%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET667+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:41:35 PM UTC 2026
% Result : Theorem 1.75s 1.14s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 11 unt; 4 def)
% Number of atoms : 394 ( 10 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 478 ( 199 ~; 196 |; 38 &)
% ( 11 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 188 ( 0 sgn 178 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(ordered_pair(X0,X1),X2)
=> ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [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))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f7,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/benchmark/theBenchmark.p',p7) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f24,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/benchmark/theBenchmark.p',p24) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f31,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f32,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_30) ).
fof(f33,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,domain(X0,X1,X3))
& subset(X2,range(X0,X1,X3)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( ! [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)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f41,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,[],[f7]) ).
fof(f42,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,[],[f41]) ).
fof(f49,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f63,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,[],[f24]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f71,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ subset(X2,domain(X0,X1,X3))
| ~ subset(X2,range(X0,X1,X3)) )
& subset(identity_relation_of(X2),X3)
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f72,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ subset(X2,domain(X0,X1,X3))
| ~ subset(X2,range(X0,X1,X3)) )
& subset(identity_relation_of(X2),X3)
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,X0)
| ~ member(ordered_pair(X1,X1),identity_relation_of(X0)) )
& ( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f36]) ).
fof(f77,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,[],[f42]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0)
& ilf_type(sK1(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(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f78]) ).
fof(f83,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f49]) ).
fof(f84,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f83]) ).
fof(f99,plain,
( ( ~ subset(sK14,domain(sK12,sK13,sK15))
| ~ subset(sK14,range(sK12,sK13,sK15)) )
& subset(identity_relation_of(sK14),sK15)
& ilf_type(sK15,relation_type(sK12,sK13))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f72]) ).
fof(f100,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f35]) ).
fof(f101,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f35]) ).
fof(f102,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f108,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f111,plain,
! [X3,X0,X1] :
( 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(cnf_transformation,[],[f79]) ).
fof(f113,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f114,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f126,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f148,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,[],[f63]) ).
fof(f153,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,[],[f67]) ).
fof(f155,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,[],[f69]) ).
fof(f157,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f31]) ).
fof(f161,plain,
ilf_type(sK15,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f99]) ).
fof(f162,plain,
subset(identity_relation_of(sK14),sK15),
inference(cnf_transformation,[],[f99]) ).
fof(f163,plain,
( ~ subset(sK14,domain(sK12,sK13,sK15))
| ~ subset(sK14,range(sK12,sK13,sK15)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f165,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f168,definition,
( spl16_1
<=> subset(sK14,range(sK12,sK13,sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f170,plain,
( ~ subset(sK14,range(sK12,sK13,sK15))
| spl16_1 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f172,definition,
( spl16_2
<=> subset(sK14,domain(sK12,sK13,sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f174,plain,
( ~ subset(sK14,domain(sK12,sK13,sK15))
| spl16_2 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f163,f172,f168]) ).
fof(f182,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f165,f157]) ).
fof(f190,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f113,f157]) ).
fof(f191,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f190,f157]) ).
fof(f192,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f114,f157]) ).
fof(f193,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f192,f157]) ).
fof(f196,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f148,f157]) ).
fof(f197,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f196,f157]) ).
fof(f198,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f102,f157]) ).
fof(f199,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[],[f198,f157]) ).
fof(f223,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f108,f157]) ).
fof(f224,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f223,f157]) ).
fof(f230,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f100,f157]) ).
fof(f231,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f230,f157]) ).
fof(f232,plain,
! [X2,X0,X1] :
( subset(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X0,sK1(X1,range_of(X2))),X2) ),
inference(resolution,[],[f231,f193]) ).
fof(f233,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f101,f157]) ).
fof(f234,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f233,f157]) ).
fof(f235,plain,
! [X2,X0,X1] :
( subset(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(ordered_pair(sK1(X0,domain_of(X1)),X2),X1) ),
inference(resolution,[],[f234,f193]) ).
fof(f244,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f111,f157]) ).
fof(f245,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f244,f157]) ).
fof(f246,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f245,f157]) ).
fof(f247,plain,
! [X0] :
( member(X0,sK15)
| ~ member(X0,identity_relation_of(sK14)) ),
inference(resolution,[],[f246,f162]) ).
fof(f280,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f153,f157]) ).
fof(f281,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f280,f157]) ).
fof(f293,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f155,f157]) ).
fof(f294,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f293,f157]) ).
