TSTP Solution File: SWC224+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWC224+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n002.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 : Thu Aug 31 20:57:36 EDT 2023
% Result : Theorem 7.28s 1.44s
% Output : Refutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 29
% Syntax : Number of formulae : 169 ( 16 unt; 0 def)
% Number of atoms : 920 ( 270 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 1213 ( 462 ~; 474 |; 217 &)
% ( 14 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 268 (; 204 !; 64 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25659,plain,
$false,
inference(avatar_sat_refutation,[],[f588,f918,f1070,f1181,f1193,f1291,f9256,f9372,f25278,f25620,f25658]) ).
fof(f25658,plain,
( ~ spl53_43
| ~ spl53_111
| ~ spl53_115
| ~ spl53_254 ),
inference(avatar_contradiction_clause,[],[f25657]) ).
fof(f25657,plain,
( $false
| ~ spl53_43
| ~ spl53_111
| ~ spl53_115
| ~ spl53_254 ),
inference(subsumption_resolution,[],[f25652,f25554]) ).
fof(f25554,plain,
( ssItem(sK5(hd(sK0),nil,tl(sK0)))
| ~ spl53_43
| ~ spl53_111
| ~ spl53_115
| ~ spl53_254 ),
inference(subsumption_resolution,[],[f25553,f9163]) ).
fof(f9163,plain,
( ssList(cons(hd(sK0),nil))
| ~ spl53_111 ),
inference(avatar_component_clause,[],[f9162]) ).
fof(f9162,plain,
( spl53_111
<=> ssList(cons(hd(sK0),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_111])]) ).
fof(f25553,plain,
( ssItem(sK5(hd(sK0),nil,tl(sK0)))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_43
| ~ spl53_115
| ~ spl53_254 ),
inference(subsumption_resolution,[],[f25552,f1163]) ).
fof(f1163,plain,
( ssItem(hd(sK0))
| ~ spl53_43 ),
inference(avatar_component_clause,[],[f1162]) ).
fof(f1162,plain,
( spl53_43
<=> ssItem(hd(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_43])]) ).
fof(f25552,plain,
( ssItem(sK5(hd(sK0),nil,tl(sK0)))
| ~ ssItem(hd(sK0))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_115
| ~ spl53_254 ),
inference(subsumption_resolution,[],[f25484,f9203]) ).
fof(f9203,plain,
( ssList(tl(sK0))
| ~ spl53_115 ),
inference(avatar_component_clause,[],[f9202]) ).
fof(f9202,plain,
( spl53_115
<=> ssList(tl(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_115])]) ).
fof(f25484,plain,
( ssItem(sK5(hd(sK0),nil,tl(sK0)))
| ~ ssList(tl(sK0))
| ~ ssItem(hd(sK0))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_254 ),
inference(trivial_inequality_removal,[],[f25452]) ).
fof(f25452,plain,
( sK0 != sK0
| ssItem(sK5(hd(sK0),nil,tl(sK0)))
| ~ ssList(tl(sK0))
| ~ ssItem(hd(sK0))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_254 ),
inference(superposition,[],[f1511,f20283]) ).
fof(f20283,plain,
( sK0 = cons(hd(sK0),tl(sK0))
| ~ spl53_254 ),
inference(avatar_component_clause,[],[f20281]) ).
fof(f20281,plain,
( spl53_254
<=> sK0 = cons(hd(sK0),tl(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_254])]) ).
fof(f1511,plain,
! [X0,X1] :
( cons(X0,X1) != sK0
| ssItem(sK5(X0,nil,X1))
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(duplicate_literal_removal,[],[f1504]) ).
fof(f1504,plain,
! [X0,X1] :
( cons(X0,X1) != sK0
| ssItem(sK5(X0,nil,X1))
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(superposition,[],[f721,f504]) ).
fof(f504,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax81) ).
fof(f721,plain,
! [X11,X12] :
( sK0 != app(cons(X11,nil),X12)
| ssItem(sK5(X11,nil,X12))
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssList(cons(X11,nil)) ),
inference(subsumption_resolution,[],[f710,f364]) ).
