%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET674+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 : n008.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 12:41:37 PM UTC 2026
% Result : Theorem 9.45s 2.19s
% Output : Refutation 10.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 26
% Syntax : Number of formulae : 245 ( 30 unt; 9 def)
% Number of atoms : 1011 ( 97 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1336 ( 570 ~; 602 |; 88 &)
% ( 19 <=>; 55 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 10 con; 0-4 aty)
% Number of variables : 513 ( 0 sgn 487 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,domain_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( member(X0,range_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) ) ) ) ),
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,binary_relation_type)
=> ( member(ordered_pair(X0,X1),X2)
=> ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) ) ) ) ) ),
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,binary_relation_type)
=> ( member(X1,image(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f7,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',p7) ).
fof(f8,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',p8) ).
fof(f17,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',p17) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f29,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',p29) ).
fof(f32,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
fof(f34,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
fof(f36,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p36) ).
fof(f38,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38) ).
fof(f40,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p40) ).
fof(f41,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( image4(X0,X1,X2,X0) = range(X0,X1,X2)
& inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_38) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( image4(X0,X1,X2,X0) = range(X0,X1,X2)
& inverse4(X0,X1,X2,X1) = domain(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ( member(X0,domain_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( member(X0,range_of(X1))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X0,domain_of(X2))
& member(X1,range_of(X2)) )
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,image(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,inverse2(X2,X0))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( member(X2,X0)
<~> member(X2,X1) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( member(X2,X0)
<~> member(X2,X1) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f49]) ).
fof(f51,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,[],[f7]) ).
fof(f52,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,[],[f51]) ).
fof(f53,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,[],[f8]) ).
fof(f62,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2] :
( ( member(X2,X0)
<=> member(X2,X1) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f78,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,[],[f29]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f32]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f38]) ).
fof(f90,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != image4(X0,X1,X2,X0)
| domain(X0,X1,X2) != inverse4(X0,X1,X2,X1) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f42]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X0,X2),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f43]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X0,X3),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,domain_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X0,X2),X1) ) )
& ( ( ilf_type(sK0(X0,X1),set_type)
& member(ordered_pair(X0,sK0(X0,X1)),X1) )
| ~ member(X0,domain_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f44]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) )
& ( ( ilf_type(sK1(X0,X1),set_type)
& member(ordered_pair(sK1(X0,X1),X0),X1) )
| ~ member(X0,range_of(X1)) ) )
| ~ ilf_type(X1,binary_relation_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f95]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2)
& member(X3,X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f47]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X1),X2)
& member(X4,X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0) ) )
& ( ( ilf_type(sK2(X0,X1,X2),set_type)
& member(ordered_pair(sK2(X0,X1,X2),X1),X2)
& member(sK2(X0,X1,X2),X0) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X4,sK2(X0,X1,X2))],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2)
& member(X3,X0) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0) ) )
& ( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X1,X4),X2)
& member(X4,X0) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,inverse2(X2,X0))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0) ) )
& ( ( ilf_type(sK3(X0,X1,X2),set_type)
& member(ordered_pair(X1,sK3(X0,X1,X2)),X2)
& member(sK3(X0,X1,X2),X0) )
| ~ member(X1,inverse2(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X1,X2))],[f101]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f50]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( ( ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0) )
& ( member(sK4(X0,X1),X1)
| member(sK4(X0,X1),X0) )
& ilf_type(sK4(X0,X1),set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f104]) ).
fof(f109,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,[],[f62]) ).
fof(f110,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,[],[f109]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f65]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ~ ilf_type(X3,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ member(sK8(X0,X1),X1)
| ~ member(sK8(X0,X1),X0) )
& ( member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0) )
& ilf_type(sK8(X0,X1),set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| ~ ilf_type(X3,set_type) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f116]) ).
fof(f132,plain,
( ( range(sK16,sK17,sK18) != image4(sK16,sK17,sK18,sK16)
| domain(sK16,sK17,sK18) != inverse4(sK16,sK17,sK18,sK17) )
& ilf_type(sK18,relation_type(sK16,sK17))
& ilf_type(sK17,set_type)
& ilf_type(sK16,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f90]) ).
fof(f133,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f93]) ).
fof(f136,plain,
! [X0,X1] :
( member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f96]) ).
fof(f139,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f140,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f142,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK2(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
fof(f146,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK3(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
fof(f150,plain,
! [X0,X1] :
( X0 = X1
| member(sK4(X0,X1),X1)
| member(sK4(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f105]) ).
fof(f151,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f105]) ).
fof(f152,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,[],[f52]) ).
fof(f153,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ 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,[],[f52]) ).
