%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET673+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 : n002.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 12:41:36 PM UTC 2026
% Result : Theorem 6.67s 1.96s
% Output : Refutation 8.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 171 ( 28 unt; 10 def)
% Number of atoms : 690 ( 46 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 895 ( 376 ~; 395 |; 61 &)
% ( 19 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 310 ( 0 sgn 294 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( 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)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),restrict(X0,X3))
<=> ( member(X2,X0)
& member(ordered_pair(X1,X2),X3) ) ) ) ) ) ),
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)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X2,X0)
& member(X3,X1) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f10,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',p10) ).
fof(f22,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',p22) ).
fof(f25,axiom,
! [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))
=> restrict4(X0,X1,X2,X3) = restrict(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
fof(f26,axiom,
! [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))
=> ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
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)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( subset(X1,X2)
=> restrict4(X0,X1,X2,X3) = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_36) ).
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))
=> ( subset(X1,X2)
=> restrict4(X0,X1,X2,X3) = X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X2,X3),X0)
<=> member(ordered_pair(X2,X3),X1) )
| ~ 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] :
( ! [X2] :
( ! [X3] :
( ( member(ordered_pair(X1,X2),restrict(X0,X3))
<=> ( member(X2,X0)
& member(ordered_pair(X1,X2),X3) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X2,X0)
& member(X3,X1) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ( 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,[],[f6]) ).
fof(f37,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,[],[f36]) ).
fof(f41,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( restrict4(X0,X1,X2,X3) = restrict(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,[],[f25]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ 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,[],[f26]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( restrict4(X0,X1,X2,X3) != X3
& subset(X1,X2)
& 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(f64,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( restrict4(X0,X1,X2,X3) != X3
& subset(X1,X2)
& ilf_type(X3,relation_type(X0,X1)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ? [X3] :
( ( ~ member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) )
& ( 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),X0)
| ~ member(ordered_pair(X2,X3),X1) )
& ( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f30]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ? [X3] :
( ( ~ member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) )
& ( 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),X0)
| ~ member(ordered_pair(X2,X3),X1) )
& ( member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ? [X3] :
( ( ~ member(ordered_pair(X2,X3),X1)
| ~ member(ordered_pair(X2,X3),X0) )
& ( 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),X0)
| ~ member(ordered_pair(X4,X5),X1) )
& ( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0) ) )
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0) )
& ( 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),X0)
| ~ member(ordered_pair(X4,X5),X1) )
& ( member(ordered_pair(X4,X5),X1)
| ~ member(ordered_pair(X4,X5),X0) ) )
| ~ ilf_type(X5,set_type) )
| ~ ilf_type(X4,set_type) )
| 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))],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3) )
& ( ( member(X2,X0)
& member(ordered_pair(X1,X2),X3) )
| ~ member(ordered_pair(X1,X2),restrict(X0,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f31]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3) )
& ( ( member(X2,X0)
& member(ordered_pair(X1,X2),X3) )
| ~ member(ordered_pair(X1,X2),restrict(X0,X3)) ) )
| ~ ilf_type(X3,binary_relation_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f69]) ).
fof(f72,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,[],[f37]) ).
fof(f73,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,[],[f72]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,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) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f73]) ).
fof(f75,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,[],[f41]) ).
fof(f76,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,[],[f75]) ).
fof(f91,plain,
( sK15 != restrict4(sK12,sK13,sK14,sK15)
& subset(sK13,sK14)
& ilf_type(sK15,relation_type(sK12,sK13))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f64]) ).
fof(f96,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| X0 = X1
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f68]) ).
fof(f97,plain,
! [X0,X1] :
( ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| X0 = X1
| ~ member(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f68]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f101,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f33]) ).
fof(f103,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f34]) ).
fof(f106,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,[],[f74]) ).
fof(f115,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f138,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f57]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( restrict4(X0,X1,X2,X3) = restrict(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(cnf_transformation,[],[f61]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f62]) ).
