TSTP Solution File: SWC091+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWC091+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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:56:28 EDT 2023
% Result : Theorem 7.77s 1.50s
% Output : Refutation 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 38
% Syntax : Number of formulae : 209 ( 14 unt; 0 def)
% Number of atoms : 968 ( 154 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 1296 ( 537 ~; 514 |; 175 &)
% ( 21 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 12 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 306 (; 249 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38785,plain,
$false,
inference(avatar_sat_refutation,[],[f1213,f1368,f2580,f3528,f3642,f3658,f6075,f6081,f6552,f6557,f6599,f38399]) ).
fof(f38399,plain,
( ~ spl69_82
| ~ spl69_6
| spl69_9
| ~ spl69_200
| ~ spl69_201 ),
inference(avatar_split_clause,[],[f38386,f6555,f6550,f1173,f1159,f2526]) ).
fof(f2526,plain,
( spl69_82
<=> ssItem(sK23(sK21)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_82])]) ).
fof(f1159,plain,
( spl69_6
<=> nil = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).
fof(f1173,plain,
( spl69_9
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_9])]) ).
fof(f6550,plain,
( spl69_200
<=> ! [X8] :
( ssList(cons(X8,nil))
| ~ ssItem(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_200])]) ).
fof(f6555,plain,
( spl69_201
<=> ! [X9] :
( nil != cons(X9,nil)
| ~ ssItem(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_201])]) ).
fof(f38386,plain,
( ~ ssItem(sK23(sK21))
| ~ spl69_6
| spl69_9
| ~ spl69_200
| ~ spl69_201 ),
inference(subsumption_resolution,[],[f38385,f378]) ).
fof(f378,plain,
ssList(sK21),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,sK20)
| ~ frontsegP(sK21,X4)
| ~ neq(sK20,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(sK19,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(sK20)
& frontsegP(sK21,sK20)
& neq(sK19,nil)
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f100,f254,f253,f252,f251]) ).
fof(f251,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(X0,X5)
| ~ segmentP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(sK19,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(sK19,nil)
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(sK19,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(sK19,nil)
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,sK20)
| ~ frontsegP(X3,X4)
| ~ neq(sK20,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(sK19,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(sK20)
& frontsegP(X3,sK20)
& neq(sK19,nil)
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,sK20)
| ~ frontsegP(X3,X4)
| ~ neq(sK20,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(sK19,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(sK20)
& frontsegP(X3,sK20)
& neq(sK19,nil)
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,sK20)
| ~ frontsegP(sK21,X4)
| ~ neq(sK20,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(sK19,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(sK20)
& frontsegP(sK21,sK20)
& neq(sK19,nil)
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(X0,X5)
| ~ segmentP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ totalorderedP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& ! [X5] :
( ~ segmentP(X0,X5)
| ~ segmentP(X1,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) )
& totalorderedP(X2)
& frontsegP(X3,X2)
& neq(X1,nil)
& 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)
=> ( ? [X4] :
( totalorderedP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| ? [X5] :
( segmentP(X0,X5)
& segmentP(X1,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X2)
& frontsegP(X3,X5)
& neq(X2,X5)
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X2)
& frontsegP(X3,X5)
& neq(X2,X5)
& ssList(X5) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ totalorderedP(X2)
| ~ frontsegP(X3,X2)
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',co1) ).
fof(f38385,plain,
( ~ ssItem(sK23(sK21))
| ~ ssList(sK21)
| ~ spl69_6
| spl69_9
| ~ spl69_200
| ~ spl69_201 ),
inference(subsumption_resolution,[],[f38379,f1175]) ).
fof(f1175,plain,
( nil != sK21
| spl69_9 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f38379,plain,
( ~ ssItem(sK23(sK21))
| nil = sK21
| ~ ssList(sK21)
| ~ spl69_6
| ~ spl69_200
| ~ spl69_201 ),
inference(resolution,[],[f38377,f4578]) ).
