%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU234+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Sep 24 02:19:49 PM UTC 2026
% Result : Theorem 143.89s 18.66s
% Output : CNFRefutation 143.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 459
% Syntax : Number of formulae : 1674 ( 75 unt; 371 def)
% Number of atoms : 6867 (1266 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 8886 (3693 ~;4124 |; 514 &)
% ( 468 <=>; 86 =>; 0 <=; 1 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 387 ( 385 usr; 371 prp; 0-4 aty)
% Number of functors : 91 ( 91 usr; 5 con; 0-5 aty)
% Number of variables : 3063 (2921 !; 142 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B] :
( ( A = empty_set
=> ( B = set_meet(A)
<=> B = empty_set ) )
& ( A != empty_set
=> ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(D,A)
=> in(C,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A] : cast_to_subset(A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f135,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f140,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f145,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f154,lemma,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f156,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f157,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f158,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f164,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f166,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f167,lemma,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f169,lemma,
! [A,B] :
( relation(B)
=> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f171,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f172,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f173,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f180,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f182,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f185,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,lemma,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,conjecture,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
~ ! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
inference(negated_conjecture,[status(cth)],[f200]) ).
fof(f204,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f212,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f213,axiom,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f214,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f218,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f221,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f230,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f232,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f233,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f234,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f237,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f240,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f241,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f244,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f245,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f246,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f247,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f248,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f252,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f255,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f256,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f257,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f258,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f259,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f262,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f263,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f268,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f270,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f272,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f273,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f287,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f288,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_transitive(X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f293,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f294,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f296,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f297,plain,
! [A,B] :
( ( ( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ( ! [C,D] :
( ( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [B] :
( ( ! [A] :
( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f297]) ).
fof(f299,plain,
! [B] :
( ( ! [A] :
( ( ( ( sK0_skl(A,B) = sK1_skl(A,B)
& in(sK0_skl(A,B),A) )
| in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) )
& ( sK0_skl(A,B) != sK1_skl(A,B)
| ~ in(sK0_skl(A,B),A)
| ~ in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f298]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ relation(X0)
| in(X2,X1)
| X0 != identity_relation(X1) ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f302,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| ~ in(X2,X1)
| in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f303,plain,
! [X0,X1] :
( ~ in(sK0_skl(X0,X1),X0)
| sK0_skl(X0,X1) != sK1_skl(X0,X1)
| ~ relation(X1)
| identity_relation(X0) = X1
| ~ in(ordered_pair(sK0_skl(X0,X1),sK1_skl(X0,X1)),X1) ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f305,plain,
! [X0,X1] :
( X1 = identity_relation(X0)
| in(ordered_pair(sK0_skl(X0,X1),sK1_skl(X0,X1)),X1)
| ~ relation(X1)
| sK0_skl(X0,X1) = sK1_skl(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f306,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f307,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f306]) ).
fof(f309,plain,
! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f310,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f311,plain,
! [A] :
( ! [B,C] :
( ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f312,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f311]) ).
fof(f313,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f312]) ).
fof(f314,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ( ( in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
& in(sK2_skl(B,C,A),B) )
| in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) )
& ( ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
| ~ in(sK2_skl(B,C,A),B)
| ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(D,sK2_skl(B,C,A)),skolemize(E,sK3_skl(B,C,A))],[f313]) ).
fof(f317,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X3,X2)
| ~ relation(X1)
| ~ relation(X0)
| in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X1)
| X0 != relation_dom_restriction(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f318,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(X0,X1,X2),sK3_skl(X0,X1,X2)),X1)
| X1 = relation_dom_restriction(X2,X0)
| ~ in(ordered_pair(sK2_skl(X0,X1,X2),sK3_skl(X0,X1,X2)),X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(sK2_skl(X0,X1,X2),X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f319,plain,
! [X0,X1,X2] :
( in(sK2_skl(X1,X2,X0),X1)
| ~ relation(X2)
| in(ordered_pair(sK2_skl(X1,X2,X0),sK3_skl(X1,X2,X0)),X2)
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f331,plain,
! [A,B] :
( ! [C] :
( ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f332,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f331]) ).
fof(f333,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f332]) ).
fof(f334,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( ( ( in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),B)
& in(sK8_skl(A,C,B),A) )
| in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),C) )
& ( ~ in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),B)
| ~ in(sK8_skl(A,C,B),A)
| ~ in(ordered_pair(sK7_skl(A,C,B),sK8_skl(A,C,B)),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(D,sK7_skl(A,C,B)),skolemize(E,sK8_skl(A,C,B))],[f333]) ).
fof(f337,plain,
! [X0,X1,X2,X3,X4] :
( relation_rng_restriction(X1,X3) != X4
| in(ordered_pair(X2,X0),X4)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(ordered_pair(X2,X0),X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f338,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK7_skl(X0,X2,X1),sK8_skl(X0,X2,X1)),X1)
| ~ in(sK8_skl(X0,X2,X1),X0)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(ordered_pair(sK7_skl(X0,X2,X1),sK8_skl(X0,X2,X1)),X2)
| relation_rng_restriction(X0,X1) = X2 ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f339,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| X1 = relation_rng_restriction(X0,X2)
| ~ relation(X1)
| in(sK8_skl(X0,X1,X2),X0)
| in(ordered_pair(sK7_skl(X0,X1,X2),sK8_skl(X0,X1,X2)),X1) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f340,plain,
! [X0,X1,X2] :
( relation_rng_restriction(X2,X1) = X0
| in(ordered_pair(sK7_skl(X2,X0,X1),sK8_skl(X2,X0,X1)),X0)
| in(ordered_pair(sK7_skl(X2,X0,X1),sK8_skl(X2,X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f351,plain,
! [A] :
( ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f352,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f351]) ).
fof(f353,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f352]) ).
fof(f354,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK12_skl(C,B,A),B)
& in(ordered_pair(sK12_skl(C,B,A),sK11_skl(C,B,A)),A) )
| in(sK11_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,sK11_skl(C,B,A)),A) )
| ~ in(sK11_skl(C,B,A),C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ( in(sK10_skl(D,C,B,A),B)
& in(ordered_pair(sK10_skl(D,C,B,A),D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(E,sK10_skl(D,C,B,A)),skolemize(D,sK11_skl(C,B,A)),skolemize(E,sK12_skl(C,B,A))],[f353]) ).
fof(f355,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| X1 != relation_image(X3,X2)
| in(ordered_pair(sK10_skl(X0,X1,X2,X3),X0),X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f357,plain,
! [X0,X1,X2,X3,X4] :
( in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X2)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f358,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| relation_image(X3,X1) = X2
| ~ in(sK11_skl(X2,X1,X3),X2)
| ~ in(ordered_pair(X0,sK11_skl(X2,X1,X3)),X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f359,plain,
! [X0,X1,X2] :
( in(sK11_skl(X0,X1,X2),X0)
| ~ relation(X2)
| relation_image(X2,X1) = X0
| in(ordered_pair(sK12_skl(X0,X1,X2),sK11_skl(X0,X1,X2)),X2) ),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f361,plain,
! [A] :
( ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f362,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f361]) ).
fof(f363,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f362]) ).
fof(f364,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK15_skl(C,B,A),B)
& in(ordered_pair(sK14_skl(C,B,A),sK15_skl(C,B,A)),A) )
| in(sK14_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK14_skl(C,B,A),E),A) )
| ~ in(sK14_skl(C,B,A),C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ( in(sK13_skl(D,C,B,A),B)
& in(ordered_pair(D,sK13_skl(D,C,B,A)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(E,sK13_skl(D,C,B,A)),skolemize(D,sK14_skl(C,B,A)),skolemize(E,sK15_skl(C,B,A))],[f363]) ).
fof(f365,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| in(ordered_pair(X3,sK13_skl(X3,X2,X1,X0)),X0)
| ~ in(X3,X2)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f364]) ).
fof(f369,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK14_skl(X2,X1,X0),sK15_skl(X2,X1,X0)),X0)
| ~ relation(X0)
| in(sK14_skl(X2,X1,X0),X2)
| relation_inverse_image(X0,X1) = X2 ),
inference(cnf_transformation,[status(thm)],[f364]) ).
fof(f381,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f382,plain,
! [A] :
( relation(A)
<=> ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f383,plain,
! [A] :
( ( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(NNF_transformation,[status(thm)],[f382]) ).
fof(f384,plain,
( ! [A] :
( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ! [A] :
( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(miniscoping,[status(thm)],[f383]) ).
fof(f385,plain,
( ! [A] :
( ( ! [C,D] : sK19_skl(A) != ordered_pair(C,D)
& in(sK19_skl(A),A) )
| relation(A) )
& ! [A] :
( ! [B] :
( B = ordered_pair(sK17_skl(B,A),sK18_skl(B,A))
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(C,sK17_skl(B,A)),skolemize(D,sK18_skl(B,A)),skolemize(B,sK19_skl(A))],[f384]) ).
fof(f387,plain,
! [X0] :
( relation(X0)
| in(sK19_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f389,plain,
! [A,B] :
( ( ( B = set_meet(A)
<=> B = empty_set )
| A != empty_set )
& ( ( B = set_meet(A)
<=> ! [C] :
( in(C,B)
<=> ! [D] :
( in(C,D)
| ~ in(D,A) ) ) )
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f390,plain,
! [A,B] :
( ( ( ( B != empty_set
| B = set_meet(A) )
& ( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ( ( ( ? [C] :
( ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| in(C,B) )
& ( ? [D] :
( ~ in(C,D)
& in(D,A) )
| ~ in(C,B) ) )
| B = set_meet(A) )
& ( ! [C] :
( ( ? [D] :
( ~ in(C,D)
& in(D,A) )
| in(C,B) )
& ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f389]) ).
fof(f391,plain,
( ! [A] :
( ( ! [B] :
( B != empty_set
| B = set_meet(A) )
& ! [B] :
( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ! [A] :
( ( ! [B] :
( ? [C] :
( ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| in(C,B) )
& ( ? [D] :
( ~ in(C,D)
& in(D,A) )
| ~ in(C,B) ) )
| B = set_meet(A) )
& ! [B] :
( ( ! [C] :
( ? [D] :
( ~ in(C,D)
& in(D,A) )
| in(C,B) )
& ! [C] :
( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(miniscoping,[status(thm)],[f390]) ).
fof(f392,plain,
( ! [A] :
( ( ! [B] :
( B != empty_set
| B = set_meet(A) )
& ! [B] :
( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ! [A] :
( ( ! [B] :
( ( ( ! [D] :
( in(sK21_skl(B,A),D)
| ~ in(D,A) )
| in(sK21_skl(B,A),B) )
& ( ( ~ in(sK21_skl(B,A),sK22_skl(B,A))
& in(sK22_skl(B,A),A) )
| ~ in(sK21_skl(B,A),B) ) )
| B = set_meet(A) )
& ! [B] :
( ( ! [C] :
( ( ~ in(C,sK20_skl(C,B,A))
& in(sK20_skl(C,B,A),A) )
| in(C,B) )
& ! [C] :
( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl]),skolemize(D,sK20_skl(C,B,A)),skolemize(C,sK21_skl(B,A)),skolemize(D,sK22_skl(B,A))],[f391]) ).
fof(f393,plain,
! [X0,X1,X2,X3] :
( in(X0,X3)
| set_meet(X2) != X1
| ~ in(X3,X2)
| X2 = empty_set
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f394,plain,
! [X0,X1,X2] :
( in(sK20_skl(X0,X1,X2),X2)
| set_meet(X2) != X1
| X2 = empty_set
| in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f395,plain,
! [X0,X1,X2] :
( empty_set = X2
| in(X0,X1)
| set_meet(X2) != X1
| ~ in(X0,sK20_skl(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f396,plain,
! [X0,X1] :
( X1 = empty_set
| in(sK22_skl(X0,X1),X1)
| ~ in(sK21_skl(X0,X1),X0)
| X0 = set_meet(X1) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f398,plain,
! [X0,X1,X2] :
( set_meet(X0) = X1
| in(sK21_skl(X1,X0),X2)
| ~ in(X2,X0)
| in(sK21_skl(X1,X0),X1)
| empty_set = X0 ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f399,plain,
! [X0,X1] :
( set_meet(X0) != X1
| empty_set = X1
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f400,plain,
! [X0,X1] :
( empty_set != X1
| empty_set != X0
| set_meet(X0) = X1 ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f401,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f402,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f401]) ).
fof(f403,plain,
( ! [A,B] :
( ( ( sK23_skl(B,A) = A
| in(sK23_skl(B,A),B) )
& ( sK23_skl(B,A) != A
| ~ in(sK23_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(C,sK23_skl(B,A))],[f402]) ).
fof(f404,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f405,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f407,plain,
! [X0,X1] :
( singleton(X1) = X0
| in(sK23_skl(X0,X1),X0)
| sK23_skl(X0,X1) = X1 ),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f408,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f409,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f408]) ).
fof(f410,plain,
( ! [A] :
( in(sK24_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(B,sK24_skl(A))],[f409]) ).
fof(f411,plain,
! [X0,X1] :
( X1 != empty_set
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f412,plain,
! [X0] :
( in(sK24_skl(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f413,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f414,plain,
( ! [A,B] :
( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(miniscoping,[status(thm)],[f413]) ).
fof(f415,plain,
( ! [A,B] :
( ( ( subset(sK25_skl(B,A),A)
| in(sK25_skl(B,A),B) )
& ( ~ subset(sK25_skl(B,A),A)
| ~ in(sK25_skl(B,A),B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(C,sK25_skl(B,A))],[f414]) ).
fof(f416,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f415]) ).
fof(f420,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f421,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(NNF_transformation,[status(thm)],[f420]) ).
fof(f422,plain,
( ! [A] :
( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(miniscoping,[status(thm)],[f421]) ).
fof(f423,plain,
( ! [A] :
( ( ~ subset(sK26_skl(A),A)
& in(sK26_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl]),skolemize(B,sK26_skl(A))],[f422]) ).
fof(f425,plain,
! [X0] :
( epsilon_transitive(X0)
| in(sK26_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f426,plain,
! [X0] :
( ~ subset(sK26_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f442,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f443,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f442]) ).
fof(f444,plain,
( ! [A,B,C] :
( ( ( sK29_skl(C,B,A) = B
| sK29_skl(C,B,A) = A
| in(sK29_skl(C,B,A),C) )
& ( ( sK29_skl(C,B,A) != B
& sK29_skl(C,B,A) != A )
| ~ in(sK29_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl]),skolemize(D,sK29_skl(C,B,A))],[f443]) ).
fof(f447,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f444]) ).
fof(f469,plain,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f470,plain,
! [A] :
( ( ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(NNF_transformation,[status(thm)],[f469]) ).
fof(f471,plain,
( ! [A] :
( ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ! [A] :
( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(miniscoping,[status(thm)],[f470]) ).
fof(f472,plain,
( ! [A] :
( ( ~ in(sK37_skl(A),sK36_skl(A))
& sK36_skl(A) != sK37_skl(A)
& ~ in(sK36_skl(A),sK37_skl(A))
& in(sK37_skl(A),A)
& in(sK36_skl(A),A) )
| epsilon_connected(A) )
& ! [A] :
( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36_skl,sK37_skl]),skolemize(B,sK36_skl(A)),skolemize(C,sK37_skl(A))],[f471]) ).
fof(f474,plain,
! [X0] :
( epsilon_connected(X0)
| in(sK36_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f475,plain,
! [X0] :
( in(sK37_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f476,plain,
! [X0] :
( epsilon_connected(X0)
| ~ in(sK36_skl(X0),sK37_skl(X0)) ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f477,plain,
! [X0] :
( sK37_skl(X0) != sK36_skl(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f478,plain,
! [X0] :
( ~ in(sK37_skl(X0),sK36_skl(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f479,plain,
! [A] :
( ! [B] :
( ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f480,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f479]) ).
