%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET660+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:41:34 PM UTC 2026
% Result : Theorem 3.41s 1.34s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 22
% Syntax : Number of formulae : 199 ( 13 unt; 8 def)
% Number of atoms : 796 ( 44 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1023 ( 426 ~; 444 |; 83 &)
% ( 27 <=>; 41 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 316 ( 0 sgn 283 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,range_of(X0))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X1),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
fof(f20,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/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f27,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f32,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/sandbox2/benchmark/theBenchmark.p',p32) ).
fof(f33,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(f35,conjecture,
! [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)
=> ( member(X3,X1)
=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X3),X2) ) ) )
<=> range(X0,X1,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_23) ).
fof(f36,negated_conjecture,
~ ! [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)
=> ( member(X3,X1)
=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X3),X2) ) ) )
<=> range(X0,X1,X2) = X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( member(X1,range_of(X0))
<=> ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X1),X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f45,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,[],[f7]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f57,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,[],[f20]) ).
fof(f58,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,[],[f57]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f63]) ).
fof(f69,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,[],[f27]) ).
fof(f75,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,[],[f32]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f77,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ! [X3] :
( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X3),X2) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
<~> range(X0,X1,X2) = X1 )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ! [X3] :
( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X3),X2) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
<~> range(X0,X1,X2) = X1 )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X1),X0) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f37]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0) ) )
& ( ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X0) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0) ) )
& ( ( ilf_type(sK0(X0,X1),set_type)
& member(ordered_pair(sK0(X0,X1),X1),X0) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f80]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f47]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f87]) ).
fof(f89,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,[],[f53]) ).
fof(f90,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,[],[f89]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f54]) ).
fof(f98,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,[],[f58]) ).
fof(f99,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,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(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,[sK6]),skolemize(X2,sK6(X0,X1))],[f99]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f61]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f64]) ).
fof(f112,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,X3),X2) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(X0,X1,X2) = X1
| ! [X3] :
( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X3),X2) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f78]) ).
fof(f113,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,X3),X2) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(X0,X1,X2) = X1
| ! [X3] :
( ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X3),X2) )
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) ) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ? [X3] :
( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,X3),X2) )
& member(X3,X1)
& ilf_type(X3,set_type) ) )
& ( range(X0,X1,X2) = X1
| ! [X5] :
( ? [X6] :
( ilf_type(X6,set_type)
& member(ordered_pair(X6,X5),X2) )
| ~ member(X5,X1)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
( ( sK14 != range(sK13,sK14,sK15)
| ( ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,sK16),sK15) )
& member(sK16,sK14)
& ilf_type(sK16,set_type) ) )
& ( sK14 = range(sK13,sK14,sK15)
| ! [X5] :
( ( ilf_type(sK17(X5),set_type)
& member(ordered_pair(sK17(X5),X5),sK15) )
| ~ member(X5,sK14)
| ~ ilf_type(X5,set_type) ) )
& ilf_type(sK15,relation_type(sK13,sK14))
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16),skolemize(X6,sK17(X5))],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f118,plain,
! [X2,X0,X1] :
( member(X1,range_of(X0))
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f128,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,[],[f45]) ).
fof(f133,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f141,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
fof(f143,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f151,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,[],[f100]) ).
fof(f153,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f100]) ).
fof(f154,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f100]) ).
fof(f156,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f103]) ).
fof(f161,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f62]) ).
fof(f162,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f104]) ).
fof(f171,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,[],[f69]) ).
fof(f178,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,[],[f75]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f180,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f183,plain,
ilf_type(sK15,relation_type(sK13,sK14)),
inference(cnf_transformation,[],[f115]) ).
fof(f184,plain,
! [X5] :
( sK14 = range(sK13,sK14,sK15)
| member(ordered_pair(sK17(X5),X5),sK15)
| ~ member(X5,sK14)
| ~ ilf_type(X5,set_type) ),
inference(cnf_transformation,[],[f115]) ).
