TSTP Solution File: SWC310+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWC310+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 : n005.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 20:58:20 EDT 2023
% Result : Theorem 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 154 ( 7 unt; 0 def)
% Number of atoms : 802 ( 289 equ)
% Maximal formula atoms : 54 ( 5 avg)
% Number of connectives : 1066 ( 418 ~; 416 |; 174 &)
% ( 22 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 180 (; 126 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1420,plain,
$false,
inference(avatar_sat_refutation,[],[f618,f623,f624,f633,f638,f643,f648,f657,f667,f786,f804,f806,f816,f824,f978,f982,f1053,f1380,f1398,f1409]) ).
fof(f1409,plain,
( spl53_6
| spl53_7 ),
inference(avatar_contradiction_clause,[],[f1408]) ).
fof(f1408,plain,
( $false
| spl53_6
| spl53_7 ),
inference(subsumption_resolution,[],[f1407,f361]) ).
fof(f361,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/tmp/tmp.vTZqYcSv2O/Vampire---4.8_22698',ax17) ).
fof(f1407,plain,
( ~ ssList(nil)
| spl53_6
| spl53_7 ),
inference(subsumption_resolution,[],[f1406,f658]) ).
fof(f658,plain,
ssList(sK1),
inference(forward_demodulation,[],[f341,f342]) ).
fof(f342,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK1)
| ! [X7] :
( ~ neq(nil,sK1)
| hd(sK1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(sK3,nil)
| ( sK2 = app(sK5,cons(sK4,nil))
& sK3 = app(cons(sK4,nil),sK5)
& ssList(sK5)
& ssItem(sK4) ) )
& ( nil != sK3
| nil = sK2 )
& 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])],[f99,f228,f227,f226,f225,f224,f223]) ).
fof(f223,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X1)
| ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X0 != X4
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X1)
| ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f224,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X1)
| ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK1)
| ! [X7] :
( ~ neq(nil,sK1)
| hd(sK1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK0 = X2
& sK1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK1)
| ! [X7] :
( ~ neq(nil,sK1)
| hd(sK1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& sK0 = X2
& sK1 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK1)
| ! [X7] :
( ~ neq(nil,sK1)
| hd(sK1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = sK2 )
& sK0 = sK2
& sK1 = X3
& ssList(X3) )
& ssList(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK1)
| ! [X7] :
( ~ neq(nil,sK1)
| hd(sK1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = sK2 )
& sK0 = sK2
& sK1 = X3
& ssList(X3) )
=> ( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK1)
| ! [X7] :
( ~ neq(nil,sK1)
| hd(sK1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK0 != X4
| ~ ssList(X4) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( ~ neq(sK3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK2
& app(cons(X8,nil),X9) = sK3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != sK3
| nil = sK2 )
& sK0 = sK2
& sK1 = sK3
& ssList(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
( ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = sK2
& app(cons(X8,nil),X9) = sK3
& ssList(X9) )
& ssItem(X8) )
=> ( ? [X9] :
( sK2 = app(X9,cons(sK4,nil))
& sK3 = app(cons(sK4,nil),X9)
& ssList(X9) )
& ssItem(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
( ? [X9] :
( sK2 = app(X9,cons(sK4,nil))
& sK3 = app(cons(sK4,nil),X9)
& ssList(X9) )
=> ( sK2 = app(sK5,cons(sK4,nil))
& sK3 = app(cons(sK4,nil),sK5)
& ssList(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X1)
| ! [X7] :
( ~ neq(nil,X1)
| hd(X1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X1) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X0 != X4
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X8] :
( ? [X9] :
( app(X9,cons(X8,nil)) = X2
& app(cons(X8,nil),X9) = X3
& ssList(X9) )
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& 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] :
( ( ( ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X1)
& ? [X7] :
( neq(nil,X1)
& hd(X1) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X1) = X5
& ssList(X6) )
& ssList(X5) )
& X0 = X4
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( app(X9,cons(X8,nil)) != X2
| app(cons(X8,nil),X9) != X3
| ~ ssList(X9) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X1)
& ? [X9] :
( neq(nil,X1)
& hd(X1) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X1) = X7
& ssList(X8) )
& ssList(X7) )
& X0 = X6
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X1)
& ? [X9] :
( neq(nil,X1)
& hd(X1) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X1) = X7
& ssList(X8) )
& ssList(X7) )
& X0 = X6
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vTZqYcSv2O/Vampire---4.8_22698',co1) ).