fof(f154,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,[],[f53]) ).
fof(f168,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f110]) ).
fof(f176,plain,
! [X0,X1] :
( X0 = X1
| member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f117]) ).
fof(f177,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK8(X0,X1),X1)
| ~ member(sK8(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f117]) ).
fof(f198,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,[],[f78]) ).
fof(f203,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f205,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f86]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f211,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f40]) ).
fof(f214,plain,
ilf_type(sK18,relation_type(sK16,sK17)),
inference(cnf_transformation,[],[f132]) ).
fof(f215,plain,
( range(sK16,sK17,sK18) != image4(sK16,sK17,sK18,sK16)
| domain(sK16,sK17,sK18) != inverse4(sK16,sK17,sK18,sK17) ),
inference(cnf_transformation,[],[f132]) ).
fof(f220,definition,
sF19 = range(sK16,sK17,sK18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f221,plain,
range(sK16,sK17,sK18) = sF19,
inference(reorient_equations,[],[f220]) ).
fof(f222,definition,
sF20 = image4(sK16,sK17,sK18,sK16),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f223,plain,
image4(sK16,sK17,sK18,sK16) = sF20,
inference(reorient_equations,[],[f222]) ).
fof(f224,definition,
sF21 = domain(sK16,sK17,sK18),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f225,plain,
domain(sK16,sK17,sK18) = sF21,
inference(reorient_equations,[],[f224]) ).
fof(f226,definition,
sF22 = inverse4(sK16,sK17,sK18,sK17),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f227,plain,
inverse4(sK16,sK17,sK18,sK17) = sF22,
inference(reorient_equations,[],[f226]) ).
fof(f228,plain,
( sF19 != sF20
| sF21 != sF22 ),
inference(definition_folding,[],[f215,f227,f225,f223,f221]) ).
fof(f229,definition,
sF23 = relation_type(sK16,sK17),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f230,plain,
relation_type(sK16,sK17) = sF23,
inference(reorient_equations,[],[f229]) ).
fof(f231,plain,
ilf_type(sK18,sF23),
inference(definition_folding,[],[f214,f230]) ).
fof(f234,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f168]) ).
fof(f238,definition,
( spl24_1
<=> sF21 = sF22 ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f239,plain,
( sF21 = sF22
| ~ spl24_1 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( sF21 != sF22
| spl24_1 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f242,definition,
( spl24_2
<=> sF19 = sF20 ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f244,plain,
( sF19 != sF20
| spl24_2 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f228,f242,f238]) ).
fof(f247,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f209,f211]) ).
fof(f249,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f207,f211]) ).
fof(f251,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f205,f211]) ).
fof(f253,plain,
! [X2,X0,X1] :
( domain_of(X2) = domain(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f203,f211]) ).
fof(f257,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,[],[f198,f211]) ).
fof(f272,plain,
! [X0,X1] :
( X0 = X1
| member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f176,f211]) ).
fof(f273,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK8(X0,X1),X1)
| ~ member(sK8(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f177,f211]) ).
fof(f278,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f234,f211]) ).
fof(f283,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,[],[f154,f211]) ).
fof(f285,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,[],[f152,f211]) ).
fof(f286,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ 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,[],[f153,f211]) ).
fof(f287,plain,
! [X0,X1] :
( X0 = X1
| member(sK4(X0,X1),X1)
| member(sK4(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f150,f211]) ).
fof(f288,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK4(X0,X1),X1)
| ~ member(sK4(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f151,f211]) ).
fof(f290,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK3(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f146,f211]) ).
fof(f291,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f148,f211]) ).
fof(f293,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK2(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f142,f211]) ).
fof(f294,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f144,f211]) ).
fof(f295,plain,
! [X2,X0,X1] :
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f139,f211]) ).
fof(f296,plain,
! [X2,X0,X1] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f140,f211]) ).
fof(f297,plain,
! [X0,X1] :
( member(ordered_pair(sK1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f136,f211]) ).
fof(f299,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f133,f211]) ).
fof(f302,plain,
! [X2,X3,X0,X1] :
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f247,f211]) ).
fof(f304,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f249,f211]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range_of(X2) = range(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f251,f211]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain_of(X2) = domain(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f253,f211]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f257,f211]) ).
fof(f321,plain,
! [X0,X1] :
( member(sK8(X0,X1),X1)
| member(sK8(X0,X1),X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f272,f211]) ).
fof(f322,plain,
! [X0,X1] :
( ~ member(sK8(X0,X1),X1)
| X0 = X1
| ~ member(sK8(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f273,f211]) ).