fof(f481,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK38_skl(B,A),sK39_skl(B,A)),B)
& in(ordered_pair(sK38_skl(B,A),sK39_skl(B,A)),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl]),skolemize(C,sK38_skl(B,A)),skolemize(D,sK39_skl(B,A))],[f480]) ).
fof(f483,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ relation(X1)
| ~ relation(X0)
| in(ordered_pair(sK38_skl(X0,X1),sK39_skl(X0,X1)),X1) ),
inference(cnf_transformation,[status(thm)],[f481]) ).
fof(f484,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK38_skl(X1,X0),sK39_skl(X1,X0)),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f481]) ).
fof(f485,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f486,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f485]) ).
fof(f487,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f486]) ).
fof(f488,plain,
( ! [A,B] :
( ( ~ in(sK40_skl(B,A),B)
& in(sK40_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40_skl]),skolemize(C,sK40_skl(B,A))],[f487]) ).
fof(f489,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| in(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f488]) ).
fof(f501,plain,
! [A] :
( ! [B,C] :
( ( ( C = apply(A,B)
<=> C = empty_set )
| in(B,relation_dom(A)) )
& ( ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f502,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f501]) ).
fof(f503,plain,
! [A] :
( ( ! [B] :
( ( ! [C] :
( C != empty_set
| C = apply(A,B) )
& ! [C] :
( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ! [B] :
( ( ! [C] :
( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ! [C] :
( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f502]) ).
fof(f505,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| apply(X2,X0) = X1
| ~ function(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f503]) ).
fof(f506,plain,
! [X0,X1,X2] :
( X2 != apply(X1,X0)
| X2 = empty_set
| ~ relation(X1)
| ~ function(X1)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[status(thm)],[f503]) ).
fof(f507,plain,
! [X0,X1,X2] :
( ~ relation(X1)
| in(X2,relation_dom(X1))
| X0 = apply(X1,X2)
| ~ function(X1)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f503]) ).
fof(f513,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f514,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f513]) ).
fof(f515,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f514]) ).
fof(f516,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK43_skl(B,A),sK44_skl(B,A)),A)
| in(sK43_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK43_skl(B,A),D),A)
| ~ in(sK43_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK42_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42_skl,sK43_skl,sK44_skl]),skolemize(D,sK42_skl(C,B,A)),skolemize(C,sK43_skl(B,A)),skolemize(D,sK44_skl(B,A))],[f515]) ).
fof(f517,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| relation_dom(X2) != X1
| ~ relation(X2)
| in(ordered_pair(X0,sK42_skl(X0,X1,X2)),X2) ),
inference(cnf_transformation,[status(thm)],[f516]) ).
fof(f518,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
| relation_dom(X0) != X2
| in(X1,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f516]) ).
fof(f519,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK43_skl(X0,X1),X2),X1)
| ~ relation(X1)
| relation_dom(X1) = X0
| ~ in(sK43_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f516]) ).
fof(f520,plain,
! [X0,X1] :
( in(ordered_pair(sK43_skl(X1,X0),sK44_skl(X1,X0)),X0)
| ~ relation(X0)
| in(sK43_skl(X1,X0),X1)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[status(thm)],[f516]) ).
fof(f521,plain,
! [X0] : X0 = cast_to_subset(X0),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f522,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(NNF_transformation,[status(thm)],[f41]) ).
fof(f523,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
| in(C,B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| ~ in(C,B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(miniscoping,[status(thm)],[f522]) ).
fof(f524,plain,
( ! [A,B] :
( ( ( ( in(sK47_skl(B,A),A)
& in(sK46_skl(B,A),sK47_skl(B,A)) )
| in(sK46_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK46_skl(B,A),D) )
| ~ in(sK46_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK45_skl(C,B,A),A)
& in(C,sK45_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl,sK47_skl]),skolemize(D,sK45_skl(C,B,A)),skolemize(C,sK46_skl(B,A)),skolemize(D,sK47_skl(B,A))],[f523]) ).
fof(f527,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X0,X3)
| X1 != union(X2)
| in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f524]) ).
fof(f531,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f532,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f531]) ).
fof(f533,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK48_skl(C,B,A),B)
& in(sK48_skl(C,B,A),A) )
| in(sK48_skl(C,B,A),C) )
& ( in(sK48_skl(C,B,A),B)
| ~ in(sK48_skl(C,B,A),A)
| ~ in(sK48_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48_skl]),skolemize(D,sK48_skl(C,B,A))],[f532]) ).
fof(f537,plain,
! [X0,X1,X2] :
( ~ in(sK48_skl(X0,X1,X2),X2)
| X0 = set_difference(X2,X1)
| in(sK48_skl(X0,X1,X2),X1)
| ~ in(sK48_skl(X0,X1,X2),X0) ),
inference(cnf_transformation,[status(thm)],[f533]) ).
fof(f538,plain,
! [X0,X1,X2] :
( in(sK48_skl(X0,X2,X1),X0)
| in(sK48_skl(X0,X2,X1),X1)
| X0 = set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f533]) ).
fof(f540,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f541,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f540]) ).
fof(f542,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f541]) ).
fof(f543,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK50_skl(B,A) = apply(A,sK51_skl(B,A))
& in(sK51_skl(B,A),relation_dom(A)) )
| in(sK50_skl(B,A),B) )
& ( ! [D] :
( sK50_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK50_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK49_skl(C,B,A))
& in(sK49_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(D,sK49_skl(C,B,A)),skolemize(C,sK50_skl(B,A)),skolemize(D,sK51_skl(B,A))],[f542]) ).
fof(f544,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ~ function(X2)
| relation_rng(X2) != X1
| ~ in(X0,X1)
| in(sK49_skl(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[status(thm)],[f543]) ).
fof(f550,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f551,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f550]) ).
fof(f552,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f551]) ).
fof(f553,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK54_skl(B,A),sK53_skl(B,A)),A)
| in(sK53_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK53_skl(B,A)),A)
| ~ in(sK53_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK52_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(D,sK52_skl(C,B,A)),skolemize(C,sK53_skl(B,A)),skolemize(D,sK54_skl(B,A))],[f552]) ).
fof(f554,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| relation_rng(X2) != X1
| ~ relation(X2)
| in(ordered_pair(sK52_skl(X0,X1,X2),X0),X2) ),
inference(cnf_transformation,[status(thm)],[f553]) ).
fof(f556,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ in(ordered_pair(X2,sK53_skl(X1,X0)),X0)
| ~ in(sK53_skl(X1,X0),X1)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[status(thm)],[f553]) ).
fof(f557,plain,
! [X0,X1] :
( in(ordered_pair(sK54_skl(X0,X1),sK53_skl(X0,X1)),X1)
| in(sK53_skl(X0,X1),X0)
| ~ relation(X1)
| X0 = relation_rng(X1) ),
inference(cnf_transformation,[status(thm)],[f553]) ).
fof(f563,plain,
! [A] :
( ! [B] :
( ( B = relation_inverse(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> in(ordered_pair(D,C),A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f564,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ( ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B = relation_inverse(A) )
& ( ! [C,D] :
( ( ~ in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f563]) ).
fof(f565,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ( ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B = relation_inverse(A) )
& ( ( ! [C,D] :
( ~ in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f564]) ).
fof(f566,plain,
! [A] :
( ! [B] :
( ( ( ( ( in(ordered_pair(sK56_skl(B,A),sK55_skl(B,A)),A)
| in(ordered_pair(sK55_skl(B,A),sK56_skl(B,A)),B) )
& ( ~ in(ordered_pair(sK56_skl(B,A),sK55_skl(B,A)),A)
| ~ in(ordered_pair(sK55_skl(B,A),sK56_skl(B,A)),B) ) )
| B = relation_inverse(A) )
& ( ( ! [C,D] :
( ~ in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl]),skolemize(C,sK55_skl(B,A)),skolemize(D,sK56_skl(B,A))],[f565]) ).
fof(f567,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| in(ordered_pair(X1,X0),X3)
| relation_inverse(X3) != X2
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f566]) ).
fof(f569,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK56_skl(X0,X1),sK55_skl(X0,X1)),X1)
| ~ in(ordered_pair(sK55_skl(X0,X1),sK56_skl(X0,X1)),X0)
| X0 = relation_inverse(X1) ),
inference(cnf_transformation,[status(thm)],[f566]) ).
fof(f571,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f572,plain,
( ! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ! [A,B] :
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f571]) ).
fof(f574,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f572]) ).
fof(f583,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f584,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ! [D,E] :
( ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f583]) ).
fof(f585,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f584]) ).
fof(f586,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ( ( in(ordered_pair(sK62_skl(C,B,A),sK61_skl(C,B,A)),B)
& in(ordered_pair(sK60_skl(C,B,A),sK62_skl(C,B,A)),A) )
| in(ordered_pair(sK60_skl(C,B,A),sK61_skl(C,B,A)),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,sK61_skl(C,B,A)),B)
| ~ in(ordered_pair(sK60_skl(C,B,A),F),A) )
| ~ in(ordered_pair(sK60_skl(C,B,A),sK61_skl(C,B,A)),C) ) )
| C = relation_composition(A,B) )
& ( ( ! [D,E] :
( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(sK59_skl(E,D,C,B,A),E),B)
& in(ordered_pair(D,sK59_skl(E,D,C,B,A)),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59_skl,sK60_skl,sK61_skl,sK62_skl]),skolemize(F,sK59_skl(E,D,C,B,A)),skolemize(D,sK60_skl(C,B,A)),skolemize(E,sK61_skl(C,B,A)),skolemize(F,sK62_skl(C,B,A))],[f585]) ).
fof(f589,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(ordered_pair(X5,X2),X1)
| ~ relation(X4)
| in(ordered_pair(X5,X3),X0)
| X0 != relation_composition(X1,X4)
| ~ in(ordered_pair(X2,X3),X4)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f586]) ).
fof(f591,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK60_skl(X1,X2,X0),sK61_skl(X1,X2,X0)),X1)
| ~ relation(X2)
| X1 = relation_composition(X0,X2)
| ~ relation(X1)
| in(ordered_pair(sK60_skl(X1,X2,X0),sK62_skl(X1,X2,X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f586]) ).
fof(f601,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f602,plain,
( ! [A,B] :
( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ! [A,B] :
( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f601]) ).
fof(f605,plain,
! [X0,X1] :
( X1 = X0
| proper_subset(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f602]) ).
fof(f657,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f658,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f657]) ).
fof(f660,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f662,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f663,plain,
one_to_one(empty_set),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f665,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f666,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f667,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f761,plain,
( ordinal(sK67_skl)
& epsilon_connected(sK67_skl)
& epsilon_transitive(sK67_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(A,sK67_skl)],[f135]) ).
fof(f762,plain,
epsilon_transitive(sK67_skl),
inference(cnf_transformation,[status(thm)],[f761]) ).
fof(f763,plain,
epsilon_connected(sK67_skl),
inference(cnf_transformation,[status(thm)],[f761]) ).
fof(f778,plain,
( ordinal(sK72_skl)
& epsilon_connected(sK72_skl)
& epsilon_transitive(sK72_skl)
& empty(sK72_skl)
& one_to_one(sK72_skl)
& function(sK72_skl)
& relation(sK72_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72_skl]),skolemize(A,sK72_skl)],[f140]) ).
fof(f783,plain,
epsilon_transitive(sK72_skl),
inference(cnf_transformation,[status(thm)],[f778]) ).
fof(f784,plain,
epsilon_connected(sK72_skl),
inference(cnf_transformation,[status(thm)],[f778]) ).
fof(f798,plain,
( ordinal(sK77_skl)
& epsilon_connected(sK77_skl)
& epsilon_transitive(sK77_skl)
& ~ empty(sK77_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77_skl]),skolemize(A,sK77_skl)],[f145]) ).
fof(f800,plain,
epsilon_transitive(sK77_skl),
inference(cnf_transformation,[status(thm)],[f798]) ).
fof(f801,plain,
epsilon_connected(sK77_skl),
inference(cnf_transformation,[status(thm)],[f798]) ).
fof(f825,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f829,plain,
! [A,B,C] :
( ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f156]) ).
fof(f830,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f829]) ).
fof(f831,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ! [A,B] :
( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f830]) ).
fof(f832,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f831]) ).
fof(f833,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_rng(relation_rng_restriction(X2,X1)))
| ~ relation(X1)
| in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[status(thm)],[f831]) ).
fof(f835,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f157]) ).
fof(f836,plain,
! [B] :
( ! [A] : subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f835]) ).
fof(f837,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f836]) ).
fof(f838,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f158]) ).
fof(f839,plain,
! [B] :
( ! [A] : subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f838]) ).
fof(f840,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f839]) ).
fof(f841,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f159]) ).
fof(f842,plain,
! [B] :
( ! [A] : subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f841]) ).
fof(f843,plain,
! [X0,X1] :
( ~ relation(X1)
| subset(relation_rng(relation_rng_restriction(X0,X1)),relation_rng(X1)) ),
inference(cnf_transformation,[status(thm)],[f842]) ).
fof(f855,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( in(powerset(C),B)
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f164]) ).
fof(f856,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( in(powerset(C),B)
| ~ in(C,B) )
& ! [D] :
( in(D,B)
| ! [C] :
( ~ subset(D,C)
| ~ in(C,B) ) )
& in(A,B) ),
inference(miniscoping,[status(thm)],[f855]) ).
fof(f857,plain,
! [A] :
( ! [C] :
( in(C,sK80_skl(A))
| are_equipotent(C,sK80_skl(A))
| ~ subset(C,sK80_skl(A)) )
& ! [C] :
( in(powerset(C),sK80_skl(A))
| ~ in(C,sK80_skl(A)) )
& ! [D] :
( in(D,sK80_skl(A))
| ! [C] :
( ~ subset(D,C)
| ~ in(C,sK80_skl(A)) ) )
& in(A,sK80_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80_skl]),skolemize(B,sK80_skl(A))],[f856]) ).
fof(f858,plain,
! [X0] : in(X0,sK80_skl(X0)),
inference(cnf_transformation,[status(thm)],[f857]) ).
fof(f865,plain,
! [A,B,C] :
( ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f166]) ).
fof(f866,plain,
! [A,B,C] :
( ( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) )
| in(A,relation_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f865]) ).
fof(f867,plain,
! [C] :
( ( ! [A,B] :
( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) )
| in(A,relation_image(C,B)) )
& ! [A,B] :
( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f866]) ).
fof(f868,plain,
! [C] :
( ( ! [A,B] :
( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) )
| in(A,relation_image(C,B)) )
& ! [A,B] :
( ( in(sK81_skl(B,A,C),B)
& in(ordered_pair(sK81_skl(B,A,C),A),C)
& in(sK81_skl(B,A,C),relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81_skl]),skolemize(D,sK81_skl(B,A,C))],[f867]) ).
fof(f870,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK81_skl(X2,X1,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f868]) ).
fof(f872,plain,
! [X0,X1,X2,X3] :
( in(X1,relation_image(X2,X3))
| ~ in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(X0,X3)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f868]) ).
fof(f873,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f167]) ).
fof(f874,plain,
! [B] :
( ! [A] : subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f873]) ).
fof(f875,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_image(X0,X1),relation_rng(X0)) ),
inference(cnf_transformation,[status(thm)],[f874]) ).
fof(f879,plain,
! [A,B] :
( relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f169]) ).
