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0.3 | å
¥ãç¥æµãçºçããªã | ¬{B} | fact1: ãéããšããããšãèµ·ãããªãããšããããšãæãç«ã€ fact2: 颚åºã«èªã蟌ãããšãèµ·ãããªãããããèªã¿åããããšãèµ·ãã fact3: å°é接ã«åŸ
ã€ããšã¯èµ·ãããªãããããéŠæ¬ãã¯èµ·ãã | fact1: ¬{HT} fact2: (¬{AA} & {AB}) fact3: (¬{BL} & {DT}) | [] | [] | null | null | [] | null | 1 | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãéããšããããšãèµ·ãããªãããšããããšãæãç«ã€ fact2: 颚åºã«èªã蟌ãããšãèµ·ãããªãããããèªã¿åããããšãèµ·ãã fact3: å°é接ã«åŸ
ã€ããšã¯èµ·ãããªãããããéŠæ¬ãã¯èµ·ãã ; $hypothesis$ = å
¥ãç¥æµãçºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{HT} fact2: (¬{AA} & {AB}) fact3: (¬{BL} & {DT}) ; $hypothesis$ = ¬{B} ; $proof$ = | __UNKNOWN__ |
0.3 | åé«ããšããããšãçºçããªã | ¬{A} | fact1: äžã¶å±±ããããã ããããšãçºçãã fact2: ã匱ããšããããšãçãã | fact1: {FQ} fact2: {EN} | [] | [] | null | null | [] | null | 1 | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: äžã¶å±±ããããã ããããšãçºçãã fact2: ã匱ããšããããšãçãã ; $hypothesis$ = åé«ããšããããšãçºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {FQ} fact2: {EN} ; $hypothesis$ = ¬{A} ; $proof$ = | __UNKNOWN__ |
0.3 | 調å³ãèµ·ãããªããŠãããããšããããšã¯çºçããªã | (¬{AA} & ¬{AB}) | fact1: ããå£ããããšããããšã¯èµ·ããªããªãã°ãäžè»æã«æã¡åºãããšãçããªããèŽçœªãèµ·ããªãããšããããšã¯èª€ãã fact2: æ³¥åã¯èµ·ããªã fact3: ã銬鹿銬鹿ãããšããããšãèµ·ãããªãããšããããšã¯ããéªã«ãããåºãããšã¯çããªãããšããããšã«ããçºçãã fact4: ãã銬鹿銬鹿ãããšããããšã¯çããã°ã空暡æ§ãèµ·ãããªããè¶è²ããšããããšã¯èµ·ãããªãããšããããšãæãç«ã€ãšããããšããªã fact5: ã調å³ã¯çºçããããããããšããããšã¯çºçããªãããšããããšãæãç«ããªã fact6: ãããäžè»æã«æã¡åºãããšã¯çºçããªããèŽçœªã¯èµ·ããªãããšããããšã¯æãç«ããªããªãã°éŠ³ãåããããšãçããªã fact7: ãããå¿ç¡ããšããããšã¯çãããããããéªã«ãããåºãããšãçºçããªãããšããããšãæãç«ãŠã°éŠ¬é¹¿éŠ¬é¹¿ãããšããããšãçºçãã fact8: ãããèŽçœªã¯èµ·ãããªãããšããããšã¯æãç«ãŠã°å¿ç¡ããšããããšãšã¡ãã¥ããããšäž¡æ¹ãèµ·ãã fact9: ãæåã¯çºçããªããã»ããè¶ã«è«åãããšãèµ·ãããªãããšããããšãæãç«ããªã fact10: ã調å³ãçºçããªããŠãããããšããããšã¯çºçããããšããããšãäºå®ã ãšããããšã¯ãªã fact11: ã調å³ã¯çããªãããããããšããããšã¯çããªãããšããããšã¯ã銬鹿銬鹿ãããšããããšã¯çºçããªãããšããããšã«èªçºããã fact12: ãäžå®æŸã«ããã¡ããããšãçããªããŠæªãããšããããšãçããªãããšããããšãæãç«ã€ãšããããšããªã fact13: ãã銳ãåããããšã¯èµ·ããªããªãã°ã¡ãã¥ããããšãèµ·ããªãããããã¯å¿ç¡ããšããããšã¯èµ·ãããªããäž¡æ¹ã fact14: ããæ³¥åãçºçããªããªãã°èŽçœªãçããªããŠæåã決ãŸãããšãçãã | fact1: ¬{H} -> ¬(¬{F} & ¬{G}) fact2: ¬{J} fact3: ¬{B} -> ¬{A} fact4: {A} -> ¬(¬{GR} & ¬{HO}) fact5: ¬({AA} & ¬{AB}) fact6: ¬(¬{F} & ¬{G}) -> ¬{E} fact7: ({C} & ¬{B}) -> {A} fact8: ¬{G} -> ({C} & {D}) fact9: ¬(¬{L} & ¬{FF}) fact10: ¬(¬{AA} & {AB}) fact11: ¬{A} -> (¬{AA} & ¬{AB}) fact12: ¬(¬{GT} & ¬{IE}) fact13: ¬{E} -> (¬{D} v ¬{C}) fact14: ¬{J} -> (¬{G} & {I}) | [] | [] | ã空暡æ§ãçããªããŠè¶è²ããšããããšã¯èµ·ããªãããšããããšãæãç«ããªã | ¬(¬{GR} & ¬{HO}) | [
"fact19 & fact17 -> int1: èŽçœªã¯çºçããªããæåã決ãŸãããšã¯çºçãã; int1 -> int2: èŽçœªãçºçããªã; fact15 & int2 -> int3: å¿ç¡ããšããããšãçãããã¡ãã¥ããããšãèµ·ãã; int3 -> int4: å¿ç¡ããšããããšãèµ·ãã;"
] | 7 | 1 | null | 14 | 0 | 14 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããå£ããããšããããšã¯èµ·ããªããªãã°ãäžè»æã«æã¡åºãããšãçããªããèŽçœªãèµ·ããªãããšããããšã¯èª€ãã fact2: æ³¥åã¯èµ·ããªã fact3: ã銬鹿銬鹿ãããšããããšãèµ·ãããªãããšããããšã¯ããéªã«ãããåºãããšã¯çããªãããšããããšã«ããçºçãã fact4: ãã銬鹿銬鹿ãããšããããšã¯çããã°ã空暡æ§ãèµ·ãããªããè¶è²ããšããããšã¯èµ·ãããªãããšããããšãæãç«ã€ãšããããšããªã fact5: ã調å³ã¯çºçããããããããšããããšã¯çºçããªãããšããããšãæãç«ããªã fact6: ãããäžè»æã«æã¡åºãããšã¯çºçããªããèŽçœªã¯èµ·ããªãããšããããšã¯æãç«ããªããªãã°éŠ³ãåããããšãçããªã fact7: ãããå¿ç¡ããšããããšã¯çãããããããéªã«ãããåºãããšãçºçããªãããšããããšãæãç«ãŠã°éŠ¬é¹¿éŠ¬é¹¿ãããšããããšãçºçãã fact8: ãããèŽçœªã¯èµ·ãããªãããšããããšã¯æãç«ãŠã°å¿ç¡ããšããããšãšã¡ãã¥ããããšäž¡æ¹ãèµ·ãã fact9: ãæåã¯çºçããªããã»ããè¶ã«è«åãããšãèµ·ãããªãããšããããšãæãç«ããªã fact10: ã調å³ãçºçããªããŠãããããšããããšã¯çºçããããšããããšãäºå®ã ãšããããšã¯ãªã fact11: ã調å³ã¯çããªãããããããšããããšã¯çããªãããšããããšã¯ã銬鹿銬鹿ãããšããããšã¯çºçããªãããšããããšã«èªçºããã fact12: ãäžå®æŸã«ããã¡ããããšãçããªããŠæªãããšããããšãçããªãããšããããšãæãç«ã€ãšããããšããªã fact13: ãã銳ãåããããšã¯èµ·ããªããªãã°ã¡ãã¥ããããšãèµ·ããªãããããã¯å¿ç¡ããšããããšã¯èµ·ãããªããäž¡æ¹ã fact14: ããæ³¥åãçºçããªããªãã°èŽçœªãçããªããŠæåã決ãŸãããšãçãã ; $hypothesis$ = 調å³ãèµ·ãããªããŠãããããšããããšã¯çºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{H} -> ¬(¬{F} & ¬{G}) fact2: ¬{J} fact3: ¬{B} -> ¬{A} fact4: {A} -> ¬(¬{GR} & ¬{HO}) fact5: ¬({AA} & ¬{AB}) fact6: ¬(¬{F} & ¬{G}) -> ¬{E} fact7: ({C} & ¬{B}) -> {A} fact8: ¬{G} -> ({C} & {D}) fact9: ¬(¬{L} & ¬{FF}) fact10: ¬(¬{AA} & {AB}) fact11: ¬{A} -> (¬{AA} & ¬{AB}) fact12: ¬(¬{GT} & ¬{IE}) fact13: ¬{E} -> (¬{D} v ¬{C}) fact14: ¬{J} -> (¬{G} & {I}) ; $hypothesis$ = (¬{AA} & ¬{AB}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®è¿éã¯æèš±ã§ãã£ãŠæ°å³æªããã®ããšããããšãæãç«ã€ãšããããšã¯ãªã | ¬({A}{a} & {B}{a}) | fact1: ããäœãã¯ïŒªïŒŠïŒ¬ãªãã°ããã¯çµã¿èŸŒãã fact2: ãã®è©å
ã¯æèš±ã ãããã¯æ±æšªé¢ã fact3: ãã®è¿éããã©ãã©ãã fact4: ãã®è¿éã¯æèš±ã fact5: ãã®è»ã¯æ°å³æªã fact6: ããã®è¿éãå°å³è¡éã«å ±ããããšããããšãäºå®ã fact7: ããããããªããã®ã¯ïŒªïŒŠïŒ¬ã ãšããããšã¯ãªã fact8: ãããã®éç©ãã ãšããããšããªããªãã°ããã®è¿éã¯æèš±ã§ãããæ°å³æªãããšããããšãäºå®ãšç°ãªã fact9: ãã®éç©ã¯ãããããå«ç¥ fact10: ãã®é·é³¥ã¯æ°å³æªããŠç©æ²ãã fact11: ãã®è¿éãæ°å³æªã | fact1: (x): {C}x -> {DP}x fact2: ({A}{cr} & {GS}{cr}) fact3: {GG}{a} fact4: {A}{a} fact5: {B}{q} fact6: {BD}{a} fact7: (x): ¬{D}x -> ¬{C}x fact8: ¬{C}{b} -> ¬({A}{a} & {B}{a}) fact9: ({D}{b} & {E}{b}) fact10: ({B}{cd} & {CH}{cd}) fact11: {B}{a} | [
"fact4 & fact11 -> hypothesis;"
] | [
"fact4 & fact11 -> hypothesis;"
] | ããã®è¿éã¯æèš±ã§ãããæ°å³æªãããšããããšãæãç«ããªã | ¬({A}{a} & {B}{a}) | [
"fact12 -> int1: ãããã®éç©ãããããããªããªãã°ããã¯ïŒªïŒŠïŒ¬ã ãšããããšã¯ãªã;"
] | 6 | 1 | 1 | 9 | 0 | 9 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããäœãã¯ïŒªïŒŠïŒ¬ãªãã°ããã¯çµã¿èŸŒãã fact2: ãã®è©å
ã¯æèš±ã ãããã¯æ±æšªé¢ã fact3: ãã®è¿éããã©ãã©ãã fact4: ãã®è¿éã¯æèš±ã fact5: ãã®è»ã¯æ°å³æªã fact6: ããã®è¿éãå°å³è¡éã«å ±ããããšããããšãäºå®ã fact7: ããããããªããã®ã¯ïŒªïŒŠïŒ¬ã ãšããããšã¯ãªã fact8: ãããã®éç©ãã ãšããããšããªããªãã°ããã®è¿éã¯æèš±ã§ãããæ°å³æªãããšããããšãäºå®ãšç°ãªã fact9: ãã®éç©ã¯ãããããå«ç¥ fact10: ãã®é·é³¥ã¯æ°å³æªããŠç©æ²ãã fact11: ãã®è¿éãæ°å³æªã ; $hypothesis$ = ããã®è¿éã¯æèš±ã§ãã£ãŠæ°å³æªããã®ããšããããšãæãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact4 & fact11 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {C}x -> {DP}x fact2: ({A}{cr} & {GS}{cr}) fact3: {GG}{a} fact4: {A}{a} fact5: {B}{q} fact6: {BD}{a} fact7: (x): ¬{D}x -> ¬{C}x fact8: ¬{C}{b} -> ¬({A}{a} & {B}{a}) fact9: ({D}{b} & {E}{b}) fact10: ({B}{cd} & {CH}{cd}) fact11: {B}{a} ; $hypothesis$ = ¬({A}{a} & {B}{a}) ; $proof$ = | fact4 & fact11 -> hypothesis; __DISPROVED__ |
0.3 | ããããã®ãžã£ã³ã«ã倧島å·ã ãšããããšããªããªãã°ããã®ãžã£ã³ã«ãããããããããããè¥è€ã§ãªãããšããããšã¯æ£ãããªãããšããããšãäºå®ãšç°ãªã | ¬(¬{A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa})) | fact1: ãããã®èãããããããšããããšããªããªãã°ãããã¯äžå·éŠã ããããããããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact2: ãããããã®ã¯å€§å³¶å·ãªãã°ãããã¯ããããããã¯è¥è€ã ãšããããšã¯ãªãããšããããšãééãã fact3: ãããã®ãžã£ã³ã«ã倧島å·ã ãšããããšã¯ãªããªãã°ãããããããè¥è€ããšããããšãæãç«ã€ãšããããšããªã fact4: ãããã®ãžã£ã³ã«ã¯é·åºæž¯ã ãšããããšããªããªãã°ããããã¯ã¬ã«ã·ã¢ã«ããã¿ããŠããé
žéå±±ã ãšããããšããªãããšããããšã¯æ£ããããšããããšãåã fact5: ãããã®çé·ã¯ããããšããããšã¯ãªããªãã°ããããå£ç¥ã«åºããåŒæ»ããšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact6: ãããããã®ã倧島å·ã ãšããããšããªããªãã°ãããã¯ããããè¥è€ã§ãªãããšããããšã¯åœã fact7: ããäœãã¯å€§å³¶å·ã ãšããããšã¯ãªããªãã°ããã¯ããããã®ã§ãã£ãŠè¥è€ã ãšããããšã¯ãªããã® fact8: ããäœãã¯å€§å³¶å·ã ãšããããšã¯ãªããªãã°ãããã¯ããããŠè¥è€ã ããšããããšã¯åã fact9: ãããã®ãžã£ã³ã«ã¯å€§å³¶å·ãªãã°ããããããããããã¯è¥è€ã ãšããããšã¯ãªãããšããããšã¯æãç«ããªã fact10: ãããã®ãžã£ã³ã«ã倧島å·ã ãšããããšããªããªãã°ããããããããããè¥è€ã ãšããããšã¯ãªã | fact1: ¬{IJ}{ch} -> ¬({P}{ch} & ¬{AA}{ch}) fact2: (x): {A}x -> ¬({AA}x & ¬{AB}x) fact3: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact4: ¬{BI}{aa} -> ¬({L}{aa} & ¬{EO}{aa}) fact5: ¬{AA}{b} -> ¬({CR}{b} & ¬{DF}{b}) fact6: (x): ¬{A}x -> ¬({AA}x & ¬{AB}x) fact7: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact8: (x): ¬{A}x -> ¬({AA}x & {AB}x) fact9: {A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa}) fact10: ¬{A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) | [
"fact6 -> hypothesis;"
] | [
"fact6 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 9 | 0 | 9 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããã®èãããããããšããããšããªããªãã°ãããã¯äžå·éŠã ããããããããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact2: ãããããã®ã¯å€§å³¶å·ãªãã°ãããã¯ããããããã¯è¥è€ã ãšããããšã¯ãªãããšããããšãééãã fact3: ãããã®ãžã£ã³ã«ã倧島å·ã ãšããããšã¯ãªããªãã°ãããããããè¥è€ããšããããšãæãç«ã€ãšããããšããªã fact4: ãããã®ãžã£ã³ã«ã¯é·åºæž¯ã ãšããããšããªããªãã°ããããã¯ã¬ã«ã·ã¢ã«ããã¿ããŠããé
žéå±±ã ãšããããšããªãããšããããšã¯æ£ããããšããããšãåã fact5: ãããã®çé·ã¯ããããšããããšã¯ãªããªãã°ããããå£ç¥ã«åºããåŒæ»ããšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact6: ãããããã®ã倧島å·ã ãšããããšããªããªãã°ãããã¯ããããè¥è€ã§ãªãããšããããšã¯åœã fact7: ããäœãã¯å€§å³¶å·ã ãšããããšã¯ãªããªãã°ããã¯ããããã®ã§ãã£ãŠè¥è€ã ãšããããšã¯ãªããã® fact8: ããäœãã¯å€§å³¶å·ã ãšããããšã¯ãªããªãã°ãããã¯ããããŠè¥è€ã ããšããããšã¯åã fact9: ãããã®ãžã£ã³ã«ã¯å€§å³¶å·ãªãã°ããããããããããã¯è¥è€ã ãšããããšã¯ãªãããšããããšã¯æãç«ããªã fact10: ãããã®ãžã£ã³ã«ã倧島å·ã ãšããããšããªããªãã°ããããããããããè¥è€ã ãšããããšã¯ãªã ; $hypothesis$ = ããããã®ãžã£ã³ã«ã倧島å·ã ãšããããšããªããªãã°ããã®ãžã£ã³ã«ãããããããããããè¥è€ã§ãªãããšããããšã¯æ£ãããªãããšããããšãäºå®ãšç°ãªã ; $proof$ = | fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{IJ}{ch} -> ¬({P}{ch} & ¬{AA}{ch}) fact2: (x): {A}x -> ¬({AA}x & ¬{AB}x) fact3: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact4: ¬{BI}{aa} -> ¬({L}{aa} & ¬{EO}{aa}) fact5: ¬{AA}{b} -> ¬({CR}{b} & ¬{DF}{b}) fact6: (x): ¬{A}x -> ¬({AA}x & ¬{AB}x) fact7: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact8: (x): ¬{A}x -> ¬({AA}x & {AB}x) fact9: {A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa}) fact10: ¬{A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) ; $hypothesis$ = ¬(¬{A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa})) ; $proof$ = | fact6 -> hypothesis; __DISPROVED__ |
0.3 | ããã®é«å§ãèžèŠãããã¿ããããããšããããšãæãç«ããªã | ¬({AA}{b} & {AB}{b}) | fact1: ãããã®éœæ¥µãããã°ã§ãªããªãã°ããã®é«å§ã¯èžèŠãããã¿ããããããšããããšãæãç«ã€ãšããããšã¯ãªã fact2: ãããã®éœæ¥µã¯ããã°ãªãã°ããã®é«å§ã¯èžèŠããããšããããšã¯äºå®ã fact3: ãããäœãã¯ãã£ããããšããããšã¯ãªããããããããå
·åã ããšããããšã誀ããªãã°ããã¯ããã°ã ãšããããšã¯ãªã fact4: ããããã®é«å§ãããã°ã§ãªãããšããããšãäºå®ãªãã°ããã®éœæ¥µã¯äºé·ãæ±ãããããèžèŠããããšããããšã¯æãç«ããªã fact5: ãã®åºæã¯çŠå³¶æ°ç°ã ãšããããšã¯ãªã | fact1: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact2: {A}{a} -> {AA}{b} fact3: (x): ¬(¬{B}x & {C}x) -> ¬{A}x fact4: ¬{A}{b} -> ¬({AG}{a} & {AA}{a}) fact5: ¬{D}{c} | [] | [] | ãã®é«å§ã¯èžèŠãããããã¯ã¿ãããã | ({AA}{b} & {AB}{b}) | [
"fact6 -> int1: ãçŠå³¶æ°ç°ã§ãªãããã®ããã;"
] | 5 | 1 | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®éœæ¥µãããã°ã§ãªããªãã°ããã®é«å§ã¯èžèŠãããã¿ããããããšããããšãæãç«ã€ãšããããšã¯ãªã fact2: ãããã®éœæ¥µã¯ããã°ãªãã°ããã®é«å§ã¯èžèŠããããšããããšã¯äºå®ã fact3: ãããäœãã¯ãã£ããããšããããšã¯ãªããããããããå
·åã ããšããããšã誀ããªãã°ããã¯ããã°ã ãšããããšã¯ãªã fact4: ããããã®é«å§ãããã°ã§ãªãããšããããšãäºå®ãªãã°ããã®éœæ¥µã¯äºé·ãæ±ãããããèžèŠããããšããããšã¯æãç«ããªã fact5: ãã®åºæã¯çŠå³¶æ°ç°ã ãšããããšã¯ãªã ; $hypothesis$ = ããã®é«å§ãèžèŠãããã¿ããããããšããããšãæãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact2: {A}{a} -> {AA}{b} fact3: (x): ¬(¬{B}x & {C}x) -> ¬{A}x fact4: ¬{A}{b} -> ¬({AG}{a} & {AA}{a}) fact5: ¬{D}{c} ; $hypothesis$ = ¬({AA}{b} & {AB}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãããèŠæããªããªãã°æ¥ã€ãã°ãã«æ£ãããã®ã¯ãã | (Ex): ¬{B}x -> {C}x | fact1: ãããããã®ã¯èŠæããªããªãã°ãããæŽèœèã fact2: ããäœãã¯å€åãã§ãªããªãã°ãããã¯èŠæãããšããããšã¯äºå®ã fact3: ããããã®ã¯ã©ã³ã±ã¯æ¥ã€ãã°ãã«æ£ãããšããããšã¯æãç«ãŠã°ãããå ªãé£ã fact4: ãããã®ã»ãŒãã«ãèŠæããªãã°ãããæ¥ã€ãã°ãã«æ£ã fact5: ãããã®ã»ãŒãã«ã¯æŽ¥ä¹é·çºæŽ¥ä¹é·ãã€ããã¯ãããšããããšããªããªãã°ããã¯å€§è寺äžãã fact6: ããã倧è寺äžããªãã°ãšãŠã€ããªãããã®ã¯ãã fact7: ããããã®éä¹ãã·ã§ãŒãã©ã»ã¢ãžã¢ã§ãªãããšããããšãæãç«ãŠã°ãããæ¥ã€ãã°ãã«æ£ã fact8: ããããèŠæãããšããããšã¯äºå®ãªãã°æ¥ã€ãã°ãã«æ£ãããã®ããã fact9: ãããã®ã»ãŒãã«ãèŠæããšããããšã¯ãªããªãã°ããã¯å¹³ä»®åã«åºãæã fact10: ãããããµãšã ãšããããšã¯ãªããªãã°ãæçãããšããããšã¯æ£ããããã®ã¯ãã fact11: ããããã®ã»ãŒãã«ã¯ã¡ãªãŸããããªãã°ãã®ã»ãŒãã«ã¯ããŽã€ã ããšããããšã¯æ£ãã fact12: ãããåç©ã±åŽå±±ã«è¿œãããããšããããšã¯ãªããªãã°ãã£é
·ãããã®ã¯ãã fact13: ãããã®ã»ãŒãã«ã¯å·äžå³¶çºåãããããããšããããšã¯ãªããªãã°ãããã¯ãããããšããããšãæ£ãã fact14: ãããæ°éã£ãœããšããããšããªããªãã°ãã£ããããã®ã¯ãã fact15: ãããç¢ä¹ã«æ±ãç· ãããšããããšããªããªãã°è
«ããŒã£ããããã®ã¯ãã fact16: ãããããããããããšããããšã¯çå®ãªãã°ãæ±æ±°äžã«å®ããããšããããšãæãç«ã€ããã®ã¯ãã fact17: ãããã倧è寺äžãã ããšããããšã¯æ¬åœãªãã°æ¡äºãå·®ç«ãŠãããã®ã¯ãã fact18: ãããã®ã»ãŒãã«ã¯èŠæããªããªãã°ããã¯æ¥ã€ãã°ãã«æ£ã fact19: ãããèãåããšããããšã¯ãªããªãã°å€§é¿åãåãèœãšãããã®ããã fact20: ãããååè·¯ãªãã°å·äžå³¶çºåããããããããã®ã¯ãã | fact1: (x): ¬{B}x -> {FN}x fact2: (x): ¬{AT}x -> {B}x fact3: {C}{ao} -> {EK}{ao} fact4: {B}{aa} -> {C}{aa} fact5: ¬{CJ}{aa} -> {FA}{aa} fact6: (Ex): {FA}x -> {AK}x fact7: ¬{DJ}{fl} -> {C}{fl} fact8: (Ex): {B}x -> {C}x fact9: ¬{B}{aa} -> {FM}{aa} fact10: (Ex): ¬{D}x -> {EF}x fact11: {BF}{aa} -> {EL}{aa} fact12: (Ex): ¬{BB}x -> {JK}x fact13: ¬{GE}{aa} -> {IJ}{aa} fact14: (Ex): ¬{FR}x -> {FT}x fact15: (Ex): ¬{BE}x -> {AP}x fact16: (Ex): {CO}x -> {CL}x fact17: (Ex): {FA}x -> {CD}x fact18: ¬{B}{aa} -> {C}{aa} fact19: (Ex): ¬{HF}x -> {HJ}x fact20: (Ex): {CP}x -> {GE}x | [
"fact18 -> hypothesis;"
] | [
"fact18 -> hypothesis;"
] | ãããã®åªŒã¯èŠæããšããããšããªããªãã°ããã¯æŽèœèã | ¬{B}{jf} -> {FN}{jf} | [
"fact21 -> hypothesis;"
] | 1 | 1 | 1 | 19 | 0 | 19 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãããããã®ã¯èŠæããªããªãã°ãããæŽèœèã fact2: ããäœãã¯å€åãã§ãªããªãã°ãããã¯èŠæãããšããããšã¯äºå®ã fact3: ããããã®ã¯ã©ã³ã±ã¯æ¥ã€ãã°ãã«æ£ãããšããããšã¯æãç«ãŠã°ãããå ªãé£ã fact4: ãããã®ã»ãŒãã«ãèŠæããªãã°ãããæ¥ã€ãã°ãã«æ£ã fact5: ãããã®ã»ãŒãã«ã¯æŽ¥ä¹é·çºæŽ¥ä¹é·ãã€ããã¯ãããšããããšããªããªãã°ããã¯å€§è寺äžãã fact6: ããã倧è寺äžããªãã°ãšãŠã€ããªãããã®ã¯ãã fact7: ããããã®éä¹ãã·ã§ãŒãã©ã»ã¢ãžã¢ã§ãªãããšããããšãæãç«ãŠã°ãããæ¥ã€ãã°ãã«æ£ã fact8: ããããèŠæãããšããããšã¯äºå®ãªãã°æ¥ã€ãã°ãã«æ£ãããã®ããã fact9: ãããã®ã»ãŒãã«ãèŠæããšããããšã¯ãªããªãã°ããã¯å¹³ä»®åã«åºãæã fact10: ãããããµãšã ãšããããšã¯ãªããªãã°ãæçãããšããããšã¯æ£ããããã®ã¯ãã fact11: ããããã®ã»ãŒãã«ã¯ã¡ãªãŸããããªãã°ãã®ã»ãŒãã«ã¯ããŽã€ã ããšããããšã¯æ£ãã fact12: ãããåç©ã±åŽå±±ã«è¿œãããããšããããšã¯ãªããªãã°ãã£é
·ãããã®ã¯ãã fact13: ãããã®ã»ãŒãã«ã¯å·äžå³¶çºåãããããããšããããšã¯ãªããªãã°ãããã¯ãããããšããããšãæ£ãã fact14: ãããæ°éã£ãœããšããããšããªããªãã°ãã£ããããã®ã¯ãã fact15: ãããç¢ä¹ã«æ±ãç· ãããšããããšããªããªãã°è
«ããŒã£ããããã®ã¯ãã fact16: ãããããããããããšããããšã¯çå®ãªãã°ãæ±æ±°äžã«å®ããããšããããšãæãç«ã€ããã®ã¯ãã fact17: ãããã倧è寺äžãã ããšããããšã¯æ¬åœãªãã°æ¡äºãå·®ç«ãŠãããã®ã¯ãã fact18: ãããã®ã»ãŒãã«ã¯èŠæããªããªãã°ããã¯æ¥ã€ãã°ãã«æ£ã fact19: ãããèãåããšããããšã¯ãªããªãã°å€§é¿åãåãèœãšãããã®ããã fact20: ãããååè·¯ãªãã°å·äžå³¶çºåããããããããã®ã¯ãã ; $hypothesis$ = ãããèŠæããªããªãã°æ¥ã€ãã°ãã«æ£ãããã®ã¯ãã ; $proof$ = | fact18 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬{B}x -> {FN}x fact2: (x): ¬{AT}x -> {B}x fact3: {C}{ao} -> {EK}{ao} fact4: {B}{aa} -> {C}{aa} fact5: ¬{CJ}{aa} -> {FA}{aa} fact6: (Ex): {FA}x -> {AK}x fact7: ¬{DJ}{fl} -> {C}{fl} fact8: (Ex): {B}x -> {C}x fact9: ¬{B}{aa} -> {FM}{aa} fact10: (Ex): ¬{D}x -> {EF}x fact11: {BF}{aa} -> {EL}{aa} fact12: (Ex): ¬{BB}x -> {JK}x fact13: ¬{GE}{aa} -> {IJ}{aa} fact14: (Ex): ¬{FR}x -> {FT}x fact15: (Ex): ¬{BE}x -> {AP}x fact16: (Ex): {CO}x -> {CL}x fact17: (Ex): {FA}x -> {CD}x fact18: ¬{B}{aa} -> {C}{aa} fact19: (Ex): ¬{HF}x -> {HJ}x fact20: (Ex): {CP}x -> {GE}x ; $hypothesis$ = (Ex): ¬{B}x -> {C}x ; $proof$ = | fact18 -> hypothesis; __PROVED__ |
0.3 | ãã®äžã髪ã¯ã¢ã³ããŒããŒã ãšããããšããªãããããå
äžã§ããããããã¯äž¡æ¹ã | (¬{AA}{b} v {AB}{b}) | fact1: ãã®ç·åž¥ã¯ã¢ã³ããŒããŒã fact2: ãããããªããªããã®ãã¢ã³ããŒããŒã§ãªãããããã¯å
äžã§ããããããã¯äž¡æ¹ã fact3: ãããã®ç·åž¥ããããããªããªãã°ããã®äžã髪ãã¢ã³ããŒããŒã§ãªãããããå
äžã§ãããäž¡æ¹ã ããšããããšãæãç«ããªã | fact1: {AA}{a} fact2: (x): ¬{A}x -> (¬{AA}x v {AB}x) fact3: {A}{a} -> ¬(¬{AA}{b} v {AB}{b}) | [] | [] | ãã®äžã髪ãã¢ã³ããŒããŒã§ãªãããããã¯å
äžã | (¬{AA}{b} v {AB}{b}) | [
"fact4 -> int1: ãããã®äžã髪ããããããªããªããªãã°ãããã¢ã³ããŒããŒã ãšããããšã¯ãªãããããã¯ãããå
äžã ;"
] | 4 | 1 | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ç·åž¥ã¯ã¢ã³ããŒããŒã fact2: ãããããªããªããã®ãã¢ã³ããŒããŒã§ãªãããããã¯å
äžã§ããããããã¯äž¡æ¹ã fact3: ãããã®ç·åž¥ããããããªããªãã°ããã®äžã髪ãã¢ã³ããŒããŒã§ãªãããããå
äžã§ãããäž¡æ¹ã ããšããããšãæãç«ããªã ; $hypothesis$ = ãã®äžã髪ã¯ã¢ã³ããŒããŒã ãšããããšããªãããããå
äžã§ããããããã¯äž¡æ¹ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {AA}{a} fact2: (x): ¬{A}x -> (¬{AA}x v {AB}x) fact3: {A}{a} -> ¬(¬{AA}{b} v {AB}{b}) ; $hypothesis$ = (¬{AA}{b} v {AB}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã圫ããããããããšãèµ·ããããããããããšããããšã¯çããªãããšããããšã¯æãç«ã€ããšããããšãæãç«ã€ãšããããšã¯ãªã | ¬({A} & ¬{B}) | fact1: ãããããŸããããšããããšãšçŽ°ããããšããããšäž¡æ¹ã¯çºçããããšããããšãåœã ããšããããšã¯æãç«ãŠã°çŽ°ããããšããããšã¯çããªã fact2: ããããŸãããããšãèµ·ããªããŠããããã«å¥ãããšãèµ·ãããªãããšããããšãäºå®ã ãšããããšããªããªãã°ããããã«å¥ãããšãçºçãã fact3: ããããªãããªããŒã·ã§ã³ãèµ·ãããããããšããããšã¯èµ·ãããªãããšããããšãåœãªãã°ãªãããªããŒã·ã§ã³ã¯çºçããªã fact4: ããåãã¯çããªããªãã°ãããŸãããããšã¯èµ·ãããªããŠããããã«å¥ãããšãçããªãããšããããšã¯æ£ããããšããããšã¯äºå®ãšç°ãªã fact5: ããã现ããããšããããšãçºçããªãããšããããšãæãç«ãŠã°ãããªãããªããŒã·ã§ã³ã¯çãããããããšããããšã¯èµ·ãããªãããšããããšãäºå®ã ããšããããšã¯äºå®ã ãšããããšããªã fact6: ãããã€ããšããããšãçããããšããããšã¯ããŸããããšããããšãçããããšããããšããããã¯ãå²åœãŠã¯èµ·ãããªãããšããããšããããã¯äž¡æ¹ããããã fact7: ããããããããšããããšãçããã°ãå®å°ã¯èµ·ãããªãããããã¯çŠçŠãããšããããšã¯èµ·ãããäž¡æ¹ã ããšããããšã¯èª€ãã fact8: 圫ããããããããšã¯çºçãã fact9: ããããšããããšãèµ·ããªã fact10: ããããŸãããããšãšããããã«å¥ãããšäž¡æ¹ãèµ·ããããšããããšã¯åãªãã°ããããã«å¥ãããšã¯çããªã fact11: ãã现ããããšããããšã¯èµ·ããã°ã圫ããããããããšã¯èµ·ããããããããããšããããšã¯çºçããªãããšããããšã¯æãç«ããªã fact12: ãããå®å°ãçããªããçŠçŠãããšããããšã¯èµ·ãããäž¡æ¹ã ããšããããšã¯èª€ããªãã°åããçããªã fact13: ããå²åœãŠã¯èµ·ãããªããªãã°çŽ°ããããšããããšãšå¿ããŸãããšããããšäž¡æ¹ãèµ·ãã fact14: å²åœãŠãèµ·ããªããšããããšã¯ããŸããããšããããšãèµ·ããããããã¯å²åœãŠãçããªããäž¡æ¹ã ããšããããšã«èªçºããã fact15: ãå¿ããŸãããšããããšã¯èµ·ãããªãããããå²åœãŠã¯èµ·ããããšããããšã¯ããã€ããšããããšã¯èµ·ãããšããããšããã£ããã fact16: ããããããã«å¥ãããšã¯èµ·ããªããªãã°çã£é»ããšããããšãšããã€ããšããããšäž¡æ¹ãèµ·ãã fact17: 転ããããšã¯èµ·ãããªã fact18: ããå¿ããŸãããšããããšã¯çããªããªãã°ãµã¿ãã ãããšãçããã圫ããããããããšãèµ·ãã | fact1: ¬({G} & {C}) -> ¬{C} fact2: ¬(¬{K} & ¬{I}) -> {I} fact3: ¬({ES} & ¬{B}) -> ¬{ES} fact4: ¬{J} -> ¬(¬{K} & ¬{I}) fact5: ¬{C} -> ¬({ES} & ¬{B}) fact6: {F} -> ({G} v ¬{E}) fact7: {N} -> ¬(¬{L} v {M}) fact8: {A} fact9: ¬{B} fact10: ¬({K} & {I}) -> ¬{I} fact11: {C} -> ¬({A} & ¬{B}) fact12: ¬(¬{L} v {M}) -> ¬{J} fact13: ¬{E} -> ({C} & {D}) fact14: ({G} v ¬{E}) -> ¬{E} fact15: {F} -> (¬{D} & {E}) fact16: ¬{I} -> ({H} & {F}) fact17: ¬{CT} fact18: ¬{D} -> ({FR} & {A}) | [
"fact8 & fact9 -> hypothesis;"
] | [
"fact8 & fact9 -> hypothesis;"
] | ãµã¿ãã ãããšãèµ·ããããªãããªããŒã·ã§ã³ãèµ·ããªã | ({FR} & ¬{ES}) | [] | 8 | 1 | 1 | 16 | 0 | 16 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããããŸããããšããããšãšçŽ°ããããšããããšäž¡æ¹ã¯çºçããããšããããšãåœã ããšããããšã¯æãç«ãŠã°çŽ°ããããšããããšã¯çããªã fact2: ããããŸãããããšãèµ·ããªããŠããããã«å¥ãããšãèµ·ãããªãããšããããšãäºå®ã ãšããããšããªããªãã°ããããã«å¥ãããšãçºçãã fact3: ããããªãããªããŒã·ã§ã³ãèµ·ãããããããšããããšã¯èµ·ãããªãããšããããšãåœãªãã°ãªãããªããŒã·ã§ã³ã¯çºçããªã fact4: ããåãã¯çããªããªãã°ãããŸãããããšã¯èµ·ãããªããŠããããã«å¥ãããšãçããªãããšããããšã¯æ£ããããšããããšã¯äºå®ãšç°ãªã fact5: ããã现ããããšããããšãçºçããªãããšããããšãæãç«ãŠã°ãããªãããªããŒã·ã§ã³ã¯çãããããããšããããšã¯èµ·ãããªãããšããããšãäºå®ã ããšããããšã¯äºå®ã ãšããããšããªã fact6: ãããã€ããšããããšãçããããšããããšã¯ããŸããããšããããšãçããããšããããšããããã¯ãå²åœãŠã¯èµ·ãããªãããšããããšããããã¯äž¡æ¹ããããã fact7: ããããããããšããããšãçããã°ãå®å°ã¯èµ·ãããªãããããã¯çŠçŠãããšããããšã¯èµ·ãããäž¡æ¹ã ããšããããšã¯èª€ãã fact8: 圫ããããããããšã¯çºçãã fact9: ããããšããããšãèµ·ããªã fact10: ããããŸãããããšãšããããã«å¥ãããšäž¡æ¹ãèµ·ããããšããããšã¯åãªãã°ããããã«å¥ãããšã¯çããªã fact11: ãã现ããããšããããšã¯èµ·ããã°ã圫ããããããããšã¯èµ·ããããããããããšããããšã¯çºçããªãããšããããšã¯æãç«ããªã fact12: ãããå®å°ãçããªããçŠçŠãããšããããšã¯èµ·ãããäž¡æ¹ã ããšããããšã¯èª€ããªãã°åããçããªã fact13: ããå²åœãŠã¯èµ·ãããªããªãã°çŽ°ããããšããããšãšå¿ããŸãããšããããšäž¡æ¹ãèµ·ãã fact14: å²åœãŠãèµ·ããªããšããããšã¯ããŸããããšããããšãèµ·ããããããã¯å²åœãŠãçããªããäž¡æ¹ã ããšããããšã«èªçºããã fact15: ãå¿ããŸãããšããããšã¯èµ·ãããªãããããå²åœãŠã¯èµ·ããããšããããšã¯ããã€ããšããããšã¯èµ·ãããšããããšããã£ããã fact16: ããããããã«å¥ãããšã¯èµ·ããªããªãã°çã£é»ããšããããšãšããã€ããšããããšäž¡æ¹ãèµ·ãã fact17: 転ããããšã¯èµ·ãããªã fact18: ããå¿ããŸãããšããããšã¯çããªããªãã°ãµã¿ãã ãããšãçããã圫ããããããããšãèµ·ãã ; $hypothesis$ = ãã圫ããããããããšãèµ·ããããããããããšããããšã¯çããªãããšããããšã¯æãç«ã€ããšããããšãæãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact8 & fact9 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({G} & {C}) -> ¬{C} fact2: ¬(¬{K} & ¬{I}) -> {I} fact3: ¬({ES} & ¬{B}) -> ¬{ES} fact4: ¬{J} -> ¬(¬{K} & ¬{I}) fact5: ¬{C} -> ¬({ES} & ¬{B}) fact6: {F} -> ({G} v ¬{E}) fact7: {N} -> ¬(¬{L} v {M}) fact8: {A} fact9: ¬{B} fact10: ¬({K} & {I}) -> ¬{I} fact11: {C} -> ¬({A} & ¬{B}) fact12: ¬(¬{L} v {M}) -> ¬{J} fact13: ¬{E} -> ({C} & {D}) fact14: ({G} v ¬{E}) -> ¬{E} fact15: {F} -> (¬{D} & {E}) fact16: ¬{I} -> ({H} & {F}) fact17: ¬{CT} fact18: ¬{D} -> ({FR} & {A}) ; $hypothesis$ = ¬({A} & ¬{B}) ; $proof$ = | fact8 & fact9 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŽã«ãã¯ã©ãã¯çæ·±ãããããé£ãç«ã€ããšããããšã¯æãç«ã€ãšããããšããªã | ¬({AA}{aa} & {AB}{aa}) | fact1: ããã¯å¹ç°ã§ãã£ãŠäžåœãã¯ããããã®ãšãããã®ã¯ãªã fact2: åºæãã¯çž®ãŸããšããããšã¯ãªãããããæš«éåŽãæ¿¡ãããŒã€ fact3: ããã¯éç®ã«ããŠã¯ãããããã朮é ã«ãããšãããšãããã®ããªã fact4: ããã¯æ¢ããã±ããã ãšãããã®ããªã fact5: ãããããã®ãçž®ãŸããšããããšããªããªãã°ãããã¯ãã ãã ãããŠããã¯çæ·±ãããšããããšãæãç«ã€ãšããããšã¯ãªã fact6: ãããããã®ã¯ãããããã fact7: å
šãŠã®ãã®ã¯çæ·±ããçž®ãŸããšããããšã¯ãªã fact8: ããã¯åæ¥ã ãå
ã€ããã³ããããšãããã®ã¯ãªã fact9: ããããããšããããããã¯å©è±ã ãšãããã®ã¯ãªã fact10: ããã®ã¯ã±ã®ãé£ãç«ã€ããããããããããããšããããšã¯æãç«ããªã | fact1: (x): ¬({HA}x & {ER}x) fact2: (x): {C}x -> (¬{A}x & {B}x) fact3: (x): ¬({CE}x & {CB}x) fact4: (x): ¬({IN}x & {N}x) fact5: (x): ¬{A}x -> ¬({GN}x & {AA}x) fact6: (x): {D}x fact7: (x): ({AA}x & ¬{A}x) fact8: (x): ¬({CR}x & {GS}x) fact9: (x): ¬({DL}x & {FI}x) fact10: ¬({AB}{bo} & {HI}{bo}) | [] | [] | ãã®ãŽã«ãã¯ã©ãã¯çæ·±ããŠé£ãç«ã€ | ({AA}{aa} & {AB}{aa}) | [
"fact11 -> int1: ãã®ãŽã«ãã¯ã©ãã¯çæ·±ããã®ã§ãã£ãŠçž®ãŸããšããããšã¯ãªããã®; int1 -> int2: ãã®ãŽã«ãã¯ã©ããçæ·±ã;"
] | 4 | 1 | null | 10 | 0 | 10 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã¯å¹ç°ã§ãã£ãŠäžåœãã¯ããããã®ãšãããã®ã¯ãªã fact2: åºæãã¯çž®ãŸããšããããšã¯ãªãããããæš«éåŽãæ¿¡ãããŒã€ fact3: ããã¯éç®ã«ããŠã¯ãããããã朮é ã«ãããšãããšãããã®ããªã fact4: ããã¯æ¢ããã±ããã ãšãããã®ããªã fact5: ãããããã®ãçž®ãŸããšããããšããªããªãã°ãããã¯ãã ãã ãããŠããã¯çæ·±ãããšããããšãæãç«ã€ãšããããšã¯ãªã fact6: ãããããã®ã¯ãããããã fact7: å
šãŠã®ãã®ã¯çæ·±ããçž®ãŸããšããããšã¯ãªã fact8: ããã¯åæ¥ã ãå
ã€ããã³ããããšãããã®ã¯ãªã fact9: ããããããšããããããã¯å©è±ã ãšãããã®ã¯ãªã fact10: ããã®ã¯ã±ã®ãé£ãç«ã€ããããããããããããšããããšã¯æãç«ããªã ; $hypothesis$ = ããã®ãŽã«ãã¯ã©ãã¯çæ·±ãããããé£ãç«ã€ããšããããšã¯æãç«ã€ãšããããšããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬({HA}x & {ER}x) fact2: (x): {C}x -> (¬{A}x & {B}x) fact3: (x): ¬({CE}x & {CB}x) fact4: (x): ¬({IN}x & {N}x) fact5: (x): ¬{A}x -> ¬({GN}x & {AA}x) fact6: (x): {D}x fact7: (x): ({AA}x & ¬{A}x) fact8: (x): ¬({CR}x & {GS}x) fact9: (x): ¬({DL}x & {FI}x) fact10: ¬({AB}{bo} & {HI}{bo}) ; $hypothesis$ = ¬({AA}{aa} & {AB}{aa}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã®ã¯ã®ãã¯è¡çãªãã°ããããæ家ã«äœãããšããããšããªãããããã¯ãããåãŸããããšããããšã¯èª€ãã | {A}{aa} -> ¬(¬{AA}{aa} v {AB}{aa}) | fact1: ããããã®ã¯ã®ããè¡çã ããšããããšã¯æãç«ãŠã°ããããæ家ã«äœããããããã¯åãŸããããšããããšãæãç«ã€ãšããããšã¯ãªã fact2: ãããããã®ã¯è¡çãªãã°ããããæ家ã«äœãããšããããšã¯ãªããåãŸããããããã¯äž¡æ¹ã ããšããããšãæãç«ã€ãšããããšããªã fact3: ããäœãã袎è
°å±±ã«ã©ããã°ããããåžæããªã ã蟌ããšããããšããªããããã¯ç¢åã ããšããããšãæãç«ã€ãšããããšããªã fact4: è¡çãåãŸãããšããããšã¯ãªã fact5: è¡çãæ家ã«äœããªãããããã¯åãŸããããããã¯äž¡æ¹ã fact6: ãããã®ã¯ã®ããè¡çãªãã°ããã¯åãŸãããªã fact7: ãããã®ã¯ã®ãã¯è¡çãªãã°ãããæ家ã«äœãããšããããšããªãããããã¯ãããåãŸãã fact8: ãããããã®ã¯è¡çãªãã°ãããã¯æ家ã«äœãããåãŸãããäž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact9: ãããã®ã¯ã®ããç¢åãªãã°ããããè¡çã ãšããããšã¯ãªãããããå¿æŽã«æãã€ãããäž¡æ¹ã ããšããããšãæãç«ããªã fact10: ãããã®ç§æãåãŸãããªãã°ããããææŒããã¯ããŸãããšããããšã¯ãªãããããããããŸããããšããããšãåã fact11: ãããããã®ã¯å®æ²»å£å°åãªãã°ãããã¯äŒŒåãããšããããšããªãããããã¯ãŸããããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã | fact1: {A}{aa} -> ¬({AA}{aa} v {AB}{aa}) fact2: (x): {A}x -> ¬(¬{AA}x v {AB}x) fact3: (x): {DE}x -> ¬(¬{BN}x v {CR}x) fact4: (x): {A}x -> ¬{AB}x fact5: (x): {A}x -> (¬{AA}x v {AB}x) fact6: {A}{aa} -> ¬{AB}{aa} fact7: {A}{aa} -> (¬{AA}{aa} v {AB}{aa}) fact8: (x): {A}x -> ¬({AA}x v {AB}x) fact9: {CR}{aa} -> ¬(¬{A}{aa} v {BF}{aa}) fact10: {AB}{gj} -> ¬(¬{FR}{gj} v {I}{gj}) fact11: (x): {DU}x -> ¬(¬{CP}x v {P}x) | [
"fact2 -> hypothesis;"
] | [
"fact2 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 10 | 0 | 10 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ã¯ã®ããè¡çã ããšããããšã¯æãç«ãŠã°ããããæ家ã«äœããããããã¯åãŸããããšããããšãæãç«ã€ãšããããšã¯ãªã fact2: ãããããã®ã¯è¡çãªãã°ããããæ家ã«äœãããšããããšã¯ãªããåãŸããããããã¯äž¡æ¹ã ããšããããšãæãç«ã€ãšããããšããªã fact3: ããäœãã袎è
°å±±ã«ã©ããã°ããããåžæããªã ã蟌ããšããããšããªããããã¯ç¢åã ããšããããšãæãç«ã€ãšããããšããªã fact4: è¡çãåãŸãããšããããšã¯ãªã fact5: è¡çãæ家ã«äœããªãããããã¯åãŸããããããã¯äž¡æ¹ã fact6: ãããã®ã¯ã®ããè¡çãªãã°ããã¯åãŸãããªã fact7: ãããã®ã¯ã®ãã¯è¡çãªãã°ãããæ家ã«äœãããšããããšããªãããããã¯ãããåãŸãã fact8: ãããããã®ã¯è¡çãªãã°ãããã¯æ家ã«äœãããåãŸãããäž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact9: ãããã®ã¯ã®ããç¢åãªãã°ããããè¡çã ãšããããšã¯ãªãããããå¿æŽã«æãã€ãããäž¡æ¹ã ããšããããšãæãç«ããªã fact10: ãããã®ç§æãåãŸãããªãã°ããããææŒããã¯ããŸãããšããããšã¯ãªãããããããããŸããããšããããšãåã fact11: ãããããã®ã¯å®æ²»å£å°åãªãã°ãããã¯äŒŒåãããšããããšããªãããããã¯ãŸããããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã ; $hypothesis$ = ãããã®ã¯ã®ãã¯è¡çãªãã°ããããæ家ã«äœãããšããããšããªãããããã¯ãããåãŸããããšããããšã¯èª€ãã ; $proof$ = | fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{aa} -> ¬({AA}{aa} v {AB}{aa}) fact2: (x): {A}x -> ¬(¬{AA}x v {AB}x) fact3: (x): {DE}x -> ¬(¬{BN}x v {CR}x) fact4: (x): {A}x -> ¬{AB}x fact5: (x): {A}x -> (¬{AA}x v {AB}x) fact6: {A}{aa} -> ¬{AB}{aa} fact7: {A}{aa} -> (¬{AA}{aa} v {AB}{aa}) fact8: (x): {A}x -> ¬({AA}x v {AB}x) fact9: {CR}{aa} -> ¬(¬{A}{aa} v {BF}{aa}) fact10: {AB}{gj} -> ¬(¬{FR}{gj} v {I}{gj}) fact11: (x): {DU}x -> ¬(¬{CP}x v {P}x) ; $hypothesis$ = {A}{aa} -> ¬(¬{AA}{aa} v {AB}{aa}) ; $proof$ = | fact2 -> hypothesis; __PROVED__ |
0.3 | æ œå¹ã¯çããªã | ¬{B} | fact1: ããã£ãããšããããšã¯èµ·ãã fact2: ãåšæ³¢ã¯èµ·ããªãããšããããšãããã£ãããšããããšãäž¡æ¹ããæšããšããããšã¯èµ·ããããšããããšã«èªçºããã fact3: ãæå€ããšããããšã¯çºçããããšããããšã¯è財ãããã ãã¶ãããšãçºçãããšããããšã«èµ·å ãã fact4: ããã¬ã¹ãçããããšããããšãæãç«ã€ fact5: ãå
±æ¯ã¯èµ·ããããšããããšãç·è£ã¯çãããšããããšããã£ããã fact6: ãå®è¡ã¯çºçããããšããããšã¯è±æ¯ã«ã²ãŸã©ãããšã¯çºçãããšããããšã«åŒãèµ·ãããã fact7: å®è¡ãèµ·ãã fact8: éåã¯çºçãã fact9: å®éåã«ãã¡ããŠãããšã¯èµ·ããªããšããããšãæšããšããããšããããã fact10: ã¢ã€ãã£ãã«å
ãããããšã¯èµ·ããªããšããããšããå®éåã«ãã¡ããŠãããšã¯èµ·ããªããçã¿èãã¯çºçããªãããšããããšãçºçããã fact11: 床é£ããšããããšã¯èµ·ãã fact12: åæ°ãªããšããããšã¯å±éºã¯çãããšããããšã«ãããããã fact13: æ œå¹ã¯ãããã£ãããšããããšãšåšæ³¢äž¡æ¹ã¯çããããšããããšã«å¶æ¢ããã fact14: æ€æ£ã«ããããããããšãèµ·ãããšããããšã¯è³è³ã¯èµ·ãããšããããšã«ãããããã fact15: ãããåšæ³¢ãèµ·ãããªããããã£ãããšããããšã¯èµ·ããããããã¯äž¡æ¹ã ããšããããšãçå®ã§ãªããªãã°æ œå¹ã¯èµ·ããªã | fact1: {A} fact2: {D} -> (¬{C} v {A}) fact3: {ED} -> {BM} fact4: {EO} fact5: {HD} -> {EE} fact6: {R} -> {EI} fact7: {EI} fact8: {EJ} fact9: ¬{E} -> {D} fact10: ¬{G} -> (¬{E} & ¬{F}) fact11: {HF} fact12: {CL} -> {GR} fact13: ({A} & {C}) -> ¬{B} fact14: {JJ} -> {CJ} fact15: ¬(¬{C} v {A}) -> ¬{B} | [] | [] | æ œå¹ãèµ·ããªã | ¬{B} | [] | 8 | 1 | null | 14 | 0 | 14 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã£ãããšããããšã¯èµ·ãã fact2: ãåšæ³¢ã¯èµ·ããªãããšããããšãããã£ãããšããããšãäž¡æ¹ããæšããšããããšã¯èµ·ããããšããããšã«èªçºããã fact3: ãæå€ããšããããšã¯çºçããããšããããšã¯è財ãããã ãã¶ãããšãçºçãããšããããšã«èµ·å ãã fact4: ããã¬ã¹ãçããããšããããšãæãç«ã€ fact5: ãå
±æ¯ã¯èµ·ããããšããããšãç·è£ã¯çãããšããããšããã£ããã fact6: ãå®è¡ã¯çºçããããšããããšã¯è±æ¯ã«ã²ãŸã©ãããšã¯çºçãããšããããšã«åŒãèµ·ãããã fact7: å®è¡ãèµ·ãã fact8: éåã¯çºçãã fact9: å®éåã«ãã¡ããŠãããšã¯èµ·ããªããšããããšãæšããšããããšããããã fact10: ã¢ã€ãã£ãã«å
ãããããšã¯èµ·ããªããšããããšããå®éåã«ãã¡ããŠãããšã¯èµ·ããªããçã¿èãã¯çºçããªãããšããããšãçºçããã fact11: 床é£ããšããããšã¯èµ·ãã fact12: åæ°ãªããšããããšã¯å±éºã¯çãããšããããšã«ãããããã fact13: æ œå¹ã¯ãããã£ãããšããããšãšåšæ³¢äž¡æ¹ã¯çããããšããããšã«å¶æ¢ããã fact14: æ€æ£ã«ããããããããšãèµ·ãããšããããšã¯è³è³ã¯èµ·ãããšããããšã«ãããããã fact15: ãããåšæ³¢ãèµ·ãããªããããã£ãããšããããšã¯èµ·ããããããã¯äž¡æ¹ã ããšããããšãçå®ã§ãªããªãã°æ œå¹ã¯èµ·ããªã ; $hypothesis$ = æ œå¹ã¯çããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} fact2: {D} -> (¬{C} v {A}) fact3: {ED} -> {BM} fact4: {EO} fact5: {HD} -> {EE} fact6: {R} -> {EI} fact7: {EI} fact8: {EJ} fact9: ¬{E} -> {D} fact10: ¬{G} -> (¬{E} & ¬{F}) fact11: {HF} fact12: {CL} -> {GR} fact13: ({A} & {C}) -> ¬{B} fact14: {JJ} -> {CJ} fact15: ¬(¬{C} v {A}) -> ¬{B} ; $hypothesis$ = ¬{B} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããæ°æ€èŠå·ã§ãªããæ·ãããšããããšããªãããšããããšã¯èª€ããªããã®ãããããšããããšã¯æãç«ã€ãšããããšããªã | ¬((Ex): ¬(¬{AA}x & ¬{AB}x)) | fact1: ããäœãã¯ã¢ãžããšããããšããªããªãã°ãããæšæ¢¶ãããããçªåºãã fact2: ããæ°æ€èŠå·ã ãšããããšã¯ãªããæ·ããããšããããšãééããªããã®ã¯ãã fact3: ãããç¡ããªããåžžç€åºç·ã ãšããããšããªãããšããããšã¯çå®ã ããšããããšã¯æãç«ã€ãšããããšããªãããã®ããã fact4: ãããééãããªããåç¬ã§ãªãããã®ãããã°ãã®èŸºå¢ã¯ã¢ãžããšããããšããªã fact5: ãããã€ãããã®ã§ãã£ãŠå¹³äžéä¿£ã«éŠŽæããã®ããšããããšã¯åœãªããã®ããã fact6: ãããã®æ¯ãè
ãè
ç¡ç°é·ã«ããããããšããããšããªããªãã°ãããééãããšããããšããªããåç¬ã ãšããããšããªã fact7: ãããã®èŸºå¢ãæšæ¢¶ããããã°ãã®äž»ä»»ããºãã³ããã fact8: ãããããã€ãããã®ã§ãã£ãŠå¹³äžéä¿£ã«éŠŽæããã®ããšããããšã¯æãç«ããªãããã®ãããã°ãã®ãæŒã¯å¹³äžéä¿£ã«éŠŽæããšããããšã¯ãªã fact9: ããæ°æ€èŠå·ã ãæ·ãããªãããšããããšã誀ããªããã®ããã fact10: ãããå¹³äžéä¿£ã«éŠŽæããšããããšã¯ãªãããã®ã¯ããã°ããã®å·ãåŒãããè
ç¡ç°é·ã«ããããããšããããšããªãããšããããšãæãç«ããªã fact11: ããäœãã¯ãºãã³ãããªãã°ãããã¯äžèŠæš¡ã§ãªããèŒããããšããããšããªãããšããããšã¯ééãã fact12: ããé¢ã¯ãããªãã通åãæã¡åºããªãããšããããšã誀ããªããã®ã¯ãã fact13: ããã®å·Ÿã¯æ°æ€èŠå·ã§ãªããŠæ·ãããšããããšã¯ãªãããšããããšã¯æ£ãããšããããšããªã fact14: ããã®å·Ÿãæ°æ€èŠå·ã ãšããããšããªããæ·ããããšããããšãäºå®ãšç°ãªã fact15: ããããã®å·ã¯åŒããããããããã¯è
ç¡ç°é·ã«ãããããªãããšããããšãééããªãã°ãã®æ¯ãè
ãè
ç¡ç°é·ã«ãããããªã fact16: ãããã®ãæ°æ€èŠå·ã ãšããããšã¯ãªããŠããã¯æ·ãããšããããšã¯ãªã fact17: ããã®å·Ÿãæ°æ€èŠå·ã ããããæ·ãããªãããšããããšã¯ééãã | fact1: (x): ¬{D}x -> ({B}x & {C}x) fact2: (Ex): ¬(¬{AA}x & {AB}x) fact3: (Ex): ¬(¬{DC}x & ¬{DH}x) fact4: (x): (¬{E}x & ¬{F}x) -> ¬{D}{b} fact5: (Ex): ¬({K}x & {I}x) fact6: ¬{G}{c} -> (¬{E}{c} & ¬{F}{c}) fact7: {B}{b} -> {A}{a} fact8: (x): ¬({K}x & {I}x) -> ¬{I}{e} fact9: (Ex): ¬({AA}x & ¬{AB}x) fact10: (x): ¬{I}x -> ¬({H}{d} & ¬{G}{d}) fact11: (x): {A}x -> ¬(¬{AL}x & ¬{BL}x) fact12: (Ex): ¬(¬{II}x & ¬{HU}x) fact13: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact14: ¬(¬{AA}{aa} & {AB}{aa}) fact15: ¬({H}{d} & ¬{G}{d}) -> ¬{G}{c} fact16: (Ex): (¬{AA}x & ¬{AB}x) fact17: ¬({AA}{aa} & ¬{AB}{aa}) | [
"fact13 -> hypothesis;"
] | [
"fact13 -> hypothesis;"
] | ããäžèŠæš¡ã ãšããããšããªããŠèŒããããªãããšããããšãäºå®ãšç°ãªãããã®ããã | (Ex): ¬(¬{AL}x & ¬{BL}x) | [
"fact23 -> int1: ãããã®äž»ä»»ã¯ãºãã³ãããªãã°ããããäžèŠæš¡ã§ãªããŠèŒããããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã; fact19 -> int2: ãããã®èŸºå¢ãã¢ãžããšããããšããªããªãã°ãããæšæ¢¶ãããããçªåºãã ; fact24 & fact25 -> int3: ãã®ãæŒãå¹³äžéä¿£ã«éŠŽæããšããããšããªã; int3 -> int4: ãå¹³äžéä¿£ã«éŠŽæãŸãªãããã®ããã; int4 & fact21 -> int5: ããã®å·ã¯åŒãããããããããè
ç¡ç°é·ã«ããããããšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšããªã; fact22 & int5 -> int6: ãã®æ¯ãè
ãè
ç¡ç°é·ã«ããããããšããããšã¯ãªã; fact26 & int6 -> int7: ããã®æ¯ãè
ãééãããšããããšããªããŠãããåç¬ã ãšããããšã¯ãªãããšããããšãæãç«ã€; int7 -> int8: ãããã®ã¯ééãããšããããšããªããã®ã§ãã£ãŠåç¬ã ãšããããšããªããã®; int8 & fact20 -> int9: ãã®èŸºå¢ãã¢ãžããªã; int2 & int9 -> int10: ãã®èŸºå¢ãæšæ¢¶ãããããçªåºãã ; int10 -> int11: ãã®èŸºå¢ã¯æšæ¢¶ãããã; fact18 & int11 -> int12: ãã®äž»ä»»ããºãã³ããã ; int1 & int12 -> int13: ããã®äž»ä»»ã¯äžèŠæš¡ã§ãªããŠããã¯èŒããããšããããšã¯ãªãããšããããšãæ¬åœã§ãªã; int13 -> hypothesis;"
] | 12 | 1 | 1 | 16 | 0 | 16 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ããäœãã¯ã¢ãžããšããããšããªããªãã°ãããæšæ¢¶ãããããçªåºãã fact2: ããæ°æ€èŠå·ã ãšããããšã¯ãªããæ·ããããšããããšãééããªããã®ã¯ãã fact3: ãããç¡ããªããåžžç€åºç·ã ãšããããšããªãããšããããšã¯çå®ã ããšããããšã¯æãç«ã€ãšããããšããªãããã®ããã fact4: ãããééãããªããåç¬ã§ãªãããã®ãããã°ãã®èŸºå¢ã¯ã¢ãžããšããããšããªã fact5: ãããã€ãããã®ã§ãã£ãŠå¹³äžéä¿£ã«éŠŽæããã®ããšããããšã¯åœãªããã®ããã fact6: ãããã®æ¯ãè
ãè
ç¡ç°é·ã«ããããããšããããšããªããªãã°ãããééãããšããããšããªããåç¬ã ãšããããšããªã fact7: ãããã®èŸºå¢ãæšæ¢¶ããããã°ãã®äž»ä»»ããºãã³ããã fact8: ãããããã€ãããã®ã§ãã£ãŠå¹³äžéä¿£ã«éŠŽæããã®ããšããããšã¯æãç«ããªãããã®ãããã°ãã®ãæŒã¯å¹³äžéä¿£ã«éŠŽæããšããããšã¯ãªã fact9: ããæ°æ€èŠå·ã ãæ·ãããªãããšããããšã誀ããªããã®ããã fact10: ãããå¹³äžéä¿£ã«éŠŽæããšããããšã¯ãªãããã®ã¯ããã°ããã®å·ãåŒãããè
ç¡ç°é·ã«ããããããšããããšããªãããšããããšãæãç«ããªã fact11: ããäœãã¯ãºãã³ãããªãã°ãããã¯äžèŠæš¡ã§ãªããèŒããããšããããšããªãããšããããšã¯ééãã fact12: ããé¢ã¯ãããªãã通åãæã¡åºããªãããšããããšã誀ããªããã®ã¯ãã fact13: ããã®å·Ÿã¯æ°æ€èŠå·ã§ãªããŠæ·ãããšããããšã¯ãªãããšããããšã¯æ£ãããšããããšããªã fact14: ããã®å·Ÿãæ°æ€èŠå·ã ãšããããšããªããæ·ããããšããããšãäºå®ãšç°ãªã fact15: ããããã®å·ã¯åŒããããããããã¯è
ç¡ç°é·ã«ãããããªãããšããããšãééããªãã°ãã®æ¯ãè
ãè
ç¡ç°é·ã«ãããããªã fact16: ãããã®ãæ°æ€èŠå·ã ãšããããšã¯ãªããŠããã¯æ·ãããšããããšã¯ãªã fact17: ããã®å·Ÿãæ°æ€èŠå·ã ããããæ·ãããªãããšããããšã¯ééãã ; $hypothesis$ = ãããæ°æ€èŠå·ã§ãªããæ·ãããšããããšããªãããšããããšã¯èª€ããªããã®ãããããšããããšã¯æãç«ã€ãšããããšããªã ; $proof$ = | fact13 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{D}x -> ({B}x & {C}x) fact2: (Ex): ¬(¬{AA}x & {AB}x) fact3: (Ex): ¬(¬{DC}x & ¬{DH}x) fact4: (x): (¬{E}x & ¬{F}x) -> ¬{D}{b} fact5: (Ex): ¬({K}x & {I}x) fact6: ¬{G}{c} -> (¬{E}{c} & ¬{F}{c}) fact7: {B}{b} -> {A}{a} fact8: (x): ¬({K}x & {I}x) -> ¬{I}{e} fact9: (Ex): ¬({AA}x & ¬{AB}x) fact10: (x): ¬{I}x -> ¬({H}{d} & ¬{G}{d}) fact11: (x): {A}x -> ¬(¬{AL}x & ¬{BL}x) fact12: (Ex): ¬(¬{II}x & ¬{HU}x) fact13: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact14: ¬(¬{AA}{aa} & {AB}{aa}) fact15: ¬({H}{d} & ¬{G}{d}) -> ¬{G}{c} fact16: (Ex): (¬{AA}x & ¬{AB}x) fact17: ¬({AA}{aa} & ¬{AB}{aa}) ; $hypothesis$ = ¬((Ex): ¬(¬{AA}x & ¬{AB}x)) ; $proof$ = | fact13 -> hypothesis; __DISPROVED__ |
0.3 | ããããããšããããšã¯çºçããªããåããããšãçããªã | (¬{AA} & ¬{AB}) | fact1: ããããããšããããšãçããªããŠåããããšãçºçããªã fact2: åããããšãçºçããªã | fact1: (¬{AA} & ¬{AB}) fact2: ¬{AB} | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 0 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ããããããšããããšãçããªããŠåããããšãçºçããªã fact2: åããããšãçºçããªã ; $hypothesis$ = ããããããšããããšã¯çºçããªããåããããšãçããªã ; $proof$ = | fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: (¬{AA} & ¬{AB}) fact2: ¬{AB} ; $hypothesis$ = (¬{AA} & ¬{AB}) ; $proof$ = | fact1 -> hypothesis; __PROVED__ |
0.3 | ãç§çã§ã¯ãªãè¿ãå¿ ãçºçããããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬(¬{A} & {B}) | fact1: è¿ãå¿ ãçºçãã fact2: ãããè¬ã¯èµ·ããªããçç°ãæŒé ãããšãçºçããªãããšããããšãçå®ã ãšããããšã¯ãªããªãã°ãè¬ã¯çããããšããããšãäºå®ã fact3: ããŠã¥ãããšããããšãçºçããããšããããšãæãç«ã€ fact4: ããããããããšããããšãçããã°éæ°Žãããã¯ããããšã¯çããªããã²ã£ãããããããšãçºçããªã fact5: ãã¢ã ãã¹ãã£ã¯èµ·ããªãããšããããšã¯ãäžé·¹å°ãæ±ãç· ããããšãçããããããé è€ã«çãããããšã¯èµ·ãããªãããšããããšã«ããçãã fact6: ãåºç€ãèµ·ãããè²æã«å·®ãåããããšãçããããšããããšãã¢ã ãã¹ãã£ã¯èµ·ããªããšããããšã«ããçºçãã fact7: ç§çãèµ·ããªã fact8: ãç«ã¡ä»£ããããšãèµ·ãããªããŠãã¬ããŒã¯ããã³ã€ã¥ããããšã¯çããªãããšããããšã¯è¬ã«èµ·å ãã fact9: ããã³ã¯ããšããããšãèµ·ãããªããªãã°ãè¬ãçºçããªããçç°ãæŒé ãããšãèµ·ããªãããšããããšã¯æãç«ã€ãšããããšããªã fact10: ã³ã¯ããšããããšã¯èµ·ãããšããããšãåºç€ãèµ·ãããšããããšã«é²ããã fact11: ããäœçœ°ã¯èµ·ãããªããªãã°ãç§çã¯çºçããªããè¿ãå¿ ã¯èµ·ããããšããããšã¯çå®ã§ãªã fact12: ãç«ã¡ä»£ããããšãçºçããªãããšããããšã¯ãããããããšããããšãšãã·ã£ãŽã黎ã³ãããšäž¡æ¹ã¯èµ·ããããšããããšãåŒãèµ·ãã fact13: ãäœçœ°ãèµ·ãããªãããªãã§ã³ã¹ãèµ·ãããªãããšããããšãã²ã£ãããããããšãçããªããšããããšã«åŒãèµ·ãããã fact14: äžé·¹å°ãæ±ãç· ããããšãçãã | fact1: {B} fact2: ¬(¬{K} & ¬{L}) -> {K} fact3: {CK} fact4: {G} -> (¬{F} & ¬{E}) fact5: ({R} & ¬{Q}) -> ¬{P} fact6: ¬{P} -> ({N} & {O}) fact7: ¬{A} fact8: {K} -> (¬{I} & ¬{J}) fact9: ¬{M} -> ¬(¬{K} & ¬{L}) fact10: {N} -> ¬{M} fact11: ¬{C} -> ¬(¬{A} & {B}) fact12: ¬{I} -> ({G} & {H}) fact13: ¬{E} -> (¬{C} & ¬{D}) fact14: {R} | [
"fact7 & fact1 -> hypothesis;"
] | [
"fact7 & fact1 -> hypothesis;"