fof(f4578,plain,
! [X0] :
( frontsegP(X0,cons(sK23(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4577,f459]) ).
fof(f459,plain,
! [X0] :
( ssItem(sK23(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0] :
( ( cons(sK23(X0),sK22(X0)) = X0
& ssItem(sK23(X0))
& ssList(sK22(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f150,f276,f275]) ).
fof(f275,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK22(X0)) = X0
& ssItem(X2) )
& ssList(sK22(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f276,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK22(X0)) = X0
& ssItem(X2) )
=> ( cons(sK23(X0),sK22(X0)) = X0
& ssItem(sK23(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax20) ).
fof(f4577,plain,
! [X0] :
( frontsegP(X0,cons(sK23(X0),nil))
| ~ ssItem(sK23(X0))
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4568,f458]) ).
fof(f458,plain,
! [X0] :
( ssList(sK22(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f4568,plain,
! [X0] :
( frontsegP(X0,cons(sK23(X0),nil))
| ~ ssList(sK22(X0))
| ~ ssItem(sK23(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f2232,f460]) ).
fof(f460,plain,
! [X0] :
( cons(sK23(X0),sK22(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f2232,plain,
! [X8,X7] :
( frontsegP(cons(X7,X8),cons(X7,nil))
| ~ ssList(X8)
| ~ ssItem(X7) ),
inference(subsumption_resolution,[],[f2227,f394]) ).
fof(f394,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax17) ).
fof(f2227,plain,
! [X8,X7] :
( frontsegP(cons(X7,X8),cons(X7,nil))
| ~ ssList(nil)
| ~ ssList(X8)
| ~ ssItem(X7) ),
inference(duplicate_literal_removal,[],[f2223]) ).
fof(f2223,plain,
! [X8,X7] :
( frontsegP(cons(X7,X8),cons(X7,nil))
| ~ ssList(nil)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssList(X8) ),
inference(resolution,[],[f637,f453]) ).
fof(f453,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax45) ).
fof(f637,plain,
! [X2,X3,X1] :
( ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f610]) ).
fof(f610,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f430]) ).
fof(f430,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,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,[],[f263]) ).
fof(f263,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.iGBhoF9uFW/Vampire---4.8_24056',ax44) ).
fof(f38377,plain,
( ! [X0] :
( ~ frontsegP(sK21,cons(X0,nil))
| ~ ssItem(X0) )
| ~ spl69_6
| ~ spl69_200
| ~ spl69_201 ),
inference(subsumption_resolution,[],[f38376,f6556]) ).
fof(f6556,plain,
( ! [X9] :
( nil != cons(X9,nil)
| ~ ssItem(X9) )
| ~ spl69_201 ),
inference(avatar_component_clause,[],[f6555]) ).
fof(f38376,plain,
( ! [X0] :
( ~ frontsegP(sK21,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0) )
| ~ spl69_6
| ~ spl69_200 ),
inference(duplicate_literal_removal,[],[f38371]) ).
fof(f38371,plain,
( ! [X0] :
( ~ frontsegP(sK21,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0)
| ~ ssItem(X0) )
| ~ spl69_6
| ~ spl69_200 ),
inference(resolution,[],[f4535,f6551]) ).
fof(f6551,plain,
( ! [X8] :
( ssList(cons(X8,nil))
| ~ ssItem(X8) )
| ~ spl69_200 ),
inference(avatar_component_clause,[],[f6550]) ).
fof(f4535,plain,
( ! [X3] :
( ~ ssList(cons(X3,nil))
| ~ frontsegP(sK21,cons(X3,nil))
| nil = cons(X3,nil)
| ~ ssItem(X3) )
| ~ spl69_6 ),
inference(resolution,[],[f4128,f405]) ).
fof(f405,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax65) ).
fof(f4128,plain,
( ! [X0] :
( ~ totalorderedP(X0)
| ~ frontsegP(sK21,X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl69_6 ),
inference(subsumption_resolution,[],[f4127,f394]) ).
