%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET648+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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:41:32 PM UTC 2026
% Result : Theorem 3.85s 6.24s
% Output : Refutation 4.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 10
% Syntax : Number of formulae : 82 ( 12 unt; 0 def)
% Number of atoms : 344 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 474 ( 212 ~; 179 |; 41 &)
% ( 13 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 132 ( 122 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
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)
=> ( subset(X0,X1)
=> ( subset(cross_product(X0,X2),cross_product(X1,X2))
& subset(cross_product(X2,X0),cross_product(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
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/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f15,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/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f20,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/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f22,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/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(range_of(X1),X0)
=> ilf_type(X1,relation_type(domain_of(X1),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_10) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(range_of(X1),X0)
=> ilf_type(X1,relation_type(domain_of(X1),X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(domain_of(X1),X0))
& subset(range_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(domain_of(X1),X0))
& subset(range_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f29]) ).
fof(f33,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f36,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,[],[f22]) ).
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(flattening,[],[f36]) ).
fof(f39,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,[],[f20]) ).
fof(f40,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,[],[f39]) ).
fof(f46,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,[],[f15]) ).
fof(f49,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,[],[f12]) ).
fof(f50,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,[],[f49]) ).
fof(f57,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(f58,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(cross_product(X0,X2),cross_product(X1,X2))
& subset(cross_product(X2,X0),cross_product(X2,X1)) )
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(cross_product(X0,X2),cross_product(X1,X2))
& subset(cross_product(X2,X0),cross_product(X2,X1)) )
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f58]) ).
fof(f62,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f63,plain,
( ~ ilf_type(sK1,relation_type(domain_of(sK1),sK0))
& subset(range_of(sK1),sK0)
& ilf_type(sK1,binary_relation_type)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f30]) ).
fof(f64,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,[],[f33]) ).
fof(f65,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,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK2(X0),X0)
& ilf_type(sK2(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,[sK2]),skolemize(X1,sK2(X0))],[f65]) ).
fof(f68,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,[],[f37]) ).
fof(f69,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,[],[f40]) ).
fof(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0)
& ilf_type(sK4(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,[sK4]),skolemize(X2,sK4(X0,X1))],[f70]) ).
fof(f76,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,[],[f46]) ).
fof(f77,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,[],[f50]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK9(X0,X1),X1)
& member(sK9(X0,X1),X0)
& ilf_type(sK9(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,[sK9]),skolemize(X2,sK9(X0,X1))],[f78]) ).
fof(f91,plain,
ilf_type(sK1,binary_relation_type),
inference(cnf_transformation,[],[f63]) ).
fof(f92,plain,
subset(range_of(sK1),sK0),
inference(cnf_transformation,[],[f63]) ).
fof(f93,plain,
~ ilf_type(sK1,relation_type(domain_of(sK1),sK0)),
inference(cnf_transformation,[],[f63]) ).
fof(f94,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f96,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f66]) ).
fof(f101,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,[],[f68]) ).
fof(f106,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f107,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK4(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f118,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,[],[f76]) ).
fof(f121,plain,
! [X3,X0,X1] :
( 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(cnf_transformation,[],[f79]) ).
fof(f138,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,[],[f57]) ).
fof(f139,plain,
! [X2,X0,X1] :
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f143,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f62]) ).
fof(f145,plain,
( ~ ilf_type(sK1,subset_type(cross_product(domain_of(sK1),sK0)))
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(domain_of(sK1),set_type) ),
inference(resolution,[],[f138,f93]) ).
fof(f146,plain,
( ~ ilf_type(sK1,subset_type(cross_product(domain_of(sK1),sK0)))
| ~ ilf_type(sK0,set_type) ),
inference(forward_subsumption_resolution,[],[f145,f94]) ).
fof(f147,plain,
~ ilf_type(sK1,subset_type(cross_product(domain_of(sK1),sK0))),
inference(forward_subsumption_resolution,[],[f146,f94]) ).
fof(f149,plain,
( ~ ilf_type(sK1,member_type(power_set(cross_product(domain_of(sK1),sK0))))
| ~ ilf_type(sK1,set_type)
| ~ ilf_type(cross_product(domain_of(sK1),sK0),set_type) ),
inference(resolution,[],[f147,f118]) ).
fof(f150,plain,
( ~ ilf_type(sK1,member_type(power_set(cross_product(domain_of(sK1),sK0))))
| ~ ilf_type(sK1,set_type) ),
inference(forward_subsumption_resolution,[],[f149,f94]) ).