fof(f297,plain,
( ~ subset(sK14,range_of(sK15))
| ~ ilf_type(sK15,relation_type(sK12,sK13))
| spl16_1 ),
inference(superposition,[],[f170,f294]) ).
fof(f298,plain,
( ~ subset(sK14,range_of(sK15))
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f297,f161]) ).
fof(f368,plain,
( ! [X0] :
( ~ ilf_type(sK15,binary_relation_type)
| ~ member(ordered_pair(X0,sK1(sK14,range_of(sK15))),sK15) )
| spl16_1 ),
inference(resolution,[],[f232,f298]) ).
fof(f371,definition,
( spl16_6
<=> ! [X0] : ~ member(ordered_pair(X0,sK1(sK14,range_of(sK15))),sK15) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
fof(f372,plain,
( ! [X0] : ~ member(ordered_pair(X0,sK1(sK14,range_of(sK15))),sK15)
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f374,definition,
( spl16_7
<=> ilf_type(sK15,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
fof(f375,plain,
( ilf_type(sK15,binary_relation_type)
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f376,plain,
( ~ ilf_type(sK15,binary_relation_type)
| spl16_7 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f377,plain,
( spl16_6
| ~ spl16_7
| spl16_1 ),
inference(avatar_split_clause,[],[f368,f168,f374,f371]) ).
fof(f378,plain,
( ~ relation_like(sK15)
| spl16_7 ),
inference(resolution,[],[f376,f182]) ).
fof(f380,plain,
( ! [X0,X1] : ~ ilf_type(sK15,subset_type(cross_product(X0,X1)))
| spl16_7 ),
inference(resolution,[],[f378,f197]) ).
fof(f387,plain,
( ! [X0,X1] : ~ ilf_type(sK15,relation_type(X0,X1))
| spl16_7 ),
inference(resolution,[],[f380,f224]) ).
fof(f393,plain,
( $false
| spl16_7 ),
inference(resolution,[],[f387,f161]) ).
fof(f395,plain,
spl16_7,
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f400,plain,
( ! [X0] : ~ member(ordered_pair(X0,sK1(sK14,range_of(sK15))),identity_relation_of(sK14))
| ~ spl16_6 ),
inference(resolution,[],[f372,f247]) ).
fof(f401,plain,
( ~ member(sK1(sK14,range_of(sK15)),sK14)
| ~ spl16_6 ),
inference(resolution,[],[f400,f199]) ).
fof(f404,plain,
( subset(sK14,range_of(sK15))
| ~ spl16_6 ),
inference(resolution,[],[f401,f191]) ).
fof(f405,plain,
( $false
| spl16_1
| ~ spl16_6 ),
inference(forward_subsumption_resolution,[],[f404,f298]) ).
fof(f406,plain,
( spl16_1
| ~ spl16_6 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f412,plain,
( ~ subset(sK14,domain_of(sK15))
| ~ ilf_type(sK15,relation_type(sK12,sK13))
| spl16_2 ),
inference(superposition,[],[f174,f281]) ).
fof(f413,plain,
( ~ subset(sK14,domain_of(sK15))
| spl16_2 ),
inference(forward_subsumption_resolution,[],[f412,f161]) ).
fof(f414,plain,
( ! [X0] :
( ~ ilf_type(sK15,binary_relation_type)
| ~ member(ordered_pair(sK1(sK14,domain_of(sK15)),X0),sK15) )
| spl16_2 ),
inference(resolution,[],[f413,f235]) ).
fof(f416,plain,
( ! [X0] : ~ member(ordered_pair(sK1(sK14,domain_of(sK15)),X0),sK15)
| spl16_2
| ~ spl16_7 ),
inference(forward_subsumption_resolution,[],[f414,f375]) ).
fof(f423,plain,
( ! [X0] : ~ member(ordered_pair(sK1(sK14,domain_of(sK15)),X0),identity_relation_of(sK14))
| spl16_2
| ~ spl16_7 ),
inference(resolution,[],[f416,f247]) ).
fof(f424,plain,
( ~ member(sK1(sK14,domain_of(sK15)),sK14)
| spl16_2
| ~ spl16_7 ),
inference(resolution,[],[f423,f199]) ).
fof(f429,plain,
( subset(sK14,domain_of(sK15))
| spl16_2
| ~ spl16_7 ),
inference(resolution,[],[f424,f191]) ).
fof(f430,plain,
( $false
| spl16_2
| ~ spl16_7 ),
inference(forward_subsumption_resolution,[],[f429,f413]) ).
