%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC073+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 : n003.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 05:18:09 PM UTC 2026
% Result : Theorem 16.14s 9.70s
% Output : CNFRefutation 16.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 22
% Syntax : Number of formulae : 140 ( 14 unt; 0 def)
% Number of atoms : 560 ( 202 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 692 ( 272 ~; 307 |; 61 &)
% ( 5 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 169 ( 0 sgn 84 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( nil != X3
& nil = X4 )
| ( nil = X2
& nil = X1 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssList(X6)
& X4 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X3) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X3) = X9
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
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(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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( nil != X3
& nil = X4 )
| ( nil = X2
& nil = X1 )
| ( neq(X4,nil)
& ( ~ neq(X3,nil)
| ? [X6] :
( ssList(X6)
& X4 != X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X3) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X3) = X9
& neq(nil,X3) )
& neq(nil,X3) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_23,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
& ( ~ ssList(X470)
| ~ neq(X470,nil)
| ~ segmentP(esk49_0,X470)
| ~ segmentP(esk48_0,X470) )
& ( nil = esk50_0
| nil != esk51_0 )
& ( nil != esk49_0
| nil != esk48_0 )
& ( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) )
& ( ~ ssList(X471)
| esk51_0 = X471
| ~ ssList(X472)
| ~ ssList(X473)
| tl(esk50_0) != X472
| app(X472,X473) != X471
| ~ ssItem(X474)
| cons(X474,nil) != X473
| hd(esk50_0) != X474
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ) ),
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_22])])])])]) ).
cnf(c_0_24,negated_conjecture,
( esk51_0 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| tl(esk50_0) != X2
| app(X2,X3) != X1
| ~ ssItem(X4)
| cons(X4,nil) != X3
| hd(esk50_0) != X4
| ~ neq(nil,esk50_0)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_25,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_26,negated_conjecture,
( esk51_0 = X1
| hd(esk50_0) != X4
| tl(esk50_0) != X2
| app(X2,X3) != X1
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[c_0_24]) ).
cnf(c_0_27,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_28,plain,
! [X342] :
( ~ ssList(X342)
| nil = X342
| ssList(tl(X342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssList(tl(esk50_0))
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])])])]),c_0_27]) ).
cnf(c_0_32,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_34,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])])]) ).
cnf(c_0_35,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_37,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_38,plain,
! [X339] :
( ~ ssList(X339)
| nil = X339
| ssItem(hd(X339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_39,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil)
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_40,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_41,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_42,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_43,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_44,plain,
! [X428] :
( ~ ssList(X428)
| nil = X428
| cons(hd(X428),tl(X428)) = X428 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_45,plain,
! [X445,X446] :
( ~ ssList(X445)
| ~ ssList(X446)
| nil = X445
| tl(app(X445,X446)) = app(tl(X445),X446) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_46,plain,
! [X440,X441] :
( ( nil = X441
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil = X440
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil != X441
| nil != X440
| nil = app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_47,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(nil,esk50_0)
| ~ neq(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_33])]) ).
cnf(c_0_48,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_50,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_51,negated_conjecture,
( esk50_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_30]),c_0_43]) ).
cnf(c_0_52,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil
| ~ neq(esk51_0,nil) ),
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_37])]) ).
cnf(c_0_56,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_49,c_0_43]) ).
cnf(c_0_57,negated_conjecture,
esk51_0 != nil,
inference(csr,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,plain,
( cons(hd(app(X1,X2)),app(tl(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_27]),c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( app(tl(esk50_0),cons(hd(esk50_0),nil)) = esk51_0
| esk50_0 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_48]),c_0_37]),c_0_56])]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_33])]) ).
cnf(c_0_61,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_36]),c_0_37])]) ).
fof(c_0_62,plain,
! [X443,X444] :
( ~ ssList(X443)
| ~ ssList(X444)
| nil = X443
| hd(app(X443,X444)) = hd(X443) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_63,negated_conjecture,
( cons(hd(app(esk50_0,cons(hd(esk50_0),nil))),esk51_0) = app(esk50_0,cons(hd(esk50_0),nil))
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_40]),c_0_33])]) ).
cnf(c_0_64,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_65,plain,
! [X337,X338] :
( ~ ssList(X337)
| ~ ssItem(X338)
| nil != cons(X338,X337) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_66,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_33])]) ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_68,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_36]),c_0_37])]) ).
cnf(c_0_69,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil
| ~ ssItem(hd(app(esk50_0,cons(hd(esk50_0),nil)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_63]),c_0_56])]) ).
