%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n014.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 12:41:32 PM UTC 2026
% Result : Theorem 3.25s 1.33s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 105 ( 10 unt; 4 def)
% Number of atoms : 402 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 507 ( 210 ~; 212 |; 44 &)
% ( 13 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 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 : 211 ( 0 sgn 198 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,range_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
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(f4,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,domain_of(X0))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X1,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
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(f30,plain,
! [X0] :
( ! [X1] :
( ( member(X0,range_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
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(f33,plain,
! [X0] :
( ! [X1] :
( ( member(X1,domain_of(X0))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X1,X2),X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f4]) ).
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(f64,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f30]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ( ilf_type(sK1(X0,X1),set_type)
& member(ordered_pair(sK1(X0,X1),X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,domain_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X1,X2),X0) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X1,X2),X0) )
| ~ member(X1,domain_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,domain_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X1,X2),X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X0) )
| ~ member(X1,domain_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,domain_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X1,X2),X0) ) )
& ( ( ilf_type(sK2(X0,X1),set_type)
& member(ordered_pair(X1,sK2(X0,X1)),X0) )
| ~ member(X1,domain_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f68]) ).
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(f97,plain,
! [X0,X1] :
( member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f66]) ).
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(f102,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK2(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f69]) ).
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(f156,plain,
( ~ subset(range_of(sK16),sK15)
| spl17_1 ),
inference(avatar_component_clause,[],[f154]) ).
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(f167,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f152,f147]) ).
fof(f175,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f115,f147]) ).
fof(f176,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f175,f147]) ).
fof(f177,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f116,f147]) ).
fof(f178,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f177,f147]) ).
fof(f181,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(f182,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f181,f147]) ).
fof(f211,plain,
! [X0,X1] :
( member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f97,f147]) ).
fof(f212,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK2(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f102,f147]) ).
fof(f214,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(f215,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f214,f147]) ).
fof(f271,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(f272,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,[],[f271,f147]) ).
fof(f273,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,[],[f272,f147]) ).
fof(f274,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f273,f147]) ).
fof(f275,plain,
! [X2,X3,X0,X1,X4] :
( subset(X1,X2)
| ~ ilf_type(X3,relation_type(X4,X2))
| ~ member(ordered_pair(X0,sK5(X1,X2)),X3) ),
inference(resolution,[],[f274,f178]) ).
fof(f280,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(f281,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,[],[f280,f147]) ).
fof(f282,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,[],[f281,f147]) ).
fof(f283,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f282,f147]) ).
fof(f284,plain,
! [X2,X3,X0,X1,X4] :
( subset(X0,X1)
| ~ ilf_type(X3,relation_type(X1,X4))
| ~ member(ordered_pair(sK5(X0,X1),X2),X3) ),
inference(resolution,[],[f283,f178]) ).
fof(f326,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,sK15))
| ~ member(ordered_pair(X2,sK5(range_of(sK16),sK15)),X0) )
| spl17_1 ),
inference(resolution,[],[f275,f156]) ).
fof(f384,plain,
( ! [X0] : ~ member(ordered_pair(X0,sK5(range_of(sK16),sK15)),sK16)
| spl17_1 ),
inference(resolution,[],[f326,f150]) ).
fof(f401,plain,
( ~ member(sK5(range_of(sK16),sK15),range_of(sK16))
| ~ ilf_type(sK16,binary_relation_type)
| spl17_1 ),
inference(resolution,[],[f384,f211]) ).
fof(f416,definition,
( spl17_21
<=> ilf_type(sK16,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl17_21])],[avatar_definition]) ).
fof(f417,plain,
( ilf_type(sK16,binary_relation_type)
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f418,plain,
( ~ ilf_type(sK16,binary_relation_type)
| spl17_21 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f420,definition,
( spl17_22
<=> member(sK5(range_of(sK16),sK15),range_of(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_22])],[avatar_definition]) ).
fof(f422,plain,
( ~ member(sK5(range_of(sK16),sK15),range_of(sK16))
| spl17_22 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f423,plain,
( ~ spl17_21
| ~ spl17_22
| spl17_1 ),
inference(avatar_split_clause,[],[f401,f154,f420,f416]) ).
fof(f425,plain,
( ~ relation_like(sK16)
| spl17_21 ),
inference(resolution,[],[f418,f167]) ).
fof(f434,plain,
( ! [X0,X1] : ~ ilf_type(sK16,subset_type(cross_product(X0,X1)))
| spl17_21 ),
inference(resolution,[],[f425,f182]) ).
fof(f1076,plain,
( ! [X0,X1] : ~ ilf_type(sK16,relation_type(X0,X1))
| spl17_21 ),
inference(resolution,[],[f434,f215]) ).
fof(f1082,plain,
( $false
| spl17_21 ),
inference(resolution,[],[f1076,f150]) ).
fof(f1084,plain,
spl17_21,
inference(avatar_contradiction_clause,[],[f1082]) ).
fof(f1214,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(sK14,X1))
| ~ member(ordered_pair(sK5(domain_of(sK16),sK14),X2),X0) )
| spl17_2 ),
inference(resolution,[],[f160,f284]) ).
fof(f1263,plain,
( ! [X0] : ~ member(ordered_pair(sK5(domain_of(sK16),sK14),X0),sK16)
| spl17_2 ),
inference(resolution,[],[f1214,f150]) ).
