%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL487+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:40:28 PM UTC 2026
% Result : Theorem 6.54s 4.65s
% Output : CNFRefutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of formulae : 155 ( 72 unt; 0 def)
% Number of atoms : 282 ( 31 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 226 ( 99 ~; 96 |; 14 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 21 con; 0-2 aty)
% Number of variables : 246 ( 31 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(principia_r2,axiom,
r2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',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(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(r4,axiom,
( r4
<=> ! [X4,X5,X6] : is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(principia_r4,axiom,
r4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
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_and,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
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(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(principia_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_equiv) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',use_substitution_of_equivalents) ).
fof(r5,axiom,
( r5
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r5) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(hilbert_and_1,conjecture,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
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(c_0_28,plain,
! [X162,X163] :
( ( ~ r2
| is_a_theorem(implies(X163,or(X162,X163))) )
& ( ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))
| r2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])]) ).
fof(c_0_29,plain,
! [X188,X189] :
( ~ op_implies_or
| implies(X188,X189) = or(not(X188),X189) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])]) ).
fof(c_0_30,plain,
! [X186,X187] :
( ~ op_implies_and
| implies(X186,X187) = not(and(X186,not(X187))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
cnf(c_0_31,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ r2 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_33,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_35,plain,
! [X182,X183] :
( ~ op_or
| or(X182,X183) = not(and(not(X182),not(X183))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_36,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_38,plain,
! [X72,X73] :
( ( ~ modus_ponens
| ~ is_a_theorem(X72)
| ~ is_a_theorem(implies(X72,X73))
| is_a_theorem(X73) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
inference(distribute,[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_39,plain,
! [X166,X167] :
( ( ~ r3
| is_a_theorem(implies(or(X166,X167),or(X167,X166))) )
& ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_41,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_42,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_44,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_45,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_47,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
fof(c_0_49,plain,
! [X170,X171,X172] :
( ( ~ r4
| is_a_theorem(implies(or(X170,or(X171,X172)),or(X171,or(X170,X172)))) )
& ( ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))
| r4 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_52,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
fof(c_0_54,plain,
! [X160] :
( ( ~ r1
| is_a_theorem(implies(or(X160,X160),X160)) )
& ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])]) ).
cnf(c_0_55,plain,
( is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))
| ~ r4 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
r4,
inference(split_conjunct,[status(thm)],[principia_r4]) ).
cnf(c_0_57,plain,
is_a_theorem(or(X1,implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]) ).
fof(c_0_61,plain,
! [X184,X185] :
( ~ op_and
| and(X184,X185) = not(or(not(X184),not(X185))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])]) ).
cnf(c_0_62,plain,
is_a_theorem(or(X1,or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_57,c_0_41]) ).
cnf(c_0_65,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_66,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_41]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_68,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(X1,or(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_62,c_0_41]) ).
cnf(c_0_71,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(or(X2,or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_52,c_0_63]) ).
cnf(c_0_72,plain,
is_a_theorem(or(X1,implies(X2,not(not(not(X1)))))),
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_73,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_67,c_0_41]) ).
cnf(c_0_75,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_41]),c_0_69])]) ).
cnf(c_0_76,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_67]) ).
cnf(c_0_77,plain,
( is_a_theorem(or(X1,not(not(X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_70]) ).
cnf(c_0_78,plain,
is_a_theorem(or(X1,or(X2,not(X2)))),
inference(spm,[status(thm)],[c_0_71,c_0_62]) ).
cnf(c_0_79,plain,
is_a_theorem(or(implies(X1,not(not(not(X2)))),X2)),
inference(spm,[status(thm)],[c_0_58,c_0_72]) ).
cnf(c_0_80,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(not(not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_81,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,not(X1))) ),
inference(spm,[status(thm)],[c_0_76,c_0_41]) ).
cnf(c_0_83,plain,
is_a_theorem(or(or(X1,not(X1)),X2)),
inference(spm,[status(thm)],[c_0_58,c_0_78]) ).
cnf(c_0_84,plain,
or(implies(X1,not(X2)),X3) = implies(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_51,c_0_75]) ).
cnf(c_0_85,plain,
implies(and(X1,not(X2)),X3) = or(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_86,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X2,not(not(X1)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_79]),c_0_75]) ).
cnf(c_0_87,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(or(X1,not(not(X1)))) ),
inference(spm,[status(thm)],[c_0_82,c_0_51]) ).
cnf(c_0_89,plain,
is_a_theorem(or(implies(X1,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_41]),c_0_84]),c_0_85]) ).
cnf(c_0_90,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_41]) ).
cnf(c_0_92,plain,
is_a_theorem(not(not(implies(X1,X1)))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_90,c_0_75]) ).
cnf(c_0_94,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_41]),c_0_41]) ).
cnf(c_0_96,plain,
( is_a_theorem(implies(X1,not(not(X2))))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_93,c_0_43]) ).
