%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL486+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 146.47s 107.61s
% Output : CNFRefutation 148.57s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named i_0_173)
% Comments :
%------------------------------------------------------------------------------
fof(kn3,axiom,
( kn3
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(or_3,axiom,
( or_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
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(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(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(equivalence_3,axiom,
( equivalence_3
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
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(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(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(equivalence_2,axiom,
( equivalence_2
<=> ! [X1,X2] : is_a_theorem(implies(equiv(X1,X2),implies(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
fof(equivalence_1,axiom,
( equivalence_1
<=> ! [X1,X2] : is_a_theorem(implies(equiv(X1,X2),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_1) ).
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(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(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
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(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
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(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(or_2,axiom,
( or_2
<=> ! [X1,X2] : is_a_theorem(implies(X2,or(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_2) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
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(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(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(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(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(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(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(hilbert_implies_3,conjecture,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(principia_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_equiv) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(principia_r4,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',use_substitution_of_equivalents) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(i_0_45,plain,
! [X142,X143,X144] :
( ( ~ kn3
| is_a_theorem(implies(implies(X142,X143),implies(not(and(X143,X144)),not(and(X144,X142))))) )
& ( ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))
| kn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])]) ).
fof(i_0_46,plain,
! [X118,X119,X120] :
( ( ~ or_3
| is_a_theorem(implies(implies(X118,X120),implies(implies(X119,X120),implies(or(X118,X119),X120)))) )
& ( ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0))))
| or_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_3])])])]) ).
fof(i_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])])])]) ).
fof(i_0_48,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])])])]) ).
fof(i_0_49,plain,
! [X148,X149,X150] :
( ( ~ cn1
| is_a_theorem(implies(implies(X148,X149),implies(implies(X149,X150),implies(X148,X150)))) )
& ( ~ is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0))))
| cn1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn1])])])]) ).
fof(i_0_50,plain,
! [X132,X133] :
( ( ~ equivalence_3
| is_a_theorem(implies(implies(X132,X133),implies(implies(X133,X132),equiv(X132,X133)))) )
& ( ~ is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0))))
| equivalence_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_3])])])]) ).
fof(i_0_51,plain,
! [X92,X93,X94] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X92,X93),implies(implies(X93,X94),implies(X92,X94)))) )
& ( ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))
| implies_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])]) ).
fof(i_0_52,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(i_0_53,plain,
! [X106,X107] :
( ( ~ and_3
| is_a_theorem(implies(X106,implies(X107,and(X106,X107)))) )
& ( ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))
| and_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])]) ).
fof(i_0_54,plain,
! [X80,X81] :
( ( ~ modus_tollens
| is_a_theorem(implies(implies(not(X81),not(X80)),implies(X80,X81))) )
& ( ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))
| modus_tollens ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])]) ).
fof(i_0_55,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])])])]) ).
fof(i_0_56,plain,
! [X128,X129] :
( ( ~ equivalence_2
| is_a_theorem(implies(equiv(X128,X129),implies(X129,X128))) )
& ( ~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))
| equivalence_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_2])])])]) ).
fof(i_0_57,plain,
! [X124,X125] :
( ( ~ equivalence_1
| is_a_theorem(implies(equiv(X124,X125),implies(X124,X125))) )
& ( ~ is_a_theorem(implies(equiv(esk27_0,esk28_0),implies(esk27_0,esk28_0)))
| equivalence_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_1])])])]) ).
fof(i_0_58,plain,
! [X158] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(X158),X158),X158)) )
& ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
| cn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])]) ).
fof(i_0_59,plain,
! [X154,X155] :
( ( ~ cn2
| is_a_theorem(implies(X154,implies(not(X154),X155))) )
& ( ~ is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0)))
| cn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn2])])])]) ).
fof(i_0_60,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])])])]) ).
fof(i_0_61,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])])])]) ).
fof(i_0_62,plain,
! [X102,X103] :
( ( ~ and_2
| is_a_theorem(implies(and(X102,X103),X103)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])]) ).
fof(i_0_63,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(i_0_64,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(i_0_65,plain,
! [X136] :
( ( ~ kn1
| is_a_theorem(implies(X136,and(X136,X136))) )
& ( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
| kn1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])]) ).
