%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET644+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 : n005.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 3.25s 1.36s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 130 ( 15 unt; 5 def)
% Number of atoms : 516 ( 16 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 689 ( 303 ~; 276 |; 59 &)
% ( 17 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 264 ( 0 sgn 244 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,X1)
=> ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& X0 = ordered_pair(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
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)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f5,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',p5) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f14,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',p14) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p21) ).
fof(f24,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/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f28,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(X0,X1))
=> ( member(X2,X3)
=> ? [X4] :
( ilf_type(X4,set_type)
& ? [X5] :
( ilf_type(X5,set_type)
& X2 = ordered_pair(X4,X5)
& member(X4,X0)
& member(X5,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_6) ).
fof(f29,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(X0,X1))
=> ( member(X2,X3)
=> ? [X4] :
( ilf_type(X4,set_type)
& ? [X5] :
( ilf_type(X5,set_type)
& X2 = ordered_pair(X4,X5)
& member(X4,X0)
& member(X5,X1) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& X0 = ordered_pair(X2,X3) ) )
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,set_type)
& X0 = ordered_pair(X2,X3) ) )
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,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(f35,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,[],[f5]) ).
fof(f42,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f43,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,[],[f14]) ).
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(ennf_transformation,[],[f19]) ).
fof(f50,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,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),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(ennf_transformation,[],[f21]) ).
fof(f53,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,[],[f52]) ).
fof(f58,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,[],[f24]) ).
fof(f62,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ordered_pair(X4,X5) != X2
| ~ member(X4,X0)
| ~ member(X5,X1) ) )
& member(X2,X3)
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ordered_pair(X4,X5) != X2
| ~ member(X4,X0)
| ~ member(X5,X1) ) )
& member(X2,X3)
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(sK0(X0),set_type)
& ilf_type(sK1(X0),set_type)
& ordered_pair(sK0(X0),sK1(X0)) = X0 )
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0)),skolemize(X3,sK1(X0))],[f31]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) )
& ( ( member(X0,X2)
& member(X1,X3) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f65]) ).
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(nnf_transformation,[],[f42]) ).
fof(f72,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,[],[f71]) ).
fof(f74,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,[],[f43]) ).
fof(f83,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,[],[f50]) ).
fof(f84,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,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f84]) ).
fof(f86,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,[],[f53]) ).
fof(f94,plain,
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ! [X5] :
( ~ ilf_type(X5,set_type)
| ordered_pair(X4,X5) != sK15
| ~ member(X4,sK13)
| ~ member(X5,sK14) ) )
& member(sK15,sK16)
& ilf_type(sK16,relation_type(sK13,sK14))
& ilf_type(sK15,set_type)
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16)],[f63]) ).
fof(f95,plain,
! [X0,X1] :
( ordered_pair(sK0(X0),sK1(X0)) = X0
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f64]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(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,[],[f66]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(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,[],[f66]) ).
fof(f104,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,[],[f35]) ).
fof(f116,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f118,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,[],[f74]) ).
fof(f131,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,[],[f85]) ).
fof(f136,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f51]) ).
fof(f137,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,[],[f86]) ).
fof(f146,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,[],[f58]) ).
fof(f151,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f155,plain,
ilf_type(sK16,relation_type(sK13,sK14)),
inference(cnf_transformation,[],[f94]) ).
fof(f156,plain,
member(sK15,sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f157,plain,
! [X4,X5] :
( ordered_pair(X4,X5) != sK15
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X4,sK13)
| ~ member(X5,sK14) ),
inference(cnf_transformation,[],[f94]) ).
fof(f166,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f116]) ).
fof(f181,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f136,f151]) ).
fof(f185,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f166,f151]) ).
fof(f199,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,[],[f146,f151]) ).
fof(f200,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f199,f151]) ).
fof(f206,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,[],[f118,f151]) ).
fof(f207,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f206,f151]) ).
fof(f216,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f137,f151]) ).
fof(f217,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f216,f151]) ).
fof(f226,plain,
! [X0,X1] :
( ordered_pair(sK0(X0),sK1(X0)) = X0
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f95,f151]) ).
fof(f227,plain,
! [X0,X1] :
( sK15 != X0
| ~ ilf_type(sK1(X0),set_type)
| ~ ilf_type(sK0(X0),set_type)
| ~ member(sK0(X0),sK13)
| ~ member(sK1(X0),sK14)
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(superposition,[],[f157,f226]) ).
fof(f228,plain,
! [X0,X1] :
( sK15 != X0
| ~ ilf_type(sK0(X0),set_type)
| ~ member(sK0(X0),sK13)
| ~ member(sK1(X0),sK14)
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f227,f151]) ).
