%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC115+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 : n025.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 05:18:20 PM UTC 2026
% Result : Theorem 23.38s 13.99s
% Output : CNFRefutation 23.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 21
% Syntax : Number of formulae : 122 ( 35 unt; 0 def)
% Number of atoms : 437 ( 124 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 526 ( 211 ~; 213 |; 44 &)
% ( 5 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn 94 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( nil = X2
& nil = X1 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5)
| ? [X6] :
( ssItem(X6)
& X5 != X6
& memberP(X4,X6)
& leq(X6,X5) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
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(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/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
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(c_0_21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( nil = X2
& nil = X1 )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5)
| ? [X6] :
( ssItem(X6)
& X5 != X6
& memberP(X4,X6)
& leq(X6,X5) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_22,negated_conjecture,
! [X465] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( nil != esk49_0
| nil != esk48_0 )
& ( nil = esk51_0
| ssItem(esk52_0) )
& ( nil = esk50_0
| ssItem(esk52_0) )
& ( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk52_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk52_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk52_0) )
& ( nil = esk51_0
| ~ ssItem(X465)
| esk52_0 = X465
| ~ memberP(esk51_0,X465)
| ~ leq(X465,esk52_0) )
& ( nil = esk50_0
| ~ ssItem(X465)
| esk52_0 = X465
| ~ memberP(esk51_0,X465)
| ~ leq(X465,esk52_0) )
& ( ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,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_21])])])])]) ).
fof(c_0_23,plain,
! [X322,X323] :
( ~ ssList(X322)
| ~ ssItem(X323)
| cons(X323,X322) != X322 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_24,negated_conjecture,
( nil != esk49_0
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( nil = esk51_0
| cons(esk52_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_30,negated_conjecture,
( nil = esk51_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( esk50_0 != nil
| esk51_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
fof(c_0_32,plain,
! [X229,X230,X232] :
( ( ssList(esk6_2(X229,X230))
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( app(X230,esk6_2(X229,X230)) = X229
| ~ frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) )
& ( ~ ssList(X232)
| app(X230,X232) != X229
| frontsegP(X229,X230)
| ~ ssList(X230)
| ~ ssList(X229) ) ),
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_33,plain,
! [X339,X340] :
( ~ ssList(X339)
| ~ ssList(X340)
| ssList(app(X339,X340)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_34,plain,
! [X220,X221,X224,X225] :
( ( ssList(esk3_2(X220,X221))
| ~ memberP(X220,X221)
| ~ ssItem(X221)
| ~ ssList(X220) )
& ( ssList(esk4_2(X220,X221))
| ~ memberP(X220,X221)
| ~ ssItem(X221)
| ~ ssList(X220) )
& ( app(esk3_2(X220,X221),cons(X221,esk4_2(X220,X221))) = X220
| ~ memberP(X220,X221)
| ~ ssItem(X221)
| ~ ssList(X220) )
& ( ~ ssList(X224)
| ~ ssList(X225)
| app(X224,cons(X221,X225)) != X220
| memberP(X220,X221)
| ~ ssItem(X221)
| ~ ssList(X220) ) ),
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_35,negated_conjecture,
( nil = esk50_0
| memberP(esk51_0,esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_36,negated_conjecture,
esk50_0 != nil,
inference(csr,[status(thm)],[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]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_38,negated_conjecture,
( nil = esk50_0
| ssItem(esk52_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_39,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,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_34]) ).
cnf(c_0_42,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(sr,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_44,negated_conjecture,
ssItem(esk52_0),
inference(sr,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_45,plain,
( ssList(esk3_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_39]),c_0_40]) ).
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_41,c_0_42]),c_0_43]),c_0_44])]) ).
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_45,c_0_42]),c_0_43]),c_0_44])]) ).
fof(c_0_49,plain,
! [X320,X321] :
( ~ ssList(X320)
| ~ ssItem(X321)
| ssList(cons(X321,X320)) ),
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_34]) ).
fof(c_0_51,plain,
! [X373,X374,X375] :
( ~ ssList(X373)
| ~ ssList(X374)
| ~ ssList(X375)
| ~ frontsegP(X373,X374)
| frontsegP(app(X373,X375),X374) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_52,plain,
! [X380] :
( ~ ssList(X380)
| frontsegP(X380,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_53,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_46,c_0_47]),c_0_48])]) ).
cnf(c_0_54,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,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_42]),c_0_43]),c_0_44])]) ).
cnf(c_0_56,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_59,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_53,c_0_54]),c_0_55]),c_0_44])]) ).
cnf(c_0_60,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_61,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_29])]) ).
cnf(c_0_62,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_58,c_0_59]),c_0_43]),c_0_48])]) ).
cnf(c_0_63,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_60,c_0_59]),c_0_48]),c_0_43])]) ).
fof(c_0_64,plain,
! [X344] :
( ~ ssList(X344)
| app(nil,X344) = X344 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_65,negated_conjecture,
frontsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_48])]) ).
fof(c_0_66,plain,
! [X341,X342,X343] :
( ~ ssList(X341)
| ~ ssList(X342)
| ~ ssItem(X343)
| cons(X343,app(X342,X341)) = app(cons(X343,X342),X341) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_67,negated_conjecture,
( nil = esk50_0
| cons(esk52_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_68,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,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_58,c_0_65]),c_0_43]),c_0_29])]) ).
cnf(c_0_70,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_60,c_0_65]),c_0_29]),c_0_43])]) ).