] | ãç§çãçºçããªããè¿ãå¿ ãçºçããããšããããšã¯åœã | ¬(¬{A} & {B}) | [] | 16 | 1 | 1 | 12 | 0 | 12 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: è¿ãå¿ ãçºçãã fact2: ãããè¬ã¯èµ·ããªããçç°ãæŒé ãããšãçºçããªãããšããããšãçå®ã ãšããããšã¯ãªããªãã°ãè¬ã¯çããããšããããšãäºå®ã fact3: ããŠã¥ãããšããããšãçºçããããšããããšãæãç«ã€ fact4: ããããããããšããããšãçããã°éæ°Žãããã¯ããããšã¯çããªããã²ã£ãããããããšãçºçããªã fact5: ãã¢ã ãã¹ãã£ã¯èµ·ããªãããšããããšã¯ãäžé·¹å°ãæ±ãç· ããããšãçããããããé è€ã«çãããããšã¯èµ·ãããªãããšããããšã«ããçãã fact6: ãåºç€ãèµ·ãããè²æã«å·®ãåããããšãçããããšããããšãã¢ã ãã¹ãã£ã¯èµ·ããªããšããããšã«ããçºçãã fact7: ç§çãèµ·ããªã fact8: ãç«ã¡ä»£ããããšãèµ·ãããªããŠãã¬ããŒã¯ããã³ã€ã¥ããããšã¯çããªãããšããããšã¯è¬ã«èµ·å ãã fact9: ããã³ã¯ããšããããšãèµ·ãããªããªãã°ãè¬ãçºçããªããçç°ãæŒé ãããšãèµ·ããªãããšããããšã¯æãç«ã€ãšããããšããªã fact10: ã³ã¯ããšããããšã¯èµ·ãããšããããšãåºç€ãèµ·ãããšããããšã«é²ããã fact11: ããäœçœ°ã¯èµ·ãããªããªãã°ãç§çã¯çºçããªããè¿ãå¿ ã¯èµ·ããããšããããšã¯çå®ã§ãªã fact12: ãç«ã¡ä»£ããããšãçºçããªãããšããããšã¯ãããããããšããããšãšãã·ã£ãŽã黎ã³ãããšäž¡æ¹ã¯èµ·ããããšããããšãåŒãèµ·ãã fact13: ãäœçœ°ãèµ·ãããªãããªãã§ã³ã¹ãèµ·ãããªãããšããããšãã²ã£ãããããããšãçããªããšããããšã«åŒãèµ·ãããã fact14: äžé·¹å°ãæ±ãç· ããããšãçãã ; $hypothesis$ = ãç§çã§ã¯ãªãè¿ãå¿ ãçºçããããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact7 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} fact2: ¬(¬{K} & ¬{L}) -> {K} fact3: {CK} fact4: {G} -> (¬{F} & ¬{E}) fact5: ({R} & ¬{Q}) -> ¬{P} fact6: ¬{P} -> ({N} & {O}) fact7: ¬{A} fact8: {K} -> (¬{I} & ¬{J}) fact9: ¬{M} -> ¬(¬{K} & ¬{L}) fact10: {N} -> ¬{M} fact11: ¬{C} -> ¬(¬{A} & {B}) fact12: ¬{I} -> ({G} & {H}) fact13: ¬{E} -> (¬{C} & ¬{D}) fact14: {R} ; $hypothesis$ = ¬(¬{A} & {B}) ; $proof$ = | fact7 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¯ããŒãºã¢ãããçœã | {A}{a} | fact1: ããããã®ãã€ã¯ãããã»ããµããšããã ããããããããããªãããšããããšã¯æãç«ããªããªãã°ããããšããã ãšããããšã¯ãªã fact2: ãããã®ã¯ããŒãºã¢ãããæ匷ããªãã°ããã®ã«ãã§ãŒã¯çœããªããããããããå€æ²»èŠãããããããããšããããšãæãç«ã€ãšããããšã¯ãªã fact3: ããäœããèãããããªããªãã°ããããæ§ã³ããé®ååç°ã ããšããããšã¯åœã fact4: å
šãŠã®ãã®ãèãããããšããããšããªã fact5: ããé èŠã±åã¯ããã°ããã®ãã€ã¯ãããã»ããµããšããã ãããããããšããããšããªãããšããããšã¯æãç«ã€ãšããããšããªã fact6: ããäœããæ§ã³ããšããããšã¯ãªããªãã°ããã¯æ匷ããŠé®ååç°ã fact7: ãã®å€å
µãé èŠã±åã fact8: ãããããšããã ãšããããšã¯ãªãããšããããšãæãç«ã€ããã®ã¯ããã°ããã®è»å¶ãéã
ãããããã¯åŒµæã ãšããããšã¯ãªãããšããããšã¯èª€ãã fact9: ããããã®è»å¶ã¯éã
ãããŠåŒµæã ãšããããšããªãããšããããšã¯èª€ããªãã°ãã®ã¯ããŒãºã¢ãããèãããããªã fact10: èãããããªããã®ã¯æ§ã³ãªã fact11: ããããããã®ã¯çœããªãããããå€æ²»èŠãããããããããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯çœã | fact1: ¬({I}{c} & ¬{K}{c}) -> ¬{I}{c} fact2: {B}{a} -> ¬(¬{A}{l} & {C}{l}) fact3: (x): ¬{F}x -> ¬({E}x & {D}x) fact4: (x): ¬{F}x fact5: (x): {J}x -> ¬({I}{c} & ¬{K}{c}) fact6: (x): ¬{E}x -> ({B}x & {D}x) fact7: {J}{d} fact8: (x): ¬{I}x -> ¬({H}{b} & ¬{G}{b}) fact9: ¬({H}{b} & ¬{G}{b}) -> ¬{F}{a} fact10: (x): ¬{F}x -> ¬{E}x fact11: (x): ¬(¬{A}x & {C}x) -> {A}x | [] | [] | ãã®ã¯ããŒãºã¢ãããçœããªã | ¬{A}{a} | [
"fact12 -> int1: ãããã®å€å
µãèãããããšããããšã¯ãªããªãã°ãããã¯æ§ã³ãããããé®ååç°ã ããšããããšã¯æãç«ããªã; fact13 -> int2: ãã®å€å
µãèãããããªã; int1 & int2 -> int3: ãããã®å€å
µãæ§ã³ããé®ååç°ã ããšããããšã¯æãç«ã€ããšããããšãåœã ; int3 -> int4: ããã¯æ§ã³ããé®ååç°ã ãšãããã®ããªã; int4 -> int5: ããã®ãã€ã¯ãããã»ããµãæ§ã³ããé®ååç°ã ããšããããšãçå®ã ãšããããšã¯ãªã;"
] | 8 | 1 | null | 11 | 0 | 11 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®ãã€ã¯ãããã»ããµããšããã ããããããããããªãããšããããšã¯æãç«ããªããªãã°ããããšããã ãšããããšã¯ãªã fact2: ãããã®ã¯ããŒãºã¢ãããæ匷ããªãã°ããã®ã«ãã§ãŒã¯çœããªããããããããå€æ²»èŠãããããããããšããããšãæãç«ã€ãšããããšã¯ãªã fact3: ããäœããèãããããªããªãã°ããããæ§ã³ããé®ååç°ã ããšããããšã¯åœã fact4: å
šãŠã®ãã®ãèãããããšããããšããªã fact5: ããé èŠã±åã¯ããã°ããã®ãã€ã¯ãããã»ããµããšããã ãããããããšããããšããªãããšããããšã¯æãç«ã€ãšããããšããªã fact6: ããäœããæ§ã³ããšããããšã¯ãªããªãã°ããã¯æ匷ããŠé®ååç°ã fact7: ãã®å€å
µãé èŠã±åã fact8: ãããããšããã ãšããããšã¯ãªãããšããããšãæãç«ã€ããã®ã¯ããã°ããã®è»å¶ãéã
ãããããã¯åŒµæã ãšããããšã¯ãªãããšããããšã¯èª€ãã fact9: ããããã®è»å¶ã¯éã
ãããŠåŒµæã ãšããããšããªãããšããããšã¯èª€ããªãã°ãã®ã¯ããŒãºã¢ãããèãããããªã fact10: èãããããªããã®ã¯æ§ã³ãªã fact11: ããããããã®ã¯çœããªãããããå€æ²»èŠãããããããããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯çœã ; $hypothesis$ = ãã®ã¯ããŒãºã¢ãããçœã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({I}{c} & ¬{K}{c}) -> ¬{I}{c} fact2: {B}{a} -> ¬(¬{A}{l} & {C}{l}) fact3: (x): ¬{F}x -> ¬({E}x & {D}x) fact4: (x): ¬{F}x fact5: (x): {J}x -> ¬({I}{c} & ¬{K}{c}) fact6: (x): ¬{E}x -> ({B}x & {D}x) fact7: {J}{d} fact8: (x): ¬{I}x -> ¬({H}{b} & ¬{G}{b}) fact9: ¬({H}{b} & ¬{G}{b}) -> ¬{F}{a} fact10: (x): ¬{F}x -> ¬{E}x fact11: (x): ¬(¬{A}x & {C}x) -> {A}x ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ããŠããŠã¯ã€ãŸããšããããšããªã | ¬{C}{a} | fact1: ãããµãããã®ããã fact2: ãä¹
çåŒã ãæ°æ¥æ¬éç Žå£æ€æ»ã«ããããããã®ã¯ãã fact3: ãã®çé
žãããã€ããšããããšããªã fact4: äœããããããããŠç¥æ°Žæ¬ã fact5: ããããµããã®ããã¶ã«æã¿èŸŒããã°ãã®ããŠããŠã¯ããããªã fact6: ããããããäœçšãªããã®ããã fact7: ãããæ西çºæž
æ°Žæ°ã«ãšãããã玢ãããã®ãããã°ãã®å
èãã€ãŸãŸãªã fact8: ãã®ããŠããŠã¯æ¥å¥³äœå€§ãããŒããšãããšããããšããªã fact9: ãã®ææ¯çŽ ã¯ããµããšããããšã¯ãªã fact10: ãã®ããŠããŠã¯ããµããšããããšã¯ãªã fact11: ãããã€ãããã®ã¯ãã fact12: ãäœããåæ¯æ¹§å¥ã«å±
æ®ãããæšãããšããããšãæ£ãã fact13: ããäœããããµããŠããã€ãã°ãã®ããŠããŠãã€ãŸããšããããšããªã fact14: ãããã®ãä»åŸ³å¯ºã§ãã£ãŠäœæã ãã® fact15: ãã®ããŠããŠã¯ããã€ããšããããšããªã fact16: ããããµãå°ç°å·»ãèžãã¯ããã°ãã®ããŠããŠã¯æ西çºæž
æ°Žæ°ã«ãšããããšããããšããªã fact17: ãããã®ã¯ããµããŠãããããã€ã fact18: ãããããã®ãããã€ããã€ãã座ã«è¡ããã°ããã®ããŠããŠã¯ã¿ã
ãç¹°ããããªãããšããããšãæ£ãã | fact1: (Ex): {A}x fact2: (Ex): ({I}x & {AA}x) fact3: ¬{B}{do} fact4: (Ex): ({FU}x & {HU}x) fact5: (x): ({A}x & {DG}x) -> ¬{AI}{a} fact6: (Ex): ({CM}x & {HM}x) fact7: (x): ({IU}x & {CQ}x) -> ¬{C}{ab} fact8: ¬{DJ}{a} fact9: ¬{A}{cu} fact10: ¬{A}{a} fact11: (Ex): {B}x fact12: (Ex): ({HD}x & {HE}x) fact13: (x): ({A}x & {B}x) -> ¬{C}{a} fact14: (Ex): ({FM}x & {K}x) fact15: ¬{B}{a} fact16: (x): ({HK}x & {A}x) -> ¬{IU}{a} fact17: (Ex): ({A}x & {B}x) fact18: (x): ({B}x & {IO}x) -> ¬{EN}{a} | [
"fact17 & fact13 -> hypothesis;"
] | [
"fact17 & fact13 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 16 | 0 | 16 | PROVED | null | PROVED | null | $facts$ = fact1: ãããµãããã®ããã fact2: ãä¹
çåŒã ãæ°æ¥æ¬éç Žå£æ€æ»ã«ããããããã®ã¯ãã fact3: ãã®çé
žãããã€ããšããããšããªã fact4: äœããããããããŠç¥æ°Žæ¬ã fact5: ããããµããã®ããã¶ã«æã¿èŸŒããã°ãã®ããŠããŠã¯ããããªã fact6: ããããããäœçšãªããã®ããã fact7: ãããæ西çºæž
æ°Žæ°ã«ãšãããã玢ãããã®ãããã°ãã®å
èãã€ãŸãŸãªã fact8: ãã®ããŠããŠã¯æ¥å¥³äœå€§ãããŒããšãããšããããšããªã fact9: ãã®ææ¯çŽ ã¯ããµããšããããšã¯ãªã fact10: ãã®ããŠããŠã¯ããµããšããããšã¯ãªã fact11: ãããã€ãããã®ã¯ãã fact12: ãäœããåæ¯æ¹§å¥ã«å±
æ®ãããæšãããšããããšãæ£ãã fact13: ããäœããããµããŠããã€ãã°ãã®ããŠããŠãã€ãŸããšããããšããªã fact14: ãããã®ãä»åŸ³å¯ºã§ãã£ãŠäœæã ãã® fact15: ãã®ããŠããŠã¯ããã€ããšããããšããªã fact16: ããããµãå°ç°å·»ãèžãã¯ããã°ãã®ããŠããŠã¯æ西çºæž
æ°Žæ°ã«ãšããããšããããšããªã fact17: ãããã®ã¯ããµããŠãããããã€ã fact18: ãããããã®ãããã€ããã€ãã座ã«è¡ããã°ããã®ããŠããŠã¯ã¿ã
ãç¹°ããããªãããšããããšãæ£ãã ; $hypothesis$ = ãã®ããŠããŠã¯ã€ãŸããšããããšããªã ; $proof$ = | fact17 & fact13 -> hypothesis; __PROVED__ | $facts$ = fact1: (Ex): {A}x fact2: (Ex): ({I}x & {AA}x) fact3: ¬{B}{do} fact4: (Ex): ({FU}x & {HU}x) fact5: (x): ({A}x & {DG}x) -> ¬{AI}{a} fact6: (Ex): ({CM}x & {HM}x) fact7: (x): ({IU}x & {CQ}x) -> ¬{C}{ab} fact8: ¬{DJ}{a} fact9: ¬{A}{cu} fact10: ¬{A}{a} fact11: (Ex): {B}x fact12: (Ex): ({HD}x & {HE}x) fact13: (x): ({A}x & {B}x) -> ¬{C}{a} fact14: (Ex): ({FM}x & {K}x) fact15: ¬{B}{a} fact16: (x): ({HK}x & {A}x) -> ¬{IU}{a} fact17: (Ex): ({A}x & {B}x) fact18: (x): ({B}x & {IO}x) -> ¬{EN}{a} ; $hypothesis$ = ¬{C}{a} ; $proof$ = | fact17 & fact13 -> hypothesis; __PROVED__ |
0.3 | ãã®å°çã西é²å¯ºã«æç³ããããã座æ·ç¢ã§ãªãããããã¯äž¡æ¹ã | ({AA}{aa} v ¬{AB}{aa}) | fact1: ãå
šãŠã¯è¥¿é²å¯ºã«æç³ãããããã¯ããã¯åº§æ·ç¢ã ãšããããšããªããäž¡æ¹ã ããšããããšãæãç«ã€ | fact1: (x): ({AA}x v ¬{AB}x) | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãå
šãŠã¯è¥¿é²å¯ºã«æç³ãããããã¯ããã¯åº§æ·ç¢ã ãšããããšããªããäž¡æ¹ã ããšããããšãæãç«ã€ ; $hypothesis$ = ãã®å°çã西é²å¯ºã«æç³ããããã座æ·ç¢ã§ãªãããããã¯äž¡æ¹ã ; $proof$ = | fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ({AA}x v ¬{AB}x) ; $hypothesis$ = ({AA}{aa} v ¬{AB}{aa}) ; $proof$ = | fact1 -> hypothesis; __PROVED__ |
0.3 | ããããåºããšããããšã¯ãªããªãã°ãæ³çé¢ã§ããããããã¯ãªã³ç¬ã«çªã£ããã°ããšããããšã¯ãªãããšããããšã¯ééããªããã®ãããããšããããšãæãç«ããªã | ¬((Ex): ¬{A}x -> ¬({AA}x v ¬{AB}x)) | fact1: ãããã®æ°Žä»ãåºããªããªãã°ããã¯æ³çé¢ã ãšããããšã¯ãªã fact2: ãããã®æ°Žä»ãåºããšããããšããªããªãã°ããã¯æ³çé¢ã§ããããªã³ç¬ã«çªã£ããã°ããªããäž¡æ¹ã fact3: ãããã®æ°Žä»ã液åã«ã»ããšããããšã¯ãªããªãã°ããããç©ãã®ãããæ³çé¢ã§ãªãããããã¯äž¡æ¹ã ããšããããšãæãç«ã€ãšããããšã¯ãªã fact4: ãããçŠãŸãªããªãã°æ°èŠå±äžã«ãã£ããªãããã®ã¯ãã fact5: ãããåºããªãã°ãæ³çé¢ã§ããããããã¯ãªã³ç¬ã«çªã£ããã°ããªãããããã¯äž¡æ¹ã ããšããããšãæãç«ã€ãšããããšããªãããã®ããã fact6: ããã被çšè
ã«ã€ããããšããããšããªããªãã°ãæ®å€ãããããã¯æåŒã«èœå»¶ã³ããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšããªãããã®ã¯ãã fact7: ãããã®æ°Žä»ãåºããªãã°ãããã¯æ³çé¢ã§ããããããã¯ããããªã³ç¬ã«çªã£ããã°ããšããããšã¯ãªãããããã¯äž¡æ¹ã ããšããããšã¯æãç«ããªã fact8: ãããåºããªããªãã°ãªã³ç¬ã«çªã£ããã°ãããã®ããã fact9: ãããã€ã³ãã£ã¢ãããªã¹ã ãšããããšããªããªãã°å
ã€åãã§ãªãããã®ã¯ãã fact10: ããã西å±æ·ã ãšããããšã¯ãªããªãã°ãããããããããã¯ãã€ãŸããããããã¯äž¡æ¹ã ããšããããšãæãç«ããªãããã®ã¯ãã fact11: ãããã®ã¢ã³ã¢ããŠã ã¯åºããšããããšã¯ãªããªãã°ãããã¯æ³¥ã¶ããã倧島åããã¹ããããããããã¯äž¡æ¹ã ããšããããšã誀ãã fact12: ããäœãã¯æ°ç«å·èªç©ºæ©ã§ãªããªãã°ãããããªã³ç¬ã«çªã£ããã°ãããããã¯ããã¯çºç«äžåœç
é¢ã ãšããããšã¯ãªãããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã fact13: ãããã®æ°Žä»ãåºããªããªãã°ãããã¯æ³çé¢ã§ãããããããªã³ç¬ã«çªã£ããã°ããªããäž¡æ¹ã ããšããããšãæãç«ããªã fact14: ãããåºããšããããšã¯ãªããªãã°æ³çé¢ã§ããããªã³ç¬ã«çªã£ããã°ããªãããããã¯äž¡æ¹ãªããã®ã¯ãã fact15: ãããã®é£ãåããæ
æ·±ããšããããšããªããªãã°ããããæ³¥ã¶ããããããåã¿åãããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã | fact1: ¬{A}{aa} -> ¬{AA}{aa} fact2: ¬{A}{aa} -> ({AA}{aa} v ¬{AB}{aa}) fact3: ¬{DL}{aa} -> ¬({GM}{aa} v ¬{AA}{aa}) fact4: (Ex): ¬{IN}x -> ¬{JF}x fact5: (Ex): {A}x -> ¬({AA}x v ¬{AB}x) fact6: (Ex): ¬{CA}x -> ¬({DJ}x v ¬{FP}x) fact7: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact8: (Ex): ¬{A}x -> {AB}x fact9: (Ex): ¬{DC}x -> ¬{HJ}x fact10: (Ex): ¬{BQ}x -> ¬({M}x v {CG}x) fact11: ¬{A}{ai} -> ¬({CR}{ai} v {DF}{ai}) fact12: (x): ¬{AM}x -> ¬({AB}x v ¬{CE}x) fact13: ¬{A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact14: (Ex): ¬{A}x -> ({AA}x v ¬{AB}x) fact15: ¬{U}{ga} -> ¬({CR}{ga} v {AL}{ga}) | [
"fact13 -> hypothesis;"
] | [
"fact13 -> hypothesis;"
] | ãããã®æ°Žä»ã¯æ°ç«å·èªç©ºæ©ã§ãªããªãã°ãããããªã³ç¬ã«çªã£ããã°ããããã¯çºç«äžåœç
é¢ã ãšããããšããªããäž¡æ¹ã ããšããããšã¯çå®ã ãšããããšããªã | ¬{AM}{aa} -> ¬({AB}{aa} v ¬{CE}{aa}) | [
"fact16 -> hypothesis;"
] | 1 | 1 | 1 | 14 | 0 | 14 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãããã®æ°Žä»ãåºããªããªãã°ããã¯æ³çé¢ã ãšããããšã¯ãªã fact2: ãããã®æ°Žä»ãåºããšããããšããªããªãã°ããã¯æ³çé¢ã§ããããªã³ç¬ã«çªã£ããã°ããªããäž¡æ¹ã fact3: ãããã®æ°Žä»ã液åã«ã»ããšããããšã¯ãªããªãã°ããããç©ãã®ãããæ³çé¢ã§ãªãããããã¯äž¡æ¹ã ããšããããšãæãç«ã€ãšããããšã¯ãªã fact4: ãããçŠãŸãªããªãã°æ°èŠå±äžã«ãã£ããªãããã®ã¯ãã fact5: ãããåºããªãã°ãæ³çé¢ã§ããããããã¯ãªã³ç¬ã«çªã£ããã°ããªãããããã¯äž¡æ¹ã ããšããããšãæãç«ã€ãšããããšããªãããã®ããã fact6: ããã被çšè
ã«ã€ããããšããããšããªããªãã°ãæ®å€ãããããã¯æåŒã«èœå»¶ã³ããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšããªãããã®ã¯ãã fact7: ãããã®æ°Žä»ãåºããªãã°ãããã¯æ³çé¢ã§ããããããã¯ããããªã³ç¬ã«çªã£ããã°ããšããããšã¯ãªãããããã¯äž¡æ¹ã ããšããããšã¯æãç«ããªã fact8: ãããåºããªããªãã°ãªã³ç¬ã«çªã£ããã°ãããã®ããã fact9: ãããã€ã³ãã£ã¢ãããªã¹ã ãšããããšããªããªãã°å
ã€åãã§ãªãããã®ã¯ãã fact10: ããã西å±æ·ã ãšããããšã¯ãªããªãã°ãããããããããã¯ãã€ãŸããããããã¯äž¡æ¹ã ããšããããšãæãç«ããªãããã®ã¯ãã fact11: ãããã®ã¢ã³ã¢ããŠã ã¯åºããšããããšã¯ãªããªãã°ãããã¯æ³¥ã¶ããã倧島åããã¹ããããããããã¯äž¡æ¹ã ããšããããšã誀ãã fact12: ããäœãã¯æ°ç«å·èªç©ºæ©ã§ãªããªãã°ãããããªã³ç¬ã«çªã£ããã°ãããããã¯ããã¯çºç«äžåœç
é¢ã ãšããããšã¯ãªãããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã fact13: ãããã®æ°Žä»ãåºããªããªãã°ãããã¯æ³çé¢ã§ãããããããªã³ç¬ã«çªã£ããã°ããªããäž¡æ¹ã ããšããããšãæãç«ããªã fact14: ãããåºããšããããšã¯ãªããªãã°æ³çé¢ã§ããããªã³ç¬ã«çªã£ããã°ããªãããããã¯äž¡æ¹ãªããã®ã¯ãã fact15: ãããã®é£ãåããæ
æ·±ããšããããšããªããªãã°ããããæ³¥ã¶ããããããåã¿åãããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã ; $hypothesis$ = ããããåºããšããããšã¯ãªããªãã°ãæ³çé¢ã§ããããããã¯ãªã³ç¬ã«çªã£ããã°ããšããããšã¯ãªãããšããããšã¯ééããªããã®ãããããšããããšãæãç«ããªã ; $proof$ = | fact13 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A}{aa} -> ¬{AA}{aa} fact2: ¬{A}{aa} -> ({AA}{aa} v ¬{AB}{aa}) fact3: ¬{DL}{aa} -> ¬({GM}{aa} v ¬{AA}{aa}) fact4: (Ex): ¬{IN}x -> ¬{JF}x fact5: (Ex): {A}x -> ¬({AA}x v ¬{AB}x) fact6: (Ex): ¬{CA}x -> ¬({DJ}x v ¬{FP}x) fact7: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact8: (Ex): ¬{A}x -> {AB}x fact9: (Ex): ¬{DC}x -> ¬{HJ}x fact10: (Ex): ¬{BQ}x -> ¬({M}x v {CG}x) fact11: ¬{A}{ai} -> ¬({CR}{ai} v {DF}{ai}) fact12: (x): ¬{AM}x -> ¬({AB}x v ¬{CE}x) fact13: ¬{A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact14: (Ex): ¬{A}x -> ({AA}x v ¬{AB}x) fact15: ¬{U}{ga} -> ¬({CR}{ga} v {AL}{ga}) ; $hypothesis$ = ¬((Ex): ¬{A}x -> ¬({AA}x v ¬{AB}x)) ; $proof$ = | fact13 -> hypothesis; __DISPROVED__ |
0.3 | ãã®äºå¡ãã²ãã£ãã | {A}{a} | fact1: ãããããã®ããããããªããªãã°ãããããæžããããŠããã fact2: ããããã²ãã£ããããšããããšã¯æãç«ã€ããã®ãããã°ããã®äºå¡ãé埳éŸã§ãªããã²ãã£ãããšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact3: ãã®äºå¡ãã²ãã£ãã fact4: ãããã®ã©ã€ã³ããªã³ã¿ã¯å®ãããšããããšããªããããæžããã°ãã®ç«¯æŠè
ã¯å®ãããšããããšããªã fact5: ãã®ç·šç©ããããã fact6: ãããäœããã²ãã£ãããŠé埳éŸã ããšããããšã¯åœãªãã°ãããã²ãã£ãããšããããšããªã fact7: ãã®äºå¡ãæšå£ã fact8: ãããããã®ã¯ãããããªããããç¡ããšããããšã¯ãªã fact9: ãããã®ç«¯æŠè
ã¯å®ãããšããããšã¯ãªããªãã°ããããªãŸãŒãã«é åºã¥ããããããã»ãŠãã ãšããããšããªã fact10: ããããã®äºå¡ã¯é埳éŸã ãšããããšã¯ãªããŠã²ãã£ãããšããããšããªãããšããããšã¯åãªãã°ãã®å
ç· ãã¯ã²ãã£ãã fact11: ãããã®ç·šç©ã¯ç³ã®è«ã«çãæãã°ããããè»é ã ãšããããšããªãããããä¿¡çšè²žã ããšããããšãäºå®ãšç°ãªã fact12: ããããªãŸãŒãã«é åºã¥ããããããã»ãŠãã§ãªãããã®ã¯ããã°ãã®ã¬ãã§ãŠã¯ã²ãã£ãã fact13: ããããè»é ã ãšããããšããªããä¿¡çšè²žã ããšããããšã¯æãç«ã€ãšããããšããªãããã®ãããã°ãã®ã©ã€ã³ããªã³ã¿ã¯å®ãããšããããšã¯ãªã fact14: ããäœãã¯ãããããªãã°ããã¯ç³ã®è«ã«çãæã fact15: ãã®äºå¡ãæã fact16: ãã®ç®è³ªãã²ãã£ãã fact17: ãã®æš©èŒ¿ã¯ã²ãã£ãã fact18: ãã®åž¯é©ãã²ãã£ãã fact19: ãããããã®ã¯ãªãŸãŒãã«é åºã¥ãããšããããšã¯ãªããªãã°ããããã²ãã£ãããŠé埳éŸã ããšããããšãåã | fact1: (x): ¬{L}x -> ({G}x & {I}x) fact2: (x): {A}x -> ¬(¬{B}{a} & ¬{A}{a}) fact3: {A}{a} fact4: (¬{E}{d} & {G}{d}) -> ¬{E}{c} fact5: {K}{e} fact6: (x): ¬({A}x & {B}x) -> ¬{A}x fact7: {CT}{a} fact8: (x): (¬{L}x & ¬{M}x) fact9: ¬{E}{c} -> ({C}{c} & ¬{D}{c}) fact10: ¬(¬{B}{a} & ¬{A}{a}) -> {A}{bn} fact11: {J}{e} -> ¬(¬{H}{e} & {F}{e}) fact12: (x): ({C}x & ¬{D}x) -> {A}{b} fact13: (x): ¬(¬{H}x & {F}x) -> ¬{E}{d} fact14: (x): {K}x -> {J}x fact15: {DT}{a} fact16: {A}{eq} fact17: {A}{if} fact18: {A}{bh} fact19: (x): ¬{C}x -> ¬({A}x & {B}x) | [
"fact3 -> hypothesis;"
] | [
"fact3 -> hypothesis;"
] | ãã®å
ç· ãã¯ã²ãã£ãã | {A}{bn} | [
"fact23 -> int1: ãã®å°çºã¯ãããããªãããããããç¡ããªã; int1 -> int2: ãã®å°çºããããããšããããšããªã; int2 -> int3: å
šãŠããããããšããããšã¯ãªã; int3 -> int4: ãã®ç·šè
ã¯ãããããšããããšã¯ãªã; fact22 -> int5: ãããã®ç·šè
ããããããªããªãã°ãããããæžããããŠããã; int4 & int5 -> int6: ãã®ç·šè
ãããæžããããŠããã; int6 -> int7: å
šãŠã¯ããæžãããããã¯ãŠããã; int7 -> int8: ãã®ã©ã€ã³ããªã³ã¿ã¯ããæžããããŠããã; int8 -> int9: ãã®ã©ã€ã³ããªã³ã¿ã¯ããæžãã; fact20 -> int10: ãããã®ç·šç©ã¯ãããããªãã°ããã¯ç³ã®è«ã«çãæã; fact25 & int10 -> int11: ãã®ç·šç©ã¯ç³ã®è«ã«çãæã; fact27 & int11 -> int12: ããã®ç·šç©ãè»é ã§ãªããŠä¿¡çšè²žã ããšããããšãæãç«ã€ãšããããšããªã; int12 -> int13: ããè»é ã ãšããããšããªãããããä¿¡çšè²žã ããšããããšãæãç«ããªãããã®ã¯ãã; int13 & fact30 -> int14: ããã®ã©ã€ã³ããªã³ã¿ãå®ãããšããããšããªãããšããããšã¯æãç«ã€; int9 & int14 -> int15: ãã®ã©ã€ã³ããªã³ã¿ãå®ãããªããããæžãã; int15 & fact24 -> int16: ãã®ç«¯æŠè
ãå®ãããšããããšããªã; int16 & fact26 -> int17: ãã®ç«¯æŠè
ããªãŸãŒãã«é åºã¥ããããããããã¯ã»ãŠãã§ãªã; int17 -> int18: äœãã¯ãªãŸãŒãã«é åºã¥ãããããã¯ã»ãŠãã§ãªã; fact28 & int18 -> int19: ãã®ã¬ãã§ãŠã¯ã²ãã£ãã; int19 -> int20: ãã²ãã£ããããã®ã¯ãã; fact29 & int20 -> int21: ããã®äºå¡ã¯é埳éŸã§ãªããŠãããã²ãã£ãããªãããšããããšã¯åœã ; int21 & fact21 -> hypothesis;"
] | 16 | 1 | 0 | 18 | 0 | 18 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãããããã®ããããããªããªãã°ãããããæžããããŠããã fact2: ããããã²ãã£ããããšããããšã¯æãç«ã€ããã®ãããã°ããã®äºå¡ãé埳éŸã§ãªããã²ãã£ãããšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact3: ãã®äºå¡ãã²ãã£ãã fact4: ãããã®ã©ã€ã³ããªã³ã¿ã¯å®ãããšããããšããªããããæžããã°ãã®ç«¯æŠè
ã¯å®ãããšããããšããªã fact5: ãã®ç·šç©ããããã fact6: ãããäœããã²ãã£ãããŠé埳éŸã ããšããããšã¯åœãªãã°ãããã²ãã£ãããšããããšããªã fact7: ãã®äºå¡ãæšå£ã fact8: ãããããã®ã¯ãããããªããããç¡ããšããããšã¯ãªã fact9: ãããã®ç«¯æŠè
ã¯å®ãããšããããšã¯ãªããªãã°ããããªãŸãŒãã«é åºã¥ããããããã»ãŠãã ãšããããšããªã fact10: ããããã®äºå¡ã¯é埳éŸã ãšããããšã¯ãªããŠã²ãã£ãããšããããšããªãããšããããšã¯åãªãã°ãã®å
ç· ãã¯ã²ãã£ãã fact11: ãããã®ç·šç©ã¯ç³ã®è«ã«çãæãã°ããããè»é ã ãšããããšããªãããããä¿¡çšè²žã ããšããããšãäºå®ãšç°ãªã fact12: ããããªãŸãŒãã«é åºã¥ããããããã»ãŠãã§ãªãããã®ã¯ããã°ãã®ã¬ãã§ãŠã¯ã²ãã£ãã fact13: ããããè»é ã ãšããããšããªããä¿¡çšè²žã ããšããããšã¯æãç«ã€ãšããããšããªãããã®ãããã°ãã®ã©ã€ã³ããªã³ã¿ã¯å®ãããšããããšã¯ãªã fact14: ããäœãã¯ãããããªãã°ããã¯ç³ã®è«ã«çãæã fact15: ãã®äºå¡ãæã fact16: ãã®ç®è³ªãã²ãã£ãã fact17: ãã®æš©èŒ¿ã¯ã²ãã£ãã fact18: ãã®åž¯é©ãã²ãã£ãã fact19: ãããããã®ã¯ãªãŸãŒãã«é åºã¥ãããšããããšã¯ãªããªãã°ããããã²ãã£ãããŠé埳éŸã ããšããããšãåã ; $hypothesis$ = ãã®äºå¡ãã²ãã£ãã ; $proof$ = | fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬{L}x -> ({G}x & {I}x) fact2: (x): {A}x -> ¬(¬{B}{a} & ¬{A}{a}) fact3: {A}{a} fact4: (¬{E}{d} & {G}{d}) -> ¬{E}{c} fact5: {K}{e} fact6: (x): ¬({A}x & {B}x) -> ¬{A}x fact7: {CT}{a} fact8: (x): (¬{L}x & ¬{M}x) fact9: ¬{E}{c} -> ({C}{c} & ¬{D}{c}) fact10: ¬(¬{B}{a} & ¬{A}{a}) -> {A}{bn} fact11: {J}{e} -> ¬(¬{H}{e} & {F}{e}) fact12: (x): ({C}x & ¬{D}x) -> {A}{b} fact13: (x): ¬(¬{H}x & {F}x) -> ¬{E}{d} fact14: (x): {K}x -> {J}x fact15: {DT}{a} fact16: {A}{eq} fact17: {A}{if} fact18: {A}{bh} fact19: (x): ¬{C}x -> ¬({A}x & {B}x) ; $hypothesis$ = {A}{a} ; $proof$ = | fact3 -> hypothesis; __PROVED__ |
0.3 | ãèªãµããšãšã念䞡æ¹ã¯èµ·ããããšããããšãæãç«ã€ãšããããšããªã | ¬({AA} & {AB}) | fact1: ããªããããšããããšãèµ·ãããªã fact2: æ¥äžŠé·ãäžç«ã€ããšã¯èµ·ãããšããããšã¯å°æžãããããã°ããããšã«ããçºçãã fact3: ãã¡çŽ°ãããšããããšãçºçããªããšããããšãèªãµããšãèµ·ãããªããšããããšãåé¿ãã fact4: ããã¡çŽ°ãããšããããšãèµ·ãããªãããšããããšããèªãµããšãšã念䞡æ¹ã¯èµ·ããããšããããšãèªçºãã fact5: èªãµããšãçãã fact6: ã床ãé£ããšããããšã¯èµ·ããããã¡çŽ°ãããšããããšã¯çºçããããšããããšãåããšããããšã¯çºçããªããšããããšãåå ã | fact1: ¬{AS} fact2: {B} -> {HK} fact3: ¬{A} -> {AA} fact4: ¬{A} -> ({AA} & {AB}) fact5: {AA} fact6: ¬{D} -> ({DM} & {A}) | [] | [] | ããèªãµããšã¯çãããã念ã¯çºçããããšããããšãäºå®ã ããšããããšã誀ãã | ¬({AA} & {AB}) | [
" -> hypothesis;"
] | 0 | 1 | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããªããããšããããšãèµ·ãããªã fact2: æ¥äžŠé·ãäžç«ã€ããšã¯èµ·ãããšããããšã¯å°æžãããããã°ããããšã«ããçºçãã fact3: ãã¡çŽ°ãããšããããšãçºçããªããšããããšãèªãµããšãèµ·ãããªããšããããšãåé¿ãã fact4: ããã¡çŽ°ãããšããããšãèµ·ãããªãããšããããšããèªãµããšãšã念䞡æ¹ã¯èµ·ããããšããããšãèªçºãã fact5: èªãµããšãçãã fact6: ã床ãé£ããšããããšã¯èµ·ããããã¡çŽ°ãããšããããšã¯çºçããããšããããšãåããšããããšã¯çºçããªããšããããšãåå ã ; $hypothesis$ = ãèªãµããšãšã念䞡æ¹ã¯èµ·ããããšããããšãæãç«ã€ãšããããšããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{AS} fact2: {B} -> {HK} fact3: ¬{A} -> {AA} fact4: ¬{A} -> ({AA} & {AB}) fact5: {AA} fact6: ¬{D} -> ({DM} & {A}) ; $hypothesis$ = ¬({AA} & {AB}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®é¡ç«ã¡ãåç«ããªã | ¬{A}{aa} | fact1: ãããããã®ã¯æã«ã®ãããªããªãã°ããã¯åç«ã€ fact2: ãå
šãŠã¯çŠèãããšããããšã¯äºå®ã fact3: ããããããã®ãåç«ã€ãæã«ã®ãããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯åç«ããªã fact4: å
šãŠã®ãã®ã¯çã£ããã fact5: ããäœãã¯ãã®ãããªãã°ããããåç«ã€ãæã«ã®ãããªãããšããããšãäºå®ãšç°ãªã fact6: ãã®éèã¯åç«ã€ fact7: ãããããã®ã¯åç«ã€ fact8: ãã®ã ãŒããŒã¯åç«ã€ | fact1: (x): ¬{B}x -> {A}x fact2: (x): {CM}x fact3: (x): ¬({A}x & ¬{B}x) -> ¬{A}x fact4: (x): {CL}x fact5: (x): {C}x -> ¬({A}x & ¬{B}x) fact6: {A}{eq} fact7: (x): {A}x fact8: {A}{ao} | [
"fact7 -> hypothesis;"
] | [
"fact7 -> hypothesis;"
] | ãã®é¡ç«ã¡ãåç«ããªã | ¬{A}{aa} | [
"fact9 -> int1: ããããã®é¡ç«ã¡ã¯åç«ã€ãããããããæã«ã®ãããªãããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãããã¯åç«ã€ãšããããšã¯ãªãããšããããšãæãç«ã€; fact10 -> int2: ãããã®é¡ç«ã¡ã¯ãã®ãããªãã°ããããã¯åç«ã€ãããã¯æã«ã®ãããªãããšããããšã¯æãç«ã€ããšããããšãåœã ;"
] | 5 | 1 | 1 | 7 | 0 | 7 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããããã®ã¯æã«ã®ãããªããªãã°ããã¯åç«ã€ fact2: ãå
šãŠã¯çŠèãããšããããšã¯äºå®ã fact3: ããããããã®ãåç«ã€ãæã«ã®ãããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯åç«ããªã fact4: å
šãŠã®ãã®ã¯çã£ããã fact5: ããäœãã¯ãã®ãããªãã°ããããåç«ã€ãæã«ã®ãããªãããšããããšãäºå®ãšç°ãªã fact6: ãã®éèã¯åç«ã€ fact7: ãããããã®ã¯åç«ã€ fact8: ãã®ã ãŒããŒã¯åç«ã€ ; $hypothesis$ = ãã®é¡ç«ã¡ãåç«ããªã ; $proof$ = | fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{B}x -> {A}x fact2: (x): {CM}x fact3: (x): ¬({A}x & ¬{B}x) -> ¬{A}x fact4: (x): {CL}x fact5: (x): {C}x -> ¬({A}x & ¬{B}x) fact6: {A}{eq} fact7: (x): {A}x fact8: {A}{ao} ; $hypothesis$ = ¬{A}{aa} ; $proof$ = | fact7 -> hypothesis; __DISPROVED__ |
0.3 | ããããçç æ²¢ã ããšããããšãæãç«ãŠã°ããã€ããŸãããŠæšå±±ãåã ãšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšããªãããã®ã¯ãã | (Ex): {A}x -> ¬({AA}x & ¬{AB}x) | fact1: ãããã®ã°ãèãæšå±±ãåãªãã°ããã¯ãªã€ããããŠããã¯èŠå®ãããšããããšããªã fact2: ãããã®ã°ãèã¯çç æ²¢ãªãã°ãããããã€ããŸãããããã¯æšå±±ãåã ãšããããšããªãããšããããšãçå®ã§ãªã fact3: ãããã®ã°ãèãçç æ²¢ãªãã°ãããã¹ãã³ãµãŒã§ããã倧槻島ã ãšããããšããªã fact4: ããäœãã¯ãŸãç¶ã«åãã°ãããã¯ããããããããã¯ããããããšããããšã¯ãªãããšããããšãåœã fact5: ãããã®ã°ãèãçç æ²¢ãªãã°ãããã¯ãã€ããŸãããã®ã§ãã£ãŠæšå±±ãåãªãã®ããšããããšã¯äºå®ãšç°ãªã fact6: ãããã®ã°ãèããã€ããŸãããªãã°ããããé£åãããããå¡ãã€ã¶ããšããããšããªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact7: ããããäžç«ããŸãããããšããããšã¯åœã§ãªããªãã°å¡ãã€ã¶ãããã¡ã ãããšããããšããªãããã®ã¯ãã fact8: ããã京åŠãªãã°ããªã€ããããã®ã§ãã£ãŠäº¬ã¶å³¶ãåãããšããããšã¯ãªããã®ããšããããšãæãç«ããªãããã®ã¯ãã fact9: ããããçä¹æµŠãããããããšããããšãæãç«ãŠã°ãåºå°Ÿå·ã«ãããèµ·ããããé ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ããã fact10: ãããã®ãããããªãã°ãè±ããã宿èã§ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ããã fact11: ãããã®ã°ãèãæ€æ¢šå·ãªãã°ãããã¡ããããŠããã¯çç æ²¢ã§ãªã fact12: ããããšããšããªãã°ã西äœå·ã§ãã£ãŠãšãã§ããªããªããã®ããšããããšã¯æãç«ããªãããã®ã¯ãã fact13: ãããçç æ²¢ãªãã°ããã€ããŸããæšå±±ãåããšããããšã¯èª€ããªããã®ããã fact14: ããããããããªãã°çŽ 質ã§ãŠãŒã¶ã§ãªãããã®ã¯ãã fact15: ããããã®ããªãµã€ãæšå±±ãåã ããšããããšã¯æãç«ãŠã°ãããã¯ç¬åž°æ°ç°ã ããŠãŒã¶ã§ãªãããšããããšã¯æãç«ã€ãšããããšããªã | fact1: {AB}{aa} -> ({GP}{aa} & ¬{HB}{aa}) fact2: {A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa}) fact3: {A}{aa} -> ({FO}{aa} & ¬{AJ}{aa}) fact4: (x): {HR}x -> ¬({II}x & ¬{CB}x) fact5: {A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact6: {AA}{aa} -> ¬({GN}{aa} & ¬{Q}{aa}) fact7: (Ex): {HK}x -> ({Q}x & ¬{GC}x) fact8: (Ex): {AI}x -> ¬({GP}x & ¬{BI}x) fact9: (Ex): {R}x -> ¬({FF}x & ¬{JH}x) fact10: (Ex): {S}x -> ¬({JB}x & ¬{EP}x) fact11: {EL}{aa} -> ({BB}{aa} & ¬{A}{aa}) fact12: (Ex): {JC}x -> ¬({M}x & ¬{DJ}x) fact13: (Ex): {A}x -> ¬({AA}x & {AB}x) fact14: (Ex): {IS}x -> ({FB}x & ¬{F}x) fact15: {AB}{fu} -> ¬({GL}{fu} & ¬{F}{fu}) | [
"fact2 -> hypothesis;"
] | [
"fact2 -> hypothesis;"
] | ãããã®ã°ãèã¯ãŸãç¶ã«åãã°ãããã¯ããããããŠããããããããªãããšããããšã¯åã | {HR}{aa} -> ¬({II}{aa} & ¬{CB}{aa}) | [
"fact16 -> hypothesis;"
] | 1 | 1 | 1 | 14 | 0 | 14 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãããã®ã°ãèãæšå±±ãåãªãã°ããã¯ãªã€ããããŠããã¯èŠå®ãããšããããšããªã fact2: ãããã®ã°ãèã¯çç æ²¢ãªãã°ãããããã€ããŸãããããã¯æšå±±ãåã ãšããããšããªãããšããããšãçå®ã§ãªã fact3: ãããã®ã°ãèãçç æ²¢ãªãã°ãããã¹ãã³ãµãŒã§ããã倧槻島ã ãšããããšããªã fact4: ããäœãã¯ãŸãç¶ã«åãã°ãããã¯ããããããããã¯ããããããšããããšã¯ãªãããšããããšãåœã fact5: ãããã®ã°ãèãçç æ²¢ãªãã°ãããã¯ãã€ããŸãããã®ã§ãã£ãŠæšå±±ãåãªãã®ããšããããšã¯äºå®ãšç°ãªã fact6: ãããã®ã°ãèããã€ããŸãããªãã°ããããé£åãããããå¡ãã€ã¶ããšããããšããªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact7: ããããäžç«ããŸãããããšããããšã¯åœã§ãªããªãã°å¡ãã€ã¶ãããã¡ã ãããšããããšããªãããã®ã¯ãã fact8: ããã京åŠãªãã°ããªã€ããããã®ã§ãã£ãŠäº¬ã¶å³¶ãåãããšããããšã¯ãªããã®ããšããããšãæãç«ããªãããã®ã¯ãã fact9: ããããçä¹æµŠãããããããšããããšãæãç«ãŠã°ãåºå°Ÿå·ã«ãããèµ·ããããé ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ããã fact10: ãããã®ãããããªãã°ãè±ããã宿èã§ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ããã fact11: ãããã®ã°ãèãæ€æ¢šå·ãªãã°ãããã¡ããããŠããã¯çç æ²¢ã§ãªã fact12: ããããšããšããªãã°ã西äœå·ã§ãã£ãŠãšãã§ããªããªããã®ããšããããšã¯æãç«ããªãããã®ã¯ãã fact13: ãããçç æ²¢ãªãã°ããã€ããŸããæšå±±ãåããšããããšã¯èª€ããªããã®ããã fact14: ããããããããªãã°çŽ 質ã§ãŠãŒã¶ã§ãªãããã®ã¯ãã fact15: ããããã®ããªãµã€ãæšå±±ãåã ããšããããšã¯æãç«ãŠã°ãããã¯ç¬åž°æ°ç°ã ããŠãŒã¶ã§ãªãããšããããšã¯æãç«ã€ãšããããšããªã ; $hypothesis$ = ããããçç æ²¢ã ããšããããšãæãç«ãŠã°ããã€ããŸãããŠæšå±±ãåã ãšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšããªãããã®ã¯ãã ; $proof$ = | fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {AB}{aa} -> ({GP}{aa} & ¬{HB}{aa}) fact2: {A}{aa} -> ¬({AA}{aa} & ¬{AB}{aa}) fact3: {A}{aa} -> ({FO}{aa} & ¬{AJ}{aa}) fact4: (x): {HR}x -> ¬({II}x & ¬{CB}x) fact5: {A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact6: {AA}{aa} -> ¬({GN}{aa} & ¬{Q}{aa}) fact7: (Ex): {HK}x -> ({Q}x & ¬{GC}x) fact8: (Ex): {AI}x -> ¬({GP}x & ¬{BI}x) fact9: (Ex): {R}x -> ¬({FF}x & ¬{JH}x) fact10: (Ex): {S}x -> ¬({JB}x & ¬{EP}x) fact11: {EL}{aa} -> ({BB}{aa} & ¬{A}{aa}) fact12: (Ex): {JC}x -> ¬({M}x & ¬{DJ}x) fact13: (Ex): {A}x -> ¬({AA}x & {AB}x) fact14: (Ex): {IS}x -> ({FB}x & ¬{F}x) fact15: {AB}{fu} -> ¬({GL}{fu} & ¬{F}{fu}) ; $hypothesis$ = (Ex): {A}x -> ¬({AA}x & ¬{AB}x) ; $proof$ = | fact2 -> hypothesis; __PROVED__ |
0.3 | ãç¹è¡£ã«ãã ãããããšã¯çããªããããã¬ãªã³ã¯çããããšããããšãæ£ãããšããããšã¯ãªã | ¬(¬{AA} & {AB}) | fact1: èããããšããããšã¯èµ·ãããšããããšã¯ã¯ãããªããšããããšã¯çããªããšããããšãæã fact2: 姫路ç¬å倧åŠããã¿ãªãããããšãçãã fact3: ããç«ã¡ãããããšã¯èµ·ãããªããªãã°ã颚èã¯èµ·ãããããã桧æšæ²¢ã«ãã¡ãŸããããšã¯èµ·ãããªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact4: ãã颚èãèµ·ããªããªãã°ç¹è¡£ã«ãã ãããããšã§ã¯ãªãããã¬ãªã³ã¯çºçãã fact5: ãæœè¡ã¯èµ·ãããªãããããè¿æ»ãèµ·ããããšããããšã¯æ¢šãæšå³ ã«çåããããšãèµ·ãããšããããšã«åž°çµãã fact6: ãè¿æ»ã¯èµ·ããããšããããšã姫路ç¬å倧åŠããã¿ãªãããããšãåå ã fact7: æ©ãŸãããšããããšã¯èµ·ããªããŠæœè¡ãèµ·ãããªã fact8: ãã匱ãããšã¯çããªããªãã°ãæ²ã€ããšã¯çºçãããç«ã¡ãããããšã¯çããªãããšããããšãäºå®ã fact9: ãã家ã®æµŠãäžèè±ãããšãçããªããŠãªãã©ãŒã ã¯èµ·ããªããªãã°èããããšããããšãèµ·ãã fact10: ããã颚èãèµ·ãããããã桧æšæ²¢ã«ãã¡ãŸããããšã¯èµ·ããªãããšããããšã¯æãç«ããªããªãã°é¢šèãçºçããªã fact11: ãç¹è¡£ã«ãã ãããããšã¯çããªããããã¬ãªã³ãèµ·ããããšããããšãééãã fact12: ããæ¶æ£ã¯èµ·ããã°å®¶ã®æµŠãäžèè±ãããšã¯èµ·ãããªãããªãã©ãŒã ãçããªã fact13: ã梚ãæšå³ ã«çåããããšã¯çºçãããã¯ãããªããšããããšã¯çºçããªãããšããããšã匱ãããšã¯èµ·ãããªããšããããšã«ç¹ãã | fact1: {J} -> ¬{G} fact2: {K} fact3: ¬{B} -> ¬({A} & ¬{C}) fact4: ¬{A} -> (¬{AA} & {AB}) fact5: (¬{I} & {H}) -> {F} fact6: {K} -> {H} fact7: (¬{R} & ¬{I}) fact8: ¬{E} -> ({D} & ¬{B}) fact9: (¬{L} & ¬{M}) -> {J} fact10: ¬({A} & ¬{C}) -> ¬{A} fact11: ¬(¬{AA} & {AB}) fact12: {N} -> (¬{L} & ¬{M}) fact13: ({F} & ¬{G}) -> ¬{E} | [
"fact11 -> hypothesis;"
] | [
"fact11 -> hypothesis;"
] | ç¹è¡£ã«ãã ãããããšã§ã¯ãªãããã¬ãªã³ã¯èµ·ãã | (¬{AA} & {AB}) | [
"fact22 -> int1: æœè¡ãçºçããªã; fact18 & fact16 -> int2: è¿æ»ãèµ·ãã; int1 & int2 -> int3: æœè¡ã¯çããªããè¿æ»ã¯çãã; fact15 & int3 -> int4: 梚ãæšå³ ã«çåããããšã¯èµ·ãã;"
] | 13 | 1 | 0 | 12 | 0 | 12 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: èããããšããããšã¯èµ·ãããšããããšã¯ã¯ãããªããšããããšã¯çããªããšããããšãæã fact2: 姫路ç¬å倧åŠããã¿ãªãããããšãçãã fact3: ããç«ã¡ãããããšã¯èµ·ãããªããªãã°ã颚èã¯èµ·ãããããã桧æšæ²¢ã«ãã¡ãŸããããšã¯èµ·ãããªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact4: ãã颚èãèµ·ããªããªãã°ç¹è¡£ã«ãã ãããããšã§ã¯ãªãããã¬ãªã³ã¯çºçãã fact5: ãæœè¡ã¯èµ·ãããªãããããè¿æ»ãèµ·ããããšããããšã¯æ¢šãæšå³ ã«çåããããšãèµ·ãããšããããšã«åž°çµãã fact6: ãè¿æ»ã¯èµ·ããããšããããšã姫路ç¬å倧åŠããã¿ãªãããããšãåå ã fact7: æ©ãŸãããšããããšã¯èµ·ããªããŠæœè¡ãèµ·ãããªã fact8: ãã匱ãããšã¯çããªããªãã°ãæ²ã€ããšã¯çºçãããç«ã¡ãããããšã¯çããªãããšããããšãäºå®ã fact9: ãã家ã®æµŠãäžèè±ãããšãçããªããŠãªãã©ãŒã ã¯èµ·ããªããªãã°èããããšããããšãèµ·ãã fact10: ããã颚èãèµ·ãããããã桧æšæ²¢ã«ãã¡ãŸããããšã¯èµ·ããªãããšããããšã¯æãç«ããªããªãã°é¢šèãçºçããªã fact11: ãç¹è¡£ã«ãã ãããããšã¯çããªããããã¬ãªã³ãèµ·ããããšããããšãééãã fact12: ããæ¶æ£ã¯èµ·ããã°å®¶ã®æµŠãäžèè±ãããšã¯èµ·ãããªãããªãã©ãŒã ãçããªã fact13: ã梚ãæšå³ ã«çåããããšã¯çºçãããã¯ãããªããšããããšã¯çºçããªãããšããããšã匱ãããšã¯èµ·ãããªããšããããšã«ç¹ãã ; $hypothesis$ = ãç¹è¡£ã«ãã ãããããšã¯çããªããããã¬ãªã³ã¯çããããšããããšãæ£ãããšããããšã¯ãªã ; $proof$ = | fact11 -> hypothesis; __PROVED__ | $facts$ = fact1: {J} -> ¬{G} fact2: {K} fact3: ¬{B} -> ¬({A} & ¬{C}) fact4: ¬{A} -> (¬{AA} & {AB}) fact5: (¬{I} & {H}) -> {F} fact6: {K} -> {H} fact7: (¬{R} & ¬{I}) fact8: ¬{E} -> ({D} & ¬{B}) fact9: (¬{L} & ¬{M}) -> {J} fact10: ¬({A} & ¬{C}) -> ¬{A} fact11: ¬(¬{AA} & {AB}) fact12: {N} -> (¬{L} & ¬{M}) fact13: ({F} & ¬{G}) -> ¬{E} ; $hypothesis$ = ¬(¬{AA} & {AB}) ; $proof$ = | fact11 -> hypothesis; __PROVED__ |
0.3 | ãããã®è³æã¯ããŒãã¹ã©ã€ã³ãªãã°ãããããããã | {A}{aa} -> {C}{aa} | fact1: ããããåãç«ãŠã§ãªããçžãããããã¯äž¡æ¹ã ããšããããšã¯èª€ãã | fact1: ããããåãç«ãŠã§ãªããçžãããããã¯äž¡æ¹ã ããšããããšã¯èª€ãã | [] | [] | null | null | [] | null | 1 | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããããåãç«ãŠã§ãªããçžãããããã¯äž¡æ¹ã ããšããããšã¯èª€ãã ; $hypothesis$ = ãããã®è³æã¯ããŒãã¹ã©ã€ã³ãªãã°ãããããããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ããããåãç«ãŠã§ãªããçžãããããã¯äž¡æ¹ã ããšããããšã¯èª€ãã ; $hypothesis$ = {A}{aa} -> {C}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã®æ°çããåéŠã«æããªããäžä¿çºå¥è¯åã ããšããããšãæãç«ã€ããšããããšã¯æãç«ã€ãšããããšããªã | ¬(¬{AA}{b} & {AB}{b}) | fact1: ãã®ä»ããã®ã¯ã¬ã¹ãã¥ãŒã«ãããããšããããšã¯ãªã fact2: ãããã®ä»ããã®ãã¬ã¹ãã¥ãŒã«ãããããšããããšã¯ãªããªãã°ããã®æ°çãã¯åéŠã«æãããšããããšããªããããããããäžä¿çºå¥è¯åã ããšããããšãééãã fact3: ãã®ã¬ã¹ãã¥ãŒã¯ä»ããã®ããããããšããããšã¯ãªã | fact1: ¬{A}{a} fact2: ¬{A}{a} -> ¬(¬{AA}{b} & {AB}{b}) fact3: ¬{AC}{aa} | [
"fact2 & fact1 -> hypothesis;"
] | [
"fact2 & fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ä»ããã®ã¯ã¬ã¹ãã¥ãŒã«ãããããšããããšã¯ãªã fact2: ãããã®ä»ããã®ãã¬ã¹ãã¥ãŒã«ãããããšããããšã¯ãªããªãã°ããã®æ°çãã¯åéŠã«æãããšããããšããªããããããããäžä¿çºå¥è¯åã ããšããããšãééãã fact3: ãã®ã¬ã¹ãã¥ãŒã¯ä»ããã®ããããããšããããšã¯ãªã ; $hypothesis$ = ãããã®æ°çããåéŠã«æããªããäžä¿çºå¥è¯åã ããšããããšãæãç«ã€ããšããããšã¯æãç«ã€ãšããããšããªã ; $proof$ = | fact2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A}{a} fact2: ¬{A}{a} -> ¬(¬{AA}{b} & {AB}{b}) fact3: ¬{AC}{aa} ; $hypothesis$ = ¬(¬{AA}{b} & {AB}{b}) ; $proof$ = | fact2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ç¬èº«ã¯ç®ããšããšããããšã¯ãªãããããã¯ããã¯çãæ·±ãããããã¯äž¡æ¹ã | (¬{B}{a} v {C}{a}) | fact1: äœãããããããããšããããšã¯ãªã fact2: ãããã®ééŠã¯èªå°œãªãã°ãããã¯ã¿ãã¿ããããªããããã¯è³ãããããšããããšãäºå®ãšç°ãªã fact3: ãã®ã¯ããã³ã¯ãããããã fact4: ãããã®ééŠããããããããšããããšã¯ãªããªãã°ãã®ç¬èº«ã¯ç®ããšããšããããšã¯ãªããçãæ·±ãããããã¯äž¡æ¹ã fact5: ãããã€ã±ããã³ã ãšããããšã¯ãªãããã®ã¯ããã°ããã®ç¬èº«ãäºåå·»ã§ãªãããããç®ããšããäž¡æ¹ã ããšããããšã¯ééãã fact6: ãã®ç¬èº«ã¯é«æŽ¥éã fact7: ãã®ç¬èº«ããããããã fact8: ããããããããããªããç®ããšããªãããã®ã¯ããã°ãã®ç¬èº«ã¯è³ã
ãããªã fact9: äœããèªå°œã ãšããããšã¯ãªã fact10: ããããã®çŸ©å
ã¯æããããããããªããããŒã¯ãã§ã³ãžã«è¬ããšããããšããªãããšããããšãçå®ã§ãªããªãã°ãã®ä»£èšºãããŒã¯ãã§ã³ãžã«è¬ããšããããšããªã fact11: ãããããã®ãçãæ·±ããªãã°ããã¯ãããããããªããã®ã§ãã£ãŠç®ããšããªããã® fact12: ãããã®ä»£èšºãããŒã¯ãã§ã³ãžã«è¬ããšããããšããªããªãã°ããã¯çœã£ãœãããããã¿ãã¿ããã fact13: ããäœããè³ããããªããªãã°ããããçãæ·±ãããã«ãã³ãåå²ãããšããããšãæ£ãã fact14: ããããã®ééŠãã¿ãã¿ããããªããŠè³ãããããšããããšãæãç«ããªããªãã°ãããè³ããããšããããšããªã fact15: ãããããã®ã¯ãããããããšããããšã¯ãªããªãã°ããã®ç¬èº«ãç®ããšããªãããããã¯çãæ·±ãããšããããšãåã fact16: ããããããããããšããããšããªãããã®ãããã°ãã®ç¬èº«ãçãæ·±ããªã fact17: ãããããã®ã¯ã¿ãã¿ããããªãã°ããã¯èªå°œã fact18: ãããããã®ã¯ãã«ãã³ãåå²ããããããããè³ããããªããªãã°ããã¯ãããããããšããããšã¯ãªã fact19: ãçãæ·±ããªãããã®ã¯ãã fact20: ãã®ç¬èº«ãçãæ·±ããšããããšããªã | fact1: (Ex): ¬{A}x fact2: {F}{b} -> ¬(¬{G}{b} & {E}{b}) fact3: {A}{br} fact4: ¬{A}{b} -> (¬{B}{a} v {C}{a}) fact5: (x): ¬{BT}x -> ¬(¬{CF}{a} v {B}{a}) fact6: {JE}{a} fact7: {A}{a} fact8: (x): (¬{A}x & ¬{B}x) -> ¬{AT}{a} fact9: (Ex): ¬{F}x fact10: ¬(¬{K}{d} & ¬{I}{d}) -> ¬{I}{c} fact11: (x): {C}x -> (¬{A}x & ¬{B}x) fact12: ¬{I}{c} -> ({H}{c} & {G}{c}) fact13: (x): ¬{E}x -> ({C}x & {D}x) fact14: ¬(¬{G}{b} & {E}{b}) -> ¬{E}{b} fact15: (x): ¬{A}x -> ¬(¬{B}{a} v {C}{a}) fact16: (x): ¬{A}x -> ¬{C}{a} fact17: (x): {G}x -> {F}x fact18: (x): ({D}x & ¬{E}x) -> ¬{A}x fact19: (Ex): ¬{C}x fact20: ¬{C}{a} | [
"fact1 & fact15 -> hypothesis;"
] | [
"fact1 & fact15 -> hypothesis;"
] | è³ã
ãããªããã®ã¯ãã | (Ex): ¬{AT}x | [
"fact24 -> int1: ãããã®ééŠãçãæ·±ããªãã°ããããããããããšããããšã¯ãªããŠããã¯ç®ããšããªã; fact21 -> int2: ãããã®ééŠãè³ããããªããªãã°ãããçãæ·±ããããã¯ãã«ãã³ãåå²ã;"
] | 8 | 1 | 1 | 18 | 0 | 18 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: äœãããããããããšããããšã¯ãªã fact2: ãããã®ééŠã¯èªå°œãªãã°ãããã¯ã¿ãã¿ããããªããããã¯è³ãããããšããããšãäºå®ãšç°ãªã fact3: ãã®ã¯ããã³ã¯ãããããã fact4: ãããã®ééŠããããããããšããããšã¯ãªããªãã°ãã®ç¬èº«ã¯ç®ããšããšããããšã¯ãªããçãæ·±ãããããã¯äž¡æ¹ã fact5: ãããã€ã±ããã³ã ãšããããšã¯ãªãããã®ã¯ããã°ããã®ç¬èº«ãäºåå·»ã§ãªãããããç®ããšããäž¡æ¹ã ããšããããšã¯ééãã fact6: ãã®ç¬èº«ã¯é«æŽ¥éã fact7: ãã®ç¬èº«ããããããã fact8: ããããããããããªããç®ããšããªãããã®ã¯ããã°ãã®ç¬èº«ã¯è³ã
ãããªã fact9: äœããèªå°œã ãšããããšã¯ãªã fact10: ããããã®çŸ©å
ã¯æããããããããªããããŒã¯ãã§ã³ãžã«è¬ããšããããšããªãããšããããšãçå®ã§ãªããªãã°ãã®ä»£èšºãããŒã¯ãã§ã³ãžã«è¬ããšããããšããªã fact11: ãããããã®ãçãæ·±ããªãã°ããã¯ãããããããªããã®ã§ãã£ãŠç®ããšããªããã® fact12: ãããã®ä»£èšºãããŒã¯ãã§ã³ãžã«è¬ããšããããšããªããªãã°ããã¯çœã£ãœãããããã¿ãã¿ããã fact13: ããäœããè³ããããªããªãã°ããããçãæ·±ãããã«ãã³ãåå²ãããšããããšãæ£ãã fact14: ããããã®ééŠãã¿ãã¿ããããªããŠè³ãããããšããããšãæãç«ããªããªãã°ãããè³ããããšããããšããªã fact15: ãããããã®ã¯ãããããããšããããšã¯ãªããªãã°ããã®ç¬èº«ãç®ããšããªãããããã¯çãæ·±ãããšããããšãåã fact16: ããããããããããšããããšããªãããã®ãããã°ãã®ç¬èº«ãçãæ·±ããªã fact17: ãããããã®ã¯ã¿ãã¿ããããªãã°ããã¯èªå°œã fact18: ãããããã®ã¯ãã«ãã³ãåå²ããããããããè³ããããªããªãã°ããã¯ãããããããšããããšã¯ãªã fact19: ãçãæ·±ããªãããã®ã¯ãã fact20: ãã®ç¬èº«ãçãæ·±ããšããããšããªã ; $hypothesis$ = ãã®ç¬èº«ã¯ç®ããšããšããããšã¯ãªãããããã¯ããã¯çãæ·±ãããããã¯äž¡æ¹ã ; $proof$ = | fact1 & fact15 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (Ex): ¬{A}x fact2: {F}{b} -> ¬(¬{G}{b} & {E}{b}) fact3: {A}{br} fact4: ¬{A}{b} -> (¬{B}{a} v {C}{a}) fact5: (x): ¬{BT}x -> ¬(¬{CF}{a} v {B}{a}) fact6: {JE}{a} fact7: {A}{a} fact8: (x): (¬{A}x & ¬{B}x) -> ¬{AT}{a} fact9: (Ex): ¬{F}x fact10: ¬(¬{K}{d} & ¬{I}{d}) -> ¬{I}{c} fact11: (x): {C}x -> (¬{A}x & ¬{B}x) fact12: ¬{I}{c} -> ({H}{c} & {G}{c}) fact13: (x): ¬{E}x -> ({C}x & {D}x) fact14: ¬(¬{G}{b} & {E}{b}) -> ¬{E}{b} fact15: (x): ¬{A}x -> ¬(¬{B}{a} v {C}{a}) fact16: (x): ¬{A}x -> ¬{C}{a} fact17: (x): {G}x -> {F}x fact18: (x): ({D}x & ¬{E}x) -> ¬{A}x fact19: (Ex): ¬{C}x fact20: ¬{C}{a} ; $hypothesis$ = (¬{B}{a} v {C}{a}) ; $proof$ = | fact1 & fact15 -> hypothesis; __DISPROVED__ |
0.3 | é£å¢ã¯çºçããªã | ¬{B} | fact1: ãã¡ãããããšããããšã¯ãé£å¢ã¯èµ·ãããªãããšããããšãåé¿ãã fact2: ããåºæ¥åãããšãçããã°çŽåã«é£ãããããšãçºçããããµãã¹ã€ããããšããããšãèµ·ãããªã fact3: ãé£å¢ãçããããšããããšãããã¡ãããããšããããšã¯èµ·ããªããå¹ãã ãŸãã«åºããããšã¯èµ·ããããšããããšã«é»ãŸãã fact4: èžåœãçºçãã fact5: ããŒã©ãŒã¹ã±ãŒãã¯çºçãã fact6: ãæå®ãçºçããããšããããšã¯çå®ã fact7: ããã£ãŒã«ãã¯ãŒã¯ã¯èµ·ãããšããããšã¯ãæ¯ã©ããããšããããšãèµ·ããªãããšããããšãå¶æ¢ããããšããããšã¯æ£ãã fact8: ãã¡ãããããšããããšã¯çãã fact9: 西æ¥æ¬é¶åšã«ãã¶ãããšããé€èã¯çããããšããããšã«ããçºçãã fact10: ãããè¡°ããããšãçããããšããããšãæ¬åœã fact11: ææ¡ãèµ·ãã fact12: ãããå£ãããŸãããšããããšã¯çããªãããšããããšã¯çå®ãªãã°ãã¡ãããããšããããšãçããªãããããå¹ãã ãŸãã«åºããããšã¯èµ·ãã fact13: ãæãçºçããªãããšããããšã¯ããã«ãŒããçããããããã¯çŽåã«é£ãããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšããã£ããã fact14: äºåç°å·ã«ææ°ä»ãããšãçºçãããšããããšã¯ãçŽãããããšãçããããšããããšãèªçºãã fact15: ããæã¯çºçããªããªãã°å£ãããŸãããšããããšãèµ·ããªãããªãŸããããšããããšãçºçããªã fact16: ç©æããšããããšã¯çãã fact17: ããªããããšããããšã¯çºçããªããšããããšã¯ç©æããšããããšãèµ·ãããšããããšã«å¶æ¢ããã fact18: ã¡ãã¡ãããã䜿ãåãããšã嚯楜ãèµ·ããªããšããããšãææ¢ãã fact19: ã貞ãä»ããçããããšããããšãæ¬åœã fact20: ããšããããããšãèµ·ããªãããšããããšã¯ããã¹ããŒã¯ãçºçããããšããããšã«é»æ¢ããã | fact1: {A} -> {B} fact2: {J} -> ({H} & ¬{I}) fact3: (¬{A} & {C}) -> ¬{B} fact4: {BS} fact5: {DD} fact6: {II} fact7: {IA} -> {AP} fact8: {A} fact9: {BT} -> {AB} fact10: {AA} fact11: {FA} fact12: ¬{D} -> (¬{A} & {C}) fact13: ({G} v {H}) -> ¬{F} fact14: {CP} -> {IU} fact15: ¬{F} -> (¬{D} & ¬{E}) fact16: {FT} fact17: {FT} -> {EC} fact18: {FR} -> {IP} fact19: {HD} fact20: {ET} -> {AU} | [
"fact1 & fact8 -> hypothesis;"
] | [
"fact1 & fact8 -> hypothesis;"
] | é£å¢ãçããªã | ¬{B} | [] | 10 | 1 | 1 | 18 | 0 | 18 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã¡ãããããšããããšã¯ãé£å¢ã¯èµ·ãããªãããšããããšãåé¿ãã fact2: ããåºæ¥åãããšãçããã°çŽåã«é£ãããããšãçºçããããµãã¹ã€ããããšããããšãèµ·ãããªã fact3: ãé£å¢ãçããããšããããšãããã¡ãããããšããããšã¯èµ·ããªããå¹ãã ãŸãã«åºããããšã¯èµ·ããããšããããšã«é»ãŸãã fact4: èžåœãçºçãã fact5: ããŒã©ãŒã¹ã±ãŒãã¯çºçãã fact6: ãæå®ãçºçããããšããããšã¯çå®ã fact7: ããã£ãŒã«ãã¯ãŒã¯ã¯èµ·ãããšããããšã¯ãæ¯ã©ããããšããããšãèµ·ããªãããšããããšãå¶æ¢ããããšããããšã¯æ£ãã fact8: ãã¡ãããããšããããšã¯çãã fact9: 西æ¥æ¬é¶åšã«ãã¶ãããšããé€èã¯çããããšããããšã«ããçºçãã fact10: ãããè¡°ããããšãçããããšããããšãæ¬åœã fact11: ææ¡ãèµ·ãã fact12: ãããå£ãããŸãããšããããšã¯çããªãããšããããšã¯çå®ãªãã°ãã¡ãããããšããããšãçããªãããããå¹ãã ãŸãã«åºããããšã¯èµ·ãã fact13: ãæãçºçããªãããšããããšã¯ããã«ãŒããçããããããã¯çŽåã«é£ãããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšããã£ããã fact14: äºåç°å·ã«ææ°ä»ãããšãçºçãããšããããšã¯ãçŽãããããšãçããããšããããšãèªçºãã fact15: ããæã¯çºçããªããªãã°å£ãããŸãããšããããšãèµ·ããªãããªãŸããããšããããšãçºçããªã fact16: ç©æããšããããšã¯çãã fact17: ããªããããšããããšã¯çºçããªããšããããšã¯ç©æããšããããšãèµ·ãããšããããšã«å¶æ¢ããã fact18: ã¡ãã¡ãããã䜿ãåãããšã嚯楜ãèµ·ããªããšããããšãææ¢ãã fact19: ã貞ãä»ããçããããšããããšãæ¬åœã fact20: ããšããããããšãèµ·ããªãããšããããšã¯ããã¹ããŒã¯ãçºçããããšããããšã«é»æ¢ããã ; $hypothesis$ = é£å¢ã¯çºçããªã ; $proof$ = | fact1 & fact8 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} -> {B} fact2: {J} -> ({H} & ¬{I}) fact3: (¬{A} & {C}) -> ¬{B} fact4: {BS} fact5: {DD} fact6: {II} fact7: {IA} -> {AP} fact8: {A} fact9: {BT} -> {AB} fact10: {AA} fact11: {FA} fact12: ¬{D} -> (¬{A} & {C}) fact13: ({G} v {H}) -> ¬{F} fact14: {CP} -> {IU} fact15: ¬{F} -> (¬{D} & ¬{E}) fact16: {FT} fact17: {FT} -> {EC} fact18: {FR} -> {IP} fact19: {HD} fact20: {ET} -> {AU} ; $hypothesis$ = ¬{B} ; $proof$ = | fact1 & fact8 -> hypothesis; __DISPROVED__ |
0.3 | æŽç€Œã¯çãã | {B} | fact1: æ
ããããšã¯èµ·ãããšããããšããç