fof(f431,plain,
( spl16_2
| ~ spl16_7 ),
inference(avatar_contradiction_clause,[],[f430]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f175]) ).
cnf(s3,plain,
( spl16_1
| spl16_6
| ~ spl16_7 ),
inference(sat_conversion,[],[f377]) ).
cnf(s4,plain,
spl16_7,
inference(sat_conversion,[],[f395]) ).
cnf(s5,plain,
( spl16_1
| ~ spl16_6 ),
inference(sat_conversion,[],[f406]) ).
cnf(s6,plain,
( spl16_2
| ~ spl16_7 ),
inference(sat_conversion,[],[f431]) ).
cnf(s7,plain,
spl16_2,
inference(rat,[],[s6,s4]) ).
cnf(s8,plain,
( spl16_1
| spl16_6 ),
inference(rat,[],[s3,s4]) ).
cnf(s9,plain,
~ spl16_1,
inference(rat,[],[s1,s7]) ).
cnf(s10,plain,
~ spl16_6,
inference(rat,[],[s5,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s8,s10,s9]) ).
fof(f432,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET667+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:29:02 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.75/1.14 % (1506903)Detected formulas, will run a generic FOF schedule.
% 1.75/1.14 % (1506913)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2640938701:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.75/1.14 % (1506913)First to succeed.
% 1.75/1.14 % (1506913)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1506903"
% 1.75/1.14 % (1506914)dis-21_1_sil=8000:lcm=predicate:random_seed=308878428:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.75/1.14 % (1506911)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=859063419:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.75/1.14 % (1506908)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2920885791:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.75/1.14 % (1506910)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2570650158:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.75/1.14 % (1506909)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1947611628:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.75/1.14 % (1506911)Refutation not found, incomplete strategy
% 1.75/1.14 % (1506911)------------------------------
% 1.75/1.14 % (1506911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.14 % (1506911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.14 % (1506911)CaDiCaL version: 2.1.3
% 1.75/1.14 % (1506911)Termination reason: Refutation not found, incomplete strategy
% 1.75/1.14 % (1506911)Time elapsed: 0.003 s
% 1.75/1.14 % (1506911)Peak memory usage: 88 MB
% 1.75/1.14 % (1506911)Instructions burned: 3 (million)
% 1.75/1.14 % (1506912)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3409589137:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.75/1.14 % (1506914)Instruction limit reached!
% 1.75/1.14 % (1506914)------------------------------
% 1.75/1.14 % (1506914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.14 % (1506912)Instruction limit reached!
% 1.75/1.14 % (1506912)------------------------------
% 1.75/1.14 % (1506912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.14 % (1506912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.14 % (1506912)CaDiCaL version: 2.1.3
% 1.75/1.14 % (1506914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.14 % (1506912)Termination reason: Instruction limit
% 1.75/1.14 % (1506912)Termination phase: Saturation
% 1.75/1.14 % (1506914)CaDiCaL version: 2.1.3
% 1.75/1.14 % (1506912)Time elapsed: 0.076 s
% 1.75/1.14 % (1506912)Peak memory usage: 88 MB
% 1.75/1.14 % (1506914)Termination reason: Instruction limit
% 1.75/1.14 % (1506914)Termination phase: Saturation
% 1.75/1.14 % (1506912)Instructions burned: 119 (million)
% 1.75/1.14 % (1506914)Time elapsed: 0.083 s
% 1.75/1.14 % (1506914)Peak memory usage: 90 MB
% 1.75/1.14 % (1506914)Instructions burned: 131 (million)
% 1.75/1.14 % (1506913)Refutation found. Thanks to Tanya!
% 1.75/1.14 % SZS status Theorem for theBenchmark
% 1.75/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.33 % (1506913)------------------------------
% 2.57/1.33 % (1506913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.33 % (1506913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.33 % (1506913)CaDiCaL version: 2.1.3
% 2.57/1.33 % (1506913)Termination reason: Refutation
% 2.57/1.33 % (1506913)Time elapsed: 0.008 s
% 2.57/1.33 % (1506913)Peak memory usage: 89 MB
% 2.57/1.33 % (1506913)Instructions burned: 18 (million)
% 2.57/1.33 % (1506913)------------------------------
% 2.57/1.33 % (1506913)------------------------------
% 2.57/1.33 % (1506903)Success in time 0.275 s
% 2.57/1.33 % Vampire exiting
%------------------------------------------------------------------------------