fof(f327,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f283,f211]) ).
fof(f329,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,[],[f285,f211]) ).
fof(f330,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ 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,[],[f286,f211]) ).
fof(f331,plain,
! [X0,X1] :
( member(sK4(X0,X1),X1)
| member(sK4(X0,X1),X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f287,f211]) ).
fof(f332,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| X0 = X1
| ~ member(sK4(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f288,f211]) ).
fof(f334,plain,
! [X2,X0,X1] :
( member(ordered_pair(X1,sK3(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f290,f211]) ).
fof(f335,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse2(X2,X0))
| ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f291,f211]) ).
fof(f337,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK2(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f293,f211]) ).
fof(f338,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f294,f211]) ).
fof(f339,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),X2)
| member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f295,f211]) ).
fof(f340,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),X2)
| member(X0,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f296,f211]) ).
fof(f344,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| inverse4(X0,X1,X2,X3) = inverse2(X2,X3) ),
inference(forward_subsumption_resolution,[],[f302,f211]) ).
fof(f346,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| image4(X0,X1,X2,X3) = image(X2,X3) ),
inference(forward_subsumption_resolution,[],[f304,f211]) ).
fof(f351,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,[],[f329,f211]) ).
fof(f352,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f330,f211]) ).
fof(f353,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X1,X3),X2)
| member(X1,inverse2(X2,X0))
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f335,f211]) ).
fof(f354,plain,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X3,X1),X2)
| member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ ilf_type(X2,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f338,f211]) ).
fof(f355,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,[],[f351,f211]) ).
fof(f356,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f352,f211]) ).
fof(f357,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF23)
| inverse2(X0,X1) = inverse4(sK16,sK17,X0,X1) ),
inference(superposition,[],[f344,f230]) ).
fof(f358,plain,
! [X0] : inverse2(sK18,X0) = inverse4(sK16,sK17,sK18,X0),
inference(resolution,[],[f357,f231]) ).
fof(f360,plain,
sF22 = inverse2(sK18,sK17),
inference(superposition,[],[f227,f358]) ).
fof(f361,plain,
! [X0,X1] :
( ~ ilf_type(X0,sF23)
| image(X0,X1) = image4(sK16,sK17,X0,X1) ),
inference(superposition,[],[f346,f230]) ).
fof(f362,plain,
! [X0] : image(sK18,X0) = image4(sK16,sK17,sK18,X0),
inference(resolution,[],[f361,f231]) ).
fof(f364,plain,
sF20 = image(sK18,sK16),
inference(superposition,[],[f223,f362]) ).
fof(f365,plain,
! [X0] :
( ~ ilf_type(X0,sF23)
| domain_of(X0) = domain(sK16,sK17,X0) ),
inference(superposition,[],[f308,f230]) ).
fof(f366,plain,
domain(sK16,sK17,sK18) = domain_of(sK18),
inference(resolution,[],[f365,f231]) ).
fof(f367,plain,
sF21 = domain_of(sK18),
inference(forward_demodulation,[],[f366,f225]) ).
fof(f368,plain,
! [X0] :
( ~ ilf_type(X0,sF23)
| range_of(X0) = range(sK16,sK17,X0) ),
inference(superposition,[],[f306,f230]) ).
fof(f369,plain,
range(sK16,sK17,sK18) = range_of(sK18),
inference(resolution,[],[f368,f231]) ).
fof(f370,plain,
sF19 = range_of(sK18),
inference(forward_demodulation,[],[f369,f221]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f337,f339]) ).
fof(f425,plain,
! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,range_of(X1)) ),
inference(duplicate_literal_removal,[],[f415]) ).
fof(f436,plain,
! [X0] :
( ~ member(X0,sF20)
| ~ ilf_type(sK18,binary_relation_type)
| member(X0,range_of(sK18)) ),
inference(superposition,[],[f425,f364]) ).
fof(f437,plain,
! [X0] :
( member(X0,sF19)
| ~ member(X0,sF20)
| ~ ilf_type(sK18,binary_relation_type) ),
inference(forward_demodulation,[],[f436,f370]) ).
fof(f439,definition,
( spl24_3
<=> ilf_type(sK18,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl24_3])],[avatar_definition]) ).
fof(f440,plain,
( ilf_type(sK18,binary_relation_type)
| ~ spl24_3 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f441,plain,
( ~ ilf_type(sK18,binary_relation_type)
| spl24_3 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f443,definition,
( spl24_4
<=> ! [X0] :
( member(X0,sF19)
| ~ member(X0,sF20) ) ),
introduced(definition,[new_symbols(definition,[spl24_4])],[avatar_definition]) ).
