%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET652+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 : n006.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 12:41:33 PM UTC 2026
% Result : Theorem 2.94s 11.32s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 126 ( 16 unt; 2 def)
% Number of atoms : 497 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 638 ( 267 ~; 255 |; 54 &)
% ( 17 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 254 ( 0 sgn 240 !; 14 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X0,X1)
& subset(X2,X3) )
=> subset(cross_product(X0,X2),cross_product(X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [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(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f9,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',p9) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
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(f18,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',p18) ).
fof(f20,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',p20) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
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,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_14) ).
fof(f28,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(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,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] :
( ! [X3] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ 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(f36,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f39,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,[],[f9]) ).
fof(f40,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,[],[f39]) ).
fof(f44,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
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(f48,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,[],[f18]) ).
fof(f49,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,[],[f48]) ).
fof(f51,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,[],[f20]) ).
fof(f52,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,[],[f51]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
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] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f61]) ).
fof(f67,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,[],[f40]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0)
& ilf_type(sK2(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,[sK2]),skolemize(X2,sK2(X0,X1))],[f68]) ).
fof(f70,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f71,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f70]) ).
fof(f73,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(f75,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,[],[f49]) ).
fof(f76,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,[],[f75]) ).
fof(f77,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))],[f76]) ).
fof(f78,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,[],[f52]) ).
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,[],[f58]) ).
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(sK10(X0),X0)
& ilf_type(sK10(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,[sK10]),skolemize(X1,sK10(X0))],[f84]) ).
fof(f86,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK12))
& subset(range_of(sK14),sK12)
& ilf_type(sK14,relation_type(sK13,sK11))
& 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)],[f62]) ).
fof(f87,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(f88,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f31]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f33]) ).
fof(f90,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,[],[f34]) ).
fof(f91,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(f94,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f99,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,[],[f69]) ).
fof(f108,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
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,[],[f73]) ).
fof(f116,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,[],[f77]) ).
fof(f117,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,[],[f77]) ).
fof(f121,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,[],[f78]) ).
fof(f129,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f57]) ).
fof(f130,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f85]) ).
fof(f134,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f138,plain,
ilf_type(sK14,relation_type(sK13,sK11)),
inference(cnf_transformation,[],[f86]) ).
fof(f139,plain,
subset(range_of(sK14),sK12),
inference(cnf_transformation,[],[f86]) ).
fof(f140,plain,
~ ilf_type(sK14,relation_type(sK13,sK12)),
inference(cnf_transformation,[],[f86]) ).
fof(f141,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f108]) ).
fof(f147,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f141,f134]) ).
fof(f151,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f130,f134]) ).
fof(f152,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(forward_subsumption_resolution,[],[f151,f134]) ).
fof(f159,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f129,f134]) ).
fof(f160,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f159,f134]) ).
fof(f163,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f94,f134]) ).
fof(f164,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f163,f134]) ).
fof(f167,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,f134]) ).
fof(f168,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(forward_subsumption_resolution,[],[f167,f134]) ).
fof(f169,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f116,f134]) ).
fof(f170,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f169,f134]) ).
fof(f171,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f117,f134]) ).
fof(f172,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f171,f134]) ).
fof(f175,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,[],[f121,f152]) ).
fof(f176,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f175,f134]) ).
fof(f177,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f176,f134]) ).
fof(f178,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f90,f134]) ).
fof(f179,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f178,f134]) ).
fof(f180,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,[],[f91,f134]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f180,f134]) ).
fof(f182,plain,
~ ilf_type(sK14,subset_type(cross_product(sK13,sK12))),
inference(resolution,[],[f181,f140]) ).
fof(f185,plain,
~ ilf_type(sK14,member_type(power_set(cross_product(sK13,sK12)))),
inference(resolution,[],[f182,f168]) ).
fof(f187,plain,
~ member(sK14,power_set(cross_product(sK13,sK12))),
inference(resolution,[],[f185,f177]) ).