cnf(c_0_97,plain,
is_a_theorem(or(X1,implies(or(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_98,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_96]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_41]),c_0_41]) ).
cnf(c_0_100,plain,
( is_a_theorem(not(not(implies(X1,X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_98,c_0_50]) ).
cnf(c_0_101,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_66,c_0_41]) ).
cnf(c_0_102,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_99]) ).
fof(c_0_103,plain,
! [X190,X191] :
( ~ op_equiv
| equiv(X190,X191) = and(implies(X190,X191),implies(X191,X190)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).
fof(c_0_104,plain,
! [X76,X77] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X76,X77))
| X76 = X77 )
& ( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents )
& ( esk3_0 != esk4_0
| substitution_of_equivalents ) ),
inference(distribute,[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_105,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X3),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_91,c_0_100]) ).
cnf(c_0_106,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_75]) ).
cnf(c_0_107,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).
cnf(c_0_109,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_110,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_111,plain,
( is_a_theorem(and(X1,implies(X2,X3)))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]) ).
cnf(c_0_113,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_53,c_0_41]) ).
cnf(c_0_114,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_115,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_116,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_52,c_0_113]) ).
cnf(c_0_117,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_118,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_116,c_0_89]) ).
cnf(c_0_119,plain,
is_a_theorem(or(implies(X1,not(X2)),X2)),
inference(spm,[status(thm)],[c_0_58,c_0_57]) ).
cnf(c_0_120,plain,
( X1 = implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(rw,[status(thm)],[c_0_119,c_0_84]) ).
fof(c_0_122,plain,
! [X176,X177,X178] :
( ( ~ r5
| is_a_theorem(implies(implies(X177,X178),implies(or(X176,X177),or(X176,X178)))) )
& ( ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))
| r5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])]) ).
cnf(c_0_123,plain,
implies(and(X1,X2),X2) = implies(X3,X3),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,plain,
( is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))
| ~ r5 ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_125,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
cnf(c_0_126,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_113,c_0_41]) ).
cnf(c_0_127,plain,
implies(implies(X1,not(X2)),X3) = or(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_41,c_0_75]) ).
fof(c_0_128,plain,
! [X98,X99] :
( ( ~ and_1
| is_a_theorem(implies(and(X98,X99),X98)) )
& ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
| and_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])]) ).
fof(c_0_129,negated_conjecture,
~ and_1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_and_1])]) ).
fof(c_0_130,plain,
! [X110,X111] :
( ( ~ or_1
| is_a_theorem(implies(X110,or(X110,X111))) )
& ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])]) ).
cnf(c_0_131,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(and(X2,X3),X3),X1)) ),
inference(spm,[status(thm)],[c_0_94,c_0_123]) ).
cnf(c_0_132,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125])]) ).
cnf(c_0_133,plain,
is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
inference(rw,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_134,plain,
( and_1
| ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_135,negated_conjecture,
~ and_1,
inference(split_conjunct,[status(thm)],[c_0_129]) ).
fof(c_0_136,plain,
! [X138,X139] :
( ( ~ kn2
| is_a_theorem(implies(and(X138,X139),X138)) )
& ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
| kn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])]) ).
cnf(c_0_137,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_138,plain,
is_a_theorem(implies(or(X1,and(X2,X3)),or(X1,X3))),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_139,plain,
is_a_theorem(implies(and(X1,X2),and(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_133]),c_0_84]) ).
cnf(c_0_140,plain,
~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)),
inference(sr,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_141,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_142,plain,
( is_a_theorem(or(X1,implies(X1,X2)))
| ~ or_1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_51]),c_0_41]) ).
cnf(c_0_143,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,and(X3,X2))) ),
inference(spm,[status(thm)],[c_0_52,c_0_138]) ).
cnf(c_0_144,plain,
is_a_theorem(or(implies(X1,X2),and(not(X2),X1))),
inference(spm,[status(thm)],[c_0_139,c_0_85]) ).
cnf(c_0_145,plain,
( kn2
| ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_146,plain,
~ kn2,
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_147,plain,
( is_a_theorem(or(implies(X1,X2),X1))
| ~ or_1 ),
inference(spm,[status(thm)],[c_0_58,c_0_142]) ).
cnf(c_0_148,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_149,plain,
~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)),
inference(sr,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_150,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ or_1 ),
inference(spm,[status(thm)],[c_0_147,c_0_84]) ).
cnf(c_0_151,plain,
( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_152,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_148]),c_0_51]) ).
cnf(c_0_153,plain,
~ or_1,
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_154,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_152])]),c_0_153]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL487+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 22:39:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.54/4.65 % Version : CSE_E---1.7
% 6.54/4.65 % Problem : theBenchmark.p
% 6.54/4.65 % SZS status Theorem for theBenchmark.p
% 6.54/4.65 % SZS output start CNFRefutation
% See solution above
% 6.54/4.67 % Total time : 3.372s
%------------------------------------------------------------------------------