TSTP Solution File: SWC057+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWC057+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 : n024.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 20:56:09 EDT 2023
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 112 ( 7 unt; 0 def)
% Number of atoms : 574 ( 148 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 749 ( 287 ~; 278 |; 144 &)
% ( 15 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 149 (; 110 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4530,plain,
$false,
inference(avatar_sat_refutation,[],[f652,f657,f662,f663,f667,f668,f673,f1222,f3700,f3777,f4529]) ).
fof(f4529,plain,
( ~ spl69_3
| ~ spl69_6 ),
inference(avatar_contradiction_clause,[],[f4528]) ).
fof(f4528,plain,
( $false
| ~ spl69_3
| ~ spl69_6 ),
inference(subsumption_resolution,[],[f4527,f395]) ).
fof(f395,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/tmp/tmp.dciKYA3vO2/Vampire---4.8_3399',ax17) ).
fof(f4527,plain,
( ~ ssList(nil)
| ~ spl69_3
| ~ spl69_6 ),
inference(resolution,[],[f3790,f638]) ).
fof(f638,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f631]) ).
fof(f631,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f574]) ).
fof(f574,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f197]) ).
fof(f197,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.dciKYA3vO2/Vampire---4.8_3399',ax15) ).
fof(f3790,plain,
( neq(nil,nil)
| ~ spl69_3
| ~ spl69_6 ),
inference(backward_demodulation,[],[f672,f656]) ).
fof(f656,plain,
( nil = sK21
| ~ spl69_3 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f654,plain,
( spl69_3
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_3])]) ).
fof(f672,plain,
( neq(sK21,nil)
| ~ spl69_6 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f670,plain,
( spl69_6
<=> neq(sK21,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).
fof(f3777,plain,
( spl69_1
| ~ spl69_3
| ~ spl69_2
| ~ spl69_11 ),
inference(avatar_split_clause,[],[f3776,f1180,f649,f654,f645]) ).
fof(f645,plain,
( spl69_1
<=> nil = sK20 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_1])]) ).
fof(f649,plain,
( spl69_2
<=> frontsegP(sK21,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_2])]) ).
fof(f1180,plain,
( spl69_11
<=> ssList(sK66(sK21,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_11])]) ).
fof(f3776,plain,
( nil != sK21
| nil = sK20
| ~ spl69_2
| ~ spl69_11 ),
inference(subsumption_resolution,[],[f3775,f375]) ).
fof(f375,plain,
ssList(sK20),
inference(cnf_transformation,[],[f253]) ).
fof(f253,plain,
( ( ( frontsegP(sK21,sK20)
& neq(sK20,nil) )
| ( nil = sK20
& nil = sK21 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK19,nil) )
| ( nil != sK18
& nil = sK19 ) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f98,f252,f251,f250,f249]) ).
fof(f249,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( frontsegP(X3,X2)
& neq(X2,nil) )
| ( nil = X2
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( frontsegP(X3,X2)
& neq(X2,nil) )
| ( nil = X2
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK18
& nil = X1 ) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f250,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( frontsegP(X3,X2)
& neq(X2,nil) )
| ( nil = X2
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK18
& nil = X1 ) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( frontsegP(X3,X2)
& neq(X2,nil) )
| ( nil = X2
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK19,nil) )
| ( nil != sK18
& nil = sK19 ) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
( ? [X2] :
( ? [X3] :
( ( ( frontsegP(X3,X2)
& neq(X2,nil) )
| ( nil = X2
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK19,nil) )
| ( nil != sK18
& nil = sK19 ) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( frontsegP(X3,sK20)
& neq(sK20,nil) )
| ( nil = sK20
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK19,nil) )
| ( nil != sK18
& nil = sK19 ) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X3] :
( ( ( frontsegP(X3,sK20)
& neq(sK20,nil) )
| ( nil = sK20
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK19,nil) )
| ( nil != sK18
& nil = sK19 ) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ( ( frontsegP(sK21,sK20)
& neq(sK20,nil) )
| ( nil = sK20
& nil = sK21 ) )
& ( ( ! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK19,nil) )
| ( nil != sK18
& nil = sK19 ) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( frontsegP(X3,X2)
& neq(X2,nil) )
| ( nil = X2
& nil = X3 ) )
& ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ~ frontsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ~ frontsegP(X3,X2)
| ~ neq(X2,nil) )
& ( nil != X2
| nil != X3 ) )
| ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dciKYA3vO2/Vampire---4.8_3399',co1) ).
fof(f3775,plain,
( nil != sK21
| nil = sK20
| ~ ssList(sK20)
| ~ spl69_2
| ~ spl69_11 ),
inference(subsumption_resolution,[],[f1171,f1181]) ).
fof(f1181,plain,
( ssList(sK66(sK21,sK20))
| ~ spl69_11 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f1171,plain,
( nil != sK21
| nil = sK20
| ~ ssList(sK66(sK21,sK20))
| ~ ssList(sK20)
| ~ spl69_2 ),
inference(superposition,[],[f587,f1166]) ).
fof(f1166,plain,
( sK21 = app(sK20,sK66(sK21,sK20))
| ~ spl69_2 ),
inference(subsumption_resolution,[],[f1165,f376]) ).
