%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC061+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:18:06 PM UTC 2026
% Result : Theorem 1.76s 1.85s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 114 ( 12 unt; 0 def)
% Number of atoms : 408 ( 116 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 489 ( 195 ~; 214 |; 39 &)
% ( 5 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 69 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_18,plain,
! [X239,X240,X243,X244] :
( ( ssList(esk8_2(X239,X240))
| ~ segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( ssList(esk9_2(X239,X240))
| ~ segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( app(app(esk8_2(X239,X240),X240),esk9_2(X239,X240)) = X239
| ~ segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) )
& ( ~ ssList(X243)
| ~ ssList(X244)
| app(app(X243,X240),X244) != X239
| segmentP(X239,X240)
| ~ ssList(X240)
| ~ ssList(X239) ) ),
inference(distribute,[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_19,negated_conjecture,
! [X468] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( nil = esk50_0
| nil != esk51_0 )
& ( ssItem(esk52_0)
| ~ neq(esk51_0,nil) )
& ( ssList(esk53_0)
| ~ neq(esk51_0,nil) )
& ( app(cons(esk52_0,nil),esk53_0) = esk51_0
| ~ neq(esk51_0,nil) )
& ( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ ssList(X468)
| ~ neq(X468,nil)
| ~ segmentP(esk49_0,X468)
| ~ segmentP(esk48_0,X468)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ ssList(X468)
| ~ neq(X468,nil)
| ~ segmentP(esk49_0,X468)
| ~ segmentP(esk48_0,X468)
| nil != esk48_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
cnf(c_0_20,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X346] :
( ~ ssList(X346)
| app(nil,X346) = X346 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_22,plain,
! [X341,X342] :
( ~ ssList(X341)
| ~ ssList(X342)
| ssList(app(X341,X342)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_23,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( neq(esk49_0,nil)
| nil = esk49_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_30,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk48_0
| ~ neq(esk51_0,nil) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( esk51_0 = nil
| neq(esk51_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( ssList(esk53_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_34,plain,
! [X438] :
( ~ ssList(X438)
| app(X438,nil) = X438 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_35,plain,
! [X375,X376,X377] :
( ~ ssList(X375)
| ~ ssList(X376)
| ~ ssList(X377)
| ~ frontsegP(X375,X376)
| frontsegP(app(X375,X377),X376) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_36,plain,
! [X382] :
( ~ ssList(X382)
| frontsegP(X382,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_37,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
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]) ).
cnf(c_0_38,negated_conjecture,
( app(esk53_0,cons(esk52_0,nil)) = esk48_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( esk51_0 = nil
| ssList(esk53_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
fof(c_0_40,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| ssList(cons(X323,X322)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_41,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_42,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk51_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_44,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( nil = esk49_0
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_47,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,esk53_0)
| ~ ssList(cons(esk52_0,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_48,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( esk51_0 = nil
| ssItem(esk52_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_50,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_42]),c_0_29])]),c_0_30]) ).
cnf(c_0_51,negated_conjecture,
( app(cons(esk52_0,nil),esk53_0) = esk51_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_43,c_0_32]) ).
cnf(c_0_52,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_29])]) ).
fof(c_0_53,plain,
! [X231,X232,X234] :
( ( ssList(esk6_2(X231,X232))
| ~ frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( app(X232,esk6_2(X231,X232)) = X231
| ~ frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) )
& ( ~ ssList(X234)
| app(X232,X234) != X231
| frontsegP(X231,X232)
| ~ ssList(X232)
| ~ ssList(X231) ) ),
inference(distribute,[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_54,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk48_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_26]),c_0_26]) ).
cnf(c_0_55,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,esk53_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_29])]),c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( esk51_0 = nil
| segmentP(esk51_0,esk53_0)
| ~ ssList(cons(esk52_0,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_39]) ).
cnf(c_0_57,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,nil)
| ~ ssList(cons(esk52_0,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_39]) ).
cnf(c_0_58,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_59,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_61,plain,
! [X431,X432] :
( ~ ssList(X431)
| ~ ssItem(X432)
| cons(X432,X431) = app(cons(X432,nil),X431) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_62,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,esk53_0)
| ~ neq(esk53_0,nil) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_39]) ).
cnf(c_0_63,negated_conjecture,
( esk51_0 = nil
| segmentP(esk51_0,esk53_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_48]),c_0_29])]),c_0_49]) ).
fof(c_0_64,plain,
! [X320,X321] :
( ( ~ neq(X320,X321)
| X320 != X321
| ~ ssList(X321)
| ~ ssList(X320) )
& ( X320 = X321
| neq(X320,X321)
| ~ ssList(X321)
| ~ ssList(X320) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
fof(c_0_65,plain,
! [X390,X391,X392] :
( ~ ssList(X390)
| ~ ssList(X391)
| ~ ssList(X392)
| ~ rearsegP(X390,X391)
| rearsegP(app(X392,X390),X391) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_66,plain,
! [X393] :
( ~ ssList(X393)
| rearsegP(X393,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_67,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,nil) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_29])]),c_0_49]) ).
