®ã«ããã®ãœããœãLv.23ã¯å±±æ·±ãããšããããšã¯äºå®ãªããã®ãœããœãLv.23ã¯ç· ãã£ãœã fact6: ããã®ã¿ã®ã¿ãªLv.83ã¯å±±æ·±ããªãäžæ¹ã§æç»ããããšããããšã¯åœã§ãããšããããã®ãŽã¡ããŽãLv.20ã¯æç»ããªã fact7: ããããã®ãŽã¡ããŽãLv.20ãèãåãé£ããšãããšãã®ã¿ãã¿ã«ã
Lv.0ã¯èãåãé£ã ; $hypothesis$ = ããã®ãœããœãLv.23ã¯çãæããŠæŽã«ããã¯æç»ããããšããããšã¯äºå®ã§ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact2: {AB}{fb} fact3: {A}{aa} -> {C}{aa} fact4: {D}{aa} fact5: {B}{aa} -> {A}{aa} fact6: ¬(¬{B}{b} & {C}{b}) -> ¬{C}{a} fact7: {GH}{a} -> {GH}{di} ; $hypothesis$ = ¬({D}{aa} & {C}{aa}) ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ãããè²·ãæããšããããšãèµ·ãã | {B} | fact1: åãç¶ããããšãèµ·ãã fact2: ãããšããããšãšãœãªãœãLv.75äºä»¶ãèµ·ãã fact3: ããåãç¶ããããšããã³è²·ãæããšããããšãèµ·ãããªãå¿ç¡ããšããããšã¯èµ·ãããªã fact4: ä»®ã«çããããšãçºçãããšããããåãç¶ããããšãèµ·ããããã©å¿ç¡ããšããããšã¯çããªãããšããããšã¯ééã£ãŠãã fact5: å¿ç¡ããšããããšãçºçãã | fact1: {A} fact2: ({GJ} & {BI}) fact3: ({A} & {B}) -> ¬{C} fact4: {D} -> ¬({A} & ¬{C}) fact5: {C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããè²·ãæããšããããšãèµ·ãã; fact1 & assump1 -> int1: åãç¶ããããšãçºçãããããŸãã«è²·ãæããšããããšãçãã; int1 & fact3 -> int2: å¿ç¡ããšããããšã¯çããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; fact1 & assump1 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ãããè²·ãæããšããããšãèµ·ãã | {B} | [] | 6 | 5 | 4 | 5 | 4 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: åãç¶ããããšãèµ·ãã fact2: ãããšããããšãšãœãªãœãLv.75äºä»¶ãèµ·ãã fact3: ããåãç¶ããããšããã³è²·ãæããšããããšãèµ·ãããªãå¿ç¡ããšããããšã¯èµ·ãããªã fact4: ä»®ã«çããããšãçºçãããšããããåãç¶ããããšãèµ·ããããã©å¿ç¡ããšããããšã¯çããªãããšããããšã¯ééã£ãŠãã fact5: å¿ç¡ããšããããšãçºçãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããè²·ãæããšããããšãèµ·ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããè²·ãæããšããããšãèµ·ãã; fact1 & assump1 -> int1: åãç¶ããããšãçºçãããããŸãã«è²·ãæããšããããšãçãã; int1 & fact3 -> int2: å¿ç¡ããšããããšã¯çããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} fact2: ({GJ} & {BI}) fact3: ({A} & {B}) -> ¬{C} fact4: {D} -> ¬({A} & ¬{C}) fact5: {C} ; $hypothesis$ = {B} ; $proof$ = | void -> assump1: {B}; fact1 & assump1 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãç³ãè¿°ã¹ãããšã¯èµ·ããªãããšããããšã¯æãç«ã€ | ¬{D} | fact1: äžè¶³ãæããšããããšã¯ãæºãããªããšããããšã¯çºçããªããŠãã€ãœããœãLv.14äºä»¶ã¯èµ·ããªãããšããããšã®åå ãšãªã fact2: ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ããªããšããããšã¯ãæºãããªããšããããšã¯èµ·ãããªããããããœããœãLv.14äºä»¶ã¯èµ·ããªãããšããããšã¯å¥æ©ã§ãã fact3: ããœã¡ã
ãœãLv.59äºä»¶ãèµ·ããããœããœãLv.14äºä»¶ãèµ·ããããããã¯äž¡æ¹ãšãã ããšããããšã¯ãç³ãè¿°ã¹ãããšã¯èµ·ããªãããšããããšã«åž°çµãã fact4: ããä»®ã«ãã©ããªããšããããšãèµ·ãããšããã°ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ãã fact5: ãã©ããªããšããããšãšæºãããªããšããããšäž¡æ¹ãšããèµ·ãã | fact1: {F} -> (¬{E} & ¬{C}) fact2: (¬{E} & ¬{C}) -> ¬{B} fact3: ({B} v {C}) -> ¬{D} fact4: {A} -> {B} fact5: ({A} & {E}) | [
"fact5 -> int1: ãã©ããªããšããããšãçãã; fact4 & int1 -> int2: ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ãã; int2 -> int3: ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ããããããã¯ãœããœãLv.14äºä»¶ãèµ·ããããããã¯ã©ã¡ããã§ãã; int3 & fact3 -> hypothesis;"
] | [
"fact5 -> int1: {A}; fact4 & int1 -> int2: {B}; int2 -> int3: ({B} v {C}); int3 & fact3 -> hypothesis;"
] | ç³ãè¿°ã¹ãããšãèµ·ãã | {D} | [] | 7 | 4 | 4 | 4 | 4 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: äžè¶³ãæããšããããšã¯ãæºãããªããšããããšã¯çºçããªããŠãã€ãœããœãLv.14äºä»¶ã¯èµ·ããªãããšããããšã®åå ãšãªã fact2: ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ããªããšããããšã¯ãæºãããªããšããããšã¯èµ·ãããªããããããœããœãLv.14äºä»¶ã¯èµ·ããªãããšããããšã¯å¥æ©ã§ãã fact3: ããœã¡ã
ãœãLv.59äºä»¶ãèµ·ããããœããœãLv.14äºä»¶ãèµ·ããããããã¯äž¡æ¹ãšãã ããšããããšã¯ãç³ãè¿°ã¹ãããšã¯èµ·ããªãããšããããšã«åž°çµãã fact4: ããä»®ã«ãã©ããªããšããããšãèµ·ãããšããã°ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ãã fact5: ãã©ããªããšããããšãšæºãããªããšããããšäž¡æ¹ãšããèµ·ãã ; $hypothesis$ = ãç³ãè¿°ã¹ãããšã¯èµ·ããªãããšããããšã¯æãç«ã€ ; $proof$ = | fact5 -> int1: ãã©ããªããšããããšãçãã; fact4 & int1 -> int2: ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ãã; int2 -> int3: ãœã¡ã
ãœãLv.59äºä»¶ãèµ·ããããããã¯ãœããœãLv.14äºä»¶ãèµ·ããããããã¯ã©ã¡ããã§ãã; int3 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {F} -> (¬{E} & ¬{C}) fact2: (¬{E} & ¬{C}) -> ¬{B} fact3: ({B} v {C}) -> ¬{D} fact4: {A} -> {B} fact5: ({A} & {E}) ; $hypothesis$ = ¬{D} ; $proof$ = | fact5 -> int1: {A}; fact4 & int1 -> int2: {B}; int2 -> int3: ({B} v {C}); int3 & fact3 -> hypothesis; __PROVED__ |
0.3 | åã£ä»ãé£ããšããããšãèµ·ãã | {C} | fact1: ä»®ã«ãèãæããšããããšã¯èµ·ãããªããããã«æµ
é»ããšããããšã¯èµ·ãããªãããšããããšã¯ééãã§ãããšãããšãåã£ä»ãé£ããšããããšã¯çããªãããšããããšã¯æ£ãã fact2: 貯氎ããããšãèµ·ãããšããããšã¯ã·ã«ã
ã·ãLv.74äºä»¶ã®ãã£ãããšãªã fact3: ããŸã«ãŸãLv.8äºä»¶ã¯èµ·ããªãããšããããšã¯æž
æããããšã¯èµ·ããªããšããããšã«é»ãŸãã fact4: èãæããšããããšã¯æµ
é»ããšããããšã«ããçãã fact5: é
ãæããšããããšã¯èµ·ãããªããšããããšã¯è²¯æ°Žããããšããã³ãŽããŽã«ãLv.60äºä»¶ãçããã«ç¹ãã fact6: èãæããšããããšã¯èµ·ãããªã fact7: ä»®ã«ãã·ã«ã
ã·ãLv.74äºä»¶ãèµ·ããããšããããšã¯åœã§ãªããšããã°ãèãæããšããããšã¯èµ·ããªããŠæµ
é»ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã | fact1: ¬(¬{B} & ¬{A}) -> ¬{C} fact2: {E} -> {D} fact3: ¬{GM} -> {JB} fact4: {A} -> {B} fact5: ¬{G} -> ({E} & {F}) fact6: ¬{B} fact7: {D} -> ¬(¬{B} & ¬{A}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããæµ
é»ããšããããšãçããããšããããšã¯æ£ãã; fact4 & assump1 -> int1: èãæããšããããšãçºçãã; int1 & fact6 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: æµ
é»ããšããããšã¯çºçããªã;"
] | [
"void -> assump1: {A}; fact4 & assump1 -> int1: {B}; int1 & fact6 -> int2: #F#; [assump1] & int2 -> int3: ¬{A};"
] | åã£ä»ãé£ããšããããšã¯çããªã | ¬{C} | [] | 8 | 5 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ãèãæããšããããšã¯èµ·ãããªããããã«æµ
é»ããšããããšã¯èµ·ãããªãããšããããšã¯ééãã§ãããšãããšãåã£ä»ãé£ããšããããšã¯çããªãããšããããšã¯æ£ãã fact2: 貯氎ããããšãèµ·ãããšããããšã¯ã·ã«ã
ã·ãLv.74äºä»¶ã®ãã£ãããšãªã fact3: ããŸã«ãŸãLv.8äºä»¶ã¯èµ·ããªãããšããããšã¯æž
æããããšã¯èµ·ããªããšããããšã«é»ãŸãã fact4: èãæããšããããšã¯æµ
é»ããšããããšã«ããçãã fact5: é
ãæããšããããšã¯èµ·ãããªããšããããšã¯è²¯æ°Žããããšããã³ãŽããŽã«ãLv.60äºä»¶ãçããã«ç¹ãã fact6: èãæããšããããšã¯èµ·ãããªã fact7: ä»®ã«ãã·ã«ã
ã·ãLv.74äºä»¶ãèµ·ããããšããããšã¯åœã§ãªããšããã°ãèãæããšããããšã¯èµ·ããªããŠæµ
é»ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã ; $hypothesis$ = åã£ä»ãé£ããšããããšãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{B} & ¬{A}) -> ¬{C} fact2: {E} -> {D} fact3: ¬{GM} -> {JB} fact4: {A} -> {B} fact5: ¬{G} -> ({E} & {F}) fact6: ¬{B} fact7: {D} -> ¬(¬{B} & ¬{A}) ; $hypothesis$ = {C} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŽã«ããŽãLv.52ã¯çºå£°ããªã | ¬{F}{d} | fact1: ãã®ãŸããŸã«ãLv.89ã¯çºå£°ãã fact2: ãã®ãããã¡ã
Lv.43ã¯ç¿æ
£åãã fact3: ä»®ã«ãã®ãããã¡ã
Lv.43ãç¿æ
£åãããšããããã®ãããã¡ã
Lv.43ã¯åãæã fact4: ãã®ãŸããŸã¡ã
Lv.92ã¯è¡æ£èã fact5: ããä»®ã«ãã®ãœã«ããœã¡ã
Lv.86ãåµé ãããªããã®ãŽã«ããŽãLv.52ã¯çºå£°ãã fact6: ããä»®ã«ãã®ãããã¡ã
Lv.43ãåãæããªãæ¥é£ã fact7: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯åãæããã©è¡æ£èããªãããšããããšã¯åœã§ãããšãããããã¯åãæããªã fact8: ããä»®ã«ãã®ãããã¡ã
Lv.43ãæ¥é£ããªãã°ãã®ã¿ã®ã¿ãLv.84ã¯è¡æ£èã fact9: ããããã®ãŸããŸã«ãLv.89ãçºå£°ãããªãããã¯æ¥é£ããšããããšã¯ãªã fact10: ä»®ã«ãã®ãããã¡ã
Lv.43ãçºå£°ããªããªãã°ãã®ãŽã«ããŽãLv.52ã¯çºå£°ããªã | fact1: {F}{gn} fact2: {A}{a} fact3: {A}{a} -> {B}{a} fact4: {D}{ik} fact5: {E}{c} -> {F}{d} fact6: {B}{a} -> {C}{a} fact7: (x): ¬({B}x & ¬{D}x) -> ¬{B}x fact8: {C}{a} -> {D}{b} fact9: {F}{gn} -> ¬{C}{gn} fact10: ¬{F}{a} -> ¬{F}{d} | [
"fact3 & fact2 -> int1: ãã®ãããã¡ã
Lv.43ã¯åãæã; int1 & fact6 -> int2: ãã®ãããã¡ã
Lv.43ã¯æ¥é£ã; int2 & fact8 -> int3: ãã®ã¿ã®ã¿ãLv.84ã¯è¡æ£èã;"
] | [
"fact3 & fact2 -> int1: {B}{a}; int1 & fact6 -> int2: {C}{a}; int2 & fact8 -> int3: {D}{b};"
] | ãã®ãŽã«ããŽãLv.52ã¯çºå£°ããªã | ¬{F}{d} | [] | 5 | 5 | 5 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãŸããŸã«ãLv.89ã¯çºå£°ãã fact2: ãã®ãããã¡ã
Lv.43ã¯ç¿æ
£åãã fact3: ä»®ã«ãã®ãããã¡ã
Lv.43ãç¿æ
£åãããšããããã®ãããã¡ã
Lv.43ã¯åãæã fact4: ãã®ãŸããŸã¡ã
Lv.92ã¯è¡æ£èã fact5: ããä»®ã«ãã®ãœã«ããœã¡ã
Lv.86ãåµé ãããªããã®ãŽã«ããŽãLv.52ã¯çºå£°ãã fact6: ããä»®ã«ãã®ãããã¡ã
Lv.43ãåãæããªãæ¥é£ã fact7: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯åãæããã©è¡æ£èããªãããšããããšã¯åœã§ãããšãããããã¯åãæããªã fact8: ããä»®ã«ãã®ãããã¡ã
Lv.43ãæ¥é£ããªãã°ãã®ã¿ã®ã¿ãLv.84ã¯è¡æ£èã fact9: ããããã®ãŸããŸã«ãLv.89ãçºå£°ãããªãããã¯æ¥é£ããšããããšã¯ãªã fact10: ä»®ã«ãã®ãããã¡ã
Lv.43ãçºå£°ããªããªãã°ãã®ãŽã«ããŽãLv.52ã¯çºå£°ããªã ; $hypothesis$ = ãã®ãŽã«ããŽãLv.52ã¯çºå£°ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {F}{gn} fact2: {A}{a} fact3: {A}{a} -> {B}{a} fact4: {D}{ik} fact5: {E}{c} -> {F}{d} fact6: {B}{a} -> {C}{a} fact7: (x): ¬({B}x & ¬{D}x) -> ¬{B}x fact8: {C}{a} -> {D}{b} fact9: {F}{gn} -> ¬{C}{gn} fact10: ¬{F}{a} -> ¬{F}{d} ; $hypothesis$ = ¬{F}{d} ; $proof$ = | __UNKNOWN__ |
0.3 | äœçœ®ä»ãããããšã¯çºçããªãããããçæãããšããããšã¯èµ·ããªã | (¬{A} & ¬{D}) | fact1: ããã¿ããšããããšãšäœçœ®ä»ãããããšãèµ·ããããšããããšã¯ããœã¡ããœãLv.37äºä»¶ã¯çºçããªãããšããããšãåŒãèµ·ãã fact2: ãã¿ããšããããšã¯èµ·ããªã fact3: äœçœ®ä»ãããããšã¯ãã¿ããšããããšã¯çããªããšããããšãé»æ¢ãã fact4: ééç¡ããšããããšã¯çããªã | fact1: ({B} & {A}) -> ¬{O} fact2: ¬{B} fact3: {A} -> {B} fact4: ¬{FF} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããäœçœ®ä»ãããããšãçãã; fact3 & assump1 -> int1: ãã¿ããšããããšãçãã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: äœçœ®ä»ãããããšã¯èµ·ãããªã;"
] | [
"void -> assump1: {A}; fact3 & assump1 -> int1: {B}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬{A};"