fof(f880,plain,
! [B] :
( ! [A] : relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f879]) ).
fof(f881,plain,
! [X0,X1] :
( relation_image(X0,X1) = relation_image(X0,set_intersection2(relation_dom(X0),X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f880]) ).
fof(f885,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f171]) ).
fof(f886,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
inference(cnf_transformation,[status(thm)],[f885]) ).
fof(f887,plain,
! [A,B] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B))
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f172]) ).
fof(f888,plain,
! [B] :
( ! [A] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B)) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f887]) ).
fof(f889,plain,
! [X0,X1] :
( ~ function(X0)
| relation_image(X0,relation_inverse_image(X0,X1)) = X1
| ~ subset(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f888]) ).
fof(f890,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f173]) ).
fof(f891,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| relation_image(X0,relation_rng(X1)) = relation_rng(relation_composition(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f890]) ).
fof(f912,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f180]) ).
fof(f915,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f182]) ).
fof(f916,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f915]) ).
fof(f917,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f916]) ).
fof(f923,plain,
! [A,B] :
( ! [C] :
( ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f185]) ).
fof(f924,plain,
! [A,B] :
( ! [C] :
( ( ( ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C))
| in(A,relation_dom(relation_composition(C,B))) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f923]) ).
fof(f925,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C))
| in(A,relation_dom(relation_composition(C,B))) )
& ! [A] :
( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f924]) ).
fof(f926,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X1)
| in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[status(thm)],[f925]) ).
fof(f927,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(apply(X0,X1),relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_composition(X0,X2)))
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f925]) ).
fof(f928,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(relation_composition(X0,X2)))
| ~ in(apply(X0,X1),relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f925]) ).
fof(f939,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f190]) ).
fof(f940,plain,
! [B] :
( ! [A] :
( ordinal(A)
| ~ in(A,B) )
| ~ ordinal(B) ),
inference(miniscoping,[status(thm)],[f939]) ).
fof(f941,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ordinal(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f940]) ).
fof(f942,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f191]) ).
fof(f943,plain,
! [X0,X1] :
( X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| in(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f942]) ).
fof(f944,plain,
! [A] :
( ! [B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f192]) ).
fof(f945,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ relation(X0)
| ~ relation(X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f944]) ).
fof(f952,plain,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f955,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f197]) ).
fof(f956,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f955]) ).
fof(f957,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK83_skl(B,A),B)
| ~ in(sK83_skl(B,A),A) )
& ( in(sK83_skl(B,A),B)
| in(sK83_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl]),skolemize(C,sK83_skl(B,A))],[f956]) ).
fof(f958,plain,
! [X0,X1] :
( in(sK83_skl(X0,X1),X1)
| X0 = X1
| in(sK83_skl(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f957]) ).
fof(f960,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f961,plain,
! [A,B,C] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f199]) ).
fof(f962,plain,
! [C] :
( ! [A,B] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f961]) ).
fof(f963,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X0,X2),X1)
| ~ relation(X1)
| in(X0,relation_field(X1)) ),
inference(cnf_transformation,[status(thm)],[f962]) ).
fof(f965,plain,
? [A] :
( ~ ordinal(A)
& ! [B] :
( ( subset(B,A)
& ordinal(B) )
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f201]) ).
fof(f966,plain,
( ~ ordinal(sK84_skl)
& ! [B] :
( ( subset(B,sK84_skl)
& ordinal(B) )
| ~ in(B,sK84_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84_skl]),skolemize(A,sK84_skl)],[f965]) ).
fof(f967,plain,
! [X0] :
( ordinal(X0)
| ~ in(X0,sK84_skl) ),
inference(cnf_transformation,[status(thm)],[f966]) ).
fof(f968,plain,
! [X0] :
( ~ in(X0,sK84_skl)
| subset(X0,sK84_skl) ),
inference(cnf_transformation,[status(thm)],[f966]) ).
fof(f969,plain,
~ ordinal(sK84_skl),
inference(cnf_transformation,[status(thm)],[f966]) ).
fof(f976,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A ) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f204]) ).
fof(f977,plain,
! [A,B] :
( ( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f976]) ).
fof(f978,plain,
! [B] :
( ( ! [A] :
( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f977]) ).
fof(f979,plain,
! [B] :
( ( ! [A] :
( ( apply(B,sK85_skl(A,B)) != sK85_skl(A,B)
& in(sK85_skl(A,B),A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ! [A] :
( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85_skl]),skolemize(C,sK85_skl(A,B))],[f978]) ).
fof(f980,plain,
! [X0,X1] :
( ~ function(X0)
| X1 = relation_dom(X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f979]) ).
fof(f1004,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f212]) ).
fof(f1005,plain,
( ! [A,B] :
( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ! [A,B] :
( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(miniscoping,[status(thm)],[f1004]) ).
fof(f1007,plain,
! [X0,X1] :
( X0 != empty_set
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f1005]) ).
fof(f1009,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f1010,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f214]) ).
fof(f1011,plain,
! [A,C] :
( ~ in(C,A)
| ! [B] :
( ~ in(B,C)
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f1010]) ).
fof(f1012,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1011]) ).
fof(f1025,plain,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f1032,plain,
! [A] :
( ! [B] :
( subset(relation_rng(relation_composition(A,B)),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f221]) ).
fof(f1033,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X1,X0)),relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1032]) ).
fof(f1049,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f1053,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f232]) ).
fof(f1054,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f1053]) ).
fof(f1055,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ! [A,B] :
( in(sK87_skl(B,A),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87_skl]),skolemize(C,sK87_skl(B,A))],[f1054]) ).
fof(f1057,plain,
! [X0,X1,X2] :
( ~ disjoint(X1,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f1055]) ).
fof(f1058,plain,
! [A] :
( ! [B] :
( ! [C] :
( in(C,subset_complement(A,B))
| in(C,B)
| ~ element(C,A) )
| ~ element(B,powerset(A)) )
| A = empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f233]) ).
fof(f1059,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,X0)
| in(X1,subset_complement(X0,X2))
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f1058]) ).
fof(f1060,plain,
! [A] :
( ! [B] :
( ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f234]) ).
fof(f1061,definition,
! [A,B,C,D] :
( sP3_prd(D,C,B,A)
<=> ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f1062,plain,
! [A] :
( ! [B] :
( ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& sP3_prd(D,C,B,A) )
& relation_dom(B) = relation_rng(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(formula_renaming,[status(thm)],[f1060,f1061]) ).
fof(f1063,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ sP3_prd(D,C,B,A) )
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& sP3_prd(D,C,B,A) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f1062]) ).
fof(f1064,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ? [C,D] : ~ sP3_prd(D,C,B,A)
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ! [C,D] : sP3_prd(D,C,B,A)
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f1063]) ).
fof(f1065,plain,
! [A] :
( ! [B] :
( ( ( ( ( sK91_skl(B,A) != apply(B,sK90_skl(B,A))
| ~ in(sK90_skl(B,A),relation_rng(A)) )
& sK90_skl(B,A) = apply(A,sK91_skl(B,A))
& in(sK91_skl(B,A),relation_dom(A)) )
| ~ sP3_prd(sK89_skl(B,A),sK88_skl(B,A),B,A)
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ! [C,D] : sP3_prd(D,C,B,A)
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88_skl,sK89_skl,sK90_skl,sK91_skl]),skolemize(C,sK88_skl(B,A)),skolemize(D,sK89_skl(B,A)),skolemize(C,sK90_skl(B,A)),skolemize(D,sK91_skl(B,A))],[f1064]) ).
fof(f1066,plain,
! [X0,X1] :
( ~ relation(X1)
| relation_dom(X1) = relation_rng(X0)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| function_inverse(X0) != X1 ),
inference(cnf_transformation,[status(thm)],[f1065]) ).
fof(f1068,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,relation_dom(X2))
| ~ one_to_one(X2)
| ~ relation(X2)
| X0 != function_inverse(X2)
| apply(X2,X3) != X1
| ~ function(X0)
| ~ function(X2)
| in(X1,relation_rng(X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1065]) ).
fof(f1069,plain,
! [X0,X1,X2,X3] :
( ~ one_to_one(X0)
| ~ function(X1)
| X2 = apply(X1,X3)
| X1 != function_inverse(X0)
| ~ in(X2,relation_dom(X0))
| apply(X0,X2) != X3
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f1065]) ).
fof(f1079,plain,
! [A] :
( A = empty_set
| ? [B,C] : in(ordered_pair(B,C),A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f237]) ).
fof(f1080,plain,
! [A] :
( A = empty_set
| in(ordered_pair(sK92_skl(A),sK93_skl(A)),A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92_skl,sK93_skl]),skolemize(B,sK92_skl(A)),skolemize(C,sK93_skl(A))],[f1079]) ).
fof(f1081,plain,
! [X0] :
( in(ordered_pair(sK92_skl(X0),sK93_skl(X0)),X0)
| X0 = empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1080]) ).
fof(f1089,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f1090,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f1091,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f241]) ).
fof(f1092,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1091]) ).
fof(f1098,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f244]) ).
fof(f1100,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) != empty_set
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f1098]) ).
fof(f1101,plain,
! [A] :
( ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f245]) ).
fof(f1102,plain,
! [A] :
( ( ( relation_rng(A) != empty_set
| relation_dom(A) = empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) != empty_set ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f1101]) ).
fof(f1103,plain,
! [X0] :
( ~ relation(X0)
| empty_set != relation_dom(X0)
| empty_set = relation_rng(X0) ),
inference(cnf_transformation,[status(thm)],[f1102]) ).
fof(f1105,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(NNF_transformation,[status(thm)],[f246]) ).
fof(f1106,plain,
( ! [A,B] :
( in(B,A)
| set_difference(A,singleton(B)) = A )
& ! [A,B] :
( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(miniscoping,[status(thm)],[f1105]) ).
fof(f1107,plain,
! [X0,X1] :
( set_difference(X1,singleton(X0)) != X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1106]) ).
fof(f1109,plain,
! [A,B] :
( ! [C] :
( ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f247]) ).
fof(f1110,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f1109]) ).
fof(f1111,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1110]) ).
fof(f1112,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK94_skl(A,C,B)) != apply(C,sK94_skl(A,C,B))
& in(sK94_skl(A,C,B),relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94_skl]),skolemize(D,sK94_skl(A,C,B))],[f1111]) ).
fof(f1113,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X1)
| X1 != relation_dom_restriction(X0,X2)
| ~ relation(X1)
| relation_dom(X1) = set_intersection2(relation_dom(X0),X2)
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f1112]) ).
fof(f1115,plain,
! [X0,X1,X2] :
( relation_dom_restriction(X0,X1) = X2
| ~ relation(X0)
| ~ relation(X2)
| ~ function(X0)
| ~ function(X2)
| in(sK94_skl(X1,X0,X2),relation_dom(X2))
| set_intersection2(relation_dom(X0),X1) != relation_dom(X2) ),
inference(cnf_transformation,[status(thm)],[f1112]) ).
fof(f1117,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f1125,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f252]) ).
fof(f1126,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1125]) ).
fof(f1127,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1125]) ).
fof(f1137,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f255]) ).
fof(f1138,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f1137]) ).
fof(f1139,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1138]) ).
fof(f1140,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f256]) ).
fof(f1141,plain,
! [B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f1140]) ).
fof(f1142,plain,
! [B] :
( ( ! [D] :
( ~ in(D,sK95_skl(B))
| ~ in(D,B) )
& in(sK95_skl(B),B) )
| ! [A] : ~ in(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95_skl]),skolemize(C,sK95_skl(B))],[f1141]) ).
fof(f1143,plain,
! [X0,X1] :
( ~ in(X1,X0)
| in(sK95_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f1142]) ).
fof(f1144,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,sK95_skl(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1142]) ).
fof(f1145,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f1146,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f258]) ).
fof(f1147,plain,
( ! [A,B] :
( set_difference(A,B) != A
| disjoint(A,B) )
& ! [A,B] :
( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f1146]) ).
fof(f1149,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1147]) ).
fof(f1150,plain,
! [A,B,C] :
( ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f259]) ).
fof(f1151,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f1150]) ).
fof(f1152,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ! [A,B] :
( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f1151]) ).
fof(f1155,plain,
! [X0,X1,X2] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[status(thm)],[f1152]) ).
fof(f1162,plain,
! [A,B,C] :
( ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f262]) ).
fof(f1163,plain,
! [A,B,C] :
( ( ( B != apply(C,A)
| ~ in(A,relation_dom(C))
| in(ordered_pair(A,B),C) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f1162]) ).
fof(f1164,plain,
! [C] :
( ( ! [A,B] :
( B != apply(C,A)
| ~ in(A,relation_dom(C))
| in(ordered_pair(A,B),C) )
& ! [A,B] :
( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f1163]) ).
fof(f1165,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1164]) ).
fof(f1166,plain,
! [X0,X1,X2] :
( ~ relation(X1)
| ~ in(ordered_pair(X2,X0),X1)
| ~ function(X1)
| X0 = apply(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1164]) ).
fof(f1167,plain,
! [X0,X1,X2] :
( ~ in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| in(ordered_pair(X2,X0),X1)
| X0 != apply(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1164]) ).
fof(f1168,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f263]) ).
fof(f1169,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| subset(set_union2(X2,X0),X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1168]) ).
fof(f1181,plain,
! [A,B] :
( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f268]) ).
fof(f1182,plain,
! [B] :
( ! [A] : subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1181]) ).
fof(f1183,plain,
! [X0,X1] :
( ~ relation(X0)
| subset(relation_rng(relation_dom_restriction(X0,X1)),relation_rng(X0)) ),
inference(cnf_transformation,[status(thm)],[f1182]) ).
fof(f1185,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f270]) ).
fof(f1186,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [D] :
( in(D,B)
| ! [C] :
( ~ subset(D,C)
| ~ in(C,B) ) )
& in(A,B) ),
inference(miniscoping,[status(thm)],[f1185]) ).
fof(f1187,plain,
! [A] :
( ! [C] :
( in(C,sK96_skl(A))
| are_equipotent(C,sK96_skl(A))
| ~ subset(C,sK96_skl(A)) )
& ! [C] :
( ( ! [E] :
( in(E,sK97_skl(C,A))
| ~ subset(E,C) )
& in(sK97_skl(C,A),sK96_skl(A)) )
| ~ in(C,sK96_skl(A)) )
& ! [D] :
( in(D,sK96_skl(A))
| ! [C] :
( ~ subset(D,C)
| ~ in(C,sK96_skl(A)) ) )
& in(A,sK96_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96_skl,sK97_skl]),skolemize(B,sK96_skl(A)),skolemize(D,sK97_skl(C,A))],[f1186]) ).
fof(f1188,plain,
! [X0] : in(X0,sK96_skl(X0)),
inference(cnf_transformation,[status(thm)],[f1187]) ).
fof(f1189,plain,
! [X0,X1,X2] :
( ~ in(X1,sK96_skl(X2))
| in(X0,sK96_skl(X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1187]) ).
fof(f1191,plain,
! [X0,X1,X2] :
( in(X2,sK97_skl(X0,X1))
| ~ subset(X2,X0)
| ~ in(X0,sK96_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f1187]) ).
fof(f1221,plain,
! [X0,X1,X2] :
( in(X2,X0)
| X0 != unordered_pair(X1,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f447]) ).
fof(f1223,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1)
| identity_relation(X1) != X0
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f302]) ).
fof(f1225,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f309]) ).
fof(f1228,plain,
! [X0,X1] :
( in(X1,X0)
| X0 != singleton(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f405]) ).