fof(f145,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f149,plain,
ilf_type(sK15,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f91]) ).
fof(f150,plain,
subset(sK13,sK14),
inference(cnf_transformation,[],[f91]) ).
fof(f151,plain,
sK15 != restrict4(sK12,sK13,sK14,sK15),
inference(cnf_transformation,[],[f91]) ).
fof(f155,definition,
sF16 = restrict4(sK12,sK13,sK14,sK15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f156,plain,
restrict4(sK12,sK13,sK14,sK15) = sF16,
inference(reorient_equations,[],[f155]) ).
fof(f157,plain,
sK15 != sF16,
inference(definition_folding,[],[f151,f156]) ).
fof(f158,definition,
sF17 = relation_type(sK12,sK13),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f159,plain,
relation_type(sK12,sK13) = sF17,
inference(reorient_equations,[],[f158]) ).
fof(f160,plain,
ilf_type(sK15,sF17),
inference(definition_folding,[],[f149,f159]) ).
fof(f162,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f115]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f144,f145]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( restrict4(X0,X1,X2,X3) = restrict(X2,X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f143,f145]) ).
fof(f170,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,[],[f138,f145]) ).
fof(f186,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f162,f145]) ).
fof(f188,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,[],[f106,f145]) ).
fof(f192,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,[],[f103,f145]) ).
fof(f194,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f101,f145]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f98,f145]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f99,f145]) ).
fof(f198,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f100,f145]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f165,f145]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( restrict4(X0,X1,X2,X3) = restrict(X2,X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f166,f145]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f170,f145]) ).
fof(f212,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f188,f145]) ).
fof(f216,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f192,f145]) ).
fof(f218,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f194,f145]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f196,f145]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f197,f145]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f198,f145]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( ilf_type(restrict4(X0,X1,X2,X3),relation_type(X0,X1))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f199,f145]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| restrict4(X0,X1,X2,X3) = restrict(X2,X3) ),
inference(forward_subsumption_resolution,[],[f200,f145]) ).
fof(f228,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f212,f145]) ).
fof(f229,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f218,f145]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f220,f145]) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| member(X2,X0)
| ~ ilf_type(X3,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f221,f145]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ member(X2,X0)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f222,f145]) ).
fof(f234,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f229,f145]) ).
fof(f236,plain,
! [X0] :
( ~ member(X0,sK13)
| member(X0,sK14) ),
inference(resolution,[],[f228,f150]) ).
fof(f237,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF17)
| restrict4(sK12,sK13,X1,X0) = restrict(X1,X0) ),
inference(superposition,[],[f224,f159]) ).
fof(f238,plain,
! [X0] : restrict4(sK12,sK13,X0,sK15) = restrict(X0,sK15),
inference(resolution,[],[f237,f160]) ).
fof(f240,plain,
sF16 = restrict(sK14,sK15),
inference(superposition,[],[f156,f238]) ).
fof(f241,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(X1,sK14)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[],[f232,f240]) ).
fof(f242,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(ordered_pair(X0,X1),sK15)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[],[f231,f240]) ).
fof(f244,definition,
( spl18_1
<=> ilf_type(sK15,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f245,plain,
( ilf_type(sK15,binary_relation_type)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f246,plain,
( ~ ilf_type(sK15,binary_relation_type)
| spl18_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f248,definition,
( spl18_2
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(ordered_pair(X0,X1),sK15) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f249,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(ordered_pair(X0,X1),sK15) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( ~ spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f242,f248,f244]) ).
fof(f252,definition,
( spl18_3
<=> ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(X1,sK14) ) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f253,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sF16)
| member(X1,sK14) )
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( ~ spl18_1
| spl18_3 ),
inference(avatar_split_clause,[],[f241,f252,f244]) ).
fof(f255,plain,
( ~ relation_like(sK15)
| spl18_1 ),
inference(resolution,[],[f186,f246]) ).
fof(f256,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f216,f202]) ).
