%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL481+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 : n012.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 01:12:53 PM UTC 2026
% Result : Theorem 96.44s 25.00s
% Output : CNFRefutation 96.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 18
% Syntax : Number of formulae : 162 ( 74 unt; 0 def)
% Number of atoms : 301 ( 41 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 259 ( 120 ~; 118 |; 10 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 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 : 320 ( 58 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(cn1,axiom,
( cn1
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn1) ).
fof(luka_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_modus_ponens) ).
fof(luka_cn1,axiom,
cn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn1) ).
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/theBenchmark.p',rosser_op_implies_and) ).
fof(cn3,axiom,
( cn3
<=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(luka_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_op_or) ).
fof(luka_cn3,axiom,
cn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn3) ).
fof(cn2,axiom,
( cn2
<=> ! [X4,X5] : is_a_theorem(implies(X4,implies(not(X4),X5))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn2) ).
fof(luka_cn2,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_cn2) ).
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(luka_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+3.ax',luka_op_equiv) ).
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+3.ax',use_substitution_of_equivalents) ).
fof(rosser_kn2,conjecture,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
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(c_0_18,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_19,plain,
! [X83,X84,X85] :
( ( cn1
| ~ is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0)))) )
& ( is_a_theorem(implies(implies(X83,X84),implies(implies(X84,X85),implies(X83,X85))))
| ~ cn1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn1])])])])]) ).
cnf(c_0_20,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[luka_modus_ponens]) ).
cnf(c_0_22,plain,
( ~ cn1
| is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
cn1,
inference(split_conjunct,[status(thm)],[luka_cn1]) ).
fof(c_0_24,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])])])]) ).
cnf(c_0_25,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_20,c_0_21])]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
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_24]) ).
cnf(c_0_29,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_30,plain,
! [X93] :
( ( cn3
| ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) )
& ( is_a_theorem(implies(implies(not(X93),X93),X93))
| ~ cn3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])])]) ).
cnf(c_0_31,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,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_34,plain,
op_or,
inference(split_conjunct,[status(thm)],[luka_op_or]) ).
cnf(c_0_35,plain,
( ~ cn3
| is_a_theorem(implies(implies(not(X1),X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
cn3,
inference(split_conjunct,[status(thm)],[luka_cn3]) ).
fof(c_0_37,plain,
! [X89,X90] :
( ( cn2
| ~ is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0))) )
& ( is_a_theorem(implies(X89,implies(not(X89),X90)))
| ~ cn2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn2])])])])]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_39,plain,
implies(not(X1),X2) = or(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_40,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_41,plain,
( ~ cn2
| is_a_theorem(implies(X1,implies(not(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
cn2,
inference(split_conjunct,[status(thm)],[luka_cn2]) ).
cnf(c_0_43,plain,
( ~ is_a_theorem(or(X3,X2))
| ~ is_a_theorem(implies(X1,not(X3)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(spm,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_46,plain,
( ~ is_a_theorem(or(X3,X2))
| ~ is_a_theorem(or(X1,not(X3)))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_39]) ).
cnf(c_0_47,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_48,plain,
( ~ is_a_theorem(implies(X1,or(X2,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_49,plain,
( ~ is_a_theorem(or(X3,X1))
| is_a_theorem(implies(implies(X1,X2),or(X3,X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_39]) ).
cnf(c_0_50,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(implies(implies(X3,X4),X2))
| ~ is_a_theorem(or(X1,implies(X3,X4)))
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_33]),c_0_47]) ).
cnf(c_0_52,plain,
( ~ is_a_theorem(or(X2,X1))
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_54,plain,
( ~ is_a_theorem(implies(or(X3,X4),X2))
| ~ is_a_theorem(or(X1,or(X3,X4)))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_55,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_39]),c_0_39]) ).
cnf(c_0_56,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( ~ is_a_theorem(implies(or(not(X1),X3),X2))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(or(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_39]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_61,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,or(X2,X2)),X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_60]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_45,c_0_39]) ).
fof(c_0_63,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_64,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,or(X1,X1)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_38,c_0_62]) ).
