%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC368+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 02:44:07 PM UTC 2026
% Result : Timeout 289.36s 37.65s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 21 unt; 0 def)
% Number of atoms : 356 ( 113 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 457 ( 185 ~; 187 |; 39 &)
% ( 3 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 70 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ( ? [X6] :
( leq(X6,X5)
& memberP(X4,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X4,X5)
| cons(X5,nil) != X3 ) ) )
| segmentP(X2,X1)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
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(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(app(X3,X2),X4) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(X3,cons(X2,X4)) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ( ? [X6] :
( leq(X6,X5)
& memberP(X4,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X4,X5)
| cons(X5,nil) != X3 ) ) )
| segmentP(X2,X1)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_14,plain,
! [X86,X87,X88] :
( X88 = X86
| app(X88,X87) != app(X86,X87)
| ~ ssList(X88)
| ~ ssList(X87)
| ~ ssList(X86) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_15,plain,
! [X92,X93,X94] :
( app(app(X92,X93),X94) = app(X92,app(X93,X94))
| ~ ssList(X94)
| ~ ssList(X93)
| ~ ssList(X92) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_16,plain,
! [X83,X84] :
( ssList(app(X83,X84))
| ~ ssList(X84)
| ~ ssList(X83) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_17,plain,
! [X85] :
( app(nil,X85) = X85
| ~ ssList(X85) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X5] :
( ssItem(X5)
=> ( ? [X6] :
( leq(X6,X5)
& memberP(X4,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X4,X5)
| cons(X5,nil) != X3 ) ) )
| segmentP(X2,X1)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_24,negated_conjecture,
! [X12] :
( ( ~ leq(X12,esk5_0)
| ~ memberP(esk4_0,X12)
| esk5_0 = X12
| ~ ssItem(X12)
| nil = esk3_0 )
& ( ~ leq(X12,esk5_0)
| ~ memberP(esk4_0,X12)
| esk5_0 = X12
| ~ ssItem(X12)
| nil = esk4_0 )
& ( memberP(esk4_0,esk5_0)
| nil = esk3_0 )
& ( memberP(esk4_0,esk5_0)
| nil = esk4_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 )
& ( ssItem(esk5_0)
| nil = esk3_0 )
& ( ssItem(esk5_0)
| nil = esk4_0 )
& ~ segmentP(esk2_0,esk1_0)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_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_18])])])])])]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X4)
| app(X1,X4) != app(X2,app(X3,X4))
| X1 = app(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X95,X96] :
( ( ~ ssList(X95)
| ~ ssList(X96)
| nil = app(X95,X96)
| nil != X95
| nil != X96 )
& ( ~ ssList(X95)
| ~ ssList(X96)
| nil != app(X95,X96)
| nil = X95 )
& ( ~ ssList(X95)
| ~ ssList(X96)
| nil != app(X95,X96)
| nil = X96 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_30,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,X3) != app(X2,X3)
| X1 = app(nil,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,plain,
! [X89,X90,X91] :
( X91 = X89
| app(X90,X91) != app(X90,X89)
| ~ ssList(X91)
| ~ ssList(X90)
| ~ ssList(X89) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_33,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_34,plain,
! [X97] :
( app(X97,nil) = X97
| ~ ssList(X97) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_35,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_37,plain,
! [X71,X72,X73,X74] :
( segmentP(app(app(X73,X71),X74),X72)
| ~ segmentP(X71,X72)
| ~ ssList(X74)
| ~ ssList(X73)
| ~ ssList(X72)
| ~ ssList(X71) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_38,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,esk4_0) != app(X2,esk4_0)
| X1 = app(nil,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_39,plain,
! [X57,X58] :
( cons(X58,X57) = app(cons(X58,nil),X57)
| ~ ssItem(X58)
| ~ ssList(X57) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_40,plain,
! [X59,X60,X63,X64] :
( ( ~ ssList(X59)
| ~ ssList(X60)
| segmentP(X59,X60)
| app(app(X63,X60),X64) != X59
| ~ ssList(X64)
| ~ ssList(X63) )
& ( ~ ssList(X59)
| ~ ssList(X60)
| ~ segmentP(X59,X60)
| app(app(esk12_2(X59,X60),X60),esk13_2(X59,X60)) = X59 )
& ( ~ ssList(X59)
| ~ ssList(X60)
| ~ segmentP(X59,X60)
| ssList(esk13_2(X59,X60)) )
& ( ~ ssList(X59)
| ~ ssList(X60)
| ~ segmentP(X59,X60)
| ssList(esk12_2(X59,X60)) ) ),
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)],[ax7])])])])])]) ).
cnf(c_0_41,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_33])]),c_0_23])]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_21]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( ~ ssList(X1)
| app(esk4_0,esk4_0) != app(X1,esk4_0)
| app(nil,X1) = esk4_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_31]) ).
