TSTP Solution File: SET674+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET674+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n015.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 15:45:09 EDT 2023
% Result : Theorem 0.22s 0.72s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 39
% Syntax : Number of formulae : 267 ( 17 unt; 0 def)
% Number of atoms : 1095 ( 83 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1436 ( 608 ~; 617 |; 118 &)
% ( 26 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 10 con; 0-4 aty)
% Number of variables : 565 (; 527 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13073,plain,
$false,
inference(avatar_sat_refutation,[],[f260,f355,f375,f12107,f12125,f12136,f13042,f13060,f13072]) ).
fof(f13072,plain,
( spl24_1
| ~ spl24_25
| ~ spl24_26 ),
inference(avatar_contradiction_clause,[],[f13071]) ).
fof(f13071,plain,
( $false
| spl24_1
| ~ spl24_25
| ~ spl24_26 ),
inference(subsumption_resolution,[],[f13070,f255]) ).
fof(f255,plain,
( sF21 != sF22
| spl24_1 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl24_1
<=> sF21 = sF22 ),
introduced(avatar_definition,[new_symbols(naming,[spl24_1])]) ).
fof(f13070,plain,
( sF21 = sF22
| ~ spl24_25
| ~ spl24_26 ),
inference(subsumption_resolution,[],[f13069,f12988]) ).
fof(f12988,plain,
( subset(sF22,sF21)
| ~ spl24_25 ),
inference(avatar_component_clause,[],[f12986]) ).
fof(f12986,plain,
( spl24_25
<=> subset(sF22,sF21) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_25])]) ).
fof(f13069,plain,
( ~ subset(sF22,sF21)
| sF21 = sF22
| ~ spl24_26 ),
inference(resolution,[],[f12991,f284]) ).
fof(f284,plain,
! [X2,X1] :
( ~ member(sK11(X2,X1),X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(resolution,[],[f282,f278]) ).
fof(f278,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK11(X0,X1),X1) ),
inference(subsumption_resolution,[],[f277,f157]) ).
fof(f157,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p40) ).
fof(f277,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f201,f157]) ).
fof(f201,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f128,f129]) ).
fof(f129,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p22) ).
fof(f282,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f281,f157]) ).
fof(f281,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f192,f157]) ).
fof(f192,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p10) ).
fof(f12991,plain,
( member(sK11(sF21,sF22),sF22)
| ~ spl24_26 ),
inference(avatar_component_clause,[],[f12990]) ).
fof(f12990,plain,
( spl24_26
<=> member(sK11(sF21,sF22),sF22) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_26])]) ).
fof(f13060,plain,
( spl24_1
| ~ spl24_3
| ~ spl24_25
| spl24_26 ),
inference(avatar_contradiction_clause,[],[f13059]) ).
fof(f13059,plain,
( $false
| spl24_1
| ~ spl24_3
| ~ spl24_25
| spl24_26 ),
inference(subsumption_resolution,[],[f13058,f13012]) ).
fof(f13012,plain,
( subset(sF21,sF22)
| ~ spl24_3
| spl24_26 ),
inference(resolution,[],[f12998,f276]) ).
fof(f276,plain,
! [X0,X1] :
( member(sK11(X0,X1),X0)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f275,f157]) ).
fof(f275,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK11(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f200,f157]) ).
fof(f200,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK11(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f130]) ).
fof(f12998,plain,
( ~ member(sK11(sF21,sF22),sF21)
| ~ spl24_3
| spl24_26 ),
inference(resolution,[],[f12992,f12866]) ).
fof(f12866,plain,
( ! [X8] :
( member(X8,sF22)
| ~ member(X8,sF21) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f12861,f467]) ).
fof(f467,plain,
! [X3,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ member(X3,X0)
| member(X3,X1) ),
inference(subsumption_resolution,[],[f466,f157]) ).
fof(f466,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f465,f157]) ).
fof(f465,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f202,f157]) ).
fof(f202,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f132,f133]) ).
fof(f133,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p24) ).
