%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC087+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 05:18:13 PM UTC 2026
% Result : Theorem 22.59s 13.80s
% Output : CNFRefutation 22.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 86 ( 12 unt; 0 def)
% Number of atoms : 357 ( 99 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 451 ( 180 ~; 196 |; 45 &)
% ( 2 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 49 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& X3 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X4) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X4) = X9
& neq(nil,X4) )
& neq(nil,X4) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ? [X6] :
( ssList(X6)
& X3 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X4) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X4) = X9
& neq(nil,X4) )
& neq(nil,X4) ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_15,negated_conjecture,
! [X470,X471,X472,X473,X474] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( neq(esk49_0,nil)
| neq(esk49_0,nil) )
& ( ~ neq(esk51_0,nil)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ ssList(X470)
| ~ neq(X470,nil)
| ~ segmentP(esk49_0,X470)
| ~ segmentP(esk48_0,X470) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X470)
| ~ neq(X470,nil)
| ~ segmentP(esk49_0,X470)
| ~ segmentP(esk48_0,X470) )
& ( neq(esk49_0,nil)
| ~ ssList(X471)
| esk50_0 = X471
| ~ ssList(X472)
| ~ ssList(X473)
| tl(esk51_0) != X472
| app(X472,X473) != X471
| ~ ssItem(X474)
| cons(X474,nil) != X473
| hd(esk51_0) != X474
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X471)
| esk50_0 = X471
| ~ ssList(X472)
| ~ ssList(X473)
| tl(esk51_0) != X472
| app(X472,X473) != X471
| ~ ssItem(X474)
| cons(X474,nil) != X473
| hd(esk51_0) != X474
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_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_14])])])])]) ).
cnf(c_0_16,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_17,negated_conjecture,
( esk50_0 = X1
| ~ neq(esk51_0,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk51_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk51_0) != X4
| ~ neq(nil,esk51_0)
| ~ neq(nil,esk51_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X345,X346] :
( ~ ssList(X345)
| ~ ssList(X346)
| ssList(app(X345,X346)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_21,negated_conjecture,
( esk50_0 = X1
| hd(esk51_0) != X4
| tl(esk51_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk51_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X342] :
( ~ ssList(X342)
| nil = X342
| ssList(tl(X342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
| ~ ssList(cons(hd(esk51_0),nil))
| ~ ssList(tl(esk51_0))
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23])])])])])]),c_0_24]) ).
cnf(c_0_28,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_26,c_0_19]) ).
fof(c_0_30,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| ssList(cons(X327,X326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_31,plain,
! [X243,X244,X247,X248] :
( ( ssList(esk8_2(X243,X244))
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( ssList(esk9_2(X243,X244))
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( app(app(esk8_2(X243,X244),X244),esk9_2(X243,X244)) = X243
| ~ segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) )
& ( ~ ssList(X247)
| ~ ssList(X248)
| app(app(X247,X244),X248) != X243
| segmentP(X243,X244)
| ~ ssList(X244)
| ~ ssList(X243) ) ),
inference(distribute,[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_32,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil))
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_33,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_35,plain,
! [X339] :
( ~ ssList(X339)
| nil = X339
| ssItem(hd(X339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_36,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_31]) ).
fof(c_0_37,plain,
! [X350] :
( ~ ssList(X350)
| app(nil,X350) = X350 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_38,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
| esk51_0 = nil
| ~ neq(nil,esk51_0)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_39,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_40,plain,
! [X324,X325] :
( ( ~ neq(X324,X325)
| X324 != X325
| ~ ssList(X325)
| ~ ssList(X324) )
& ( X324 = X325
| neq(X324,X325)
| ~ ssList(X325)
| ~ ssList(X324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_41,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_36]) ).
cnf(c_0_42,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
| esk51_0 = nil
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_29])]) ).
cnf(c_0_44,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,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_41,c_0_42]),c_0_34])]),c_0_24]) ).
cnf(c_0_46,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk48_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_29]),c_0_34])]) ).
