%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC152+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:43:14 PM UTC 2026
% Result : Theorem 0.79s 0.54s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 24 unt; 0 def)
% Number of atoms : 340 ( 68 equ)
% Maximal formula atoms : 42 ( 5 avg)
% Number of connectives : 430 ( 155 ~; 170 |; 57 &)
% ( 2 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 12 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 80 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( nil != X3
| nil != X4 )
& ! [X11] :
( ? [X12] :
( leq(X11,X12)
& memberP(X4,X12)
& X11 != X12
& ssItem(X12) )
| ~ memberP(X4,X11)
| cons(X11,nil) != X3
| ~ ssItem(X11) ) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ( leq(X5,X6)
& ! [X10] :
( ( leq(X10,X6)
& leq(X5,X10) )
| ~ memberP(X8,X10)
| ~ ssItem(X10) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
| ~ ssList(X9) ) ) ) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
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(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(X3,X2)
& leq(X2,X3) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax8) ).
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(ax59,axiom,
! [X1] :
( ssItem(X1)
=> cyclefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax59) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(ax66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax66) ).
fof(ax60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax60) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( nil != X3
| nil != X4 )
& ! [X11] :
( ? [X12] :
( leq(X11,X12)
& memberP(X4,X12)
& X11 != X12
& ssItem(X12) )
| ~ memberP(X4,X11)
| cons(X11,nil) != X3
| ~ ssItem(X11) ) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ( leq(X5,X6)
& ! [X10] :
( ( leq(X10,X6)
& leq(X5,X10) )
| ~ memberP(X8,X10)
| ~ ssItem(X10) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
| ~ ssList(X9) ) ) ) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( nil != X3
| nil != X4 )
& ! [X11] :
( ? [X12] :
( leq(X11,X12)
& memberP(X4,X12)
& X11 != X12
& ssItem(X12) )
| ~ memberP(X4,X11)
| cons(X11,nil) != X3
| ~ ssItem(X11) ) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ( leq(X5,X6)
& ! [X10] :
( ( leq(X10,X6)
& leq(X5,X10) )
| ~ memberP(X8,X10)
| ~ ssItem(X10) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1
| ~ ssList(X9) ) ) ) ) )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_14,negated_conjecture,
! [X268] :
( ( ~ leq(esk58_0,X268)
| ~ memberP(esk51_0,X268)
| esk58_0 = X268
| ~ ssItem(X268)
| nil = esk50_0 )
& ( ~ leq(esk58_0,X268)
| ~ memberP(esk51_0,X268)
| esk58_0 = X268
| ~ ssItem(X268)
| nil = esk51_0 )
& ( memberP(esk51_0,esk58_0)
| nil = esk50_0 )
& ( memberP(esk51_0,esk58_0)
| nil = esk51_0 )
& ( cons(esk58_0,nil) = esk50_0
| nil = esk50_0 )
& ( cons(esk58_0,nil) = esk50_0
| nil = esk51_0 )
& ( ssItem(esk58_0)
| nil = esk50_0 )
& ( ssItem(esk58_0)
| nil = esk51_0 )
& ( ~ leq(esk52_0,esk53_0)
| ~ leq(esk57_0,esk53_0)
| ~ leq(esk52_0,esk57_0) )
& ( ~ leq(esk52_0,esk53_0)
| memberP(esk55_0,esk57_0) )
& ( ~ leq(esk52_0,esk53_0)
| ssItem(esk57_0) )
& leq(esk53_0,esk52_0)
& app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
& ssList(esk56_0)
& ssList(esk55_0)
& ssList(esk54_0)
& ssItem(esk53_0)
& ssItem(esk52_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])])]) ).
cnf(c_0_15,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_14]) ).
cnf(c_0_16,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X228,X229,X230] :
( app(app(X228,X229),X230) = app(X228,app(X229,X230))
| ~ ssList(X230)
| ~ ssList(X229)
| ~ ssList(X228) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_18,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_15,c_0_16]) ).
cnf(c_0_19,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_22,plain,
! [X117,X118] :
( ssList(cons(X118,X117))
| ~ ssItem(X118)
| ~ ssList(X117) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_23,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| 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_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_26,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_27,plain,
! [X226,X227] :
( cons(X227,X226) = app(cons(X227,nil),X226)
| ~ ssItem(X227)
| ~ ssList(X226) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_28,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_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_29,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,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_28,c_0_29]),c_0_20]),c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,negated_conjecture,
( ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| 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(spm,[status(thm)],[c_0_19,c_0_30]),c_0_31])]) ).
cnf(c_0_33,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_34,plain,
! [X136,X137] :
( ssList(app(X136,X137))
| ~ ssList(X137)
| ~ ssList(X136) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| 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_32,c_0_24]),c_0_25]),c_0_33])]) ).
