TSTP Solution File: LCL531+1 by PyRes---1.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : PyRes---1.3
% Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:55:05 EDT 2022
% Result : Theorem 17.64s 17.81s
% Output : Refutation 17.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL531+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 18:25:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 17.64/17.81 # Version: 1.3
% 17.64/17.81 # SZS status Theorem
% 17.64/17.81 # SZS output start CNFRefutation
% 17.64/17.81 fof(s1_0_axiom_m4,conjecture,axiom_m4,input).
% 17.64/17.81 fof(c10,negated_conjecture,(~axiom_m4),inference(assume_negation,status(cth),[s1_0_axiom_m4])).
% 17.64/17.81 fof(c11,negated_conjecture,~axiom_m4,inference(fof_simplification,status(thm),[c10])).
% 17.64/17.81 cnf(c12,negated_conjecture,~axiom_m4,inference(split_conjunct,status(thm),[c11])).
% 17.64/17.81 fof(axiom_m4,axiom,(axiom_m4<=>(![X]:is_a_theorem(strict_implies(X,and(X,X))))),input).
% 17.64/17.81 fof(c76,axiom,((~axiom_m4|(![X]:is_a_theorem(strict_implies(X,and(X,X)))))&((?[X]:~is_a_theorem(strict_implies(X,and(X,X))))|axiom_m4)),inference(fof_nnf,status(thm),[axiom_m4])).
% 17.64/17.81 fof(c77,axiom,((~axiom_m4|(![X28]:is_a_theorem(strict_implies(X28,and(X28,X28)))))&((?[X29]:~is_a_theorem(strict_implies(X29,and(X29,X29))))|axiom_m4)),inference(variable_rename,status(thm),[c76])).
% 17.64/17.81 fof(c79,axiom,(![X28]:((~axiom_m4|is_a_theorem(strict_implies(X28,and(X28,X28))))&(~is_a_theorem(strict_implies(skolem0011,and(skolem0011,skolem0011)))|axiom_m4))),inference(shift_quantors,status(thm),[fof(c78,axiom,((~axiom_m4|(![X28]:is_a_theorem(strict_implies(X28,and(X28,X28)))))&(~is_a_theorem(strict_implies(skolem0011,and(skolem0011,skolem0011)))|axiom_m4)),inference(skolemize,status(esa),[c77])).])).
% 17.64/17.81 cnf(c81,axiom,~is_a_theorem(strict_implies(skolem0011,and(skolem0011,skolem0011)))|axiom_m4,inference(split_conjunct,status(thm),[c79])).
% 17.64/17.81 cnf(c9,plain,X234!=X235|~is_a_theorem(X234)|is_a_theorem(X235),eq_axiom).
% 17.64/17.81 cnf(symmetry,axiom,X207!=X208|X208=X207,eq_axiom).
% 17.64/17.81 fof(s1_0_op_strict_implies,axiom,op_strict_implies,input).
% 17.64/17.81 cnf(c15,axiom,op_strict_implies,inference(split_conjunct,status(thm),[s1_0_op_strict_implies])).
% 17.64/17.81 fof(op_strict_implies,axiom,(op_strict_implies=>(![X]:(![Y]:strict_implies(X,Y)=necessarily(implies(X,Y))))),input).
% 17.64/17.81 fof(c28,axiom,(~op_strict_implies|(![X]:(![Y]:strict_implies(X,Y)=necessarily(implies(X,Y))))),inference(fof_nnf,status(thm),[op_strict_implies])).
% 17.64/17.81 fof(c30,axiom,(![X4]:(![X5]:(~op_strict_implies|strict_implies(X4,X5)=necessarily(implies(X4,X5))))),inference(shift_quantors,status(thm),[fof(c29,axiom,(~op_strict_implies|(![X4]:(![X5]:strict_implies(X4,X5)=necessarily(implies(X4,X5))))),inference(variable_rename,status(thm),[c28])).])).
% 17.64/17.81 cnf(c31,axiom,~op_strict_implies|strict_implies(X270,X271)=necessarily(implies(X270,X271)),inference(split_conjunct,status(thm),[c30])).
