%------------------------------------------------------------------------------
% File : PyRes---1.5
% Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:58:39 PM UTC 2026
% Result : Theorem 8.47s 8.76s
% Output : CNFRefutation 8.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 18:27:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:155: SyntaxWarning: invalid escape sequence '\.'
% 0.11/0.40 (re.compile("\."), Token.FullStop),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:156: SyntaxWarning: invalid escape sequence '\('
% 0.11/0.40 (re.compile("\("), Token.OpenPar),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:157: SyntaxWarning: invalid escape sequence '\)'
% 0.11/0.40 (re.compile("\)"), Token.ClosePar),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:158: SyntaxWarning: invalid escape sequence '\['
% 0.11/0.40 (re.compile("\["), Token.OpenSquare),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:159: SyntaxWarning: invalid escape sequence '\]'
% 0.11/0.40 (re.compile("\]"), Token.CloseSquare),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:162: SyntaxWarning: invalid escape sequence '\|'
% 0.11/0.40 (re.compile("~\|"), Token.Nor),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:164: SyntaxWarning: invalid escape sequence '\|'
% 0.11/0.40 (re.compile("\|"), Token.Or),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:175: SyntaxWarning: invalid escape sequence '\?'
% 0.11/0.40 (re.compile("\?"), Token.Existential),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:176: SyntaxWarning: invalid escape sequence '\s'
% 0.11/0.40 (re.compile("\s+"), Token.WhiteSpace),
% 0.11/0.40 /export/starexec/sandbox/solver/bin/lexer.py:180: SyntaxWarning: invalid escape sequence '\$'
% 0.11/0.40 (re.compile("\$[_a-z0-9_A-Z]*"), Token.DefFunctor),
% 0.11/0.43 /export/starexec/sandbox/solver/bin/signature.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.11/0.43 """
% 0.11/0.44 /export/starexec/sandbox/solver/bin/literals.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.11/0.44 """
% 0.23/0.48 /export/starexec/sandbox/solver/bin/unification.py:6: SyntaxWarning: invalid escape sequence '\c'
% 0.23/0.48 """
% 8.47/8.76 % Version: 1.5
% 8.47/8.76 % SZS status Theorem
% 8.47/8.76 % SZS output start CNFRefutation
% 8.47/8.76 fof(s1_0_axiom_m4,conjecture,axiom_m4,file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_axiom_m4)).
% 8.47/8.76 fof(c10,negated_conjecture,(~axiom_m4),inference(assume_negation,[status(cth)],[s1_0_axiom_m4])).
% 8.47/8.76 fof(c11,negated_conjecture,~axiom_m4,inference(fof_simplification,[status(thm)],[c10])).
% 8.47/8.76 cnf(c12,negated_conjecture,~axiom_m4,inference(split_conjunct,[status(thm)],[c11])).
% 8.47/8.76 fof(axiom_m4,axiom,(axiom_m4<=>(![X]:is_a_theorem(strict_implies(X,and(X,X))))),file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', axiom_m4)).
% 8.47/8.76 fof(c76,plain,((~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])).
% 8.47/8.76 fof(c77,plain,((~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])).
% 8.47/8.76 fof(c79,plain,(![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,plain,((~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])).])).
% 8.47/8.76 cnf(c81,plain,~is_a_theorem(strict_implies(skolem0011,and(skolem0011,skolem0011)))|axiom_m4,inference(split_conjunct,[status(thm)],[c79])).
% 8.47/8.76 cnf(c9,axiom,X235!=X236|~is_a_theorem(X235)|is_a_theorem(X236),theory(equality)).
% 8.47/8.76 cnf(symmetry,axiom,X208!=X207|X207=X208,theory(equality)).
% 8.47/8.76 fof(s1_0_op_strict_implies,axiom,op_strict_implies,file('/export/starexec/sandbox/benchmark/theBenchmark.p', s1_0_op_strict_implies)).
% 8.47/8.76 cnf(c15,plain,op_strict_implies,inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])).
% 8.47/8.76 fof(op_strict_implies,axiom,(op_strict_implies=>(![X]:(![Y]:strict_implies(X,Y)=necessarily(implies(X,Y))))),file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax', op_strict_implies)).
% 8.47/8.76 fof(c28,plain,(~op_strict_implies|(![X]:(![Y]:strict_implies(X,Y)=necessarily(implies(X,Y))))),inference(fof_nnf,[status(thm)],[op_strict_implies])).
% 8.47/8.76 fof(c30,plain,(![X4]:(![X5]:(~op_strict_implies|strict_implies(X4,X5)=necessarily(implies(X4,X5))))),inference(shift_quantors,[status(thm)],[fof(c29,plain,(~op_strict_implies|(![X4]:(![X5]:strict_implies(X4,X5)=necessarily(implies(X4,X5))))),inference(variable_rename,[status(thm)],[c28])).])).
% 8.47/8.76 cnf(c31,plain,~op_strict_implies|strict_implies(X270,X269)=necessarily(implies(X270,X269)),inference(split_conjunct,[status(thm)],[c30])).
% 8.47/8.76 cnf(c421,plain,strict_implies(X299,X300)=necessarily(implies(X299,X300)),inference(resolution,[status(thm)],[c31, c15])).
% 8.47/8.76 cnf(c443,plain,necessarily(implies(X303,X304))=strict_implies(X303,X304),inference(resolution,[status(thm)],[c421, symmetry])).
% 8.47/8.76 cnf(c473,plain,~is_a_theorem(necessarily(implies(X568,X567)))|is_a_theorem(strict_implies(X568,X567)),inference(resolution,[status(thm)],[c443, c9])).
% 8.47/8.76 fof(km5_necessitation,axiom,necessitation,file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax', km5_necessitation)).