fof(f4127,plain,
( ! [X0] :
( ~ totalorderedP(X0)
| ~ frontsegP(sK21,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(nil) )
| ~ spl69_6 ),
inference(duplicate_literal_removal,[],[f4125]) ).
fof(f4125,plain,
( ! [X0] :
( ~ totalorderedP(X0)
| ~ frontsegP(sK21,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl69_6 ),
inference(resolution,[],[f3789,f574]) ).
fof(f574,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax15) ).
fof(f3789,plain,
( ! [X4] :
( ~ neq(nil,X4)
| ~ totalorderedP(X4)
| ~ frontsegP(sK21,X4)
| ~ ssList(X4) )
| ~ spl69_6 ),
inference(forward_demodulation,[],[f3788,f1161]) ).
fof(f1161,plain,
( nil = sK20
| ~ spl69_6 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f3788,plain,
( ! [X4] :
( ~ totalorderedP(X4)
| ~ frontsegP(sK21,X4)
| ~ neq(sK20,X4)
| ~ ssList(X4) )
| ~ spl69_6 ),
inference(subsumption_resolution,[],[f3663,f451]) ).
fof(f451,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax57) ).
fof(f3663,plain,
( ! [X4] :
( ~ segmentP(X4,nil)
| ~ totalorderedP(X4)
| ~ frontsegP(sK21,X4)
| ~ neq(sK20,X4)
| ~ ssList(X4) )
| ~ spl69_6 ),
inference(backward_demodulation,[],[f385,f1161]) ).
fof(f385,plain,
! [X4] :
( ~ segmentP(X4,sK20)
| ~ totalorderedP(X4)
| ~ frontsegP(sK21,X4)
| ~ neq(sK20,X4)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f255]) ).
fof(f6599,plain,
( ~ spl69_6
| ~ spl69_106
| spl69_180 ),
inference(avatar_contradiction_clause,[],[f6598]) ).
fof(f6598,plain,
( $false
| ~ spl69_6
| ~ spl69_106
| spl69_180 ),
inference(subsumption_resolution,[],[f6597,f394]) ).
fof(f6597,plain,
( ~ ssList(nil)
| ~ spl69_6
| ~ spl69_106
| spl69_180 ),
inference(subsumption_resolution,[],[f6596,f3782]) ).
fof(f3782,plain,
( segmentP(nil,nil)
| ~ spl69_6
| ~ spl69_106 ),
inference(backward_demodulation,[],[f3526,f1161]) ).
fof(f3526,plain,
( segmentP(sK20,sK20)
| ~ spl69_106 ),
inference(avatar_component_clause,[],[f3525]) ).
fof(f3525,plain,
( spl69_106
<=> segmentP(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_106])]) ).
fof(f6596,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| spl69_180 ),
inference(duplicate_literal_removal,[],[f6595]) ).
fof(f6595,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl69_180 ),
inference(resolution,[],[f6432,f579]) ).
fof(f579,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
& ssList(sK65(X0,X1))
& ssList(sK64(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f362,f364,f363]) ).
fof(f363,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK64(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f364,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK64(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f362,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax7) ).
fof(f6432,plain,
( ~ ssList(sK65(nil,nil))
| spl69_180 ),
inference(avatar_component_clause,[],[f6430]) ).
fof(f6430,plain,
( spl69_180
<=> ssList(sK65(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_180])]) ).
fof(f6557,plain,
( ~ spl69_180
| spl69_201
| ~ spl69_170
| ~ spl69_171 ),
inference(avatar_split_clause,[],[f6553,f6072,f6068,f6555,f6430]) ).
fof(f6068,plain,
( spl69_170
<=> ssList(sK64(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_170])]) ).
fof(f6072,plain,
( spl69_171
<=> nil = app(sK64(nil,nil),sK65(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_171])]) ).
