%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET680+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 : n019.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 12:41:38 PM UTC 2026
% Result : Theorem 2.78s 1.25s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 117 ( 10 unt; 5 def)
% Number of atoms : 458 ( 5 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 580 ( 239 ~; 213 |; 79 &)
% ( 16 <=>; 31 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 213 ( 0 sgn 180 !; 33 ?)
% 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f6,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',p6) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f17,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',p17) ).
fof(f26,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',p26) ).
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(f31,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f32,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
<=> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(ordered_pair(X3,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_47) ).
fof(f33,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,member_type(X0))
=> ( member(X3,domain(X0,X1,X2))
<=> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(ordered_pair(X3,X4),X2) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f34,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(f37,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(f38,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,[],[f37]) ).
fof(f41,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,[],[f6]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f54,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f65,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,[],[f26]) ).
fof(f66,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(f70,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( member(X3,domain(X0,X1,X2))
<~> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(ordered_pair(X3,X4),X2) ) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f71,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( member(X3,domain(X0,X1,X2))
<~> ? [X4] :
( ilf_type(X4,member_type(X1))
& member(ordered_pair(X3,X4),X2) ) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f70]) ).
fof(f72,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,[],[f34]) ).
fof(f73,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,[],[f72]) ).
fof(f74,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))],[f73]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f79,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK3(X0),X0)
& ilf_type(sK3(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f80]) ).
fof(f82,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,[],[f54]) ).
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(flattening,[],[f82]) ).
fof(f97,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ ilf_type(X4,member_type(X1))
| ~ member(ordered_pair(X3,X4),X2) )
| ~ member(X3,domain(X0,X1,X2)) )
& ( ? [X4] :
( ilf_type(X4,member_type(X1))
& member(ordered_pair(X3,X4),X2) )
| member(X3,domain(X0,X1,X2)) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f71]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ ilf_type(X4,member_type(X1))
| ~ member(ordered_pair(X3,X4),X2) )
| ~ member(X3,domain(X0,X1,X2)) )
& ( ? [X4] :
( ilf_type(X4,member_type(X1))
& member(ordered_pair(X3,X4),X2) )
| member(X3,domain(X0,X1,X2)) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ ilf_type(X4,member_type(X1))
| ~ member(ordered_pair(X3,X4),X2) )
| ~ member(X3,domain(X0,X1,X2)) )
& ( ? [X5] :
( ilf_type(X5,member_type(X1))
& member(ordered_pair(X3,X5),X2) )
| member(X3,domain(X0,X1,X2)) )
& ilf_type(X3,member_type(X0)) )
& ilf_type(X2,relation_type(X0,X1)) )
& ~ empty(X1)
& ilf_type(X1,set_type) )
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
( ( ! [X4] :
( ~ ilf_type(X4,member_type(sK12))
| ~ member(ordered_pair(sK14,X4),sK13) )
| ~ member(sK14,domain(sK11,sK12,sK13)) )
& ( ( ilf_type(sK15,member_type(sK12))
& member(ordered_pair(sK14,sK15),sK13) )
| member(sK14,domain(sK11,sK12,sK13)) )
& ilf_type(sK14,member_type(sK11))
& ilf_type(sK13,relation_type(sK11,sK12))
& ~ empty(sK12)
& ilf_type(sK12,set_type)
& ~ empty(sK11)
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14),skolemize(X5,sK15)],[f99]) ).
fof(f101,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,[],[f74]) ).
fof(f103,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X1))
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f74]) ).
fof(f106,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,[],[f38]) ).
fof(f111,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,[],[f41]) ).
fof(f115,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f128,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f151,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,[],[f65]) ).
fof(f152,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,[],[f66]) ).
fof(f156,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f31]) ).
fof(f161,plain,
ilf_type(sK13,relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f100]) ).
fof(f163,plain,
( member(ordered_pair(sK14,sK15),sK13)
| member(sK14,domain(sK11,sK12,sK13)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f165,plain,
! [X4] :
( ~ ilf_type(X4,member_type(sK12))
| ~ member(ordered_pair(sK14,X4),sK13)
| ~ member(sK14,domain(sK11,sK12,sK13)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f172,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f128]) ).
fof(f174,definition,
( spl16_1
<=> member(sK14,domain(sK11,sK12,sK13)) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f175,plain,
( ~ member(sK14,domain(sK11,sK12,sK13))
| spl16_1 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( member(sK14,domain(sK11,sK12,sK13))
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f178,definition,
( spl16_2
<=> member(ordered_pair(sK14,sK15),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f180,plain,
( member(ordered_pair(sK14,sK15),sK13)
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f163,f178,f174]) ).
fof(f188,definition,
( spl16_4
<=> ! [X4] :
( ~ ilf_type(X4,member_type(sK12))
| ~ member(ordered_pair(sK14,X4),sK13) ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f189,plain,
( ! [X4] :
( ~ ilf_type(X4,member_type(sK12))
| ~ member(ordered_pair(sK14,X4),sK13) )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( ~ spl16_1
| spl16_4 ),
inference(avatar_split_clause,[],[f165,f188,f174]) ).