fof(f229,plain,
! [X0,X1] :
( ~ member(sK1(X0),sK14)
| ~ member(sK0(X0),sK13)
| sK15 != X0
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f228,f151]) ).
fof(f230,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,[],[f104,f151]) ).
fof(f231,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f230,f151]) ).
fof(f286,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,[],[f131,f151]) ).
fof(f287,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f286,f151]) ).
fof(f288,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f287,f151]) ).
fof(f323,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f98,f151]) ).
fof(f324,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f323,f151]) ).
fof(f325,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type) ),
inference(forward_subsumption_resolution,[],[f324,f151]) ).
fof(f326,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
inference(forward_subsumption_resolution,[],[f325,f151]) ).
fof(f329,definition,
( spl17_8
<=> ! [X0] :
( ~ member(sK15,X0)
| ~ relation_like(X0) ) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
fof(f330,plain,
( ! [X0] :
( ~ relation_like(X0)
| ~ member(sK15,X0) )
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f342,plain,
! [X2,X3,X0,X1] :
( member(sK1(X0),X2)
| ~ member(X0,cross_product(X1,X2))
| ~ member(X0,X3)
| ~ ilf_type(X3,binary_relation_type) ),
inference(superposition,[],[f326,f226]) ).
fof(f347,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f99,f151]) ).
fof(f348,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f347,f151]) ).
fof(f349,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ ilf_type(X3,set_type) ),
inference(forward_subsumption_resolution,[],[f348,f151]) ).
fof(f350,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
inference(forward_subsumption_resolution,[],[f349,f151]) ).
fof(f352,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X0,X2),X3)
| member(X0,X1)
| ~ member(X3,power_set(cross_product(X1,X4))) ),
inference(resolution,[],[f350,f288]) ).
fof(f437,definition,
( spl17_15
<=> ! [X0] : ~ member(sK15,cross_product(X0,sK14)) ),
introduced(definition,[new_symbols(definition,[spl17_15])],[avatar_definition]) ).
fof(f438,plain,
( ! [X0] : ~ member(sK15,cross_product(X0,sK14))
| ~ spl17_15 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f441,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ member(sK15,X0) )
| ~ spl17_8 ),
inference(resolution,[],[f330,f200]) ).
fof(f448,plain,
! [X2,X3,X0,X1,X4] :
( member(sK0(X0),X2)
| ~ member(X0,X1)
| ~ member(X1,power_set(cross_product(X2,X3)))
| ~ member(X0,X4)
| ~ ilf_type(X4,binary_relation_type) ),
inference(superposition,[],[f352,f226]) ).
fof(f466,plain,
! [X2,X3,X0,X1] :
( sK15 != X0
| ~ member(X0,X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(sK0(X0),sK13)
| ~ member(X0,cross_product(X1,sK14))
| ~ member(X0,X3)
| ~ ilf_type(X3,binary_relation_type) ),
inference(resolution,[],[f342,f229]) ).
fof(f524,plain,
! [X2,X0,X1] :
( ~ member(sK15,X0)
| ~ ilf_type(X0,binary_relation_type)
| ~ member(sK0(sK15),sK13)
| ~ member(sK15,cross_product(X1,sK14))
| ~ member(sK15,X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(equality_resolution,[],[f466]) ).
fof(f533,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ member(sK15,X0) )
| ~ spl17_8 ),
inference(resolution,[],[f441,f231]) ).
fof(f561,plain,
( ~ member(sK15,sK16)
| ~ spl17_8 ),
inference(resolution,[],[f533,f155]) ).
fof(f564,plain,
( $false
| ~ spl17_8 ),
inference(forward_subsumption_resolution,[],[f561,f156]) ).
fof(f565,plain,
~ spl17_8,
inference(avatar_contradiction_clause,[],[f564]) ).
fof(f567,definition,
( spl17_21
<=> ! [X1] :
( ~ member(sK15,X1)
| ~ ilf_type(X1,binary_relation_type) ) ),
introduced(definition,[new_symbols(definition,[spl17_21])],[avatar_definition]) ).
fof(f568,plain,
( ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ member(sK15,X1) )
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f570,definition,
( spl17_22
<=> member(sK0(sK15),sK13) ),
introduced(definition,[new_symbols(definition,[spl17_22])],[avatar_definition]) ).
fof(f572,plain,
( ~ member(sK0(sK15),sK13)
| spl17_22 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f577,plain,
( spl17_21
| spl17_15
| ~ spl17_22
| spl17_21 ),
inference(avatar_split_clause,[],[f524,f567,f570,f437,f567]) ).
fof(f610,plain,
( ! [X0,X1] :
( ~ member(sK15,X0)
| ~ member(X0,power_set(cross_product(X1,sK14))) )
| ~ spl17_15 ),
inference(resolution,[],[f438,f288]) ).
