TSTP Solution File: SEV515+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV515+1 : TPTP v8.1.2. Released v7.0.0.
% 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 : n023.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 19:42:08 EDT 2023
% Result : Theorem 0.24s 0.45s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 24
% Syntax : Number of formulae : 135 ( 2 unt; 0 def)
% Number of atoms : 660 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 770 ( 245 ~; 383 |; 118 &)
% ( 21 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 17 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 146 (; 118 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f369,plain,
$false,
inference(avatar_sat_refutation,[],[f79,f87,f91,f100,f121,f164,f247,f271,f279,f280,f287,f293,f301,f307,f340,f342,f351,f353,f357,f367,f368]) ).
fof(f368,plain,
( spl4_24
| spl4_22
| ~ spl4_25 ),
inference(avatar_split_clause,[],[f322,f255,f241,f252]) ).
fof(f252,plain,
( spl4_24
<=> g_both(sK1(sK3),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
fof(f241,plain,
( spl4_22
<=> g_true_only(sK1(sK3),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
fof(f255,plain,
( spl4_25
<=> g_both(sK1(sK3),sK1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
fof(f322,plain,
( g_true_only(sK1(sK3),sK3)
| g_both(sK1(sK3),sK3)
| ~ spl4_25 ),
inference(resolution,[],[f256,f148]) ).
fof(f148,plain,
! [X0] :
( ~ g_both(X0,X0)
| g_true_only(X0,sK3)
| g_both(X0,sK3) ),
inference(resolution,[],[f47,f42]) ).
fof(f42,plain,
! [X3] :
( ~ g_false_only(X3,sK3)
| ~ g_both(X3,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( ( ! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,sK2) )
| ( g_false_only(X1,X1)
& g_true_only(X1,sK2) ) )
| sP0 )
& ! [X3] :
( ( ( ~ g_both(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_false_only(X3,sK3) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_both(X3,sK3) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_both(X3,X3) )
| ~ g_true_only(X3,sK3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f19,f21,f20]) ).
fof(f20,plain,
( ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
=> ! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,sK2) )
| ( g_false_only(X1,X1)
& g_true_only(X1,sK2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( ? [X2] :
! [X3] :
( ( ( ~ g_both(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_false_only(X3,X2) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_both(X3,X2) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_both(X3,X3) )
| ~ g_true_only(X3,X2) ) )
=> ! [X3] :
( ( ( ~ g_both(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_false_only(X3,sK3) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_both(X3,sK3) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_both(X3,X3) )
| ~ g_true_only(X3,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
( ( ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
| sP0 )
& ? [X2] :
! [X3] :
( ( ( ~ g_both(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_false_only(X3,X2) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_false_only(X3,X3) )
| ~ g_both(X3,X2) )
& ( ( ~ g_true_only(X3,X3)
& ~ g_both(X3,X3) )
| ~ g_true_only(X3,X2) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
( ( ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
| sP0 )
& ? [X5] :
! [X6] :
( ( ( ~ g_both(X6,X6)
& ~ g_false_only(X6,X6) )
| ~ g_false_only(X6,X5) )
& ( ( ~ g_true_only(X6,X6)
& ~ g_false_only(X6,X6) )
| ~ g_both(X6,X5) )
& ( ( ~ g_true_only(X6,X6)
& ~ g_both(X6,X6) )
| ~ g_true_only(X6,X5) ) ) ),
inference(definition_folding,[],[f12,f13]) ).