fof(f187,plain,
( sK14 != range(sK13,sK14,sK15)
| member(sK16,sK14) ),
inference(cnf_transformation,[],[f115]) ).
fof(f188,plain,
! [X4] :
( sK14 != range(sK13,sK14,sK15)
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,sK16),sK15) ),
inference(cnf_transformation,[],[f115]) ).
fof(f197,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f201,definition,
( spl18_1
<=> ! [X5] :
( member(ordered_pair(sK17(X5),X5),sK15)
| ~ ilf_type(X5,set_type)
| ~ member(X5,sK14) ) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f202,plain,
( ! [X5] :
( member(ordered_pair(sK17(X5),X5),sK15)
| ~ ilf_type(X5,set_type)
| ~ member(X5,sK14) )
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,definition,
( spl18_2
<=> sK14 = range(sK13,sK14,sK15) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f205,plain,
( sK14 != range(sK13,sK14,sK15)
| spl18_2 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f206,plain,
( sK14 = range(sK13,sK14,sK15)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f184,f204,f201]) ).
fof(f218,definition,
( spl18_5
<=> member(sK16,sK14) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f220,plain,
( member(sK16,sK14)
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,plain,
( spl18_5
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f187,f204,f218]) ).
fof(f223,definition,
( spl18_6
<=> ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X4,sK16),sK15) ) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f224,plain,
( ! [X4] :
( ~ member(ordered_pair(X4,sK16),sK15)
| ~ ilf_type(X4,set_type) )
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f225,plain,
( spl18_6
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f188,f204,f223]) ).
fof(f246,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[],[f161,f180]) ).
fof(f250,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f197,f180]) ).
fof(f275,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK6(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f153,f180]) ).
fof(f276,plain,
! [X0,X1] :
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(forward_subsumption_resolution,[],[f275,f180]) ).
fof(f277,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f154,f180]) ).
fof(f278,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK6(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f277,f180]) ).
fof(f279,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,[],[f171,f180]) ).
fof(f280,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f279,f180]) ).
fof(f281,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f133,f180]) ).
fof(f282,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(forward_subsumption_resolution,[],[f281,f180]) ).
fof(f284,plain,
! [X0,X1] :
( ~ member(sK6(X0,X1),X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(resolution,[],[f282,f278]) ).
fof(f286,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f143,f180]) ).
fof(f287,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(forward_subsumption_resolution,[],[f286,f180]) ).
fof(f303,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f162,f180]) ).
fof(f304,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(forward_subsumption_resolution,[],[f303,f180]) ).
fof(f325,plain,
! [X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ member(X1,range_of(X0))
| member(ordered_pair(sK0(X0,X1),X1),X0) ),
inference(forward_subsumption_resolution,[],[f116,f180]) ).
fof(f327,plain,
! [X0,X1] :
( member(ordered_pair(sK0(X1,X0),X0),X1)
| ~ member(X0,range_of(X1))
| ~ relation_like(X1) ),
inference(resolution,[],[f325,f250]) ).
fof(f331,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,[],[f128,f180]) ).
fof(f332,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f331,f180]) ).
fof(f341,plain,
! [X2,X0,X1] :
( member(X1,range_of(X0))
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f118,f180]) ).
fof(f342,plain,
! [X2,X0,X1] :
( member(X1,range_of(X0))
| ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[],[f341,f180]) ).
fof(f344,plain,
( ~ member(sK16,range_of(sK15))
| ~ relation_like(sK15)
| ~ ilf_type(sK0(sK15,sK16),set_type)
| ~ spl18_6 ),
inference(resolution,[],[f327,f224]) ).
fof(f385,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,[],[f151,f180]) ).
fof(f386,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f385,f180]) ).
fof(f387,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(forward_subsumption_resolution,[],[f386,f180]) ).
fof(f389,plain,
! [X2,X0,X1] :
( ~ member(sK6(X1,X2),X2)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[],[f387,f278]) ).
fof(f415,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,[],[f178,f180]) ).