fof(i_0_66,plain,
! [X114,X115] :
( ( ~ or_2
| is_a_theorem(implies(X115,or(X114,X115))) )
& ( ~ is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0)))
| or_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_2])])])]) ).
fof(i_0_67,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])])])]) ).
fof(i_0_68,plain,
! [X84,X85] :
( ( ~ implies_1
| is_a_theorem(implies(X84,implies(X85,X84))) )
& ( ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))
| implies_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])]) ).
fof(i_0_69,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(i_0_70,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])])]) ).
fof(i_0_71,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])])]) ).
fof(i_0_72,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(i_0_73,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])])]) ).
fof(i_0_74,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])])])])]) ).
fof(i_0_75,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(i_0_76,negated_conjecture,
~ implies_3,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_3])]) ).
cnf(i_0_77,plain,
( kn3
| ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0))))) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_78,plain,
( or_3
| ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0)))) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_79,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))
| ~ kn3 ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_80,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))
| ~ or_3 ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_81,plain,
( r4
| ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0)))) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_82,plain,
( r5
| ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0)))) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_83,plain,
( cn1
| ~ is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0)))) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_84,plain,
( equivalence_3
| ~ is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0)))) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_85,plain,
( implies_3
| ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0)))) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_86,plain,
( is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))
| ~ r4 ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_87,plain,
( is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))
| ~ r5 ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_88,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))
| ~ equivalence_3 ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_89,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ cn1 ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_90,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ implies_3 ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_91,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)],[i_0_52]),
[final] ).
cnf(i_0_92,plain,
( and_3
| ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_93,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_94,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0))) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_95,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_96,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_97,plain,
( r3
| ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_98,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0))) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_99,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(esk27_0,esk28_0),implies(esk27_0,esk28_0))) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_100,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_101,plain,
( is_a_theorem(implies(equiv(X1,X2),implies(X1,X2)))
| ~ equivalence_1 ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_102,plain,
( is_a_theorem(implies(equiv(X1,X2),implies(X2,X1)))
| ~ equivalence_2 ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_103,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_104,plain,
( cn2
| ~ is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0))) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_105,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_106,plain,
( is_a_theorem(implies(X1,implies(not(X1),X2)))
| ~ cn2 ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_107,plain,
( r1
| ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_108,plain,
( kn2
| ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_109,plain,
( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_110,plain,
( and_1
| ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_111,plain,
( r2
| ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0))) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_112,plain,
( kn1
| ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_113,plain,
( or_2
| ~ is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0))) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_114,plain,
( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_115,plain,
( implies_1
| ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0))) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_116,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_117,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_118,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_119,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ and_2 ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_120,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_121,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ r2 ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_122,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ or_2 ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_123,plain,
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_124,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_125,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_126,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_127,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_128,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_129,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_130,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_131,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_132,plain,
( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_133,plain,
( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_134,plain,
( modus_ponens
| ~ is_a_theorem(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_135,plain,
( is_a_theorem(esk1_0)
| modus_ponens ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_136,plain,
( substitution_of_equivalents
| esk3_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_137,negated_conjecture,
~ implies_3,
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_138,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]),
[final] ).
cnf(i_0_139,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[principia_op_equiv]),
[final] ).
cnf(i_0_140,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]),
[final] ).
cnf(i_0_141,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]),
[final] ).
cnf(i_0_142,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]),
[final] ).
cnf(i_0_143,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]),
[final] ).
cnf(i_0_144,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]),
[final] ).
cnf(i_0_145,plain,
r4,
inference(split_conjunct,[status(thm)],[principia_r4]),
[final] ).
cnf(i_0_146,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]),
[final] ).
cnf(i_0_147,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]),
[final] ).
cnf(i_0_148,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]),
[final] ).
cnf(i_0_149,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]),
[final] ).
cnf(i_0_150,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]),
[final] ).
cnf(i_0_151,axiom,
X1 = X1 ).