fof(f364,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax17) ).
fof(f710,plain,
! [X11,X12] :
( sK0 != app(cons(X11,nil),X12)
| ssItem(sK5(X11,nil,X12))
| ~ ssList(X12)
| ~ ssList(nil)
| ~ ssItem(X11)
| ~ ssList(cons(X11,nil)) ),
inference(superposition,[],[f346,f421]) ).
fof(f421,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax28) ).
fof(f346,plain,
! [X10,X8,X9] :
( app(app(X9,cons(X8,nil)),X10) != sK0
| ssItem(sK5(X8,X9,X10))
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssItem(X8) ),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
( ( nil != sK2
| nil = sK3 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& sK3 = app(sK2,sK4)
& ssList(sK4)
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ( ~ leq(sK5(X8,X9,X10),X8)
& leq(X8,sK5(X8,X9,X10))
& memberP(X10,sK5(X8,X9,X10))
& memberP(X9,sK5(X8,X9,X10))
& ssItem(sK5(X8,X9,X10)) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = sK2
& sK1 = sK3
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f100,f229,f228,f227,f226,f225,f224]) ).
fof(f224,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = X2
& sK1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = X2
& sK1 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != sK2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& app(sK2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = sK2
& sK1 = X3
& ssList(X3) )
& ssList(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
( ? [X3] :
( ( nil != sK2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& app(sK2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = sK2
& sK1 = X3
& ssList(X3) )
=> ( ( nil != sK2
| nil = sK3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& app(sK2,X4) = sK3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != sK0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK0
& sK0 = sK2
& sK1 = sK3
& ssList(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
( ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& app(sK2,X4) = sK3
& ssList(X4) )
=> ( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& sK3 = app(sK2,sK4)
& ssList(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f229,plain,
! [X8,X9,X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
=> ( ~ leq(sK5(X8,X9,X10),X8)
& leq(X8,sK5(X8,X9,X10))
& memberP(X10,sK5(X8,X9,X10))
& memberP(X9,sK5(X8,X9,X10))
& ssItem(sK5(X8,X9,X10)) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X11,X8)
& leq(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ! [X11] :
( ssItem(X11)
=> ( leq(X11,X8)
| ~ leq(X8,X11)
| ~ memberP(X10,X11)
| ~ memberP(X9,X11) ) )
& app(app(X9,cons(X8,nil)),X10) = X0
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssList(X8)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X8
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(X2,X8) != X3 ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X7,X4)
| ~ leq(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssList(X8)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X8
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(X2,X8) != X3 ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X7,X4)
| ~ leq(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',co1) ).
fof(f25652,plain,
( ~ ssItem(sK5(hd(sK0),nil,tl(sK0)))
| ~ spl53_43
| ~ spl53_111
| ~ spl53_115
| ~ spl53_254 ),
inference(resolution,[],[f25557,f365]) ).
fof(f365,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax38) ).
fof(f25557,plain,
( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
| ~ spl53_43
| ~ spl53_111
| ~ spl53_115
| ~ spl53_254 ),
inference(subsumption_resolution,[],[f25556,f9163]) ).
fof(f25556,plain,
( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_43
| ~ spl53_115
| ~ spl53_254 ),
inference(subsumption_resolution,[],[f25555,f1163]) ).
fof(f25555,plain,
( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
| ~ ssItem(hd(sK0))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_115
| ~ spl53_254 ),
inference(subsumption_resolution,[],[f25483,f9203]) ).
fof(f25483,plain,
( memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
| ~ ssList(tl(sK0))
| ~ ssItem(hd(sK0))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_254 ),
inference(trivial_inequality_removal,[],[f25454]) ).
fof(f25454,plain,
( sK0 != sK0
| memberP(nil,sK5(hd(sK0),nil,tl(sK0)))
| ~ ssList(tl(sK0))
| ~ ssItem(hd(sK0))
| ~ ssList(cons(hd(sK0),nil))
| ~ spl53_254 ),
inference(superposition,[],[f1849,f20283]) ).
fof(f1849,plain,
! [X0,X1] :
( cons(X0,X1) != sK0
| memberP(nil,sK5(X0,nil,X1))
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(duplicate_literal_removal,[],[f1842]) ).
