%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC343+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 : n015.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 05:19:15 PM UTC 2026
% Result : Theorem 2.01s 1.90s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 20 unt; 0 def)
% Number of atoms : 422 ( 179 equ)
% Maximal formula atoms : 88 ( 4 avg)
% Number of connectives : 560 ( 226 ~; 246 |; 53 &)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn 52 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ? [X10] :
( ssList(X10)
& app(X1,X10) = X2
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(cons(X11,nil),X12) != X10
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( app(X14,cons(X13,nil)) != X1
| ~ lt(X13,X11) ) ) ) ) ) )
& strictorderedP(X1) )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
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(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ? [X10] :
( ssList(X10)
& app(X1,X10) = X2
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(cons(X11,nil),X12) != X10
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( app(X14,cons(X13,nil)) != X1
| ~ lt(X13,X11) ) ) ) ) ) )
& strictorderedP(X1) )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_11,negated_conjecture,
! [X481,X482,X483,X484,X485] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& app(esk50_0,esk52_0) = esk51_0
& strictorderedP(esk50_0)
& ( ~ ssItem(X481)
| ~ ssList(X482)
| app(cons(X481,nil),X482) != esk52_0
| ~ ssItem(X483)
| ~ ssList(X484)
| app(X484,cons(X483,nil)) != esk50_0
| ~ lt(X483,X481) )
& ( nil = esk51_0
| nil != esk50_0 )
& ( nil = esk48_0
| ssItem(esk53_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssItem(esk53_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| ssList(esk54_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssList(esk54_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| app(cons(esk53_1(X485),nil),esk54_1(X485)) = X485
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| app(cons(esk53_1(X485),nil),esk54_1(X485)) = X485
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| ssItem(esk55_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssItem(esk55_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| ssList(esk56_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssList(esk56_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| app(esk56_1(X485),cons(esk55_1(X485),nil)) = esk48_0
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| app(esk56_1(X485),cons(esk55_1(X485),nil)) = esk48_0
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| lt(esk55_1(X485),esk53_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| lt(esk55_1(X485),esk53_1(X485))
| ~ ssList(X485)
| app(esk48_0,X485) != esk49_0
| ~ strictorderedP(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_10])])])])]) ).
cnf(c_0_12,negated_conjecture,
strictorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( nil = esk48_0
| app(esk56_1(X1),cons(esk55_1(X1),nil)) = esk48_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
strictorderedP(esk48_0),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
app(esk50_0,esk52_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( nil = esk48_0
| ssItem(esk55_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( nil = esk48_0
| ssList(esk56_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk52_0
| ~ ssItem(X3)
| ~ ssList(X4)
| app(X4,cons(X3,nil)) != esk50_0
| ~ lt(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( app(esk56_1(X1),cons(esk55_1(X1),nil)) = esk48_0
| esk48_0 = nil
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
app(esk48_0,esk52_0) = esk49_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_17]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( esk48_0 = nil
| ssItem(esk55_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15])]) ).
cnf(c_0_25,negated_conjecture,
( esk48_0 = nil
| ssList(esk56_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_15])]) ).
cnf(c_0_26,negated_conjecture,
( nil = esk48_0
| app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
( nil = esk48_0
| ssItem(esk53_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
( nil = esk48_0
| ssList(esk54_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( nil = esk48_0
| lt(esk55_1(X1),esk53_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_30,plain,
! [X245,X246,X248] :
( ( ssList(esk6_2(X245,X246))
| ~ frontsegP(X245,X246)
| ~ ssList(X246)
| ~ ssList(X245) )
& ( app(X246,esk6_2(X245,X246)) = X245
| ~ frontsegP(X245,X246)
| ~ ssList(X246)
| ~ ssList(X245) )
& ( ~ ssList(X248)
| app(X246,X248) != X245
| frontsegP(X245,X246)
| ~ ssList(X246)
| ~ ssList(X245) ) ),
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_31,plain,
! [X388] :
( ~ ssList(X388)
| frontsegP(X388,X388) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
fof(c_0_32,plain,
! [X397] :
( ( ~ frontsegP(nil,X397)
| nil = X397
| ~ ssList(X397) )
& ( nil != X397
| frontsegP(nil,X397)
| ~ ssList(X397) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
cnf(c_0_33,negated_conjecture,
( app(X1,cons(X2,nil)) != esk48_0
| app(cons(X3,nil),X4) != esk52_0
| ~ lt(X2,X3)
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_34,negated_conjecture,
( app(esk56_1(esk52_0),cons(esk55_1(esk52_0),nil)) = esk48_0
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_35,negated_conjecture,
( esk48_0 = nil
| ssItem(esk55_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
cnf(c_0_36,negated_conjecture,
( esk48_0 = nil
| ssList(esk56_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_23])]) ).
cnf(c_0_37,negated_conjecture,
( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| esk48_0 = nil
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15])]) ).
cnf(c_0_38,negated_conjecture,
( esk48_0 = nil
| ssItem(esk53_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_15])]) ).
cnf(c_0_39,negated_conjecture,
( esk48_0 = nil
| ssList(esk54_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_15])]) ).
