%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC394+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 : n002.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 02:44:13 PM UTC 2026
% Result : Theorem 8.80s 2.00s
% Output : CNFRefutation 8.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 27 unt; 0 def)
% Number of atoms : 337 ( 55 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 423 ( 173 ~; 171 |; 33 &)
% ( 5 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 128 ( 0 sgn 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ~ segmentP(X4,X3)
| ~ neq(X3,nil) )
& ( nil != X3
| nil != X4 ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(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(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(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X3,X1)
| memberP(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
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(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ~ segmentP(X4,X3)
| ~ neq(X3,nil) )
& ( nil != X3
| nil != X4 ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ~ segmentP(X4,X3)
| ~ neq(X3,nil) )
& ( nil != X3
| nil != X4 ) )
| ! [X5] :
( ssItem(X5)
=> ( memberP(X2,X5)
| ~ memberP(X1,X5) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_16,negated_conjecture,
( ( nil = esk50_0
| segmentP(esk51_0,esk50_0) )
& ( nil = esk50_0
| neq(esk50_0,nil) )
& ( nil = esk51_0
| segmentP(esk51_0,esk50_0) )
& ( nil = esk51_0
| neq(esk50_0,nil) )
& ~ memberP(esk49_0,esk52_0)
& memberP(esk48_0,esk52_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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
fof(c_0_17,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_18,negated_conjecture,
memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,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_22,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_17]) ).
cnf(c_0_23,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
app(esk3_2(esk50_0,esk52_0),cons(esk52_0,esk4_2(esk50_0,esk52_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk3_2(esk50_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk52_0,esk4_2(esk50_0,esk52_0)))
| esk50_0 != X1
| frontsegP(X1,esk3_2(esk50_0,esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
fof(c_0_31,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_32,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk4_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_33,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_34,plain,
! [X182] :
( rearsegP(X182,nil)
| ~ ssList(X182) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ ssList(cons(esk52_0,esk4_2(esk50_0,esk52_0)))
| frontsegP(esk50_0,esk3_2(esk50_0,esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_24])]) ).
cnf(c_0_36,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk4_2(esk50_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_38,plain,
( ~ rearsegP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
( ~ ssList(X1)
| rearsegP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_42,negated_conjecture,
frontsegP(esk50_0,esk3_2(esk50_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_25])]) ).
cnf(c_0_43,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_44,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_45,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(app(X1,X2),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_46,negated_conjecture,
app(esk3_2(esk50_0,esk52_0),esk6_2(esk50_0,esk3_2(esk50_0,esk52_0))) = esk50_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_24]),c_0_29])]) ).
cnf(c_0_47,negated_conjecture,
ssList(esk6_2(esk50_0,esk3_2(esk50_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_29]),c_0_24])]) ).
fof(c_0_48,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_49,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(esk7_2(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,negated_conjecture,
rearsegP(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_29]),c_0_47])]) ).
cnf(c_0_51,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ssList(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_52,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_53,plain,
! [X222,X223,X224] :
( app(app(X222,X223),X224) = app(X222,app(X223,X224))
| ~ ssList(X224)
| ~ ssList(X223)
| ~ ssList(X222) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,negated_conjecture,
app(esk7_2(esk50_0,nil),nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_40]),c_0_24])]) ).
cnf(c_0_56,negated_conjecture,
ssList(esk7_2(esk50_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_40]),c_0_24])]) ).
fof(c_0_57,plain,
! [X151,X152,X153] :
( ( ~ ssItem(X151)
| ~ ssList(X152)
| ~ ssList(X153)
| memberP(app(X152,X153),X151)
| ~ memberP(X153,X151) )
& ( ~ ssItem(X151)
| ~ ssList(X152)
| ~ ssList(X153)
| memberP(app(X152,X153),X151)
| ~ memberP(X152,X151) )
& ( ~ ssItem(X151)
| ~ ssList(X152)
| ~ ssList(X153)
| memberP(X153,X151)
| memberP(X152,X151)
| ~ memberP(app(X152,X153),X151) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
cnf(c_0_58,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
esk7_2(esk50_0,nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_61,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
app(esk50_0,nil) = esk50_0,
inference(rw,[status(thm)],[c_0_55,c_0_60]) ).