fof(f6553,plain,
( ! [X9] :
( nil != cons(X9,nil)
| ~ ssList(sK65(nil,nil))
| ~ ssItem(X9) )
| ~ spl69_170
| ~ spl69_171 ),
inference(subsumption_resolution,[],[f6418,f6069]) ).
fof(f6069,plain,
( ssList(sK64(nil,nil))
| ~ spl69_170 ),
inference(avatar_component_clause,[],[f6068]) ).
fof(f6418,plain,
( ! [X9] :
( nil != cons(X9,nil)
| ~ ssList(sK65(nil,nil))
| ~ ssItem(X9)
| ~ ssList(sK64(nil,nil)) )
| ~ spl69_171 ),
inference(superposition,[],[f2349,f6074]) ).
fof(f6074,plain,
( nil = app(sK64(nil,nil),sK65(nil,nil))
| ~ spl69_171 ),
inference(avatar_component_clause,[],[f6072]) ).
fof(f2349,plain,
! [X18,X16,X17] :
( nil != cons(X16,app(X17,X18))
| ~ ssList(X18)
| ~ ssItem(X16)
| ~ ssList(X17) ),
inference(subsumption_resolution,[],[f2348,f556]) ).
fof(f556,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.iGBhoF9uFW/Vampire---4.8_24056',ax16) ).
fof(f2348,plain,
! [X18,X16,X17] :
( nil != cons(X16,app(X17,X18))
| ~ ssList(X18)
| ~ ssList(cons(X16,X17))
| ~ ssItem(X16)
| ~ ssList(X17) ),
inference(subsumption_resolution,[],[f2326,f557]) ).
fof(f557,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax21) ).
fof(f2326,plain,
! [X18,X16,X17] :
( nil != cons(X16,app(X17,X18))
| nil = cons(X16,X17)
| ~ ssList(X18)
| ~ ssList(cons(X16,X17))
| ~ ssItem(X16)
| ~ ssList(X17) ),
inference(duplicate_literal_removal,[],[f2304]) ).
fof(f2304,plain,
! [X18,X16,X17] :
( nil != cons(X16,app(X17,X18))
| nil = cons(X16,X17)
| ~ ssList(X18)
| ~ ssList(cons(X16,X17))
| ~ ssItem(X16)
| ~ ssList(X17)
| ~ ssList(X18) ),
inference(superposition,[],[f586,f588]) ).
fof(f588,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax27) ).
fof(f586,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,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,[],[f370]) ).
fof(f370,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.iGBhoF9uFW/Vampire---4.8_24056',ax83) ).
fof(f6552,plain,
( ~ spl69_180
| spl69_200
| ~ spl69_170
| ~ spl69_171 ),
inference(avatar_split_clause,[],[f6548,f6072,f6068,f6550,f6430]) ).
fof(f6548,plain,
( ! [X8] :
( ssList(cons(X8,nil))
| ~ ssList(sK65(nil,nil))
| ~ ssItem(X8) )
| ~ spl69_170
| ~ spl69_171 ),
inference(subsumption_resolution,[],[f6417,f6069]) ).
fof(f6417,plain,
( ! [X8] :
( ssList(cons(X8,nil))
| ~ ssList(sK65(nil,nil))
| ~ ssItem(X8)
| ~ ssList(sK64(nil,nil)) )
| ~ spl69_171 ),
inference(superposition,[],[f2344,f6074]) ).
fof(f2344,plain,
! [X8,X9,X7] :
( ssList(cons(X7,app(X8,X9)))
| ~ ssList(X9)
| ~ ssItem(X7)
| ~ ssList(X8) ),
inference(subsumption_resolution,[],[f2329,f556]) ).
fof(f2329,plain,
! [X8,X9,X7] :
( ssList(cons(X7,app(X8,X9)))
| ~ ssList(X9)
| ~ ssList(cons(X7,X8))
| ~ ssItem(X7)
| ~ ssList(X8) ),
inference(duplicate_literal_removal,[],[f2301]) ).