cnf(c_0_36,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_37,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ ssList(X40)
| cyclefreeP(X40)
| leq(esk11_1(X40),esk10_1(X40)) )
& ( ~ ssList(X40)
| cyclefreeP(X40)
| leq(esk10_1(X40),esk11_1(X40)) )
& ( ~ ssList(X40)
| cyclefreeP(X40)
| app(app(esk12_1(X40),cons(esk10_1(X40),esk13_1(X40))),cons(esk11_1(X40),esk14_1(X40))) = X40 )
& ( ~ ssList(X40)
| cyclefreeP(X40)
| ssList(esk14_1(X40)) )
& ( ~ ssList(X40)
| cyclefreeP(X40)
| ssList(esk13_1(X40)) )
& ( ~ ssList(X40)
| cyclefreeP(X40)
| ssList(esk12_1(X40)) )
& ( ~ ssList(X40)
| cyclefreeP(X40)
| ssItem(esk11_1(X40)) )
& ( ~ ssList(X40)
| cyclefreeP(X40)
| ssItem(esk10_1(X40)) )
& ( ~ ssList(X40)
| ~ leq(X42,X41)
| ~ leq(X41,X42)
| app(app(X43,cons(X41,X44)),cons(X42,X45)) != X40
| ~ ssList(X45)
| ~ ssList(X44)
| ~ ssList(X43)
| ~ ssItem(X42)
| ~ ssItem(X41)
| ~ cyclefreeP(X40) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax8])])])])])]) ).
cnf(c_0_38,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| 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(spm,[status(thm)],[c_0_35,c_0_36]),c_0_21])]) ).
fof(c_0_39,plain,
! [X73,X74,X75,X76,X77,X78] :
( ( ~ ssList(X73)
| totalorderedP(X73)
| ~ leq(esk25_1(X73),esk26_1(X73)) )
& ( ~ ssList(X73)
| totalorderedP(X73)
| app(app(esk27_1(X73),cons(esk25_1(X73),esk28_1(X73))),cons(esk26_1(X73),esk29_1(X73))) = X73 )
& ( ~ ssList(X73)
| totalorderedP(X73)
| ssList(esk29_1(X73)) )
& ( ~ ssList(X73)
| totalorderedP(X73)
| ssList(esk28_1(X73)) )
& ( ~ ssList(X73)
| totalorderedP(X73)
| ssList(esk27_1(X73)) )
& ( ~ ssList(X73)
| totalorderedP(X73)
| ssItem(esk26_1(X73)) )
& ( ~ ssList(X73)
| totalorderedP(X73)
| ssItem(esk25_1(X73)) )
& ( ~ ssList(X73)
| leq(X74,X75)
| app(app(X76,cons(X74,X77)),cons(X75,X78)) != X73
| ~ ssList(X78)
| ~ ssList(X77)
| ~ ssList(X76)
| ~ ssItem(X75)
| ~ ssItem(X74)
| ~ totalorderedP(X73) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])])])])]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| ~ leq(X3,X2)
| ~ leq(X2,X3)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ cyclefreeP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,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_38,c_0_24]),c_0_20]),c_0_26])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_43,plain,
! [X202] :
( cyclefreeP(cons(X202,nil))
| ~ ssItem(X202) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax59])])]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ totalorderedP(X1)
| leq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_45,plain,
! [X205] :
( totalorderedP(cons(X205,nil))
| ~ ssItem(X205) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])])]) ).
cnf(c_0_46,plain,
( ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| ~ cyclefreeP(app(app(X3,cons(X2,X4)),cons(X1,X5)))
| ~ leq(X2,X1)
| ~ leq(X1,X2) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_47,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_41,c_0_29]),c_0_31]),c_0_33])]) ).
cnf(c_0_48,negated_conjecture,
leq(esk53_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_42,c_0_16]) ).
cnf(c_0_50,plain,
( ~ ssItem(X1)
| cyclefreeP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( cons(esk58_0,nil) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,negated_conjecture,
( ssItem(esk58_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_53,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ totalorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| leq(X1,X2) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,negated_conjecture,
( ~ cyclefreeP(esk50_0)
| ~ leq(esk52_0,esk53_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_46,c_0_47]),c_0_48]),c_0_49]),c_0_31]),c_0_20]),c_0_21]),c_0_33]),c_0_26])]) ).
cnf(c_0_56,negated_conjecture,
( cyclefreeP(esk50_0)
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( ~ totalorderedP(esk50_0)
| leq(esk52_0,esk53_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_53,c_0_47]),c_0_49]),c_0_31]),c_0_20]),c_0_21]),c_0_33]),c_0_26])]) ).
cnf(c_0_58,negated_conjecture,
( totalorderedP(esk50_0)
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_51]),c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( ~ leq(esk52_0,esk53_0)
| esk50_0 = nil ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_61,plain,
totalorderedP(nil),
inference(split_conjunct,[status(thm)],[ax66]) ).
cnf(c_0_62,plain,
cyclefreeP(nil),
inference(split_conjunct,[status(thm)],[ax60]) ).
cnf(c_0_63,negated_conjecture,
leq(esk52_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_60]),c_0_61])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_60]),c_0_62])]),c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC152+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 07:59:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.79/0.54 % Version: 3.5.1
% 0.79/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.79/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.79/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.79/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.79/0.54 % Starting sh5l with 300s (1) cores
% 0.79/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2088066 completed with status 0
% 0.79/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.79/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.79/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.79/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.79/0.54 % No SInE strategy applied
% 0.79/0.54 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.79/0.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.79/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.79/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.79/0.54 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.79/0.54 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.79/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.79/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2088074 completed with status 0
% 0.79/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.79/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.79/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.79/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.79/0.54 % No SInE strategy applied
% 0.79/0.54 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.79/0.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.79/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.79/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.79/0.54 % Preprocessing time : 0.004 s
% 0.79/0.54 % Presaturation interreduction done
% 0.79/0.54
% 0.79/0.54 % Proof found!