] | ãœã¡ããœãLv.37äºä»¶ã¯çºçããªã | ¬{O} | [] | 6 | 5 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã¿ããšããããšãšäœçœ®ä»ãããããšãèµ·ããããšããããšã¯ããœã¡ããœãLv.37äºä»¶ã¯çºçããªãããšããããšãåŒãèµ·ãã fact2: ãã¿ããšããããšã¯èµ·ããªã fact3: äœçœ®ä»ãããããšã¯ãã¿ããšããããšã¯çããªããšããããšãé»æ¢ãã fact4: ééç¡ããšããããšã¯çããªã ; $hypothesis$ = äœçœ®ä»ãããããšã¯çºçããªãããããçæãããšããããšã¯èµ·ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({B} & {A}) -> ¬{O} fact2: ¬{B} fact3: {A} -> {B} fact4: ¬{FF} ; $hypothesis$ = (¬{A} & ¬{D}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸããŸãLv.72ã¯æ¡å€§è§£éããªã | ¬{D}{b} | fact1: ããä»®ã«ãã®ã·ã®ã·ãLv.60ãèãããªãã°ãã®ãããã«ãLv.37ã¯ãã°ãã£ãã fact2: ããããã®ãããã«ãLv.37ããã°ãã£ãããªãã°ãã®ãŸããŸãLv.72ã¯æ¡å€§è§£éãã fact3: ãããšããã¢ã³ã¹ã¿ãŒã¯çŸããé£ããªããšãããããã°ãã£ãããå ããŠã ããç¡ãããšããããšã¯åœã§ãã fact4: ããããã®ãŸããŸãLv.72ãã ããç¡ããªããªããã®ã·ã®ã·ãLv.60ã¯æ¡å€§è§£éãããããã«èãã fact5: ãã®ã·ã®ã·ãLv.60ãã ããç¡ããªãã°ãã®ãããã«ãLv.37ã¯ãã°ãã£ãã fact6: ãã®ã·ã®ã·ãLv.60ã¯èããããããã¯ã ããç¡ã | fact1: {A}{a} -> {C}{c} fact2: {C}{c} -> {D}{b} fact3: (x): ¬{E}x -> ¬({C}x & {B}x) fact4: ¬{B}{b} -> ({D}{a} & {A}{a}) fact5: {B}{a} -> {C}{c} fact6: ({A}{a} v {B}{a}) | [
"fact6 & fact1 & fact5 -> int1: ãã®ãããã«ãLv.37ã¯ãã°ãã£ãã; int1 & fact2 -> hypothesis;"
] | [
"fact6 & fact1 & fact5 -> int1: {C}{c}; int1 & fact2 -> hypothesis;"
] | ãã®ã·ã®ã·ãLv.60ã¯æ¡å€§è§£éãã | {D}{a} | [
"fact7 -> int2: ãããããã®ãããã«ãLv.37ã¯çŸããé£ããªãããšããããšã¯çå®ã ãšããããããã¯ãã°ãã£ãããã ããç¡ãããšããããšã¯æãç«ããªã;"
] | 6 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ã·ã®ã·ãLv.60ãèãããªãã°ãã®ãããã«ãLv.37ã¯ãã°ãã£ãã fact2: ããããã®ãããã«ãLv.37ããã°ãã£ãããªãã°ãã®ãŸããŸãLv.72ã¯æ¡å€§è§£éãã fact3: ãããšããã¢ã³ã¹ã¿ãŒã¯çŸããé£ããªããšãããããã°ãã£ãããå ããŠã ããç¡ãããšããããšã¯åœã§ãã fact4: ããããã®ãŸããŸãLv.72ãã ããç¡ããªããªããã®ã·ã®ã·ãLv.60ã¯æ¡å€§è§£éãããããã«èãã fact5: ãã®ã·ã®ã·ãLv.60ãã ããç¡ããªãã°ãã®ãããã«ãLv.37ã¯ãã°ãã£ãã fact6: ãã®ã·ã®ã·ãLv.60ã¯èããããããã¯ã ããç¡ã ; $hypothesis$ = ãã®ãŸããŸãLv.72ã¯æ¡å€§è§£éããªã ; $proof$ = | fact6 & fact1 & fact5 -> int1: ãã®ãããã«ãLv.37ã¯ãã°ãã£ãã; int1 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {C}{c} fact2: {C}{c} -> {D}{b} fact3: (x): ¬{E}x -> ¬({C}x & {B}x) fact4: ¬{B}{b} -> ({D}{a} & {A}{a}) fact5: {B}{a} -> {C}{c} fact6: ({A}{a} v {B}{a}) ; $hypothesis$ = ¬{D}{b} ; $proof$ = | fact6 & fact1 & fact5 -> int1: {C}{c}; int1 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœã«ããœã«ãLv.21ã¯å¬éããªããŠæŽã«ã¹ããã溶æ¥ããªã | (¬{G}{e} & ¬{F}{e}) | fact1: ä»®ã«ãã®ãã«ãããLv.74ã¯ãããŒããšããã°ããã®ããããLv.82ã¯ãããŒããªãããšããããšã¯æãç«ã€ fact2: ä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãç©åããšããã°å¬éããªã fact3: ããããã®ãã«ãããLv.74ãåºæ¥é£ããšãããšãã®ã·ã«ãã·ã®Lv.68ã¯æåºããã fact4: ãã®ãããã®Lv.85ã¯éºãã fact5: ããããã®ã·ã«ãã·ã®Lv.68ãæåºããããšããããã®ãããã®Lv.85ã¯ç©åã fact6: ãã®ã·ã«ãã·ã®Lv.68ã¯åºæ¥é£ããªããªãããã®ãã«ãããLv.74ã¯æåºãããªããã©å¬éããããšããããšã¯æãç«ããªã fact7: ãã®ãã«ãããLv.74ã¯åºæ¥é£ã fact8: ãã®ãããã®Lv.85ãéºãããç©åããšããããã®ãã®ããLv.13ã¯ãããŒããªã fact9: ãã®ãã«ãããLv.74ã¯æåºããã fact10: ããã®ãã®ããLv.13ã¯ãããŒãããããã¹ããã溶æ¥ããªãããšããããšã¯æãç«ããªã | fact1: {E}{a} -> ¬{E}{jh} fact2: (x): {C}x -> ¬{G}x fact3: {A}{a} -> {B}{b} fact4: {D}{c} fact5: {B}{b} -> {C}{c} fact6: ¬{A}{b} -> ¬(¬{B}{a} & {G}{a}) fact7: {A}{a} fact8: ({D}{c} & {C}{c}) -> ¬{E}{d} fact9: {B}{a} fact10: ¬({E}{d} & ¬{F}{d}) | [
"fact3 & fact7 -> int1: ãã®ã·ã«ãã·ã®Lv.68ã¯æåºããã; int1 & fact5 -> int2: ãã®ãããã®Lv.85ã¯ç©åã; int2 & fact4 -> int3: ãã®ãããã®Lv.85ãéºããããã®äžç©åã; int3 & fact8 -> int4: ãã®ãã®ããLv.13ã¯ãããŒããªã;"
] | [
"fact3 & fact7 -> int1: {B}{b}; int1 & fact5 -> int2: {C}{c}; int2 & fact4 -> int3: ({D}{c} & {C}{c}); int3 & fact8 -> int4: ¬{E}{d};"
] | ããã®ããããLv.82ã¯ãããŒããªãããšããããšã¯æãç«ã€ | ¬{E}{jh} | [] | 8 | 5 | 5 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãã«ãããLv.74ã¯ãããŒããšããã°ããã®ããããLv.82ã¯ãããŒããªãããšããããšã¯æãç«ã€ fact2: ä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãç©åããšããã°å¬éããªã fact3: ããããã®ãã«ãããLv.74ãåºæ¥é£ããšãããšãã®ã·ã«ãã·ã®Lv.68ã¯æåºããã fact4: ãã®ãããã®Lv.85ã¯éºãã fact5: ããããã®ã·ã«ãã·ã®Lv.68ãæåºããããšããããã®ãããã®Lv.85ã¯ç©åã fact6: ãã®ã·ã«ãã·ã®Lv.68ã¯åºæ¥é£ããªããªãããã®ãã«ãããLv.74ã¯æåºãããªããã©å¬éããããšããããšã¯æãç«ããªã fact7: ãã®ãã«ãããLv.74ã¯åºæ¥é£ã fact8: ãã®ãããã®Lv.85ãéºãããç©åããšããããã®ãã®ããLv.13ã¯ãããŒããªã fact9: ãã®ãã«ãããLv.74ã¯æåºããã fact10: ããã®ãã®ããLv.13ã¯ãããŒãããããã¹ããã溶æ¥ããªãããšããããšã¯æãç«ããªã ; $hypothesis$ = ãã®ãœã«ããœã«ãLv.21ã¯å¬éããªããŠæŽã«ã¹ããã溶æ¥ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {E}{a} -> ¬{E}{jh} fact2: (x): {C}x -> ¬{G}x fact3: {A}{a} -> {B}{b} fact4: {D}{c} fact5: {B}{b} -> {C}{c} fact6: ¬{A}{b} -> ¬(¬{B}{a} & {G}{a}) fact7: {A}{a} fact8: ({D}{c} & {C}{c}) -> ¬{E}{d} fact9: {B}{a} fact10: ¬({E}{d} & ¬{F}{d}) ; $hypothesis$ = (¬{G}{e} & ¬{F}{e}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ãã·ãLv.68ã¯æãç«ã€ | {E}{b} | fact1: ä»®ã«ããã¢ã³ã¹ã¿ãŒãå¿æããšãããšããã¯é ããšããããšã¯ãªã fact2: ããã®ãŽã®ãŽã¡ã
Lv.75ã¯å¿æãããšããããšã¯æãç«ã€ fact3: ããä»®ã«ãã®ãŽã®ãŽã¡ã
Lv.75ãé ããªããªããã®ããããªLv.36ã¯åãæããŠããã«ããã fact4: ããã®ããããªLv.36ã¯åãæãããšããããšã¯ç¢ºãã§ãããªããã®ã·ãã·ãLv.68ã¯æãç«ã€ | fact1: (x): {A}x -> ¬{C}x fact2: {A}{aa} fact3: ¬{C}{aa} -> ({D}{a} & {B}{a}) fact4: {D}{a} -> {E}{b} | [
"fact1 -> int1: ããä»®ã«ãã®ãŽã®ãŽã¡ã
Lv.75ãå¿æããªãã°ãã®ãŽã®ãŽã¡ã
Lv.75ã¯é ããªã; int1 & fact2 -> int2: ãã®ãŽã®ãŽã¡ã
Lv.75ã¯é ããªã; int2 & fact3 -> int3: ãã®ããããªLv.36ã¯åãæããŠããŸãã«ããã; int3 -> int4: ãã®ããããªLv.36ã¯åãæã; int4 & fact4 -> hypothesis;"
] | [
"fact1 -> int1: {A}{aa} -> ¬{C}{aa}; int1 & fact2 -> int2: ¬{C}{aa}; int2 & fact3 -> int3: ({D}{a} & {B}{a}); int3 -> int4: {D}{a}; int4 & fact4 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ããã¢ã³ã¹ã¿ãŒãå¿æããšãããšããã¯é ããšããããšã¯ãªã fact2: ããã®ãŽã®ãŽã¡ã
Lv.75ã¯å¿æãããšããããšã¯æãç«ã€ fact3: ããä»®ã«ãã®ãŽã®ãŽã¡ã
Lv.75ãé ããªããªããã®ããããªLv.36ã¯åãæããŠããã«ããã fact4: ããã®ããããªLv.36ã¯åãæãããšããããšã¯ç¢ºãã§ãããªããã®ã·ãã·ãLv.68ã¯æãç«ã€ ; $hypothesis$ = ãã®ã·ãã·ãLv.68ã¯æãç«ã€ ; $proof$ = | fact1 -> int1: ããä»®ã«ãã®ãŽã®ãŽã¡ã
Lv.75ãå¿æããªãã°ãã®ãŽã®ãŽã¡ã
Lv.75ã¯é ããªã; int1 & fact2 -> int2: ãã®ãŽã®ãŽã¡ã
Lv.75ã¯é ããªã; int2 & fact3 -> int3: ãã®ããããªLv.36ã¯åãæããŠããŸãã«ããã; int3 -> int4: ãã®ããããªLv.36ã¯åãæã; int4 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {A}x -> ¬{C}x fact2: {A}{aa} fact3: ¬{C}{aa} -> ({D}{a} & {B}{a}) fact4: {D}{a} -> {E}{b} ; $hypothesis$ = {E}{b} ; $proof$ = | fact1 -> int1: {A}{aa} -> ¬{C}{aa}; int1 & fact2 -> int2: ¬{C}{aa}; int2 & fact3 -> int3: ({D}{a} & {B}{a}); int3 -> int4: {D}{a}; int4 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽããŽãªLv.28ã¯é»ã | {D}{a} | fact1: äœããã®ã¢ã³ã¹ã¿ãŒã¯é»ããšããã°ãåè§ããã©æç«ããªãããšããããšã¯æãç«ããªã fact2: ããä»®ã«ãã®ãŽããŽãªLv.28ãæããæããªããŠæŽã«ãããæç«ããªããšãããšããã¯ç¡çç¡ã fact3: ãã®ãŽããŽãªLv.28ã¯æç«ããªã fact4: ãããã®ãœã«ãœã¡ãLv.83ã¯åãé£ããªããäžžã£ãããäž¡æ¹ã§ããããšããããšã¯ç¢ºãã ããšããããšã¯ééã£ãŠãã fact5: ããããåãé£ããªããäžžã£ããããããã¯äž¡æ¹ã ããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ãŽããŽãªLv.28ã¯æããæããªã fact6: ãã®ãŽããŽãªLv.28ãç¡çç¡ããšããã°ãã®ãŽããŽãªLv.28ã¯é»ã | fact1: (x): {D}x -> ¬({EO}x & ¬{B}x) fact2: (¬{A}{a} & ¬{B}{a}) -> {C}{a} fact3: ¬{B}{a} fact4: ¬(¬{AA}{aa} v {AB}{aa}) fact5: (x): ¬(¬{AA}x v {AB}x) -> ¬{A}{a} fact6: {C}{a} -> {D}{a} | [
"fact4 -> int1: ãããåãé£ããªãããããã¯äžžã£ãããã©ã¡ããã§ããããšããããšã¯èª€ãã§ãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ç¢ºãã§ãã; int1 & fact5 -> int2: ãã®ãŽããŽãªLv.28ã¯æããæããªã; int2 & fact3 -> int3: ãã®ãŽããŽãªLv.28ã¯æããæããšããããšã¯ãªããŠãŸãããã¯æç«ããªã; int3 & fact2 -> int4: ãã®ãŽããŽãªLv.28ã¯ç¡çç¡ã; int4 & fact6 -> hypothesis;"
] | [
"fact4 -> int1: (Ex): ¬(¬{AA}x v {AB}x); int1 & fact5 -> int2: ¬{A}{a}; int2 & fact3 -> int3: (¬{A}{a} & ¬{B}{a}); int3 & fact2 -> int4: {C}{a}; int4 & fact6 -> hypothesis;"
] | ãã®ãŽããŽãªLv.28ã¯åè§ããªããã ããç¡ããªã | (¬{EO}{a} & ¬{H}{a}) | [
"fact7 -> int5: ãã®ã·ã«ãã·ã¡ã
Lv.41ã¯é»ããšããã°ãåè§ããæç«ããªãããšããããšã¯åœã§ãã;"
] | 6 | 5 | 5 | 5 | 5 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: äœããã®ã¢ã³ã¹ã¿ãŒã¯é»ããšããã°ãåè§ããã©æç«ããªãããšããããšã¯æãç«ããªã fact2: ããä»®ã«ãã®ãŽããŽãªLv.28ãæããæããªããŠæŽã«ãããæç«ããªããšãããšããã¯ç¡çç¡ã fact3: ãã®ãŽããŽãªLv.28ã¯æç«ããªã fact4: ãããã®ãœã«ãœã¡ãLv.83ã¯åãé£ããªããäžžã£ãããäž¡æ¹ã§ããããšããããšã¯ç¢ºãã ããšããããšã¯ééã£ãŠãã fact5: ããããåãé£ããªããäžžã£ããããããã¯äž¡æ¹ã ããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ãŽããŽãªLv.28ã¯æããæããªã fact6: ãã®ãŽããŽãªLv.28ãç¡çç¡ããšããã°ãã®ãŽããŽãªLv.28ã¯é»ã ; $hypothesis$ = ãã®ãŽããŽãªLv.28ã¯é»ã ; $proof$ = | fact4 -> int1: ãããåãé£ããªãããããã¯äžžã£ãããã©ã¡ããã§ããããšããããšã¯èª€ãã§ãããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ç¢ºãã§ãã; int1 & fact5 -> int2: ãã®ãŽããŽãªLv.28ã¯æããæããªã; int2 & fact3 -> int3: ãã®ãŽããŽãªLv.28ã¯æããæããšããããšã¯ãªããŠãŸãããã¯æç«ããªã; int3 & fact2 -> int4: ãã®ãŽããŽãªLv.28ã¯ç¡çç¡ã; int4 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {D}x -> ¬({EO}x & ¬{B}x) fact2: (¬{A}{a} & ¬{B}{a}) -> {C}{a} fact3: ¬{B}{a} fact4: ¬(¬{AA}{aa} v {AB}{aa}) fact5: (x): ¬(¬{AA}x v {AB}x) -> ¬{A}{a} fact6: {C}{a} -> {D}{a} ; $hypothesis$ = {D}{a} ; $proof$ = | fact4 -> int1: (Ex): ¬(¬{AA}x v {AB}x); int1 & fact5 -> int2: ¬{A}{a}; int2 & fact3 -> int3: (¬{A}{a} & ¬{B}{a}); int3 & fact2 -> int4: {C}{a}; int4 & fact6 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã¿ã«ã
ã¿ãLv.67ã¯äº¬éœãããããããã¶ãã¶ãããªã | ({AA}{a} & ¬{AB}{a}) | fact1: ããä»®ã«ãã®ãŽã«ãŽã«ãLv.70ãæ¬åœããããªããªããã®ãŽã«ãŽã«ãLv.70ã¯äœåç¡ãã京éœããã fact2: ããä»®ã«ããã®ãŽã«ãŽã«ãLv.70ã¯äœåç¡ãããšããããšã¯çå®ã ãšããã°æã fact3: ãã®ãŽã«ãŽã«ãLv.70ã¯æããªã | fact1: ¬{D}{b} -> ({B}{b} v {AA}{b}) fact2: {B}{b} -> {A}{b} fact3: ¬{A}{b} | [] | [] | 以äžã®ããã«ä»®å®ããããã®ã¿ã«ã
ã¿ãLv.67ã¯äº¬éœãããããããã¶ãã¶ãããªã | ({AA}{a} & ¬{AB}{a}) | [] | 4 | 5 | 4 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãŽã«ãŽã«ãLv.70ãæ¬åœããããªããªããã®ãŽã«ãŽã«ãLv.70ã¯äœåç¡ãã京éœããã fact2: ããä»®ã«ããã®ãŽã«ãŽã«ãLv.70ã¯äœåç¡ãããšããããšã¯çå®ã ãšããã°æã fact3: ãã®ãŽã«ãŽã«ãLv.70ã¯æããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã¿ã«ã