fof(f13,plain,
( ! [X2] :
( ? [X3] :
( ( ( g_both(X3,X3)
| g_false_only(X3,X3) )
& g_false_only(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_false_only(X3,X3) )
& g_both(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_both(X3,X3) )
& g_true_only(X3,X2) ) )
| ! [X4] :
( ~ g_both(X4,X4)
| ~ g_both(X4,X2) ) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f12,plain,
( ( ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
| ! [X2] :
( ? [X3] :
( ( ( g_both(X3,X3)
| g_false_only(X3,X3) )
& g_false_only(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_false_only(X3,X3) )
& g_both(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_both(X3,X3) )
& g_true_only(X3,X2) ) )
| ! [X4] :
( ~ g_both(X4,X4)
| ~ g_both(X4,X2) ) ) )
& ? [X5] :
! [X6] :
( ( ( ~ g_both(X6,X6)
& ~ g_false_only(X6,X6) )
| ~ g_false_only(X6,X5) )
& ( ( ~ g_true_only(X6,X6)
& ~ g_false_only(X6,X6) )
| ~ g_both(X6,X5) )
& ( ( ~ g_true_only(X6,X6)
& ~ g_both(X6,X6) )
| ~ g_true_only(X6,X5) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
& ? [X2] :
( ~ ? [X3] :
( ( ( g_both(X3,X3)
| g_false_only(X3,X3) )
& g_false_only(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_false_only(X3,X3) )
& g_both(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_both(X3,X3) )
& g_true_only(X3,X2) ) )
& ? [X4] :
( g_both(X4,X4)
& g_both(X4,X2) ) ) )
| ! [X5] :
? [X6] :
( ( ( g_both(X6,X6)
| g_false_only(X6,X6) )
& g_false_only(X6,X5) )
| ( ( g_true_only(X6,X6)
| g_false_only(X6,X6) )
& g_both(X6,X5) )
| ( ( g_true_only(X6,X6)
| g_both(X6,X6) )
& g_true_only(X6,X5) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( g_both(X1,X1)
& g_both(X1,X0) ) ) )
| ! [X0] :
? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
( ( ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( g_both(X1,X1)
& g_both(X1,X0) ) ) )
| ! [X0] :
? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qh5Qu8hA3D/Vampire---4.8_3036',nc1) ).
fof(f47,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X3] :
( g_false_only(X2,X3)
| g_both(X2,X3)
| g_true_only(X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.Qh5Qu8hA3D/Vampire---4.8_3036',exhaustion_g) ).
fof(f256,plain,
( g_both(sK1(sK3),sK1(sK3))
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f367,plain,
( ~ spl4_20
| ~ spl4_24 ),
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f364,plain,
( $false
| ~ spl4_20
| ~ spl4_24 ),
inference(resolution,[],[f274,f236]) ).
fof(f236,plain,
( g_true_only(sK1(sK3),sK1(sK3))
| ~ spl4_20 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f235,plain,
( spl4_20
<=> g_true_only(sK1(sK3),sK1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
fof(f274,plain,
( ~ g_true_only(sK1(sK3),sK1(sK3))
| ~ spl4_24 ),
inference(resolution,[],[f253,f40]) ).
fof(f40,plain,
! [X3] :
( ~ g_both(X3,sK3)
| ~ g_true_only(X3,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f253,plain,
( g_both(sK1(sK3),sK3)
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f357,plain,
( spl4_15
| spl4_25
| spl4_22
| spl4_24
| spl4_21
| ~ spl4_26 ),
inference(avatar_split_clause,[],[f332,f291,f238,f252,f241,f255,f119]) ).
fof(f119,plain,
( spl4_15
<=> g_true_only(sK3,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
fof(f238,plain,
( spl4_21
<=> g_false_only(sK1(sK3),sK1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
fof(f291,plain,
( spl4_26
<=> ! [X4] :
( g_both(sK1(X4),sK1(X4))
| g_false_only(sK1(X4),sK1(X4))
| g_both(sK1(X4),X4)
| g_true_only(sK1(X4),X4)
| ~ g_both(sK3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
fof(f332,plain,
( g_false_only(sK1(sK3),sK1(sK3))
| g_both(sK1(sK3),sK3)
| g_true_only(sK1(sK3),sK3)
| g_both(sK1(sK3),sK1(sK3))
| g_true_only(sK3,sK3)
| ~ spl4_26 ),
inference(duplicate_literal_removal,[],[f331]) ).
fof(f331,plain,
( g_false_only(sK1(sK3),sK1(sK3))
| g_both(sK1(sK3),sK3)
| g_true_only(sK1(sK3),sK3)
| g_both(sK1(sK3),sK1(sK3))
| g_true_only(sK3,sK3)
| g_true_only(sK3,sK3)
| ~ spl4_26 ),
inference(resolution,[],[f292,f200]) ).
fof(f200,plain,
! [X0] :
( g_both(X0,sK3)
| g_true_only(X0,X0)
| g_true_only(X0,sK3) ),
inference(duplicate_literal_removal,[],[f194]) ).