ãããšããããšãèµ·ããããšããããšã«ããçãã fact2: ãç²ç¶ãçããªãããšããããšããæ
ããããšãèµ·ããããšããããšã«å¶æ¢ããã fact3: ãããè¡è
¥ããšããããšãçºçããªããçªç«ã€ããšãçºçããããšããããšã誀ããªãã°ã³ãŠããæããããšã¯èµ·ãã fact4: æŽç€Œãçãããšããããšã¯ã³ãŠããæããããšãçãããšããããšã«ããçãã fact5: ãããç«ã¡ä»£ãããããšãèµ·ããããšããããšã¯äºå®ãšç°ãªãã°åäžååæ¡è¥¿ãã€ãã°ãããšã¯èµ·ããã家äžèãèŠãããããšã¯çºçãã fact6: ãã家äžèãèŠãããããšã¯èµ·ããã°ãè¡è
¥ããšããããšã¯èµ·ããªãããããçªç«ã€ããšãçºçããããšããããšãæãç«ã€ãšããããšããªã fact7: ãããã ãŠãããšãšèå¯ããšããããšãçããããšããããšã¯æŽç€Œã¯èµ·ãããšããããšãåé¿ãã fact8: ãç«ã¡ä»£ãããããšãèµ·ããªããçŠãããããšããããšã¯èµ·ãããªãããšããããšãç²ç¶ããã£ããã | fact1: {K} -> {J} fact2: {J} -> {I} fact3: ¬(¬{D} & {C}) -> {A} fact4: {A} -> {B} fact5: ¬{G} -> ({F} & {E}) fact6: {E} -> ¬(¬{D} & {C}) fact7: ({AA} & {AB}) -> ¬{B} fact8: {I} -> (¬{G} & ¬{H}) | [] | [] | æŽç€Œãèµ·ãã | {B} | [] | 12 | 1 | null | 7 | 0 | 7 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: æ
ããããšã¯èµ·ãããšããããšããç
ãããšããããšãèµ·ããããšããããšã«ããçãã fact2: ãç²ç¶ãçããªãããšããããšããæ
ããããšãèµ·ããããšããããšã«å¶æ¢ããã fact3: ãããè¡è
¥ããšããããšãçºçããªããçªç«ã€ããšãçºçããããšããããšã誀ããªãã°ã³ãŠããæããããšã¯èµ·ãã fact4: æŽç€Œãçãããšããããšã¯ã³ãŠããæããããšãçãããšããããšã«ããçãã fact5: ãããç«ã¡ä»£ãããããšãèµ·ããããšããããšã¯äºå®ãšç°ãªãã°åäžååæ¡è¥¿ãã€ãã°ãããšã¯èµ·ããã家äžèãèŠãããããšã¯çºçãã fact6: ãã家äžèãèŠãããããšã¯èµ·ããã°ãè¡è
¥ããšããããšã¯èµ·ããªãããããçªç«ã€ããšãçºçããããšããããšãæãç«ã€ãšããããšããªã fact7: ãããã ãŠãããšãšèå¯ããšããããšãçããããšããããšã¯æŽç€Œã¯èµ·ãããšããããšãåé¿ãã fact8: ãç«ã¡ä»£ãããããšãèµ·ããªããçŠãããããšããããšã¯èµ·ãããªãããšããããšãç²ç¶ããã£ããã ; $hypothesis$ = æŽç€Œã¯çãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {K} -> {J} fact2: {J} -> {I} fact3: ¬(¬{D} & {C}) -> {A} fact4: {A} -> {B} fact5: ¬{G} -> ({F} & {E}) fact6: {E} -> ¬(¬{D} & {C}) fact7: ({AA} & {AB}) -> ¬{B} fact8: {I} -> (¬{G} & ¬{H}) ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãªã«ãŽãŒã«ã¯è¥¿éè°·æ°ç°ã«ãããããªãããããã¯ããã¯å€§ãããªãããšããããšãæãç«ããªã | ¬(¬{AA}{b} v ¬{AB}{b}) | fact1: ããäœãããã°ãã°ãããªãã°ãããã¯ãã
ã€ãªããšããããšããªããŠäžè±é»æ©ããŒã æ©åšã§ãªãããšããããšãæ£ãããªã fact2: ãããã®ãªã«ãŽãŒã«ã¯è¥¿éè°·æ°ç°ã«ããããããšããããšããªããªãã°ãã®ããã±ãŒãžã倧ãã fact3: ãããããã®ã¯æµ·å£«ã¶ç¬æžã§ãªããªãã°ããã¯è¥¿éè°·æ°ç°ã«ãããããªããããã倧ãããªãããããã¯äž¡æ¹ã fact4: ããã®å€é£ãå¿èŠãããšããããšããªãããããã¯ããã¯ããããšã«ããããããšããããšã¯ãªãããšããããšãééãã fact5: ãã®ããã±ãŒãžã海士ã¶ç¬æžã ãšããããšã¯ãªã fact6: ãããã®ãªã«ãŽãŒã«ã西éè°·æ°ç°ã«ããããããšããããšã¯ãªãããããã¯ããã海士ã¶ç¬æžã§ãªãããšããããšãåã§ãªãããšããããšã¯æãç«ããªã fact7: ãããã®ããã±ãŒãžã¯å€§ãããšããããšã¯ãªããªãã°ãã®ãªã«ãŽãŒã«ã¯æµ·å£«ã¶ç¬æžã fact8: ãããã®ãªã«ãŽãŒã«ã海士ã¶ç¬æžã§ãªããªãã°ããã®ããã±ãŒãžã西éè°·æ°ç°ã«ãããããªãã倧ãããšããããšããªãããããã¯äž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact9: ãããã®ããã±ãŒãžã¯æµ·å£«ã¶ç¬æžã ãšããããšã¯ãªããªãã°ããã®ãªã«ãŽãŒã«ã西éè°·æ°ç°ã«ãããããªãããããã¯ããã¯å€§ãããšããããšããªããäž¡æ¹ã ããšããããšãæãç«ããªã fact10: ããããã®ããã±ãŒãžã¯æµ·å£«ã¶ç¬æžã§ãªãããšããããšã¯æãç«ãŠã°ãã®ãªã«ãŽãŒã«ã¯è¥¿éè°·æ°ç°ã«ããããã | fact1: (x): {D}x -> ¬(¬{B}x & ¬{C}x) fact2: ¬{AA}{b} -> {AB}{a} fact3: (x): ¬{A}x -> (¬{AA}x v ¬{AB}x) fact4: ¬(¬{BR}{im} v ¬{EL}{im}) fact5: ¬{A}{a} fact6: ¬(¬{AA}{b} v ¬{A}{b}) fact7: ¬{AB}{a} -> {A}{b} fact8: ¬{A}{b} -> ¬(¬{AA}{a} v ¬{AB}{a}) fact9: ¬{A}{a} -> ¬(¬{AA}{b} v ¬{AB}{b}) fact10: ¬{A}{a} -> {AA}{b} | [
"fact9 & fact5 -> hypothesis;"
] | [
"fact9 & fact5 -> hypothesis;"
] | ãã®ã¹ã¯ãŒã«ãã¹ã海士ã¶ç¬æžã ãšããããšã¯ãªã | ¬{A}{bm} | [
"fact11 -> int1: ãããã®ããã±ãŒãžã¯ãã°ãã°ãããªãã°ãããããã
ã€ãªããªããã®ã§ãã£ãŠäžè±é»æ©ããŒã æ©åšã ãšããããšããªããã®ããšããããšã誀ãã ;"
] | 5 | 1 | 1 | 8 | 0 | 8 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããäœãããã°ãã°ãããªãã°ãããã¯ãã
ã€ãªããšããããšããªããŠäžè±é»æ©ããŒã æ©åšã§ãªãããšããããšãæ£ãããªã fact2: ãããã®ãªã«ãŽãŒã«ã¯è¥¿éè°·æ°ç°ã«ããããããšããããšããªããªãã°ãã®ããã±ãŒãžã倧ãã fact3: ãããããã®ã¯æµ·å£«ã¶ç¬æžã§ãªããªãã°ããã¯è¥¿éè°·æ°ç°ã«ãããããªããããã倧ãããªãããããã¯äž¡æ¹ã fact4: ããã®å€é£ãå¿èŠãããšããããšããªãããããã¯ããã¯ããããšã«ããããããšããããšã¯ãªãããšããããšãééãã fact5: ãã®ããã±ãŒãžã海士ã¶ç¬æžã ãšããããšã¯ãªã fact6: ãããã®ãªã«ãŽãŒã«ã西éè°·æ°ç°ã«ããããããšããããšã¯ãªãããããã¯ããã海士ã¶ç¬æžã§ãªãããšããããšãåã§ãªãããšããããšã¯æãç«ããªã fact7: ãããã®ããã±ãŒãžã¯å€§ãããšããããšã¯ãªããªãã°ãã®ãªã«ãŽãŒã«ã¯æµ·å£«ã¶ç¬æžã fact8: ãããã®ãªã«ãŽãŒã«ã海士ã¶ç¬æžã§ãªããªãã°ããã®ããã±ãŒãžã西éè°·æ°ç°ã«ãããããªãã倧ãããšããããšããªãããããã¯äž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact9: ãããã®ããã±ãŒãžã¯æµ·å£«ã¶ç¬æžã ãšããããšã¯ãªããªãã°ããã®ãªã«ãŽãŒã«ã西éè°·æ°ç°ã«ãããããªãããããã¯ããã¯å€§ãããšããããšããªããäž¡æ¹ã ããšããããšãæãç«ããªã fact10: ããããã®ããã±ãŒãžã¯æµ·å£«ã¶ç¬æžã§ãªãããšããããšã¯æãç«ãŠã°ãã®ãªã«ãŽãŒã«ã¯è¥¿éè°·æ°ç°ã«ããããã ; $hypothesis$ = ããã®ãªã«ãŽãŒã«ã¯è¥¿éè°·æ°ç°ã«ãããããªãããããã¯ããã¯å€§ãããªãããšããããšãæãç«ããªã ; $proof$ = | fact9 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {D}x -> ¬(¬{B}x & ¬{C}x) fact2: ¬{AA}{b} -> {AB}{a} fact3: (x): ¬{A}x -> (¬{AA}x v ¬{AB}x) fact4: ¬(¬{BR}{im} v ¬{EL}{im}) fact5: ¬{A}{a} fact6: ¬(¬{AA}{b} v ¬{A}{b}) fact7: ¬{AB}{a} -> {A}{b} fact8: ¬{A}{b} -> ¬(¬{AA}{a} v ¬{AB}{a}) fact9: ¬{A}{a} -> ¬(¬{AA}{b} v ¬{AB}{b}) fact10: ¬{A}{a} -> {AA}{b} ; $hypothesis$ = ¬(¬{AA}{b} v ¬{AB}{b}) ; $proof$ = | fact9 & fact5 -> hypothesis; __PROVED__ |
0.3 | ãããããããšã¯èµ·ããªãããããåŒãæž¡ãã¯çããããšããããšãåã | ¬(¬{AA} & {AB}) | fact1: åŒãæž¡ãã¯èµ·ãããªããšããããšãçœé³¥å£å°ãã¿ãããã€ããšã¯èµ·ããªããšããããšã«ææ¢ããã fact2: ããçœé³¥å£å°ãã¿ãããã€ããšã¯çºçããªããªãã°ããããããšã§ã¯ãªãåŒãæž¡ãã¯çãã fact3: ç¥ãã¯èµ·ãããªããšããããšã¯ã緩解ã¯çããªããã«ãã¯èµ·ããããšããããšã®åå ãšãªã fact4: ããçœé³¥å£å°ãã¿ãããã€ããšã¯çããã°ãããããããšã§ã¯ãªãåŒãæž¡ãã¯èµ·ããããšããããšãæãç«ã€ãšããããšããªã | fact1: ¬{A} -> {AB} fact2: ¬{A} -> (¬{AA} & {AB}) fact3: ¬{CI} -> (¬{K} & {JG}) fact4: {A} -> ¬(¬{AA} & {AB}) | [] | [] | ãããããããšã§ã¯ãªãåŒãæž¡ãã¯èµ·ããããšããããšã¯æãç«ããªã | ¬(¬{AA} & {AB}) | [] | 6 | 1 | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: åŒãæž¡ãã¯èµ·ãããªããšããããšãçœé³¥å£å°ãã¿ãããã€ããšã¯èµ·ããªããšããããšã«ææ¢ããã fact2: ããçœé³¥å£å°ãã¿ãããã€ããšã¯çºçããªããªãã°ããããããšã§ã¯ãªãåŒãæž¡ãã¯çãã fact3: ç¥ãã¯èµ·ãããªããšããããšã¯ã緩解ã¯çããªããã«ãã¯èµ·ããããšããããšã®åå ãšãªã fact4: ããçœé³¥å£å°ãã¿ãããã€ããšã¯çããã°ãããããããšã§ã¯ãªãåŒãæž¡ãã¯èµ·ããããšããããšãæãç«ã€ãšããããšããªã ; $hypothesis$ = ãããããããšã¯èµ·ããªãããããåŒãæž¡ãã¯çããããšããããšãåã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A} -> {AB} fact2: ¬{A} -> (¬{AA} & {AB}) fact3: ¬{CI} -> (¬{K} & {JG}) fact4: {A} -> ¬(¬{AA} & {AB}) ; $hypothesis$ = ¬(¬{AA} & {AB}) ; $proof$ = | __UNKNOWN__ |
0.3 | 床ããããšããããšã¯èµ·ãããªã | ¬{B} | fact1: æããããšãçºçããªããšããããšããããã¯ãã£ãªãã£ãŒãçãããšããããšãäž¡æ¹ãããã£ãªãã£ãŒãèµ·ãããªãããšããããšãé»æ¢ãã fact2: ããæ°ããããããšããããšã¯èµ·ããã°ãå£çããçããªãããã«ãããããšããããšãèµ·ãããªããäž¡æ¹ã ããšããããšã¯æãç«ããªã fact3: ããªãŒãããºã¬èŸŒãããšã¯çºçããªãããšããããšãæãå·»ãã€ãããããšãèµ·ãããšããããšã«å¶æ¢ããã fact4: 圹ãšçžè
°æãã«ç·æ¯ç«ã€ããšãèµ·ãã fact5: ããã£ãªãã£ãŒã¯èµ·ãããªãããšããããšããå¯æã¯çããããšããããšã«ææ¢ããã fact6: ãããã£ãªãã£ãŒã¯èµ·ããã°ãæãå·»ãã€ãããããšã¯èµ·ãããªããè®ã«è©£ã§ãããšãçããããšããããšã¯èª€ãã fact7: å¯æãæããããšãèµ·ãããªããšããããšãããã£ãªãã£ãŒã¯èµ·ããããšããããšãäž¡æ¹ãåŒãèµ·ãã fact8: ããå¯æã¯èµ·ãããªããªãã°ããã£ãªãã£ãŒãçºçããªããæããããšã¯èµ·ãããªãããšããããšã¯ééãã fact9: ããããã£ãªãã£ãŒãèµ·ãããªããæããããšãèµ·ãããªãããšããããšãäºå®ãšç°ãªãã°ãã£ãªãã£ãŒãçãã fact10: 宀ç©æŸåã«ã¶ã£ãããããšã¯çãã fact11: æãé£ããšããããšã¯èµ·ãã fact12: 鶎鳎ã«èšããããšãšåèŠå
«èŠã¯çãã fact13: ãã床ããããšããããšãçããªããªãã°ç£å¶ã¯èµ·ãããæãå·»ãã€ãããããšãçºçããªã fact14: ãããå¯æãšè®ã«è©£ã§ãããšãçããããšããããšãæãç«ã€ãšããããšããªããªãã°è®ã«è©£ã§ãããšã¯çºçããªã fact15: ããå£çããèµ·ããªããªãã°æããããšãšå¯æãèµ·ãã fact16: ã°ã£ã¡ããšããããšã¯èµ·ãããä»ãã¯çãã fact17: è®ã«è©£ã§ãããšã¯çããªããšããããšã¯åºŠããããšããããšãçºçããªããšããããšããããã fact18: ãããå£çããèµ·ãããªãããã«ãããããšããããšã¯èµ·ããªãããããã¯äž¡æ¹ã ããšããããšã¯äºå®ãšç°ãªãã°å¯æãèµ·ãã fact19: æãå·»ãã€ãããããšã¯çºçããã床ããããšããããšã¯çãã | fact1: (¬{F} v {D}) -> {D} fact2: {I} -> ¬(¬{G} v ¬{H}) fact3: {A} -> {AA} fact4: ({N} & {T}) fact5: {E} -> {D} fact6: {D} -> ¬(¬{A} & {C}) fact7: {E} -> (¬{F} v {D}) fact8: ¬{E} -> ¬(¬{D} & ¬{F}) fact9: ¬(¬{D} & ¬{F}) -> {D} fact10: {AJ} fact11: {ET} fact12: ({BE} & {IJ}) fact13: ¬{B} -> ({EN} & ¬{A}) fact14: ¬({E} & {C}) -> ¬{C} fact15: ¬{G} -> ({F} & {E}) fact16: ({JD} & {DC}) fact17: ¬{C} -> ¬{B} fact18: ¬(¬{G} v ¬{H}) -> {E} fact19: ({A} & {B}) | [
"fact19 -> hypothesis;"
] | [
"fact19 -> hypothesis;"
] | ç£å¶ã¯çãã | {EN} | [] | 8 | 1 | 1 | 18 | 0 | 18 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: æããããšãçºçããªããšããããšããããã¯ãã£ãªãã£ãŒãçãããšããããšãäž¡æ¹ãããã£ãªãã£ãŒãèµ·ãããªãããšããããšãé»æ¢ãã fact2: ããæ°ããããããšããããšã¯èµ·ããã°ãå£çããçããªãããã«ãããããšããããšãèµ·ãããªããäž¡æ¹ã ããšããããšã¯æãç«ããªã fact3: ããªãŒãããºã¬èŸŒãããšã¯çºçããªãããšããããšãæãå·»ãã€ãããããšãèµ·ãããšããããšã«å¶æ¢ããã fact4: 圹ãšçžè
°æãã«ç·æ¯ç«ã€ããšãèµ·ãã fact5: ããã£ãªãã£ãŒã¯èµ·ãããªãããšããããšããå¯æã¯çããããšããããšã«ææ¢ããã fact6: ãããã£ãªãã£ãŒã¯èµ·ããã°ãæãå·»ãã€ãããããšã¯èµ·ãããªããè®ã«è©£ã§ãããšãçããããšããããšã¯èª€ãã fact7: å¯æãæããããšãèµ·ãããªããšããããšãããã£ãªãã£ãŒã¯èµ·ããããšããããšãäž¡æ¹ãåŒãèµ·ãã fact8: ããå¯æã¯èµ·ãããªããªãã°ããã£ãªãã£ãŒãçºçããªããæããããšã¯èµ·ãããªãããšããããšã¯ééãã fact9: ããããã£ãªãã£ãŒãèµ·ãããªããæããããšãèµ·ãããªãããšããããšãäºå®ãšç°ãªãã°ãã£ãªãã£ãŒãçãã fact10: 宀ç©æŸåã«ã¶ã£ãããããšã¯çãã fact11: æãé£ããšããããšã¯èµ·ãã fact12: 鶎鳎ã«èšããããšãšåèŠå
«èŠã¯çãã fact13: ãã床ããããšããããšãçããªããªãã°ç£å¶ã¯èµ·ãããæãå·»ãã€ãããããšãçºçããªã fact14: ãããå¯æãšè®ã«è©£ã§ãããšãçããããšããããšãæãç«ã€ãšããããšããªããªãã°è®ã«è©£ã§ãããšã¯çºçããªã fact15: ããå£çããèµ·ããªããªãã°æããããšãšå¯æãèµ·ãã fact16: ã°ã£ã¡ããšããããšã¯èµ·ãããä»ãã¯çãã fact17: è®ã«è©£ã§ãããšã¯çããªããšããããšã¯åºŠããããšããããšãçºçããªããšããããšããããã fact18: ãããå£çããèµ·ãããªãããã«ãããããšããããšã¯èµ·ããªãããããã¯äž¡æ¹ã ããšããããšã¯äºå®ãšç°ãªãã°å¯æãèµ·ãã fact19: æãå·»ãã€ãããããšã¯çºçããã床ããããšããããšã¯çãã ; $hypothesis$ = 床ããããšããããšã¯èµ·ãããªã ; $proof$ = | fact19 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (¬{F} v {D}) -> {D} fact2: {I} -> ¬(¬{G} v ¬{H}) fact3: {A} -> {AA} fact4: ({N} & {T}) fact5: {E} -> {D} fact6: {D} -> ¬(¬{A} & {C}) fact7: {E} -> (¬{F} v {D}) fact8: ¬{E} -> ¬(¬{D} & ¬{F}) fact9: ¬(¬{D} & ¬{F}) -> {D} fact10: {AJ} fact11: {ET} fact12: ({BE} & {IJ}) fact13: ¬{B} -> ({EN} & ¬{A}) fact14: ¬({E} & {C}) -> ¬{C} fact15: ¬{G} -> ({F} & {E}) fact16: ({JD} & {DC}) fact17: ¬{C} -> ¬{B} fact18: ¬(¬{G} v ¬{H}) -> {E} fact19: ({A} & {B}) ; $hypothesis$ = ¬{B} ; $proof$ = | fact19 -> hypothesis; __DISPROVED__ |
0.3 | ãããªãããããšãçãã | {B} | fact1: å¯è§£ã¯çºçããªã fact2: ããããªãããããšã¯èµ·ãããäºå¡æãèµ·ããããšããããšã¯äžä¿¡ç·ããããããšã¯çºçããªããšããããšã«èµ·å ãã fact3: ããçš®å¥ãçããã°çµåãã§ã¯ãªãä»åãã¯èµ·ãã fact4: æ°äžã«æ¯ããŸããããšãèµ·ããªããšããããšã¯äºã岩ã«ä»åãããšã¯èµ·ãããšããããšããã¡ãã©ããšããããšãèµ·ãããªããšããããšããããã¯äž¡æ¹ã«åž°çµãã fact5: ãããå³å³ãããšããããšã¯èµ·ããªãããšããããšããããããããšããããšã¯èµ·ããªããšããããšã«ãããããã fact6: ããããªãããããšãèµ·ããããšããããšããäºå¡æã¯çããªãããšããããšã«é²ããã fact7: äžä¿¡ç·ããããããšã¯çºçãããšããããšãã·ãããçºçãããšããããšã«é»æ¢ããã fact8: æå¢ãçºçããªã fact9: ãªã«ããããªããšããããšãšçš®å¥äž¡æ¹ãèµ·ãã fact10: ããå·»ã¯èµ·ãããªããªãã°æ°äžã«æ¯ããŸããããšã¯çºçããªããå²æµãå·®ã延ã¹ãããšã¯çºçããªã fact11: æ°äžã«æ¯ããŸããããšãçºçããªã fact12: ãèèè²ã«ãããªããããšãèµ·ããããšããããšã¯ã¢ã«ãŽãªãºã ã¯çããªããšããããšã«å¶æ¢ããã fact13: ãããã¡ããã©ãã
ããå¢ããããšãçºçããªãããã«ã ã«ã¬ãã¿ã ããããšãçããªãããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãã«ã ã«ã¬ãã¿ã ããããšãèµ·ãã fact14: ãããçµåããèµ·ããªãããšããããšã¯æ£ãããªãã°ãã¡ããã©ãã
ããå¢ããããšãçºçããªããŠãã«ã ã«ã¬ãã¿ã ããããšã¯èµ·ãããªãããšããããšãåœã fact15: é£ã¯èµ·ããªã fact16: åºç«ãŠã¯çããªã fact17: ããã«ã ã«ã¬ãã¿ã ããããšã¯çºçããããšããããšãããŸã£ããããšããããšã¯çããªããŠå·»ã¯çºçããªãããšããããšã«ç¹ãã | fact1: ¬{BN} fact2: ¬{C} -> ({B} & {A}) fact3: {O} -> (¬{M} & {N}) fact4: ¬{G} -> ({F} v ¬{E}) fact5: ¬{GM} -> ¬{BB} fact6: ¬{A} -> ¬{B} fact7: {D} -> ¬{C} fact8: ¬{EC} fact9: ({P} & {O}) fact10: ¬{I} -> (¬{G} & ¬{H}) fact11: ¬{G} fact12: ¬{FE} -> ¬{FC} fact13: ¬(¬{L} & ¬{K}) -> {K} fact14: ¬{M} -> ¬(¬{L} & ¬{K}) fact15: ¬{DF} fact16: ¬{AU} fact17: {K} -> (¬{J} & ¬{I}) | [] | [] | ãããªãããããšã¯èµ·ãã | {B} | [
"fact22 -> int1: çš®å¥ã¯çãã; fact21 & int1 -> int2: çµåãã¯èµ·ããªãããããä»åãã¯çºçãã; int2 -> int3: çµåãã¯çããªã; fact20 & int3 -> int4: ãã¡ããã©ãã
ããå¢ããããšã¯çºçããªããŠãã«ã ã«ã¬ãã¿ã ããããšã¯èµ·ããªãããšããããšã¯èª€ãã ; fact25 & int4 -> int5: ãã«ã ã«ã¬ãã¿ã ããããšã¯èµ·ãã; fact18 & int5 -> int6: ãŸã£ããããšããããšãçããªããå·»ãèµ·ããªã; int6 -> int7: å·»ãçºçããªã; fact26 & int7 -> int8: æ°äžã«æ¯ããŸããããšã¯çããªããŠå²æµãå·®ã延ã¹ãããšã¯çããªã; int8 -> int9: æ°äžã«æ¯ããŸããããšã¯èµ·ããªã; fact24 & int9 -> int10: äºã岩ã«ä»åãããšãèµ·ããããããã¯ãã¡ãã©ããšããããšãèµ·ãããªãããããã¯äž¡æ¹ã ;"
] | 14 | 1 | null | 16 | 0 | 16 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: å¯è§£ã¯çºçããªã fact2: ããããªãããããšã¯èµ·ãããäºå¡æãèµ·ããããšããããšã¯äžä¿¡ç·ããããããšã¯çºçããªããšããããšã«èµ·å ãã fact3: ããçš®å¥ãçããã°çµåãã§ã¯ãªãä»åãã¯èµ·ãã fact4: æ°äžã«æ¯ããŸããããšãèµ·ããªããšããããšã¯äºã岩ã«ä»åãããšã¯èµ·ãããšããããšããã¡ãã©ããšããããšãèµ·ãããªããšããããšããããã¯äž¡æ¹ã«åž°çµãã fact5: ãããå³å³ãããšããããšã¯èµ·ããªãããšããããšããããããããšããããšã¯èµ·ããªããšããããšã«ãããããã fact6: ããããªãããããšãèµ·ããããšããããšããäºå¡æã¯çããªãããšããããšã«é²ããã fact7: äžä¿¡ç·ããããããšã¯çºçãããšããããšãã·ãããçºçãããšããããšã«é»æ¢ããã fact8: æå¢ãçºçããªã fact9: ãªã«ããããªããšããããšãšçš®å¥äž¡æ¹ãèµ·ãã fact10: ããå·»ã¯èµ·ãããªããªãã°æ°äžã«æ¯ããŸããããšã¯çºçããªããå²æµãå·®ã延ã¹ãããšã¯çºçããªã fact11: æ°äžã«æ¯ããŸããããšãçºçããªã fact12: ãèèè²ã«ãããªããããšãèµ·ããããšããããšã¯ã¢ã«ãŽãªãºã ã¯çããªããšããããšã«å¶æ¢ããã fact13: ãããã¡ããã©ãã
ããå¢ããããšãçºçããªãããã«ã ã«ã¬ãã¿ã ããããšãçããªãããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãã«ã ã«ã¬ãã¿ã ããããšãèµ·ãã fact14: ãããçµåããèµ·ããªãããšããããšã¯æ£ãããªãã°ãã¡ããã©ãã
ããå¢ããããšãçºçããªããŠãã«ã ã«ã¬ãã¿ã ããããšã¯èµ·ãããªãããšããããšãåœã fact15: é£ã¯èµ·ããªã fact16: åºç«ãŠã¯çããªã fact17: ããã«ã ã«ã¬ãã¿ã ããããšã¯çºçããããšããããšãããŸã£ããããšããããšã¯çããªããŠå·»ã¯çºçããªãããšããããšã«ç¹ãã ; $hypothesis$ = ãããªãããããšãçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{BN} fact2: ¬{C} -> ({B} & {A}) fact3: {O} -> (¬{M} & {N}) fact4: ¬{G} -> ({F} v ¬{E}) fact5: ¬{GM} -> ¬{BB} fact6: ¬{A} -> ¬{B} fact7: {D} -> ¬{C} fact8: ¬{EC} fact9: ({P} & {O}) fact10: ¬{I} -> (¬{G} & ¬{H}) fact11: ¬{G} fact12: ¬{FE} -> ¬{FC} fact13: ¬(¬{L} & ¬{K}) -> {K} fact14: ¬{M} -> ¬(¬{L} & ¬{K}) fact15: ¬{DF} fact16: ¬{AU} fact17: {K} -> (¬{J} & ¬{I}) ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã³ã³ãã©ãæŠå³¶ã ããšããããšã¯æ£ãã | {B}{b} | fact1: ããã®ã³ã³ãã©ãåæ山倧ãçµã¿ãããªãããããããã¯æŠå³¶ã ããšããããšã¯æãç«ããªã fact2: ããããã®ã¡ãŒã³ã¹ããªãŒããæ¥ç«ãã©ã³ã建èšã§ãªãããããæŠå³¶ã ããšããããšãééããªãã°ãã®ã³ã³ãã©ã¯åæ山倧ãçµã¿ããã fact3: ããããã®ã¡ãŒã³ã¹ããªãŒãã¯åæ山倧ãçµã¿ãããªããŠæŠå³¶ã ããšããããšãäºå®ã§ãªããªãã°ãã®ã³ã³ãã©ãæ¥ç«ãã©ã³ã建èšã fact4: ãã®ã¡ãŒã³ã¹ããªãŒãã¯æŠå³¶ã fact5: ãã®ã³ã³ãã©ã¯æ¥ç«ãã©ã³ã建èšã fact6: ãããã®ã¡ãŒã³ã¹ããªãŒãã¯æ¥ç«ãã©ã³ã建èšãªãã°ãã®ã³ã³ãã©ã¯æŠå³¶ã fact7: ããããã®ã³ã³ãã©ãæ¥ç«ãã©ã³ã建èšã ãšããããšããªããããã¯åæ山倧ãçµã¿ãããããšããããšãééããªãã°ãã®ã¡ãŒã³ã¹ããªãŒãã¯æŠå³¶ã fact8: ãããã®ã¡ãŒã³ã¹ããªãŒããææ©ããªããåæ山倧ãçµã¿ãããããšããããšãäºå®ãšç°ãªãããšããããšãäºå®ã fact9: ããããã®ã³ã³ãã©ã¯åæ山倧ãçµã¿ãããªããæ¥ç«ãã©ã³ã建èšã ããšããããšãäºå®ãšç°ãªãã°ãã®ã¡ãŒã³ã¹ããªãŒããæŠå³¶ã fact10: ãã®ã³ã³ãã©ãæž
èŒã fact11: ããã®ã¡ãŒã³ã¹ããªãŒãã¯æ¥ç«ãã©ã³ã建èšã ãåæ山倧ãçµã¿ãããããšããããšã¯æãç«ããªã fact12: ããã®ã¡ãŒã³ã¹ããªãŒãã¯æ¥ç«ãã©ã³ã建èšã ãšããããšã¯ãªããåæ山倧ãçµã¿ãããããšããããšã¯æãç«ããªã fact13: ãã®ã³ã³ãã©ãé£ã fact14: ããããã®ã¡ãŒã³ã¹ããªãŒããæ¥ç«ãã©ã³ã建èšã ãšããããšã¯ãªããåæ山倧ãçµã¿ãããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãã®ã³ã³ãã©ãæŠå³¶ã | fact1: ¬(¬{AB}{b} & {B}{b}) fact2: ¬(¬{AA}{a} & {B}{a}) -> {AB}{b} fact3: ¬(¬{AB}{a} & {B}{a}) -> {AA}{b} fact4: {B}{a} fact5: {AA}{b} fact6: {AA}{a} -> {B}{b} fact7: ¬(¬{AA}{b} & {AB}{b}) -> {B}{a} fact8: ¬(¬{FS}{a} & {AB}{a}) fact9: ¬(¬{AB}{b} & {AA}{b}) -> {B}{a} fact10: {DF}{b} fact11: ¬({AA}{a} & {AB}{a}) fact12: ¬(¬{AA}{a} & {AB}{a}) fact13: {CB}{b} fact14: ¬(¬{AA}{a} & {AB}{a}) -> {B}{b} | [
"fact14 & fact12 -> hypothesis;"
] | [
"fact14 & fact12 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 12 | 0 | 12 | PROVED | null | PROVED | null | $facts$ = fact1: ããã®ã³ã³ãã©ãåæ山倧ãçµã¿ãããªãããããããã¯æŠå³¶ã ããšããããšã¯æãç«ããªã fact2: ããããã®ã¡ãŒã³ã¹ããªãŒããæ¥ç«ãã©ã³ã建èšã§ãªãããããæŠå³¶ã ããšããããšãééããªãã°ãã®ã³ã³ãã©ã¯åæ山倧ãçµã¿ããã fact3: ããããã®ã¡ãŒã³ã¹ããªãŒãã¯åæ山倧ãçµã¿ãããªããŠæŠå³¶ã ããšããããšãäºå®ã§ãªããªãã°ãã®ã³ã³ãã©ãæ¥ç«ãã©ã³ã建èšã fact4: ãã®ã¡ãŒã³ã¹ããªãŒãã¯æŠå³¶ã fact5: ãã®ã³ã³ãã©ã¯æ¥ç«ãã©ã³ã建èšã fact6: ãããã®ã¡ãŒã³ã¹ããªãŒãã¯æ¥ç«ãã©ã³ã建èšãªãã°ãã®ã³ã³ãã©ã¯æŠå³¶ã fact7: ããããã®ã³ã³ãã©ãæ¥ç«ãã©ã³ã建èšã ãšããããšããªããããã¯åæ山倧ãçµã¿ãããããšããããšãééããªãã°ãã®ã¡ãŒã³ã¹ããªãŒãã¯æŠå³¶ã fact8: ãããã®ã¡ãŒã³ã¹ããªãŒããææ©ããªããåæ山倧ãçµã¿ãããããšããããšãäºå®ãšç°ãªãããšããããšãäºå®ã fact9: ããããã®ã³ã³ãã©ã¯åæ山倧ãçµã¿ãããªããæ¥ç«ãã©ã³ã建èšã ããšããããšãäºå®ãšç°ãªãã°ãã®ã¡ãŒã³ã¹ããªãŒããæŠå³¶ã fact10: ãã®ã³ã³ãã©ãæž
èŒã fact11: ããã®ã¡ãŒã³ã¹ããªãŒãã¯æ¥ç«ãã©ã³ã建èšã ãåæ山倧ãçµã¿ãããããšããããšã¯æãç«ããªã fact12: ããã®ã¡ãŒã³ã¹ããªãŒãã¯æ¥ç«ãã©ã³ã建èšã ãšããããšã¯ãªããåæ山倧ãçµã¿ãããããšããããšã¯æãç«ããªã fact13: ãã®ã³ã³ãã©ãé£ã fact14: ããããã®ã¡ãŒã³ã¹ããªãŒããæ¥ç«ãã©ã³ã建èšã ãšããããšã¯ãªããåæ山倧ãçµã¿ãããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãã®ã³ã³ãã©ãæŠå³¶ã ; $hypothesis$ = ããã®ã³ã³ãã©ãæŠå³¶ã ããšããããšã¯æ£ãã ; $proof$ = | fact14 & fact12 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬(¬{AB}{b} & {B}{b}) fact2: ¬(¬{AA}{a} & {B}{a}) -> {AB}{b} fact3: ¬(¬{AB}{a} & {B}{a}) -> {AA}{b} fact4: {B}{a} fact5: {AA}{b} fact6: {AA}{a} -> {B}{b} fact7: ¬(¬{AA}{b} & {AB}{b}) -> {B}{a} fact8: ¬(¬{FS}{a} & {AB}{a}) fact9: ¬(¬{AB}{b} & {AA}{b}) -> {B}{a} fact10: {DF}{b} fact11: ¬({AA}{a} & {AB}{a}) fact12: ¬(¬{AA}{a} & {AB}{a}) fact13: {CB}{b} fact14: ¬(¬{AA}{a} & {AB}{a}) -> {B}{b} ; $hypothesis$ = {B}{b} ; $proof$ = | fact14 & fact12 -> hypothesis; __PROVED__ |
0.3 | ãã®è»å¡ã¯åœŠå³¶è§åã§ãªãããããæž¡è¯å觊ã«ä»£ããªã | (¬{AA}{a} & ¬{AB}{a}) | fact1: ãã®è»å¡ãã®ã¿ã»ããšããããšããªã fact2: ãããã®ç
ãåãçºããªããªãã°ããããããªããšããããšããªããã®ã§ãã£ãŠäžããã ã ãã® fact3: ããã®ç ç³ã¯æž¡è¯å觊ã«ä»£ããªãããšããããšã¯æãç«ã€ fact4: ãããããã®ãããªãŠã®ã ãšããããšããªããªãã°ããããççœããšããããšããªããããããããããããªãããšããããšãæ£ãã fact5: ããäœãã¯åãçºãããšããããšããªãããããããã¯ãããªããªãã°ããã®æ¯æµãäžããã ã§ãªãããšããããšãæãç«ã€ fact6: ãã®è»å¡ã圊島è§åã§ãªããæž¡è¯å觊ã«ä»£ããªã fact7: ãã®èå
ã圊島è§åã§ãªã fact8: ãã®è»å¡ãç¢å¶ã«ãµãããŸãªã fact9: ãããã®åãæã¯ãããããããªããªãã°ããã®ææ¥éŠãåãçºãããšããããšã¯ãªãããããªãããšããããšãäºå®ã fact10: ãã®è»å¡ã¯æãç©ã ãšããããšããªãã峡谷ã ãšããããšã¯ãªã fact11: ãã®æå ãæž¡è¯å觊ã«ä»£ããªããããã¯å€§å³°æ²Œã ãšããããšããªã fact12: ãããããã®ã¯æ¿«ç²ãé£ã³ãã€ãšããããšã¯ãªããªãã°ãããã圊島è§åã ãšããããšã¯ãªããŠãããæž¡è¯å觊ã«ä»£ããªãããšããããšãæãç«ã€ãšããããšããªã fact13: ãããããã®ã¯æ¿«ç²ãé£ã³ãã€ãšããããšã¯ãªããªãã°ããã圊島è§åã ãšããããšã¯ãªããŠã¿ã¥ãããªã fact14: ãã®è»å¡ã¯åœŠå³¶è§åã§ãªã fact15: ãã®ã©ãžãªããŒã³ã³ã圊島è§åã ãšããããšããªã fact16: ãã®è»å¡ããããŒãã¥ãããªã fact17: ãå
šãŠã¯ããªãŠã®ã§ãªãããšããããšã¯æ£ãã fact18: ãããããªããªããã®ãäžããã ãªãã°ããããæ¿«ç²ãé£ã³ãã€ãšããããšããªãããšããããšã¯æãç«ã€ | fact1: ¬{CI}{a} fact2: ¬{D}{hi} -> (¬{C}{hi} & {B}{hi}) fact3: ¬{AB}{cj} fact4: (x): ¬{G}x -> (¬{F}x & ¬{E}x) fact5: (x): (¬{D}x & {C}x) -> ¬{B}{b} fact6: (¬{AA}{a} & ¬{AB}{a}) fact7: ¬{AA}{gh} fact8: ¬{EC}{a} fact9: ¬{E}{d} -> (¬{D}{c} & {C}{c}) fact10: (¬{FI}{a} & ¬{DE}{a}) fact11: (¬{AB}{ht} & ¬{BT}{ht}) fact12: (x): ¬{A}x -> ¬(¬{AA}x & ¬{AB}x) fact13: (x): ¬{A}x -> (¬{AA}x & ¬{AS}x) fact14: ¬{AA}{a} fact15: ¬{AA}{gg} fact16: ¬{GP}{a} fact17: (x): ¬{G}x fact18: (x): (¬{C}x & {B}x) -> ¬{A}x | [
"fact6 -> hypothesis;"
] | [
"fact6 -> hypothesis;"
] | ããã®è»å¡ã圊島è§åã ãšããããšããªããŠããã¯æž¡è¯å觊ã«ä»£ãããšããããšããªãããšããããšã¯æ¬åœã§ãªã | ¬(¬{AA}{a} & ¬{AB}{a}) | [
"fact19 -> int1: ããããã®è»å¡ãæ¿«ç²ãé£ã³ãããªããªãã°ãããã®è»å¡ã¯åœŠå³¶è§åã§ãªããæž¡è¯å觊ã«ä»£ãããšããããšã¯ãªãããšããããšãæãç«ããªãããšããããšãæãç«ã€ããšããããšãæãç«ã€; fact23 -> int2: ãããã®èæãããªãŠã®ã ãšããããšããªããªãã°ããã¯ççœããªãããããããããšããããšã¯ãªã; fact22 -> int3: ãã®èæãããªãŠã®ã ãšããããšããªã; int2 & int3 -> int4: ãã®èæã¯ççœããšããããšããªããŠããããããããããšããããšããªã; int4 -> int5: å
šãŠãççœããšããããšã¯ãªããã®ã§ãã£ãŠãããããããšããããšããªããã®; int5 -> int6: ãã®åãæãççœããšããããšã¯ãªããŠããããããããããªã; int6 -> int7: ãã®åãæããããããããªã; fact20 & int7 -> int8: ãã®ææ¥éŠãåãçºãããšããããšããªãããããªã; int8 -> int9: äœãã¯åãçºãããšããããšããªãããããããã¯ãããªã; int9 & fact21 -> int10: ããã®æ¯æµãäžããã ã ãšããããšããªãããšããããšã¯èª€ãã§ãªã; int10 -> int11: ãäžããã ã ãšããããšã¯ãªãããã®ããã;"
] | 11 | 1 | 0 | 17 | 0 | 17 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®è»å¡ãã®ã¿ã»ããšããããšããªã fact2: ãããã®ç
ãåãçºããªããªãã°ããããããªããšããããšããªããã®ã§ãã£ãŠäžããã ã ãã® fact3: ããã®ç ç³ã¯æž¡è¯å觊ã«ä»£ããªãããšããããšã¯æãç«ã€ fact4: ãããããã®ãããªãŠã®ã ãšããããšããªããªãã°ããããççœããšããããšããªããããããããããããªãããšããããšãæ£ãã fact5: ããäœãã¯åãçºãããšããããšããªãããããããã¯ãããªããªãã°ããã®æ¯æµãäžããã ã§ãªãããšããããšãæãç«ã€ fact6: ãã®è»å¡ã圊島è§åã§ãªããæž¡è¯å觊ã«ä»£ããªã fact7: ãã®èå
ã圊島è§åã§ãªã fact8: ãã®è»å¡ãç¢å¶ã«ãµãããŸãªã fact9: ãããã®åãæã¯ãããããããªããªãã°ããã®ææ¥éŠãåãçºãããšããããšã¯ãªãããããªãããšããããšãäºå®ã fact10: ãã®è»å¡ã¯æãç©ã ãšããããšããªãã峡谷ã ãšããããšã¯ãªã fact11: ãã®æå ãæž¡è¯å觊ã«ä»£ããªããããã¯å€§å³°æ²Œã ãšããããšããªã fact12: ãããããã®ã¯æ¿«ç²ãé£ã³ãã€ãšããããšã¯ãªããªãã°ãããã圊島è§åã ãšããããšã¯ãªããŠãããæž¡è¯å觊ã«ä»£ããªãããšããããšãæãç«ã€ãšããããšããªã fact13: ãããããã®ã¯æ¿«ç²ãé£ã³ãã€ãšããããšã¯ãªããªãã°ããã圊島è§åã ãšããããšã¯ãªããŠã¿ã¥ãããªã fact14: ãã®è»å¡ã¯åœŠå³¶è§åã§ãªã fact15: ãã®ã©ãžãªããŒã³ã³ã圊島è§åã ãšããããšããªã fact16: ãã®è»å¡ããããŒãã¥ãããªã fact17: ãå
šãŠã¯ããªãŠã®ã§ãªãããšããããšã¯æ£ãã fact18: ãããããªããªããã®ãäžããã ãªãã°ããããæ¿«ç²ãé£ã³ãã€ãšããããšããªãããšããããšã¯æãç«ã€ ; $hypothesis$ = ãã®è»å¡ã¯åœŠå³¶è§åã§ãªãããããæž¡è¯å觊ã«ä»£ããªã ; $proof$ = | fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{CI}{a} fact2: ¬{D}{hi} -> (¬{C}{hi} & {B}{hi}) fact3: ¬{AB}{cj} fact4: (x): ¬{G}x -> (¬{F}x & ¬{E}x) fact5: (x): (¬{D}x & {C}x) -> ¬{B}{b} fact6: (¬{AA}{a} & ¬{AB}{a}) fact7: ¬{AA}{gh} fact8: ¬{EC}{a} fact9: ¬{E}{d} -> (¬{D}{c} & {C}{c}) fact10: (¬{FI}{a} & ¬{DE}{a}) fact11: (¬{AB}{ht} & ¬{BT}{ht}) fact12: (x): ¬{A}x -> ¬(¬{AA}x & ¬{AB}x) fact13: (x): ¬{A}x -> (¬{AA}x & ¬{AS}x) fact14: ¬{AA}{a} fact15: ¬{AA}{gg} fact16: ¬{GP}{a} fact17: (x): ¬{G}x fact18: (x): (¬{C}x & {B}x) -> ¬{A}x ; $hypothesis$ = (¬{AA}{a} & ¬{AB}{a}) ; $proof$ = | fact6 -> hypothesis; __PROVED__ |
0.3 | ãŸã£ããããšããããšãèµ·ãããªã | ¬{B} | fact1: ããããè
¹ç«ããããšããããšã¯çºçããããããæãåºæ·±ããšããããšã¯çºçããªãããšããããšãæãç«ã€ãšããããšã¯ãªãããšããããšãæ£ãããªãã°çŽå±±ã«åãããšã¯çºçããªã fact2: ããããè·«é³ãšåæ¡ãèŠåç«ã€ããšãçããããšããããšãçå®ã ããšããããšã¯äºå®ãšç°ãªãã°è·«é³ãçããªã fact3: ãããããšããããšã¯èµ·ãã fact4: ãå¿å¿ãããšããããšãçããªãããŸã£ããããšããããšã¯çºçããããšããããšãæ£ãã fact5: ããã客æ±ããèµ·ããããããããšããããšãèµ·ããããšããããšãééããªãã°æããããšããããšãçããªã fact6: ãç»å±±ã¯èµ·ããªãããšããããšã¯ãå¿å¿ãããšããããšãšãŸã£ããããšããããšäž¡æ¹ãèµ·ããããšããããšã®åå ãšãªã fact7: è·«é³ãèµ·ããªããšããããšã¯ãããã ããããšããããšãçããªãã䌎å¥å²ãåºãããããšã¯èµ·ãããªããäž¡æ¹ã ããšããããšãçãããã fact8: ãç»å±±ã¯èµ·ããªããæ
ãã ãããšããããšã¯çºçããªãããšããããšã¯ãçŽå±±ã«åãããšã¯çããªãããšããããšãåå ã fact9: ããããããšããããšã¯çºçããã°å°ããšããããšã¯çããããããã¯åæãèµ·ãããªã fact10: ãããããšã¯èµ·ãããšããããšãèªãããšãèµ·ãããšããããšã«é»æ¢ããã fact11: ãå°ããšããããšã¯çããããšããããšããåæãçºçããªãããšããããšããããã¯äž¡æ¹ã¯ççªã£ãœããšããããšãèµ·ãããšããããšãå¶æ¢ãã fact12: å¿å¿ãããšããããšãçããªã fact13: ãšãŒã¯ãããã«ã«çŸãããããšã¯çããªããšããããšã¯ããã ããããšããããšãèµ·ãããªããšããããšã䌎å¥å²ãåºãããããšã¯çããªããšããããšãåå ã fact14: ãã€ãã³ã³ãã¢è²©å£²ããªãããããããšã¯çããªããŠããã ããããšããããšã¯çºçãã fact15: ãããããããšã¯èµ·ãããªããªãã°ããã€ããšããããšãšããããšããããšãçºçãã fact16: ããççªã£ãœããšããããšãçããªããªãã°ãè
¹ç«ããããšããããšãèµ·ããããããæãåºæ·±ããšããããšãèµ·ããªãããšããããšã¯èª€ãã fact17: ãããšãŒã¯ãããã«ã«çŸãããããšãçããªããªãã°ã客æ±ããšãããããšããããšãçããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact18: ãèªãããšã¯çãããæ±æã¯çããããšããããšã¯æããããšããããšãèµ·ããªããšããããšã«ç±æ¥ãã fact19: ããã«ãã«ãããšããããšãçããªããå·®ç°ã¯èµ·ããããšããããšã¯å¿å¿ãããšããããšã¯èµ·ãããšããããšã«ããçºçãã fact20: ãå¿å¿ãããšããããšã¯çããããããç»å±±ãèµ·ããªãããšããããšãããŸã£ããããšããããšãèµ·ããããšããããšãææ¢ãã | fact1: ¬({F} & ¬{G}) -> ¬{E} fact2: ¬({AB} & {AC}) -> ¬{AB} fact3: {R} fact4: (¬{A} & {B}) fact5: ¬({Q} & {R}) -> ¬{P} fact6: ¬{C} -> ({A} & {B}) fact7: ¬{AB} -> (¬{AA} v ¬{U}) fact8: ¬{E} -> (¬{C} & ¬{D}) fact9: {K} -> ({I} v ¬{J}) fact10: {N} -> ¬{M} fact11: ({I} v ¬{J}) -> ¬{H} fact12: ¬{A} fact13: (¬{AA} v ¬{U}) -> ¬{S} fact14: (¬{IO} & {AA}) fact15: ¬{M} -> ({L} & {K}) fact16: ¬{H} -> ¬({F} & ¬{G}) fact17: ¬{S} -> ¬({Q} & {R}) fact18: ¬{P} -> ({N} & {O}) fact19: {A} -> (¬{GK} & {T}) fact20: ({A} & ¬{C}) -> ¬{B} | [
"fact4 -> hypothesis;"
] | [
"fact4 -> hypothesis;"
] | ããŸã£ããããšããããšãçºçããªãããšããããšã¯æ£ãã | ¬{B} | [] | 6 | 1 | 1 | 19 | 0 | 19 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããè
¹ç«ããããšããããšã¯çºçããããããæãåºæ·±ããšããããšã¯çºçããªãããšããããšãæãç«ã€ãšããããšã¯ãªãããšããããšãæ£ãããªãã°çŽå±±ã«åãããšã¯çºçããªã fact2: ããããè·«é³ãšåæ¡ãèŠåç«ã€ããšãçããããšããããšãçå®ã ããšããããšã¯äºå®ãšç°ãªãã°è·«é³ãçããªã fact3: ãããããšããããšã¯èµ·ãã fact4: ãå¿å¿ãããšããããšãçããªãããŸã£ããããšããããšã¯çºçããããšããããšãæ£ãã fact5: ããã客æ±ããèµ·ããããããããšããããšãèµ·ããããšããããšãééããªãã°æããããšããããšãçããªã fact6: ãç»å±±ã¯èµ·ããªãããšããããšã¯ãå¿å¿ãããšããããšãšãŸã£ããããšããããšäž¡æ¹ãèµ·ããããšããããšã®åå ãšãªã fact7: è·«é³ãèµ·ããªããšããããšã¯ãããã ããããšããããšãçããªãã䌎å¥å²ãåºãããããšã¯èµ·ãããªããäž¡æ¹ã ããšããããšãçãããã fact8: ãç»å±±ã¯èµ·ããªããæ
ãã ãããšããããšã¯çºçããªãããšããããšã¯ãçŽå±±ã«åãããšã¯çããªãããšããããšãåå ã fact9: ããããããšããããšã¯çºçããã°å°ããšããããšã¯çããããããã¯åæãèµ·ãããªã fact10: ãããããšã¯èµ·ãããšããããšãèªãããšãèµ·ãããšããããšã«é»æ¢ããã fact11: ãå°ããšããããšã¯çããããšããããšããåæãçºçããªãããšããããšããããã¯äž¡æ¹ã¯ççªã£ãœããšããããšãèµ·ãããšããããšãå¶æ¢ãã fact12: å¿å¿ãããšããããšãçããªã fact13: ãšãŒã¯ãããã«ã«çŸãããããšã¯çããªããšããããšã¯ããã ããããšããããšãèµ·ãããªããšããããšã䌎å¥å²ãåºãããããšã¯çããªããšããããšãåå ã fact14: ãã€ãã³ã³ãã¢è²©å£²ããªãããããããšã¯çããªããŠããã ããããšããããšã¯çºçãã fact15: ãããããããšã¯èµ·ãããªããªãã°ããã€ããšããããšãšããããšããããšãçºçãã fact16: ããççªã£ãœããšããããšãçããªããªãã°ãè
¹ç«ããããšããããšãèµ·ããããããæãåºæ·±ããšããããšãèµ·ããªãããšããããšã¯èª€ãã fact17: ãããšãŒã¯ãããã«ã«çŸãããããšãçããªããªãã°ã客æ±ããšãããããšããããšãçããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact18: ãèªãããšã¯çãããæ±æã¯çããããšããããšã¯æããããšããããšãèµ·ããªããšããããšã«ç±æ¥ãã fact19: ããã«ãã«ãããšããããšãçããªããå·®ç°ã¯èµ·ããããšããããšã¯å¿å¿ãããšããããšã¯èµ·ãããšããããšã«ããçºçãã fact20: ãå¿å¿ãããšããããšã¯çããããããç»å±±ãèµ·ããªãããšããããšãããŸã£ããããšããããšãèµ·ããããšããããšãææ¢ãã ; $hypothesis$ = ãŸã£ããããšããããšãèµ·ãããªã ; $proof$ = | fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({F} & ¬{G}) -> ¬{E} fact2: ¬({AB} & {AC}) -> ¬{AB} fact3: {R} fact4: (¬{A} & {B}) fact5: ¬({Q} & {R}) -> ¬{P} fact6: ¬{C} -> ({A} & {B}) fact7: ¬{AB} -> (¬{AA} v ¬{U}) fact8: ¬{E} -> (¬{C} & ¬{D}) fact9: {K} -> ({I} v ¬{J}) fact10: {N} -> ¬{M} fact11: ({I} v ¬{J}) -> ¬{H} fact12: ¬{A} fact13: (¬{AA} v ¬{U}) -> ¬{S} fact14: (¬{IO} & {AA}) fact15: ¬{M} -> ({L} & {K}) fact16: ¬{H} -> ¬({F} & ¬{G}) fact17: ¬{S} -> ¬({Q} & {R}) fact18: ¬{P} -> ({N} & {O}) fact19: {A} -> (¬{GK} & {T}) fact20: ({A} & ¬{C}) -> ¬{B} ; $hypothesis$ = ¬{B} ; $proof$ = | fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ããªãããšããããšã¯çºçãã | {B} | fact1: ãããåäžã«é»ããããšãšå蚎ã«çŸœç¹ãããšäž¡æ¹ã¯çºçããããšããããšãæãç«ã€ãšããããšããªããªãã°ãããã¯ãããããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ã€ fact2: ãããéããšããããšãçããªããæšæ»åã«éããããšãçããªãããšããããšã¯åã ãšããããšã¯ãªããªãã°æšæ»åã«éããããšãèµ·ããªã fact3: å¹èŽã倪ãããšã¯çºçãã fact4: ãããäžæµ·å¹²æå°ãããæ©ãããšã¯èµ·ãããªãããããã¯ãããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšããªããªãã°å±±çäžžã«ãèœãšããããšãçãã fact5: ãåäžã«é»ããããšãšå蚎ã«çŸœç¹ãããšäž¡æ¹ãèµ·ããããšããããšãåœã fact6: ããããšããããããšããããšãèµ·ãããªããªãã°ã殎ã蟌ã¿ã§ã¯ãªãå
±æ é»è³ãããããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact7: ããç殺ãã¯èµ·ããªããªãã°ã¡ããããšããããšãèµ·ãããæ°æŽãã¯çºçãã fact8: ãã波浪ã¯çããªããªãã°ããã®ããªãããšããããšã¯èµ·ããªãã座蟌ã¿ãçºçããªãããšããããšã¯èª€ãã fact9: ãç殺ããèµ·ãããªãããšããããšã¯ãããã¯ãããããšããããšã¯èµ·ããªããå±±çäžžã«ãèœãšããããšãçããããšããããšã«èµ·å ãã fact10: ããã殎ã蟌ã¿ã¯çºçããªãããããå
±æ é»è³ãããããšããããšãèµ·ããããšããããšãæãç«ããªããªãã°æ³¢æµªãèµ·ããªã fact11: ããšããããããšããããšã§ã¯ãªãããããšããããšã¯èµ·ãã fact12: ããããã®ããªãããšããããšãçããªãã座蟌ã¿ãçºçããªãããšããããšãæãç«ã€ãšããããšããªããªãã°åº§èŸŒã¿ãèµ·ãã fact13: ããã¡ããããšããããšã¯èµ·ããã°éããšããããšãèµ·ãããªãããããã¢ã€ã·ã³ã°ã¯çºçãã fact14: ããæšæ»åã«éããããšã¯çºçããªããªãã°éé»ããšããããšãšå¹èŽã倪ãããšãèµ·ãã | fact1: ¬({P} & {Q}) -> ¬{O} fact2: (¬{F} v ¬{C}) -> ¬{C} fact3: {A} fact4: ¬(¬{R} v {S}) -> {N} fact5: ¬({P} & {Q}) fact6: ¬{H} -> ¬(¬{G} & {E}) fact7: ¬{M} -> ({K} & {L}) fact8: ¬{D} -> ¬(¬{B} & ¬{BS}) fact9: (¬{O} & {N}) -> ¬{M} fact10: ¬(¬{G} & {E}) -> ¬{D} fact11: (¬{H} & {I}) fact12: ¬(¬{B} & ¬{BS}) -> {BS} fact13: {K} -> (¬{F} & {J}) fact14: ¬{C} -> ({HC} & {A}) | [] | [] | 座蟌ã¿ãšéé»ããšããããšãçãã | ({BS} & {HC}) | [
"fact19 -> int1: ããšããããããšããããšãçããªã; fact21 & int1 -> int2: ã殎ã蟌ã¿ã§ã¯ãªãå
±æ é»è³ãããããšããããšã¯èµ·ããããšããããšã誀ãã ; fact18 & int2 -> int3: 波浪ã¯çããªã; fact27 & int3 -> int4: ããã®ããªãããšããããšãçããªããŠåº§èŸŒã¿ã¯èµ·ãããªãããšããããšã¯èª€ãã ; fact15 & int4 -> int5: 座蟌ã¿ãèµ·ãã; fact25 & fact22 -> int6: ããã¯ãããããšããããšãèµ·ãããªã;"
] | 12 | 1 | null | 14 | 0 | 14 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããåäžã«é»ããããšãšå蚎ã«çŸœç¹ãããšäž¡æ¹ã¯çºçããããšããããšãæãç«ã€ãšããããšããªããªãã°ãããã¯ãããããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ã€ fact2: ãããéããšããããšãçããªããæšæ»åã«éããããšãçããªãããšããããšã¯åã ãšããããšã¯ãªããªãã°æšæ»åã«éããããšãèµ·ããªã fact3: å¹èŽã倪ãããšã¯çºçãã fact4: ãããäžæµ·å¹²æå°ãããæ©ãããšã¯èµ·ãããªãããããã¯ãããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšããªããªãã°å±±çäžžã«ãèœãšããããšãçãã fact5: ãåäžã«é»ããããšãšå蚎ã«çŸœç¹ãããšäž¡æ¹ãèµ·ããããšããããšãåœã fact6: ããããšããããããšããããšãèµ·ãããªããªãã°ã殎ã蟌ã¿ã§ã¯ãªãå
±æ é»è³ãããããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact7: ããç殺ãã¯èµ·ããªããªãã°ã¡ããããšããããšãèµ·ãããæ°æŽãã¯çºçãã fact8: ãã波浪ã¯çããªããªãã°ããã®ããªãããšããããšã¯èµ·ããªãã座蟌ã¿ãçºçããªãããšããããšã¯èª€ãã fact9: ãç殺ããèµ·ãããªãããšããããšã¯ãããã¯ãããããšããããšã¯èµ·ããªããå±±çäžžã«ãèœãšããããšãçããããšããããšã«èµ·å ãã fact10: ããã殎ã蟌ã¿ã¯çºçããªãããããå
±æ é»è³ãããããšããããšãèµ·ããããšããããšãæãç«ããªããªãã°æ³¢æµªãèµ·ããªã fact11: ããšããããããšããããšã§ã¯ãªãããããšããããšã¯èµ·ãã fact12: ããããã®ããªãããšããããšãçããªãã座蟌ã¿ãçºçããªãããšããããšãæãç«ã€ãšããããšããªããªãã°åº§èŸŒã¿ãèµ·ãã fact13: ããã¡ããããšããããšã¯èµ·ããã°éããšããããšãèµ·ãããªãããããã¢ã€ã·ã³ã°ã¯çºçãã fact14: ããæšæ»åã«éããããšã¯çºçããªããªãã°éé»ããšããããšãšå¹èŽã倪ãããšãèµ·ãã ; $hypothesis$ = ãã®ããªãããšããããšã¯çºçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({P} & {Q}) -> ¬{O} fact2: (¬{F} v ¬{C}) -> ¬{C} fact3: {A} fact4: ¬(¬{R} v {S}) -> {N} fact5: ¬({P} & {Q}) fact6: ¬{H} -> ¬(¬{G} & {E}) fact7: ¬{M} -> ({K} & {L}) fact8: ¬{D} -> ¬(¬{B} & ¬{BS}) fact9: (¬{O} & {N}) -> ¬{M} fact10: ¬(¬{G} & {E}) -> ¬{D} fact11: (¬{H} & {I}) fact12: ¬(¬{B} & ¬{BS}) -> {BS} fact13: {K} -> (¬{F} & {J}) fact14: ¬{C} -> ({HC} & {A}) ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããèšãã¯ããç«ã€ããšãèµ·ãããªãããããã¯ãã®å¯ãããšããããšãèµ·ãããäž¡æ¹ã ããšããããšã¯æãç«ããªã | ¬(¬{A} v {B}) | fact1: ãããç©çãããšããããšãçºçããªãããšããããšã¯æ£ãããªãã°ãäžåã¯èµ·ãããå¿é
ãçºçããããšããããšã¯åã fact2: ãããå€ç¬ã«ãããšãããããšãšããŠãããšã¯çºçããããšããããšãåãªãã°å€ç¬ã«ãããšãããããšã¯çããªã fact3: ãããäžåãšå¿é
ã¯èµ·ããããšããããšã誀ããªãã°ç·ç¶ã«æ¬ããããšã¯èµ·ãããªã fact4: ãæ±æ¬é¡å¯ºã«ç³ãèããããšã¯çºçããªããæ¶ããããšã¯èµ·ãããªãããšããããšã¯ãç¬ãå ããèµ·ããããšããããšã«ããçãã fact5: ããã¢ãããšããããšã¯èµ·ããªããŠæŒãä»ãããŸãããšããããšã¯çºçããªãããšããããšã¯ããšãŸãããšããããšã¯èµ·ãããšããããšã«ç±æ¥ãã fact6: ããã浞瀌ãçºçããã圹è·ãèµ·ããããšããããšã¯æãç«ããªããªãã°æµžç€Œã¯çããªã fact7: ããå€æ»ãçããªããªãã°ç©çãããšããããšã¯èµ·ããªããŠæãããšãèµ·ããªã fact8: ãã浞瀌ãèµ·ããªããªãã°ãããèšãã¯ããç«ã€ããšã¯çããªãããããã¯ãã®å¯ãããšããããšã¯èµ·ããããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã fact9: ãããããŸãããããšããããšã¯çããããããæž
ãããšããããšãçºçããªãããšããããšã¯æãç«ããªããªãã°å€æ»ã¯èµ·ããªã fact10: ãããç·ç¶ã«æ¬ããããšã¯èµ·ããªããªãã°ã浞瀌ãçºçããã圹è·ãçºçããããšããããšãééãã ããšããããšãäºå®ã fact11: ããæ±æ¬é¡å¯ºã«ç³ãèããããšãèµ·ãããªããªãã°äœæã¯èµ·ãããããšãŸãããšããããšãçºçãã fact12: ãããã¢ãããšããããšãçºçããªããªãã°ãå€ç¬ã«ãããšãããããšãšããŠãããšãèµ·ããããšããããšãæãç«ã€ãšããããšããªã fact13: ããå€ç¬ã«ãããšãããããšã¯èµ·ããªããªãã°ããããŸãããããšããããšãèµ·ãããæž
ãããšããããšãèµ·ããªãããšããããšãæãç«ã€ãšããããšããªãããšããããšã¯æãç«ã€ | fact1: ¬{H} -> ¬({F} & {G}) fact2: ¬({M} & {O}) -> ¬{M} fact3: ¬({F} & {G}) -> ¬{E} fact4: {U} -> (¬{S} & ¬{T}) fact5: {Q} -> (¬{N} & ¬{P}) fact6: ¬({C} & {D}) -> ¬{C} fact7: ¬{J} -> (¬{H} & ¬{I}) fact8: ¬{C} -> ¬(¬{A} v {B}) fact9: ¬({L} & ¬{K}) -> ¬{J} fact10: ¬{E} -> ¬({C} & {D}) fact11: ¬{S} -> ({R} & {Q}) fact12: ¬{N} -> ¬({M} & {O}) fact13: ¬{M} -> ¬({L} & ¬{K}) | [] | [] | ããããèšãã¯ããç«ã€ããšãèµ·ããªãããã®å¯ãããšããããšã¯çããããããã¯äž¡æ¹ã ããšããããšã¯ééãã ããšããããšã誀ãã ãšããããšããªã | ¬(¬{A} v {B}) | [] | 18 | 1 | null | 13 | 0 | 13 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããç©çãããšããããšãçºçããªãããšããããšã¯æ£ãããªãã°ãäžåã¯èµ·ãããå¿é
ãçºçããããšããããšã¯åã fact2: ãããå€ç¬ã«ãããšãããããšãšããŠãããšã¯çºçããããšããããšãåãªãã°å€ç¬ã«ãããšãããããšã¯çããªã fact3: ãããäžåãšå¿é
ã¯èµ·ããããšããããšã誀ããªãã°ç·ç¶ã«æ¬ããããšã¯èµ·ãããªã fact4: ãæ±æ¬é¡å¯ºã«ç³ãèããããšã¯çºçããªããæ¶ããããšã¯èµ·ãããªãããšããããšã¯ãç¬ãå ããèµ·ããããšããããšã«ããçãã fact5: ããã¢ãããšããããšã¯èµ·ããªããŠæŒãä»ãããŸãããšããããšã¯çºçããªãããšããããšã¯ããšãŸãããšããããšã¯èµ·ãããšããããšã«ç±æ¥ãã fact6: ããã浞瀌ãçºçããã圹è·ãèµ·ããããšããããšã¯æãç«ããªããªãã°æµžç€Œã¯çããªã fact7: ããå€æ»ãçããªããªãã°ç©çãããšããããšã¯èµ·ããªããŠæãããšãèµ·ããªã fact8: ãã浞瀌ãèµ·ããªããªãã°ãããèšãã¯ããç«ã€ããšã¯çããªãããããã¯ãã®å¯ãããšããããšã¯èµ·ããããããã¯äž¡æ¹ã ããšããããšãæãç«ããªã fact9: ãããããŸãããããšããããšã¯çããããããæž
ãããšããããšãçºçããªãããšããããšã¯æãç«ããªããªãã°å€æ»ã¯èµ·ããªã fact10: ãããç·ç¶ã«æ¬ããããšã¯èµ·ããªããªãã°ã浞瀌ãçºçããã圹è·ãçºçããããšããããšãééãã ããšããããšãäºå®ã fact11: ããæ±æ¬é¡å¯ºã«ç³ãèããããšãèµ·ãããªããªãã°äœæã¯èµ·ãããããšãŸãããšããããšãçºçãã fact12: ãããã¢ãããšããããšãçºçããªããªãã°ãå€ç¬ã«ãããšãããããšãšããŠãããšãèµ·ããããšããããšãæãç«ã€ãšããããšããªã fact13: ããå€ç¬ã«ãããšãããããšã¯èµ·ããªããªãã°ããããŸãããããšããããšãèµ·ãããæž
ãããšããããšãèµ·ããªãããšããããšãæãç«ã€ãšããããšããªãããšããããšã¯æãç«ã€ ; $hypothesis$ = ãããèšãã¯ããç«ã€ããšãèµ·ãããªãããããã¯ãã®å¯ãããšããããšãèµ·ãããäž¡æ¹ã ããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{H} -> ¬({F} & {G}) fact2: ¬({M} & {O}) -> ¬{M} fact3: ¬({F} & {G}) -> ¬{E} fact4: {U} -> (¬{S} & ¬{T}) fact5: {Q} -> (¬{N} & ¬{P}) fact6: ¬({C} & {D}) -> ¬{C} fact7: ¬{J} -> (¬{H} & ¬{I}) fact8: ¬{C} -> ¬(¬{A} v {B}) fact9: ¬({L} & ¬{K}) -> ¬{J} fact10: ¬{E} -> ¬({C} & {D}) fact11: ¬{S} -> ({R} & {Q}) fact12: ¬{N} -> ¬({M} & {O}) fact13: ¬{M} -> ¬({L} & ¬{K}) ; $hypothesis$ = ¬(¬{A} v {B}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®åã¯æ
ãŸãããªããŠè³ã
ãããªãããšããããšãæãç«ããªã | ¬(¬{AA}{a} & ¬{AB}{a}) | fact1: ãããã®åãã¯å¿ããããªããªãã°ããã®åã¯æ¯é·ã«ãããããšããããšã¯ãªããããããããªãããšããããšã¯æãç«ããªã fact2: ããããããã®ãæ
ãŸãããšããããšã¯ãªããè³ã
ãããšããããšããªã fact3: ãããã®ããã³ã¯åµã蟌ããšããããšã¯ãªããªãã°ããã®åããå¿ããããã®ã§ãã£ãŠçœå±±æµŠã«ãããããããã®ããšããããšã¯èª€ãã fact4: ãããäœãã¯å¿ããããŠçœå±±æµŠã«ããããããããšããããšã¯åœãªãã°ããã¯å¿ããããšããããšããªã fact5: ãããããã®åããå¿ããããšããããšããªããã®ã§ãã£ãŠããããããªããã®ããšããããšã¯ééããªãã°ãã®åã¯ãããããããšããããšãäºå®ã fact6: ããäœãã¯ããããããªãã°ãããã¯ã€ãã¹å·ãããããããšããããšã¯ãªããŠããã¯æ
ãŸãããšããããšã¯ãªãããšããããšã誀ãã fact7: ããäœãã¯ãã奜ããªããªãã°ãããã¯ããã°ããšããããšã¯ãªããŠãããäžæ¢šé¿ã ãšããããšã¯ãªãããšããããšã¯æ¬åœã ãšããããšããªã fact8: ãããã®ããã³ã¯æ¯é·ã«ããããã°ããã®åãã¯å¿ããããªããŠããããããªãããšããããšãæãç«ã€ãšããããšããªã fact9: ããããã®çŽåãããã°ããšããããšã¯ãªããŠãããäžæ¢šé¿ã§ãªãããšããããšãééããªãã°ãã®ããã³ãåµã蟌ããšããããšããªã fact10: ãã®åãããããããšããããšããªã | fact1: ¬{C}{b} -> ¬(¬{B}{a} & ¬{A}{a}) fact2: (x): {A}x -> (¬{AA}x & ¬{AB}x) fact3: ¬{D}{c} -> ¬({C}{b} & {E}{b}) fact4: (x): ¬({C}x & {E}x) -> ¬{C}x fact5: ¬(¬{C}{b} & ¬{A}{b}) -> {A}{a} fact6: (x): {A}x -> ¬(¬{EM}x & ¬{AA}x) fact7: (x): {H}x -> ¬(¬{G}x & ¬{F}x) fact8: {B}{c} -> ¬(¬{C}{b} & ¬{A}{b}) fact9: ¬(¬{G}{d} & ¬{F}{d}) -> ¬{D}{c} fact10: ¬{A}{a} | [] | [] | ããã®ãã·ãããã€ãã¹å·ããããããªãããããæ
ãŸãããšããããšã¯ãªãããšããããšã¯åœã | ¬(¬{EM}{p} & ¬{AA}{p}) | [
"fact13 -> int1: ãããã®ãã·ããã¯ããããããªãã°ããããã€ãã¹å·ãããããããšããããšã¯ãªããæ
ãŸãããšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšããªã; fact16 -> int2: ããããã®åãã¯å¿ããããŠçœå±±æµŠã«ããããããããšããããšãäºå®ãšç°ãªãã°ããã¯å¿ããããªã; fact12 -> int3: ãããã®çŽåã¯ãã奜ããªããªãã°ããããããã°ããªããããã¯äžæ¢šé¿ã§ãªãããšããããšã¯æãç«ã€ãšããããšããªã;"
] | 9 | 1 | null | 9 | 0 | 9 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®åãã¯å¿ããããªããªãã°ããã®åã¯æ¯é·ã«ãããããšããããšã¯ãªããããããããªãããšããããšã¯æãç«ããªã fact2: ããããããã®ãæ
ãŸãããšããããšã¯ãªããè³ã
ãããšããããšããªã fact3: ãããã®ããã³ã¯åµã蟌ããšããããšã¯ãªããªãã°ããã®åããå¿ããããã®ã§ãã£ãŠçœå±±æµŠã«ãããããããã®ããšããããšã¯èª€ãã fact4: ãããäœãã¯å¿ããããŠçœå±±æµŠã«ããããããããšããããšã¯åœãªãã°ããã¯å¿ããããšããããšããªã fact5: ãããããã®åããå¿ããããšããããšããªããã®ã§ãã£ãŠããããããªããã®ããšããããšã¯ééããªãã°ãã®åã¯ãããããããšããããšãäºå®ã fact6: ããäœãã¯ããããããªãã°ãããã¯ã€ãã¹å·ãããããããšããããšã¯ãªããŠããã¯æ
ãŸãããšããããšã¯ãªãããšããããšã誀ãã fact7: ããäœãã¯ãã奜ããªããªãã°ãããã¯ããã°ããšããããšã¯ãªããŠãããäžæ¢šé¿ã ãšããããšã¯ãªãããšããããšã¯æ¬åœã ãšããããšããªã fact8: ãããã®ããã³ã¯æ¯é·ã«ããããã°ããã®åãã¯å¿ããããªããŠããããããªãããšããããšãæãç«ã€ãšããããšããªã fact9: ããããã®çŽåãããã°ããšããããšã¯ãªããŠãããäžæ¢šé¿ã§ãªãããšããããšãééããªãã°ãã®ããã³ãåµã蟌ããšããããšããªã fact10: ãã®åãããããããšããããšããªã ; $hypothesis$ = ããã®åã¯æ
ãŸãããªããŠè³ã
ãããªãããšããããšãæãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{C}{b} -> ¬(¬{B}{a} & ¬{A}{a}) fact2: (x): {A}x -> (¬{AA}x & ¬{AB}x) fact3: ¬{D}{c} -> ¬({C}{b} & {E}{b}) fact4: (x): ¬({C}x & {E}x) -> ¬{C}x fact5: ¬(¬{C}{b} & ¬{A}{b}) -> {A}{a} fact6: (x): {A}x -> ¬(¬{EM}x & ¬{AA}x) fact7: (x): {H}x -> ¬(¬{G}x & ¬{F}x) fact8: {B}{c} -> ¬(¬{C}{b} & ¬{A}{b}) fact9: ¬(¬{G}{d} & ¬{F}{d}) -> ¬{D}{c} fact10: ¬{A}{a} ; $hypothesis$ = ¬(¬{AA}{a} & ¬{AB}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ç²ããšããããšã¯èµ·ãããªã | ¬{A} | fact1: ç²ããšããããšã¯èµ·ãã | fact1: {A} | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 0 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ç²ããšããããšã¯èµ·ãã ; $hypothesis$ = ç²ããšããããšã¯èµ·ãããªã ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} ; $hypothesis$ = ¬{A} ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãããã®ãžã£ã€ãã³ã³ãã¹ã倧麻çºæŸæã ãããã座å·å