fof(f257,plain,
! [X0] :
( ~ ilf_type(X0,sF17)
| relation_like(X0) ),
inference(superposition,[],[f256,f159]) ).
fof(f258,plain,
relation_like(sK15),
inference(resolution,[],[f257,f160]) ).
fof(f259,plain,
( $false
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f258,f255]) ).
fof(f260,plain,
spl18_1,
inference(avatar_contradiction_clause,[],[f259]) ).
fof(f266,plain,
( ! [X0] :
( member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),X0)
| sF16 = X0
| ~ ilf_type(sF16,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type)
| member(sK1(X0,sF16),sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f96,f253]) ).
fof(f267,plain,
( ! [X0] :
( member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),X0)
| sF16 = X0
| ~ ilf_type(sF16,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type)
| member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),sK15) )
| ~ spl18_2 ),
inference(resolution,[],[f96,f249]) ).
fof(f288,definition,
( spl18_6
<=> ilf_type(sF16,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f289,plain,
( ilf_type(sF16,binary_relation_type)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( ~ ilf_type(sF16,binary_relation_type)
| spl18_6 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f306,definition,
( spl18_10
<=> ! [X0] :
( member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),X0)
| member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),sK15)
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl18_10])],[avatar_definition]) ).
fof(f307,plain,
( ! [X0] :
( member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),sK15)
| member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),X0)
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0 )
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f308,plain,
( ~ spl18_6
| spl18_10
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f267,f248,f306,f288]) ).
fof(f310,definition,
( spl18_11
<=> ! [X0] :
( member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),X0)
| member(sK1(X0,sF16),sK14)
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition]) ).
fof(f311,plain,
( ! [X0] :
( member(ordered_pair(sK0(X0,sF16),sK1(X0,sF16)),X0)
| member(sK1(X0,sF16),sK14)
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0 )
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( ~ spl18_6
| spl18_11
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f266,f252,f310,f288]) ).
fof(f315,plain,
( ~ relation_like(sF16)
| spl18_6 ),
inference(resolution,[],[f290,f186]) ).
fof(f331,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),sF16)
| ~ member(X1,sK14)
| ~ member(ordered_pair(X0,X1),sK15)
| ~ ilf_type(sK15,binary_relation_type) ),
inference(superposition,[],[f233,f240]) ).
fof(f334,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sK15)
| ~ member(X1,sK14)
| member(ordered_pair(X0,X1),sF16) )
| ~ spl18_1 ),
inference(forward_subsumption_resolution,[],[f331,f245]) ).
fof(f345,plain,
( ilf_type(sF16,relation_type(sK12,sK13))
| ~ ilf_type(sK15,relation_type(sK12,sK13)) ),
inference(superposition,[],[f223,f156]) ).
fof(f349,plain,
( ilf_type(sF16,sF17)
| ~ ilf_type(sK15,relation_type(sK12,sK13)) ),
inference(forward_demodulation,[],[f345,f159]) ).
fof(f351,plain,
( ~ ilf_type(sK15,sF17)
| ilf_type(sF16,sF17) ),
inference(forward_demodulation,[],[f349,f159]) ).
fof(f353,plain,
ilf_type(sF16,sF17),
inference(forward_subsumption_resolution,[],[f351,f160]) ).
fof(f354,plain,
relation_like(sF16),
inference(resolution,[],[f353,f257]) ).
fof(f356,plain,
( $false
| spl18_6 ),
inference(forward_subsumption_resolution,[],[f354,f315]) ).
fof(f357,plain,
spl18_6,
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f363,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X2,X1))
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0
| member(sK1(X0,sF16),X1)
| member(sK1(X0,sF16),sK14) )
| ~ spl18_11 ),
inference(resolution,[],[f311,f234]) ).
fof(f404,plain,
( member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sK15)
| ~ ilf_type(sK15,binary_relation_type)
| sK15 = sF16
| ~ spl18_10 ),
inference(factoring,[],[f307]) ).