fof(f1842,plain,
! [X0,X1] :
( cons(X0,X1) != sK0
| memberP(nil,sK5(X0,nil,X1))
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(superposition,[],[f807,f504]) ).
fof(f807,plain,
! [X11,X12] :
( sK0 != app(cons(X11,nil),X12)
| memberP(nil,sK5(X11,nil,X12))
| ~ ssList(X12)
| ~ ssItem(X11)
| ~ ssList(cons(X11,nil)) ),
inference(subsumption_resolution,[],[f796,f364]) ).
fof(f796,plain,
! [X11,X12] :
( sK0 != app(cons(X11,nil),X12)
| memberP(nil,sK5(X11,nil,X12))
| ~ ssList(X12)
| ~ ssList(nil)
| ~ ssItem(X11)
| ~ ssList(cons(X11,nil)) ),
inference(superposition,[],[f347,f421]) ).
fof(f347,plain,
! [X10,X8,X9] :
( app(app(X9,cons(X8,nil)),X10) != sK0
| memberP(X9,sK5(X8,X9,X10))
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssItem(X8) ),
inference(cnf_transformation,[],[f230]) ).
fof(f25620,plain,
( spl53_4
| ~ spl53_327 ),
inference(avatar_contradiction_clause,[],[f25619]) ).
fof(f25619,plain,
( $false
| spl53_4
| ~ spl53_327 ),
inference(subsumption_resolution,[],[f25618,f646]) ).
fof(f646,plain,
( nil != sK1
| spl53_4 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f644,plain,
( spl53_4
<=> nil = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).
fof(f25618,plain,
( nil = sK1
| ~ spl53_327 ),
inference(subsumption_resolution,[],[f25617,f589]) ).
fof(f589,plain,
ssList(sK1),
inference(forward_demodulation,[],[f342,f343]) ).
fof(f343,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f230]) ).
fof(f342,plain,
ssList(sK3),
inference(cnf_transformation,[],[f230]) ).
fof(f25617,plain,
( ~ ssList(sK1)
| nil = sK1
| ~ spl53_327 ),
inference(duplicate_literal_removal,[],[f25608]) ).
fof(f25608,plain,
( ~ ssList(sK1)
| nil = sK1
| ~ ssList(sK1)
| ~ spl53_327 ),
inference(resolution,[],[f25277,f416]) ).
fof(f416,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax42) ).
fof(f25277,plain,
( ! [X2] :
( ~ frontsegP(X2,sK1)
| ~ ssList(X2)
| nil = X2 )
| ~ spl53_327 ),
inference(avatar_component_clause,[],[f25276]) ).
fof(f25276,plain,
( spl53_327
<=> ! [X2] :
( ~ frontsegP(X2,sK1)
| ~ ssList(X2)
| nil = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_327])]) ).
fof(f25278,plain,
( spl53_327
| spl53_254
| ~ spl53_16 ),
inference(avatar_split_clause,[],[f25268,f916,f20281,f25276]) ).
fof(f916,plain,
( spl53_16
<=> ! [X2,X3] :
( ~ frontsegP(cons(X2,X3),sK1)
| ~ ssItem(X2)
| ~ ssList(X3)
| hd(sK0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_16])]) ).
fof(f25268,plain,
( ! [X2] :
( sK0 = cons(hd(sK0),tl(sK0))
| ~ frontsegP(X2,sK1)
| nil = X2
| ~ ssList(X2) )
| ~ spl53_16 ),
inference(duplicate_literal_removal,[],[f25175]) ).
fof(f25175,plain,
( ! [X2] :
( sK0 = cons(hd(sK0),tl(sK0))
| ~ frontsegP(X2,sK1)
| nil = X2
| ~ ssList(X2)
| ~ frontsegP(X2,sK1)
| nil = X2
| ~ ssList(X2) )
| ~ spl53_16 ),
inference(superposition,[],[f12791,f3699]) ).