fof(f151,plain,
~ ilf_type(sK1,member_type(power_set(cross_product(domain_of(sK1),sK0)))),
inference(forward_subsumption_resolution,[],[f150,f94]) ).
fof(f160,plain,
( ~ member(sK1,power_set(cross_product(domain_of(sK1),sK0)))
| empty(power_set(cross_product(domain_of(sK1),sK0)))
| ~ ilf_type(power_set(cross_product(domain_of(sK1),sK0)),set_type)
| ~ ilf_type(sK1,set_type) ),
inference(resolution,[],[f151,f101]) ).
fof(f161,plain,
( ~ member(sK1,power_set(cross_product(domain_of(sK1),sK0)))
| ~ ilf_type(power_set(cross_product(domain_of(sK1),sK0)),set_type)
| ~ ilf_type(sK1,set_type) ),
inference(forward_subsumption_resolution,[],[f160,f96]) ).
fof(f162,plain,
( ~ member(sK1,power_set(cross_product(domain_of(sK1),sK0)))
| ~ ilf_type(power_set(cross_product(domain_of(sK1),sK0)),set_type) ),
inference(forward_subsumption_resolution,[],[f161,f94]) ).
fof(f163,plain,
~ member(sK1,power_set(cross_product(domain_of(sK1),sK0))),
inference(forward_subsumption_resolution,[],[f162,f94]) ).
fof(f164,plain,
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),cross_product(domain_of(sK1),sK0))
| ~ ilf_type(cross_product(domain_of(sK1),sK0),set_type)
| ~ ilf_type(sK1,set_type) ),
inference(resolution,[],[f163,f107]) ).
fof(f168,plain,
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),cross_product(domain_of(sK1),sK0))
| ~ ilf_type(cross_product(domain_of(sK1),sK0),set_type) ),
inference(forward_subsumption_resolution,[],[f164,f94]) ).
fof(f170,plain,
~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),cross_product(domain_of(sK1),sK0)),
inference(forward_subsumption_resolution,[],[f168,f94]) ).
fof(f176,plain,
! [X0] :
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X0)
| ~ ilf_type(sK4(sK1,cross_product(domain_of(sK1),sK0)),set_type)
| ~ subset(X0,cross_product(domain_of(sK1),sK0))
| ~ ilf_type(cross_product(domain_of(sK1),sK0),set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f170,f121]) ).
fof(f179,plain,
! [X0] :
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X0)
| ~ ilf_type(sK4(sK1,cross_product(domain_of(sK1),sK0)),set_type)
| ~ subset(X0,cross_product(domain_of(sK1),sK0))
| ~ ilf_type(cross_product(domain_of(sK1),sK0),set_type) ),
inference(forward_subsumption_resolution,[],[f176,f94]) ).
fof(f181,plain,
! [X0] :
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X0)
| ~ ilf_type(sK4(sK1,cross_product(domain_of(sK1),sK0)),set_type)
| ~ subset(X0,cross_product(domain_of(sK1),sK0)) ),
inference(forward_subsumption_resolution,[],[f179,f94]) ).
fof(f191,plain,
! [X0] :
( ~ subset(X0,cross_product(domain_of(sK1),sK0))
| ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X0) ),
inference(forward_subsumption_resolution,[],[f181,f94]) ).
fof(f236,plain,
! [X0] :
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),cross_product(domain_of(sK1),X0))
| ~ subset(X0,sK0)
| ~ ilf_type(domain_of(sK1),set_type)
| ~ ilf_type(sK0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f191,f139]) ).
fof(f239,plain,
! [X0] :
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),cross_product(domain_of(sK1),X0))
| ~ subset(X0,sK0)
| ~ ilf_type(domain_of(sK1),set_type)
| ~ ilf_type(sK0,set_type) ),
inference(forward_subsumption_resolution,[],[f236,f94]) ).
fof(f243,plain,
! [X0] :
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),cross_product(domain_of(sK1),X0))
| ~ subset(X0,sK0)
| ~ ilf_type(domain_of(sK1),set_type) ),
inference(forward_subsumption_resolution,[],[f239,f94]) ).
fof(f247,plain,
! [X0] :
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),cross_product(domain_of(sK1),X0))
| ~ subset(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f243,f94]) ).
fof(f501,plain,
! [X0,X1] :
( ~ subset(X0,sK0)
| ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X1)
| ~ ilf_type(sK4(sK1,cross_product(domain_of(sK1),sK0)),set_type)
| ~ subset(X1,cross_product(domain_of(sK1),X0))
| ~ ilf_type(cross_product(domain_of(sK1),X0),set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f247,f121]) ).