fof(f341,plain,
ssList(sK3),
inference(cnf_transformation,[],[f229]) ).
fof(f1406,plain,
( ~ ssList(sK1)
| ~ ssList(nil)
| spl53_6
| spl53_7 ),
inference(subsumption_resolution,[],[f1404,f616]) ).
fof(f616,plain,
( nil != sK1
| spl53_7 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f615,plain,
( spl53_7
<=> nil = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_7])]) ).
fof(f1404,plain,
( nil = sK1
| ~ ssList(sK1)
| ~ ssList(nil)
| spl53_6 ),
inference(resolution,[],[f611,f514]) ).
fof(f514,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f198]) ).
fof(f198,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.vTZqYcSv2O/Vampire---4.8_22698',ax15) ).
fof(f611,plain,
( ~ neq(nil,sK1)
| spl53_6 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f609,plain,
( spl53_6
<=> neq(nil,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_6])]) ).
fof(f1398,plain,
( spl53_3
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(avatar_contradiction_clause,[],[f1397]) ).
fof(f1397,plain,
( $false
| spl53_3
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(subsumption_resolution,[],[f1396,f642]) ).
fof(f642,plain,
( ssList(sK5)
| ~ spl53_12 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f640,plain,
( spl53_12
<=> ssList(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_12])]) ).
fof(f1396,plain,
( ~ ssList(sK5)
| spl53_3
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(forward_demodulation,[],[f599,f1257]) ).
fof(f1257,plain,
( tl(sK1) = sK5
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(subsumption_resolution,[],[f1256,f642]) ).
fof(f1256,plain,
( tl(sK1) = sK5
| ~ ssList(sK5)
| ~ spl53_13
| ~ spl53_32 ),
inference(subsumption_resolution,[],[f1181,f647]) ).
fof(f647,plain,
( ssItem(sK4)
| ~ spl53_13 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f645,plain,
( spl53_13
<=> ssItem(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_13])]) ).
fof(f1181,plain,
( tl(sK1) = sK5
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl53_32 ),
inference(superposition,[],[f499,f798]) ).
fof(f798,plain,
( sK1 = cons(sK4,sK5)
| ~ spl53_32 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f796,plain,
( spl53_32
<=> sK1 = cons(sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_32])]) ).
fof(f499,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vTZqYcSv2O/Vampire---4.8_22698',ax25) ).
fof(f599,plain,
( ~ ssList(tl(sK1))
| spl53_3 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f597,plain,
( spl53_3
<=> ssList(tl(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_3])]) ).
fof(f1380,plain,
( spl53_2
| ~ spl53_9
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(avatar_contradiction_clause,[],[f1379]) ).
fof(f1379,plain,
( $false
| spl53_2
| ~ spl53_9
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(subsumption_resolution,[],[f1378,f671]) ).
fof(f671,plain,
( sK0 = app(sK5,cons(sK4,nil))
| ~ spl53_9 ),
inference(forward_demodulation,[],[f628,f343]) ).
fof(f343,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f229]) ).
fof(f628,plain,
( sK2 = app(sK5,cons(sK4,nil))
| ~ spl53_9 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f626,plain,
( spl53_9
<=> sK2 = app(sK5,cons(sK4,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_9])]) ).
fof(f1378,plain,
( sK0 != app(sK5,cons(sK4,nil))
| spl53_2
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(forward_demodulation,[],[f1372,f1259]) ).
fof(f1259,plain,
( hd(sK1) = sK4
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(subsumption_resolution,[],[f1258,f642]) ).
fof(f1258,plain,
( hd(sK1) = sK4
| ~ ssList(sK5)
| ~ spl53_13
| ~ spl53_32 ),
inference(subsumption_resolution,[],[f1182,f647]) ).
fof(f1182,plain,
( hd(sK1) = sK4
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl53_32 ),
inference(superposition,[],[f500,f798]) ).
fof(f500,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vTZqYcSv2O/Vampire---4.8_22698',ax23) ).
fof(f1372,plain,
( sK0 != app(sK5,cons(hd(sK1),nil))
| spl53_2
| ~ spl53_12
| ~ spl53_13
| ~ spl53_32 ),
inference(superposition,[],[f595,f1257]) ).
fof(f595,plain,
( sK0 != app(tl(sK1),cons(hd(sK1),nil))
| spl53_2 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f593,plain,
( spl53_2
<=> sK0 = app(tl(sK1),cons(hd(sK1),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_2])]) ).