ã¿ãLv.67ã¯äº¬éœãããããããã¶ãã¶ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{D}{b} -> ({B}{b} v {AA}{b}) fact2: {B}{b} -> {A}{b} fact3: ¬{A}{b} ; $hypothesis$ = ({AA}{a} & ¬{AB}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ããããLv.34ã¯æ§æãåŸãªã | ¬{A}{a} | fact1: ä»®ã«ãã®ããããLv.30ãçãããšããããšã¯ãªããšãããšãã®ããããLv.30ã¯å£ãæããŠæããã fact2: ãå
šãŠã®ã¢ã³ã¹ã¿ãŒã¯æ§æãåŸãããšããããšã¯æãç«ã€ fact3: ãã®ããããLv.30ãæãããã¢ã³ã¹ã¿ãŒã§ãããã®äžä¿¡é ŒãåŸãã°ãã®ããããLv.34ã¯æããããªã fact4: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯æããã fact5: ãæããããªãã¢ã³ã¹ã¿ãŒã¯æ§æãåŸãªãããšããããšã¯æ¬åœã | fact1: ¬{G}{b} -> ({F}{b} & {B}{b}) fact2: (x): {A}x fact3: ({B}{b} & {D}{b}) -> ¬{B}{a} fact4: (x): {AH}x fact5: (x): ¬{B}x -> ¬{A}x | [
"fact2 -> int1: ãå
šãŠã®ã¢ã³ã¹ã¿ãŒã¯æ§æãåŸãããšããããšã¯æãç«ã€; int1 -> hypothesis;"
] | [
"fact2 -> int1: (x): {A}x; int1 -> hypothesis;"
] | ãã®ããããLv.34ã¯æ§æãåŸãªã | ¬{A}{a} | [
"fact7 -> int2: ãã®ããããLv.34ãæããããªããªãã°ãã®ããããLv.34ã¯æ§æãåŸãªã;"
] | 5 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ããããLv.30ãçãããšããããšã¯ãªããšãããšãã®ããããLv.30ã¯å£ãæããŠæããã fact2: ãå
šãŠã®ã¢ã³ã¹ã¿ãŒã¯æ§æãåŸãããšããããšã¯æãç«ã€ fact3: ãã®ããããLv.30ãæãããã¢ã³ã¹ã¿ãŒã§ãããã®äžä¿¡é ŒãåŸãã°ãã®ããããLv.34ã¯æããããªã fact4: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯æããã fact5: ãæããããªãã¢ã³ã¹ã¿ãŒã¯æ§æãåŸãªãããšããããšã¯æ¬åœã ; $hypothesis$ = ãã®ããããLv.34ã¯æ§æãåŸãªã ; $proof$ = | fact2 -> int1: ãå
šãŠã®ã¢ã³ã¹ã¿ãŒã¯æ§æãåŸãããšããããšã¯æãç«ã€; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{G}{b} -> ({F}{b} & {B}{b}) fact2: (x): {A}x fact3: ({B}{b} & {D}{b}) -> ¬{B}{a} fact4: (x): {AH}x fact5: (x): ¬{B}x -> ¬{A}x ; $hypothesis$ = ¬{A}{a} ; $proof$ = | fact2 -> int1: (x): {A}x; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ããããLv.44ã¯å³èŠãããšããããšã¯ãªã | ¬{E}{b} | fact1: ãã®ããããLv.44ã¯é£ã¶ fact2: ãããã®ãããã¡ãLv.22ã¯åãããªããšããã°ããã®ãŽããŽã¡ãLv.79ã¯èš±ãé£ããŠããŸãã«é£ã¶ããšããããšã¯æãç«ããªã fact3: ãèš±ãé£ããªãã¢ã³ã¹ã¿ãŒã¯é£ã¶ããšããããšã¯æãç«ã€ fact4: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯é
è¡ããããããå³èŠããªãããšããããšã¯èª€ããªãã°å³èŠãã fact5: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯èš±ãé£ããªããªããããã¯é
è¡ããããããå³èŠããªãããšããããšã¯èª€ã£ãŠãã fact6: ããã®ã·ãªã·ãLv.56ã¯èš±ãé£ããªãããšããããšã¯æãç«ã€ fact7: ãã®ã·ãªã·ãLv.56ãé
è¡ãããªããã®ãããã¡ãLv.22ã¯åããã fact8: ãã®ããããLv.44ã¯èš±ãé£ã fact9: ãã®ãããã¡ãLv.22ãåãããã°ãã®ããããLv.44ã¯å³èŠãã | fact1: {C}{b} fact2: ¬{D}{a} -> ¬({B}{jf} & {C}{jf}) fact3: (x): ¬{B}x -> {C}x fact4: (x): ¬({A}x & ¬{E}x) -> {E}x fact5: (x): ¬{B}x -> ¬({A}x & ¬{E}x) fact6: ¬{B}{aa} fact7: {A}{aa} -> {D}{a} fact8: {B}{b} fact9: {D}{a} -> {E}{b} | [
"fact3 -> int1: ãã®ã·ãªã·ãLv.56ãèš±ãé£ããªããªãé£ã¶; int1 & fact6 -> int2: ãã®ã·ãªã·ãLv.56ã¯é£ã¶;"
] | [
"fact3 -> int1: ¬{B}{aa} -> {C}{aa}; int1 & fact6 -> int2: {C}{aa};"
] | ãã®ããããLv.44ã¯å³èŠãããšããããšã¯ãªã | ¬{E}{b} | [] | 4 | 5 | 5 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ããããLv.44ã¯é£ã¶ fact2: ãããã®ãããã¡ãLv.22ã¯åãããªããšããã°ããã®ãŽããŽã¡ãLv.79ã¯èš±ãé£ããŠããŸãã«é£ã¶ããšããããšã¯æãç«ããªã fact3: ãèš±ãé£ããªãã¢ã³ã¹ã¿ãŒã¯é£ã¶ããšããããšã¯æãç«ã€ fact4: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯é
è¡ããããããå³èŠããªãããšããããšã¯èª€ããªãã°å³èŠãã fact5: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯èš±ãé£ããªããªããããã¯é
è¡ããããããå³èŠããªãããšããããšã¯èª€ã£ãŠãã fact6: ããã®ã·ãªã·ãLv.56ã¯èš±ãé£ããªãããšããããšã¯æãç«ã€ fact7: ãã®ã·ãªã·ãLv.56ãé
è¡ãããªããã®ãããã¡ãLv.22ã¯åããã fact8: ãã®ããããLv.44ã¯èš±ãé£ã fact9: ãã®ãããã¡ãLv.22ãåãããã°ãã®ããããLv.44ã¯å³èŠãã ; $hypothesis$ = ãã®ããããLv.44ã¯å³èŠãããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C}{b} fact2: ¬{D}{a} -> ¬({B}{jf} & {C}{jf}) fact3: (x): ¬{B}x -> {C}x fact4: (x): ¬({A}x & ¬{E}x) -> {E}x fact5: (x): ¬{B}x -> ¬({A}x & ¬{E}x) fact6: ¬{B}{aa} fact7: {A}{aa} -> {D}{a} fact8: {B}{b} fact9: {D}{a} -> {E}{b} ; $hypothesis$ = ¬{E}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ã«ãã·ã¡ãLv.8ã¯çŽ°é·ããã©ããã¯ææãæããªãããšããããšã¯ééãã§ãã | ¬({E}{c} & ¬{G}{c}) | fact1: ãã®ãœããœã«ãLv.31ã¯åŸ¡å¿ãããããã«æãæã fact2: ãã®ãŽããŽã¡ãLv.45ã¯çŽ°é·ããçã
ãã fact3: ãã®ãŽãªãŽã«Lv.40ã¯å°ãè¿ããããã¯æ»ãæã fact4: ãã®ã·ã«ãã·ã¡ãLv.8ã现é·ããšãããããã¯åŸ¡å¿ãã fact5: ãããããã®ãœããœã«ãLv.31ã¯çŸšãŸãããæŽã«æ¢ãæãããšããããšã¯æ¬åœãªããã®ãœã¡ããœãLv.40ã¯çŽ°é·ããªã fact6: ãããã®ãœããœã«ãLv.31ã埡å¿ãããšããããã®ãœããœã«ãLv.31ã¯æ¢ãæã fact7: ãã®ãœã¡ããœãLv.40ã¯çŽ°é·ããªããªãããã®ã·ã«ãã·ã¡ãLv.8ã¯çŽ°é·ããã©ææãæããªãããšããããšã¯æãç«ããªã fact8: ãã®ãœããœã«ãLv.31ã¯çŸšãŸãã | fact1: ({A}{a} & {B}{a}) fact2: ({E}{jk} & {HN}{jk}) fact3: ({IO}{ar} & {CH}{ar}) fact4: {E}{c} -> {A}{c} fact5: ({D}{a} & {C}{a}) -> ¬{E}{b} fact6: {A}{a} -> {C}{a} fact7: ¬{E}{b} -> ¬({E}{c} & ¬{G}{c}) fact8: {D}{a} | [
"fact1 -> int1: ããã®ãœããœã«ãLv.31ã¯åŸ¡å¿ããããšããããšã¯æ£ãã; int1 & fact6 -> int2: ãã®ãœããœã«ãLv.31ã¯æ¢ãæã; int2 & fact8 -> int3: ãã®ãœããœã«ãLv.31ã¯çŸšãŸãããŠæŽã«æ¢ãæã; int3 & fact5 -> int4: ãã®ãœã¡ããœãLv.40ã¯çŽ°é·ããªã; int4 & fact7 -> hypothesis;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact6 -> int2: {C}{a}; int2 & fact8 -> int3: ({D}{a} & {C}{a}); int3 & fact5 -> int4: ¬{E}{b}; int4 & fact7 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãœããœã«ãLv.31ã¯åŸ¡å¿ãããããã«æãæã fact2: ãã®ãŽããŽã¡ãLv.45ã¯çŽ°é·ããçã
ãã fact3: ãã®ãŽãªãŽã«Lv.40ã¯å°ãè¿ããããã¯æ»ãæã fact4: ãã®ã·ã«ãã·ã¡ãLv.8ã现é·ããšãããããã¯åŸ¡å¿ãã fact5: ãããããã®ãœããœã«ãLv.31ã¯çŸšãŸãããæŽã«æ¢ãæãããšããããšã¯æ¬åœãªããã®ãœã¡ããœãLv.40ã¯çŽ°é·ããªã fact6: ãããã®ãœããœã«ãLv.31ã埡å¿ãããšããããã®ãœããœã«ãLv.31ã¯æ¢ãæã fact7: ãã®ãœã¡ããœãLv.40ã¯çŽ°é·ããªããªãããã®ã·ã«ãã·ã¡ãLv.8ã¯çŽ°é·ããã©ææãæããªãããšããããšã¯æãç«ããªã fact8: ãã®ãœããœã«ãLv.31ã¯çŸšãŸãã ; $hypothesis$ = ããã®ã·ã«ãã·ã¡ãLv.8ã¯çŽ°é·ããã©ããã¯ææãæããªãããšããããšã¯ééãã§ãã ; $proof$ = | fact1 -> int1: ããã®ãœããœã«ãLv.31ã¯åŸ¡å¿ããããšããããšã¯æ£ãã; int1 & fact6 -> int2: ãã®ãœããœã«ãLv.31ã¯æ¢ãæã; int2 & fact8 -> int3: ãã®ãœããœã«ãLv.31ã¯çŸšãŸãããŠæŽã«æ¢ãæã; int3 & fact5 -> int4: ãã®ãœã¡ããœãLv.40ã¯çŽ°é·ããªã; int4 & fact7 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: ({E}{jk} & {HN}{jk}) fact3: ({IO}{ar} & {CH}{ar}) fact4: {E}{c} -> {A}{c} fact5: ({D}{a} & {C}{a}) -> ¬{E}{b} fact6: {A}{a} -> {C}{a} fact7: ¬{E}{b} -> ¬({E}{c} & ¬{G}{c}) fact8: {D}{a} ; $hypothesis$ = ¬({E}{c} & ¬{G}{c}) ; $proof$ = | fact1 -> int1: {A}{a}; int1 & fact6 -> int2: {C}{a}; int2 & fact8 -> int3: ({D}{a} & {C}{a}); int3 & fact5 -> int4: ¬{E}{b}; int4 & fact7 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããœã«ããœãLv.27äºä»¶ãèµ·ãã | {B} | fact1: ãå¿ç¡ããšããããšã¯èµ·ããªãããšããããšã¯äºå®ã§ãã fact2: ããããã«ã
Lv.89äºä»¶ãçºçãããã·ãã·ãªLv.81äºä»¶ãçããããšããããšã¯ãŽã®ãŽã«ãLv.65äºä»¶ãçºçããªããšããããšã¯ãã£ããã§ãã fact3: ãããã«ã
Lv.89äºä»¶ãçºçãã fact4: ã·ãã·ãªLv.81äºä»¶ãèµ·ãã fact5: ãããããã«ã
Lv.89äºä»¶ãšãœã«ããœãLv.27äºä»¶ãçãããªãã·ãã·ãªLv.81äºä»¶ã¯çããªã | fact1: ¬{AL} fact2: ¬{D} -> ({A} v {C}) fact3: {A} fact4: {C} fact5: ({A} & {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããœã«ããœãLv.27äºä»¶ãèµ·ãã; fact3 & assump1 -> int1: ãããã«ã
Lv.89äºä»¶ãèµ·ããããœã«ããœãLv.27äºä»¶ãèµ·ãã; int1 & fact5 -> int2: ã·ãã·ãªLv.81äºä»¶ã¯çºçããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; fact3 & assump1 -> int1: ({A} & {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããœã«ããœãLv.27äºä»¶ãèµ·ãã | {B} | [] | 6 | 5 | 4 | 5 | 4 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãå¿ç¡ããšããããšã¯èµ·ããªãããšããããšã¯äºå®ã§ãã fact2: ããããã«ã
Lv.89äºä»¶ãçºçãããã·ãã·ãªLv.81äºä»¶ãçããããšããããšã¯ãŽã®ãŽã«ãLv.65äºä»¶ãçºçããªããšããããšã¯ãã£ããã§ãã fact3: ãããã«ã
Lv.89äºä»¶ãçºçãã fact4: ã·ãã·ãªLv.81äºä»¶ãèµ·ãã fact5: ãããããã«ã
Lv.89äºä»¶ãšãœã«ããœãLv.27äºä»¶ãçãããªãã·ãã·ãªLv.81äºä»¶ã¯çããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããœã«ããœãLv.27äºä»¶ãèµ·ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããœã«ããœãLv.27äºä»¶ãèµ·ãã; fact3 & assump1 -> int1: ãããã«ã
Lv.89äºä»¶ãèµ·ããããœã«ããœãLv.27äºä»¶ãèµ·ãã; int1 & fact5 -> int2: ã·ãã·ãªLv.81äºä»¶ã¯çºçããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{AL} fact2: ¬{D} -> ({A} v {C}) fact3: {A} fact4: {C} fact5: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {B} ; $proof$ = | void -> assump1: {B}; fact3 & assump1 -> int1: ({A} & {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ã«ã
ã¿ã«ã
Lv.7ã¯èªåããã | {A}{a} | fact1: ä»®ã«ãã®ãŸããŸã«ãLv.18ãå°ãããšãããšåãã¡é£ãäžæ¹ã§æŽãããŸãããªã fact2: ä»®ã«åãã¡é£ãã¢ã³ã¹ã¿ãŒãæŽãããŸãããªããªãããã¯èªåããã fact3: ãã®ãœããœã¡ãLv.28ã¯èªåããã | fact1: {D}{ib} -> ({C}{ib} & ¬{B}{ib}) fact2: (x): ({C}x & ¬{B}x) -> {A}x fact3: {A}{cb} | [] | [] | ãã®ãŸããŸã«ãLv.18ã¯èªåããã | {A}{ib} | [
"fact4 -> int1: ãããã®ãŸããŸã«ãLv.18ãåãã¡é£ãããã©æŽãããŸãããªããªãã°ãã®ãŸããŸã«ãLv.18ã¯èªåããã;"
] | 6 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãŸããŸã«ãLv.18ãå°ãããšãããšåãã¡é£ãäžæ¹ã§æŽãããŸãããªã fact2: ä»®ã«åãã¡é£ãã¢ã³ã¹ã¿ãŒãæŽãããŸãããªããªãããã¯èªåããã fact3: ãã®ãœããœã¡ãLv.28ã¯èªåããã ; $hypothesis$ = ãã®ã¿ã«ã
ã¿ã«ã
Lv.7ã¯èªåããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {D}{ib} -> ({C}{ib} & ¬{B}{ib}) fact2: (x): ({C}x & ¬{B}x) -> {A}x fact3: {A}{cb} ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŽã«ãŽãªLv.78ã¯ãã€ãã£ãããã | {A}{a} | fact1: çºçãæãã¢ã³ã¹ã¿ãŒã¯çŸšãŸãã fact2: ãã®ãŽã«ããŽãLv.11ã¯çºçãæããŠããã«ããã¯æåºã fact3: ããããã¢ã³ã¹ã¿ãŒã¯ãã€ãã£ãããã fact4: ããããªãããã®ã¢ã³ã¹ã¿ãŒãéåããªããªãããã¯æãå€ããããã«ãã€ãã£ããããããšããããšã¯æãç«ã€ fact5: 矚ãŸããã¢ã³ã¹ã¿ãŒã¯éåããªããå ããŠæ¬²æ·±ããªã fact6: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯è«ã | fact1: (x): {F}x -> {E}x fact2: ({F}{ds} & {G}{ds}) fact3: (x): {A}x fact4: (x): ¬{C}x -> ({B}x & {A}x) fact5: (x): {E}x -> (¬{C}x & ¬{D}x) fact6: (x): {DO}x | [