% 17.64/17.81 cnf(c415,plain,strict_implies(X298,X299)=necessarily(implies(X298,X299)),inference(resolution,status(thm),[c31, c15])).
% 17.64/17.81 cnf(c434,plain,necessarily(implies(X302,X301))=strict_implies(X302,X301),inference(resolution,status(thm),[c415, symmetry])).
% 17.64/17.81 cnf(c462,plain,~is_a_theorem(necessarily(implies(X545,X544)))|is_a_theorem(strict_implies(X545,X544)),inference(resolution,status(thm),[c434, c9])).
% 17.64/17.81 fof(km5_necessitation,axiom,necessitation,input).
% 17.64/17.81 cnf(c22,axiom,necessitation,inference(split_conjunct,status(thm),[km5_necessitation])).
% 17.64/17.81 fof(necessitation,axiom,(necessitation<=>(![X]:(is_a_theorem(X)=>is_a_theorem(necessarily(X))))),input).
% 17.64/17.81 fof(c180,axiom,((~necessitation|(![X]:(~is_a_theorem(X)|is_a_theorem(necessarily(X)))))&((?[X]:(is_a_theorem(X)&~is_a_theorem(necessarily(X))))|necessitation)),inference(fof_nnf,status(thm),[necessitation])).
% 17.64/17.81 fof(c181,axiom,((~necessitation|(![X84]:(~is_a_theorem(X84)|is_a_theorem(necessarily(X84)))))&((?[X85]:(is_a_theorem(X85)&~is_a_theorem(necessarily(X85))))|necessitation)),inference(variable_rename,status(thm),[c180])).
% 17.64/17.81 fof(c183,axiom,(![X84]:((~necessitation|(~is_a_theorem(X84)|is_a_theorem(necessarily(X84))))&((is_a_theorem(skolem0039)&~is_a_theorem(necessarily(skolem0039)))|necessitation))),inference(shift_quantors,status(thm),[fof(c182,axiom,((~necessitation|(![X84]:(~is_a_theorem(X84)|is_a_theorem(necessarily(X84)))))&((is_a_theorem(skolem0039)&~is_a_theorem(necessarily(skolem0039)))|necessitation)),inference(skolemize,status(esa),[c181])).])).
% 17.64/17.81 fof(c184,axiom,(![X84]:((~necessitation|(~is_a_theorem(X84)|is_a_theorem(necessarily(X84))))&((is_a_theorem(skolem0039)|necessitation)&(~is_a_theorem(necessarily(skolem0039))|necessitation)))),inference(distribute,status(thm),[c183])).
% 17.64/17.81 cnf(c185,axiom,~necessitation|~is_a_theorem(X247)|is_a_theorem(necessarily(X247)),inference(split_conjunct,status(thm),[c184])).
% 17.64/17.81 fof(hilbert_modus_ponens,axiom,modus_ponens,input).
% 17.64/17.81 cnf(c202,axiom,modus_ponens,inference(split_conjunct,status(thm),[hilbert_modus_ponens])).
% 17.64/17.81 fof(hilbert_and_3,axiom,and_3,input).
% 17.64/17.81 cnf(c195,axiom,and_3,inference(split_conjunct,status(thm),[hilbert_and_3])).
% 17.64/17.81 fof(and_3,axiom,(and_3<=>(![X]:(![Y]:is_a_theorem(implies(X,implies(Y,and(X,Y))))))),input).
% 17.64/17.81 fof(c328,axiom,((~and_3|(![X]:(![Y]:is_a_theorem(implies(X,implies(Y,and(X,Y)))))))&((?[X]:(?[Y]:~is_a_theorem(implies(X,implies(Y,and(X,Y))))))|and_3)),inference(fof_nnf,status(thm),[and_3])).
% 17.64/17.81 fof(c329,axiom,((~and_3|(![X168]:(![X169]:is_a_theorem(implies(X168,implies(X169,and(X168,X169)))))))&((?[X170]:(?[X171]:~is_a_theorem(implies(X170,implies(X171,and(X170,X171))))))|and_3)),inference(variable_rename,status(thm),[c328])).
