%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:44:51 PM UTC 2026
% Result : Theorem 0.71s 0.82s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 96 ( 38 unt; 0 def)
% Number of atoms : 330 ( 83 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 395 ( 161 ~; 155 |; 33 &)
% ( 5 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 72 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( app(X6,X8) != X4
| app(app(X6,X7),X8) != X3
| ~ ssList(X8) ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( app(X3,X2) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax79) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( app(X6,X8) != X4
| app(app(X6,X7),X8) != X3
| ~ ssList(X8) ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( app(X6,X8) != X4
| app(app(X6,X7),X8) != X3
| ~ ssList(X8) ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_15,plain,
! [X26,X27,X29] :
( ( ~ ssList(X26)
| ~ ssList(X27)
| rearsegP(X26,X27)
| app(X29,X27) != X26
| ~ ssList(X29) )
& ( ~ ssList(X26)
| ~ ssList(X27)
| ~ rearsegP(X26,X27)
| app(esk7_2(X26,X27),X27) = X26 )
& ( ~ ssList(X26)
| ~ ssList(X27)
| ~ rearsegP(X26,X27)
| ssList(esk7_2(X26,X27)) ) ),
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])])])])])]) ).
fof(c_0_16,plain,
! [X132,X133] :
( ssList(app(X132,X133))
| ~ ssList(X133)
| ~ ssList(X132) ),
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,negated_conjecture,
! [X257] :
( app(esk52_0,esk54_0) = esk51_0
& app(app(esk52_0,esk53_0),esk54_0) = esk50_0
& ssList(esk54_0)
& ssList(esk53_0)
& ssList(esk52_0)
& ( ~ segmentP(esk48_0,X257)
| ~ segmentP(esk49_0,X257)
| ~ neq(X257,nil)
| ~ ssList(X257) )
& neq(esk49_0,nil)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
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_14])])])])]) ).
cnf(c_0_18,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X1,X2) != X3
| ~ ssList(X1)
| rearsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
app(app(esk52_0,esk53_0),esk54_0) = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X216,X217,X218] :
( X218 = X216
| app(X218,X217) != app(X216,X217)
| ~ ssList(X218)
| ~ ssList(X217)
| ~ ssList(X216) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| rearsegP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
app(app(esk52_0,esk53_0),esk54_0) = esk48_0,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( ~ ssList(app(esk52_0,esk53_0))
| rearsegP(esk48_0,esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(esk52_0,esk53_0))
| app(X1,esk54_0) != esk48_0
| X1 = app(esk52_0,esk53_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| app(esk7_2(X1,X2),X2) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,negated_conjecture,
rearsegP(esk48_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_28]),c_0_29])]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ssList(esk7_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_35,plain,
! [X30,X31,X34,X35] :
( ( ~ ssList(X30)
| ~ ssList(X31)
| segmentP(X30,X31)
| app(app(X34,X31),X35) != X30
| ~ ssList(X35)
| ~ ssList(X34) )
& ( ~ ssList(X30)
| ~ ssList(X31)
| ~ segmentP(X30,X31)
| app(app(esk8_2(X30,X31),X31),esk9_2(X30,X31)) = X30 )
& ( ~ ssList(X30)
| ~ ssList(X31)
| ~ segmentP(X30,X31)
| ssList(esk9_2(X30,X31)) )
& ( ~ ssList(X30)
| ~ ssList(X31)
| ~ segmentP(X30,X31)
| ssList(esk8_2(X30,X31)) ) ),
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_36,negated_conjecture,
( ~ ssList(X1)
| app(X1,esk54_0) != esk48_0
| X1 = app(esk52_0,esk53_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_28]),c_0_29])]) ).
cnf(c_0_37,negated_conjecture,
app(esk7_2(esk48_0,esk54_0),esk54_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25]),c_0_33])]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk7_2(esk48_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_25]),c_0_33])]) ).
cnf(c_0_39,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_35]) ).
cnf(c_0_40,negated_conjecture,
esk7_2(esk48_0,esk54_0) = app(esk52_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
app(esk52_0,esk54_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_43,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_39]) ).
cnf(c_0_44,negated_conjecture,
ssList(app(esk52_0,esk53_0)),
inference(rw,[status(thm)],[c_0_38,c_0_40]) ).
fof(c_0_45,plain,
! [X229] :
( app(X229,nil) = X229
| ~ ssList(X229) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_46,negated_conjecture,
app(esk52_0,esk54_0) = esk49_0,
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(esk48_0,X1))
| segmentP(app(esk48_0,X1),esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_24]),c_0_25])]),c_0_44])]) ).
cnf(c_0_48,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_50,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(esk49_0,X1))
| segmentP(app(esk49_0,X1),esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_46]),c_0_25]),c_0_29])]) ).
cnf(c_0_51,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_52,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_53,negated_conjecture,
( ~ segmentP(esk48_0,X1)
| ~ segmentP(esk49_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_54,negated_conjecture,
segmentP(esk48_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_33]),c_0_49])]) ).
cnf(c_0_55,negated_conjecture,
segmentP(esk49_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_48]),c_0_51]),c_0_49])]) ).