fof(c_0_64,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])])])])])]) ).
cnf(c_0_65,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_66,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_67,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(X1)
| memberP(app(X1,esk50_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(X1)
| ssList(app(X1,esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_40]),c_0_24])]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| app(app(esk8_2(X1,X2),X2),esk9_2(X1,X2)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( nil = esk50_0
| segmentP(esk51_0,esk50_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_72,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
~ memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ssList(esk9_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_76,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| memberP(app(app(X1,esk50_0),X2),esk52_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_25])]),c_0_69]) ).
cnf(c_0_78,negated_conjecture,
( esk50_0 = nil
| app(app(esk8_2(esk51_0,esk50_0),esk50_0),esk9_2(esk51_0,esk50_0)) = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_24]),c_0_72])]) ).
cnf(c_0_79,negated_conjecture,
~ memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_73,c_0_66]) ).
cnf(c_0_80,negated_conjecture,
( ssList(esk8_2(esk51_0,esk50_0))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_71]),c_0_24]),c_0_72])]) ).
cnf(c_0_81,negated_conjecture,
( ssList(esk9_2(esk51_0,esk50_0))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_71]),c_0_24]),c_0_72])]) ).
fof(c_0_82,plain,
! [X157] :
( ~ memberP(nil,X157)
| ~ ssItem(X157) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
cnf(c_0_83,negated_conjecture,
esk50_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_80]),c_0_81]) ).
cnf(c_0_84,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_85,negated_conjecture,
memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_23,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC394+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.64 % Computer : n002.cluster.edu
% 0.15/0.64 % Model : x86_64 x86_64
% 0.15/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.64 % Memory : 8046.5625MB
% 0.15/0.64 % OS : Linux 6.8.0-71-generic
% 0.15/0.64 % CPULimit : 300
% 0.15/0.64 % WCLimit : 300
% 0.15/0.64 % DateTime : Mon Sep 21 08:23:18 UTC 2026
% 0.15/0.64 % CPUTime :
% 0.15/0.65 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.72 Running first-order theorem proving
% 0.21/0.72 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
% 8.80/2.00 % Version: 3.5.1
% 8.80/2.00 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.80/2.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.80/2.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.80/2.00 % Starting new_bool_3 with 300s (1) cores
% 8.80/2.00 % Starting new_bool_1 with 300s (1) cores
% 8.80/2.00 % Starting sh5l with 300s (1) cores
% 8.80/2.00 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2858575 completed with status 0
% 8.80/2.00 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 8.80/2.00 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.80/2.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.80/2.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.80/2.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.80/2.00 % No SInE strategy applied
% 8.80/2.00 % Search class: FGHSF-FSLM21-MFFFFFNN
% 8.80/2.00 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 8.80/2.00 % Starting SubtermCWHack with 136s (1) cores
% 8.80/2.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.80/2.00 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 8.80/2.00 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 8.80/2.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 8.80/2.00 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 2858581 completed with status 0
% 8.80/2.00 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 8.80/2.00 % Preprocessing class: FSLSSMSSSSSNFFN.
% 8.80/2.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.80/2.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 8.80/2.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.80/2.00 % No SInE strategy applied
% 8.80/2.00 % Search class: FGHSF-FSLM21-MFFFFFNN
% 8.80/2.00 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 8.80/2.00 % Starting SubtermCWHack with 136s (1) cores
% 8.80/2.00 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 8.80/2.00 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 8.80/2.00 % Preprocessing time : 0.006 s
% 8.80/2.00
% 8.80/2.00 % Proof found!
