%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET655+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 : n011.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 3.45s 1.35s
% Output : Refutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 101 ( 16 unt; 0 def)
% Number of atoms : 426 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 564 ( 239 ~; 221 |; 55 &)
% ( 13 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 227 ( 211 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X0,X1)
& subset(X2,X3) )
=> subset(cross_product(X0,X2),cross_product(X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f7,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',p7) ).
fof(f10,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',p10) ).
fof(f11,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',p11) ).
fof(f12,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',p12) ).
fof(f14,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',p14) ).
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,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X2))
=> ( ( subset(X0,X1)
& subset(X2,X3) )
=> ilf_type(X4,relation_type(X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_17) ).
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,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X2))
=> ( ( subset(X0,X1)
& subset(X2,X3) )
=> ilf_type(X4,relation_type(X1,X3)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f24,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,[],[f2]) ).
fof(f25,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,[],[f24]) ).
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,[],[f3]) ).
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,[],[f5]) ).
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,[],[f7]) ).
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,[],[f10]) ).
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,[],[f11]) ).
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,[],[f12]) ).
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(f41,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(X1,X3))
& subset(X0,X1)
& subset(X2,X3)
& ilf_type(X4,relation_type(X0,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(X1,X3))
& subset(X0,X1)
& subset(X2,X3)
& ilf_type(X4,relation_type(X0,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f48]) ).
fof(f51,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(f52,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,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0)
& ilf_type(sK1(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,[sK1]),skolemize(X2,sK1(X0,X1))],[f52]) ).
fof(f54,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(f56,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(f57,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,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f57]) ).
fof(f59,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(f61,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,[],[f41]) ).
fof(f62,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,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK5(X0),X0)
& ilf_type(sK5(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,[sK5]),skolemize(X1,sK5(X0))],[f62]) ).
fof(f67,plain,
( ~ ilf_type(sK13,relation_type(sK10,sK12))
& subset(sK9,sK10)
& subset(sK11,sK12)
& ilf_type(sK13,relation_type(sK9,sK11))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK9,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12),skolemize(X4,sK13)],[f49]) ).
fof(f69,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,[],[f25]) ).
fof(f70,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(f71,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,[],[f26]) ).
fof(f73,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,[],[f53]) ).
fof(f78,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,[],[f54]) ).
fof(f79,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,[],[f54]) ).
fof(f82,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,[],[f58]) ).
fof(f84,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK3(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f58]) ).
fof(f85,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK3(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f58]) ).
fof(f87,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f88,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,[],[f59]) ).
fof(f89,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,[],[f59]) ).
fof(f91,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f103,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f108,plain,
ilf_type(sK13,relation_type(sK9,sK11)),
inference(cnf_transformation,[],[f67]) ).
fof(f109,plain,
subset(sK11,sK12),
inference(cnf_transformation,[],[f67]) ).
fof(f110,plain,
subset(sK9,sK10),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
~ ilf_type(sK13,relation_type(sK10,sK12)),
inference(cnf_transformation,[],[f67]) ).
fof(f113,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f87,f103]) ).
fof(f119,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f91,f103]) ).
fof(f120,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(forward_subsumption_resolution,[],[f119,f103]) ).
fof(f129,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f78,f103]) ).
fof(f130,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f129,f103]) ).
fof(f131,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,[],[f79,f103]) ).
fof(f132,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(forward_subsumption_resolution,[],[f131,f103]) ).
fof(f133,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK3(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f84,f103]) ).
fof(f134,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f133,f103]) ).
fof(f135,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK3(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f85,f103]) ).
fof(f136,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK3(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f135,f103]) ).
fof(f137,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f88,f103]) ).
fof(f138,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f137,f103]) ).
fof(f139,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,[],[f89,f120]) ).
fof(f140,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f139,f103]) ).
fof(f141,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f140,f103]) ).
fof(f142,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,[],[f70,f103]) ).
fof(f143,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f142,f103]) ).
fof(f144,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,[],[f71,f103]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f144,f103]) ).
fof(f146,plain,
~ ilf_type(sK13,subset_type(cross_product(sK10,sK12))),
inference(resolution,[],[f145,f111]) ).
fof(f148,plain,
~ ilf_type(sK13,member_type(power_set(cross_product(sK10,sK12)))),
inference(resolution,[],[f146,f132]) ).