fof(f12861,plain,
( ! [X8] :
( member(X8,sF22)
| ~ member(X8,sF21)
| member(sF21,power_set(sF22)) )
| ~ spl24_3 ),
inference(resolution,[],[f12844,f287]) ).
fof(f287,plain,
! [X0,X1] :
( member(sK12(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f286,f157]) ).
fof(f286,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK12(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f204,f157]) ).
fof(f204,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK12(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f134]) ).
fof(f12844,plain,
( ! [X3,X4] :
( ~ member(sK12(X4,sF22),sF21)
| member(X3,sF22)
| ~ member(X3,X4) )
| ~ spl24_3 ),
inference(forward_demodulation,[],[f12843,f342]) ).
fof(f342,plain,
sF21 = range_of(sK2),
inference(subsumption_resolution,[],[f341,f246]) ).
fof(f246,plain,
ilf_type(sK2,sF23),
inference(definition_folding,[],[f155,f245]) ).
fof(f245,plain,
relation_type(sK0,sK1) = sF23,
introduced(function_definition,[]) ).
fof(f155,plain,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ( domain(sK0,sK1,sK2) != inverse4(sK0,sK1,sK2,sK1)
| range(sK0,sK1,sK2) != image4(sK0,sK1,sK2,sK0) )
& ilf_type(sK2,relation_type(sK0,sK1))
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f44,f94,f93,f92]) ).
fof(f92,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( domain(X0,X1,X2) != inverse4(X0,X1,X2,X1)
| range(X0,X1,X2) != image4(X0,X1,X2,X0) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ( domain(sK0,X1,X2) != inverse4(sK0,X1,X2,X1)
| range(sK0,X1,X2) != image4(sK0,X1,X2,sK0) )
& ilf_type(X2,relation_type(sK0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK0,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ? [X1] :
( ? [X2] :
( ( domain(sK0,X1,X2) != inverse4(sK0,X1,X2,X1)
| range(sK0,X1,X2) != image4(sK0,X1,X2,sK0) )
& ilf_type(X2,relation_type(sK0,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ( domain(sK0,sK1,X2) != inverse4(sK0,sK1,X2,sK1)
| range(sK0,sK1,X2) != image4(sK0,sK1,X2,sK0) )
& ilf_type(X2,relation_type(sK0,sK1)) )
& ilf_type(sK1,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ? [X2] :
( ( domain(sK0,sK1,X2) != inverse4(sK0,sK1,X2,sK1)
| range(sK0,sK1,X2) != image4(sK0,sK1,X2,sK0) )
& ilf_type(X2,relation_type(sK0,sK1)) )
=> ( ( domain(sK0,sK1,sK2) != inverse4(sK0,sK1,sK2,sK1)
| range(sK0,sK1,sK2) != image4(sK0,sK1,sK2,sK0) )
& ilf_type(sK2,relation_type(sK0,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( domain(X0,X1,X2) != inverse4(X0,X1,X2,X1)
| range(X0,X1,X2) != image4(X0,X1,X2,X0) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( domain(X0,X1,X2) = inverse4(X0,X1,X2,X1)
& range(X0,X1,X2) = image4(X0,X1,X2,X0) ) ) ) ),
inference(negated_conjecture,[],[f41]) ).
fof(f41,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( domain(X0,X1,X2) = inverse4(X0,X1,X2,X1)
& range(X0,X1,X2) = image4(X0,X1,X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',prove_relset_1_38) ).
fof(f341,plain,
( ~ ilf_type(sK2,sF23)
| sF21 = range_of(sK2) ),
inference(forward_demodulation,[],[f339,f245]) ).
fof(f339,plain,
( sF21 = range_of(sK2)
| ~ ilf_type(sK2,relation_type(sK0,sK1)) ),
inference(superposition,[],[f338,f242]) ).
fof(f242,plain,
range(sK0,sK1,sK2) = sF21,
introduced(function_definition,[]) ).
fof(f338,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f337,f157]) ).
fof(f337,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f220,f157]) ).
fof(f220,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range_of(X2) = range(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p34) ).
fof(f12843,plain,
( ! [X3,X4] :
( member(X3,sF22)
| ~ member(X3,X4)
| ~ member(sK12(X4,sF22),range_of(sK2)) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f12840,f350]) ).