cnf(c_0_66,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_67,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[luka_op_equiv]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_49]) ).
cnf(c_0_69,plain,
( ~ is_a_theorem(or(X1,X2))
| is_a_theorem(or(X1,or(X2,X3))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_39]),c_0_39]) ).
cnf(c_0_70,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
cnf(c_0_71,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
fof(c_0_72,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_73,plain,
( ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(or(X2,X3),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(or(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_39]) ).
cnf(c_0_75,plain,
implies(implies(X1,X2),and(X2,not(X1))) = not(equiv(X1,X2)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_78,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(or(X1,X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(or(equiv(X1,X2),and(X2,not(X1)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_75]),c_0_39]) ).
cnf(c_0_80,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_60]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_39]) ).
cnf(c_0_82,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_70,c_0_39]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_65]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(equiv(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_33]) ).
cnf(c_0_86,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(or(X1,X2),or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(X1,not(and(not(X1),or(X2,X3))))),
inference(spm,[status(thm)],[c_0_45,c_0_82]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(implies(X1,X4))
| ~ is_a_theorem(implies(X4,X2))
| is_a_theorem(or(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_83,c_0_31]) ).
cnf(c_0_89,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(implies(or(X1,X2),X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_86]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(or(and(not(X1),or(X3,X4)),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_87]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(X4)
| ~ is_a_theorem(implies(X4,X1))
| is_a_theorem(or(or(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_83,c_0_65]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(implies(X1,or(X2,X2)))
| is_a_theorem(or(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_88,c_0_44]) ).
cnf(c_0_94,plain,
( ~ is_a_theorem(implies(X4,X2))
| ~ is_a_theorem(implies(X1,X4))
| is_a_theorem(implies(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_38,c_0_65]) ).
cnf(c_0_95,plain,
( ~ is_a_theorem(implies(X2,X1))
| or(X1,X2) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_62])]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_91,c_0_59]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(or(or(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_92,c_0_44]) ).
cnf(c_0_98,plain,
is_a_theorem(or(implies(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_93,c_0_62]) ).
cnf(c_0_99,plain,
( ~ is_a_theorem(implies(or(X1,X4),X2))
| is_a_theorem(implies(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_94,c_0_62]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(or(or(X1,X1),or(X1,X1)),X1)),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(implies(X2,X4))
| ~ is_a_theorem(implies(X1,implies(X4,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_38,c_0_31]) ).
cnf(c_0_102,plain,
( ~ is_a_theorem(or(X2,X1))
| or(X1,not(X2)) = X1 ),
inference(spm,[status(thm)],[c_0_95,c_0_39]) ).
cnf(c_0_103,plain,
is_a_theorem(or(implies(or(or(X1,X1),or(X1,X1)),X1),X2)),
inference(spm,[status(thm)],[c_0_93,c_0_44]) ).
cnf(c_0_104,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_44]),c_0_62])]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(or(X2,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_96]) ).
cnf(c_0_106,plain,
is_a_theorem(or(or(implies(X1,X1),X2),X3)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(or(X1,X1),or(X1,X2))),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_108,plain,
( ~ is_a_theorem(implies(X3,implies(X2,X4)))
| is_a_theorem(implies(or(X1,X2),implies(X3,or(X1,X4)))) ),
inference(spm,[status(thm)],[c_0_101,c_0_81]) ).
cnf(c_0_109,plain,
or(X1,not(implies(X2,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_104]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(X1,or(implies(X2,X2),X3))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(implies(X1,or(X2,X2)))
| is_a_theorem(implies(X1,or(X2,X3))) ),
inference(spm,[status(thm)],[c_0_38,c_0_107]) ).
cnf(c_0_112,plain,
is_a_theorem(implies(implies(implies(X1,X2),and(X1,not(X2))),and(X1,not(X2)))),
inference(spm,[status(thm)],[c_0_40,c_0_33]) ).
cnf(c_0_113,plain,
implies(implies(X1,and(X2,not(X3))),X4) = or(and(X1,implies(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_47,c_0_33]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(X1,implies(X2,or(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_39]),c_0_110])]) ).