fof(f416,plain,
! [X2,X0,X1] :
( range_of(X2) = range(X0,X1,X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f415,f180]) ).
fof(f418,plain,
( sK14 = range_of(sK15)
| ~ ilf_type(sK15,relation_type(sK13,sK14))
| ~ spl18_2 ),
inference(superposition,[],[f206,f416]) ).
fof(f419,plain,
( sK14 = range_of(sK15)
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f418,f183]) ).
fof(f431,plain,
( ~ member(sK16,range_of(sK15))
| ~ relation_like(sK15)
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f344,f180]) ).
fof(f436,definition,
( spl18_17
<=> ilf_type(sK15,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[spl18_17])],[avatar_definition]) ).
fof(f437,plain,
( ilf_type(sK15,binary_relation_type)
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f438,plain,
( ~ ilf_type(sK15,binary_relation_type)
| spl18_17 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f443,plain,
( ~ member(sK16,sK14)
| ~ relation_like(sK15)
| ~ spl18_2
| ~ spl18_6 ),
inference(forward_demodulation,[],[f431,f419]) ).
fof(f444,plain,
( ~ relation_like(sK15)
| ~ spl18_2
| ~ spl18_5
| ~ spl18_6 ),
inference(forward_subsumption_resolution,[],[f443,f220]) ).
fof(f445,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f179,f180]) ).
fof(f446,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f445,f180]) ).
fof(f448,plain,
! [X2,X0,X1] :
( ilf_type(range_of(X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(superposition,[],[f446,f416]) ).
fof(f449,plain,
! [X2,X0,X1] :
( ilf_type(range_of(X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(duplicate_literal_removal,[],[f448]) ).
fof(f451,plain,
( ! [X0,X1] : ~ ilf_type(sK15,subset_type(cross_product(X0,X1)))
| ~ spl18_2
| ~ spl18_5
| ~ spl18_6 ),
inference(resolution,[],[f444,f280]) ).
fof(f468,plain,
( ~ relation_like(sK15)
| spl18_17 ),
inference(resolution,[],[f438,f250]) ).
fof(f490,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f156,f180]) ).
fof(f491,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f490,f180]) ).
fof(f492,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[],[f491,f180]) ).
fof(f498,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| ~ member(X2,power_set(X1))
| ~ member(sK6(X0,X1),X2)
| X0 = X1 ),
inference(resolution,[],[f492,f284]) ).
fof(f569,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,X2)
| ~ member(ordered_pair(X3,sK6(X2,range_of(X1))),X1)
| member(X0,range_of(X1)) ),
inference(resolution,[],[f389,f342]) ).
fof(f652,plain,
( ! [X0,X1] : ~ ilf_type(sK15,relation_type(X0,X1))
| ~ spl18_2
| ~ spl18_5
| ~ spl18_6 ),
inference(resolution,[],[f451,f332]) ).
fof(f656,plain,
( $false
| ~ spl18_2
| ~ spl18_5
| ~ spl18_6 ),
inference(resolution,[],[f652,f183]) ).
fof(f658,plain,
( ~ spl18_2
| ~ spl18_5
| ~ spl18_6 ),
inference(avatar_contradiction_clause,[],[f656]) ).
fof(f659,plain,
( ! [X5] :
( member(ordered_pair(sK17(X5),X5),sK15)
| ~ member(X5,sK14) )
| ~ spl18_1 ),
inference(forward_subsumption_resolution,[],[f202,f180]) ).
fof(f661,definition,
( spl18_31
<=> relation_like(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_31])],[avatar_definition]) ).
fof(f663,plain,
( ~ relation_like(sK15)
| spl18_31 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f669,plain,
( ~ spl18_31
| spl18_17 ),
inference(avatar_split_clause,[],[f468,f436,f661]) ).
fof(f671,plain,
( sK14 != range_of(sK15)
| ~ ilf_type(sK15,relation_type(sK13,sK14))
| spl18_2 ),
inference(superposition,[],[f205,f416]) ).