fof(c_0_56,plain,
! [X111,X112] :
( ( ~ ssList(X111)
| ~ ssList(X112)
| neq(X111,X112)
| X111 = X112 )
& ( ~ ssList(X111)
| ~ ssList(X112)
| X111 != X112
| ~ neq(X111,X112) ) ),
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_52])])])])]) ).
cnf(c_0_57,negated_conjecture,
~ neq(esk54_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_25])]) ).
cnf(c_0_58,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_59,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_49]),c_0_25])]) ).
cnf(c_0_60,negated_conjecture,
app(esk52_0,nil) = esk49_0,
inference(rw,[status(thm)],[c_0_46,c_0_59]) ).
fof(c_0_61,plain,
! [X22,X23,X25] :
( ( ~ ssList(X22)
| ~ ssList(X23)
| frontsegP(X22,X23)
| app(X23,X25) != X22
| ~ ssList(X25) )
& ( ~ ssList(X22)
| ~ ssList(X23)
| ~ frontsegP(X22,X23)
| app(X23,esk6_2(X22,X23)) = X22 )
& ( ~ ssList(X22)
| ~ ssList(X23)
| ~ frontsegP(X22,X23)
| ssList(esk6_2(X22,X23)) ) ),
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])])])])])]) ).
fof(c_0_62,plain,
! [X224,X225,X226] :
( app(app(X224,X225),X226) = app(X224,app(X225,X226))
| ~ ssList(X226)
| ~ ssList(X225)
| ~ ssList(X224) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_63,negated_conjecture,
esk52_0 = esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_60]),c_0_29])]) ).
cnf(c_0_64,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| app(X2,X1) != X3
| ~ ssList(X1)
| frontsegP(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_65,plain,
! [X137] :
( app(nil,X137) = X137
| ~ ssList(X137) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_66,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,negated_conjecture,
app(esk49_0,nil) = esk49_0,
inference(rw,[status(thm)],[c_0_60,c_0_63]) ).
fof(c_0_68,plain,
! [X219,X220,X221] :
( X221 = X219
| app(X220,X221) != app(X220,X219)
| ~ ssList(X221)
| ~ ssList(X220)
| ~ ssList(X219) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_69,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_64]),c_0_19]) ).
cnf(c_0_70,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_71,negated_conjecture,
( ~ ssList(X1)
| app(esk49_0,app(nil,X1)) = app(esk49_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_49]),c_0_51])]) ).
cnf(c_0_72,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,negated_conjecture,
frontsegP(esk49_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_46]),c_0_29]),c_0_25])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_76,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_66,c_0_70]),c_0_49])]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(app(nil,X1))
| ssList(app(esk49_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_71]),c_0_51])]) ).
fof(c_0_78,plain,
! [X165] :
( frontsegP(X165,X165)
| ~ ssList(X165) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(X1)
| app(esk52_0,X1) != esk49_0
| X1 = esk54_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_46]),c_0_25]),c_0_29])]) ).
cnf(c_0_80,negated_conjecture,
app(esk52_0,esk6_2(esk49_0,esk52_0)) = esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_51]),c_0_29])]) ).
cnf(c_0_81,negated_conjecture,
ssList(esk6_2(esk49_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_74]),c_0_29]),c_0_51])]) ).
cnf(c_0_82,negated_conjecture,
app(nil,esk49_0) = esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_67]),c_0_49]),c_0_51])]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssList(X1)
| ssList(app(esk49_0,X1)) ),
inference(spm,[status(thm)],[c_0_77,c_0_70]) ).
cnf(c_0_84,negated_conjecture,
app(app(esk49_0,esk53_0),nil) = esk48_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_59]),c_0_63]) ).
cnf(c_0_85,negated_conjecture,
ssList(app(esk49_0,esk53_0)),
inference(spm,[status(thm)],[c_0_44,c_0_63]) ).
cnf(c_0_86,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_87,negated_conjecture,
esk6_2(esk49_0,esk52_0) = esk54_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(esk49_0,X1),esk49_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_82]),c_0_51]),c_0_49])]),c_0_83]) ).
cnf(c_0_89,negated_conjecture,
app(esk49_0,esk53_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_84]),c_0_85])]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| app(X1,esk6_2(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_73,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
esk6_2(esk49_0,esk49_0) = nil,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_59]),c_0_63]) ).
cnf(c_0_92,negated_conjecture,
segmentP(esk48_0,esk49_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_28])]) ).
cnf(c_0_93,negated_conjecture,
segmentP(esk49_0,esk49_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_90]),c_0_91]),c_0_49]),c_0_51])]) ).
