%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET656+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 : n003.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 2.71s 1.30s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 15 unt; 2 def)
% Number of atoms : 357 ( 15 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 442 ( 182 ~; 178 |; 37 &)
% ( 15 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 176 ( 0 sgn 169 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
=> intersection(X0,X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,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,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',p6) ).
fof(f13,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',p13) ).
fof(f17,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',p17) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
fof(f19,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',p19) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f21,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',p21) ).
fof(f30,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
fof(f31,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_18) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f33]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f39,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,[],[f6]) ).
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,[],[f13]) ).
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(ennf_transformation,[],[f17]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f18]) ).
fof(f53,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,[],[f19]) ).
fof(f54,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,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f56,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,[],[f21]) ).
fof(f57,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,[],[f56]) ).
fof(f69,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( intersection(X2,cross_product(X0,X1)) != X2
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f32]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f37]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f73]) ).
fof(f83,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(f85,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,[],[f51]) ).
fof(f86,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,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(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,[sK7]),skolemize(X2,sK7(X0,X1))],[f86]) ).
fof(f88,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,[],[f54]) ).
fof(f89,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,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK8(X0,X1),X1)
& member(sK8(X0,X1),X0)
& ilf_type(sK8(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,[sK8]),skolemize(X2,sK8(X0,X1))],[f89]) ).
fof(f91,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,[],[f57]) ).
fof(f103,plain,
( sK17 != intersection(sK17,cross_product(sK15,sK16))
& ilf_type(sK17,relation_type(sK15,sK16))
& ilf_type(sK16,set_type)
& ilf_type(sK15,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X0,sK15),skolemize(X1,sK16),skolemize(X2,sK17)],[f69]) ).
fof(f104,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f34]) ).
fof(f112,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f74]) ).
fof(f116,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,[],[f39]) ).
fof(f131,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,[],[f83]) ).
fof(f138,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f139,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f87]) ).
fof(f140,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f141,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,[],[f90]) ).
fof(f146,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f147,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,[],[f91]) ).
fof(f168,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f30]) ).
fof(f171,plain,
ilf_type(sK17,relation_type(sK15,sK16)),
inference(cnf_transformation,[],[f103]) ).
fof(f172,plain,
sK17 != intersection(sK17,cross_product(sK15,sK16)),
inference(cnf_transformation,[],[f103]) ).
fof(f185,plain,
! [X0] : subset(X0,X0),
inference(forward_subsumption_resolution,[],[f140,f168]) ).
fof(f186,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f146,f168]) ).
fof(f200,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f104,f168]) ).
fof(f201,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f200,f168]) ).
fof(f202,plain,
! [X0] : intersection(X0,X0) = X0,
inference(resolution,[],[f201,f185]) ).
fof(f203,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK7(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f138,f168]) ).
fof(f204,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f203,f168]) ).
fof(f205,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f139,f168]) ).
fof(f206,plain,
! [X0,X1] :
( ~ member(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f205,f168]) ).
fof(f211,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,[],[f131,f168]) ).
fof(f212,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f211,f168]) ).
fof(f221,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f147,f168]) ).
fof(f222,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f221,f168]) ).
fof(f224,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f222,f212]) ).
fof(f226,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[],[f224,f186]) ).
fof(f235,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f112,f168]) ).
fof(f236,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f235,f168]) ).
fof(f237,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f236,f168]) ).
fof(f238,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),intersection(X2,X1)) ),
inference(resolution,[],[f237,f206]) ).
fof(f245,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,[],[f116,f168]) ).
fof(f246,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f245,f168]) ).
fof(f247,plain,
! [X2,X0,X1] :
( intersection(X0,X1) = X0
| ~ member(sK7(X0,X1),intersection(X2,X1)) ),
inference(resolution,[],[f238,f201]) ).
fof(f264,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) ),
inference(forward_subsumption_resolution,[],[f141,f168]) ).
fof(f265,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f264,f168]) ).
fof(f266,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f265,f168]) ).
fof(f274,plain,
! [X0] :
( sK17 != sK17
| ~ member(sK7(sK17,cross_product(sK15,sK16)),intersection(X0,cross_product(sK15,sK16))) ),
inference(superposition,[],[f172,f247]) ).
fof(f277,plain,
! [X0] : ~ member(sK7(sK17,cross_product(sK15,sK16)),intersection(X0,cross_product(sK15,sK16))),
inference(trivial_inequality_removal,[],[f274]) ).
fof(f287,plain,
~ member(sK7(sK17,cross_product(sK15,sK16)),cross_product(sK15,sK16)),
inference(superposition,[],[f277,f202]) ).
fof(f297,plain,
! [X0] :
( ~ member(sK7(sK17,cross_product(sK15,sK16)),X0)
| ~ member(X0,power_set(cross_product(sK15,sK16))) ),
inference(resolution,[],[f287,f266]) ).
fof(f347,plain,
( ~ member(sK17,power_set(cross_product(sK15,sK16)))
| subset(sK17,cross_product(sK15,sK16)) ),
inference(resolution,[],[f297,f204]) ).