fof(f1241,definition,
( sQ0_spl
<=> in(sK84_skl,sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1242,plain,
( ~ sQ0_spl
| in(sK84_skl,sK84_skl) ),
inference(component_clause,[status(thm)],[f1241]) ).
fof(f1244,definition,
( sQ1_spl
<=> sK84_skl = sK84_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1250,plain,
! [X0,X1] :
( ~ in(X1,sK84_skl)
| in(X0,sK84_skl)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f489,f968]) ).
fof(f1252,plain,
( ~ relation(empty_set)
| empty_set = empty_set ),
inference(resolution,[status(thm)],[f1090,f1100]) ).
fof(f1254,definition,
( sQ2_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1257,definition,
( sQ3_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1259,plain,
( sQ3_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f1257]) ).
fof(f1261,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1252,f1254,f1257]) ).
fof(f1262,plain,
! [X0] :
( ~ in(X0,X0)
| ~ in(X0,X0) ),
inference(factoring,[status(thm)],[f1012]) ).
fof(f1263,plain,
! [X0] : ~ in(X0,X0),
inference(duplicate_literals_removal,[status(thm)],[f1262]) ).
fof(f1272,definition,
( sQ4_spl
<=> ordinal(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1273,plain,
( ~ sQ4_spl
| ordinal(sK84_skl) ),
inference(component_clause,[status(thm)],[f1272]) ).
fof(f1287,plain,
! [X0,X1] :
( ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f917,f968]) ).
fof(f1290,plain,
! [X0,X1] :
( ~ in(X1,sK84_skl)
| ~ subset(X0,X1)
| subset(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f917,f968]) ).
fof(f1293,definition,
( sQ7_spl
<=> subset(sK84_skl,sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1300,definition,
! [X0] :
( sQ8_spl
<=> ( ~ in(X0,sK84_skl)
| subset(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1313,plain,
! [X0,X1] :
( ~ in(X1,sK84_skl)
| subset(X1,sK84_skl)
| ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X0) ),
inference(resolution,[status(thm)],[f1290,f1287]) ).
fof(f1316,plain,
! [X0,X1,X2] :
( ~ in(X2,sK84_skl)
| ~ subset(X1,X2)
| subset(X0,sK84_skl)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f1290,f917]) ).
fof(f1317,plain,
! [X0] :
( subset(sK84_skl,sK84_skl)
| ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X0) ),
inference(resolution,[status(thm)],[f1290,f917]) ).
fof(f1318,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ in(X2,sK84_skl)
| ~ subset(sK84_skl,X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f1290,f917]) ).
fof(f1319,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| in(X2,sK84_skl)
| ~ subset(X1,X0)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1290,f489]) ).
fof(f1320,plain,
! [X0,X1] :
( ~ subset(sK84_skl,X0)
| ~ subset(X0,X1)
| ~ in(X1,sK84_skl)
| sK84_skl = X0 ),
inference(resolution,[status(thm)],[f1290,f310]) ).
fof(f1321,definition,
! [X0] :
( sQ9_spl
<=> ( ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1322,plain,
! [X0] :
( ~ sQ9_spl
| ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X0) ),
inference(component_clause,[status(thm)],[f1321]) ).
fof(f1325,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1317,f1321,f1293]) ).
fof(f1326,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1313,f1321,f1300]) ).
fof(f1330,plain,
! [X0] :
( ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X0)
| sK84_skl = sK84_skl ),
inference(resolution,[status(thm)],[f1320,f1225]) ).
fof(f1331,plain,
( sQ9_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f1330,f1244,f1321]) ).
fof(f1334,plain,
! [X0,X1,X2] :
( ~ in(X2,ordered_pair(sK14_skl(X1,X0,sK84_skl),sK15_skl(X1,X0,sK84_skl)))
| in(X2,sK84_skl)
| ~ relation(sK84_skl)
| in(sK14_skl(X1,X0,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X0) = X1 ),
inference(resolution,[status(thm)],[f369,f1250]) ).
fof(f1335,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK14_skl(X1,X0,sK84_skl),sK15_skl(X1,X0,sK84_skl)))
| ~ relation(sK84_skl)
| in(sK14_skl(X1,X0,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X0) = X1 ),
inference(resolution,[status(thm)],[f369,f967]) ).
fof(f1342,definition,
! [X0,X1] :
( sQ10_spl
<=> ( ordinal(ordered_pair(sK14_skl(X1,X0,sK84_skl),sK15_skl(X1,X0,sK84_skl)))
| in(sK14_skl(X1,X0,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1345,definition,
( sQ11_spl
<=> relation(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1347,plain,
( sQ11_spl
| ~ relation(sK84_skl) ),
inference(component_clause,[status(thm)],[f1345]) ).
fof(f1348,plain,
( ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f1335,f1342,f1345]) ).
fof(f1349,definition,
! [X0,X1,X2] :
( sQ12_spl
<=> ( ~ in(X2,ordered_pair(sK14_skl(X1,X0,sK84_skl),sK15_skl(X1,X0,sK84_skl)))
| in(X2,sK84_skl)
| in(sK14_skl(X1,X0,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1352,plain,
( ~ sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f1334,f1349,f1345]) ).
fof(f1361,plain,
! [X0,X1,X2] :
( ~ in(X2,sK84_skl)
| subset(X2,sK84_skl)
| ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X0)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f1316,f1287]) ).
fof(f1362,plain,
! [X0,X1] :
( subset(sK84_skl,sK84_skl)
| ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X0)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f1316,f917]) ).
fof(f1365,plain,
! [X0,X1,X2,X3] :
( ~ subset(X1,X3)
| ~ subset(sK84_skl,X2)
| ~ subset(X3,X0)
| subset(X1,X2)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1316,f917]) ).
fof(f1368,definition,
! [X0,X1] :
( sQ13_spl
<=> ( ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X0)
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1369,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X0)
| ~ subset(X0,X1) ),
inference(component_clause,[status(thm)],[f1368]) ).
fof(f1371,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1362,f1368,f1293]) ).
fof(f1372,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1361,f1368,f1300]) ).
fof(f1377,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X1)
| ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X0) ),
inference(resolution,[status(thm)],[f1369,f1290]) ).
fof(f1381,plain,
( ~ sQ13_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1377,f1321,f1368]) ).
fof(f1418,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,sK84_skl)
| ~ subset(sK84_skl,X2)
| ~ subset(X2,X3)
| ~ in(X1,sK84_skl)
| ~ subset(X0,X1)
| subset(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1318,f1316]) ).
fof(f1432,definition,
! [X0,X1,X2,X3] :
( sQ17_spl
<=> ( ~ in(X3,sK84_skl)
| ~ subset(X0,X2)
| ~ subset(X2,X3)
| ~ subset(sK84_skl,X1)
| subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f1436,definition,
! [X0,X1,X2] :
( sQ18_spl
<=> ( ~ in(X2,sK84_skl)
| ~ subset(X0,X2)
| ~ subset(sK84_skl,X1)
| subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f1441,definition,
! [X0,X1] :
( sQ19_spl
<=> ( ~ in(X1,sK84_skl)
| ~ subset(X0,X1)
| subset(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f1447,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X1)
| subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1451,plain,
( sQ13_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f1418,f1441,f1368]) ).
fof(f1471,definition,
! [X0,X1,X2] :
( sQ22_spl
<=> ( ~ in(X2,sK84_skl)
| ~ subset(X1,X2)
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1488,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,sK84_skl)
| ~ subset(X0,X3)
| ~ subset(X3,X4)
| ~ subset(sK84_skl,X1)
| ~ in(X2,sK84_skl)
| ~ subset(sK84_skl,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f1365,f1316]) ).
fof(f1490,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,sK84_skl)
| ~ subset(X0,X3)
| ~ subset(sK84_skl,X1)
| ~ in(X2,sK84_skl)
| ~ subset(sK84_skl,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f1365,f1290]) ).
fof(f1492,plain,
! [X0,X1,X2] :
( ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X1)
| ~ in(X2,sK84_skl)
| ~ subset(sK84_skl,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f1365,f968]) ).
fof(f1495,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,sK84_skl)
| ~ subset(sK84_skl,X3)
| ~ subset(X3,X4)
| ~ subset(X0,X1)
| ~ in(X2,sK84_skl)
| ~ subset(X1,X2)
| subset(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1365,f1316]) ).
fof(f1505,plain,
( sQ9_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f1488,f1432,f1321]) ).
fof(f1506,definition,
! [X0,X1,X2] :
( sQ24_spl
<=> ( ~ subset(X0,X1)
| ~ in(X2,sK84_skl)
| ~ subset(X1,X2)
| subset(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1513,plain,
( sQ13_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f1495,f1506,f1368]) ).
fof(f1515,plain,
( sQ9_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1492,f1447,f1321]) ).
fof(f1521,plain,
( sQ9_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f1490,f1436,f1321]) ).
fof(f1532,plain,
! [X0,X1,X2,X3] :
( ~ subset(sK84_skl,X1)
| ~ in(X3,sK84_skl)
| ~ subset(singleton(X2),X3)
| subset(X0,X1)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1007,f1365]) ).
fof(f1534,plain,
! [X0,X1,X2,X3] :
( ~ subset(sK84_skl,X2)
| ~ subset(X1,X0)
| ~ in(singleton(X3),sK84_skl)
| subset(X1,X2)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1007,f1365]) ).
fof(f1535,plain,
! [X0,X1,X2] :
( ~ in(X1,X0)
| ~ in(singleton(X2),sK84_skl)
| in(X1,sK84_skl)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1007,f1319]) ).
fof(f1537,plain,
! [X0,X1,X2] :
( ~ in(singleton(X2),sK84_skl)
| ~ subset(sK84_skl,X1)
| subset(X0,X1)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1007,f1318]) ).
fof(f1539,plain,
! [X0,X1,X2] :
( subset(X0,singleton(X2))
| X1 != empty_set
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f1007,f917]) ).
fof(f1541,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(singleton(X1),X2)
| empty_set != X0 ),
inference(resolution,[status(thm)],[f1007,f917]) ).
fof(f1544,definition,
( sQ26_spl
<=> sK84_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1545,plain,
( ~ sQ26_spl
| sK84_skl = empty_set ),
inference(component_clause,[status(thm)],[f1544]) ).
fof(f1546,plain,
( sQ26_spl
| empty_set != sK84_skl ),
inference(component_clause,[status(thm)],[f1544]) ).
fof(f1555,definition,
! [X0,X1] :
( sQ29_spl
<=> ( ~ in(X1,X0)
| in(X1,sK84_skl)
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1558,definition,
! [X2] :
( sQ30_spl
<=> ~ in(singleton(X2),sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1561,plain,
( sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f1535,f1555,f1558]) ).
fof(f1562,definition,
! [X0,X1] :
( sQ31_spl
<=> ( ~ in(X1,sK84_skl)
| ~ subset(singleton(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1567,definition,
! [X0,X1,X2] :
( sQ32_spl
<=> ( ~ in(X2,sK84_skl)
| ~ subset(X0,X2)
| subset(X0,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1571,definition,
! [X0] :
( sQ33_spl
<=> ( ~ in(singleton(X0),sK84_skl)
| subset(sK84_skl,singleton(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1572,plain,
! [X0] :
( ~ sQ33_spl
| ~ in(singleton(X0),sK84_skl)
| subset(sK84_skl,singleton(X0)) ),
inference(component_clause,[status(thm)],[f1571]) ).
fof(f1575,definition,
! [X0,X1] :
( sQ34_spl
<=> ( ~ in(X0,sK84_skl)
| subset(X0,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f1579,definition,
! [X0,X1] :
( sQ35_spl
<=> ( ~ subset(sK84_skl,X1)
| subset(X0,X1)
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f1580,plain,
! [X0,X1] :
( ~ sQ35_spl
| ~ subset(sK84_skl,X1)
| X0 != empty_set
| subset(X0,X1) ),
inference(component_clause,[status(thm)],[f1579]) ).
fof(f1582,plain,
( sQ30_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1537,f1579,f1558]) ).
fof(f1583,definition,
! [X0,X1,X2] :
( sQ36_spl
<=> ( ~ subset(sK84_skl,X2)
| ~ subset(X1,X0)
| subset(X1,X2)
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f1586,plain,
( sQ30_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f1534,f1583,f1558]) ).
fof(f1588,plain,
( sQ31_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f1532,f1579,f1562]) ).
fof(f1590,plain,
! [X0,X1] :
( ~ in(X1,sK22_skl(X0,sK84_skl))
| in(X1,sK84_skl)
| ~ in(sK21_skl(X0,sK84_skl),X0)
| empty_set = sK84_skl
| set_meet(sK84_skl) = X0 ),
inference(resolution,[status(thm)],[f396,f1250]) ).
fof(f1591,plain,
! [X0] :
( ordinal(sK22_skl(X0,sK84_skl))
| ~ in(sK21_skl(X0,sK84_skl),X0)
| empty_set = sK84_skl
| set_meet(sK84_skl) = X0 ),
inference(resolution,[status(thm)],[f396,f967]) ).
fof(f1598,definition,
! [X0] :
( sQ37_spl
<=> ( ordinal(sK22_skl(X0,sK84_skl))
| ~ in(sK21_skl(X0,sK84_skl),X0)
| set_meet(sK84_skl) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1599,plain,
! [X0] :
( ~ sQ37_spl
| ordinal(sK22_skl(X0,sK84_skl))
| set_meet(sK84_skl) = X0
| ~ in(sK21_skl(X0,sK84_skl),X0) ),
inference(component_clause,[status(thm)],[f1598]) ).
fof(f1601,plain,
( sQ26_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f1591,f1598,f1544]) ).
fof(f1602,definition,
! [X0,X1] :
( sQ38_spl
<=> ( ~ in(X1,sK22_skl(X0,sK84_skl))
| in(X1,sK84_skl)
| ~ in(sK21_skl(X0,sK84_skl),X0)
| set_meet(sK84_skl) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1603,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ in(sK21_skl(X0,sK84_skl),X0)
| ~ in(X1,sK22_skl(X0,sK84_skl))
| in(X1,sK84_skl)
| set_meet(sK84_skl) = X0 ),
inference(component_clause,[status(thm)],[f1602]) ).
fof(f1605,plain,
( sQ26_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1590,f1602,f1544]) ).
fof(f1606,plain,
! [X0] :
( ~ sQ33_spl
| ~ sQ9_spl
| ~ in(singleton(X0),sK84_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1572,f1322]) ).
fof(f1619,plain,
( ~ sQ26_spl
| ~ ordinal(empty_set) ),
inference(backward_demodulation,[status(thm)],[f1545,f969]) ).
fof(f1620,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1619,f667]) ).
fof(f1621,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f1620]) ).
fof(f1638,plain,
! [X0] :
( ~ sQ37_spl
| ordinal(sK22_skl(sK84_skl,sK84_skl))
| set_meet(sK84_skl) = sK84_skl
| ~ in(X0,sK84_skl)
| ~ in(sK21_skl(sK84_skl,sK84_skl),X0) ),
inference(resolution,[status(thm)],[f1250,f1599]) ).
fof(f1640,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X1,sK84_skl)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f1250,f967]) ).
fof(f1661,definition,
! [X0] :
( sQ40_spl
<=> ( ~ in(X0,sK84_skl)
| ~ in(sK84_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1665,definition,
! [X0] :
( sQ41_spl
<=> ( ~ in(X0,sK84_skl)
| ~ in(sK21_skl(sK84_skl,sK84_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1668,definition,
( sQ42_spl
<=> set_meet(sK84_skl) = sK84_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1671,definition,
( sQ43_spl
<=> ordinal(sK22_skl(sK84_skl,sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1674,plain,
( ~ sQ37_spl
| sQ43_spl
| sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1638,f1665,f1668,f1671,f1598]) ).
