%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL485+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 17.98s 11.24s
% Output : CNFRefutation 18.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 26
% Syntax : Number of formulae : 172 ( 83 unt; 0 def)
% Number of atoms : 302 ( 34 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 233 ( 103 ~; 103 |; 12 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 300 ( 42 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(principia_r4,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(principia_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_equiv) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(hilbert_implies_2,conjecture,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(c_0_26,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_27,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_28,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_29,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ r2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_31,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_33,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_34,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_36,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_37,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_38,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_39,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_40,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_42,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_43,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_45,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
fof(c_0_47,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_48,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_50,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_43,c_0_44])]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
fof(c_0_52,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_53,plain,
( is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))
| ~ r4 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
r4,
inference(split_conjunct,[status(thm)],[principia_r4]) ).
cnf(c_0_55,plain,
is_a_theorem(or(X1,implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]) ).
fof(c_0_59,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_60,plain,
is_a_theorem(or(X1,or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
cnf(c_0_61,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_53,c_0_54])]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_55,c_0_39]) ).
cnf(c_0_63,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_64,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_39]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_66,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(X1,or(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_60,c_0_39]) ).
cnf(c_0_69,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(or(X2,or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_61]) ).
cnf(c_0_70,plain,
is_a_theorem(or(X1,implies(X2,not(not(not(X1)))))),
inference(spm,[status(thm)],[c_0_62,c_0_49]) ).
cnf(c_0_71,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_65,c_0_39]) ).
cnf(c_0_73,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_39]),c_0_67])]) ).
cnf(c_0_74,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_65]) ).
cnf(c_0_75,plain,
( is_a_theorem(or(X1,not(not(X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_68]) ).
cnf(c_0_76,plain,
is_a_theorem(or(X1,or(X2,not(X2)))),
inference(spm,[status(thm)],[c_0_69,c_0_60]) ).
cnf(c_0_77,plain,
is_a_theorem(or(implies(X1,not(not(not(X2)))),X2)),
inference(spm,[status(thm)],[c_0_56,c_0_70]) ).
cnf(c_0_78,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(not(not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_79,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_80,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,not(X1))) ),
inference(spm,[status(thm)],[c_0_74,c_0_39]) ).
cnf(c_0_81,plain,
is_a_theorem(or(or(X1,not(X1)),X2)),
inference(spm,[status(thm)],[c_0_56,c_0_76]) ).
cnf(c_0_82,plain,
or(implies(X1,not(X2)),X3) = implies(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_49,c_0_73]) ).
cnf(c_0_83,plain,
implies(and(X1,not(X2)),X3) = or(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_84,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X2,not(not(X1)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_77]),c_0_73]) ).
cnf(c_0_85,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(or(X1,not(not(X1)))) ),
inference(spm,[status(thm)],[c_0_80,c_0_49]) ).
cnf(c_0_87,plain,
is_a_theorem(or(implies(X1,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_39]),c_0_82]),c_0_83]) ).
cnf(c_0_88,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_39]) ).
cnf(c_0_90,plain,
is_a_theorem(not(not(implies(X1,X1)))),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(not(and(X1,X2))) ),
inference(spm,[status(thm)],[c_0_88,c_0_73]) ).
cnf(c_0_92,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_93,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_61,c_0_39]),c_0_39]) ).
cnf(c_0_94,plain,
( is_a_theorem(implies(X1,not(not(X2))))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_91,c_0_41]) ).
cnf(c_0_95,plain,
is_a_theorem(or(X1,implies(or(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_96,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_94]) ).
cnf(c_0_97,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_39]),c_0_39]) ).
cnf(c_0_98,plain,
( is_a_theorem(not(not(implies(X1,X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_48]) ).
cnf(c_0_99,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_64,c_0_39]) ).
cnf(c_0_100,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_97]) ).
fof(c_0_101,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_102,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_103,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X3),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_89,c_0_98]) ).
cnf(c_0_104,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_73]) ).
cnf(c_0_105,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_106,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).
cnf(c_0_107,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_108,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_109,plain,
( is_a_theorem(and(X1,implies(X2,X3)))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).
cnf(c_0_111,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_112,plain,
( X1 = X2
| ~ is_a_theorem(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(equiv(X1,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_50,c_0_111]) ).
cnf(c_0_115,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_114,c_0_87]) ).
cnf(c_0_117,plain,
is_a_theorem(or(implies(X1,not(X2)),X2)),
inference(spm,[status(thm)],[c_0_56,c_0_55]) ).
cnf(c_0_118,plain,
( X1 = implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_119,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(rw,[status(thm)],[c_0_117,c_0_82]) ).
fof(c_0_120,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_121,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_111,c_0_39]) ).
cnf(c_0_122,plain,
implies(implies(X1,not(X2)),X3) = or(and(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_73]) ).