ãããã€ããšããããšããªããªãã°ãããå°ãããããšããããšããªã | ({AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa} | fact1: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯éŠã ãããã¯è»ãããªããªãã°ããã¯åããåãããšããããšã¯ãªã fact2: ããäœããå¿ãããŠåããåããªããªãã°ããããã€ã³ããã¯ã¹ã ãšããããšã¯ãªãããšããããšã¯çå®ã fact3: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯å€§éº»çºæŸæã ã座å·å
ãããã€ãã°ãããå°ããããªã fact4: ãã倧麻çºæŸæã座å·å
ãããã€ããšããããšããªããªãã°ãããå°ããããªã fact5: ããäœããçå
µè¡ãåºããããããããäºèšãã€ãããªããªãã°ããããã®ãããŸãããªã fact6: ãã倧麻çºæŸæã¯åº§å·å
ãããã€ãã°ãããå°ãããããšããããšã¯ãªã fact7: ãã倧麻çºæŸæã座å·å
ãããã€ããªããªãã°ããã¯å°ãããã fact8: ãããã®ãžã£ã€ãã³ã³ãã¹ã西éšã¬ã¹ãèããããããããã¯åº§å·å
ãããã€ããªããªãã°ããã¯ãã¶ãããšããããšã¯ãªã fact9: ããéšåã¡ãäžäžäŸã§ãªããªãã°ããããã©ã³ãã³ã§ãªã fact10: ãããã®ãžã£ã€ãã³ã³ãã¹ãæ°Žèåã ãããããã£æ¯ã ãšããããšããªããªãã°ããã¯å°ããããªã fact11: ãããã®ã·ã§ã«ã¿ãŒã¯åããåãããäžåºžã ãšããããšããªããªãã°ãããã ã ã£ãŽãããªã fact12: ãããã®çœæ³¢ãèžèŠãããããã¯ç
è¬ã§ãªããªãã°ããã座å·å
ãããã€ããšããããšã¯ãªã fact13: ããäœãã¯ç³æŽ¥ã ã女ããããšããããšã¯ãªããªãã°ããããããŸãããªã fact14: ããéœè°äŒãããã©ãããšããããšããªããªãã°ãããã¯ã ã ã£ãŽãããšããããšããªãããšããããšãäºå®ã fact15: ããæŽããŸãããã®ã¯ãããããªããªãã°ãããæ±æžå ã§ãªã fact16: ãããããã®ã¯é»èš±ãããã€ããããããäžéšãä¹æããªããªãã°ããããããªããšããããšããªã fact17: ãããã®çºæ±ã倧麻çºæŸæã§ãã£ãŠç³æŽ¥ã ãšããããšã¯ãªããã®ãªãã°ããã¯äœå¿ç¡ããšããããšããªã fact18: ããããããã®ã§ãã£ãŠèããšããããšã¯ãªããã®ã¯æ£®æ¯ã ãšããããšããªã fact19: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯å€§éº»çºæŸæã ãããã¯åº§å·å
ãããã€ããªããªãã°ãããå°ãããã fact20: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯é»èš±ãããã€ãããããã¯ãã¢ã³ããªã«ã¬ã³ã§ãªããªãã°ããã倧麻çºæŸæã ãšããããšããªã | fact1: ({DP}{aa} & ¬{EG}{aa}) -> ¬{AP}{aa} fact2: (x): ({EH}x & ¬{AP}x) -> ¬{O}x fact3: ({AA}{aa} & {AB}{aa}) -> ¬{B}{aa} fact4: (x): ({AA}x & ¬{AB}x) -> ¬{B}x fact5: (x): ({JA}x & ¬{IE}x) -> ¬{AQ}x fact6: (x): ({AA}x & {AB}x) -> ¬{B}x fact7: (x): ({AA}x & ¬{AB}x) -> {B}x fact8: ({AN}{aa} & ¬{AB}{aa}) -> ¬{AG}{aa} fact9: (x): ({BE}x & ¬{IU}x) -> ¬{HE}x fact10: ({DI}{aa} & ¬{DT}{aa}) -> ¬{B}{aa} fact11: ({AP}{gr} & ¬{EU}{gr}) -> ¬{C}{gr} fact12: ({AI}{aj} & ¬{H}{aj}) -> ¬{AB}{aj} fact13: (x): ({EN}x & ¬{L}x) -> ¬{BM}x fact14: (x): ({DS}x & ¬{EK}x) -> ¬{C}x fact15: (x): ({BN}x & ¬{ET}x) -> ¬{AL}x fact16: (x): ({CK}x & ¬{IG}x) -> ¬{DU}x fact17: ({AA}{db} & ¬{EN}{db}) -> ¬{IJ}{db} fact18: (x): ({GE}x & ¬{IL}x) -> ¬{DJ}x fact19: ({AA}{aa} & ¬{AB}{aa}) -> {B}{aa} fact20: ({CK}{aa} & ¬{GJ}{aa}) -> ¬{AA}{aa} | [
"fact4 -> hypothesis;"
] | [
"fact4 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 19 | 0 | 19 | PROVED | null | PROVED | null | $facts$ = fact1: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯éŠã ãããã¯è»ãããªããªãã°ããã¯åããåãããšããããšã¯ãªã fact2: ããäœããå¿ãããŠåããåããªããªãã°ããããã€ã³ããã¯ã¹ã ãšããããšã¯ãªãããšããããšã¯çå®ã fact3: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯å€§éº»çºæŸæã ã座å·å
ãããã€ãã°ãããå°ããããªã fact4: ãã倧麻çºæŸæã座å·å
ãããã€ããšããããšããªããªãã°ãããå°ããããªã fact5: ããäœããçå
µè¡ãåºããããããããäºèšãã€ãããªããªãã°ããããã®ãããŸãããªã fact6: ãã倧麻çºæŸæã¯åº§å·å
ãããã€ãã°ãããå°ãããããšããããšã¯ãªã fact7: ãã倧麻çºæŸæã座å·å
ãããã€ããªããªãã°ããã¯å°ãããã fact8: ãããã®ãžã£ã€ãã³ã³ãã¹ã西éšã¬ã¹ãèããããããããã¯åº§å·å
ãããã€ããªããªãã°ããã¯ãã¶ãããšããããšã¯ãªã fact9: ããéšåã¡ãäžäžäŸã§ãªããªãã°ããããã©ã³ãã³ã§ãªã fact10: ãããã®ãžã£ã€ãã³ã³ãã¹ãæ°Žèåã ãããããã£æ¯ã ãšããããšããªããªãã°ããã¯å°ããããªã fact11: ãããã®ã·ã§ã«ã¿ãŒã¯åããåãããäžåºžã ãšããããšããªããªãã°ãããã ã ã£ãŽãããªã fact12: ãããã®çœæ³¢ãèžèŠãããããã¯ç
è¬ã§ãªããªãã°ããã座å·å
ãããã€ããšããããšã¯ãªã fact13: ããäœãã¯ç³æŽ¥ã ã女ããããšããããšã¯ãªããªãã°ããããããŸãããªã fact14: ããéœè°äŒãããã©ãããšããããšããªããªãã°ãããã¯ã ã ã£ãŽãããšããããšããªãããšããããšãäºå®ã fact15: ããæŽããŸãããã®ã¯ãããããªããªãã°ãããæ±æžå ã§ãªã fact16: ãããããã®ã¯é»èš±ãããã€ããããããäžéšãä¹æããªããªãã°ããããããªããšããããšããªã fact17: ãããã®çºæ±ã倧麻çºæŸæã§ãã£ãŠç³æŽ¥ã ãšããããšã¯ãªããã®ãªãã°ããã¯äœå¿ç¡ããšããããšããªã fact18: ããããããã®ã§ãã£ãŠèããšããããšã¯ãªããã®ã¯æ£®æ¯ã ãšããããšããªã fact19: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯å€§éº»çºæŸæã ãããã¯åº§å·å
ãããã€ããªããªãã°ãããå°ãããã fact20: ãããã®ãžã£ã€ãã³ã³ãã¹ã¯é»èš±ãããã€ãããããã¯ãã¢ã³ããªã«ã¬ã³ã§ãªããªãã°ããã倧麻çºæŸæã ãšããããšããªã ; $hypothesis$ = ãããã®ãžã£ã€ãã³ã³ãã¹ã倧麻çºæŸæã ãããã座å·å
ãããã€ããšããããšããªããªãã°ãããå°ãããããšããããšããªã ; $proof$ = | fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ({DP}{aa} & ¬{EG}{aa}) -> ¬{AP}{aa} fact2: (x): ({EH}x & ¬{AP}x) -> ¬{O}x fact3: ({AA}{aa} & {AB}{aa}) -> ¬{B}{aa} fact4: (x): ({AA}x & ¬{AB}x) -> ¬{B}x fact5: (x): ({JA}x & ¬{IE}x) -> ¬{AQ}x fact6: (x): ({AA}x & {AB}x) -> ¬{B}x fact7: (x): ({AA}x & ¬{AB}x) -> {B}x fact8: ({AN}{aa} & ¬{AB}{aa}) -> ¬{AG}{aa} fact9: (x): ({BE}x & ¬{IU}x) -> ¬{HE}x fact10: ({DI}{aa} & ¬{DT}{aa}) -> ¬{B}{aa} fact11: ({AP}{gr} & ¬{EU}{gr}) -> ¬{C}{gr} fact12: ({AI}{aj} & ¬{H}{aj}) -> ¬{AB}{aj} fact13: (x): ({EN}x & ¬{L}x) -> ¬{BM}x fact14: (x): ({DS}x & ¬{EK}x) -> ¬{C}x fact15: (x): ({BN}x & ¬{ET}x) -> ¬{AL}x fact16: (x): ({CK}x & ¬{IG}x) -> ¬{DU}x fact17: ({AA}{db} & ¬{EN}{db}) -> ¬{IJ}{db} fact18: (x): ({GE}x & ¬{IL}x) -> ¬{DJ}x fact19: ({AA}{aa} & ¬{AB}{aa}) -> {B}{aa} fact20: ({CK}{aa} & ¬{GJ}{aa}) -> ¬{AA}{aa} ; $hypothesis$ = ({AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa} ; $proof$ = | fact4 -> hypothesis; __PROVED__ |
0.3 | ããªãŒããŒã©ã³ã¯çºçããªããä¿ã¯èµ·ããªãããšããããšãåœã | ¬(¬{AA} & ¬{AB}) | fact1: ãããäžããªããšããããšã¯èµ·ããããšããããšã¯äºå®ãšç°ãªããªããªãã°ããªãŒããŒã©ã³ã¯çºçããªããŠä¿ãèµ·ããªãããšããããšãééãã fact2: ãèŠã«ãããšããããšãçããããšããããšããåŸ
åœãæ¹ãããšãçºçããªãããšããããšãé»æ¢ãã fact3: ãåéæ²¢ã«ããããããããšã¯èµ·ããªãããšããããšã¯ãææãèµ·ããã西å€è³ã«ãããã ãããšã¯èµ·ããããšããããšã«ç¹ãã fact4: ãããç¹°åºãèµ·ãããªããäžå€§æ¡ã«åŒ·ãŸãããšãèµ·ãããªãããšããããšã¯èª€ããªãã°å±ãªããªããšããããšã¯èµ·ããªã fact5: ããšã»ããããšããããšã¯çºçããããã
ãè¡ã«èæµãããšãçºçããªãããšããããšã¯ããŒã€ããªããšããããšãçããªããšããããšãåŒãèµ·ãã fact6: ãåäœäžãæ³£ãäŒããããšãçºçããªããŠããšãããããšããããšãçããªãããšããããšããåŸ
åœãæ¹ãããšãèµ·ããããšããããšã«èµ·å ãã fact7: ããäœãäºã¯èµ·ããã°ãç¹°åºãçºçããªããäžå€§æ¡ã«åŒ·ãŸãããšã¯çºçããªãããšããããšãæãç«ããªã fact8: ã解èªãšããã§ãããšããããšãèµ·ããããšããããšã¯ãåäœäžãæ³£ãäŒããããšãçããªãããšããããšãå¥æ©ã fact9: ãããå°å»¶ãããããããšãšåéæ²¢ã«ããããããããšã¯èµ·ããããšããããšã誀ããªãã°åéæ²¢ã«ããããããããšã¯èµ·ããªã fact10: äœãäºãšãããããšããããšäž¡æ¹ãçãã fact11: ããå±ãªããªããšããããšã¯çºçããªããæããšããããšãçºçããªããªãã°æããšããããšã¯èµ·ããªã fact12: ããå
å®ããã©ããããšã¯èµ·ããªããªãã°ãå°å»¶ãããããããšãšåéæ²¢ã«ããããããããšãçºçããããšããããšã誀ãã fact13: æ¹ãçºçããªããç»èžã¯çããªã fact14: ããæããšããããšã¯çºçããªããªãã°ãšã»ããããšããããšãçºçããããã
ãè¡ã«èæµãããšã¯èµ·ããªã fact15: 空ã¯ãããããšããããšãçºçããªãããã©ã¡ãŒã¿ãŒã¯èµ·ããªã fact16: ãã西å€è³ã«ãããã ãããšã¯çºçããã°ãèŠã«ãããšããããšãçºçããããšããããšã¯æ¬åœã fact17: ä¿ãèµ·ãããªã fact18: å°å²±åæ²¢ãå€ããããšã¯çºçããªããããã£ã±ããšããããšãèµ·ããªã fact19: äžããªããšããããšãçºçãããšããããšã¯ãããŒã€ããªããšããããšãèµ·ããªããããã§ãããšããããšãèµ·ããããšããããšã«åŒãèµ·ãããã | fact1: {A} -> ¬(¬{AA} & ¬{AB}) fact2: {K} -> {J} fact3: ¬{N} -> ({M} & {L}) fact4: ¬(¬{R} & ¬{S}) -> ¬{P} fact5: ({G} & ¬{H}) -> ¬{B} fact6: {J} -> (¬{E} & ¬{F}) fact7: {T} -> ¬(¬{R} & ¬{S}) fact8: ¬{E} -> ({D} & {C}) fact9: ¬({O} & {N}) -> ¬{N} fact10: ({T} & {U}) fact11: (¬{P} v ¬{I}) -> ¬{I} fact12: ¬{Q} -> ¬({O} & {N}) fact13: (¬{FF} & ¬{HM}) fact14: ¬{I} -> ({G} & ¬{H}) fact15: (¬{IC} & ¬{IN}) fact16: {L} -> {K} fact17: ¬{AB} fact18: (¬{HL} & ¬{HJ}) fact19: (¬{B} & {C}) -> {A} | [] | [] | ãããªãŒããŒã©ã³ã¯èµ·ãããªããŠä¿ãèµ·ããªãããšããããšãæãç«ããªãããšããããšãæ£ãã | ¬(¬{AA} & ¬{AB}) | [
"fact32 -> int1: äœãäºãèµ·ãã; fact25 & int1 -> int2: ãç¹°åºãçããªããäžå€§æ¡ã«åŒ·ãŸãããšã¯çºçããªãããšããããšãäºå®ã§ãªã; fact28 & int2 -> int3: å±ãªããªããšããããšã¯çºçããªã; int3 -> int4: å±ãªããªããšããããšãçºçããªãããããã¯æããšããããšã¯èµ·ãããªããäž¡æ¹ã ; fact20 & int4 -> int5: æããšããããšãçºçããªã; fact27 & int5 -> int6: ãšã»ããããšããããšãèµ·ããããã
ãè¡ã«èæµãããšã¯çããªã; fact21 & int6 -> int7: ããŒã€ããªããšããããšãçºçããªã;"
] | 13 | 1 | null | 19 | 0 | 19 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããäžããªããšããããšã¯èµ·ããããšããããšã¯äºå®ãšç°ãªããªããªãã°ããªãŒããŒã©ã³ã¯çºçããªããŠä¿ãèµ·ããªãããšããããšãééãã fact2: ãèŠã«ãããšããããšãçããããšããããšããåŸ
åœãæ¹ãããšãçºçããªãããšããããšãé»æ¢ãã fact3: ãåéæ²¢ã«ããããããããšã¯èµ·ããªãããšããããšã¯ãææãèµ·ããã西å€è³ã«ãããã ãããšã¯èµ·ããããšããããšã«ç¹ãã fact4: ãããç¹°åºãèµ·ãããªããäžå€§æ¡ã«åŒ·ãŸãããšãèµ·ãããªãããšããããšã¯èª€ããªãã°å±ãªããªããšããããšã¯èµ·ããªã fact5: ããšã»ããããšããããšã¯çºçããããã
ãè¡ã«èæµãããšãçºçããªãããšããããšã¯ããŒã€ããªããšããããšãçããªããšããããšãåŒãèµ·ãã fact6: ãåäœäžãæ³£ãäŒããããšãçºçããªããŠããšãããããšããããšãçããªãããšããããšããåŸ
åœãæ¹ãããšãèµ·ããããšããããšã«èµ·å ãã fact7: ããäœãäºã¯èµ·ããã°ãç¹°åºãçºçããªããäžå€§æ¡ã«åŒ·ãŸãããšã¯çºçããªãããšããããšãæãç«ããªã fact8: ã解èªãšããã§ãããšããããšãèµ·ããããšããããšã¯ãåäœäžãæ³£ãäŒããããšãçããªãããšããããšãå¥æ©ã fact9: ãããå°å»¶ãããããããšãšåéæ²¢ã«ããããããããšã¯èµ·ããããšããããšã誀ããªãã°åéæ²¢ã«ããããããããšã¯èµ·ããªã fact10: äœãäºãšãããããšããããšäž¡æ¹ãçãã fact11: ããå±ãªããªããšããããšã¯çºçããªããæããšããããšãçºçããªããªãã°æããšããããšã¯èµ·ããªã fact12: ããå
å®ããã©ããããšã¯èµ·ããªããªãã°ãå°å»¶ãããããããšãšåéæ²¢ã«ããããããããšãçºçããããšããããšã誀ãã fact13: æ¹ãçºçããªããç»èžã¯çããªã fact14: ããæããšããããšã¯çºçããªããªãã°ãšã»ããããšããããšãçºçããããã
ãè¡ã«èæµãããšã¯èµ·ããªã fact15: 空ã¯ãããããšããããšãçºçããªãããã©ã¡ãŒã¿ãŒã¯èµ·ããªã fact16: ãã西å€è³ã«ãããã ãããšã¯çºçããã°ãèŠã«ãããšããããšãçºçããããšããããšã¯æ¬åœã fact17: ä¿ãèµ·ãããªã fact18: å°å²±åæ²¢ãå€ããããšã¯çºçããªããããã£ã±ããšããããšãèµ·ããªã fact19: äžããªããšããããšãçºçãããšããããšã¯ãããŒã€ããªããšããããšãèµ·ããªããããã§ãããšããããšãèµ·ããããšããããšã«åŒãèµ·ãããã ; $hypothesis$ = ããªãŒããŒã©ã³ã¯çºçããªããä¿ã¯èµ·ããªãããšããããšãåœã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} -> ¬(¬{AA} & ¬{AB}) fact2: {K} -> {J} fact3: ¬{N} -> ({M} & {L}) fact4: ¬(¬{R} & ¬{S}) -> ¬{P} fact5: ({G} & ¬{H}) -> ¬{B} fact6: {J} -> (¬{E} & ¬{F}) fact7: {T} -> ¬(¬{R} & ¬{S}) fact8: ¬{E} -> ({D} & {C}) fact9: ¬({O} & {N}) -> ¬{N} fact10: ({T} & {U}) fact11: (¬{P} v ¬{I}) -> ¬{I} fact12: ¬{Q} -> ¬({O} & {N}) fact13: (¬{FF} & ¬{HM}) fact14: ¬{I} -> ({G} & ¬{H}) fact15: (¬{IC} & ¬{IN}) fact16: {L} -> {K} fact17: ¬{AB} fact18: (¬{HL} & ¬{HJ}) fact19: (¬{B} & {C}) -> {A} ; $hypothesis$ = ¬(¬{AA} & ¬{AB}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¯ã¬ãªãœãŒãã暪çžã«å¶ããšããããšããªã | ¬{B}{a} | fact1: ããã®äŸè
ãå¡å±±å³ ã ããšããããšã¯æãç«ã€ fact2: ãããã®ä¹³çã¯å
ä»ããçŠã蟌ãã°ããã¯è±äœè¥¿ã ãšããããšããªã fact3: ããäœãã¯æ°žä»£ã«æãå
¥ããã°ããã暪çžã«å¶ã fact4: ãããããžã£ãã«ã ãäž¡åºã ããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ã¯ããã°ãã®ç«¯æŠè
ãã€ã³ãç£æ¥é£çã fact5: ãããã®äŸè
ã¯å¡å±±å³ ãªãã°ãããã®ä¹³çãèŠããšããããšã¯ãªããããããããæºå€ªã¶å²³ã ããšããããšã¯æ¬åœã ããšããããšãæãç«ããªã fact6: ãããããã®ã¯ã»ãã«ãããªãã°ãããã¯ããµããšããããšã¯ãªããã±ã¿ã«ç«¶åããªãããšããããšãçå®ã§ãªã fact7: ãããã®ä¹³çã¯è±äœè¥¿ã ãšããããšããªããªãã°ããã®ãããŒãžã£ãŒã¯å²©æžè¶ã ãšããããšã¯ãªããããããããåäžåå ã«ç± ãããšããããšãæãç«ããªã fact8: ãããã®ç«¯æŠè
ã¯æŸæµŠçºæå·ã ãšããããšã¯ãªããªãã°ãã®ã¯ã¬ãªãœãŒãã氞代ã«æãå
¥ãããããã¯ã»ãã«ãã fact9: ããããã®åŒå€©ã¯æšªçžã«å¶ããªããããã¯ãããŸãããšããããšã¯ãªãããšããããšã¯æãç«ããªããªãã°ããããããããšããããšã¯ãªã fact10: ããã®ã¯ã¬ãªãœãŒãã¯æ®ºé¢šæ¯ããããããµããªãããšããããšãäºå®ã ãšããããšããªã fact11: äžåºæ±ããããããªã fact12: ããããã®ä¹³çã¯èŠããªããã®ã§ãã£ãŠæºå€ªã¶å²³ãªãã®ããšããããšã¯æãç«ããªããªãã°ããã¯å
ä»ããçŠã蟌ã fact13: ããã®ã¯ã¬ãªãœãŒãã殺颚æ¯ããããšããããšããªããŠããµããšããããšã¯ãªãããšããããšã¯ééãã fact14: ããã€ã³ãç£æ¥é£çã¯ãããããªããªãã°ãããæŸæµŠçºæå·ã§ãªã fact15: ãããã岩æžè¶ã§ãªãããããåäžåå ã«ç± ãããšããããšãæãç«ããªãããã®ãããã°ãã®ç«¯æŠè
ãäžåºæ±ã fact16: ããããã®ã¯ã¬ãªãœãŒãã暪çžã«å¶ããªããããã¯æ°žä»£ã«æãå
¥ããããšããããšã¯æãç«ããªããªãã°ãã®ãã¥ãŒã¢ãŒãã»ãã«ãã fact17: ãããã®ã¯ã¬ãªãœãŒãã殺颚æ¯ãããã°ããã¯æšªçžã«å¶ããªã fact18: ããã¯ãžã£ãã«ã ããããäž¡åºã ãšãããã®ããªã | fact1: {P}{f} fact2: {M}{e} -> ¬{L}{e} fact3: (x): {C}x -> {B}x fact4: (x): ¬({H}x & {I}x) -> {E}{b} fact5: {P}{f} -> ¬(¬{N}{e} & {O}{e}) fact6: (x): {A}x -> ¬(¬{AB}x & ¬{GK}x) fact7: ¬{L}{e} -> ¬(¬{K}{d} & {J}{d}) fact8: ¬{D}{b} -> ({C}{a} v {A}{a}) fact9: ¬(¬{B}{gg} & ¬{BH}{gg}) -> ¬{EF}{gg} fact10: ¬({AA}{a} & ¬{AB}{a}) fact11: (x): {G}x -> {F}x fact12: ¬(¬{N}{e} & {O}{e}) -> {M}{e} fact13: ¬(¬{AA}{a} & ¬{AB}{a}) fact14: (x): ({E}x & {F}x) -> ¬{D}x fact15: (x): ¬(¬{K}x & {J}x) -> {G}{b} fact16: ¬(¬{B}{a} & {C}{a}) -> {A}{fc} fact17: {AA}{a} -> ¬{B}{a} fact18: (x): ¬({H}x & {I}x) | [] | [] | ããã®ãã¥ãŒã¢ãŒã¯ããµããšããããšã¯ãªããã±ã¿ã«ç«¶åããªãããšããããšã¯æãç«ããªã | ¬(¬{AB}{fc} & ¬{GK}{fc}) | [
"fact20 -> int1: ãããã®ãã¥ãŒã¢ãŒãã»ãã«ãããªãã°ããããããµããªããããã¯ã±ã¿ã«ç«¶åããªãããšããããšãæãç«ããªã;"
] | 5 | 1 | null | 17 | 0 | 17 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã®äŸè
ãå¡å±±å³ ã ããšããããšã¯æãç«ã€ fact2: ãããã®ä¹³çã¯å
ä»ããçŠã蟌ãã°ããã¯è±äœè¥¿ã ãšããããšããªã fact3: ããäœãã¯æ°žä»£ã«æãå
¥ããã°ããã暪çžã«å¶ã fact4: ãããããžã£ãã«ã ãäž¡åºã ããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ã¯ããã°ãã®ç«¯æŠè
ãã€ã³ãç£æ¥é£çã fact5: ãããã®äŸè
ã¯å¡å±±å³ ãªãã°ãããã®ä¹³çãèŠããšããããšã¯ãªããããããããæºå€ªã¶å²³ã ããšããããšã¯æ¬åœã ããšããããšãæãç«ããªã fact6: ãããããã®ã¯ã»ãã«ãããªãã°ãããã¯ããµããšããããšã¯ãªããã±ã¿ã«ç«¶åããªãããšããããšãçå®ã§ãªã fact7: ãããã®ä¹³çã¯è±äœè¥¿ã ãšããããšããªããªãã°ããã®ãããŒãžã£ãŒã¯å²©æžè¶ã ãšããããšã¯ãªããããããããåäžåå ã«ç± ãããšããããšãæãç«ããªã fact8: ãããã®ç«¯æŠè
ã¯æŸæµŠçºæå·ã ãšããããšã¯ãªããªãã°ãã®ã¯ã¬ãªãœãŒãã氞代ã«æãå
¥ãããããã¯ã»ãã«ãã fact9: ããããã®åŒå€©ã¯æšªçžã«å¶ããªããããã¯ãããŸãããšããããšã¯ãªãããšããããšã¯æãç«ããªããªãã°ããããããããšããããšã¯ãªã fact10: ããã®ã¯ã¬ãªãœãŒãã¯æ®ºé¢šæ¯ããããããµããªãããšããããšãäºå®ã ãšããããšããªã fact11: äžåºæ±ããããããªã fact12: ããããã®ä¹³çã¯èŠããªããã®ã§ãã£ãŠæºå€ªã¶å²³ãªãã®ããšããããšã¯æãç«ããªããªãã°ããã¯å
ä»ããçŠã蟌ã fact13: ããã®ã¯ã¬ãªãœãŒãã殺颚æ¯ããããšããããšããªããŠããµããšããããšã¯ãªãããšããããšã¯ééãã fact14: ããã€ã³ãç£æ¥é£çã¯ãããããªããªãã°ãããæŸæµŠçºæå·ã§ãªã fact15: ãããã岩æžè¶ã§ãªãããããåäžåå ã«ç± ãããšããããšãæãç«ããªãããã®ãããã°ãã®ç«¯æŠè
ãäžåºæ±ã fact16: ããããã®ã¯ã¬ãªãœãŒãã暪çžã«å¶ããªããããã¯æ°žä»£ã«æãå
¥ããããšããããšã¯æãç«ããªããªãã°ãã®ãã¥ãŒã¢ãŒãã»ãã«ãã fact17: ãããã®ã¯ã¬ãªãœãŒãã殺颚æ¯ãããã°ããã¯æšªçžã«å¶ããªã fact18: ããã¯ãžã£ãã«ã ããããäž¡åºã ãšãããã®ããªã ; $hypothesis$ = ãã®ã¯ã¬ãªãœãŒãã暪çžã«å¶ããšããããšããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {P}{f} fact2: {M}{e} -> ¬{L}{e} fact3: (x): {C}x -> {B}x fact4: (x): ¬({H}x & {I}x) -> {E}{b} fact5: {P}{f} -> ¬(¬{N}{e} & {O}{e}) fact6: (x): {A}x -> ¬(¬{AB}x & ¬{GK}x) fact7: ¬{L}{e} -> ¬(¬{K}{d} & {J}{d}) fact8: ¬{D}{b} -> ({C}{a} v {A}{a}) fact9: ¬(¬{B}{gg} & ¬{BH}{gg}) -> ¬{EF}{gg} fact10: ¬({AA}{a} & ¬{AB}{a}) fact11: (x): {G}x -> {F}x fact12: ¬(¬{N}{e} & {O}{e}) -> {M}{e} fact13: ¬(¬{AA}{a} & ¬{AB}{a}) fact14: (x): ({E}x & {F}x) -> ¬{D}x fact15: (x): ¬(¬{K}x & {J}x) -> {G}{b} fact16: ¬(¬{B}{a} & {C}{a}) -> {A}{fc} fact17: {AA}{a} -> ¬{B}{a} fact18: (x): ¬({H}x & {I}x) ; $hypothesis$ = ¬{B}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããè«žè²ã ãšããããšããªããªãã°å·å¿µæ·±ããšããããšããªããå
è·ãªããã®ãããããšããããšãåã | ¬((Ex): ¬{A}x -> (¬{AA}x & {AB}x)) | fact1: ãããè«žè²ã ãšããããšã¯ãªããªãã°å·å¿µæ·±ããªãããã®ã¯ãã fact2: ãããã®ã¢ã«ãããè«žè²ã§ãªããªãã°ããã¯ã¡ããã¥ãããšããããšããªãã京éœå¥³åäžåŠæ ¡ãããããã fact3: ãããè«žè²ã ãšããããšããªããªãã°å
è·ãªããã®ã¯ãã fact4: ãããã®æåžãè«žè²ãªãã°ããã¯å·å¿µæ·±ããšããããšããªãããããå
è·ã fact5: ãããè©©æ Œã§ãªããªãã°èãå¯ããšããããšã¯ãªããé£ãæ¶æã«åž°ãããã®ããã fact6: ãããã®æåžã¯è«žè²ã§ãªããªãã°ãããå·å¿µæ·±ããšããããšããªã fact7: ãããè«žè²ãªãã°å·å¿µæ·±ããªããå
è·ãªããã®ã¯ãã fact8: ãããã®æåžãè«žè²ã ãšããããšã¯ãªããªãã°ãããç©ããããšããããšããªããŠãããåäžãã fact9: ãããã®æåžã¯è«žè²ã ãšããããšããªããªãã°ãããå·å¿µæ·±ããšããããšã¯ãªããã®ã§ãã£ãŠå
è·ã ãã® fact10: ããããè«žè²ã ãšããããšããªãããšããããšãæ£ãããªãã°å·å¿µæ·±ããå
è·ãªããã®ã¯ãã fact11: ãããã®äžçºãã¡ããã¥ãããªããªãã°ããã京éã§ãªããããã匷ã fact12: ãããã®æåžã¯å°çºæ¿ã§ãªããªãã°ãããå
è·ã ãšããããšã¯ãªããã«ã¡ã«ããããã fact13: ãããããã®ã¯å®åã§ãªããªãã°ãããå
è·ã ãšããããšã¯ãªããããããžã£ã³ãŠãã³ã | fact1: (Ex): ¬{A}x -> ¬{AA}x fact2: ¬{A}{ac} -> (¬{GL}{ac} & {CI}{ac}) fact3: (Ex): ¬{A}x -> {AB}x fact4: {A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact5: (Ex): ¬{EP}x -> (¬{JE}x & {HP}x) fact6: ¬{A}{aa} -> ¬{AA}{aa} fact7: (Ex): {A}x -> (¬{AA}x & {AB}x) fact8: ¬{A}{aa} -> (¬{IL}{aa} & {HR}{aa}) fact9: ¬{A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact10: (Ex): ¬{A}x -> ({AA}x & {AB}x) fact11: ¬{GL}{fs} -> (¬{K}{fs} & {IR}{fs}) fact12: ¬{HE}{aa} -> (¬{AB}{aa} & {G}{aa}) fact13: (x): ¬{CL}x -> (¬{AB}x & {HK}x) | [
"fact9 -> hypothesis;"
] | [
"fact9 -> hypothesis;"
] | ãããã®é²æ©ãå®åã ãšããããšã¯ãªããªãã°ãããå
è·ã ãšããããšããªããããã¯ãžã£ã³ãŠãã³ã | ¬{CL}{ck} -> (¬{AB}{ck} & {HK}{ck}) | [
"fact14 -> hypothesis;"
] | 1 | 1 | 1 | 12 | 0 | 12 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãããè«žè²ã ãšããããšã¯ãªããªãã°å·å¿µæ·±ããªãããã®ã¯ãã fact2: ãããã®ã¢ã«ãããè«žè²ã§ãªããªãã°ããã¯ã¡ããã¥ãããšããããšããªãã京éœå¥³åäžåŠæ ¡ãããããã fact3: ãããè«žè²ã ãšããããšããªããªãã°å
è·ãªããã®ã¯ãã fact4: ãããã®æåžãè«žè²ãªãã°ããã¯å·å¿µæ·±ããšããããšããªãããããå
è·ã fact5: ãããè©©æ Œã§ãªããªãã°èãå¯ããšããããšã¯ãªããé£ãæ¶æã«åž°ãããã®ããã fact6: ãããã®æåžã¯è«žè²ã§ãªããªãã°ãããå·å¿µæ·±ããšããããšããªã fact7: ãããè«žè²ãªãã°å·å¿µæ·±ããªããå
è·ãªããã®ã¯ãã fact8: ãããã®æåžãè«žè²ã ãšããããšã¯ãªããªãã°ãããç©ããããšããããšããªããŠãããåäžãã fact9: ãããã®æåžã¯è«žè²ã ãšããããšããªããªãã°ãããå·å¿µæ·±ããšããããšã¯ãªããã®ã§ãã£ãŠå
è·ã ãã® fact10: ããããè«žè²ã ãšããããšããªãããšããããšãæ£ãããªãã°å·å¿µæ·±ããå
è·ãªããã®ã¯ãã fact11: ãããã®äžçºãã¡ããã¥ãããªããªãã°ããã京éã§ãªããããã匷ã fact12: ãããã®æåžã¯å°çºæ¿ã§ãªããªãã°ãããå
è·ã ãšããããšã¯ãªããã«ã¡ã«ããããã fact13: ãããããã®ã¯å®åã§ãªããªãã°ãããå
è·ã ãšããããšã¯ãªããããããžã£ã³ãŠãã³ã ; $hypothesis$ = ããããè«žè²ã ãšããããšããªããªãã°å·å¿µæ·±ããšããããšããªããå
è·ãªããã®ãããããšããããšãåã ; $proof$ = | fact9 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (Ex): ¬{A}x -> ¬{AA}x fact2: ¬{A}{ac} -> (¬{GL}{ac} & {CI}{ac}) fact3: (Ex): ¬{A}x -> {AB}x fact4: {A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact5: (Ex): ¬{EP}x -> (¬{JE}x & {HP}x) fact6: ¬{A}{aa} -> ¬{AA}{aa} fact7: (Ex): {A}x -> (¬{AA}x & {AB}x) fact8: ¬{A}{aa} -> (¬{IL}{aa} & {HR}{aa}) fact9: ¬{A}{aa} -> (¬{AA}{aa} & {AB}{aa}) fact10: (Ex): ¬{A}x -> ({AA}x & {AB}x) fact11: ¬{GL}{fs} -> (¬{K}{fs} & {IR}{fs}) fact12: ¬{HE}{aa} -> (¬{AB}{aa} & {G}{aa}) fact13: (x): ¬{CL}x -> (¬{AB}x & {HK}x) ; $hypothesis$ = ¬((Ex): ¬{A}x -> (¬{AA}x & {AB}x)) ; $proof$ = | fact9 -> hypothesis; __DISPROVED__ |
0.3 | ãããææãã ãšããããšããªããã±ã³ãçŽãªããã®ã¯ããããšããããšãäºå®ã ããšããããšã¯åœã | ¬((Ex): (¬{AA}x & {AB}x)) | fact1: äœããç«æžã§ãªããããã涌ãã fact2: ãææãã§ã±ã³ãçŽãªããã®ããã fact3: ããã®ãªããã¯ããŒã»ã³ããŒãžã«éã³æ©ããšããããšããªããã±ã³ãçŽã ããšããããšãæãç«ã€ fact4: ãããããã®ã¯å°ã蟌ããã°ããã¯èº«çœ·ããšããããšã¯ãªãã銳äžãã«ãã¡ãŸãã fact5: ãããã®ã¯ã±ã³ãçŽã fact6: ãã®ãªããã¯ã±ã³ãçŽã fact7: ãææãã§ãªãããã®ã¯ãã fact8: å
ããªããŠã¯ãã°ããããã®ããã fact9: ãå£ãããªããªããæãããããã®ã¯ãã fact10: ãçŠãããããšããããšããªãããã®ããã fact11: ãã®ãªããã¯ææãã ãšããããšããªããããã¯ã±ã³ãçŽã fact12: äœãã鶎島ã ãšããããšã¯ãªããç³é«ã | fact1: (Ex): (¬{ES}x & {T}x) fact2: (Ex): ({AA}x & {AB}x) fact3: (¬{DB}{aa} & {AB}{aa}) fact4: (x): {A}x -> (¬{IS}x & {FH}x) fact5: (Ex): {AB}x fact6: {AB}{aa} fact7: (Ex): ¬{AA}x fact8: (Ex): (¬{EE}x & {CT}x) fact9: (Ex): (¬{HG}x & {GD}x) fact10: (Ex): ¬{AM}x fact11: (¬{AA}{aa} & {AB}{aa}) fact12: (Ex): (¬{IB}x & {FF}x) | [
"fact11 -> hypothesis;"
] | [
"fact11 -> hypothesis;"
] | äœãã¯èº«çœ·ããªãã銳äžãã«ãã¡ãŸãã | (Ex): (¬{IS}x & {FH}x) | [
"fact13 -> int1: ãããã®æ²¹çµµã®å
·ã¯å°ã蟌ããã°ããã身眷ããšããããšããªããããã銳äžãã«ãã¡ãŸãã;"
] | 7 | 1 | 1 | 11 | 0 | 11 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: äœããç«æžã§ãªããããã涌ãã fact2: ãææãã§ã±ã³ãçŽãªããã®ããã fact3: ããã®ãªããã¯ããŒã»ã³ããŒãžã«éã³æ©ããšããããšããªããã±ã³ãçŽã ããšããããšãæãç«ã€ fact4: ãããããã®ã¯å°ã蟌ããã°ããã¯èº«çœ·ããšããããšã¯ãªãã銳äžãã«ãã¡ãŸãã fact5: ãããã®ã¯ã±ã³ãçŽã fact6: ãã®ãªããã¯ã±ã³ãçŽã fact7: ãææãã§ãªãããã®ã¯ãã fact8: å
ããªããŠã¯ãã°ããããã®ããã fact9: ãå£ãããªããªããæãããããã®ã¯ãã fact10: ãçŠãããããšããããšããªãããã®ããã fact11: ãã®ãªããã¯ææãã ãšããããšããªããããã¯ã±ã³ãçŽã fact12: äœãã鶎島ã ãšããããšã¯ãªããç³é«ã ; $hypothesis$ = ãããææãã ãšããããšããªããã±ã³ãçŽãªããã®ã¯ããããšããããšãäºå®ã ããšããããšã¯åœã ; $proof$ = | fact11 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (Ex): (¬{ES}x & {T}x) fact2: (Ex): ({AA}x & {AB}x) fact3: (¬{DB}{aa} & {AB}{aa}) fact4: (x): {A}x -> (¬{IS}x & {FH}x) fact5: (Ex): {AB}x fact6: {AB}{aa} fact7: (Ex): ¬{AA}x fact8: (Ex): (¬{EE}x & {CT}x) fact9: (Ex): (¬{HG}x & {GD}x) fact10: (Ex): ¬{AM}x fact11: (¬{AA}{aa} & {AB}{aa}) fact12: (Ex): (¬{IB}x & {FF}x) ; $hypothesis$ = ¬((Ex): (¬{AA}x & {AB}x)) ; $proof$ = | fact11 -> hypothesis; __DISPROVED__ |
0.3 | ãã®è»éªšãããã€ãããŸãããªã | ¬{B}{b} | fact1: ããããã®è»éªšãããã€ãããŸããããããã¯ãããè·¡éšã ããšããããšã¯èª€ããªãã°ãã®éŠåœŠãæã°ãããšããããšããªã fact2: ãããããã®è»éªšã¯ããã€ãããŸãããšããããšããªãããããã¯ããã¯æã°ããããããã¯äž¡æ¹ã ããšããããšã¯çå®ã ããšããããšã¯èª€ããªãã°ãã®éŠåœŠã¯è·¡éšã ãšããããšããªã fact3: ãã®å·ã¯æã°ãããªã fact4: ããã®éŠåœŠãæã°ãããšããããšã¯ãªãããããã¯ãããè·¡éšã ããšããããšãäºå®ãšç°ãªã fact5: ããããã®è»éªšã¯æã°ãããªããè·¡éšã§ããããããã¯äž¡æ¹ã ããšããããšã¯ééããªãã°ãã®éŠåœŠã¯ããã€ãããŸãããšããããšã¯ãªã fact6: ããããã®ç
ۍ
ããã®ããããããªãããšããããšã¯æ¬åœãªãã°ããããè接ä¹
ä¿å±±å°ã§ãã£ãŠæµ®è¢ã«ãã³ããããã®ããšããããšã誀ãã fact7: ããããã®è»éªšã¯è·¡éšã§ãªãããããã¯ãããæã°ããããšããããšã¯æãç«ããªããªãã°ãã®éŠåœŠãããã€ãããŸãããšããããšã¯ãªã fact8: ãããããã®ã¯æµ®è¢ã«ãã³ããããªããªãã°ãããç³
飯ã ãšããããšããªããå¿è¡ã«æ·»ãéãããšããããšããªã fact9: ããããã®éŠåœŠãæã°ããããããã¯è·¡éšã§ããããããã¯äž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ãã®è»éªšãããã€ãããŸãããªã fact10: ãã®éŠåœŠãæã°ãã fact11: ããã®éŠåœŠãæã°ãããªãããããäºæè¿ãããšããããšãåã fact12: ããäœããç³
飯ã ãšããããšã¯ãªãããããå¿è¡ã«æ·»ãéããªããªãã°ãããã¯ããã€ãããŸããããšããããšãæãç«ã€ fact13: ãããã®ãªã»ããã¯éŠ¬å Žãªãã°ãã®ç
ۍ
ããŠããããã®ããããããªã fact14: ãã®ãªã»ããã¯éŠ¬å Žã fact15: ãããããã®ãå¿è¡ã«æ·»ãéããªããªãã°ããããããã€ãããŸãããšããããšããªããããã¯ç³
飯ã ããšããããšã¯äºå®ãšç°ãªã fact16: ããããã®è»éªšã¯æã°ããããããã¯ããã€ãããŸãããäž¡æ¹ã ããšããããšãäºå®ãšç°ãªãã°ãã®éŠåœŠãè·¡éšã ãšããããšããªã fact17: ããããã®éŠåœŠãæã°ããããããã¯ããã€ãããŸããããšããããšã¯åãªãã°ãã®è»éªšã¯è·¡éšã§ãªã | fact1: ¬({B}{b} v {AB}{b}) -> ¬{AA}{a} fact2: ¬(¬{B}{b} v {AA}{b}) -> ¬{AB}{a} fact3: ¬{AA}{jf} fact4: ¬(¬{AA}{a} v {AB}{a}) fact5: ¬(¬{AA}{b} v {AB}{b}) -> ¬{B}{a} fact6: ¬{F}{c} -> ¬({E}{c} & {D}{c}) fact7: ¬(¬{AB}{b} v {AA}{b}) -> ¬{B}{a} fact8: (x): ¬{D}x -> (¬{A}x & ¬{C}x) fact9: ¬({AA}{a} v {AB}{a}) -> ¬{B}{b} fact10: {AA}{a} fact11: ¬(¬{AA}{a} v {IT}{a}) fact12: (x): (¬{A}x & ¬{C}x) -> {B}x fact13: {H}{d} -> ({G}{c} & ¬{F}{c}) fact14: {H}{d} fact15: (x): ¬{C}x -> ¬(¬{B}x & {A}x) fact16: ¬({AA}{b} v {B}{b}) -> ¬{AB}{a} fact17: ¬({AA}{a} v {B}{a}) -> ¬{AB}{b} | [] | [] | ããã®è»éªšã¯ããã€ãããŸããããšããããšã¯æ£ãã | {B}{b} | [
"fact19 -> int1: ãããã®è»éªšãç³
飯ã ãšããããšããªããŠãããå¿è¡ã«æ·»ãéãããšããããšã¯ãªããªãã°ããã¯ããã€ãããŸãã; fact18 -> int2: ããããã®è»éªšã¯æµ®è¢ã«ãã³ããããšããããšããªããªãã°ãã®è»éªšã¯ç³
飯ã ãšããããšã¯ãªããå¿è¡ã«æ·»ãéãããšããããšããªãããšããããšã¯æ£ãã;"
] | 5 | 1 | null | 16 | 0 | 16 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®è»éªšãããã€ãããŸããããããã¯ãããè·¡éšã ããšããããšã¯èª€ããªãã°ãã®éŠåœŠãæã°ãããšããããšããªã fact2: ãããããã®è»éªšã¯ããã€ãããŸãããšããããšããªãããããã¯ããã¯æã°ããããããã¯äž¡æ¹ã ããšããããšã¯çå®ã ããšããããšã¯èª€ããªãã°ãã®éŠåœŠã¯è·¡éšã ãšããããšããªã fact3: ãã®å·ã¯æã°ãããªã fact4: ããã®éŠåœŠãæã°ãããšããããšã¯ãªãããããã¯ãããè·¡éšã ããšããããšãäºå®ãšç°ãªã fact5: ããããã®è»éªšã¯æã°ãããªããè·¡éšã§ããããããã¯äž¡æ¹ã ããšããããšã¯ééããªãã°ãã®éŠåœŠã¯ããã€ãããŸãããšããããšã¯ãªã fact6: ããããã®ç
ۍ
ããã®ããããããªãããšããããšã¯æ¬åœãªãã°ããããè接ä¹
ä¿å±±å°ã§ãã£ãŠæµ®è¢ã«ãã³ããããã®ããšããããšã誀ãã fact7: ããããã®è»éªšã¯è·¡éšã§ãªãããããã¯ãããæã°ããããšããããšã¯æãç«ããªããªãã°ãã®éŠåœŠãããã€ãããŸãããšããããšã¯ãªã fact8: ãããããã®ã¯æµ®è¢ã«ãã³ããããªããªãã°ãããç³
飯ã ãšããããšããªããå¿è¡ã«æ·»ãéãããšããããšããªã fact9: ããããã®éŠåœŠãæã°ããããããã¯è·¡éšã§ããããããã¯äž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ãã®è»éªšãããã€ãããŸãããªã fact10: ãã®éŠåœŠãæã°ãã fact11: ããã®éŠåœŠãæã°ãããªãããããäºæè¿ãããšããããšãåã fact12: ããäœããç³
飯ã ãšããããšã¯ãªãããããå¿è¡ã«æ·»ãéããªããªãã°ãããã¯ããã€ãããŸããããšããããšãæãç«ã€ fact13: ãããã®ãªã»ããã¯éŠ¬å Žãªãã°ãã®ç
ۍ
ããŠããããã®ããããããªã fact14: ãã®ãªã»ããã¯éŠ¬å Žã fact15: ãããããã®ãå¿è¡ã«æ·»ãéããªããªãã°ããããããã€ãããŸãããšããããšããªããããã¯ç³
飯ã ããšããããšã¯äºå®ãšç°ãªã fact16: ããããã®è»éªšã¯æã°ããããããã¯ããã€ãããŸãããäž¡æ¹ã ããšããããšãäºå®ãšç°ãªãã°ãã®éŠåœŠãè·¡éšã ãšããããšããªã fact17: ããããã®éŠåœŠãæã°ããããããã¯ããã€ãããŸããããšããããšã¯åãªãã°ãã®è»éªšã¯è·¡éšã§ãªã ; $hypothesis$ = ãã®è»éªšãããã€ãããŸãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({B}{b} v {AB}{b}) -> ¬{AA}{a} fact2: ¬(¬{B}{b} v {AA}{b}) -> ¬{AB}{a} fact3: ¬{AA}{jf} fact4: ¬(¬{AA}{a} v {AB}{a}) fact5: ¬(¬{AA}{b} v {AB}{b}) -> ¬{B}{a} fact6: ¬{F}{c} -> ¬({E}{c} & {D}{c}) fact7: ¬(¬{AB}{b} v {AA}{b}) -> ¬{B}{a} fact8: (x): ¬{D}x -> (¬{A}x & ¬{C}x) fact9: ¬({AA}{a} v {AB}{a}) -> ¬{B}{b} fact10: {AA}{a} fact11: ¬(¬{AA}{a} v {IT}{a}) fact12: (x): (¬{A}x & ¬{C}x) -> {B}x fact13: {H}{d} -> ({G}{c} & ¬{F}{c}) fact14: {H}{d} fact15: (x): ¬{C}x -> ¬(¬{B}x & {A}x) fact16: ¬({AA}{b} v {B}{b}) -> ¬{AB}{a} fact17: ¬({AA}{a} v {B}{a}) -> ¬{AB}{b} ; $hypothesis$ = ¬{B}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãçºè°ãçããªãããããå°å Žã¹ãŒããŒã«æµ®ãåºãããšã¯çºçããããšããããšãæ¬åœã ãšããããšã¯ãªã | ¬(¬{AA} & {AB}) | fact1: ãŸã¢ãããšããããšã¯èµ·ããªããšããããšãæé
·ããšããããšã«ææ¢ããã fact2: ããã©ããããšã§ã¯ãªãçŒç±ãèµ·ãã fact3: ããç®åºåºŠããšããããšãèµ·ãããªããªãã°ç
§èããšããããšãšå°éåã«å€ªããããšã¯èµ·ãã fact4: çºè°ã¯èµ·ããªã fact5: ããç
§èããšããããšãçºçããã°ã空ããããšã¯çããããã€ãããããšããããšã¯çããªãããšããããšã¯åœã fact6: ããæé
·ããšããããšã¯èµ·ãããªããªãã°ãå«ãããã¯èµ·ããããŸã¢ãããšããããšãèµ·ããªãããšããããšã¯ééãã fact7: ãããçããšæé
·ããšããããšãçºçããããšããããšãééããªãã°æé
·ããšããããšã¯çºçããªã fact8: ãçããšæé
·ããšããããšäž¡æ¹ã¯èµ·ããããšããããšã¯ã空ããããšãçããªãããšããããšãå¥æ©ã fact9: ããµãããããã€ããããšãèµ·ãããªãããªããšã©ãããããããããšã¯èµ·ããããšããããšããŸã¢ãããšããããšãçºçãããšããããšã«èµ·å ãã fact10: ããªããšã©ãããããããããšãçããªãããšããããšã¯ãæ»
ã³ãããšãšçžŠç£åã«æºãããããšãçããããšããããšããããã fact11: ãç
§èããšããããšãšãã€ãããããšããããšäž¡æ¹ãçããããšããããšã¯ãå°éåã«å€ªããããšã¯çããªãããšããããšãåå ã fact12: çºè°ã§ã¯ãªãå°å Žã¹ãŒããŒã«æµ®ãåºãããšãèµ·ãã fact13: åã»è«èšªããšãããããããšãçºçããªã fact14: ããç
§èããšããããšã¯çºçããã°çžŠç£åã«æºãããããšã¯çºçããªããå«ãããã¯èµ·ãããªã fact15: ã空ããããšã§ã¯ãªãç®åºåºŠããšããããšãçããããšããããšãåã»è«èšªããšãããããããšãèµ·ããªããšããããšãå¥æ©ã fact16: ããã瞊ç£åã«æºãããããšã¯çºçããªãããšããããšã¯æ¬åœãªãã°ãŠã°ããããšããããšãšæ»
ã³ãããšäž¡æ¹ãèµ·ãã fact17: ããã空ããããšãçããããã€ãããããšããããšã¯çºçããªãããšããããšã¯èª€ããªãã°ã空ããããšãèµ·ããªãããšããããšã¯äºå®ã fact18: å°éåã«å€ªããããšãèµ·ããªã fact19: ããã¡èŸããšããããšãçããªããæ¥è®åŽããŸãããããšã¯èµ·ããããšããããšã¯æãç«ã€ | fact1: {F} -> {D} fact2: (¬{BL} & {U}) fact3: ¬{L} -> ({I} & {K}) fact4: ¬{AA} fact5: {I} -> ¬({H} & ¬{J}) fact6: ¬{F} -> ¬({E} & ¬{D}) fact7: ¬({G} & {F}) -> ¬{F} fact8: ¬{H} -> ({G} & {F}) fact9: {D} -> (¬{ET} & {C}) fact10: ¬{C} -> ({A} & {B}) fact11: ¬{K} -> ({I} & {J}) fact12: (¬{AA} & {AB}) fact13: ¬{M} fact14: {I} -> (¬{B} & ¬{E}) fact15: ¬{M} -> (¬{H} & {L}) fact16: ¬{B} -> ({Q} & {A}) fact17: ¬({H} & ¬{J}) -> ¬{H} fact18: ¬{K} fact19: (¬{HQ} & {JC}) | [
"fact12 -> hypothesis;"
] | [
"fact12 -> hypothesis;"
] | ãµãããããã€ããããšã¯çºçããªããããããŠã°ããããšããããšãèµ·ãã | (¬{ET} & {Q}) | [
"fact26 & fact20 -> int1: 空ããããšã¯èµ·ãããªããŠç®åºåºŠããšããããšã¯èµ·ãã; int1 -> int2: 空ããããšã¯èµ·ãããªã; fact25 & int2 -> int3: çããèµ·ãããæé
·ããšããããšã¯èµ·ãã; int3 -> int4: æé
·ããšããããšã¯èµ·ãã; fact27 & int4 -> int5: ãŸã¢ãããšããããšã¯çãã; fact23 & int5 -> int6: ãµãããããã€ããããšã¯çºçããªãããªããšã©ãããããããããšãçºçãã; int6 -> int7: ãµãããããã€ããããšãèµ·ããªã; fact22 & fact24 -> int8: ç
§èããšããããšãšãã€ãããããšããããšã¯çºçãã; int8 -> int9: ç
§èããšããããšãçºçãã; fact21 & int9 -> int10: 瞊ç£åã«æºãããããšã¯çºçããªããå«ããããèµ·ãããªã; int10 -> int11: 瞊ç£åã«æºãããããšã¯çºçããªã; fact28 & int11 -> int12: ãŠã°ããããšããããšãšæ»
ã³ãããšãèµ·ãã; int12 -> int13: ãŠã°ããããšããããšãçºçãã; int7 & int13 -> hypothesis;"
] | 8 | 1 | 0 | 18 | 0 | 18 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãŸã¢ãããšããããšã¯èµ·ããªããšããããšãæé
·ããšããããšã«ææ¢ããã fact2: ããã©ããããšã§ã¯ãªãçŒç±ãèµ·ãã fact3: ããç®åºåºŠããšããããšãèµ·ãããªããªãã°ç
§èããšããããšãšå°éåã«å€ªããããšã¯èµ·ãã fact4: çºè°ã¯èµ·ããªã fact5: ããç
§èããšããããšãçºçããã°ã空ããããšã¯çããããã€ãããããšããããšã¯çããªãããšããããšã¯åœã fact6: ããæé
·ããšããããšã¯èµ·ãããªããªãã°ãå«ãããã¯èµ·ããããŸã¢ãããšããããšãèµ·ããªãããšããããšã¯ééãã fact7: ãããçããšæé
·ããšããããšãçºçããããšããããšãééããªãã°æé
·ããšããããšã¯çºçããªã fact8: ãçããšæé
·ããšããããšäž¡æ¹ã¯èµ·ããããšããããšã¯ã空ããããšãçããªãããšããããšãå¥æ©ã fact9: ããµãããããã€ããããšãèµ·ãããªãããªããšã©ãããããããããšã¯èµ·ããããšããããšããŸã¢ãããšããããšãçºçãããšããããšã«èµ·å ãã fact10: ããªããšã©ãããããããããšãçããªãããšããããšã¯ãæ»
ã³ãããšãšçžŠç£åã«æºãããããšãçããããšããããšããããã fact11: ãç
§èããšããããšãšãã€ãããããšããããšäž¡æ¹ãçããããšããããšã¯ãå°éåã«å€ªããããšã¯çããªãããšããããšãåå ã fact12: çºè°ã§ã¯ãªãå°å Žã¹ãŒããŒã«æµ®ãåºãããšãèµ·ãã fact13: åã»è«èšªããšãããããããšãçºçããªã fact14: ããç
§èããšããããšã¯çºçããã°çžŠç£åã«æºãããããšã¯çºçããªããå«ãããã¯èµ·ãããªã fact15: ã空ããããšã§ã¯ãªãç®åºåºŠããšããããšãçããããšããããšãåã»è«èšªããšãããããããšãèµ·ããªããšããããšãå¥æ©ã fact16: ããã瞊ç£åã«æºãããããšã¯çºçããªãããšããããšã¯æ¬åœãªãã°ãŠã°ããããšããããšãšæ»
ã³ãããšäž¡æ¹ãèµ·ãã fact17: ããã空ããããšãçããããã€ãããããšããããšã¯çºçããªãããšããããšã¯èª€ããªãã°ã空ããããšãèµ·ããªãããšããããšã¯äºå®ã fact18: å°éåã«å€ªããããšãèµ·ããªã fact19: ããã¡èŸããšããããšãçããªããæ¥è®åŽããŸãããããšã¯èµ·ããããšããããšã¯æãç«ã€ ; $hypothesis$ = ãçºè°ãçããªãããããå°å Žã¹ãŒããŒã«æµ®ãåºãããšã¯çºçããããšããããšãæ¬åœã ãšããããšã¯ãªã ; $proof$ = | fact12 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {F} -> {D} fact2: (¬{BL} & {U}) fact3: ¬{L} -> ({I} & {K}) fact4: ¬{AA} fact5: {I} -> ¬({H} & ¬{J}) fact6: ¬{F} -> ¬({E} & ¬{D}) fact7: ¬({G} & {F}) -> ¬{F} fact8: ¬{H} -> ({G} & {F}) fact9: {D} -> (¬{ET} & {C}) fact10: ¬{C} -> ({A} & {B}) fact11: ¬{K} -> ({I} & {J}) fact12: (¬{AA} & {AB}) fact13: ¬{M} fact14: {I} -> (¬{B} & ¬{E}) fact15: ¬{M} -> (¬{H} & {L}) fact16: ¬{B} -> ({Q} & {A}) fact17: ¬({H} & ¬{J}) -> ¬{H} fact18: ¬{K} fact19: (¬{HQ} & {JC}) ; $hypothesis$ = ¬(¬{AA} & {AB}) ; $proof$ = | fact12 -> hypothesis; __DISPROVED__ |
0.3 | ããããå°éå°ãªãã°åå
åã§ã²ãããªãããã®ãããããšããããšãééãã | ¬((Ex): {A}x -> ({AA}x & ¬{AB}x)) | fact1: ãããã®ãã¬ãããå°éå°ãªãã°ããã¯åå
åã ãããã¯ã²ãããªã fact2: ãããåé宿ã«ã§ãããã°åè¡ãã²ãããããã¹ãã ãšããããšã¯ãªãããã®ããã fact3: ãããã®ãã¬ãããåçã培ãã°ãããã¡ã£ã¡ãããªã fact4: ãããããã®ãã¬ããã¯çºå®ã«ãŸããåºãããšããããšãæãç«ãŠã°ãã®ãã¬ãããå°éå°ã ãé梚åãå²ãæ»ããªãããšããããšã¯æ¬åœã fact5: ããããã€ãªããªãã°ãããµããããããæã¡ç ããªãããã®ããã fact6: ãããéã©ããªãã°ãšãããããžãããã§ãªãããã®ã¯ãã fact7: ã°ã°ã£ã¡ããã®ãæŸå³¶å
é·ã ããããåçã培ããšããããšããªã fact8: ãããäŒé»ãªãã°ãããã ãåœéæŸæ ããããããªãããã®ã¯ãã fact9: ãããåè¿«ãªãã°ããããšããããšããªãããã®ããã fact10: ããããã®ãã¬ãããèãããããšããããšã¯äºå®ãªãã°ããã¯å°éå°ã§ãªã | fact1: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) fact2: (Ex): {EU}x -> ({FS}x & ¬{T}x) fact3: {CA}{aa} -> ¬{DT}{aa} fact4: {FI}{aa} -> ({A}{aa} & ¬{CH}{aa}) fact5: (Ex): {AH}x -> ({IJ}x & ¬{GE}x) fact6: (Ex): {EI}x -> ({O}x & ¬{GF}x) fact7: (x): {GN}x -> ({BR}x & ¬{CA}x) fact8: (Ex): {AI}x -> ({AN}x & ¬{FF}x) fact9: (Ex): {EC}x -> ¬{D}x fact10: {IR}{aa} -> ¬{A}{aa} | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | ãããã®ã¿ã©ããã¯ã°ã°ã£ã¡ããªãã°ãããæŸå³¶å
é·ã ãåçã培ããšããããšããªã | {GN}{bs} -> ({BR}{bs} & ¬{CA}{bs}) | [
"fact11 -> hypothesis;"
] | 1 | 1 | 1 | 9 | 0 | 9 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãããã®ãã¬ãããå°éå°ãªãã°ããã¯åå
åã ãããã¯ã²ãããªã fact2: ãããåé宿ã«ã§ãããã°åè¡ãã²ãããããã¹ãã ãšããããšã¯ãªãããã®ããã fact3: ãããã®ãã¬ãããåçã培ãã°ãããã¡ã£ã¡ãããªã fact4: ãããããã®ãã¬ããã¯çºå®ã«ãŸããåºãããšããããšãæãç«ãŠã°ãã®ãã¬ãããå°éå°ã ãé梚åãå²ãæ»ããªãããšããããšã¯æ¬åœã fact5: ããããã€ãªããªãã°ãããµããããããæã¡ç ããªãããã®ããã fact6: ãããéã©ããªãã°ãšãããããžãããã§ãªãããã®ã¯ãã fact7: ã°ã°ã£ã¡ããã®ãæŸå³¶å
é·ã ããããåçã培ããšããããšããªã fact8: ãããäŒé»ãªãã°ãããã ãåœéæŸæ ããããããªãããã®ã¯ãã fact9: ãããåè¿«ãªãã°ããããšããããšããªãããã®ããã fact10: ããããã®ãã¬ãããèãããããšããããšã¯äºå®ãªãã°ããã¯å°éå°ã§ãªã ; $hypothesis$ = ããããå°éå°ãªãã°åå
åã§ã²ãããªãããã®ãããããšããããšãééãã ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) fact2: (Ex): {EU}x -> ({FS}x & ¬{T}x) fact3: {CA}{aa} -> ¬{DT}{aa} fact4: {FI}{aa} -> ({A}{aa} & ¬{CH}{aa}) fact5: (Ex): {AH}x -> ({IJ}x & ¬{GE}x) fact6: (Ex): {EI}x -> ({O}x & ¬{GF}x) fact7: (x): {GN}x -> ({BR}x & ¬{CA}x) fact8: (Ex): {AI}x -> ({AN}x & ¬{FF}x) fact9: (Ex): {EC}x -> ¬{D}x fact10: {IR}{aa} -> ¬{A}{aa} ; $hypothesis$ = ¬((Ex): {A}x -> ({AA}x & ¬{AB}x)) ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ |
0.3 | äºå·å³ ã«èª¬ãããããšãèµ·ãããªã | ¬{A} | fact1: ããæãããšããããšãèµ·ããªããªãã°ãç©ºæŒ ã«ããããããšã¯çºçãããçžä¹ã¯çºçããããšããããšã¯åã fact2: ããæ·æ±°ãçããã°ãåŒãã¯çºçããªããŠäºå·å³ ã«èª¬ãããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšããªã fact3: ããã¿ãã€ããå± ãããšãçºçãããå€åœ¢ãèµ·ããããšããããšãé ã¶æ ¹å³ ãå£èª¬ãèœãšãããšãèµ·ãããªããšããããšã«èªçºããã fact4: ããåŒããšæ·æ±°äž¡æ¹ã¯çºçããã°äºå·å³ ã«èª¬ãããããšã¯çºçããªã fact5: ãããç©ºæŒ ã«ããããããšãšçžä¹äž¡æ¹ã¯èµ·ããããšããããšãæãç«ããªããªãã°ç©ºæŒ ã«ããããããšã¯èµ·ãããªã fact6: ããã女女ãããšããããšãæ±äžæ¡ã«ãªããããšãäž¡æ¹ã¯çããããšããããšã¯ééããªãã°ãããããçºçããªã fact7: ããããåŒãã¯èµ·ãããªããäºå·å³ ã«èª¬ãããããšã¯çããªãããšããããšãäºå®ã ããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°é²æ¢ãçãã fact8: ã»ãããããšãèµ·ãã fact9: åŒãã¯èµ·ãã fact10: äºå·å³ ã«èª¬ãããããšãšåŒãäž¡æ¹ã¯èµ·ãã fact11: ããæããããšããããšãçããªããªãã°ã女女ãããšããããšãæ±äžæ¡ã«ãªããããšãäž¡æ¹ã¯èµ·ããããšããããšãåã fact12: ãããåã³ãèµ·ããªããŠæŠåŸ³ãã€ããããããšã¯çºçããªãããšããããšãæãç«ã€ãšããããšããªããªãã°åã³ã¯èµ·ãã fact13: åã³ã¯èµ·ãããšããããšã¯ãæ·æ±°ãèµ·ããããšããããšã®åå ãšãªã fact14: ãããããã¯çããªãããšããããšã¯ãã¡ããããæããããšãšå°æããšããããšãçããããšããããšããããã fact15: ããç©ºæŒ ã«ããããããšãèµ·ããªããªãã°ãçŽããšé ã¶æ ¹å³ ãå£èª¬ãèœãšãããšäž¡æ¹ã¯èµ·ããããšããããšãééãã fact16: ãããçŽããšé ã¶æ ¹å³ ãå£èª¬ãèœãšãããšäž¡æ¹ã¯çããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°é ã¶æ ¹å³ ãå£èª¬ãèœãšãããšãèµ·ãããªã fact17: ããå°æããšããããšã¯èµ·ããã°ãåã³ã¯èµ·ããªããŠæŠåŸ³ãã€ããããããšã¯èµ·ããªãããšããããšãééãã fact18: ãæŽåã¯èµ·ãããªããããããã€ããšã¯èµ·ããããšããããšãå€åœ¢ã¯çãããšããããšã«ããçãã fact19: ããæŽåãèµ·ãããªããããããã€ããšãçããã°æããããšããããšãçããªã | fact1: ¬{T} -> ¬({Q} & {S}) fact2: {C} -> ¬(¬{B} & ¬{A}) fact3: ¬{P} -> ({O} & {N}) fact4: ({B} & {C}) -> ¬{A} fact5: ¬({Q} & {S}) -> ¬{Q} fact6: ¬({I} v {J}) -> ¬{H} fact7: ¬(¬{B} & ¬{A}) -> {HN} fact8: {HE} fact9: {B} fact10: ({A} & {B}) fact11: ¬{K} -> ¬({I} v {J}) fact12: ¬(¬{D} & ¬{F}) -> {D} fact13: {D} -> {C} fact14: ¬{H} -> ({G} & {E}) fact15: ¬{Q} -> ¬({R} & {P}) fact16: ¬({R} & {P}) -> ¬{P} fact17: {E} -> ¬(¬{D} & ¬{F}) fact18: {N} -> (¬{M} & {L}) fact19: (¬{M} & {L}) -> ¬{K} | [
"fact10 -> hypothesis;"
] | [
"fact10 -> hypothesis;"
] | äºå·å³ ã«èª¬ãããããšã¯çºçããªã | ¬{A} | [] | 5 | 1 | 1 | 18 | 0 | 18 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããæãããšããããšãèµ·ããªããªãã°ãç©ºæŒ ã«ããããããšã¯çºçãããçžä¹ã¯çºçããããšããããšã¯åã fact2: ããæ·æ±°ãçããã°ãåŒãã¯çºçããªããŠäºå·å³ ã«èª¬ãããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšããªã fact3: ããã¿ãã€ããå± ãããšãçºçãããå€åœ¢ãèµ·ããããšããããšãé ã¶æ ¹å³ ãå£èª¬ãèœãšãããšãèµ·ãããªããšããããšã«èªçºããã fact4: ããåŒããšæ·æ±°äž¡æ¹ã¯çºçããã°äºå·å³ ã«èª¬ãããããšã¯çºçããªã fact5: ãããç©ºæŒ ã«ããããããšãšçžä¹äž¡æ¹ã¯èµ·ããããšããããšãæãç«ããªããªãã°ç©ºæŒ ã«ããããããšã¯èµ·ãããªã fact6: ããã女女ãããšããããšãæ±äžæ¡ã«ãªããããšãäž¡æ¹ã¯çããããšããããšã¯ééããªãã°ãããããçºçããªã fact7: ããããåŒãã¯èµ·ãããªããäºå·å³ ã«èª¬ãããããšã¯çããªãããšããããšãäºå®ã ããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°é²æ¢ãçãã fact8: ã»ãããããšãèµ·ãã fact9: åŒãã¯èµ·ãã fact10: äºå·å³ ã«èª¬ãããããšãšåŒãäž¡æ¹ã¯èµ·ãã fact11: ããæããããšããããšãçããªããªãã°ã女女ãããšããããšãæ±äžæ¡ã«ãªããããšãäž¡æ¹ã¯èµ·ããããšããããšãåã fact12: ãããåã³ãèµ·ããªããŠæŠåŸ³ãã€ããããããšã¯çºçããªãããšããããšãæãç«ã€ãšããããšããªããªãã°åã³ã¯èµ·ãã fact13: åã³ã¯èµ·ãããšããããšã¯ãæ·æ±°ãèµ·ããããšããããšã®åå ãšãªã fact14: ãããããã¯çããªãããšããããšã¯ãã¡ããããæããããšãšå°æããšããããšãçããããšããããšããããã fact15: ããç©ºæŒ ã«ããããããšãèµ·ããªããªãã°ãçŽããšé ã¶æ ¹å³ ãå£èª¬ãèœãšãããšäž¡æ¹ã¯èµ·ããããšããããšãééãã fact16: ãããçŽããšé ã¶æ ¹å³ ãå£èª¬ãèœãšãããšäž¡æ¹ã¯çããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°é ã¶æ ¹å³ ãå£èª¬ãèœãšãããšãèµ·ãããªã fact17: ããå°æããšããããšã¯èµ·ããã°ãåã³ã¯èµ·ããªããŠæŠåŸ³ãã€ããããããšã¯èµ·ããªãããšããããšãééãã fact18: ãæŽåã¯èµ·ãããªããããããã€ããšã¯èµ·ããããšããããšãå€åœ¢ã¯çãããšããããšã«ããçãã fact19: ããæŽåãèµ·ãããªããããããã€ããšãçããã°æããããšããããšãçããªã ; $hypothesis$ = äºå·å³ ã«èª¬ãããããšãèµ·ãããªã ; $proof$ = | fact10 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{T} -> ¬({Q} & {S}) fact2: {C} -> ¬(¬{B} & ¬{A}) fact3: ¬{P} -> ({O} & {N}) fact4: ({B} & {C}) -> ¬{A} fact5: ¬({Q} & {S}) -> ¬{Q} fact6: ¬({I} v {J}) -> ¬{H} fact7: ¬(¬{B} & ¬{A}) -> {HN} fact8: {HE} fact9: {B} fact10: ({A} & {B}) fact11: ¬{K} -> ¬({I} v {J}) fact12: ¬(¬{D} & ¬{F}) -> {D} fact13: {D} -> {C} fact14: ¬{H} -> ({G} & {E}) fact15: ¬{Q} -> ¬({R} & {P}) fact16: ¬({R} & {P}) -> ¬{P} fact17: {E} -> ¬(¬{D} & ¬{F}) fact18: {N} -> (¬{M} & {L}) fact19: (¬{M} & {L}) -> ¬{K} ; $hypothesis$ = ¬{A} ; $proof$ = | fact10 -> hypothesis; __DISPROVED__ |
