%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:44:17 PM UTC 2026
% Result : Theorem 0.37s 0.55s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 109 ( 19 unt; 5 def)
% Number of atoms : 396 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 461 ( 174 ~; 199 |; 41 &)
% ( 16 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 172 ( 0 sgn 160 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f4,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',p4) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f8,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',p8) ).
fof(f11,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',p11) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f13,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',p13) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_2) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f22]) ).
fof(f26,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,[],[f4]) ).
fof(f28,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,[],[f6]) ).
fof(f29,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,[],[f28]) ).
fof(f31,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,[],[f8]) ).
fof(f34,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,[],[f11]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,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,[],[f13]) ).
fof(f38,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,[],[f37]) ).
fof(f47,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(X0,cross_product(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ subset(X0,cross_product(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f47]) ).
fof(f53,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,[],[f29]) ).
fof(f54,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,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0)
& ilf_type(sK3(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,[sK3]),skolemize(X2,sK3(X0,X1))],[f54]) ).
fof(f56,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,[],[f31]) ).
fof(f58,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,[],[f35]) ).
fof(f59,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,[],[f58]) ).
fof(f60,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))],[f59]) ).
fof(f61,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,[],[f38]) ).
fof(f69,plain,
( ~ subset(sK11,cross_product(sK12,sK13))
& subset(sK11,sK14)
& ilf_type(sK14,relation_type(sK12,sK13))
& 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)],[f48]) ).
fof(f70,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f23]) ).
fof(f78,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,[],[f26]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f84,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f86,plain,
! [X0,X1] :
( 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(cnf_transformation,[],[f56]) ).
fof(f90,plain,
! [X3,X0,X1] :
( 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(cnf_transformation,[],[f60]) ).
fof(f95,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f96,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f114,plain,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f69]) ).
fof(f115,plain,
subset(sK11,sK14),
inference(cnf_transformation,[],[f69]) ).
fof(f116,plain,
~ subset(sK11,cross_product(sK12,sK13)),
inference(cnf_transformation,[],[f69]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2)
| ilf_type(X1,set_type)
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f70]) ).
fof(f127,plain,
! [X3,X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f78]) ).
fof(f129,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ~ member(sK3(X0,X1),X1)
| subset(X0,X1)
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f84]) ).
fof(f130,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| member(sK3(X0,X1),X0)
| subset(X0,X1)
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f83]) ).
fof(f135,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f141,plain,
! [X3,X0,X1] :
( ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1)
| ~ member(X0,power_set(X1))
| ilf_type(X1,set_type)
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f142,plain,
! [X0] :
( empty(power_set(X0))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f95]) ).
fof(f145,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| ~ empty(X1)
| member(X0,X1)
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f158,plain,
! [X0] : ~ ilf_type(X0,set_type),
inference(consistent_polarity_flipping,[],[f110]) ).
fof(f159,plain,
~ ilf_type(sK14,relation_type(sK12,sK13)),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f164,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(resolution,[],[f129,f158]) ).
fof(f165,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[],[f164,f158]) ).
fof(f166,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(resolution,[],[f130,f158]) ).
fof(f168,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[],[f166,f158]) ).
fof(f179,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f135,f158]) ).
fof(f180,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[],[f179,f158]) ).
fof(f227,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| ~ empty(X1)
| member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(resolution,[],[f145,f158]) ).
fof(f228,plain,
! [X0,X1] :
( ilf_type(X1,member_type(X0))
| member(X1,X0)
| ~ empty(X0) ),
inference(resolution,[],[f227,f158]) ).
fof(f295,plain,
! [X2,X0,X1] :
( ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[],[f127,f158]) ).
fof(f296,plain,
! [X2,X0,X1] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[],[f295,f158]) ).
fof(f300,plain,
~ ilf_type(sK14,subset_type(cross_product(sK12,sK13))),
inference(resolution,[],[f296,f159]) ).
fof(f303,plain,
~ ilf_type(sK14,member_type(power_set(cross_product(sK12,sK13)))),
inference(resolution,[],[f300,f180]) ).
fof(f305,plain,
( member(sK14,power_set(cross_product(sK12,sK13)))
| ~ empty(power_set(cross_product(sK12,sK13))) ),
inference(resolution,[],[f303,f228]) ).
fof(f307,definition,
( spl15_7
<=> empty(power_set(cross_product(sK12,sK13))) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f309,plain,
( ~ empty(power_set(cross_product(sK12,sK13)))
| spl15_7 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f311,definition,
( spl15_8
<=> member(sK14,power_set(cross_product(sK12,sK13))) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f314,plain,
( ~ spl15_7
| spl15_8 ),
inference(avatar_split_clause,[],[f305,f311,f307]) ).