fof(f407,plain,
( member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sK15)
| sK15 = sF16
| ~ spl18_1
| ~ spl18_10 ),
inference(forward_subsumption_resolution,[],[f404,f245]) ).
fof(f411,plain,
( member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sK15)
| ~ spl18_1
| ~ spl18_10 ),
inference(forward_subsumption_resolution,[],[f407,f157]) ).
fof(f412,plain,
( ~ member(sK1(sK15,sF16),sK14)
| member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sF16)
| ~ spl18_1
| ~ spl18_10 ),
inference(resolution,[],[f411,f334]) ).
fof(f416,definition,
( spl18_12
<=> member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sF16) ),
introduced(definition,[new_symbols(definition,[spl18_12])],[avatar_definition]) ).
fof(f418,plain,
( member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sF16)
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f420,definition,
( spl18_13
<=> member(sK1(sK15,sF16),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_13])],[avatar_definition]) ).
fof(f422,plain,
( ~ member(sK1(sK15,sF16),sK14)
| spl18_13 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f423,plain,
( spl18_12
| ~ spl18_13
| ~ spl18_1
| ~ spl18_10 ),
inference(avatar_split_clause,[],[f412,f306,f244,f420,f416]) ).
fof(f431,plain,
( ! [X0] :
( ~ ilf_type(X0,sF17)
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0
| member(sK1(X0,sF16),sK13)
| member(sK1(X0,sF16),sK14) )
| ~ spl18_11 ),
inference(superposition,[],[f363,f159]) ).
fof(f432,plain,
( ! [X0] :
( member(sK1(X0,sF16),sK14)
| ~ ilf_type(X0,binary_relation_type)
| sF16 = X0
| ~ ilf_type(X0,sF17) )
| ~ spl18_11 ),
inference(forward_subsumption_resolution,[],[f431,f236]) ).
fof(f433,plain,
( ~ ilf_type(sK15,binary_relation_type)
| sK15 = sF16
| ~ ilf_type(sK15,sF17)
| ~ spl18_11
| spl18_13 ),
inference(resolution,[],[f432,f422]) ).
fof(f434,plain,
( sK15 = sF16
| ~ ilf_type(sK15,sF17)
| ~ spl18_1
| ~ spl18_11
| spl18_13 ),
inference(forward_subsumption_resolution,[],[f433,f245]) ).
fof(f435,plain,
( ~ ilf_type(sK15,sF17)
| ~ spl18_1
| ~ spl18_11
| spl18_13 ),
inference(forward_subsumption_resolution,[],[f434,f157]) ).
fof(f436,plain,
( $false
| ~ spl18_1
| ~ spl18_11
| spl18_13 ),
inference(forward_subsumption_resolution,[],[f435,f160]) ).
fof(f437,plain,
( ~ spl18_1
| ~ spl18_11
| spl18_13 ),
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f438,plain,
( sK15 = sF16
| ~ member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sK15)
| ~ ilf_type(sF16,binary_relation_type)
| ~ ilf_type(sK15,binary_relation_type)
| ~ spl18_12 ),
inference(resolution,[],[f418,f97]) ).
fof(f443,plain,
( ~ member(ordered_pair(sK0(sK15,sF16),sK1(sK15,sF16)),sK15)
| ~ ilf_type(sF16,binary_relation_type)
| ~ ilf_type(sK15,binary_relation_type)
| ~ spl18_12 ),
inference(forward_subsumption_resolution,[],[f438,f157]) ).
fof(f444,plain,
( ~ ilf_type(sF16,binary_relation_type)
| ~ ilf_type(sK15,binary_relation_type)
| ~ spl18_1
| ~ spl18_10
| ~ spl18_12 ),
inference(forward_subsumption_resolution,[],[f443,f411]) ).
fof(f445,plain,
( ~ ilf_type(sK15,binary_relation_type)
| ~ spl18_1
| ~ spl18_6
| ~ spl18_10
| ~ spl18_12 ),
inference(forward_subsumption_resolution,[],[f444,f289]) ).
