%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC363+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 : n021.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 05:19:21 PM UTC 2026
% Result : Theorem 207.06s 122.36s
% Output : CNFRefutation 207.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 127 ( 47 unt; 0 def)
% Number of atoms : 375 ( 97 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 424 ( 176 ~; 169 |; 26 &)
% ( 3 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 155 ( 0 sgn 85 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& neq(X4,nil) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(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(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
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(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5) ) )
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_21,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& neq(esk49_0,nil)
& ~ segmentP(esk49_0,esk48_0)
& ( nil = esk50_0
| nil != esk51_0 )
& ( ssItem(esk52_0)
| ~ neq(esk51_0,nil) )
& ( cons(esk52_0,nil) = esk50_0
| ~ neq(esk51_0,nil) )
& ( memberP(esk51_0,esk52_0)
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_22,negated_conjecture,
neq(esk49_0,nil),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_23,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X228,X229,X231] :
( ( ssList(esk6_2(X228,X229))
| ~ frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( app(X229,esk6_2(X228,X229)) = X228
| ~ frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( ~ ssList(X231)
| app(X229,X231) != X228
| frontsegP(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) ) ),
inference(distribute,[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_25,plain,
! [X338,X339] :
( ~ ssList(X338)
| ~ ssList(X339)
| ssList(app(X338,X339)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_26,plain,
! [X428,X429] :
( ~ ssList(X428)
| ~ ssItem(X429)
| cons(X429,X428) = app(cons(X429,nil),X428) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_27,negated_conjecture,
( cons(esk52_0,nil) = esk50_0
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( ssItem(esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_30,plain,
! [X219,X220,X223,X224] :
( ( ssList(esk3_2(X219,X220))
| ~ memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) )
& ( ssList(esk4_2(X219,X220))
| ~ memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) )
& ( app(esk3_2(X219,X220),cons(X220,esk4_2(X219,X220))) = X219
| ~ memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) )
& ( ~ ssList(X223)
| ~ ssList(X224)
| app(X223,cons(X220,X224)) != X219
| memberP(X219,X220)
| ~ ssItem(X220)
| ~ ssList(X219) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_31,negated_conjecture,
( memberP(esk51_0,esk52_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
cons(esk52_0,nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_37,negated_conjecture,
ssItem(esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_39,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_40,plain,
( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_28])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_43,plain,
( ssList(esk3_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34]) ).
cnf(c_0_45,negated_conjecture,
( app(esk50_0,X1) = cons(esk52_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_37])]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_42]),c_0_37])]) ).
fof(c_0_49,plain,
! [X319,X320] :
( ~ ssList(X319)
| ~ ssItem(X320)
| ssList(cons(X320,X319)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_50,plain,
( ssList(esk4_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_51,plain,
! [X425,X426,X427] :
( ~ ssList(X425)
| ~ ssList(X426)
| ~ ssList(X427)
| app(X426,X427) != app(X426,X425)
| X427 = X425 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(c_0_52,plain,
! [X435] :
( ~ ssList(X435)
| app(X435,nil) = X435 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_53,negated_conjecture,
( frontsegP(cons(esk52_0,X1),esk50_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_54,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_55,plain,
! [X372,X373,X374] :
( ~ ssList(X372)
| ~ ssList(X373)
| ~ ssList(X374)
| ~ frontsegP(X372,X373)
| frontsegP(app(X372,X374),X373) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_56,plain,
! [X379] :
( ~ ssList(X379)
| frontsegP(X379,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_57,negated_conjecture,
( frontsegP(esk51_0,esk3_2(esk51_0,esk52_0))
| ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_47]),c_0_48])]) ).
cnf(c_0_58,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,negated_conjecture,
ssList(esk4_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_42]),c_0_37])]) ).
cnf(c_0_60,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_63,negated_conjecture,
frontsegP(esk50_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_36]),c_0_54])]) ).
cnf(c_0_64,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_65,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,negated_conjecture,
frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_37])]) ).
cnf(c_0_68,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_54])]) ).
cnf(c_0_69,negated_conjecture,
app(esk50_0,esk6_2(esk50_0,esk50_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_46])]) ).
cnf(c_0_70,negated_conjecture,
ssList(esk6_2(esk50_0,esk50_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_63]),c_0_46])]) ).
cnf(c_0_71,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_54])]) ).
cnf(c_0_72,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_67]),c_0_42]),c_0_48])]) ).
cnf(c_0_73,negated_conjecture,
ssList(esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_67]),c_0_48]),c_0_42])]) ).
cnf(c_0_74,negated_conjecture,
esk6_2(esk50_0,esk50_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_46]),c_0_70])]) ).
fof(c_0_75,plain,
! [X343] :
( ~ ssList(X343)
| app(nil,X343) = X343 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_76,negated_conjecture,
frontsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_48])]) ).
cnf(c_0_77,negated_conjecture,
app(esk50_0,nil) = esk50_0,
inference(rw,[status(thm)],[c_0_69,c_0_74]) ).
fof(c_0_78,plain,
! [X340,X341,X342] :
( ~ ssList(X340)
| ~ ssList(X341)
| ~ ssItem(X342)
| cons(X342,app(X341,X340)) = app(cons(X342,X341),X340) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_79,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_80,negated_conjecture,
app(nil,esk6_2(esk51_0,nil)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_76]),c_0_42]),c_0_54])]) ).
cnf(c_0_81,negated_conjecture,
ssList(esk6_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_76]),c_0_54]),c_0_42])]) ).