fof(f444,plain,
( ! [X0] :
( ~ member(X0,sF20)
| member(X0,sF19) )
| ~ spl24_4 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( ~ spl24_3
| spl24_4 ),
inference(avatar_split_clause,[],[f437,f443,f439]) ).
fof(f446,plain,
( ~ relation_like(sK18)
| spl24_3 ),
inference(resolution,[],[f441,f278]) ).
fof(f450,plain,
! [X2,X0,X1] :
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f334,f340]) ).
fof(f459,plain,
! [X2,X0,X1] :
( ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,domain_of(X1)) ),
inference(duplicate_literal_removal,[],[f450]) ).
fof(f472,plain,
! [X0] :
( ~ member(X0,sF22)
| ~ ilf_type(sK18,binary_relation_type)
| member(X0,domain_of(sK18)) ),
inference(superposition,[],[f459,f360]) ).
fof(f476,plain,
! [X2,X0,X1] :
( ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,inverse2(X1,X2))
| ~ member(sK0(X0,X1),X2)
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f299,f353]) ).
fof(f477,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,relation_type(X3,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(sK0(X0,X1),X2)
| ~ member(X0,domain_of(X1)) ),
inference(resolution,[],[f299,f355]) ).
fof(f478,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,X2)
| ~ member(X0,domain_of(X1)) ),
inference(resolution,[],[f299,f356]) ).
fof(f482,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,X1),X2)
| ~ ilf_type(X1,binary_relation_type)
| member(X0,inverse2(X1,X2))
| ~ member(X0,domain_of(X1)) ),
inference(duplicate_literal_removal,[],[f476]) ).
fof(f486,plain,
! [X0,X1] :
( member(sK0(X1,X0),sK17)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,sF23)
| ~ member(X1,domain_of(X0)) ),
inference(superposition,[],[f477,f230]) ).
fof(f487,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,sF23)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type)
| member(X1,inverse2(X0,sK17))
| ~ member(X1,domain_of(X0)) ),
inference(resolution,[],[f486,f482]) ).
fof(f488,plain,
! [X0,X1] :
( member(X1,inverse2(X0,sK17))
| ~ ilf_type(X0,sF23)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(duplicate_literal_removal,[],[f487]) ).
fof(f506,plain,
! [X0] :
( member(X0,sF22)
| ~ ilf_type(sK18,sF23)
| ~ member(X0,domain_of(sK18))
| ~ ilf_type(sK18,binary_relation_type) ),
inference(superposition,[],[f488,f360]) ).
fof(f508,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type)
| member(X1,sK16)
| ~ ilf_type(X0,sF23) ),
inference(superposition,[],[f478,f230]) ).
fof(f519,plain,
! [X0] :
( ~ member(X0,sF21)
| ~ ilf_type(sK18,binary_relation_type)
| member(X0,sK16)
| ~ ilf_type(sK18,sF23) ),
inference(superposition,[],[f508,f367]) ).
fof(f629,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f327,f310]) ).
fof(f630,plain,
! [X0] :
( ~ ilf_type(X0,sF23)
| relation_like(X0) ),
inference(superposition,[],[f629,f230]) ).
fof(f631,plain,
relation_like(sK18),
inference(resolution,[],[f630,f231]) ).
fof(f632,plain,
( $false
| spl24_3 ),
inference(forward_subsumption_resolution,[],[f631,f446]) ).
fof(f633,plain,
spl24_3,
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f634,plain,
( ! [X0] :
( ~ member(X0,sF22)
| member(X0,domain_of(sK18)) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f472,f440]) ).
fof(f636,plain,
! [X0] :
( member(X0,sF22)
| ~ member(X0,domain_of(sK18))
| ~ ilf_type(sK18,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f506,f231]) ).
fof(f637,plain,
( ! [X0] :
( ~ member(X0,sF21)
| member(X0,sK16)
| ~ ilf_type(sK18,sF23) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f519,f440]) ).
fof(f655,plain,
( ! [X0] :
( ~ member(X0,sF22)
| member(X0,sF21) )
| ~ spl24_3 ),
inference(forward_demodulation,[],[f634,f367]) ).
fof(f657,plain,
( ! [X0] :
( member(X0,sF22)
| ~ member(X0,domain_of(sK18)) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f636,f440]) ).
fof(f658,plain,
( ! [X0] :
( ~ member(X0,sF21)
| member(X0,sK16) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f637,f231]) ).
fof(f673,plain,
( ! [X0] :
( ~ member(X0,sF21)
| member(X0,sF22) )
| ~ spl24_3 ),
inference(forward_demodulation,[],[f657,f367]) ).