cnf(i_0_152,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_153,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_154,axiom,
( X1 != X2
| implies(X1,X3) = implies(X2,X3) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| implies(X3,X1) = implies(X3,X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| not(X1) = not(X2) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| and(X1,X3) = and(X2,X3) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| and(X3,X1) = and(X3,X2) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| or(X1,X3) = or(X2,X3) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| or(X3,X1) = or(X3,X2) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| equiv(X1,X3) = equiv(X2,X3) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| equiv(X3,X1) = equiv(X3,X2) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ) ).
cnf(i_0_165,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
inference(scs_inference,[],[i_0_145,i_0_86]) ).
cnf(i_0_166,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(scs_inference,[],[i_0_144,i_0_87]) ).
cnf(i_0_167,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(scs_inference,[],[i_0_146,i_0_100]) ).
cnf(i_0_168,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(scs_inference,[],[i_0_148,i_0_116]) ).
cnf(i_0_169,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(scs_inference,[],[i_0_147,i_0_121]) ).
cnf(i_0_170,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(scs_inference,[],[i_0_139,i_0_125]) ).
cnf(i_0_171,plain,
or(X1,X2) = not(and(not(X1),not(X2))),
inference(scs_inference,[],[i_0_143,i_0_126]) ).
cnf(i_0_172,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(scs_inference,[],[i_0_142,i_0_127]) ).
cnf(i_0_174,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(scs_inference,[],[i_0_141,i_0_129]) ).
cnf(i_0_176,plain,
implies(X1,X2) = or(not(X1),X2),
inference(scs_inference,[],[i_0_140,i_0_131]) ).
cnf(i_0_177,plain,
or_2,
inference(scs_inference,[],[i_0_169,i_0_113]) ).
cnf(i_0_178,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(scs_inference,[],[i_0_170,i_0_152]) ).
cnf(i_0_179,plain,
is_a_theorem(or(X1,implies(or(X2,X2),X2))),
inference(scs_inference,[],[i_0_168,i_0_170,i_0_169,i_0_152,i_0_173]) ).
cnf(i_0_180,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_183,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(scs_inference,[],[i_0_164,i_0_168,i_0_170,i_0_176,i_0_169,i_0_171,i_0_152,i_0_173,i_0_163,i_0_153]) ).
cnf(i_0_184,plain,
or(X1,X2) = not(and(not(X1),not(X2))),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_187,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(scs_inference,[],[i_0_172,i_0_152]) ).
cnf(i_0_189,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rename_variables,[],[i_0_167]) ).
cnf(i_0_193,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_194,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(scs_inference,[],[i_0_174,i_0_152]) ).
cnf(i_0_203,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rename_variables,[],[i_0_167]) ).
cnf(i_0_210,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_221,plain,
implies(X1,X2) = or(not(X1),X2),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_223,plain,
or(not(X1),X2) = implies(X1,X2),
inference(scs_inference,[],[i_0_176,i_0_152]) ).
cnf(i_0_225,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_229,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_237,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_239,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(scs_inference,[],[i_0_171,i_0_152]) ).
cnf(i_0_250,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_252,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_274,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_323,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_336,plain,
or(X1,X2) = not(and(not(X1),not(X2))),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_414,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_433,plain,
implies(X1,X2) = or(not(X1),X2),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_450,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_506,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_641,plain,
implies(X1,X2) = or(not(X1),X2),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_674,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_740,plain,
or(X1,X2) = not(and(not(X1),not(X2))),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_775,plain,
implies(X1,X2) = or(not(X1),X2),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_791,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_806,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_873,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_1031,plain,
implies(X1,X2) = or(not(X1),X2),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_1104,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_1108,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_1139,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rename_variables,[],[i_0_168]) ).
cnf(i_0_1151,plain,
implies(X1,X2) = or(not(X1),X2),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_1160,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_1169,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_1219,plain,
implies(X1,X2) = or(not(X1),X2),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_1261,plain,
or(X1,X2) = not(and(not(X1),not(X2))),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_1294,plain,
implies(X1,X2) = not(and(X1,not(X2))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_1319,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_1321,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_1330,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_1338,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_1349,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(rename_variables,[],[i_0_166]) ).
cnf(i_0_1355,plain,
or(X1,X2) = not(and(not(X1),not(X2))),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_1367,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rename_variables,[],[i_0_167]) ).
