%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL502+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 : Thu Sep 24 01:12:55 PM UTC 2026
% Result : Theorem 27.34s 10.93s
% Output : CNFRefutation 27.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 18
% Syntax : Number of formulae : 153 ( 85 unt; 0 def)
% Number of atoms : 258 ( 25 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 191 ( 86 ~; 84 |; 10 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 268 ( 34 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
fof(kn3,axiom,
( kn3
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(hilbert_modus_tollens,conjecture,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',use_substitution_of_equivalents) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(c_0_18,plain,
! [X121,X122] :
( implies(X121,X122) = not(and(X121,not(X122)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
fof(c_0_19,plain,
! [X117,X118] :
( or(X117,X118) = not(and(not(X117),not(X118)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_20,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_22,plain,
! [X77,X78,X79] :
( ( kn3
| ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0))))) )
& ( is_a_theorem(implies(implies(X77,X78),implies(not(and(X78,X79)),not(and(X79,X77)))))
| ~ kn3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])])]) ).
cnf(c_0_23,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_25,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_26,plain,
( ~ kn3
| is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1))))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
fof(c_0_29,plain,
! [X7,X8] :
( ( modus_ponens
| ~ is_a_theorem(esk2_0) )
& ( modus_ponens
| is_a_theorem(implies(esk1_0,esk2_0)) )
& ( modus_ponens
| is_a_theorem(esk1_0) )
& ( is_a_theorem(X8)
| ~ is_a_theorem(implies(X7,X8))
| ~ is_a_theorem(X7)
| ~ modus_ponens ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
fof(c_0_31,plain,
! [X71] :
( ( kn1
| ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))) )
& ( is_a_theorem(implies(X71,and(X71,X71)))
| ~ kn1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_24]),c_0_27]) ).
cnf(c_0_35,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_36,plain,
( ~ kn1
| is_a_theorem(implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27]),c_0_35]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(or(X3,X1))
| is_a_theorem(implies(implies(X1,X2),or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_40,c_0_27]) ).
fof(c_0_43,plain,
! [X73,X74] :
( ( kn2
| ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)) )
& ( is_a_theorem(implies(and(X73,X74),X73))
| ~ kn2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(implies(and(not(X1),not(X1)),X2),or(X2,X1))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
( ~ kn2
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_46,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_47,plain,
( ~ is_a_theorem(implies(and(not(X2),not(X2)),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_49,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(implies(X1,X2),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_41,c_0_49]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_52,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_38,c_0_50]) ).
cnf(c_0_54,plain,
( ~ is_a_theorem(implies(X2,and(X3,not(X4))))
| ~ is_a_theorem(or(and(X2,implies(X3,X4)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,plain,
( ~ is_a_theorem(or(X3,X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_38,c_0_34]) ).
cnf(c_0_56,plain,
is_a_theorem(or(X1,not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_53,c_0_48]) ).
cnf(c_0_57,plain,
( ~ is_a_theorem(or(and(not(X2),or(X2,X2)),X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_27]) ).
cnf(c_0_58,plain,
is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_55,c_0_49]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(or(and(X1,X2),X3),or(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_27]) ).
cnf(c_0_60,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_56,c_0_24]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
( ~ is_a_theorem(or(and(X2,X3),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_63,plain,
is_a_theorem(or(and(implies(X1,X2),X3),implies(X3,X1))),
inference(spm,[status(thm)],[c_0_55,c_0_60]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(or(and(X1,X2),not(and(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_38,c_0_61]) ).
cnf(c_0_66,plain,
is_a_theorem(or(implies(X1,X2),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
is_a_theorem(or(and(X1,X2),not(and(X2,and(X1,X3))))),
inference(spm,[status(thm)],[c_0_64,c_0_48]) ).
cnf(c_0_68,plain,
is_a_theorem(not(not(implies(X1,X1)))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(implies(X1,X2),not(and(not(X2),and(X1,X3))))),
inference(spm,[status(thm)],[c_0_67,c_0_35]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(or(not(implies(X2,X2)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_68]) ).
cnf(c_0_71,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(not(and(not(X1),and(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_38,c_0_69]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_70,c_0_49]) ).
cnf(c_0_73,plain,
is_a_theorem(not(and(not(X1),and(X1,X2)))),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(or(and(not(X2),and(X2,X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_73]) ).
cnf(c_0_75,plain,
is_a_theorem(implies(and(X1,X2),not(not(X1)))),
inference(spm,[status(thm)],[c_0_74,c_0_58]) ).
