%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC078+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 : n009.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 02:42:54 PM UTC 2026
% Result : Theorem 75.06s 12.63s
% Output : CNFRefutation 75.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 110 ( 26 unt; 0 def)
% Number of atoms : 422 ( 102 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 522 ( 210 ~; 206 |; 45 &)
% ( 6 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 169 ( 0 sgn 92 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax51) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( app(X3,X2) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(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(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X4,X6)
| cons(X6,nil) != X3 ) ) )
| ( nil = X1
& nil = X2 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_21,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_22,negated_conjecture,
! [X255] :
( ( memberP(esk51_0,esk52_0)
| nil = esk50_0 )
& ( memberP(esk51_0,esk52_0)
| nil = esk51_0 )
& ( cons(esk52_0,nil) = esk50_0
| nil = esk50_0 )
& ( cons(esk52_0,nil) = esk50_0
| nil = esk51_0 )
& ( ssItem(esk52_0)
| nil = esk50_0 )
& ( ssItem(esk52_0)
| nil = esk51_0 )
& ( nil != esk48_0
| nil != esk49_0 )
& ( ~ segmentP(esk48_0,X255)
| ~ segmentP(esk49_0,X255)
| ~ neq(X255,nil)
| ~ ssList(X255) )
& 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_20])])])])])]) ).
fof(c_0_23,plain,
! [X122,X123] :
( nil != cons(X123,X122)
| ~ ssItem(X123)
| ~ ssList(X122) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_24,negated_conjecture,
( nil != esk48_0
| nil != esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( cons(esk52_0,nil) = esk50_0
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_30,negated_conjecture,
( ssItem(esk52_0)
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( esk51_0 != nil
| esk50_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
fof(c_0_32,plain,
! [X179,X180,X181] :
( rearsegP(app(X181,X179),X180)
| ~ rearsegP(X179,X180)
| ~ ssList(X181)
| ~ ssList(X180)
| ~ ssList(X179) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])])]) ).
fof(c_0_33,plain,
! [X182] :
( rearsegP(X182,nil)
| ~ ssList(X182) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])])]) ).
fof(c_0_34,plain,
! [X11,X12,X15,X16] :
( ( ~ ssList(X11)
| ~ ssItem(X12)
| memberP(X11,X12)
| app(X15,cons(X12,X16)) != X11
| ~ ssList(X16)
| ~ ssList(X15) )
& ( ~ ssList(X11)
| ~ ssItem(X12)
| ~ memberP(X11,X12)
| app(esk3_2(X11,X12),cons(X12,esk4_2(X11,X12))) = X11 )
& ( ~ ssList(X11)
| ~ ssItem(X12)
| ~ memberP(X11,X12)
| ssList(esk4_2(X11,X12)) )
& ( ~ ssList(X11)
| ~ ssItem(X12)
| ~ memberP(X11,X12)
| ssList(esk3_2(X11,X12)) ) ),
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_35,negated_conjecture,
( memberP(esk51_0,esk52_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_36,negated_conjecture,
esk50_0 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),c_0_30]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_38,negated_conjecture,
( ssItem(esk52_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_39,plain,
( ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| rearsegP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_44,negated_conjecture,
ssItem(esk52_0),
inference(sr,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(app(X1,X2),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29])]) ).
cnf(c_0_47,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44])]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_42]),c_0_43]),c_0_44])]) ).
fof(c_0_49,plain,
! [X111,X112] :
( ssList(cons(X112,X111))
| ~ ssItem(X112)
| ~ ssList(X111) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_50,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_51,plain,
! [X24,X25,X27] :
( ( ~ ssList(X24)
| ~ ssList(X25)
| rearsegP(X24,X25)
| app(X27,X25) != X24
| ~ ssList(X27) )
& ( ~ ssList(X24)
| ~ ssList(X25)
| ~ rearsegP(X24,X25)
| app(esk7_2(X24,X25),X25) = X24 )
& ( ~ ssList(X24)
| ~ ssList(X25)
| ~ rearsegP(X24,X25)
| ssList(esk7_2(X24,X25)) ) ),
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)],[ax6])])])])])]) ).
cnf(c_0_52,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0)))
| rearsegP(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_53,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
ssList(esk4_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_43]),c_0_44])]) ).
fof(c_0_55,plain,
! [X28,X29,X32,X33] :
( ( ~ ssList(X28)
| ~ ssList(X29)
| segmentP(X28,X29)
| app(app(X32,X29),X33) != X28
| ~ ssList(X33)
| ~ ssList(X32) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| app(app(esk8_2(X28,X29),X29),esk9_2(X28,X29)) = X28 )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk9_2(X28,X29)) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ segmentP(X28,X29)
| ssList(esk8_2(X28,X29)) ) ),
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])])])])])]) ).