fof(f626,plain,
( ! [X0] :
( ~ member(sK15,X0)
| ~ relation_like(X0) )
| ~ spl17_21 ),
inference(resolution,[],[f568,f185]) ).
fof(f627,plain,
( spl17_8
| ~ spl17_21 ),
inference(avatar_split_clause,[],[f626,f567,f329]) ).
fof(f750,plain,
( ! [X0] : ~ member(sK16,power_set(cross_product(X0,sK14)))
| ~ spl17_15 ),
inference(resolution,[],[f610,f156]) ).
fof(f761,plain,
( ! [X0] :
( ~ ilf_type(sK16,member_type(power_set(cross_product(X0,sK14))))
| empty(power_set(cross_product(X0,sK14))) )
| ~ spl17_15 ),
inference(resolution,[],[f750,f217]) ).
fof(f762,plain,
( ! [X0] : ~ ilf_type(sK16,member_type(power_set(cross_product(X0,sK14))))
| ~ spl17_15 ),
inference(forward_subsumption_resolution,[],[f761,f181]) ).
fof(f765,plain,
( ! [X0] : ~ ilf_type(sK16,subset_type(cross_product(X0,sK14)))
| ~ spl17_15 ),
inference(resolution,[],[f762,f207]) ).
fof(f774,plain,
( ! [X0] : ~ ilf_type(sK16,relation_type(X0,sK14))
| ~ spl17_15 ),
inference(resolution,[],[f765,f231]) ).
fof(f794,plain,
( $false
| ~ spl17_15 ),
inference(resolution,[],[f774,f155]) ).
fof(f796,plain,
~ spl17_15,
inference(avatar_contradiction_clause,[],[f794]) ).
fof(f799,definition,
( spl17_30
<=> ! [X0,X1] :
( ~ member(sK15,X0)
| ~ member(X0,power_set(cross_product(sK13,X1))) ) ),
introduced(definition,[new_symbols(definition,[spl17_30])],[avatar_definition]) ).
fof(f800,plain,
( ! [X0,X1] :
( ~ member(sK15,X0)
| ~ member(X0,power_set(cross_product(sK13,X1))) )
| ~ spl17_30 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f892,plain,
( ! [X2,X0,X1] :
( ~ member(sK15,X0)
| ~ member(X0,power_set(cross_product(sK13,X1)))
| ~ member(sK15,X2)
| ~ ilf_type(X2,binary_relation_type) )
| spl17_22 ),
inference(resolution,[],[f572,f448]) ).
fof(f897,plain,
( spl17_21
| spl17_30
| spl17_22 ),
inference(avatar_split_clause,[],[f892,f570,f799,f567]) ).
fof(f933,plain,
( ! [X0] : ~ member(sK16,power_set(cross_product(sK13,X0)))
| ~ spl17_30 ),
inference(resolution,[],[f800,f156]) ).
fof(f945,plain,
( ! [X0] :
( ~ ilf_type(sK16,member_type(power_set(cross_product(sK13,X0))))
| empty(power_set(cross_product(sK13,X0))) )
| ~ spl17_30 ),
inference(resolution,[],[f933,f217]) ).
fof(f946,plain,
( ! [X0] : ~ ilf_type(sK16,member_type(power_set(cross_product(sK13,X0))))
| ~ spl17_30 ),
inference(forward_subsumption_resolution,[],[f945,f181]) ).
fof(f949,plain,
( ! [X0] : ~ ilf_type(sK16,subset_type(cross_product(sK13,X0)))
| ~ spl17_30 ),
inference(resolution,[],[f946,f207]) ).
fof(f954,plain,
( ! [X0] : ~ ilf_type(sK16,relation_type(sK13,X0))
| ~ spl17_30 ),
inference(resolution,[],[f949,f231]) ).
fof(f959,plain,
( $false
| ~ spl17_30 ),
inference(resolution,[],[f954,f155]) ).
fof(f961,plain,
~ spl17_30,
inference(avatar_contradiction_clause,[],[f959]) ).
cnf(s15,plain,
~ spl17_8,
inference(sat_conversion,[],[f565]) ).
cnf(s17,plain,
( spl17_21
| spl17_15
| spl17_21
| ~ spl17_22 ),
inference(sat_conversion,[],[f577]) ).
cnf(s18,plain,
( spl17_15
| spl17_21
| ~ spl17_22 ),
inference(rat,[],[s17]) ).
cnf(s24,plain,
( spl17_8
| ~ spl17_21 ),
inference(sat_conversion,[],[f627]) ).
cnf(s32,plain,
~ spl17_15,
inference(sat_conversion,[],[f796]) ).