fof(f3699,plain,
( ! [X1] :
( hd(X1) = hd(sK0)
| ~ frontsegP(X1,sK1)
| nil = X1
| ~ ssList(X1) )
| ~ spl53_16 ),
inference(subsumption_resolution,[],[f3698,f426]) ).
fof(f426,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax24) ).
fof(f3698,plain,
( ! [X1] :
( ~ frontsegP(X1,sK1)
| ~ ssList(tl(X1))
| hd(X1) = hd(sK0)
| nil = X1
| ~ ssList(X1) )
| ~ spl53_16 ),
inference(subsumption_resolution,[],[f3689,f425]) ).
fof(f425,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax22) ).
fof(f3689,plain,
( ! [X1] :
( ~ frontsegP(X1,sK1)
| ~ ssItem(hd(X1))
| ~ ssList(tl(X1))
| hd(X1) = hd(sK0)
| nil = X1
| ~ ssList(X1) )
| ~ spl53_16 ),
inference(superposition,[],[f917,f427]) ).
fof(f427,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax78) ).
fof(f917,plain,
( ! [X2,X3] :
( ~ frontsegP(cons(X2,X3),sK1)
| ~ ssItem(X2)
| ~ ssList(X3)
| hd(sK0) = X2 )
| ~ spl53_16 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f12791,plain,
( ! [X19] :
( sK0 = cons(hd(X19),tl(sK0))
| ~ frontsegP(X19,sK1)
| nil = X19
| ~ ssList(X19) )
| ~ spl53_16 ),
inference(subsumption_resolution,[],[f12790,f590]) ).
fof(f590,plain,
ssList(sK0),
inference(forward_demodulation,[],[f341,f344]) ).
fof(f344,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f230]) ).
fof(f341,plain,
ssList(sK2),
inference(cnf_transformation,[],[f230]) ).
fof(f12790,plain,
( ! [X19] :
( sK0 = cons(hd(X19),tl(sK0))
| ~ ssList(sK0)
| ~ frontsegP(X19,sK1)
| nil = X19
| ~ ssList(X19) )
| ~ spl53_16 ),
inference(subsumption_resolution,[],[f12780,f345]) ).
fof(f345,plain,
nil != sK0,
inference(cnf_transformation,[],[f230]) ).
fof(f12780,plain,
( ! [X19] :
( sK0 = cons(hd(X19),tl(sK0))
| nil = sK0
| ~ ssList(sK0)
| ~ frontsegP(X19,sK1)
| nil = X19
| ~ ssList(X19) )
| ~ spl53_16 ),
inference(superposition,[],[f427,f3699]) ).
fof(f9372,plain,
( ~ spl53_43
| spl53_111 ),
inference(avatar_contradiction_clause,[],[f9371]) ).
fof(f9371,plain,
( $false
| ~ spl53_43
| spl53_111 ),
inference(subsumption_resolution,[],[f9370,f364]) ).
fof(f9370,plain,
( ~ ssList(nil)
| ~ spl53_43
| spl53_111 ),
inference(subsumption_resolution,[],[f9369,f1163]) ).
fof(f9369,plain,
( ~ ssItem(hd(sK0))
| ~ ssList(nil)
| spl53_111 ),
inference(resolution,[],[f9164,f499]) ).
fof(f499,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax16) ).
fof(f9164,plain,
( ~ ssList(cons(hd(sK0),nil))
| spl53_111 ),
inference(avatar_component_clause,[],[f9162]) ).
fof(f9256,plain,
spl53_115,
inference(avatar_contradiction_clause,[],[f9255]) ).
fof(f9255,plain,
( $false
| spl53_115 ),
inference(subsumption_resolution,[],[f9254,f590]) ).
fof(f9254,plain,
( ~ ssList(sK0)
| spl53_115 ),
inference(subsumption_resolution,[],[f9253,f345]) ).
fof(f9253,plain,
( nil = sK0
| ~ ssList(sK0)
| spl53_115 ),
inference(resolution,[],[f9204,f426]) ).
fof(f9204,plain,
( ~ ssList(tl(sK0))
| spl53_115 ),
inference(avatar_component_clause,[],[f9202]) ).