fof(f376,plain,
ssList(sK21),
inference(cnf_transformation,[],[f253]) ).
fof(f1165,plain,
( sK21 = app(sK20,sK66(sK21,sK20))
| ~ ssList(sK21)
| ~ spl69_2 ),
inference(subsumption_resolution,[],[f1159,f375]) ).
fof(f1159,plain,
( sK21 = app(sK20,sK66(sK21,sK20))
| ~ ssList(sK20)
| ~ ssList(sK21)
| ~ spl69_2 ),
inference(resolution,[],[f584,f651]) ).
fof(f651,plain,
( frontsegP(sK21,sK20)
| ~ spl69_2 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f584,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK66(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f367,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])],[f365,f366]) ).
fof(f366,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK66(X0,X1)) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f365,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,[],[f364]) ).
fof(f364,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,[],[f200]) ).
fof(f200,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.dciKYA3vO2/Vampire---4.8_3399',ax5) ).
fof(f587,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f369,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,[],[f368]) ).
fof(f368,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,[],[f201]) ).
fof(f201,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.dciKYA3vO2/Vampire---4.8_3399',ax83) ).
fof(f3700,plain,
( ~ spl69_2
| ~ spl69_4
| ~ spl69_5
| ~ spl69_11 ),
inference(avatar_contradiction_clause,[],[f3699]) ).
fof(f3699,plain,
( $false
| ~ spl69_2
| ~ spl69_4
| ~ spl69_5
| ~ spl69_11 ),
inference(subsumption_resolution,[],[f3698,f375]) ).
fof(f3698,plain,
( ~ ssList(sK20)
| ~ spl69_2
| ~ spl69_4
| ~ spl69_5
| ~ spl69_11 ),
inference(resolution,[],[f3691,f456]) ).
fof(f456,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,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.dciKYA3vO2/Vampire---4.8_3399',ax55) ).
fof(f3691,plain,
( ~ segmentP(sK20,sK20)
| ~ spl69_2
| ~ spl69_4
| ~ spl69_5
| ~ spl69_11 ),
inference(subsumption_resolution,[],[f3690,f661]) ).
fof(f661,plain,
( neq(sK20,nil)
| ~ spl69_4 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f659,plain,
( spl69_4
<=> neq(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_4])]) ).
fof(f3690,plain,
( ~ neq(sK20,nil)
| ~ segmentP(sK20,sK20)
| ~ spl69_2
| ~ spl69_5
| ~ spl69_11 ),
inference(subsumption_resolution,[],[f3685,f375]) ).
fof(f3685,plain,
( ~ ssList(sK20)
| ~ neq(sK20,nil)
| ~ segmentP(sK20,sK20)
| ~ spl69_2
| ~ spl69_5
| ~ spl69_11 ),
inference(resolution,[],[f3682,f666]) ).
fof(f666,plain,
( ! [X4] :
( ~ segmentP(sK21,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK20,X4) )
| ~ spl69_5 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f665,plain,
( spl69_5
<=> ! [X4] :
( ~ segmentP(sK20,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK21,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).
fof(f3682,plain,
( segmentP(sK21,sK20)
| ~ spl69_2
| ~ spl69_11 ),
inference(subsumption_resolution,[],[f3681,f1181]) ).
fof(f3681,plain,
( segmentP(sK21,sK20)
| ~ ssList(sK66(sK21,sK20))
| ~ spl69_2 ),
inference(subsumption_resolution,[],[f3657,f375]) ).
fof(f3657,plain,
( segmentP(sK21,sK20)
| ~ ssList(sK20)
| ~ ssList(sK66(sK21,sK20))
| ~ spl69_2 ),
inference(superposition,[],[f3404,f1166]) ).
fof(f3404,plain,
! [X16,X15] :
( segmentP(app(X15,X16),X15)
| ~ ssList(X15)
| ~ ssList(X16) ),
inference(subsumption_resolution,[],[f3403,f567]) ).
fof(f567,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,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.dciKYA3vO2/Vampire---4.8_3399',ax26) ).
fof(f3403,plain,
! [X16,X15] :
( ~ ssList(app(X15,X16))
| ~ ssList(X16)
| ~ ssList(X15)
| segmentP(app(X15,X16),X15) ),
inference(subsumption_resolution,[],[f3393,f395]) ).
fof(f3393,plain,
! [X16,X15] :
( ~ ssList(app(X15,X16))
| ~ ssList(X16)
| ~ ssList(nil)
| ~ ssList(X15)
| segmentP(app(X15,X16),X15) ),
inference(duplicate_literal_removal,[],[f3377]) ).
fof(f3377,plain,
! [X16,X15] :
( ~ ssList(app(X15,X16))
| ~ ssList(X16)
| ~ ssList(nil)
| ~ ssList(X15)
| segmentP(app(X15,X16),X15)
| ~ ssList(X15) ),
inference(superposition,[],[f633,f458]) ).
fof(f458,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,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.dciKYA3vO2/Vampire---4.8_3399',ax28) ).
fof(f633,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,[],[f582]) ).