% 8.80/2.00 % SZS status Theorem
% 8.80/2.00 % SZS output start CNFRefutation
% See solution above
% 8.80/2.00 % Parsed axioms : 96
% 8.80/2.00 % Removed by relevancy pruning/SinE : 0
% 8.80/2.00 % Initial clauses : 203
% 8.80/2.00 % Removed in clause preprocessing : 2
% 8.80/2.00 % Initial clauses in saturation : 201
% 8.80/2.00 % Processed clauses : 4382
% 8.80/2.00 % ...of these trivial : 9
% 8.80/2.00 % ...subsumed : 2815
% 8.80/2.00 % ...remaining for further processing : 1558
% 8.80/2.00 % Other redundant clauses eliminated : 379
% 8.80/2.00 % Clauses deleted for lack of memory : 0
% 8.80/2.00 % Backward-subsumed : 108
% 8.80/2.00 % Backward-rewritten : 469
% 8.80/2.00 % Generated clauses : 16533
% 8.80/2.00 % ...of the previous two non-redundant : 15263
% 8.80/2.00 % ...aggressively subsumed : 0
% 8.80/2.00 % Contextual simplify-reflections : 947
% 8.80/2.00 % Paramodulations : 15970
% 8.80/2.00 % Factorizations : 0
% 8.80/2.00 % NegExts : 0
% 8.80/2.00 % Equation resolutions : 563
% 8.80/2.00 % Disequality decompositions : 0
% 8.80/2.00 % Total rewrite steps : 9156
% 8.80/2.00 % ...of those cached : 9099
% 8.80/2.00 % Propositional unsat checks : 0
% 8.80/2.00 % Propositional check models : 0
% 8.80/2.00 % Propositional check unsatisfiable : 0
% 8.80/2.00 % Propositional clauses : 0
% 8.80/2.00 % Propositional clauses after purity: 0
% 8.80/2.00 % Propositional unsat core size : 0
% 8.80/2.00 % Propositional preprocessing time : 0.000
% 8.80/2.00 % Propositional encoding time : 0.000
% 8.80/2.00 % Propositional solver time : 0.000
% 8.80/2.00 % Success case prop preproc time : 0.000
% 8.80/2.00 % Success case prop encoding time : 0.000
% 8.80/2.00 % Success case prop solver time : 0.000
% 8.80/2.00 % Current number of processed clauses : 975
% 8.80/2.00 % Positive orientable unit clauses : 40
% 8.80/2.00 % Positive unorientable unit clauses: 0
% 8.80/2.00 % Negative unit clauses : 3
% 8.80/2.00 % Non-unit-clauses : 932
% 8.80/2.00 % Current number of unprocessed clauses: 10906
% 8.80/2.00 % ...number of literals in the above : 81452
% 8.80/2.00 % Current number of archived formulas : 0
% 8.80/2.00 % Current number of archived clauses : 577
% 8.80/2.00 % Clause-clause subsumption calls (NU) : 451728
% 8.80/2.00 % Rec. Clause-clause subsumption calls : 126278
% 8.80/2.00 % Non-unit clause-clause subsumptions : 3833
% 8.80/2.00 % Unit Clause-clause subsumption calls : 1784
% 8.80/2.00 % Rewrite failures with RHS unbound : 0
% 8.80/2.00 % BW rewrite match attempts : 23
% 8.80/2.00 % BW rewrite match successes : 15
% 8.80/2.00 % Condensation attempts : 0
% 8.80/2.00 % Condensation successes : 0
% 8.80/2.00 % Termbank termtop insertions : 385107
% 8.80/2.00 % Search garbage collected termcells : 4259
% 8.80/2.00
% 8.80/2.00 % -------------------------------------------------
% 8.80/2.00 % User time : 1.105 s
% 8.80/2.00 % System time : 0.033 s
% 8.80/2.00 % Total time : 1.139 s
% 8.80/2.00 % Maximum resident set size: 4272 pages
% 8.80/2.00
% 8.80/2.00 % -------------------------------------------------
% 8.80/2.00 % User time : 5.516 s
% 8.80/2.00 % System time : 0.190 s
% 8.80/2.00 % Total time : 5.706 s
% 8.80/2.00 % Maximum resident set size: 4864 pages
% 8.80/2.00 % E exiting
%------------------------------------------------------------------------------