fof(f504,plain,
! [X0,X1] :
( ~ subset(X0,sK0)
| ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X1)
| ~ ilf_type(sK4(sK1,cross_product(domain_of(sK1),sK0)),set_type)
| ~ subset(X1,cross_product(domain_of(sK1),X0))
| ~ ilf_type(cross_product(domain_of(sK1),X0),set_type) ),
inference(forward_subsumption_resolution,[],[f501,f94]) ).
fof(f507,plain,
! [X0,X1] :
( ~ subset(X0,sK0)
| ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X1)
| ~ ilf_type(sK4(sK1,cross_product(domain_of(sK1),sK0)),set_type)
| ~ subset(X1,cross_product(domain_of(sK1),X0)) ),
inference(forward_subsumption_resolution,[],[f504,f94]) ).
fof(f509,plain,
! [X0,X1] :
( ~ subset(X0,sK0)
| ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X1)
| ~ subset(X1,cross_product(domain_of(sK1),X0)) ),
inference(forward_subsumption_resolution,[],[f507,f94]) ).
fof(f2100,plain,
! [X0] :
( ~ subset(X0,cross_product(domain_of(sK1),range_of(sK1)))
| ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),X0) ),
inference(resolution,[],[f509,f92]) ).
fof(f6624,plain,
( ~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),sK1)
| ~ ilf_type(sK1,binary_relation_type) ),
inference(resolution,[],[f2100,f143]) ).
fof(f6635,plain,
~ member(sK4(sK1,cross_product(domain_of(sK1),sK0)),sK1),
inference(forward_subsumption_resolution,[],[f6624,f91]) ).
fof(f6643,plain,
( member(sK1,power_set(cross_product(domain_of(sK1),sK0)))
| ~ ilf_type(cross_product(domain_of(sK1),sK0),set_type)
| ~ ilf_type(sK1,set_type) ),
inference(resolution,[],[f6635,f106]) ).
fof(f6650,plain,
( ~ ilf_type(cross_product(domain_of(sK1),sK0),set_type)
| ~ ilf_type(sK1,set_type) ),
inference(forward_subsumption_resolution,[],[f6643,f163]) ).
fof(f6654,plain,
~ ilf_type(cross_product(domain_of(sK1),sK0),set_type),
inference(forward_subsumption_resolution,[],[f6650,f94]) ).
fof(f6658,plain,
$false,
inference(forward_subsumption_resolution,[],[f6654,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET648+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n007.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Mon Sep 28 02:26:15 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.85/6.24 % (1970538)Detected formulas, will run a generic FOF schedule.
% 3.85/6.24 % (1970548)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3437491748:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.85/6.24 % (1970546)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3609721656:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.85/6.24 % (1970547)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1876154679:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.85/6.24 % (1970544)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=475532572:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.85/6.24 % (1970549)dis-21_1_sil=8000:lcm=predicate:random_seed=2728287464: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)
% 3.85/6.24 % (1970543)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=3110991828:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.85/6.24 % (1970545)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=3125817515:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.85/6.24 % (1970546)Refutation not found, incomplete strategy
% 3.85/6.24 % (1970546)------------------------------
% 3.85/6.24 % (1970546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/6.24 % (1970546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/6.24 % (1970546)CaDiCaL version: 2.1.3
% 3.85/6.24 % (1970546)Termination reason: Refutation not found, incomplete strategy
% 3.85/6.24 % (1970546)Time elapsed: 0.002 s
% 3.85/6.24 % (1970546)Peak memory usage: 87 MB
% 3.85/6.24 % (1970546)Instructions burned: 2 (million)
% 3.85/6.24 % (1970547)Instruction limit reached!
% 3.85/6.24 % (1970547)------------------------------
% 3.85/6.24 % (1970547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/6.24 % (1970547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/6.24 % (1970547)CaDiCaL version: 2.1.3
% 3.85/6.24 % (1970547)Termination reason: Instruction limit
% 3.85/6.24 % (1970547)Termination phase: Saturation
% 3.85/6.24 % (1970547)Time elapsed: 0.067 s
% 3.85/6.24 % (1970547)Peak memory usage: 87 MB
% 3.85/6.24 % (1970547)Instructions burned: 120 (million)
% 3.85/6.24 % (1970549)Instruction limit reached!