fof(f446,plain,
( $false
| ~ spl18_1
| ~ spl18_6
| ~ spl18_10
| ~ spl18_12 ),
inference(forward_subsumption_resolution,[],[f445,f245]) ).
fof(f447,plain,
( ~ spl18_1
| ~ spl18_6
| ~ spl18_10
| ~ spl18_12 ),
inference(avatar_contradiction_clause,[],[f446]) ).
cnf(s1,plain,
( ~ spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f250]) ).
cnf(s2,plain,
( ~ spl18_1
| spl18_3 ),
inference(sat_conversion,[],[f254]) ).
cnf(s3,plain,
spl18_1,
inference(sat_conversion,[],[f260]) ).
cnf(s8,plain,
( ~ spl18_2
| ~ spl18_6
| spl18_10 ),
inference(sat_conversion,[],[f308]) ).
cnf(s9,plain,
( ~ spl18_3
| ~ spl18_6
| spl18_11 ),
inference(sat_conversion,[],[f312]) ).
cnf(s10,plain,
spl18_6,
inference(sat_conversion,[],[f357]) ).
cnf(s11,plain,
( ~ spl18_1
| ~ spl18_10
| spl18_12
| ~ spl18_13 ),
inference(sat_conversion,[],[f423]) ).
cnf(s12,plain,
( ~ spl18_1
| ~ spl18_11
| spl18_13 ),
inference(sat_conversion,[],[f437]) ).
cnf(s13,plain,
( ~ spl18_1
| ~ spl18_6
| ~ spl18_10
| ~ spl18_12 ),
inference(sat_conversion,[],[f447]) ).
cnf(s14,plain,
( ~ spl18_3
| spl18_11 ),
inference(rat,[],[s9,s10]) ).
cnf(s15,plain,
( ~ spl18_2
| spl18_10 ),
inference(rat,[],[s8,s10]) ).
cnf(s18,plain,
spl18_3,
inference(rat,[],[s2,s3]) ).
cnf(s19,plain,
spl18_11,
inference(rat,[],[s14,s18]) ).
cnf(s21,plain,
spl18_13,
inference(rat,[],[s12,s3,s19]) ).
cnf(s22,plain,
spl18_2,
inference(rat,[],[s1,s3]) ).
cnf(s23,plain,
spl18_10,
inference(rat,[],[s15,s22]) ).
cnf(s25,plain,
spl18_12,
inference(rat,[],[s11,s21,s3,s23]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s13,s3,s10,s25,s23]) ).
fof(f448,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET673+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:31:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 6.67/1.96 % (4097368)Detected formulas, will run a generic FOF schedule.
% 6.67/1.96 % (4097441)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=628798073:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.67/1.96 % (4097441)Instruction limit reached!
% 6.67/1.96 % (4097441)------------------------------
% 6.67/1.96 % (4097441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097441)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097441)Termination reason: Instruction limit
% 6.67/1.96 % (4097441)Termination phase: Saturation
% 6.67/1.96 % (4097441)Time elapsed: 0.038 s
% 6.67/1.96 % (4097441)Peak memory usage: 88 MB
% 6.67/1.96 % (4097441)Instructions burned: 120 (million)
% 6.67/1.96 % (4097442)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1519977188:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.67/1.96 % (4097437)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=1152229015:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.67/1.96 % (4097439)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=387080782:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.67/1.96 % (4097436)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=2452619629:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.67/1.96 % (4097439)Refutation not found, incomplete strategy
% 6.67/1.96 % (4097439)------------------------------
% 6.67/1.96 % (4097439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097439)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097439)Termination reason: Refutation not found, incomplete strategy
% 6.67/1.96 % (4097439)Time elapsed: 0.002 s
% 6.67/1.96 % (4097439)Peak memory usage: 88 MB
% 6.67/1.96 % (4097439)Instructions burned: 1 (million)
% 6.67/1.96 % (4097443)dis-21_1_sil=8000:lcm=predicate:random_seed=1561045200: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)
% 6.67/1.96 % (4097438)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=3846263010:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.67/1.96 % (4097443)Instruction limit reached!