fof(f315,plain,
( ilf_type(cross_product(sK12,sK13),set_type)
| spl15_7 ),
inference(resolution,[],[f309,f142]) ).
fof(f331,plain,
( $false
| spl15_7 ),
inference(resolution,[],[f315,f158]) ).
fof(f332,plain,
spl15_7,
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f370,plain,
! [X2,X0,X1] :
( ilf_type(X1,set_type)
| ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1)
| ilf_type(X0,set_type) ),
inference(resolution,[],[f118,f158]) ).
fof(f371,plain,
! [X2,X0,X1] :
( ilf_type(X2,set_type)
| subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f370,f158]) ).
fof(f373,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X0,X2)
| ~ subset(X2,X1) ),
inference(resolution,[],[f371,f158]) ).
fof(f374,plain,
! [X0] :
( ~ subset(sK11,X0)
| ~ subset(X0,cross_product(sK12,sK13)) ),
inference(resolution,[],[f373,f116]) ).
fof(f426,definition,
( spl15_18
<=> member(sK3(sK14,cross_product(sK12,sK13)),sK14) ),
introduced(definition,[new_symbols(definition,[spl15_18])],[avatar_definition]) ).
fof(f427,plain,
( ~ member(sK3(sK14,cross_product(sK12,sK13)),sK14)
| spl15_18 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
( member(sK3(sK14,cross_product(sK12,sK13)),sK14)
| ~ spl15_18 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f440,plain,
( subset(sK14,cross_product(sK12,sK13))
| spl15_18 ),
inference(resolution,[],[f427,f168]) ).
fof(f443,plain,
( ~ subset(sK11,sK14)
| spl15_18 ),
inference(resolution,[],[f440,f374]) ).
fof(f444,plain,
( $false
| spl15_18 ),
inference(resolution,[],[f443,f115]) ).
fof(f447,plain,
spl15_18,
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f476,definition,
( spl15_22
<=> subset(sK11,sK14) ),
introduced(definition,[new_symbols(definition,[spl15_22])],[avatar_definition]) ).
fof(f478,plain,
( ~ subset(sK11,sK14)
| spl15_22 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f481,plain,
( $false
| spl15_22 ),
inference(resolution,[],[f478,f115]) ).
fof(f484,plain,
spl15_22,
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f567,plain,
! [X2,X0,X1] :
( ilf_type(X2,set_type)
| member(X0,X2)
| ~ member(X1,power_set(X2))
| ~ member(X0,X1)
| ilf_type(X1,set_type) ),
inference(resolution,[],[f141,f158]) ).
fof(f1212,plain,
! [X2,X0,X1] :
( ilf_type(X2,set_type)
| ~ member(X2,power_set(X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(resolution,[],[f567,f158]) ).
fof(f1623,definition,
( spl15_132
<=> subset(sK14,cross_product(sK12,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_132])],[avatar_definition]) ).
fof(f1624,plain,
( subset(sK14,cross_product(sK12,sK13))
| ~ spl15_132 ),
inference(avatar_component_clause,[],[f1623]) ).
fof(f1682,plain,
( ~ subset(sK11,sK14)
| ~ spl15_132 ),
inference(resolution,[],[f1624,f374]) ).
fof(f1718,plain,
( ~ spl15_22
| ~ spl15_132 ),
inference(avatar_split_clause,[],[f1682,f1623,f476]) ).
fof(f2163,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[],[f1212,f158]) ).
fof(f3337,plain,
! [X2,X0,X1] :
( ~ member(X2,power_set(X1))
| ~ member(sK3(X0,X1),X2)
| subset(X0,X1) ),
inference(resolution,[],[f2163,f165]) ).
fof(f4511,plain,
( ~ member(sK14,power_set(cross_product(sK12,sK13)))
| subset(sK14,cross_product(sK12,sK13))
| ~ spl15_18 ),
inference(resolution,[],[f3337,f428]) ).
fof(f4574,plain,
( spl15_132
| ~ spl15_8
| ~ spl15_18 ),
inference(avatar_split_clause,[],[f4511,f426,f311,f1623]) ).
cnf(s8,plain,
( ~ spl15_7
| spl15_8 ),
inference(sat_conversion,[],[f314]) ).
cnf(s11,plain,
spl15_7,
inference(sat_conversion,[],[f332]) ).