cnf(c_0_76,plain,
is_a_theorem(not(not(or(X1,not(X1))))),
inference(spm,[status(thm)],[c_0_68,c_0_27]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_72]),c_0_35]),c_0_27]) ).
cnf(c_0_78,plain,
( ~ is_a_theorem(and(X1,X2))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_38,c_0_75]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_80,plain,
( ~ is_a_theorem(or(not(or(X2,not(X2))),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_76]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),or(X3,X1))),
inference(spm,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(or(X1,X2),or(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_50,c_0_27]) ).
cnf(c_0_83,plain,
is_a_theorem(or(X1,not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_53,c_0_77]) ).
cnf(c_0_84,plain,
is_a_theorem(not(and(not(implies(X1,X1)),X2))),
inference(spm,[status(thm)],[c_0_70,c_0_56]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,plain,
is_a_theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_80,c_0_49]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_81]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_38,c_0_82]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(or(or(X1,X1),X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_83]),c_0_27]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(or(and(not(implies(X2,X2)),X3),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_84]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(or(not(X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_85]) ).
cnf(c_0_92,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_86]),c_0_27]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(implies(or(X2,X3),X1))
| is_a_theorem(or(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_87,c_0_27]) ).
cnf(c_0_94,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_88,c_0_49]) ).
cnf(c_0_95,plain,
( ~ is_a_theorem(or(or(X2,X2),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_89]) ).
cnf(c_0_96,plain,
is_a_theorem(or(or(X1,not(X2)),not(implies(X2,X1)))),
inference(spm,[status(thm)],[c_0_53,c_0_50]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(implies(or(implies(X2,X2),X3),X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_35]),c_0_27]) ).
cnf(c_0_98,plain,
( ~ is_a_theorem(and(X2,not(X3)))
| ~ is_a_theorem(or(implies(X2,X3),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_24]) ).
cnf(c_0_99,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_92]) ).
cnf(c_0_100,plain,
is_a_theorem(or(or(X1,X2),not(X2))),
inference(spm,[status(thm)],[c_0_93,c_0_92]) ).
cnf(c_0_101,plain,
is_a_theorem(implies(or(not(not(X1)),X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_94]),c_0_27]) ).
cnf(c_0_102,plain,
is_a_theorem(or(not(implies(X1,not(X1))),not(X1))),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,plain,
is_a_theorem(or(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_97,c_0_92]) ).
cnf(c_0_104,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(or(X2,X2),X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_79]),c_0_27]) ).
cnf(c_0_105,plain,
is_a_theorem(or(not(X1),or(X2,X1))),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_106,plain,
( ~ is_a_theorem(or(not(not(X2)),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_101]) ).
cnf(c_0_107,plain,
is_a_theorem(or(not(X1),not(implies(X1,not(X1))))),
inference(spm,[status(thm)],[c_0_99,c_0_102]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),or(X2,X3))),
inference(spm,[status(thm)],[c_0_41,c_0_103]) ).
cnf(c_0_109,plain,
is_a_theorem(or(and(X1,X2),not(and(X2,X1)))),
inference(spm,[status(thm)],[c_0_64,c_0_72]) ).
cnf(c_0_110,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(or(or(not(X2),not(X2)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_85]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_91,c_0_105]) ).
cnf(c_0_112,plain,
is_a_theorem(or(not(or(X1,not(not(X1)))),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_27]) ).
cnf(c_0_113,plain,
( ~ is_a_theorem(implies(implies(X3,X3),X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_108]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X1)))),
inference(spm,[status(thm)],[c_0_109,c_0_35]) ).
cnf(c_0_115,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(implies(X1,not(X1)))) ),
inference(spm,[status(thm)],[c_0_110,c_0_96]) ).
cnf(c_0_116,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(or(and(X1,X2),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_55,c_0_111]) ).
fof(c_0_117,plain,
! [X125,X126] :
( equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).
cnf(c_0_118,plain,
( ~ is_a_theorem(or(X1,not(not(X1))))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_112]) ).
cnf(c_0_119,plain,
is_a_theorem(or(not(and(not(X1),X1)),X2)),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_120,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(or(implies(X2,not(X2)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_115]) ).
cnf(c_0_121,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(or(implies(X1,X2),and(X3,X1))) ),
inference(spm,[status(thm)],[c_0_99,c_0_116]) ).
cnf(c_0_122,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_123,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_124,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_125,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_87,c_0_72]) ).
fof(c_0_126,negated_conjecture,
~ modus_tollens,
inference(assume_negation,[status(cth)],[hilbert_modus_tollens]) ).