fof(f718,plain,
( ! [X0] :
( member(sK8(sF21,X0),sF22)
| member(sK8(sF21,X0),X0)
| sF21 = X0 )
| ~ spl24_3 ),
inference(resolution,[],[f673,f321]) ).
fof(f834,plain,
( ! [X0] :
( member(sK4(sF20,X0),sF19)
| member(sK4(sF20,X0),X0)
| sF20 = X0 )
| ~ spl24_4 ),
inference(resolution,[],[f444,f331]) ).
fof(f944,plain,
( member(sK8(sF21,sF22),sF22)
| sF21 = sF22
| ~ spl24_3 ),
inference(factoring,[],[f718]) ).
fof(f1029,plain,
( ! [X0] :
( member(sK8(X0,sF22),sF21)
| member(sK8(X0,sF22),X0)
| sF22 = X0 )
| ~ spl24_3 ),
inference(resolution,[],[f655,f321]) ).
fof(f1239,plain,
( member(sK8(sF21,sF22),sF21)
| sF21 = sF22
| ~ spl24_3 ),
inference(factoring,[],[f1029]) ).
fof(f1409,plain,
( member(sK4(sF20,sF19),sF19)
| sF19 = sF20
| ~ spl24_4 ),
inference(factoring,[],[f834]) ).
fof(f1412,plain,
( member(sK4(sF20,sF19),sF19)
| spl24_2
| ~ spl24_4 ),
inference(forward_subsumption_resolution,[],[f1409,f244]) ).
fof(f1413,plain,
( sF19 = sF20
| ~ member(sK4(sF20,sF19),sF20)
| spl24_2
| ~ spl24_4 ),
inference(resolution,[],[f1412,f332]) ).
fof(f1414,plain,
( ~ member(sK4(sF20,sF19),sF20)
| spl24_2
| ~ spl24_4 ),
inference(forward_subsumption_resolution,[],[f1413,f244]) ).
fof(f1656,plain,
! [X2,X0,X1] :
( ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,image(X1,X2))
| ~ member(sK1(X0,X1),X2)
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f297,f354]) ).
fof(f1657,plain,
! [X2,X0,X1] :
( ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(sK1(X0,X1),inverse2(X1,X2))
| ~ member(X0,X2)
| ~ ilf_type(X1,binary_relation_type) ),
inference(resolution,[],[f297,f353]) ).
fof(f1658,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,relation_type(X3,X2))
| ~ ilf_type(X1,binary_relation_type)
| member(X0,X2)
| ~ member(X0,range_of(X1)) ),
inference(resolution,[],[f297,f355]) ).
fof(f1671,plain,
! [X2,X0,X1] :
( member(sK1(X0,X1),inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,range_of(X1))
| ~ member(X0,X2) ),
inference(duplicate_literal_removal,[],[f1657]) ).
fof(f1672,plain,
! [X2,X0,X1] :
( ~ member(sK1(X0,X1),X2)
| ~ ilf_type(X1,binary_relation_type)
| member(X0,image(X1,X2))
| ~ member(X0,range_of(X1)) ),
inference(duplicate_literal_removal,[],[f1656]) ).
fof(f1686,plain,
! [X0] :
( member(sK1(X0,sK18),sF22)
| ~ ilf_type(sK18,binary_relation_type)
| ~ member(X0,range_of(sK18))
| ~ member(X0,sK17) ),
inference(superposition,[],[f1671,f360]) ).
fof(f1690,plain,
( ! [X0] :
( member(sK1(X0,sK18),sF22)
| ~ member(X0,range_of(sK18))
| ~ member(X0,sK17) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f1686,f440]) ).
fof(f1737,plain,
! [X0,X1] :
( ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type)
| member(X1,sK17)
| ~ ilf_type(X0,sF23) ),
inference(superposition,[],[f1658,f230]) ).
fof(f1772,plain,
! [X0] :
( ~ member(X0,sF19)
| ~ ilf_type(sK18,binary_relation_type)
| member(X0,sK17)
| ~ ilf_type(sK18,sF23) ),
inference(superposition,[],[f1737,f370]) ).
fof(f1774,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(X0,sK17)
| ~ ilf_type(sK18,sF23) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f1772,f440]) ).
fof(f1787,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(X0,sK17) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f1774,f231]) ).
fof(f2018,plain,
( member(sK8(sF21,sF22),sF22)
| spl24_1
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f944,f240]) ).
fof(f2026,plain,
( member(sK8(sF21,sF22),sF21)
| spl24_1
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f1239,f240]) ).