"fact3 -> int1: ããããã¢ã³ã¹ã¿ãŒã¯ãã€ãã£ãããã; int1 -> hypothesis;"
] | [
"fact3 -> int1: (x): {A}x; int1 -> hypothesis;"
] | ããã®ãŽã«ããŽãLv.11ã¯ãã€ãã£ããããããšããããšã¯æ£ãã | {A}{ds} | [
"fact9 -> int2: ä»®ã«ãã®ãŽã«ããŽãLv.11ãéåããªããªããã®ãŽã«ããŽãLv.11ã¯æãå€ãããã€ãã£ãããã; fact8 -> int3: ãããããã®ãŽã«ããŽãLv.11ã¯çŸšãŸããããšããããšã¯èª€ã£ãŠããªããšãããšãã®ãŽã«ããŽãLv.11ã¯éåããªããŠããã«ããã¯æ¬²æ·±ããªã; fact7 -> int4: ãã®ãŽã«ããŽãLv.11ãçºçãæããšããã°çŸšãŸãã; fact10 -> int5: ãã®ãŽã«ããŽãLv.11ã¯çºçãæã; int4 & int5 -> int6: ãã®ãŽã«ããŽãLv.11ã¯çŸšãŸãã; int3 & int6 -> int7: ãã®ãŽã«ããŽãLv.11ã¯éåããªããããã¯æ¬²æ·±ããšããããšã¯ãªã; int7 -> int8: ãã®ãŽã«ããŽãLv.11ã¯éåãããšããããšã¯ãªã; int2 & int8 -> int9: ãã®ãŽã«ããŽãLv.11ã¯æãå€ããæŽã«ãã€ãã£ãããã; int9 -> hypothesis;"
] | 6 | 2 | 2 | 2 | 2 | 5 | 0 | 5 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: çºçãæãã¢ã³ã¹ã¿ãŒã¯çŸšãŸãã fact2: ãã®ãŽã«ããŽãLv.11ã¯çºçãæããŠããã«ããã¯æåºã fact3: ããããã¢ã³ã¹ã¿ãŒã¯ãã€ãã£ãããã fact4: ããããªãããã®ã¢ã³ã¹ã¿ãŒãéåããªããªãããã¯æãå€ããããã«ãã€ãã£ããããããšããããšã¯æãç«ã€ fact5: 矚ãŸããã¢ã³ã¹ã¿ãŒã¯éåããªããå ããŠæ¬²æ·±ããªã fact6: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯è«ã ; $hypothesis$ = ãã®ãŽã«ãŽãªLv.78ã¯ãã€ãã£ãããã ; $proof$ = | fact3 -> int1: ããããã¢ã³ã¹ã¿ãŒã¯ãã€ãã£ãããã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {F}x -> {E}x fact2: ({F}{ds} & {G}{ds}) fact3: (x): {A}x fact4: (x): ¬{C}x -> ({B}x & {A}x) fact5: (x): {E}x -> (¬{C}x & ¬{D}x) fact6: (x): {DO}x ; $hypothesis$ = {A}{a} ; $proof$ = | fact3 -> int1: (x): {A}x; int1 -> hypothesis; __PROVED__ |
0.3 | ãŸã«ãŸã¡ãLv.46äºä»¶ãèµ·ãã | {F} | fact1: 䜿çšãæããšããããšãçãããããã«æž©ãããšããããšãçºçãã fact2: èéããšããããšã¯ã¿ãã¿ãLv.46äºä»¶ãçºçããã fact3: ãŸã«ãŸã¡ãLv.46äºä»¶ã¯ãã¿ãã¿ãLv.46äºä»¶ãçããããããã¯æãããæããšããããšãçãããäž¡æ¹ã§ããããšããããšã«é»ãŸãã fact4: èéããšããããšã¯äœ¿çšãæããšããããšã«ãããããã | fact1: ({A} & {B}) fact2: {C} -> {D} fact3: ({D} v {E}) -> ¬{F} fact4: {A} -> {C} | [
"fact1 -> int1: 䜿çšãæããšããããšãèµ·ãã; int1 & fact4 -> int2: èéããšããããšãçãã; int2 & fact2 -> int3: ã¿ãã¿ãLv.46äºä»¶ãçãã; int3 -> int4: ã¿ãã¿ãLv.46äºä»¶ããŸãã¯æãããæããšããããšããŸãã¯äž¡æ¹ãšããèµ·ãã; int4 & fact3 -> hypothesis;"
] | [
"fact1 -> int1: {A}; int1 & fact4 -> int2: {C}; int2 & fact2 -> int3: {D}; int3 -> int4: ({D} v {E}); int4 & fact3 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: 䜿çšãæããšããããšãçãããããã«æž©ãããšããããšãçºçãã fact2: èéããšããããšã¯ã¿ãã¿ãLv.46äºä»¶ãçºçããã fact3: ãŸã«ãŸã¡ãLv.46äºä»¶ã¯ãã¿ãã¿ãLv.46äºä»¶ãçããããããã¯æãããæããšããããšãçãããäž¡æ¹ã§ããããšããããšã«é»ãŸãã fact4: èéããšããããšã¯äœ¿çšãæããšããããšã«ãããããã ; $hypothesis$ = ãŸã«ãŸã¡ãLv.46äºä»¶ãèµ·ãã ; $proof$ = | fact1 -> int1: 䜿çšãæããšããããšãèµ·ãã; int1 & fact4 -> int2: èéããšããããšãçãã; int2 & fact2 -> int3: ã¿ãã¿ãLv.46äºä»¶ãçãã; int3 -> int4: ã¿ãã¿ãLv.46äºä»¶ããŸãã¯æãããæããšããããšããŸãã¯äž¡æ¹ãšããèµ·ãã; int4 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} & {B}) fact2: {C} -> {D} fact3: ({D} v {E}) -> ¬{F} fact4: {A} -> {C} ; $hypothesis$ = {F} ; $proof$ = | fact1 -> int1: {A}; int1 & fact4 -> int2: {C}; int2 & fact2 -> int3: {D}; int3 -> int4: ({D} v {E}); int4 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ã«ã
ã¿ãLv.16ã¯å± 殺ããªã | ¬{F}{c} | fact1: ããä»®ã«ãã®ãŽã¡ããŽã®Lv.33ã銬鹿ããããªããšããã°ãŸã³ããèã£ãœã fact2: ä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãè¬æ®ºãããšãããå± æ®ºãã fact3: ãã®ãã¡ããã¡ãLv.51ãèã£ãœããšããã°ãã®ãã¡ããã¡ãLv.51ã¯éŠ¬é¹¿ããããšããããšã¯ãªã fact4: ãã®ãã¡ããã¡ãLv.51ã¯ãŸã³ã fact5: ãã®ãŽã¡ããŽã®Lv.33ã銬鹿ããããå¯ããªãããã®ã¿ã«ã
ã¿ãLv.16ã¯å± 殺ããªãããšããããšã¯ééã£ãŠãããšããããšã¯ãªã fact6: ä»®ã«ãã®ãã¡ããã¡ãLv.51ã¯èã£ãœããªããšãããããã®ãŽã¡ããŽã®Lv.33ã¯éŠ¬é¹¿ãããããšããããšã¯æ¬åœã fact7: ãã®ãã¡ããã¡ãLv.51ãè¬æ®ºããããããã¯ããããŸã³ããšããããã®ãã¡ããã¡ãLv.51ã¯èã£ãœããªã fact8: ãã®ãŽã¡ããŽã®Lv.33ã¯å¯ã fact9: ãããã®ã¿ã«ã
ã¿ãLv.16ãèã£ãœããªããªãã°ããã¯è¬æ®ºãããããã«ãŸã³ã | fact1: ¬{D}{b} -> ({B}{b} & {C}{b}) fact2: (x): {A}x -> {F}x fact3: {C}{a} -> ¬{D}{a} fact4: {B}{a} fact5: ({D}{b} & {E}{b}) -> ¬{F}{c} fact6: ¬{C}{a} -> {D}{b} fact7: ({A}{a} v {B}{a}) -> ¬{C}{a} fact8: {E}{b} fact9: ¬{C}{c} -> ({A}{c} & {B}{c}) | [
"fact4 -> int1: ãã®ãã¡ããã¡ãLv.51ã¯è¬æ®ºããããããã¯ãŸã³ã; int1 & fact7 -> int2: ãã®ãã¡ããã¡ãLv.51ã¯èã£ãœããªã; int2 & fact6 -> int3: ãã®ãŽã¡ããŽã®Lv.33ã¯éŠ¬é¹¿ããã; int3 & fact8 -> int4: ãã®ãŽã¡ããŽã®Lv.33ã銬鹿ãããããã®äžå¯ã; int4 & fact5 -> hypothesis;"
] | [
"fact4 -> int1: ({A}{a} v {B}{a}); int1 & fact7 -> int2: ¬{C}{a}; int2 & fact6 -> int3: {D}{b}; int3 & fact8 -> int4: ({D}{b} & {E}{b}); int4 & fact5 -> hypothesis;"
] | ãã®ãŽã¡ããŽã®Lv.33ã¯è¬æ®ºãã | {A}{b} | [] | 7 | 5 | 5 | 5 | 5 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãŽã¡ããŽã®Lv.33ã銬鹿ããããªããšããã°ãŸã³ããèã£ãœã fact2: ä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãè¬æ®ºãããšãããå± æ®ºãã fact3: ãã®ãã¡ããã¡ãLv.51ãèã£ãœããšããã°ãã®ãã¡ããã¡ãLv.51ã¯éŠ¬é¹¿ããããšããããšã¯ãªã fact4: ãã®ãã¡ããã¡ãLv.51ã¯ãŸã³ã fact5: ãã®ãŽã¡ããŽã®Lv.33ã銬鹿ããããå¯ããªãããã®ã¿ã«ã
ã¿ãLv.16ã¯å± 殺ããªãããšããããšã¯ééã£ãŠãããšããããšã¯ãªã fact6: ä»®ã«ãã®ãã¡ããã¡ãLv.51ã¯èã£ãœããªããšãããããã®ãŽã¡ããŽã®Lv.33ã¯éŠ¬é¹¿ãããããšããããšã¯æ¬åœã fact7: ãã®ãã¡ããã¡ãLv.51ãè¬æ®ºããããããã¯ããããŸã³ããšããããã®ãã¡ããã¡ãLv.51ã¯èã£ãœããªã fact8: ãã®ãŽã¡ããŽã®Lv.33ã¯å¯ã fact9: ãããã®ã¿ã«ã
ã¿ãLv.16ãèã£ãœããªããªãã°ããã¯è¬æ®ºãããããã«ãŸã³ã ; $hypothesis$ = ãã®ã¿ã«ã
ã¿ãLv.16ã¯å± 殺ããªã ; $proof$ = | fact4 -> int1: ãã®ãã¡ããã¡ãLv.51ã¯è¬æ®ºããããããã¯ãŸã³ã; int1 & fact7 -> int2: ãã®ãã¡ããã¡ãLv.51ã¯èã£ãœããªã; int2 & fact6 -> int3: ãã®ãŽã¡ããŽã®Lv.33ã¯éŠ¬é¹¿ããã; int3 & fact8 -> int4: ãã®ãŽã¡ããŽã®Lv.33ã銬鹿ãããããã®äžå¯ã; int4 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{D}{b} -> ({B}{b} & {C}{b}) fact2: (x): {A}x -> {F}x fact3: {C}{a} -> ¬{D}{a} fact4: {B}{a} fact5: ({D}{b} & {E}{b}) -> ¬{F}{c} fact6: ¬{C}{a} -> {D}{b} fact7: ({A}{a} v {B}{a}) -> ¬{C}{a} fact8: {E}{b} fact9: ¬{C}{c} -> ({A}{c} & {B}{c}) ; $hypothesis$ = ¬{F}{c} ; $proof$ = | fact4 -> int1: ({A}{a} v {B}{a}); int1 & fact7 -> int2: ¬{C}{a}; int2 & fact6 -> int3: {D}{b}; int3 & fact8 -> int4: ({D}{b} & {E}{b}); int4 & fact5 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸããŸãLv.12ã¯åŸé£ã | {B}{aa} | fact1: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãçã£é»ããªããªãããã¯éããæããªã fact2: ãã®ãŸããŸãLv.12ã¯éããæã | fact1: (x): ¬{GA}x -> ¬{C}x fact2: {C}{aa} | [] | [] | ããä»®ã«ãã®ãŸã«ã
ãŸãLv.48ãçã£é»ããªããªãéããæããšããããšã¯ãªã | ¬{GA}{hf} -> ¬{C}{hf} | [
"fact3 -> hypothesis;"
] | 1 | 5 | 4 | null | null | 1 | 0 | 1 | UNKNOWN | PROVED | UNKNOWN | PROVED | $facts$ = fact1: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãçã£é»ããªããªãããã¯éããæããªã fact2: ãã®ãŸããŸãLv.12ã¯éããæã ; $hypothesis$ = ãã®ãŸããŸãLv.12ã¯åŸé£ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{GA}x -> ¬{C}x fact2: {C}{aa} ; $hypothesis$ = {B}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããä»®ã«ä¿¡å¿æ·±ããªãä¿¡å¿æ·±ãããã©åéããæããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯åã | ¬((Ex): {A}x -> ({A}x & ¬{B}x)) | fact1: ããã®ãœã«ããœã¡ãLv.34ã¯åéããæããªãããšããããšã¯çå®ã§ãã fact2: ä»®ã«ãã®ãœã«ããœã¡ãLv.34ãä¿¡å¿æ·±ããšããããã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ãããŸãããã¯åéããæã | fact1: ¬{B}{a} fact2: {A}{a} -> ({A}{a} & {B}{a}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ã; assump1 & fact1 -> int1: ãã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ãäžæ¹ã§åéããæããªã; [assump1] & int1 -> int2: ããã®ãœã«ããœã¡ãLv.34ãä¿¡å¿æ·±ããšããã°ãã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ãããã©åéããæããšããããšã¯ãªãããšããããšã¯åã§ãããšããããšã¯ãªã; int2 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; assump1 & fact1 -> int1: ({A}{a} & ¬{B}{a}); [assump1] & int1 -> int2: {A}{a} -> ({A}{a} & ¬{B}{a}); int2 -> hypothesis;"
] | null | null | [] | null | 4 | 3 | 4 | 3 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããã®ãœã«ããœã¡ãLv.34ã¯åéããæããªãããšããããšã¯çå®ã§ãã fact2: ä»®ã«ãã®ãœã«ããœã¡ãLv.34ãä¿¡å¿æ·±ããšããããã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ãããŸãããã¯åéããæã ; $hypothesis$ = ããããä»®ã«ä¿¡å¿æ·±ããªãä¿¡å¿æ·±ãããã©åéããæããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯åã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ã; assump1 & fact1 -> int1: ãã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ãäžæ¹ã§åéããæããªã; [assump1] & int1 -> int2: ããã®ãœã«ããœã¡ãLv.34ãä¿¡å¿æ·±ããšããã°ãã®ãœã«ããœã¡ãLv.34ã¯ä¿¡å¿æ·±ãããã©åéããæããšããããšã¯ãªãããšããããšã¯åã§ãããšããããšã¯ãªã; int2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{B}{a} fact2: {A}{a} -> ({A}{a} & {B}{a}) ; $hypothesis$ = ¬((Ex): {A}x -> ({A}x & ¬{B}x)) ; $proof$ = | void -> assump1: {A}{a}; assump1 & fact1 -> int1: ({A}{a} & ¬{B}{a}); [assump1] & int1 -> int2: {A}{a} -> ({A}{a} & ¬{B}{a}); int2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ãããšããããšã¯ãªããå£ç
©ããªããäž¡æ¹ãšãã ããšããããšã¯æ£ãã | (¬{AA}{aa} v ¬{AB}{aa}) | fact1: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯ç»ãç¶ããªãããŸãã¯ããã¯å£ç
©ããäž¡æ¹ãšãã§ããããšããããšã¯ééãã ãšãããšãããã¯åŸ¡å®ãããšããããšã¯ãªãããšããããšã¯åã§ãªã fact2: ãã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãã fact3: ããä»®ã«ãããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ããªããå£ç
©ãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯æ£ããããšããããšã¯ééãã§ãããšããããã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãããªã fact4: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ç»ãç¶ããªãããããã¯å£ç
©ããªãããšããããšã¯åã§ãããšãããã埡å®ãããšããããšã¯ãªãããšããããšã¯æ£ãã fact5: ããããšããã¢ã³ã¹ã¿ãŒã¯ç»ãç¶ããããããã¯å£ç
©ããšããããšã¯ãªãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªããšããã°ãããã¯åŸ¡å®ãããªãããšããããšã¯åã§ãªã | fact1: (x): ¬(¬{AA}x v {AB}x) -> ¬{B}x fact2: {B}{aa} fact3: ¬(¬{AA}{aa} v {AB}{aa}) -> ¬{B}{aa} fact4: (x): ¬(¬{AA}x v ¬{AB}x) -> ¬{B}x fact5: (x): ¬({AA}x v ¬{AB}x) -> ¬{B}x | [