fof(f214,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f172,f156]) ).
fof(f219,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f117,f156]) ).
fof(f220,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(forward_subsumption_resolution,[],[f219,f156]) ).
fof(f239,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,[],[f151,f156]) ).
fof(f240,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f239,f156]) ).
fof(f253,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f115,f220]) ).
fof(f254,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f253,f156]) ).
fof(f255,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f254,f156]) ).
fof(f274,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,[],[f101,f156]) ).
fof(f275,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,[],[f111,f156]) ).
fof(f276,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f275,f156]) ).
fof(f282,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X1))
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f103,f156]) ).
fof(f283,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X1))
| ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f282,f156]) ).
fof(f301,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,[],[f152,f156]) ).
fof(f302,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f301,f156]) ).
fof(f304,plain,
( ~ member(sK14,domain_of(sK13))
| ~ ilf_type(sK13,relation_type(sK11,sK12))
| spl16_1 ),
inference(superposition,[],[f175,f302]) ).
fof(f305,plain,
( ~ member(sK14,domain_of(sK13))
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f304,f161]) ).
fof(f307,plain,
( ! [X0] :
( ~ member(ordered_pair(sK14,X0),sK13)
| ~ ilf_type(sK13,binary_relation_type) )
| spl16_1 ),
inference(resolution,[],[f305,f283]) ).
fof(f319,definition,
( spl16_12
<=> ilf_type(sK13,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
fof(f320,plain,
( ilf_type(sK13,binary_relation_type)
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f321,plain,
( ~ ilf_type(sK13,binary_relation_type)
| spl16_12 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f323,definition,
( spl16_13
<=> ! [X0] : ~ member(ordered_pair(sK14,X0),sK13) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
fof(f324,plain,
( ! [X0] : ~ member(ordered_pair(sK14,X0),sK13)
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f325,plain,
( ~ spl16_12
| spl16_13
| spl16_1 ),
inference(avatar_split_clause,[],[f307,f174,f323,f319]) ).
fof(f328,plain,
( ~ relation_like(sK13)
| spl16_12 ),
inference(resolution,[],[f321,f214]) ).
fof(f332,plain,
( ! [X0,X1] : ~ ilf_type(sK13,subset_type(cross_product(X0,X1)))
| spl16_12 ),
inference(resolution,[],[f328,f240]) ).
fof(f346,plain,
( ! [X0,X1] : ~ ilf_type(sK13,relation_type(X0,X1))
| spl16_12 ),
inference(resolution,[],[f332,f276]) ).
fof(f348,plain,
( $false
| spl16_12 ),
inference(resolution,[],[f346,f161]) ).
fof(f350,plain,
spl16_12,
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f360,plain,
( $false
| ~ spl16_2
| ~ spl16_13 ),
inference(resolution,[],[f324,f180]) ).
fof(f361,plain,
( ~ member(sK14,domain_of(sK13))
| ~ ilf_type(sK13,binary_relation_type)
| ~ spl16_13 ),
inference(resolution,[],[f324,f274]) ).
fof(f363,plain,
( ~ spl16_2
| ~ spl16_13 ),
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f373,plain,
( ~ member(sK14,domain_of(sK13))
| ~ spl16_12
| ~ spl16_13 ),
inference(forward_subsumption_resolution,[],[f361,f320]) ).
fof(f374,plain,
( member(sK14,domain_of(sK13))
| ~ ilf_type(sK13,relation_type(sK11,sK12))
| ~ spl16_1 ),
inference(superposition,[],[f176,f302]) ).
fof(f375,plain,
( member(sK14,domain_of(sK13))
| ~ spl16_1 ),
inference(forward_subsumption_resolution,[],[f374,f161]) ).
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(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f106,f156]) ).
fof(f390,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,[],[f389,f156]) ).
fof(f391,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,[],[f390,f156]) ).
fof(f392,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f391,f156]) ).
fof(f395,plain,
! [X0,X1] :
( member(X1,sK12)
| ~ member(ordered_pair(X0,X1),sK13) ),
inference(resolution,[],[f392,f161]) ).
fof(f398,plain,
( $false
| ~ spl16_1
| ~ spl16_12
| ~ spl16_13 ),
inference(forward_subsumption_resolution,[],[f373,f375]) ).
fof(f399,plain,
( ~ spl16_1
| ~ spl16_12
| ~ spl16_13 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f437,plain,
( ! [X0] :
( ~ member(ordered_pair(sK14,X0),sK13)
| ~ member(X0,sK12) )
| ~ spl16_4 ),
inference(resolution,[],[f189,f255]) ).
fof(f449,plain,
( ! [X0] : ~ member(ordered_pair(sK14,X0),sK13)
| ~ spl16_4 ),
inference(forward_subsumption_resolution,[],[f437,f395]) ).