cnf(c_0_115,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_89,c_0_96]) ).
cnf(c_0_116,plain,
is_a_theorem(implies(or(or(X1,X1),or(X1,X1)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_111,c_0_44]) ).
cnf(c_0_117,plain,
( ~ is_a_theorem(or(X1,X3))
| ~ is_a_theorem(implies(or(X3,X4),X2))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_69]) ).
cnf(c_0_118,plain,
is_a_theorem(or(and(implies(X1,X2),implies(X1,X2)),and(X1,not(X2)))),
inference(rw,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_119,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,implies(X1,X2)))
| implies(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_89,c_0_60]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_114,c_0_109]) ).
cnf(c_0_121,plain,
( ~ is_a_theorem(X1)
| or(X1,X2) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_104]),c_0_104]),c_0_104]),c_0_104]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(not(X3))
| ~ is_a_theorem(or(X1,X3))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_117,c_0_74]) ).
cnf(c_0_123,plain,
is_a_theorem(or(equiv(X1,X1),and(X1,not(X1)))),
inference(spm,[status(thm)],[c_0_118,c_0_71]) ).
cnf(c_0_124,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_62]) ).
cnf(c_0_125,plain,
( ~ is_a_theorem(X1)
| implies(X1,X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_126,plain,
is_a_theorem(or(or(or(implies(X1,X1),X2),X3),X4)),
inference(spm,[status(thm)],[c_0_97,c_0_106]) ).
cnf(c_0_127,plain,
or(implies(X1,X1),X2) = implies(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_44]),c_0_104]),c_0_104]) ).
cnf(c_0_128,plain,
is_a_theorem(or(equiv(X1,X1),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_33]),c_0_124])]) ).
cnf(c_0_129,plain,
( ~ is_a_theorem(or(X1,X3))
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_49]) ).
cnf(c_0_130,plain,
is_a_theorem(implies(implies(or(not(X1),X2),X1),X1)),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
cnf(c_0_131,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(or(X2,X3),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_132,plain,
implies(implies(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_127]),c_0_127]) ).
cnf(c_0_133,plain,
is_a_theorem(implies(X1,equiv(X2,X2))),
inference(spm,[status(thm)],[c_0_105,c_0_128]) ).
cnf(c_0_134,plain,
( ~ is_a_theorem(or(X1,implies(or(not(X2),X3),X2)))
| is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_135,plain,
is_a_theorem(or(X1,implies(or(X1,X2),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_132]),c_0_39]) ).
cnf(c_0_136,plain,
( ~ is_a_theorem(X1)
| X1 = equiv(X2,X2) ),
inference(spm,[status(thm)],[c_0_115,c_0_133]) ).
cnf(c_0_137,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_115,c_0_96]) ).
cnf(c_0_138,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_139,plain,
implies(X1,X1) = equiv(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_44]),c_0_104]) ).
fof(c_0_140,negated_conjecture,
~ kn2,
inference(assume_negation,[status(cth)],[rosser_kn2]) ).
cnf(c_0_141,plain,
( ~ is_a_theorem(or(X3,not(X1)))
| is_a_theorem(implies(or(X1,X2),or(X3,X2))) ),
inference(spm,[status(thm)],[c_0_49,c_0_39]) ).
cnf(c_0_142,plain,
( ~ is_a_theorem(X2)
| or(not(X1),X1) = X2 ),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_143,plain,
is_a_theorem(or(or(X1,not(X1)),X2)),
inference(spm,[status(thm)],[c_0_98,c_0_39]) ).
cnf(c_0_144,plain,
or(X1,not(X1)) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_139]),c_0_139]) ).
fof(c_0_145,negated_conjecture,
~ kn2,
inference(fof_simplification,[status(thm)],[c_0_140]) ).
cnf(c_0_146,plain,
is_a_theorem(implies(and(X1,not(X2)),implies(implies(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_45,c_0_33]) ).