cnf(c_0_48,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_50,negated_conjecture,
( ssItem(esk5_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_51,plain,
! [X31,X32,X35,X36] :
( ( ~ ssList(X31)
| ~ ssItem(X32)
| memberP(X31,X32)
| app(X35,cons(X32,X36)) != X31
| ~ ssList(X36)
| ~ ssList(X35) )
& ( ~ ssList(X31)
| ~ ssItem(X32)
| ~ memberP(X31,X32)
| app(esk8_2(X31,X32),cons(X32,esk9_2(X31,X32))) = X31 )
& ( ~ ssList(X31)
| ~ ssItem(X32)
| ~ memberP(X31,X32)
| ssList(esk9_2(X31,X32)) )
& ( ~ ssList(X31)
| ~ ssItem(X32)
| ~ memberP(X31,X32)
| ssList(esk8_2(X31,X32)) ) ),
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)],[ax3])])])])])]) ).
cnf(c_0_52,plain,
( ~ ssList(X4)
| ~ ssList(X3)
| app(app(X1,X3),X2) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_23])]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_20]),c_0_23])]),c_0_21]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_23])]) ).
cnf(c_0_56,negated_conjecture,
( ~ ssList(X1)
| app(esk3_0,esk4_0) != app(X1,esk4_0)
| app(nil,X1) = esk3_0 ),
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_57,negated_conjecture,
~ segmentP(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_22]),c_0_23])]) ).
cnf(c_0_59,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_31])]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssList(X1)
| esk3_0 = nil
| cons(esk5_0,X1) = app(esk3_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk9_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| app(X1,nil) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_23])]),c_0_55]) ).
cnf(c_0_64,negated_conjecture,
app(nil,esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_56]),c_0_45])]) ).
cnf(c_0_65,negated_conjecture,
~ segmentP(esk4_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_28]),c_0_36]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| segmentP(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_31]),c_0_23])]) ).
cnf(c_0_67,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| esk3_0 = nil
| cons(esk5_0,esk9_2(X1,X2)) = app(esk3_0,esk9_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,negated_conjecture,
( memberP(esk4_0,esk5_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_69,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_22]),c_0_23])]),c_0_21]) ).
cnf(c_0_70,negated_conjecture,
( esk3_0 != nil
| app(esk3_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_45])]) ).
cnf(c_0_71,negated_conjecture,
~ segmentP(nil,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_45])]) ).
cnf(c_0_72,negated_conjecture,
( esk3_0 = nil
| cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_31])]),c_0_50]) ).
cnf(c_0_73,negated_conjecture,
esk3_0 != nil,
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_45]),c_0_23])]),c_0_71]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(esk8_2(X1,X2),cons(X2,esk9_2(X1,X2))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_75,negated_conjecture,
cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0)),
inference(sr,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
memberP(esk4_0,esk5_0),
inference(sr,[status(thm)],[c_0_68,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_50,c_0_73]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(X1,app(X2,X3)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_20]),c_0_44]) ).
cnf(c_0_79,negated_conjecture,
app(esk8_2(esk4_0,esk5_0),app(esk3_0,esk9_2(esk4_0,esk5_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_31]),c_0_77])]) ).
cnf(c_0_80,negated_conjecture,
( ~ ssList(esk8_2(esk4_0,esk5_0))
| ~ ssList(esk9_2(esk4_0,esk5_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_45])]),c_0_65]) ).
cnf(c_0_81,negated_conjecture,
~ ssList(esk8_2(esk4_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_61]),c_0_76]),c_0_31]),c_0_77])]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_76]),c_0_31]),c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC368+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n019.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 08:19:20 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 289.36/37.65 % Version: 3.5.1
% 289.36/37.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 289.36/37.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 289.36/37.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 289.36/37.65 % Starting new_bool_3 with 300s (1) cores
% 289.36/37.65 % Starting new_bool_1 with 300s (1) cores
% 289.36/37.65 % Starting sh5l with 300s (1) cores
% 289.36/37.65 % new_bool_3 with pid 2120893 completed with status 0
% 289.36/37.65 % Result found by new_bool_3
% 289.36/37.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 289.36/37.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 289.36/37.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 289.36/37.65 % Starting new_bool_3 with 300s (1) cores
% 289.36/37.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 289.36/37.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 289.36/37.65 % Search class: FGHSF-FFMM21-MFFFFFNN
% 289.36/37.65 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 289.36/37.65 % Starting SubtermCWHack with 31s (1) cores
% 289.36/37.65 % SubtermCWHack with pid 2120899 completed with status 8
% 289.36/37.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 289.36/37.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2120961 completed with status 0
% 289.36/37.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 289.36/37.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 289.36/37.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 289.36/37.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 289.36/37.65 % Starting new_bool_3 with 300s (1) cores
% 289.36/37.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 289.36/37.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 289.36/37.65 % Search class: FGHSF-FFMM21-MFFFFFNN
% 289.36/37.65 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 289.36/37.65 % Starting SubtermCWHack with 31s (1) cores
% 289.36/37.65 % SubtermCWHack with pid 2120899 completed with status 8
% 289.36/37.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 289.36/37.65 % Preprocessing time : 0.004 s
% 289.36/37.65 % Presaturation interreduction done
% 289.36/37.65
% 289.36/37.65 % Proof found!