0.3 | ãããšããšããããšã¯èµ·ãããªãããšããããšãæ£ãã | ¬{A} | fact1: ãããæªå€©åã¯çããªãããšããããšãæãç«ãŠã°ããšããšããããšã¯çãããå€ããããšããããšãèµ·ãã | fact1: ¬{C} -> ({A} & {B}) | [] | [] | ããšããšããããšã¯èµ·ãã | {A} | [] | 6 | 1 | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããæªå€©åã¯çããªãããšããããšãæãç«ãŠã°ããšããšããããšã¯çãããå€ããããšããããšãèµ·ãã ; $hypothesis$ = ãããšããšããããšã¯èµ·ãããªãããšããããšãæ£ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{C} -> ({A} & {B}) ; $hypothesis$ = ¬{A} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããããã®èã¯è³ºããªããŠããã¯èå£æ²Œã«ãã¿ã€ããšããããšã¯ãªãããšããããšãæ¬åœã ãšããããšããªããªãã°ãã®èã倩éã«æ³ããšããããšããªãããšããããšã¯åœã | ¬(¬(¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa}) | fact1: ãããäœãã¯ã¢ã¹ã¿ãã³ã«ãããšããããšããªããããã¯ããããªãããšããããšã¯ééããªãã°ããã¯è³ºããªã fact2: ããããäœãã¯è³ºããªããããã¯èå£æ²Œã«ãã¿ã€ããšããããšã¯ãªãããšããããšãäºå®ãšç°ãªãã°ããã倩éã«æ³ãããšããããšãåœã ãšããããšããªã fact3: ããããã®èãèçµµã«æ··ãããããšããããšããªããããã倩éã«æ³ããšããããšããªãããšããããšãæãç«ããªããªãã°ããããã³ããšããããšã¯ãªã fact4: ããããããã®ã¯ãµãããããªããããã¯å
èŠãããªãããšããããšã¯ééããªãã°ãããæ²ç°ã«ããè¿«ããšããããšããªã fact5: ããããã®èã賺ããªããããã¯èå£æ²Œã«ãã¿ã€ãããšããããšã¯èª€ããªãã°ããã倩éã«æ³ããšããããšã¯ãªã fact6: ããããã®èã¯ãããã§ãªããããã倩éã«æ³ããªãããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãããè³è°ããšããããšããªã fact7: ããããã®èã賺ããšããããšã¯ãªãããããã€ã³ãã¢ã§ãªãããšããããšã¯ééããªãã°ããã¯é£ããšããããšã¯ãªã fact8: ãããããã®ã賺ããªããŠèå£æ²Œã«ãã¿ã€ããšããããšã¯ãªããªãã°ããã倩éã«æ³ããšããããšã¯ãªã fact9: ããããã®èã賺ãã°ããã®èã倩éã«æ³ããªãããšããããšãæ¬åœã ããšããããšã¯æ¬åœã fact10: ãããã®èã賺ããšããããšã¯ãªããŠèå£æ²Œã«ãã¿ã€ããªããªãã°ããã¯å€©éã«æ³ããšããããšããªã fact11: ãããããããã®ã賺ããšããããšã¯ãªãããããèå£æ²Œã«ãã¿ã€ãããšããããšãäºå®ãšç°ãªããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯å€©éã«æ³ããšããããšããªã fact12: ããããã®èã¯è³ºããšããããšããªããŠããã¯èå£æ²Œã«ãã¿ã€ããªãããšããããšãåœãªãã°ããã¯å€©éã«æ³ã fact13: ãããããã®ã¯è³ºãã°ããã¯å€©éã«æ³ããšããããšããªã fact14: ããããããã®ã¯ã±ã€ããå
¥ãçŽããšããããšããªãããããããšããããšããªãããšããããšãæãç«ããªããªãã°ããããã£ãŽã©ããšããããšã¯ãªã fact15: ããããã®ãããã³ãŒããçå°Ÿã§ãªããããã倩éã«æ³ããšããããšããªãããšããããšãåœãªãã°ãããæ£ãããšããããšã¯ãªã fact16: ãããäœãã¯è³ºããªããŠããã¯èå£æ²Œã«ãã¿ã€ããªãããšããããšã誀ããªãã°ããã¯å€©éã«æ³ããšããããšã¯ãªã fact17: ããããã®èã倧ãªãŒã°ã ãšããããšã¯ãªããããã倧åçŸäºã ãšããããšããªãããšããããšã¯èª€ããªãã°ãããèå£æ²Œã«ãã¿ã€ããšããããšã¯ãªã fact18: ããããããã®ã¯ããããã°ããªããã®ã§ãã£ãŠäºæœ
æšã§ãªããã®ããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯ç
ãããšããããšããªã fact19: ããããã®ãããŒã«ã¯ãããããšããããšããªããŠè³ºããšããããšããªãããšããããšã¯åœãªãã°ããã¯æå±±èäžã ãšããããšã¯ãªã fact20: ãããäœãã¯èšãæãããšããããšã¯ãªããŠåæšæœå²³ã ãšããããšã¯ãªãããšããããšãåãªãã°ãããèå
ã ãšããããšã¯ãªã | fact1: (x): ¬(¬{BE}x & ¬{FO}x) -> ¬{AA}x fact2: (x): ¬(¬{AA}x & ¬{AB}x) -> {B}x fact3: ¬(¬{HE}{aa} & ¬{B}{aa}) -> ¬{EN}{aa} fact4: (x): ¬(¬{FN}x & ¬{DE}x) -> ¬{IG}x fact5: ¬(¬{AA}{aa} & {AB}{aa}) -> ¬{B}{aa} fact6: ¬(¬{CQ}{aa} & ¬{B}{aa}) -> ¬{BM}{aa} fact7: ¬(¬{AA}{aa} & ¬{GC}{aa}) -> ¬{EQ}{aa} fact8: (x): (¬{AA}x & ¬{AB}x) -> ¬{B}x fact9: {AA}{aa} -> ¬{B}{aa} fact10: (¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa} fact11: (x): ¬(¬{AA}x & {AB}x) -> ¬{B}x fact12: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa} fact13: (x): {AA}x -> ¬{B}x fact14: (x): ¬(¬{IJ}x & ¬{S}x) -> ¬{GQ}x fact15: ¬(¬{IC}{da} & ¬{B}{da}) -> ¬{AG}{da} fact16: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x fact17: ¬(¬{HH}{aa} & ¬{FA}{aa}) -> ¬{AB}{aa} fact18: (x): ¬(¬{GI}x & ¬{HD}x) -> ¬{DK}x fact19: ¬(¬{H}{cd} & ¬{AA}{cd}) -> ¬{AP}{cd} fact20: (x): ¬(¬{DD}x & ¬{JJ}x) -> ¬{AE}x | [
"fact16 -> hypothesis;"
] | [
"fact16 -> hypothesis;"
] | ããããã®èãã¢ã¹ã¿ãã³ã«ãããªããããããªãããšããããšãäºå®ãšç°ãªãã°ããã¯è³ºããšããããšã¯ãªã | ¬(¬{BE}{aa} & ¬{FO}{aa}) -> ¬{AA}{aa} | [
"fact21 -> hypothesis;"
] | 1 | 1 | 1 | 19 | 0 | 19 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãããäœãã¯ã¢ã¹ã¿ãã³ã«ãããšããããšããªããããã¯ããããªãããšããããšã¯ééããªãã°ããã¯è³ºããªã fact2: ããããäœãã¯è³ºããªããããã¯èå£æ²Œã«ãã¿ã€ããšããããšã¯ãªãããšããããšãäºå®ãšç°ãªãã°ããã倩éã«æ³ãããšããããšãåœã ãšããããšããªã fact3: ããããã®èãèçµµã«æ··ãããããšããããšããªããããã倩éã«æ³ããšããããšããªãããšããããšãæãç«ããªããªãã°ããããã³ããšããããšã¯ãªã fact4: ããããããã®ã¯ãµãããããªããããã¯å
èŠãããªãããšããããšã¯ééããªãã°ãããæ²ç°ã«ããè¿«ããšããããšããªã fact5: ããããã®èã賺ããªããããã¯èå£æ²Œã«ãã¿ã€ãããšããããšã¯èª€ããªãã°ããã倩éã«æ³ããšããããšã¯ãªã fact6: ããããã®èã¯ãããã§ãªããããã倩éã«æ³ããªãããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãããè³è°ããšããããšããªã fact7: ããããã®èã賺ããšããããšã¯ãªãããããã€ã³ãã¢ã§ãªãããšããããšã¯ééããªãã°ããã¯é£ããšããããšã¯ãªã fact8: ãããããã®ã賺ããªããŠèå£æ²Œã«ãã¿ã€ããšããããšã¯ãªããªãã°ããã倩éã«æ³ããšããããšã¯ãªã fact9: ããããã®èã賺ãã°ããã®èã倩éã«æ³ããªãããšããããšãæ¬åœã ããšããããšã¯æ¬åœã fact10: ãããã®èã賺ããšããããšã¯ãªããŠèå£æ²Œã«ãã¿ã€ããªããªãã°ããã¯å€©éã«æ³ããšããããšããªã fact11: ãããããããã®ã賺ããšããããšã¯ãªãããããèå£æ²Œã«ãã¿ã€ãããšããããšãäºå®ãšç°ãªããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯å€©éã«æ³ããšããããšããªã fact12: ããããã®èã¯è³ºããšããããšããªããŠããã¯èå£æ²Œã«ãã¿ã€ããªãããšããããšãåœãªãã°ããã¯å€©éã«æ³ã fact13: ãããããã®ã¯è³ºãã°ããã¯å€©éã«æ³ããšããããšããªã fact14: ããããããã®ã¯ã±ã€ããå
¥ãçŽããšããããšããªãããããããšããããšããªãããšããããšãæãç«ããªããªãã°ããããã£ãŽã©ããšããããšã¯ãªã fact15: ããããã®ãããã³ãŒããçå°Ÿã§ãªããããã倩éã«æ³ããšããããšããªãããšããããšãåœãªãã°ãããæ£ãããšããããšã¯ãªã fact16: ãããäœãã¯è³ºããªããŠããã¯èå£æ²Œã«ãã¿ã€ããªãããšããããšã誀ããªãã°ããã¯å€©éã«æ³ããšããããšã¯ãªã fact17: ããããã®èã倧ãªãŒã°ã ãšããããšã¯ãªããããã倧åçŸäºã ãšããããšããªãããšããããšã¯èª€ããªãã°ãããèå£æ²Œã«ãã¿ã€ããšããããšã¯ãªã fact18: ããããããã®ã¯ããããã°ããªããã®ã§ãã£ãŠäºæœ
æšã§ãªããã®ããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯ç
ãããšããããšããªã fact19: ããããã®ãããŒã«ã¯ãããããšããããšããªããŠè³ºããšããããšããªãããšããããšã¯åœãªãã°ããã¯æå±±èäžã ãšããããšã¯ãªã fact20: ãããäœãã¯èšãæãããšããããšã¯ãªããŠåæšæœå²³ã ãšããããšã¯ãªãããšããããšãåãªãã°ãããèå
ã ãšããããšã¯ãªã ; $hypothesis$ = ãããããã®èã¯è³ºããªããŠããã¯èå£æ²Œã«ãã¿ã€ããšããããšã¯ãªãããšããããšãæ¬åœã ãšããããšããªããªãã°ãã®èã倩éã«æ³ããšããããšããªãããšããããšã¯åœã ; $proof$ = | fact16 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬(¬{BE}x & ¬{FO}x) -> ¬{AA}x fact2: (x): ¬(¬{AA}x & ¬{AB}x) -> {B}x fact3: ¬(¬{HE}{aa} & ¬{B}{aa}) -> ¬{EN}{aa} fact4: (x): ¬(¬{FN}x & ¬{DE}x) -> ¬{IG}x fact5: ¬(¬{AA}{aa} & {AB}{aa}) -> ¬{B}{aa} fact6: ¬(¬{CQ}{aa} & ¬{B}{aa}) -> ¬{BM}{aa} fact7: ¬(¬{AA}{aa} & ¬{GC}{aa}) -> ¬{EQ}{aa} fact8: (x): (¬{AA}x & ¬{AB}x) -> ¬{B}x fact9: {AA}{aa} -> ¬{B}{aa} fact10: (¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa} fact11: (x): ¬(¬{AA}x & {AB}x) -> ¬{B}x fact12: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa} fact13: (x): {AA}x -> ¬{B}x fact14: (x): ¬(¬{IJ}x & ¬{S}x) -> ¬{GQ}x fact15: ¬(¬{IC}{da} & ¬{B}{da}) -> ¬{AG}{da} fact16: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x fact17: ¬(¬{HH}{aa} & ¬{FA}{aa}) -> ¬{AB}{aa} fact18: (x): ¬(¬{GI}x & ¬{HD}x) -> ¬{DK}x fact19: ¬(¬{H}{cd} & ¬{AA}{cd}) -> ¬{AP}{cd} fact20: (x): ¬(¬{DD}x & ¬{JJ}x) -> ¬{AE}x ; $hypothesis$ = ¬(¬(¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa}) ; $proof$ = | fact16 -> hypothesis; __DISPROVED__ |
0.3 | ãã®åå
žã¯ããŸã | {B}{b} | fact1: ãã®é·ç®¡ãç®ã°ãã fact2: ããã®åŸè¢ããªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ãããšããããšã¯ãªããŠãããæ±åæ±ã ãšããããšããªãããšããããšã¯èª€ãã fact3: ããŸããããšããããšã¯ãªããã®ãããŸããŠå¥å
šãåŸ
ã¡ä»ãã fact4: ãããããã®ã¯ããŸãããããããã¯å€åœ¢ãæ±ç· ããããããã¯äž¡æ¹ã fact5: ããããã®åŸè¢ã¯ãªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ãããšããããšããªããæ±åæ±ã§ãªãããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãã®ç äžããªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ããªã fact6: ããããã®ç äžã¯ãããšã©ããããããããããšããããšããªãããšããããšã¯æãç«ããªããªãã°ãã®çå Žãæ±äžå±±ã«åžãå¯ãã fact7: ãããã®ç äžããªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ãããšããããšããªããªãã°ãããããããšã©ããããããããããªãããšããããšãåœã fact8: ãããã®åå
žã¯ããŸããããªãã°ãã®é·ç®¡ã¯ããŸã fact9: ãã®é·ç®¡ã¯æ ¹ã¶ãããç®ã°ãã fact10: ãããã®é·ç®¡ãæ ¹ã¶ãããŠç®ã°ãããªãã°ãã®åå
žãããŸããšããããšã¯ãªã | fact1: {AB}{a} fact2: ¬(¬{G}{e} & ¬{K}{e}) fact3: (x): ¬{C}x -> ({B}x & {A}x) fact4: (x): ({C}x v {D}x) fact5: ¬(¬{G}{e} & ¬{K}{e}) -> ¬{G}{c} fact6: ¬({E}{c} & ¬{F}{c}) -> {DN}{ef} fact7: ¬{G}{c} -> ¬({E}{c} & ¬{F}{c}) fact8: {C}{b} -> {B}{a} fact9: ({AA}{a} & {AB}{a}) fact10: ({AA}{a} & {AB}{a}) -> ¬{B}{b} | [
"fact10 & fact9 -> hypothesis;"
] | [
"fact10 & fact9 -> hypothesis;"
] | ãã®åå
žãããŸã | {B}{b} | [
"fact11 -> int1: ãããã®åå
žã¯ããŸããããšããããšããªããªãã°ããã¯ããŸããå¥å
šãåŸ
ã¡ä»ãã;"
] | 5 | 1 | 1 | 8 | 0 | 8 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®é·ç®¡ãç®ã°ãã fact2: ããã®åŸè¢ããªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ãããšããããšã¯ãªããŠãããæ±åæ±ã ãšããããšããªãããšããããšã¯èª€ãã fact3: ããŸããããšããããšã¯ãªããã®ãããŸããŠå¥å
šãåŸ
ã¡ä»ãã fact4: ãããããã®ã¯ããŸãããããããã¯å€åœ¢ãæ±ç· ããããããã¯äž¡æ¹ã fact5: ããããã®åŸè¢ã¯ãªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ãããšããããšããªããæ±åæ±ã§ãªãããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãã®ç äžããªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ããªã fact6: ããããã®ç äžã¯ãããšã©ããããããããããšããããšããªãããšããããšã¯æãç«ããªããªãã°ãã®çå Žãæ±äžå±±ã«åžãå¯ãã fact7: ãããã®ç äžããªã¹ãã³ã»ãã«ã³åžåœããã¡ã¥ãããšããããšããªããªãã°ãããããããšã©ããããããããããªãããšããããšãåœã fact8: ãããã®åå
žã¯ããŸããããªãã°ãã®é·ç®¡ã¯ããŸã fact9: ãã®é·ç®¡ã¯æ ¹ã¶ãããç®ã°ãã fact10: ãããã®é·ç®¡ãæ ¹ã¶ãããŠç®ã°ãããªãã°ãã®åå
žãããŸããšããããšã¯ãªã ; $hypothesis$ = ãã®åå
žã¯ããŸã ; $proof$ = | fact10 & fact9 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {AB}{a} fact2: ¬(¬{G}{e} & ¬{K}{e}) fact3: (x): ¬{C}x -> ({B}x & {A}x) fact4: (x): ({C}x v {D}x) fact5: ¬(¬{G}{e} & ¬{K}{e}) -> ¬{G}{c} fact6: ¬({E}{c} & ¬{F}{c}) -> {DN}{ef} fact7: ¬{G}{c} -> ¬({E}{c} & ¬{F}{c}) fact8: {C}{b} -> {B}{a} fact9: ({AA}{a} & {AB}{a}) fact10: ({AA}{a} & {AB}{a}) -> ¬{B}{b} ; $hypothesis$ = {B}{b} ; $proof$ = | fact10 & fact9 -> hypothesis; __DISPROVED__ |
0.3 | æŠé²ãçãã | {A} | fact1: ããæãããšãçãã fact2: çªã£ã±ãã¯èµ·ãã fact3: æŠé²ãçãã fact4: ã¬ãžã¹ã¿ã³ã¹ããéºãããšããããšãçºçãããæŠé²ã¯çºçããªãããšããããšã«ç¹ãã fact5: çªçµãçºçãã fact6: ããèŸããšããããšãçºçãã fact7: ããç«èšŒã¯çºçããªããªãã°å§Šèšã¯çºçãããæçµãèµ·ããªã fact8: äžæºè¶³ã¯èµ·ãã fact9: ããæçµã¯çºçããªããªãã°ã¬ãžã¹ã¿ã³ã¹ã¯èµ·ããããããŒã«ã«ç£ãããšãèµ·ãã fact10: ããçŠãã£ãããšããããšã¯èµ·ãããªããªãã°èªãåºãããšã¯èµ·ããããããç«èšŒã¯çããªã fact11: çŸã
ãããšããããšã¯çºçãã | fact1: {DJ} fact2: {CD} fact3: {A} fact4: {B} -> ({CO} & ¬{A}) fact5: {BK} fact6: {BD} fact7: ¬{F} -> ({E} & ¬{D}) fact8: {K} fact9: ¬{D} -> ({B} & {C}) fact10: ¬{H} -> ({G} & ¬{F}) fact11: {IR} | [
"fact3 -> hypothesis;"
] | [
"fact3 -> hypothesis;"
] | éºãããšããããšã¯èµ·ãã | {CO} | [] | 9 | 1 | 0 | 10 | 0 | 10 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããæãããšãçãã fact2: çªã£ã±ãã¯èµ·ãã fact3: æŠé²ãçãã fact4: ã¬ãžã¹ã¿ã³ã¹ããéºãããšããããšãçºçãããæŠé²ã¯çºçããªãããšããããšã«ç¹ãã fact5: çªçµãçºçãã fact6: ããèŸããšããããšãçºçãã fact7: ããç«èšŒã¯çºçããªããªãã°å§Šèšã¯çºçãããæçµãèµ·ããªã fact8: äžæºè¶³ã¯èµ·ãã fact9: ããæçµã¯çºçããªããªãã°ã¬ãžã¹ã¿ã³ã¹ã¯èµ·ããããããŒã«ã«ç£ãããšãèµ·ãã fact10: ããçŠãã£ãããšããããšã¯èµ·ãããªããªãã°èªãåºãããšã¯èµ·ããããããç«èšŒã¯çããªã fact11: çŸã
ãããšããããšã¯çºçãã ; $hypothesis$ = æŠé²ãçãã ; $proof$ = | fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {DJ} fact2: {CD} fact3: {A} fact4: {B} -> ({CO} & ¬{A}) fact5: {BK} fact6: {BD} fact7: ¬{F} -> ({E} & ¬{D}) fact8: {K} fact9: ¬{D} -> ({B} & {C}) fact10: ¬{H} -> ({G} & ¬{F}) fact11: {IR} ; $hypothesis$ = {A} ; $proof$ = | fact3 -> hypothesis; __PROVED__ |
0.3 | ããããã©ããããŠå±±æ¬åã«åºã§ç«ã€ããšããããšãæãç«ããªãããã®ã¯ããããšããããšãééãã | ¬((Ex): ¬({AA}x & {AB}x)) | fact1: ããäœãã¯å奜ãããã¯ããã°ãããæ±äº¬ã fact2: ãããã®å£°éã芳å
ã«ç©ºããã¶ããšããããšã¯ãªããªãã°ããã¯ç«åãããããçæãã fact3: ããããã®å£°éã¯æ±äº¬ã ããšããããšã¯æãç«ãŠã°ãã®æ°å
µã¯ç¯èŸãç·ŽãçŽããªããé²æ¥ã ãšããããšããªã fact4: ããäœããç«åãã°ããããå奜ãããã¯ããããšããããšã¯çå®ã fact5: ããäœãã¯ç«åããããã¯çæãããšããããšããªããäž¡æ¹ãªãã°ããã¯å奜ãããã¯ãããªã fact6: ãããããã®ã¯èŠ³å
ã«ç©ºããã¶ããªããªãã°ããã¯ç«åãããããã¯ããã¯çæãããšããããšããªã fact7: ããäœããé²æ¥ã§ãªããªãã°ãããããã©ããããŠãããã¹ãã¬ãŒãåã¡ã ããšããããšã¯æãç«ã€ãšããããšããªã fact8: ããã®ç£åããã©ãããã最ãããšããããšãçå®ã ãšããããšããªã fact9: ããããã®ã€ãã§ãŠã¯ãããããããã·ã£ãŠãŠãŠã§ãªãããšããããšãåãªãã°ãã®å£°éã芳å
ã«ç©ºããã¶ããšããããšã¯ãªã fact10: ããã®èŽè
ã泰次ã ãéãããšããããšã¯æãç«ããªã fact11: ãã®åžžç¿ç¯ã¯ããã fact12: ãããããã®ã¯æ±äº¬ã ãšããããšã¯ãªããªãã°ãããã¯é²æ¥ã ããããç¯èŸãç·ŽãçŽããããšããããšã¯æãç«ããªã fact13: ããããã®é¬Œçã芳å
ã«ç©ºããã¶ãããããããã¯ã·ã£ãŠãŠãŠã ãšããããšããªãããšããããšãæãç«ããªããªãã°ãããã芳å
ã«ç©ºããã¶ããšããããšããªãããšããããšã¯äºå®ã fact14: ããããã®ã€ãã§ãŠã¯é²æ¥ã ãšããããšããªããªãã°ããã®å£°éã¯è¿·ã蟌ããããã¯ã¯ãããããšããããšãäºå®ãšç°ãªãããšããããšã¯äºå®ã fact15: ãããããã®é¬Œçã¯é²æ¥ã ãããã¯ç¯èŸãç·ŽãçŽããããšããããšã¯äºå®ãšç°ãªãããšããããšã¯æãç«ãŠã°ãã®ã€ãã§ãŠã¯é²æ¥ã§ãªã fact16: ããã©ããããŠå±±æ¬åã«åºã§ç«ã€ããã®ããã fact17: ããã®èŽè
ã¯ãã©ããããå±±æ¬åã«åºã§ç«ã€ããšããããšãäºå®ãšç°ãªã fact18: ããæã²ã©ããã®ã§ãã£ãŠç©ãã®ãããã®ããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ããã fact19: ããäœãã¯ãããã°ããã®é¬Œçã芳å
ã«ç©ºããã¶ãããããã·ã£ãŠãŠãŠã§ãªãããšããããšã¯äºå®ãšç°ãªã fact20: ãããããã®ã¯å奜ãããã¯ãããªããªãã°ãããã¯æ±äº¬ã ãšããããšããªãããšããããšãæãç«ã€ | fact1: (x): {D}x -> {C}x fact2: ¬{G}{a} -> ({E}{a} & {F}{a}) fact3: {C}{a} -> (¬{B}{k} & ¬{A}{k}) fact4: (x): {E}x -> {D}x fact5: (x): ({E}x v ¬{F}x) -> ¬{D}x fact6: (x): ¬{G}x -> ({E}x v ¬{F}x) fact7: (x): ¬{A}x -> ¬({AA}x & {BO}x) fact8: ¬({AA}{el} & {AQ}{el}) fact9: ¬({I}{b} & ¬{H}{b}) -> ¬{G}{a} fact10: ¬({HB}{aa} & {BH}{aa}) fact11: {I}{d} fact12: (x): ¬{C}x -> ¬({A}x & {B}x) fact13: ¬({G}{c} & ¬{H}{c}) -> ¬{G}{c} fact14: ¬{A}{b} -> ¬({FB}{a} & {DD}{a}) fact15: ¬({A}{c} & {B}{c}) -> ¬{A}{b} fact16: (Ex): ({AA}x & {AB}x) fact17: ¬({AA}{aa} & {AB}{aa}) fact18: (Ex): ¬({IO}x & {N}x) fact19: (x): {I}x -> ¬({G}{c} & ¬{H}{c}) fact20: (x): ¬{D}x -> ¬{C}x | [
"fact17 -> hypothesis;"
] | [
"fact17 -> hypothesis;"
] | ããã®æ°å
µããã©ããããã¹ãã¬ãŒãåã¡ã ããšããããšã¯èª€ãã | ¬({AA}{k} & {BO}{k}) | [
"fact22 -> int1: ããããã®æ°å
µã¯é²æ¥ã ãšããããšã¯ãªãããšããããšãäºå®ãªãã°ãããããã©ãããããããã¹ãã¬ãŒãåã¡ã ããšããããšã¯äºå®ãšç°ãªã; fact23 -> int2: ãããã®å£°éã¯å奜ãããã¯ããã°ããã¯æ±äº¬ã ; fact24 -> int3: ãããã®å£°éã¯ç«åãã°ããã¯å奜ãããã¯ãã;"
] | 8 | 1 | 1 | 19 | 0 | 19 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããäœãã¯å奜ãããã¯ããã°ãããæ±äº¬ã fact2: ãããã®å£°éã芳å
ã«ç©ºããã¶ããšããããšã¯ãªããªãã°ããã¯ç«åãããããçæãã fact3: ããããã®å£°éã¯æ±äº¬ã ããšããããšã¯æãç«ãŠã°ãã®æ°å
µã¯ç¯èŸãç·ŽãçŽããªããé²æ¥ã ãšããããšããªã fact4: ããäœããç«åãã°ããããå奜ãããã¯ããããšããããšã¯çå®ã fact5: ããäœãã¯ç«åããããã¯çæãããšããããšããªããäž¡æ¹ãªãã°ããã¯å奜ãããã¯ãããªã fact6: ãããããã®ã¯èŠ³å
ã«ç©ºããã¶ããªããªãã°ããã¯ç«åãããããã¯ããã¯çæãããšããããšããªã fact7: ããäœããé²æ¥ã§ãªããªãã°ãããããã©ããããŠãããã¹ãã¬ãŒãåã¡ã ããšããããšã¯æãç«ã€ãšããããšããªã fact8: ããã®ç£åããã©ãããã最ãããšããããšãçå®ã ãšããããšããªã fact9: ããããã®ã€ãã§ãŠã¯ãããããããã·ã£ãŠãŠãŠã§ãªãããšããããšãåãªãã°ãã®å£°éã芳å
ã«ç©ºããã¶ããšããããšã¯ãªã fact10: ããã®èŽè
ã泰次ã ãéãããšããããšã¯æãç«ããªã fact11: ãã®åžžç¿ç¯ã¯ããã fact12: ãããããã®ã¯æ±äº¬ã ãšããããšã¯ãªããªãã°ãããã¯é²æ¥ã ããããç¯èŸãç·ŽãçŽããããšããããšã¯æãç«ããªã fact13: ããããã®é¬Œçã芳å
ã«ç©ºããã¶ãããããããã¯ã·ã£ãŠãŠãŠã ãšããããšããªãããšããããšãæãç«ããªããªãã°ãããã芳å
ã«ç©ºããã¶ããšããããšããªãããšããããšã¯äºå®ã fact14: ããããã®ã€ãã§ãŠã¯é²æ¥ã ãšããããšããªããªãã°ããã®å£°éã¯è¿·ã蟌ããããã¯ã¯ãããããšããããšãäºå®ãšç°ãªãããšããããšã¯äºå®ã fact15: ãããããã®é¬Œçã¯é²æ¥ã ãããã¯ç¯èŸãç·ŽãçŽããããšããããšã¯äºå®ãšç°ãªãããšããããšã¯æãç«ãŠã°ãã®ã€ãã§ãŠã¯é²æ¥ã§ãªã fact16: ããã©ããããŠå±±æ¬åã«åºã§ç«ã€ããã®ããã fact17: ããã®èŽè
ã¯ãã©ããããå±±æ¬åã«åºã§ç«ã€ããšããããšãäºå®ãšç°ãªã fact18: ããæã²ã©ããã®ã§ãã£ãŠç©ãã®ãããã®ããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ããã fact19: ããäœãã¯ãããã°ããã®é¬Œçã芳å
ã«ç©ºããã¶ãããããã·ã£ãŠãŠãŠã§ãªãããšããããšã¯äºå®ãšç°ãªã fact20: ãããããã®ã¯å奜ãããã¯ãããªããªãã°ãããã¯æ±äº¬ã ãšããããšããªãããšããããšãæãç«ã€ ; $hypothesis$ = ããããã©ããããŠå±±æ¬åã«åºã§ç«ã€ããšããããšãæãç«ããªãããã®ã¯ããããšããããšãééãã ; $proof$ = | fact17 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {D}x -> {C}x fact2: ¬{G}{a} -> ({E}{a} & {F}{a}) fact3: {C}{a} -> (¬{B}{k} & ¬{A}{k}) fact4: (x): {E}x -> {D}x fact5: (x): ({E}x v ¬{F}x) -> ¬{D}x fact6: (x): ¬{G}x -> ({E}x v ¬{F}x) fact7: (x): ¬{A}x -> ¬({AA}x & {BO}x) fact8: ¬({AA}{el} & {AQ}{el}) fact9: ¬({I}{b} & ¬{H}{b}) -> ¬{G}{a} fact10: ¬({HB}{aa} & {BH}{aa}) fact11: {I}{d} fact12: (x): ¬{C}x -> ¬({A}x & {B}x) fact13: ¬({G}{c} & ¬{H}{c}) -> ¬{G}{c} fact14: ¬{A}{b} -> ¬({FB}{a} & {DD}{a}) fact15: ¬({A}{c} & {B}{c}) -> ¬{A}{b} fact16: (Ex): ({AA}x & {AB}x) fact17: ¬({AA}{aa} & {AB}{aa}) fact18: (Ex): ¬({IO}x & {N}x) fact19: (x): {I}x -> ¬({G}{c} & ¬{H}{c}) fact20: (x): ¬{D}x -> ¬{C}x ; $hypothesis$ = ¬((Ex): ¬({AA}x & {AB}x)) ; $proof$ = | fact17 -> hypothesis; __DISPROVED__ |
0.3 | ãã®æã¯ãã®æããããšããããšã¯ãªã | ¬{B}{a} | fact1: ãã®ææ°ã¯ãã®æããããªã fact2: ããããããããã®ã¯ããã°ãã®å±±çŸãããªèããªã fact3: ãããå ªãžãããã®ãããã°ãã®æãéæœéšå·ã«ã¯ãããããšããããšã¯ãªã fact4: ãã®çç±ã¯å€§äºç¡ããªã fact5: ãããèžããããã®ãããã°ãã®æã岡è±çºå°ç¯ãããªãããªã fact6: ãã®ã ãã¿ãŒããã®æããããšããããšã¯ãªã fact7: ãããã劬ãŸãããŠé»åŒã ããšããããšã¯æãç«ããªãããã®ãããã°ããã®å¹žãã¯åŠ¬ãŸãããšããããšããªãããšããããšã¯æãç«ã€ fact8: ãã®æã錻翌ã ãšããããšã¯ãªã fact9: ãã®æã倧äºç¡ããšããããšã¯ãªã fact10: ããã劬ãŸãããªãããã®ã¯ããã°ãã®æã¯éŒ»ç¿Œã§ãã®æããã fact11: ãã®å
¬çµã¯ãã®æããããšããããšããªã fact12: ãããã錻翌ã ããšããããšãæãç«ã€ããã®ãããã°ããã®æã¯ãã®æããããªãããšããããšãæ¬åœã fact13: ãã®æã¯æ°é£ããããªã fact14: ããã錻翌ãªããã®ãããã°ãã®æã垯ç¶ç±ç¹ã§ãªã fact15: ã錻翌ãªããã®ã¯ãã | fact1: ¬{B}{bk} fact2: (x): {JD}x -> ¬{CT}{ff} fact3: (x): {AN}x -> ¬{EC}{a} fact4: ¬{AD}{do} fact5: (x): {DM}x -> ¬{AB}{a} fact6: ¬{B}{fs} fact7: (x): ¬({C}x & {D}x) -> ¬{C}{b} fact8: ¬{A}{a} fact9: ¬{AD}{a} fact10: (x): ¬{C}x -> ({A}{a} & {B}{a}) fact11: ¬{B}{em} fact12: (x): {A}x -> ¬{B}{a} fact13: ¬{HN}{a} fact14: (x): {A}x -> ¬{DI}{a} fact15: (Ex): {A}x | [
"fact15 & fact12 -> hypothesis;"
] | [
"fact15 & fact12 -> hypothesis;"
] | ãã®æã¯ãã®æããã | {B}{a} | [] | 9 | 1 | 1 | 13 | 0 | 13 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ææ°ã¯ãã®æããããªã fact2: ããããããããã®ã¯ããã°ãã®å±±çŸãããªèããªã fact3: ãããå ªãžãããã®ãããã°ãã®æãéæœéšå·ã«ã¯ãããããšããããšã¯ãªã fact4: ãã®çç±ã¯å€§äºç¡ããªã fact5: ãããèžããããã®ãããã°ãã®æã岡è±çºå°ç¯ãããªãããªã fact6: ãã®ã ãã¿ãŒããã®æããããšããããšã¯ãªã fact7: ãããã劬ãŸãããŠé»åŒã ããšããããšã¯æãç«ããªãããã®ãããã°ããã®å¹žãã¯åŠ¬ãŸãããšããããšããªãããšããããšã¯æãç«ã€ fact8: ãã®æã錻翌ã ãšããããšã¯ãªã fact9: ãã®æã倧äºç¡ããšããããšã¯ãªã fact10: ããã劬ãŸãããªãããã®ã¯ããã°ãã®æã¯éŒ»ç¿Œã§ãã®æããã fact11: ãã®å
¬çµã¯ãã®æããããšããããšããªã fact12: ãããã錻翌ã ããšããããšãæãç«ã€ããã®ãããã°ããã®æã¯ãã®æããããªãããšããããšãæ¬åœã fact13: ãã®æã¯æ°é£ããããªã fact14: ããã錻翌ãªããã®ãããã°ãã®æã垯ç¶ç±ç¹ã§ãªã fact15: ã錻翌ãªããã®ã¯ãã ; $hypothesis$ = ãã®æã¯ãã®æããããšããããšã¯ãªã ; $proof$ = | fact15 & fact12 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{B}{bk} fact2: (x): {JD}x -> ¬{CT}{ff} fact3: (x): {AN}x -> ¬{EC}{a} fact4: ¬{AD}{do} fact5: (x): {DM}x -> ¬{AB}{a} fact6: ¬{B}{fs} fact7: (x): ¬({C}x & {D}x) -> ¬{C}{b} fact8: ¬{A}{a} fact9: ¬{AD}{a} fact10: (x): ¬{C}x -> ({A}{a} & {B}{a}) fact11: ¬{B}{em} fact12: (x): {A}x -> ¬{B}{a} fact13: ¬{HN}{a} fact14: (x): {A}x -> ¬{DI}{a} fact15: (Ex): {A}x ; $hypothesis$ = ¬{B}{a} ; $proof$ = | fact15 & fact12 -> hypothesis; __PROVED__ |
0.3 | ãã®ã¹ãŒããŒãã³ã¯ã®ãããã | {A}{a} | fact1: ãã®çžåãã®ãããã fact2: ãã®ç·çµ±ãã®ãããã fact3: ãã®ã¹ãŒããŒãã³ãã®ãããã fact4: ãã®ãã«ãããŠã ã¯åžãã fact5: ãã®åœäœã¯ã²ããã fact6: ãããã®åœäœã¯ã²ããããªãã°ãããç Žæã fact7: ããäœãã銬鹿銬鹿ãããªããéå°»åãå£ãæ°ããããªããªãã°ããã¯ã®ãããã fact8: ããããããã®ã¯åžãããšããããšã¯ãªããŠãã®ãããšããããšããªãããšããããšã¯çå®ã§ãªããªãã°ããã¯æç·©ããšããããšããªã fact9: ãã®ã¹ãŒããŒãã³ã¯ããããªã fact10: ãããã®åœäœãå¯ä»ãå°œãããªããç Žæãªãã°ããã®ç«¯åœ¹ã¯å¯ä»ãå°œãããªãããšããããšãæ¬åœã fact11: ãããèŠã«ãããªãããã®ãããã°ããã®å°¿çŽ ã¯éŠ¬é¹¿éŠ¬é¹¿ãããªããããã¯éå°»åãå£ãæ°ããããªããäž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact12: ãã®åœäœãå¯ä»ãå°œãããªã fact13: ãããæç·©ããšããããšããªããå¯ä»ãå°œãããšããããšã¯ãªãããã®ã¯ããã°ãã®ããŒã¡ã©ã³ã¯èŠã«ãããªã fact14: ãããåžããããã®ãããã°ããã®ç«¯åœ¹ãåžããªããããã¯ãã®ãããšããããšããªãããšããããšã誀ãã | fact1: {A}{n} fact2: {A}{cr} fact3: {A}{a} fact4: {H}{f} fact5: {J}{e} fact6: {J}{e} -> {I}{e} fact7: (x): (¬{C}x & ¬{B}x) -> {A}x fact8: (x): ¬(¬{H}x & ¬{G}x) -> ¬{E}x fact9: {FN}{a} fact10: (¬{F}{e} & {I}{e}) -> ¬{F}{d} fact11: (x): ¬{D}x -> ¬(¬{C}{b} v ¬{B}{b}) fact12: ¬{F}{e} fact13: (x): (¬{E}x & ¬{F}x) -> ¬{D}{c} fact14: (x): {H}x -> ¬(¬{H}{d} & ¬{G}{d}) | [
"fact3 -> hypothesis;"
] | [
"fact3 -> hypothesis;"
] | ãã®ã¹ãŒããŒãã³ã¯ã®ãããããšããããšããªã | ¬{A}{a} | [
"fact20 -> int1: ããããã®ç«¯åœ¹ã¯åžãããšããããšã¯ãªãããã®ãããšããããšããªãããšããããšã¯ééããªãã°ããã¯æç·©ããšããããšã¯ãªã; fact22 -> int2: ãããã®ãåžãã; int2 & fact18 -> int3: ããã®ç«¯åœ¹ãåžããªããããããã®ãããªãããšããããšã¯æãç«ããªã; int1 & int3 -> int4: ãã®ç«¯åœ¹ãæç·©ããªã; fact16 & fact21 -> int5: ãã®åœäœã¯ç Žæã ; fact23 & int5 -> int6: ãã®åœäœã¯å¯ä»ãå°œãããšããããšããªãããããç Žæã ; fact15 & int6 -> int7: ããã®ç«¯åœ¹ãå¯ä»ãå°œãããªãããšããããšãæãç«ã€; int4 & int7 -> int8: ãã®ç«¯åœ¹ã¯æç·©ããšããããšããªããå¯ä»ãå°œãããªã; int8 -> int9: äœãã¯æç·©ããšããããšããªããå¯ä»ãå°œãããšããããšããªã; int9 & fact17 -> int10: ãã®ããŒã¡ã©ã³ãèŠã«ãããšããããšã¯ãªã; int10 -> int11: ããèŠã«ãããªãããšããããšãäºå®ãªããã®ã¯ãã; int11 & fact19 -> int12: ããã®å°¿çŽ ã¯éŠ¬é¹¿éŠ¬é¹¿ãããšããããšããªãããããã¯éå°»åãå£ãæ°ããããªããäž¡æ¹ã ããšããããšãæãç«ããªã; int12 -> int13: ããã銬鹿銬鹿ãããªããéå°»åãå£ãæ°ãããããšããããšã¯ãªããäž¡æ¹ã ããšããããšãæãç«ã€ããšããããšãééããªããã®ã¯ãã;"
] | 10 | 1 | 0 | 13 | 0 | 13 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®çžåãã®ãããã fact2: ãã®ç·çµ±ãã®ãããã fact3: ãã®ã¹ãŒããŒãã³ãã®ãããã fact4: ãã®ãã«ãããŠã ã¯åžãã fact5: ãã®åœäœã¯ã²ããã fact6: ãããã®åœäœã¯ã²ããããªãã°ãããç Žæã fact7: ããäœãã銬鹿銬鹿ãããªããéå°»åãå£ãæ°ããããªããªãã°ããã¯ã®ãããã fact8: ããããããã®ã¯åžãããšããããšã¯ãªããŠãã®ãããšããããšããªãããšããããšã¯çå®ã§ãªããªãã°ããã¯æç·©ããšããããšããªã fact9: ãã®ã¹ãŒããŒãã³ã¯ããããªã fact10: ãããã®åœäœãå¯ä»ãå°œãããªããç Žæãªãã°ããã®ç«¯åœ¹ã¯å¯ä»ãå°œãããªãããšããããšãæ¬åœã fact11: ãããèŠã«ãããªãããã®ãããã°ããã®å°¿çŽ ã¯éŠ¬é¹¿éŠ¬é¹¿ãããªããããã¯éå°»åãå£ãæ°ããããªããäž¡æ¹ã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact12: ãã®åœäœãå¯ä»ãå°œãããªã fact13: ãããæç·©ããšããããšããªããå¯ä»ãå°œãããšããããšã¯ãªãããã®ã¯ããã°ãã®ããŒã¡ã©ã³ã¯èŠã«ãããªã fact14: ãããåžããããã®ãããã°ããã®ç«¯åœ¹ãåžããªããããã¯ãã®ãããšããããšããªãããšããããšã誀ãã ; $hypothesis$ = ãã®ã¹ãŒããŒãã³ã¯ã®ãããã ; $proof$ = | fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{n} fact2: {A}{cr} fact3: {A}{a} fact4: {H}{f} fact5: {J}{e} fact6: {J}{e} -> {I}{e} fact7: (x): (¬{C}x & ¬{B}x) -> {A}x fact8: (x): ¬(¬{H}x & ¬{G}x) -> ¬{E}x fact9: {FN}{a} fact10: (¬{F}{e} & {I}{e}) -> ¬{F}{d} fact11: (x): ¬{D}x -> ¬(¬{C}{b} v ¬{B}{b}) fact12: ¬{F}{e} fact13: (x): (¬{E}x & ¬{F}x) -> ¬{D}{c} fact14: (x): {H}x -> ¬(¬{H}{d} & ¬{G}{d}) ; $hypothesis$ = {A}{a} ; $proof$ = | fact3 -> hypothesis; __PROVED__ |
0.3 | ããã®ã€ã³ã¯ã¯äºäºãããšããããšããªãå°æŸå³¶ç·ããšããããšãæãç«ã€ãšããããšããªã | ¬(¬{B}{a} & {C}{a}) | fact1: ãããã®åŠç©¶ã¯ããŸã ããªãã°ãã®åœ±é¿ãããŸã ã fact2: ãããããã®ãåŸããããã®ã§ãã£ãŠåãäžãããã® fact3: ãããããã®ãæ°ééã§ãªããªãã°ããã®ã€ã³ã¯ã¯äºäºãããªãå°æŸå³¶ç·ããšããããšã¯åã fact4: ãäºäºãããªãããã®ããã fact5: ããäœããæŠéã§ãªãããããããŸã ããªãã°ããã¯è çã fact6: ããäœãã¯åãäžããã°ãããã¯å
æå±±ãçµã殺ããªããŠããã¯ãããè²ããããã®ã¹ããšããããšããªãããšããããšã¯ééãã fact7: äœãã被æžæ°ãæŠãããããã¯ããŠã fact8: ããã®ã€ã³ã¯ãäºäºãããããã¯å°æŸå³¶ç·ã ããšããããšã¯æãç«ããªã fact9: ãããã®æ颚ãå¯ç©¢ããšããããšã¯ãªããªãã°ãããã¯åé·çºåæ±å³¶ã ãããã¯æ®ãæããããšããããšãäºå®ãšç°ãªã fact10: ãããã®èµ·ç¹ã¯æ°ééãªãã°ãã®ã€ã³ã¯ãæ°ééã fact11: ããäœããåè海岞ãæ±ãããããªããäºäºãããšããããšã¯ãªãããããã¯äž¡æ¹ãªãã°ããã¯åè海岞ãæ±ããããããšããããšã¯ãªã fact12: ãããäœãã¯å
æå±±ãçµã殺ããªãããããè²ããããã®ã¹ãªãããšããããšã誀ããªãã°ããã¯æŠéã§ãªã fact13: æ°ééãäºäºãããªããå°æŸå³¶ç·ã fact14: ãæ°ééã ãšããããšã¯ãªãããã®ã¯ãã fact15: ããäœãã¯è¢«æžæ°ãæŠãããããŠãã°ãã®æ颚ãå¯ç©¢ããªã fact16: ãããã®åœ±é¿ãè çãªãã°ãã®èµ·ç¹ã¯æ°ééã | fact1: {F}{d} -> {F}{c} fact2: (x): ({L}x & {K}x) fact3: (x): ¬{A}x -> ¬(¬{B}{a} & {C}{a}) fact4: (Ex): ¬{B}x fact5: (x): (¬{E}x & {F}x) -> {D}x fact6: (x): {K}x -> ¬(¬{J}x & ¬{I}x) fact7: (Ex): ({O}x & {N}x) fact8: ¬({B}{a} & {C}{a}) fact9: ¬{M}{e} -> ¬({H}{e} & {G}{e}) fact10: {A}{b} -> {A}{a} fact11: (x): (¬{AC}x v ¬{B}x) -> ¬{AC}x fact12: (x): ¬(¬{J}x & ¬{I}x) -> ¬{E}x fact13: (x): {A}x -> (¬{B}x & {C}x) fact14: (Ex): ¬{A}x fact15: (x): ({O}x & {N}x) -> ¬{M}{e} fact16: {D}{c} -> {A}{b} | [
"fact14 & fact3 -> hypothesis;"
] | [
"fact14 & fact3 -> hypothesis;"
] | ãã®ã€ã³ã¯ãäºäºãããšããããšã¯ãªãããããå°æŸå³¶ç·ã | (¬{B}{a} & {C}{a}) | [
"fact18 -> int1: ãããã®ã€ã³ã¯ã¯æ°ééãªãã°ããã¯äºäºãããªãããããå°æŸå³¶ç·ã ; fact21 -> int2: ãããã®åœ±é¿ãæŠéã ãšããããšã¯ãªãããããããŸã ããªãã°ãããè çã ; fact24 -> int3: ããããã®åœ±é¿ã¯å
æå±±ãçµã殺ããšããããšããªããŠããããããè²ããããã®ã¹ãªãããšããããšã¯çå®ã ãšããããšã¯ãªããªãã°ããããæŠéã§ãªãããšããããšãæãç«ã€; fact23 -> int4: ããããã®åœ±é¿ãåãäžããããšããããšãæãç«ãŠã°ããããå
æå±±ãçµã殺ããªãããããè²ããããã®ã¹ãªãããšããããšã¯åã ; fact27 -> int5: ããã®åœ±é¿ã¯åŸããããã®ã§ãã£ãŠåãäžãããã®ããšããããšãæãç«ã€; int5 -> int6: ããã®åœ±é¿ãåãäžããããšããããšã¯æ£ãã; int4 & int6 -> int7: ããã®åœ±é¿ãå
æå±±ãçµã殺ããªããããã¯ãããè²ããããã®ã¹ãªãããšããããšã¯åœã ; int3 & int7 -> int8: ãã®åœ±é¿ã¯æŠéã ãšããããšããªã; fact17 & fact25 -> int9: ããã®æ颚ã¯å¯ç©¢ããšããããšããªãããšããããšã¯æ¬åœã ; fact19 & int9 -> int10: ãããã®æ颚ã¯åé·çºåæ±å³¶ã§ãããæ®ãæããããšããããšãæãç«ã€ãšããããšããªãããšããããšãæãç«ã€; int10 -> int11: ããåé·çºåæ±å³¶ã ãæ®ãæããããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ããã;"
] | 10 | 1 | 1 | 14 | 0 | 14 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããã®åŠç©¶ã¯ããŸã ããªãã°ãã®åœ±é¿ãããŸã ã fact2: ãããããã®ãåŸããããã®ã§ãã£ãŠåãäžãããã® fact3: ãããããã®ãæ°ééã§ãªããªãã°ããã®ã€ã³ã¯ã¯äºäºãããªãå°æŸå³¶ç·ããšããããšã¯åã fact4: ãäºäºãããªãããã®ããã fact5: ããäœããæŠéã§ãªãããããããŸã ããªãã°ããã¯è çã fact6: ããäœãã¯åãäžããã°ãããã¯å
æå±±ãçµã殺ããªããŠããã¯ãããè²ããããã®ã¹ããšããããšããªãããšããããšã¯ééãã fact7: äœãã被æžæ°ãæŠãããããã¯ããŠã fact8: ããã®ã€ã³ã¯ãäºäºãããããã¯å°æŸå³¶ç·ã ããšããããšã¯æãç«ããªã fact9: ãããã®æ颚ãå¯ç©¢ããšããããšã¯ãªããªãã°ãããã¯åé·çºåæ±å³¶ã ãããã¯æ®ãæããããšããããšãäºå®ãšç°ãªã fact10: ãããã®èµ·ç¹ã¯æ°ééãªãã°ãã®ã€ã³ã¯ãæ°ééã fact11: ããäœããåè海岞ãæ±ãããããªããäºäºãããšããããšã¯ãªãããããã¯äž¡æ¹ãªãã°ããã¯åè海岞ãæ±ããããããšããããšã¯ãªã fact12: ãããäœãã¯å
æå±±ãçµã殺ããªãããããè²ããããã®ã¹ãªãããšããããšã誀ããªãã°ããã¯æŠéã§ãªã fact13: æ°ééãäºäºãããªããå°æŸå³¶ç·ã fact14: ãæ°ééã ãšããããšã¯ãªãããã®ã¯ãã fact15: ããäœãã¯è¢«æžæ°ãæŠãããããŠãã°ãã®æ颚ãå¯ç©¢ããªã fact16: ãããã®åœ±é¿ãè çãªãã°ãã®èµ·ç¹ã¯æ°ééã ; $hypothesis$ = ããã®ã€ã³ã¯ã¯äºäºãããšããããšããªãå°æŸå³¶ç·ããšããããšãæãç«ã€ãšããããšããªã ; $proof$ = | fact14 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {F}{d} -> {F}{c} fact2: (x): ({L}x & {K}x) fact3: (x): ¬{A}x -> ¬(¬{B}{a} & {C}{a}) fact4: (Ex): ¬{B}x fact5: (x): (¬{E}x & {F}x) -> {D}x fact6: (x): {K}x -> ¬(¬{J}x & ¬{I}x) fact7: (Ex): ({O}x & {N}x) fact8: ¬({B}{a} & {C}{a}) fact9: ¬{M}{e} -> ¬({H}{e} & {G}{e}) fact10: {A}{b} -> {A}{a} fact11: (x): (¬{AC}x v ¬{B}x) -> ¬{AC}x fact12: (x): ¬(¬{J}x & ¬{I}x) -> ¬{E}x fact13: (x): {A}x -> (¬{B}x & {C}x) fact14: (Ex): ¬{A}x fact15: (x): ({O}x & {N}x) -> ¬{M}{e} fact16: {D}{c} -> {A}{b} ; $hypothesis$ = ¬(¬{B}{a} & {C}{a}) ; $proof$ = | fact14 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®è³ç¥çµã¯ã¯ã£ãããå³ä»ãããããããããªã | ({AA}{a} & ¬{AB}{a}) | fact1: ããäœããç©ã¿èŸŒãã°ããã¯æ±é«é ããããããããã¯ã¯ã£ãããå³ä»ãããšããããšããªã fact2: ãã®è³ç¥çµãç©ã¿èŸŒããšããããšããªã fact3: ãããã®æ¯è»ãç©ã¿èŸŒããšããããšã¯ãªãããããã¯çŠäžéã§ããããããã¯äž¡æ¹ãªãã°ããããã¯ã£ãããå³ä»ãããšããããšã¯ãªãããšããããšãæ¬åœã fact4: ãããã®è³ç¥çµã¯ç©ã¿èŸŒããšããããšã¯ãªããªãã°ããããããããããªãããšããããšã¯äºå®ã fact5: ãã®è³ç¥çµãããããããšããããšããªã fact6: ãã®è³ç¥çµã¯ä¹
äžéãã¯ããã¬ããããããããªã fact7: ãããããã®ãã¿ãããã°ããããç©ã¿èŸŒããšããããšã¯ãªããŠããã¯çŠäžéã§ãªãããšããããšãééãã fact8: ãã®è³ç¥çµã¯ææ¶ã座ãã fact9: ããããäœããç©ã¿èŸŒããšããããšããªããŠãããçŠäžéã§ãªãããšããããšãæãç«ã€ããšããããšãæãç«ããªããªãã°ããã¯ç©ã¿èŸŒã | fact1: (x): {A}x -> ({II}x & ¬{AA}x) fact2: ¬{A}{a} fact3: (¬{A}{b} v {B}{b}) -> ¬{AA}{b} fact4: ¬{A}{a} -> ¬{AB}{a} fact5: ¬{AB}{a} fact6: ({DK}{a} & ¬{DD}{a}) fact7: (x): {C}x -> ¬(¬{A}x & ¬{B}x) fact8: {E}{a} fact9: (x): ¬(¬{A}x & ¬{B}x) -> {A}x | [] | [] | ãã®éãå Žãæ±é«é ããããããã¯ã£ãããå³ä»ããªã | ({II}{fc} & ¬{AA}{fc}) | [
"fact12 -> int1: ããããã®éãå Žã¯ç©ã¿èŸŒãããšããããšã¯æãç«ãŠã°ããã¯æ±é«é ãããããããããã¯ã£ãããå³ä»ããªã; fact10 -> int2: ããããã®éãå Žãç©ã¿èŸŒããšããããšã¯ãªããŠãããçŠäžéã§ãªãããšããããšã¯ééããªãã°ãããç©ã¿èŸŒã; fact13 -> int3: ãããã®éãå Žã¯ã¿ãããã°ããããç©ã¿èŸŒããªããçŠäžéã ãšããããšã¯ãªãããšããããšã¯æãç«ããªã; fact11 -> int4: ãææ¶ã座ããããã®ã¯ãã;"
] | 6 | 1 | null | 8 | 0 | 8 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããäœããç©ã¿èŸŒãã°ããã¯æ±é«é ããããããããã¯ã¯ã£ãããå³ä»ãããšããããšããªã fact2: ãã®è³ç¥çµãç©ã¿èŸŒããšããããšããªã fact3: ãããã®æ¯è»ãç©ã¿èŸŒããšããããšã¯ãªãããããã¯çŠäžéã§ããããããã¯äž¡æ¹ãªãã°ããããã¯ã£ãããå³ä»ãããšããããšã¯ãªãããšããããšãæ¬åœã fact4: ãããã®è³ç¥çµã¯ç©ã¿èŸŒããšããããšã¯ãªããªãã°ããããããããããªãããšããããšã¯äºå®ã fact5: ãã®è³ç¥çµãããããããšããããšããªã fact6: ãã®è³ç¥çµã¯ä¹
äžéãã¯ããã¬ããããããããªã fact7: ãããããã®ãã¿ãããã°ããããç©ã¿èŸŒããšããããšã¯ãªããŠããã¯çŠäžéã§ãªãããšããããšãééãã fact8: ãã®è³ç¥çµã¯ææ¶ã座ãã fact9: ããããäœããç©ã¿èŸŒããšããããšããªããŠãããçŠäžéã§ãªãããšããããšãæãç«ã€ããšããããšãæãç«ããªããªãã°ããã¯ç©ã¿èŸŒã ; $hypothesis$ = ãã®è³ç¥çµã¯ã¯ã£ãããå³ä»ãããããããããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): {A}x -> ({II}x & ¬{AA}x) fact2: ¬{A}{a} fact3: (¬{A}{b} v {B}{b}) -> ¬{AA}{b} fact4: ¬{A}{a} -> ¬{AB}{a} fact5: ¬{AB}{a} fact6: ({DK}{a} & ¬{DD}{a}) fact7: (x): {C}x -> ¬(¬{A}x & ¬{B}x) fact8: {E}{a} fact9: (x): ¬(¬{A}x & ¬{B}x) -> {A}x ; $hypothesis$ = ({AA}{a} & ¬{AB}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãåçãçºçããªããããŸããšããããšã¯çºçããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬(¬{AA} & ¬{AB}) | fact1: éäžã¯ãè®ã«ã©ãããªã¥ãããšãèµ·ãããããã糶売ãèµ·ããªãããšããããšããããã fact2: ããé£èŸŒãããšã¯èµ·ãããªããªãã°ããè¬ãã®ãããããšãšæ®ºæ®ã¯èµ·ããããšããããšãæãç«ããªãããšããããšãæ£ãã fact3: ãããè¬ãã®ãããããšã¯çºçããã殺æ®ãçºçããããšããããšãæãç«ããªããªãã°è¬ãã®ãããããšãçããªã fact4: ããŸãããšããããšã¯çºçãããæçãèµ·ãããªãããšããããšãçå®ã§ãªã fact5: ããäžæ¹¯å·ãæãããšã¯èµ·ãããªããªãã°ãåçãçããªããããŸããšããããšãèµ·ãããªãããšããããšã¯æãç«ããªã fact6: ããããããããšããããšã¯èµ·ããªããæ°é«ããšããããšã¯èµ·ããããšããããšã¯ãé£èŸŒãããšãèµ·ããªãããšããããšãçãããã fact7: ããè¬ãã®ãããããšã¯èµ·ããªããªãã°çµæ«ãšç«¹ã®è¢ã«äœãäžããããšãèµ·ãã fact8: ãããã¥ãããšããããšãçºçãããã¬ã¿ã¬ã¿ãèµ·ããããšããããšã¯ç³¶å£²ã¯çããªããšããããšããã£ããã fact9: äžæ¹¯å·ãæãããšã¯çãããšããããšã¯ãåçãçºçããªããããŸããšããããšã¯èµ·ããªãããšããããšãèªçºãã fact10: çµæ«ãçãããšããããšã¯ãäžæ¹¯å·ãæãããšãçããããšããããšãçºçããã fact11: ããããããããšããããšã§ã¯ãªãæ°é«ããšããããšãçºçããããšããããšããããã¥ãããšããããšãèµ·ããããšããããšã«èµ·å ãã fact12: ããäžæ¹¯å·ãæãããšãèµ·ãããªããªãã°ãåçãèµ·ãããããŸããšããããšã¯çããªãããšããããšã¯åã | fact1: {M} -> ({L} & ¬{K}) fact2: ¬{F} -> ¬({D} & {E}) fact3: ¬({D} & {E}) -> ¬{D} fact4: ¬({FJ} & ¬{DR}) fact5: ¬{A} -> ¬(¬{AA} & ¬{AB}) fact6: (¬{G} & {H}) -> ¬{F} fact7: ¬{D} -> ({B} & {C}) fact8: ¬{K} -> ({I} & {J}) fact9: {A} -> (¬{AA} & ¬{AB}) fact10: {B} -> {A} fact11: {I} -> (¬{G} & {H}) fact12: ¬{A} -> ¬({AA} & ¬{AB}) | [] | [] | åçãçºçããªããããŸããšããããšã¯èµ·ãããªã | (¬{AA} & ¬{AB}) | [] | 14 | 1 | null | 11 | 0 | 11 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: éäžã¯ãè®ã«ã©ãããªã¥ãããšãèµ·ãããããã糶売ãèµ·ããªãããšããããšããããã fact2: ããé£èŸŒãããšã¯èµ·ãããªããªãã°ããè¬ãã®ãããããšãšæ®ºæ®ã¯èµ·ããããšããããšãæãç«ããªãããšããããšãæ£ãã fact3: ãããè¬ãã®ãããããšã¯çºçããã殺æ®ãçºçããããšããããšãæãç«ããªããªãã°è¬ãã®ãããããšãçããªã fact4: ããŸãããšããããšã¯çºçãããæçãèµ·ãããªãããšããããšãçå®ã§ãªã fact5: ããäžæ¹¯å·ãæãããšã¯èµ·ãããªããªãã°ãåçãçããªããããŸããšããããšãèµ·ãããªãããšããããšã¯æãç«ããªã fact6: ããããããããšããããšã¯èµ·ããªããæ°é«ããšããããšã¯èµ·ããããšããããšã¯ãé£èŸŒãããšãèµ·ããªãããšããããšãçãããã fact7: ããè¬ãã®ãããããšã¯èµ·ããªããªãã°çµæ«ãšç«¹ã®è¢ã«äœãäžããããšãèµ·ãã fact8: ãããã¥ãããšããããšãçºçãããã¬ã¿ã¬ã¿ãèµ·ããããšããããšã¯ç³¶å£²ã¯çããªããšããããšããã£ããã fact9: äžæ¹¯å·ãæãããšã¯çãããšããããšã¯ãåçãçºçããªããããŸããšããããšã¯èµ·ããªãããšããããšãèªçºãã fact10: çµæ«ãçãããšããããšã¯ãäžæ¹¯å·ãæãããšãçããããšããããšãçºçããã fact11: ããããããããšããããšã§ã¯ãªãæ°é«ããšããããšãçºçããããšããããšããããã¥ãããšããããšãèµ·ããããšããããšã«èµ·å ãã fact12: ããäžæ¹¯å·ãæãããšãèµ·ãããªããªãã°ãåçãèµ·ãããããŸããšããããšã¯çããªãããšããããšã¯åã ; $hypothesis$ = ãåçãçºçããªããããŸããšããããšã¯çºçããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {M} -> ({L} & ¬{K}) fact2: ¬{F} -> ¬({D} & {E}) fact3: ¬({D} & {E}) -> ¬{D} fact4: ¬({FJ} & ¬{DR}) fact5: ¬{A} -> ¬(¬{AA} & ¬{AB}) fact6: (¬{G} & {H}) -> ¬{F} fact7: ¬{D} -> ({B} & {C}) fact8: ¬{K} -> ({I} & {J}) fact9: {A} -> (¬{AA} & ¬{AB}) fact10: {B} -> {A} fact11: {I} -> (¬{G} & {H}) fact12: ¬{A} -> ¬({AA} & ¬{AB}) ; $hypothesis$ = ¬(¬{AA} & ¬{AB}) ; $proof$ = | __UNKNOWN__ |
0.3 | 貫çŠã¯èµ·ããªããããããããšããããšã¯çºçããªã | (¬{AA} & ¬{AB}) | fact1: ããç¥ç°äœä¹
éãããã¹ããããšãèµ·ããã°ãããŸã³ããããšããããšã¯èµ·ãããªããäžæ¿èªãèšãããããšã¯èµ·ããããšããããšãäºå®ã§ãªã fact2: ããŸã³ããããšããããšãèµ·ããªã fact3: ãçã¯çããªãããšããããšãããã€ãããšããããšã¯èµ·ãããªãããã¿ããããšãçããªãããšããããšããããã fact4: ãã奜ããªããšããããšãèµ·ãããšããããšã¯ãç¥ç°äœä¹
éãããã¹ããããšã¯èµ·ããããšããããšãçºçããã fact5: å¿èš±ç¡ããšããããšã¯èµ·ããªããšããããšããååã¯èµ·ãããªããŠããããªããšããããšãçºçããªãããšããããšã«åž°çµãã fact6: ãåãåŒãã¯çºçããªãããšããããšããçŸèµ°ãèµ·ãããªãããšããããšã«ç¹ãã fact7: åŸããããšããããšãèµ·ãããªããåŸå³ã¯èµ·ããªã fact8: æéããšããããšãèµ·ããªããŠè²°ããããšã¯çºçããªã fact9: ãããããããŸã³ããããšããããšãçºçããªããäžæ¿èªãèšãããããšã¯çºçããããšããããšãäºå®ã ããšããããšãäºå®ã§ãªããªãã°äžæ¿èªãèšãããããšã¯çºçããªãããšããããšãäºå®ã fact10: å°ã蟌ãããšã¯çããªããšããããšãå
å°èµè¶ãæŸãããšã¯çºçããªããšããããšã«ç±æ¥ãã fact11: ããããããšããããšãèµ·ãããªã fact12: ããããããšããããšã¯èµ·ãããšããããšããããŸã³ããããšããããšã¯èµ·ãããªãããšããããšã«é²ããã fact13: ããæéããšããããšã¯èµ·ããªããªãã°ãã©ãã¯ã¹ãããããçºçããªããŠéå¯ãçºçããªã fact14: ããå¡©èŸããšããããšã¯èµ·ããªããªãã°ãã¿ããããšãèµ·ãããªããå埩ãçããªã fact15: ããè©£ãããšã¯çºçããªããªãã°ãã奜ããªããšããããšã¯èµ·ãããäºæ°ãããšããããšã¯èµ·ãã | fact1: {B} -> ¬(¬{A} & {IK}) fact2: ¬{A} fact3: ¬{HR} -> (¬{GN} & ¬{FQ}) fact4: {C} -> {B} fact5: ¬{IJ} -> (¬{IB} & ¬{EJ}) fact6: ¬{AP} -> ¬{IM} fact7: (¬{F} & ¬{EP}) fact8: (¬{BB} & ¬{M}) fact9: ¬(¬{A} & {IK}) -> ¬{IK} fact10: ¬{CO} -> ¬{FE} fact11: ¬{AB} fact12: ¬{A} -> ¬{AB} fact13: ¬{BB} -> (¬{JH} & ¬{AS}) fact14: ¬{BA} -> (¬{FQ} & ¬{HD}) fact15: ¬{E} -> ({C} & {D}) | [] | [] | äžæ¿èªãèšãããããšãçºçããªã | ¬{IK} | [] | 9 | 1 | null | 14 | 0 | 14 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããç¥ç°äœä¹
éãããã¹ããããšãèµ·ããã°ãããŸã³ããããšããããšã¯èµ·ãããªããäžæ¿èªãèšãããããšã¯èµ·ããããšããããšãäºå®ã§ãªã fact2: ããŸã³ããããšããããšãèµ·ããªã fact3: ãçã¯çããªãããšããããšãããã€ãããšããããšã¯èµ·ãããªãããã¿ããããšãçããªãããšããããšããããã fact4: ãã奜ããªããšããããšãèµ·ãããšããããšã¯ãç¥ç°äœä¹
éãããã¹ããããšã¯èµ·ããããšããããšãçºçããã fact5: å¿èš±ç¡ããšããããšã¯èµ·ããªããšããããšããååã¯èµ·ãããªããŠããããªããšããããšãçºçããªãããšããããšã«åž°çµãã fact6: ãåãåŒãã¯çºçããªãããšããããšããçŸèµ°ãèµ·ãããªãããšããããšã«ç¹ãã fact7: åŸããããšããããšãèµ·ãããªããåŸå³ã¯èµ·ããªã fact8: æéããšããããšãèµ·ããªããŠè²°ããããšã¯çºçããªã fact9: ãããããããŸã³ããããšããããšãçºçããªããäžæ¿èªãèšãããããšã¯çºçããããšããããšãäºå®ã ããšããããšãäºå®ã§ãªããªãã°äžæ¿èªãèšãããããšã¯çºçããªãããšããããšãäºå®ã fact10: å°ã蟌ãããšã¯çããªããšããããšãå
å°èµè¶ãæŸãããšã¯çºçããªããšããããšã«ç±æ¥ãã fact11: ããããããšããããšãèµ·ãããªã fact12: ããããããšããããšã¯èµ·ãããšããããšããããŸã³ããããšããããšã¯èµ·ãããªãããšããããšã«é²ããã fact13: ããæéããšããããšã¯èµ·ããªããªãã°ãã©ãã¯ã¹ãããããçºçããªããŠéå¯ãçºçããªã fact14: ããå¡©èŸããšããããšã¯èµ·ããªããªãã°ãã¿ããããšãèµ·ãããªããå埩ãçããªã fact15: ããè©£ãããšã¯çºçããªããªãã°ãã奜ããªããšããããšã¯èµ·ãããäºæ°ãããšããããšã¯èµ·ãã ; $hypothesis$ = 貫çŠã¯èµ·ããªããããããããšããããšã¯çºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B} -> ¬(¬{A} & {IK}) fact2: ¬{A} fact3: ¬{HR} -> (¬{GN} & ¬{FQ}) fact4: {C} -> {B} fact5: ¬{IJ} -> (¬{IB} & ¬{EJ}) fact6: ¬{AP} -> ¬{IM} fact7: (¬{F} & ¬{EP}) fact8: (¬{BB} & ¬{M}) fact9: ¬(¬{A} & {IK}) -> ¬{IK} fact10: ¬{CO} -> ¬{FE} fact11: ¬{AB} fact12: ¬{A} -> ¬{AB} fact13: ¬{BB} -> (¬{JH} & ¬{AS}) fact14: ¬{BA} -> (¬{FQ} & ¬{HD}) fact15: ¬{E} -> ({C} & {D}) ; $hypothesis$ = (¬{AA} & ¬{AB}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã祥é
ãªãã°ããŸããããªãããã®ãããããšããããšã¯æãç«ããªã | ¬((Ex): {A}x -> ¬{C}x) | fact1: ãããã®çŒç®ã祥é
ãªãã°ãããããŸããããšããããšã¯ãªã fact2: ãããã®çŒç®ã¯è¿æšå·ãªãã°ããããããŸããããšããããšããªãããšããããšãæ¬åœã fact3: ããã祥é
ãªãã°ããŸãããããã®ããã fact4: ããããå
«å¹¡éã ããšããããšãæ¬åœãªãã°éšããããããã®ã¯ãã fact5: ãããå£å§ãããªãã°è¡çºãªããã®ããã fact6: ãããã®çŒç®ãããŸããããªãã°ããã¯é³æ²»ã«ç²ããªã fact7: ãããäºåç¬ãªãã°å€å
ã§ãªãããã®ã¯ãã fact8: ããããåžžç€ç¥ç°ã ããšããããšã¯æãç«ãŠã°ãããããšããããšããªãããã®ããã fact9: ãããã®çŒç®ã祥é
ãªãã°ãããããŸããã fact10: ããããã«ãã³å·ãããããã°é¢šã³ãªããã®ã¯ãã | fact1: {A}{aa} -> ¬{C}{aa} fact2: {DP}{aa} -> ¬{C}{aa} fact3: (Ex): {A}x -> {C}x fact4: (Ex): {EP}x -> {GU}x fact5: (Ex): {AL}x -> {HA}x fact6: {C}{aa} -> ¬{F}{aa} fact7: (Ex): {FB}x -> ¬{FR}x fact8: (Ex): {JD}x -> ¬{CP}x fact9: {A}{aa} -> {C}{aa} fact10: (Ex): {R}x -> {IK}x | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 9 | 0 | 9 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããã®çŒç®ã祥é
ãªãã°ãããããŸããããšããããšã¯ãªã fact2: ãããã®çŒç®ã¯è¿æšå·ãªãã°ããããããŸããããšããããšããªãããšããããšãæ¬åœã fact3: ããã祥é
ãªãã°ããŸãããããã®ããã fact4: ããããå
«å¹¡éã ããšããããšãæ¬åœãªãã°éšããããããã®ã¯ãã fact5: ãããå£å§ãããªãã°è¡çºãªããã®ããã fact6: ãããã®çŒç®ãããŸããããªãã°ããã¯é³æ²»ã«ç²ããªã fact7: ãããäºåç¬ãªãã°å€å
ã§ãªãããã®ã¯ãã fact8: ããããåžžç€ç¥ç°ã ããšããããšã¯æãç«ãŠã°ãããããšããããšããªãããã®ããã fact9: ãããã®çŒç®ã祥é
ãªãã°ãããããŸããã fact10: ããããã«ãã³å·ãããããã°é¢šã³ãªããã®ã¯ãã ; $hypothesis$ = ãããã祥é
ãªãã°ããŸããããªãããã®ãããããšããããšã¯æãç«ããªã ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{aa} -> ¬{C}{aa} fact2: {DP}{aa} -> ¬{C}{aa} fact3: (Ex): {A}x -> {C}x fact4: (Ex): {EP}x -> {GU}x fact5: (Ex): {AL}x -> {HA}x fact6: {C}{aa} -> ¬{F}{aa} fact7: (Ex): {FB}x -> ¬{FR}x fact8: (Ex): {JD}x -> ¬{CP}x fact9: {A}{aa} -> {C}{aa} fact10: (Ex): {R}x -> {IK}x ; $hypothesis$ = ¬((Ex): {A}x -> ¬{C}x) ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãããã¹ãšåãè§ç®ç«ããªããªãã°è¥¿æš©çŸãèšãã€ãããšããããšã¯ãªããŠé£ã³æ£ãããã®ããã | (Ex): ¬{A}x -> (¬{AA}x & {AB}x) | fact1: ããäœãã¯åºŠéã«ãªããããšããããšã¯ãªããªãã°ããã¯æšªããã§ãªãããããéæç·ç ã | fact1: (x): ¬{FP}x -> (¬{HD}x & {AF}x) | [] | [] | ããã床éã«ãªããããªããªãã°æšªããã ãšããããšã¯ãªããŠéæç·ç ãªããã®ããã | (Ex): ¬{FP}x -> (¬{HD}x & {AF}x) | [
"fact2 -> int1: ããããã®æåã¯åºŠéã«ãªããããšããããšããªãããšããããšã¯çå®ãªãã°ããã¯æšªããã ãšããããšã¯ãªãããããéæç·ç ã ; int1 -> hypothesis;"