fof(f672,plain,
( sK14 != range_of(sK15)
| spl18_2 ),
inference(forward_subsumption_resolution,[],[f671,f183]) ).
fof(f674,plain,
( ! [X0,X1] : ~ ilf_type(sK15,subset_type(cross_product(X0,X1)))
| spl18_31 ),
inference(resolution,[],[f663,f280]) ).
fof(f690,plain,
( ! [X0,X1] : ~ ilf_type(sK15,relation_type(X0,X1))
| spl18_31 ),
inference(resolution,[],[f674,f332]) ).
fof(f699,plain,
( $false
| spl18_31 ),
inference(resolution,[],[f690,f183]) ).
fof(f701,plain,
spl18_31,
inference(avatar_contradiction_clause,[],[f699]) ).
fof(f850,plain,
! [X2,X0,X1] :
( ~ member(sK6(X1,X2),X2)
| ~ member(sK6(X2,X1),X0)
| X1 = X2
| ~ member(X0,power_set(X1)) ),
inference(resolution,[],[f498,f278]) ).
fof(f896,plain,
( ! [X2,X0,X1] :
( ~ member(ordered_pair(X2,sK6(X1,range_of(sK15))),sK15)
| ~ member(X0,X1)
| member(X0,range_of(sK15)) )
| ~ spl18_17 ),
inference(resolution,[],[f569,f437]) ).
fof(f1340,plain,
( ! [X0,X1] :
( ~ member(sK6(X1,range_of(sK15)),sK14)
| member(X0,range_of(sK15))
| ~ member(X0,X1) )
| ~ spl18_1
| ~ spl18_17 ),
inference(resolution,[],[f896,f659]) ).
fof(f1447,plain,
( ! [X0] :
( member(X0,range_of(sK15))
| ~ member(X0,sK14)
| subset(sK14,range_of(sK15)) )
| ~ spl18_1
| ~ spl18_17 ),
inference(resolution,[],[f1340,f276]) ).
fof(f1452,definition,
( spl18_50
<=> member(sK6(sK14,range_of(sK15)),range_of(sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_50])],[avatar_definition]) ).
fof(f1454,plain,
( member(sK6(sK14,range_of(sK15)),range_of(sK15))
| ~ spl18_50 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f1456,definition,
( spl18_51
<=> member(sK6(sK14,range_of(sK15)),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_51])],[avatar_definition]) ).
fof(f1457,plain,
( member(sK6(sK14,range_of(sK15)),sK14)
| ~ spl18_51 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f1458,plain,
( ~ member(sK6(sK14,range_of(sK15)),sK14)
| spl18_51 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f1468,plain,
( ! [X0] :
( ~ member(X0,sK14)
| member(X0,range_of(sK15)) )
| ~ spl18_1
| ~ spl18_17 ),
inference(forward_subsumption_resolution,[],[f1447,f387]) ).
fof(f1472,plain,
( subset(sK14,range_of(sK15))
| spl18_51 ),
inference(resolution,[],[f1458,f276]) ).
fof(f1486,plain,
( ! [X0] :
( ~ member(X0,power_set(sK14))
| ~ member(sK6(range_of(sK15),sK14),X0)
| sK14 = range_of(sK15) )
| spl18_51 ),
inference(resolution,[],[f1472,f498]) ).
fof(f1488,plain,
( sK14 = range_of(sK15)
| ~ subset(range_of(sK15),sK14)
| spl18_51 ),
inference(resolution,[],[f1472,f282]) ).
fof(f1489,plain,
( ~ subset(range_of(sK15),sK14)
| spl18_2
| spl18_51 ),
inference(forward_subsumption_resolution,[],[f1488,f672]) ).
fof(f1490,plain,
( ! [X0] :
( ~ member(sK6(range_of(sK15),sK14),X0)
| ~ member(X0,power_set(sK14)) )
| spl18_2
| spl18_51 ),
inference(forward_subsumption_resolution,[],[f1486,f672]) ).