% 289.36/37.65 % SZS status Theorem
% 289.36/37.65 % SZS output start CNFRefutation
% See solution above
% 289.36/37.65 % Parsed axioms : 96
% 289.36/37.65 % Removed by relevancy pruning/SinE : 59
% 289.36/37.65 % Initial clauses : 71
% 289.36/37.65 % Removed in clause preprocessing : 0
% 289.36/37.65 % Initial clauses in saturation : 71
% 289.36/37.65 % Processed clauses : 12241
% 289.36/37.65 % ...of these trivial : 494
% 289.36/37.65 % ...subsumed : 8543
% 289.36/37.65 % ...remaining for further processing : 3204
% 289.36/37.65 % Other redundant clauses eliminated : 97
% 289.36/37.65 % Clauses deleted for lack of memory : 0
% 289.36/37.65 % Backward-subsumed : 433
% 289.36/37.65 % Backward-rewritten : 424
% 289.36/37.65 % Generated clauses : 146394
% 289.36/37.65 % ...of the previous two non-redundant : 142199
% 289.36/37.65 % ...aggressively subsumed : 0
% 289.36/37.65 % Contextual simplify-reflections : 1104
% 289.36/37.65 % Paramodulations : 145971
% 289.36/37.65 % Factorizations : 2
% 289.36/37.65 % NegExts : 0
% 289.36/37.65 % Equation resolutions : 137
% 289.36/37.65 % Disequality decompositions : 0
% 289.36/37.65 % Total rewrite steps : 96198
% 289.36/37.65 % ...of those cached : 95940
% 289.36/37.65 % Propositional unsat checks : 0
% 289.36/37.65 % Propositional check models : 0
% 289.36/37.65 % Propositional check unsatisfiable : 0
% 289.36/37.65 % Propositional clauses : 0
% 289.36/37.65 % Propositional clauses after purity: 0
% 289.36/37.65 % Propositional unsat core size : 0
% 289.36/37.65 % Propositional preprocessing time : 0.000
% 289.36/37.65 % Propositional encoding time : 0.000
% 289.36/37.65 % Propositional solver time : 0.000
% 289.36/37.65 % Success case prop preproc time : 0.000
% 289.36/37.65 % Success case prop encoding time : 0.000
% 289.36/37.65 % Success case prop solver time : 0.000
% 289.36/37.65 % Current number of processed clauses : 1989
% 289.36/37.65 % Positive orientable unit clauses : 290
% 289.36/37.65 % Positive unorientable unit clauses: 0
% 289.36/37.65 % Negative unit clauses : 235
% 289.36/37.65 % Non-unit-clauses : 1464
% 289.36/37.65 % Current number of unprocessed clauses: 123743
% 289.36/37.65 % ...number of literals in the above : 670641
% 289.36/37.65 % Current number of archived formulas : 0
% 289.36/37.65 % Current number of archived clauses : 1209
% 289.36/37.65 % Clause-clause subsumption calls (NU) : 379177
% 289.36/37.65 % Rec. Clause-clause subsumption calls : 128399
% 289.36/37.65 % Non-unit clause-clause subsumptions : 7019
% 289.36/37.65 % Unit Clause-clause subsumption calls : 22439
% 289.36/37.65 % Rewrite failures with RHS unbound : 0
% 289.36/37.65 % BW rewrite match attempts : 2261
% 289.36/37.65 % BW rewrite match successes : 105
% 289.36/37.65 % Condensation attempts : 0
% 289.36/37.65 % Condensation successes : 0
% 289.36/37.65 % Termbank termtop insertions : 3612169
% 289.36/37.65 % Search garbage collected termcells : 1956
% 289.36/37.65
% 289.36/37.65 % -------------------------------------------------
% 289.36/37.65 % User time : 35.238 s
% 289.36/37.65 % System time : 1.280 s
% 289.36/37.65 % Total time : 36.518 s
% 289.36/37.65 % Maximum resident set size: 3760 pages
% 289.36/37.65
% 289.36/37.65 % -------------------------------------------------
% 289.36/37.65 % User time : 35.243 s
% 289.36/37.65 % System time : 1.287 s
% 289.36/37.65 % Total time : 36.529 s
% 289.36/37.65 % Maximum resident set size: 4864 pages
% 289.36/37.65 % E exiting
%------------------------------------------------------------------------------