cnf(c_0_70,negated_conjecture,
( app(esk50_0,cons(hd(esk50_0),nil)) = cons(hd(esk50_0),esk51_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_40]),c_0_33])]) ).
cnf(c_0_71,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_64]),c_0_33])]) ).
fof(c_0_72,plain,
! [X235,X236,X238] :
( ( ssList(esk6_2(X235,X236))
| ~ frontsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( app(X236,esk6_2(X235,X236)) = X235
| ~ frontsegP(X235,X236)
| ~ ssList(X236)
| ~ ssList(X235) )
& ( ~ ssList(X238)
| app(X236,X238) != X235
| frontsegP(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)],[ax5])])])])]) ).
cnf(c_0_73,negated_conjecture,
( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
| esk50_0 = nil
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_70]),c_0_33])]) ).
cnf(c_0_74,negated_conjecture,
( esk50_0 = nil
| ssList(cons(hd(esk50_0),esk51_0))
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_70]),c_0_33])]) ).
cnf(c_0_75,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_36]),c_0_37])]) ).
fof(c_0_76,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_77,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
| esk50_0 = nil
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_36]),c_0_37])]) ).
cnf(c_0_79,negated_conjecture,
( esk50_0 = nil
| ssList(cons(hd(esk50_0),esk51_0))
| ~ ssItem(hd(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_36]),c_0_37])]) ).
cnf(c_0_80,negated_conjecture,
( esk50_0 = nil
| app(esk50_0,cons(hd(esk50_0),nil)) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_40]),c_0_33])]) ).
cnf(c_0_81,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_76]) ).
fof(c_0_82,plain,
! [X442] :
( ~ ssList(X442)
| app(X442,nil) = X442 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_83,plain,
! [X340,X341] :
( ~ ssList(X340)
| ~ ssItem(X341)
| hd(cons(X341,X340)) = X341 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_84,plain,
! [X382,X383,X384,X385] :
( ( X382 = X383
| ~ frontsegP(cons(X382,X384),cons(X383,X385))
| ~ ssList(X385)
| ~ ssList(X384)
| ~ ssItem(X383)
| ~ ssItem(X382) )
& ( frontsegP(X384,X385)
| ~ frontsegP(cons(X382,X384),cons(X383,X385))
| ~ ssList(X385)
| ~ ssList(X384)
| ~ ssItem(X383)
| ~ ssItem(X382) )
& ( X382 != X383
| ~ frontsegP(X384,X385)
| frontsegP(cons(X382,X384),cons(X383,X385))
| ~ ssList(X385)
| ~ ssList(X384)
| ~ ssItem(X383)
| ~ ssItem(X382) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
fof(c_0_85,plain,
! [X334] :
( ( ssList(esk44_1(X334))
| nil = X334
| ~ ssList(X334) )
& ( ssItem(esk45_1(X334))
| nil = X334
| ~ ssList(X334) )
& ( cons(esk45_1(X334),esk44_1(X334)) = X334
| nil = X334
| ~ ssList(X334) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_86,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_27]) ).
cnf(c_0_87,negated_conjecture,
( hd(cons(hd(esk50_0),esk51_0)) = hd(esk50_0)
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_40]),c_0_33])]) ).
cnf(c_0_88,negated_conjecture,
( esk50_0 = nil
| ssList(cons(hd(esk50_0),esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_40]),c_0_33])]) ).
cnf(c_0_89,negated_conjecture,
( esk50_0 = nil
| cons(hd(esk50_0),esk51_0) != nil ),
inference(spm,[status(thm)],[c_0_80,c_0_70]) ).
cnf(c_0_90,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_81]) ).
cnf(c_0_91,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
fof(c_0_92,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_93,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_94,plain,
( X1 = X2
| ~ frontsegP(cons(X1,X3),cons(X2,X4))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_95,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_96,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_97,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_98,negated_conjecture,
( esk50_0 = nil
| frontsegP(cons(hd(esk50_0),esk51_0),esk50_0)
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_70]),c_0_33])]) ).
cnf(c_0_99,negated_conjecture,
( esk50_0 = nil
| ssItem(hd(esk50_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_87]),c_0_88]),c_0_89]) ).
fof(c_0_100,plain,
! [X350] :
( ~ ssList(X350)
| app(nil,X350) = X350 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_101,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_90,c_0_91]),c_0_37])]),c_0_27]) ).
cnf(c_0_102,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_103,plain,
( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_93]),c_0_36]),c_0_67]) ).
cnf(c_0_104,plain,
( X1 = esk45_1(X2)
| nil = X2
| ~ frontsegP(cons(X1,X3),X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_97]) ).