% 17.64/17.81 fof(c331,axiom,(![X168]:(![X169]:((~and_3|is_a_theorem(implies(X168,implies(X169,and(X168,X169)))))&(~is_a_theorem(implies(skolem0076,implies(skolem0077,and(skolem0076,skolem0077))))|and_3)))),inference(shift_quantors,status(thm),[fof(c330,axiom,((~and_3|(![X168]:(![X169]:is_a_theorem(implies(X168,implies(X169,and(X168,X169)))))))&(~is_a_theorem(implies(skolem0076,implies(skolem0077,and(skolem0076,skolem0077))))|and_3)),inference(skolemize,status(esa),[c329])).])).
% 17.64/17.81 cnf(c332,axiom,~and_3|is_a_theorem(implies(X364,implies(X363,and(X364,X363)))),inference(split_conjunct,status(thm),[c331])).
% 17.64/17.81 cnf(c527,plain,is_a_theorem(implies(X366,implies(X365,and(X366,X365)))),inference(resolution,status(thm),[c332, c195])).
% 17.64/17.81 fof(modus_ponens,axiom,(modus_ponens<=>(![X]:(![Y]:((is_a_theorem(X)&is_a_theorem(implies(X,Y)))=>is_a_theorem(Y))))),input).
% 17.64/17.81 fof(c378,axiom,((~modus_ponens|(![X]:(![Y]:((~is_a_theorem(X)|~is_a_theorem(implies(X,Y)))|is_a_theorem(Y)))))&((?[X]:(?[Y]:((is_a_theorem(X)&is_a_theorem(implies(X,Y)))&~is_a_theorem(Y))))|modus_ponens)),inference(fof_nnf,status(thm),[modus_ponens])).
% 17.64/17.81 fof(c379,axiom,((~modus_ponens|(![X202]:(![X203]:((~is_a_theorem(X202)|~is_a_theorem(implies(X202,X203)))|is_a_theorem(X203)))))&((?[X204]:(?[X205]:((is_a_theorem(X204)&is_a_theorem(implies(X204,X205)))&~is_a_theorem(X205))))|modus_ponens)),inference(variable_rename,status(thm),[c378])).
% 17.64/17.81 fof(c381,axiom,(![X202]:(![X203]:((~modus_ponens|((~is_a_theorem(X202)|~is_a_theorem(implies(X202,X203)))|is_a_theorem(X203)))&(((is_a_theorem(skolem0093)&is_a_theorem(implies(skolem0093,skolem0094)))&~is_a_theorem(skolem0094))|modus_ponens)))),inference(shift_quantors,status(thm),[fof(c380,axiom,((~modus_ponens|(![X202]:(![X203]:((~is_a_theorem(X202)|~is_a_theorem(implies(X202,X203)))|is_a_theorem(X203)))))&(((is_a_theorem(skolem0093)&is_a_theorem(implies(skolem0093,skolem0094)))&~is_a_theorem(skolem0094))|modus_ponens)),inference(skolemize,status(esa),[c379])).])).
% 17.64/17.81 fof(c382,axiom,(![X202]:(![X203]:((~modus_ponens|((~is_a_theorem(X202)|~is_a_theorem(implies(X202,X203)))|is_a_theorem(X203)))&(((is_a_theorem(skolem0093)|modus_ponens)&(is_a_theorem(implies(skolem0093,skolem0094))|modus_ponens))&(~is_a_theorem(skolem0094)|modus_ponens))))),inference(distribute,status(thm),[c381])).
% 17.64/17.81 cnf(c383,axiom,~modus_ponens|~is_a_theorem(X368)|~is_a_theorem(implies(X368,X367))|is_a_theorem(X367),inference(split_conjunct,status(thm),[c382])).
% 17.64/17.81 fof(hilbert_implies_2,axiom,implies_2,input).
% 17.64/17.81 cnf(c199,axiom,implies_2,inference(split_conjunct,status(thm),[hilbert_implies_2])).