fof(f1690,plain,
( ordinal(sK72_skl)
| ~ epsilon_transitive(sK72_skl) ),
inference(resolution,[status(thm)],[f288,f784]) ).
fof(f1691,definition,
( sQ46_spl
<=> epsilon_transitive(sK72_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1693,plain,
( sQ46_spl
| ~ epsilon_transitive(sK72_skl) ),
inference(component_clause,[status(thm)],[f1691]) ).
fof(f1694,definition,
( sQ47_spl
<=> ordinal(sK72_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1697,plain,
( sQ47_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1690,f1691,f1694]) ).
fof(f1698,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1693,f783]) ).
fof(f1699,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f1698]) ).
fof(f1717,plain,
( ordinal(sK77_skl)
| ~ epsilon_transitive(sK77_skl) ),
inference(resolution,[status(thm)],[f801,f288]) ).
fof(f1718,definition,
( sQ48_spl
<=> epsilon_transitive(sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1720,plain,
( sQ48_spl
| ~ epsilon_transitive(sK77_skl) ),
inference(component_clause,[status(thm)],[f1718]) ).
fof(f1721,definition,
( sQ49_spl
<=> ordinal(sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1724,plain,
( sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f1717,f1718,f1721]) ).
fof(f1732,plain,
! [X0,X1,X2] :
( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X2)
| ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X1)
| X1 = relation_dom_restriction(sK84_skl,X0)
| ~ relation(X1)
| ~ relation(sK84_skl)
| ~ in(sK2_skl(X0,X1,sK84_skl),X0) ),
inference(resolution,[status(thm)],[f318,f1250]) ).
fof(f1733,plain,
! [X0,X1,X2] :
( ~ ordinal(ordered_pair(sK2_skl(X1,X2,X0),sK3_skl(X1,X2,X0)))
| in(X0,ordered_pair(sK2_skl(X1,X2,X0),sK3_skl(X1,X2,X0)))
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = X2
| ~ relation(X2)
| X0 = ordered_pair(sK2_skl(X1,X2,X0),sK3_skl(X1,X2,X0))
| ~ in(ordered_pair(sK2_skl(X1,X2,X0),sK3_skl(X1,X2,X0)),X2)
| ~ in(sK2_skl(X1,X2,X0),X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f318,f943]) ).
fof(f1734,definition,
! [X0,X1,X2] :
( sQ50_spl
<=> ( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X2)
| ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X1)
| X1 = relation_dom_restriction(sK84_skl,X0)
| ~ relation(X1)
| ~ in(sK2_skl(X0,X1,sK84_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1737,plain,
( ~ sQ11_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f1732,f1734,f1345]) ).
fof(f1759,definition,
! [X1] :
( sQ51_spl
<=> singleton(X1) != empty_set ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1760,plain,
! [X0] :
( ~ sQ51_spl
| singleton(X0) != empty_set ),
inference(component_clause,[status(thm)],[f1759]) ).
fof(f1771,plain,
! [X0] :
( in(X0,sK84_skl)
| ~ in(X0,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl)))
| empty_set = sK84_skl
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f1081,f1250]) ).
fof(f1772,plain,
( ordinal(ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl)))
| empty_set = sK84_skl
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f1081,f967]) ).
fof(f1780,definition,
! [X0] :
( sQ53_spl
<=> ( in(X0,sK84_skl)
| ~ in(X0,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1783,plain,
( sQ53_spl
| sQ26_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1771,f1345,f1544,f1780]) ).
fof(f1784,definition,
( sQ54_spl
<=> ordinal(ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1787,plain,
( sQ54_spl
| sQ26_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1772,f1345,f1544,f1784]) ).
fof(f1793,plain,
! [X0,X1,X2] :
( ~ function(X1)
| ~ relation(X1)
| ordinal(sK94_skl(X2,X0,X1))
| relation_dom(X1) != set_intersection2(relation_dom(X0),X2)
| X1 = relation_dom_restriction(X0,X2)
| ~ ordinal(relation_dom(X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1115,f941]) ).
fof(f1794,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| relation_dom(X0) != set_intersection2(relation_dom(X2),X1)
| ~ function(X0)
| ~ function(X2)
| ~ relation(X2)
| X0 = relation_dom_restriction(X2,X1)
| ~ in(relation_dom(X0),sK94_skl(X1,X2,X0)) ),
inference(resolution,[status(thm)],[f1115,f273]) ).
fof(f1805,plain,
! [X0,X1] :
( ~ sQ35_spl
| ~ subset(sK84_skl,X1)
| ~ in(X1,sK84_skl)
| X0 != empty_set
| subset(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1580,f1290]) ).
fof(f1810,plain,
! [X0] :
( ~ sQ35_spl
| subset(X0,sK84_skl)
| empty_set != X0 ),
inference(resolution,[status(thm)],[f1580,f1225]) ).
fof(f1811,definition,
! [X0] :
( sQ55_spl
<=> ( X0 != empty_set
| subset(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1812,plain,
! [X0] :
( ~ sQ55_spl
| empty_set != X0
| subset(X0,sK84_skl) ),
inference(component_clause,[status(thm)],[f1811]) ).
fof(f1814,plain,
( ~ sQ35_spl
| sQ9_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1805,f1811,f1321,f1579]) ).
fof(f1817,definition,
! [X0,X1] :
( sQ56_spl
<=> ( X0 != empty_set
| subset(X0,singleton(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1822,plain,
! [X0,X1,X2] :
( ~ subset(singleton(X2),X1)
| ~ in(X1,sK84_skl)
| X0 != empty_set
| subset(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1541,f1290]) ).
fof(f1823,plain,
! [X0,X1] :
( ~ in(singleton(X1),sK84_skl)
| X0 != empty_set
| subset(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1541,f968]) ).
fof(f1827,plain,
( sQ30_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1823,f1811,f1558]) ).
fof(f1830,plain,
( sQ31_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1822,f1811,f1562]) ).
fof(f1839,plain,
! [X0,X1] :
( ~ sQ35_spl
| X1 != empty_set
| subset(X0,sK84_skl)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f1810,f917]) ).
fof(f1842,plain,
! [X0,X1] :
( ~ sQ35_spl
| in(X0,sK84_skl)
| empty_set != X1
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f1810,f489]) ).
fof(f1856,definition,
! [X0] :
( sQ57_spl
<=> ( ~ in(singleton(X0),sK84_skl)
| singleton(X0) = sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1860,definition,
! [X0,X1] :
( sQ58_spl
<=> ( ~ subset(singleton(X0),X1)
| ~ in(X1,sK84_skl)
| singleton(X0) = sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1869,plain,
! [X0,X1,X2,X3] :
( X2 != empty_set
| subset(X2,singleton(X3))
| ~ subset(singleton(X1),X0)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1539,f1541]) ).
fof(f1870,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| X1 != empty_set
| subset(X1,singleton(X2))
| ~ subset(sK84_skl,X0)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1539,f1580]) ).
fof(f1871,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ in(singleton(X1),sK84_skl)
| ~ subset(sK84_skl,X0)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1539,f1322]) ).
fof(f1872,plain,
! [X0,X1,X2] :
( subset(X1,singleton(X2))
| ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X0)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f1539,f1287]) ).
fof(f1879,definition,
! [X0] :
( sQ60_spl
<=> ( ~ subset(sK84_skl,X0)
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1880,plain,
! [X0] :
( ~ sQ60_spl
| empty_set != X0
| ~ subset(sK84_skl,X0) ),
inference(component_clause,[status(thm)],[f1879]) ).
fof(f1882,plain,
( sQ34_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1872,f1879,f1575]) ).
fof(f1883,definition,
! [X0,X1] :
( sQ61_spl
<=> ( ~ subset(singleton(X1),X0)
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1886,plain,
( sQ56_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f1869,f1883,f1817]) ).
fof(f1887,plain,
( ~ sQ9_spl
| sQ30_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1871,f1879,f1558,f1321]) ).
fof(f1888,plain,
( ~ sQ35_spl
| sQ56_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1870,f1879,f1817,f1579]) ).
fof(f1898,plain,
! [X0,X1,X2] :
( in(X2,sK84_skl)
| ~ in(X2,sK20_skl(X1,X0,sK84_skl))
| in(X1,X0)
| X0 != set_meet(sK84_skl)
| sK84_skl = empty_set ),
inference(resolution,[status(thm)],[f394,f1250]) ).
fof(f1899,plain,
! [X0,X1] :
( ordinal(sK20_skl(X1,X0,sK84_skl))
| in(X1,X0)
| X0 != set_meet(sK84_skl)
| sK84_skl = empty_set ),
inference(resolution,[status(thm)],[f394,f967]) ).
fof(f1907,definition,
! [X0,X1] :
( sQ62_spl
<=> ( ordinal(sK20_skl(X1,X0,sK84_skl))
| in(X1,X0)
| X0 != set_meet(sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1910,plain,
( sQ62_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1899,f1544,f1907]) ).
fof(f1911,definition,
! [X0,X1,X2] :
( sQ63_spl
<=> ( in(X2,sK84_skl)
| ~ in(X2,sK20_skl(X1,X0,sK84_skl))
| in(X1,X0)
| X0 != set_meet(sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1914,plain,
( sQ63_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1898,f1544,f1911]) ).
fof(f1943,plain,
! [X0,X1,X2] :
( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(X1,X0))
| ~ in(X1,relation_dom(sK84_skl))
| ~ relation(sK84_skl)
| ~ function(sK84_skl)
| X0 != apply(sK84_skl,X1) ),
inference(resolution,[status(thm)],[f1167,f1250]) ).
fof(f1944,plain,
! [X0,X1] :
( ordinal(ordered_pair(X1,X0))
| ~ in(X1,relation_dom(sK84_skl))
| ~ relation(sK84_skl)
| ~ function(sK84_skl)
| X0 != apply(sK84_skl,X1) ),
inference(resolution,[status(thm)],[f1167,f967]) ).
fof(f1958,definition,
! [X0,X1] :
( sQ67_spl
<=> ( ordinal(ordered_pair(X1,X0))
| ~ in(X1,relation_dom(sK84_skl))
| X0 != apply(sK84_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1961,definition,
( sQ68_spl
<=> function(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1964,plain,
( ~ sQ11_spl
| ~ sQ68_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1944,f1958,f1961,f1345]) ).
fof(f1966,definition,
! [X0,X1,X2] :
( sQ69_spl
<=> ( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(X1,X0))
| ~ in(X1,relation_dom(sK84_skl))
| X0 != apply(sK84_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1969,plain,
( ~ sQ11_spl
| ~ sQ68_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1943,f1966,f1961,f1345]) ).
fof(f1973,plain,
( ~ relation(identity_relation(empty_set))
| identity_relation(empty_set) = empty_set ),
inference(resolution,[status(thm)],[f1127,f1100]) ).
fof(f1975,definition,
( sQ70_spl
<=> identity_relation(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1976,plain,
( ~ sQ70_spl
| identity_relation(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f1975]) ).
fof(f1978,definition,
( sQ71_spl
<=> relation(identity_relation(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1980,plain,
( sQ71_spl
| ~ relation(identity_relation(empty_set)) ),
inference(component_clause,[status(thm)],[f1978]) ).
fof(f1981,plain,
( ~ sQ71_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1973,f1975,f1978]) ).
fof(f2027,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(resolution,[status(thm)],[f1221,f293]) ).
fof(f2030,plain,
! [X0,X1] : in(X0,cast_to_subset(unordered_pair(X1,X0))),
inference(resolution,[status(thm)],[f1221,f521]) ).
fof(f2034,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(forward_demodulation,[status(thm)],[f521,f2030]) ).
fof(f2056,plain,
! [X0,X1,X2] :
( X1 = set_union2(X2,X0)
| ~ subset(X1,set_union2(X2,X0))
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f1169,f310]) ).
fof(f2062,plain,
! [X0] : in(X0,singleton(X0)),
inference(resolution,[status(thm)],[f1117,f1221]) ).
fof(f2078,plain,
! [X0,X1,X2] :
( in(X1,X2)
| X2 != set_meet(sK84_skl)
| sK84_skl = empty_set
| ordinal(X0)
| ~ in(X0,sK20_skl(X1,X2,sK84_skl)) ),
inference(resolution,[status(thm)],[f1640,f394]) ).
fof(f2080,plain,
! [X0,X1] :
( ~ in(sK21_skl(X1,sK84_skl),X1)
| empty_set = sK84_skl
| set_meet(sK84_skl) = X1
| ordinal(X0)
| ~ in(X0,sK22_skl(X1,sK84_skl)) ),
inference(resolution,[status(thm)],[f1640,f396]) ).
fof(f2081,plain,
! [X0] :
( empty_set = sK84_skl
| ~ relation(sK84_skl)
| ordinal(X0)
| ~ in(X0,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f1640,f1081]) ).
fof(f2082,plain,
! [X0,X1,X2] :
( ~ relation(sK84_skl)
| in(sK14_skl(X1,X2,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X2) = X1
| ordinal(X0)
| ~ in(X0,ordered_pair(sK14_skl(X1,X2,sK84_skl),sK15_skl(X1,X2,sK84_skl))) ),
inference(resolution,[status(thm)],[f1640,f369]) ).
fof(f2083,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(sK84_skl))
| ~ relation(sK84_skl)
| ~ function(sK84_skl)
| X2 != apply(sK84_skl,X1)
| ordinal(X0)
| ~ in(X0,ordered_pair(X1,X2)) ),
inference(resolution,[status(thm)],[f1640,f1167]) ).
fof(f2086,definition,
! [X0,X1,X2] :
( sQ72_spl
<=> ( in(sK14_skl(X1,X2,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X2) = X1
| ordinal(X0)
| ~ in(X0,ordered_pair(sK14_skl(X1,X2,sK84_skl),sK15_skl(X1,X2,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f2089,plain,
( ~ sQ11_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f2082,f2086,f1345]) ).
fof(f2090,definition,
! [X0,X1] :
( sQ73_spl
<=> ( ~ in(sK21_skl(X1,sK84_skl),X1)
| set_meet(sK84_skl) = X1
| ordinal(X0)
| ~ in(X0,sK22_skl(X1,sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f2093,plain,
( sQ26_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f2080,f2090,f1544]) ).
fof(f2098,definition,
! [X0,X1,X2] :
( sQ75_spl
<=> ( ~ in(X1,relation_dom(sK84_skl))
| X2 != apply(sK84_skl,X1)
| ordinal(X0)
| ~ in(X0,ordered_pair(X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f2101,plain,
( ~ sQ11_spl
| ~ sQ68_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f2083,f2098,f1961,f1345]) ).
fof(f2102,definition,
! [X0] :
( sQ76_spl
<=> ( ordinal(X0)
| ~ in(X0,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f2105,plain,
( sQ26_spl
| ~ sQ11_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f2081,f2102,f1345,f1544]) ).
fof(f2106,definition,
! [X0,X1,X2] :
( sQ77_spl
<=> ( in(X1,X2)
| X2 != set_meet(sK84_skl)
| ordinal(X0)
| ~ in(X0,sK20_skl(X1,X2,sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f2109,plain,
( sQ26_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f2078,f2106,f1544]) ).
fof(f2110,plain,
( ordinal(empty_set)
| ~ epsilon_transitive(empty_set) ),
inference(resolution,[status(thm)],[f666,f288]) ).