fof(f2301,plain,
! [X8,X9,X7] :
( ssList(cons(X7,app(X8,X9)))
| ~ ssList(X9)
| ~ ssList(cons(X7,X8))
| ~ ssItem(X7)
| ~ ssList(X8)
| ~ ssList(X9) ),
inference(superposition,[],[f566,f588]) ).
fof(f566,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax26) ).
fof(f6081,plain,
( ~ spl69_6
| ~ spl69_106
| spl69_170 ),
inference(avatar_contradiction_clause,[],[f6080]) ).
fof(f6080,plain,
( $false
| ~ spl69_6
| ~ spl69_106
| spl69_170 ),
inference(subsumption_resolution,[],[f6079,f394]) ).
fof(f6079,plain,
( ~ ssList(nil)
| ~ spl69_6
| ~ spl69_106
| spl69_170 ),
inference(subsumption_resolution,[],[f6078,f3782]) ).
fof(f6078,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| spl69_170 ),
inference(duplicate_literal_removal,[],[f6077]) ).
fof(f6077,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl69_170 ),
inference(resolution,[],[f6070,f578]) ).
fof(f578,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f6070,plain,
( ~ ssList(sK64(nil,nil))
| spl69_170 ),
inference(avatar_component_clause,[],[f6068]) ).
fof(f6075,plain,
( ~ spl69_170
| spl69_171 ),
inference(avatar_split_clause,[],[f6066,f6072,f6068]) ).
fof(f6066,plain,
( nil = app(sK64(nil,nil),sK65(nil,nil))
| ~ ssList(sK64(nil,nil)) ),
inference(subsumption_resolution,[],[f6027,f394]) ).
fof(f6027,plain,
( nil = app(sK64(nil,nil),sK65(nil,nil))
| ~ ssList(nil)
| ~ ssList(sK64(nil,nil)) ),
inference(superposition,[],[f2789,f456]) ).
fof(f456,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax84) ).
fof(f2789,plain,
! [X1] :
( app(app(sK64(X1,X1),X1),sK65(X1,X1)) = X1
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f2788]) ).
fof(f2788,plain,
! [X1] :
( app(app(sK64(X1,X1),X1),sK65(X1,X1)) = X1
| ~ ssList(X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(resolution,[],[f580,f455]) ).
fof(f455,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax55) ).
fof(f580,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| app(app(sK64(X0,X1),X1),sK65(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f3658,plain,
( spl69_6
| spl69_105 ),
inference(avatar_split_clause,[],[f3657,f3521,f1159]) ).
fof(f3521,plain,
( spl69_105
<=> neq(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_105])]) ).
fof(f3657,plain,
( nil = sK20
| spl69_105 ),
inference(subsumption_resolution,[],[f3656,f377]) ).
fof(f377,plain,
ssList(sK20),
inference(cnf_transformation,[],[f255]) ).
fof(f3656,plain,
( nil = sK20
| ~ ssList(sK20)
| spl69_105 ),
inference(subsumption_resolution,[],[f3643,f394]) ).
fof(f3643,plain,
( nil = sK20
| ~ ssList(nil)
| ~ ssList(sK20)
| spl69_105 ),
inference(resolution,[],[f3523,f574]) ).
fof(f3523,plain,
( ~ neq(sK20,nil)
| spl69_105 ),
inference(avatar_component_clause,[],[f3521]) ).
fof(f3642,plain,
spl69_106,
inference(avatar_contradiction_clause,[],[f3641]) ).
fof(f3641,plain,
( $false
| spl69_106 ),
inference(subsumption_resolution,[],[f3640,f377]) ).
fof(f3640,plain,
( ~ ssList(sK20)
| spl69_106 ),
inference(resolution,[],[f3527,f455]) ).
fof(f3527,plain,
( ~ segmentP(sK20,sK20)
| spl69_106 ),
inference(avatar_component_clause,[],[f3525]) ).
