%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET665+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 12:44:22 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 119 ( 12 unt; 2 def)
% Number of atoms : 490 ( 15 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 643 ( 272 ~; 271 |; 50 &)
% ( 21 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 231 ( 0 sgn 222 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(ordered_pair(X2,X3),X0)
=> member(ordered_pair(X2,X3),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/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)
=> ( member(ordered_pair(X1,X2),identity_relation_of(X0))
<=> ( member(X1,X0)
& X1 = X2 ) ) ) ) ),
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)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X0,X2)
& member(X1,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(identity_relation_of(X0),binary_relation_type) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(f11,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',p11) ).
fof(f17,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',p17) ).
fof(f20,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',p20) ).
fof(f21,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',p21) ).
fof(f23,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',p23) ).
fof(f25,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',p25) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f28,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_28) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> subset(identity_relation_of(X0),cross_product(X0,X0)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
<=> ( member(X1,X0)
& X1 = X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f33,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,[],[f3]) ).
fof(f38,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
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,[],[f11]) ).
fof(f47,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,[],[f17]) ).
fof(f51,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,[],[f20]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
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(flattening,[],[f52]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
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(flattening,[],[f55]) ).
fof(f59,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f62,plain,
? [X0] :
( ~ subset(identity_relation_of(X0),cross_product(X0,X0))
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ? [X3] :
( ~ member(ordered_pair(X2,X3),X1)
& member(ordered_pair(X2,X3),X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ! [X3] :
( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f31]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ? [X3] :
( ~ member(ordered_pair(X2,X3),X1)
& member(ordered_pair(X2,X3),X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) )
& ( ! [X4] :
( ! [X5] :
( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0)
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
& member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& ilf_type(sK1(X0,X1),set_type)
& ilf_type(sK0(X0,X1),set_type) ) )
& ( ! [X4] :
( ! [X5] :
( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0)
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ member(X1,X0)
| X1 != X2 )
& ( ( member(X1,X0)
& X1 = X2 )
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ member(X1,X0)
| X1 != X2 )
& ( ( member(X1,X0)
& X1 = X2 )
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f66]) ).
fof(f68,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,[],[f33]) ).
fof(f69,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,[],[f68]) ).
fof(f78,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(f79,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,[],[f78]) ).
fof(f82,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,[],[f47]) ).
fof(f87,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,[],[f53]) ).
fof(f88,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,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(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,[sK11]),skolemize(X2,sK11(X0,X1))],[f88]) ).
fof(f90,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,[],[f56]) ).
fof(f92,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,[],[f59]) ).
fof(f93,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,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK13(X0),X0)
& ilf_type(sK13(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,[sK13]),skolemize(X1,sK13(X0))],[f93]) ).
fof(f95,plain,
( ~ subset(identity_relation_of(sK14),cross_product(sK14,sK14))
& ilf_type(sK14,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f62]) ).
fof(f99,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| subset(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f100,plain,
! [X0,X1] :
( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| subset(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f101,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f102,plain,
! [X2,X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f69]) ).
fof(f118,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f126,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f134,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,[],[f82]) ).
fof(f142,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,[],[f51]) ).
fof(f145,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK11(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f89]) ).
fof(f146,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f89]) ).
fof(f150,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,[],[f90]) ).
fof(f152,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f156,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f158,plain,
~ subset(identity_relation_of(sK14),cross_product(sK14,sK14)),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f167,plain,
! [X0] : ilf_type(identity_relation_of(X0),binary_relation_type),
inference(forward_subsumption_resolution,[],[f118,f156]) ).
fof(f173,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f162,f156]) ).
fof(f178,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f152,f156]) ).
fof(f179,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f178,f156]) ).
fof(f194,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,[],[f142,f156]) ).
fof(f195,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f194,f156]) ).
fof(f199,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,[],[f134,f156]) ).
fof(f200,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f199,f156]) ).
fof(f205,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK11(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f145,f156]) ).
fof(f206,plain,
! [X0,X1] :
( member(sK11(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f205,f156]) ).
fof(f208,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f146,f156]) ).
fof(f209,plain,
! [X0,X1] :
( ~ member(sK11(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f208,f156]) ).
fof(f212,plain,
! [X0] :
( member(X0,power_set(X0))
| member(X0,power_set(X0)) ),
inference(resolution,[],[f209,f206]) ).
fof(f214,plain,
! [X0] : member(X0,power_set(X0)),
inference(duplicate_literal_removal,[],[f212]) ).
fof(f222,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,[],[f150,f179]) ).
fof(f223,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f222,f156]) ).
fof(f224,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[],[f223,f156]) ).
fof(f226,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f224,f200]) ).
fof(f238,plain,
! [X0] : ilf_type(X0,subset_type(X0)),
inference(resolution,[],[f226,f214]) ).
fof(f249,plain,
! [X0,X1] : relation_like(cross_product(X0,X1)),
inference(resolution,[],[f238,f195]) ).
fof(f275,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f101,f156]) ).
fof(f276,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f275,f156]) ).
fof(f277,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| X1 = X2 ),
inference(forward_subsumption_resolution,[],[f276,f156]) ).
fof(f279,plain,
! [X0,X1] :
( sK0(identity_relation_of(X0),X1) = sK1(identity_relation_of(X0),X1)
| subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(resolution,[],[f277,f99]) ).
fof(f280,plain,
! [X0,X1] :
( subset(identity_relation_of(X0),X1)
| sK0(identity_relation_of(X0),X1) = sK1(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f279,f167]) ).
fof(f282,plain,
! [X2,X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f102,f156]) ).
