%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC152+1 : TPTP v9.2.1. Released v2.4.0.
% 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 05:18:30 PM UTC 2026
% Result : Theorem 1.63s 1.82s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 25 unt; 0 def)
% Number of atoms : 394 ( 68 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 507 ( 186 ~; 208 |; 61 &)
% ( 4 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 12 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 85 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
| ~ leq(X6,X5)
| ( ! [X10] :
( ~ ssItem(X10)
| ~ memberP(X8,X10)
| ( leq(X5,X10)
& leq(X10,X6) ) )
& leq(X5,X6) ) ) ) ) ) )
| ( ! [X11] :
( ~ ssItem(X11)
| cons(X11,nil) != X3
| ~ memberP(X4,X11)
| ? [X12] :
( ssItem(X12)
& X11 != X12
& memberP(X4,X12)
& leq(X11,X12) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax11,axiom,
! [X1] :
( ssList(X1)
=> ( totalorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> leq(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax11) ).
fof(ax8,axiom,
! [X1] :
( ssList(X1)
=> ( cyclefreeP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> ~ ( leq(X2,X3)
& leq(X3,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax8) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(ax12,axiom,
! [X1] :
( ssList(X1)
=> ( strictorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> lt(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).
fof(ax59,axiom,
! [X1] :
( ssItem(X1)
=> cyclefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax59) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(ax69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax69) ).
fof(ax60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax60) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
| ~ leq(X6,X5)
| ( ! [X10] :
( ~ ssItem(X10)
| ~ memberP(X8,X10)
| ( leq(X5,X10)
& leq(X10,X6) ) )
& leq(X5,X6) ) ) ) ) ) )
| ( ! [X11] :
( ~ ssItem(X11)
| cons(X11,nil) != X3
| ~ memberP(X4,X11)
| ? [X12] :
( ssItem(X12)
& X11 != X12
& memberP(X4,X12)
& leq(X11,X12) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_15,negated_conjecture,
! [X483] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& ssList(esk56_0)
& app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
& leq(esk53_0,esk52_0)
& ( ssItem(esk57_0)
| ~ leq(esk52_0,esk53_0) )
& ( memberP(esk55_0,esk57_0)
| ~ leq(esk52_0,esk53_0) )
& ( ~ leq(esk52_0,esk57_0)
| ~ leq(esk57_0,esk53_0)
| ~ leq(esk52_0,esk53_0) )
& ( nil = esk51_0
| ssItem(esk58_0) )
& ( nil = esk50_0
| ssItem(esk58_0) )
& ( nil = esk51_0
| cons(esk58_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk58_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk58_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk58_0) )
& ( nil = esk51_0
| ~ ssItem(X483)
| esk58_0 = X483
| ~ memberP(esk51_0,X483)
| ~ leq(esk58_0,X483) )
& ( nil = esk50_0
| ~ ssItem(X483)
| esk58_0 = X483
| ~ memberP(esk51_0,X483)
| ~ leq(esk58_0,X483) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
cnf(c_0_16,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_17,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X443,X444,X445] :
( ~ ssList(X443)
| ~ ssList(X444)
| ~ ssList(X445)
| app(app(X443,X444),X445) = app(X443,app(X444,X445)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_19,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,plain,
! [X332,X333] :
( ~ ssList(X332)
| ~ ssItem(X333)
| ssList(cons(X333,X332)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_24,negated_conjecture,
( app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_25,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_27,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_28,plain,
! [X441,X442] :
( ~ ssList(X441)
| ~ ssItem(X442)
| cons(X442,X441) = app(cons(X442,nil),X441) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_29,negated_conjecture,
app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
cnf(c_0_30,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21]),c_0_27])]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_31]),c_0_32])]) ).
cnf(c_0_34,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_35,plain,
! [X351,X352] :
( ~ ssList(X351)
| ~ ssList(X352)
| ssList(app(X351,X352)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_36,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_26]),c_0_34])]) ).