fof(f1594,plain,
( ! [X0] :
( member(sK6(sK14,X0),range_of(sK15))
| subset(sK14,X0) )
| ~ spl18_1
| ~ spl18_17 ),
inference(resolution,[],[f1468,f276]) ).
fof(f1666,plain,
( subset(sK14,range_of(sK15))
| ~ subset(range_of(sK15),sK14)
| sK14 = range_of(sK15)
| ~ spl18_1
| ~ spl18_17 ),
inference(resolution,[],[f1594,f284]) ).
fof(f2281,plain,
( ~ member(range_of(sK15),power_set(sK14))
| subset(range_of(sK15),sK14)
| spl18_2
| spl18_51 ),
inference(resolution,[],[f1490,f276]) ).
fof(f2287,plain,
( ~ member(range_of(sK15),power_set(sK14))
| spl18_2
| spl18_51 ),
inference(forward_subsumption_resolution,[],[f2281,f1489]) ).
fof(f2292,plain,
( ~ ilf_type(range_of(sK15),member_type(power_set(sK14)))
| empty(power_set(sK14))
| spl18_2
| spl18_51 ),
inference(resolution,[],[f2287,f304]) ).
fof(f2293,plain,
( ~ ilf_type(range_of(sK15),member_type(power_set(sK14)))
| spl18_2
| spl18_51 ),
inference(forward_subsumption_resolution,[],[f2292,f246]) ).
fof(f2300,plain,
( ~ ilf_type(range_of(sK15),subset_type(sK14))
| spl18_2
| spl18_51 ),
inference(resolution,[],[f2293,f287]) ).
fof(f2303,plain,
( ! [X0] : ~ ilf_type(sK15,relation_type(X0,sK14))
| spl18_2
| spl18_51 ),
inference(resolution,[],[f2300,f449]) ).
fof(f2310,plain,
( $false
| spl18_2
| spl18_51 ),
inference(resolution,[],[f2303,f183]) ).
fof(f2312,plain,
( spl18_2
| spl18_51 ),
inference(avatar_contradiction_clause,[],[f2310]) ).
fof(f2314,plain,
( ~ subset(range_of(sK15),sK14)
| sK14 = range_of(sK15)
| ~ spl18_1
| ~ spl18_17 ),
inference(forward_subsumption_resolution,[],[f1666,f282]) ).
fof(f2316,plain,
( ~ subset(range_of(sK15),sK14)
| ~ spl18_1
| spl18_2
| ~ spl18_17 ),
inference(forward_subsumption_resolution,[],[f2314,f672]) ).
fof(f2324,plain,
( member(sK6(sK14,range_of(sK15)),range_of(sK15))
| ~ spl18_1
| ~ spl18_17
| ~ spl18_51 ),
inference(resolution,[],[f1457,f1468]) ).
fof(f2327,plain,
( spl18_50
| ~ spl18_1
| ~ spl18_17
| ~ spl18_51 ),
inference(avatar_split_clause,[],[f2324,f1456,f436,f201,f1452]) ).
fof(f2347,plain,
( ! [X0] :
( ~ member(sK6(range_of(sK15),sK14),X0)
| sK14 = range_of(sK15)
| ~ member(X0,power_set(sK14)) )
| ~ spl18_50 ),
inference(resolution,[],[f1454,f850]) ).
fof(f2352,plain,
( ! [X0] :
( ~ member(sK6(range_of(sK15),sK14),X0)
| ~ member(X0,power_set(sK14)) )
| spl18_2
| ~ spl18_50 ),
inference(forward_subsumption_resolution,[],[f2347,f672]) ).
fof(f2367,plain,
( ~ member(range_of(sK15),power_set(sK14))
| subset(range_of(sK15),sK14)
| spl18_2
| ~ spl18_50 ),
inference(resolution,[],[f2352,f276]) ).