fof(f283,plain,
! [X2,X0,X1] :
( member(X1,X0)
| ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f282,f156]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X1,X2),identity_relation_of(X0))
| member(X1,X0) ),
inference(forward_subsumption_resolution,[],[f283,f156]) ).
fof(f287,plain,
! [X0,X1] :
( member(sK0(identity_relation_of(X0),X1),X0)
| subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(identity_relation_of(X0),binary_relation_type) ),
inference(resolution,[],[f284,f99]) ).
fof(f288,plain,
! [X0,X1] :
( member(sK0(identity_relation_of(X0),X1),X0)
| subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f287,f167]) ).
fof(f429,plain,
! [X2,X3,X0,X1] :
( 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) ),
inference(forward_subsumption_resolution,[],[f106,f156]) ).
fof(f430,plain,
! [X2,X3,X0,X1] :
( 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) ),
inference(forward_subsumption_resolution,[],[f429,f156]) ).
fof(f431,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,set_type) ),
inference(forward_subsumption_resolution,[],[f430,f156]) ).
fof(f432,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X0,X2)
| ~ member(X1,X3) ),
inference(forward_subsumption_resolution,[],[f431,f156]) ).
fof(f446,plain,
! [X2,X0,X1] :
( ~ member(sK1(X0,cross_product(X1,X2)),X2)
| ~ member(sK0(X0,cross_product(X1,X2)),X1)
| subset(X0,cross_product(X1,X2))
| ~ ilf_type(cross_product(X1,X2),binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[],[f432,f100]) ).
fof(f663,plain,
( sK0(identity_relation_of(sK14),cross_product(sK14,sK14)) = sK1(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type) ),
inference(resolution,[],[f280,f158]) ).
fof(f672,definition,
( spl15_6
<=> ilf_type(cross_product(sK14,sK14),binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f673,plain,
( ilf_type(cross_product(sK14,sK14),binary_relation_type)
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f674,plain,
( ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| spl15_6 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f676,definition,
( spl15_7
<=> sK0(identity_relation_of(sK14),cross_product(sK14,sK14)) = sK1(identity_relation_of(sK14),cross_product(sK14,sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f678,plain,
( sK0(identity_relation_of(sK14),cross_product(sK14,sK14)) = sK1(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f679,plain,
( ~ spl15_6
| spl15_7 ),
inference(avatar_split_clause,[],[f663,f676,f672]) ).
fof(f680,plain,
( ~ relation_like(cross_product(sK14,sK14))
| spl15_6 ),
inference(resolution,[],[f674,f173]) ).
fof(f681,plain,
( $false
| spl15_6 ),
inference(forward_subsumption_resolution,[],[f680,f249]) ).
fof(f682,plain,
spl15_6,
inference(avatar_contradiction_clause,[],[f681]) ).
fof(f1072,plain,
( ~ member(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| ~ member(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| subset(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK14),binary_relation_type)
| ~ spl15_7 ),
inference(superposition,[],[f446,f678]) ).
fof(f1073,plain,
( ~ member(sK0(identity_relation_of(sK14),cross_product(sK14,sK14)),sK14)
| subset(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK14),binary_relation_type)
| ~ spl15_7 ),
inference(duplicate_literal_removal,[],[f1072]) ).
fof(f1075,plain,
( subset(identity_relation_of(sK14),cross_product(sK14,sK14))
| ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK14),binary_relation_type)
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f1073,f288]) ).
fof(f1076,plain,
( ~ ilf_type(cross_product(sK14,sK14),binary_relation_type)
| ~ ilf_type(identity_relation_of(sK14),binary_relation_type)
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f1075,f158]) ).
fof(f1077,plain,
( ~ ilf_type(identity_relation_of(sK14),binary_relation_type)
| ~ spl15_6
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f1076,f673]) ).
fof(f1078,plain,
( $false
| ~ spl15_6
| ~ spl15_7 ),
inference(forward_subsumption_resolution,[],[f1077,f167]) ).
fof(f1079,plain,
( ~ spl15_6
| ~ spl15_7 ),
inference(avatar_contradiction_clause,[],[f1078]) ).
cnf(s4,plain,
( ~ spl15_6
| spl15_7 ),
inference(sat_conversion,[],[f679]) ).
cnf(s5,plain,
spl15_6,
inference(sat_conversion,[],[f682]) ).
cnf(s14,plain,
( ~ spl15_6
| ~ spl15_7 ),
inference(sat_conversion,[],[f1079]) ).
cnf(s17,plain,
~ spl15_7,
inference(rat,[],[s14,s5]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s4,s17,s5]) ).
fof(f1080,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET665+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 02:32:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.46 % (2206935)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2206943)dis+10_1_sil=32000:sp=arity:random_seed=4063904698:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (2206941)% WARNING: option uhcvi not known.
% 0.15/0.46 % (2206940)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3919753731_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (2206942)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=912554059:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (2206944)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2875578120:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (2206945)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3827640128:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (2206946)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3732849749:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (2206941)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1508120941:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (2206943) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2206935-2206943"...
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % (2206943)...printing done.
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % (2206941) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2206935-2206941"...
% 0.15/0.46 % (2206943)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (2206943)------------------------------
% 0.15/0.46 % (2206943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (2206943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (2206943)CaDiCaL version: 2.1.3
% 0.15/0.46 % (2206943)Termination reason: Refutation
% 0.15/0.46 % (2206943)Time elapsed: 0.016 s
% 0.15/0.46 % (2206943)Peak memory usage: 13 MB
% 0.15/0.46 % (2206943)Instructions burned: 43 (million)
% 0.15/0.46 % (2206935)Success in time 0.046 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------