%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET647+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 : n008.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 4.19s 11.53s
% Output : Refutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 87 ( 7 unt; 0 def)
% Number of atoms : 373 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 484 ( 198 ~; 198 |; 42 &)
% ( 13 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 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 : 204 ( 194 !; 10 ?)
% 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(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
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,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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(domain_of(X1),X0)
=> ilf_type(X1,relation_type(X0,range_of(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_9) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(domain_of(X1),X0)
=> ilf_type(X1,relation_type(X0,range_of(X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,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(f30,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,[],[f29]) ).
fof(f31,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,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(f33,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,[],[f32]) ).
fof(f34,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(f41,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(f42,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,[],[f41]) ).
fof(f45,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(f51,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(f52,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,[],[f51]) ).
fof(f54,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(f55,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,[],[f54]) ).
fof(f58,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f61,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f61]) ).
fof(f73,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,[],[f42]) ).
fof(f74,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,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,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) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f74]) ).
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,[],[f45]) ).
fof(f81,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,[],[f52]) ).
fof(f82,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,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f82]) ).
fof(f84,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,[],[f55]) ).
fof(f86,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,[],[f58]) ).
fof(f87,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,[],[f86]) ).
fof(f88,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK11(X0),X0)
& ilf_type(sK11(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,[sK11]),skolemize(X1,sK11(X0))],[f87]) ).
fof(f89,plain,
( ~ ilf_type(sK13,relation_type(sK12,range_of(sK13)))
& subset(domain_of(sK13),sK12)
& ilf_type(sK13,binary_relation_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f62]) ).
fof(f90,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,[],[f30]) ).
fof(f91,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f31]) ).
fof(f93,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f33]) ).
fof(f95,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,[],[f34]) ).
fof(f109,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,[],[f75]) ).
fof(f116,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(f128,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f129,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK9(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f133,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,[],[f84]) ).
fof(f135,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f139,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f141,plain,
ilf_type(sK13,binary_relation_type),
inference(cnf_transformation,[],[f89]) ).
fof(f142,plain,
subset(domain_of(sK13),sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f143,plain,
~ ilf_type(sK13,relation_type(sK12,range_of(sK13))),
inference(cnf_transformation,[],[f89]) ).
fof(f146,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f135,f139]) ).
fof(f150,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f133,f139]) ).
fof(f153,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f128,f139]) ).
fof(f154,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK9(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f129,f139]) ).
fof(f162,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,[],[f116,f139]) ).
fof(f163,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f109,f139]) ).
fof(f174,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,[],[f95,f139]) ).
fof(f176,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f93,f139]) ).
fof(f177,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f90,f139]) ).
fof(f178,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f146,f139]) ).
fof(f180,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f150,f139]) ).
fof(f182,plain,
! [X0,X1] :
( member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f153,f139]) ).
fof(f183,plain,
! [X0,X1] :
( ~ member(sK9(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f154,f139]) ).
fof(f188,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f162,f139]) ).
fof(f189,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f163,f139]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f174,f139]) ).
fof(f198,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f176,f139]) ).
fof(f199,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f177,f139]) ).
fof(f200,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f180,f178]) ).
fof(f203,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f189,f139]) ).
fof(f205,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f198,f139]) ).
fof(f206,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(forward_subsumption_resolution,[],[f199,f139]) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,cross_product(X0,X3))
| ~ subset(X0,X1)
| subset(X2,cross_product(X1,X3)) ),
inference(resolution,[],[f205,f206]) ).
fof(f215,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(X1,range_of(X0)))
| ~ subset(domain_of(X0),X1) ),
inference(resolution,[],[f211,f91]) ).
fof(f218,plain,
! [X2,X0,X1] :
( member(sK9(X0,X1),X2)
| member(X0,power_set(X1))
| ~ subset(X0,X2) ),
inference(resolution,[],[f182,f203]) ).
fof(f225,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(resolution,[],[f183,f218]) ).
fof(f226,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f228,plain,
! [X0] :
( ~ subset(domain_of(sK13),X0)
| subset(sK13,cross_product(X0,range_of(sK13))) ),
inference(resolution,[],[f215,f141]) ).
fof(f229,plain,
subset(sK13,cross_product(sK12,range_of(sK13))),
inference(resolution,[],[f228,f142]) ).
fof(f273,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ member(X0,power_set(X1)) ),
inference(resolution,[],[f188,f200]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ member(X0,power_set(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[],[f273,f196]) ).
fof(f277,plain,
! [X2,X0,X1] :
( ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[],[f274,f226]) ).
fof(f279,plain,
$false,
inference(unit_resulting_resolution,[],[f277,f143,f229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET647+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/10.40 % Computer : n008.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.12/10.40 % DateTime : Mon Sep 28 02:29:05 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.12/10.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/10.44 Running first-order theorem proving
% 0.12/10.44 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
% 4.19/11.53 % (1810896)Detected formulas, will run a generic FOF schedule.