fof(f1053,plain,
( ~ spl53_13
| ~ spl53_20 ),
inference(avatar_contradiction_clause,[],[f1052]) ).
fof(f1052,plain,
( $false
| ~ spl53_13
| ~ spl53_20 ),
inference(subsumption_resolution,[],[f1051,f361]) ).
fof(f1051,plain,
( ~ ssList(nil)
| ~ spl53_13
| ~ spl53_20 ),
inference(subsumption_resolution,[],[f1035,f647]) ).
fof(f1035,plain,
( ~ ssItem(sK4)
| ~ ssList(nil)
| ~ spl53_20 ),
inference(trivial_inequality_removal,[],[f1010]) ).
fof(f1010,plain,
( nil != nil
| ~ ssItem(sK4)
| ~ ssList(nil)
| ~ spl53_20 ),
inference(superposition,[],[f498,f722]) ).
fof(f722,plain,
( nil = cons(sK4,nil)
| ~ spl53_20 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f720,plain,
( spl53_20
<=> nil = cons(sK4,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_20])]) ).
fof(f498,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vTZqYcSv2O/Vampire---4.8_22698',ax18) ).
fof(f982,plain,
( spl53_5
| spl53_7 ),
inference(avatar_contradiction_clause,[],[f981]) ).
fof(f981,plain,
( $false
| spl53_5
| spl53_7 ),
inference(subsumption_resolution,[],[f980,f658]) ).
fof(f980,plain,
( ~ ssList(sK1)
| spl53_5
| spl53_7 ),
inference(subsumption_resolution,[],[f979,f616]) ).
fof(f979,plain,
( nil = sK1
| ~ ssList(sK1)
| spl53_5 ),
inference(resolution,[],[f607,f422]) ).
fof(f422,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f150]) ).
fof(f150,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.vTZqYcSv2O/Vampire---4.8_22698',ax22) ).
fof(f607,plain,
( ~ ssItem(hd(sK1))
| spl53_5 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f605,plain,
( spl53_5
<=> ssItem(hd(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_5])]) ).
fof(f978,plain,
( ~ spl53_5
| spl53_4 ),
inference(avatar_split_clause,[],[f977,f601,f605]) ).
fof(f601,plain,
( spl53_4
<=> ssList(cons(hd(sK1),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_4])]) ).
fof(f977,plain,
( ~ ssItem(hd(sK1))
| spl53_4 ),
inference(subsumption_resolution,[],[f976,f361]) ).
fof(f976,plain,
( ~ ssItem(hd(sK1))
| ~ ssList(nil)
| spl53_4 ),
inference(resolution,[],[f603,f496]) ).
fof(f496,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,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.vTZqYcSv2O/Vampire---4.8_22698',ax16) ).
fof(f603,plain,
( ~ ssList(cons(hd(sK1),nil))
| spl53_4 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f824,plain,
( ~ spl53_16
| spl53_20
| ~ spl53_7
| ~ spl53_11
| ~ spl53_12 ),
inference(avatar_split_clause,[],[f823,f640,f635,f615,f720,f701]) ).
fof(f701,plain,
( spl53_16
<=> ssList(cons(sK4,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_16])]) ).
fof(f635,plain,
( spl53_11
<=> sK3 = app(cons(sK4,nil),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_11])]) ).
fof(f823,plain,
( nil != sK1
| nil = cons(sK4,nil)
| ~ ssList(cons(sK4,nil))
| ~ spl53_11
| ~ spl53_12 ),
inference(subsumption_resolution,[],[f682,f642]) ).
fof(f682,plain,
( nil != sK1
| nil = cons(sK4,nil)
| ~ ssList(sK5)
| ~ ssList(cons(sK4,nil))
| ~ spl53_11 ),
inference(superposition,[],[f526,f668]) ).
fof(f668,plain,
( sK1 = app(cons(sK4,nil),sK5)
| ~ spl53_11 ),
inference(forward_demodulation,[],[f637,f342]) ).
fof(f637,plain,
( sK3 = app(cons(sK4,nil),sK5)
| ~ spl53_11 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f526,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f333]) ).
fof(f333,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,[],[f202]) ).
fof(f202,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.vTZqYcSv2O/Vampire---4.8_22698',ax83) ).
fof(f816,plain,
( spl53_1
| ~ spl53_14 ),
inference(avatar_contradiction_clause,[],[f815]) ).
fof(f815,plain,
( $false
| spl53_1
| ~ spl53_14 ),
inference(subsumption_resolution,[],[f812,f591]) ).