fof(f3528,plain,
( ~ spl69_105
| ~ spl69_106
| ~ spl69_5 ),
inference(avatar_split_clause,[],[f3519,f1155,f3525,f3521]) ).
fof(f1155,plain,
( spl69_5
<=> ssList(sK66(sK21,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).
fof(f3519,plain,
( ~ segmentP(sK20,sK20)
| ~ neq(sK20,nil)
| ~ spl69_5 ),
inference(subsumption_resolution,[],[f3503,f377]) ).
fof(f3503,plain,
( ~ segmentP(sK20,sK20)
| ~ neq(sK20,nil)
| ~ ssList(sK20)
| ~ spl69_5 ),
inference(resolution,[],[f3499,f603]) ).
fof(f603,plain,
! [X5] :
( ~ segmentP(sK21,X5)
| ~ segmentP(sK20,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) ),
inference(definition_unfolding,[],[f384,f380,f379]) ).
fof(f379,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f255]) ).
fof(f380,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f255]) ).
fof(f384,plain,
! [X5] :
( ~ segmentP(sK18,X5)
| ~ segmentP(sK19,X5)
| ~ neq(X5,nil)
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f255]) ).
fof(f3499,plain,
( segmentP(sK21,sK20)
| ~ spl69_5 ),
inference(subsumption_resolution,[],[f3498,f1156]) ).
fof(f1156,plain,
( ssList(sK66(sK21,sK20))
| ~ spl69_5 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f3498,plain,
( segmentP(sK21,sK20)
| ~ ssList(sK66(sK21,sK20)) ),
inference(subsumption_resolution,[],[f3474,f377]) ).
fof(f3474,plain,
( segmentP(sK21,sK20)
| ~ ssList(sK20)
| ~ ssList(sK66(sK21,sK20)) ),
inference(superposition,[],[f3134,f1140]) ).
fof(f1140,plain,
sK21 = app(sK20,sK66(sK21,sK20)),
inference(subsumption_resolution,[],[f1139,f378]) ).
fof(f1139,plain,
( sK21 = app(sK20,sK66(sK21,sK20))
| ~ ssList(sK21) ),
inference(subsumption_resolution,[],[f1132,f377]) ).
fof(f1132,plain,
( sK21 = app(sK20,sK66(sK21,sK20))
| ~ ssList(sK20)
| ~ ssList(sK21) ),
inference(resolution,[],[f583,f382]) ).
fof(f382,plain,
frontsegP(sK21,sK20),
inference(cnf_transformation,[],[f255]) ).
fof(f583,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK66(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK66(X0,X1)) = X0
& ssList(sK66(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f367,f368]) ).
fof(f368,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK66(X0,X1)) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056',ax5) ).
fof(f3134,plain,
! [X14,X13] :
( segmentP(app(X13,X14),X13)
| ~ ssList(X13)
| ~ ssList(X14) ),
inference(subsumption_resolution,[],[f3133,f566]) ).
fof(f3133,plain,
! [X14,X13] :
( ~ ssList(app(X13,X14))
| ~ ssList(X14)
| ~ ssList(X13)
| segmentP(app(X13,X14),X13) ),
inference(subsumption_resolution,[],[f3125,f394]) ).
fof(f3125,plain,
! [X14,X13] :
( ~ ssList(app(X13,X14))
| ~ ssList(X14)
| ~ ssList(nil)
| ~ ssList(X13)
| segmentP(app(X13,X14),X13) ),
inference(duplicate_literal_removal,[],[f3114]) ).
fof(f3114,plain,
! [X14,X13] :
( ~ ssList(app(X13,X14))
| ~ ssList(X14)
| ~ ssList(nil)
| ~ ssList(X13)
| segmentP(app(X13,X14),X13)
| ~ ssList(X13) ),
inference(superposition,[],[f630,f457]) ).
fof(f457,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.iGBhoF9uFW/Vampire---4.8_24056',ax28) ).
fof(f630,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f581]) ).
