%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET665+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 : n026.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 3.45s 1.60s
% Output : Refutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 103 ( 12 unt; 4 def)
% Number of atoms : 371 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 464 ( 196 ~; 196 |; 34 &)
% ( 13 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 174 ( 0 sgn 169 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X2,X3),X0)
=> member(ordered_pair(X2,X3),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(ordered_pair(X1,X2),identity_relation_of(X0))
<=> ( member(X1,X0)
& X1 = X2 ) ) ) ) ),
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)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),binary_relation_type) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(f11,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',p11) ).
fof(f13,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',p13) ).
fof(f20,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',p20) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_28) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
<=> ( member(X1,X0)
& X1 = X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,X3) ) )
| ~ 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(f34,plain,
! [X0] :
( ! [X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f42,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f11]) ).
fof(f43,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,[],[f13]) ).
fof(f51,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,[],[f20]) ).
fof(f62,plain,
? [X0] :
( ~ subset(identity_relation_of(X0),cross_product(X0,X0))
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ? [X3] :
( ~ member(ordered_pair(X2,X3),X1)
& member(ordered_pair(X2,X3),X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f31]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ? [X3] :
( ~ member(ordered_pair(X2,X3),X1)
& member(ordered_pair(X2,X3),X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X4] :
( ! [X5] :
( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0)
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
& member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& ilf_type(sK1(X0,X1),set_type)
& ilf_type(sK0(X0,X1),set_type) ) )
& ( ! [X4] :
( ! [X5] :
( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0)
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ member(X1,X0)
| X1 != X2 )
& ( ( member(X1,X0)
& X1 = X2 )
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ member(X1,X0)
| X1 != X2 )
& ( ( member(X1,X0)
& X1 = X2 )
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f68]) ).
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(nnf_transformation,[],[f42]) ).
fof(f79,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,[],[f78]) ).
fof(f95,plain,
( ~ subset(identity_relation_of(sK14),cross_product(sK14,sK14))
& ilf_type(sK14,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f62]) ).
fof(f99,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| subset(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f100,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f101,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f102,plain,
! [X2,X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f69]) ).
fof(f107,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f34]) ).
fof(f118,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
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,[],[f79]) ).
fof(f128,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,[],[f43]) ).
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,[],[f51]) ).
fof(f156,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f158,plain,
~ subset(identity_relation_of(sK14),cross_product(sK14,sK14)),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f167,plain,
! [X0] : ilf_type(identity_relation_of(X0),binary_relation_type),
inference(forward_subsumption_resolution,[],[f118,f156]) ).
fof(f171,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f162,f156]) ).
fof(f177,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f107,f156]) ).
fof(f178,plain,
! [X0,X1] : ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
inference(forward_subsumption_resolution,[],[f177,f156]) ).
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,f156]) ).
fof(f188,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f187,f156]) ).
fof(f216,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,[],[f128,f156]) ).
fof(f217,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f216,f156]) ).
fof(f225,plain,
( ~ member(ordered_pair(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK1(identity_relation_of(sK14),cross_product(sK14,sK14))),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK14),binary_relation_type) ),
inference(resolution,[],[f100,f158]) ).
fof(f226,plain,
( ~ member(ordered_pair(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK1(identity_relation_of(sK14),cross_product(sK14,sK14))),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f225,f167]) ).
fof(f228,definition,
( spl15_3
<=> ilf_type(cross_product(sK14,sK14),binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f229,plain,
( ilf_type(cross_product(sK14,sK14),binary_relation_type)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f230,plain,
( ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| spl15_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f232,definition,
( spl15_4
<=> member(ordered_pair(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK1(identity_relation_of(sK14),cross_product(sK14,sK14))),cross_product(sK14,sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f234,plain,
( ~ member(ordered_pair(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK1(identity_relation_of(sK14),cross_product(sK14,sK14))),cross_product(sK14,sK14))
| spl15_4 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f235,plain,
( ~ spl15_3
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f226,f232,f228]) ).
fof(f236,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f101,f156]) ).
fof(f237,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f236,f156]) ).
fof(f238,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| X1 = X2 ),
inference(forward_subsumption_resolution,[],[f237,f156]) ).
fof(f239,plain,
( ~ relation_like(cross_product(sK14,sK14))
| spl15_3 ),
inference(resolution,[],[f230,f171]) ).
