%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 12:44:19 PM UTC 2026
% Result : Theorem 0.17s 5.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 11 unt; 4 def)
% Number of atoms : 400 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 506 ( 209 ~; 212 |; 44 &)
% ( 13 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 207 ( 0 sgn 194 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,domain_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f3,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(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,range_of(X0))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X1),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f8,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/sandbox/benchmark/theBenchmark.p',p8) ).
fof(f10,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/sandbox/benchmark/theBenchmark.p',p10) ).
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/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f23,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/sandbox/benchmark/theBenchmark.p',p23) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_12) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ( member(X0,domain_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& 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(ennf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& 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(flattening,[],[f31]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ( member(X1,range_of(X0))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X1),X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f37,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,[],[f8]) ).
fof(f39,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,[],[f10]) ).
fof(f40,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,[],[f39]) ).
fof(f43,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(f56,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,[],[f23]) ).
fof(f60,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ subset(domain_of(X2),X0)
| ~ subset(range_of(X2),X1) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f29]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X0,X3),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ( ilf_type(sK0(X0,X1),set_type)
& member(ordered_pair(X0,sK0(X0,X1)),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f62]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X1),X0) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X0) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0) ) )
& ( ( ilf_type(sK3(X0,X1),set_type)
& member(ordered_pair(sK3(X0,X1),X1),X0) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f71]) ).
fof(f74,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,[],[f40]) ).
fof(f75,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,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0)
& ilf_type(sK5(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,[sK5]),skolemize(X2,sK5(X0,X1))],[f75]) ).
fof(f77,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,[],[f43]) ).
fof(f78,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,[],[f77]) ).
fof(f93,plain,
( ( ~ subset(domain_of(sK16),sK14)
| ~ subset(range_of(sK16),sK15) )
& ilf_type(sK16,relation_type(sK14,sK15))
& ilf_type(sK15,set_type)
& ilf_type(sK14,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16)],[f60]) ).
fof(f94,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f100,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,[],[f32]) ).
fof(f101,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,[],[f32]) ).
fof(f106,plain,
! [X0,X1] :
( member(ordered_pair(sK3(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f110,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,[],[f37]) ).
fof(f115,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f116,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f121,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f78]) ).
fof(f142,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,[],[f56]) ).
fof(f147,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f150,plain,
ilf_type(sK16,relation_type(sK14,sK15)),
inference(cnf_transformation,[],[f93]) ).
fof(f151,plain,
( ~ subset(domain_of(sK16),sK14)
| ~ subset(range_of(sK16),sK15) ),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f121]) ).
fof(f154,definition,
( spl17_1
<=> subset(range_of(sK16),sK15) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f158,definition,
( spl17_2
<=> subset(domain_of(sK16),sK14) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f160,plain,
( ~ subset(domain_of(sK16),sK14)
| spl17_2 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( ~ spl17_1
| ~ spl17_2 ),
inference(avatar_split_clause,[],[f151,f158,f154]) ).
fof(f168,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f152,f147]) ).
fof(f179,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f115,f147]) ).
fof(f180,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f179,f147]) ).
fof(f182,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f116,f147]) ).
fof(f183,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f182,f147]) ).
fof(f187,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,[],[f142,f147]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f187,f147]) ).
fof(f225,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f94,f147]) ).
fof(f250,plain,
! [X0,X1] :
( member(ordered_pair(sK3(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f106,f147]) ).
fof(f264,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,[],[f110,f147]) ).
fof(f265,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f264,f147]) ).
fof(f278,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f265,f188]) ).
fof(f292,plain,
relation_like(sK16),
inference(resolution,[],[f278,f150]) ).
fof(f387,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(forward_subsumption_resolution,[],[f100,f147]) ).
fof(f388,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(forward_subsumption_resolution,[],[f387,f147]) ).
fof(f389,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(forward_subsumption_resolution,[],[f388,f147]) ).
fof(f390,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f389,f147]) ).
fof(f391,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X3,X1))
| member(X0,X1)
| ~ member(X0,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(resolution,[],[f390,f250]) ).
fof(f397,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) ),
inference(forward_subsumption_resolution,[],[f101,f147]) ).
fof(f398,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) ),
inference(forward_subsumption_resolution,[],[f397,f147]) ).
fof(f399,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) ),
inference(forward_subsumption_resolution,[],[f398,f147]) ).
fof(f400,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f399,f147]) ).
fof(f413,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X1,X3))
| member(X0,X1)
| ~ member(X0,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(resolution,[],[f400,f225]) ).
fof(f511,plain,
! [X0] :
( member(X0,sK15)
| ~ member(X0,range_of(sK16))
| ~ ilf_type(sK16,binary_relation_type) ),
inference(resolution,[],[f391,f150]) ).
fof(f513,definition,
( spl17_7
<=> ilf_type(sK16,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f514,plain,
( ilf_type(sK16,binary_relation_type)
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f515,plain,
( ~ ilf_type(sK16,binary_relation_type)
| spl17_7 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f517,definition,
( spl17_8
<=> ! [X0] :
( member(X0,sK15)
| ~ member(X0,range_of(sK16)) ) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
fof(f518,plain,
( ! [X0] :
( ~ member(X0,range_of(sK16))
| member(X0,sK15) )
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f519,plain,
( ~ spl17_7
| spl17_8 ),
inference(avatar_split_clause,[],[f511,f517,f513]) ).