fof(c_0_127,plain,
! [X11,X12] :
( ( substitution_of_equivalents
| esk3_0 != esk4_0 )
& ( substitution_of_equivalents
| is_a_theorem(equiv(esk3_0,esk4_0)) )
& ( X11 = X12
| ~ is_a_theorem(equiv(X11,X12))
| ~ substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])]) ).
cnf(c_0_128,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_129,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]) ).
cnf(c_0_130,plain,
( ~ is_a_theorem(or(and(not(X2),X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_124]) ).
cnf(c_0_131,plain,
is_a_theorem(or(and(X1,X2),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_55,c_0_125]) ).
fof(c_0_132,negated_conjecture,
~ modus_tollens,
inference(fof_simplification,[status(thm)],[c_0_126]) ).
cnf(c_0_133,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_52,c_0_27]) ).
cnf(c_0_134,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_135,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_136,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(equiv(X1,X2)) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_137,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_27]) ).
fof(c_0_138,plain,
! [X15,X16] :
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0))) )
& ( is_a_theorem(implies(implies(not(X16),not(X15)),implies(X15,X16)))
| ~ modus_tollens ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])]) ).
fof(c_0_139,negated_conjecture,
~ modus_tollens,
inference(fof_nnf,[status(thm)],[c_0_132]) ).
cnf(c_0_140,plain,
not(and(not(X1),or(X2,X3))) = or(X1,and(not(X2),not(X3))),
inference(spm,[status(thm)],[c_0_27,c_0_133]) ).
cnf(c_0_141,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]) ).
cnf(c_0_142,plain,
is_a_theorem(equiv(and(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_40]),c_0_48])]) ).
cnf(c_0_143,plain,
is_a_theorem(equiv(X1,or(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_77]),c_0_137])]) ).
cnf(c_0_144,plain,
( ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))
| modus_tollens ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_145,negated_conjecture,
~ modus_tollens,
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_146,plain,
implies(or(X1,and(not(X2),not(X3))),X4) = or(and(not(X1),or(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_27,c_0_140]) ).
cnf(c_0_147,plain,
and(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_148,plain,
or(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_141,c_0_143]) ).
cnf(c_0_149,plain,
~ is_a_theorem(implies(or(esk6_0,not(esk5_0)),implies(esk5_0,esk6_0))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_27]),c_0_145]) ).
cnf(c_0_150,plain,
implies(or(X1,not(X2)),X3) = or(and(not(X1),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_148]) ).
cnf(c_0_151,plain,
is_a_theorem(or(and(not(X1),X2),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_55,c_0_86]) ).
cnf(c_0_152,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150]),c_0_151])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL502+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/5.36 % Computer : n002.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 00:38:52 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.34/10.93 % Version: 3.5.1
% 27.34/10.93 % Preprocessing class: FSMSSLSSSSSNFFN.
% 27.34/10.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.34/10.93 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 27.34/10.93 % Starting new_bool_3 with 300s (1) cores
% 27.34/10.93 % Starting new_bool_1 with 300s (1) cores
% 27.34/10.93 % Starting sh5l with 300s (1) cores
% 27.34/10.93 % new_bool_3 with pid 2078119 completed with status 9
% 27.34/10.93 % new_bool_1 with pid 2078120 completed with status 9
% 27.34/10.93 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 2078118 completed with status 0
% 27.34/10.93 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 27.34/10.93 % Preprocessing class: FSMSSLSSSSSNFFN.
% 27.34/10.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.34/10.93 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 27.34/10.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.34/10.93 % No SInE strategy applied
% 27.34/10.93 % Search class: FGUSF-FFMM21-MFFFFFNN
% 27.34/10.93 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 27.34/10.93 % Starting SubtermCWHack with 151s (1) cores
% 27.34/10.93 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 27.34/10.93 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 27.34/10.93 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 27.34/10.93 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 27.34/10.93 % H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 2078132 completed with status 0
% 27.34/10.93 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 27.34/10.93 % Preprocessing class: FSMSSLSSSSSNFFN.
% 27.34/10.93 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.34/10.93 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 27.34/10.93 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.34/10.93 % No SInE strategy applied
% 27.34/10.93 % Search class: FGUSF-FFMM21-MFFFFFNN
% 27.34/10.93 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 27.34/10.93 % Starting SubtermCWHack with 151s (1) cores
% 27.34/10.93 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 27.34/10.93 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 27.34/10.93 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 27.34/10.93 % Preprocessing time : 0.001 s
% 27.34/10.93 % Presaturation interreduction done
% 27.34/10.93
% 27.34/10.93 % Proof found!