% 4.19/11.53 % (1810902)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=1088380897:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.19/11.53 % (1810904)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3458289077:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.19/11.53 % (1810901)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=3828854186:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.19/11.53 % (1810907)dis-21_1_sil=8000:lcm=predicate:random_seed=2865104335: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)
% 4.19/11.53 % (1810905)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=345180923:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.19/11.53 % (1810903)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=2083322986:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.19/11.53 % (1810904)Refutation not found, incomplete strategy
% 4.19/11.53 % (1810904)------------------------------
% 4.19/11.53 % (1810904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/11.53 % (1810904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/11.53 % (1810904)CaDiCaL version: 2.1.3
% 4.19/11.53 % (1810904)Termination reason: Refutation not found, incomplete strategy
% 4.19/11.53 % (1810904)Time elapsed: 0.002 s
% 4.19/11.53 % (1810904)Peak memory usage: 88 MB
% 4.19/11.53 % (1810904)Instructions burned: 2 (million)
% 4.19/11.53 % (1810906)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=47054331:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.19/11.53 % (1810905)Instruction limit reached!
% 4.19/11.53 % (1810905)------------------------------
% 4.19/11.53 % (1810905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/11.53 % (1810905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/11.53 % (1810905)CaDiCaL version: 2.1.3
% 4.19/11.53 % (1810905)Termination reason: Instruction limit
% 4.19/11.53 % (1810905)Termination phase: Saturation
% 4.19/11.53 % (1810905)Time elapsed: 0.068 s
% 4.19/11.53 % (1810905)Peak memory usage: 87 MB
% 4.19/11.53 % (1810905)Instructions burned: 121 (million)
% 4.19/11.53 % (1810907)Instruction limit reached!
% 4.19/11.53 % (1810907)------------------------------
% 4.19/11.53 % (1810907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/11.53 % (1810907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/11.53 % (1810907)CaDiCaL version: 2.1.3
% 4.19/11.53 % (1810907)Termination reason: Instruction limit
% 4.19/11.53 % (1810907)Termination phase: Saturation
% 4.19/11.53 % (1810907)Time elapsed: 0.079 s
% 4.19/11.53 % (1810907)Peak memory usage: 90 MB
% 4.19/11.53 % (1810907)Instructions burned: 130 (million)
% 4.19/11.53 % (1810906)Instruction limit reached!
% 4.19/11.53 % (1810906)------------------------------
% 4.19/11.53 % (1810906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/11.53 % (1810906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/11.53 % (1810906)CaDiCaL version: 2.1.3
% 4.19/11.53 % (1810906)Termination reason: Instruction limit
% 4.19/11.53 % (1810906)Termination phase: Saturation
% 4.19/11.53 % (1810906)Time elapsed: 0.100 s
% 4.19/11.53 % (1810906)Peak memory usage: 90 MB
% 4.19/11.53 % (1810906)Instructions burned: 139 (million)
% 4.19/11.53 % (1810915)lrs+10_1_sil=8000:sp=occurrence:random_seed=729062791:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.19/11.53 % (1810916)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1695342292:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.19/11.53 % (1810904)------------------------------
% 4.19/11.53 % (1810904)------------------------------
% 4.19/11.53 % (1810917)lrs+1011_1_sil=32000:sp=occurrence:random_seed=648455343:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.19/11.53 % (1810902)First to succeed.
% 4.19/11.53 % (1810902)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1810896"
% 4.19/11.53 % (1810916)Instruction limit reached!
% 4.19/11.53 % (1810916)------------------------------
% 4.19/11.53 % (1810916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/11.53 % (1810916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/11.53 % (1810916)CaDiCaL version: 2.1.3
% 4.19/11.53 % (1810916)Termination reason: Instruction limit
% 4.19/11.53 % (1810916)Termination phase: Saturation
% 4.19/11.53 % (1810916)Time elapsed: 0.087 s
% 4.19/11.53 % (1810916)Peak memory usage: 89 MB
% 4.19/11.53 % (1810916)Instructions burned: 157 (million)
% 4.19/11.53 % (1810920)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=378249243:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.19/11.53 % (1810915)Instruction limit reached!
% 4.19/11.53 % (1810915)------------------------------
% 4.19/11.53 % (1810915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/11.53 % (1810915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/11.53 % (1810915)CaDiCaL version: 2.1.3
% 4.19/11.53 % (1810915)Termination reason: Instruction limit
% 4.19/11.53 % (1810915)Termination phase: Saturation
% 4.19/11.53 % (1810915)Time elapsed: 0.177 s
% 4.19/11.53 % (1810915)Peak memory usage: 91 MB
% 4.19/11.53 % (1810915)Instructions burned: 285 (million)
% 4.19/11.53 % (1810920)Also succeeded, but the first one will report.
% 4.19/11.53 % (1810917)Also succeeded, but the first one will report.
% 4.19/11.53 % (1810902)Refutation found. Thanks to Tanya!
% 4.19/11.53 % SZS status Theorem for theBenchmark
% 4.19/11.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.23/11.73 % (1810902)------------------------------
% 5.23/11.73 % (1810902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/11.73 % (1810902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/11.73 % (1810902)CaDiCaL version: 2.1.3
% 5.23/11.73 % (1810902)Termination reason: Refutation
% 5.23/11.73 % (1810902)Time elapsed: 0.357 s
% 5.23/11.73 % (1810902)Peak memory usage: 129 MB
% 5.23/11.73 % (1810902)Instructions burned: 952 (million)
% 5.23/11.73 % (1810902)------------------------------
% 5.23/11.73 % (1810902)------------------------------
% 5.23/11.73 % (1810896)Success in time 0.645 s
% 5.23/11.73 % Vampire exiting
%------------------------------------------------------------------------------