"fact4 -> int1: ä»®ã«ããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ããªãããããã¯ããã¯å£ç
©ããšããããšã¯ãªãããããã¯äž¡æ¹ã ããšããããšã¯èª€ã£ãŠãããšããããã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãããªã; void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ããªãããããã¯å£ç
©ããªãããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã; int1 & assump1 -> int2: ãã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"fact4 -> int1: ¬(¬{AA}{aa} v ¬{AB}{aa}) -> ¬{B}{aa}; void -> assump1: ¬(¬{AA}{aa} v ¬{AB}{aa}); int1 & assump1 -> int2: ¬{B}{aa}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯ç»ãç¶ããªãããŸãã¯ããã¯å£ç
©ããäž¡æ¹ãšãã§ããããšããããšã¯ééãã ãšãããšãããã¯åŸ¡å®ãããšããããšã¯ãªãããšããããšã¯åã§ãªã fact2: ãã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãã fact3: ããä»®ã«ãããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ããªããå£ç
©ãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯æ£ããããšããããšã¯ééãã§ãããšããããã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãããªã fact4: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ç»ãç¶ããªãããããã¯å£ç
©ããªãããšããããšã¯åã§ãããšãããã埡å®ãããšããããšã¯ãªãããšããããšã¯æ£ãã fact5: ããããšããã¢ã³ã¹ã¿ãŒã¯ç»ãç¶ããããããã¯å£ç
©ããšããããšã¯ãªãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªããšããã°ãããã¯åŸ¡å®ãããªãããšããããšã¯åã§ãªã ; $hypothesis$ = ããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ãããšããããšã¯ãªããå£ç
©ããªããäž¡æ¹ãšãã ããšããããšã¯æ£ãã ; $proof$ = | fact4 -> int1: ä»®ã«ããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ããªãããããã¯ããã¯å£ç
©ããšããããšã¯ãªãããããã¯äž¡æ¹ã ããšããããšã¯èª€ã£ãŠãããšããããã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãããªã; void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ã¿ãã¿ã¡ãLv.50ã¯ç»ãç¶ããªãããããã¯å£ç
©ããªãããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã; int1 & assump1 -> int2: ãã®ã¿ãã¿ã¡ãLv.50ã¯åŸ¡å®ãããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬(¬{AA}x v {AB}x) -> ¬{B}x fact2: {B}{aa} fact3: ¬(¬{AA}{aa} v {AB}{aa}) -> ¬{B}{aa} fact4: (x): ¬(¬{AA}x v ¬{AB}x) -> ¬{B}x fact5: (x): ¬({AA}x v ¬{AB}x) -> ¬{B}x ; $hypothesis$ = (¬{AA}{aa} v ¬{AB}{aa}) ; $proof$ = | fact4 -> int1: ¬(¬{AA}{aa} v ¬{AB}{aa}) -> ¬{B}{aa}; void -> assump1: ¬(¬{AA}{aa} v ¬{AB}{aa}); int1 & assump1 -> int2: ¬{B}{aa}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ããããã©ã³ãããããªãã°æããªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {B}x -> ¬{C}x | fact1: ãã®ãŽããŽãLv.96ã¯æã fact2: ãããã®ãœã¡ã
ãœãLv.80ããã©ã³ãããããšãããããã¯æã fact3: ãã®ãœã¡ã
ãœãLv.80ã¯åºãé£ã fact4: ãã®ãœã¡ã
ãœãLv.80ã¯æã fact5: ãããã®ãœã¡ã
ãœãLv.80ãåºãé£ããŠãã©ã³ãããããšããããã®ãœã¡ã
ãœãLv.80ã¯æããªã fact6: ããä»®ã«åœ±é¿ããæãã¢ã³ã¹ã¿ãŒããã©ã³ãããããšããã°ããã¯æŽ»åãæããªã | fact1: {C}{bj} fact2: {B}{a} -> {C}{a} fact3: {A}{a} fact4: {C}{a} fact5: ({A}{a} & {B}{a}) -> ¬{C}{a} fact6: (x): ({BI}x & {B}x) -> ¬{E}x | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã¡ã
ãœãLv.80ã¯ãã©ã³ãããã; fact3 & assump1 -> int1: ãã®ãœã¡ã
ãœãLv.80ã¯åºãé£ããŠããŸãã«ãã©ã³ãããã; int1 & fact5 -> int2: ãã®ãœã¡ã
ãœãLv.80ã¯æããªã; [assump1] & int2 -> int3: ä»®ã«ãã®ãœã¡ã
ãœãLv.80ããã©ã³ãããããšãããæããªã; int3 -> hypothesis;"
] | [
"void -> assump1: {B}{a}; fact3 & assump1 -> int1: ({A}{a} & {B}{a}); int1 & fact5 -> int2: ¬{C}{a}; [assump1] & int2 -> int3: {B}{a} -> ¬{C}{a}; int3 -> hypothesis;"
] | ãã®ãœã¡ã
ãœãLv.80ã¯åœ±é¿ããæããŠãã©ã³ãããããªã掻åãæããªã | ({BI}{a} & {B}{a}) -> ¬{E}{a} | [
"fact7 -> hypothesis;"
] | 1 | 5 | 4 | 5 | 4 | 4 | 0 | 4 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãã®ãŽããŽãLv.96ã¯æã fact2: ãããã®ãœã¡ã
ãœãLv.80ããã©ã³ãããããšãããããã¯æã fact3: ãã®ãœã¡ã
ãœãLv.80ã¯åºãé£ã fact4: ãã®ãœã¡ã
ãœãLv.80ã¯æã fact5: ãããã®ãœã¡ã
ãœãLv.80ãåºãé£ããŠãã©ã³ãããããšããããã®ãœã¡ã
ãœãLv.80ã¯æããªã fact6: ããä»®ã«åœ±é¿ããæãã¢ã³ã¹ã¿ãŒããã©ã³ãããããšããã°ããã¯æŽ»åãæããªã ; $hypothesis$ = ããããã©ã³ãããããªãã°æããªããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã¡ã
ãœãLv.80ã¯ãã©ã³ãããã; fact3 & assump1 -> int1: ãã®ãœã¡ã
ãœãLv.80ã¯åºãé£ããŠããŸãã«ãã©ã³ãããã; int1 & fact5 -> int2: ãã®ãœã¡ã
ãœãLv.80ã¯æããªã; [assump1] & int2 -> int3: ä»®ã«ãã®ãœã¡ã
ãœãLv.80ããã©ã³ãããããšãããæããªã; int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{bj} fact2: {B}{a} -> {C}{a} fact3: {A}{a} fact4: {C}{a} fact5: ({A}{a} & {B}{a}) -> ¬{C}{a} fact6: (x): ({BI}x & {B}x) -> ¬{E}x ; $hypothesis$ = (Ex): {B}x -> ¬{C}x ; $proof$ = | void -> assump1: {B}{a}; fact3 & assump1 -> int1: ({A}{a} & {B}{a}); int1 & fact5 -> int2: ¬{C}{a}; [assump1] & int2 -> int3: {B}{a} -> ¬{C}{a}; int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœã«ã
ãœã¡ã
Lv.15ã¯ãµã«ããµã«ããã | {C}{a} | fact1: ãã®ãœã«ã
ãœã¡ã
Lv.15ã¯èª¬æãé£ããªã fact2: ãã®ãœã«ã
ãœã¡ã
Lv.15ã¯èŠ³å
客ããããªã | fact1: ¬{B}{a} fact2: ¬{A}{a} | [
"fact2 & fact1 -> int1: ãã®ãœã«ã
ãœã¡ã
Lv.15ã¯èŠ³å
客ããããªãããŸã説æãé£ããšããããšã¯ãªã;"
] | [
"fact2 & fact1 -> int1: (¬{A}{a} & ¬{B}{a});"
] | null | null | [] | null | 2 | 2 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãœã«ã
ãœã¡ã
Lv.15ã¯èª¬æãé£ããªã fact2: ãã®ãœã«ã
ãœã¡ã
Lv.15ã¯èŠ³å
客ããããªã ; $hypothesis$ = ãã®ãœã«ã
ãœã¡ã
Lv.15ã¯ãµã«ããµã«ããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{B}{a} fact2: ¬{A}{a} ; $hypothesis$ = {C}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ãLv.14ã¯çæãã | {D}{c} | fact1: ããããã®ãŸããŸã®Lv.99ãæ¯èŠãããªãã°ãã®ã¿ãã¿ãLv.14ã¯æãããã fact2: ãã®ã·ãã·ã«Lv.8ã¯æãããã fact3: ããä»®ã«ãã®ãŸããŸã®Lv.99ãã§ã£ãããšãããšãã®ã¿ãã¿ãLv.14ã¯æãããã fact4: ãã®ã¿ãã¿ãLv.14ã¯åããèŸã fact5: ããä»®ã«ãã®ã¿ãã¿ãLv.14ãæãããããšãããšããã¯çæãã fact6: ããä»®ã«ãã®ãŸããŸã®Lv.99ãçæãããšããã°ãã®ã¿ãã¿ãLv.14ã¯ã§ã£ãã fact7: ãã®ãŸããŸã®Lv.99ã¯æ¯èŠããããããã¯ã§ã£ããããããã¯ã©ã¡ããã fact8: ãèšèŒã»èšé²ãããæãããããªãããšããããšã¯çå®ã§ãããšããã¢ã³ã¹ã¿ãŒã¯ãªã | fact1: {A}{a} -> {C}{c} fact2: {C}{fb} fact3: {B}{a} -> {C}{c} fact4: {EM}{c} fact5: {C}{c} -> {D}{c} fact6: {D}{a} -> {B}{c} fact7: ({A}{a} v {B}{a}) fact8: (x): ¬({E}x & ¬{C}x) | [
"fact7 & fact1 & fact3 -> int1: ãã®ã¿ãã¿ãLv.14ã¯æãããã; int1 & fact5 -> hypothesis;"
] | [
"fact7 & fact1 & fact3 -> int1: {C}{c}; int1 & fact5 -> hypothesis;"
] | ãã®ã¿ãã¿ãLv.14ã¯çæããªã | ¬{D}{c} | [
"fact9 -> int2: ããã®ãŸããŸã®Lv.99ã¯èšèŒã»èšé²ãããã©ããã¯æãããããªãããšããããšã¯ç¢ºãã§ãªã;"
] | 6 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããã®ãŸããŸã®Lv.99ãæ¯èŠãããªãã°ãã®ã¿ãã¿ãLv.14ã¯æãããã fact2: ãã®ã·ãã·ã«Lv.8ã¯æãããã fact3: ããä»®ã«ãã®ãŸããŸã®Lv.99ãã§ã£ãããšãããšãã®ã¿ãã¿ãLv.14ã¯æãããã fact4: ãã®ã¿ãã¿ãLv.14ã¯åããèŸã fact5: ããä»®ã«ãã®ã¿ãã¿ãLv.14ãæãããããšãããšããã¯çæãã fact6: ããä»®ã«ãã®ãŸããŸã®Lv.99ãçæãããšããã°ãã®ã¿ãã¿ãLv.14ã¯ã§ã£ãã fact7: ãã®ãŸããŸã®Lv.99ã¯æ¯èŠããããããã¯ã§ã£ããããããã¯ã©ã¡ããã fact8: ãèšèŒã»èšé²ãããæãããããªãããšããããšã¯çå®ã§ãããšããã¢ã³ã¹ã¿ãŒã¯ãªã ; $hypothesis$ = ãã®ã¿ãã¿ãLv.14ã¯çæãã ; $proof$ = | fact7 & fact1 & fact3 -> int1: ãã®ã¿ãã¿ãLv.14ã¯æãããã; int1 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} -> {C}{c} fact2: {C}{fb} fact3: {B}{a} -> {C}{c} fact4: {EM}{c} fact5: {C}{c} -> {D}{c} fact6: {D}{a} -> {B}{c} fact7: ({A}{a} v {B}{a}) fact8: (x): ¬({E}x & ¬{C}x) ; $hypothesis$ = {D}{c} ; $proof$ = | fact7 & fact1 & fact3 -> int1: {C}{c}; int1 & fact5 -> hypothesis; __PROVED__ |
0.3 | ããŽã«ããŽã«ãLv.19äºä»¶ã¯èµ·ããªãããšããããšã¯æãç«ã€ | ¬{F} | fact1: æããããšããããšããã³å匷ããšããããšãèµ·ãã fact2: å匷ããšããããšã¯çºçããªããšãããæããããšããããšã¯èµ·ããªããŠãŸãæºãŸãæããšããããšã¯èµ·ããªã fact3: ãœããœãLv.54äºä»¶ãçãã fact4: ããä»®ã«æããããšã§ã¯ãªãå匷ããšããããšãèµ·ãããšãããšã·ã¡ãã·ã«ã
Lv.58äºä»¶ãèµ·ãã fact5: ç¯ãæããšããããšãèµ·ãã fact6: ãããã¿ãã¿ãLv.24äºä»¶ãçºçããªããšãããã·ã¡ãã·ã«ã
Lv.58äºä»¶ã§ã¯ãªããœããœãLv.54äºä»¶ã¯çºçãã fact7: ä»®ã«ã·ã¡ãã·ã«ã
Lv.58äºä»¶ãšãœããœãLv.54äºä»¶ã©ã¡ãããèµ·ããã°ãŽã«ããŽã«ãLv.19äºä»¶ã¯çããªã fact8: ããŽã¡ããŽã¡ã
Lv.97äºä»¶ã¯çºçããªããããããŸããŸã«ãLv.6äºä»¶ãèµ·ããããšããããšã¯ãŸããŸã«ãLv.6äºä»¶ã«ããçãã fact9: ä»®ã«å匷ããšããããšãçãããªãæããããšã§ã¯ãªãå匷ããšããããšãçºçãã | fact1: ({A} & {B}) fact2: ¬{B} -> (¬{A} & ¬{JE}) fact3: {E} fact4: (¬{D} & {B}) -> {C} fact5: {DM} fact6: ¬{G} -> (¬{C} & {E}) fact7: ({C} & {E}) -> ¬{F} fact8: {HB} -> (¬{BR} & {HB}) fact9: {B} -> (¬{D} & {B}) | [
"fact1 -> int1: å匷ããšããããšãèµ·ãã; int1 & fact9 -> int2: æããããšã§ã¯ãªããŠå匷ããšããããšãèµ·ãã; int2 & fact4 -> int3: ã·ã¡ãã·ã«ã
Lv.58äºä»¶ãçãã; int3 & fact3 -> int4: ã·ã¡ãã·ã«ã
Lv.58äºä»¶ããã³ãœããœãLv.54äºä»¶äž¡æ¹ãçãã; int4 & fact7 -> hypothesis;"
] | [
"fact1 -> int1: {B}; int1 & fact9 -> int2: (¬{D} & {B}); int2 & fact4 -> int3: {C}; int3 & fact3 -> int4: ({C} & {E}); int4 & fact7 -> hypothesis;"
] | æºãŸãæããšããããšã¯èµ·ããªã | ¬{JE} | [] | 6 | 5 | 5 | 5 | 5 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: æããããšããããšããã³å匷ããšããããšãèµ·ãã fact2: å匷ããšããããšã¯çºçããªããšãããæããããšããããšã¯èµ·ããªããŠãŸãæºãŸãæããšããããšã¯èµ·ããªã fact3: ãœããœãLv.54äºä»¶ãçãã fact4: ããä»®ã«æããããšã§ã¯ãªãå匷ããšããããšãèµ·ãããšãããšã·ã¡ãã·ã«ã
Lv.58äºä»¶ãèµ·ãã fact5: ç¯ãæããšããããšãèµ·ãã fact6: ãããã¿ãã¿ãLv.24äºä»¶ãçºçããªããšãããã·ã¡ãã·ã«ã
Lv.58äºä»¶ã§ã¯ãªããœããœãLv.54äºä»¶ã¯çºçãã fact7: ä»®ã«ã·ã¡ãã·ã«ã
Lv.58äºä»¶ãšãœããœãLv.54äºä»¶ã©ã¡ãããèµ·ããã°ãŽã«ããŽã«ãLv.19äºä»¶ã¯çããªã fact8: ããŽã¡ããŽã¡ã
Lv.97äºä»¶ã¯çºçããªããããããŸããŸã«ãLv.6äºä»¶ãèµ·ããããšããããšã¯ãŸããŸã«ãLv.6äºä»¶ã«ããçãã fact9: ä»®ã«å匷ããšããããšãçãããªãæããããšã§ã¯ãªãå匷ããšããããšãçºçãã ; $hypothesis$ = ããŽã«ããŽã«ãLv.19äºä»¶ã¯èµ·ããªãããšããããšã¯æãç«ã€ ; $proof$ = | fact1 -> int1: å匷ããšããããšãèµ·ãã; int1 & fact9 -> int2: æããããšã§ã¯ãªããŠå匷ããšããããšãèµ·ãã; int2 & fact4 -> int3: ã·ã¡ãã·ã«ã
Lv.58äºä»¶ãçãã; int3 & fact3 -> int4: ã·ã¡ãã·ã«ã
Lv.58äºä»¶ããã³ãœããœãLv.54äºä»¶äž¡æ¹ãçãã; int4 & fact7 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} & {B}) fact2: ¬{B} -> (¬{A} & ¬{JE}) fact3: {E} fact4: (¬{D} & {B}) -> {C} fact5: {DM} fact6: ¬{G} -> (¬{C} & {E}) fact7: ({C} & {E}) -> ¬{F} fact8: {HB} -> (¬{BR} & {HB}) fact9: {B} -> (¬{D} & {B}) ; $hypothesis$ = ¬{F} ; $proof$ = | fact1 -> int1: {B}; int1 & fact9 -> int2: (¬{D} & {B}); int2 & fact4 -> int3: {C}; int3 & fact3 -> int4: ({C} & {E}); int4 & fact7 -> hypothesis; __PROVED__ |