fof(f1298,plain,
( ~ member(sK5(domain_of(sK16),sK14),domain_of(sK16))
| ~ ilf_type(sK16,binary_relation_type)
| spl17_2 ),
inference(resolution,[],[f1263,f212]) ).
fof(f1308,plain,
( ~ member(sK5(domain_of(sK16),sK14),domain_of(sK16))
| spl17_2
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f1298,f417]) ).
fof(f1636,plain,
( subset(range_of(sK16),sK15)
| spl17_22 ),
inference(resolution,[],[f422,f176]) ).
fof(f1647,plain,
( subset(domain_of(sK16),sK14)
| spl17_2
| ~ spl17_21 ),
inference(resolution,[],[f1308,f176]) ).
fof(f1654,plain,
( $false
| spl17_2
| ~ spl17_21 ),
inference(forward_subsumption_resolution,[],[f1647,f160]) ).
fof(f1655,plain,
( spl17_2
| ~ spl17_21 ),
inference(avatar_contradiction_clause,[],[f1654]) ).
fof(f1656,plain,
( spl17_1
| spl17_22 ),
inference(avatar_split_clause,[],[f1636,f420,f154]) ).
cnf(s1,plain,
( ~ spl17_1
| ~ spl17_2 ),
inference(sat_conversion,[],[f161]) ).
cnf(s23,plain,
( spl17_1
| ~ spl17_21
| ~ spl17_22 ),
inference(sat_conversion,[],[f423]) ).
cnf(s74,plain,
spl17_21,
inference(sat_conversion,[],[f1084]) ).
cnf(s129,plain,
( spl17_2
| ~ spl17_21 ),
inference(sat_conversion,[],[f1655]) ).
cnf(s130,plain,
( spl17_1
| spl17_22 ),
inference(sat_conversion,[],[f1656]) ).
cnf(s131,plain,
spl17_2,
inference(rat,[],[s129,s74]) ).
cnf(s133,plain,
( spl17_1
| ~ spl17_22 ),
inference(rat,[],[s23,s74]) ).
cnf(s134,plain,
~ spl17_1,
inference(rat,[],[s1,s131]) ).
cnf(s135,plain,
spl17_22,
inference(rat,[],[s130,s134]) ).
cnf(s137,plain,
$false,
inference(rat,[],[s133,s135,s134]) ).
fof(f1657,plain,
$false,
inference(avatar_sat_refutation,[],[s137]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:28:03 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.25/1.33 % (1377510)Detected formulas, will run a generic FOF schedule.
% 3.25/1.33 % (1377516)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=1191009302:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.25/1.33 % (1377518)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4288223299:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.25/1.33 % (1377518)Refutation not found, incomplete strategy
% 3.25/1.33 % (1377518)------------------------------
% 3.25/1.33 % (1377518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.33 % (1377518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.33 % (1377518)CaDiCaL version: 2.1.3
% 3.25/1.33 % (1377518)Termination reason: Refutation not found, incomplete strategy
% 3.25/1.33 % (1377518)Time elapsed: 0.003 s
% 3.25/1.33 % (1377518)Peak memory usage: 88 MB
% 3.25/1.33 % (1377518)Instructions burned: 2 (million)
% 3.25/1.33 % (1377515)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=1925467964:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.25/1.33 % (1377517)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=3552959031:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.25/1.33 % (1377520)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3892315704:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.25/1.33 % (1377519)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1835527190:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.25/1.33 % (1377521)dis-21_1_sil=8000:lcm=predicate:random_seed=3895098280: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)
% 3.25/1.33 % (1377520)First to succeed.
% 3.25/1.33 % (1377520)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1377510"
% 3.25/1.33 % (1377521)Also succeeded, but the first one will report.
% 3.25/1.33 % (1377519)Instruction limit reached!
% 3.25/1.33 % (1377519)------------------------------
% 3.25/1.33 % (1377519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.33 % (1377519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.33 % (1377519)CaDiCaL version: 2.1.3
% 3.25/1.33 % (1377519)Termination reason: Instruction limit
% 3.25/1.33 % (1377519)Termination phase: Saturation
% 3.25/1.33 % (1377519)Time elapsed: 0.069 s
% 3.25/1.33 % (1377519)Peak memory usage: 88 MB
% 3.25/1.33 % (1377519)Instructions burned: 120 (million)
% 3.25/1.33 % (1377529)lrs+10_1_sil=8000:sp=occurrence:random_seed=4168379230:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.25/1.33 % (1377518)------------------------------
% 3.25/1.33 % (1377518)------------------------------
% 3.25/1.33 % (1377529)Also succeeded, but the first one will report.
% 3.25/1.33 % (1377520)Refutation found. Thanks to Tanya!
% 3.25/1.33 % SZS status Theorem for theBenchmark
% 3.25/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.52 % (1377520)------------------------------
% 3.87/1.52 % (1377520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.52 % (1377520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.52 % (1377520)CaDiCaL version: 2.1.3
% 3.87/1.52 % (1377520)Termination reason: Refutation
% 3.87/1.52 % (1377520)Time elapsed: 0.039 s
% 3.87/1.52 % (1377520)Peak memory usage: 90 MB
% 3.87/1.52 % (1377520)Instructions burned: 53 (million)
% 3.87/1.52 % (1377520)------------------------------
% 3.87/1.52 % (1377520)------------------------------
% 3.87/1.52 % (1377510)Success in time 0.455 s
% 3.87/1.52 % Vampire exiting
%------------------------------------------------------------------------------