fof(f153,plain,
~ member(sK13,power_set(cross_product(sK10,sK12))),
inference(resolution,[],[f148,f141]) ).
fof(f154,plain,
~ member(sK3(sK13,cross_product(sK10,sK12)),cross_product(sK10,sK12)),
inference(resolution,[],[f153,f136]) ).
fof(f170,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,[],[f73,f103]) ).
fof(f171,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f170,f103]) ).
fof(f172,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f171,f103]) ).
fof(f174,plain,
! [X0] :
( ~ subset(X0,cross_product(sK10,sK12))
| ~ member(sK3(sK13,cross_product(sK10,sK12)),X0) ),
inference(resolution,[],[f172,f154]) ).
fof(f184,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f82,f103]) ).
fof(f185,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f184,f103]) ).
fof(f186,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f185,f103]) ).
fof(f197,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,[],[f69,f103]) ).
fof(f198,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,[],[f197,f103]) ).
fof(f199,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,[],[f198,f103]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ subset(X2,X3) ),
inference(forward_subsumption_resolution,[],[f199,f103]) ).
fof(f205,plain,
! [X0,X1] :
( ~ member(sK3(sK13,cross_product(sK10,sK12)),cross_product(X0,X1))
| ~ subset(X1,sK12)
| ~ subset(X0,sK10) ),
inference(resolution,[],[f200,f174]) ).
fof(f300,plain,
! [X2,X0,X1] :
( ~ subset(X1,sK10)
| ~ subset(X0,sK12)
| ~ member(sK3(sK13,cross_product(sK10,sK12)),X2)
| ~ member(X2,power_set(cross_product(X1,X0))) ),
inference(resolution,[],[f205,f186]) ).
fof(f718,plain,
! [X0,X1] :
( ~ subset(X0,sK12)
| ~ member(sK3(sK13,cross_product(sK10,sK12)),X1)
| ~ member(X1,power_set(cross_product(sK9,X0))) ),
inference(resolution,[],[f300,f110]) ).
fof(f1406,plain,
! [X0] :
( ~ member(sK3(sK13,cross_product(sK10,sK12)),X0)
| ~ member(X0,power_set(cross_product(sK9,sK11))) ),
inference(resolution,[],[f718,f109]) ).
fof(f2201,plain,
( ~ member(sK13,power_set(cross_product(sK9,sK11)))
| member(sK13,power_set(cross_product(sK10,sK12))) ),
inference(resolution,[],[f1406,f134]) ).
fof(f2207,plain,
~ member(sK13,power_set(cross_product(sK9,sK11))),
inference(forward_subsumption_resolution,[],[f2201,f153]) ).
fof(f2211,plain,
( ~ ilf_type(sK13,member_type(power_set(cross_product(sK9,sK11))))
| empty(power_set(cross_product(sK9,sK11))) ),
inference(resolution,[],[f2207,f138]) ).
fof(f2212,plain,
~ ilf_type(sK13,member_type(power_set(cross_product(sK9,sK11)))),
inference(forward_subsumption_resolution,[],[f2211,f113]) ).
fof(f2221,plain,
~ ilf_type(sK13,subset_type(cross_product(sK9,sK11))),
inference(resolution,[],[f2212,f130]) ).
fof(f2226,plain,
~ ilf_type(sK13,relation_type(sK9,sK11)),
inference(resolution,[],[f2221,f143]) ).
fof(f2228,plain,
$false,
inference(forward_subsumption_resolution,[],[f2226,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET655+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:28:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.45/1.35 % (2961764)Detected formulas, will run a generic FOF schedule.
% 3.45/1.35 % (2961775)dis-21_1_sil=8000:lcm=predicate:random_seed=2372831487: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)
% 3.45/1.35 % (2961771)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=2801631809:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.45/1.35 % (2961769)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=3704239087:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.45/1.35 % (2961770)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=1171699009:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.45/1.35 % (2961772)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3484940762:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.45/1.35 % (2961772)Refutation not found, incomplete strategy
% 3.45/1.35 % (2961772)------------------------------
% 3.45/1.35 % (2961772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.35 % (2961772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.35 % (2961772)CaDiCaL version: 2.1.3
% 3.45/1.35 % (2961772)Termination reason: Refutation not found, incomplete strategy
% 3.45/1.35 % (2961772)Time elapsed: 0.002 s
% 3.45/1.35 % (2961772)Peak memory usage: 88 MB
% 3.45/1.35 % (2961772)Instructions burned: 1 (million)
% 3.45/1.35 % (2961775)Instruction limit reached!