fof(f191,plain,
~ member(sK5(sK14,cross_product(sK13,sK12)),cross_product(sK13,sK12)),
inference(resolution,[],[f187,f172]) ).
fof(f203,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,[],[f87,f134]) ).
fof(f204,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f203,f134]) ).
fof(f205,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(forward_subsumption_resolution,[],[f204,f134]) ).
fof(f209,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,[],[f99,f134]) ).
fof(f210,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f209,f134]) ).
fof(f211,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f210,f134]) ).
fof(f213,plain,
! [X0] :
( ~ member(sK5(sK14,cross_product(sK13,sK12)),X0)
| ~ subset(X0,cross_product(sK13,sK12)) ),
inference(resolution,[],[f211,f191]) ).
fof(f220,plain,
( ~ subset(sK14,cross_product(sK13,sK12))
| member(sK14,power_set(cross_product(sK13,sK12))) ),
inference(resolution,[],[f213,f170]) ).
fof(f225,plain,
~ subset(sK14,cross_product(sK13,sK12)),
inference(forward_subsumption_resolution,[],[f220,f187]) ).
fof(f227,plain,
! [X0] :
( ~ subset(sK14,X0)
| ~ subset(X0,cross_product(sK13,sK12)) ),
inference(resolution,[],[f225,f205]) ).
fof(f233,plain,
( ~ subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,sK12))
| ~ ilf_type(sK14,binary_relation_type) ),
inference(resolution,[],[f227,f88]) ).
fof(f237,definition,
( spl15_3
<=> ilf_type(sK14,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f239,plain,
( ~ ilf_type(sK14,binary_relation_type)
| spl15_3 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f241,definition,
( spl15_4
<=> subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f243,plain,
( ~ subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,sK12))
| spl15_4 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f244,plain,
( ~ spl15_3
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f233,f241,f237]) ).
fof(f249,plain,
( ~ relation_like(sK14)
| spl15_3 ),
inference(resolution,[],[f239,f147]) ).
fof(f250,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f89,f134]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f250,f134]) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X3,set_type) ),
inference(forward_subsumption_resolution,[],[f251,f134]) ).
fof(f253,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3) ),
inference(forward_subsumption_resolution,[],[f252,f134]) ).
fof(f254,plain,
( ! [X0,X1] : ~ ilf_type(sK14,subset_type(cross_product(X0,X1)))
| spl15_3 ),
inference(resolution,[],[f249,f160]) ).
fof(f258,plain,
( ! [X0,X1] : ~ ilf_type(sK14,relation_type(X0,X1))
| spl15_3 ),
inference(resolution,[],[f254,f179]) ).
fof(f265,plain,
( $false
| spl15_3 ),
inference(resolution,[],[f258,f138]) ).
fof(f267,plain,
spl15_3,
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f287,plain,
( ~ subset(domain_of(sK14),sK13)
| ~ subset(range_of(sK14),sK12)
| spl15_4 ),
inference(resolution,[],[f243,f253]) ).
fof(f290,plain,
( ~ subset(domain_of(sK14),sK13)
| spl15_4 ),
inference(forward_subsumption_resolution,[],[f287,f139]) ).
fof(f296,plain,
( ! [X0] : ~ ilf_type(sK14,relation_type(sK13,X0))
| spl15_4 ),
inference(resolution,[],[f290,f164]) ).
fof(f305,plain,
( $false
| spl15_4 ),
inference(resolution,[],[f296,f138]) ).
fof(f307,plain,
spl15_4,
inference(avatar_contradiction_clause,[],[f305]) ).
cnf(s2,plain,
( ~ spl15_3
| ~ spl15_4 ),
inference(sat_conversion,[],[f244]) ).
cnf(s3,plain,
spl15_3,
inference(sat_conversion,[],[f267]) ).
cnf(s5,plain,
spl15_4,
inference(sat_conversion,[],[f307]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s5,s3]) ).
fof(f308,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET652+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/10.39 % Computer : n006.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Mon Sep 28 02:28:06 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.43 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
% 2.94/11.32 % (3531915)Detected formulas, will run a generic FOF schedule.