fof(f350,plain,
( ilf_type(sK2,binary_relation_type)
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f349,plain,
( spl24_3
<=> ilf_type(sK2,binary_relation_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_3])]) ).
fof(f12840,plain,
( ! [X3,X4] :
( member(X3,sF22)
| ~ member(X3,X4)
| ~ member(sK12(X4,sF22),range_of(sK2))
| ~ ilf_type(sK2,binary_relation_type) )
| ~ spl24_3 ),
inference(resolution,[],[f1014,f312]) ).
fof(f312,plain,
! [X0,X1] :
( member(ordered_pair(sK7(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(subsumption_resolution,[],[f178,f157]) ).
fof(f178,plain,
! [X0,X1] :
( member(ordered_pair(sK7(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(sK7(X0,X1),X0),X1)
& ilf_type(sK7(X0,X1),set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X3,X0),X1)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(sK7(X0,X1),X0),X1)
& ilf_type(sK7(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X3,X0),X1)
& ilf_type(X3,set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,range_of(X1))
<=> ? [X2] :
( member(ordered_pair(X2,X0),X1)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p2) ).
fof(f1014,plain,
( ! [X10,X11,X9] :
( ~ member(ordered_pair(X9,sK12(X10,sF22)),sK2)
| member(X11,sF22)
| ~ member(X11,X10) )
| ~ spl24_3 ),
inference(resolution,[],[f1009,f468]) ).
fof(f468,plain,
! [X2,X0,X1] :
( ~ member(sK12(X1,X2),X2)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[],[f467,f289]) ).
fof(f289,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK12(X0,X1),X1) ),
inference(subsumption_resolution,[],[f288,f157]) ).
fof(f288,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK12(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f205,f157]) ).
fof(f205,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK12(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f134]) ).
fof(f1009,plain,
( ! [X0,X1] :
( member(X0,sF22)
| ~ member(ordered_pair(X1,X0),sK2) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f1008,f910]) ).
fof(f910,plain,
! [X0,X1] :
( member(X0,sK0)
| ~ member(ordered_pair(X0,X1),sK2) ),
inference(resolution,[],[f904,f246]) ).
fof(f904,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,sF23)
| ~ member(ordered_pair(X1,X2),X0)
| member(X1,sK0) ),
inference(superposition,[],[f901,f245]) ).
fof(f901,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0) ),
inference(subsumption_resolution,[],[f900,f157]) ).
fof(f900,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f899,f157]) ).
fof(f899,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f898,f157]) ).
fof(f898,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f218,f157]) ).
fof(f218,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p7) ).
fof(f1008,plain,
( ! [X0,X1] :
( member(X0,sF22)
| ~ member(ordered_pair(X1,X0),sK2)
| ~ member(X1,sK0) )
| ~ spl24_3 ),
inference(superposition,[],[f832,f778]) ).
fof(f778,plain,
sF22 = image(sK2,sK0),
inference(superposition,[],[f775,f243]) ).
fof(f243,plain,
image4(sK0,sK1,sK2,sK0) = sF22,
introduced(function_definition,[]) ).
fof(f775,plain,
! [X0] : image(sK2,X0) = image4(sK0,sK1,sK2,X0),
inference(resolution,[],[f774,f246]) ).
fof(f774,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF23)
| image(X0,X1) = image4(sK0,sK1,X0,X1) ),
inference(superposition,[],[f756,f245]) ).
fof(f756,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(subsumption_resolution,[],[f755,f157]) ).
fof(f755,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f754,f157]) ).
fof(f754,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f226,f157]) ).
fof(f226,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p36) ).
fof(f832,plain,
( ! [X8,X9,X7] :
( member(X9,image(sK2,X8))
| ~ member(ordered_pair(X7,X9),sK2)
| ~ member(X7,X8) )
| ~ spl24_3 ),
inference(resolution,[],[f817,f350]) ).
fof(f817,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| member(X1,image(X2,X0)) ),
inference(subsumption_resolution,[],[f816,f157]) ).