fof(f450,plain,
( spl16_13
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f449,f188,f323]) ).
cnf(s1,plain,
( spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f181]) ).
cnf(s3,plain,
( ~ spl16_1
| spl16_4 ),
inference(sat_conversion,[],[f190]) ).
cnf(s11,plain,
( spl16_1
| ~ spl16_12
| spl16_13 ),
inference(sat_conversion,[],[f325]) ).
cnf(s13,plain,
spl16_12,
inference(sat_conversion,[],[f350]) ).
cnf(s14,plain,
( ~ spl16_2
| ~ spl16_13 ),
inference(sat_conversion,[],[f363]) ).
cnf(s18,plain,
( ~ spl16_1
| ~ spl16_12
| ~ spl16_13 ),
inference(sat_conversion,[],[f399]) ).
cnf(s24,plain,
( ~ spl16_4
| spl16_13 ),
inference(sat_conversion,[],[f450]) ).
cnf(s25,plain,
( spl16_1
| spl16_13 ),
inference(rat,[],[s11,s13]) ).
cnf(s28,plain,
spl16_1,
inference(rat,[],[s14,s1,s25]) ).
cnf(s30,plain,
~ spl16_13,
inference(rat,[],[s18,s13,s28]) ).
cnf(s33,plain,
spl16_4,
inference(rat,[],[s3,s28]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s24,s30,s33]) ).
fof(f451,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET680+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n019.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 02:32:05 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.78/1.25 % (3607961)Detected formulas, will run a generic FOF schedule.
% 2.78/1.25 % (3607970)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=904772917:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.25 % (3607966)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=3152631729:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.25 % (3607970)Instruction limit reached!
% 2.78/1.25 % (3607970)------------------------------
% 2.78/1.25 % (3607970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.25 % (3607970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.25 % (3607970)CaDiCaL version: 2.1.3
% 2.78/1.25 % (3607970)Termination reason: Instruction limit
% 2.78/1.25 % (3607970)Termination phase: Saturation
% 2.78/1.25 % (3607970)Time elapsed: 0.036 s
% 2.78/1.25 % (3607970)Peak memory usage: 88 MB
% 2.78/1.25 % (3607970)Instructions burned: 122 (million)
% 2.78/1.25 % (3607971)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2116148711:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.25 % (3607969)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2882718294:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.25 % (3607968)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=1802039772:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.25 % (3607967)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=2343814056:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.25 % (3607972)dis-21_1_sil=8000:lcm=predicate:random_seed=182631807: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)
% 2.78/1.25 % (3607969)Refutation not found, incomplete strategy
% 2.78/1.25 % (3607969)------------------------------
% 2.78/1.25 % (3607969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.25 % (3607969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.25 % (3607969)CaDiCaL version: 2.1.3
% 2.78/1.25 % (3607969)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.25 % (3607969)Time elapsed: 0.003 s
% 2.78/1.25 % (3607969)Peak memory usage: 88 MB
% 2.78/1.25 % (3607969)Instructions burned: 2 (million)
% 2.78/1.25 % (3607971)First to succeed.
% 2.78/1.25 % (3607971)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3607961"
% 2.78/1.25 % (3607975)lrs+10_1_sil=8000:sp=occurrence:random_seed=3008281919:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.78/1.25 % (3607972)Instruction limit reached!
% 2.78/1.25 % (3607972)------------------------------
% 2.78/1.25 % (3607972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.25 % (3607972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.25 % (3607972)CaDiCaL version: 2.1.3
% 2.78/1.25 % (3607972)Termination reason: Instruction limit
% 2.78/1.25 % (3607972)Termination phase: Saturation
% 2.78/1.25 % (3607972)Time elapsed: 0.081 s
% 2.78/1.25 % (3607972)Peak memory usage: 90 MB
% 2.78/1.25 % (3607972)Instructions burned: 130 (million)
% 2.78/1.25 % (3607975)Also succeeded, but the first one will report.
% 2.78/1.25 % (3607982)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2674783941:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.78/1.25 % (3607969)------------------------------
% 2.78/1.25 % (3607969)------------------------------
% 2.78/1.25 % (3607971)Refutation found. Thanks to Tanya!
% 2.78/1.25 % SZS status Theorem for theBenchmark
% 2.78/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.35 % (3607971)------------------------------
% 3.40/1.35 % (3607971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.35 % (3607971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.35 % (3607971)CaDiCaL version: 2.1.3
% 3.40/1.35 % (3607971)Termination reason: Refutation
% 3.40/1.35 % (3607971)Time elapsed: 0.014 s
% 3.40/1.35 % (3607971)Peak memory usage: 90 MB
% 3.40/1.35 % (3607971)Instructions burned: 16 (million)
% 3.40/1.35 % (3607971)------------------------------
% 3.40/1.35 % (3607971)------------------------------
% 3.40/1.35 % (3607961)Success in time 0.411 s
% 3.40/1.35 % Vampire exiting
%------------------------------------------------------------------------------