% 6.67/1.96 % (4097443)------------------------------
% 6.67/1.96 % (4097443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097443)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097443)Termination reason: Instruction limit
% 6.67/1.96 % (4097443)Termination phase: Saturation
% 6.67/1.96 % (4097443)Time elapsed: 0.076 s
% 6.67/1.96 % (4097443)Peak memory usage: 90 MB
% 6.67/1.96 % (4097443)Instructions burned: 130 (million)
% 6.67/1.96 % (4097442)Instruction limit reached!
% 6.67/1.96 % (4097442)------------------------------
% 6.67/1.96 % (4097442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097442)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097442)Termination reason: Instruction limit
% 6.67/1.96 % (4097442)Termination phase: Saturation
% 6.67/1.96 % (4097442)Time elapsed: 0.100 s
% 6.67/1.96 % (4097442)Peak memory usage: 89 MB
% 6.67/1.96 % (4097442)Instructions burned: 140 (million)
% 6.67/1.96 % (4097451)lrs+10_1_sil=8000:sp=occurrence:random_seed=779724197:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.67/1.96 % (4097451)Instruction limit reached!
% 6.67/1.96 % (4097451)------------------------------
% 6.67/1.96 % (4097451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097451)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097451)Termination reason: Instruction limit
% 6.67/1.96 % (4097451)Termination phase: Saturation
% 6.67/1.96 % (4097451)Time elapsed: 0.093 s
% 6.67/1.96 % (4097451)Peak memory usage: 91 MB
% 6.67/1.96 % (4097451)Instructions burned: 287 (million)
% 6.67/1.96 % (4097439)------------------------------
% 6.67/1.96 % (4097439)------------------------------
% 6.67/1.96 % (4097478)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1785603957:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.67/1.96 % (4097472)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1992099986:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.67/1.96 % (4097528)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1559287230:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.67/1.96 % (4097472)Instruction limit reached!
% 6.67/1.96 % (4097472)------------------------------
% 6.67/1.96 % (4097472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097472)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097472)Termination reason: Instruction limit
% 6.67/1.96 % (4097472)Termination phase: Saturation
% 6.67/1.96 % (4097472)Time elapsed: 0.086 s
% 6.67/1.96 % (4097472)Peak memory usage: 89 MB
% 6.67/1.96 % (4097472)Instructions burned: 157 (million)
% 6.67/1.96 % (4097543)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3735924904:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.67/1.96 % (4097543)Refutation not found, incomplete strategy
% 6.67/1.96 % (4097543)------------------------------
% 6.67/1.96 % (4097543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097543)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097543)Termination reason: Refutation not found, incomplete strategy
% 6.67/1.96 % (4097543)Time elapsed: 0.004 s
% 6.67/1.96 % (4097543)Peak memory usage: 88 MB
% 6.67/1.96 % (4097543)Instructions burned: 5 (million)
% 6.67/1.96 % (4097528)Instruction limit reached!
% 6.67/1.96 % (4097528)------------------------------
% 6.67/1.96 % (4097528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097528)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097528)Termination reason: Instruction limit
% 6.67/1.96 % (4097528)Termination phase: Saturation
% 6.67/1.96 % (4097528)Time elapsed: 0.091 s
% 6.67/1.96 % (4097528)Peak memory usage: 90 MB
% 6.67/1.96 % (4097528)Instructions burned: 249 (million)
% 6.67/1.96 % (4097567)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=757038182:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.67/1.96 % (4097478)Instruction limit reached!