% 2.94/11.32 % (3531923)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4224863951:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.94/11.32 % (3531923)Refutation not found, incomplete strategy
% 2.94/11.32 % (3531923)------------------------------
% 2.94/11.32 % (3531923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/11.32 % (3531923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/11.32 % (3531923)CaDiCaL version: 2.1.3
% 2.94/11.32 % (3531923)Termination reason: Refutation not found, incomplete strategy
% 2.94/11.32 % (3531923)Time elapsed: 0.001 s
% 2.94/11.32 % (3531923)Peak memory usage: 87 MB
% 2.94/11.32 % (3531921)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=314916519:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.94/11.32 % (3531920)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=774773941:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.94/11.32 % (3531924)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2148990470:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.94/11.32 % (3531922)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=129834962:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.94/11.32 % (3531926)dis-21_1_sil=8000:lcm=predicate:random_seed=707458605: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)
% 2.94/11.32 % (3531925)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3889981047:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.94/11.32 % (3531925)First to succeed.
% 2.94/11.32 % (3531925)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3531915"
% 2.94/11.32 % (3531924)Instruction limit reached!
% 2.94/11.32 % (3531924)------------------------------
% 2.94/11.32 % (3531924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/11.32 % (3531924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/11.32 % (3531924)CaDiCaL version: 2.1.3
% 2.94/11.32 % (3531924)Termination reason: Instruction limit
% 2.94/11.32 % (3531924)Termination phase: Saturation
% 2.94/11.32 % (3531924)Time elapsed: 0.058 s
% 2.94/11.32 % (3531924)Peak memory usage: 87 MB
% 2.94/11.32 % (3531924)Instructions burned: 121 (million)
% 2.94/11.32 % (3531926)Instruction limit reached!
% 2.94/11.32 % (3531926)------------------------------
% 2.94/11.32 % (3531926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/11.32 % (3531926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/11.32 % (3531926)CaDiCaL version: 2.1.3
% 2.94/11.32 % (3531926)Termination reason: Instruction limit
% 2.94/11.32 % (3531926)Termination phase: Saturation
% 2.94/11.32 % (3531926)Time elapsed: 0.077 s
% 2.94/11.32 % (3531926)Peak memory usage: 89 MB
% 2.94/11.32 % (3531926)Instructions burned: 129 (million)
% 2.94/11.32 % (3531923)------------------------------
% 2.94/11.32 % (3531923)------------------------------
% 2.94/11.32 % (3531934)lrs+10_1_sil=8000:sp=occurrence:random_seed=2040131932:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.94/11.32 % (3531935)lrs+10_1_sil=32000:urr=on:br=off:random_seed=118780709:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.94/11.32 % (3531936)lrs+1011_1_sil=32000:sp=occurrence:random_seed=959723576:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.94/11.32 % (3531936)Also succeeded, but the first one will report.
% 2.94/11.32 % (3531925)Refutation found. Thanks to Tanya!
% 2.94/11.32 % SZS status Theorem for theBenchmark
% 2.94/11.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/11.52 % (3531925)------------------------------
% 3.80/11.52 % (3531925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/11.52 % (3531925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/11.52 % (3531925)CaDiCaL version: 2.1.3
% 3.80/11.52 % (3531925)Termination reason: Refutation
% 3.80/11.52 % (3531925)Time elapsed: 0.010 s
% 3.80/11.52 % (3531925)Peak memory usage: 89 MB
% 3.80/11.52 % (3531925)Instructions burned: 12 (million)
% 3.80/11.52 % (3531925)------------------------------
% 3.80/11.52 % (3531925)------------------------------
% 3.80/11.52 % (3531915)Success in time 0.45 s
% 3.80/11.52 % Vampire exiting
%------------------------------------------------------------------------------