%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET646+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 : n015.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 12:41:31 PM UTC 2026
% Result : Theorem 2.68s 1.28s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 92 ( 15 unt; 2 def)
% Number of atoms : 428 ( 38 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 570 ( 234 ~; 224 |; 62 &)
% ( 18 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 197 ( 0 sgn 182 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,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',p3) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X2 = singleton(X1)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X2)
<=> X3 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
fof(f19,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',p19) ).
fof(f21,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',p21) ).
fof(f25,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
fof(f26,conjecture,
! [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(X2,X0)
& member(X3,X1) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_8) ).
fof(f27,negated_conjecture,
~ ! [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(X2,X0)
& member(X3,X1) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f29,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,[],[f2]) ).
fof(f30,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,[],[f3]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = singleton(X1)
<=> ! [X3] :
( ( member(X3,X2)
<=> X3 = X1 )
| ~ ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(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,[],[f17]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(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,[],[f45]) ).
fof(f48,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,[],[f19]) ).
fof(f49,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,[],[f48]) ).
fof(f52,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f58,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X2,X0)
& member(X3,X1)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X2,X0)
& member(X3,X1)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f58]) ).
fof(f61,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,[],[f29]) ).
fof(f62,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,[],[f61]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = singleton(X1)
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X3 = X1
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X2)
| X1 != X3 )
& ( X3 = X1
| ~ member(X3,X2) ) )
| ~ ilf_type(X3,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = singleton(X1)
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X3 = X1
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X2)
| X1 != X3 )
& ( X3 = X1
| ~ member(X3,X2) ) )
| ~ ilf_type(X3,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = singleton(X1)
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X3 = X1
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X4] :
( ( ( member(X4,X2)
| X1 != X4 )
& ( X1 = X4
| ~ member(X4,X2) ) )
| ~ ilf_type(X4,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = singleton(X1)
| ( ( sK1(X1,X2) != X1
| ~ member(sK1(X1,X2),X2) )
& ( sK1(X1,X2) = X1
| member(sK1(X1,X2),X2) )
& ilf_type(sK1(X1,X2),set_type) ) )
& ( ! [X4] :
( ( ( member(X4,X2)
| X1 != X4 )
& ( X1 = X4
| ~ member(X4,X2) ) )
| ~ ilf_type(X4,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X1,X2))],[f66]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f39]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f46]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f79]) ).
fof(f81,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,[],[f49]) ).
fof(f83,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,[],[f52]) ).
fof(f84,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,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK7(X0),X0)
& ilf_type(sK7(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,[sK7]),skolemize(X1,sK7(X0))],[f84]) ).
fof(f89,plain,
( ~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12))
& member(sK13,sK11)
& member(sK14,sK12)
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14)],[f59]) ).
fof(f94,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,[],[f62]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f30]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| ~ member(X4,X2)
| ~ ilf_type(X4,set_type)
| singleton(X1) != X2
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f69]) ).
fof(f125,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f130,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,[],[f81]) ).
fof(f132,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f85]) ).
fof(f143,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f25]) ).
fof(f148,plain,
member(sK14,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f149,plain,
member(sK13,sK11),
inference(cnf_transformation,[],[f89]) ).
fof(f150,plain,
~ ilf_type(singleton(ordered_pair(sK13,sK14)),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f89]) ).
fof(f153,plain,
! [X0,X1,X4] :
( X1 = X4
| ~ member(X4,singleton(X1))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(equality_resolution,[],[f98]) ).
fof(f162,definition,
( spl15_1
<=> ! [X0] : ~ ilf_type(X0,set_type) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f163,plain,
( ! [X0] : ~ ilf_type(X0,set_type)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f173,definition,
( spl15_4
<=> ! [X4,X1] :
( X1 = X4
| ~ ilf_type(X1,set_type)
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X4,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f174,plain,
( ! [X1,X4] :
( X1 = X4
| ~ ilf_type(X1,set_type)
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X4,singleton(X1)) )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f175,plain,
( spl15_1
| spl15_4 ),
inference(avatar_split_clause,[],[f153,f173,f162]) ).