fof(c_0_56,plain,
! [X135] :
( app(nil,X135) = X135
| ~ ssList(X135) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_57,plain,
! [X220,X221] :
( cons(X221,X220) = app(cons(X221,nil),X220)
| ~ ssItem(X221)
| ~ ssList(X220) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_58,negated_conjecture,
( cons(esk52_0,nil) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_59,plain,
! [X227] :
( app(X227,nil) = X227
| ~ ssList(X227) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_60,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(esk7_2(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_44])]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ssList(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,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_55]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_65,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,negated_conjecture,
cons(esk52_0,nil) = esk50_0,
inference(sr,[status(thm)],[c_0_58,c_0_36]) ).
cnf(c_0_67,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_68,plain,
! [X130,X131] :
( ssList(app(X130,X131))
| ~ ssList(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_69,plain,
! [X20,X21,X23] :
( ( ~ ssList(X20)
| ~ ssList(X21)
| frontsegP(X20,X21)
| app(X21,X23) != X20
| ~ ssList(X23) )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| app(X21,esk6_2(X20,X21)) = X20 )
& ( ~ ssList(X20)
| ~ ssList(X21)
| ~ frontsegP(X20,X21)
| ssList(esk6_2(X20,X21)) ) ),
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)],[ax5])])])])])]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_71,negated_conjecture,
app(esk7_2(esk51_0,nil),nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_29]),c_0_43])]) ).
cnf(c_0_72,negated_conjecture,
ssList(esk7_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_29]),c_0_43])]) ).
cnf(c_0_73,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(X2,X3) != X1
| segmentP(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_29])]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(X1)
| app(esk50_0,X1) = cons(esk52_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_44])]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_67,c_0_25]) ).
cnf(c_0_76,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,negated_conjecture,
esk7_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
fof(c_0_79,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_80,plain,
! [X190,X191,X192,X193] :
( segmentP(app(app(X192,X190),X193),X191)
| ~ segmentP(X190,X191)
| ~ ssList(X193)
| ~ ssList(X192)
| ~ ssList(X191)
| ~ ssList(X190) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_81,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| cons(esk52_0,X2) != X1
| segmentP(X1,esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssList(X1)
| ssList(cons(esk52_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_74]),c_0_75])]) ).
fof(c_0_83,plain,
! [X217,X218,X219] :
( X219 = X217
| app(X218,X219) != app(X218,X217)
| ~ ssList(X219)
| ~ ssList(X218)
| ~ ssList(X217) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_84,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_76]) ).
cnf(c_0_85,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(rw,[status(thm)],[c_0_71,c_0_78]) ).
cnf(c_0_86,negated_conjecture,
( ~ segmentP(esk48_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_87,plain,
! [X109,X110] :
( ( ~ ssList(X109)
| ~ ssList(X110)
| neq(X109,X110)
| X109 = X110 )
& ( ~ ssList(X109)
| ~ ssList(X110)
| X109 != X110
| ~ neq(X109,X110) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])])])]) ).
cnf(c_0_88,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_80]) ).
cnf(c_0_89,negated_conjecture,
( ~ ssList(X1)
| segmentP(cons(esk52_0,X1),esk50_0) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_81]),c_0_82]) ).
fof(c_0_90,plain,
! [X163] :
( frontsegP(X163,X163)
| ~ ssList(X163) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).
cnf(c_0_91,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_92,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_93,negated_conjecture,
frontsegP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_43]),c_0_29])]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_95,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ segmentP(esk50_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_25]),c_0_26]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_97,plain,
! [X189] :
( segmentP(X189,X189)
| ~ ssList(X189) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_98,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(app(app(X1,cons(esk52_0,X2)),X3),esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_75])]),c_0_82]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_100,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != X2
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_70]),c_0_29])]) ).
cnf(c_0_101,negated_conjecture,
app(esk51_0,esk6_2(esk51_0,esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_43])]) ).
cnf(c_0_102,negated_conjecture,
ssList(esk6_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_93]),c_0_43])]) ).
cnf(c_0_103,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk51_0,X1)
| ~ segmentP(esk50_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_29])]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(esk51_0,X1),esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_47]),c_0_48]),c_0_54])]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| app(X1,esk6_2(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_92,c_0_99]) ).
cnf(c_0_107,negated_conjecture,
esk6_2(esk51_0,esk51_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_43]),c_0_102])]) ).
cnf(c_0_108,negated_conjecture,
~ segmentP(esk51_0,esk50_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_75])]),c_0_36]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_29]),c_0_43])]),c_0_108]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC078+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 07:54:12 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 75.06/12.63 % Version: 3.5.1
% 75.06/12.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 75.06/12.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 75.06/12.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 75.06/12.63 % Starting new_bool_3 with 300s (1) cores
% 75.06/12.63 % Starting new_bool_1 with 300s (1) cores
% 75.06/12.63 % Starting sh5l with 300s (1) cores
% 75.06/12.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1250821 completed with status 0
% 75.06/12.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 75.06/12.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 75.06/12.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 75.06/12.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 75.06/12.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 75.06/12.63 % No SInE strategy applied
% 75.06/12.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 75.06/12.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 75.06/12.63 % Starting SubtermCWHack with 136s (1) cores
% 75.06/12.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 75.06/12.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 75.06/12.63 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 75.06/12.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 75.06/12.63 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 1250830 completed with status 0
% 75.06/12.63 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 75.06/12.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 75.06/12.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 75.06/12.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 75.06/12.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 75.06/12.63 % No SInE strategy applied
% 75.06/12.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 75.06/12.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 75.06/12.63 % Starting SubtermCWHack with 136s (1) cores
% 75.06/12.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 75.06/12.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 75.06/12.63 % Preprocessing time : 0.002 s
% 75.06/12.63
% 75.06/12.63 % Proof found!