fof(f816,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f815,f157]) ).
fof(f815,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f213,f157]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ( member(sK13(X0,X1,X2),X0)
& member(ordered_pair(sK13(X0,X1,X2),X1),X2)
& ilf_type(sK13(X0,X1,X2),set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f137,f138]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X4,X1),X2)
& ilf_type(X4,set_type) )
=> ( member(sK13(X0,X1,X2),X0)
& member(ordered_pair(sK13(X0,X1,X2),X1),X2)
& ilf_type(sK13(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X4,X1),X2)
& ilf_type(X4,set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,image(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,image(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p4) ).
fof(f12992,plain,
( ~ member(sK11(sF21,sF22),sF22)
| spl24_26 ),
inference(avatar_component_clause,[],[f12990]) ).
fof(f13058,plain,
( ~ subset(sF21,sF22)
| spl24_1
| ~ spl24_25 ),
inference(subsumption_resolution,[],[f13049,f255]) ).
fof(f13049,plain,
( sF21 = sF22
| ~ subset(sF21,sF22)
| ~ spl24_25 ),
inference(resolution,[],[f12988,f282]) ).
fof(f13042,plain,
( ~ spl24_3
| ~ spl24_4
| spl24_25 ),
inference(avatar_contradiction_clause,[],[f13041]) ).
fof(f13041,plain,
( $false
| ~ spl24_3
| ~ spl24_4
| spl24_25 ),
inference(subsumption_resolution,[],[f13038,f12987]) ).
fof(f12987,plain,
( ~ subset(sF22,sF21)
| spl24_25 ),
inference(avatar_component_clause,[],[f12986]) ).
fof(f13038,plain,
( subset(sF22,sF21)
| ~ spl24_3
| ~ spl24_4
| spl24_25 ),
inference(resolution,[],[f13003,f276]) ).
fof(f13003,plain,
( ~ member(sK11(sF22,sF21),sF22)
| ~ spl24_3
| ~ spl24_4
| spl24_25 ),
inference(resolution,[],[f12994,f1256]) ).
fof(f1256,plain,
( ! [X3] :
( member(X3,sF21)
| ~ member(X3,sF22) )
| ~ spl24_3
| ~ spl24_4 ),
inference(subsumption_resolution,[],[f1253,f467]) ).
fof(f1253,plain,
( ! [X3] :
( ~ member(X3,sF22)
| member(X3,sF21)
| member(sF22,power_set(sF21)) )
| ~ spl24_3
| ~ spl24_4 ),
inference(resolution,[],[f1241,f287]) ).
fof(f1241,plain,
( ! [X0,X1] :
( ~ member(sK12(X0,sF21),sF22)
| ~ member(X1,X0)
| member(X1,sF21) )
| ~ spl24_3
| ~ spl24_4 ),
inference(superposition,[],[f981,f778]) ).
fof(f981,plain,
( ! [X8,X6,X7] :
( ~ member(sK12(X6,sF21),image(sK2,X7))
| ~ member(X8,X6)
| member(X8,sF21) )
| ~ spl24_3
| ~ spl24_4 ),
inference(resolution,[],[f612,f498]) ).
fof(f498,plain,
( ! [X24,X25,X23] :
( ~ member(ordered_pair(X25,sK12(X24,sF21)),sK2)
| ~ member(X23,X24)
| member(X23,sF21) )
| ~ spl24_4 ),
inference(resolution,[],[f468,f354]) ).
fof(f354,plain,
( ! [X0,X1] :
( member(X0,sF21)
| ~ member(ordered_pair(X1,X0),sK2) )
| ~ spl24_4 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f353,plain,
( spl24_4
<=> ! [X0,X1] :
( member(X0,sF21)
| ~ member(ordered_pair(X1,X0),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_4])]) ).
fof(f612,plain,
( ! [X6,X5] :
( member(ordered_pair(sK13(X6,X5,sK2),X5),sK2)
| ~ member(X5,image(sK2,X6)) )
| ~ spl24_3 ),
inference(resolution,[],[f598,f350]) ).