% 17.64/17.81 fof(implies_2,axiom,(implies_2<=>(![X]:(![Y]:is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))),input).
% 17.64/17.81 fof(c352,axiom,((~implies_2|(![X]:(![Y]:is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))))))&((?[X]:(?[Y]:~is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))|implies_2)),inference(fof_nnf,status(thm),[implies_2])).
% 17.64/17.81 fof(c353,axiom,((~implies_2|(![X186]:(![X187]:is_a_theorem(implies(implies(X186,implies(X186,X187)),implies(X186,X187))))))&((?[X188]:(?[X189]:~is_a_theorem(implies(implies(X188,implies(X188,X189)),implies(X188,X189)))))|implies_2)),inference(variable_rename,status(thm),[c352])).
% 17.64/17.81 fof(c355,axiom,(![X186]:(![X187]:((~implies_2|is_a_theorem(implies(implies(X186,implies(X186,X187)),implies(X186,X187))))&(~is_a_theorem(implies(implies(skolem0085,implies(skolem0085,skolem0086)),implies(skolem0085,skolem0086)))|implies_2)))),inference(shift_quantors,status(thm),[fof(c354,axiom,((~implies_2|(![X186]:(![X187]:is_a_theorem(implies(implies(X186,implies(X186,X187)),implies(X186,X187))))))&(~is_a_theorem(implies(implies(skolem0085,implies(skolem0085,skolem0086)),implies(skolem0085,skolem0086)))|implies_2)),inference(skolemize,status(esa),[c353])).])).
% 17.64/17.81 cnf(c356,axiom,~implies_2|is_a_theorem(implies(implies(X607,implies(X607,X608)),implies(X607,X608))),inference(split_conjunct,status(thm),[c355])).
% 17.64/17.81 cnf(c1183,plain,is_a_theorem(implies(implies(X1587,implies(X1587,X1586)),implies(X1587,X1586))),inference(resolution,status(thm),[c356, c199])).
% 17.64/17.81 cnf(c5219,plain,~modus_ponens|~is_a_theorem(implies(X6057,implies(X6057,X6056)))|is_a_theorem(implies(X6057,X6056)),inference(resolution,status(thm),[c1183, c383])).
% 17.64/17.81 cnf(c31368,plain,~modus_ponens|is_a_theorem(implies(X6099,and(X6099,X6099))),inference(resolution,status(thm),[c5219, c527])).
% 17.64/17.81 cnf(c31688,plain,is_a_theorem(implies(X6100,and(X6100,X6100))),inference(resolution,status(thm),[c31368, c202])).
% 17.64/17.81 cnf(c31729,plain,~necessitation|is_a_theorem(necessarily(implies(X6215,and(X6215,X6215)))),inference(resolution,status(thm),[c31688, c185])).
% 17.64/17.81 cnf(c32889,plain,is_a_theorem(necessarily(implies(X6216,and(X6216,X6216)))),inference(resolution,status(thm),[c31729, c22])).
% 17.64/17.81 cnf(c32930,plain,is_a_theorem(strict_implies(X6219,and(X6219,X6219))),inference(resolution,status(thm),[c32889, c462])).
% 17.64/17.81 cnf(c32964,plain,axiom_m4,inference(resolution,status(thm),[c32930, c81])).
% 17.64/17.81 cnf(c32997,plain,$false,inference(resolution,status(thm),[c32964, c12])).
% 17.64/17.81 # SZS output end CNFRefutation
% 17.64/17.81
% 17.64/17.81 # Initial clauses : 159
% 17.64/17.81 # Processed clauses : 1340
% 17.64/17.81 # Factors computed : 0
% 17.64/17.81 # Resolvents computed: 32611
% 17.64/17.81 # Tautologies deleted: 44
% 17.64/17.81 # Forward subsumed : 1210
% 17.64/17.81 # Backward subsumed : 532
% 17.64/17.81 # -------- CPU Time ---------
% 17.64/17.81 # User time : 17.370 s
% 17.64/17.81 # System time : 0.093 s
% 17.64/17.81 # Total time : 17.463 s
%------------------------------------------------------------------------------