cnf(c_0_105,negated_conjecture,
( esk50_0 = nil
| frontsegP(cons(hd(esk50_0),esk51_0),esk50_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_36]),c_0_37])]),c_0_99]) ).
cnf(c_0_106,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(cons(X1,nil))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_108,plain,
( cons(esk45_1(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_95]),c_0_96]),c_0_97]) ).
cnf(c_0_109,negated_conjecture,
( esk45_1(esk50_0) = hd(esk50_0)
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_56]),c_0_33])]),c_0_99]) ).
cnf(c_0_110,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_90,c_0_106]),c_0_37])]),c_0_27]) ).
cnf(c_0_111,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_36]),c_0_37])]) ).
cnf(c_0_112,negated_conjecture,
( cons(hd(esk50_0),tl(esk50_0)) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_33])]) ).
cnf(c_0_113,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,tl(esk50_0))
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssList(tl(esk50_0)) ),
inference(spm,[status(thm)],[c_0_110,c_0_59]) ).
cnf(c_0_114,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk49_0,X1)
| ~ segmentP(esk48_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_115,negated_conjecture,
( esk50_0 = nil
| segmentP(esk50_0,tl(esk50_0))
| ~ ssList(tl(esk50_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_99]) ).
cnf(c_0_116,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,tl(esk50_0))
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_32]),c_0_33])]) ).
cnf(c_0_117,negated_conjecture,
( ~ segmentP(esk50_0,X1)
| ~ segmentP(esk51_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_30]),c_0_43]) ).
cnf(c_0_118,negated_conjecture,
( esk50_0 = nil
| segmentP(esk50_0,tl(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_32]),c_0_33])]) ).
cnf(c_0_119,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,tl(esk50_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_36]),c_0_37])]),c_0_99]) ).
cnf(c_0_120,negated_conjecture,
( esk50_0 = nil
| ~ ssList(tl(esk50_0))
| ~ neq(tl(esk50_0),nil) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]) ).
cnf(c_0_121,negated_conjecture,
( esk50_0 = nil
| ~ neq(tl(esk50_0),nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_32]),c_0_33])]) ).
fof(c_0_122,plain,
! [X404] :
( ~ ssList(X404)
| segmentP(X404,X404) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_123,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,cons(hd(esk50_0),nil))
| ~ ssList(cons(hd(esk50_0),nil))
| ~ ssList(tl(esk50_0)) ),
inference(spm,[status(thm)],[c_0_101,c_0_59]) ).
cnf(c_0_124,negated_conjecture,
( tl(esk50_0) = nil
| esk50_0 = nil
| ~ ssList(tl(esk50_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_48]),c_0_37])]) ).
cnf(c_0_125,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_126,negated_conjecture,
( neq(esk50_0,nil)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_127,plain,
! [X409] :
( ~ ssList(X409)
| segmentP(X409,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_128,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,cons(hd(esk50_0),nil))
| ~ ssList(cons(hd(esk50_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_32]),c_0_33])]) ).
cnf(c_0_129,negated_conjecture,
( tl(esk50_0) = nil
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_32]),c_0_33])]) ).
cnf(c_0_130,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_125]),c_0_33])]) ).
cnf(c_0_131,negated_conjecture,
neq(esk50_0,nil),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_48]),c_0_37]),c_0_56])]),c_0_57]) ).
cnf(c_0_132,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_133,negated_conjecture,
( esk50_0 = nil
| segmentP(esk51_0,cons(hd(esk50_0),nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_36]),c_0_37])]),c_0_99]) ).
cnf(c_0_134,negated_conjecture,
( cons(hd(esk50_0),nil) = esk50_0
| esk50_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_129]),c_0_33])]) ).
cnf(c_0_135,negated_conjecture,
~ segmentP(esk51_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131])]) ).
cnf(c_0_136,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_117,c_0_132]),c_0_37]),c_0_33])]) ).
cnf(c_0_137,negated_conjecture,
esk50_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]) ).
cnf(c_0_138,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_132]),c_0_56])]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_137]),c_0_138]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC073+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.11/0.31 % Computer : n003.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue May 5 04:22:26 EDT 2026
% 0.11/0.31 % CPUTime :
% 0.11/0.32 % start to proof: theBenchmark
% 16.14/9.70 % Version : CSE_E---1.7
% 16.14/9.70 % Problem : theBenchmark.p
% 16.14/9.70 % SZS status Theorem for theBenchmark.p
% 16.14/9.70 % SZS output start CNFRefutation
% See solution above
% 16.14/9.75 % Total time : 7.385s
%------------------------------------------------------------------------------