fof(f194,plain,
! [X0] :
( g_both(X0,sK3)
| g_true_only(X0,sK3)
| g_true_only(X0,X0)
| g_true_only(X0,sK3)
| g_both(X0,sK3) ),
inference(resolution,[],[f177,f148]) ).
fof(f177,plain,
! [X1] :
( g_both(X1,sK3)
| g_both(X1,X1)
| g_true_only(X1,sK3)
| g_true_only(X1,X1) ),
inference(resolution,[],[f149,f47]) ).
fof(f149,plain,
! [X1] :
( ~ g_false_only(X1,X1)
| g_true_only(X1,sK3)
| g_both(X1,sK3) ),
inference(resolution,[],[f47,f41]) ).
fof(f41,plain,
! [X3] :
( ~ g_false_only(X3,sK3)
| ~ g_false_only(X3,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f292,plain,
( ! [X4] :
( ~ g_both(sK3,X4)
| g_false_only(sK1(X4),sK1(X4))
| g_both(sK1(X4),X4)
| g_true_only(sK1(X4),X4)
| g_both(sK1(X4),sK1(X4)) )
| ~ spl4_26 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f353,plain,
( ~ spl4_20
| ~ spl4_22 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f352,plain,
( $false
| ~ spl4_20
| ~ spl4_22 ),
inference(resolution,[],[f236,f266]) ).
fof(f266,plain,
( ~ g_true_only(sK1(sK3),sK1(sK3))
| ~ spl4_22 ),
inference(resolution,[],[f242,f38]) ).
fof(f38,plain,
! [X3] :
( ~ g_true_only(X3,sK3)
| ~ g_true_only(X3,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f242,plain,
( g_true_only(sK1(sK3),sK3)
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f351,plain,
( ~ spl4_22
| ~ spl4_23 ),
inference(avatar_contradiction_clause,[],[f350]) ).
fof(f350,plain,
( $false
| ~ spl4_22
| ~ spl4_23 ),
inference(resolution,[],[f283,f242]) ).
fof(f283,plain,
( ~ g_true_only(sK1(sK3),sK3)
| ~ spl4_23 ),
inference(resolution,[],[f245,f145]) ).
fof(f145,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(resolution,[],[f54,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( g_false_only(X0,X1)
| g_true(X0,X1)
| ~ g_false(X0,X1) )
& ( ( ~ g_true(X0,X1)
& g_false(X0,X1) )
| ~ g_false_only(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( g_false_only(X0,X1)
| g_true(X0,X1)
| ~ g_false(X0,X1) )
& ( ( ~ g_true(X0,X1)
& g_false(X0,X1) )
| ~ g_false_only(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0,X1] :
( g_false_only(X0,X1)
<=> ( ~ g_true(X0,X1)
& g_false(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X3] :
( g_false_only(X2,X3)
<=> ( ~ g_true(X2,X3)
& g_false(X2,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qh5Qu8hA3D/Vampire---4.8_3036',false_only_g) ).
fof(f54,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( g_true_only(X0,X1)
| g_false(X0,X1)
| ~ g_true(X0,X1) )
& ( ( ~ g_false(X0,X1)
& g_true(X0,X1) )
| ~ g_true_only(X0,X1) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( g_true_only(X0,X1)
| g_false(X0,X1)
| ~ g_true(X0,X1) )
& ( ( ~ g_false(X0,X1)
& g_true(X0,X1) )
| ~ g_true_only(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( g_true_only(X0,X1)
<=> ( ~ g_false(X0,X1)
& g_true(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X3] :
( g_true_only(X2,X3)
<=> ( ~ g_false(X2,X3)
& g_true(X2,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qh5Qu8hA3D/Vampire---4.8_3036',true_only_g) ).
fof(f245,plain,
( g_false_only(sK1(sK3),sK3)
| ~ spl4_23 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f244,plain,
( spl4_23
<=> g_false_only(sK1(sK3),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
fof(f342,plain,
( spl4_23
| spl4_25
| spl4_20
| spl4_24
| ~ spl4_14
| ~ spl4_28 ),
inference(avatar_split_clause,[],[f336,f299,f116,f252,f235,f255,f244]) ).