cnf(c_0_82,negated_conjecture,
frontsegP(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_77]),c_0_54]),c_0_46])]) ).
cnf(c_0_83,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_84,negated_conjecture,
esk6_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
fof(c_0_85,plain,
! [X336,X337] :
( ~ ssList(X336)
| ~ ssItem(X337)
| tl(cons(X337,X336)) = X336 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
fof(c_0_86,plain,
! [X321,X322] :
( ~ ssList(X321)
| ~ ssItem(X322)
| cons(X322,X321) != X321 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
fof(c_0_87,plain,
! [X398,X399,X400,X401] :
( ~ ssList(X398)
| ~ ssList(X399)
| ~ ssList(X400)
| ~ ssList(X401)
| ~ segmentP(X398,X399)
| segmentP(app(app(X400,X398),X401),X399) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])]) ).
fof(c_0_88,plain,
! [X397] :
( ~ ssList(X397)
| segmentP(X397,X397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])]) ).
cnf(c_0_89,negated_conjecture,
app(nil,esk6_2(esk50_0,nil)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_82]),c_0_46]),c_0_54])]) ).
cnf(c_0_90,negated_conjecture,
ssList(esk6_2(esk50_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_82]),c_0_54]),c_0_46])]) ).
fof(c_0_91,plain,
! [X438,X439] :
( ~ ssList(X438)
| ~ ssList(X439)
| nil = X438
| tl(app(X438,X439)) = app(tl(X438),X439) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
cnf(c_0_92,negated_conjecture,
( cons(esk52_0,app(nil,X1)) = app(esk50_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_36]),c_0_54]),c_0_37])]) ).
cnf(c_0_93,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(rw,[status(thm)],[c_0_80,c_0_84]) ).
cnf(c_0_94,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_96,plain,
! [X433,X434] :
( ( nil = X434
| nil != app(X433,X434)
| ~ ssList(X434)
| ~ ssList(X433) )
& ( nil = X433
| nil != app(X433,X434)
| ~ ssList(X434)
| ~ ssList(X433) )
& ( nil != X434
| nil != X433
| nil = app(X433,X434)
| ~ ssList(X434)
| ~ ssList(X433) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_97,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_98,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_99,negated_conjecture,
esk6_2(esk50_0,nil) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_89]),c_0_90])]) ).
cnf(c_0_100,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_101,negated_conjecture,
app(esk50_0,esk51_0) = cons(esk52_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_42])]) ).
cnf(c_0_102,negated_conjecture,
tl(esk50_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_36]),c_0_54]),c_0_37])]) ).
cnf(c_0_103,negated_conjecture,
esk50_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_36]),c_0_54]),c_0_37])]) ).
cnf(c_0_104,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_105,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
app(nil,esk50_0) = esk50_0,
inference(rw,[status(thm)],[c_0_89,c_0_99]) ).
cnf(c_0_107,plain,
( app(tl(X1),nil) = tl(X1)
| nil = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_61]),c_0_54])]) ).
cnf(c_0_108,negated_conjecture,
tl(cons(esk52_0,esk51_0)) = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_93]),c_0_42]),c_0_46])]),c_0_103]) ).
cnf(c_0_109,negated_conjecture,
ssList(cons(esk52_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_101]),c_0_42]),c_0_46])]) ).
cnf(c_0_110,negated_conjecture,
cons(esk52_0,esk51_0) != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_101]),c_0_42]),c_0_46])]),c_0_103]) ).
cnf(c_0_111,negated_conjecture,
( segmentP(app(esk50_0,X1),esk50_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_54]),c_0_46])]) ).
fof(c_0_112,plain,
! [X371] :
( ~ ssList(X371)
| frontsegP(X371,X371) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
cnf(c_0_113,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109])]),c_0_110]) ).
cnf(c_0_114,negated_conjecture,
( segmentP(cons(esk52_0,X1),esk50_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_45]) ).
cnf(c_0_115,negated_conjecture,
( ssList(cons(esk52_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_45]),c_0_46])]) ).
cnf(c_0_116,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_117,negated_conjecture,
frontsegP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_113]),c_0_42]),c_0_54])]) ).
cnf(c_0_118,negated_conjecture,
( segmentP(app(app(X1,cons(esk52_0,X2)),X3),esk50_0)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_114]),c_0_46])]),c_0_115]) ).
cnf(c_0_119,negated_conjecture,
( X1 = nil
| app(esk51_0,X1) != esk51_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_113]),c_0_54]),c_0_42])]) ).
cnf(c_0_120,plain,
( app(X1,esk6_2(X1,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
ssList(esk6_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_117]),c_0_42])]) ).
cnf(c_0_122,negated_conjecture,
~ segmentP(esk49_0,esk48_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_123,negated_conjecture,
( segmentP(app(esk51_0,X1),esk50_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_47]),c_0_48]),c_0_59])]) ).
cnf(c_0_124,negated_conjecture,
esk6_2(esk51_0,esk51_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]),c_0_42])]) ).
cnf(c_0_125,negated_conjecture,
~ segmentP(esk51_0,esk50_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_23]),c_0_39]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_120]),c_0_124]),c_0_54]),c_0_42])]),c_0_125]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC363+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:47:55 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 207.06/122.36 % Version : CSE_E---1.7
% 207.06/122.36 % Problem : theBenchmark.p
% 207.06/122.36 % SZS status Theorem for theBenchmark.p
% 207.06/122.36 % SZS output start CNFRefutation
% See solution above
% 207.96/123.27 % Total time : 91.435s
%------------------------------------------------------------------------------