fof(f591,plain,
( nil != sK0
| spl53_1 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f589,plain,
( spl53_1
<=> nil = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_1])]) ).
fof(f812,plain,
( nil = sK0
| ~ spl53_14 ),
inference(superposition,[],[f343,f652]) ).
fof(f652,plain,
( nil = sK2
| ~ spl53_14 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f650,plain,
( spl53_14
<=> nil = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_14])]) ).
fof(f806,plain,
( ~ spl53_8
| spl53_10 ),
inference(avatar_split_clause,[],[f805,f630,f620]) ).
fof(f620,plain,
( spl53_8
<=> neq(sK1,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_8])]) ).
fof(f630,plain,
( spl53_10
<=> neq(sK3,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl53_10])]) ).
fof(f805,plain,
( ~ neq(sK1,nil)
| spl53_10 ),
inference(forward_demodulation,[],[f632,f342]) ).
fof(f632,plain,
( ~ neq(sK3,nil)
| spl53_10 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f804,plain,
( ~ spl53_13
| spl53_32
| ~ spl53_11
| ~ spl53_12 ),
inference(avatar_split_clause,[],[f803,f640,f635,f796,f645]) ).
fof(f803,plain,
( sK1 = cons(sK4,sK5)
| ~ ssItem(sK4)
| ~ spl53_11
| ~ spl53_12 ),
inference(subsumption_resolution,[],[f672,f642]) ).
fof(f672,plain,
( sK1 = cons(sK4,sK5)
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl53_11 ),
inference(superposition,[],[f668,f501]) ).
fof(f501,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,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.vTZqYcSv2O/Vampire---4.8_22698',ax81) ).
fof(f786,plain,
( ~ spl53_13
| spl53_16 ),
inference(avatar_split_clause,[],[f785,f701,f645]) ).
fof(f785,plain,
( ~ ssItem(sK4)
| spl53_16 ),
inference(subsumption_resolution,[],[f781,f361]) ).
fof(f781,plain,
( ~ ssItem(sK4)
| ~ ssList(nil)
| spl53_16 ),
inference(resolution,[],[f703,f496]) ).
fof(f703,plain,
( ~ ssList(cons(sK4,nil))
| spl53_16 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f667,plain,
( ~ spl53_7
| spl53_15 ),
inference(avatar_split_clause,[],[f664,f654,f615]) ).
fof(f654,plain,
( spl53_15
<=> nil = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl53_15])]) ).
fof(f664,plain,
( nil != sK1
| spl53_15 ),
inference(superposition,[],[f656,f342]) ).
fof(f656,plain,
( nil != sK3
| spl53_15 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f657,plain,
( spl53_14
| ~ spl53_15 ),
inference(avatar_split_clause,[],[f344,f654,f650]) ).
fof(f344,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f229]) ).
fof(f648,plain,
( spl53_13
| ~ spl53_10 ),
inference(avatar_split_clause,[],[f345,f630,f645]) ).
fof(f345,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f229]) ).
fof(f643,plain,
( spl53_12
| ~ spl53_10 ),
inference(avatar_split_clause,[],[f346,f630,f640]) ).
fof(f346,plain,
( ~ neq(sK3,nil)
| ssList(sK5) ),
inference(cnf_transformation,[],[f229]) ).
fof(f638,plain,
( spl53_11
| ~ spl53_10 ),
inference(avatar_split_clause,[],[f347,f630,f635]) ).
fof(f347,plain,
( ~ neq(sK3,nil)
| sK3 = app(cons(sK4,nil),sK5) ),
inference(cnf_transformation,[],[f229]) ).
fof(f633,plain,
( spl53_9
| ~ spl53_10 ),
inference(avatar_split_clause,[],[f348,f630,f626]) ).
fof(f348,plain,
( ~ neq(sK3,nil)
| sK2 = app(sK5,cons(sK4,nil)) ),
inference(cnf_transformation,[],[f229]) ).
fof(f624,plain,
( spl53_7
| spl53_8 ),
inference(avatar_split_clause,[],[f349,f620,f615]) ).
fof(f349,plain,
( neq(sK1,nil)
| nil = sK1 ),
inference(cnf_transformation,[],[f229]) ).
fof(f623,plain,
( ~ spl53_1
| spl53_8 ),
inference(avatar_split_clause,[],[f350,f620,f589]) ).
fof(f350,plain,
( neq(sK1,nil)
| nil != sK0 ),
inference(cnf_transformation,[],[f229]) ).