% 8.47/8.76 cnf(c22,plain,necessitation,inference(split_conjunct,[status(thm)],[km5_necessitation])).
% 8.47/8.76 fof(necessitation,axiom,(necessitation<=>(![X]:(is_a_theorem(X)=>is_a_theorem(necessarily(X))))),file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax', necessitation)).
% 8.47/8.76 fof(c180,plain,((~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])).
% 8.47/8.76 fof(c181,plain,((~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])).
% 8.47/8.76 fof(c183,plain,(![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,plain,((~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])).])).
% 8.47/8.76 fof(c184,plain,(![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])).
% 8.47/8.76 cnf(c185,plain,~necessitation|~is_a_theorem(X248)|is_a_theorem(necessarily(X248)),inference(split_conjunct,[status(thm)],[c184])).
% 8.47/8.76 fof(hilbert_modus_ponens,axiom,modus_ponens,file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 8.47/8.76 cnf(c202,plain,modus_ponens,inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 8.47/8.76 fof(hilbert_and_3,axiom,and_3,file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 8.47/8.76 cnf(c195,plain,and_3,inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 8.47/8.76 fof(and_3,axiom,(and_3<=>(![X]:(![Y]:is_a_theorem(implies(X,implies(Y,and(X,Y))))))),file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_3)).
% 8.47/8.76 fof(c328,plain,((~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])).
% 8.47/8.76 fof(c329,plain,((~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])).
% 8.47/8.76 fof(c331,plain,(![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,plain,((~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])).])).
% 8.47/8.76 cnf(c332,plain,~and_3|is_a_theorem(implies(X366,implies(X365,and(X366,X365)))),inference(split_conjunct,[status(thm)],[c331])).
% 8.47/8.76 cnf(c567,plain,is_a_theorem(implies(X367,implies(X368,and(X367,X368)))),inference(resolution,[status(thm)],[c332, c195])).
% 8.47/8.76 fof(modus_ponens,axiom,(modus_ponens<=>(![X]:(![Y]:((is_a_theorem(X)&is_a_theorem(implies(X,Y)))=>is_a_theorem(Y))))),file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', modus_ponens)).
% 8.47/8.76 fof(c378,plain,((~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])).
% 8.47/8.76 fof(c379,plain,((~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])).
% 8.47/8.76 fof(c381,plain,(![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,plain,((~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])).])).
% 8.47/8.76 fof(c382,plain,(![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])).
% 8.47/8.76 cnf(c383,plain,~modus_ponens|~is_a_theorem(X369)|~is_a_theorem(implies(X369,X370))|is_a_theorem(X370),inference(split_conjunct,[status(thm)],[c382])).
% 8.47/8.76 fof(hilbert_implies_2,axiom,implies_2,file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 8.47/8.76 cnf(c199,plain,implies_2,inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 8.47/8.76 fof(implies_2,axiom,(implies_2<=>(![X]:(![Y]:is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))),file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', implies_2)).
% 8.47/8.76 fof(c352,plain,((~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])).
% 8.47/8.76 fof(c353,plain,((~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])).
% 8.47/8.76 fof(c355,plain,(![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,plain,((~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])).])).
% 8.47/8.76 cnf(c356,plain,~implies_2|is_a_theorem(implies(implies(X599,implies(X599,X598)),implies(X599,X598))),inference(split_conjunct,[status(thm)],[c355])).
% 8.47/8.76 cnf(c1265,plain,is_a_theorem(implies(implies(X1550,implies(X1550,X1549)),implies(X1550,X1549))),inference(resolution,[status(thm)],[c356, c199])).
% 8.47/8.76 cnf(c5188,plain,~modus_ponens|~is_a_theorem(implies(X5801,implies(X5801,X5802)))|is_a_theorem(implies(X5801,X5802)),inference(resolution,[status(thm)],[c1265, c383])).
% 8.47/8.76 cnf(c28722,plain,~modus_ponens|is_a_theorem(implies(X5837,and(X5837,X5837))),inference(resolution,[status(thm)],[c5188, c567])).
% 8.47/8.76 cnf(c29102,plain,is_a_theorem(implies(X5838,and(X5838,X5838))),inference(resolution,[status(thm)],[c28722, c202])).
% 8.47/8.76 cnf(c29147,plain,~necessitation|is_a_theorem(necessarily(implies(X5972,and(X5972,X5972)))),inference(resolution,[status(thm)],[c29102, c185])).
% 8.47/8.76 cnf(c31746,plain,is_a_theorem(necessarily(implies(X5973,and(X5973,X5973)))),inference(resolution,[status(thm)],[c29147, c22])).
% 8.47/8.76 cnf(c31753,plain,is_a_theorem(strict_implies(X5978,and(X5978,X5978))),inference(resolution,[status(thm)],[c31746, c473])).
% 8.47/8.76 cnf(c31906,plain,axiom_m4,inference(resolution,[status(thm)],[c31753, c81])).
% 8.47/8.76 cnf(c31915,plain,$false,inference(resolution,[status(thm)],[c31906, c12])).
% 8.47/8.76 % SZS output end CNFRefutation
% 8.47/8.76
% 8.47/8.76 % Initial clauses : 159
% 8.47/8.76 % Processed clauses : 1340
% 8.47/8.76 % Factors computed : 8
% 8.47/8.76 % Resolvents computed: 31521
% 8.47/8.76 % Tautologies deleted: 71
% 8.47/8.76 % Forward subsumed : 1207
% 8.47/8.76 % Backward subsumed : 533
% 8.47/8.76 % -------- CPU Time ---------
% 8.47/8.76 % User time : 8.329 s
% 8.47/8.76 % System time : 0.064 s
% 8.47/8.76 % Total time : 8.393 s
%------------------------------------------------------------------------------