fof(f598,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,image(X2,X0))
| member(ordered_pair(sK13(X0,X1,X2),X1),X2) ),
inference(subsumption_resolution,[],[f597,f157]) ).
fof(f597,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK13(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f211,f157]) ).
fof(f211,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK13(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f139]) ).
fof(f12994,plain,
( ~ member(sK11(sF22,sF21),sF21)
| spl24_25 ),
inference(resolution,[],[f12987,f278]) ).
fof(f12136,plain,
( spl24_2
| ~ spl24_19
| ~ spl24_20 ),
inference(avatar_contradiction_clause,[],[f12135]) ).
fof(f12135,plain,
( $false
| spl24_2
| ~ spl24_19
| ~ spl24_20 ),
inference(subsumption_resolution,[],[f12134,f259]) ).
fof(f259,plain,
( sF19 != sF20
| spl24_2 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f257,plain,
( spl24_2
<=> sF19 = sF20 ),
introduced(avatar_definition,[new_symbols(naming,[spl24_2])]) ).
fof(f12134,plain,
( sF19 = sF20
| ~ spl24_19
| ~ spl24_20 ),
inference(subsumption_resolution,[],[f12133,f12057]) ).
fof(f12057,plain,
( subset(sF20,sF19)
| ~ spl24_19 ),
inference(avatar_component_clause,[],[f12055]) ).
fof(f12055,plain,
( spl24_19
<=> subset(sF20,sF19) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_19])]) ).
fof(f12133,plain,
( ~ subset(sF20,sF19)
| sF19 = sF20
| ~ spl24_20 ),
inference(resolution,[],[f12060,f284]) ).
fof(f12060,plain,
( member(sK11(sF19,sF20),sF20)
| ~ spl24_20 ),
inference(avatar_component_clause,[],[f12059]) ).
fof(f12059,plain,
( spl24_20
<=> member(sK11(sF19,sF20),sF20) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_20])]) ).
fof(f12125,plain,
( spl24_2
| ~ spl24_3
| ~ spl24_19
| spl24_20 ),
inference(avatar_contradiction_clause,[],[f12124]) ).
fof(f12124,plain,
( $false
| spl24_2
| ~ spl24_3
| ~ spl24_19
| spl24_20 ),
inference(subsumption_resolution,[],[f12123,f12079]) ).
fof(f12079,plain,
( subset(sF19,sF20)
| ~ spl24_3
| spl24_20 ),
inference(resolution,[],[f12065,f276]) ).
fof(f12065,plain,
( ~ member(sK11(sF19,sF20),sF19)
| ~ spl24_3
| spl24_20 ),
inference(resolution,[],[f12061,f11486]) ).
fof(f11486,plain,
( ! [X8] :
( member(X8,sF20)
| ~ member(X8,sF19) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f11483,f467]) ).
fof(f11483,plain,
( ! [X8] :
( member(X8,sF20)
| ~ member(X8,sF19)
| member(sF19,power_set(sF20)) )
| ~ spl24_3 ),
inference(resolution,[],[f11471,f287]) ).
fof(f11471,plain,
( ! [X3,X4] :
( ~ member(sK12(X4,sF20),sF19)
| member(X3,sF20)
| ~ member(X3,X4) )
| ~ spl24_3 ),
inference(forward_demodulation,[],[f11470,f360]) ).
fof(f360,plain,
sF19 = domain_of(sK2),
inference(subsumption_resolution,[],[f359,f246]) ).
fof(f359,plain,
( ~ ilf_type(sK2,sF23)
| sF19 = domain_of(sK2) ),
inference(forward_demodulation,[],[f357,f245]) ).
fof(f357,plain,
( sF19 = domain_of(sK2)
| ~ ilf_type(sK2,relation_type(sK0,sK1)) ),
inference(superposition,[],[f346,f240]) ).
fof(f240,plain,
domain(sK0,sK1,sK2) = sF19,
introduced(function_definition,[]) ).
fof(f346,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f345,f157]) ).
fof(f345,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f221,f157]) ).
fof(f221,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain_of(X2) = domain(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p32) ).