0.3 | ãã®ãã¡ã
ããLv.70ã¯çéãé£ããªã | ¬{E}{c} | fact1: ããä»®ã«ãã®ãããã«ãLv.32ã¯çžå¯Ÿç«ãããšãããšãèã£ãºãããªãããããã¯ããã¯ãã€ããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact2: ãšããã¢ã³ã¹ã¿ãŒãèµ·ããåŸãªããªãã°æ²é»ãããªã fact3: ããªèãã¢ã³ã¹ã¿ãŒã¯èµ·ããåŸãªã fact4: ä»®ã«ããã¢ã³ã¹ã¿ãŒãçéãé£ããšãããšããªèã fact5: ä»®ã«ããã®ãŸã«ããŸãLv.92ã¯èµ·ããåŸãããšããããšã¯æ£ãããšãããšãã®ãã¡ã
ããLv.70ã¯ããªèã fact6: ä»®ã«ãã®ãããã«ãLv.32ãæ蚎ãããšããããšã¯ãªããšããã°ãã®ãããã«ãLv.32ã¯çéãé£ãããŸãå®çµãã fact7: ä»®ã«ãã®ãããã«ãLv.32ãæ²é»ããšããããã®ãŸã«ããŸãLv.92ã¯èµ·ããåŸã fact8: ãã®ãããã«ãLv.32ãæ²é»ãããªããªããã®ãã«ããã«Lv.63ã¯ãã€ãããããçžå¯Ÿç«ãã fact9: ãã®ãããã«ãLv.32ã¯çžå¯Ÿç«ãã fact10: ä»®ã«ããã®ãããã«ãLv.32ã¯èã£ãºãããªãããããã¯ãã€ããªãããããã¯äž¡æ¹ã ããšããããšã¯æãç«ããªããšããã°ãã®ãããã«ãLv.32ã¯æ²é»ã fact11: ãã®ãã¡ã
ããLv.70ãããªèããšãããšããã¯çéãé£ã | fact1: {A}{a} -> ¬(¬{AA}{a} v ¬{AB}{a}) fact2: (x): ¬{C}x -> ¬{B}x fact3: (x): {D}x -> ¬{C}x fact4: (x): {E}x -> {D}x fact5: {C}{b} -> {D}{c} fact6: ¬{G}{a} -> ({E}{a} & {F}{a}) fact7: {B}{a} -> {C}{b} fact8: ¬{B}{a} -> ({AB}{em} & {A}{em}) fact9: {A}{a} fact10: ¬(¬{AA}{a} v ¬{AB}{a}) -> {B}{a} fact11: {D}{c} -> {E}{c} | [
"fact1 & fact9 -> int1: ããã®ãããã«ãLv.32ã¯èã£ãºãããªãããããã¯ããã¯ãã€ããªããäž¡æ¹ã ããšããããšã¯åã§ãã; int1 & fact10 -> int2: ãã®ãããã«ãLv.32ã¯æ²é»ã; int2 & fact7 -> int3: ãã®ãŸã«ããŸãLv.92ã¯èµ·ããåŸã; int3 & fact5 -> int4: ãã®ãã¡ã
ããLv.70ã¯ããªèã; int4 & fact11 -> hypothesis;"
] | [
"fact1 & fact9 -> int1: ¬(¬{AA}{a} v ¬{AB}{a}); int1 & fact10 -> int2: {B}{a}; int2 & fact7 -> int3: {C}{b}; int3 & fact5 -> int4: {D}{c}; int4 & fact11 -> hypothesis;"
] | ãã®ãã«ããã«Lv.63ã¯ãã€ã | {AB}{em} | [
"fact14 -> int5: ãããã®ãããã«ãLv.32ãèµ·ããåŸãªããšãããæ²é»ãããªã; fact16 -> int6: ããããã®ãããã«ãLv.32ãããªèããšããã°ããã¯èµ·ããåŸãªã; fact15 -> int7: ããä»®ã«ããã®ãããã«ãLv.32ã¯çéãé£ãããšããããšã¯äºå®ã§ãããšãããããã¯ããªèã;"
] | 7 | 5 | 5 | 5 | 5 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãããã«ãLv.32ã¯çžå¯Ÿç«ãããšãããšãèã£ãºãããªãããããã¯ããã¯ãã€ããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact2: ãšããã¢ã³ã¹ã¿ãŒãèµ·ããåŸãªããªãã°æ²é»ãããªã fact3: ããªèãã¢ã³ã¹ã¿ãŒã¯èµ·ããåŸãªã fact4: ä»®ã«ããã¢ã³ã¹ã¿ãŒãçéãé£ããšãããšããªèã fact5: ä»®ã«ããã®ãŸã«ããŸãLv.92ã¯èµ·ããåŸãããšããããšã¯æ£ãããšãããšãã®ãã¡ã
ããLv.70ã¯ããªèã fact6: ä»®ã«ãã®ãããã«ãLv.32ãæ蚎ãããšããããšã¯ãªããšããã°ãã®ãããã«ãLv.32ã¯çéãé£ãããŸãå®çµãã fact7: ä»®ã«ãã®ãããã«ãLv.32ãæ²é»ããšããããã®ãŸã«ããŸãLv.92ã¯èµ·ããåŸã fact8: ãã®ãããã«ãLv.32ãæ²é»ãããªããªããã®ãã«ããã«Lv.63ã¯ãã€ãããããçžå¯Ÿç«ãã fact9: ãã®ãããã«ãLv.32ã¯çžå¯Ÿç«ãã fact10: ä»®ã«ããã®ãããã«ãLv.32ã¯èã£ãºãããªãããããã¯ãã€ããªãããããã¯äž¡æ¹ã ããšããããšã¯æãç«ããªããšããã°ãã®ãããã«ãLv.32ã¯æ²é»ã fact11: ãã®ãã¡ã
ããLv.70ãããªèããšãããšããã¯çéãé£ã ; $hypothesis$ = ãã®ãã¡ã
ããLv.70ã¯çéãé£ããªã ; $proof$ = | fact1 & fact9 -> int1: ããã®ãããã«ãLv.32ã¯èã£ãºãããªãããããã¯ããã¯ãã€ããªããäž¡æ¹ã ããšããããšã¯åã§ãã; int1 & fact10 -> int2: ãã®ãããã«ãLv.32ã¯æ²é»ã; int2 & fact7 -> int3: ãã®ãŸã«ããŸãLv.92ã¯èµ·ããåŸã; int3 & fact5 -> int4: ãã®ãã¡ã
ããLv.70ã¯ããªèã; int4 & fact11 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> ¬(¬{AA}{a} v ¬{AB}{a}) fact2: (x): ¬{C}x -> ¬{B}x fact3: (x): {D}x -> ¬{C}x fact4: (x): {E}x -> {D}x fact5: {C}{b} -> {D}{c} fact6: ¬{G}{a} -> ({E}{a} & {F}{a}) fact7: {B}{a} -> {C}{b} fact8: ¬{B}{a} -> ({AB}{em} & {A}{em}) fact9: {A}{a} fact10: ¬(¬{AA}{a} v ¬{AB}{a}) -> {B}{a} fact11: {D}{c} -> {E}{c} ; $hypothesis$ = ¬{E}{c} ; $proof$ = | fact1 & fact9 -> int1: ¬(¬{AA}{a} v ¬{AB}{a}); int1 & fact10 -> int2: {B}{a}; int2 & fact7 -> int3: {C}{b}; int3 & fact5 -> int4: {D}{c}; int4 & fact11 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœãLv.70ã¯ã¡ããæããªã | ¬{F}{c} | fact1: ããããã®ãŸã¡ããŸãªLv.77ã幌ããªããã®ãŸã¡ããŸãªLv.77ã¯å¿ã fact2: ãã®ãŸã¡ããŸãªLv.77ãå¿ããšããããã®ãœããœãLv.70ã¯ã¿ã€ãã«ããã fact3: ãã®ã·ãã·ãLv.28ã¯ãæããŠç®èŠãŸãã fact4: ãããã®ãŽã«ããŽã¡ãLv.30ãç®èŠãŸãããšãããšãã®ãŸã¡ããŸãªLv.77ã¯å¹Œã fact5: ãã®ãœããœãLv.70ã¯å匷ã fact6: ããä»®ã«ãã®ãœããœãLv.70ãã¿ã€ãã«ããããããã«ãããå匷ããšããã°ãã®ãœããœãLv.70ã¯ã¡ããæããšããããšã¯ãªã fact7: 幌ããªãã¢ã³ã¹ã¿ãŒã¯ã¡ããæããŠå ããŠç®èŠãŸãã | fact1: {B}{b} -> {C}{b} fact2: {C}{b} -> {D}{c} fact3: ({EB}{fb} & {A}{fb}) fact4: {A}{a} -> {B}{b} fact5: {E}{c} fact6: ({D}{c} & {E}{c}) -> ¬{F}{c} fact7: (x): ¬{B}x -> ({F}x & {A}x) | [] | [] | ãã®ãœããœãLv.70ã¯ã¡ããæã | {F}{c} | [
"fact8 -> int1: ããããã®ãœããœãLv.70ã¯å¹Œããªãããšããããšã¯æ¬åœã§ãããšããã°ããã®ãœããœãLv.70ã¯ã¡ããæããŠããã«ç®èŠãŸããããšããããšã¯çå®ã§ãã;"
] | 4 | 5 | 5 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®ãŸã¡ããŸãªLv.77ã幌ããªããã®ãŸã¡ããŸãªLv.77ã¯å¿ã fact2: ãã®ãŸã¡ããŸãªLv.77ãå¿ããšããããã®ãœããœãLv.70ã¯ã¿ã€ãã«ããã fact3: ãã®ã·ãã·ãLv.28ã¯ãæããŠç®èŠãŸãã fact4: ãããã®ãŽã«ããŽã¡ãLv.30ãç®èŠãŸãããšãããšãã®ãŸã¡ããŸãªLv.77ã¯å¹Œã fact5: ãã®ãœããœãLv.70ã¯å匷ã fact6: ããä»®ã«ãã®ãœããœãLv.70ãã¿ã€ãã«ããããããã«ãããå匷ããšããã°ãã®ãœããœãLv.70ã¯ã¡ããæããšããããšã¯ãªã fact7: 幌ããªãã¢ã³ã¹ã¿ãŒã¯ã¡ããæããŠå ããŠç®èŠãŸãã ; $hypothesis$ = ãã®ãœããœãLv.70ã¯ã¡ããæããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{b} -> {C}{b} fact2: {C}{b} -> {D}{c} fact3: ({EB}{fb} & {A}{fb}) fact4: {A}{a} -> {B}{b} fact5: {E}{c} fact6: ({D}{c} & {E}{c}) -> ¬{F}{c} fact7: (x): ¬{B}x -> ({F}x & {A}x) ; $hypothesis$ = ¬{F}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | 転å«ããããšã¯èµ·ãããªããçšé ããšããããšã¯èµ·ããªã | (¬{D} & ¬{C}) | fact1: ä»®ã«ç©çããããšããããšã¯çããªããšãããã転å«ããããšã¯çºçããªããæŽã«çšé ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact2: ãç©çããããšããããšãèµ·ãããæãé£ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact3: ãããããã¡ãLv.20äºä»¶ãèµ·ãããšããã°è»¢å«ããããšã¯èµ·ãããªããŠç©çããããšããããšãèµ·ãã fact4: æãé£ããšããããšã¯èµ·ããªã | fact1: ¬{A} -> ¬(¬{D} & ¬{C}) fact2: ¬({A} & ¬{B}) fact3: {F} -> (¬{D} & {A}) fact4: ¬{B} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããç©çããããšããããšãèµ·ãã; assump1 & fact4 -> int1: ç©çããããšããããšãçãããæãé£ããšããããšã¯èµ·ãããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãç©çããããšããããšã¯èµ·ãããªãããšããããšã¯çå®ã ; int3 & fact1 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact4 -> int1: ({A} & ¬{B}); int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}; int3 & fact1 -> hypothesis;"
] | 転å«ããããšã¯èµ·ãããªããçšé ããšããããšã¯èµ·ããªã | (¬{D} & ¬{C}) | [] | 4 | 5 | 4 | 5 | 4 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ç©çããããšããããšã¯çããªããšãããã転å«ããããšã¯çºçããªããæŽã«çšé ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact2: ãç©çããããšããããšãèµ·ãããæãé£ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact3: ãããããã¡ãLv.20äºä»¶ãèµ·ãããšããã°è»¢å«ããããšã¯èµ·ãããªããŠç©çããããšããããšãèµ·ãã fact4: æãé£ããšããããšã¯èµ·ããªã ; $hypothesis$ = 転å«ããããšã¯èµ·ãããªããçšé ããšããããšã¯èµ·ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããç©çããããšããããšãèµ·ãã; assump1 & fact4 -> int1: ç©çããããšããããšãçãããæãé£ããšããããšã¯èµ·ãããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãç©çããããšããããšã¯èµ·ãããªãããšããããšã¯çå®ã ; int3 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A} -> ¬(¬{D} & ¬{C}) fact2: ¬({A} & ¬{B}) fact3: {F} -> (¬{D} & {A}) fact4: ¬{B} ; $hypothesis$ = (¬{D} & ¬{C}) ; $proof$ = | void -> assump1: {A}; assump1 & fact4 -> int1: ({A} & ¬{B}); int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}; int3 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãæµ
ããšããããšã¯çããªãããŸãã¯ããã«ã»ã¯ãªãã¯ããããšãèµ·ããããšããããšã¯æãç«ããªã | ¬(¬{C} v {D}) | fact1: ãŸããŸã«ãLv.20äºä»¶ãèµ·ãããšããããšã¯å®¹æããšããããšããã£ããã§ãã fact2: 容æããšããããšã¯èµ·ãããªããšãããæµ
ããšããããšã¯çããªãããããã¯ããã«ã»ã¯ãªãã¯ããããšãèµ·ãã fact3: ãŸããŸã«ãLv.20äºä»¶ã¯çºçããªã | fact1: {A} -> {B} fact2: ¬{A} -> (¬{C} v {D}) fact3: ¬{B} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããã容æããšããããšãçºçãã; fact1 & assump1 -> int1: ãŸããŸã«ãLv.20äºä»¶ãèµ·ãã; int1 & fact3 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: 容æããšããããšã¯èµ·ãããªã; int3 & fact2 -> hypothesis;"
] | [
"void -> assump1: {A}; fact1 & assump1 -> int1: {B}; int1 & fact3 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}; int3 & fact2 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãŸããŸã«ãLv.20äºä»¶ãèµ·ãããšããããšã¯å®¹æããšããããšããã£ããã§ãã fact2: 容æããšããããšã¯èµ·ãããªããšãããæµ
ããšããããšã¯çããªãããããã¯ããã«ã»ã¯ãªãã¯ããããšãèµ·ãã fact3: ãŸããŸã«ãLv.20äºä»¶ã¯çºçããªã ; $hypothesis$ = ãæµ
ããšããããšã¯çããªãããŸãã¯ããã«ã»ã¯ãªãã¯ããããšãèµ·ããããšããããšã¯æãç«ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããã容æããšããããšãçºçãã; fact1 & assump1 -> int1: ãŸããŸã«ãLv.20äºä»¶ãèµ·ãã; int1 & fact3 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: 容æããšããããšã¯èµ·ãããªã; int3 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} -> {B} fact2: ¬{A} -> (¬{C} v {D}) fact3: ¬{B} ; $hypothesis$ = ¬(¬{C} v {D}) ; $proof$ = | void -> assump1: {A}; fact1 & assump1 -> int1: {B}; int1 & fact3 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}; int3 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã¿ãªã¿ã«ãLv.3ã¯æ°ä»ãæããªãããã©éè¿ãããšããããšã¯èª€ãã | ¬(¬{AA}{aa} & {AB}{aa}) | fact1: ä»®ã«æ°ä»ãæããªãã¢ã³ã¹ã¿ãŒãéè¿ããšãããšèãæããªã fact2: ãã®ã¿ãªã¿ã«ãLv.3ã¯èãæã | fact1: (x): (¬{AA}x & {AB}x) -> ¬{B}x fact2: {B}{aa} | [