cnf(c_0_37,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_38,plain,
! [X288,X289,X290,X291,X292,X293] :
( ( ~ totalorderedP(X288)
| ~ ssItem(X289)
| ~ ssItem(X290)
| ~ ssList(X291)
| ~ ssList(X292)
| ~ ssList(X293)
| app(app(X291,cons(X289,X292)),cons(X290,X293)) != X288
| leq(X289,X290)
| ~ ssList(X288) )
& ( ssItem(esk25_1(X288))
| totalorderedP(X288)
| ~ ssList(X288) )
& ( ssItem(esk26_1(X288))
| totalorderedP(X288)
| ~ ssList(X288) )
& ( ssList(esk27_1(X288))
| totalorderedP(X288)
| ~ ssList(X288) )
& ( ssList(esk28_1(X288))
| totalorderedP(X288)
| ~ ssList(X288) )
& ( ssList(esk29_1(X288))
| totalorderedP(X288)
| ~ ssList(X288) )
& ( app(app(esk27_1(X288),cons(esk25_1(X288),esk28_1(X288))),cons(esk26_1(X288),esk29_1(X288))) = X288
| totalorderedP(X288)
| ~ ssList(X288) )
& ( ~ leq(esk25_1(X288),esk26_1(X288))
| totalorderedP(X288)
| ~ ssList(X288) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])])])]) ).
cnf(c_0_39,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_22])]) ).
fof(c_0_40,plain,
! [X255,X256,X257,X258,X259,X260] :
( ( ~ cyclefreeP(X255)
| ~ ssItem(X256)
| ~ ssItem(X257)
| ~ ssList(X258)
| ~ ssList(X259)
| ~ ssList(X260)
| app(app(X258,cons(X256,X259)),cons(X257,X260)) != X255
| ~ leq(X256,X257)
| ~ leq(X257,X256)
| ~ ssList(X255) )
& ( ssItem(esk10_1(X255))
| cyclefreeP(X255)
| ~ ssList(X255) )
& ( ssItem(esk11_1(X255))
| cyclefreeP(X255)
| ~ ssList(X255) )
& ( ssList(esk12_1(X255))
| cyclefreeP(X255)
| ~ ssList(X255) )
& ( ssList(esk13_1(X255))
| cyclefreeP(X255)
| ~ ssList(X255) )
& ( ssList(esk14_1(X255))
| cyclefreeP(X255)
| ~ ssList(X255) )
& ( app(app(esk12_1(X255),cons(esk10_1(X255),esk13_1(X255))),cons(esk11_1(X255),esk14_1(X255))) = X255
| cyclefreeP(X255)
| ~ ssList(X255) )
& ( leq(esk10_1(X255),esk11_1(X255))
| cyclefreeP(X255)
| ~ ssList(X255) )
& ( leq(esk11_1(X255),esk10_1(X255))
| cyclefreeP(X255)
| ~ ssList(X255) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])])])]) ).
cnf(c_0_41,plain,
( leq(X2,X3)
| ~ totalorderedP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_25]),c_0_21]),c_0_27])]) ).
cnf(c_0_43,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_44,plain,
! [X420] :
( ~ ssItem(X420)
| totalorderedP(cons(X420,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])]) ).
fof(c_0_45,plain,
! [X299,X300,X301,X302,X303,X304] :
( ( ~ strictorderedP(X299)
| ~ ssItem(X300)
| ~ ssItem(X301)
| ~ ssList(X302)
| ~ ssList(X303)
| ~ ssList(X304)
| app(app(X302,cons(X300,X303)),cons(X301,X304)) != X299
| lt(X300,X301)
| ~ ssList(X299) )
& ( ssItem(esk30_1(X299))
| strictorderedP(X299)
| ~ ssList(X299) )
& ( ssItem(esk31_1(X299))
| strictorderedP(X299)
| ~ ssList(X299) )
& ( ssList(esk32_1(X299))
| strictorderedP(X299)
| ~ ssList(X299) )
& ( ssList(esk33_1(X299))
| strictorderedP(X299)
| ~ ssList(X299) )
& ( ssList(esk34_1(X299))
| strictorderedP(X299)
| ~ ssList(X299) )
& ( app(app(esk32_1(X299),cons(esk30_1(X299),esk33_1(X299))),cons(esk31_1(X299),esk34_1(X299))) = X299
| strictorderedP(X299)
| ~ ssList(X299) )
& ( ~ lt(esk30_1(X299),esk31_1(X299))
| strictorderedP(X299)
| ~ ssList(X299) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])]) ).