cnf(c_0_68,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_58,c_0_26]) ).
cnf(c_0_69,plain,
( app(nil,esk6_2(X1,nil)) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_45]),c_0_29])]) ).
cnf(c_0_70,plain,
( ssList(esk6_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_45]),c_0_29])]) ).
cnf(c_0_71,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,negated_conjecture,
( esk51_0 = nil
| ~ neq(esk53_0,nil) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_73,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_75,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_76,negated_conjecture,
( app(nil,esk6_2(esk51_0,nil)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_67]),c_0_68]),c_0_29])]) ).
cnf(c_0_77,plain,
( esk6_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_69]),c_0_70]) ).
fof(c_0_78,plain,
! [X235,X236,X238] :
( ( ssList(esk7_2(X235,X236))
| ~ rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( app(esk7_2(X235,X236),X236) = X235
| ~ rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ~ ssList(X238)
| app(X238,X236) != X235
| rearsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) ) ),
inference(distribute,[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_79,negated_conjecture,
( cons(esk52_0,esk53_0) = esk51_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_71]),c_0_49]),c_0_39]) ).
cnf(c_0_80,negated_conjecture,
( esk53_0 = nil
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_29])]),c_0_39]) ).
cnf(c_0_81,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_29])]) ).
cnf(c_0_82,negated_conjecture,
( app(nil,esk51_0) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_68])]) ).
cnf(c_0_83,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_84,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_85,negated_conjecture,
( cons(esk52_0,nil) = esk51_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,negated_conjecture,
( esk51_0 = nil
| rearsegP(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_29]),c_0_68])]) ).
cnf(c_0_87,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_75]),c_0_29])]) ).
cnf(c_0_88,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_75]),c_0_29])]) ).
fof(c_0_89,plain,
! [X400] :
( ~ ssList(X400)
| segmentP(X400,X400) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_90,negated_conjecture,
( app(esk53_0,esk51_0) = esk48_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_38,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( app(esk7_2(esk51_0,nil),nil) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_86]),c_0_29]),c_0_68])]) ).
cnf(c_0_92,plain,
( esk7_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_87]),c_0_88]) ).
cnf(c_0_93,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_94,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_95,negated_conjecture,
( app(nil,esk51_0) = esk48_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_90,c_0_80]) ).
cnf(c_0_96,negated_conjecture,
( app(esk51_0,nil) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_68])]) ).
cnf(c_0_97,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_98,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_99,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,esk48_0)
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_93]),c_0_94])]) ).
cnf(c_0_100,negated_conjecture,
( esk51_0 = nil
| esk48_0 = esk51_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_95]),c_0_68])]) ).
cnf(c_0_101,negated_conjecture,
( esk51_0 = nil
| segmentP(esk51_0,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_96]),c_0_68]),c_0_29])]) ).
fof(c_0_102,plain,
! [X406] :
( ( ~ segmentP(nil,X406)
| nil = X406
| ~ ssList(X406) )
& ( nil != X406
| segmentP(nil,X406)
| ~ ssList(X406) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])]) ).
cnf(c_0_103,negated_conjecture,
( esk48_0 != nil
| ~ segmentP(esk48_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[c_0_97,c_0_26]) ).
cnf(c_0_104,negated_conjecture,
( esk48_0 = nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[c_0_98,c_0_24]) ).
cnf(c_0_105,negated_conjecture,
esk51_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_32]),c_0_101]) ).
cnf(c_0_106,plain,
( segmentP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_108,negated_conjecture,
( esk48_0 != nil
| ~ segmentP(esk51_0,esk48_0)
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_93]),c_0_94])]) ).
cnf(c_0_109,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).
cnf(c_0_110,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_106]),c_0_29])]) ).
cnf(c_0_111,negated_conjecture,
( neq(esk51_0,nil)
| esk48_0 != nil ),
inference(rw,[status(thm)],[c_0_107,c_0_26]) ).
cnf(c_0_112,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_105]),c_0_109]),c_0_109]),c_0_110]),c_0_109])]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_105]),c_0_109])]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC061+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:21:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.76/1.85 % Version : CSE_E---1.7
% 1.76/1.85 % Problem : theBenchmark.p
% 1.76/1.85 % SZS status Theorem for theBenchmark.p
% 1.76/1.85 % SZS output start CNFRefutation
% See solution above
% 1.76/1.85 % Total time : 1.372s
%------------------------------------------------------------------------------