fof(f2066,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(sK1(X0,sK18),sF22)
| ~ member(X0,sK17) )
| ~ spl24_3 ),
inference(forward_demodulation,[],[f1690,f370]) ).
fof(f2140,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(sK1(X0,sK18),sF22) )
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f2066,f1787]) ).
fof(f2233,plain,
( sF21 = sF22
| ~ member(sK8(sF21,sF22),sF21)
| spl24_1
| ~ spl24_3 ),
inference(resolution,[],[f2018,f322]) ).
fof(f2235,plain,
( ~ member(sK8(sF21,sF22),sF21)
| spl24_1
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f2233,f240]) ).
fof(f2236,plain,
( $false
| spl24_1
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f2235,f2026]) ).
fof(f2237,plain,
( spl24_1
| ~ spl24_3 ),
inference(avatar_contradiction_clause,[],[f2236]) ).
fof(f2360,plain,
( ! [X0] :
( member(sK1(X0,sK18),sF21)
| ~ member(X0,sF19) )
| ~ spl24_1
| ~ spl24_3 ),
inference(forward_demodulation,[],[f2140,f239]) ).
fof(f2951,plain,
( ! [X0] :
( member(sK1(X0,sK18),sK16)
| ~ member(X0,sF19) )
| ~ spl24_1
| ~ spl24_3 ),
inference(resolution,[],[f2360,f658]) ).
fof(f2996,plain,
( ! [X0] :
( ~ member(X0,sF19)
| ~ ilf_type(sK18,binary_relation_type)
| member(X0,image(sK18,sK16))
| ~ member(X0,range_of(sK18)) )
| ~ spl24_1
| ~ spl24_3 ),
inference(resolution,[],[f2951,f1672]) ).
fof(f2997,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(X0,image(sK18,sK16))
| ~ member(X0,range_of(sK18)) )
| ~ spl24_1
| ~ spl24_3 ),
inference(forward_subsumption_resolution,[],[f2996,f440]) ).
fof(f2998,plain,
( ! [X0] :
( member(X0,sF20)
| ~ member(X0,sF19)
| ~ member(X0,range_of(sK18)) )
| ~ spl24_1
| ~ spl24_3 ),
inference(forward_demodulation,[],[f2997,f364]) ).
fof(f2999,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(X0,sF20)
| ~ member(X0,sF19) )
| ~ spl24_1
| ~ spl24_3 ),
inference(forward_demodulation,[],[f2998,f370]) ).
fof(f3000,plain,
( ! [X0] :
( ~ member(X0,sF19)
| member(X0,sF20) )
| ~ spl24_1
| ~ spl24_3 ),
inference(duplicate_literal_removal,[],[f2999]) ).
fof(f3020,plain,
( member(sK4(sF20,sF19),sF20)
| ~ spl24_1
| spl24_2
| ~ spl24_3
| ~ spl24_4 ),
inference(resolution,[],[f3000,f1412]) ).
fof(f3046,plain,
( $false
| ~ spl24_1
| spl24_2
| ~ spl24_3
| ~ spl24_4 ),
inference(forward_subsumption_resolution,[],[f3020,f1414]) ).
fof(f3047,plain,
( ~ spl24_1
| spl24_2
| ~ spl24_3
| ~ spl24_4 ),
inference(avatar_contradiction_clause,[],[f3046]) ).
cnf(s1,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(sat_conversion,[],[f245]) ).
cnf(s2,plain,
( ~ spl24_3
| spl24_4 ),
inference(sat_conversion,[],[f445]) ).
cnf(s3,plain,
spl24_3,
inference(sat_conversion,[],[f633]) ).
cnf(s63,plain,
( spl24_1
| ~ spl24_3 ),
inference(sat_conversion,[],[f2237]) ).
cnf(s90,plain,
( ~ spl24_1
| spl24_2
| ~ spl24_3
| ~ spl24_4 ),
inference(sat_conversion,[],[f3047]) ).
cnf(s91,plain,
spl24_1,
inference(rat,[],[s63,s3]) ).
cnf(s92,plain,
spl24_4,
inference(rat,[],[s2,s3]) ).
cnf(s93,plain,
spl24_2,
inference(rat,[],[s90,s91,s3,s92]) ).
cnf(s94,plain,
$false,
inference(rat,[],[s1,s93,s91]) ).
fof(f3066,plain,
$false,
inference(avatar_sat_refutation,[],[s94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET674+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 02:30:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 9.45/2.19 % (1812915)Detected formulas, will run a generic FOF schedule.
% 9.45/2.19 % (1812926)dis-21_1_sil=8000:lcm=predicate:random_seed=3073256370: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)
% 9.45/2.19 % (1812926)Instruction limit reached!