cnf(i_0_1369,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_1446,plain,
or(X1,X2) = not(and(not(X1),not(X2))),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_1459,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_1476,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_186,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(scs_inference,[],[i_0_177,i_0_122]) ).
cnf(i_0_188,plain,
is_a_theorem(or(implies(or(X1,X1),X1),X2)),
inference(scs_inference,[],[i_0_179,i_0_167,i_0_172,i_0_152,i_0_173]) ).
cnf(i_0_192,plain,
equiv(X1,X2) = not(or(not(implies(X1,X2)),not(implies(X2,X1)))),
inference(scs_inference,[],[i_0_164,i_0_179,i_0_167,i_0_172,i_0_170,i_0_152,i_0_173,i_0_163,i_0_153]) ).
cnf(i_0_200,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_201,plain,
not(and(not(not(X1)),not(X2))) = implies(X1,X2),
inference(scs_inference,[],[i_0_183,i_0_152]) ).
cnf(i_0_207,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_233,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_244,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_248,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_259,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_263,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_266,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_268,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_270,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_272,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_285,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(rename_variables,[],[i_0_239]) ).
cnf(i_0_291,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(rename_variables,[],[i_0_239]) ).
cnf(i_0_303,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(rename_variables,[],[i_0_239]) ).
cnf(i_0_315,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(rename_variables,[],[i_0_239]) ).
cnf(i_0_356,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_395,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_397,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_431,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_469,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_487,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_504,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_537,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_539,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_573,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_604,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_606,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_639,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_692,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_708,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_773,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_789,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_868,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(rename_variables,[],[i_0_239]) ).
cnf(i_0_904,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_935,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_966,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_1060,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_1122,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_1131,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(rename_variables,[],[i_0_178]) ).
cnf(i_0_1149,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(rename_variables,[],[i_0_187]) ).
cnf(i_0_1192,plain,
implies(X1,X2) = not(and(not(not(X1)),not(X2))),
inference(rename_variables,[],[i_0_183]) ).
cnf(c_0_184,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
i_0_128 ).
cnf(c_0_185,plain,
implies(X1,X2) = or(not(X1),X2),
i_0_176 ).
cnf(c_0_186,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(or(not(X2),X1)) ),
inference(rw,[status(thm)],[c_0_184,c_0_185]) ).
cnf(c_0_187,plain,
modus_ponens,
i_0_150 ).
cnf(c_0_188,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
i_0_165 ).
cnf(c_0_189,plain,
( implies_3
| ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0)))) ),
i_0_85 ).
cnf(c_0_190,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(not(X2),X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187])]) ).
cnf(c_0_191,plain,
is_a_theorem(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))),
inference(rw,[status(thm)],[c_0_188,c_0_185]) ).
cnf(c_0_192,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
i_0_166 ).
cnf(c_0_193,plain,
( implies_3
| ~ is_a_theorem(or(not(or(not(esk11_0),esk12_0)),or(not(or(not(esk12_0),esk13_0)),or(not(esk11_0),esk13_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_185]),c_0_185]),c_0_185]),c_0_185]),c_0_185]) ).
cnf(c_0_194,negated_conjecture,
~ implies_3,
i_0_137 ).
cnf(c_0_195,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(or(X2,or(X1,X3))) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_196,plain,
is_a_theorem(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_185]),c_0_185]),c_0_185]) ).
cnf(c_0_197,plain,
~ is_a_theorem(or(not(or(not(esk11_0),esk12_0)),or(not(or(not(esk12_0),esk13_0)),or(not(esk11_0),esk13_0)))),
inference(sr,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_198,plain,
is_a_theorem(or(not(or(X1,X2)),or(not(or(not(X2),X3)),or(X1,X3)))),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_199,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_198])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LCL486+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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 22:39:01 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 146.47/107.61 % Version : CSE_E---1.7
% 146.47/107.61 % Problem : theBenchmark.p
% 146.47/107.61 % SZS status Theorem for theBenchmark.p
% 146.47/107.61 % SZS output start CNFRefutation
% See solution above
% 148.57/109.78 % Total time : 107.302s
%------------------------------------------------------------------------------