fof(f116,plain,
( spl4_14
<=> g_both(sK3,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
fof(f299,plain,
( spl4_28
<=> ! [X2] :
( g_false_only(sK1(X2),X2)
| g_both(sK1(X2),X2)
| g_true_only(sK1(X2),sK1(X2))
| g_both(sK1(X2),sK1(X2))
| ~ g_both(sK3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
fof(f336,plain,
( g_both(sK1(sK3),sK3)
| g_true_only(sK1(sK3),sK1(sK3))
| g_both(sK1(sK3),sK1(sK3))
| g_false_only(sK1(sK3),sK3)
| ~ spl4_14
| ~ spl4_28 ),
inference(resolution,[],[f300,f154]) ).
fof(f154,plain,
( g_both(sK3,sK3)
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f300,plain,
( ! [X2] :
( ~ g_both(sK3,X2)
| g_both(sK1(X2),X2)
| g_true_only(sK1(X2),sK1(X2))
| g_both(sK1(X2),sK1(X2))
| g_false_only(sK1(X2),X2) )
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f340,plain,
( ~ spl4_22
| ~ spl4_25 ),
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f339,plain,
( $false
| ~ spl4_22
| ~ spl4_25 ),
inference(resolution,[],[f267,f256]) ).
fof(f267,plain,
( ~ g_both(sK1(sK3),sK1(sK3))
| ~ spl4_22 ),
inference(resolution,[],[f242,f37]) ).
fof(f37,plain,
! [X3] :
( ~ g_true_only(X3,sK3)
| ~ g_both(X3,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f307,plain,
( spl4_15
| spl4_14 ),
inference(avatar_split_clause,[],[f206,f116,f119]) ).
fof(f206,plain,
( g_both(sK3,sK3)
| g_true_only(sK3,sK3) ),
inference(duplicate_literal_removal,[],[f188]) ).
fof(f188,plain,
( g_both(sK3,sK3)
| g_true_only(sK3,sK3)
| g_true_only(sK3,sK3)
| g_true_only(sK3,sK3)
| g_both(sK3,sK3) ),
inference(resolution,[],[f177,f148]) ).
fof(f301,plain,
( spl4_28
| spl4_15
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f223,f89,f119,f299]) ).
fof(f89,plain,
( spl4_8
<=> ! [X2,X0] :
( g_false_only(sK1(X0),X0)
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| g_both(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f223,plain,
( ! [X2] :
( g_true_only(sK3,sK3)
| g_false_only(sK1(X2),X2)
| ~ g_both(sK3,X2)
| g_both(sK1(X2),sK1(X2))
| g_true_only(sK1(X2),sK1(X2))
| g_both(sK1(X2),X2) )
| ~ spl4_8 ),
inference(duplicate_literal_removal,[],[f213]) ).
fof(f213,plain,
( ! [X2] :
( g_true_only(sK3,sK3)
| g_true_only(sK3,sK3)
| g_false_only(sK1(X2),X2)
| ~ g_both(sK3,X2)
| g_both(sK1(X2),sK1(X2))
| g_true_only(sK1(X2),sK1(X2))
| g_both(sK1(X2),X2) )
| ~ spl4_8 ),
inference(resolution,[],[f200,f90]) ).
fof(f90,plain,
( ! [X2,X0] :
( ~ g_both(X2,X2)
| g_false_only(sK1(X0),X0)
| ~ g_both(X2,X0)
| g_both(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),X0) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f293,plain,
( spl4_26
| spl4_15
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f221,f77,f119,f291]) ).
fof(f77,plain,
( spl4_5
<=> ! [X2,X0] :
( g_both(sK1(X0),sK1(X0))
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| g_true_only(sK1(X0),X0)
| g_both(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f221,plain,
( ! [X4] :
( g_true_only(sK3,sK3)
| g_both(sK1(X4),sK1(X4))
| ~ g_both(sK3,X4)
| g_true_only(sK1(X4),X4)
| g_both(sK1(X4),X4)
| g_false_only(sK1(X4),sK1(X4)) )
| ~ spl4_5 ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f215,plain,
( ! [X4] :
( g_true_only(sK3,sK3)
| g_true_only(sK3,sK3)
| g_both(sK1(X4),sK1(X4))
| ~ g_both(sK3,X4)
| g_true_only(sK1(X4),X4)
| g_both(sK1(X4),X4)
| g_false_only(sK1(X4),sK1(X4)) )
| ~ spl4_5 ),
inference(resolution,[],[f200,f78]) ).