% 3.85/6.24 % (1970549)------------------------------
% 3.85/6.24 % (1970549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/6.24 % (1970549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/6.24 % (1970549)CaDiCaL version: 2.1.3
% 3.85/6.24 % (1970549)Termination reason: Instruction limit
% 3.85/6.24 % (1970549)Termination phase: Saturation
% 3.85/6.24 % (1970549)Time elapsed: 0.078 s
% 3.85/6.24 % (1970549)Peak memory usage: 90 MB
% 3.85/6.24 % (1970549)Instructions burned: 130 (million)
% 3.85/6.24 % (1970548)Instruction limit reached!
% 3.85/6.24 % (1970548)------------------------------
% 3.85/6.24 % (1970548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/6.24 % (1970548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/6.24 % (1970548)CaDiCaL version: 2.1.3
% 3.85/6.24 % (1970548)Termination reason: Instruction limit
% 3.85/6.24 % (1970548)Termination phase: Saturation
% 3.85/6.24 % (1970548)Time elapsed: 0.098 s
% 3.85/6.24 % (1970548)Peak memory usage: 90 MB
% 3.85/6.24 % (1970548)Instructions burned: 140 (million)
% 3.85/6.24 % (1970557)lrs+10_1_sil=8000:sp=occurrence:random_seed=629675396:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.85/6.24 % (1970558)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2591083159:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.85/6.24 % (1970559)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3458853411:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.85/6.24 % (1970546)------------------------------
% 3.85/6.24 % (1970546)------------------------------
% 3.85/6.24 % (1970558)Instruction limit reached!
% 3.85/6.24 % (1970558)------------------------------
% 3.85/6.24 % (1970558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/6.24 % (1970558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/6.24 % (1970558)CaDiCaL version: 2.1.3
% 3.85/6.24 % (1970558)Termination reason: Instruction limit
% 3.85/6.24 % (1970558)Termination phase: Saturation
% 3.85/6.24 % (1970558)Time elapsed: 0.085 s
% 3.85/6.24 % (1970558)Peak memory usage: 89 MB
% 3.85/6.24 % (1970558)Instructions burned: 157 (million)
% 3.85/6.24 % (1970559)First to succeed.
% 3.85/6.24 % (1970559)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1970538"
% 3.85/6.24 % (1970563)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3497746368:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.85/6.24 % (1970557)Instruction limit reached!
% 3.85/6.24 % (1970557)------------------------------
% 3.85/6.24 % (1970557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/6.24 % (1970557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/6.24 % (1970557)CaDiCaL version: 2.1.3
% 3.85/6.24 % (1970557)Termination reason: Instruction limit
% 3.85/6.24 % (1970557)Termination phase: Saturation
% 3.85/6.24 % (1970557)Time elapsed: 0.177 s
% 3.85/6.24 % (1970557)Peak memory usage: 91 MB
% 3.85/6.24 % (1970557)Instructions burned: 287 (million)
% 3.85/6.24 % (1970563)Also succeeded, but the first one will report.
% 3.85/6.24 % (1970564)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2971831778:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.85/6.24 % (1970564)Refutation not found, incomplete strategy
% 3.85/6.24 % (1970564)------------------------------
% 3.85/6.24 % (1970564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/6.24 % (1970564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/6.24 % (1970564)CaDiCaL version: 2.1.3
% 3.85/6.24 % (1970564)Termination reason: Refutation not found, incomplete strategy
% 3.85/6.24 % (1970564)Time elapsed: 0.002 s
% 3.85/6.24 % (1970564)Peak memory usage: 88 MB
% 3.85/6.24 % (1970564)Instructions burned: 2 (million)
% 3.85/6.24 % (1970559)Refutation found. Thanks to Tanya!
% 3.85/6.24 % SZS status Theorem for theBenchmark
% 3.85/6.24 % SZS output start Proof for theBenchmark
% See solution above
% 4.61/6.42 % (1970559)------------------------------
% 4.61/6.42 % (1970559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/6.42 % (1970559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/6.42 % (1970559)CaDiCaL version: 2.1.3
% 4.61/6.42 % (1970559)Termination reason: Refutation
% 4.61/6.42 % (1970559)Time elapsed: 0.086 s
% 4.61/6.42 % (1970559)Peak memory usage: 91 MB
% 4.61/6.42 % (1970559)Instructions burned: 231 (million)
% 4.61/6.42 % (1970559)------------------------------
% 4.61/6.42 % (1970559)------------------------------
% 4.61/6.42 % (1970538)Success in time 0.61 s
% 4.61/6.42 % Vampire exiting
%------------------------------------------------------------------------------