% 75.06/12.63 % SZS status Theorem
% 75.06/12.63 % SZS output start CNFRefutation
% See solution above
% 75.06/12.64 % Parsed axioms : 96
% 75.06/12.64 % Removed by relevancy pruning/SinE : 0
% 75.06/12.64 % Initial clauses : 204
% 75.06/12.64 % Removed in clause preprocessing : 2
% 75.06/12.64 % Initial clauses in saturation : 202
% 75.06/12.64 % Processed clauses : 26093
% 75.06/12.64 % ...of these trivial : 308
% 75.06/12.64 % ...subsumed : 17675
% 75.06/12.64 % ...remaining for further processing : 8110
% 75.06/12.64 % Other redundant clauses eliminated : 889
% 75.06/12.64 % Clauses deleted for lack of memory : 0
% 75.06/12.64 % Backward-subsumed : 752
% 75.06/12.64 % Backward-rewritten : 882
% 75.06/12.64 % Generated clauses : 189673
% 75.06/12.64 % ...of the previous two non-redundant : 173481
% 75.06/12.64 % ...aggressively subsumed : 0
% 75.06/12.64 % Contextual simplify-reflections : 2961
% 75.06/12.64 % Paramodulations : 188144
% 75.06/12.64 % Factorizations : 1
% 75.06/12.64 % NegExts : 0
% 75.06/12.64 % Equation resolutions : 1479
% 75.06/12.64 % Disequality decompositions : 0
% 75.06/12.64 % Total rewrite steps : 240540
% 75.06/12.64 % ...of those cached : 239602
% 75.06/12.64 % Propositional unsat checks : 0
% 75.06/12.64 % Propositional check models : 0
% 75.06/12.64 % Propositional check unsatisfiable : 0
% 75.06/12.64 % Propositional clauses : 0
% 75.06/12.64 % Propositional clauses after purity: 0
% 75.06/12.64 % Propositional unsat core size : 0
% 75.06/12.64 % Propositional preprocessing time : 0.000
% 75.06/12.64 % Propositional encoding time : 0.000
% 75.06/12.64 % Propositional solver time : 0.000
% 75.06/12.64 % Success case prop preproc time : 0.000
% 75.06/12.64 % Success case prop encoding time : 0.000
% 75.06/12.64 % Success case prop solver time : 0.000
% 75.06/12.64 % Current number of processed clauses : 6421
% 75.06/12.64 % Positive orientable unit clauses : 1100
% 75.06/12.64 % Positive unorientable unit clauses: 0
% 75.06/12.64 % Negative unit clauses : 248
% 75.06/12.64 % Non-unit-clauses : 5073
% 75.06/12.64 % Current number of unprocessed clauses: 144761
% 75.06/12.64 % ...number of literals in the above : 943349
% 75.06/12.64 % Current number of archived formulas : 0
% 75.06/12.64 % Current number of archived clauses : 1683
% 75.06/12.64 % Clause-clause subsumption calls (NU) : 2981948
% 75.06/12.64 % Rec. Clause-clause subsumption calls : 1225835
% 75.06/12.64 % Non-unit clause-clause subsumptions : 16148
% 75.06/12.64 % Unit Clause-clause subsumption calls : 55704
% 75.06/12.64 % Rewrite failures with RHS unbound : 0
% 75.06/12.64 % BW rewrite match attempts : 13276
% 75.06/12.64 % BW rewrite match successes : 349
% 75.06/12.64 % Condensation attempts : 0
% 75.06/12.64 % Condensation successes : 0
% 75.06/12.64 % Termbank termtop insertions : 5805084
% 75.06/12.64 % Search garbage collected termcells : 4321
% 75.06/12.64
% 75.06/12.64 % -------------------------------------------------
% 75.06/12.64 % User time : 9.191 s
% 75.06/12.64 % System time : 0.182 s
% 75.06/12.64 % Total time : 9.374 s
% 75.06/12.64 % Maximum resident set size: 4272 pages
% 75.06/12.64
% 75.06/12.64 % -------------------------------------------------
% 75.06/12.64 % User time : 49.368 s
% 75.06/12.64 % System time : 1.304 s
% 75.06/12.64 % Total time : 50.671 s
% 75.06/12.64 % Maximum resident set size: 4864 pages
% 75.06/12.64 % E exiting
%------------------------------------------------------------------------------