fof(f78,plain,
( ! [X2,X0] :
( ~ g_both(X2,X2)
| g_both(sK1(X0),sK1(X0))
| ~ g_both(X2,X0)
| g_true_only(sK1(X0),X0)
| g_both(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0)) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f287,plain,
( spl4_20
| spl4_22
| ~ spl4_23 ),
inference(avatar_split_clause,[],[f285,f244,f241,f235]) ).
fof(f285,plain,
( g_true_only(sK1(sK3),sK3)
| g_true_only(sK1(sK3),sK1(sK3))
| ~ spl4_23 ),
inference(resolution,[],[f216,f245]) ).
fof(f216,plain,
! [X5] :
( ~ g_false_only(X5,sK3)
| g_true_only(X5,sK3)
| g_true_only(X5,X5) ),
inference(resolution,[],[f200,f144]) ).
fof(f144,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(resolution,[],[f52,f48]) ).
fof(f48,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( g_both(X0,X1)
| ~ g_false(X0,X1)
| ~ g_true(X0,X1) )
& ( ( g_false(X0,X1)
& g_true(X0,X1) )
| ~ g_both(X0,X1) ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( g_both(X0,X1)
| ~ g_false(X0,X1)
| ~ g_true(X0,X1) )
& ( ( g_false(X0,X1)
& g_true(X0,X1) )
| ~ g_both(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0,X1] :
( g_both(X0,X1)
<=> ( g_false(X0,X1)
& g_true(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X3] :
( g_both(X2,X3)
<=> ( g_false(X2,X3)
& g_true(X2,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qh5Qu8hA3D/Vampire---4.8_3036',both_g) ).
fof(f280,plain,
( spl4_20
| spl4_22
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f262,f238,f241,f235]) ).
fof(f262,plain,
( g_true_only(sK1(sK3),sK3)
| g_true_only(sK1(sK3),sK1(sK3))
| ~ spl4_21 ),
inference(resolution,[],[f239,f211]) ).
fof(f211,plain,
! [X1] :
( ~ g_false_only(X1,X1)
| g_true_only(X1,sK3)
| g_true_only(X1,X1) ),
inference(resolution,[],[f200,f39]) ).
fof(f39,plain,
! [X3] :
( ~ g_both(X3,sK3)
| ~ g_false_only(X3,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f239,plain,
( g_false_only(sK1(sK3),sK1(sK3))
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f279,plain,
( ~ spl4_22
| ~ spl4_24 ),
inference(avatar_contradiction_clause,[],[f278]) ).
fof(f278,plain,
( $false
| ~ spl4_22
| ~ spl4_24 ),
inference(resolution,[],[f276,f242]) ).
fof(f276,plain,
( ~ g_true_only(sK1(sK3),sK3)
| ~ spl4_24 ),
inference(resolution,[],[f253,f147]) ).
fof(f147,plain,
! [X2,X3] :
( ~ g_both(X2,X3)
| ~ g_true_only(X2,X3) ),
inference(resolution,[],[f55,f49]) ).
fof(f49,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f55,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f271,plain,
( ~ spl4_20
| ~ spl4_21 ),
inference(avatar_contradiction_clause,[],[f268]) ).
fof(f268,plain,
( $false
| ~ spl4_20
| ~ spl4_21 ),
inference(resolution,[],[f264,f236]) ).
fof(f264,plain,
( ~ g_true_only(sK1(sK3),sK1(sK3))
| ~ spl4_21 ),
inference(resolution,[],[f239,f145]) ).
fof(f247,plain,
( spl4_15
| spl4_20
| spl4_21
| spl4_22
| spl4_23
| ~ spl4_7
| ~ spl4_14 ),
inference(avatar_split_clause,[],[f233,f116,f85,f244,f241,f238,f235,f119]) ).