% 0.79/0.54 % SZS status Theorem
% 0.79/0.54 % SZS output start CNFRefutation
% See solution above
% 0.79/0.54 % Parsed axioms : 96
% 0.79/0.54 % Removed by relevancy pruning/SinE : 0
% 0.79/0.54 % Initial clauses : 214
% 0.79/0.54 % Removed in clause preprocessing : 2
% 0.79/0.54 % Initial clauses in saturation : 212
% 0.79/0.54 % Processed clauses : 789
% 0.79/0.54 % ...of these trivial : 4
% 0.79/0.54 % ...subsumed : 129
% 0.79/0.54 % ...remaining for further processing : 655
% 0.79/0.54 % Other redundant clauses eliminated : 69
% 0.79/0.54 % Clauses deleted for lack of memory : 0
% 0.79/0.54 % Backward-subsumed : 19
% 0.79/0.54 % Backward-rewritten : 166
% 0.79/0.54 % Generated clauses : 1699
% 0.79/0.54 % ...of the previous two non-redundant : 1599
% 0.79/0.54 % ...aggressively subsumed : 0
% 0.79/0.54 % Contextual simplify-reflections : 90
% 0.79/0.54 % Paramodulations : 1627
% 0.79/0.54 % Factorizations : 0
% 0.79/0.54 % NegExts : 0
% 0.79/0.54 % Equation resolutions : 74
% 0.79/0.54 % Disequality decompositions : 0
% 0.79/0.54 % Total rewrite steps : 1549
% 0.79/0.54 % ...of those cached : 1507
% 0.79/0.54 % Propositional unsat checks : 0
% 0.79/0.54 % Propositional check models : 0
% 0.79/0.54 % Propositional check unsatisfiable : 0
% 0.79/0.54 % Propositional clauses : 0
% 0.79/0.54 % Propositional clauses after purity: 0
% 0.79/0.54 % Propositional unsat core size : 0
% 0.79/0.54 % Propositional preprocessing time : 0.000
% 0.79/0.54 % Propositional encoding time : 0.000
% 0.79/0.54 % Propositional solver time : 0.000
% 0.79/0.54 % Success case prop preproc time : 0.000
% 0.79/0.54 % Success case prop encoding time : 0.000
% 0.79/0.54 % Success case prop solver time : 0.000
% 0.79/0.54 % Current number of processed clauses : 241
% 0.79/0.54 % Positive orientable unit clauses : 32
% 0.79/0.54 % Positive unorientable unit clauses: 0
% 0.79/0.54 % Negative unit clauses : 2
% 0.79/0.54 % Non-unit-clauses : 207
% 0.79/0.54 % Current number of unprocessed clauses: 1213
% 0.79/0.54 % ...number of literals in the above : 6649
% 0.79/0.54 % Current number of archived formulas : 0
% 0.79/0.54 % Current number of archived clauses : 391
% 0.79/0.54 % Clause-clause subsumption calls (NU) : 29703
% 0.79/0.54 % Rec. Clause-clause subsumption calls : 10359
% 0.79/0.54 % Non-unit clause-clause subsumptions : 213
% 0.79/0.54 % Unit Clause-clause subsumption calls : 134
% 0.79/0.54 % Rewrite failures with RHS unbound : 0
% 0.79/0.54 % BW rewrite match attempts : 34
% 0.79/0.54 % BW rewrite match successes : 15
% 0.79/0.54 % Condensation attempts : 0
% 0.79/0.54 % Condensation successes : 0
% 0.79/0.54 % Termbank termtop insertions : 56335
% 0.79/0.54 % Search garbage collected termcells : 4467
% 0.79/0.54
% 0.79/0.54 % -------------------------------------------------
% 0.79/0.54 % User time : 0.114 s
% 0.79/0.54 % System time : 0.005 s
% 0.79/0.54 % Total time : 0.119 s
% 0.79/0.54 % Maximum resident set size: 4280 pages
% 0.79/0.54
% 0.79/0.54 % -------------------------------------------------
% 0.79/0.54 % User time : 0.480 s
% 0.79/0.54 % System time : 0.036 s
% 0.79/0.54 % Total time : 0.516 s
% 0.79/0.54 % Maximum resident set size: 4608 pages
% 0.79/0.54 % E exiting
%------------------------------------------------------------------------------