fof(f2373,plain,
( ~ member(range_of(sK15),power_set(sK14))
| ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(forward_subsumption_resolution,[],[f2367,f2316]) ).
fof(f2379,plain,
( ~ ilf_type(range_of(sK15),member_type(power_set(sK14)))
| empty(power_set(sK14))
| ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(resolution,[],[f2373,f304]) ).
fof(f2380,plain,
( ~ ilf_type(range_of(sK15),member_type(power_set(sK14)))
| ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(forward_subsumption_resolution,[],[f2379,f246]) ).
fof(f2392,plain,
( ~ ilf_type(range_of(sK15),subset_type(sK14))
| ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(resolution,[],[f2380,f287]) ).
fof(f2399,plain,
( ! [X0] : ~ ilf_type(sK15,relation_type(X0,sK14))
| ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(resolution,[],[f2392,f449]) ).
fof(f2404,plain,
( $false
| ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(resolution,[],[f2399,f183]) ).
fof(f2406,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(avatar_contradiction_clause,[],[f2404]) ).
cnf(s1,plain,
( spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f207]) ).
cnf(s4,plain,
( ~ spl18_2
| spl18_5 ),
inference(sat_conversion,[],[f221]) ).
cnf(s5,plain,
( ~ spl18_2
| spl18_6 ),
inference(sat_conversion,[],[f225]) ).
cnf(s29,plain,
( ~ spl18_2
| ~ spl18_5
| ~ spl18_6 ),
inference(sat_conversion,[],[f658]) ).
cnf(s31,plain,
( spl18_17
| ~ spl18_31 ),
inference(sat_conversion,[],[f669]) ).
cnf(s35,plain,
spl18_31,
inference(sat_conversion,[],[f701]) ).
cnf(s71,plain,
( spl18_2
| spl18_51 ),
inference(sat_conversion,[],[f2312]) ).
cnf(s73,plain,
( ~ spl18_1
| ~ spl18_17
| spl18_50
| ~ spl18_51 ),
inference(sat_conversion,[],[f2327]) ).
cnf(s74,plain,
( ~ spl18_1
| spl18_2
| ~ spl18_17
| ~ spl18_50 ),
inference(sat_conversion,[],[f2406]) ).
cnf(s76,plain,
spl18_17,
inference(rat,[],[s31,s35]) ).
cnf(s82,plain,
~ spl18_2,
inference(rat,[],[s29,s4,s5]) ).
cnf(s83,plain,
spl18_51,
inference(rat,[],[s71,s82]) ).
cnf(s85,plain,
spl18_1,
inference(rat,[],[s1,s82]) ).
cnf(s87,plain,
spl18_50,
inference(rat,[],[s73,s83,s76,s85]) ).
cnf(s88,plain,
$false,
inference(rat,[],[s74,s82,s76,s87,s85]) ).
fof(f2407,plain,
$false,
inference(avatar_sat_refutation,[],[s88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET660+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:31:27 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.41/1.34 % (3416647)Detected formulas, will run a generic FOF schedule.
% 3.41/1.34 % (3416702)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3389798175:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.41/1.34 % (3416702)Refutation not found, incomplete strategy
% 3.41/1.34 % (3416702)------------------------------
% 3.41/1.34 % (3416702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.34 % (3416702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.34 % (3416702)CaDiCaL version: 2.1.3
% 3.41/1.34 % (3416702)Termination reason: Refutation not found, incomplete strategy
% 3.41/1.34 % (3416702)Time elapsed: 0.002 s
% 3.41/1.34 % (3416702)Peak memory usage: 88 MB
% 3.41/1.34 % (3416702)Instructions burned: 2 (million)
% 3.41/1.34 % (3416704)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3122021022:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.41/1.34 % (3416703)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1741976960:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.41/1.34 % (3416705)dis-21_1_sil=8000:lcm=predicate:random_seed=939476474:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.41/1.34 % (3416699)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=2159514359:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.41/1.34 % (3416700)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=541933856:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.41/1.34 % (3416701)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=169417887:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.41/1.34 % (3416703)Instruction limit reached!