fof(f85,plain,
( spl4_7
<=> ! [X2,X0] :
( g_false_only(sK1(X0),X0)
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| g_true_only(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f233,plain,
( g_false_only(sK1(sK3),sK3)
| g_true_only(sK1(sK3),sK3)
| g_false_only(sK1(sK3),sK1(sK3))
| g_true_only(sK1(sK3),sK1(sK3))
| g_true_only(sK3,sK3)
| ~ spl4_7
| ~ spl4_14 ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f232,plain,
( g_false_only(sK1(sK3),sK3)
| g_true_only(sK1(sK3),sK3)
| g_false_only(sK1(sK3),sK1(sK3))
| g_true_only(sK1(sK3),sK1(sK3))
| g_true_only(sK3,sK3)
| g_true_only(sK3,sK3)
| ~ spl4_7
| ~ spl4_14 ),
inference(resolution,[],[f170,f200]) ).
fof(f170,plain,
( ! [X0] :
( ~ g_both(sK3,X0)
| g_false_only(sK1(X0),X0)
| g_true_only(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0)) )
| ~ spl4_7
| ~ spl4_14 ),
inference(resolution,[],[f154,f86]) ).
fof(f86,plain,
( ! [X2,X0] :
( ~ g_both(X2,X2)
| g_false_only(sK1(X0),X0)
| ~ g_both(X2,X0)
| g_true_only(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0)) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f164,plain,
~ spl4_15,
inference(avatar_contradiction_clause,[],[f162]) ).
fof(f162,plain,
( $false
| ~ spl4_15 ),
inference(resolution,[],[f158,f120]) ).
fof(f120,plain,
( g_true_only(sK3,sK3)
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f158,plain,
( ~ g_true_only(sK3,sK3)
| ~ spl4_15 ),
inference(resolution,[],[f120,f38]) ).
fof(f121,plain,
( ~ spl4_14
| spl4_15
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f113,f98,f119,f116]) ).
fof(f98,plain,
( spl4_10
<=> ! [X1] :
( g_true_only(X1,X1)
| g_false_only(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f113,plain,
( g_true_only(sK3,sK3)
| ~ g_both(sK3,sK3)
| ~ spl4_10 ),
inference(resolution,[],[f99,f42]) ).
fof(f99,plain,
( ! [X1] :
( g_false_only(X1,X1)
| g_true_only(X1,X1) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( spl4_1
| spl4_10 ),
inference(avatar_split_clause,[],[f46,f98,f62]) ).
fof(f62,plain,
( spl4_1
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f46,plain,
! [X1] :
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| sP0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f91,plain,
( ~ spl4_1
| spl4_8 ),
inference(avatar_split_clause,[],[f30,f89,f62]) ).
fof(f30,plain,
! [X2,X0] :
( g_false_only(sK1(X0),X0)
| g_both(sK1(X0),X0)
| g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),sK1(X0))
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ! [X0] :
( ( ( g_both(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0)) )
& g_false_only(sK1(X0),X0) )
| ( ( g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0)) )
& g_both(sK1(X0),X0) )
| ( ( g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),sK1(X0)) )
& g_true_only(sK1(X0),X0) )
| ! [X2] :
( ~ g_both(X2,X2)
| ~ g_both(X2,X0) ) )
| ~ sP0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f17]) ).
fof(f17,plain,
! [X0] :
( ? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
=> ( ( ( g_both(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0)) )
& g_false_only(sK1(X0),X0) )
| ( ( g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0)) )
& g_both(sK1(X0),X0) )
| ( ( g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),sK1(X0)) )
& g_true_only(sK1(X0),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ! [X0] :
( ? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
| ! [X2] :
( ~ g_both(X2,X2)
| ~ g_both(X2,X0) ) )
| ~ sP0 ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
( ! [X2] :
( ? [X3] :
( ( ( g_both(X3,X3)
| g_false_only(X3,X3) )
& g_false_only(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_false_only(X3,X3) )
& g_both(X3,X2) )
| ( ( g_true_only(X3,X3)
| g_both(X3,X3) )
& g_true_only(X3,X2) ) )
| ! [X4] :
( ~ g_both(X4,X4)
| ~ g_both(X4,X2) ) )
| ~ sP0 ),
inference(nnf_transformation,[],[f13]) ).
fof(f87,plain,
( ~ spl4_1
| spl4_7 ),
inference(avatar_split_clause,[],[f31,f85,f62]) ).
fof(f31,plain,
! [X2,X0] :
( g_false_only(sK1(X0),X0)
| g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),X0)
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f79,plain,
( ~ spl4_1
| spl4_5 ),
inference(avatar_split_clause,[],[f33,f77,f62]) ).
fof(f33,plain,
! [X2,X0] :
( g_both(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),X0)
| g_true_only(sK1(X0),X0)
| ~ g_both(X2,X2)
| ~ g_both(X2,X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SEV515+1 : TPTP v8.1.2. Released v7.0.0.