% 3.45/1.35 % (2961775)------------------------------
% 3.45/1.35 % (2961775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.35 % (2961775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.35 % (2961775)CaDiCaL version: 2.1.3
% 3.45/1.35 % (2961775)Termination reason: Instruction limit
% 3.45/1.35 % (2961775)Termination phase: Saturation
% 3.45/1.35 % (2961775)Time elapsed: 0.047 s
% 3.45/1.35 % (2961775)Peak memory usage: 90 MB
% 3.45/1.35 % (2961775)Instructions burned: 143 (million)
% 3.45/1.35 % (2961774)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3907757841:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.45/1.35 % (2961773)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3197580913:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.45/1.35 % (2961773)Instruction limit reached!
% 3.45/1.35 % (2961773)------------------------------
% 3.45/1.35 % (2961773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.35 % (2961773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.35 % (2961773)CaDiCaL version: 2.1.3
% 3.45/1.35 % (2961773)Termination reason: Instruction limit
% 3.45/1.35 % (2961773)Termination phase: Saturation
% 3.45/1.35 % (2961773)Time elapsed: 0.057 s
% 3.45/1.35 % (2961773)Peak memory usage: 87 MB
% 3.45/1.35 % (2961773)Instructions burned: 121 (million)
% 3.45/1.35 % (2961774)First to succeed.
% 3.45/1.35 % (2961774)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2961764"
% 3.45/1.35 % (2961781)lrs+10_1_sil=8000:sp=occurrence:random_seed=4243604013:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.45/1.35 % (2961781)Instruction limit reached!
% 3.45/1.35 % (2961781)------------------------------
% 3.45/1.35 % (2961781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.35 % (2961781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.35 % (2961781)CaDiCaL version: 2.1.3
% 3.45/1.35 % (2961781)Termination reason: Instruction limit
% 3.45/1.35 % (2961781)Termination phase: Saturation
% 3.45/1.35 % (2961781)Time elapsed: 0.096 s
% 3.45/1.35 % (2961781)Peak memory usage: 91 MB
% 3.45/1.35 % (2961781)Instructions burned: 287 (million)
% 3.45/1.35 % (2961784)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2738892344:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.45/1.35 % (2961772)------------------------------
% 3.45/1.35 % (2961772)------------------------------
% 3.45/1.35 % (2961786)lrs+1011_1_sil=32000:sp=occurrence:random_seed=321888262:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.45/1.35 % (2961784)Instruction limit reached!
% 3.45/1.35 % (2961784)------------------------------
% 3.45/1.35 % (2961784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.35 % (2961784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.35 % (2961784)CaDiCaL version: 2.1.3
% 3.45/1.35 % (2961784)Termination reason: Instruction limit
% 3.45/1.35 % (2961784)Termination phase: Saturation
% 3.45/1.35 % (2961784)Time elapsed: 0.086 s
% 3.45/1.35 % (2961784)Peak memory usage: 91 MB
% 3.45/1.35 % (2961784)Instructions burned: 159 (million)
% 3.45/1.35 % (2961774)Refutation found. Thanks to Tanya!
% 3.45/1.35 % SZS status Theorem for theBenchmark
% 3.45/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.14/1.55 % (2961774)------------------------------
% 4.14/1.55 % (2961774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.14/1.55 % (2961774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.14/1.55 % (2961774)CaDiCaL version: 2.1.3
% 4.14/1.55 % (2961774)Termination reason: Refutation
% 4.14/1.55 % (2961774)Time elapsed: 0.081 s
% 4.14/1.55 % (2961774)Peak memory usage: 89 MB
% 4.14/1.55 % (2961774)Instructions burned: 111 (million)
% 4.14/1.55 % (2961774)------------------------------
% 4.14/1.55 % (2961774)------------------------------
% 4.14/1.55 % (2961764)Success in time 0.497 s
% 4.14/1.55 % Vampire exiting
%------------------------------------------------------------------------------