% 3.41/1.34 % (3416703)------------------------------
% 3.41/1.34 % (3416703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.34 % (3416703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.34 % (3416703)CaDiCaL version: 2.1.3
% 3.41/1.34 % (3416703)Termination reason: Instruction limit
% 3.41/1.34 % (3416703)Termination phase: Saturation
% 3.41/1.34 % (3416703)Time elapsed: 0.060 s
% 3.41/1.34 % (3416703)Peak memory usage: 88 MB
% 3.41/1.34 % (3416703)Instructions burned: 120 (million)
% 3.41/1.34 % (3416705)Instruction limit reached!
% 3.41/1.34 % (3416705)------------------------------
% 3.41/1.34 % (3416705)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.34 % (3416705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.34 % (3416705)CaDiCaL version: 2.1.3
% 3.41/1.34 % (3416705)Termination reason: Instruction limit
% 3.41/1.34 % (3416705)Termination phase: Saturation
% 3.41/1.34 % (3416705)Time elapsed: 0.079 s
% 3.41/1.34 % (3416705)Peak memory usage: 90 MB
% 3.41/1.34 % (3416705)Instructions burned: 129 (million)
% 3.41/1.34 % (3416704)First to succeed.
% 3.41/1.34 % (3416704)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3416647"
% 3.41/1.34 % (3416702)------------------------------
% 3.41/1.34 % (3416702)------------------------------
% 3.41/1.34 % (3416713)lrs+10_1_sil=8000:sp=occurrence:random_seed=439608715:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.41/1.34 % (3416715)lrs+1011_1_sil=32000:sp=occurrence:random_seed=781762161:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.41/1.34 % (3416714)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1746187102:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.41/1.34 % (3416714)Instruction limit reached!
% 3.41/1.34 % (3416714)------------------------------
% 3.41/1.34 % (3416714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.34 % (3416714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.34 % (3416714)CaDiCaL version: 2.1.3
% 3.41/1.34 % (3416714)Termination reason: Instruction limit
% 3.41/1.34 % (3416714)Termination phase: Saturation
% 3.41/1.34 % (3416714)Time elapsed: 0.076 s
% 3.41/1.34 % (3416714)Peak memory usage: 93 MB
% 3.41/1.34 % (3416714)Instructions burned: 160 (million)
% 3.41/1.34 % (3416715)Instruction limit reached!
% 3.41/1.34 % (3416715)------------------------------
% 3.41/1.34 % (3416715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.41/1.34 % (3416715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.41/1.34 % (3416715)CaDiCaL version: 2.1.3
% 3.41/1.34 % (3416715)Termination reason: Instruction limit
% 3.41/1.34 % (3416715)Termination phase: Saturation
% 3.41/1.34 % (3416715)Time elapsed: 0.103 s
% 3.41/1.34 % (3416715)Peak memory usage: 92 MB
% 3.41/1.34 % (3416715)Instructions burned: 331 (million)
% 3.41/1.34 % (3416704)Refutation found. Thanks to Tanya!
% 3.41/1.34 % SZS status Theorem for theBenchmark
% 3.41/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 4.16/1.54 % (3416704)------------------------------
% 4.16/1.54 % (3416704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.16/1.54 % (3416704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.54 % (3416704)CaDiCaL version: 2.1.3
% 4.16/1.54 % (3416704)Termination reason: Refutation
% 4.16/1.54 % (3416704)Time elapsed: 0.096 s
% 4.16/1.54 % (3416704)Peak memory usage: 91 MB
% 4.16/1.54 % (3416704)Instructions burned: 125 (million)
% 4.16/1.54 % (3416704)------------------------------
% 4.16/1.54 % (3416704)------------------------------
% 4.16/1.54 % (3416647)Success in time 0.494 s
% 4.16/1.54 % Vampire exiting
%------------------------------------------------------------------------------