fof(f1291,plain,
spl53_43,
inference(avatar_contradiction_clause,[],[f1290]) ).
fof(f1290,plain,
( $false
| spl53_43 ),
inference(subsumption_resolution,[],[f1289,f590]) ).
fof(f1289,plain,
( ~ ssList(sK0)
| spl53_43 ),
inference(subsumption_resolution,[],[f1288,f345]) ).
fof(f1288,plain,
( nil = sK0
| ~ ssList(sK0)
| spl53_43 ),
inference(resolution,[],[f1164,f425]) ).
fof(f1164,plain,
( ~ ssItem(hd(sK0))
| spl53_43 ),
inference(avatar_component_clause,[],[f1162]) ).
fof(f1193,plain,
~ spl53_4,
inference(avatar_split_clause,[],[f1192,f644]) ).
fof(f1192,plain,
nil != sK1,
inference(subsumption_resolution,[],[f1191,f590]) ).
fof(f1191,plain,
( ~ ssList(sK0)
| nil != sK1 ),
inference(forward_demodulation,[],[f1190,f344]) ).
fof(f1190,plain,
( nil != sK1
| ~ ssList(sK2) ),
inference(subsumption_resolution,[],[f1189,f345]) ).
fof(f1189,plain,
( nil = sK0
| nil != sK1
| ~ ssList(sK2) ),
inference(forward_demodulation,[],[f1170,f344]) ).
fof(f1170,plain,
( nil != sK1
| nil = sK2
| ~ ssList(sK2) ),
inference(forward_demodulation,[],[f1169,f343]) ).
fof(f1169,plain,
( nil != sK3
| nil = sK2
| ~ ssList(sK2) ),
inference(subsumption_resolution,[],[f600,f351]) ).
fof(f351,plain,
ssList(sK4),
inference(cnf_transformation,[],[f230]) ).
fof(f600,plain,
( nil != sK3
| nil = sK2
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f529,f352]) ).
fof(f352,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f230]) ).
fof(f529,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f335]) ).
fof(f335,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f334]) ).
fof(f334,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax83) ).
fof(f1181,plain,
( spl53_4
| ~ spl53_1 ),
inference(avatar_split_clause,[],[f1174,f581,f644]) ).
fof(f581,plain,
( spl53_1
<=> nil = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_1])]) ).
fof(f1174,plain,
( nil = sK1
| ~ spl53_1 ),
inference(superposition,[],[f583,f343]) ).
fof(f583,plain,
( nil = sK3
| ~ spl53_1 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f1070,plain,
( spl53_4
| spl53_13 ),
inference(avatar_contradiction_clause,[],[f1069]) ).
fof(f1069,plain,
( $false
| spl53_4
| spl53_13 ),
inference(subsumption_resolution,[],[f1068,f589]) ).
fof(f1068,plain,
( ~ ssList(sK1)
| spl53_4
| spl53_13 ),
inference(subsumption_resolution,[],[f1067,f646]) ).
fof(f1067,plain,
( nil = sK1
| ~ ssList(sK1)
| spl53_13 ),
inference(resolution,[],[f904,f426]) ).
fof(f904,plain,
( ~ ssList(tl(sK1))
| spl53_13 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f902,plain,
( spl53_13
<=> ssList(tl(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_13])]) ).
fof(f918,plain,
( ~ spl53_13
| spl53_16
| spl53_2
| spl53_4 ),
inference(avatar_split_clause,[],[f914,f644,f585,f916,f902]) ).
fof(f585,plain,
( spl53_2
<=> nil = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).
fof(f914,plain,
( ! [X2,X3] :
( ~ frontsegP(cons(X2,X3),sK1)
| hd(sK0) = X2
| ~ ssList(tl(sK1))
| ~ ssList(X3)
| ~ ssItem(X2) )
| spl53_2
| spl53_4 ),
inference(subsumption_resolution,[],[f866,f821]) ).
fof(f821,plain,
( ssItem(hd(sK0))
| spl53_2
| spl53_4 ),
inference(subsumption_resolution,[],[f820,f589]) ).