% 6.67/1.96 % (4097478)------------------------------
% 6.67/1.96 % (4097478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097478)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097478)Termination reason: Instruction limit
% 6.67/1.96 % (4097478)Termination phase: Saturation
% 6.67/1.96 % (4097478)Time elapsed: 0.236 s
% 6.67/1.96 % (4097478)Peak memory usage: 91 MB
% 6.67/1.96 % (4097478)Instructions burned: 326 (million)
% 6.67/1.96 % (4097569)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1080012009:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.67/1.96 % (4097569)Instruction limit reached!
% 6.67/1.96 % (4097569)------------------------------
% 6.67/1.96 % (4097569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097569)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097569)Termination reason: Instruction limit
% 6.67/1.96 % (4097569)Termination phase: Saturation
% 6.67/1.96 % (4097569)Time elapsed: 0.040 s
% 6.67/1.96 % (4097569)Peak memory usage: 90 MB
% 6.67/1.96 % (4097569)Instructions burned: 113 (million)
% 6.67/1.96 % (4097583)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3319380387:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.67/1.96 % (4097543)------------------------------
% 6.67/1.96 % (4097543)------------------------------
% 6.67/1.96 % (4097436)First to succeed.
% 6.67/1.96 % (4097436)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4097368"
% 6.67/1.96 % (4097620)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=749208134:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.67/1.96 % (4097583)Instruction limit reached!
% 6.67/1.96 % (4097583)------------------------------
% 6.67/1.96 % (4097583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097583)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097583)Termination reason: Instruction limit
% 6.67/1.96 % (4097583)Termination phase: Saturation
% 6.67/1.96 % (4097583)Time elapsed: 0.069 s
% 6.67/1.96 % (4097583)Peak memory usage: 89 MB
% 6.67/1.96 % (4097583)Instructions burned: 128 (million)
% 6.67/1.96 % (4097620)Instruction limit reached!
% 6.67/1.96 % (4097620)------------------------------
% 6.67/1.96 % (4097620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097620)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097620)Termination reason: Instruction limit
% 6.67/1.96 % (4097620)Termination phase: Saturation
% 6.67/1.96 % (4097620)Time elapsed: 0.039 s
% 6.67/1.96 % (4097620)Peak memory usage: 89 MB
% 6.67/1.96 % (4097620)Instructions burned: 118 (million)
% 6.67/1.96 % (4097622)lrs+10_1_sil=8000:sp=occurrence:random_seed=3886653409:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.67/1.96 % (4097625)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2059255929:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.67/1.96 % (4097624)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2437729361:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.67/1.96 % (4097624)Refutation not found, incomplete strategy
% 6.67/1.96 % (4097624)------------------------------
% 6.67/1.96 % (4097624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.96 % (4097624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.96 % (4097624)CaDiCaL version: 2.1.3
% 6.67/1.96 % (4097624)Termination reason: Refutation not found, incomplete strategy
% 6.67/1.96 % (4097624)Time elapsed: 0.003 s
% 6.67/1.96 % (4097624)Peak memory usage: 88 MB
% 6.67/1.96 % (4097624)Instructions burned: 4 (million)
% 6.67/1.96 % (4097436)Refutation found. Thanks to Tanya!
% 6.67/1.96 % SZS status Theorem for theBenchmark
% 6.67/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 8.22/2.08 % (4097436)------------------------------
% 8.22/2.08 % (4097436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.22/2.08 % (4097436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/2.08 % (4097436)CaDiCaL version: 2.1.3
% 8.22/2.08 % (4097436)Termination reason: Refutation
% 8.22/2.08 % (4097436)Time elapsed: 0.661 s
% 8.22/2.08 % (4097436)Peak memory usage: 129 MB
% 8.22/2.08 % (4097436)Instructions burned: 979 (million)
% 8.22/2.08 % (4097436)------------------------------
% 8.22/2.08 % (4097436)------------------------------
% 8.22/2.08 % (4097368)Success in time 1.1 s
% 8.22/2.08 % Vampire exiting
%------------------------------------------------------------------------------