fof(f241,plain,
! [X0,X1] :
( sK0(identity_relation_of(X0),X1) = sK1(identity_relation_of(X0),X1)
| subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(resolution,[],[f238,f99]) ).
fof(f243,plain,
! [X0,X1] :
( subset(identity_relation_of(X0),X1)
| sK0(identity_relation_of(X0),X1) = sK1(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f241,f167]) ).
fof(f244,plain,
( ! [X0,X1] : ~ ilf_type(cross_product(sK14,sK14),subset_type(cross_product(X0,X1)))
| spl15_3 ),
inference(resolution,[],[f239,f188]) ).
fof(f247,plain,
! [X2,X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f102,f156]) ).
fof(f248,plain,
! [X2,X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f247,f156]) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| member(X1,X0) ),
inference(forward_subsumption_resolution,[],[f248,f156]) ).
fof(f250,plain,
( ! [X0,X1] : ~ ilf_type(cross_product(sK14,sK14),relation_type(X0,X1))
| spl15_3 ),
inference(resolution,[],[f244,f217]) ).
fof(f253,plain,
! [X0,X1] :
( member(sK0(identity_relation_of(X0),X1),X0)
| subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(resolution,[],[f249,f99]) ).
fof(f255,plain,
! [X0,X1] :
( member(sK0(identity_relation_of(X0),X1),X0)
| subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f253,f167]) ).
fof(f256,plain,
( $false
| spl15_3 ),
inference(resolution,[],[f250,f178]) ).
fof(f258,plain,
spl15_3,
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f341,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f106,f156]) ).
fof(f342,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f341,f156]) ).
fof(f343,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,set_type) ),
inference(forward_subsumption_resolution,[],[f342,f156]) ).
fof(f344,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) ),
inference(forward_subsumption_resolution,[],[f343,f156]) ).
fof(f349,plain,
( ~ member(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| ~ member(sK1(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| spl15_4 ),
inference(resolution,[],[f344,f234]) ).
fof(f353,definition,
( spl15_7
<=> member(sK1(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f355,plain,
( ~ member(sK1(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| spl15_7 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f357,definition,
( spl15_8
<=> member(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f359,plain,
( ~ member(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| spl15_8 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f360,plain,
( ~ spl15_7
| ~ spl15_8
| spl15_4 ),
inference(avatar_split_clause,[],[f349,f232,f357,f353]) ).
fof(f475,plain,
( sK0(identity_relation_of(sK14),cross_product(sK14,sK14)) = sK1(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type) ),
inference(resolution,[],[f243,f158]) ).
fof(f477,plain,
( sK0(identity_relation_of(sK14),cross_product(sK14,sK14)) = sK1(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f475,f229]) ).
fof(f495,plain,
( ~ member(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| ~ spl15_3
| spl15_7 ),
inference(superposition,[],[f355,f477]) ).
fof(f503,plain,
( ~ spl15_8
| ~ spl15_3
| spl15_7 ),
inference(avatar_split_clause,[],[f495,f353,f228,f357]) ).
fof(f506,plain,
( subset(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| spl15_8 ),
inference(resolution,[],[f359,f255]) ).
fof(f514,plain,
( ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| spl15_8 ),
inference(forward_subsumption_resolution,[],[f506,f158]) ).
fof(f515,plain,
( $false
| ~ spl15_3
| spl15_8 ),
inference(forward_subsumption_resolution,[],[f514,f229]) ).
fof(f516,plain,
( ~ spl15_3
| spl15_8 ),
inference(avatar_contradiction_clause,[],[f515]) ).
cnf(s2,plain,
( ~ spl15_3
| ~ spl15_4 ),
inference(sat_conversion,[],[f235]) ).
cnf(s3,plain,
spl15_3,
inference(sat_conversion,[],[f258]) ).
cnf(s6,plain,
( spl15_4
| ~ spl15_7
| ~ spl15_8 ),
inference(sat_conversion,[],[f360]) ).
cnf(s10,plain,
( ~ spl15_3
| spl15_7
| ~ spl15_8 ),
inference(sat_conversion,[],[f503]) ).
cnf(s12,plain,
( ~ spl15_3
| spl15_8 ),
inference(sat_conversion,[],[f516]) ).
cnf(s13,plain,
spl15_8,
inference(rat,[],[s12,s3]) ).
cnf(s14,plain,
spl15_7,
inference(rat,[],[s10,s13,s3]) ).
cnf(s15,plain,
spl15_4,
inference(rat,[],[s6,s13,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s15,s3]) ).
fof(f517,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET665+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:31:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.45/1.60 % (3417354)Detected formulas, will run a generic FOF schedule.
