%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL519+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:12:58 PM UTC 2026
% Result : Theorem 1.25s 0.63s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 108 ( 49 unt; 0 def)
% Number of atoms : 196 ( 36 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 155 ( 67 ~; 65 |; 10 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 169 ( 14 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
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/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',use_substitution_of_equivalents) ).
fof(principia_r2,conjecture,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(c_0_22,plain,
! [X123,X124] :
( implies(X123,X124) = or(not(X123),X124)
| ~ op_implies_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])]) ).
fof(c_0_23,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_24,plain,
! [X119,X120] :
( and(X119,X120) = not(or(not(X119),not(X120)))
| ~ op_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])]) ).
cnf(c_0_25,plain,
( ~ op_implies_or
| implies(X1,X2) = or(not(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_27,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_28,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_30,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])])])])])]) ).
fof(c_0_31,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_32,plain,
( ~ op_and
| and(X1,X2) = not(or(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_34,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_35,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_37,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_40,plain,
( ~ kn2
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_42,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_43,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
fof(c_0_44,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_45,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_38,c_0_39])]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_47,plain,
not(or(X1,not(X2))) = and(not(X1),X2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
( ~ kn1
| is_a_theorem(implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_50,plain,
( ~ is_a_theorem(and(X1,X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
and(not(not(X1)),X2) = and(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_33]),c_0_42]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(and(X1,X2))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
fof(c_0_55,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_56,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_58,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_59,plain,
or(and(X1,X2),X3) = implies(implies(X1,not(X2)),X3),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
fof(c_0_60,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])])])])]) ).
fof(c_0_61,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_62,plain,
( ~ is_a_theorem(and(X1,not(X2)))
| is_a_theorem(not(implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_63,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_64,plain,
and(X1,implies(X2,not(X3))) = not(implies(X1,and(X2,X3))),
inference(spm,[status(thm)],[c_0_42,c_0_42]) ).
cnf(c_0_65,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_36]),c_0_59]) ).
cnf(c_0_66,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_60]) ).
cnf(c_0_67,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(and(X1,implies(X2,X3)))
| is_a_theorem(not(implies(X1,and(X2,not(X3))))) ),
inference(spm,[status(thm)],[c_0_62,c_0_36]) ).
cnf(c_0_71,plain,
not(implies(or(X1,X2),and(X2,X1))) = equiv(not(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_43]),c_0_64]) ).
cnf(c_0_72,plain,
( ~ is_a_theorem(implies(implies(X2,X3),X1))
| ~ is_a_theorem(implies(X2,not(not(X3))))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_65]) ).
cnf(c_0_73,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_66,c_0_43]),c_0_67])]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(equiv(X1,X2))
| is_a_theorem(equiv(not(not(X1)),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_33]),c_0_63]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(implies(implies(and(X2,X3),X2),X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_46]),c_0_51]) ).
cnf(c_0_77,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,not(X2)),not(and(X2,X3)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_73]),c_0_59]) ).
cnf(c_0_78,plain,
( ~ is_a_theorem(equiv(X1,X2))
| not(not(X1)) = X2 ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(implies(X1,X1))
| is_a_theorem(equiv(X1,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_80,plain,
( ~ is_a_theorem(implies(X2,and(not(X1),X3)))
| is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,plain,
( ~ is_a_theorem(implies(X1,X1))
| not(not(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_52]),c_0_36]) ).
cnf(c_0_83,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_84,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_36,c_0_83]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(implies(X2,and(not(X1),X3)))
| is_a_theorem(implies(X1,not(X2))) ),
inference(rw,[status(thm)],[c_0_80,c_0_84]) ).
cnf(c_0_86,plain,
( ~ is_a_theorem(implies(X2,and(X1,X3)))
| is_a_theorem(or(X1,not(X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_83]),c_0_43]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(implies(implies(X2,X2),X1))
| is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_82]),c_0_43]),c_0_33]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(or(X2,and(X1,X3)))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_43]),c_0_83]) ).
cnf(c_0_89,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_42,c_0_83]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(implies(X2,not(X1)))
| is_a_theorem(implies(X1,not(X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_77]),c_0_84]) ).
fof(c_0_91,negated_conjecture,
~ r2,
inference(assume_negation,[status(cth)],[principia_r2]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(or(X2,not(implies(X1,X3))))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(or(X1,not(X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_83]),c_0_43]) ).
fof(c_0_94,negated_conjecture,
~ r2,
inference(fof_simplification,[status(thm)],[c_0_91]) ).
cnf(c_0_95,plain,
( ~ is_a_theorem(implies(implies(X1,X3),X2))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(implies(or(X2,not(X2)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_43]) ).
cnf(c_0_97,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,not(X3)),implies(X3,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_43]),c_0_36]),c_0_59]) ).
fof(c_0_98,plain,
! [X97,X98] :
( ( r2
| ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))) )
& ( is_a_theorem(implies(X98,or(X97,X98)))
| ~ r2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])]) ).
fof(c_0_99,negated_conjecture,
~ r2,
inference(fof_nnf,[status(thm)],[c_0_94]) ).
cnf(c_0_100,plain,
( ~ is_a_theorem(implies(or(X1,X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_43]),c_0_33]) ).
cnf(c_0_101,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_43]) ).
cnf(c_0_102,plain,
( ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))
| r2 ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_103,negated_conjecture,
~ r2,
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_104,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,plain,
~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))),
inference(sr,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_106,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(spm,[status(thm)],[c_0_104,c_0_43]) ).