fof(f11470,plain,
( ! [X3,X4] :
( member(X3,sF20)
| ~ member(X3,X4)
| ~ member(sK12(X4,sF20),domain_of(sK2)) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f11467,f350]) ).
fof(f11467,plain,
( ! [X3,X4] :
( member(X3,sF20)
| ~ member(X3,X4)
| ~ member(sK12(X4,sF20),domain_of(sK2))
| ~ ilf_type(sK2,binary_relation_type) )
| ~ spl24_3 ),
inference(resolution,[],[f1039,f313]) ).
fof(f313,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK8(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(subsumption_resolution,[],[f181,f157]) ).
fof(f181,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK8(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(X0,sK8(X0,X1)),X1)
& ilf_type(sK8(X0,X1),set_type) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f113,f114]) ).
fof(f114,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X0,X3),X1)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(X0,sK8(X0,X1)),X1)
& ilf_type(sK8(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X0,X3),X1)
& ilf_type(X3,set_type) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( member(X0,domain_of(X1))
<=> ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,domain_of(X1))
<=> ? [X2] :
( member(ordered_pair(X0,X2),X1)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p1) ).
fof(f1039,plain,
( ! [X10,X11,X9] :
( ~ member(ordered_pair(sK12(X9,sF20),X10),sK2)
| member(X11,sF20)
| ~ member(X11,X9) )
| ~ spl24_3 ),
inference(resolution,[],[f1020,f468]) ).
fof(f1020,plain,
( ! [X0,X1] :
( member(X0,sF20)
| ~ member(ordered_pair(X0,X1),sK2) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f1019,f929]) ).
fof(f929,plain,
! [X0,X1] :
( member(X1,sK1)
| ~ member(ordered_pair(X0,X1),sK2) ),
inference(resolution,[],[f923,f246]) ).
fof(f923,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,sF23)
| ~ member(ordered_pair(X1,X2),X0)
| member(X2,sK1) ),
inference(superposition,[],[f920,f245]) ).
fof(f920,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) ),
inference(subsumption_resolution,[],[f919,f157]) ).
fof(f919,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f918,f157]) ).
fof(f918,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f917,f157]) ).
fof(f917,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f219,f157]) ).
fof(f219,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f74]) ).
fof(f1019,plain,
( ! [X0,X1] :
( member(X0,sF20)
| ~ member(ordered_pair(X0,X1),sK2)
| ~ member(X1,sK1) )
| ~ spl24_3 ),
inference(superposition,[],[f890,f810]) ).
fof(f810,plain,
sF20 = inverse2(sK2,sK1),
inference(superposition,[],[f807,f241]) ).
fof(f241,plain,
inverse4(sK0,sK1,sK2,sK1) = sF20,
introduced(function_definition,[]) ).
fof(f807,plain,
! [X0] : inverse2(sK2,X0) = inverse4(sK0,sK1,sK2,X0),
inference(resolution,[],[f806,f246]) ).
fof(f806,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF23)
| inverse2(X0,X1) = inverse4(sK0,sK1,X0,X1) ),
inference(superposition,[],[f785,f245]) ).
fof(f785,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(subsumption_resolution,[],[f784,f157]) ).
fof(f784,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f783,f157]) ).
fof(f783,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f227,f157]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p38) ).
fof(f890,plain,
( ! [X8,X9,X7] :
( member(X9,inverse2(sK2,X8))
| ~ member(ordered_pair(X9,X7),sK2)
| ~ member(X7,X8) )
| ~ spl24_3 ),
inference(resolution,[],[f859,f350]) ).
fof(f859,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| member(X1,inverse2(X2,X0)) ),
inference(subsumption_resolution,[],[f858,f157]) ).
fof(f858,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f857,f157]) ).
fof(f857,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f217,f157]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ( member(sK14(X0,X1,X2),X0)
& member(ordered_pair(X1,sK14(X0,X1,X2)),X2)
& ilf_type(sK14(X0,X1,X2),set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f141,f142]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
=> ( member(sK14(X0,X1,X2),X0)
& member(ordered_pair(X1,sK14(X0,X1,X2)),X2)
& ilf_type(sK14(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X1,X4),X2)
& ilf_type(X4,set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X1,X3),X2)
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p5) ).