fof(f199,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f132,f143]) ).
fof(f200,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(forward_subsumption_resolution,[],[f199,f143]) ).
fof(f219,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f111,f143]) ).
fof(f220,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(forward_subsumption_resolution,[],[f219,f143]) ).
fof(f221,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f125,f143]) ).
fof(f222,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f221,f143]) ).
fof(f223,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f126,f143]) ).
fof(f224,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f223,f143]) ).
fof(f227,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,[],[f130,f200]) ).
fof(f228,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f227,f143]) ).
fof(f229,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f228,f143]) ).
fof(f232,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f96,f143]) ).
fof(f233,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f232,f143]) ).
fof(f234,plain,
~ ilf_type(singleton(ordered_pair(sK13,sK14)),subset_type(cross_product(sK11,sK12))),
inference(resolution,[],[f233,f150]) ).
fof(f239,plain,
~ ilf_type(singleton(ordered_pair(sK13,sK14)),member_type(power_set(cross_product(sK11,sK12)))),
inference(resolution,[],[f234,f220]) ).
fof(f241,plain,
~ member(singleton(ordered_pair(sK13,sK14)),power_set(cross_product(sK11,sK12))),
inference(resolution,[],[f239,f229]) ).
fof(f242,plain,
( ! [X1,X4] :
( X1 = X4
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X4,singleton(X1)) )
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f174,f143]) ).
fof(f243,plain,
( ! [X1,X4] :
( X1 = X4
| ~ ilf_type(X4,set_type)
| ~ member(X4,singleton(X1)) )
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f242,f143]) ).
fof(f244,plain,
( ! [X1,X4] :
( ~ member(X4,singleton(X1))
| X1 = X4 )
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f243,f143]) ).
fof(f245,plain,
~ member(sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12)),cross_product(sK11,sK12)),
inference(resolution,[],[f241,f224]) ).
fof(f252,plain,
( ! [X0,X1] :
( member(singleton(X0),power_set(X1))
| sK5(singleton(X0),X1) = X0 )
| ~ spl15_4 ),
inference(resolution,[],[f244,f222]) ).
fof(f402,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,[],[f94,f143]) ).
fof(f403,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,[],[f402,f143]) ).
fof(f404,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,[],[f403,f143]) ).
fof(f405,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) ),
inference(forward_subsumption_resolution,[],[f404,f143]) ).
fof(f456,plain,
( ordered_pair(sK13,sK14) = sK5(singleton(ordered_pair(sK13,sK14)),cross_product(sK11,sK12))
| ~ spl15_4 ),
inference(resolution,[],[f252,f241]) ).
fof(f462,plain,
( ~ member(ordered_pair(sK13,sK14),cross_product(sK11,sK12))
| ~ spl15_4 ),
inference(superposition,[],[f245,f456]) ).
fof(f472,plain,
( ~ member(sK13,sK11)
| ~ member(sK14,sK12)
| ~ spl15_4 ),
inference(resolution,[],[f462,f405]) ).
fof(f482,plain,
( ~ member(sK14,sK12)
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f472,f149]) ).
fof(f483,plain,
( $false
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f482,f148]) ).
fof(f484,plain,
~ spl15_4,
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f485,plain,
( $false
| ~ spl15_1 ),
inference(forward_subsumption_resolution,[],[f163,f143]) ).
fof(f486,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f485]) ).
cnf(s5,plain,
( spl15_1
| spl15_4 ),
inference(sat_conversion,[],[f175]) ).
cnf(s12,plain,
~ spl15_4,
inference(sat_conversion,[],[f484]) ).
cnf(s13,plain,
~ spl15_1,
inference(sat_conversion,[],[f486]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s5,s12,s13]) ).
fof(f487,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET646+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 02:27:31 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.68/1.28 % (2204093)Detected formulas, will run a generic FOF schedule.