] | 2 | 1 | null | 1 | 0 | 1 | UNKNOWN | PROVED | UNKNOWN | PROVED | $facts$ = fact1: ããäœãã¯åºŠéã«ãªããããšããããšã¯ãªããªãã°ããã¯æšªããã§ãªãããããéæç·ç ã ; $hypothesis$ = ãããã¹ãšåãè§ç®ç«ããªããªãã°è¥¿æš©çŸãèšãã€ãããšããããšã¯ãªããŠé£ã³æ£ãããã®ããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{FP}x -> (¬{HD}x & {AF}x) ; $hypothesis$ = (Ex): ¬{A}x -> (¬{AA}x & {AB}x) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®é£ãã£åãéã | {B}{a} | fact1: ãã®é£ãã£åãèèãããªãããããã¯ãããä»°ãããããããããã¯äž¡æ¹ã fact2: ãã®æ²³åã¯ã²ããéžã§ãªãããããã¯ç·äŒã§ãããäž¡æ¹ã fact3: ãã®å€§æžãæ°ã¥ããããããããã¯ä»°ããããã fact4: ãã®å
çãéããªã fact5: ãã®æºæ³ãä»°ããããããªã fact6: ãã®é£ãã£åã¯ãã³ããã³ã«ææ®ããããããã¯ããã¯éã fact7: ãã®é£ãã£åãéç§ã§ããããããã¯ããã¯é倪ããäž¡æ¹ã fact8: ãããã®é£ãã£åãç·äŒã ãšããããšããªããªãã°ãããã¯ã»ã¬ã»ãªãã»ã¢ã¡ãªã«ã ãšããããšã¯ãªãããšããããšã¯æ¬åœã fact9: ãã®é£ãã£åãç·äŒã ãšããããšã¯ãªããä»°ããããã fact10: ãã®é£ãã£åã¯ä»°ããããããšããããšã¯ãªãããããã¯ããã¯é·ºãéŠã§ããããããã¯äž¡æ¹ã fact11: ãããã®é£ãã£åãç·äŒã ãšããããšããªããããã¯ã¯ãããªããäž¡æ¹ãªãã°ãããéç§ã ãšããããšã¯ãªã fact12: ããã®è·æš©ãä»°ããããããšããããšããªãããšããããšã¯æãç«ã€ fact13: ããã®é£ãã£åã¯é倪ããšããããšããªãããšããããšã¯äºå®ã fact14: ãã®é£ãã£åã¯äžå
æ¢ã«ãããããè¬åã«æº¶ã蟌ããäž¡æ¹ã fact15: ãã®é£ãã£åãå倩æ¹ã§ããããããã¯ãããä»°ããããã fact16: ãã®é£ãã£åãèåäœåã ãšããããšã¯ãªãããããã¯ããã¯ä»°ããããã fact17: ãã®ééãç·äŒã ãšããããšã¯ãªã | fact1: (¬{DK}{a} v {AB}{a}) fact2: (¬{BH}{gh} v {AA}{gh}) fact3: ({BQ}{hq} v {AB}{hq}) fact4: ¬{B}{co} fact5: ¬{AB}{ij} fact6: ({HQ}{a} v {B}{a}) fact7: ({HS}{a} v {JB}{a}) fact8: ¬{AA}{a} -> ¬{II}{a} fact9: (¬{AA}{a} v {AB}{a}) fact10: (¬{AB}{a} v {EK}{a}) fact11: (¬{AA}{a} v {FR}{a}) -> ¬{HS}{a} fact12: ¬{AB}{al} fact13: ¬{JB}{a} fact14: ({GG}{a} v {HU}{a}) fact15: ({EF}{a} v {AB}{a}) fact16: (¬{EH}{a} v {AB}{a}) fact17: ¬{AA}{cl} | [] | [] | null | null | [] | null | 1 | null | 16 | 0 | 16 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®é£ãã£åãèèãããªãããããã¯ãããä»°ãããããããããã¯äž¡æ¹ã fact2: ãã®æ²³åã¯ã²ããéžã§ãªãããããã¯ç·äŒã§ãããäž¡æ¹ã fact3: ãã®å€§æžãæ°ã¥ããããããããã¯ä»°ããããã fact4: ãã®å
çãéããªã fact5: ãã®æºæ³ãä»°ããããããªã fact6: ãã®é£ãã£åã¯ãã³ããã³ã«ææ®ããããããã¯ããã¯éã fact7: ãã®é£ãã£åãéç§ã§ããããããã¯ããã¯é倪ããäž¡æ¹ã fact8: ãããã®é£ãã£åãç·äŒã ãšããããšããªããªãã°ãããã¯ã»ã¬ã»ãªãã»ã¢ã¡ãªã«ã ãšããããšã¯ãªãããšããããšã¯æ¬åœã fact9: ãã®é£ãã£åãç·äŒã ãšããããšã¯ãªããä»°ããããã fact10: ãã®é£ãã£åã¯ä»°ããããããšããããšã¯ãªãããããã¯ããã¯é·ºãéŠã§ããããããã¯äž¡æ¹ã fact11: ãããã®é£ãã£åãç·äŒã ãšããããšããªããããã¯ã¯ãããªããäž¡æ¹ãªãã°ãããéç§ã ãšããããšã¯ãªã fact12: ããã®è·æš©ãä»°ããããããšããããšããªãããšããããšã¯æãç«ã€ fact13: ããã®é£ãã£åã¯é倪ããšããããšããªãããšããããšã¯äºå®ã fact14: ãã®é£ãã£åã¯äžå
æ¢ã«ãããããè¬åã«æº¶ã蟌ããäž¡æ¹ã fact15: ãã®é£ãã£åãå倩æ¹ã§ããããããã¯ãããä»°ããããã fact16: ãã®é£ãã£åãèåäœåã ãšããããšã¯ãªãããããã¯ããã¯ä»°ããããã fact17: ãã®ééãç·äŒã ãšããããšã¯ãªã ; $hypothesis$ = ãã®é£ãã£åãéã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (¬{DK}{a} v {AB}{a}) fact2: (¬{BH}{gh} v {AA}{gh}) fact3: ({BQ}{hq} v {AB}{hq}) fact4: ¬{B}{co} fact5: ¬{AB}{ij} fact6: ({HQ}{a} v {B}{a}) fact7: ({HS}{a} v {JB}{a}) fact8: ¬{AA}{a} -> ¬{II}{a} fact9: (¬{AA}{a} v {AB}{a}) fact10: (¬{AB}{a} v {EK}{a}) fact11: (¬{AA}{a} v {FR}{a}) -> ¬{HS}{a} fact12: ¬{AB}{al} fact13: ¬{JB}{a} fact14: ({GG}{a} v {HU}{a}) fact15: ({EF}{a} v {AB}{a}) fact16: (¬{EH}{a} v {AB}{a}) fact17: ¬{AA}{cl} ; $hypothesis$ = {B}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãã¬ãžãã³ããå®å ã«èª€ããããã¯ãžãžãããããšããããšãééãã | ¬({A}{a} & {B}{a}) | fact1: ãããããã©ããããã®ãããã°ããã®ãã¬ãžãã³ããããã©ãããªããæ°åžã«çºãããªãããšããããšã¯æãç«ã€ãšããããšããªã fact2: ãããæããããã®ãããã°ãã®ã³ã³ããŒã¿ã¯ããã©ãããŠççœã fact3: ãæããããã®ããã fact4: ãã®ãã¬ãžãã³ããå®å ã«èª€ã fact5: ãã®ãã¬ãžãã³ãããžãžããã fact6: ãããäœãã¯èèã§ãªãããžãžããããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯ãžãžããã fact7: ããããã®ãã¬ãžãã³ããããã©ãããšããããšã¯ãªããæ°åžã«çºãããªãããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãããã»ãããã fact8: ããäœããã»ããããã°ãã®çç°è«ãå®å ã«èª€ã fact9: ãã®å®å ããã¬ãžãã³ãã誀ã | fact1: (x): {F}x -> ¬(¬{F}{a} & ¬{E}{a}) fact2: (x): {H}x -> ({F}{b} & {G}{b}) fact3: (Ex): {H}x fact4: {A}{a} fact5: {B}{a} fact6: (x): ¬(¬{C}x & ¬{B}x) -> {B}x fact7: ¬(¬{F}{a} & ¬{E}{a}) -> {D}{a} fact8: (x): {D}x -> {A}{jc} fact9: {AA}{aa} | [
"fact4 & fact5 -> hypothesis;"
] | [
"fact4 & fact5 -> hypothesis;"
] | ããã®çç°è«ããžãžãããããšããããšãæãç«ã€ | {B}{jc} | [
"fact13 -> int1: ããããã®çç°è«ã¯èèã ãšããããšããªããããããžãžããããªãããšããããšã¯æãç«ããªããªãã°ããã¯ãžãžããã; fact12 & fact14 -> int2: ãã®ã³ã³ããŒã¿ãããã©ãããŠççœã; int2 -> int3: ãã®ã³ã³ããŒã¿ã¯ããã©ãã; int3 -> int4: ãããã©ããããã®ããã; int4 & fact15 -> int5: ããã®ãã¬ãžãã³ãã¯ããã©ãããªããã®ã§ãã£ãŠæ°åžã«çºãããªããã®ããšããããšã¯åã ; fact11 & int5 -> int6: ãã®ãã¬ãžãã³ããã»ãããã; int6 -> int7: äœããã»ãããã; int7 & fact10 -> int8: ããã®çç°è«ã¯å®å ã«èª€ãããšããããšã¯æ¬åœã ;"
] | 9 | 1 | 1 | 7 | 0 | 7 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããããã©ããããã®ãããã°ããã®ãã¬ãžãã³ããããã©ãããªããæ°åžã«çºãããªãããšããããšã¯æãç«ã€ãšããããšããªã fact2: ãããæããããã®ãããã°ãã®ã³ã³ããŒã¿ã¯ããã©ãããŠççœã fact3: ãæããããã®ããã fact4: ãã®ãã¬ãžãã³ããå®å ã«èª€ã fact5: ãã®ãã¬ãžãã³ãããžãžããã fact6: ãããäœãã¯èèã§ãªãããžãžããããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯ãžãžããã fact7: ããããã®ãã¬ãžãã³ããããã©ãããšããããšã¯ãªããæ°åžã«çºãããªãããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãããã»ãããã fact8: ããäœããã»ããããã°ãã®çç°è«ãå®å ã«èª€ã fact9: ãã®å®å ããã¬ãžãã³ãã誀ã ; $hypothesis$ = ããã®ãã¬ãžãã³ããå®å ã«èª€ããããã¯ãžãžãããããšããããšãééãã ; $proof$ = | fact4 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {F}x -> ¬(¬{F}{a} & ¬{E}{a}) fact2: (x): {H}x -> ({F}{b} & {G}{b}) fact3: (Ex): {H}x fact4: {A}{a} fact5: {B}{a} fact6: (x): ¬(¬{C}x & ¬{B}x) -> {B}x fact7: ¬(¬{F}{a} & ¬{E}{a}) -> {D}{a} fact8: (x): {D}x -> {A}{jc} fact9: {AA}{aa} ; $hypothesis$ = ¬({A}{a} & {B}{a}) ; $proof$ = | fact4 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | æ±æ©è²¿ã«ç«ãŠãããšãèµ·ãããªããããããããšããããšã¯çãã | (¬{AA} & {AB}) | fact1: ãã°ãèããšããããšãèµ·ãããªãããšããããšã¯ãç« å®ã«åŒãä»ããããšã§ã¯ãªãå ªãé£ããšããããšãçããããšããããšã«åž°çµãã fact2: æãããšã¯èµ·ãããªããšããããšããæ±æ©è²¿ã«ç«ãŠãããšãçºçããããšããããšãé²ã fact3: äžçµæžãçããªãããããæ²çžå€§äº¬ã«èšªããããšã¯èµ·ãã fact4: æ±æ©è²¿ã«ç«ãŠãããšã¯çºçããªã fact5: çããšããããšã¯çºçããªã fact6: æãããšã¯èµ·ããªã fact7: å±éãçããªã fact8: ããŒã²ã³ãããŒã«çšã¿ããããããšã¯èµ·ãããªããæ°Žæžã«ãããŸãããšãèµ·ãã fact9: ææŽã¯çºçããªã fact10: ææŽã¯çºçããªããšããããšãããµãã¯ããããšãèµ·ãããªãã人ä»ãã¯çºçããããšããããšããããã fact11: èèŠãããšããããšãçããªãããããåŒãæãã¯èµ·ãã fact12: ããããŸãããããšããããšã§ã¯ãªããžã³ããŒãŒã«èŠè¿ããããšãçºçããããšããããšã¯ãæãããšã¯èµ·ããããšããããšã«èªçºãããããšããããšã¯æãç«ã€ fact13: ããæãããšãèµ·ãããªããªãã°æ±æ©è²¿ã«ç«ãŠãããšãèµ·ãããªããããããããšããããšãèµ·ãã fact14: äžãæ°Žè°·ã«å¥®ãèµ·ã€ããšãçããªããŠãã®ããããããšããããšã¯çãã fact15: ãç°èŠãçããªãã絊油ãèµ·ããããšããããšã¯ã謊å³ã«ãã¿ããããããšã¯çããªãããšããããšã«åŒãèµ·ãããã fact16: ããããããšããããšãæãããšãèµ·ãããªããšããããšãé»æ¢ãã fact17: ãããæãããšã¯èµ·ããããšããããšã¯åœã ãšããããšã¯ãªããªãã°ããæ±æ©è²¿ã«ç«ãŠãããšãçããªããŠããããããšããããšãçºçããããšããããšãæãç«ã€ããšããããšã¯æãç«ããªã fact18: è©Šã¿ã§ã¯ãªãéèã¯çãã | fact1: ¬{R} -> (¬{EO} & {AM}) fact2: ¬{A} -> ¬{AA} fact3: (¬{HA} & {ET}) fact4: ¬{AA} fact5: ¬{HG} fact6: ¬{A} fact7: ¬{IH} fact8: (¬{CQ} & {HH}) fact9: ¬{AJ} fact10: ¬{AJ} -> (¬{EC} & {AS}) fact11: (¬{HR} & {CB}) fact12: {A} -> (¬{JF} & {AH}) fact13: ¬{A} -> (¬{AA} & {AB}) fact14: (¬{DN} & {DG}) fact15: ¬{EN} -> (¬{H} & {IA}) fact16: {B} -> {A} fact17: {A} -> ¬(¬{AA} & {AB}) fact18: (¬{T} & {IP}) | [
"fact13 & fact6 -> hypothesis;"
] | [
"fact13 & fact6 -> hypothesis;"
] | ãæ±æ©è²¿ã«ç«ãŠãããšãçºçããªããããããããšããããšã¯çããããšããããšã¯æãç«ã€ãšããããšããªã | ¬(¬{AA} & {AB}) | [] | 7 | 1 | 1 | 16 | 0 | 16 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã°ãèããšããããšãèµ·ãããªãããšããããšã¯ãç« å®ã«åŒãä»ããããšã§ã¯ãªãå ªãé£ããšããããšãçããããšããããšã«åž°çµãã fact2: æãããšã¯èµ·ãããªããšããããšããæ±æ©è²¿ã«ç«ãŠãããšãçºçããããšããããšãé²ã fact3: äžçµæžãçããªãããããæ²çžå€§äº¬ã«èšªããããšã¯èµ·ãã fact4: æ±æ©è²¿ã«ç«ãŠãããšã¯çºçããªã fact5: çããšããããšã¯çºçããªã fact6: æãããšã¯èµ·ããªã fact7: å±éãçããªã fact8: ããŒã²ã³ãããŒã«çšã¿ããããããšã¯èµ·ãããªããæ°Žæžã«ãããŸãããšãèµ·ãã fact9: ææŽã¯çºçããªã fact10: ææŽã¯çºçããªããšããããšãããµãã¯ããããšãèµ·ãããªãã人ä»ãã¯çºçããããšããããšããããã fact11: èèŠãããšããããšãçããªãããããåŒãæãã¯èµ·ãã fact12: ããããŸãããããšããããšã§ã¯ãªããžã³ããŒãŒã«èŠè¿ããããšãçºçããããšããããšã¯ãæãããšã¯èµ·ããããšããããšã«èªçºãããããšããããšã¯æãç«ã€ fact13: ããæãããšãèµ·ãããªããªãã°æ±æ©è²¿ã«ç«ãŠãããšãèµ·ãããªããããããããšããããšãèµ·ãã fact14: äžãæ°Žè°·ã«å¥®ãèµ·ã€ããšãçããªããŠãã®ããããããšããããšã¯çãã fact15: ãç°èŠãçããªãã絊油ãèµ·ããããšããããšã¯ã謊å³ã«ãã¿ããããããšã¯çããªãããšããããšã«åŒãèµ·ãããã fact16: ããããããšããããšãæãããšãèµ·ãããªããšããããšãé»æ¢ãã fact17: ãããæãããšã¯èµ·ããããšããããšã¯åœã ãšããããšã¯ãªããªãã°ããæ±æ©è²¿ã«ç«ãŠãããšãçããªããŠããããããšããããšãçºçããããšããããšãæãç«ã€ããšããããšã¯æãç«ããªã fact18: è©Šã¿ã§ã¯ãªãéèã¯çãã ; $hypothesis$ = æ±æ©è²¿ã«ç«ãŠãããšãèµ·ãããªããããããããšããããšã¯çãã ; $proof$ = | fact13 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{R} -> (¬{EO} & {AM}) fact2: ¬{A} -> ¬{AA} fact3: (¬{HA} & {ET}) fact4: ¬{AA} fact5: ¬{HG} fact6: ¬{A} fact7: ¬{IH} fact8: (¬{CQ} & {HH}) fact9: ¬{AJ} fact10: ¬{AJ} -> (¬{EC} & {AS}) fact11: (¬{HR} & {CB}) fact12: {A} -> (¬{JF} & {AH}) fact13: ¬{A} -> (¬{AA} & {AB}) fact14: (¬{DN} & {DG}) fact15: ¬{EN} -> (¬{H} & {IA}) fact16: {B} -> {A} fact17: {A} -> ¬(¬{AA} & {AB}) fact18: (¬{T} & {IP}) ; $hypothesis$ = (¬{AA} & {AB}) ; $proof$ = | fact13 & fact6 -> hypothesis; __PROVED__ |
0.3 | ãããã®ãŠãŒãã£ãªãã£ã¯éèŠãããšããããšããªããçæäºã ãšããããšããªãããšããããšãæ£ããããšããããšãééãã | ¬(¬{AA}{b} & ¬{AB}{b}) | fact1: ããããããã®ãããããããããã¯äžæå°å·ã«ãµããããšããããšããããšãæ£ãããšããããšããªããªãã°ããããããŒã«ããåºããªã fact2: ãããããã®ã¯ãããŒã«ããåºãããšããããšããªããªãã°ãããã¯éèŠãããªããããã¯çæäºã ãšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšããªã fact3: ãã®ãããŒã¯åããããåºããªã fact4: ãã®åãã鷹峰倧æ¥ã ãšããããšã¯ãªã fact5: ãã®åãã¯çæäºã ãšããããšããªã fact6: ãã®ç
§æã¯å°è³¢ãã fact7: ãããã®åãã¯ãããŒã«ããåºãããšããããšã¯ãªããªãã°ãã®ãŠãŒãã£ãªãã£ãéèŠãããšããããšã¯ãªãããããçæäºã ãšããããšããªã fact8: ããããã®åããç æããã£åãããããããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãããããããããšããããšããªã fact9: ãã®åãã¯ãããŒã«ããåºããªã | fact1: (x): ¬({C}x & {B}x) -> ¬{A}x fact2: (x): ¬{A}x -> ¬(¬{AA}x & ¬{AB}x) fact3: ¬{AC}{aa} fact4: ¬{AM}{a} fact5: ¬{AB}{a} fact6: {E}{c} fact7: ¬{A}{a} -> (¬{AA}{b} & ¬{AB}{b}) fact8: ¬({D}{a} & {C}{a}) -> ¬{C}{a} fact9: ¬{A}{a} | [
"fact7 & fact9 -> hypothesis;"
] | [
"fact7 & fact9 -> hypothesis;"
] | ããã®ãŠãŒãã£ãªãã£ãéèŠãããšããããšã¯ãªããã®ã§ãã£ãŠçæäºã ãšããããšããªããã®ããšããããšã¯åã | ¬(¬{AA}{b} & ¬{AB}{b}) | [
"fact12 -> int1: ãããã®ãŠãŒãã£ãªãã£ã¯ãããŒã«ããåºããªããªãã°ãããã¯éèŠãããªããçæäºã§ãªãããšããããšãæãç«ã€ãšããããšããªã; fact10 -> int2: ããããã®ãŠãŒãã£ãªãã£ãããããããäžæå°å·ã«ãµããããšããããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããããããŒã«ããåºãããšããããšã¯ãªã; fact13 -> int3: ãå°è³¢ããããã®ããã;"
] | 7 | 1 | 1 | 7 | 0 | 7 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããããã®ãããããããããã¯äžæå°å·ã«ãµããããšããããšããããšãæ£ãããšããããšããªããªãã°ããããããŒã«ããåºããªã fact2: ãããããã®ã¯ãããŒã«ããåºãããšããããšããªããªãã°ãããã¯éèŠãããªããããã¯çæäºã ãšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšããªã fact3: ãã®ãããŒã¯åããããåºããªã fact4: ãã®åãã鷹峰倧æ¥ã ãšããããšã¯ãªã fact5: ãã®åãã¯çæäºã ãšããããšããªã fact6: ãã®ç
§æã¯å°è³¢ãã fact7: ãããã®åãã¯ãããŒã«ããåºãããšããããšã¯ãªããªãã°ãã®ãŠãŒãã£ãªãã£ãéèŠãããšããããšã¯ãªãããããçæäºã ãšããããšããªã fact8: ããããã®åããç æããã£åãããããããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãããããããããšããããšããªã fact9: ãã®åãã¯ãããŒã«ããåºããªã ; $hypothesis$ = ãããã®ãŠãŒãã£ãªãã£ã¯éèŠãããšããããšããªããçæäºã ãšããããšããªãããšããããšãæ£ããããšããããšãééãã ; $proof$ = | fact7 & fact9 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬({C}x & {B}x) -> ¬{A}x fact2: (x): ¬{A}x -> ¬(¬{AA}x & ¬{AB}x) fact3: ¬{AC}{aa} fact4: ¬{AM}{a} fact5: ¬{AB}{a} fact6: {E}{c} fact7: ¬{A}{a} -> (¬{AA}{b} & ¬{AB}{b}) fact8: ¬({D}{a} & {C}{a}) -> ¬{C}{a} fact9: ¬{A}{a} ; $hypothesis$ = ¬(¬{AA}{b} & ¬{AB}{b}) ; $proof$ = | fact7 & fact9 -> hypothesis; __DISPROVED__ |
0.3 | ãã®å¥é¢ãã³ããªããªã | ¬{A}{a} | fact1: ããäœãããŠã§ã«ããŒãé
ãããããšããããšããªããªãã°ãããã¯ãããªãããå
å
äžè°·å°ã«åšãåãããšããããšã¯ãªãããšããããšã¯èª€ãã fact2: ç©¢ãããããŠç®ç€é«ããšããããšã¯ãªããã®ã¯ãŠã§ã«ããŒãé
ããããªã fact3: å
šãŠã®ãã®ã¯ç©¢ãããããã®ã§ãã£ãŠç®ç€é«ããšããããšããªããã® | fact1: (x): ¬{F}x -> ¬({D}x & ¬{E}x) fact2: (x): ({H}x & ¬{G}x) -> ¬{F}x fact3: (x): ({H}x & ¬{G}x) | [] | [] | ããã®æ¬å±ã¯ã³ããªãããšããããšã¯äºå®ã | {A}{de} | [
"fact4 -> int1: ãããã®åœäž»ãç©¢ããããããããããã¯ç®ç€é«ããšããããšããªããªãã°ããã¯ãŠã§ã«ããŒãé
ããããªã; fact6 -> int2: ãã®åœäž»ã¯ç©¢ããããããããããã¯ç®ç€é«ããªã; int1 & int2 -> int3: ãã®åœäž»ã¯ãŠã§ã«ããŒãé
ãããããšããããšããªã; int3 -> int4: ãããããã®ããŠã§ã«ããŒãé
ãããããšããããšã¯ãªã; int4 -> int5: ãã®çŒç®ããŠã§ã«ããŒãé
ãããããšããããšããªã; fact5 -> int6: ãããã®çŒç®ã¯ãŠã§ã«ããŒãé
ãããããšããããšããªããªãã°ãããã¯ãããªãããããã¯å
å
äžè°·å°ã«åšãåãããšããããšã¯ãªãããšããããšã¯æãç«ããªã; int5 & int6 -> int7: ããã®çŒç®ããããªãããããã¯å
å
äžè°·å°ã«åšãåããªãããšããããšã¯æãç«ããªã;"
] | 9 | 1 | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããäœãããŠã§ã«ããŒãé
ãããããšããããšããªããªãã°ãããã¯ãããªãããå
å
äžè°·å°ã«åšãåãããšããããšã¯ãªãããšããããšã¯èª€ãã fact2: ç©¢ãããããŠç®ç€é«ããšããããšã¯ãªããã®ã¯ãŠã§ã«ããŒãé
ããããªã fact3: å
šãŠã®ãã®ã¯ç©¢ãããããã®ã§ãã£ãŠç®ç€é«ããšããããšããªããã® ; $hypothesis$ = ãã®å¥é¢ãã³ããªããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{F}x -> ¬({D}x & ¬{E}x) fact2: (x): ({H}x & ¬{G}x) -> ¬{F}x fact3: (x): ({H}x & ¬{G}x) ; $hypothesis$ = ¬{A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã³ãŒã³ããŒãã鶎å·ã ãšããããšããªããŠãããããªãããšããããšãæãç«ã€ãšããããšã¯ãªã | ¬(¬{AA}{b} & ¬{AB}{b}) | fact1: ãããäœãã¯ãããããšããããšã¯ãªãããããæ
ãšããããªãããšããããšã¯èª€ããªãã°ããã¯é è¡ã§ãªã fact2: ããäœãã¯ãã
ãåã§ãªããªãã°ãããã¯ããããŸãªããŠæ
ãšããããšããããšããªãããšããããšã¯çå®ã ãšããããšããªã fact3: ãããããã®ããŠã£ã³ããŠã«é£ããããšããããšããªãã矚ããªããªãã°ããããããã fact4: ãããã®ããã°ãªã矚ããªãã°ãã®ã³ãŒã³ããŒãã鶎å·ã§ãªããŠãããããšããããšã¯ãªã fact5: ããäœãã¯é è¡ã ãšããããšããªããªãã°ããããŠã£ã³ããŠã«é£ããããšããããšã¯ãªããŠçŸšããšããããšã¯ãªã fact6: ããäœãã矚ããªãã°ãããã¯é¶Žå·ã ãšããããšããªããããããããããšããããšããªãããšããããšãåœã fact7: ãã®ããã°ãªã¯çŸšã | fact1: (x): ¬(¬{E}x & ¬{D}x) -> ¬{C}x fact2: (x): ¬{F}x -> ¬(¬{E}x & ¬{D}x) fact3: (x): (¬{B}x & ¬{A}x) -> {AB}x fact4: {A}{a} -> (¬{AA}{b} & ¬{AB}{b}) fact5: (x): ¬{C}x -> (¬{B}x & ¬{A}x) fact6: (x): {A}x -> ¬(¬{AA}x & ¬{AB}x) fact7: {A}{a} | [
"fact4 & fact7 -> hypothesis;"
] | [
"fact4 & fact7 -> hypothesis;"
] | ããã®ã³ãŒã³ããŒãã¯é¶Žå·ã§ãªããããããããããªãããšããããšã¯æãç«ããªã | ¬(¬{AA}{b} & ¬{AB}{b}) | [
"fact8 -> int1: ãããã®ã³ãŒã³ããŒãã矚ããªãã°ãããã¯é¶Žå·ã ãšããããšããªããŠãããããªãããšããããšã¯æãç«ããªã;"
] | 5 | 1 | 1 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããäœãã¯ãããããšããããšã¯ãªãããããæ
ãšããããªãããšããããšã¯èª€ããªãã°ããã¯é è¡ã§ãªã fact2: ããäœãã¯ãã
ãåã§ãªããªãã°ãããã¯ããããŸãªããŠæ
ãšããããšããããšããªãããšããããšã¯çå®ã ãšããããšããªã fact3: ãããããã®ããŠã£ã³ããŠã«é£ããããšããããšããªãã矚ããªããªãã°ããããããã fact4: ãããã®ããã°ãªã矚ããªãã°ãã®ã³ãŒã³ããŒãã鶎å·ã§ãªããŠãããããšããããšã¯ãªã fact5: ããäœãã¯é è¡ã ãšããããšããªããªãã°ããããŠã£ã³ããŠã«é£ããããšããããšã¯ãªããŠçŸšããšããããšã¯ãªã fact6: ããäœãã矚ããªãã°ãããã¯é¶Žå·ã ãšããããšããªããããããããããšããããšããªãããšããããšãåœã fact7: ãã®ããã°ãªã¯çŸšã ; $hypothesis$ = ããã®ã³ãŒã³ããŒãã鶎å·ã ãšããããšããªããŠãããããªãããšããããšãæãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact4 & fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬(¬{E}x & ¬{D}x) -> ¬{C}x fact2: (x): ¬{F}x -> ¬(¬{E}x & ¬{D}x) fact3: (x): (¬{B}x & ¬{A}x) -> {AB}x fact4: {A}{a} -> (¬{AA}{b} & ¬{AB}{b}) fact5: (x): ¬{C}x -> (¬{B}x & ¬{A}x) fact6: (x): {A}x -> ¬(¬{AA}x & ¬{AB}x) fact7: {A}{a} ; $hypothesis$ = ¬(¬{AA}{b} & ¬{AB}{b}) ; $proof$ = | fact4 & fact7 -> hypothesis; __DISPROVED__ |
0.3 | ãé¢ãããšãçºçãããåç©çºäžåç©ãåŽããããšãèµ·ããªãããšããããšãäºå®ãšç°ãªã | ¬({AA} & ¬{AB}) | fact1: ãããç·©æ ãèµ·ããããããããããšãèµ·ãããªãããšããããšãæãç«ããªããªãã°ãã ããªããšããããšã¯çºçããªã fact2: ãäžè®ç°ã«ãã¡ã¿ãããšã¯çããªãããšããããšããéç§ãèãæ»ããããšãèµ·ãããªããã§ãããšããããšãèµ·ããããšããããšã®ãã£ãããšãªã fact3: ãèåã«ãã¿ããããšã¯èµ·ããããããããããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ããªã fact4: 貧å¯ã埮ç¡ãããšã¯çãããšããããšã¯ãããããšããããšã§ã¯ãªãã§ãããšããããšãèµ·ããããšããããšãå¥æ©ã fact5: ãé¢ãããšã¯èµ·ãããåç©çºäžåç©ãåŽããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact6: ãããå¯ç¬ãããšããããšãšãã£ãšããããšããããšäž¡æ¹ãçããããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããããšããããšã¯èµ·ããªã fact7: ããèŠæ
£ããããšã¯èµ·ããªããªãã°ãç¡èª¿æ³ãèµ·ãããç¥é¡ã¯çºçããªãããšããããšãåœã fact8: ãèŠæ
£ããããšã¯çºçããªããŠéºã
ãããšããããšãèµ·ããªãããšããããšã¯ãäžè¡ãå±ããèµ·ããããšããããšã«ç±æ¥ãã fact9: èŠæ
£ããããšãèµ·ãããšããããšã¯ãé¢ãããšã¯èµ·ããããããåç©çºäžåç©ãåŽããããšã¯çºçããªãããšããããšã®ãã£ãããšãªã fact10: ãé¢ãããšãšåç©çºäžåç©ãåŽããããšã¯èµ·ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact11: ãããåããšããããšã¯çããªãããããã¯ãããã«ãããšããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯åœãªãã°ãäžè®ç°ã«ãã¡ã¿ãããšã¯çããªãããšããããšãåœã ãšããããšããªã fact12: ããç·šä¿®ãèµ·ãããªããªãã°æ¥å»ã¯èµ·ãããçŠãŸããããšããããšã¯èµ·ãã fact13: ãèŠæ
£ããããšãšéºã
ãããšããããšãçºçããããšããããšã¯äžè¡ãå±ããèµ·ããªããšããããšã«ãããããã fact14: ããçŠãŸããããšããããšã¯çããã°äžè¡ãå±ããçããªããåé¿ã¯èµ·ããªã fact15: ãããããã¡ãç³ããããããšãèµ·ããªããªãã°ããç·©æ ãçºçããããããããããšã¯èµ·ãããªãããšããããšãäºå®ãšç°ãªãããšããããšã¯äºå®ã fact16: ããããããããšãçºçãããç·šä¿®ãèµ·ããããšããããšãäºå®ãšç°ãªãã°ç·šä¿®ãèµ·ããªã fact17: ãå¯ç¬ãããšããããšãçºçããããã£ãšããããšããããšãçºçããããšããããšãééãã fact18: ãç¡ããšããããšãèµ·ããããããã¡ãç³ããããããšãèµ·ããªãããšããããšã¯ã貧å¯ã埮ç¡ãããšã¯çããããšããããšãåå ã fact19: ãã²ãããšããããšãèµ·ãããç¹°åºãã¯èµ·ããªãããšããããšãåã fact20: ãããã ããªããšããããšã¯èµ·ããªããªãã°ããããããšãšç·šä¿®ã¯èµ·ããããšããããšãæãç«ããªã | fact1: ¬({K} & ¬{J}) -> ¬{I} fact2: ¬{T} -> (¬{Q} & {O}) fact3: ¬({HJ} & ¬{FO}) fact4: (¬{P} & {O}) -> {N} fact5: ¬({AA} & ¬{AB}) fact6: ¬({S} & {R}) -> ¬{P} fact7: ¬{A} -> ¬({JJ} & ¬{HL}) fact8: {C} -> (¬{A} & ¬{B}) fact9: {A} -> ({AA} & ¬{AB}) fact10: ¬({AA} & {AB}) fact11: ¬(¬{AC} v {U}) -> ¬{T} fact12: ¬{G} -> ({F} & {E}) fact13: ¬{C} -> ({A} & {B}) fact14: {E} -> (¬{C} & ¬{D}) fact15: ¬{L} -> ¬({K} & ¬{J}) fact16: ¬({H} & {G}) -> ¬{G} fact17: ¬({S} & {R}) fact18: {N} -> ({M} & ¬{L}) fact19: ¬({IF} & ¬{ES}) fact20: ¬{I} -> ¬({H} & {G}) | [
"fact5 -> hypothesis;"
] | [
"fact5 -> hypothesis;"
] | é¢ãããšãçããããããåç©çºäžåç©ãåŽããããšãçããªã | ({AA} & ¬{AB}) | [
"fact30 & fact26 -> int1: ããããšããããšãèµ·ãããªã;"
] | 18 | 1 | 0 | 19 | 0 | 19 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããç·©æ ãèµ·ããããããããããšãèµ·ãããªãããšããããšãæãç«ããªããªãã°ãã ããªããšããããšã¯çºçããªã fact2: ãäžè®ç°ã«ãã¡ã¿ãããšã¯çããªãããšããããšããéç§ãèãæ»ããããšãèµ·ãããªããã§ãããšããããšãèµ·ããããšããããšã®ãã£ãããšãªã fact3: ãèåã«ãã¿ããããšã¯èµ·ããããããããããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ããªã fact4: 貧å¯ã埮ç¡ãããšã¯çãããšããããšã¯ãããããšããããšã§ã¯ãªãã§ãããšããããšãèµ·ããããšããããšãå¥æ©ã fact5: ãé¢ãããšã¯èµ·ãããåç©çºäžåç©ãåŽããããšã¯èµ·ããªãããšããããšã¯æãç«ããªã fact6: ãããå¯ç¬ãããšããããšãšãã£ãšããããšããããšäž¡æ¹ãçããããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããããšããããšã¯èµ·ããªã fact7: ããèŠæ
£ããããšã¯èµ·ããªããªãã°ãç¡èª¿æ³ãèµ·ãããç¥é¡ã¯çºçããªãããšããããšãåœã fact8: ãèŠæ
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ãããšããããšãèµ·ããªãããšããããšã¯ãäžè¡ãå±ããèµ·ããããšããããšã«ç±æ¥ãã fact9: èŠæ
£ããããšãèµ·ãããšããããšã¯ãé¢ãããšã¯èµ·ããããããåç©çºäžåç©ãåŽããããšã¯çºçããªãããšããããšã®ãã£ãããšãªã fact10: ãé¢ãããšãšåç©çºäžåç©ãåŽããããšã¯èµ·ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact11: ãããåããšããããšã¯çããªãããããã¯ãããã«ãããšããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯åœãªãã°ãäžè®ç°ã«ãã¡ã¿ãããšã¯çããªãããšããããšãåœã ãšããããšããªã fact12: ããç·šä¿®ãèµ·ãããªããªãã°æ¥å»ã¯èµ·ãããçŠãŸããããšããããšã¯èµ·ãã fact13: ãèŠæ
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ãããšããããšãçºçããããšããããšã¯äžè¡ãå±ããèµ·ããªããšããããšã«ãããããã fact14: ããçŠãŸããããšããããšã¯çããã°äžè¡ãå±ããçããªããåé¿ã¯èµ·ããªã fact15: ãããããã¡ãç³ããããããšãèµ·ããªããªãã°ããç·©æ ãçºçããããããããããšã¯èµ·ãããªãããšããããšãäºå®ãšç°ãªãããšããããšã¯äºå®ã fact16: ããããããããšãçºçãããç·šä¿®ãèµ·ããããšããããšãäºå®ãšç°ãªãã°ç·šä¿®ãèµ·ããªã fact17: ãå¯ç¬ãããšããããšãçºçããããã£ãšããããšããããšãçºçããããšããããšãééãã fact18: ãç¡ããšããããšãèµ·ããããããã¡ãç³ããããããšãèµ·ããªãããšããããšã¯ã貧å¯ã埮ç¡ãããšã¯çããããšããããšãåå ã fact19: ãã²ãããšããããšãèµ·ãããç¹°åºãã¯èµ·ããªãããšããããšãåã fact20: ãããã ããªããšããããšã¯èµ·ããªããªãã°ããããããšãšç·šä¿®ã¯èµ·ããããšããããšãæãç«ããªã ; $hypothesis$ = ãé¢ãããšãçºçãããåç©çºäžåç©ãåŽããããšãèµ·ããªãããšããããšãäºå®ãšç°ãªã ; $proof$ = | fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({K} & ¬{J}) -> ¬{I} fact2: ¬{T} -> (¬{Q} & {O}) fact3: ¬({HJ} & ¬{FO}) fact4: (¬{P} & {O}) -> {N} fact5: ¬({AA} & ¬{AB}) fact6: ¬({S} & {R}) -> ¬{P} fact7: ¬{A} -> ¬({JJ} & ¬{HL}) fact8: {C} -> (¬{A} & ¬{B}) fact9: {A} -> ({AA} & ¬{AB}) fact10: ¬({AA} & {AB}) fact11: ¬(¬{AC} v {U}) -> ¬{T} fact12: ¬{G} -> ({F} & {E}) fact13: ¬{C} -> ({A} & {B}) fact14: {E} -> (¬{C} & ¬{D}) fact15: ¬{L} -> ¬({K} & ¬{J}) fact16: ¬({H} & {G}) -> ¬{G} fact17: ¬({S} & {R}) fact18: {N} -> ({M} & ¬{L}) fact19: ¬({IF} & ¬{ES}) fact20: ¬{I} -> ¬({H} & {G}) ; $hypothesis$ = ¬({AA} & ¬{AB}) ; $proof$ = | fact5 -> hypothesis; __PROVED__ |
0.3 | è
æœã¯èµ·ãããªã | ¬{B} | fact1: èªè·¡ãçãã fact2: ããŸããããšããããšãçºçãã fact3: ããèªè·¡ãçºçããªããªãã°çŽãã¯çºçãã fact4: ãªããŒãµã«ãšæ®å€ããšããããšãçãã fact5: åå±ã¿ãçºçãã fact6: è¥ããšããããšãçãããã¬ãããšã¯çãã fact7: ãã³ãã ãããšããããšãèµ·ãã fact8: å§æ®ºã¯èµ·ãã fact9: çé·ã¯èµ·ãããå¿ããããšããããšã¯èµ·ãã fact10: æ¯è¢ã«ä»£ããããšãšå¿ããããšããããšäž¡æ¹ã¯èµ·ãã | fact1: {A} fact2: {HH} fact3: ¬{A} -> {ED} fact4: ({BA} & {AT}) fact5: {EO} fact6: ({FH} & {CE}) fact7: {FF} fact8: {DC} fact9: ({BP} & {GF}) fact10: ({JI} & {N}) | [] | [] | çŽãã¯çãã | {ED} | [] | 6 | 1 | null | 10 | 0 | 10 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: èªè·¡ãçãã fact2: ããŸããããšããããšãçºçãã fact3: ããèªè·¡ãçºçããªããªãã°çŽãã¯çºçãã fact4: ãªããŒãµã«ãšæ®å€ããšããããšãçãã fact5: åå±ã¿ãçºçãã fact6: è¥ããšããããšãçãããã¬ãããšã¯çãã fact7: ãã³ãã ãããšããããšãèµ·ãã fact8: å§æ®ºã¯èµ·ãã fact9: çé·ã¯èµ·ãããå¿ããããšããããšã¯èµ·ãã fact10: æ¯è¢ã«ä»£ããããšãšå¿ããããšããããšäž¡æ¹ã¯èµ·ãã ; $hypothesis$ = è
æœã¯èµ·ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} fact2: {HH} fact3: ¬{A} -> {ED} fact4: ({BA} & {AT}) fact5: {EO} fact6: ({FH} & {CE}) fact7: {FF} fact8: {DC} fact9: ({BP} & {GF}) fact10: ({JI} & {N}) ; $hypothesis$ = ¬{B} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããæŸå³°ãªãã°æ©æŽ¥ã«åãèããæ¥æš¹ãèããã ããšããããšã¯ãªãããã®ã¯ãã | (Ex): {A}x -> ({AA}x & ¬{AB}x) | fact1: ãããæŸå³°ãªãã°æ©æŽ¥ã«åãèããæ¥æš¹ãèããã ãããã®ããã fact2: ãããã®æ§æ¬ã¯æŸå³°ãªãã°ãããæ©æŽ¥ã«åãèããæ¥æš¹ãèããã ããªã | fact1: (Ex): {A}x -> ({AA}x & {AB}x) fact2: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) | [
"fact2 -> hypothesis;"
] | [
"fact2 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãããæŸå³°ãªãã°æ©æŽ¥ã«åãèããæ¥æš¹ãèããã ãããã®ããã fact2: ãããã®æ§æ¬ã¯æŸå³°ãªãã°ãããæ©æŽ¥ã«åãèããæ¥æš¹ãèããã ããªã ; $hypothesis$ = ãããæŸå³°ãªãã°æ©æŽ¥ã«åãèããæ¥æš¹ãèããã ããšããããšã¯ãªãããã®ã¯ãã ; $proof$ = | fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: (Ex): {A}x -> ({AA}x & {AB}x) fact2: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) ; $hypothesis$ = (Ex): {A}x -> ({AA}x & ¬{AB}x) ; $proof$ = | fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®é»å§ã¯ãŠã€ã ã | {A}{a} | fact1: ããæ°ŽæžæŸéå±ã西èšæžäºæ¡ã§ãªããªãã°ãããããŠã€ã ããªãããšããããšãçå®ã fact2: ããããã®é£èãäŒè³éã ãšããããšã¯ãªãããšããããšã¯æ¬åœãªãã°ããã®ããã¯åµ¯å³šæšååçŠç°ã§ãªããå¬ã«æãŠãããšããããšãåã fact3: ããäœããã¹ã¿ãžãªã«æ±ãéããªããªãã°ãããæããããããããã¯èŠæ²Œã§ããããããã¯äž¡æ¹ã fact4: ãããäœãã¯åµ¯å³šæšååçŠç°ã ãšããããšããªãããããããã¯å¬ã«æãŠãããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯ã¹ã¿ãžãªã«æ±ãéãããšããããšã¯ãªã fact5: ããäœãã¯å¬ã«æãŠãªããªãã°ããããã¯ã¹ã¿ãžãªã«æ±ãéãããšããããšã¯ãªããŠããã¯èŠæ²Œã ããšããããšã¯ééãã§ãªãããšããããšãäºå®ãšç°ãªã fact6: ãã®é£èã¯ç©ãã®ãã fact7: ãããã®ããããŠã€ã ããªããªãã°ããã®é»å§ã¯å¹žã±è°·ã ãå®å€«ã ãšããããšã¯ãªãããšããããšãåã fact8: äœããæ¿ãæšã ããããçªã£åŒµããšããããšã¯ãªã fact9: ããããã®é£èã¯è¥¿èšæžäºæ¡ã ãšããããšã¯ãªãããšããããšãæãç«ãŠã°ããã®ããããŠã€ã ããªãããšããããšã誀ãã ãšããããšããªã fact10: ããæ¿ãæšã§çªã£åŒµãããšããããšã¯æ¬åœã ãšããããšããªãããã®ã¯ãã fact11: ãããã®é£èãç©ãã®ãããªãã°ããã¯ããããããæ°è€ã±åŽããã¡ããããªã fact12: ãããããŠã€ã ããç©ããããšããããšã¯ãªãããšããããšã¯æãç«ããªãããã®ã¯ããã°ããã®é»å§ãã¬ããšãããšããããšã¯æãç«ã€ fact13: ããäœããçªã£åŒµãã°ãã®é»å§ããŠã€ã ã fact14: ããããããµãããããŠè¥¿èšæžäºæ¡ã ãšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ã¯ããã°ãã®é倩ã¯çªã£åŒµãããšããããšã¯æ¬åœã fact15: æãããããã®ãæ°ŽæžæŸéå±ã§ãã£ãŠè¥¿èšæžäºæ¡ã§ãªããã® fact16: ããæ¿ãæšã ãçªã£åŒµããšããããšã¯ãªãããšããããšã誀ããªããã®ããã fact17: ããããããããã®ã¯æ°è€ã±åŽããã¡ããããšããããšã¯ãªããªãã°ãããäŒè³éã ãšããããšããªã fact18: ããããã¹ã¿ãžãªã«æ±ãéãããšããããšã¯ãªããŠèŠæ²Œã ããšããããšãåãªããã®ãããã°ãã®é£èã¯æãããã fact19: ããäœããæ°ŽæžæŸéå±ã§ãªããªãã°ããã¯è¥¿èšæžäºæ¡ã§ãªãããããã¯ããããŠã€ã ããšããããšã¯ãªã fact20: ããäœãã¯æãããããªãã°ããã¯æ°ŽæžæŸéå±ã ãšããããšã¯ãªã | fact1: (x): ({C}x & ¬{B}x) -> ¬{A}x fact2: ¬{I}{c} -> ¬(¬{H}{b} & {G}{b}) fact3: (x): ¬{E}x -> ({D}x v {F}x) fact4: (x): ¬(¬{H}x & {G}x) -> ¬{E}x fact5: (x): ¬{G}x -> ¬(¬{E}x & {F}x) fact6: {L}{c} fact7: ¬{A}{b} -> ¬({DI}{a} & ¬{CP}{a}) fact8: (Ex): ({AA}x & ¬{AB}x) fact9: ¬{B}{c} -> ¬{A}{b} fact10: (Ex): ¬({AA}x & {AB}x) fact11: {L}{c} -> ({J}{c} & ¬{K}{c}) fact12: (x): ¬({A}x & ¬{HK}x) -> {GK}{a} fact13: (x): {AB}x -> {A}{a} fact14: (x): ¬({BN}x & ¬{B}x) -> {AB}{gk} fact15: (x): {D}x -> ({C}x & ¬{B}x) fact16: (Ex): ¬({AA}x & ¬{AB}x) fact17: (x): ({J}x & ¬{K}x) -> ¬{I}x fact18: (x): ¬(¬{E}x & {F}x) -> {D}{c} fact19: (x): ¬{C}x -> (¬{B}x v ¬{A}x) fact20: (x): {D}x -> ¬{C}x | [] | [] | ãã幞ã±è°·ã ãå®å€«ã§ãªãããšããããšãæãç«ããªãããã®ã¯ãã | (Ex): ¬({DI}x & ¬{CP}x) | [
"fact26 -> int1: ãããã®é£èã¯æ°ŽæžæŸéå±ã§ãªããªãã°ããã¯è¥¿èšæžäºæ¡ã ãšããããšã¯ãªãããããã¯ããã¯ãŠã€ã ããªãããããã¯äž¡æ¹ã ; fact23 -> int2: ãããã®é£èã¯æãããããªãã°ãããæ°ŽæžæŸéå±ã§ãªã; fact25 -> int3: ãããã®å
šç²ç²ã¯å¬ã«æãŠãªããªãã°ããããã¹ã¿ãžãªã«æ±ãéãããšããããšããªãããããèŠæ²Œã ããšããããšã¯åã ;"
] | 9 | 1 | null | 19 | 0 | 19 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããæ°ŽæžæŸéå±ã西èšæžäºæ¡ã§ãªããªãã°ãããããŠã€ã ããªãããšããããšãçå®ã fact2: ããããã®é£èãäŒè³éã ãšããããšã¯ãªãããšããããšã¯æ¬åœãªãã°ããã®ããã¯åµ¯å³šæšååçŠç°ã§ãªããå¬ã«æãŠãããšããããšãåã fact3: ããäœããã¹ã¿ãžãªã«æ±ãéããªããªãã°ãããæããããããããã¯èŠæ²Œã§ããããããã¯äž¡æ¹ã fact4: ãããäœãã¯åµ¯å³šæšååçŠç°ã ãšããããšããªãããããããã¯å¬ã«æãŠãããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯ã¹ã¿ãžãªã«æ±ãéãããšããããšã¯ãªã fact5: ããäœãã¯å¬ã«æãŠãªããªãã°ããããã¯ã¹ã¿ãžãªã«æ±ãéãããšããããšã¯ãªããŠããã¯èŠæ²Œã ããšããããšã¯ééãã§ãªãããšããããšãäºå®ãšç°ãªã fact6: ãã®é£èã¯ç©ãã®ãã fact7: ãããã®ããããŠã€ã ããªããªãã°ããã®é»å§ã¯å¹žã±è°·ã ãå®å€«ã ãšããããšã¯ãªãããšããããšãåã fact8: äœããæ¿ãæšã ããããçªã£åŒµããšããããšã¯ãªã fact9: ããããã®é£èã¯è¥¿èšæžäºæ¡ã ãšããããšã¯ãªãããšããããšãæãç«ãŠã°ããã®ããããŠã€ã ããªãããšããããšã誀ãã ãšããããšããªã fact10: ããæ¿ãæšã§çªã£åŒµãããšããããšã¯æ¬åœã ãšããããšããªãããã®ã¯ãã fact11: ãããã®é£èãç©ãã®ãããªãã°ããã¯ããããããæ°è€ã±åŽããã¡ããããªã fact12: ãããããŠã€ã ããç©ããããšããããšã¯ãªãããšããããšã¯æãç«ããªãããã®ã¯ããã°ããã®é»å§ãã¬ããšãããšããããšã¯æãç«ã€ fact13: ããäœããçªã£åŒµãã°ãã®é»å§ããŠã€ã ã fact14: ããããããµãããããŠè¥¿èšæžäºæ¡ã ãšããããšã¯ãªãããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ã¯ããã°ãã®é倩ã¯çªã£åŒµãããšããããšã¯æ¬åœã fact15: æãããããã®ãæ°ŽæžæŸéå±ã§ãã£ãŠè¥¿èšæžäºæ¡ã§ãªããã® fact16: ããæ¿ãæšã ãçªã£åŒµããšããããšã¯ãªãããšããããšã誀ããªããã®ããã fact17: ããããããããã®ã¯æ°è€ã±åŽããã¡ããããšããããšã¯ãªããªãã°ãããäŒè³éã ãšããããšããªã fact18: ããããã¹ã¿ãžãªã«æ±ãéãããšããããšã¯ãªããŠèŠæ²Œã ããšããããšãåãªããã®ãããã°ãã®é£èã¯æãããã fact19: ããäœããæ°ŽæžæŸéå±ã§ãªããªãã°ããã¯è¥¿èšæžäºæ¡ã§ãªãããããã¯ããããŠã€ã ããšããããšã¯ãªã fact20: ããäœãã¯æãããããªãã°ããã¯æ°ŽæžæŸéå±ã ãšããããšã¯ãªã ; $hypothesis$ = ãã®é»å§ã¯ãŠã€ã ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ({C}x & ¬{B}x) -> ¬{A}x fact2: ¬{I}{c} -> ¬(¬{H}{b} & {G}{b}) fact3: (x): ¬{E}x -> ({D}x v {F}x) fact4: (x): ¬(¬{H}x & {G}x) -> ¬{E}x fact5: (x): ¬{G}x -> ¬(¬{E}x & {F}x) fact6: {L}{c} fact7: ¬{A}{b} -> ¬({DI}{a} & ¬{CP}{a}) fact8: (Ex): ({AA}x & ¬{AB}x) fact9: ¬{B}{c} -> ¬{A}{b} fact10: (Ex): ¬({AA}x & {AB}x) fact11: {L}{c} -> ({J}{c} & ¬{K}{c}) fact12: (x): ¬({A}x & ¬{HK}x) -> {GK}{a} fact13: (x): {AB}x -> {A}{a} fact14: (x): ¬({BN}x & ¬{B}x) -> {AB}{gk} fact15: (x): {D}x -> ({C}x & ¬{B}x) fact16: (Ex): ¬({AA}x & ¬{AB}x) fact17: (x): ({J}x & ¬{K}x) -> ¬{I}x fact18: (x): ¬(¬{E}x & {F}x) -> {D}{c} fact19: (x): ¬{C}x -> (¬{B}x v ¬{A}x) fact20: (x): {D}x -> ¬{C}x ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããã®ã¹ãºã¡ããã¶ããšããããšããªããªãã°ãã®ã¹ãºã¡ãèžããããšããããšã¯ééãã | ¬(¬{B}{aa} -> {C}{aa}) | fact1: ããäœãã¯ãã¶ããªãã°ããã¯èžãã fact2: ããäœãã¯éããšããããšããªããªãã°ããã¯ããŸãããã fact3: ãããããã®ã¯é²ãããã¡ããã€ãããšããããšã¯ãªããªãã°ããã¯ããã¹ã«ãŒãã fact4: ããäœãã端åŽã«ãããªããªãã°ãããå èçºäžå èãç¹°ãè¿ãã fact5: ãããã®ãã¯ãã³ã¹ã¢ã¹ã¯èžãããšããããšã¯ãªããªãã°ããã¯ããæ¥ãã fact6: ãããã®ã¹ãºã¡ããšã¹ãã©ã³ãã«è§Šãåããšããããšããªããªãã°ãããççãã fact7: ããããã®ç ç³ããã¶ããšããããšã¯ãªãããšããããšã¯æ¬åœãªãã°ããã¯è»œçºæ²¢ã«ã§ãããã fact8: ããããã®ã¹ãºã¡ãã€ãã¢ã€ãã€ã ãšããããšããªãããšããããšã¯æ£ãããªãã°ããã¯ãã¬ãå±±å£ãæµ®ã¹ã fact9: ããäœãã¯æ¢
挬ãã§ãªããªãã°ãããã¬ã³ãã©ã³ãã fact10: ãããããã®ã¯èžãããªããªãã°ããã¯å¥¥æ·±ã fact11: ããããã®ãšã¹ãã¹ã¯ãµãããªããªãã°ãã®ãšã¹ãã¹ã¯ãã¶ãããšããããšãæãç«ã€ fact12: ãããã®ã¹ãºã¡ãã¯ãããªããªãã°ãããå°ãªã fact13: ããäœãã¯ãã¶ããšããããšããªããªãã°ããã¯èžãã fact14: ããããã®ã¹ãºã¡ã¯ãã¶ããªãã°ãã®ã¹ãºã¡ã¯èžããããšããããšã¯æãç«ã€ fact15: ãããã®ã¹ãºã¡ã¯ã€ãã«ãããªããªãã°ãããåå¡©åå°ããµã | fact1: (x): {B}x -> {C}x fact2: (x): ¬{HC}x -> {CA}x fact3: (x): ¬{IG}x -> {EH}x fact4: (x): ¬{AM}x -> {CS}x fact5: ¬{C}{cm} -> {ET}{cm} fact6: ¬{DK}{aa} -> {CB}{aa} fact7: ¬{B}{i} -> {P}{i} fact8: ¬{JI}{aa} -> {BS}{aa} fact9: (x): ¬{BF}x -> {F}x fact10: (x): ¬{C}x -> {HK}x fact11: ¬{FN}{gc} -> {B}{gc} fact12: ¬{AA}{aa} -> {BU}{aa} fact13: (x): ¬{B}x -> {C}x fact14: {B}{aa} -> {C}{aa} fact15: ¬{EC}{aa} -> {AF}{aa} | [
"fact13 -> hypothesis;"
] | [
"fact13 -> hypothesis;"
] | ãããã®ãã«ã¯èžãããªããªãã°ããã¯å¥¥æ·±ã | ¬{C}{bp} -> {HK}{bp} | [
"fact16 -> hypothesis;"
] | 1 | 1 | 1 | 14 | 0 | 14 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ããäœãã¯ãã¶ããªãã°ããã¯èžãã fact2: ããäœãã¯éããšããããšããªããªãã°ããã¯ããŸãããã fact3: ãããããã®ã¯é²ãããã¡ããã€ãããšããããšã¯ãªããªãã°ããã¯ããã¹ã«ãŒãã fact4: ããäœãã端åŽã«ãããªããªãã°ãããå èçºäžå èãç¹°ãè¿ãã fact5: ãããã®ãã¯ãã³ã¹ã¢ã¹ã¯èžãããšããããšã¯ãªããªãã°ããã¯ããæ¥ãã fact6: ãããã®ã¹ãºã¡ããšã¹ãã©ã³ãã«è§Šãåããšããããšããªããªãã°ãããççãã fact7: ããããã®ç ç³ããã¶ããšããããšã¯ãªãããšããããšã¯æ¬åœãªãã°ããã¯è»œçºæ²¢ã«ã§ãããã fact8: ããããã®ã¹ãºã¡ãã€ãã¢ã€ãã€ã ãšããããšããªãããšããããšã¯æ£ãããªãã°ããã¯ãã¬ãå±±å£ãæµ®ã¹ã fact9: ããäœãã¯æ¢
挬ãã§ãªããªãã°ãããã¬ã³ãã©ã³ãã fact10: ãããããã®ã¯èžãããªããªãã°ããã¯å¥¥æ·±ã fact11: ããããã®ãšã¹ãã¹ã¯ãµãããªããªãã°ãã®ãšã¹ãã¹ã¯ãã¶ãããšããããšãæãç«ã€ fact12: ãããã®ã¹ãºã¡ãã¯ãããªããªãã°ãããå°ãªã fact13: ããäœãã¯ãã¶ããšããããšããªããªãã°ããã¯èžãã fact14: ããããã®ã¹ãºã¡ã¯ãã¶ããªãã°ãã®ã¹ãºã¡ã¯èžããããšããããšã¯æãç«ã€ fact15: ãããã®ã¹ãºã¡ã¯ã€ãã«ãããªããªãã°ãããåå¡©åå°ããµã ; $hypothesis$ = ããããã®ã¹ãºã¡ããã¶ããšããããšããªããªãã°ãã®ã¹ãºã¡ãèžããããšããããšã¯ééãã ; $proof$ = | fact13 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {B}x -> {C}x fact2: (x): ¬{HC}x -> {CA}x fact3: (x): ¬{IG}x -> {EH}x fact4: (x): ¬{AM}x -> {CS}x fact5: ¬{C}{cm} -> {ET}{cm} fact6: ¬{DK}{aa} -> {CB}{aa} fact7: ¬{B}{i} -> {P}{i} fact8: ¬{JI}{aa} -> {BS}{aa} fact9: (x): ¬{BF}x -> {F}x fact10: (x): ¬{C}x -> {HK}x fact11: ¬{FN}{gc} -> {B}{gc} fact12: ¬{AA}{aa} -> {BU}{aa} fact13: (x): ¬{B}x -> {C}x fact14: {B}{aa} -> {C}{aa} fact15: ¬{EC}{aa} -> {AF}{aa} ; $hypothesis$ = ¬(¬{B}{aa} -> {C}{aa}) ; $proof$ = | fact13 -> hypothesis; __DISPROVED__ |
0.3 | ã«ãã«ããããšããããšãçãã | {B} | fact1: ãããåãåããšç©é³äž¡æ¹ãçããããšããããšã¯äºå®ã§ãªããªãã°ã«ãã«ããããšããããšã¯èµ·ãããªã fact2: ããªã¿ã ããããšããããšãšãã¿ãããããšããããšäž¡æ¹ãèµ·ããããšããããšã¯ãåã
ãããšããããšãèµ·ãããªãããšããããšã«ããçãã fact3: ãããè£ä»ãããããããããšãšç±ã£ãœããšããããšã¯èµ·ããããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãåã
ãããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact4: ããããã«ãã«ããããšããããšã¯èµ·ããªããããã女童ããã°ããšããããšã¯çããããšããããšãäºå®ãšç°ãªãã°å¥³ç«¥ããã°ããšããããšãçããªãããšããããšãçå®ã fact5: è£ä»ãããããããããšã¯èµ·ãããªããšããããšã¯ãç±ã£ãœããšããããšã¯çºçãããåã
ãããšããããšã¯çºçããããšããããšãçãããã fact6: ãã«ãã«ããããšããããšã¯èµ·ããªãããšããããšã¯ç©é³ãçããªããšããããšã«ããçºçãã fact7: ãçµæ±ºã¯èµ·ãããªãããšããããšããã«ããããšãèµ·ããããããããã¶ããããšã¯èµ·ããªãããšããããšããããã fact8: ããããã¶ããããšã¯çããªããªãã°ãè£ä»ãããããããããšãšç±ã£ãœããšããããšã¯èµ·ããããšããããšãäºå®ãšç°ãªã fact9: ãªã¿ã ããããšããããšãèµ·ãããšããããšã¯ãã¿ãããããšããããšãèµ·ãããšããããšã«èªçºããã fact10: ãããªã¿ã ããããšããããšãèµ·ããã°ãã«ãã«ããããšããããšã¯èµ·ãããªãã女童ããã°ããšããããšã¯èµ·ããããšããããšã¯åœã fact11: ãåãåããšç©é³ãçºçããããšããããšãäºå®ãšç°ãªã fact12: ããªã¿ã ããããšããããšãçºçããããšããããšã¯ã女童ããã°ããšããããšã§ã¯ãªãã«ãã«ããããšããããšãçºçããããšããããšã®åå ãšãªã fact13: ãçŠçã¯çºçããããšããããšã¯å¥³ç«¥ããã°ããšããããšã¯çããªããšããããšã«ææ¢ããã | fact1: ¬({AA} & {AB}) -> ¬{B} fact2: ¬{E} -> ({C} & {D}) fact3: ¬({G} & {F}) -> ¬{E} fact4: ¬(¬{B} & {A}) -> ¬{A} fact5: ¬{G} -> ({F} & {E}) fact6: ¬{AB} -> ¬{B} fact7: ¬{J} -> ({I} & ¬{H}) fact8: ¬{H} -> ¬({G} & {F}) fact9: {D} -> {C} fact10: {C} -> ¬(¬{B} & {A}) fact11: ¬({AA} & {AB}) fact12: {C} -> (¬{A} & {B}) fact13: ¬{A} -> ¬{CE} | [
"fact1 & fact11 -> hypothesis;"
] | [
"fact1 & fact11 -> hypothesis;"
] | ãã«ãã«ããããšããããšãèµ·ããããšããããšãäºå®ã | {B} | [] | 8 | 1 | 1 | 11 | 0 | 11 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããåãåããšç©é³äž¡æ¹ãçããããšããããšã¯äºå®ã§ãªããªãã°ã«ãã«ããããšããããšã¯èµ·ãããªã fact2: ããªã¿ã ããããšããããšãšãã¿ãããããšããããšäž¡æ¹ãèµ·ããããšããããšã¯ãåã
ãããšããããšãèµ·ãããªãããšããããšã«ããçãã fact3: ãããè£ä»ãããããããããšãšç±ã£ãœããšããããšã¯èµ·ããããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãåã
ãããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact4: ããããã«ãã«ããããšããããšã¯èµ·ããªããããã女童ããã°ããšããããšã¯çããããšããããšãäºå®ãšç°ãªãã°å¥³ç«¥ããã°ããšããããšãçããªãããšããããšãçå®ã fact5: è£ä»ãããããããããšã¯èµ·ãããªããšããããšã¯ãç±ã£ãœããšããããšã¯çºçãããåã
ãããšããããšã¯çºçããããšããããšãçãããã fact6: ãã«ãã«ããããšããããšã¯èµ·ããªãããšããããšã¯ç©é³ãçããªããšããããšã«ããçºçãã fact7: ãçµæ±ºã¯èµ·ãããªãããšããããšããã«ããããšãèµ·ããããããããã¶ããããšã¯èµ·ããªãããšããããšããããã fact8: ããããã¶ããããšã¯çããªããªãã°ãè£ä»ãããããããããšãšç±ã£ãœããšããããšã¯èµ·ããããšããããšãäºå®ãšç°ãªã fact9: ãªã¿ã ããããšããããšãèµ·ãããšããããšã¯ãã¿ãããããšããããšãèµ·ãããšããããšã«èªçºããã fact10: ãããªã¿ã ããããšããããšãèµ·ããã°ãã«ãã«ããããšããããšã¯èµ·ãããªãã女童ããã°ããšããããšã¯èµ·ããããšããããšã¯åœã fact11: ãåãåããšç©é³ãçºçããããšããããšãäºå®ãšç°ãªã fact12: ããªã¿ã ããããšããããšãçºçããããšããããšã¯ã女童ããã°ããšããããšã§ã¯ãªãã«ãã«ããããšããããšãçºçããããšããããšã®åå ãšãªã fact13: ãçŠçã¯çºçããããšããããšã¯å¥³ç«¥ããã°ããšããããšã¯çããªããšããããšã«ææ¢ããã ; $hypothesis$ = ã«ãã«ããããšããããšãçãã ; $proof$ = | fact1 & fact11 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({AA} & {AB}) -> ¬{B} fact2: ¬{E} -> ({C} & {D}) fact3: ¬({G} & {F}) -> ¬{E} fact4: ¬(¬{B} & {A}) -> ¬{A} fact5: ¬{G} -> ({F} & {E}) fact6: ¬{AB} -> ¬{B} fact7: ¬{J} -> ({I} & ¬{H}) fact8: ¬{H} -> ¬({G} & {F}) fact9: {D} -> {C} fact10: {C} -> ¬(¬{B} & {A}) fact11: ¬({AA} & {AB}) fact12: {C} -> (¬{A} & {B}) fact13: ¬{A} -> ¬{CE} ; $hypothesis$ = {B} ; $proof$ = | fact1 & fact11 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãã¿ã³ã¯å
¥éãããå€åŽã§ãªã | ({AA}{a} & ¬{AB}{a}) | fact1: ãã®ãã¿ã³ã¯å
¥éããããããããã¯å€åŽã§ãªã fact2: ããäœãã¯å¬ãªãã°ãããã解æãããšããããšããªãããããã¿ã¯ã©ãã«ã³ã«ãããããšããããšã¯æãç«ããªã fact3: ããå¬ã¯è©äžãéãã°ãããã¯è§£æãããªãããšããããšã¯åã§ãªã fact4: ããäœããè³ãããªãã°ããããã¶ãããåŸæåæã ãšããããšããªã fact5: ãã®ããŒããã©ãªãªãè©äžãéã fact6: ããããã®ããããã³ãèå·å²žã«çœ·ãåºã§ããæ¥æ¬ã©ã³ãã£ãã¯ã ããšããããšãééããªãã°ããã¯è©äžãéããªã fact7: ããäœãã¯è³ãããšããããšããªããªãã°ãããã¯å
¥éãããå€åŽã§ãªãããšããããšãæãç«ããªã fact8: ãã®ãã¿ã³ãå€åŽã§ãªã fact9: ããããããã®ã¯æ¥æ¬ã©ã³ãã£ãã¯ã ãããã¯èå·å²žã«çœ·ãåºã§ãããšããããšãåœãªãã°ããã¯æ¥æ¬ã©ã³ãã£ãã¯ã ãšããããšããªã fact10: ãã®è³æ®»ã¯å
¥éãããåé ããªã fact11: ããããããã®ã¯è§£æãããªããŠã¿ã¯ã©ãã«ã³ã«ãããããšããããšã¯æãç«ããªããªãã°ãããè³ãããšããããšããªã fact12: ãããã®ããããã³ãæ¥æ¬ã©ã³ãã£ãã¯ã§ãªããªãã°ãã®ããŒããã©ãªãªãå¬ã§ãããæ®å²ã fact13: ããã®ããããã³ãæ¥æ¬ã©ã³ãã£ãã¯ã ãèå·å²žã«çœ·ãåºã§ãããšããããšãæãç«ã€ãšããããšããªã fact14: ããããè©äžãéããªãããšããããšãæãç«ã€ããã®ã¯ããã°ãããã®ããŒããã©ãªãªãå¬ã§ãªããæ®å²ã ããšããããšã¯æãç«ããªãããšããããšã¯åã§ãªã fact15: ããã®ããããã³ãèå·å²žã«çœ·ãåºã§ããæ¥æ¬ã©ã³ãã£ãã¯ã ããšããããšã誀ãã fact16: ããã解æãããšããããšããªãããã®ã¯ããã°ãã®ãã¿ã³ã¯è³ããããããã¯ããã¯ã¿ã¯ã©ãã«ã³ã«ããã | fact1: ({AA}{a} & ¬{AB}{a}) fact2: (x): {D}x -> ¬(¬{B}x & {C}x) fact3: (x): ({D}x & {E}x) -> ¬{B}x fact4: (x): {A}x -> ({DQ}x & ¬{GM}x) fact5: {E}{b} fact6: ¬({H}{c} & {G}{c}) -> ¬{E}{c} fact7: (x): ¬{A}x -> ¬({AA}x & ¬{AB}x) fact8: ¬{AB}{a} fact9: (x): ¬({G}x & {H}x) -> ¬{G}x fact10: ({AA}{iq} & ¬{FM}{iq}) fact11: (x): ¬(¬{B}x & {C}x) -> ¬{A}x fact12: ¬{G}{c} -> ({D}{b} & {F}{b}) fact13: ¬({G}{c} & {H}{c}) fact14: (x): ¬{E}x -> ¬(¬{D}{b} & {F}{b}) fact15: ¬({H}{c} & {G}{c}) fact16: (x): ¬{B}x -> ({A}{a} v {C}{a}) | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | ããã®ãã¿ã³ã¯å
¥éããããããããã¯å€åŽã§ãªãããšããããšã¯èª€ãã | ¬({AA}{a} & ¬{AB}{a}) | [
"fact22 -> int1: ããããã®ãã¿ã³ã¯è³ãããªãããšããããšã¯äºå®ãªãã°ããããå
¥éãããå€åŽã ãšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã; fact19 -> int2: ããããã®ãã¿ã³ã解æãããšããããšããªããã¿ã¯ã©ãã«ã³ã«ãããããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯è³ãããªã; fact20 -> int3: ãããã®ãã¿ã³ãå¬ãªãã°ãããã¯è§£æãããšããããšã¯ãªãããããã¿ã¯ã©ãã«ã³ã«ãããããšããããšãæ¬åœã ãšããããšããªã; fact17 & fact18 -> int4: ãã®ããããã³ã¯è©äžãéããªã; int4 -> int5: ãè©äžãéããšããããšã¯ãªãããã®ããã; int5 & fact21 -> int6: ããã®ããŒããã©ãªãªãå¬ã§ãªããããã¯æ®å²ã ããšããããšãæãç«ã€ãšããããšã¯ãªã; int6 -> int7: ããå¬ã§ãªãããããæ®å²ã ããšããããšã¯äºå®ãšç°ãªãããã®ããã;"