cnf(c_0_147,plain,
( ~ is_a_theorem(or(X2,not(X1)))
| is_a_theorem(implies(or(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_141]) ).
cnf(c_0_148,plain,
or(not(X1),X1) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]),c_0_127]) ).
cnf(c_0_149,plain,
or(X1,not(not(X1))) = X1,
inference(spm,[status(thm)],[c_0_102,c_0_138]) ).
fof(c_0_150,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])])])])]) ).
fof(c_0_151,negated_conjecture,
~ kn2,
inference(fof_nnf,[status(thm)],[c_0_145]) ).
cnf(c_0_152,plain,
( ~ is_a_theorem(implies(X1,implies(or(not(X2),X3),X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_130]) ).
cnf(c_0_153,plain,
is_a_theorem(implies(and(not(X1),not(X2)),implies(or(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_146,c_0_39]) ).
cnf(c_0_154,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149]),c_0_124])]) ).
cnf(c_0_155,plain,
( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
| kn2 ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_156,negated_conjecture,
~ kn2,
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_157,plain,
is_a_theorem(implies(and(not(not(X1)),not(X2)),X1)),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_158,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_154]),c_0_39]),c_0_148]),c_0_124])]) ).
cnf(c_0_159,plain,
~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)),
inference(sr,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_160,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_158]) ).
cnf(c_0_161,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL481+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/5.51 % Computer : n012.cluster.edu
% 0.05/5.51 % Model : x86_64 x86_64
% 0.05/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.51 % Memory : 8046.5625MB
% 0.05/5.51 % OS : Linux 6.8.0-71-generic
% 0.05/5.51 % CPULimit : 300
% 0.05/5.51 % WCLimit : 300
% 0.05/5.51 % DateTime : Mon Sep 21 00:34:00 UTC 2026
% 0.05/5.51 % CPUTime :
% 0.05/5.51 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/5.54 Running first-order theorem proving
% 0.05/5.54 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
% 96.44/25.00 % Version: 3.5.1
% 96.44/25.00 % Preprocessing class: FSMSSLSSSSSNFFN.
% 96.44/25.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 96.44/25.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 96.44/25.00 % Starting new_bool_3 with 300s (1) cores
% 96.44/25.00 % Starting new_bool_1 with 300s (1) cores
% 96.44/25.00 % Starting sh5l with 300s (1) cores
% 96.44/25.00 % new_bool_1 with pid 1233112 completed with status 9
% 96.44/25.00 % new_bool_3 with pid 1233111 completed with status 9
% 96.44/25.00 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1233110 completed with status 0
% 96.44/25.00 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 96.44/25.00 % Preprocessing class: FSMSSLSSSSSNFFN.
% 96.44/25.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 96.44/25.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 96.44/25.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 96.44/25.00 % No SInE strategy applied
% 96.44/25.00 % Search class: FGUSF-FFMM21-MFFFFFNN
% 96.44/25.00 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 96.44/25.00 % Starting SubtermCWHack with 151s (1) cores
% 96.44/25.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 96.44/25.00 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 96.44/25.00 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 96.44/25.00 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 96.44/25.00 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 1233117 completed with status 0
% 96.44/25.00 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 96.44/25.00 % Preprocessing class: FSMSSLSSSSSNFFN.
% 96.44/25.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 96.44/25.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 96.44/25.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 96.44/25.00 % No SInE strategy applied
% 96.44/25.00 % Search class: FGUSF-FFMM21-MFFFFFNN
% 96.44/25.00 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 96.44/25.00 % Starting SubtermCWHack with 151s (1) cores
% 96.44/25.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 96.44/25.00 % Preprocessing time : 0.001 s
% 96.44/25.00 % Presaturation interreduction done
% 96.44/25.00
% 96.44/25.00 % Proof found!