cnf(c_0_40,negated_conjecture,
( esk48_0 = nil
| lt(esk55_1(X1),esk53_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15])]) ).
cnf(c_0_41,negated_conjecture,
( ssList(esk54_1(X1))
| nil != esk49_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_42,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_46,negated_conjecture,
( ssItem(esk53_1(X1))
| nil != esk49_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_47,negated_conjecture,
( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| nil != esk49_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_48,plain,
! [X452] :
( ~ ssList(X452)
| app(X452,nil) = X452 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_49,negated_conjecture,
( nil = esk51_0
| nil != esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_50,negated_conjecture,
( esk48_0 = nil
| app(cons(X1,nil),X2) != esk52_0
| ~ lt(esk55_1(esk52_0),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]) ).
cnf(c_0_51,negated_conjecture,
( app(cons(esk53_1(esk52_0),nil),esk54_1(esk52_0)) = esk52_0
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_23])]) ).
cnf(c_0_52,negated_conjecture,
( esk48_0 = nil
| ssItem(esk53_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_23])]) ).
cnf(c_0_53,negated_conjecture,
( esk48_0 = nil
| ssList(esk54_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_22]),c_0_23])]) ).
cnf(c_0_54,negated_conjecture,
( esk48_0 = nil
| lt(esk55_1(esk52_0),esk53_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_22]),c_0_23])]) ).
cnf(c_0_55,negated_conjecture,
( ssList(esk54_1(X1))
| app(esk48_0,X1) != esk49_0
| esk49_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_15])]) ).
cnf(c_0_56,plain,
( app(X1,esk6_2(X1,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_57,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_58,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_59,plain,
! [X450,X451] :
( ( nil = X451
| nil != app(X450,X451)
| ~ ssList(X451)
| ~ ssList(X450) )
& ( nil = X450
| nil != app(X450,X451)
| ~ ssList(X451)
| ~ ssList(X450) )
& ( nil != X451
| nil != X450
| nil = app(X450,X451)
| ~ ssList(X451)
| ~ ssList(X450) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_60,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_44]),c_0_45])]) ).
cnf(c_0_61,negated_conjecture,
( ssItem(esk53_1(X1))
| app(esk48_0,X1) != esk49_0
| esk49_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_15])]) ).
fof(c_0_62,plain,
! [X347,X348] :
( ~ ssList(X347)
| ~ ssItem(X348)
| nil != cons(X348,X347) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
fof(c_0_63,plain,
! [X357,X358,X359] :
( ~ ssList(X357)
| ~ ssList(X358)
| ~ ssItem(X359)
| cons(X359,app(X358,X357)) = app(cons(X359,X358),X357) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(c_0_64,plain,
! [X355,X356] :
( ~ ssList(X355)
| ~ ssList(X356)
| ssList(app(X355,X356)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_65,negated_conjecture,
( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| app(esk48_0,X1) != esk49_0
| esk49_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_15])]) ).
cnf(c_0_66,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,negated_conjecture,
( esk49_0 = nil
| esk48_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_17]),c_0_13]) ).
cnf(c_0_68,negated_conjecture,
esk48_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]),c_0_54]) ).
cnf(c_0_69,negated_conjecture,
( ssList(esk54_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil
| ~ ssList(esk6_2(esk48_0,esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_70,plain,
( ssList(esk6_2(X1,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_71,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_60]),c_0_45])]) ).
cnf(c_0_73,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_60]),c_0_45])]) ).
cnf(c_0_74,negated_conjecture,
( ssItem(esk53_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil
| ~ ssList(esk6_2(esk48_0,esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_56]),c_0_57])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_77,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_78,negated_conjecture,
( app(cons(esk53_1(nil),nil),esk54_1(nil)) = nil
| esk49_0 != esk48_0
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_45]),c_0_57])]) ).
cnf(c_0_79,negated_conjecture,
esk49_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_80,negated_conjecture,
( ssList(esk54_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_57])]) ).
cnf(c_0_81,plain,
esk6_2(nil,nil) = 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_45]),c_0_73])]) ).
cnf(c_0_82,negated_conjecture,
( ssItem(esk53_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_70]),c_0_57])]) ).
cnf(c_0_83,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_84,negated_conjecture,
app(cons(esk53_1(nil),nil),esk54_1(nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_68])]),c_0_79])]) ).
cnf(c_0_85,negated_conjecture,
ssList(esk54_1(nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_68]),c_0_68]),c_0_81]),c_0_68])]),c_0_79])]) ).
cnf(c_0_86,negated_conjecture,
ssItem(esk53_1(nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_68]),c_0_68]),c_0_81]),c_0_68])]),c_0_79])]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_45]),c_0_85]),c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC343+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
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:45:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 2.01/1.90 % Version : CSE_E---1.7
% 2.01/1.90 % Problem : theBenchmark.p
% 2.01/1.90 % SZS status Theorem for theBenchmark.p
% 2.01/1.90 % SZS output start CNFRefutation
% See solution above
% 2.01/1.90 % Total time : 1.372s
%------------------------------------------------------------------------------