% 9.45/2.19 % (1812926)------------------------------
% 9.45/2.19 % (1812926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812926)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812926)Termination reason: Instruction limit
% 9.45/2.19 % (1812926)Termination phase: Saturation
% 9.45/2.19 % (1812926)Time elapsed: 0.043 s
% 9.45/2.19 % (1812926)Peak memory usage: 90 MB
% 9.45/2.19 % (1812926)Instructions burned: 130 (million)
% 9.45/2.19 % (1812922)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=3220497785:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.45/2.19 % (1812924)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2185804068:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.45/2.19 % (1812920)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=2282926499:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.45/2.19 % (1812923)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2366618985:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.45/2.19 % (1812921)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=2898336833:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.45/2.19 % (1812925)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=442151669:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.45/2.19 % (1812923)Refutation not found, incomplete strategy
% 9.45/2.19 % (1812923)------------------------------
% 9.45/2.19 % (1812923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812923)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812923)Termination reason: Refutation not found, incomplete strategy
% 9.45/2.19 % (1812923)Time elapsed: 0.003 s
% 9.45/2.19 % (1812923)Peak memory usage: 88 MB
% 9.45/2.19 % (1812923)Instructions burned: 2 (million)
% 9.45/2.19 % (1812924)Instruction limit reached!
% 9.45/2.19 % (1812924)------------------------------
% 9.45/2.19 % (1812924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812924)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812924)Termination reason: Instruction limit
% 9.45/2.19 % (1812924)Termination phase: Saturation
% 9.45/2.19 % (1812924)Time elapsed: 0.072 s
% 9.45/2.19 % (1812924)Peak memory usage: 89 MB
% 9.45/2.19 % (1812924)Instructions burned: 121 (million)
% 9.45/2.19 % (1812925)Instruction limit reached!
% 9.45/2.19 % (1812925)------------------------------
% 9.45/2.19 % (1812925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812925)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812925)Termination reason: Instruction limit
% 9.45/2.19 % (1812925)Termination phase: Saturation
% 9.45/2.19 % (1812925)Time elapsed: 0.098 s
% 9.45/2.19 % (1812925)Peak memory usage: 90 MB
% 9.45/2.19 % (1812925)Instructions burned: 140 (million)
% 9.45/2.19 % (1812933)lrs+10_1_sil=8000:sp=occurrence:random_seed=2445022009:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.45/2.19 % (1812933)Instruction limit reached!
% 9.45/2.19 % (1812933)------------------------------
% 9.45/2.19 % (1812933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812933)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812933)Termination reason: Instruction limit
% 9.45/2.19 % (1812933)Termination phase: Saturation
% 9.45/2.19 % (1812933)Time elapsed: 0.095 s
% 9.45/2.19 % (1812933)Peak memory usage: 92 MB
% 9.45/2.19 % (1812933)Instructions burned: 287 (million)
% 9.45/2.19 % (1812935)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3314379893:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.45/2.19 % (1812935)Refutation not found, incomplete strategy
% 9.45/2.19 % (1812935)------------------------------
% 9.45/2.19 % (1812935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812935)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812935)Termination reason: Refutation not found, incomplete strategy
% 9.45/2.19 % (1812935)Time elapsed: 0.005 s
% 9.45/2.19 % (1812935)Peak memory usage: 89 MB
% 9.45/2.19 % (1812935)Instructions burned: 5 (million)
% 9.45/2.19 % (1812923)------------------------------
% 9.45/2.19 % (1812923)------------------------------
% 9.45/2.19 % (1812936)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1071698334:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.45/2.19 % (1812936)Refutation not found, incomplete strategy
% 9.45/2.19 % (1812936)------------------------------
% 9.45/2.19 % (1812936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812936)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812936)Termination reason: Refutation not found, incomplete strategy
% 9.45/2.19 % (1812936)Time elapsed: 0.005 s
% 9.45/2.19 % (1812936)Peak memory usage: 88 MB
% 9.45/2.19 % (1812936)Instructions burned: 5 (million)
% 9.45/2.19 % (1812938)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=1055837295:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 9.45/2.19 % (1812938)Instruction limit reached!