fof(f355,definition,
( spl18_1
<=> subset(sK17,cross_product(sK15,sK16)) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f357,plain,
( subset(sK17,cross_product(sK15,sK16))
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f359,definition,
( spl18_2
<=> member(sK17,power_set(cross_product(sK15,sK16))) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f361,plain,
( ~ member(sK17,power_set(cross_product(sK15,sK16)))
| spl18_2 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f362,plain,
( spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f347,f359,f355]) ).
fof(f376,plain,
( ~ ilf_type(sK17,subset_type(cross_product(sK15,sK16)))
| spl18_2 ),
inference(resolution,[],[f361,f226]) ).
fof(f385,plain,
( ~ ilf_type(sK17,relation_type(sK15,sK16))
| spl18_2 ),
inference(resolution,[],[f376,f246]) ).
fof(f387,plain,
( $false
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f385,f171]) ).
fof(f388,plain,
spl18_2,
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f391,plain,
( sK17 = intersection(sK17,cross_product(sK15,sK16))
| ~ spl18_1 ),
inference(resolution,[],[f357,f201]) ).
fof(f392,plain,
( $false
| ~ spl18_1 ),
inference(forward_subsumption_resolution,[],[f391,f172]) ).
fof(f393,plain,
~ spl18_1,
inference(avatar_contradiction_clause,[],[f392]) ).
cnf(s1,plain,
( spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f362]) ).
cnf(s2,plain,
spl18_2,
inference(sat_conversion,[],[f388]) ).
cnf(s3,plain,
~ spl18_1,
inference(sat_conversion,[],[f393]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f394,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET656+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 02:30:12 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.71/1.30 % (1129535)Detected formulas, will run a generic FOF schedule.
% 2.71/1.30 % (1129657)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1297140749:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.30 % (1129656)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4285509644:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.30 % (1129659)dis-21_1_sil=8000:lcm=predicate:random_seed=3177414588: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)
% 2.71/1.30 % (1129658)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1378058197:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.30 % (1129654)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=3196361036:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.30 % (1129653)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=350945932:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.30 % (1129655)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=1621638146:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.30 % (1129656)Refutation not found, incomplete strategy
% 2.71/1.30 % (1129656)------------------------------
% 2.71/1.30 % (1129656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.30 % (1129656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.30 % (1129656)CaDiCaL version: 2.1.3
% 2.71/1.30 % (1129656)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.30 % (1129656)Time elapsed: 0.002 s
% 2.71/1.30 % (1129656)Peak memory usage: 88 MB
% 2.71/1.30 % (1129656)Instructions burned: 1 (million)
% 2.71/1.30 % (1129657)Instruction limit reached!
% 2.71/1.30 % (1129657)------------------------------
% 2.71/1.30 % (1129657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.30 % (1129657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.30 % (1129657)CaDiCaL version: 2.1.3
% 2.71/1.30 % (1129657)Termination reason: Instruction limit
% 2.71/1.30 % (1129657)Termination phase: Saturation
% 2.71/1.30 % (1129657)Time elapsed: 0.037 s
% 2.71/1.30 % (1129657)Peak memory usage: 88 MB
% 2.71/1.30 % (1129657)Instructions burned: 121 (million)
% 2.71/1.30 % (1129658)First to succeed.
% 2.71/1.30 % (1129658)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1129535"
% 2.71/1.30 % (1129659)Also succeeded, but the first one will report.
% 2.71/1.30 % (1129667)lrs+10_1_sil=8000:sp=occurrence:random_seed=1910893571:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.71/1.30 % (1129667)Instruction limit reached!
% 2.71/1.30 % (1129667)------------------------------
% 2.71/1.30 % (1129667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.30 % (1129667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.30 % (1129667)CaDiCaL version: 2.1.3
% 2.71/1.30 % (1129667)Termination reason: Instruction limit
% 2.71/1.30 % (1129667)Termination phase: Saturation
% 2.71/1.30 % (1129667)Time elapsed: 0.089 s
% 2.71/1.30 % (1129667)Peak memory usage: 91 MB
% 2.71/1.30 % (1129667)Instructions burned: 285 (million)
% 2.71/1.30 % (1129656)------------------------------
% 2.71/1.30 % (1129656)------------------------------
% 2.71/1.30 % (1129658)Refutation found. Thanks to Tanya!
% 2.71/1.30 % SZS status Theorem for theBenchmark
% 2.71/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.50 % (1129658)------------------------------
% 3.65/1.50 % (1129658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.50 % (1129658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.50 % (1129658)CaDiCaL version: 2.1.3
% 3.65/1.50 % (1129658)Termination reason: Refutation
% 3.65/1.50 % (1129658)Time elapsed: 0.011 s
% 3.65/1.50 % (1129658)Peak memory usage: 90 MB
% 3.65/1.50 % (1129658)Instructions burned: 15 (million)
% 3.65/1.50 % (1129658)------------------------------
% 3.65/1.50 % (1129658)------------------------------
% 3.65/1.50 % (1129535)Success in time 0.443 s
% 3.65/1.50 % Vampire exiting
%------------------------------------------------------------------------------