fof(f12061,plain,
( ~ member(sK11(sF19,sF20),sF20)
| spl24_20 ),
inference(avatar_component_clause,[],[f12059]) ).
fof(f12123,plain,
( ~ subset(sF19,sF20)
| spl24_2
| ~ spl24_19 ),
inference(subsumption_resolution,[],[f12114,f259]) ).
fof(f12114,plain,
( sF19 = sF20
| ~ subset(sF19,sF20)
| ~ spl24_19 ),
inference(resolution,[],[f12057,f282]) ).
fof(f12107,plain,
( ~ spl24_3
| spl24_19 ),
inference(avatar_contradiction_clause,[],[f12106]) ).
fof(f12106,plain,
( $false
| ~ spl24_3
| spl24_19 ),
inference(subsumption_resolution,[],[f12103,f12056]) ).
fof(f12056,plain,
( ~ subset(sF20,sF19)
| spl24_19 ),
inference(avatar_component_clause,[],[f12055]) ).
fof(f12103,plain,
( subset(sF20,sF19)
| ~ spl24_3
| spl24_19 ),
inference(resolution,[],[f12072,f276]) ).
fof(f12072,plain,
( ~ member(sK11(sF20,sF19),sF20)
| ~ spl24_3
| spl24_19 ),
inference(resolution,[],[f12063,f1316]) ).
fof(f1316,plain,
( ! [X3] :
( member(X3,sF19)
| ~ member(X3,sF20) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f1313,f467]) ).
fof(f1313,plain,
( ! [X3] :
( ~ member(X3,sF20)
| member(X3,sF19)
| member(sF20,power_set(sF19)) )
| ~ spl24_3 ),
inference(resolution,[],[f1300,f287]) ).
fof(f1300,plain,
( ! [X0,X1] :
( ~ member(sK12(X0,sF19),sF20)
| ~ member(X1,X0)
| member(X1,sF19) )
| ~ spl24_3 ),
inference(superposition,[],[f985,f810]) ).
fof(f985,plain,
( ! [X8,X6,X7] :
( ~ member(sK12(X6,sF19),inverse2(sK2,X7))
| ~ member(X8,X6)
| member(X8,sF19) )
| ~ spl24_3 ),
inference(resolution,[],[f662,f497]) ).
fof(f497,plain,
( ! [X21,X22,X20] :
( ~ member(ordered_pair(sK12(X21,sF19),X22),sK2)
| ~ member(X20,X21)
| member(X20,sF19) )
| ~ spl24_3 ),
inference(resolution,[],[f468,f383]) ).
fof(f383,plain,
( ! [X0,X1] :
( member(X0,sF19)
| ~ member(ordered_pair(X0,X1),sK2) )
| ~ spl24_3 ),
inference(subsumption_resolution,[],[f367,f350]) ).
fof(f367,plain,
! [X0,X1] :
( member(X0,sF19)
| ~ member(ordered_pair(X0,X1),sK2)
| ~ ilf_type(sK2,binary_relation_type) ),
inference(superposition,[],[f327,f360]) ).
fof(f327,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X1))
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(subsumption_resolution,[],[f326,f157]) ).
fof(f326,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X1))
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f182,f157]) ).
fof(f182,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X1))
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f115]) ).
fof(f662,plain,
( ! [X6,X5] :
( member(ordered_pair(X5,sK14(X6,X5,sK2)),sK2)
| ~ member(X5,inverse2(sK2,X6)) )
| ~ spl24_3 ),
inference(resolution,[],[f624,f350]) ).
fof(f624,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,inverse2(X2,X0))
| member(ordered_pair(X1,sK14(X0,X1,X2)),X2) ),
inference(subsumption_resolution,[],[f623,f157]) ).
fof(f623,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK14(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f215,f157]) ).
fof(f215,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK14(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f143]) ).
fof(f12063,plain,
( ~ member(sK11(sF20,sF19),sF19)
| spl24_19 ),
inference(resolution,[],[f12056,f278]) ).