cnf(c_0_123,plain,
implies(and(X1,X2),X2) = implies(X3,X3),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
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_120]) ).
cnf(c_0_125,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
cnf(c_0_126,plain,
is_a_theorem(or(and(X1,X2),implies(X2,not(X1)))),
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_92,c_0_97]) ).
cnf(c_0_128,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(and(X2,X3),X3),X1)) ),
inference(spm,[status(thm)],[c_0_92,c_0_123]) ).
cnf(c_0_129,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_130,plain,
is_a_theorem(or(implies(X1,not(X2)),and(X2,X1))),
inference(spm,[status(thm)],[c_0_56,c_0_126]) ).
cnf(c_0_131,plain,
is_a_theorem(implies(X1,and(implies(X2,X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_127]),c_0_73]) ).
cnf(c_0_132,plain,
is_a_theorem(implies(or(X1,and(X2,X3)),or(X1,X3))),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,plain,
is_a_theorem(implies(and(X1,X2),and(X2,X1))),
inference(rw,[status(thm)],[c_0_130,c_0_82]) ).
cnf(c_0_134,plain,
( is_a_theorem(and(implies(X1,X1),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_131]) ).
cnf(c_0_135,plain,
implies(or(X1,X1),X1) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_118,c_0_65]) ).
cnf(c_0_136,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,and(X3,X2))) ),
inference(spm,[status(thm)],[c_0_50,c_0_132]) ).
cnf(c_0_137,plain,
is_a_theorem(or(implies(X1,X2),and(not(X2),X1))),
inference(spm,[status(thm)],[c_0_133,c_0_83]) ).
cnf(c_0_138,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_79,c_0_73]) ).
cnf(c_0_139,plain,
( is_a_theorem(and(implies(or(X1,X1),X1),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_140,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_141,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_138,c_0_41]) ).
cnf(c_0_142,plain,
is_a_theorem(equiv(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_110]),c_0_38])]) ).
cnf(c_0_143,plain,
is_a_theorem(or(implies(and(X1,X2),X3),X2)),
inference(spm,[status(thm)],[c_0_136,c_0_140]) ).
cnf(c_0_144,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_140]),c_0_49]) ).
cnf(c_0_145,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,not(not(X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_49]),c_0_49]) ).
cnf(c_0_146,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_38]) ).
cnf(c_0_147,plain,
( is_a_theorem(implies(or(X1,X2),or(X1,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_50,c_0_129]) ).
cnf(c_0_148,plain,
or(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_112,c_0_142]) ).
cnf(c_0_149,plain,
is_a_theorem(or(X1,implies(and(X2,X1),X3))),
inference(spm,[status(thm)],[c_0_56,c_0_143]) ).
cnf(c_0_150,plain,
implies(X1,or(X1,X2)) = implies(X3,X3),
inference(spm,[status(thm)],[c_0_118,c_0_144]) ).
cnf(c_0_151,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(not(X2))) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,plain,
( is_a_theorem(not(not(or(X1,X2))))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_51]) ).
cnf(c_0_153,plain,
( is_a_theorem(implies(or(X1,X2),X1))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_154,plain,
is_a_theorem(or(X1,implies(X2,or(X2,X3)))),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(or(X3,X2)) ),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_156,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_153]) ).
cnf(c_0_157,plain,
is_a_theorem(or(X1,or(X2,implies(X2,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_39]),c_0_49]) ).
cnf(c_0_158,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_155]) ).
cnf(c_0_159,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(or(X2,implies(X2,X3)),X1)) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
fof(c_0_160,plain,
! [X88,X89] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X88,implies(X88,X89)),implies(X88,X89))) )
& ( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
| implies_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])]) ).
fof(c_0_161,negated_conjecture,
~ implies_2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_2])]) ).
cnf(c_0_162,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,or(X1,X2))) ),
inference(spm,[status(thm)],[c_0_74,c_0_158]) ).
cnf(c_0_163,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(implies(X1,X3),X2)) ),
inference(spm,[status(thm)],[c_0_159,c_0_147]) ).
cnf(c_0_164,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_39]),c_0_39]) ).
cnf(c_0_165,plain,
( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) ),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_166,negated_conjecture,
~ implies_2,
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_167,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_162,c_0_39]) ).
cnf(c_0_168,plain,
is_a_theorem(or(X1,implies(implies(X2,X1),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_169,plain,
~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))),
inference(sr,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_170,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_171,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LCL485+1 : TPTP v9.2.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 22:38:46 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 17.98/11.24 % Version : CSE_E---1.7
% 17.98/11.24 % Problem : theBenchmark.p
% 17.98/11.24 % SZS status Theorem for theBenchmark.p
% 17.98/11.24 % SZS output start CNFRefutation
% See solution above
% 18.09/11.32 % Total time : 8.368s
%------------------------------------------------------------------------------