"fact1 -> int1: ããããã®ã¿ãªã¿ã«ãLv.3ãæ°ä»ãæããªããã©éè¿ããšããã°ãã®ã¿ãªã¿ã«ãLv.3ã¯èãæããšããããšã¯ãªã; void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãªã¿ã«ãLv.3ã¯æ°ä»ãæããªãããã©éè¿ã; int1 & assump1 -> int2: ããã®ã¿ãªã¿ã«ãLv.3ã¯èãæããªãããšããããšã¯ç¢ºãã ; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"fact1 -> int1: (¬{AA}{aa} & {AB}{aa}) -> ¬{B}{aa}; void -> assump1: (¬{AA}{aa} & {AB}{aa}); int1 & assump1 -> int2: ¬{B}{aa}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«æ°ä»ãæããªãã¢ã³ã¹ã¿ãŒãéè¿ããšãããšèãæããªã fact2: ãã®ã¿ãªã¿ã«ãLv.3ã¯èãæã ; $hypothesis$ = ããã®ã¿ãªã¿ã«ãLv.3ã¯æ°ä»ãæããªãããã©éè¿ãããšããããšã¯èª€ãã ; $proof$ = | fact1 -> int1: ããããã®ã¿ãªã¿ã«ãLv.3ãæ°ä»ãæããªããã©éè¿ããšããã°ãã®ã¿ãªã¿ã«ãLv.3ã¯èãæããšããããšã¯ãªã; void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãªã¿ã«ãLv.3ã¯æ°ä»ãæããªãããã©éè¿ã; int1 & assump1 -> int2: ããã®ã¿ãªã¿ã«ãLv.3ã¯èãæããªãããšããããšã¯ç¢ºãã ; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): (¬{AA}x & {AB}x) -> ¬{B}x fact2: {B}{aa} ; $hypothesis$ = ¬(¬{AA}{aa} & {AB}{aa}) ; $proof$ = | fact1 -> int1: (¬{AA}{aa} & {AB}{aa}) -> ¬{B}{aa}; void -> assump1: (¬{AA}{aa} & {AB}{aa}); int1 & assump1 -> int2: ¬{B}{aa}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.21ã¯ããããšããªã | ¬{B}{aa} | fact1: ããã®ã·ãã·ãLv.21ã¯éãããšããããšã¯æãç«ã€ fact2: ãããããã¢ã³ã¹ã¿ãŒãããããšããªããšãããéããªã | fact1: {C}{aa} fact2: (x): ¬{B}x -> ¬{C}x | [
"fact2 -> int1: ããããã®ã·ãã·ãLv.21ãããããšããªããšãããšãã®ã·ãã·ãLv.21ã¯éããªã; void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.21ã¯ããããšããªã; int1 & assump1 -> int2: ããã®ã·ãã·ãLv.21ã¯éããªãããšããããšã¯æãç«ã€; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"fact2 -> int1: ¬{B}{aa} -> ¬{C}{aa}; void -> assump1: ¬{B}{aa}; int1 & assump1 -> int2: ¬{C}{aa}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããã®ã·ãã·ãLv.21ã¯éãããšããããšã¯æãç«ã€ fact2: ãããããã¢ã³ã¹ã¿ãŒãããããšããªããšãããéããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.21ã¯ããããšããªã ; $proof$ = | fact2 -> int1: ããããã®ã·ãã·ãLv.21ãããããšããªããšãããšãã®ã·ãã·ãLv.21ã¯éããªã; void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.21ã¯ããããšããªã; int1 & assump1 -> int2: ããã®ã·ãã·ãLv.21ã¯éããªãããšããããšã¯æãç«ã€; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{aa} fact2: (x): ¬{B}x -> ¬{C}x ; $hypothesis$ = ¬{B}{aa} ; $proof$ = | fact2 -> int1: ¬{B}{aa} -> ¬{C}{aa}; void -> assump1: ¬{B}{aa}; int1 & assump1 -> int2: ¬{C}{aa}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãã¡ããã«ã
Lv.29ã¯å ãé£ããšããããšã¯ãªã | ¬{E}{a} | fact1: ãã®ãã¡ããã«ã
Lv.29ãæã¡æããªããã®ãã¡ããã«ã
Lv.29ã¯å ãé£ã fact2: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯çœªæ·±ãããã®äžèµ·ããæã fact3: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çŽçšãããæŽã«ãã©ããã©ããã fact4: ããããã®ãã«ãããLv.28ãèµ·ããæããšãããšãã®ãã«ãããLv.28ã¯å¯æã fact5: ãããã®ãã«ãããLv.28ãå¯æããªããã®ãã¡ããã«ã
Lv.29ã¯æã¡æã fact6: ãã®ãã¡ããã«ã
Lv.29ã¯å¯æã fact7: ãã®ãã«ãããLv.28ãæã¡æããªãèµ·ããæã | fact1: {D}{a} -> {E}{a} fact2: (x): ({A}x & {B}x) fact3: (x): ({FA}x & {CB}x) fact4: {B}{aa} -> {C}{aa} fact5: {C}{aa} -> {D}{a} fact6: {C}{a} fact7: {D}{aa} -> {B}{aa} | [
"fact2 -> int1: ãã®ãã«ãããLv.28ã¯çœªæ·±ããããã«èµ·ããæã; int1 -> int2: ãã®ãã«ãããLv.28ã¯èµ·ããæã; int2 & fact4 -> int3: ãã®ãã«ãããLv.28ã¯å¯æã; int3 & fact5 -> int4: ãã®ãã¡ããã«ã
Lv.29ã¯æã¡æã; int4 & fact1 -> hypothesis;"
] | [
"fact2 -> int1: ({A}{aa} & {B}{aa}); int1 -> int2: {B}{aa}; int2 & fact4 -> int3: {C}{aa}; int3 & fact5 -> int4: {D}{a}; int4 & fact1 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ãã¡ããã«ã
Lv.29ãæã¡æããªããã®ãã¡ããã«ã
Lv.29ã¯å ãé£ã fact2: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯çœªæ·±ãããã®äžèµ·ããæã fact3: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çŽçšãããæŽã«ãã©ããã©ããã fact4: ããããã®ãã«ãããLv.28ãèµ·ããæããšãããšãã®ãã«ãããLv.28ã¯å¯æã fact5: ãããã®ãã«ãããLv.28ãå¯æããªããã®ãã¡ããã«ã
Lv.29ã¯æã¡æã fact6: ãã®ãã¡ããã«ã
Lv.29ã¯å¯æã fact7: ãã®ãã«ãããLv.28ãæã¡æããªãèµ·ããæã ; $hypothesis$ = ãã®ãã¡ããã«ã
Lv.29ã¯å ãé£ããšããããšã¯ãªã ; $proof$ = | fact2 -> int1: ãã®ãã«ãããLv.28ã¯çœªæ·±ããããã«èµ·ããæã; int1 -> int2: ãã®ãã«ãããLv.28ã¯èµ·ããæã; int2 & fact4 -> int3: ãã®ãã«ãããLv.28ã¯å¯æã; int3 & fact5 -> int4: ãã®ãã¡ããã«ã
Lv.29ã¯æã¡æã; int4 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {D}{a} -> {E}{a} fact2: (x): ({A}x & {B}x) fact3: (x): ({FA}x & {CB}x) fact4: {B}{aa} -> {C}{aa} fact5: {C}{aa} -> {D}{a} fact6: {C}{a} fact7: {D}{aa} -> {B}{aa} ; $hypothesis$ = ¬{E}{a} ; $proof$ = | fact2 -> int1: ({A}{aa} & {B}{aa}); int1 -> int2: {B}{aa}; int2 & fact4 -> int3: {C}{aa}; int3 & fact5 -> int4: {D}{a}; int4 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ããããLv.2ã¯èŠªãããããšããããšã¯æãç«ã€ | {E}{c} | fact1: ããä»®ã«çãŸãæãã¢ã³ã¹ã¿ãŒãçèŠãããªãã°ãã®ãœã«ããœãLv.7ã¯é€é¬Œã£ãœããªã fact2: ãããã®ãœã«ããœãLv.7ãé€é¬Œã£ãœããšããããšã¯ãªããšããã°ãã®ããããLv.2ã¯é€é¬Œã£ãœããªã fact3: ãã®ãœã¡ããœã¡ã
Lv.47ã¯çèŠãã fact4: ãã®ãœã¡ããœã¡ã
Lv.47ã¯çãŸãæã fact5: ä»®ã«ãããã®ãœã¡ããœã¡ã
Lv.47ã¯èŠªããããªããã©çèŠããããšããããšã¯æãç«ããªãããšããããšã¯çå®ãªããã®ããããLv.2ã¯èŠªããã fact6: ããããã®ãœã«ããœãLv.7ãé€é¬Œã£ãœããªããªããã®ããããLv.2ã¯é€é¬Œã£ãœããªããããã«èŠªããããªã | fact1: (x): ({A}x & {B}x) -> ¬{C}{b} fact2: ¬{C}{b} -> ¬{C}{c} fact3: {B}{a} fact4: {A}{a} fact5: ¬(¬{E}{a} & {B}{a}) -> {E}{c} fact6: ¬{C}{b} -> (¬{C}{c} & ¬{E}{c}) | [
"fact4 & fact3 -> int1: ãã®ãœã¡ããœã¡ã
Lv.47ã¯çãŸãæããŠããã¯çèŠãã; int1 -> int2: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çãŸãæããçèŠãã; int2 & fact1 -> int3: ãã®ãœã«ããœãLv.7ã¯é€é¬Œã£ãœããªã; int3 & fact6 -> int4: ãã®ããããLv.2ã¯é€é¬Œã£ãœããªãã芪ããããªã; int4 -> hypothesis;"
] | [
"fact4 & fact3 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact1 -> int3: ¬{C}{b}; int3 & fact6 -> int4: (¬{C}{c} & ¬{E}{c}); int4 -> hypothesis;"
] | ããã®ããããLv.2ã¯èŠªãããããšããããšã¯æãç«ã€ | {E}{c} | [] | 5 | 5 | 5 | 5 | 5 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«çãŸãæãã¢ã³ã¹ã¿ãŒãçèŠãããªãã°ãã®ãœã«ããœãLv.7ã¯é€é¬Œã£ãœããªã fact2: ãããã®ãœã«ããœãLv.7ãé€é¬Œã£ãœããšããããšã¯ãªããšããã°ãã®ããããLv.2ã¯é€é¬Œã£ãœããªã fact3: ãã®ãœã¡ããœã¡ã
Lv.47ã¯çèŠãã fact4: ãã®ãœã¡ããœã¡ã
Lv.47ã¯çãŸãæã fact5: ä»®ã«ãããã®ãœã¡ããœã¡ã
Lv.47ã¯èŠªããããªããã©çèŠããããšããããšã¯æãç«ããªãããšããããšã¯çå®ãªããã®ããããLv.2ã¯èŠªããã fact6: ããããã®ãœã«ããœãLv.7ãé€é¬Œã£ãœããªããªããã®ããããLv.2ã¯é€é¬Œã£ãœããªããããã«èŠªããããªã ; $hypothesis$ = ããã®ããããLv.2ã¯èŠªãããããšããããšã¯æãç«ã€ ; $proof$ = | fact4 & fact3 -> int1: ãã®ãœã¡ããœã¡ã
Lv.47ã¯çãŸãæããŠããã¯çèŠãã; int1 -> int2: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çãŸãæããçèŠãã; int2 & fact1 -> int3: ãã®ãœã«ããœãLv.7ã¯é€é¬Œã£ãœããªã; int3 & fact6 -> int4: ãã®ããããLv.2ã¯é€é¬Œã£ãœããªãã芪ããããªã; int4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ({A}x & {B}x) -> ¬{C}{b} fact2: ¬{C}{b} -> ¬{C}{c} fact3: {B}{a} fact4: {A}{a} fact5: ¬(¬{E}{a} & {B}{a}) -> {E}{c} fact6: ¬{C}{b} -> (¬{C}{c} & ¬{E}{c}) ; $hypothesis$ = {E}{c} ; $proof$ = | fact4 & fact3 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact1 -> int3: ¬{C}{b}; int3 & fact6 -> int4: (¬{C}{c} & ¬{E}{c}); int4 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãã«ããã¡ã
Lv.61ã¯åãæããŠããã¯é話åºæ¥ãããšããããšã¯ééãã§ãã | ¬({E}{c} & {D}{c}) | fact1: ããä»®ã«ãã®ãŽã«ã
ãŽã¡ã
Lv.41ããã©ã³ã¹è¯ããšããããã®ãã«ããã¡ã
Lv.61ã¯é話åºæ¥ã fact2: ä»®ã«ããã¢ã³ã¹ã¿ãŒã調ã¹æããç解ãèŸããªããã®ãŽã«ã
ãŽã¡ã
Lv.41ã¯ãã©ã³ã¹è¯ã fact3: ãã®ã¿ãã¿ãLv.56ã¯èª¿ã¹æã fact4: ãã®ã¿ãã¿ãLv.56ã¯ç解ãèŸã fact5: ãã®ãã«ããã¡ã
Lv.61ã¯åãæã | fact1: {C}{b} -> {D}{c} fact2: (x): ({A}x & {B}x) -> {C}{b} fact3: {A}{a} fact4: {B}{a} fact5: {E}{c} | [
"fact3 & fact4 -> int1: ãã®ã¿ãã¿ãLv.56ã¯èª¿ã¹æããŠãŸãããã¯ç解ãèŸã; int1 -> int2: äœããã®ã¢ã³ã¹ã¿ãŒã¯èª¿ã¹æããããã«ããã¯ç解ãèŸã; int2 & fact2 -> int3: ãã®ãŽã«ã
ãŽã¡ã
Lv.41ã¯ãã©ã³ã¹è¯ã; int3 & fact1 -> int4: ãã®ãã«ããã¡ã
Lv.61ã¯é話åºæ¥ã; int4 & fact5 -> hypothesis;"
] | [
"fact3 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact2 -> int3: {C}{b}; int3 & fact1 -> int4: {D}{c}; int4 & fact5 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããä»®ã«ãã®ãŽã«ã
ãŽã¡ã
Lv.41ããã©ã³ã¹è¯ããšããããã®ãã«ããã¡ã
Lv.61ã¯é話åºæ¥ã fact2: ä»®ã«ããã¢ã³ã¹ã¿ãŒã調ã¹æããç解ãèŸããªããã®ãŽã«ã
ãŽã¡ã
Lv.41ã¯ãã©ã³ã¹è¯ã fact3: ãã®ã¿ãã¿ãLv.56ã¯èª¿ã¹æã fact4: ãã®ã¿ãã¿ãLv.56ã¯ç解ãèŸã fact5: ãã®ãã«ããã¡ã
Lv.61ã¯åãæã ; $hypothesis$ = ããã®ãã«ããã¡ã
Lv.61ã¯åãæããŠããã¯é話åºæ¥ãããšããããšã¯ééãã§ãã ; $proof$ = | fact3 & fact4 -> int1: ãã®ã¿ãã¿ãLv.56ã¯èª¿ã¹æããŠãŸãããã¯ç解ãèŸã; int1 -> int2: äœããã®ã¢ã³ã¹ã¿ãŒã¯èª¿ã¹æããããã«ããã¯ç解ãèŸã; int2 & fact2 -> int3: ãã®ãŽã«ã
ãŽã¡ã
Lv.41ã¯ãã©ã³ã¹è¯ã; int3 & fact1 -> int4: ãã®ãã«ããã¡ã
Lv.61ã¯é話åºæ¥ã; int4 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{b} -> {D}{c} fact2: (x): ({A}x & {B}x) -> {C}{b} fact3: {A}{a} fact4: {B}{a} fact5: {E}{c} ; $hypothesis$ = ¬({E}{c} & {D}{c}) ; $proof$ = | fact3 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact2 -> int3: {C}{b}; int3 & fact1 -> int4: {D}{c}; int4 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœã«ãœã«Lv.20ã¯æããããªã | ¬{D}{a} | fact1: ããä»®ã«ãã®ãŸã¡ã
ãŸã¡ãLv.38ãã¡ã£ããããã€å¿æ·±ããªãã°ãã®ããããLv.19ã¯ã¡ã£ãããªã fact2: ãã®ãœã«ãœã«Lv.20ã¯è¿·ä¿¡æ·±ããŠã¡ã£ãã fact3: ãã®ãœã«ãœã«Lv.20ã¯å¯ç¬ãã fact4: ããã®ããããLv.19ã¯ã¡ã£ãããªãããšããããšã¯æ£ãããªãã°ãã®ãœã«ãœã«Lv.20ã¯è¿·ä¿¡æ·±ããŠæããã fact5: ã䌌ä»ãããããã¢ã³ã¹ã¿ãŒã¯ãã fact6: ãã®ãœã«ãœã«Lv.20ã¯ææãããå ããŠå¿æ·±ã fact7: ããã®ã¿ã¡ã
ã¿ãLv.55ã¯ææããããšããããšã¯ééãã§ãªã | fact1: ({B}{c} & {E}{c}) -> ¬{B}{b} fact2: ({A}{a} & {B}{a}) fact3: {GR}{a} fact4: ¬{B}{b} -> ({A}{a} & {D}{a}) fact5: (Ex): {F}x fact6: ({C}{a} & {E}{a}) fact7: {C}{hk} | [
"fact2 -> int1: ãã®ãœã«ãœã«Lv.20ã¯ã¡ã£ãã; fact6 -> int2: ãã®ãœã«ãœã«Lv.20ã¯ææãã; int1 & int2 -> int3: ãã®ãœã«ãœã«Lv.20ã¯ã¡ã£ãããããŸãã«ããã¯ææãã;"
] | [
"fact2 -> int1: {B}{a}; fact6 -> int2: {C}{a}; int1 & int2 -> int3: ({B}{a} & {C}{a});"
] | ãã®ã·ãã·ãLv.58ã¯ããããŒã«ããããã€ããã¯æããã | ({U}{dl} & {D}{dl}) | [] | 3 | 4 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãŸã¡ã
ãŸã¡ãLv.38ãã¡ã£ããããã€å¿æ·±ããªãã°ãã®ããããLv.19ã¯ã¡ã£ãããªã fact2: ãã®ãœã«ãœã«Lv.20ã¯è¿·ä¿¡æ·±ããŠã¡ã£ãã fact3: ãã®ãœã«ãœã«Lv.20ã¯å¯ç¬ãã fact4: ããã®ããããLv.19ã¯ã¡ã£ãããªãããšããããšã¯æ£ãããªãã°ãã®ãœã«ãœã«Lv.20ã¯è¿·ä¿¡æ·±ããŠæããã fact5: ã䌌ä»ãããããã¢ã³ã¹ã¿ãŒã¯ãã fact6: ãã®ãœã«ãœã«Lv.20ã¯ææãããå ããŠå¿æ·±ã fact7: ããã®ã¿ã¡ã