cnf(s36,plain,
( spl17_21
| spl17_22
| spl17_30 ),
inference(sat_conversion,[],[f897]) ).
cnf(s42,plain,
~ spl17_30,
inference(sat_conversion,[],[f961]) ).
cnf(s43,plain,
( spl17_21
| spl17_22 ),
inference(rat,[],[s36,s42]) ).
cnf(s46,plain,
( spl17_21
| ~ spl17_22 ),
inference(rat,[],[s18,s32]) ).
cnf(s48,plain,
~ spl17_21,
inference(rat,[],[s24,s15]) ).
cnf(s50,plain,
spl17_22,
inference(rat,[],[s43,s48]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s46,s50,s48]) ).
fof(f962,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET644+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:27:53 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.25/1.36 % (372327)Detected formulas, will run a generic FOF schedule.
% 3.25/1.36 % (372432)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1553961638:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.25/1.36 % (372432)Instruction limit reached!
% 3.25/1.36 % (372432)------------------------------
% 3.25/1.36 % (372432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.36 % (372432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.36 % (372432)CaDiCaL version: 2.1.3
% 3.25/1.36 % (372432)Termination reason: Instruction limit
% 3.25/1.36 % (372432)Termination phase: Saturation
% 3.25/1.36 % (372432)Time elapsed: 0.037 s
% 3.25/1.36 % (372432)Peak memory usage: 88 MB
% 3.25/1.36 % (372432)Instructions burned: 121 (million)
% 3.25/1.36 % (372428)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=332833272:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.25/1.36 % (372426)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=3063544950:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.25/1.36 % (372431)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1989590873:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.25/1.36 % (372430)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=2286085765:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.25/1.36 % (372431)Refutation not found, incomplete strategy
% 3.25/1.36 % (372431)------------------------------
% 3.25/1.36 % (372431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.36 % (372431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.36 % (372431)CaDiCaL version: 2.1.3
% 3.25/1.36 % (372431)Termination reason: Refutation not found, incomplete strategy
% 3.25/1.36 % (372431)Time elapsed: 0.002 s
% 3.25/1.36 % (372431)Peak memory usage: 88 MB
% 3.25/1.36 % (372431)Instructions burned: 1 (million)
% 3.25/1.36 % (372434)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3413031302:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.25/1.36 % (372435)dis-21_1_sil=8000:lcm=predicate:random_seed=4090692964: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)
% 3.25/1.36 % (372434)First to succeed.
% 3.25/1.36 % (372434)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-372327"
% 3.25/1.36 % (372435)Instruction limit reached!
% 3.25/1.36 % (372435)------------------------------
% 3.25/1.36 % (372435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.36 % (372435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.36 % (372435)CaDiCaL version: 2.1.3
% 3.25/1.36 % (372435)Termination reason: Instruction limit
% 3.25/1.36 % (372435)Termination phase: Saturation
% 3.25/1.36 % (372435)Time elapsed: 0.081 s
% 3.25/1.36 % (372435)Peak memory usage: 89 MB
% 3.25/1.36 % (372435)Instructions burned: 129 (million)
% 3.25/1.36 % (372443)lrs+10_1_sil=8000:sp=occurrence:random_seed=2835167169:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.25/1.36 % (372443)Instruction limit reached!
% 3.25/1.36 % (372443)------------------------------
% 3.25/1.36 % (372443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.36 % (372443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.36 % (372443)CaDiCaL version: 2.1.3
% 3.25/1.36 % (372443)Termination reason: Instruction limit
% 3.25/1.36 % (372443)Termination phase: Saturation
% 3.25/1.36 % (372443)Time elapsed: 0.113 s
% 3.25/1.36 % (372443)Peak memory usage: 91 MB
% 3.25/1.36 % (372443)Instructions burned: 288 (million)
% 3.25/1.36 % (372431)------------------------------
% 3.25/1.36 % (372431)------------------------------
% 3.25/1.36 % (372434)Refutation found. Thanks to Tanya!
% 3.25/1.36 % SZS status Theorem for theBenchmark
% 3.25/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 4.02/1.56 % (372434)------------------------------
% 4.02/1.56 % (372434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.56 % (372434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.56 % (372434)CaDiCaL version: 2.1.3
% 4.02/1.56 % (372434)Termination reason: Refutation
% 4.02/1.56 % (372434)Time elapsed: 0.034 s
% 4.02/1.56 % (372434)Peak memory usage: 90 MB
% 4.02/1.56 % (372434)Instructions burned: 44 (million)
% 4.02/1.56 % (372434)------------------------------
% 4.02/1.56 % (372434)------------------------------
% 4.02/1.56 % (372327)Success in time 0.483 s
% 4.02/1.56 % Vampire exiting
%------------------------------------------------------------------------------