fof(f2111,definition,
( sQ78_spl
<=> epsilon_transitive(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f2113,plain,
( sQ78_spl
| ~ epsilon_transitive(empty_set) ),
inference(component_clause,[status(thm)],[f2111]) ).
fof(f2114,definition,
( sQ79_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f2117,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f2110,f2111,f2114]) ).
fof(f2118,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2113,f665]) ).
fof(f2119,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f2118]) ).
fof(f2120,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X1)
| X1 = relation_dom_restriction(sK84_skl,X0)
| ~ relation(X1)
| ~ relation(sK84_skl)
| ~ in(sK2_skl(X0,X1,sK84_skl),X0)
| X2 != empty_set
| ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X2) ),
inference(resolution,[status(thm)],[f1842,f318]) ).
fof(f2125,plain,
! [X0] :
( ~ sQ37_spl
| ~ sQ35_spl
| ordinal(sK22_skl(sK84_skl,sK84_skl))
| set_meet(sK84_skl) = sK84_skl
| X0 != empty_set
| ~ in(sK21_skl(sK84_skl,sK84_skl),X0) ),
inference(resolution,[status(thm)],[f1842,f1599]) ).
fof(f2142,plain,
! [X0,X1] :
( ~ sQ35_spl
| ~ in(sK84_skl,X0)
| X1 != empty_set
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f1842,f273]) ).
fof(f2147,definition,
! [X0] :
( sQ81_spl
<=> ( X0 != empty_set
| ~ in(sK84_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f2154,definition,
! [X0] :
( sQ82_spl
<=> ( X0 != empty_set
| ~ in(sK21_skl(sK84_skl,sK84_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f2157,plain,
( ~ sQ37_spl
| ~ sQ35_spl
| sQ43_spl
| sQ42_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f2125,f2154,f1668,f1671,f1579,f1598]) ).
fof(f2158,definition,
! [X0,X1,X2] :
( sQ83_spl
<=> ( ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X1)
| X1 = relation_dom_restriction(sK84_skl,X0)
| ~ relation(X1)
| ~ in(sK2_skl(X0,X1,sK84_skl),X0)
| X2 != empty_set
| ~ in(ordered_pair(sK2_skl(X0,X1,sK84_skl),sK3_skl(X0,X1,sK84_skl)),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f2161,plain,
( ~ sQ35_spl
| ~ sQ11_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f2120,f2158,f1345,f1579]) ).
fof(f2199,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| X2 != empty_set
| ~ in(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)),X2)
| ~ ordinal(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK84_skl
| ~ relation(sK84_skl)
| X0 = ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0))
| ~ in(sK2_skl(X1,sK84_skl,X0),X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1733,f1842]) ).
fof(f2200,plain,
! [X0,X1,X2] :
( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)),X2)
| ~ ordinal(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK84_skl
| ~ relation(sK84_skl)
| X0 = ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0))
| ~ in(sK2_skl(X1,sK84_skl,X0),X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1733,f1250]) ).
fof(f2203,definition,
! [X0,X1,X2] :
( sQ86_spl
<=> ( X2 != empty_set
| ~ in(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)),X2)
| ~ ordinal(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK84_skl
| X0 = ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0))
| ~ in(sK2_skl(X1,sK84_skl,X0),X1)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f2206,plain,
( ~ sQ35_spl
| ~ sQ11_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f2199,f2203,f1345,f1579]) ).
fof(f2208,definition,
! [X0,X1,X2] :
( sQ87_spl
<=> ( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)),X2)
| ~ ordinal(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK84_skl
| X0 = ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0))
| ~ in(sK2_skl(X1,sK84_skl,X0),X1)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f2211,plain,
( ~ sQ11_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f2200,f2208,f1345]) ).
fof(f2228,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| X2 != empty_set
| subset(X2,sK84_skl)
| ~ subset(singleton(X1),X0)
| empty_set != X0 ),
inference(resolution,[status(thm)],[f1839,f1541]) ).
fof(f2230,plain,
! [X0,X1] :
( ~ sQ35_spl
| X1 != empty_set
| subset(X1,sK84_skl)
| ~ subset(sK84_skl,X0)
| empty_set != X0 ),
inference(resolution,[status(thm)],[f1839,f1580]) ).
fof(f2240,plain,
( ~ sQ35_spl
| sQ55_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f2228,f1883,f1811,f1579]) ).
fof(f2244,plain,
( ~ sQ35_spl
| sQ55_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f2230,f1879,f1811,f1579]) ).
fof(f2275,plain,
! [X0,X1] :
( ~ sQ35_spl
| X1 != empty_set
| ~ in(sK84_skl,X1)
| ~ in(sK84_skl,X0)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f2142,f1842]) ).
fof(f2284,plain,
( ~ sQ35_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f2275,f2147,f1579]) ).
fof(f2291,plain,
! [X0,X1,X2] :
( ~ subset(sK84_skl,X2)
| X2 != empty_set
| ~ in(X1,sK84_skl)
| singleton(X0) = sK84_skl
| ~ subset(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f1320,f1539]) ).
fof(f2296,plain,
( sQ60_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f2291,f1860,f1879]) ).
fof(f2302,plain,
! [X0,X1,X2] :
( in(X2,X0)
| empty_set = X1
| sK20_skl(X2,X0,X1) = X2
| ~ ordinal(sK20_skl(X2,X0,X1))
| ~ ordinal(X2)
| in(sK20_skl(X2,X0,X1),X2)
| X0 != set_meet(X1) ),
inference(resolution,[status(thm)],[f395,f943]) ).
fof(f2311,plain,
! [X0,X1,X2] :
( sK95_skl(X0) = X1
| ~ in(X1,X0)
| ~ ordinal(sK95_skl(X0))
| ~ ordinal(X1)
| ~ in(X2,X0)
| in(sK95_skl(X0),X1) ),
inference(resolution,[status(thm)],[f1144,f943]) ).
fof(f2353,plain,
! [X0,X1] :
( ~ ordinal(X0)
| sK23_skl(X0,X1) = X1
| ordinal(sK23_skl(X0,X1))
| X0 = singleton(X1) ),
inference(resolution,[status(thm)],[f407,f941]) ).
fof(f2367,plain,
! [X0,X1,X2] :
( ordinal(X2)
| ~ in(X2,ordered_pair(X1,X1))
| ~ in(X1,X0)
| identity_relation(X0) != sK84_skl
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f1223,f1640]) ).
fof(f2368,plain,
! [X0,X1,X2] :
( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(X1,X1))
| ~ in(X1,X0)
| identity_relation(X0) != sK84_skl
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f1223,f1250]) ).
fof(f2369,plain,
! [X0,X1] :
( ordinal(ordered_pair(X1,X1))
| ~ in(X1,X0)
| identity_relation(X0) != sK84_skl
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f1223,f967]) ).
fof(f2385,definition,
! [X0,X1] :
( sQ90_spl
<=> ( ordinal(ordered_pair(X1,X1))
| ~ in(X1,X0)
| identity_relation(X0) != sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f2388,plain,
( sQ90_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2369,f1345,f2385]) ).
fof(f2389,definition,
! [X0,X1,X2] :
( sQ91_spl
<=> ( ordinal(X2)
| ~ in(X2,ordered_pair(X1,X1))
| ~ in(X1,X0)
| identity_relation(X0) != sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f2392,plain,
( sQ91_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2367,f1345,f2389]) ).
fof(f2393,definition,
! [X0,X1,X2] :
( sQ92_spl
<=> ( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(X1,X1))
| ~ in(X1,X0)
| identity_relation(X0) != sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f2396,plain,
( sQ92_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2368,f1345,f2393]) ).
fof(f2447,plain,
! [X0,X1,X2,X3] :
( X3 != empty_set
| subset(X3,sK84_skl)
| ~ subset(X2,X0)
| ~ subset(singleton(X1),X2)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1316,f1541]) ).
fof(f2467,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| X3 != empty_set
| subset(X1,sK84_skl)
| ~ subset(X1,X2)
| ~ in(singleton(X0),sK84_skl) ),
inference(resolution,[status(thm)],[f1316,f1539]) ).
fof(f2468,plain,
! [X0,X1,X2] :
( X2 != empty_set
| subset(X1,sK84_skl)
| ~ subset(X1,X2)
| ~ in(singleton(X0),sK84_skl) ),
inference(resolution,[status(thm)],[f1316,f1007]) ).
fof(f2473,definition,
! [X1,X2,X3] :
( sQ93_spl
<=> ( ~ subset(X2,X3)
| X3 != empty_set
| subset(X1,sK84_skl)
| ~ subset(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f2476,plain,
( sQ93_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f2467,f1558,f2473]) ).
fof(f2480,definition,
! [X0,X1] :
( sQ94_spl
<=> ( X1 != empty_set
| subset(X0,sK84_skl)
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f2486,plain,
( sQ94_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f2468,f1558,f2480]) ).
fof(f2489,definition,
! [X0,X1,X2] :
( sQ95_spl
<=> ( ~ subset(X2,X0)
| ~ subset(singleton(X1),X2)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f2492,plain,
( sQ55_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f2447,f2489,f1811]) ).
fof(f2595,plain,
! [X0,X1] :
( ordinal(X1)
| ~ in(X1,sK95_skl(sK84_skl))
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1143,f1640]) ).
fof(f2596,plain,
! [X0,X1] :
( in(X1,sK84_skl)
| ~ in(X1,sK95_skl(sK84_skl))
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1143,f1250]) ).
fof(f2597,plain,
! [X0] :
( ordinal(sK95_skl(sK84_skl))
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1143,f967]) ).
fof(f2603,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X1,X0)
| ~ in(X0,sK95_skl(X1)) ),
inference(resolution,[status(thm)],[f1143,f1012]) ).
fof(f2606,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,sK95_skl(X0)) ),
inference(resolution,[status(thm)],[f1143,f273]) ).
fof(f2607,definition,
! [X0] :
( sQ97_spl
<=> ~ in(X0,sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f2608,plain,
! [X0] :
( ~ sQ97_spl
| ~ in(X0,sK84_skl) ),
inference(component_clause,[status(thm)],[f2607]) ).
fof(f2610,definition,
! [X1] :
( sQ98_spl
<=> ( ordinal(X1)
| ~ in(X1,sK95_skl(sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f2611,plain,
! [X0] :
( ~ sQ98_spl
| ordinal(X0)
| ~ in(X0,sK95_skl(sK84_skl)) ),
inference(component_clause,[status(thm)],[f2610]) ).
fof(f2613,plain,
( sQ98_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f2595,f2607,f2610]) ).
fof(f2614,definition,
( sQ99_spl
<=> ordinal(sK95_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f2615,plain,
( ~ sQ99_spl
| ordinal(sK95_skl(sK84_skl)) ),
inference(component_clause,[status(thm)],[f2614]) ).
fof(f2617,plain,
( sQ99_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f2597,f2607,f2614]) ).
fof(f2619,definition,
! [X1] :
( sQ100_spl
<=> ( in(X1,sK84_skl)
| ~ in(X1,sK95_skl(sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f2622,plain,
( sQ100_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f2596,f2607,f2619]) ).
fof(f2631,plain,
( ~ sQ97_spl
| empty_set = sK84_skl
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f2608,f1081]) ).
fof(f2652,plain,
( ~ sQ97_spl
| sQ26_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2631,f1345,f1544,f2607]) ).
fof(f2678,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(ordered_pair(X5,X3),X1)
| ~ in(X2,X4)
| ~ relation(X2)
| ~ in(X4,ordered_pair(X5,X3))
| ~ relation(X1)
| ~ in(X3,X0)
| relation_rng_restriction(X0,X1) != X2 ),
inference(resolution,[status(thm)],[f337,f1012]) ).
fof(f2681,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(X1)
| ~ ordinal(X2)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(X4,X0)
| ordinal(ordered_pair(X3,X4))
| ~ relation(X2)
| relation_rng_restriction(X0,X1) != X2 ),
inference(resolution,[status(thm)],[f337,f941]) ).
fof(f2682,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X1,X2),X4)
| ~ in(X2,X3)
| ~ relation(X4)
| relation_rng_restriction(X3,X4) != X0
| ~ in(X0,ordered_pair(X1,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f337,f273]) ).
fof(f2687,plain,
( ordinal(sK67_skl)
| ~ epsilon_transitive(sK67_skl) ),
inference(resolution,[status(thm)],[f763,f288]) ).
fof(f2688,definition,
( sQ107_spl
<=> epsilon_transitive(sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f2690,plain,
( sQ107_spl
| ~ epsilon_transitive(sK67_skl) ),
inference(component_clause,[status(thm)],[f2688]) ).
fof(f2691,definition,
( sQ108_spl
<=> ordinal(sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f2694,plain,
( sQ108_spl
| ~ sQ107_spl ),
inference(split_clause,[status(thm)],[f2687,f2688,f2691]) ).
fof(f2695,plain,
( sQ107_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2690,f762]) ).
fof(f2696,plain,
sQ107_spl,
inference(contradiction_clause,[status(thm)],[f2695]) ).
fof(f2706,plain,
! [X0,X1,X2,X3] :
( relation_rng_restriction(X2,X3) != sK84_skl
| ~ relation(X3)
| ~ relation(sK84_skl)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X1,X2)
| ordinal(ordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[f967,f337]) ).
fof(f2717,definition,
! [X0,X1,X2,X3] :
( sQ109_spl
<=> ( relation_rng_restriction(X2,X3) != sK84_skl
| ~ relation(X3)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X1,X2)
| ordinal(ordered_pair(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f2720,plain,
( ~ sQ11_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f2706,f2717,f1345]) ).
fof(f2730,plain,
! [X0] :
( ~ in(X0,sK84_skl)
| ~ subset(sK84_skl,X0)
| sK84_skl = X0 ),
inference(resolution,[status(thm)],[f968,f310]) ).
fof(f2735,plain,
( sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1720,f800]) ).
fof(f2736,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f2735]) ).
fof(f2752,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f960,f917]) ).
fof(f2756,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f960,f310]) ).
fof(f2761,plain,
! [X0] :
( ~ sQ37_spl
| ordinal(sK22_skl(X0,sK84_skl))
| set_meet(sK84_skl) = X0
| set_meet(sK84_skl) = X0
| ~ in(X0,sK84_skl)
| in(sK21_skl(X0,sK84_skl),X0)
| empty_set = sK84_skl ),
inference(resolution,[status(thm)],[f398,f1599]) ).
fof(f2784,plain,
! [X0,X1,X2] :
( ordinal(sK21_skl(X0,X1))
| ~ ordinal(X2)
| empty_set = X1
| in(sK21_skl(X0,X1),X0)
| ~ in(X2,X1)
| X0 = set_meet(X1) ),
inference(resolution,[status(thm)],[f398,f941]) ).
fof(f2791,definition,
! [X0] :
( sQ110_spl
<=> ( ordinal(sK22_skl(X0,sK84_skl))
| set_meet(sK84_skl) = X0
| set_meet(sK84_skl) = X0
| ~ in(X0,sK84_skl)
| in(sK21_skl(X0,sK84_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f2794,plain,
( ~ sQ37_spl
| sQ110_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f2761,f1544,f2791,f1598]) ).
fof(f2800,plain,
! [X0] :
( ~ sQ98_spl
| ~ in(X0,sK95_skl(sK84_skl))
| ordinal(sK95_skl(sK95_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f2611,f1143]) ).
fof(f2804,plain,
! [X0,X1] :
( ~ sQ98_spl
| in(X0,X1)
| X1 != set_meet(sK95_skl(sK84_skl))
| sK95_skl(sK84_skl) = empty_set
| ordinal(sK20_skl(X0,X1,sK95_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f2611,f394]) ).