% 96.44/25.00 % SZS status Theorem
% 96.44/25.00 % SZS output start CNFRefutation
% See solution above
% 96.44/25.01 % Parsed axioms : 43
% 96.44/25.01 % Removed by relevancy pruning/SinE : 0
% 96.44/25.01 % Initial clauses : 72
% 96.44/25.01 % Removed in clause preprocessing : 0
% 96.44/25.01 % Initial clauses in saturation : 72
% 96.44/25.01 % Processed clauses : 63812
% 96.44/25.01 % ...of these trivial : 1572
% 96.44/25.01 % ...subsumed : 55072
% 96.44/25.01 % ...remaining for further processing : 7168
% 96.44/25.01 % Other redundant clauses eliminated : 0
% 96.44/25.01 % Clauses deleted for lack of memory : 0
% 96.44/25.01 % Backward-subsumed : 1219
% 96.44/25.01 % Backward-rewritten : 1145
% 96.44/25.01 % Generated clauses : 1210544
% 96.44/25.01 % ...of the previous two non-redundant : 1064357
% 96.44/25.01 % ...aggressively subsumed : 0
% 96.44/25.01 % Contextual simplify-reflections : 9
% 96.44/25.01 % Paramodulations : 1210544
% 96.44/25.01 % Factorizations : 0
% 96.44/25.01 % NegExts : 0
% 96.44/25.01 % Equation resolutions : 0
% 96.44/25.01 % Disequality decompositions : 0
% 96.44/25.01 % Total rewrite steps : 752040
% 96.44/25.01 % ...of those cached : 726949
% 96.44/25.01 % Propositional unsat checks : 1
% 96.44/25.01 % Propositional check models : 0
% 96.44/25.01 % Propositional check unsatisfiable : 0
% 96.44/25.01 % Propositional clauses : 0
% 96.44/25.01 % Propositional clauses after purity: 0
% 96.44/25.01 % Propositional unsat core size : 0
% 96.44/25.01 % Propositional preprocessing time : 0.000
% 96.44/25.01 % Propositional encoding time : 0.986
% 96.44/25.01 % Propositional solver time : 0.460
% 96.44/25.01 % Success case prop preproc time : 0.000
% 96.44/25.01 % Success case prop encoding time : 0.000
% 96.44/25.01 % Success case prop solver time : 0.000
% 96.44/25.01 % Current number of processed clauses : 4744
% 96.44/25.01 % Positive orientable unit clauses : 451
% 96.44/25.01 % Positive unorientable unit clauses: 2
% 96.44/25.01 % Negative unit clauses : 3
% 96.44/25.01 % Non-unit-clauses : 4288
% 96.44/25.01 % Current number of unprocessed clauses: 990766
% 96.44/25.01 % ...number of literals in the above : 2384697
% 96.44/25.01 % Current number of archived formulas : 0
% 96.44/25.01 % Current number of archived clauses : 2424
% 96.44/25.01 % Clause-clause subsumption calls (NU) : 2002444
% 96.44/25.01 % Rec. Clause-clause subsumption calls : 1839684
% 96.44/25.01 % Non-unit clause-clause subsumptions : 53631
% 96.44/25.01 % Unit Clause-clause subsumption calls : 40087
% 96.44/25.01 % Rewrite failures with RHS unbound : 0
% 96.44/25.01 % BW rewrite match attempts : 36783
% 96.44/25.01 % BW rewrite match successes : 328
% 96.44/25.01 % Condensation attempts : 0
% 96.44/25.01 % Condensation successes : 0
% 96.44/25.01 % Termbank termtop insertions : 22291828
% 96.44/25.01 % Search garbage collected termcells : 1092
% 96.44/25.01
% 96.44/25.01 % -------------------------------------------------
% 96.44/25.01 % User time : 18.487 s
% 96.44/25.01 % System time : 0.673 s
% 96.44/25.01 % Total time : 19.160 s
% 96.44/25.01 % Maximum resident set size: 3688 pages
% 96.44/25.01
% 96.44/25.01 % -------------------------------------------------
% 96.44/25.01 % User time : 93.151 s
% 96.44/25.01 % System time : 3.422 s
% 96.44/25.01 % Total time : 96.573 s
% 96.44/25.01 % Maximum resident set size: 4608 pages
% 96.44/25.01 % E exiting
%------------------------------------------------------------------------------