cnf(c_0_46,plain,
( ~ cyclefreeP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ leq(X2,X3)
| ~ leq(X3,X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
( leq(X1,X2)
| ~ totalorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_32]),c_0_34])]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_43,c_0_17]) ).
cnf(c_0_50,plain,
( totalorderedP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( nil = esk50_0
| cons(esk58_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_52,negated_conjecture,
( nil = esk50_0
| ssItem(esk58_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_53,plain,
! [X417] :
( ~ ssItem(X417)
| cyclefreeP(cons(X417,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax59])]) ).
cnf(c_0_54,plain,
( lt(X2,X3)
| ~ strictorderedP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
( ~ leq(X1,X2)
| ~ leq(X2,X1)
| ~ cyclefreeP(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| ~ ssList(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_56,negated_conjecture,
leq(esk53_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_57,negated_conjecture,
( leq(esk52_0,esk53_0)
| ~ totalorderedP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_32]),c_0_21]),c_0_22]),c_0_34]),c_0_27])]) ).
cnf(c_0_58,negated_conjecture,
( esk50_0 = nil
| totalorderedP(esk50_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_59,plain,
( cyclefreeP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( lt(X1,X2)
| ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( ~ leq(esk52_0,esk53_0)
| ~ cyclefreeP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_48]),c_0_56]),c_0_49]),c_0_32]),c_0_21]),c_0_22]),c_0_34]),c_0_27])]) ).
cnf(c_0_62,negated_conjecture,
( esk50_0 = nil
| leq(esk52_0,esk53_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( esk50_0 = nil
| cyclefreeP(esk50_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_52]) ).
fof(c_0_64,plain,
! [X465,X466] :
( ( X465 != X466
| ~ lt(X465,X466)
| ~ ssItem(X466)
| ~ ssItem(X465) )
& ( leq(X465,X466)
| ~ lt(X465,X466)
| ~ ssItem(X466)
| ~ ssItem(X465) )
& ( X465 = X466
| ~ leq(X465,X466)
| lt(X465,X466)
| ~ ssItem(X466)
| ~ ssItem(X465) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax93])])])]) ).
cnf(c_0_65,negated_conjecture,
( lt(esk52_0,esk53_0)
| ~ strictorderedP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_48]),c_0_49]),c_0_32]),c_0_21]),c_0_22]),c_0_34]),c_0_27])]) ).
cnf(c_0_66,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_67,plain,
strictorderedP(nil),
inference(split_conjunct,[status(thm)],[ax69]) ).
cnf(c_0_68,plain,
cyclefreeP(nil),
inference(split_conjunct,[status(thm)],[ax60]) ).
cnf(c_0_69,plain,
( leq(X1,X2)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,negated_conjecture,
lt(esk52_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
cnf(c_0_71,negated_conjecture,
~ leq(esk52_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_66]),c_0_68])]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_34]),c_0_27])]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC152+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:30:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.63/1.82 % Version : CSE_E---1.7
% 1.63/1.82 % Problem : theBenchmark.p
% 1.63/1.82 % SZS status Theorem for theBenchmark.p
% 1.63/1.82 % SZS output start CNFRefutation
% See solution above
% 1.63/1.82 % Total time : 1.371s
%------------------------------------------------------------------------------