% 2.68/1.28 % (2204104)dis-21_1_sil=8000:lcm=predicate:random_seed=1398334129: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)
% 2.68/1.28 % (2204104)Instruction limit reached!
% 2.68/1.28 % (2204104)------------------------------
% 2.68/1.28 % (2204104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (2204104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (2204104)CaDiCaL version: 2.1.3
% 2.68/1.28 % (2204104)Termination reason: Instruction limit
% 2.68/1.28 % (2204104)Termination phase: Saturation
% 2.68/1.28 % (2204104)Time elapsed: 0.031 s
% 2.68/1.28 % (2204104)Peak memory usage: 89 MB
% 2.68/1.28 % (2204104)Instructions burned: 131 (million)
% 2.68/1.28 % (2204098)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=3256834683:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.28 % (2204099)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=3375004331:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.28 % (2204101)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2795627377:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.28 % (2204102)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3336965360:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.28 % (2204103)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4052923272:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.28 % (2204100)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=1969352946:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.28 % (2204101)Refutation not found, incomplete strategy
% 2.68/1.28 % (2204101)------------------------------
% 2.68/1.28 % (2204101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (2204101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (2204101)CaDiCaL version: 2.1.3
% 2.68/1.28 % (2204101)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.28 % (2204101)Time elapsed: 0.002 s
% 2.68/1.28 % (2204101)Peak memory usage: 88 MB
% 2.68/1.28 % (2204101)Instructions burned: 1 (million)
% 2.68/1.28 % (2204103)First to succeed.
% 2.68/1.28 % (2204103)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2204093"
% 2.68/1.28 % (2204102)Instruction limit reached!
% 2.68/1.28 % (2204102)------------------------------
% 2.68/1.28 % (2204102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (2204102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (2204102)CaDiCaL version: 2.1.3
% 2.68/1.28 % (2204102)Termination reason: Instruction limit
% 2.68/1.28 % (2204102)Termination phase: Saturation
% 2.68/1.28 % (2204102)Time elapsed: 0.057 s
% 2.68/1.28 % (2204102)Peak memory usage: 88 MB
% 2.68/1.28 % (2204102)Instructions burned: 119 (million)
% 2.68/1.28 % (2204106)lrs+10_1_sil=8000:sp=occurrence:random_seed=1831770457:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.68/1.28 % (2204106)Instruction limit reached!
% 2.68/1.28 % (2204106)------------------------------
% 2.68/1.28 % (2204106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (2204106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (2204106)CaDiCaL version: 2.1.3
% 2.68/1.28 % (2204106)Termination reason: Instruction limit
% 2.68/1.28 % (2204106)Termination phase: Saturation
% 2.68/1.28 % (2204106)Time elapsed: 0.096 s
% 2.68/1.28 % (2204106)Peak memory usage: 91 MB
% 2.68/1.28 % (2204106)Instructions burned: 287 (million)
% 2.68/1.28 % (2204113)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1444590992:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.68/1.28 % (2204101)------------------------------
% 2.68/1.28 % (2204101)------------------------------
% 2.68/1.28 % (2204103)Refutation found. Thanks to Tanya!
% 2.68/1.28 % SZS status Theorem for theBenchmark
% 2.68/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.37 % (2204103)------------------------------
% 3.63/1.37 % (2204103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.37 % (2204103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.37 % (2204103)CaDiCaL version: 2.1.3
% 3.63/1.37 % (2204103)Termination reason: Refutation
% 3.63/1.37 % (2204103)Time elapsed: 0.016 s
% 3.63/1.37 % (2204103)Peak memory usage: 90 MB
% 3.63/1.37 % (2204103)Instructions burned: 20 (million)
% 3.63/1.37 % (2204103)------------------------------
% 3.63/1.37 % (2204103)------------------------------
% 3.63/1.37 % (2204093)Success in time 0.445 s
% 3.63/1.37 % Vampire exiting
%------------------------------------------------------------------------------