ã¿ãLv.55ã¯ææããããšããããšã¯ééãã§ãªã ; $hypothesis$ = ãã®ãœã«ãœã«Lv.20ã¯æããããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({B}{c} & {E}{c}) -> ¬{B}{b} fact2: ({A}{a} & {B}{a}) fact3: {GR}{a} fact4: ¬{B}{b} -> ({A}{a} & {D}{a}) fact5: (Ex): {F}x fact6: ({C}{a} & {E}{a}) fact7: {C}{hk} ; $hypothesis$ = ¬{D}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãŽã«ã
ãŽãLv.21ã決ãé£ããšããã°ãã®ãœããœãLv.28ã¯æ±ãæãããšããããšã¯èª€ãã§ãã | ¬({A}{a} -> {D}{d}) | fact1: ãããããã®ãŽã«ã
ãŽãLv.21ã¯æ±ºãé£ãããšããããšã¯ééã£ãŠããªããšããã°ãã®ãŽã«ããŽãLv.7ã¯ç²ã匷ã fact2: ãããããã®ã¿ãã¿ãªLv.84ã¯åãããšããããšã¯æ£ãããšããã°ãã®ãœããœãLv.28ã¯æ±ãæã fact3: ãã®ãœããœãLv.28ã¯ç²ã匷ã fact4: åŒè§£ããŸãããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯åããã©æ±ãæããªã fact5: ãã®ãŽã«ã
ãŽãLv.21ã¯æµžããªããåŒè§£ããŸãããªã fact6: ãã®ãœããœãLv.28ã¯åã | fact1: {A}{a} -> {B}{b} fact2: {C}{c} -> {D}{d} fact3: {B}{d} fact4: (x): ¬{E}x -> ({C}x & ¬{D}x) fact5: (¬{F}{a} & ¬{E}{a}) fact6: {C}{d} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ãŽã«ã
ãŽãLv.21ã¯æ±ºãé£ãããšããããšã¯æ¬åœã ; fact1 & assump1 -> int1: ããã®ãŽã«ããŽãLv.7ã¯ç²ã匷ãããšããããšã¯æãç«ã€;"
] | [
"void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{b};"
] | ãã®ãœã«ããœã¡ãLv.52ã¯ç²ã匷ã | {B}{hm} | [
"fact8 -> int2: ä»®ã«ãã®ãŽã«ã
ãŽãLv.21ãåŒè§£ããŸãããªããªãåãããããæ±ãæããªã; fact7 -> int3: ãã®ãŽã«ã
ãŽãLv.21ã¯åŒè§£ããŸãããªã; int2 & int3 -> int4: ãã®ãŽã«ã
ãŽãLv.21ã¯åãããã©ããã¯æ±ãæããšããããšã¯ãªã; int4 -> int5: ãã®ãŽã«ã
ãŽãLv.21ã¯åã; int5 -> int6: ãšããã¢ã³ã¹ã¿ãŒã¯åã;"
] | 6 | 5 | 4 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããããã®ãŽã«ã
ãŽãLv.21ã¯æ±ºãé£ãããšããããšã¯ééã£ãŠããªããšããã°ãã®ãŽã«ããŽãLv.7ã¯ç²ã匷ã fact2: ãããããã®ã¿ãã¿ãªLv.84ã¯åãããšããããšã¯æ£ãããšããã°ãã®ãœããœãLv.28ã¯æ±ãæã fact3: ãã®ãœããœãLv.28ã¯ç²ã匷ã fact4: åŒè§£ããŸãããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯åããã©æ±ãæããªã fact5: ãã®ãŽã«ã
ãŽãLv.21ã¯æµžããªããåŒè§£ããŸãããªã fact6: ãã®ãœããœãLv.28ã¯åã ; $hypothesis$ = ããã®ãŽã«ã
ãŽãLv.21ã決ãé£ããšããã°ãã®ãœããœãLv.28ã¯æ±ãæãããšããããšã¯èª€ãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} -> {B}{b} fact2: {C}{c} -> {D}{d} fact3: {B}{d} fact4: (x): ¬{E}x -> ({C}x & ¬{D}x) fact5: (¬{F}{a} & ¬{E}{a}) fact6: {C}{d} ; $hypothesis$ = ¬({A}{a} -> {D}{d}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã¿ã«ãã¿ã¡ã
Lv.17äºä»¶ãèµ·ããããããã¯èãèœã¡ãããšãèµ·ãããäž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã | ¬({C} v {A}) | fact1: èšãåºãé£ããšããããšãçºçããããµãŠã¶ãŠãããšããããšãèµ·ãã fact2: èãèœã¡ãããšãèµ·ãããããã奜ãŸãããšããããšãçãã fact3: ãŸã«ããŸãLv.55äºä»¶ãèµ·ãããããŸãã«éããšããããšãçãã fact4: ã·ã«ã
ã·ãLv.38äºä»¶ãçºçãããããªãã«ãLv.70äºä»¶ãèµ·ãã fact5: ãå¿ãŸå¿ãŸãããšããããšããã³ãŸã¡ããŸãªLv.88äºä»¶ãçããããšããããšã¯æ¬åœã§ãã | fact1: ({FH} v {IU}) fact2: ({A} & {B}) fact3: ({DM} & {AE}) fact4: ({FP} & {IN}) fact5: ({BF} & {AG}) | [
"fact2 -> int1: èãèœã¡ãããšãèµ·ãã; int1 -> hypothesis;"
] | [
"fact2 -> int1: {A}; int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: èšãåºãé£ããšããããšãçºçããããµãŠã¶ãŠãããšããããšãèµ·ãã fact2: èãèœã¡ãããšãèµ·ãããããã奜ãŸãããšããããšãçãã fact3: ãŸã«ããŸãLv.55äºä»¶ãèµ·ãããããŸãã«éããšããããšãçãã fact4: ã·ã«ã
ã·ãLv.38äºä»¶ãçºçãããããªãã«ãLv.70äºä»¶ãèµ·ãã fact5: ãå¿ãŸå¿ãŸãããšããããšããã³ãŸã¡ããŸãªLv.88äºä»¶ãçããããšããããšã¯æ¬åœã§ãã ; $hypothesis$ = ãã¿ã«ãã¿ã¡ã
Lv.17äºä»¶ãèµ·ããããããã¯èãèœã¡ãããšãèµ·ãããäž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã ; $proof$ = | fact2 -> int1: èãèœã¡ãããšãèµ·ãã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({FH} v {IU}) fact2: ({A} & {B}) fact3: ({DM} & {AE}) fact4: ({FP} & {IN}) fact5: ({BF} & {AG}) ; $hypothesis$ = ¬({C} v {A}) ; $proof$ = | fact2 -> int1: {A}; int1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŸãªãŸãLv.71ã¯é Œã¿é£ããªãããšããããšã¯æ¬åœã | ¬{F}{b} | fact1: ãããã®ãŸãªãŸãLv.71ãäžžã£ããããããäœåç¡ããªãã°ãã®ãŸãªãŸãLv.71ã¯é Œã¿é£ããªã fact2: ãäœããã®ã¢ã³ã¹ã¿ãŒã¯å€å¥ãæããªããŠæŽã«çç®ããªãããšããããšã¯æãç«ããªããšããã°ãæ ãããªãããšããããšã¯æ¬åœã§ãã fact3: ãã®ãŽããŽãLv.84ã¯å€å¥ãæããçç®ãã fact4: ä»®ã«ãã®ãŽããŽãLv.84ãçç®ãããšããã°ãã®ãŸãªãŸãLv.71ã¯æ ã fact5: ãã®ãŸãªãŸãLv.71ã¯äœåç¡ã fact6: ãããã®ãŸãªãŸãLv.71ãæ ããªããã®ãŸãªãŸãLv.71ã¯äžžã£ãã | fact1: ({D}{b} & {E}{b}) -> ¬{F}{b} fact2: (x): ¬(¬{A}x & ¬{B}x) -> ¬{C}x fact3: ({A}{a} & {B}{a}) fact4: {B}{a} -> {C}{b} fact5: {E}{b} fact6: {C}{b} -> {D}{b} | [
"fact3 -> int1: ãã®ãŽããŽãLv.84ã¯çç®ãã; int1 & fact4 -> int2: ãã®ãŸãªãŸãLv.71ã¯æ ã; int2 & fact6 -> int3: ãã®ãŸãªãŸãLv.71ã¯äžžã£ãã; int3 & fact5 -> int4: ãã®ãŸãªãŸãLv.71ã¯äžžã£ããããã®äžäœåç¡ã; int4 & fact1 -> hypothesis;"
] | [
"fact3 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{b}; int2 & fact6 -> int3: {D}{b}; int3 & fact5 -> int4: ({D}{b} & {E}{b}); int4 & fact1 -> hypothesis;"
] | ãã®ã¿ã¡ãã¿ã«Lv.31ã¯æ ãããªã | ¬{C}{dn} | [
"fact7 -> int5: ããã®ã¿ã¡ãã¿ã«Lv.31ã¯å€å¥ãæããšããããšã¯ãªãããããçç®ããªãããšããããšã¯èª€ã£ãŠãããšããããã®ã¿ã¡ãã¿ã«Lv.31ã¯æ ãããªã;"
] | 4 | 5 | 5 | 5 | 5 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããã®ãŸãªãŸãLv.71ãäžžã£ããããããäœåç¡ããªãã°ãã®ãŸãªãŸãLv.71ã¯é Œã¿é£ããªã fact2: ãäœããã®ã¢ã³ã¹ã¿ãŒã¯å€å¥ãæããªããŠæŽã«çç®ããªãããšããããšã¯æãç«ããªããšããã°ãæ ãããªãããšããããšã¯æ¬åœã§ãã fact3: ãã®ãŽããŽãLv.84ã¯å€å¥ãæããçç®ãã fact4: ä»®ã«ãã®ãŽããŽãLv.84ãçç®ãããšããã°ãã®ãŸãªãŸãLv.71ã¯æ ã fact5: ãã®ãŸãªãŸãLv.71ã¯äœåç¡ã fact6: ãããã®ãŸãªãŸãLv.71ãæ ããªããã®ãŸãªãŸãLv.71ã¯äžžã£ãã ; $hypothesis$ = ããã®ãŸãªãŸãLv.71ã¯é Œã¿é£ããªãããšããããšã¯æ¬åœã ; $proof$ = | fact3 -> int1: ãã®ãŽããŽãLv.84ã¯çç®ãã; int1 & fact4 -> int2: ãã®ãŸãªãŸãLv.71ã¯æ ã; int2 & fact6 -> int3: ãã®ãŸãªãŸãLv.71ã¯äžžã£ãã; int3 & fact5 -> int4: ãã®ãŸãªãŸãLv.71ã¯äžžã£ããããã®äžäœåç¡ã; int4 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({D}{b} & {E}{b}) -> ¬{F}{b} fact2: (x): ¬(¬{A}x & ¬{B}x) -> ¬{C}x fact3: ({A}{a} & {B}{a}) fact4: {B}{a} -> {C}{b} fact5: {E}{b} fact6: {C}{b} -> {D}{b} ; $hypothesis$ = ¬{F}{b} ; $proof$ = | fact3 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{b}; int2 & fact6 -> int3: {D}{b}; int3 & fact5 -> int4: ({D}{b} & {E}{b}); int4 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ãããã¡ãLv.16ã¯åŒ±ã | {D}{c} | fact1: ä»®ã«ãã®ã·ãã·ãLv.64ãã ã ã£åºããšãããšãã®ã¿ã«ãã¿ãLv.8ã¯åŸ¡ãã§ãã fact2: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãæ«æããããªãã°ã ã ã£åºã fact3: ãã®ã·ãã·ãLv.64ã¯æ«æããã fact4: ããä»®ã«ãã®ã¿ã«ãã¿ãLv.8ã埡ãã§ãããšããã°ãã®ãããã¡ãLv.16ã¯åŒ±ã | fact1: {B}{a} -> {C}{b} fact2: (x): {A}x -> {B}x fact3: {A}{a} fact4: {C}{b} -> {D}{c} | [
"fact2 -> int1: ãããããã®ã·ãã·ãLv.64ã¯æ«æãããããšããããšã¯æãç«ãŠã°ãã ã ã£åºãããšããããšã¯æ¬åœã§ãã; int1 & fact3 -> int2: ãã®ã·ãã·ãLv.64ã¯ã ã ã£åºã; int2 & fact1 -> int3: ãã®ã¿ã«ãã¿ãLv.8ã¯åŸ¡ãã§ãã; int3 & fact4 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a} -> {B}{a}; int1 & fact3 -> int2: {B}{a}; int2 & fact1 -> int3: {C}{b}; int3 & fact4 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ãã®ã·ãã·ãLv.64ãã ã ã£åºããšãããšãã®ã¿ã«ãã¿ãLv.8ã¯åŸ¡ãã§ãã fact2: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãæ«æããããªãã°ã ã ã£åºã fact3: ãã®ã·ãã·ãLv.64ã¯æ«æããã fact4: ããä»®ã«ãã®ã¿ã«ãã¿ãLv.8ã埡ãã§ãããšããã°ãã®ãããã¡ãLv.16ã¯åŒ±ã ; $hypothesis$ = ãã®ãããã¡ãLv.16ã¯åŒ±ã ; $proof$ = | fact2 -> int1: ãããããã®ã·ãã·ãLv.64ã¯æ«æãããããšããããšã¯æãç«ãŠã°ãã ã ã£åºãããšããããšã¯æ¬åœã§ãã; int1 & fact3 -> int2: ãã®ã·ãã·ãLv.64ã¯ã ã ã£åºã; int2 & fact1 -> int3: ãã®ã¿ã«ãã¿ãLv.8ã¯åŸ¡ãã§ãã; int3 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{a} -> {C}{b} fact2: (x): {A}x -> {B}x fact3: {A}{a} fact4: {C}{b} -> {D}{c} ; $hypothesis$ = {D}{c} ; $proof$ = | fact2 -> int1: {A}{a} -> {B}{a}; int1 & fact3 -> int2: {B}{a}; int2 & fact1 -> int3: {C}{b}; int3 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœã«ããœã®Lv.99ã¯çãããŠçŽ æŽãã | ({E}{c} & {D}{c}) | fact1: ãã®ãœã«ããœã®Lv.99ãæãåããšãããçãã fact2: ãã®ãœã«ããœã®Lv.99ã埮ç¬ãŸãããªãã°ããã¯çŽ æŽãã fact3: ããä»®ã«ãã®ã·ã¡ãã·ã«ã
Lv.77ãããŠããã°ãã®ãœã«ããœã®Lv.99ã¯åŸ®ç¬ãŸãã fact4: ããããã®ã·ã¡ãã·ã«ã
Lv.77ãæãåããªããã®ãœã«ããœã®Lv.99ã¯åŸ®ç¬ãŸãã fact5: ããä»®ã«ãã®ãœã«ããœã®Lv.99ãããŠãããšããã°ãã®ã·ã¡ãã·ã«ã
Lv.77ã¯çãã fact6: ãã®ãœã«ããœã®Lv.99ã¯çãã fact7: ããããã¢ã³ã¹ã¿ãŒã¯æãåããããã¯ããŠãã | fact1: {A}{c} -> {E}{c} fact2: {C}{c} -> {D}{c} fact3: {B}{a} -> {C}{c} fact4: {A}{a} -> {C}{c} fact5: {B}{c} -> {E}{a} fact6: {E}{c} fact7: (x): ({A}x v {B}x) | [
"fact7 -> int1: ãã®ã·ã¡ãã·ã«ã
Lv.77ã¯æãåããããŠããããããã¯äž¡æ¹ãšãã ; int1 & fact4 & fact3 -> int2: ãã®ãœã«ããœã®Lv.99ã¯åŸ®ç¬ãŸãã; int2 & fact2 -> int3: ãã®ãœã«ããœã®Lv.99ã¯çŽ æŽãã; int3 & fact6 -> hypothesis;"
] | [
"fact7 -> int1: ({A}{a} v {B}{a}); int1 & fact4 & fact3 -> int2: {C}{c}; int2 & fact2 -> int3: {D}{c}; int3 & fact6 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãœã«ããœã®Lv.99ãæãåããšãããçãã fact2: ãã®ãœã«ããœã®Lv.99ã埮ç¬ãŸãããªãã°ããã¯çŽ æŽãã fact3: ããä»®ã«ãã®ã·ã¡ãã·ã«ã
Lv.77ãããŠããã°ãã®ãœã«ããœã®Lv.99ã¯åŸ®ç¬ãŸãã fact4: ããããã®ã·ã¡ãã·ã«ã
Lv.77ãæãåããªããã®ãœã«ããœã®Lv.99ã¯åŸ®ç¬ãŸãã fact5: ããä»®ã«ãã®ãœã«ããœã®Lv.99ãããŠãããšããã°ãã®ã·ã¡ãã·ã«ã
Lv.77ã¯çãã fact6: ãã®ãœã«ããœã®Lv.99ã¯çãã fact7: ããããã¢ã³ã¹ã¿ãŒã¯æãåããããã¯ããŠãã ; $hypothesis$ = ãã®ãœã«ããœã®Lv.99ã¯çãããŠçŽ æŽãã ; $proof$ = | fact7 -> int1: ãã®ã·ã¡ãã·ã«ã
Lv.77ã¯æãåããããŠããããããã¯äž¡æ¹ãšãã ; int1 & fact4 & fact3 -> int2: ãã®ãœã«ããœã®Lv.99ã¯åŸ®ç¬ãŸãã; int2 & fact2 -> int3: ãã®ãœã«ããœã®Lv.99ã¯çŽ æŽãã; int3 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{c} -> {E}{c} fact2: {C}{c} -> {D}{c} fact3: {B}{a} -> {C}{c} fact4: {A}{a} -> {C}{c} fact5: {B}{c} -> {E}{a} fact6: {E}{c} fact7: (x): ({A}x v {B}x) ; $hypothesis$ = ({E}{c} & {D}{c}) ; $proof$ = | fact7 -> int1: ({A}{a} v {B}{a}); int1 & fact4 & fact3 -> int2: {C}{c}; int2 & fact2 -> int3: {D}{c}; int3 & fact6 -> hypothesis; __PROVED__ |
Subsets and Splits