fof(f520,plain,
( ~ relation_like(sK16)
| spl17_7 ),
inference(resolution,[],[f515,f168]) ).
fof(f521,plain,
( $false
| spl17_7 ),
inference(forward_subsumption_resolution,[],[f520,f292]) ).
fof(f522,plain,
spl17_7,
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f530,plain,
! [X0] :
( member(X0,sK14)
| ~ member(X0,domain_of(sK16))
| ~ ilf_type(sK16,binary_relation_type) ),
inference(resolution,[],[f413,f150]) ).
fof(f531,plain,
( ! [X0] :
( ~ member(X0,domain_of(sK16))
| member(X0,sK14) )
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f530,f514]) ).
fof(f535,plain,
( ! [X0] :
( member(sK5(range_of(sK16),X0),sK15)
| subset(range_of(sK16),X0) )
| ~ spl17_8 ),
inference(resolution,[],[f518,f180]) ).
fof(f689,plain,
( ! [X0] :
( member(sK5(domain_of(sK16),X0),sK14)
| subset(domain_of(sK16),X0) )
| ~ spl17_7 ),
inference(resolution,[],[f531,f180]) ).
fof(f875,plain,
( subset(range_of(sK16),sK15)
| subset(range_of(sK16),sK15)
| ~ spl17_8 ),
inference(resolution,[],[f535,f183]) ).
fof(f878,plain,
( subset(range_of(sK16),sK15)
| ~ spl17_8 ),
inference(duplicate_literal_removal,[],[f875]) ).
fof(f920,plain,
( spl17_1
| ~ spl17_8 ),
inference(avatar_split_clause,[],[f878,f517,f154]) ).
fof(f1211,plain,
( subset(domain_of(sK16),sK14)
| subset(domain_of(sK16),sK14)
| ~ spl17_7 ),
inference(resolution,[],[f689,f183]) ).
fof(f1214,plain,
( subset(domain_of(sK16),sK14)
| ~ spl17_7 ),
inference(duplicate_literal_removal,[],[f1211]) ).
fof(f1215,plain,
( $false
| spl17_2
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f1214,f160]) ).
fof(f1216,plain,
( spl17_2
| ~ spl17_7 ),
inference(avatar_contradiction_clause,[],[f1215]) ).
cnf(s1,plain,
( ~ spl17_1
| ~ spl17_2 ),
inference(sat_conversion,[],[f161]) ).
cnf(s4,plain,
( ~ spl17_7
| spl17_8 ),
inference(sat_conversion,[],[f519]) ).
cnf(s5,plain,
spl17_7,
inference(sat_conversion,[],[f522]) ).
cnf(s39,plain,
( spl17_1
| ~ spl17_8 ),
inference(sat_conversion,[],[f920]) ).
cnf(s61,plain,
( spl17_2
| ~ spl17_7 ),
inference(sat_conversion,[],[f1216]) ).
cnf(s62,plain,
spl17_2,
inference(rat,[],[s61,s5]) ).
cnf(s63,plain,
spl17_8,
inference(rat,[],[s4,s5]) ).
cnf(s64,plain,
spl17_1,
inference(rat,[],[s39,s63]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s1,s62,s64]) ).
fof(f1217,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/5.40 % Computer : n017.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Mon Sep 28 02:23:42 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/5.44 Running first-order model finding
% 0.12/5.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.51 % (3156052)Will run a generic schedule for satisfiability detection.
% 0.17/5.51 % (3156058)% WARNING: option uhcvi not known.
% 0.17/5.51 % (3156057)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3541154502_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/5.51 % (3156058)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=750579211:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/5.51 % (3156060)dis+10_1_sil=32000:sp=arity:random_seed=1772713593:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/5.51 % (3156059)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1289550160:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/5.51 % (3156061)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=927096798:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/5.51 % (3156062)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1807685614:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/5.51 % (3156063)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3710298747:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/5.51 % TRYING [1]
% 0.17/5.51 % TRYING [2]
% 0.17/5.51 % TRYING [3]
% 0.17/5.51 % (3156060) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3156052-3156060"...
% 0.17/5.51 % (3156060)...printing done.
% 0.17/5.51 % (3156060)Refutation found. Thanks to Tanya!
% 0.17/5.51 % SZS status Theorem for theBenchmark
% 0.17/5.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/5.51 % (3156060)------------------------------
% 0.17/5.51 % (3156060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/5.51 % (3156060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/5.51 % (3156060)CaDiCaL version: 2.1.3
% 0.17/5.51 % (3156060)Termination reason: Refutation
% 0.17/5.51 % (3156060)Time elapsed: 0.028 s
% 0.17/5.51 % (3156060)Peak memory usage: 13 MB
% 0.17/5.51 % (3156060)Instructions burned: 40 (million)
% 0.17/5.51 % (3156052)Success in time 0.062 s
% 0.17/5.51 % Vampire exiting
%------------------------------------------------------------------------------