cnf(c_0_107,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL519+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 00:37:33 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.25/0.63 % Version: 3.5.1
% 1.25/0.63 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.25/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.25/0.63 % Starting new_bool_3 with 300s (1) cores
% 1.25/0.63 % Starting new_bool_1 with 300s (1) cores
% 1.25/0.63 % Starting sh5l with 300s (1) cores
% 1.25/0.63 % new_bool_1 with pid 1615630 completed with status 9
% 1.25/0.63 % sh5l with pid 1615631 completed with status 9
% 1.25/0.63 % new_bool_3 with pid 1615629 completed with status 9
% 1.25/0.63 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1615628 completed with status 0
% 1.25/0.63 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 1.25/0.63 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.25/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.25/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.25/0.63 % No SInE strategy applied
% 1.25/0.63 % Search class: FGUSF-FFMM21-MFFFFFNN
% 1.25/0.63 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.25/0.63 % Starting SubtermCWHack with 151s (1) cores
% 1.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 1.25/0.63 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 1.25/0.63 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 1.25/0.63 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.25/0.63 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1615644 completed with status 0
% 1.25/0.63 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 1.25/0.63 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.25/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.25/0.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.25/0.63 % No SInE strategy applied
% 1.25/0.63 % Search class: FGUSF-FFMM21-MFFFFFNN
% 1.25/0.63 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.25/0.63 % Starting SubtermCWHack with 151s (1) cores
% 1.25/0.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 1.25/0.63 % Preprocessing time : 0.001 s
% 1.25/0.63 % Presaturation interreduction done
% 1.25/0.63
% 1.25/0.63 % Proof found!
% 1.25/0.63 % SZS status Theorem
% 1.25/0.63 % SZS output start CNFRefutation
% See solution above
% 1.25/0.63 % Parsed axioms : 43
% 1.25/0.63 % Removed by relevancy pruning/SinE : 0
% 1.25/0.63 % Initial clauses : 72
% 1.25/0.63 % Removed in clause preprocessing : 0
% 1.25/0.63 % Initial clauses in saturation : 72
% 1.25/0.63 % Processed clauses : 2779
% 1.25/0.63 % ...of these trivial : 158
% 1.25/0.63 % ...subsumed : 1892
% 1.25/0.63 % ...remaining for further processing : 729
% 1.25/0.63 % Other redundant clauses eliminated : 0
% 1.25/0.63 % Clauses deleted for lack of memory : 0
% 1.25/0.63 % Backward-subsumed : 57
% 1.25/0.63 % Backward-rewritten : 138
% 1.25/0.63 % Generated clauses : 9122
% 1.25/0.63 % ...of the previous two non-redundant : 7781
% 1.25/0.63 % ...aggressively subsumed : 0
% 1.25/0.63 % Contextual simplify-reflections : 1
% 1.25/0.63 % Paramodulations : 9122
% 1.25/0.63 % Factorizations : 0
% 1.25/0.63 % NegExts : 0
% 1.25/0.63 % Equation resolutions : 0
% 1.25/0.63 % Disequality decompositions : 0
% 1.25/0.63 % Total rewrite steps : 6168
% 1.25/0.63 % ...of those cached : 4685
% 1.25/0.63 % Propositional unsat checks : 0
% 1.25/0.63 % Propositional check models : 0
% 1.25/0.63 % Propositional check unsatisfiable : 0
% 1.25/0.63 % Propositional clauses : 0
% 1.25/0.63 % Propositional clauses after purity: 0
% 1.25/0.63 % Propositional unsat core size : 0
% 1.25/0.63 % Propositional preprocessing time : 0.000
% 1.25/0.63 % Propositional encoding time : 0.000
% 1.25/0.63 % Propositional solver time : 0.000
% 1.25/0.63 % Success case prop preproc time : 0.000
% 1.25/0.63 % Success case prop encoding time : 0.000
% 1.25/0.63 % Success case prop solver time : 0.000
% 1.25/0.63 % Current number of processed clauses : 473
% 1.25/0.63 % Positive orientable unit clauses : 115
% 1.25/0.63 % Positive unorientable unit clauses: 0
% 1.25/0.63 % Negative unit clauses : 12
% 1.25/0.63 % Non-unit-clauses : 346
% 1.25/0.63 % Current number of unprocessed clauses: 4573
% 1.25/0.63 % ...number of literals in the above : 9590
% 1.25/0.63 % Current number of archived formulas : 0
% 1.25/0.63 % Current number of archived clauses : 256
% 1.25/0.63 % Clause-clause subsumption calls (NU) : 18172
% 1.25/0.63 % Rec. Clause-clause subsumption calls : 17946
% 1.25/0.63 % Non-unit clause-clause subsumptions : 1918
% 1.25/0.63 % Unit Clause-clause subsumption calls : 2973
% 1.25/0.63 % Rewrite failures with RHS unbound : 0
% 1.25/0.63 % BW rewrite match attempts : 685
% 1.25/0.63 % BW rewrite match successes : 57
% 1.25/0.63 % Condensation attempts : 0
% 1.25/0.63 % Condensation successes : 0
% 1.25/0.63 % Termbank termtop insertions : 121911
% 1.25/0.63 % Search garbage collected termcells : 1092
% 1.25/0.63
% 1.25/0.63 % -------------------------------------------------
% 1.25/0.63 % User time : 0.184 s
% 1.25/0.63 % System time : 0.016 s
% 1.25/0.63 % Total time : 0.200 s
% 1.25/0.63 % Maximum resident set size: 3944 pages
% 1.25/0.63
% 1.25/0.63 % -------------------------------------------------
% 1.25/0.63 % User time : 0.946 s
% 1.25/0.63 % System time : 0.109 s
% 1.25/0.63 % Total time : 1.054 s
% 1.25/0.63 % Maximum resident set size: 4864 pages
% 1.25/0.63 % E exiting
%------------------------------------------------------------------------------