fof(f618,plain,
( spl53_7
| ~ spl53_2
| ~ spl53_3
| ~ spl53_4
| ~ spl53_5
| ~ spl53_6 ),
inference(avatar_split_clause,[],[f613,f609,f605,f601,f597,f593,f615]) ).
fof(f613,plain,
( ~ neq(nil,sK1)
| ~ ssItem(hd(sK1))
| ~ ssList(cons(hd(sK1),nil))
| ~ ssList(tl(sK1))
| sK0 != app(tl(sK1),cons(hd(sK1),nil))
| nil = sK1 ),
inference(subsumption_resolution,[],[f585,f506]) ).
fof(f506,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f185,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.vTZqYcSv2O/Vampire---4.8_22698',ax26) ).
fof(f585,plain,
( ~ neq(nil,sK1)
| ~ ssItem(hd(sK1))
| ~ ssList(cons(hd(sK1),nil))
| ~ ssList(tl(sK1))
| sK0 != app(tl(sK1),cons(hd(sK1),nil))
| ~ ssList(app(tl(sK1),cons(hd(sK1),nil)))
| nil = sK1 ),
inference(duplicate_literal_removal,[],[f550]) ).
fof(f550,plain,
( ~ neq(nil,sK1)
| ~ neq(nil,sK1)
| ~ ssItem(hd(sK1))
| ~ ssList(cons(hd(sK1),nil))
| ~ ssList(tl(sK1))
| sK0 != app(tl(sK1),cons(hd(sK1),nil))
| ~ ssList(app(tl(sK1),cons(hd(sK1),nil)))
| nil = sK1 ),
inference(equality_resolution,[],[f549]) ).
fof(f549,plain,
! [X5] :
( ~ neq(nil,sK1)
| ~ neq(nil,sK1)
| ~ ssItem(hd(sK1))
| tl(sK1) != X5
| ~ ssList(cons(hd(sK1),nil))
| ~ ssList(X5)
| sK0 != app(X5,cons(hd(sK1),nil))
| ~ ssList(app(X5,cons(hd(sK1),nil)))
| nil = sK1 ),
inference(equality_resolution,[],[f548]) ).
fof(f548,plain,
! [X4,X5] :
( ~ neq(nil,sK1)
| ~ neq(nil,sK1)
| ~ ssItem(hd(sK1))
| app(X5,cons(hd(sK1),nil)) != X4
| tl(sK1) != X5
| ~ ssList(cons(hd(sK1),nil))
| ~ ssList(X5)
| sK0 != X4
| ~ ssList(X4)
| nil = sK1 ),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X6,X4,X5] :
( ~ neq(nil,sK1)
| ~ neq(nil,sK1)
| cons(hd(sK1),nil) != X6
| ~ ssItem(hd(sK1))
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6)
| ~ ssList(X5)
| sK0 != X4
| ~ ssList(X4)
| nil = sK1 ),
inference(equality_resolution,[],[f351]) ).
fof(f351,plain,
! [X6,X7,X4,X5] :
( ~ neq(nil,sK1)
| ~ neq(nil,sK1)
| hd(sK1) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7)
| app(X5,X6) != X4
| tl(sK1) != X5
| ~ ssList(X6)
| ~ ssList(X5)
| sK0 != X4
| ~ ssList(X4)
| nil = sK1 ),
inference(cnf_transformation,[],[f229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC310+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 18:48:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.vTZqYcSv2O/Vampire---4.8_22698
% 0.13/0.36 % (22805)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.42 % (22809)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.17/0.44 % (22808)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)
% 0.17/0.44 % (22812)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)
% 0.17/0.45 % (22810)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)
% 0.17/0.46 % (22807)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.17/0.46 % (22806)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)
% 0.17/0.48 % (22813)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.17/0.49 % (22813)First to succeed.
% 0.17/0.51 % (22813)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Theorem for Vampire---4
% 0.17/0.51 % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.51 % (22813)------------------------------
% 0.17/0.51 % (22813)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.51 % (22813)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.51 % (22813)Termination reason: Refutation
% 0.17/0.51
% 0.17/0.51 % (22813)Memory used [KB]: 6396
% 0.17/0.51 % (22813)Time elapsed: 0.072 s
% 0.17/0.51 % (22813)------------------------------
% 0.17/0.51 % (22813)------------------------------
% 0.17/0.51 % (22805)Success in time 0.147 s
% 0.17/0.51 % Vampire---4.8 exiting
%------------------------------------------------------------------------------