fof(f2806,plain,
! [X0] :
( ~ sQ98_spl
| ~ in(sK21_skl(X0,sK95_skl(sK84_skl)),X0)
| empty_set = sK95_skl(sK84_skl)
| set_meet(sK95_skl(sK84_skl)) = X0
| ordinal(sK22_skl(X0,sK95_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f2611,f396]) ).
fof(f2807,plain,
( ~ sQ98_spl
| empty_set = sK95_skl(sK84_skl)
| ~ relation(sK95_skl(sK84_skl))
| ordinal(ordered_pair(sK92_skl(sK95_skl(sK84_skl)),sK93_skl(sK95_skl(sK84_skl)))) ),
inference(resolution,[status(thm)],[f2611,f1081]) ).
fof(f2808,plain,
! [X0,X1] :
( ~ sQ98_spl
| ~ relation(sK95_skl(sK84_skl))
| in(sK14_skl(X0,X1,sK95_skl(sK84_skl)),X0)
| relation_inverse_image(sK95_skl(sK84_skl),X1) = X0
| ordinal(ordered_pair(sK14_skl(X0,X1,sK95_skl(sK84_skl)),sK15_skl(X0,X1,sK95_skl(sK84_skl)))) ),
inference(resolution,[status(thm)],[f2611,f369]) ).
fof(f2809,plain,
! [X0,X1,X2,X3] :
( ~ sQ98_spl
| relation_rng_restriction(X2,X3) != sK95_skl(sK84_skl)
| ~ relation(X3)
| ~ relation(sK95_skl(sK84_skl))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X1,X2)
| ordinal(ordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[f2611,f337]) ).
fof(f2810,plain,
! [X0,X1] :
( ~ sQ98_spl
| ~ in(X0,X1)
| identity_relation(X1) != sK95_skl(sK84_skl)
| ~ relation(sK95_skl(sK84_skl))
| ordinal(ordered_pair(X0,X0)) ),
inference(resolution,[status(thm)],[f2611,f1223]) ).
fof(f2811,plain,
! [X0,X1] :
( ~ sQ98_spl
| ~ in(X0,relation_dom(sK95_skl(sK84_skl)))
| ~ relation(sK95_skl(sK84_skl))
| ~ function(sK95_skl(sK84_skl))
| X1 != apply(sK95_skl(sK84_skl),X0)
| ordinal(ordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[f2611,f1167]) ).
fof(f2812,plain,
! [X0] :
( ~ sQ98_spl
| sK95_skl(sK84_skl) = X0
| in(sK95_skl(sK84_skl),X0)
| ~ ordinal(X0)
| ~ ordinal(sK95_skl(sK84_skl))
| ordinal(X0) ),
inference(resolution,[status(thm)],[f2611,f943]) ).
fof(f2813,definition,
( sQ111_spl
<=> ordinal(ordered_pair(sK92_skl(sK95_skl(sK84_skl)),sK93_skl(sK95_skl(sK84_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f2816,definition,
( sQ112_spl
<=> relation(sK95_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f2818,plain,
( sQ112_spl
| ~ relation(sK95_skl(sK84_skl)) ),
inference(component_clause,[status(thm)],[f2816]) ).
fof(f2819,definition,
( sQ113_spl
<=> empty_set = sK95_skl(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f2820,plain,
( ~ sQ113_spl
| empty_set = sK95_skl(sK84_skl) ),
inference(component_clause,[status(thm)],[f2819]) ).
fof(f2822,plain,
( ~ sQ98_spl
| sQ113_spl
| ~ sQ112_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f2807,f2813,f2816,f2819,f2610]) ).
fof(f2823,definition,
! [X0] :
( sQ114_spl
<=> ( ~ in(sK21_skl(X0,sK95_skl(sK84_skl)),X0)
| set_meet(sK95_skl(sK84_skl)) = X0
| ordinal(sK22_skl(X0,sK95_skl(sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f2826,plain,
( ~ sQ98_spl
| sQ113_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f2806,f2823,f2819,f2610]) ).
fof(f2827,definition,
! [X0,X1,X2,X3] :
( sQ115_spl
<=> ( relation_rng_restriction(X2,X3) != sK95_skl(sK84_skl)
| ~ relation(X3)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X1,X2)
| ordinal(ordered_pair(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f2830,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f2809,f2827,f2816,f2610]) ).
fof(f2831,definition,
( sQ116_spl
<=> ordinal(sK95_skl(sK95_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f2834,definition,
! [X0] :
( sQ117_spl
<=> ~ in(X0,sK95_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f2835,plain,
! [X0] :
( ~ sQ117_spl
| ~ in(X0,sK95_skl(sK84_skl)) ),
inference(component_clause,[status(thm)],[f2834]) ).
fof(f2837,plain,
( ~ sQ98_spl
| sQ117_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f2800,f2831,f2834,f2610]) ).
fof(f2838,definition,
! [X0] :
( sQ118_spl
<=> ( sK95_skl(sK84_skl) = X0
| in(sK95_skl(sK84_skl),X0)
| ~ ordinal(X0)
| ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f2841,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f2812,f2838,f2614,f2610]) ).
fof(f2842,definition,
! [X0,X1] :
( sQ119_spl
<=> ( in(X0,X1)
| X1 != set_meet(sK95_skl(sK84_skl))
| ordinal(sK20_skl(X0,X1,sK95_skl(sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f2845,plain,
( ~ sQ98_spl
| sQ113_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f2804,f2842,f2819,f2610]) ).
fof(f2846,definition,
! [X0,X1] :
( sQ120_spl
<=> ( ~ in(X0,X1)
| identity_relation(X1) != sK95_skl(sK84_skl)
| ordinal(ordered_pair(X0,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f2849,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f2810,f2846,f2816,f2610]) ).
fof(f2851,definition,
! [X0,X1] :
( sQ121_spl
<=> ( ~ in(X0,relation_dom(sK95_skl(sK84_skl)))
| X1 != apply(sK95_skl(sK84_skl),X0)
| ordinal(ordered_pair(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f2854,definition,
( sQ122_spl
<=> function(sK95_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f2856,plain,
( sQ122_spl
| ~ function(sK95_skl(sK84_skl)) ),
inference(component_clause,[status(thm)],[f2854]) ).
fof(f2857,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| ~ sQ122_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f2811,f2851,f2854,f2816,f2610]) ).
fof(f2858,definition,
! [X0,X1] :
( sQ123_spl
<=> ( in(sK14_skl(X0,X1,sK95_skl(sK84_skl)),X0)
| relation_inverse_image(sK95_skl(sK84_skl),X1) = X0
| ordinal(ordered_pair(sK14_skl(X0,X1,sK95_skl(sK84_skl)),sK15_skl(X0,X1,sK95_skl(sK84_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f2861,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f2808,f2858,f2816,f2610]) ).
fof(f2876,plain,
! [X0,X1,X2,X3] :
( X3 = relation_dom(X0)
| ~ ordinal(X3)
| ~ relation(X0)
| X2 != apply(X0,X3)
| in(relation_dom(X0),X3)
| in(X2,relation_rng(X0))
| ~ function(X1)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ relation(X1)
| X1 != function_inverse(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f1068,f943]) ).
fof(f2895,plain,
( ordinal(sK36_skl(sK84_skl))
| epsilon_connected(sK84_skl) ),
inference(resolution,[status(thm)],[f474,f967]) ).
fof(f2897,plain,
( ~ sQ98_spl
| ordinal(sK36_skl(sK95_skl(sK84_skl)))
| epsilon_connected(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f474,f2611]) ).
fof(f2908,definition,
( sQ124_spl
<=> epsilon_connected(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f2909,plain,
( ~ sQ124_spl
| epsilon_connected(sK84_skl) ),
inference(component_clause,[status(thm)],[f2908]) ).
fof(f2911,definition,
( sQ125_spl
<=> ordinal(sK36_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f2914,plain,
( sQ125_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f2895,f2908,f2911]) ).
fof(f2915,definition,
( sQ126_spl
<=> epsilon_connected(sK95_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f2918,definition,
( sQ127_spl
<=> ordinal(sK36_skl(sK95_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f2921,plain,
( ~ sQ98_spl
| sQ127_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f2897,f2915,f2918,f2610]) ).
fof(f2922,plain,
( ~ sQ124_spl
| ordinal(sK84_skl)
| ~ epsilon_transitive(sK84_skl) ),
inference(resolution,[status(thm)],[f2909,f288]) ).
fof(f2923,definition,
( sQ128_spl
<=> epsilon_transitive(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f2925,plain,
( sQ128_spl
| ~ epsilon_transitive(sK84_skl) ),
inference(component_clause,[status(thm)],[f2923]) ).
fof(f2926,plain,
( ~ sQ124_spl
| sQ4_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f2922,f2923,f1272,f2908]) ).
fof(f2947,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK12_skl(X1,X0,sK84_skl),sK11_skl(X1,X0,sK84_skl)))
| in(sK11_skl(X1,X0,sK84_skl),X1)
| ~ relation(sK84_skl)
| relation_image(sK84_skl,X0) = X1 ),
inference(resolution,[status(thm)],[f359,f967]) ).
fof(f2949,plain,
! [X0,X1] :
( ~ sQ98_spl
| ordinal(ordered_pair(sK12_skl(X1,X0,sK95_skl(sK84_skl)),sK11_skl(X1,X0,sK95_skl(sK84_skl))))
| in(sK11_skl(X1,X0,sK95_skl(sK84_skl)),X1)
| ~ relation(sK95_skl(sK84_skl))
| relation_image(sK95_skl(sK84_skl),X0) = X1 ),
inference(resolution,[status(thm)],[f359,f2611]) ).
fof(f2960,definition,
! [X0,X1] :
( sQ129_spl
<=> ( ordinal(ordered_pair(sK12_skl(X1,X0,sK95_skl(sK84_skl)),sK11_skl(X1,X0,sK95_skl(sK84_skl))))
| in(sK11_skl(X1,X0,sK95_skl(sK84_skl)),X1)
| relation_image(sK95_skl(sK84_skl),X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f2963,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f2949,f2960,f2816,f2610]) ).
fof(f2964,definition,
! [X0,X1] :
( sQ130_spl
<=> ( ordinal(ordered_pair(sK12_skl(X1,X0,sK84_skl),sK11_skl(X1,X0,sK84_skl)))
| in(sK11_skl(X1,X0,sK84_skl),X1)
| relation_image(sK84_skl,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f2967,plain,
( ~ sQ11_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f2947,f2964,f1345]) ).
fof(f2983,plain,
! [X0,X1,X2] :
( in(sK96_skl(X1),X2)
| X2 = sK96_skl(X1)
| ~ ordinal(X2)
| ~ subset(X0,X2)
| ~ ordinal(sK96_skl(X1))
| in(X0,sK96_skl(X1)) ),
inference(resolution,[status(thm)],[f1189,f943]) ).
fof(f2985,plain,
( sQ112_spl
| ~ sQ113_spl
| ~ relation(empty_set) ),
inference(backward_demodulation,[status(thm)],[f2820,f2818]) ).
fof(f2988,plain,
! [X0] :
( ~ sQ113_spl
| ~ in(X0,sK84_skl)
| in(empty_set,sK84_skl) ),
inference(paramodulation,[status(thm)],[f2820,f1143]) ).
fof(f2989,plain,
! [X0,X1] :
( ~ sQ113_spl
| ~ in(X1,sK84_skl)
| ~ in(X0,empty_set)
| ~ in(X0,sK84_skl) ),
inference(paramodulation,[status(thm)],[f2820,f1144]) ).
fof(f2990,plain,
( sQ112_spl
| ~ sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2985,f660]) ).
fof(f2991,plain,
( sQ112_spl
| ~ sQ113_spl ),
inference(contradiction_clause,[status(thm)],[f2990]) ).
fof(f2999,definition,
( sQ131_spl
<=> in(empty_set,sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f3002,plain,
( ~ sQ113_spl
| sQ97_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f2988,f2999,f2607,f2819]) ).
fof(f3003,definition,
! [X0] :
( sQ132_spl
<=> ( ~ in(X0,empty_set)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f3006,plain,
( ~ sQ113_spl
| sQ97_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f2989,f3003,f2607,f2819]) ).
fof(f3022,definition,
( sQ135_spl
<=> epsilon_transitive(sK95_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f3080,plain,
! [X0] :
( ordinal(ordered_pair(sK38_skl(X0,sK84_skl),sK39_skl(X0,sK84_skl)))
| subset(sK84_skl,X0)
| ~ relation(sK84_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f483,f967]) ).
fof(f3093,definition,
! [X0] :
( sQ136_spl
<=> ( ordinal(ordered_pair(sK38_skl(X0,sK84_skl),sK39_skl(X0,sK84_skl)))
| subset(sK84_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f3096,plain,
( ~ sQ11_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f3080,f3093,f1345]) ).
fof(f3118,plain,
( ~ relation(identity_relation(empty_set))
| empty_set = relation_rng(identity_relation(empty_set)) ),
inference(resolution,[status(thm)],[f1126,f1103]) ).
fof(f3143,definition,
( sQ137_spl
<=> empty_set = relation_rng(identity_relation(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f3146,plain,
( ~ sQ71_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f3118,f3143,f1978]) ).
fof(f3156,plain,
( sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1980,f658]) ).
fof(f3157,plain,
sQ71_spl,
inference(contradiction_clause,[status(thm)],[f3156]) ).
fof(f3213,plain,
! [X0,X1] :
( subset(sK84_skl,X1)
| ~ relation(sK84_skl)
| ~ relation(X1)
| ~ in(X0,ordered_pair(sK38_skl(X1,sK84_skl),sK39_skl(X1,sK84_skl)))
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f483]) ).
fof(f3214,plain,
! [X0,X1,X2] :
( in(sK11_skl(X1,X2,sK84_skl),X1)
| ~ relation(sK84_skl)
| relation_image(sK84_skl,X2) = X1
| ~ in(X0,ordered_pair(sK12_skl(X1,X2,sK84_skl),sK11_skl(X1,X2,sK84_skl)))
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f359]) ).
fof(f3217,plain,
! [X0,X1,X2,X3,X4] :
( relation_rng_restriction(X3,X4) != sK84_skl
| ~ relation(X4)
| ~ relation(sK84_skl)
| ~ in(ordered_pair(X1,X2),X4)
| ~ in(X2,X3)
| ~ in(X0,ordered_pair(X1,X2))
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f337]) ).
fof(f3229,definition,
! [X0,X1] :
( sQ139_spl
<=> ( subset(sK84_skl,X1)
| ~ relation(X1)
| ~ in(X0,ordered_pair(sK38_skl(X1,sK84_skl),sK39_skl(X1,sK84_skl)))
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f3232,plain,
( ~ sQ11_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f3213,f3229,f1345]) ).
fof(f3237,definition,
! [X0,X1,X2,X3,X4] :
( sQ140_spl
<=> ( relation_rng_restriction(X3,X4) != sK84_skl
| ~ relation(X4)
| ~ in(ordered_pair(X1,X2),X4)
| ~ in(X2,X3)
| ~ in(X0,ordered_pair(X1,X2))
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f3240,plain,
( ~ sQ11_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f3217,f3237,f1345]) ).
fof(f3243,definition,
! [X0,X1,X2] :
( sQ141_spl
<=> ( in(sK11_skl(X1,X2,sK84_skl),X1)
| relation_image(sK84_skl,X2) = X1
| ~ in(X0,ordered_pair(sK12_skl(X1,X2,sK84_skl),sK11_skl(X1,X2,sK84_skl)))
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f3246,plain,
( ~ sQ11_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f3214,f3243,f1345]) ).