fof(f820,plain,
( ssItem(hd(sK0))
| ~ ssList(sK1)
| spl53_2
| spl53_4 ),
inference(subsumption_resolution,[],[f815,f646]) ).
fof(f815,plain,
( ssItem(hd(sK0))
| nil = sK1
| ~ ssList(sK1)
| spl53_2 ),
inference(superposition,[],[f425,f634]) ).
fof(f634,plain,
( hd(sK1) = hd(sK0)
| spl53_2 ),
inference(subsumption_resolution,[],[f633,f590]) ).
fof(f633,plain,
( ~ ssList(sK0)
| hd(sK1) = hd(sK0)
| spl53_2 ),
inference(forward_demodulation,[],[f632,f344]) ).
fof(f632,plain,
( hd(sK1) = hd(sK0)
| ~ ssList(sK2)
| spl53_2 ),
inference(forward_demodulation,[],[f631,f344]) ).
fof(f631,plain,
( hd(sK2) = hd(sK1)
| ~ ssList(sK2)
| spl53_2 ),
inference(forward_demodulation,[],[f630,f343]) ).
fof(f630,plain,
( hd(sK2) = hd(sK3)
| ~ ssList(sK2)
| spl53_2 ),
inference(subsumption_resolution,[],[f629,f351]) ).
fof(f629,plain,
( hd(sK2) = hd(sK3)
| ~ ssList(sK4)
| ~ ssList(sK2)
| spl53_2 ),
inference(subsumption_resolution,[],[f598,f587]) ).
fof(f587,plain,
( nil != sK2
| spl53_2 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f598,plain,
( hd(sK2) = hd(sK3)
| nil = sK2
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f510,f352]) ).
fof(f510,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax85) ).
fof(f866,plain,
( ! [X2,X3] :
( ~ frontsegP(cons(X2,X3),sK1)
| hd(sK0) = X2
| ~ ssList(tl(sK1))
| ~ ssList(X3)
| ~ ssItem(hd(sK0))
| ~ ssItem(X2) )
| spl53_2
| spl53_4 ),
inference(superposition,[],[f398,f819]) ).
fof(f819,plain,
( sK1 = cons(hd(sK0),tl(sK1))
| spl53_2
| spl53_4 ),
inference(subsumption_resolution,[],[f818,f589]) ).
fof(f818,plain,
( sK1 = cons(hd(sK0),tl(sK1))
| ~ ssList(sK1)
| spl53_2
| spl53_4 ),
inference(subsumption_resolution,[],[f814,f646]) ).
fof(f814,plain,
( sK1 = cons(hd(sK0),tl(sK1))
| nil = sK1
| ~ ssList(sK1)
| spl53_2 ),
inference(superposition,[],[f427,f634]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( ~ frontsegP(cons(X0,X2),cons(X1,X3))
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f238]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355',ax44) ).
fof(f588,plain,
( spl53_1
| ~ spl53_2 ),
inference(avatar_split_clause,[],[f355,f585,f581]) ).
fof(f355,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWC224+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 16:10:50 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.JFXQD3IDzR/Vampire---4.8_14355
% 0.15/0.37 % (14612)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (14614)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.21/0.43 % (14617)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.43 % (14615)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.21/0.43 % (14613)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.21/0.43 % (14618)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.21/0.43 % (14616)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.21/0.43 % (14619)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 7.28/1.43 % (14619)First to succeed.
% 7.28/1.44 % (14619)Refutation found. Thanks to Tanya!
% 7.28/1.44 % SZS status Theorem for Vampire---4
% 7.28/1.44 % SZS output start Proof for Vampire---4
% See solution above
% 7.28/1.44 % (14619)------------------------------
% 7.28/1.44 % (14619)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 7.28/1.44 % (14619)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 7.28/1.44 % (14619)Termination reason: Refutation
% 7.28/1.44
% 7.28/1.44 % (14619)Memory used [KB]: 19701
% 7.28/1.44 % (14619)Time elapsed: 1.007 s
% 7.28/1.44 % (14619)------------------------------
% 7.28/1.44 % (14619)------------------------------
% 7.28/1.44 % (14612)Success in time 1.073 s
% 7.28/1.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------