fof(f581,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f2580,plain,
( spl69_9
| spl69_82 ),
inference(avatar_contradiction_clause,[],[f2579]) ).
fof(f2579,plain,
( $false
| spl69_9
| spl69_82 ),
inference(subsumption_resolution,[],[f2578,f378]) ).
fof(f2578,plain,
( ~ ssList(sK21)
| spl69_9
| spl69_82 ),
inference(subsumption_resolution,[],[f2576,f1175]) ).
fof(f2576,plain,
( nil = sK21
| ~ ssList(sK21)
| spl69_82 ),
inference(resolution,[],[f2528,f459]) ).
fof(f2528,plain,
( ~ ssItem(sK23(sK21))
| spl69_82 ),
inference(avatar_component_clause,[],[f2526]) ).
fof(f1368,plain,
~ spl69_9,
inference(avatar_contradiction_clause,[],[f1367]) ).
fof(f1367,plain,
( $false
| ~ spl69_9 ),
inference(subsumption_resolution,[],[f1366,f394]) ).
fof(f1366,plain,
( ~ ssList(nil)
| ~ spl69_9 ),
inference(resolution,[],[f1340,f635]) ).
fof(f635,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f628]) ).
fof(f628,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f573]) ).
fof(f573,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f1340,plain,
( neq(nil,nil)
| ~ spl69_9 ),
inference(backward_demodulation,[],[f604,f1174]) ).
fof(f1174,plain,
( nil = sK21
| ~ spl69_9 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f604,plain,
neq(sK21,nil),
inference(definition_unfolding,[],[f381,f379]) ).
fof(f381,plain,
neq(sK19,nil),
inference(cnf_transformation,[],[f255]) ).
fof(f1213,plain,
spl69_5,
inference(avatar_contradiction_clause,[],[f1212]) ).
fof(f1212,plain,
( $false
| spl69_5 ),
inference(subsumption_resolution,[],[f1211,f378]) ).
fof(f1211,plain,
( ~ ssList(sK21)
| spl69_5 ),
inference(subsumption_resolution,[],[f1210,f377]) ).
fof(f1210,plain,
( ~ ssList(sK20)
| ~ ssList(sK21)
| spl69_5 ),
inference(subsumption_resolution,[],[f1209,f382]) ).
fof(f1209,plain,
( ~ frontsegP(sK21,sK20)
| ~ ssList(sK20)
| ~ ssList(sK21)
| spl69_5 ),
inference(resolution,[],[f1157,f582]) ).
fof(f582,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f1157,plain,
( ~ ssList(sK66(sK21,sK20))
| spl69_5 ),
inference(avatar_component_clause,[],[f1155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC091+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 16:39:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.iGBhoF9uFW/Vampire---4.8_24056
% 0.14/0.36 % (24163)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (24167)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.21/0.42 % (24168)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)
% 0.21/0.42 % (24169)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)
% 0.21/0.42 % (24166)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)
% 0.21/0.42 % (24165)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.21/0.42 % (24170)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.21/0.42 % (24164)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)
% 7.77/1.49 % (24167)First to succeed.
% 7.77/1.50 % (24167)Refutation found. Thanks to Tanya!
% 7.77/1.50 % SZS status Theorem for Vampire---4
% 7.77/1.50 % SZS output start Proof for Vampire---4
% See solution above
% 7.77/1.50 % (24167)------------------------------
% 7.77/1.50 % (24167)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 7.77/1.50 % (24167)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 7.77/1.50 % (24167)Termination reason: Refutation
% 7.77/1.50
% 7.77/1.50 % (24167)Memory used [KB]: 32366
% 7.77/1.50 % (24167)Time elapsed: 1.075 s
% 7.77/1.50 % (24167)------------------------------
% 7.77/1.50 % (24167)------------------------------
% 7.77/1.50 % (24163)Success in time 1.14 s
% 7.77/1.50 % Vampire---4.8 exiting
%------------------------------------------------------------------------------