fof(f582,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,[],[f363]) ).
fof(f363,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])],[f360,f362,f361]) ).
fof(f361,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(f362,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(f360,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,[],[f359]) ).
fof(f359,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,[],[f199]) ).
fof(f199,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.dciKYA3vO2/Vampire---4.8_3399',ax7) ).
fof(f1222,plain,
( ~ spl69_2
| spl69_11 ),
inference(avatar_contradiction_clause,[],[f1221]) ).
fof(f1221,plain,
( $false
| ~ spl69_2
| spl69_11 ),
inference(subsumption_resolution,[],[f1220,f376]) ).
fof(f1220,plain,
( ~ ssList(sK21)
| ~ spl69_2
| spl69_11 ),
inference(subsumption_resolution,[],[f1219,f375]) ).
fof(f1219,plain,
( ~ ssList(sK20)
| ~ ssList(sK21)
| ~ spl69_2
| spl69_11 ),
inference(subsumption_resolution,[],[f1218,f651]) ).
fof(f1218,plain,
( ~ frontsegP(sK21,sK20)
| ~ ssList(sK20)
| ~ ssList(sK21)
| spl69_11 ),
inference(resolution,[],[f1182,f583]) ).
fof(f583,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f1182,plain,
( ~ ssList(sK66(sK21,sK20))
| spl69_11 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f673,plain,
( ~ spl69_1
| spl69_6 ),
inference(avatar_split_clause,[],[f606,f670,f645]) ).
fof(f606,plain,
( neq(sK21,nil)
| nil != sK20 ),
inference(definition_unfolding,[],[f380,f377,f378]) ).
fof(f378,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f253]) ).
fof(f377,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f253]) ).
fof(f380,plain,
( neq(sK19,nil)
| nil != sK18 ),
inference(cnf_transformation,[],[f253]) ).
fof(f668,plain,
( spl69_3
| spl69_5 ),
inference(avatar_split_clause,[],[f605,f665,f654]) ).
fof(f605,plain,
! [X4] :
( ~ segmentP(sK20,X4)
| ~ segmentP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK21 ),
inference(definition_unfolding,[],[f381,f378,f377,f377]) ).
fof(f381,plain,
! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK19 ),
inference(cnf_transformation,[],[f253]) ).
fof(f667,plain,
( ~ spl69_1
| spl69_5 ),
inference(avatar_split_clause,[],[f604,f665,f645]) ).
fof(f604,plain,
! [X4] :
( ~ segmentP(sK20,X4)
| ~ segmentP(sK21,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK20 ),
inference(definition_unfolding,[],[f382,f378,f377,f378]) ).
fof(f382,plain,
! [X4] :
( ~ segmentP(sK18,X4)
| ~ segmentP(sK19,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK18 ),
inference(cnf_transformation,[],[f253]) ).
fof(f663,plain,
( spl69_3
| spl69_4 ),
inference(avatar_split_clause,[],[f383,f659,f654]) ).
fof(f383,plain,
( neq(sK20,nil)
| nil = sK21 ),
inference(cnf_transformation,[],[f253]) ).
fof(f662,plain,
( spl69_1
| spl69_4 ),
inference(avatar_split_clause,[],[f384,f659,f645]) ).
fof(f384,plain,
( neq(sK20,nil)
| nil = sK20 ),
inference(cnf_transformation,[],[f253]) ).
fof(f657,plain,
( spl69_3
| spl69_2 ),
inference(avatar_split_clause,[],[f385,f649,f654]) ).
fof(f385,plain,
( frontsegP(sK21,sK20)
| nil = sK21 ),
inference(cnf_transformation,[],[f253]) ).
fof(f652,plain,
( spl69_1
| spl69_2 ),
inference(avatar_split_clause,[],[f386,f649,f645]) ).
fof(f386,plain,
( frontsegP(sK21,sK20)
| nil = sK20 ),
inference(cnf_transformation,[],[f253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC057+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 17:18:38 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.33 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.33 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.dciKYA3vO2/Vampire---4.8_3399
% 0.13/0.34 % (3507)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.40 % (3510)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)
% 0.18/0.40 % (3514)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.18/0.40 % (3509)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.18/0.40 % (3511)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.18/0.40 % (3512)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)
% 0.18/0.40 % (3513)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)
% 0.18/0.40 % (3508)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)
% 0.18/0.51 % (3511)First to succeed.
% 0.18/0.51 % (3511)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for Vampire---4
% 0.18/0.51 % SZS output start Proof for Vampire---4
% See solution above
% 0.18/0.51 % (3511)------------------------------
% 0.18/0.51 % (3511)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.18/0.51 % (3511)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.18/0.51 % (3511)Termination reason: Refutation
% 0.18/0.51
% 0.18/0.51 % (3511)Memory used [KB]: 8187
% 0.18/0.51 % (3511)Time elapsed: 0.108 s
% 0.18/0.51 % (3511)------------------------------
% 0.18/0.51 % (3511)------------------------------
% 0.18/0.51 % (3507)Success in time 0.17 s
% 0.18/0.51 % Vampire---4.8 exiting
%------------------------------------------------------------------------------