cnf(c_0_71,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_72,negated_conjecture,
cons(esk52_0,nil) = esk50_0,
inference(sr,[status(thm)],[c_0_67,c_0_36]) ).
cnf(c_0_73,negated_conjecture,
esk6_2(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
fof(c_0_74,plain,
! [X337,X338] :
( ~ ssList(X337)
| ~ ssItem(X338)
| tl(cons(X338,X337)) = X337 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
fof(c_0_75,plain,
! [X237,X238,X241,X242] :
( ( ssList(esk8_2(X237,X238))
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ssList(esk9_2(X237,X238))
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( app(app(esk8_2(X237,X238),X238),esk9_2(X237,X238)) = X237
| ~ segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ~ ssList(X241)
| ~ ssList(X242)
| app(app(X241,X238),X242) != X237
| segmentP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) ) ),
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_76,plain,
! [X439,X440] :
( ~ ssList(X439)
| ~ ssList(X440)
| nil = X439
| tl(app(X439,X440)) = app(tl(X439),X440) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_77,plain,
! [X436] :
( ~ ssList(X436)
| app(X436,nil) = X436 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_78,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_71,c_0_72]),c_0_29]),c_0_44])]) ).
cnf(c_0_79,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(rw,[status(thm)],[c_0_69,c_0_73]) ).
cnf(c_0_80,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_81,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_82,plain,
! [X434,X435] :
( ( nil = X435
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil = X434
| nil != app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) )
& ( nil != X435
| nil != X434
| nil = app(X434,X435)
| ~ ssList(X435)
| ~ ssList(X434) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_83,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_75]) ).
fof(c_0_84,plain,
! [X429,X430] :
( ~ ssList(X429)
| ~ ssItem(X430)
| cons(X430,X429) = app(cons(X430,nil),X429) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_85,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_86,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_87,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_78,c_0_79]),c_0_43])]) ).
cnf(c_0_88,negated_conjecture,
tl(esk50_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_72]),c_0_29]),c_0_44])]) ).
cnf(c_0_89,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_81,c_0_25]) ).
cnf(c_0_90,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_91,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_83]) ).
cnf(c_0_92,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_93,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_85,c_0_86]),c_0_29])]) ).
cnf(c_0_94,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_85,c_0_87]),c_0_88]),c_0_79]),c_0_43]),c_0_89])]),c_0_36]) ).
cnf(c_0_95,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_40,c_0_87]),c_0_43]),c_0_89])]) ).
cnf(c_0_96,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_90,c_0_87]),c_0_43]),c_0_89])]),c_0_36]) ).
fof(c_0_97,plain,
! [X399,X400,X401,X402] :
( ~ ssList(X399)
| ~ ssList(X400)
| ~ ssList(X401)
| ~ ssList(X402)
| ~ segmentP(X399,X400)
| segmentP(app(app(X401,X399),X402),X400) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])]) ).
cnf(c_0_98,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_91,c_0_68]),c_0_29])]),c_0_40]) ).
cnf(c_0_99,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_92,c_0_72]),c_0_44])]) ).
fof(c_0_100,plain,
! [X426,X427,X428] :
( ~ ssList(X426)
| ~ ssList(X427)
| ~ ssList(X428)
| app(X427,X428) != app(X427,X426)
| X428 = X426 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(c_0_101,plain,
! [X372] :
( ~ ssList(X372)
| frontsegP(X372,X372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
cnf(c_0_102,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_93,c_0_94]),c_0_95])]),c_0_96]) ).
cnf(c_0_103,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_97]) ).
cnf(c_0_104,negated_conjecture,
( segmentP(cons(esk52_0,X1),esk50_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_89])]) ).
cnf(c_0_105,negated_conjecture,
( ssList(cons(esk52_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_99]),c_0_89])]) ).
cnf(c_0_106,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_108,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_46,c_0_102]),c_0_43]),c_0_29])]) ).
cnf(c_0_109,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_103,c_0_104]),c_0_89])]),c_0_105]) ).
cnf(c_0_110,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_106,c_0_102]),c_0_29]),c_0_43])]) ).
cnf(c_0_111,plain,
( app(X1,esk6_2(X1,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
ssList(esk6_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_108]),c_0_43])]) ).
cnf(c_0_113,negated_conjecture,
( ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_114,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_109,c_0_47]),c_0_48]),c_0_55])]) ).
cnf(c_0_115,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_110,c_0_111]),c_0_112]),c_0_43])]) ).
cnf(c_0_116,negated_conjecture,
( ~ segmentP(esk51_0,esk50_0)
| ~ neq(esk50_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_25]),c_0_26]),c_0_25]) ).
cnf(c_0_117,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_111]),c_0_115]),c_0_29]),c_0_43])]) ).
fof(c_0_118,plain,
! [X318,X319] :
( ( ~ neq(X318,X319)
| X318 != X319
| ~ ssList(X319)
| ~ ssList(X318) )
& ( X318 = X319
| neq(X318,X319)
| ~ ssList(X319)
| ~ ssList(X318) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_119,negated_conjecture,
~ neq(esk50_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_120,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_121,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_29]),c_0_89])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC115+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n025.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 04:28:28 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 23.38/13.99 % Version : CSE_E---1.7
% 23.38/13.99 % Problem : theBenchmark.p
% 23.38/13.99 % SZS status Theorem for theBenchmark.p
% 23.38/13.99 % SZS output start CNFRefutation
% See solution above
% 23.51/14.08 % Total time : 10.386s
%------------------------------------------------------------------------------