cnf(c_0_94,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_95,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_53,c_0_92]),c_0_93]),c_0_51]),c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 07:57:02 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.71/0.82 % Version: 3.5.1
% 0.71/0.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.71/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.71/0.82 % Starting new_bool_3 with 300s (1) cores
% 0.71/0.82 % Starting new_bool_1 with 300s (1) cores
% 0.71/0.82 % Starting sh5l with 300s (1) cores
% 0.71/0.82 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2813937 completed with status 0
% 0.71/0.82 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.71/0.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.71/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.71/0.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.71/0.82 % No SInE strategy applied
% 0.71/0.82 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.71/0.82 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.71/0.82 % Starting SubtermCWHack with 136s (1) cores
% 0.71/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.71/0.82 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.71/0.82 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.71/0.82 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.71/0.82 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2813945 completed with status 0
% 0.71/0.82 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.71/0.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.71/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.71/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.71/0.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.71/0.82 % No SInE strategy applied
% 0.71/0.82 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.71/0.82 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.71/0.82 % Starting SubtermCWHack with 136s (1) cores
% 0.71/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.71/0.82 % Preprocessing time : 0.004 s
% 0.71/0.82 % Presaturation interreduction done
% 0.71/0.82
% 0.71/0.82 % Proof found!
% 0.71/0.82 % SZS status Theorem
% 0.71/0.82 % SZS output start CNFRefutation
% See solution above
% 0.71/0.82 % Parsed axioms : 96
% 0.71/0.82 % Removed by relevancy pruning/SinE : 0
% 0.71/0.82 % Initial clauses : 203
% 0.71/0.82 % Removed in clause preprocessing : 2
% 0.71/0.82 % Initial clauses in saturation : 201
% 0.71/0.82 % Processed clauses : 2416
% 0.71/0.82 % ...of these trivial : 65
% 0.71/0.82 % ...subsumed : 1133
% 0.71/0.82 % ...remaining for further processing : 1218
% 0.71/0.82 % Other redundant clauses eliminated : 116
% 0.71/0.82 % Clauses deleted for lack of memory : 0
% 0.71/0.82 % Backward-subsumed : 53
% 0.71/0.82 % Backward-rewritten : 241
% 0.71/0.82 % Generated clauses : 7479
% 0.71/0.82 % ...of the previous two non-redundant : 6793
% 0.71/0.82 % ...aggressively subsumed : 0
% 0.71/0.82 % Contextual simplify-reflections : 208
% 0.71/0.82 % Paramodulations : 7356
% 0.71/0.82 % Factorizations : 0
% 0.71/0.82 % NegExts : 0
% 0.71/0.82 % Equation resolutions : 125
% 0.71/0.82 % Disequality decompositions : 0
% 0.71/0.82 % Total rewrite steps : 8117
% 0.71/0.82 % ...of those cached : 7976
% 0.71/0.82 % Propositional unsat checks : 0
% 0.71/0.82 % Propositional check models : 0
% 0.71/0.82 % Propositional check unsatisfiable : 0
% 0.71/0.82 % Propositional clauses : 0
% 0.71/0.82 % Propositional clauses after purity: 0
% 0.71/0.82 % Propositional unsat core size : 0
% 0.71/0.82 % Propositional preprocessing time : 0.000
% 0.71/0.82 % Propositional encoding time : 0.000
% 0.71/0.82 % Propositional solver time : 0.000
% 0.71/0.82 % Success case prop preproc time : 0.000
% 0.71/0.82 % Success case prop encoding time : 0.000
% 0.71/0.82 % Success case prop solver time : 0.000
% 0.71/0.82 % Current number of processed clauses : 706
% 0.71/0.82 % Positive orientable unit clauses : 108
% 0.71/0.82 % Positive unorientable unit clauses: 0
% 0.71/0.82 % Negative unit clauses : 3
% 0.71/0.82 % Non-unit-clauses : 595
% 0.71/0.82 % Current number of unprocessed clauses: 4368
% 0.71/0.82 % ...number of literals in the above : 22640
% 0.71/0.82 % Current number of archived formulas : 0
% 0.71/0.82 % Current number of archived clauses : 489
% 0.71/0.82 % Clause-clause subsumption calls (NU) : 66301
% 0.71/0.82 % Rec. Clause-clause subsumption calls : 23314
% 0.71/0.82 % Non-unit clause-clause subsumptions : 1229
% 0.71/0.82 % Unit Clause-clause subsumption calls : 3000
% 0.71/0.82 % Rewrite failures with RHS unbound : 0
% 0.71/0.82 % BW rewrite match attempts : 54
% 0.71/0.82 % BW rewrite match successes : 50
% 0.71/0.82 % Condensation attempts : 0
% 0.71/0.82 % Condensation successes : 0
% 0.71/0.82 % Termbank termtop insertions : 147995
% 0.71/0.82 % Search garbage collected termcells : 4287
% 0.71/0.82
% 0.71/0.82 % -------------------------------------------------
% 0.71/0.82 % User time : 0.238 s
% 0.71/0.82 % System time : 0.013 s
% 0.71/0.82 % Total time : 0.251 s
% 0.71/0.82 % Maximum resident set size: 4272 pages
% 0.71/0.82
% 0.71/0.82 % -------------------------------------------------
% 0.71/0.82 % User time : 1.091 s
% 0.71/0.82 % System time : 0.050 s
% 0.71/0.82 % Total time : 1.141 s
% 0.71/0.82 % Maximum resident set size: 4864 pages
% 0.71/0.82 % E exiting
%------------------------------------------------------------------------------