fof(f375,plain,
spl24_3,
inference(avatar_contradiction_clause,[],[f374]) ).
fof(f374,plain,
( $false
| spl24_3 ),
inference(subsumption_resolution,[],[f373,f246]) ).
fof(f373,plain,
( ~ ilf_type(sK2,sF23)
| spl24_3 ),
inference(superposition,[],[f370,f245]) ).
fof(f370,plain,
( ! [X0,X1] : ~ ilf_type(sK2,relation_type(X0,X1))
| spl24_3 ),
inference(resolution,[],[f364,f318]) ).
fof(f318,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f317,f157]) ).
fof(f317,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f186,f157]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p8) ).
fof(f364,plain,
( ! [X2,X3] : ~ ilf_type(sK2,subset_type(cross_product(X2,X3)))
| spl24_3 ),
inference(resolution,[],[f356,f280]) ).
fof(f280,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f279,f157]) ).
fof(f279,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f228,f157]) ).
fof(f228,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p29) ).
fof(f356,plain,
( ~ relation_like(sK2)
| spl24_3 ),
inference(resolution,[],[f351,f266]) ).
fof(f266,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(subsumption_resolution,[],[f251,f157]) ).
fof(f251,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223',p17) ).
fof(f351,plain,
( ~ ilf_type(sK2,binary_relation_type)
| spl24_3 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f355,plain,
( ~ spl24_3
| spl24_4 ),
inference(avatar_split_clause,[],[f347,f353,f349]) ).
fof(f347,plain,
! [X0,X1] :
( member(X0,sF21)
| ~ member(ordered_pair(X1,X0),sK2)
| ~ ilf_type(sK2,binary_relation_type) ),
inference(superposition,[],[f324,f342]) ).
fof(f324,plain,
! [X2,X0,X1] :
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(subsumption_resolution,[],[f323,f157]) ).
fof(f323,plain,
! [X2,X0,X1] :
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f179,f157]) ).
fof(f179,plain,
! [X2,X0,X1] :
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f111]) ).
fof(f260,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f244,f257,f253]) ).
fof(f244,plain,
( sF19 != sF20
| sF21 != sF22 ),
inference(definition_folding,[],[f156,f243,f242,f241,f240]) ).
fof(f156,plain,
( domain(sK0,sK1,sK2) != inverse4(sK0,sK1,sK2,sK1)
| range(sK0,sK1,sK2) != image4(sK0,sK1,sK2,sK0) ),
inference(cnf_transformation,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET674+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 14:22:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.oUSfqRglMY/Vampire---4.8_16223
% 0.15/0.37 % (16330)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (16334)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.43 % (16333)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.43 % (16335)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (16331)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.43 % (16336)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.43 % (16332)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.43 % (16337)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.22/0.43 % (16334)Refutation not found, incomplete strategy% (16334)------------------------------
% 0.22/0.43 % (16334)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (16334)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (16334)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.43
% 0.22/0.43 % (16334)Memory used [KB]: 5756
% 0.22/0.43 % (16334)Time elapsed: 0.008 s
% 0.22/0.43 % (16334)------------------------------
% 0.22/0.43 % (16334)------------------------------
% 0.22/0.48 % (16338)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_401 on Vampire---4 for (401ds/0Mi)
% 0.22/0.72 % (16338)First to succeed.
% 0.22/0.72 % (16338)Refutation found. Thanks to Tanya!
% 0.22/0.72 % SZS status Theorem for Vampire---4
% 0.22/0.72 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.72 % (16338)------------------------------
% 0.22/0.72 % (16338)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.72 % (16338)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.72 % (16338)Termination reason: Refutation
% 0.22/0.72
% 0.22/0.72 % (16338)Memory used [KB]: 12153
% 0.22/0.72 % (16338)Time elapsed: 0.237 s
% 0.22/0.72 % (16338)------------------------------
% 0.22/0.72 % (16338)------------------------------
% 0.22/0.72 % (16330)Success in time 0.354 s
% 0.22/0.72 % Vampire---4.8 exiting
%------------------------------------------------------------------------------