fof(c_0_47,plain,
! [X442] :
( ~ ssList(X442)
| app(X442,nil) = X442 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_48,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,tl(esk51_0))
| ~ ssList(cons(hd(esk51_0),nil))
| ~ ssList(tl(esk51_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,tl(esk51_0))
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_28]),c_0_29])]) ).
fof(c_0_51,plain,
! [X435,X436] :
( ~ ssList(X435)
| ~ ssItem(X436)
| cons(X436,X435) = app(cons(X436,nil),X435) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_52,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_41,c_0_49]),c_0_34])]),c_0_24]) ).
cnf(c_0_53,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_54,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,tl(esk51_0))
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_33]),c_0_34])]) ).
cnf(c_0_55,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,cons(hd(esk51_0),nil))
| ~ ssList(cons(hd(esk51_0),nil))
| ~ ssList(tl(esk51_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
( ~ segmentP(esk48_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_19]),c_0_23])]) ).
cnf(c_0_58,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_39]),c_0_29])]) ).
cnf(c_0_59,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
fof(c_0_60,plain,
! [X428] :
( ~ ssList(X428)
| nil = X428
| cons(hd(X428),tl(X428)) = X428 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_61,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,cons(hd(esk51_0),nil))
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_28]),c_0_29])]) ).
cnf(c_0_62,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,tl(esk51_0))
| ~ ssList(tl(esk51_0))
| ~ neq(tl(esk51_0),nil) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_33]),c_0_34])]) ).
cnf(c_0_64,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,cons(hd(esk51_0),nil))
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_33]),c_0_34])]) ).
cnf(c_0_66,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,tl(esk51_0))
| ~ neq(tl(esk51_0),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_28]),c_0_29])]) ).
cnf(c_0_67,plain,
( nil = X1
| segmentP(X1,tl(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_39]),c_0_28]) ).
cnf(c_0_68,negated_conjecture,
( esk51_0 = nil
| segmentP(esk48_0,cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_39]),c_0_29])]) ).
cnf(c_0_69,negated_conjecture,
( esk51_0 = nil
| ~ neq(tl(esk51_0),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_29])]) ).
cnf(c_0_70,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,cons(hd(esk51_0),nil))
| ~ ssList(cons(hd(esk51_0),nil))
| ~ neq(cons(hd(esk51_0),nil),nil) ),
inference(spm,[status(thm)],[c_0_57,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( tl(esk51_0) = nil
| esk51_0 = nil
| ~ ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_44]),c_0_34])]) ).
cnf(c_0_72,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,cons(hd(esk51_0),nil))
| ~ neq(cons(hd(esk51_0),nil),nil)
| ~ ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_33]),c_0_34])]) ).
cnf(c_0_73,negated_conjecture,
( tl(esk51_0) = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_28]),c_0_29])]) ).
fof(c_0_74,plain,
! [X409] :
( ~ ssList(X409)
| segmentP(X409,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_75,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,cons(hd(esk51_0),nil))
| ~ neq(cons(hd(esk51_0),nil),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_39]),c_0_29])]) ).
cnf(c_0_76,negated_conjecture,
( cons(hd(esk51_0),nil) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_73]),c_0_29])]) ).
fof(c_0_77,plain,
! [X404] :
( ~ ssList(X404)
| segmentP(X404,X404) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_78,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_79,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_80,negated_conjecture,
( esk51_0 = nil
| ~ segmentP(esk51_0,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_23])]) ).
cnf(c_0_81,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( ~ segmentP(esk51_0,nil)
| ~ neq(nil,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_78]),c_0_34]),c_0_79])]) ).
cnf(c_0_83,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_29])]) ).
cnf(c_0_84,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_78]),c_0_29])]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_83]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC087+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 04:23:46 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 22.59/13.80 % Version : CSE_E---1.7
% 22.59/13.80 % Problem : theBenchmark.p
% 22.59/13.80 % SZS status Theorem for theBenchmark.p
% 22.59/13.80 % SZS output start CNFRefutation
% See solution above
% 22.59/13.88 % Total time : 10.388s
%------------------------------------------------------------------------------