% 27.34/10.93 % SZS status Theorem
% 27.34/10.93 % SZS output start CNFRefutation
% See solution above
% 27.34/10.93 % Parsed axioms : 43
% 27.34/10.93 % Removed by relevancy pruning/SinE : 0
% 27.34/10.93 % Initial clauses : 72
% 27.34/10.93 % Removed in clause preprocessing : 0
% 27.34/10.93 % Initial clauses in saturation : 72
% 27.34/10.93 % Processed clauses : 15205
% 27.34/10.93 % ...of these trivial : 2759
% 27.34/10.93 % ...subsumed : 8563
% 27.34/10.93 % ...remaining for further processing : 3883
% 27.34/10.93 % Other redundant clauses eliminated : 0
% 27.34/10.93 % Clauses deleted for lack of memory : 0
% 27.34/10.93 % Backward-subsumed : 138
% 27.34/10.93 % Backward-rewritten : 1186
% 27.34/10.93 % Generated clauses : 559461
% 27.34/10.93 % ...of the previous two non-redundant : 478838
% 27.34/10.93 % ...aggressively subsumed : 0
% 27.34/10.93 % Contextual simplify-reflections : 1
% 27.34/10.93 % Paramodulations : 559461
% 27.34/10.93 % Factorizations : 0
% 27.34/10.93 % NegExts : 0
% 27.34/10.93 % Equation resolutions : 0
% 27.34/10.93 % Disequality decompositions : 0
% 27.34/10.93 % Total rewrite steps : 293795
% 27.34/10.93 % ...of those cached : 227243
% 27.34/10.93 % Propositional unsat checks : 0
% 27.34/10.93 % Propositional check models : 0
% 27.34/10.93 % Propositional check unsatisfiable : 0
% 27.34/10.93 % Propositional clauses : 0
% 27.34/10.93 % Propositional clauses after purity: 0
% 27.34/10.93 % Propositional unsat core size : 0
% 27.34/10.93 % Propositional preprocessing time : 0.000
% 27.34/10.93 % Propositional encoding time : 0.000
% 27.34/10.93 % Propositional solver time : 0.000
% 27.34/10.93 % Success case prop preproc time : 0.000
% 27.34/10.93 % Success case prop encoding time : 0.000
% 27.34/10.93 % Success case prop solver time : 0.000
% 27.34/10.93 % Current number of processed clauses : 2500
% 27.34/10.93 % Positive orientable unit clauses : 1135
% 27.34/10.93 % Positive unorientable unit clauses: 0
% 27.34/10.93 % Negative unit clauses : 3
% 27.34/10.93 % Non-unit-clauses : 1362
% 27.34/10.93 % Current number of unprocessed clauses: 463564
% 27.34/10.93 % ...number of literals in the above : 878251
% 27.34/10.93 % Current number of archived formulas : 0
% 27.34/10.93 % Current number of archived clauses : 1383
% 27.34/10.93 % Clause-clause subsumption calls (NU) : 538178
% 27.34/10.93 % Rec. Clause-clause subsumption calls : 528128
% 27.34/10.93 % Non-unit clause-clause subsumptions : 8697
% 27.34/10.93 % Unit Clause-clause subsumption calls : 10914
% 27.34/10.93 % Rewrite failures with RHS unbound : 0
% 27.34/10.93 % BW rewrite match attempts : 94384
% 27.34/10.93 % BW rewrite match successes : 1049
% 27.34/10.93 % Condensation attempts : 0
% 27.34/10.93 % Condensation successes : 0
% 27.34/10.93 % Termbank termtop insertions : 10703199
% 27.34/10.93 % Search garbage collected termcells : 1092
% 27.34/10.93
% 27.34/10.93 % -------------------------------------------------
% 27.34/10.93 % User time : 5.099 s
% 27.34/10.93 % System time : 0.297 s
% 27.34/10.93 % Total time : 5.396 s
% 27.34/10.93 % Maximum resident set size: 3380 pages
% 27.34/10.93
% 27.34/10.93 % -------------------------------------------------
% 27.34/10.93 % User time : 26.026 s
% 27.34/10.93 % System time : 1.208 s
% 27.34/10.93 % Total time : 27.234 s
% 27.34/10.93 % Maximum resident set size: 4608 pages
% 27.34/10.93 % E exiting
%------------------------------------------------------------------------------