] | 8 | 1 | 0 | 15 | 0 | 15 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãã¿ã³ã¯å
¥éããããããããã¯å€åŽã§ãªã fact2: ããäœãã¯å¬ãªãã°ãããã解æãããšããããšããªãããããã¿ã¯ã©ãã«ã³ã«ãããããšããããšã¯æãç«ããªã fact3: ããå¬ã¯è©äžãéãã°ãããã¯è§£æãããªãããšããããšã¯åã§ãªã fact4: ããäœããè³ãããªãã°ããããã¶ãããåŸæåæã ãšããããšããªã fact5: ãã®ããŒããã©ãªãªãè©äžãéã fact6: ããããã®ããããã³ãèå·å²žã«çœ·ãåºã§ããæ¥æ¬ã©ã³ãã£ãã¯ã ããšããããšãééããªãã°ããã¯è©äžãéããªã fact7: ããäœãã¯è³ãããšããããšããªããªãã°ãããã¯å
¥éãããå€åŽã§ãªãããšããããšãæãç«ããªã fact8: ãã®ãã¿ã³ãå€åŽã§ãªã fact9: ããããããã®ã¯æ¥æ¬ã©ã³ãã£ãã¯ã ãããã¯èå·å²žã«çœ·ãåºã§ãããšããããšãåœãªãã°ããã¯æ¥æ¬ã©ã³ãã£ãã¯ã ãšããããšããªã fact10: ãã®è³æ®»ã¯å
¥éãããåé ããªã fact11: ããããããã®ã¯è§£æãããªããŠã¿ã¯ã©ãã«ã³ã«ãããããšããããšã¯æãç«ããªããªãã°ãããè³ãããšããããšããªã fact12: ãããã®ããããã³ãæ¥æ¬ã©ã³ãã£ãã¯ã§ãªããªãã°ãã®ããŒããã©ãªãªãå¬ã§ãããæ®å²ã fact13: ããã®ããããã³ãæ¥æ¬ã©ã³ãã£ãã¯ã ãèå·å²žã«çœ·ãåºã§ãããšããããšãæãç«ã€ãšããããšããªã fact14: ããããè©äžãéããªãããšããããšãæãç«ã€ããã®ã¯ããã°ãããã®ããŒããã©ãªãªãå¬ã§ãªããæ®å²ã ããšããããšã¯æãç«ããªãããšããããšã¯åã§ãªã fact15: ããã®ããããã³ãèå·å²žã«çœ·ãåºã§ããæ¥æ¬ã©ã³ãã£ãã¯ã ããšããããšã誀ãã fact16: ããã解æãããšããããšããªãããã®ã¯ããã°ãã®ãã¿ã³ã¯è³ããããããã¯ããã¯ã¿ã¯ã©ãã«ã³ã«ããã ; $hypothesis$ = ãã®ãã¿ã³ã¯å
¥éãããå€åŽã§ãªã ; $proof$ = | fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({AA}{a} & ¬{AB}{a}) fact2: (x): {D}x -> ¬(¬{B}x & {C}x) fact3: (x): ({D}x & {E}x) -> ¬{B}x fact4: (x): {A}x -> ({DQ}x & ¬{GM}x) fact5: {E}{b} fact6: ¬({H}{c} & {G}{c}) -> ¬{E}{c} fact7: (x): ¬{A}x -> ¬({AA}x & ¬{AB}x) fact8: ¬{AB}{a} fact9: (x): ¬({G}x & {H}x) -> ¬{G}x fact10: ({AA}{iq} & ¬{FM}{iq}) fact11: (x): ¬(¬{B}x & {C}x) -> ¬{A}x fact12: ¬{G}{c} -> ({D}{b} & {F}{b}) fact13: ¬({G}{c} & {H}{c}) fact14: (x): ¬{E}x -> ¬(¬{D}{b} & {F}{b}) fact15: ¬({H}{c} & {G}{c}) fact16: (x): ¬{B}x -> ({A}{a} v {C}{a}) ; $hypothesis$ = ({AA}{a} & ¬{AB}{a}) ; $proof$ = | fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ç¥æ¯ã¯ãªãŸããã§ãªã | ¬{B}{a} | fact1: ããäœãã空管çã ãšããããšã¯ãªããªãã°ãããä¿ä¿¡ã§ããã¯æ¹éäžåã«æ
Žãããšããããšããªã fact2: ããããããã®ã¯è±çã«ãããããšããããšããªããŠåãéããªãããšããããšãæãç«ããªããªãã°ããã¯ãªãŸããã fact3: ãã®ç¥æ¯ã¯çå·ã§ãããæž
ã
ããããããã¯äž¡æ¹ã fact4: ãããã®ææãã¯å€§å
éè¡ãªãã°ãã®å€è£
ã銬鹿ãããããããèšäŒã ãšããããšã¯ãªã fact5: ãã銬鹿ããããã®ãèšäŒã ãšããããšã¯ãªããªãã°ããã空管çã ãšããããšã¯ãªã fact6: ãããããã®ããªãŸããã ãšããããšã¯ãªãããããããã¯åãéããã°ãããèŠå€ªéã«å
¥ããããšããããšããªã fact7: ãä¿ä¿¡ã§ãªãããã®ã¯ãã fact8: ãããã®ç¥æ¯ãããããããããã¯ããã¯èŠå€ªéã«å
¥ããããšããããšã¯ãªããäž¡æ¹ãªãã°ããããªãŸããã ãšããããšããªã fact9: ããããä¿ä¿¡ã§ãªãããã®ã¯ããããšããããšãæãç«ãŠã°ãã®åæ§ã¯ãªãŸããã§ãªã fact10: ãããã®åºåã¯æ¹éäžåã«æ
Žããªããªãã°ããã®ç¥æ¯ã¯è±çã«ããããªãããããåãéããªãããšããããšã¯åã fact11: ãããã®å€è£
ã¯ä¿ä¿¡ã ããããããã¯æ¹éäžåã«æ
Žãããšããããšã¯ãªããªãã°ãã®åºåã¯æ¹éäžåã«æ
Žããªã fact12: ãããã®ç¥æ¯ã¯æ²Œå²¡ã ãšããããšã¯ãªããªãã°ããã¯ãªãŸããã§ãªã | fact1: (x): ¬{F}x -> ({E}x & ¬{D}x) fact2: (x): ¬(¬{C}x & ¬{A}x) -> {B}x fact3: ({HM}{a} v {JG}{a}) fact4: {I}{d} -> ({G}{c} & ¬{H}{c}) fact5: (x): ({G}x & ¬{H}x) -> ¬{F}x fact6: (x): (¬{B}x & {A}x) -> ¬{AB}x fact7: (Ex): ¬{E}x fact8: ({AA}{a} v ¬{AB}{a}) -> ¬{B}{a} fact9: (x): ¬{E}x -> ¬{B}{ea} fact10: ¬{D}{b} -> ¬(¬{C}{a} & ¬{A}{a}) fact11: ({E}{c} & ¬{D}{c}) -> ¬{D}{b} fact12: ¬{BQ}{a} -> ¬{B}{a} | [] | [] | ãã®ç¥æ¯ããªãŸããã | {B}{a} | [
"fact15 -> int1: ããããããã®ç¥æ¯ãè±çã«ããããªããŠããã¯åãéãããšããããšã¯ãªãããšããããšãæ¬åœã ããšããããšã¯æãç«ããªããªãã°ãã®ç¥æ¯ã¯ãªãŸããã ããšããããšã¯èª€ãã§ãªã; fact16 -> int2: ãããã®å€è£
ã¯ç©ºç®¡çã ãšããããšã¯ãªããªãã°ããã¯ä¿ä¿¡ã§ããã¯æ¹éäžåã«æ
Žãããšããããšã¯ãªã; fact17 -> int3: ãããã®å€è£
ã¯éŠ¬é¹¿ãããããããèšäŒã§ãªããªãã°ãããã空管çã ãšããããšããªãããšããããšã¯æãç«ã€;"
] | 8 | 1 | null | 11 | 0 | 11 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããäœãã空管çã ãšããããšã¯ãªããªãã°ãããä¿ä¿¡ã§ããã¯æ¹éäžåã«æ
Žãããšããããšããªã fact2: ããããããã®ã¯è±çã«ãããããšããããšããªããŠåãéããªãããšããããšãæãç«ããªããªãã°ããã¯ãªãŸããã fact3: ãã®ç¥æ¯ã¯çå·ã§ãããæž
ã
ããããããã¯äž¡æ¹ã fact4: ãããã®ææãã¯å€§å
éè¡ãªãã°ãã®å€è£
ã銬鹿ãããããããèšäŒã ãšããããšã¯ãªã fact5: ãã銬鹿ããããã®ãèšäŒã ãšããããšã¯ãªããªãã°ããã空管çã ãšããããšã¯ãªã fact6: ãããããã®ããªãŸããã ãšããããšã¯ãªãããããããã¯åãéããã°ãããèŠå€ªéã«å
¥ããããšããããšããªã fact7: ãä¿ä¿¡ã§ãªãããã®ã¯ãã fact8: ãããã®ç¥æ¯ãããããããããã¯ããã¯èŠå€ªéã«å
¥ããããšããããšã¯ãªããäž¡æ¹ãªãã°ããããªãŸããã ãšããããšããªã fact9: ããããä¿ä¿¡ã§ãªãããã®ã¯ããããšããããšãæãç«ãŠã°ãã®åæ§ã¯ãªãŸããã§ãªã fact10: ãããã®åºåã¯æ¹éäžåã«æ
Žããªããªãã°ããã®ç¥æ¯ã¯è±çã«ããããªãããããåãéããªãããšããããšã¯åã fact11: ãããã®å€è£
ã¯ä¿ä¿¡ã ããããããã¯æ¹éäžåã«æ
Žãããšããããšã¯ãªããªãã°ãã®åºåã¯æ¹éäžåã«æ
Žããªã fact12: ãããã®ç¥æ¯ã¯æ²Œå²¡ã ãšããããšã¯ãªããªãã°ããã¯ãªãŸããã§ãªã ; $hypothesis$ = ãã®ç¥æ¯ã¯ãªãŸããã§ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{F}x -> ({E}x & ¬{D}x) fact2: (x): ¬(¬{C}x & ¬{A}x) -> {B}x fact3: ({HM}{a} v {JG}{a}) fact4: {I}{d} -> ({G}{c} & ¬{H}{c}) fact5: (x): ({G}x & ¬{H}x) -> ¬{F}x fact6: (x): (¬{B}x & {A}x) -> ¬{AB}x fact7: (Ex): ¬{E}x fact8: ({AA}{a} v ¬{AB}{a}) -> ¬{B}{a} fact9: (x): ¬{E}x -> ¬{B}{ea} fact10: ¬{D}{b} -> ¬(¬{C}{a} & ¬{A}{a}) fact11: ({E}{c} & ¬{D}{c}) -> ¬{D}{b} fact12: ¬{BQ}{a} -> ¬{B}{a} ; $hypothesis$ = ¬{B}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | æ±ãçãããšãèµ·ãã | {B} | fact1: ãäŒãããšã¯èµ·ããªãããããå€±æ Œãçããããšããããšã¯æ¬åœã fact2: ãäŒãããšãçããªãããããå€±æ Œã¯çããããšããããšãæ±ãçãããšã¯èµ·ããªããšããããšãææ¢ãã fact3: å
¬åŒã¯èµ·ãããªã fact4: ãããã€ããšããããšãšçžèšã¡äž¡æ¹ã¯èµ·ããã°æº¢æ°Žãèµ·ãã | fact1: (¬{AA} & {AB}) fact2: (¬{AA} & {AB}) -> {B} fact3: ¬{CL} fact4: ({HU} & {JA}) -> {FU} | [
"fact2 & fact1 -> hypothesis;"
] | [
"fact2 & fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãäŒãããšã¯èµ·ããªãããããå€±æ Œãçããããšããããšã¯æ¬åœã fact2: ãäŒãããšãçããªãããããå€±æ Œã¯çããããšããããšãæ±ãçãããšã¯èµ·ããªããšããããšãææ¢ãã fact3: å
¬åŒã¯èµ·ãããªã fact4: ãããã€ããšããããšãšçžèšã¡äž¡æ¹ã¯èµ·ããã°æº¢æ°Žãèµ·ãã ; $hypothesis$ = æ±ãçãããšãèµ·ãã ; $proof$ = | fact2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: (¬{AA} & {AB}) fact2: (¬{AA} & {AB}) -> {B} fact3: ¬{CL} fact4: ({HU} & {JA}) -> {FU} ; $hypothesis$ = {B} ; $proof$ = | fact2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ããããããšããããšãèµ·ãããªã | ¬{A} | fact1: ããããããšããããšã¯çºçãã fact2: çç£æè¡ç 究æãçªãåãããããšã¯èµ·ãã fact3: ããã¯ãªã°ãªãããšããããšã¯çããªããªãã°äºéžãšããããããšããããšã¯èµ·ãã fact4: çããããããšããããšã¯èµ·ãã | fact1: {A} fact2: {P} fact3: ¬{B} -> ({HQ} & {A}) fact4: {U} | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | äºéžãçºçãã | {HQ} | [] | 6 | 1 | 0 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããããšããããšã¯çºçãã fact2: çç£æè¡ç 究æãçªãåãããããšã¯èµ·ãã fact3: ããã¯ãªã°ãªãããšããããšã¯çããªããªãã°äºéžãšããããããšããããšã¯èµ·ãã fact4: çããããããšããããšã¯èµ·ãã ; $hypothesis$ = ããããããšããããšãèµ·ãããªã ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} fact2: {P} fact3: ¬{B} -> ({HQ} & {A}) fact4: {U} ; $hypothesis$ = ¬{A} ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãããã®åœ«å»ãææ¥çåœã ãšããããšããªããªãã°ãããããç¡ããåŸ
ã¡äŸã³ããšããããšããªã | ¬{A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) | fact1: ããäœããææ¥çåœã ãšããããšããªããªãã°ãããããç¡ããŠãããåŸ
ã¡äŸã³ãªã fact2: ãããã®åœ«å»ã¯ææ¥çåœã§ãªããªãã°ããããããç¡ããã®ã§ãã£ãŠåŸ
ã¡äŸã³ããã®ããšããããšãæãç«ã€ fact3: ãããã®åœ«å»ã¯ææ¥çåœãªãã°ãããããç¡ããŠåŸ
ã¡äŸã³ãªã fact4: ããäœããææ¥çåœã ãšããããšã¯ãªããªãã°ãããããç¡ã fact5: ããäœãã¯è€ããããã°ããã飯岡å©äºéãããããªãããããã¯ãããªã | fact1: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact2: ¬{A}{aa} -> ({AA}{aa} & {AB}{aa}) fact3: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) fact4: (x): ¬{A}x -> {AA}x fact5: (x): {H}x -> ({K}x & ¬{AU}x) | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 4 | 0 | 4 | PROVED | null | PROVED | null | $facts$ = fact1: ããäœããææ¥çåœã ãšããããšããªããªãã°ãããããç¡ããŠãããåŸ
ã¡äŸã³ãªã fact2: ãããã®åœ«å»ã¯ææ¥çåœã§ãªããªãã°ããããããç¡ããã®ã§ãã£ãŠåŸ
ã¡äŸã³ããã®ããšããããšãæãç«ã€ fact3: ãããã®åœ«å»ã¯ææ¥çåœãªãã°ãããããç¡ããŠåŸ
ã¡äŸã³ãªã fact4: ããäœããææ¥çåœã ãšããããšã¯ãªããªãã°ãããããç¡ã fact5: ããäœãã¯è€ããããã°ããã飯岡å©äºéãããããªãããããã¯ãããªã ; $hypothesis$ = ãããã®åœ«å»ãææ¥çåœã ãšããããšããªããªãã°ãããããç¡ããåŸ
ã¡äŸã³ããšããããšããªã ; $proof$ = | fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact2: ¬{A}{aa} -> ({AA}{aa} & {AB}{aa}) fact3: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) fact4: (x): ¬{A}x -> {AA}x fact5: (x): {H}x -> ({K}x & ¬{AU}x) ; $hypothesis$ = ¬{A}{aa} -> ({AA}{aa} & ¬{AB}{aa}) ; $proof$ = | fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ç©äœãé»ããšããããšã¯ãªã | ¬{B}{b} | fact1: ããäœãã¯èŠè¿ãã°ãããäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽãããããæç¡ããªã fact2: ãããããã®ã¯æŽå
ãªãã°ãããã¯äžæšé£å·ã ããããªããããªãããšããããšãåã fact3: ãããäœããåŠæå®ç ã«èšãäºããªãã奜ãããããããšããããšãééããªãã°ãããåŠæå®ç ã«èšãäºã fact4: ããããããã®ã¯äžæšé£å·ã ããããããã¯ãããªããããªãããšããããšã¯äºå®ãšç°ãªãã°ããã¯äžæšé£å·ã ãšããããšããªã fact5: ãããã®åãæãäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽããããããããæç¡ããšããããšããªããªãã°ãã®éºéªžãäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽããšããããšããªã fact6: ãããã®ããªã³ãããåŠæå®ç ã«èšãäºãã°ãã®ã ã¯ããžã¯é¹¿å®ãé ãæãŠãªããŠããã¯é»ããšããããšããªã fact7: ãããã®ã ã¯ããžã鹿å®ãé ãæãŠããšããããšã¯ãªããŠé»ããªããªãã°ãã®ç©äœãé»ããªã fact8: ããäœããåŠæå®ç ã«èšãäºããšããããšã¯ãªããªãã°ããã¯æ±äžéã«ããŒããªããããã¯ççãããšããããšã¯ãªã fact9: ãããã®ã¹ãã¬ã鹿å®ãé ãæãŠãªããªãã°ãããåŠæå®ç ã«èšãäºããªããããã¯é»ããšããããšããªã fact10: ãããã®éºéªžãäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽããšããããšããªããªãã°ããã®ããªã³ããã¯åŠæå®ç ã«èšãäºããªããããã奜ãããããããšããããšã¯çå®ã ãšããããšã¯ãªã fact11: ãããã®ã ã¯ããžãé»ããªããã®ã§ãã£ãŠæ±äžéã«ããŒããã®ãªãã°ãã®ç©äœã¯å²¡è°·ç¶²æ©ã fact12: ãããã®ã ã¯ããžã¯å²¡è°·ç¶²æ©ã§ãªããæ±äžéã«ããŒããšããããšããªããªãã°ããã®ç©äœãé»ãããšããããšãæ£ãã fact13: ãã®ã ã¯ããžã¯æ±äžéã«ããŒãŸãªã fact14: ããã®ç©äœã¯å²¡è°·ç¶²æ©ã ããšããããšãæãç«ã€ fact15: ããäœãã¯ç©æ·ãããªãã°ããã¯èŠè¿ã fact16: ããäœãã¯äžæšé£å·ã§ãªããªãã°ãããç©æ·ãããå°ç°å倧è¡é¢äžã fact17: ãããã®ç©äœã岡谷網æ©ã§ãªããŠæ±äžéã«ããŒãã°ãã®ã ã¯ããžãé»ã | fact1: (x): {G}x -> ({E}x & ¬{F}x) fact2: (x): {L}x -> ¬({J}x & ¬{K}x) fact3: (x): ¬(¬{A}x & {D}x) -> {A}x fact4: (x): ¬({J}x & ¬{K}x) -> ¬{J}x fact5: ({E}{e} & ¬{F}{e}) -> ¬{E}{d} fact6: {A}{c} -> (¬{C}{a} & ¬{B}{a}) fact7: (¬{C}{a} & ¬{B}{a}) -> ¬{B}{b} fact8: (x): ¬{A}x -> (¬{AB}x & ¬{BI}x) fact9: ¬{C}{u} -> (¬{A}{u} & ¬{B}{u}) fact10: ¬{E}{d} -> ¬(¬{A}{c} & {D}{c}) fact11: (¬{B}{a} & {AB}{a}) -> {AA}{b} fact12: (¬{AA}{a} & ¬{AB}{a}) -> {B}{b} fact13: ¬{AB}{a} fact14: {AA}{b} fact15: (x): {H}x -> {G}x fact16: (x): ¬{J}x -> ({H}x & {I}x) fact17: (¬{AA}{b} & {AB}{b}) -> {B}{a} | [] | [] | ãã®ã¹ãã¬ã¯æ±äžéã«ããŒããšããããšã¯ãªããŠççãããªã | (¬{AB}{u} & ¬{BI}{u}) | [
"fact19 -> int1: ããããã®ã¹ãã¬ãåŠæå®ç ã«èšãäºããªãããšããããšãæãç«ãŠã°ããã¯æ±äžéã«ããŒãŸãªããŠççãããªã;"
] | 5 | 1 | null | 16 | 0 | 16 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããäœãã¯èŠè¿ãã°ãããäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽãããããæç¡ããªã fact2: ãããããã®ã¯æŽå
ãªãã°ãããã¯äžæšé£å·ã ããããªããããªãããšããããšãåã fact3: ãããäœããåŠæå®ç ã«èšãäºããªãã奜ãããããããšããããšãééããªãã°ãããåŠæå®ç ã«èšãäºã fact4: ããããããã®ã¯äžæšé£å·ã ããããããã¯ãããªããããªãããšããããšã¯äºå®ãšç°ãªãã°ããã¯äžæšé£å·ã ãšããããšããªã fact5: ãããã®åãæãäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽããããããããæç¡ããšããããšããªããªãã°ãã®éºéªžãäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽããšããããšããªã fact6: ãããã®ããªã³ãããåŠæå®ç ã«èšãäºãã°ãã®ã ã¯ããžã¯é¹¿å®ãé ãæãŠãªããŠããã¯é»ããšããããšããªã fact7: ãããã®ã ã¯ããžã鹿å®ãé ãæãŠããšããããšã¯ãªããŠé»ããªããªãã°ãã®ç©äœãé»ããªã fact8: ããäœããåŠæå®ç ã«èšãäºããšããããšã¯ãªããªãã°ããã¯æ±äžéã«ããŒããªããããã¯ççãããšããããšã¯ãªã fact9: ãããã®ã¹ãã¬ã鹿å®ãé ãæãŠãªããªãã°ãããåŠæå®ç ã«èšãäºããªããããã¯é»ããšããããšããªã fact10: ãããã®éºéªžãäžæ¥ããŒã ãµãŒãã¹ãæã¡çŽããšããããšããªããªãã°ããã®ããªã³ããã¯åŠæå®ç ã«èšãäºããªããããã奜ãããããããšããããšã¯çå®ã ãšããããšã¯ãªã fact11: ãããã®ã ã¯ããžãé»ããªããã®ã§ãã£ãŠæ±äžéã«ããŒããã®ãªãã°ãã®ç©äœã¯å²¡è°·ç¶²æ©ã fact12: ãããã®ã ã¯ããžã¯å²¡è°·ç¶²æ©ã§ãªããæ±äžéã«ããŒããšããããšããªããªãã°ããã®ç©äœãé»ãããšããããšãæ£ãã fact13: ãã®ã ã¯ããžã¯æ±äžéã«ããŒãŸãªã fact14: ããã®ç©äœã¯å²¡è°·ç¶²æ©ã ããšããããšãæãç«ã€ fact15: ããäœãã¯ç©æ·ãããªãã°ããã¯èŠè¿ã fact16: ããäœãã¯äžæšé£å·ã§ãªããªãã°ãããç©æ·ãããå°ç°å倧è¡é¢äžã fact17: ãããã®ç©äœã岡谷網æ©ã§ãªããŠæ±äžéã«ããŒãã°ãã®ã ã¯ããžãé»ã ; $hypothesis$ = ãã®ç©äœãé»ããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): {G}x -> ({E}x & ¬{F}x) fact2: (x): {L}x -> ¬({J}x & ¬{K}x) fact3: (x): ¬(¬{A}x & {D}x) -> {A}x fact4: (x): ¬({J}x & ¬{K}x) -> ¬{J}x fact5: ({E}{e} & ¬{F}{e}) -> ¬{E}{d} fact6: {A}{c} -> (¬{C}{a} & ¬{B}{a}) fact7: (¬{C}{a} & ¬{B}{a}) -> ¬{B}{b} fact8: (x): ¬{A}x -> (¬{AB}x & ¬{BI}x) fact9: ¬{C}{u} -> (¬{A}{u} & ¬{B}{u}) fact10: ¬{E}{d} -> ¬(¬{A}{c} & {D}{c}) fact11: (¬{B}{a} & {AB}{a}) -> {AA}{b} fact12: (¬{AA}{a} & ¬{AB}{a}) -> {B}{b} fact13: ¬{AB}{a} fact14: {AA}{b} fact15: (x): {H}x -> {G}x fact16: (x): ¬{J}x -> ({H}x & {I}x) fact17: (¬{AA}{b} & {AB}{b}) -> {B}{a} ; $hypothesis$ = ¬{B}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®éºäººã¯é¿æµã§ãã£ãŠå€§åæ¬è°·ã ãã® | ({A}{a} & {B}{a}) | fact1: ãã®éºäººãé¿æµã fact2: ãããã®éã¯ãããããããªããããã¯ãè¶åãçž«ããã°ãã®ã¹ã«ãŠãã¯ãè¶åãçž«ããªã fact3: ãã®éã¯ç¥æ²åã ãæžããšããã fact4: ãã®éºäººã¯ãªããªã³ã ãããã貎ã fact5: ããç¥æ²åã ãšããããšããªããåºåŒã網ã§ãªãããšããããšãæãç«ããªãããã®ã¯ãã fact6: ãããããã®ããããããããªããªãã°ããããè¶åãçž«ããªã fact7: ãããã®ã¹ã«ãŠãã¯åå±±åãã²ãã¯ãããšããããšã¯ãªããªãã°ããã®éºäººã倧åæ¬è°·ã§ããããããã¯é¿æµã§ããããããã¯äž¡æ¹ã ããšããããšã¯åã ãšããããšããªã fact8: ããäœãã¯ãè¶åãçž«ãããšããããšã¯ãªããªãã°ãããã€ã€ãåå±±åãã²ãã¯ãããšããããšããªã fact9: ãããäœããåºåŒã網ãªãã°ãããããããããããšããããšãäºå®ã fact10: ãã®ãã£ããããã¯åºåŒã網ã fact11: ãããã®ãã£ãããããåºåŒã網ãªãã°ããã®éãåºåŒã網ã ããšããããšãåœã ãšããããšã¯ãªã fact12: ãã®éºäººã¯å€§åæ¬è°·ã fact13: ããã®ã¿ã³ã°ã¹ãã³ã倧åæ¬è°·ã ããšããããšã¯èª€ãã§ãªã fact14: ãããã®éã¯æžããšãããããããããããªãã°ãã®ã¹ã«ãŠãã¯ãããããããšããããšã¯ãªã | fact1: {A}{a} fact2: (¬{F}{c} & {E}{c}) -> ¬{E}{b} fact3: ({I}{c} & {G}{c}) fact4: ({HT}{a} & {AS}{a}) fact5: (Ex): ¬(¬{I}x & ¬{H}x) fact6: (x): ¬{F}x -> ¬{E}x fact7: ¬{C}{b} -> ({B}{a} v {A}{a}) fact8: (x): ¬{E}x -> ({D}x & ¬{C}x) fact9: (x): {H}x -> {F}x fact10: {H}{d} fact11: {H}{d} -> {H}{c} fact12: {B}{a} fact13: {B}{hb} fact14: ({G}{c} & {F}{c}) -> ¬{F}{b} | [
"fact1 & fact12 -> hypothesis;"
] | [
"fact1 & fact12 -> hypothesis;"
] | ãã®ãµããžã§ã¯ãã¯å€§åæ¬è°·ã | {B}{ii} | [
"fact22 -> int1: ãããã®ã¹ã«ãŠãããè¶åãçž«ãããšããããšããªããªãã°ããã¯ã€ã€ãåå±±åãã²ãã¯ãããªã; fact16 -> int2: ãããã®ã¹ã«ãŠãã¯ãããããããšããããšã¯ãªããªãã°ããã¯ãè¶åãçž«ããªã; fact15 -> int3: ãã®éã¯æžããšããã; fact17 -> int4: ãããã®éã¯åºåŒã網ãªãã°ããããããããã; fact20 & fact19 -> int5: ãã®éã¯åºåŒã網ã ; int4 & int5 -> int6: ãã®éããããããã; int3 & int6 -> int7: ãã®éã¯æžããšãããããããããã; fact21 & int7 -> int8: ãã®ã¹ã«ãŠãããããããããšããããšããªã; int2 & int8 -> int9: ãã®ã¹ã«ãŠãããè¶åãçž«ãããšããããšã¯ãªã; int1 & int9 -> int10: ããã®ã¹ã«ãŠãã¯ã€ã€ãããã¯åå±±åãã²ãã¯ãããªãããšããããšãäºå®ã ; int10 -> int11: ãã®ã¹ã«ãŠããåå±±åãã²ãã¯ãããšããããšããªã; fact18 & int11 -> int12: ãã®éºäººã¯å€§åæ¬è°·ã§ããããããã¯ããã¯é¿æµã§ããããããã¯äž¡æ¹ã ;"
] | 9 | 1 | 1 | 12 | 0 | 12 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®éºäººãé¿æµã fact2: ãããã®éã¯ãããããããªããããã¯ãè¶åãçž«ããã°ãã®ã¹ã«ãŠãã¯ãè¶åãçž«ããªã fact3: ãã®éã¯ç¥æ²åã ãæžããšããã fact4: ãã®éºäººã¯ãªããªã³ã ãããã貎ã fact5: ããç¥æ²åã ãšããããšããªããåºåŒã網ã§ãªãããšããããšãæãç«ããªãããã®ã¯ãã fact6: ãããããã®ããããããããªããªãã°ããããè¶åãçž«ããªã fact7: ãããã®ã¹ã«ãŠãã¯åå±±åãã²ãã¯ãããšããããšã¯ãªããªãã°ããã®éºäººã倧åæ¬è°·ã§ããããããã¯é¿æµã§ããããããã¯äž¡æ¹ã ããšããããšã¯åã ãšããããšããªã fact8: ããäœãã¯ãè¶åãçž«ãããšããããšã¯ãªããªãã°ãããã€ã€ãåå±±åãã²ãã¯ãããšããããšããªã fact9: ãããäœããåºåŒã網ãªãã°ãããããããããããšããããšãäºå®ã fact10: ãã®ãã£ããããã¯åºåŒã網ã fact11: ãããã®ãã£ãããããåºåŒã網ãªãã°ããã®éãåºåŒã網ã ããšããããšãåœã ãšããããšã¯ãªã fact12: ãã®éºäººã¯å€§åæ¬è°·ã fact13: ããã®ã¿ã³ã°ã¹ãã³ã倧åæ¬è°·ã ããšããããšã¯èª€ãã§ãªã fact14: ãããã®éã¯æžããšãããããããããããªãã°ãã®ã¹ã«ãŠãã¯ãããããããšããããšã¯ãªã ; $hypothesis$ = ãã®éºäººã¯é¿æµã§ãã£ãŠå€§åæ¬è°·ã ãã® ; $proof$ = | fact1 & fact12 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} fact2: (¬{F}{c} & {E}{c}) -> ¬{E}{b} fact3: ({I}{c} & {G}{c}) fact4: ({HT}{a} & {AS}{a}) fact5: (Ex): ¬(¬{I}x & ¬{H}x) fact6: (x): ¬{F}x -> ¬{E}x fact7: ¬{C}{b} -> ({B}{a} v {A}{a}) fact8: (x): ¬{E}x -> ({D}x & ¬{C}x) fact9: (x): {H}x -> {F}x fact10: {H}{d} fact11: {H}{d} -> {H}{c} fact12: {B}{a} fact13: {B}{hb} fact14: ({G}{c} & {F}{c}) -> ¬{F}{b} ; $hypothesis$ = ({A}{a} & {B}{a}) ; $proof$ = | fact1 & fact12 -> hypothesis; __PROVED__ |
0.3 | ãã®è·¡ç¶ãã¯åè¹ã«ç¯ãã | {B}{b} | fact1: ããã®é£å±±ãå€ãããšããããšã¯çå®ã fact2: ãã®ã©ãŠã³ãžã¯åè¹ã«ç¯ãã fact3: ãã®è·¡ç¶ããåæã«ã²ãããã fact4: ããããã«ã«ãœããã¯ã³ãã¥ãã±ãŒã·ã§ã³ã§ãªããåè¹ã«ç¯ããããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ã¯ããã°ãã®ã±ãŒãžã¯å€ã fact5: ãããã®ã©ãŠã³ãžã¯åè¹ã«ç¯ããã°ãã®è·¡ç¶ãã¯å€ã fact6: ãã®è·¡ç¶ãã¯æ ä¹èŒã«ãããã fact7: ãã®è·¡ç¶ããå€ã fact8: ããããããã®ã¯é£ãããªããããã¯äœãåºãããšããããšãæãç«ã€ãšããããšããªããªãã°ãããäœãåºããšããããšã¯ãªã fact9: ããããã®ã©ãŠã³ãžã¯å€ããªãã°ãã®è·¡ç¶ããåè¹ã«ç¯ããããšããããšã¯æãç«ã€ fact10: ãããã®ã©ãŠã³ãžãåè¹ã«ç¯ããã°ãã®æ°Žç©ã¯å€ã fact11: ãããã®ã©ãŠã³ãžã¯å€ãããããã«ã«ãœããã¯ã³ãã¥ãã±ãŒã·ã§ã³ãªãã°ãã®è·¡ç¶ãã¯åè¹ã«ç¯ãããšããããšã¯ãªã fact12: ãã®è·¡ç¶ãããªãããã fact13: ãã®ãã»ãªã¯å€ã fact14: ãããã®è·¡ç¶ããå€ããªãã°ãã®ã©ãŠã³ãžãæã fact15: ãã®ã©ãŠã³ãžãå€ã fact16: ãããã®è·¡ç¶ããå€ããªãã°ãã®ã©ãŠã³ãžã¯åè¹ã«ç¯ãã | fact1: {A}{dg} fact2: {B}{a} fact3: {IA}{b} fact4: (x): ¬(¬{C}x & {B}x) -> {A}{hc} fact5: {B}{a} -> {A}{b} fact6: {FT}{b} fact7: {A}{b} fact8: (x): ¬({E}x & {D}x) -> ¬{D}x fact9: {A}{a} -> {B}{b} fact10: {B}{a} -> {A}{hq} fact11: ({A}{a} & {C}{a}) -> ¬{B}{b} fact12: {HH}{b} fact13: {A}{dp} fact14: {A}{b} -> {GG}{a} fact15: {A}{a} fact16: {A}{b} -> {B}{a} | [
"fact9 & fact15 -> hypothesis;"
] | [
"fact9 & fact15 -> hypothesis;"
] | ãã®ã±ãŒãžã¯å€ã | {A}{hc} | [
"fact17 -> int1: ããããã®è·¡ç¶ãã¯é£ãããªãããããäœãåºãããšããããšãåœãªãã°ããã¯äœãåºããšããããšã¯ãªã;"
] | 8 | 1 | 1 | 14 | 0 | 14 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããã®é£å±±ãå€ãããšããããšã¯çå®ã fact2: ãã®ã©ãŠã³ãžã¯åè¹ã«ç¯ãã fact3: ãã®è·¡ç¶ããåæã«ã²ãããã fact4: ããããã«ã«ãœããã¯ã³ãã¥ãã±ãŒã·ã§ã³ã§ãªããåè¹ã«ç¯ããããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ã¯ããã°ãã®ã±ãŒãžã¯å€ã fact5: ãããã®ã©ãŠã³ãžã¯åè¹ã«ç¯ããã°ãã®è·¡ç¶ãã¯å€ã fact6: ãã®è·¡ç¶ãã¯æ ä¹èŒã«ãããã fact7: ãã®è·¡ç¶ããå€ã fact8: ããããããã®ã¯é£ãããªããããã¯äœãåºãããšããããšãæãç«ã€ãšããããšããªããªãã°ãããäœãåºããšããããšã¯ãªã fact9: ããããã®ã©ãŠã³ãžã¯å€ããªãã°ãã®è·¡ç¶ããåè¹ã«ç¯ããããšããããšã¯æãç«ã€ fact10: ãããã®ã©ãŠã³ãžãåè¹ã«ç¯ããã°ãã®æ°Žç©ã¯å€ã fact11: ãããã®ã©ãŠã³ãžã¯å€ãããããã«ã«ãœããã¯ã³ãã¥ãã±ãŒã·ã§ã³ãªãã°ãã®è·¡ç¶ãã¯åè¹ã«ç¯ãããšããããšã¯ãªã fact12: ãã®è·¡ç¶ãããªãããã fact13: ãã®ãã»ãªã¯å€ã fact14: ãããã®è·¡ç¶ããå€ããªãã°ãã®ã©ãŠã³ãžãæã fact15: ãã®ã©ãŠã³ãžãå€ã fact16: ãããã®è·¡ç¶ããå€ããªãã°ãã®ã©ãŠã³ãžã¯åè¹ã«ç¯ãã ; $hypothesis$ = ãã®è·¡ç¶ãã¯åè¹ã«ç¯ãã ; $proof$ = | fact9 & fact15 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{dg} fact2: {B}{a} fact3: {IA}{b} fact4: (x): ¬(¬{C}x & {B}x) -> {A}{hc} fact5: {B}{a} -> {A}{b} fact6: {FT}{b} fact7: {A}{b} fact8: (x): ¬({E}x & {D}x) -> ¬{D}x fact9: {A}{a} -> {B}{b} fact10: {B}{a} -> {A}{hq} fact11: ({A}{a} & {C}{a}) -> ¬{B}{b} fact12: {HH}{b} fact13: {A}{dp} fact14: {A}{b} -> {GG}{a} fact15: {A}{a} fact16: {A}{b} -> {B}{a} ; $hypothesis$ = {B}{b} ; $proof$ = | fact9 & fact15 -> hypothesis; __PROVED__ |
0.3 | ããã®èãããããããããšããããšãæãç«ã€ | {A}{a} | fact1: ãã®åèµã¯ãããã fact2: ãããããã®ã¯å¯
己山ã§ãªããªãã°ããã®çªé ãè±ç°çºå°å·ã§ãªããããã¯ååœç¹ç¶è²©å£²ã§ãªãããšããããšã¯äºå®ãšç°ãªã fact3: ãã®èãããå¹³å島ã§èœç»åžãç¬ãå
〠fact4: ãã®èŸ²å Žã¯ç°äºåºã«ç¹æ§ã¥ãã fact5: ãããã®èŸ²å Žã¯ç°äºåºã«ç¹æ§ã¥ããã°ãã®éç ²çŸåãç©ã¯ä»ãã ãšããããšããªããããããŠããã fact6: ãã®èããããããããã fact7: ããããã®èããããããããããããããããããšããããšã¯ãªãããšããããšã¯äºå®ã§ãªããªãã°ãã®éŠ¬éããããã fact8: ãã®ç²ã¯ãããã fact9: ããã®èããã¯éããããããšããããšãæãç«ã€ fact10: ãã®èããã¯ããããããããããã fact11: ããäœããåã¿ã圢ã¥ããã°ãããã¯ãããããããããããããããšããããšããªãããšããããšã¯äºå®ãšç°ãªã fact12: ãã®ã¢ãã¿ãŒã¯ãããã fact13: ããããè±ç°çºå°å·ã§ãªããååœç¹ç¶è²©å£²ã ãšããããšã¯ãªãããšããããšã¯æãç«ããªãããã®ãããã°ããã®ããŒã«ãã¢ãªã³ã°ãåã¿ã圢ã¥ããããšããããšãæãç«ã€ fact14: ããäœãã¯ç©ã¯ä»ãã ãšããããšã¯ãªãããŠããããªãã°ãããå¯
己山ã ãšããããšã¯ãªã | fact1: {A}{ir} fact2: (x): ¬{F}x -> ¬(¬{E}{c} & ¬{D}{c}) fact3: ({CS}{a} & {II}{a}) fact4: {I}{e} fact5: {I}{e} -> (¬{G}{d} & {H}{d}) fact6: {B}{a} fact7: ¬({B}{a} & ¬{A}{a}) -> {A}{bn} fact8: {A}{cf} fact9: {HO}{a} fact10: ({A}{a} & {B}{a}) fact11: (x): {C}x -> ¬({A}x & ¬{B}x) fact12: {A}{fk} fact13: (x): ¬(¬{E}x & ¬{D}x) -> {C}{b} fact14: (x): (¬{G}x & {H}x) -> ¬{F}x | [
"fact10 -> hypothesis;"
] | [
"fact10 -> hypothesis;"
] | ãã®èããã¯ãããããšããããšããªã | ¬{A}{a} | [
"fact15 -> int1: ãããã®ããŒã«ãã¢ãªã³ã°ã¯åã¿ã圢ã¥ããã°ãããããããããããããããããããªãããšããããšã¯æãç«ããªã; fact18 -> int2: ãããã®éç ²çŸåãç©ã¯ä»ãã§ãªãããŠããããªãã°ãããã¯å¯
己山ã§ãªãããšããããšã¯æãç«ã€; fact20 & fact16 -> int3: ãã®éç ²çŸåãç©ã¯ä»ãã ãšããããšã¯ãªãããŠããã; int2 & int3 -> int4: ãã®éç ²çŸåãå¯
己山ã ãšããããšããªã; int4 -> int5: äœãã¯å¯
己山ã ãšããããšããªã; int5 & fact19 -> int6: ããã®çªé ã¯è±ç°çºå°å·ã ãšããããšããªããããã¯ååœç¹ç¶è²©å£²ã ãšããããšããªãããšããããšãæ¬åœã§ãªã; int6 -> int7: ããè±ç°çºå°å·ã§ãªããååœç¹ç¶è²©å£²ã§ãªãããšããããšã¯æãç«ã€ãšããããšããªãããã®ããã; int7 & fact17 -> int8: ãã®ããŒã«ãã¢ãªã³ã°ã¯åã¿ã圢ã¥ãã; int1 & int8 -> int9: ããã®ããŒã«ãã¢ãªã³ã°ã¯ããããããããããããªãããšããããšãåœã ; int9 -> int10: ããããããããããããããšããããšã¯ãªãããšããããšãæãç«ããªãããã®ã¯ãã;"
] | 9 | 1 | 1 | 13 | 0 | 13 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®åèµã¯ãããã fact2: ãããããã®ã¯å¯
己山ã§ãªããªãã°ããã®çªé ãè±ç°çºå°å·ã§ãªããããã¯ååœç¹ç¶è²©å£²ã§ãªãããšããããšã¯äºå®ãšç°ãªã fact3: ãã®èãããå¹³å島ã§èœç»åžãç¬ãå
〠fact4: ãã®èŸ²å Žã¯ç°äºåºã«ç¹æ§ã¥ãã fact5: ãããã®èŸ²å Žã¯ç°äºåºã«ç¹æ§ã¥ããã°ãã®éç ²çŸåãç©ã¯ä»ãã ãšããããšããªããããããŠããã fact6: ãã®èããããããããã fact7: ããããã®èããããããããããããããããããšããããšã¯ãªãããšããããšã¯äºå®ã§ãªããªãã°ãã®éŠ¬éããããã fact8: ãã®ç²ã¯ãããã fact9: ããã®èããã¯éããããããšããããšãæãç«ã€ fact10: ãã®èããã¯ããããããããããã fact11: ããäœããåã¿ã圢ã¥ããã°ãããã¯ãããããããããããããããšããããšããªãããšããããšã¯äºå®ãšç°ãªã fact12: ãã®ã¢ãã¿ãŒã¯ãããã fact13: ããããè±ç°çºå°å·ã§ãªããååœç¹ç¶è²©å£²ã ãšããããšã¯ãªãããšããããšã¯æãç«ããªãããã®ãããã°ããã®ããŒã«ãã¢ãªã³ã°ãåã¿ã圢ã¥ããããšããããšãæãç«ã€ fact14: ããäœãã¯ç©ã¯ä»ãã ãšããããšã¯ãªãããŠããããªãã°ãããå¯
己山ã ãšããããšã¯ãªã ; $hypothesis$ = ããã®èãããããããããšããããšãæãç«ã€ ; $proof$ = | fact10 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{ir} fact2: (x): ¬{F}x -> ¬(¬{E}{c} & ¬{D}{c}) fact3: ({CS}{a} & {II}{a}) fact4: {I}{e} fact5: {I}{e} -> (¬{G}{d} & {H}{d}) fact6: {B}{a} fact7: ¬({B}{a} & ¬{A}{a}) -> {A}{bn} fact8: {A}{cf} fact9: {HO}{a} fact10: ({A}{a} & {B}{a}) fact11: (x): {C}x -> ¬({A}x & ¬{B}x) fact12: {A}{fk} fact13: (x): ¬(¬{E}x & ¬{D}x) -> {C}{b} fact14: (x): (¬{G}x & {H}x) -> ¬{F}x ; $hypothesis$ = {A}{a} ; $proof$ = | fact10 -> hypothesis; __PROVED__ |
0.3 | ãã®æžåºããã®ã©ãã | {B}{b} | fact1: ãã®ãã©ãã¿ãªãŠã ã¯ç²å倧åŠã fact2: ãã®çéã¯ç²å倧åŠã§ãªã fact3: ãããã®äžå€ãé²æ°Žãªãã°ããã¯å®åãã¯ãŸããšããããšã¯ãªãããããã¯ç©éšãããããããã¯äž¡æ¹ã fact4: ãããã®çéãç²å倧åŠã ãšããããšããªããªãã°ãã®æžåºããã®ã©ãã fact5: ãããã®çéã¯ç²å倧åŠã ãããã¯å
é極楜æ©ã圩ããã°ãã®æžåºããã®ã©ãããšããããšã¯ãªã | fact1: {A}{eq} fact2: ¬{A}{a} fact3: {F}{c} -> (¬{E}{c} v {D}{c}) fact4: ¬{A}{a} -> {B}{b} fact5: ({A}{a} & {C}{a}) -> ¬{B}{b} | [
"fact4 & fact2 -> hypothesis;"
] | [
"fact4 & fact2 -> hypothesis;"
] | ãã®æžåºãã¯ã®ã©ãããšããããšããªã | ¬{B}{b} | [] | 5 | 1 | 1 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãã©ãã¿ãªãŠã ã¯ç²å倧åŠã fact2: ãã®çéã¯ç²å倧åŠã§ãªã fact3: ãããã®äžå€ãé²æ°Žãªãã°ããã¯å®åãã¯ãŸããšããããšã¯ãªãããããã¯ç©éšãããããããã¯äž¡æ¹ã fact4: ãããã®çéãç²å倧åŠã ãšããããšããªããªãã°ãã®æžåºããã®ã©ãã fact5: ãããã®çéã¯ç²å倧åŠã ãããã¯å
é極楜æ©ã圩ããã°ãã®æžåºããã®ã©ãããšããããšã¯ãªã ; $hypothesis$ = ãã®æžåºããã®ã©ãã ; $proof$ = | fact4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{eq} fact2: ¬{A}{a} fact3: {F}{c} -> (¬{E}{c} v {D}{c}) fact4: ¬{A}{a} -> {B}{b} fact5: ({A}{a} & {C}{a}) -> ¬{B}{b} ; $hypothesis$ = {B}{b} ; $proof$ = | fact4 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãããããããšããããšã¯çºçããªãããšããããšã¯æ£ãã | ¬{B} | fact1: æãããšããããšã¯çºçãã fact2: ããŸããã©ãããšããããšã¯çºçãããæ¥æ¬æ³ä»€ã«ãããã€ããããšãçããããšããããšã¯å¥ãéãŠãçºçããªããšããããšã«ãããããã fact3: æ¥æ¬æ³ä»€ã«ãããã€ããããšãšããããããšããããšãçãã fact4: ããã¯ã ããããšããããšã¯çºçããªããªãã°ããããããšããããšãèµ·ãããªããŠæ¥æ¬æ³ä»€ã«ãããã€ããããšãèµ·ããªã | fact1: {HB} fact2: ¬{E} -> ({ED} & {A}) fact3: ({A} & {B}) fact4: ¬{C} -> (¬{B} & ¬{A}) | [
"fact3 -> hypothesis;"
] | [
"fact3 -> hypothesis;"
] | ãŸããã©ãããšããããšã¯èµ·ãããçèŠãããšããããšã¯èµ·ãã | ({ED} & {G}) | [] | 4 | 1 | 1 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: æãããšããããšã¯çºçãã fact2: ããŸããã©ãããšããããšã¯çºçãããæ¥æ¬æ³ä»€ã«ãããã€ããããšãçããããšããããšã¯å¥ãéãŠãçºçããªããšããããšã«ãããããã fact3: æ¥æ¬æ³ä»€ã«ãããã€ããããšãšããããããšããããšãçãã fact4: ããã¯ã ããããšããããšã¯çºçããªããªãã°ããããããšããããšãèµ·ãããªããŠæ¥æ¬æ³ä»€ã«ãããã€ããããšãèµ·ããªã ; $hypothesis$ = ãããããããšããããšã¯çºçããªãããšããããšã¯æ£ãã ; $proof$ = | fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {HB} fact2: ¬{E} -> ({ED} & {A}) fact3: ({A} & {B}) fact4: ¬{C} -> (¬{B} & ¬{A}) ; $hypothesis$ = ¬{B} ; $proof$ = | fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®æªæ²ã¯æµ
èå²³ã§ãªã | ¬{B}{a} | fact1: ããã®æªæ²ãå»ã¿ä»ãããæäžãæã代ãããšããããšã¯ééãã fact2: ãããããã®ã¹ãã©ã€ãã¯ãµã³ããŒã«ã§ãã£ãŠåŒãè£ããã®ããšããããšãäºå®ã ããšããããšã¯æãç«ããªããªãã°ããã®å£²è¬ã¯ãµã³ããŒã«ã ãšããããšããªãããšããããšã¯æãç«ã€ fact3: ããããã®éªã ããŸãçãåå°Ÿã§ãªãããšããããšã¯çå®ãªãã°ãã®åæ¥ã¯æã¥ããããããäžæž
æ°Žã«è¡ãè©°ããšããããšããªããäž¡æ¹ã fact4: ããã®æªæ²ãå»ã¿ä»ãããããã¯æäžãæã代ããšããããšã¯ãªãããšããããšã¯èª€ãã fact5: ããäœãããµã³ããŒã«ã§ãªããªãã°ãããã¯ä»åã§å«ãããšããããšã¯ãªãããšããããšã¯èª€ãã fact6: ããããã®æªæ²ãå»ã¿ä»ããããããæäžãæã代ããªãããšããããšã¯åœãªãã°ãããæµ
èå²³ã ãšããããšããªã fact7: ãããã®èèã¯èŠããªããªãã°ããã®éªã ããŸã¯é²æ£ã ãããŸãã£ã±ãããšããããšã¯æãç«ããªã fact8: ããæµå寺äžåç°ãããã°ããã®æªæ²ãå»ã¿ä»ãããããããŸãããªãããšããããšã¯ééãã fact9: ãããã®æªæ²ãæäžãæã代ãã°ãããæµ
èå²³ã ãšããããšããªã fact10: ãããäœããæµ
èå²³ã§ãã£ãŠç£¯èããªããã®ããšããããšãæãç«ããªããªãã°ãããæµå寺äžåç°ã fact11: ããã®æªæ²ã¯åŒæãã«å»¶ãããããããã¯ããæ
šã§ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact12: ãããããã®ã埳ä¹
ã ãšããããšããªããããããããæŠã°ãããªãã°ããã¯çãåå°Ÿã ãšããããšããªã fact13: ããããä»åã§ãã£ãŠå«ãããšããããšã¯ãªããã®ããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ãããã°ãã®èèãèŠããªã fact14: ãããäœããé²æ£ã§ããã¯ããŸãã£ã±ãããšããããšãäºå®ãšç°ãªãã°ãããé²æ£ã§ãªã fact15: ãããã®åæ¥ãæã¥ãããªãã°ãã®ãããã©ã€ã³ãäžæž
æ°Žã«è¡ãè©°ããªã fact16: ãããã®ãããã©ã€ã³ãäžæž
æ°Žã«è¡ãè©°ããªããªãã°ããã®åãåãã¯æµ
èå²³ã ãããã磯èããšããããšããªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact17: ãã®ãããã©ã€ã³ã¯çãåå°Ÿã ãšããããšã¯ãªã fact18: ãããã®åæ¥ãäžæž
æ°Žã«è¡ãè©°ããªããªãã°ãã®ãããã©ã€ã³ã¯äžæž
æ°Žã«è¡ãè©°ããšããããšããªã fact19: ãããããã®ã¯é²æ£ã ãšããããšã¯ãªããªãã°ããã¯åŸ³ä¹
ã ãšããããšã¯ãªããŠæŠã°ãã fact20: ããã¯ãµã³ããŒã«ã§ãã£ãŠåŒãè£ããã®ãšãããã®ã¯ãªã | fact1: ¬({AA}{a} & {AB}{a}) fact2: ¬({N}{h} & {O}{h}) -> ¬{N}{g} fact3: ¬{E}{e} -> ({F}{d} v ¬{D}{d}) fact4: ¬({AA}{a} & ¬{AB}{a}) fact5: (x): ¬{N}x -> ¬({L}x & ¬{M}x) fact6: ¬({AA}{a} & ¬{AB}{a}) -> ¬{B}{a} fact7: ¬{K}{f} -> ¬({I}{e} & {J}{e}) fact8: (x): {A}x -> ¬({AA}{a} & ¬{DO}{a}) fact9: {AB}{a} -> ¬{B}{a} fact10: (x): ¬({B}x & ¬{C}x) -> {A}x fact11: ¬({HE}{a} & ¬{AS}{a}) fact12: (x): (¬{H}x & {G}x) -> ¬{E}x fact13: (x): ¬({L}x & ¬{M}x) -> ¬{K}{f} fact14: (x): ¬({I}x & {J}x) -> ¬{I}x fact15: {F}{d} -> ¬{D}{c} fact16: ¬{D}{c} -> ¬({B}{b} & ¬{C}{b}) fact17: ¬{E}{c} fact18: ¬{D}{d} -> ¬{D}{c} fact19: (x): ¬{I}x -> (¬{H}x & {G}x) fact20: (x): ¬({N}x & {O}x) | [
"fact6 & fact4 -> hypothesis;"
] | [
"fact6 & fact4 -> hypothesis;"
] | ãããã®æªæ²ãå»ã¿ä»ãããããããŸããããšããããšããªãããšããããšãæãç«ã€ãšããããšããªãããšããããšãäºå®ã | ¬({AA}{a} & ¬{DO}{a}) | [
"fact31 -> int1: ãããããã®åãåãã¯æµ
èå²³ã ãããã磯èããªãããšããããšã¯åœã ããšããããšã¯äºå®ãªãã°ããããæµå寺äžåç°ã ããšããããšãæãç«ã€; fact25 -> int2: ãããã®éªã ããŸã埳ä¹
ã ãšããããšããªããæŠã°ãããªãã°ãããçãåå°Ÿã ãšããããšã¯ãªã; fact29 -> int3: ãããã®éªã ããŸã¯é²æ£ã§ãªããªãã°ããã¯åŸ³ä¹
ã§ãªããŠæŠã°ãã; fact34 -> int4: ããããã®éªã ããŸãé²æ£ã ããããããŸãã£ã±ãããšããããšã誀ããªãã°ããã¯é²æ£ã ãšããããšããªã; fact33 -> int5: ãããã®å£²è¬ããµã³ããŒã«ã ãšããããšã¯ãªããªãã°ãããã¯ä»åã ããããå«ãããšããããšã¯ãªãããšããããšã誀ãã ; fact27 -> int6: ããã®ã¹ãã©ã€ãã¯ãµã³ããŒã«ã ããããåŒãè£ãããšããããšãäºå®ã§ãªã; fact23 & int6 -> int7: ãã®å£²è¬ããµã³ããŒã«ã§ãªã; int5 & int7 -> int8: ããã®å£²è¬ã¯ä»åã ããããããã¯å«ãããšããããšããªãããšããããšã¯æãç«ããªã; int8 -> int9: ããä»åã ãå«ãããšããããšã¯ãªãããšããããšãééããªããã®ã¯ãã; int9 & fact22 -> int10: ãã®èèã¯èŠããªã; fact26 & int10 -> int11: ããã®éªã ããŸã¯é²æ£ã§ããŸãã£ã±ãããšããããšãæãç«ã€ãšããããšã¯ãªã; int4 & int11 -> int12: ãã®éªã ããŸã¯é²æ£ã§ãªã; int3 & int12 -> int13: ãã®éªã ããŸã¯åŸ³ä¹
ã ãšããããšã¯ãªããæŠã°ãã; int2 & int13 -> int14: ãã®éªã ããŸãçãåå°Ÿã§ãªã; fact32 & int14 -> int15: ãã®åæ¥ã¯æã¥ããããããã¯äžæž
æ°Žã«è¡ãè©°ããªã; int15 & fact24 & fact28 -> int16: ãã®ãããã©ã€ã³ãäžæž
æ°Žã«è¡ãè©°ããšããããšããªã; fact30 & int16 -> int17: ããã®åãåãã¯æµ
èå²³ã ãããã¯ç£¯èããšããããšã¯ãªãããšããããšã¯äºå®ãšç°ãªã; int1 & int17 -> int18: ãã®åãåãã¯æµå寺äžåç°ã ; int18 -> int19: ãæµå寺äžåç°ãªããã®ã¯ãã; int19 & fact21 -> hypothesis;"
] | 15 | 1 | 1 | 18 | 0 | 18 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ããã®æªæ²ãå»ã¿ä»ãããæäžãæã代ãããšããããšã¯ééãã fact2: ãããããã®ã¹ãã©ã€ãã¯ãµã³ããŒã«ã§ãã£ãŠåŒãè£ããã®ããšããããšãäºå®ã ããšããããšã¯æãç«ããªããªãã°ããã®å£²è¬ã¯ãµã³ããŒã«ã ãšããããšããªãããšããããšã¯æãç«ã€ fact3: ããããã®éªã ããŸãçãåå°Ÿã§ãªãããšããããšã¯çå®ãªãã°ãã®åæ¥ã¯æã¥ããããããäžæž
æ°Žã«è¡ãè©°ããšããããšããªããäž¡æ¹ã fact4: ããã®æªæ²ãå»ã¿ä»ãããããã¯æäžãæã代ããšããããšã¯ãªãããšããããšã¯èª€ãã fact5: ããäœãããµã³ããŒã«ã§ãªããªãã°ãããã¯ä»åã§å«ãããšããããšã¯ãªãããšããããšã¯èª€ãã fact6: ããããã®æªæ²ãå»ã¿ä»ããããããæäžãæã代ããªãããšããããšã¯åœãªãã°ãããæµ
èå²³ã ãšããããšããªã fact7: ãããã®èèã¯èŠããªããªãã°ããã®éªã ããŸã¯é²æ£ã ãããŸãã£ã±ãããšããããšã¯æãç«ããªã fact8: ããæµå寺äžåç°ãããã°ããã®æªæ²ãå»ã¿ä»ãããããããŸãããªãããšããããšã¯ééãã fact9: ãããã®æªæ²ãæäžãæã代ãã°ãããæµ
èå²³ã ãšããããšããªã fact10: ãããäœããæµ
èå²³ã§ãã£ãŠç£¯èããªããã®ããšããããšãæãç«ããªããªãã°ãããæµå寺äžåç°ã fact11: ããã®æªæ²ã¯åŒæãã«å»¶ãããããããã¯ããæ
šã§ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact12: ãããããã®ã埳ä¹
ã ãšããããšããªããããããããæŠã°ãããªãã°ããã¯çãåå°Ÿã ãšããããšããªã fact13: ããããä»åã§ãã£ãŠå«ãããšããããšã¯ãªããã®ããšããããšãæãç«ã€ãšããããšã¯ãªãããã®ãããã°ãã®èèãèŠããªã fact14: ãããäœããé²æ£ã§ããã¯ããŸãã£ã±ãããšããããšãäºå®ãšç°ãªãã°ãããé²æ£ã§ãªã fact15: ãããã®åæ¥ãæã¥ãããªãã°ãã®ãããã©ã€ã³ãäžæž
æ°Žã«è¡ãè©°ããªã fact16: ãããã®ãããã©ã€ã³ãäžæž
æ°Žã«è¡ãè©°ããªããªãã°ããã®åãåãã¯æµ
èå²³ã ãããã磯èããšããããšããªãããšããããšãæãç«ã€ãšããããšã¯ãªã fact17: ãã®ãããã©ã€ã³ã¯çãåå°Ÿã ãšããããšã¯ãªã fact18: ãããã®åæ¥ãäžæž
æ°Žã«è¡ãè©°ããªããªãã°ãã®ãããã©ã€ã³ã¯äžæž
æ°Žã«è¡ãè©°ããšããããšããªã fact19: ãããããã®ã¯é²æ£ã ãšããããšã¯ãªããªãã°ããã¯åŸ³ä¹
ã ãšããããšã¯ãªããŠæŠã°ãã fact20: ããã¯ãµã³ããŒã«ã§ãã£ãŠåŒãè£ããã®ãšãããã®ã¯ãªã ; $hypothesis$ = ãã®æªæ²ã¯æµ
èå²³ã§ãªã ; $proof$ = | fact6 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({AA}{a} & {AB}{a}) fact2: ¬({N}{h} & {O}{h}) -> ¬{N}{g} fact3: ¬{E}{e} -> ({F}{d} v ¬{D}{d}) fact4: ¬({AA}{a} & ¬{AB}{a}) fact5: (x): ¬{N}x -> ¬({L}x & ¬{M}x) fact6: ¬({AA}{a} & ¬{AB}{a}) -> ¬{B}{a} fact7: ¬{K}{f} -> ¬({I}{e} & {J}{e}) fact8: (x): {A}x -> ¬({AA}{a} & ¬{DO}{a}) fact9: {AB}{a} -> ¬{B}{a} fact10: (x): ¬({B}x & ¬{C}x) -> {A}x fact11: ¬({HE}{a} & ¬{AS}{a}) fact12: (x): (¬{H}x & {G}x) -> ¬{E}x fact13: (x): ¬({L}x & ¬{M}x) -> ¬{K}{f} fact14: (x): ¬({I}x & {J}x) -> ¬{I}x fact15: {F}{d} -> ¬{D}{c} fact16: ¬{D}{c} -> ¬({B}{b} & ¬{C}{b}) fact17: ¬{E}{c} fact18: ¬{D}{d} -> ¬{D}{c} fact19: (x): ¬{I}x -> (¬{H}x & {G}x) fact20: (x): ¬({N}x & {O}x) ; $hypothesis$ = ¬{B}{a} ; $proof$ = | fact6 & fact4 -> hypothesis; __PROVED__ |
0.3 | ããã®æ²¹åœ©ãçŠäºå€§åŠã«ããã蟌ãããã殺ãããšããããšãæãç«ã€ãšããããšããªã | ¬({A}{a} & {B}{a}) | fact1: ãã®åœ±æ³åž«ã¯çå Žå±±ãããããããããããççãã fact2: ãã®çŠäºå€§åŠã油圩ãããã蟌ã fact3: ãã®æ²¹åœ©ãéé ã fact4: ããäœãã¯ãã殺ããšããããšã¯ãªãããããã¯ããã¯é²ããã°ããã¯çŠäºå€§åŠã«ããã蟌ã fact5: ãã®æ²¹åœ©ããŸãããŠãããéã
äºã fact6: ããã®æ²¹åœ©ã圌æ°ã«é ãã ãããšããããšãæãç«ã€ fact7: ãããäœãã¯è¡éããããããããã¯é²ãããšããããšã¯ãªãããšããããšãæãç«ããªããªãã°ããããã殺ããšããããšã¯ãªã fact8: ãã®æ²¹åœ©ãå
±ãèã蟌ããããã¯å¯Ÿå¯©ã fact9: ãã®ãšã¢ããã殺ãããã€ãŒã£ãã fact10: ãã®ç€ç³ãè¥ãããã殺ã fact11: ãã®æ²¹åœ©ãçŠäºå€§åŠã«ããã蟌ã fact12: ãã®ãšã³ããã¹ãããã殺ã fact13: ãã®ã®ã€ãçŠäºå€§åŠã«ããã蟌ã fact14: ãã®æ²¹åœ©ã¯ãã殺ã fact15: ãã®æ²¹åœ©ã¯ãšãã»ã³ã fact16: ããäœããæ±è¥¿æ±è¥¿ã§ãªããªãã°ããããè¡éãããããã¯é²ããªãããšããããšãäºå®ãšç°ãªã | fact1: ({AL}{fa} & {CH}{fa}) fact2: {AA}{aa} fact3: {CM}{a} fact4: (x): (¬{B}x v {C}x) -> {A}x fact5: ({HR}{a} & {HK}{a}) fact6: {FE}{a} fact7: (x): ¬({D}x & ¬{C}x) -> ¬{B}x fact8: ({HN}{a} & {DK}{a}) fact9: ({B}{bg} & {DN}{bg}) fact10: ({J}{df} & {B}{df}) fact11: {A}{a} fact12: {B}{ds} fact13: {A}{ei} fact14: {B}{a} fact15: {JE}{a} fact16: (x): ¬{E}x -> ¬({D}x & ¬{C}x) | [
"fact11 & fact14 -> hypothesis;"
] | [
"fact11 & fact14 -> hypothesis;"
] | ããã®æ²¹åœ©ãçŠäºå€§åŠã«ããã蟌ãããã殺ãããšããããšãæ£ãããšããããšããªã | ¬({A}{a} & {B}{a}) | [
"fact18 -> int1: ããããã®ä»€å¬¢ã¯è¡éãããé²ãããšããããšããªãããšããããšã¯åœãªãã°ããã¯ãã殺ããšããããšããªã; fact17 -> int2: ãããã®ä»€å¬¢ã¯æ±è¥¿æ±è¥¿ã§ãªããªãã°ãããã¯è¡éãããé²ãããšããããšã¯ãªãããšããããšã¯æ¬åœã§ãªã;"
] | 5 | 1 | 1 | 14 | 0 | 14 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®åœ±æ³åž«ã¯çå Žå±±ãããããããããããççãã fact2: ãã®çŠäºå€§åŠã油圩ãããã蟌ã fact3: ãã®æ²¹åœ©ãéé ã fact4: ããäœãã¯ãã殺ããšããããšã¯ãªãããããã¯ããã¯é²ããã°ããã¯çŠäºå€§åŠã«ããã蟌ã fact5: ãã®æ²¹åœ©ããŸãããŠãããéã
äºã fact6: ããã®æ²¹åœ©ã圌æ°ã«é ãã ãããšããããšãæãç«ã€ fact7: ãããäœãã¯è¡éããããããããã¯é²ãããšããããšã¯ãªãããšããããšãæãç«ããªããªãã°ããããã殺ããšããããšã¯ãªã fact8: ãã®æ²¹åœ©ãå
±ãèã蟌ããããã¯å¯Ÿå¯©ã fact9: ãã®ãšã¢ããã殺ãããã€ãŒã£ãã fact10: ãã®ç€ç³ãè¥ãããã殺ã fact11: ãã®æ²¹åœ©ãçŠäºå€§åŠã«ããã蟌ã fact12: ãã®ãšã³ããã¹ãããã殺ã fact13: ãã®ã®ã€ãçŠäºå€§åŠã«ããã蟌ã fact14: ãã®æ²¹åœ©ã¯ãã殺ã fact15: ãã®æ²¹åœ©ã¯ãšãã»ã³ã fact16: ããäœããæ±è¥¿æ±è¥¿ã§ãªããªãã°ããããè¡éãããããã¯é²ããªãããšããããšãäºå®ãšç°ãªã ; $hypothesis$ = ããã®æ²¹åœ©ãçŠäºå€§åŠã«ããã蟌ãããã殺ãããšããããšãæãç«ã€ãšããããšããªã ; $proof$ = | fact11 & fact14 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({AL}{fa} & {CH}{fa}) fact2: {AA}{aa} fact3: {CM}{a} fact4: (x): (¬{B}x v {C}x) -> {A}x fact5: ({HR}{a} & {HK}{a}) fact6: {FE}{a} fact7: (x): ¬({D}x & ¬{C}x) -> ¬{B}x fact8: ({HN}{a} & {DK}{a}) fact9: ({B}{bg} & {DN}{bg}) fact10: ({J}{df} & {B}{df}) fact11: {A}{a} fact12: {B}{ds} fact13: {A}{ei} fact14: {B}{a} fact15: {JE}{a} fact16: (x): ¬{E}x -> ¬({D}x & ¬{C}x) ; $hypothesis$ = ¬({A}{a} & {B}{a}) ; $proof$ = | fact11 & fact14 -> hypothesis; __DISPROVED__ |
0.3 | ããã®åŸ¡çšèã¯å¹³ãããªãããããã¯ãããéœéã§ããããããã¯äž¡æ¹ã ããšããããšã¯äºå®ãšç°ãªã | ¬(¬{AA}{a} v {AB}{a}) | fact1: ããããé»ãããã®ãããã°ãã®æã€ãã¯ã³ãŒã³ã¹ããã¯ã§ãªãããããã¯ãããäžéŽ«ã fact2: ãããã®äŒœèã空空ãããªãã°ãããããã©ããéžæ©ããšããããšã¯ãªã fact3: ããå¯ãããã®ãè¯ç·ã fact4: ããã©ããŠéžæ©ããªããã®ã¯åæåã«ã€ãã°ã fact5: ãããã®åŸ¡çšèã¯è¯ç·ãªãã°ãããã¯å¹³ãããªãããããã¯ããã¯éœéã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact6: ãã®æžåã貪æ
Ÿã§ããããããã¯ããã¯ãããã§ããããããã¯äž¡æ¹ã fact7: ãããã®åŸ¡çšèã¯è¯ç·ãªãã°ããã¯å¹³ãã fact8: ããããã®ç€ç³ãã³ãŒã³ã¹ããã¯ã§ãã£ãŠèŽå·ãåŸ
ã¡ããããã®ããšããããšã¯åãªãã°ãã®å®¿äž»ã¯èçã«ããããªã fact9: ããäœããã³ãŒã³ã¹ããã¯ã ãšããããšã¯ãªãããããã¯ããã¯äžéŽ«ãªãã°ãããã³ãŒã³ã¹ããã¯ã§ãªã fact10: ãããã®ã°ãªã¹ã¯éœéãªãã°ãã®åŸ¡çšèã¯éœéã fact11: ãããããã®ãåæåã«ã€ãã°ãã°ããã¯ãé»ã fact12: ãããæš¡ããããã®ãããã°ãã®ã°ãªã¹ãã«ã€ããããããããã¯åæ©å·ä¹
ä¿ã§ããããããã¯äž¡æ¹ã fact13: ãããã³ãŒã³ã¹ããã¯ã ãšããããšã¯ãªãããã®ãããã°ããã®ç€ç³ã¯ã³ãŒã³ã¹ããã¯ã§ããã¯èŽå·ãåŸ
ã¡ãããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact14: ãããã®ã°ãªã¹ã¯ã«ã€ãããããªãã°ãã®åŸ¡çšèãåæ©å·ä¹
ä¿ã fact15: ãããã®æªé»ã¯ã¯ã°ã²ãããªããããã¯æš¡ãããšããããšããªããªãã°ããã®æŒç®ã¯æš¡ããããšããããšã¯åã§ãªã fact16: ãããã®æžåãããããªãã°ãã®äŒœèã¯ç©ºç©ºãã fact17: ãããã®åŸ¡çšèã¯ããå¯ãããªãã°ãã®ãã£ããã³ãããå¯ãã fact18: ãã®åŸ¡çšèãè¯ç·ã fact19: ãããèçã«ãããããšããããšããªãããã®ãããã°ãã®æªé»ã¯ã¯ã°ã²ãããšããããšããªããŠæš¡ãããšããããšã¯ãªã fact20: ãããã®æžåã貪æ
Ÿãªãã°ãã®äŒœèã¯ç©ºç©ºãã fact21: ãããããã®ã¯åæ©å·ä¹
ä¿ãªãã°ããã¯ããå¯ãã | fact1: (x): {K}x -> (¬{H}{g} v {J}{g}) fact2: {O}{h} -> ({N}{h} & ¬{M}{h}) fact3: (x): {B}x -> {A}x fact4: (x): ({N}x & ¬{M}x) -> {L}x fact5: {A}{a} -> ¬(¬{AA}{a} v {AB}{a}) fact6: ({Q}{i} v {P}{i}) fact7: {A}{a} -> {AA}{a} fact8: ¬({H}{f} & {I}{f}) -> ¬{F}{e} fact9: (x): (¬{H}x v {J}x) -> ¬{H}x fact10: {AB}{b} -> {AB}{a} fact11: (x): {L}x -> {K}x fact12: (x): {D}x -> ({E}{b} v {C}{b}) fact13: (x): ¬{H}x -> ¬({H}{f} & {I}{f}) fact14: {E}{b} -> {C}{a} fact15: (¬{G}{d} & ¬{D}{d}) -> {D}{c} fact16: {P}{i} -> {O}{h} fact17: {B}{a} -> {B}{jb} fact18: {A}{a} fact19: (x): ¬{F}x -> (¬{G}{d} & ¬{D}{d}) fact20: {Q}{i} -> {O}{h} fact21: (x): {C}x -> {B}x | [
"fact5 & fact18 -> hypothesis;"
] | [
"fact5 & fact18 -> hypothesis;"
] | ãã®ãã£ããã³ãè¯ç·ã | {A}{jb} | [
"fact33 -> int1: ãããã®ãã£ããã³ãããå¯ãããªãã°ããã¯è¯ç·ã ; fact35 -> int2: ãããã®åŸ¡çšèã¯åæ©å·ä¹
ä¿ãªãã°ãããããå¯ãã; fact36 -> int3: ãããã®æã€ããã³ãŒã³ã¹ããã¯ã§ãªããããã¯äžéŽ«ã§ããããããã¯äž¡æ¹ãªãã°ãããã³ãŒã³ã¹ããã¯ã ãšããããšããªã; fact24 -> int4: ãããã®äŒœèã¯åæåã«ã€ãã°ãã°ããã¯ãé»ã; fact32 -> int5: ãããã®äŒœèãããã©ããã®ã§ãã£ãŠéžæ©ããªããã®ãªãã°ãããã¯åæåã«ã€ãã°ãããšããããšãäºå®ãšç°ãªããšããããšã¯ãªã; fact30 & fact27 & fact26 -> int6: ãã®äŒœèã空空ãã; fact28 & int6 -> int7: ãã®äŒœèãããã©ããéžæ©ããšããããšããªã; int5 & int7 -> int8: ãã®äŒœèãåæåã«ã€ãã°ã; int4 & int8 -> int9: ãã®äŒœèã¯ãé»ã; int9 -> int10: ããé»ãããã®ããã; int10 & fact37 -> int11: ãã®æã€ããã³ãŒã³ã¹ããã¯ã§ãªãããããã¯ããã¯äžéŽ«ã ; int3 & int11 -> int12: ãã®æã€ããã³ãŒã³ã¹ããã¯ã§ãªã; int12 -> int13: ãã³ãŒã³ã¹ããã¯ã§ãªãããã®ã¯ãã; int13 & fact29 -> int14: ããã®ç€ç³ãã³ãŒã³ã¹ããã¯ã ãããã¯èŽå·ãåŸ