% 3.45/1.60 % (3417384)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1192494940:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.45/1.60 % (3417383)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2746754958:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.45/1.60 % (3417383)Refutation not found, incomplete strategy
% 3.45/1.60 % (3417383)------------------------------
% 3.45/1.60 % (3417383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.60 % (3417383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.60 % (3417383)CaDiCaL version: 2.1.3
% 3.45/1.60 % (3417383)Termination reason: Refutation not found, incomplete strategy
% 3.45/1.60 % (3417383)Time elapsed: 0.002 s
% 3.45/1.60 % (3417383)Peak memory usage: 88 MB
% 3.45/1.60 % (3417383)Instructions burned: 2 (million)
% 3.45/1.60 % (3417380)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=2158159853:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.45/1.60 % (3417384)Instruction limit reached!
% 3.45/1.60 % (3417384)------------------------------
% 3.45/1.60 % (3417384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.60 % (3417384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.60 % (3417384)CaDiCaL version: 2.1.3
% 3.45/1.60 % (3417384)Termination reason: Instruction limit
% 3.45/1.60 % (3417384)Termination phase: Saturation
% 3.45/1.60 % (3417384)Time elapsed: 0.052 s
% 3.45/1.60 % (3417384)Peak memory usage: 88 MB
% 3.45/1.60 % (3417384)Instructions burned: 120 (million)
% 3.45/1.60 % (3417386)dis-21_1_sil=8000:lcm=predicate:random_seed=1622686351: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)
% 3.45/1.60 % (3417381)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=2320749517:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.45/1.60 % (3417382)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=3122570329:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.45/1.60 % (3417385)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2330896803:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.45/1.60 % (3417385)First to succeed.
% 3.45/1.60 % (3417385)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3417354"
% 3.45/1.60 % (3417386)Instruction limit reached!
% 3.45/1.60 % (3417386)------------------------------
% 3.45/1.60 % (3417386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.60 % (3417386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.60 % (3417386)CaDiCaL version: 2.1.3
% 3.45/1.60 % (3417386)Termination reason: Instruction limit
% 3.45/1.60 % (3417386)Termination phase: Saturation
% 3.45/1.60 % (3417386)Time elapsed: 0.123 s
% 3.45/1.60 % (3417386)Peak memory usage: 90 MB
% 3.45/1.60 % (3417386)Instructions burned: 129 (million)
% 3.45/1.60 % (3417392)lrs+10_1_sil=8000:sp=occurrence:random_seed=411363240:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.45/1.60 % (3417392)Also succeeded, but the first one will report.
% 3.45/1.60 % (3417383)------------------------------
% 3.45/1.60 % (3417383)------------------------------
% 3.45/1.60 % (3417402)lrs+10_1_sil=32000:urr=on:br=off:random_seed=11531392:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.45/1.60 % (3417404)lrs+1011_1_sil=32000:sp=occurrence:random_seed=5845936:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 3.45/1.60 % (3417404)Also succeeded, but the first one will report.
% 3.45/1.60 % (3417385)Refutation found. Thanks to Tanya!
% 3.45/1.60 % SZS status Theorem for theBenchmark
% 3.45/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.45/1.83 % (3417385)------------------------------
% 5.45/1.83 % (3417385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.83 % (3417385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.83 % (3417385)CaDiCaL version: 2.1.3
% 5.45/1.83 % (3417385)Termination reason: Refutation
% 5.45/1.83 % (3417385)Time elapsed: 0.027 s
% 5.45/1.83 % (3417385)Peak memory usage: 90 MB
% 5.45/1.83 % (3417385)Instructions burned: 21 (million)
% 5.45/1.83 % (3417385)------------------------------
% 5.45/1.83 % (3417385)------------------------------
% 5.45/1.83 % (3417354)Success in time 0.673 s
% 5.45/1.83 % Vampire exiting
%------------------------------------------------------------------------------