% 0.14/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n023.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 24 03:27:57 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.16/0.38 This is a FOF_THM_RFO_NEQ problem
% 0.16/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.Qh5Qu8hA3D/Vampire---4.8_3036
% 0.16/0.38 % (3143)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.44 % (3147)dis-1_128_add=large:amm=sco:anc=all_dependent:bs=on:bsr=on:bce=on:cond=fast:fsr=off:gsp=on:gs=on:gsem=off:lcm=predicate:lma=on:nm=32:nwc=4.0:nicw=on:sac=on:sp=weighted_frequency_692 on Vampire---4 for (692ds/0Mi)
% 0.24/0.44 % (3145)dis-1002_1_av=off:bsr=on:cond=on:flr=on:fsr=off:gsp=on:nwc=2.0:sims=off_1218 on Vampire---4 for (1218ds/0Mi)
% 0.24/0.44 % (3146)lrs+11_4:3_aac=none:add=off:amm=off:anc=none:bd=preordered:bs=on:bce=on:flr=on:fsd=off:fsr=off:fde=none:nwc=2.5:sims=off:sp=reverse_arity:tgt=full:stl=188_1106 on Vampire---4 for (1106ds/0Mi)
% 0.24/0.44 % (3149)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_415 on Vampire---4 for (415ds/0Mi)
% 0.24/0.44 % (3150)dis+3_1024_av=off:fsr=off:gsp=on:lcm=predicate:nm=4:sos=all:sp=weighted_frequency_338 on Vampire---4 for (338ds/0Mi)
% 0.24/0.44 % (3148)ott-1010_5_add=off:amm=off:anc=none:bce=on:cond=fast:flr=on:lma=on:nm=2:nwc=1.1:sp=occurrence:tgt=ground_470 on Vampire---4 for (470ds/0Mi)
% 0.24/0.44 % (3144)lrs-1_7_acc=on:amm=off:anc=all:bs=on:bsr=on:cond=fast:flr=on:fsr=off:gsp=on:lcm=reverse:lma=on:msp=off:nm=0:nwc=1.2:sp=frequency:stl=188_1354 on Vampire---4 for (1354ds/0Mi)
% 0.24/0.44 % (3149)Refutation not found, incomplete strategy% (3149)------------------------------
% 0.24/0.44 % (3149)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.44 % (3149)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.44 % (3149)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.44
% 0.24/0.44 % (3149)Memory used [KB]: 5500
% 0.24/0.44 % (3149)Time elapsed: 0.005 s
% 0.24/0.44 % (3149)------------------------------
% 0.24/0.44 % (3149)------------------------------
% 0.24/0.45 % (3145)Refutation not found, incomplete strategy% (3145)------------------------------
% 0.24/0.45 % (3145)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.45 % (3145)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.45 % (3145)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.45
% 0.24/0.45 % (3145)Memory used [KB]: 1023
% 0.24/0.45 % (3145)Time elapsed: 0.008 s
% 0.24/0.45 % (3145)------------------------------
% 0.24/0.45 % (3145)------------------------------
% 0.24/0.45 % (3146)First to succeed.
% 0.24/0.45 % (3148)Also succeeded, but the first one will report.
% 0.24/0.45 % (3146)Refutation found. Thanks to Tanya!
% 0.24/0.45 % SZS status Theorem for Vampire---4
% 0.24/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.45 % (3146)------------------------------
% 0.24/0.45 % (3146)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.45 % (3146)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.45 % (3146)Termination reason: Refutation
% 0.24/0.45
% 0.24/0.45 % (3146)Memory used [KB]: 5628
% 0.24/0.45 % (3146)Time elapsed: 0.012 s
% 0.24/0.45 % (3146)------------------------------
% 0.24/0.45 % (3146)------------------------------
% 0.24/0.45 % (3143)Success in time 0.069 s
% 0.24/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------