ã¡ãããããšããããšã¯æãç«ã€ãšããããšã¯ãªã; fact31 & int14 -> int15: ãã®å®¿äž»ãèçã«ãããããšããããšã¯ãªã; int15 -> int16: äœããèçã«ãããããšããããšã¯ãªã; int16 & fact22 -> int17: ãã®æªé»ãã¯ã°ã²ãããšããããšããªããæš¡ããªã; fact23 & int17 -> int18: ãã®æŒç®ãæš¡ãã; int18 -> int19: ãããã®ã¯æš¡ãã; int19 & fact34 -> int20: ãã®ã°ãªã¹ã¯ã«ã€ããããããããã¯ããã¯åæ©å·ä¹
ä¿ã§ããããããã¯äž¡æ¹ã ;"
] | 19 | 1 | 1 | 19 | 0 | 19 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããé»ãããã®ãããã°ãã®æã€ãã¯ã³ãŒã³ã¹ããã¯ã§ãªãããããã¯ãããäžéŽ«ã fact2: ãããã®äŒœèã空空ãããªãã°ãããããã©ããéžæ©ããšããããšã¯ãªã fact3: ããå¯ãããã®ãè¯ç·ã fact4: ããã©ããŠéžæ©ããªããã®ã¯åæåã«ã€ãã°ã fact5: ãããã®åŸ¡çšèã¯è¯ç·ãªãã°ãããã¯å¹³ãããªãããããã¯ããã¯éœéã ããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact6: ãã®æžåã貪æ
Ÿã§ããããããã¯ããã¯ãããã§ããããããã¯äž¡æ¹ã fact7: ãããã®åŸ¡çšèã¯è¯ç·ãªãã°ããã¯å¹³ãã fact8: ããããã®ç€ç³ãã³ãŒã³ã¹ããã¯ã§ãã£ãŠèŽå·ãåŸ
ã¡ããããã®ããšããããšã¯åãªãã°ãã®å®¿äž»ã¯èçã«ããããªã fact9: ããäœããã³ãŒã³ã¹ããã¯ã ãšããããšã¯ãªãããããã¯ããã¯äžéŽ«ãªãã°ãããã³ãŒã³ã¹ããã¯ã§ãªã fact10: ãããã®ã°ãªã¹ã¯éœéãªãã°ãã®åŸ¡çšèã¯éœéã fact11: ãããããã®ãåæåã«ã€ãã°ãã°ããã¯ãé»ã fact12: ãããæš¡ããããã®ãããã°ãã®ã°ãªã¹ãã«ã€ããããããããã¯åæ©å·ä¹
ä¿ã§ããããããã¯äž¡æ¹ã fact13: ãããã³ãŒã³ã¹ããã¯ã ãšããããšã¯ãªãããã®ãããã°ããã®ç€ç³ã¯ã³ãŒã³ã¹ããã¯ã§ããã¯èŽå·ãåŸ
ã¡ãããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact14: ãããã®ã°ãªã¹ã¯ã«ã€ãããããªãã°ãã®åŸ¡çšèãåæ©å·ä¹
ä¿ã fact15: ãããã®æªé»ã¯ã¯ã°ã²ãããªããããã¯æš¡ãããšããããšããªããªãã°ããã®æŒç®ã¯æš¡ããããšããããšã¯åã§ãªã fact16: ãããã®æžåãããããªãã°ãã®äŒœèã¯ç©ºç©ºãã fact17: ãããã®åŸ¡çšèã¯ããå¯ãããªãã°ãã®ãã£ããã³ãããå¯ãã fact18: ãã®åŸ¡çšèãè¯ç·ã fact19: ãããèçã«ãããããšããããšããªãããã®ãããã°ãã®æªé»ã¯ã¯ã°ã²ãããšããããšããªããŠæš¡ãããšããããšã¯ãªã fact20: ãããã®æžåã貪æ
Ÿãªãã°ãã®äŒœèã¯ç©ºç©ºãã fact21: ãããããã®ã¯åæ©å·ä¹
ä¿ãªãã°ããã¯ããå¯ãã ; $hypothesis$ = ããã®åŸ¡çšèã¯å¹³ãããªãããããã¯ãããéœéã§ããããããã¯äž¡æ¹ã ããšããããšã¯äºå®ãšç°ãªã ; $proof$ = | fact5 & fact18 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {K}x -> (¬{H}{g} v {J}{g}) fact2: {O}{h} -> ({N}{h} & ¬{M}{h}) fact3: (x): {B}x -> {A}x fact4: (x): ({N}x & ¬{M}x) -> {L}x fact5: {A}{a} -> ¬(¬{AA}{a} v {AB}{a}) fact6: ({Q}{i} v {P}{i}) fact7: {A}{a} -> {AA}{a} fact8: ¬({H}{f} & {I}{f}) -> ¬{F}{e} fact9: (x): (¬{H}x v {J}x) -> ¬{H}x fact10: {AB}{b} -> {AB}{a} fact11: (x): {L}x -> {K}x fact12: (x): {D}x -> ({E}{b} v {C}{b}) fact13: (x): ¬{H}x -> ¬({H}{f} & {I}{f}) fact14: {E}{b} -> {C}{a} fact15: (¬{G}{d} & ¬{D}{d}) -> {D}{c} fact16: {P}{i} -> {O}{h} fact17: {B}{a} -> {B}{jb} fact18: {A}{a} fact19: (x): ¬{F}x -> (¬{G}{d} & ¬{D}{d}) fact20: {Q}{i} -> {O}{h} fact21: (x): {C}x -> {B}x ; $hypothesis$ = ¬(¬{AA}{a} v {AB}{a}) ; $proof$ = | fact5 & fact18 -> hypothesis; __PROVED__ |
0.3 | è©åãèµ·ãã | {A} | fact1: å¿ã¥ãããšããããšãçºçãããšããããšããæããããšããããšã¯çºçããªãããšããããšãé»ã fact2: ããã·ã§ãŒãã³ããŸãšããããšãçãããèªãåãããããšãèµ·ãããªãããšããããšãåã ãšããããšããªãããšããããšã¯ã®ãããããšããããšãèµ·ãããšããããšã«ããçãã fact3: ãããç©ã
ãããšããããšã¯çºçããªããç°å®¶æ°ãæã代ããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯æãç«ããªããªãã°å¿ã¥ãããšããããšã¯èµ·ãã fact4: ããããããããããšããããšãèµ·ããªããŠã¡ããããããšã¯èµ·ããããšããããšãåãªãã°éããããšãçºçããªã fact5: ãããã±ã³ãèœããããšãèµ·ããã°ãã®ãããããšããããšã¯çããªããŠèžã¿è¶ããããšã¯çããªãããšããããšãäºå®ã ãšããããšããªã fact6: ãè©åãšåŒç¢äž¡æ¹ãçããããšããããšã¯èªãåãããããšãèµ·ããªããšããããšãåå ã fact7: ããããéããããšã¯èµ·ãããªãããšããããšã¯çå®ãªãã°ãç©ã
ãããšããããšã¯èµ·ããªãããããã¯ç°å®¶æ°ãæã代ããããšã¯èµ·ããããããã¯äž¡æ¹ã ããšããããšã¯äºå®ãšç°ãªãããšããããšã¯æãç«ã€ fact8: ãè©åã¯èµ·ããããšããããšãæãç«ã€ fact9: ãããééãããšããããšãçºçããã眵ãããšãèµ·ããªãããšããããšã¯æãç«ããªããªãã°ééãããšããããšã¯èµ·ããªã fact10: ããããã®ãããããšããããšã¯èµ·ãããªããèžã¿è¶ããããšã¯èµ·ããªãããšããããšãæãç«ã€ããšããããšãåœãªãã°ã®ãããããšããããšã¯èµ·ãã fact11: ããééãããšããããšãçããªããªãã°ã¬ã€ããçããããããã¯åæã«ãã ããããšãèµ·ãããäž¡æ¹ã fact12: ããæšå¹Žããžãããããšã¯çºçããã°ããããããããšããããšãèµ·ããªããŠã¡ããããããšã¯çããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact13: ããæããããšããããšã¯èµ·ããã°ããã±ã³ãèœããããšã¯èµ·ããããããéãããšããããšãèµ·ãããªãããšããããšãééãã ãšããããšããªã fact14: ããåçç®ãããè¡šãããšãçããªããªãã°ãééãããšããããšãçããã眵ãããšãèµ·ããªãããšããããšãééãã | fact1: {I} -> {H} fact2: {D} -> ({C} & ¬{B}) fact3: ¬(¬{J} v {K}) -> {I} fact4: ¬(¬{N} & {M}) -> ¬{L} fact5: {F} -> ¬(¬{D} & ¬{E}) fact6: ¬{B} -> ({A} & {IJ}) fact7: ¬{L} -> ¬(¬{J} v {K}) fact8: {A} fact9: ¬({R} & ¬{T}) -> ¬{R} fact10: ¬(¬{D} & ¬{E}) -> {D} fact11: ¬{R} -> ({Q} v {P}) fact12: {O} -> ¬(¬{N} & {M}) fact13: {H} -> ({F} & ¬{G}) fact14: ¬{S} -> ¬({R} & ¬{T}) | [
"fact8 -> hypothesis;"
] | [
"fact8 -> hypothesis;"
] | åŒç¢ã¯èµ·ãã | {IJ} | [] | 18 | 1 | 0 | 13 | 0 | 13 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: å¿ã¥ãããšããããšãçºçãããšããããšããæããããšããããšã¯çºçããªãããšããããšãé»ã fact2: ããã·ã§ãŒãã³ããŸãšããããšãçãããèªãåãããããšãèµ·ãããªãããšããããšãåã ãšããããšããªãããšããããšã¯ã®ãããããšããããšãèµ·ãããšããããšã«ããçãã fact3: ãããç©ã
ãããšããããšã¯çºçããªããç°å®¶æ°ãæã代ããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯æãç«ããªããªãã°å¿ã¥ãããšããããšã¯èµ·ãã fact4: ããããããããããšããããšãèµ·ããªããŠã¡ããããããšã¯èµ·ããããšããããšãåãªãã°éããããšãçºçããªã fact5: ãããã±ã³ãèœããããšãèµ·ããã°ãã®ãããããšããããšã¯çããªããŠèžã¿è¶ããããšã¯çããªãããšããããšãäºå®ã ãšããããšããªã fact6: ãè©åãšåŒç¢äž¡æ¹ãçããããšããããšã¯èªãåãããããšãèµ·ããªããšããããšãåå ã fact7: ããããéããããšã¯èµ·ãããªãããšããããšã¯çå®ãªãã°ãç©ã
ãããšããããšã¯èµ·ããªãããããã¯ç°å®¶æ°ãæã代ããããšã¯èµ·ããããããã¯äž¡æ¹ã ããšããããšã¯äºå®ãšç°ãªãããšããããšã¯æãç«ã€ fact8: ãè©åã¯èµ·ããããšããããšãæãç«ã€ fact9: ãããééãããšããããšãçºçããã眵ãããšãèµ·ããªãããšããããšã¯æãç«ããªããªãã°ééãããšããããšã¯èµ·ããªã fact10: ããããã®ãããããšããããšã¯èµ·ãããªããèžã¿è¶ããããšã¯èµ·ããªãããšããããšãæãç«ã€ããšããããšãåœãªãã°ã®ãããããšããããšã¯èµ·ãã fact11: ããééãããšããããšãçããªããªãã°ã¬ã€ããçããããããã¯åæã«ãã ããããšãèµ·ãããäž¡æ¹ã fact12: ããæšå¹Žããžãããããšã¯çºçããã°ããããããããšããããšãèµ·ããªããŠã¡ããããããšã¯çããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact13: ããæããããšããããšã¯èµ·ããã°ããã±ã³ãèœããããšã¯èµ·ããããããéãããšããããšãèµ·ãããªãããšããããšãééãã ãšããããšããªã fact14: ããåçç®ãããè¡šãããšãçããªããªãã°ãééãããšããããšãçããã眵ãããšãèµ·ããªãããšããããšãééãã ; $hypothesis$ = è©åãèµ·ãã ; $proof$ = | fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: {I} -> {H} fact2: {D} -> ({C} & ¬{B}) fact3: ¬(¬{J} v {K}) -> {I} fact4: ¬(¬{N} & {M}) -> ¬{L} fact5: {F} -> ¬(¬{D} & ¬{E}) fact6: ¬{B} -> ({A} & {IJ}) fact7: ¬{L} -> ¬(¬{J} v {K}) fact8: {A} fact9: ¬({R} & ¬{T}) -> ¬{R} fact10: ¬(¬{D} & ¬{E}) -> {D} fact11: ¬{R} -> ({Q} v {P}) fact12: {O} -> ¬(¬{N} & {M}) fact13: {H} -> ({F} & ¬{G}) fact14: ¬{S} -> ¬({R} & ¬{T}) ; $hypothesis$ = {A} ; $proof$ = | fact8 -> hypothesis; __PROVED__ |
0.3 | ããããã®ãç¥æ¯ãããæªè°·ãããã€ãããšããããšããªããè±å²ã«ãã«ããããªãããšããããšã¯æãç«ããªããªãã°ããã¯å°æè©ã | ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa} | fact1: ããããã®ãç¥æ¯ããã¯æµ
çç°ã ããšããããšãæãç«ãŠã°ããããçç³ã ããšããããšã¯äºå®ã fact2: ãããäœããçèç·ããããããšããããšã¯ãªãããããããªãããšããããšãæãç«ããªããªãã°ããã¯äžæšæã fact3: ããããããã®ãé«æ±ãã¥ãŒã¿ãŠã³äžå€®ã«ãŸã延ããªããæ°Žèã ããšããããšãåãªãã°ããã¯èŠè¶ãã fact4: ããäœãã¯å²©ä»£ã売é£ã°ãã°ãããçåã fact5: ããããã®ãç¥æ¯ããã¯æªè°·ãããã€ããªããŠããããªãŸã¬ãããªãããšããããšã¯ééããªãã°ãããå°ãããã fact6: ãããã®ãç¥æ¯ããã¯æªè°·ãããã€ãããšããããšããªããé¿ããªããªãã°ããããäœèã«è²è€ªããããšããããšãæ£ãã fact7: ããããããã®ãé£äžã ãšããããšã¯ãªãããããããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãããæµ
çç°ã fact8: ãããã®ãç¥æ¯ããã¯æããããªããããã¯ããããªããšããããšããªããªãã°ããããå°æè©ã ããšããããšãäºå®ã fact9: ãããäœãã¯æ¥å€ã ãšããããšããªããæãããããšããããšãåœãªãã°ããã¯ãªãŒã«ã¹ã¿ãŒãºã fact10: ãé£äžã¯ãã£ã®ã¥ã¢ã ããšããããšã¯äºå®ã fact11: ãããã®ãç¥æ¯ãããè±å²ã«ãã«ããããªããæå€ããªããªãã°ããã¯ç°å©ã | fact1: {BR}{aa} -> {EK}{aa} fact2: (x): ¬(¬{CN}x & ¬{IO}x) -> {FR}x fact3: (x): ¬(¬{GA}x & {IM}x) -> {IP}x fact4: (x): {AN}x -> {FK}x fact5: ¬(¬{AA}{aa} & ¬{AR}{aa}) -> {GU}{aa} fact6: (¬{AA}{aa} & ¬{BP}{aa}) -> {EP}{aa} fact7: (x): ¬(¬{FH}x & {JG}x) -> {BR}x fact8: (¬{ES}{aa} & ¬{IG}{aa}) -> {B}{aa} fact9: (x): ¬(¬{DB}x & {ES}x) -> {CI}x fact10: (x): {FH}x -> {R}x fact11: (¬{AB}{aa} & ¬{GD}{aa}) -> {BT}{aa} | [] | [] | null | null | [] | null | 1 | null | 11 | 0 | 11 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããããã®ãç¥æ¯ããã¯æµ
çç°ã ããšããããšãæãç«ãŠã°ããããçç³ã ããšããããšã¯äºå®ã fact2: ãããäœããçèç·ããããããšããããšã¯ãªãããããããªãããšããããšãæãç«ããªããªãã°ããã¯äžæšæã fact3: ããããããã®ãé«æ±ãã¥ãŒã¿ãŠã³äžå€®ã«ãŸã延ããªããæ°Žèã ããšããããšãåãªãã°ããã¯èŠè¶ãã fact4: ããäœãã¯å²©ä»£ã売é£ã°ãã°ãããçåã fact5: ããããã®ãç¥æ¯ããã¯æªè°·ãããã€ããªããŠããããªãŸã¬ãããªãããšããããšã¯ééããªãã°ãããå°ãããã fact6: ãããã®ãç¥æ¯ããã¯æªè°·ãããã€ãããšããããšããªããé¿ããªããªãã°ããããäœèã«è²è€ªããããšããããšãæ£ãã fact7: ããããããã®ãé£äžã ãšããããšã¯ãªãããããããããšããããšãæãç«ã€ãšããããšã¯ãªããªãã°ãããæµ
çç°ã fact8: ãããã®ãç¥æ¯ããã¯æããããªããããã¯ããããªããšããããšããªããªãã°ããããå°æè©ã ããšããããšãäºå®ã fact9: ãããäœãã¯æ¥å€ã ãšããããšããªããæãããããšããããšãåœãªãã°ããã¯ãªãŒã«ã¹ã¿ãŒãºã fact10: ãé£äžã¯ãã£ã®ã¥ã¢ã ããšããããšã¯äºå®ã fact11: ãããã®ãç¥æ¯ãããè±å²ã«ãã«ããããªããæå€ããªããªãã°ããã¯ç°å©ã ; $hypothesis$ = ããããã®ãç¥æ¯ãããæªè°·ãããã€ãããšããããšããªããè±å²ã«ãã«ããããªãããšããããšã¯æãç«ããªããªãã°ããã¯å°æè©ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {BR}{aa} -> {EK}{aa} fact2: (x): ¬(¬{CN}x & ¬{IO}x) -> {FR}x fact3: (x): ¬(¬{GA}x & {IM}x) -> {IP}x fact4: (x): {AN}x -> {FK}x fact5: ¬(¬{AA}{aa} & ¬{AR}{aa}) -> {GU}{aa} fact6: (¬{AA}{aa} & ¬{BP}{aa}) -> {EP}{aa} fact7: (x): ¬(¬{FH}x & {JG}x) -> {BR}x fact8: (¬{ES}{aa} & ¬{IG}{aa}) -> {B}{aa} fact9: (x): ¬(¬{DB}x & {ES}x) -> {CI}x fact10: (x): {FH}x -> {R}x fact11: (¬{AB}{aa} & ¬{GD}{aa}) -> {BT}{aa} ; $hypothesis$ = ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | åŒãå
·ããããšãšåŒ·æ¬²äž¡æ¹ã¯çºçãã | ({A} & {B}) | fact1: ãåŒãå
·ããããšãèµ·ããããšããããšã¯æ¬åœã fact2: 匷欲ã¯çºçãã fact3: ãæŠç«ã¯èµ·ããããšããããšã¯äºå®ã fact4: ã¿ã€ããããšãçºçãã fact5: ãããŸããªããšããããšãçºçããããšããããšãæãç«ã€ fact6: èå³æ·±ããšããããšãçºçãã fact7: 玳士é²ãé
ããããšãçºçãã fact8: ãããããããšãšäžåŒµãã¯èµ·ãã fact9: 仲è£ã¯èµ·ãããæ±æŽä¿¡èšéè¡ãçŒãä»ããããšã¯èµ·ãã fact10: æ¥ãããããšããããšãèµ·ãã fact11: ãµãããããšããããšã¯èµ·ãã fact12: ååºã¯èµ·ãã fact13: 仲è£ãèµ·ãã fact14: ããã¡ã«èŠããããšãšãã©ã³ãã³ã°ã¯çºçãã fact15: çŠã
ãããšããããšãçºçãã fact16: éæã¯èµ·ãã fact17: èé£ããšããããšãšæ¶ããšããããšäž¡æ¹ãèµ·ãã | fact1: {A} fact2: {B} fact3: {EQ} fact4: {IT} fact5: {IL} fact6: {HT} fact7: {BE} fact8: ({CQ} & {IK}) fact9: ({BJ} & {GI}) fact10: {GF} fact11: {M} fact12: {FS} fact13: {BJ} fact14: ({FF} & {DO}) fact15: {EH} fact16: {AP} fact17: ({HF} & {DL}) | [
"fact1 & fact2 -> hypothesis;"
] | [
"fact1 & fact2 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 15 | 0 | 15 | PROVED | null | PROVED | null | $facts$ = fact1: ãåŒãå
·ããããšãèµ·ããããšããããšã¯æ¬åœã fact2: 匷欲ã¯çºçãã fact3: ãæŠç«ã¯èµ·ããããšããããšã¯äºå®ã fact4: ã¿ã€ããããšãçºçãã fact5: ãããŸããªããšããããšãçºçããããšããããšãæãç«ã€ fact6: èå³æ·±ããšããããšãçºçãã fact7: 玳士é²ãé
ããããšãçºçãã fact8: ãããããããšãšäžåŒµãã¯èµ·ãã fact9: 仲è£ã¯èµ·ãããæ±æŽä¿¡èšéè¡ãçŒãä»ããããšã¯èµ·ãã fact10: æ¥ãããããšããããšãèµ·ãã fact11: ãµãããããšããããšã¯èµ·ãã fact12: ååºã¯èµ·ãã fact13: 仲è£ãèµ·ãã fact14: ããã¡ã«èŠããããšãšãã©ã³ãã³ã°ã¯çºçãã fact15: çŠã
ãããšããããšãçºçãã fact16: éæã¯èµ·ãã fact17: èé£ããšããããšãšæ¶ããšããããšäž¡æ¹ãèµ·ãã ; $hypothesis$ = åŒãå
·ããããšãšåŒ·æ¬²äž¡æ¹ã¯çºçãã ; $proof$ = | fact1 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} fact2: {B} fact3: {EQ} fact4: {IT} fact5: {IL} fact6: {HT} fact7: {BE} fact8: ({CQ} & {IK}) fact9: ({BJ} & {GI}) fact10: {GF} fact11: {M} fact12: {FS} fact13: {BJ} fact14: ({FF} & {DO}) fact15: {EH} fact16: {AP} fact17: ({HF} & {DL}) ; $hypothesis$ = ({A} & {B}) ; $proof$ = | fact1 & fact2 -> hypothesis; __PROVED__ |
0.3 | æŽãããšã¯èµ·ãããªã | ¬{B} | fact1: ãã»ã©è¿ããšããããšã¯çºçããªãããšããããšã¯é¥é¥ãèµ·ããªããšããããšãèªçºãã fact2: é¥é¥ã¯çºçããªããšããããšããæããçããããããããããšããããšã¯çºçããããšããããšãèªçºãã fact3: ãã»ã©è¿ããšããããšã¯çããªããããã€ãã«ããããããããšãèµ·ããªãããšããããšã¯ãå¿ããŸãããšããããšã¯çºçããããšããããšãå¥æ©ã fact4: ãããæé£ããšããããšã¯çºçããªããŠæœè¡ãèµ·ããªãããšããããšãééããªãã°äžå¡æãçºçãã fact5: åçŽã圢ã¥ããããšãçããªããšããããšããé»éå¯å±±ã«çž®ããããšã¯èµ·ããªããããããããšããããšã¯èµ·ãããªãããšããããšã®ãã£ãããšãªã fact6: ããããžã ããŒã«åŒµãåãããããšãçºçããªããæãŠåãããšã¯èµ·ããããšããããšã¯æãç«ããªããªãã°æãŠåãããšã¯èµ·ããªã fact7: å¿ããŸãããšããããšãçãããšããããšã¯æãŠãèµ·ããªããšããããšãåå ã fact8: ãããæãŠã¯èµ·ãããéãããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšããªããªãã°æãŠãçºçããªã fact9: ãäžéãçºçããããããšããããšãèµ·ãããªãããšããããšã¯èª€ãã fact10: ãããããããããšããããšã¯çºçããã°ãæé£ããšããããšãçºçããªããæœè¡ã¯çããªãããšããããšãäºå®ã ãšããããšããªã fact11: ãããæãŠåãããšã¯çããªãããšããããšã¯æãç«ãŠã°ãæãŠãèµ·ããããããéãããããšã¯çºçããªãããšããããšãæãç«ããªã fact12: ããããããšããããšãçããã°ãå¿ããªããšããããšã¯èµ·ãããå
çŸã«çµäžããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ãšããããšããªã fact13: ãããé»éå¯å±±ã«çž®ããããšã¯çããªãããšããããšã¯äºå®ãªãã°ãããžã ããŒã«åŒµãåãããããšã§ã¯ãªãæãŠåãããšãèµ·ããããšããããšã¯æ¬åœã ããšããããšã誀ãã fact14: äžå¡æã¯çãããšããããšããæŽãããšã¯èµ·ããããããããããšããããšãçããªãããšããããšãèªçºãã fact15: ãèšæŸã€ããšãèµ·ããããããæ€åãèµ·ããªãããšããããšã¯äºå®ãšç°ãªã | fact1: ¬{I} -> ¬{H} fact2: ¬{H} -> ({G} & {F}) fact3: {K} -> (¬{I} & ¬{J}) fact4: ¬(¬{E} & ¬{D}) -> {C} fact5: ¬{R} -> (¬{P} & ¬{Q}) fact6: ¬(¬{O} & {M}) -> ¬{M} fact7: ¬{L} -> {K} fact8: ¬({L} & ¬{N}) -> ¬{L} fact9: ¬({AA} & ¬{AB}) fact10: {F} -> ¬(¬{E} & ¬{D}) fact11: ¬{M} -> ¬({L} & ¬{N}) fact12: {A} -> ¬({HG} & ¬{EH}) fact13: ¬{P} -> ¬(¬{O} & {M}) fact14: {C} -> ({B} & ¬{A}) fact15: ¬({IA} & ¬{BK}) | [] | [] | ãå¿ããªããšããããšãçãããå
çŸã«çµäžããããšã¯èµ·ãããªãããšããããšãåã | ¬({HG} & ¬{EH}) | [] | 6 | 1 | null | 14 | 0 | 14 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã»ã©è¿ããšããããšã¯çºçããªãããšããããšã¯é¥é¥ãèµ·ããªããšããããšãèªçºãã fact2: é¥é¥ã¯çºçããªããšããããšããæããçããããããããããšããããšã¯çºçããããšããããšãèªçºãã fact3: ãã»ã©è¿ããšããããšã¯çããªããããã€ãã«ããããããããšãèµ·ããªãããšããããšã¯ãå¿ããŸãããšããããšã¯çºçããããšããããšãå¥æ©ã fact4: ãããæé£ããšããããšã¯çºçããªããŠæœè¡ãèµ·ããªãããšããããšãééããªãã°äžå¡æãçºçãã fact5: åçŽã圢ã¥ããããšãçããªããšããããšããé»éå¯å±±ã«çž®ããããšã¯èµ·ããªããããããããšããããšã¯èµ·ãããªãããšããããšã®ãã£ãããšãªã fact6: ããããžã ããŒã«åŒµãåãããããšãçºçããªããæãŠåãããšã¯èµ·ããããšããããšã¯æãç«ããªããªãã°æãŠåãããšã¯èµ·ããªã fact7: å¿ããŸãããšããããšãçãããšããããšã¯æãŠãèµ·ããªããšããããšãåå ã fact8: ãããæãŠã¯èµ·ãããéãããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšããªããªãã°æãŠãçºçããªã fact9: ãäžéãçºçããããããšããããšãèµ·ãããªãããšããããšã¯èª€ãã fact10: ãããããããããšããããšã¯çºçããã°ãæé£ããšããããšãçºçããªããæœè¡ã¯çããªãããšããããšãäºå®ã ãšããããšããªã fact11: ãããæãŠåãããšã¯çããªãããšããããšã¯æãç«ãŠã°ãæãŠãèµ·ããããããéãããããšã¯çºçããªãããšããããšãæãç«ããªã fact12: ããããããšããããšãçããã°ãå¿ããªããšããããšã¯èµ·ãããå
çŸã«çµäžããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ãšããããšããªã fact13: ãããé»éå¯å±±ã«çž®ããããšã¯çããªãããšããããšã¯äºå®ãªãã°ãããžã ããŒã«åŒµãåãããããšã§ã¯ãªãæãŠåãããšãèµ·ããããšããããšã¯æ¬åœã ããšããããšã誀ãã fact14: äžå¡æã¯çãããšããããšããæŽãããšã¯èµ·ããããããããããšããããšãçããªãããšããããšãèªçºãã fact15: ãèšæŸã€ããšãèµ·ããããããæ€åãèµ·ããªãããšããããšã¯äºå®ãšç°ãªã ; $hypothesis$ = æŽãããšã¯èµ·ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{I} -> ¬{H} fact2: ¬{H} -> ({G} & {F}) fact3: {K} -> (¬{I} & ¬{J}) fact4: ¬(¬{E} & ¬{D}) -> {C} fact5: ¬{R} -> (¬{P} & ¬{Q}) fact6: ¬(¬{O} & {M}) -> ¬{M} fact7: ¬{L} -> {K} fact8: ¬({L} & ¬{N}) -> ¬{L} fact9: ¬({AA} & ¬{AB}) fact10: {F} -> ¬(¬{E} & ¬{D}) fact11: ¬{M} -> ¬({L} & ¬{N}) fact12: {A} -> ¬({HG} & ¬{EH}) fact13: ¬{P} -> ¬(¬{O} & {M}) fact14: {C} -> ({B} & ¬{A}) fact15: ¬({IA} & ¬{BK}) ; $hypothesis$ = ¬{B} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¯ã€ã·ã£ãã¯ãŸãããã©ããªã | ¬{B}{b} | fact1: æ°åŸ¡éå£ã¯ããã«ãã£ãŒãšãªã¢ã fact2: ããã®çœäººãã»ã©ãšãããªãããšããããšã¯æ¬åœã fact3: ãã®äžå±
ãçå±ã£ãœã fact4: ããããšããããšããªããã®ã¯æ°åŸ¡éå£ã ãåž°ããå·æããšããããšããªã fact5: ãããã®äžå±
ã¯ã»ã©ãšãããããã¯çå±ã£ãœããªãã°ãã®ã¯ã€ã·ã£ãããŸãããã©ããªã fact6: ãããã®ã¯ã€ã·ã£ããããã«ãã£ãŒãšãªã¢ãªãã°ããããŸãããã©ã fact7: ããæ°åŸ¡éå£ãåž°ããå·æããšããããšããªããªãã°ããããããã«ãã£ãŒãšãªã¢ã§ãªãããšããããšãæ£ãã fact8: ããããããã®ãããã«ãã£ãŒãšãªã¢ã ãããããŸãããã©ããšããããšããªãããšããããšã誀ããªãã°ããã¯çå±ã£ãœããªã fact9: ããã®äžå±
ã¯ã»ã©ãšãããçå±ã£ãœãããšããããšãééãã§ãªã | fact1: (x): {C}x -> {A}x fact2: ¬{AA}{je} fact3: {AB}{a} fact4: (x): ¬{E}x -> ({C}x & ¬{D}x) fact5: ({AA}{a} & {AB}{a}) -> ¬{B}{b} fact6: {A}{b} -> {B}{b} fact7: (x): ({C}x & ¬{D}x) -> ¬{A}x fact8: (x): ¬({A}x & ¬{B}x) -> ¬{AB}x fact9: ({AA}{a} & {AB}{a}) | [
"fact5 & fact9 -> hypothesis;"
] | [
"fact5 & fact9 -> hypothesis;"
] | ãã®ã¯ã€ã·ã£ãããŸãããã©ã | {B}{b} | [
"fact11 -> int1: ããããã®ã¯ã€ã·ã£ãã¯æ°åŸ¡éå£ã ããšããããšã¯äºå®ãªãã°ããã¯ããã«ãã£ãŒãšãªã¢ã ;"
] | 5 | 1 | 1 | 7 | 0 | 7 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: æ°åŸ¡éå£ã¯ããã«ãã£ãŒãšãªã¢ã fact2: ããã®çœäººãã»ã©ãšãããªãããšããããšã¯æ¬åœã fact3: ãã®äžå±
ãçå±ã£ãœã fact4: ããããšããããšããªããã®ã¯æ°åŸ¡éå£ã ãåž°ããå·æããšããããšããªã fact5: ãããã®äžå±
ã¯ã»ã©ãšãããããã¯çå±ã£ãœããªãã°ãã®ã¯ã€ã·ã£ãããŸãããã©ããªã fact6: ãããã®ã¯ã€ã·ã£ããããã«ãã£ãŒãšãªã¢ãªãã°ããããŸãããã©ã fact7: ããæ°åŸ¡éå£ãåž°ããå·æããšããããšããªããªãã°ããããããã«ãã£ãŒãšãªã¢ã§ãªãããšããããšãæ£ãã fact8: ããããããã®ãããã«ãã£ãŒãšãªã¢ã ãããããŸãããã©ããšããããšããªãããšããããšã誀ããªãã°ããã¯çå±ã£ãœããªã fact9: ããã®äžå±
ã¯ã»ã©ãšãããçå±ã£ãœãããšããããšãééãã§ãªã ; $hypothesis$ = ãã®ã¯ã€ã·ã£ãã¯ãŸãããã©ããªã ; $proof$ = | fact5 & fact9 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {C}x -> {A}x fact2: ¬{AA}{je} fact3: {AB}{a} fact4: (x): ¬{E}x -> ({C}x & ¬{D}x) fact5: ({AA}{a} & {AB}{a}) -> ¬{B}{b} fact6: {A}{b} -> {B}{b} fact7: (x): ({C}x & ¬{D}x) -> ¬{A}x fact8: (x): ¬({A}x & ¬{B}x) -> ¬{AB}x fact9: ({AA}{a} & {AB}{a}) ; $hypothesis$ = ¬{B}{b} ; $proof$ = | fact5 & fact9 -> hypothesis; __PROVED__ |
0.3 | ããããã®æé ã¯ãããããããªããªãã°ãã®æé ãæ²åã ããšããããšã誀ãã | ¬(¬{B}{aa} -> {C}{aa}) | fact1: ããäœãã¯äº¬éœæ°è瀟ã§ãªããªãã°ããããµãããã fact2: ãããããã®ã¯ã€ãåã«é£åºãã°ããã¯çŒãæã fact3: ãããã®æé ãä¿®åŠé¢å®®ãèã«æ©ããªããªãã°ããã¯ãããããã fact4: ãããããããã®ãæ²åã fact5: ããããã®æé ãããããããããšããããšãçå®ãªãã°ããã¯æ²åã fact6: ãããã®æé ãæ²åãªãã°ãããå±å³¶äžã fact7: ããäœãã¯å€©åã§ãªããªãã°ããã¯éåŒã fact8: ãããã®æé ãæ²åã ãšããããšã¯ãªããªãã°ãããå³èã«ä»°ã fact9: ãããã®æé ãæ²åã§ãªããªãã°ããã¯æ°ãç«ãŠã fact10: ããããããªããã®ããããªã fact11: ããäœãã¯èŽã蟌ãŸãªããªãã°ãããçŒãæã fact12: ããäœãã¯äžåã ãšããããšã¯ãªããªãã°ããããã¥ãŒãºãŠã£ãŒã¯ãæ±ãèµ·ããã fact13: ãããããã®ããããããšããããšããªããªãã°ããã¯åäžã«äºåãã fact14: æ³¥èããªããã®ã¯è±èœã fact15: ãããããããªããã®ãæ²åã fact16: ãããã®æé ã¯ã·ã¡åã ãšããããšã¯ãªããªãã°ããã¯æ©æ¬åäŒã | fact1: (x): ¬{IU}x -> {IT}x fact2: (x): {AU}x -> {BN}x fact3: ¬{AI}{aa} -> {B}{aa} fact4: (x): {B}x -> {C}x fact5: {B}{aa} -> {C}{aa} fact6: {C}{aa} -> {GA}{aa} fact7: (x): ¬{DR}x -> {EA}x fact8: ¬{C}{aa} -> {GF}{aa} fact9: ¬{C}{aa} -> {HP}{aa} fact10: (x): ¬{J}x -> {DC}x fact11: (x): ¬{CM}x -> {BN}x fact12: (x): ¬{EU}x -> {IA}x fact13: (x): ¬{CI}x -> {AO}x fact14: (x): ¬{BQ}x -> {AB}x fact15: (x): ¬{B}x -> {C}x fact16: ¬{FE}{aa} -> {JJ}{aa} | [
"fact15 -> hypothesis;"
] | [
"fact15 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 15 | 0 | 15 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããäœãã¯äº¬éœæ°è瀟ã§ãªããªãã°ããããµãããã fact2: ãããããã®ã¯ã€ãåã«é£åºãã°ããã¯çŒãæã fact3: ãããã®æé ãä¿®åŠé¢å®®ãèã«æ©ããªããªãã°ããã¯ãããããã fact4: ãããããããã®ãæ²åã fact5: ããããã®æé ãããããããããšããããšãçå®ãªãã°ããã¯æ²åã fact6: ãããã®æé ãæ²åãªãã°ãããå±å³¶äžã fact7: ããäœãã¯å€©åã§ãªããªãã°ããã¯éåŒã fact8: ãããã®æé ãæ²åã ãšããããšã¯ãªããªãã°ãããå³èã«ä»°ã fact9: ãããã®æé ãæ²åã§ãªããªãã°ããã¯æ°ãç«ãŠã fact10: ããããããªããã®ããããªã fact11: ããäœãã¯èŽã蟌ãŸãªããªãã°ãããçŒãæã fact12: ããäœãã¯äžåã ãšããããšã¯ãªããªãã°ããããã¥ãŒãºãŠã£ãŒã¯ãæ±ãèµ·ããã fact13: ãããããã®ããããããšããããšããªããªãã°ããã¯åäžã«äºåãã fact14: æ³¥èããªããã®ã¯è±èœã fact15: ãããããããªããã®ãæ²åã fact16: ãããã®æé ã¯ã·ã¡åã ãšããããšã¯ãªããªãã°ããã¯æ©æ¬åäŒã ; $hypothesis$ = ããããã®æé ã¯ãããããããªããªãã°ãã®æé ãæ²åã ããšããããšã誀ãã ; $proof$ = | fact15 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{IU}x -> {IT}x fact2: (x): {AU}x -> {BN}x fact3: ¬{AI}{aa} -> {B}{aa} fact4: (x): {B}x -> {C}x fact5: {B}{aa} -> {C}{aa} fact6: {C}{aa} -> {GA}{aa} fact7: (x): ¬{DR}x -> {EA}x fact8: ¬{C}{aa} -> {GF}{aa} fact9: ¬{C}{aa} -> {HP}{aa} fact10: (x): ¬{J}x -> {DC}x fact11: (x): ¬{CM}x -> {BN}x fact12: (x): ¬{EU}x -> {IA}x fact13: (x): ¬{CI}x -> {AO}x fact14: (x): ¬{BQ}x -> {AB}x fact15: (x): ¬{B}x -> {C}x fact16: ¬{FE}{aa} -> {JJ}{aa} ; $hypothesis$ = ¬(¬{B}{aa} -> {C}{aa}) ; $proof$ = | fact15 -> hypothesis; __DISPROVED__ |
0.3 | ãéåŠä¿ã«å¯ãŒããããšã¯èµ·ããªããŠç®æããšããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšããªã | ¬(¬{AA} & ¬{AB}) | fact1: 身æ§ããããšãèµ·ããªããšããããšãç®æããšããããšã¯èµ·ãããªããšããããšã«ç¹ãã fact2: æ Œå¥œãããšããããšã¯çããªãã倧é£ã¯çããªã fact3: ãéåŠä¿ã«å¯ãŒããããšã¯çããªããç®æããšããããšã¯èµ·ããªãããšããããšã¯ã身æ§ããããšã¯çããªãããšããããšãå¥æ©ã fact4: 身æ§ããããšãçºçããªã fact5: ãç®æããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact6: ãã身æ§ããããšãçããã°ãéåŠä¿ã«å¯ãŒããããšã¯çããªããŠç®æããšããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | fact1: ¬{A} -> ¬{AB} fact2: (¬{L} & ¬{CN}) fact3: ¬{A} -> (¬{AA} & ¬{AB}) fact4: ¬{A} fact5: ¬{AB} fact6: {A} -> ¬(¬{AA} & ¬{AB}) | [
"fact3 & fact4 -> hypothesis;"
] | [
"fact3 & fact4 -> hypothesis;"
] | ãéåŠä¿ã«å¯ãŒããããšã¯çºçããªããç®æããšããããšã¯çããªãããšããããšãåœã | ¬(¬{AA} & ¬{AB}) | [] | 6 | 1 | 1 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: 身æ§ããããšãèµ·ããªããšããããšãç®æããšããããšã¯èµ·ãããªããšããããšã«ç¹ãã fact2: æ Œå¥œãããšããããšã¯çããªãã倧é£ã¯çããªã fact3: ãéåŠä¿ã«å¯ãŒããããšã¯çããªããç®æããšããããšã¯èµ·ããªãããšããããšã¯ã身æ§ããããšã¯çããªãããšããããšãå¥æ©ã fact4: 身æ§ããããšãçºçããªã fact5: ãç®æããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact6: ãã身æ§ããããšãçããã°ãéåŠä¿ã«å¯ãŒããããšã¯çããªããŠç®æããšããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $hypothesis$ = ãéåŠä¿ã«å¯ãŒããããšã¯èµ·ããªããŠç®æããšããããšãçºçããªãããšããããšã¯æãç«ã€ãšããããšããªã ; $proof$ = | fact3 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A} -> ¬{AB} fact2: (¬{L} & ¬{CN}) fact3: ¬{A} -> (¬{AA} & ¬{AB}) fact4: ¬{A} fact5: ¬{AB} fact6: {A} -> ¬(¬{AA} & ¬{AB}) ; $hypothesis$ = ¬(¬{AA} & ¬{AB}) ; $proof$ = | fact3 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®åæ§ãåäžãã¯ãã€ãããšããããšããªã | ¬{B}{a} | fact1: ããããç¯ãããã€ããªããšããããšããªãããšããããšãåœãªããã®ãããã°ãã®æ²¹çŽã¯ç¯ãããšããããšããªã fact2: ããäœãã¯äžäžé¢ã§ãªããªãã°ãããã¯å²ãæ®ããªããŠããããªãããšããããšãæãç«ã€ãšããããšããªã fact3: ããç¢éšå±±ãç¯ããªããªãã°ãã®æ²¹çŽã¯éæœéšæ²¢ã«è³éŠŽãã fact4: ããããããã®ã¯ããããªããããã¯æŸå
ã§ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯ããã fact5: ãããã®åæ§ãåäžãã¯ãã€ãããšããããšã¯ãªãããããå²ãæ®ããªããªãã°ãã®ç·šè
ãå²ãæ®ã fact6: ãã®ãµã©ã»ã³ãå·®ãé£ãããªã fact7: ããããã®ãããã¢ããã¯äžäžé¢ã§ãªãããšããããšãæ£ãããªãã°ããã®ç çã¯ããããªããããã¯æŸå
ã§ãªãããšããããšãåã fact8: ãã®ã·ã£ãã³ã¯ç¢éšå±±ã fact9: ãã®ã·ã£ãã³ãç¯ãããšããããšããªã fact10: ãããäœããäžäžé¢ã ãšããããšã¯ãªããããããããéæœéšæ²¢ã«è³éŠŽããããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãããäžäžé¢ã fact11: ãããç¯ããªãããã®ãããã°ãã®ãããã¢ãããéæœéšæ²¢ã«è³éŠŽãããšããããšã¯ãªã fact12: ãããã®åæ§ã¯å²ãæ®ãã°ãããåäžãã¯ãã€ãã fact13: ãããã®åæ§ã¯åè§ããªãã°ããããåäžãã¯ãã€ããããšããããšã¯æ£ãã fact14: ãã®ç·šè
ã¯åäžãã¯ãã€ãã fact15: ãããã®åºç€ãç¢éšå±±ã§ãªããªãã°ããã®ã·ã£ãã³ã¯ç¯ããããããããã¯ã€ããªããšããããšããªãããšããããšãæãç«ããªã fact16: ãããã®ãµã©ã»ã³ã¯ãšãåããããŸèŠããšããããšã¯ãªããªãã°ããã¯è±ç°åäºããããåããããã¯ç¢éšå±±ã fact17: ããããã®åæ§ã¯çããããããšããããšãæãç«ãŠã°ããã¯èžãããã fact18: ãã®ãµã©ã»ã³ããšãåããããŸèŠãªã fact19: ããããéæœéšæ²¢ã«è³éŠŽããªãããšããããšã¯åã ãšããããšã¯ãªãããã®ãããã°ãã®ç çãäžäžé¢ã ãšããããšã¯ãªããŠãããæŸå
ã ãšããããšã¯ãªã fact20: ãã®åæ§ãå²ãæ®ã fact21: ãããã®ãµã©ã»ã³ã¯å·®ãé£ãããªããªãã°ããã¯åæšå·ã«ãããã ãã空ã
ãã fact22: ãããã®ãµã©ã»ã³ã¯åæšå·ã«ãããã ããç¢éšå±±ãªãã°ãã®åºç€ã¯ç¢éšå±±ã§ãªã | fact1: (x): ¬({G}x & ¬{I}x) -> ¬{G}{d} fact2: (x): ¬{D}x -> ¬(¬{A}x & ¬{C}x) fact3: (x): ({H}x & ¬{G}x) -> {F}{d} fact4: (x): ¬(¬{C}x & ¬{E}x) -> {C}x fact5: (¬{B}{a} & ¬{A}{a}) -> {A}{fp} fact6: ¬{L}{g} fact7: ¬{D}{c} -> ¬(¬{C}{b} & ¬{E}{b}) fact8: {H}{e} fact9: ¬{G}{e} fact10: (x): ¬(¬{D}x & {F}x) -> {D}x fact11: (x): ¬{G}x -> ¬{F}{c} fact12: {A}{a} -> {B}{a} fact13: {HN}{a} -> {B}{a} fact14: {B}{fp} fact15: ¬{H}{f} -> ¬({G}{e} & ¬{I}{e}) fact16: ¬{N}{g} -> ({M}{g} & {H}{g}) fact17: {P}{a} -> {IQ}{a} fact18: ¬{N}{g} fact19: (x): ¬{F}x -> (¬{D}{b} & ¬{E}{b}) fact20: {A}{a} fact21: ¬{L}{g} -> ({K}{g} & {J}{g}) fact22: ({K}{g} & {H}{g}) -> ¬{H}{f} | [
"fact12 & fact20 -> hypothesis;"
] | [
"fact12 & fact20 -> hypothesis;"
] | ãã®ç·šè
ãå²ãæ®ã | {A}{fp} | [
"fact27 -> int1: ããããã®ç çã¯ããããšããããšããªãããããæŸå
ã§ãªãããšããããšã¯åãªãã°ãããããã; fact23 & fact28 -> int2: ãã®ã·ã£ãã³ãç¢éšå±±ã ãããã¯ç¯ããªã; int2 -> int3: ãç¢éšå±±ã§ç¯ããªãããã®ã¯ãã; int3 & fact26 -> int4: ãã®æ²¹çŽãéæœéšæ²¢ã«è³éŠŽãã; int4 -> int5: ãéæœéšæ²¢ã«è³éŠŽããããã®ã¯ãã;"
] | 10 | 1 | 1 | 20 | 0 | 20 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããç¯ãããã€ããªããšããããšããªãããšããããšãåœãªããã®ãããã°ãã®æ²¹çŽã¯ç¯ãããšããããšããªã fact2: ããäœãã¯äžäžé¢ã§ãªããªãã°ãããã¯å²ãæ®ããªããŠããããªãããšããããšãæãç«ã€ãšããããšããªã fact3: ããç¢éšå±±ãç¯ããªããªãã°ãã®æ²¹çŽã¯éæœéšæ²¢ã«è³éŠŽãã fact4: ããããããã®ã¯ããããªããããã¯æŸå
ã§ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ããã¯ããã fact5: ãããã®åæ§ãåäžãã¯ãã€ãããšããããšã¯ãªãããããå²ãæ®ããªããªãã°ãã®ç·šè
ãå²ãæ®ã fact6: ãã®ãµã©ã»ã³ãå·®ãé£ãããªã fact7: ããããã®ãããã¢ããã¯äžäžé¢ã§ãªãããšããããšãæ£ãããªãã°ããã®ç çã¯ããããªããããã¯æŸå
ã§ãªãããšããããšãåã fact8: ãã®ã·ã£ãã³ã¯ç¢éšå±±ã fact9: ãã®ã·ã£ãã³ãç¯ãããšããããšããªã fact10: ãããäœããäžäžé¢ã ãšããããšã¯ãªããããããããéæœéšæ²¢ã«è³éŠŽããããšããããšã¯æãç«ã€ãšããããšããªããªãã°ãããäžäžé¢ã fact11: ãããç¯ããªãããã®ãããã°ãã®ãããã¢ãããéæœéšæ²¢ã«è³éŠŽãããšããããšã¯ãªã fact12: ãããã®åæ§ã¯å²ãæ®ãã°ãããåäžãã¯ãã€ãã fact13: ãããã®åæ§ã¯åè§ããªãã°ããããåäžãã¯ãã€ããããšããããšã¯æ£ãã fact14: ãã®ç·šè
ã¯åäžãã¯ãã€ãã fact15: ãããã®åºç€ãç¢éšå±±ã§ãªããªãã°ããã®ã·ã£ãã³ã¯ç¯ããããããããã¯ã€ããªããšããããšããªãããšããããšãæãç«ããªã fact16: ãããã®ãµã©ã»ã³ã¯ãšãåããããŸèŠããšããããšã¯ãªããªãã°ããã¯è±ç°åäºããããåããããã¯ç¢éšå±±ã fact17: ããããã®åæ§ã¯çããããããšããããšãæãç«ãŠã°ããã¯èžãããã fact18: ãã®ãµã©ã»ã³ããšãåããããŸèŠãªã fact19: ããããéæœéšæ²¢ã«è³éŠŽããªãããšããããšã¯åã ãšããããšã¯ãªãããã®ãããã°ãã®ç çãäžäžé¢ã ãšããããšã¯ãªããŠãããæŸå
ã ãšããããšã¯ãªã fact20: ãã®åæ§ãå²ãæ®ã fact21: ãããã®ãµã©ã»ã³ã¯å·®ãé£ãããªããªãã°ããã¯åæšå·ã«ãããã ãã空ã
ãã fact22: ãããã®ãµã©ã»ã³ã¯åæšå·ã«ãããã ããç¢éšå±±ãªãã°ãã®åºç€ã¯ç¢éšå±±ã§ãªã ; $hypothesis$ = ãã®åæ§ãåäžãã¯ãã€ãããšããããšããªã ; $proof$ = | fact12 & fact20 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬({G}x & ¬{I}x) -> ¬{G}{d} fact2: (x): ¬{D}x -> ¬(¬{A}x & ¬{C}x) fact3: (x): ({H}x & ¬{G}x) -> {F}{d} fact4: (x): ¬(¬{C}x & ¬{E}x) -> {C}x fact5: (¬{B}{a} & ¬{A}{a}) -> {A}{fp} fact6: ¬{L}{g} fact7: ¬{D}{c} -> ¬(¬{C}{b} & ¬{E}{b}) fact8: {H}{e} fact9: ¬{G}{e} fact10: (x): ¬(¬{D}x & {F}x) -> {D}x fact11: (x): ¬{G}x -> ¬{F}{c} fact12: {A}{a} -> {B}{a} fact13: {HN}{a} -> {B}{a} fact14: {B}{fp} fact15: ¬{H}{f} -> ¬({G}{e} & ¬{I}{e}) fact16: ¬{N}{g} -> ({M}{g} & {H}{g}) fact17: {P}{a} -> {IQ}{a} fact18: ¬{N}{g} fact19: (x): ¬{F}x -> (¬{D}{b} & ¬{E}{b}) fact20: {A}{a} fact21: ¬{L}{g} -> ({K}{g} & {J}{g}) fact22: ({K}{g} & {H}{g}) -> ¬{H}{f} ; $hypothesis$ = ¬{B}{a} ; $proof$ = | fact12 & fact20 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¹ããªã³ã°ã¯éŠçã ãšããããšã¯ãªã | ¬{A}{a} | fact1: ãã®å±äœã¯ãããã fact2: ããã®ææãéŠçã ããšããããšã¯çå®ã fact3: ãããããã®ã¯çããšããããšã¯ãªããªãã°ããã¯ããµæ±ã§ãªã fact4: ãããããã®ãäžç³žç°ã§ãªããªãã°ããããããã§ããã¯éŠçã fact5: ãã®èèã¯éŠçã fact6: ãã®ã¹ããªã³ã°ããããã fact7: ããã®ã¹ããªã³ã°ãä¹
ç±³å·åã§ãªããããã¯ããµæ±ã ãšããããšããªãããšããããšã¯åœã fact8: ãã®ã¹ããªã³ã°ãäžæåã§ãã£ãŠããããã® fact9: ãã®åå£ã¯éŠçã ãäžæåã fact10: ãããããã®ã¯ããµæ±ã ãšããããšã¯ãªããªãã°ãããã¯äžç³žç°ã ããããã ããšããããšãæãç«ã€ãšããããšããªã fact11: ããããä¹
ç±³å·åã ãšããããšã¯ãªããŠããµæ±ã ãšããããšããªãããšããããšãæãç«ããªãããã®ã¯ããã°ãã®æ¯åã¯ä¹
ç±³å·åã fact12: ããã®ã¹ããªã³ã°ã¯ã«ããã©ãŒã¡ã³ã ããšããããšãæãç«ã€ fact13: ãã®ã¹ããªã³ã°ã¯æ«æ°žã fact14: ãããã®æŒãå
¥ãã¯èŠæç¡ããªãã°ããã®è«äžãããšãããããªãããããã¯çãããšããããšã¯åœã | fact1: {B}{fj} fact2: {A}{er} fact3: (x): ¬{E}x -> ¬{D}x fact4: (x): ¬{C}x -> ({B}x & {A}x) fact5: {A}{bc} fact6: {B}{a} fact7: ¬(¬{CR}{a} & ¬{D}{a}) fact8: ({HT}{a} & {R}{a}) fact9: ({A}{fk} & {HT}{fk}) fact10: (x): ¬{D}x -> ¬({C}x & {B}x) fact11: (x): ¬(¬{CR}x & ¬{D}x) -> {CR}{dh} fact12: {FE}{a} fact13: {IA}{a} fact14: {G}{c} -> ¬(¬{F}{b} v {E}{b}) | [] | [] | ãã®æ¯åãä¹
ç±³å·åã ãããããããã | ({CR}{dh} & {B}{dh}) | [
"fact18 -> int1: ããä¹
ç±³å·åã§ãªããããµæ±ã§ãªãããšããããšã¯æãç«ããªãããã®ã¯ãã; int1 & fact17 -> int2: ãã®æ¯åãä¹
ç±³å·åã ; fact15 -> int3: ãããã®æ¯åã¯äžç³žç°ã§ãªããªãã°ããã¯ãããã§ãã£ãŠéŠçã ãã®;"
] | 6 | 1 | null | 14 | 0 | 14 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®å±äœã¯ãããã fact2: ããã®ææãéŠçã ããšããããšã¯çå®ã fact3: ãããããã®ã¯çããšããããšã¯ãªããªãã°ããã¯ããµæ±ã§ãªã fact4: ãããããã®ãäžç³žç°ã§ãªããªãã°ããããããã§ããã¯éŠçã fact5: ãã®èèã¯éŠçã fact6: ãã®ã¹ããªã³ã°ããããã fact7: ããã®ã¹ããªã³ã°ãä¹
ç±³å·åã§ãªããããã¯ããµæ±ã ãšããããšããªãããšããããšã¯åœã fact8: ãã®ã¹ããªã³ã°ãäžæåã§ãã£ãŠããããã® fact9: ãã®åå£ã¯éŠçã ãäžæåã fact10: ãããããã®ã¯ããµæ±ã ãšããããšã¯ãªããªãã°ãããã¯äžç³žç°ã ããããã ããšããããšãæãç«ã€ãšããããšããªã fact11: ããããä¹
ç±³å·åã ãšããããšã¯ãªããŠããµæ±ã ãšããããšããªãããšããããšãæãç«ããªãããã®ã¯ããã°ãã®æ¯åã¯ä¹
ç±³å·åã fact12: ããã®ã¹ããªã³ã°ã¯ã«ããã©ãŒã¡ã³ã ããšããããšãæãç«ã€ fact13: ãã®ã¹ããªã³ã°ã¯æ«æ°žã fact14: ãããã®æŒãå
¥ãã¯èŠæç¡ããªãã°ããã®è«äžãããšãããããªãããããã¯çãããšããããšã¯åœã ; $hypothesis$ = ãã®ã¹ããªã³ã°ã¯éŠçã ãšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{fj} fact2: {A}{er} fact3: (x): ¬{E}x -> ¬{D}x fact4: (x): ¬{C}x -> ({B}x & {A}x) fact5: {A}{bc} fact6: {B}{a} fact7: ¬(¬{CR}{a} & ¬{D}{a}) fact8: ({HT}{a} & {R}{a}) fact9: ({A}{fk} & {HT}{fk}) fact10: (x): ¬{D}x -> ¬({C}x & {B}x) fact11: (x): ¬(¬{CR}x & ¬{D}x) -> {CR}{dh} fact12: {FE}{a} fact13: {IA}{a} fact14: {G}{c} -> ¬(¬{F}{b} v {E}{b}) ; $hypothesis$ = ¬{A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®æšªæ§ãããã€ãããã | {B}{a} | fact1: ããã®æšªæ§ãã»ããªãããšããããšã¯ãªãããšããããšã¯çå®ã fact2: ãããäœããå®ç©æ®¿ã ããããããã¯åéœã ãšããããšããªãããšããããšã¯äºå®ãšç°ãªãã°ãããæ¬èŠå¯ºã fact3: ãããäœããæ¬èŠå¯ºã§ãªãããšããããšãæãç«ãŠã°ãããè«èšªã«æ
ãã湿å°ã fact4: æ¬èŠå¯ºãè«èšªã«æ
ãŸãªãã湿å°ã ãšããããšã¯ãªã fact5: ãããã®æšªæ§ã¯ãŸã¶ãããªãã°ããããããã€ããããããšããããšã¯äºå®ã fact6: ãããããã®ãè«èšªã«æ
ããšããããšããªããªãã°ããããã¿ãããããšããããšã¯ãªã fact7: ãããã®æšªæ§ãã»ããªãããšããããšã¯ãªããªãã°ããããå®ç©æ®¿ã§ããã¯åéœã ãšããããšã¯ãªãããšããããšãåœã fact8: ãããã®èŠç¿ã¯ããµããªãã°ããã¯ããã€ãããã fact9: ããããã®ããªãŠã ã¯åéœã§ãããå®ç©æ®¿ã ããšããããšã¯äºå®ãšç°ãªãã°ãã®ãã³ããæ¬èŠå¯ºã ãšããããšã¯ãªã fact10: ãããã®ãã³ãããã¿ãããããšããããšã¯ãªããã®ã§ãã£ãŠãŸã¶ãããšããããšããªããã®ãªãã°ãã®æšªæ§ãããã€ãããããšããããšã¯ãªã fact11: ãããã®æšªæ§ã¯ãã¿ãããããšããããšã¯ãªããªãã°ãããã¯ãŸã¶ãããšããããšããªããŠããã¯ããã€ãããããªãããšããããšãäºå®ãšç°ãªã | fact1: ¬{I}{a} fact2: (x): ¬({H}x & ¬{G}x) -> {F}x fact3: (x): ¬{F}x -> ({D}x & {E}x) fact4: (x): {F}x -> (¬{D}x v ¬{E}x) fact5: {A}{a} -> {B}{a} fact6: (x): ¬{D}x -> ¬{C}x fact7: ¬{I}{a} -> ¬({H}{a} & ¬{G}{a}) fact8: {HH}{jk} -> {B}{jk} fact9: ¬({G}{c} & {H}{c}) -> ¬{F}{b} fact10: (¬{C}{b} & ¬{A}{b}) -> ¬{B}{a} fact11: ¬{C}{a} -> ¬(¬{A}{a} & ¬{B}{a}) | [] | [] | ãã®æ°ŽèŸºã¯ãŸã¶ãã | {A}{ej} | [
"fact15 -> int1: ãããã®æšªæ§ã¯æ¬èŠå¯ºãªãã°ããã¯è«èšªã«æ
ãŸãªãããããã¯ããã湿å°ã ãšããããšã¯ãªã; fact17 -> int2: ããããã®æšªæ§ãå®ç©æ®¿ã ããããåéœã§ãªãããšããããšãæãç«ããªããªãã°ãããæ¬èŠå¯ºã ; fact13 & fact12 -> int3: ããã®æšªæ§ãå®ç©æ®¿ã§åéœã§ãªãããšããããšã¯èª€ãã ; int2 & int3 -> int4: ãã®æšªæ§ã¯æ¬èŠå¯ºã ; int1 & int4 -> int5: ãã®æšªæ§ãè«èšªã«æ
ããšããããšã¯ãªãããããã¯æ¹¿å°ã ãšããããšããªã; fact16 -> int6: ãããã®æšªæ§ã¯è«èšªã«æ
ããšããããšããªããªãã°ããã¯ãã¿ãããããªã;"
] | 7 | 1 | null | 10 | 0 | 10 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã®æšªæ§ãã»ããªãããšããããšã¯ãªãããšããããšã¯çå®ã fact2: ãããäœããå®ç©æ®¿ã ããããããã¯åéœã ãšããããšããªãããšããããšã¯äºå®ãšç°ãªãã°ãããæ¬èŠå¯ºã fact3: ãããäœããæ¬èŠå¯ºã§ãªãããšããããšãæãç«ãŠã°ãããè«èšªã«æ
ãã湿å°ã fact4: æ¬èŠå¯ºãè«èšªã«æ
ãŸãªãã湿å°ã ãšããããšã¯ãªã fact5: ãããã®æšªæ§ã¯ãŸã¶ãããªãã°ããããããã€ããããããšããããšã¯äºå®ã fact6: ãããããã®ãè«èšªã«æ
ããšããããšããªããªãã°ããããã¿ãããããšããããšã¯ãªã fact7: ãããã®æšªæ§ãã»ããªãããšããããšã¯ãªããªãã°ããããå®ç©æ®¿ã§ããã¯åéœã ãšããããšã¯ãªãããšããããšãåœã fact8: ãããã®èŠç¿ã¯ããµããªãã°ããã¯ããã€ãããã fact9: ããããã®ããªãŠã ã¯åéœã§ãããå®ç©æ®¿ã ããšããããšã¯äºå®ãšç°ãªãã°ãã®ãã³ããæ¬èŠå¯ºã ãšããããšã¯ãªã fact10: ãããã®ãã³ãããã¿ãããããšããããšã¯ãªããã®ã§ãã£ãŠãŸã¶ãããšããããšããªããã®ãªãã°ãã®æšªæ§ãããã€ãããããšããããšã¯ãªã fact11: ãããã®æšªæ§ã¯ãã¿ãããããšããããšã¯ãªããªãã°ãããã¯ãŸã¶ãããšããããšããªããŠããã¯ããã€ãããããªãããšããããšãäºå®ãšç°ãªã ; $hypothesis$ = ãã®æšªæ§ãããã€ãããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{I}{a} fact2: (x): ¬({H}x & ¬{G}x) -> {F}x fact3: (x): ¬{F}x -> ({D}x & {E}x) fact4: (x): {F}x -> (¬{D}x v ¬{E}x) fact5: {A}{a} -> {B}{a} fact6: (x): ¬{D}x -> ¬{C}x fact7: ¬{I}{a} -> ¬({H}{a} & ¬{G}{a}) fact8: {HH}{jk} -> {B}{jk} fact9: ¬({G}{c} & {H}{c}) -> ¬{F}{b} fact10: (¬{C}{b} & ¬{A}{b}) -> ¬{B}{a} fact11: ¬{C}{a} -> ¬(¬{A}{a} & ¬{B}{a}) ; $hypothesis$ = {B}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®å¹Žéãæãã€ã | {B}{b} | fact1: ããåæ°ã«é»ãããããã°ãã ãããªãããšããããšãåœãªããã®ããã fact2: ãã®çã¯ç·ã fact3: ãããããã®ãåæ°ã«é»ãããšããããšããªããŠããããã
ããšããããšã¯ãªããªãã°ãããæªå¢Ÿã«äº€ãããããšããããšã¯ãªã fact4: ããããåæ°ã«é»ãããããã°ãã ãããšããããšããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ãããã°ãã®èã¯åæ°ã«é»ãããšããããšã¯ãªã fact5: ãã®èã¯ç·ã§ãªãããããããã¯çªã·ã fact6: ããããã®èãã®ããããããã®ã§ãã£ãŠäººæãããšããããšããªããã®ããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯äººæãã fact7: ãã®èãçªã·ã fact8: 人æãããã®ããã
ããšããããšã¯ãªã fact9: ããäœãã¯æªå¢Ÿã«äº€ãããããªããªãã°ããããçŸä»£ã§ãããäžå
«ãæã«ããããªããäž¡æ¹ã ããšããããšãæãç«ã€ãšããããšã¯ãªã | fact1: (Ex): ¬({F}x & ¬{J}x) fact2: {AA}{gc} fact3: (x): (¬{F}x & ¬{E}x) -> ¬{D}x fact4: (x): ¬({F}x & ¬{J}x) -> ¬{F}{a} fact5: (¬{AA}{a} & {AB}{a}) fact6: ¬({H}{a} & ¬{G}{a}) -> {G}{a} fact7: {AB}{a} fact8: (x): {G}x -> ¬{E}x fact9: (x): ¬{D}x -> ¬({A}x v {C}x) | [] | [] | ãã®å¹Žéã¯æãã€ããªã | ¬{B}{b} | [
"fact12 -> int1: ãããã®èãæªå¢Ÿã«äº€ãããããšããããšããªããªãã°ããããçŸä»£ã§ããããããã¯ããã¯äžå
«ãæã«ããããªãããšããããšã¯æãç«ããªã; fact11 -> int2: ãããã®èã¯åæ°ã«é»ãããšããããšããªãããã
ããšããããšããªããªãã°ãããæªå¢Ÿã«äº€ãããããšããããšããªã; fact15 & fact13 -> int3: ãã®èãåæ°ã«é»ããªã; fact14 -> int4: ãããã®èã¯äººæãããªãã°ããããã
ããšããããšããªã;"
] | 7 | 1 | null | 8 | 0 | 8 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããåæ°ã«é»ãããããã°ãã ãããªãããšããããšãåœãªããã®ããã fact2: ãã®çã¯ç·ã fact3: ãããããã®ãåæ°ã«é»ãããšããããšããªããŠããããã
ããšããããšã¯ãªããªãã°ãããæªå¢Ÿã«äº€ãããããšããããšã¯ãªã fact4: ããããåæ°ã«é»ãããããã°ãã ãããšããããšããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããã®ãããã°ãã®èã¯åæ°ã«é»ãããšããããšã¯ãªã fact5: ãã®èã¯ç·ã§ãªãããããããã¯çªã·ã fact6: ããããã®èãã®ããããããã®ã§ãã£ãŠäººæãããšããããšããªããã®ããšããããšã¯æãç«ã€ãšããããšããªããªãã°ããã¯äººæãã fact7: ãã®èãçªã·ã fact8: 人æãããã®ããã
ããšããããšã¯ãªã fact9: ããäœãã¯æªå¢Ÿã«äº€ãããããªããªãã°ããããçŸä»£ã§ãããäžå
«ãæã«ããããªããäž¡æ¹ã ããšããããšãæãç«ã€ãšããããšã¯ãªã ; $hypothesis$ = ãã®å¹Žéãæãã€ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (Ex): ¬({F}x & ¬{J}x) fact2: {AA}{gc} fact3: (x): (¬{F}x & ¬{E}x) -> ¬{D}x fact4: (x): ¬({F}x & ¬{J}x) -> ¬{F}{a} fact5: (¬{AA}{a} & {AB}{a}) fact6: ¬({H}{a} & ¬{G}{a}) -> {G}{a} fact7: {AB}{a} fact8: (x): {G}x -> ¬{E}x fact9: (x): ¬{D}x -> ¬({A}x v {C}x) ; $hypothesis$ = {B}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã®æŽçŸã¯ããã ããããªããå¿æããªããªãã°ããã¯é·è
å²³ã«å·£ç¯ããªã | (¬{AA}{aa} v ¬{AB}{aa}) -> ¬{B}{aa} | fact1: ãããããã®ã溶æãæãåºãããããã¯ããã¯ããã§ãããªãããããã¯äž¡æ¹ãªãã°ããã¯ã¶åããªã fact2: ãããã®æŽçŸãå®®åŽç£æ¥çµå¶å€§ãé£ããšããããšããªããªãã°ãããããããšããããšã¯ãªã fact3: ãããã®èæ¯ãé«ç°ååé«çåŠæ ¡ã§ãªããè
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å²³ã«å·£ç¯ã fact4: ãããã®æå§ãåé£å±±äžã§ãããããã¯é·è
å²³ã«å·£ç¯ããªãããããã¯äž¡æ¹ãªãã°ãããããããããªã fact5: ãããã®è²§ä¹äººããããããããã¯é·è
å²³ã«å·£ç¯ããšããããšã¯ãªããªãã°ããã¯èããããšããããšã¯ãªã fact6: ããããã®æŽçŸã¯å°äžã ãšããããšããªãããšããããšãæãç«ãŠã°ããã¯çžãããªããªã fact7: ããäœãã¯èµäœã«éã«åããªããªãã°ããããã±ããã»ã»ãŸã³ãåãä»ãããšããããšã¯ãªã fact8: ããäœãã¯å°äžã§ãªãããããã¯ãããæ¥å°é£é森äŒã ãšããããšã¯ãªããªãã°ãããè¿œä»ã fact9: ãããã®æŽçŸã¯çå€ã«é£ã³æãããšããããšããªãããããã¯ããã第äžååãã€ã¿ããŠããšããããšã¯ãªããªãã°ããã¯ä¹
çŠæšã§ãªã | fact1: (x): ({DQ}x v ¬{K}x) -> ¬{IR}x fact2: ¬{FO}{aa} -> ¬{IE}{aa} fact3: (¬{EB}{c} v ¬{CC}{c}) -> {B}{c} fact4: ({P}{at} v ¬{B}{at}) -> ¬{JK}{at} fact5: ({IE}{gl} v ¬{B}{gl}) -> ¬{BS}{gl} fact6: ¬{AM}{aa} -> ¬{CO}{aa} fact7: (x): ¬{BG}x -> ¬{FR}x fact8: (x): (¬{AM}x v ¬{ID}x) -> {S}x fact9: (¬{FC}{aa} v ¬{CK}{aa}) -> ¬{DD}{aa} | [] | [] | null | null | [] | null | 1 | null | 9 | 0 | 9 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããããã®ã溶æãæãåºãããããã¯ããã¯ããã§ãããªãããããã¯äž¡æ¹ãªãã°ããã¯ã¶åããªã fact2: ãããã®æŽçŸãå®®åŽç£æ¥çµå¶å€§ãé£ããšããããšããªããªãã°ãããããããšããããšã¯ãªã fact3: ãããã®èæ¯ãé«ç°ååé«çåŠæ ¡ã§ãªããè
¹ç©¢ããªããªãã°ããã¯é·è
å²³ã«å·£ç¯ã fact4: ãããã®æå§ãåé£å±±äžã§ãããããã¯é·è
å²³ã«å·£ç¯ããªãããããã¯äž¡æ¹ãªãã°ãããããããããªã fact5: ãããã®è²§ä¹äººããããããããã¯é·è
å²³ã«å·£ç¯ããšããããšã¯ãªããªãã°ããã¯èããããšããããšã¯ãªã fact6: ããããã®æŽçŸã¯å°äžã ãšããããšããªãããšããããšãæãç«ãŠã°ããã¯çžãããªããªã fact7: ããäœãã¯èµäœã«éã«åããªããªãã°ããããã±ããã»ã»ãŸã³ãåãä»ãããšããããšã¯ãªã fact8: ããäœãã¯å°äžã§ãªãããããã¯ãããæ¥å°é£é森äŒã ãšããããšã¯ãªããªãã°ãããè¿œä»ã fact9: ãããã®æŽçŸã¯çå€ã«é£ã³æãããšããããšããªãããããã¯ããã第äžååãã€ã¿ããŠããšããããšã¯ãªããªãã°ããã¯ä¹
çŠæšã§ãªã ; $hypothesis$ = ãããã®æŽçŸã¯ããã ããããªããå¿æããªããªãã°ããã¯é·è
å²³ã«å·£ç¯ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ({DQ}x v ¬{K}x) -> ¬{IR}x fact2: ¬{FO}{aa} -> ¬{IE}{aa} fact3: (¬{EB}{c} v ¬{CC}{c}) -> {B}{c} fact4: ({P}{at} v ¬{B}{at}) -> ¬{JK}{at} fact5: ({IE}{gl} v ¬{B}{gl}) -> ¬{BS}{gl} fact6: ¬{AM}{aa} -> ¬{CO}{aa} fact7: (x): ¬{BG}x -> ¬{FR}x fact8: (x): (¬{AM}x v ¬{ID}x) -> {S}x fact9: (¬{FC}{aa} v ¬{CK}{aa}) -> ¬{DD}{aa} ; $hypothesis$ = (¬{AA}{aa} v ¬{AB}{aa}) -> ¬{B}{aa} ; $proof$ = | __UNKNOWN__ |