cnf(s19,plain,
spl15_18,
inference(sat_conversion,[],[f447]) ).
cnf(s24,plain,
spl15_22,
inference(sat_conversion,[],[f484]) ).
cnf(s184,plain,
( ~ spl15_22
| ~ spl15_132 ),
inference(sat_conversion,[],[f1718]) ).
cnf(s556,plain,
( ~ spl15_8
| ~ spl15_18
| spl15_132 ),
inference(sat_conversion,[],[f4574]) ).
cnf(s631,plain,
~ spl15_132,
inference(rat,[],[s184,s24]) ).
cnf(s636,plain,
~ spl15_8,
inference(rat,[],[s556,s631,s19]) ).
cnf(s663,plain,
$false,
inference(rat,[],[s8,s636,s11]) ).
fof(f4638,plain,
$false,
inference(avatar_sat_refutation,[],[s663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET640+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 02:23:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.55 % (749187)Will run a generic schedule for satisfiability detection.
% 0.37/0.55 % (749201)% WARNING: option uhcvi not known.
% 0.37/0.55 % (749201)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1051726860:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.37/0.55 % (749205)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1674245891:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.37/0.55 % (749204)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1824351220:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.37/0.55 % (749203)dis+10_1_sil=32000:sp=arity:random_seed=2759850430:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.37/0.55 % (749206)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4023212526:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.37/0.55 % (749200)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3841374796_2999 on theBenchmark for (2999ds/0Mi)
% 0.37/0.55 % (749202)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=475201406:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.37/0.55 % TRYING [1]
% 0.37/0.55 % TRYING [2]
% 0.37/0.55 % TRYING [3]
% 0.37/0.55 % (749204)Instruction limit reached!
% 0.37/0.55 % (749204)------------------------------
% 0.37/0.55 % (749204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.55 % (749204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.55 % (749204)CaDiCaL version: 2.1.3
% 0.37/0.55 % (749204)Termination reason: Instruction limit
% 0.37/0.55 % (749204)Termination phase: Saturation
% 0.37/0.55 % (749204)Time elapsed: 0.068 s
% 0.37/0.55 % (749204)Peak memory usage: 13 MB
% 0.37/0.55 % (749204)Instructions burned: 116 (million)
% 0.37/0.55 % (749203)Instruction limit reached!
% 0.37/0.55 % (749203)------------------------------
% 0.37/0.55 % (749203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.55 % (749203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.55 % (749203)CaDiCaL version: 2.1.3
% 0.37/0.55 % (749203)Termination reason: Instruction limit
% 0.37/0.55 % (749203)Termination phase: Saturation
% 0.37/0.55 % (749203)Time elapsed: 0.069 s
% 0.37/0.55 % (749203)Peak memory usage: 13 MB
% 0.37/0.55 % (749203)Instructions burned: 103 (million)
% 0.37/0.55 % (749227)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2465011658:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.37/0.55 % (749228)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1978694368:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.37/0.55 % TRYING [4]
% 0.37/0.55 % (749205)Instruction limit reached!
% 0.37/0.55 % (749205)------------------------------
% 0.37/0.55 % (749205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.55 % (749205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.55 % (749205)CaDiCaL version: 2.1.3
% 0.37/0.55 % (749205)Termination reason: Instruction limit
% 0.37/0.55 % (749205)Termination phase: Saturation
% 0.37/0.55 % (749205)Time elapsed: 0.097 s
% 0.37/0.55 % (749205)Peak memory usage: 13 MB
% 0.37/0.55 % (749205)Instructions burned: 131 (million)
% 0.37/0.55 % TRYING [1]
% 0.37/0.55 % TRYING [2]
% 0.37/0.55 % (749206) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-749187-749206"...
% 0.37/0.55 % (749206)...printing done.
% 0.37/0.55 % (749206)Refutation found. Thanks to Tanya!
% 0.37/0.55 % SZS status Theorem for theBenchmark
% 0.37/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.55 % (749206)------------------------------
% 0.37/0.55 % (749206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.55 % (749206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.55 % (749206)CaDiCaL version: 2.1.3
% 0.37/0.55 % (749206)Termination reason: Refutation
% 0.37/0.55 % (749206)Time elapsed: 0.099 s
% 0.37/0.55 % (749206)Peak memory usage: 15 MB
% 0.37/0.55 % (749206)Instructions burned: 144 (million)
% 0.37/0.55 % (749187)Success in time 0.141 s
% 0.37/0.55 % Vampire exiting
%------------------------------------------------------------------------------