% 9.45/2.19 % (1812938)------------------------------
% 9.45/2.19 % (1812938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812940)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3244399499:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.45/2.19 % (1812938)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812938)Termination reason: Instruction limit
% 9.45/2.19 % (1812938)Termination phase: Saturation
% 9.45/2.19 % (1812938)Time elapsed: 0.092 s
% 9.45/2.19 % (1812938)Peak memory usage: 91 MB
% 9.45/2.19 % (1812938)Instructions burned: 250 (million)
% 9.45/2.19 % (1812940)Refutation not found, incomplete strategy
% 9.45/2.19 % (1812940)------------------------------
% 9.45/2.19 % (1812940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812940)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812940)Termination reason: Refutation not found, incomplete strategy
% 9.45/2.19 % (1812940)Time elapsed: 0.004 s
% 9.45/2.19 % (1812940)Peak memory usage: 88 MB
% 9.45/2.19 % (1812940)Instructions burned: 4 (million)
% 9.45/2.19 % (1812935)------------------------------
% 9.45/2.19 % (1812935)------------------------------
% 9.45/2.19 % (1812936)------------------------------
% 9.45/2.19 % (1812936)------------------------------
% 9.45/2.19 % (1812944)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4290044551:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 9.45/2.19 % (1812945)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3262782982:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 9.45/2.19 % (1812940)------------------------------
% 9.45/2.19 % (1812940)------------------------------
% 9.45/2.19 % (1812946)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=711363097:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 9.45/2.19 % (1812945)Instruction limit reached!
% 9.45/2.19 % (1812945)------------------------------
% 9.45/2.19 % (1812945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812945)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812945)Termination reason: Instruction limit
% 9.45/2.19 % (1812945)Termination phase: Saturation
% 9.45/2.19 % (1812945)Time elapsed: 0.073 s
% 9.45/2.19 % (1812945)Peak memory usage: 90 MB
% 9.45/2.19 % (1812945)Instructions burned: 114 (million)
% 9.45/2.19 % (1812946)Instruction limit reached!
% 9.45/2.19 % (1812946)------------------------------
% 9.45/2.19 % (1812946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812946)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812946)Termination reason: Instruction limit
% 9.45/2.19 % (1812946)Termination phase: Saturation
% 9.45/2.19 % (1812946)Time elapsed: 0.065 s
% 9.45/2.19 % (1812946)Peak memory usage: 89 MB
% 9.45/2.19 % (1812946)Instructions burned: 128 (million)
% 9.45/2.19 % (1812949)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2475544332:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 9.45/2.19 % (1812949)Refutation not found, incomplete strategy
% 9.45/2.19 % (1812949)------------------------------
% 9.45/2.19 % (1812949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812949)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812949)Termination reason: Refutation not found, incomplete strategy
% 9.45/2.19 % (1812949)Time elapsed: 0.005 s
% 9.45/2.19 % (1812949)Peak memory usage: 89 MB
% 9.45/2.19 % (1812949)Instructions burned: 6 (million)
% 9.45/2.19 % (1812951)lrs+10_1_sil=8000:sp=occurrence:random_seed=3461363930:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.45/2.19 % (1812920)First to succeed.
% 9.45/2.19 % (1812920)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1812915"
% 9.45/2.19 % (1812952)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4165683211:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.45/2.19 % (1812952)Refutation not found, incomplete strategy
% 9.45/2.19 % (1812952)------------------------------
% 9.45/2.19 % (1812952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.45/2.19 % (1812952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.45/2.19 % (1812952)CaDiCaL version: 2.1.3
% 9.45/2.19 % (1812952)Termination reason: Refutation not found, incomplete strategy
% 9.45/2.19 % (1812952)Time elapsed: 0.004 s
% 9.45/2.19 % (1812952)Peak memory usage: 88 MB
% 9.45/2.19 % (1812952)Instructions burned: 6 (million)
% 9.45/2.19 % (1812949)------------------------------
% 9.45/2.19 % (1812949)------------------------------
% 9.45/2.19 % (1812920)Refutation found. Thanks to Tanya!
% 9.45/2.19 % SZS status Theorem for theBenchmark
% 9.45/2.19 % SZS output start Proof for theBenchmark
% See solution above
% 10.00/2.39 % (1812920)------------------------------
% 10.00/2.39 % (1812920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.00/2.39 % (1812920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.00/2.39 % (1812920)CaDiCaL version: 2.1.3
% 10.00/2.39 % (1812920)Termination reason: Refutation
% 10.00/2.39 % (1812920)Time elapsed: 0.902 s
% 10.00/2.39 % (1812920)Peak memory usage: 132 MB
% 10.00/2.39 % (1812920)Instructions burned: 1364 (million)
% 10.00/2.39 % (1812920)------------------------------
% 10.00/2.39 % (1812920)------------------------------
% 10.00/2.39 % (1812915)Success in time 1.338 s
% 10.00/2.39 % Vampire exiting
%------------------------------------------------------------------------------