fof(f3247,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1242,f1263]) ).
fof(f3248,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f3247]) ).
fof(f3279,plain,
! [X0,X1] :
( in(X0,X1)
| X0 = X1
| X0 != empty_set
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f411,f943]) ).
fof(f3332,plain,
! [X0] :
( in(sK83_skl(X0,sK84_skl),X0)
| ordinal(sK83_skl(X0,sK84_skl))
| sK84_skl = X0 ),
inference(resolution,[status(thm)],[f958,f967]) ).
fof(f3350,plain,
! [X0,X1] :
( ~ subset(sK84_skl,X1)
| X1 != empty_set
| sK84_skl = singleton(X0)
| ~ in(singleton(X0),sK84_skl) ),
inference(resolution,[status(thm)],[f2730,f1539]) ).
fof(f3356,plain,
( sQ60_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f3350,f1856,f1879]) ).
fof(f3483,plain,
! [X0,X1,X2] :
( in(set_intersection2(X1,X2),X0)
| X0 = set_intersection2(X1,X2)
| ~ ordinal(set_intersection2(X1,X2))
| ~ disjoint(X1,X2)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f1057,f943]) ).
fof(f3558,plain,
! [X0,X1,X2] :
( X1 = X2
| X0 = X2
| ~ ordinal(X2)
| in(X0,X2)
| singleton(X1) != X0
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f404,f943]) ).
fof(f3597,plain,
! [X0,X1,X2] :
( ~ subset(X1,relation_dom(X2))
| ~ subset(X2,X0)
| ~ relation(X2)
| subset(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f945,f917]) ).
fof(f3599,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ relation(X2)
| ~ relation(X0)
| ~ subset(relation_dom(X2),X1)
| subset(relation_dom(X0),X1) ),
inference(resolution,[status(thm)],[f945,f917]) ).
fof(f3600,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ relation(X1)
| ~ subset(X2,X1)
| in(X0,relation_dom(X1)) ),
inference(resolution,[status(thm)],[f945,f489]) ).
fof(f3601,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(relation_dom(X1),relation_dom(X0))
| relation_dom(X0) = relation_dom(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f945,f310]) ).
fof(f3612,plain,
! [X0,X1] :
( ~ relation(X0)
| relation_rng(X0) = relation_rng(relation_dom_restriction(X0,X1))
| ~ subset(relation_rng(X0),relation_rng(relation_dom_restriction(X0,X1))) ),
inference(resolution,[status(thm)],[f1183,f310]) ).
fof(f3614,plain,
! [X0] :
( ~ relation(empty_set)
| subset(relation_rng(relation_dom_restriction(empty_set,X0)),empty_set) ),
inference(paramodulation,[status(thm)],[f1090,f1183]) ).
fof(f3616,definition,
! [X0] :
( sQ145_spl
<=> subset(relation_rng(relation_dom_restriction(empty_set,X0)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f3619,plain,
( ~ sQ3_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f3614,f3616,f1257]) ).
fof(f3620,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1259,f660]) ).
fof(f3621,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f3620]) ).
fof(f3654,plain,
! [X0] :
( subset(relation_dom(X0),empty_set)
| ~ relation(X0)
| ~ relation(empty_set)
| ~ subset(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f945]) ).
fof(f3655,plain,
! [X0] :
( subset(empty_set,relation_dom(X0))
| ~ relation(empty_set)
| ~ relation(X0)
| ~ subset(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f1089,f945]) ).
fof(f3656,plain,
! [X0,X1,X2] :
( ~ in(X2,empty_set)
| ~ one_to_one(empty_set)
| ~ relation(empty_set)
| X0 != function_inverse(empty_set)
| apply(empty_set,X2) != X1
| ~ function(X0)
| ~ function(empty_set)
| in(X1,relation_rng(empty_set))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1089,f1068]) ).
fof(f3657,plain,
! [X0,X1] :
( ~ relation(empty_set)
| relation_dom(empty_set) != set_intersection2(relation_dom(X1),X0)
| ~ function(empty_set)
| ~ function(X1)
| ~ relation(X1)
| empty_set = relation_dom_restriction(X1,X0)
| ~ in(empty_set,sK94_skl(X0,X1,empty_set)) ),
inference(paramodulation,[status(thm)],[f1089,f1794]) ).
fof(f3658,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ordinal(sK94_skl(X1,empty_set,X0))
| relation_dom(X0) != set_intersection2(empty_set,X1)
| X0 = relation_dom_restriction(empty_set,X1)
| ~ ordinal(relation_dom(X0))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f1793]) ).
fof(f3660,plain,
! [X0,X1] :
( relation_dom_restriction(X0,X1) = empty_set
| ~ relation(X0)
| ~ relation(empty_set)
| ~ function(X0)
| ~ function(empty_set)
| in(sK94_skl(X1,X0,empty_set),empty_set)
| set_intersection2(relation_dom(X0),X1) != relation_dom(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f1115]) ).
fof(f3661,plain,
( ~ relation(empty_set)
| empty_set = relation_rng(empty_set)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f1089,f1103]) ).
fof(f3663,plain,
! [X0,X1] :
( ~ relation(empty_set)
| ~ function(X0)
| X0 != relation_dom_restriction(empty_set,X1)
| ~ relation(X0)
| relation_dom(X0) = set_intersection2(empty_set,X1)
| ~ function(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f1113]) ).
fof(f3664,definition,
( sQ146_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f3666,plain,
( sQ146_spl
| ~ function(empty_set) ),
inference(component_clause,[status(thm)],[f3664]) ).
fof(f3667,definition,
! [X0,X1] :
( sQ147_spl
<=> ( ~ function(X0)
| X0 != relation_dom_restriction(empty_set,X1)
| ~ relation(X0)
| relation_dom(X0) = set_intersection2(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f3670,plain,
( ~ sQ3_spl
| sQ147_spl
| ~ sQ146_spl ),
inference(split_clause,[status(thm)],[f3663,f3664,f3667,f1257]) ).
fof(f3672,definition,
! [X0] :
( sQ148_spl
<=> ( subset(empty_set,relation_dom(X0))
| ~ relation(X0)
| ~ subset(empty_set,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f3675,plain,
( ~ sQ3_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f3655,f3672,f1257]) ).
fof(f3676,definition,
( sQ149_spl
<=> relation_rng(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f3680,definition,
! [X0] :
( sQ150_spl
<=> ( subset(relation_dom(X0),empty_set)
| ~ relation(X0)
| ~ subset(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f3683,plain,
( ~ sQ3_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f3654,f3680,f1257]) ).
fof(f3684,definition,
! [X0,X1] :
( sQ151_spl
<=> ( relation_dom(empty_set) != set_intersection2(relation_dom(X1),X0)
| ~ function(X1)
| ~ relation(X1)
| empty_set = relation_dom_restriction(X1,X0)
| ~ in(empty_set,sK94_skl(X0,X1,empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f3687,plain,
( ~ sQ3_spl
| ~ sQ146_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f3657,f3684,f3664,f1257]) ).
fof(f3689,plain,
( ~ sQ3_spl
| sQ149_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3661,f1254,f3676,f1257]) ).
fof(f3691,definition,
! [X0,X1] :
( sQ152_spl
<=> ( relation_dom_restriction(X0,X1) = empty_set
| ~ relation(X0)
| ~ function(X0)
| in(sK94_skl(X1,X0,empty_set),empty_set)
| set_intersection2(relation_dom(X0),X1) != relation_dom(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f3694,plain,
( ~ sQ3_spl
| ~ sQ146_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f3660,f3691,f3664,f1257]) ).
fof(f3695,definition,
! [X0,X1] :
( sQ153_spl
<=> ( ~ function(X0)
| ~ relation(X0)
| ordinal(sK94_skl(X1,empty_set,X0))
| relation_dom(X0) != set_intersection2(empty_set,X1)
| X0 = relation_dom_restriction(empty_set,X1)
| ~ ordinal(relation_dom(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f3698,plain,
( sQ153_spl
| ~ sQ146_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3658,f1257,f3664,f3695]) ).
fof(f3699,definition,
! [X0] :
( sQ154_spl
<=> ( X0 != function_inverse(empty_set)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f3702,definition,
! [X1,X2] :
( sQ155_spl
<=> ( ~ in(X2,empty_set)
| apply(empty_set,X2) != X1
| in(X1,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f3705,definition,
( sQ156_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f3707,plain,
( sQ156_spl
| ~ one_to_one(empty_set) ),
inference(component_clause,[status(thm)],[f3705]) ).
fof(f3708,plain,
( ~ sQ156_spl
| ~ sQ3_spl
| ~ sQ146_spl
| sQ155_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f3656,f3699,f3702,f3664,f1257,f3705]) ).
fof(f3709,plain,
( sQ146_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3666,f662]) ).
fof(f3710,plain,
sQ146_spl,
inference(contradiction_clause,[status(thm)],[f3709]) ).
fof(f3712,plain,
( sQ156_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3707,f663]) ).
fof(f3713,plain,
sQ156_spl,
inference(contradiction_clause,[status(thm)],[f3712]) ).
fof(f3741,definition,
! [X0] :
( sQ157_spl
<=> ( ordinal(sK22_skl(X0,sK84_skl))
| set_meet(sK84_skl) = X0
| ordinal(sK21_skl(X0,sK84_skl))
| set_meet(sK84_skl) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f3789,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,ordered_pair(sK10_skl(X0,X1,X2,sK84_skl),X0))
| in(X3,sK84_skl)
| ~ relation(sK84_skl)
| X1 != relation_image(sK84_skl,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f355,f1250]) ).
fof(f3790,plain,
! [X0,X1,X2] :
( ordinal(ordered_pair(sK10_skl(X0,X1,X2,sK84_skl),X0))
| ~ relation(sK84_skl)
| X1 != relation_image(sK84_skl,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f355,f967]) ).
fof(f3807,definition,
! [X0,X1,X2] :
( sQ158_spl
<=> ( ordinal(ordered_pair(sK10_skl(X0,X1,X2,sK84_skl),X0))
| X1 != relation_image(sK84_skl,X2)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f3810,plain,
( ~ sQ11_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f3790,f3807,f1345]) ).
fof(f3812,definition,
! [X0,X1,X2,X3] :
( sQ159_spl
<=> ( ~ in(X3,ordered_pair(sK10_skl(X0,X1,X2,sK84_skl),X0))
| in(X3,sK84_skl)
| X1 != relation_image(sK84_skl,X2)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f3815,plain,
( ~ sQ11_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f3789,f3812,f1345]) ).
fof(f3914,plain,
! [X0,X1,X2] :
( ~ ordinal(X2)
| ~ function(X0)
| ~ function(X1)
| ~ ordinal(relation_dom(relation_composition(X0,X1)))
| in(X2,relation_dom(X0))
| ~ relation(X0)
| relation_dom(relation_composition(X0,X1)) = X2
| ~ relation(X1)
| in(relation_dom(relation_composition(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f926,f943]) ).
fof(f3916,plain,
( ~ sQ98_spl
| epsilon_transitive(sK95_skl(sK84_skl))
| ordinal(sK26_skl(sK95_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f2611,f425]) ).
fof(f3928,plain,
! [X0,X1,X2] :
( ~ sQ98_spl
| ~ relation(sK95_skl(sK84_skl))
| X1 != relation_image(sK95_skl(sK84_skl),X2)
| ~ in(X0,X1)
| ordinal(ordered_pair(sK10_skl(X0,X1,X2,sK95_skl(sK84_skl)),X0)) ),
inference(resolution,[status(thm)],[f2611,f355]) ).
fof(f3929,plain,
! [X0] :
( ~ sQ98_spl
| subset(sK95_skl(sK84_skl),X0)
| ~ relation(sK95_skl(sK84_skl))
| ~ relation(X0)
| ordinal(ordered_pair(sK38_skl(X0,sK95_skl(sK84_skl)),sK39_skl(X0,sK95_skl(sK84_skl)))) ),
inference(resolution,[status(thm)],[f2611,f483]) ).
fof(f3944,definition,
! [X0,X1,X2] :
( sQ160_spl
<=> ( X1 != relation_image(sK95_skl(sK84_skl),X2)
| ~ in(X0,X1)
| ordinal(ordered_pair(sK10_skl(X0,X1,X2,sK95_skl(sK84_skl)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f3947,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f3928,f3944,f2816,f2610]) ).
fof(f3950,definition,
! [X0] :
( sQ161_spl
<=> ( subset(sK95_skl(sK84_skl),X0)
| ~ relation(X0)
| ordinal(ordered_pair(sK38_skl(X0,sK95_skl(sK84_skl)),sK39_skl(X0,sK95_skl(sK84_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f3953,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f3929,f3950,f2816,f2610]) ).
fof(f3958,definition,
( sQ162_spl
<=> ordinal(sK26_skl(sK95_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f3961,plain,
( ~ sQ98_spl
| sQ135_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f3916,f3958,f3022,f2610]) ).
fof(f3963,plain,
! [X0] :
( sK36_skl(X0) = sK37_skl(X0)
| in(sK36_skl(X0),sK37_skl(X0))
| ~ ordinal(sK37_skl(X0))
| ~ ordinal(sK36_skl(X0))
| epsilon_connected(X0) ),
inference(resolution,[status(thm)],[f478,f943]) ).
fof(f3964,plain,
! [X0] :
( ~ ordinal(sK36_skl(X0))
| ~ ordinal(sK37_skl(X0))
| epsilon_connected(X0)
| sK36_skl(X0) = sK37_skl(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3963,f476]) ).
fof(f4012,plain,
! [X0,X1] :
( ~ in(X1,ordered_pair(sK43_skl(X0,sK84_skl),sK44_skl(X0,sK84_skl)))
| in(X1,sK84_skl)
| ~ relation(sK84_skl)
| in(sK43_skl(X0,sK84_skl),X0)
| relation_dom(sK84_skl) = X0 ),
inference(resolution,[status(thm)],[f520,f1250]) ).
fof(f4013,plain,
! [X0] :
( ordinal(ordered_pair(sK43_skl(X0,sK84_skl),sK44_skl(X0,sK84_skl)))
| ~ relation(sK84_skl)
| in(sK43_skl(X0,sK84_skl),X0)
| relation_dom(sK84_skl) = X0 ),
inference(resolution,[status(thm)],[f520,f967]) ).
fof(f4015,plain,
! [X0] :
( ~ sQ98_spl
| ordinal(ordered_pair(sK43_skl(X0,sK95_skl(sK84_skl)),sK44_skl(X0,sK95_skl(sK84_skl))))
| ~ relation(sK95_skl(sK84_skl))
| in(sK43_skl(X0,sK95_skl(sK84_skl)),X0)
| relation_dom(sK95_skl(sK84_skl)) = X0 ),
inference(resolution,[status(thm)],[f520,f2611]) ).
fof(f4031,definition,
! [X0] :
( sQ163_spl
<=> ( ordinal(ordered_pair(sK43_skl(X0,sK95_skl(sK84_skl)),sK44_skl(X0,sK95_skl(sK84_skl))))
| in(sK43_skl(X0,sK95_skl(sK84_skl)),X0)
| relation_dom(sK95_skl(sK84_skl)) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f4034,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ163_spl ),
inference(split_clause,[status(thm)],[f4015,f4031,f2816,f2610]) ).
fof(f4036,definition,
! [X0,X1] :
( sQ164_spl
<=> ( ~ in(X1,ordered_pair(sK43_skl(X0,sK84_skl),sK44_skl(X0,sK84_skl)))
| in(X1,sK84_skl)
| in(sK43_skl(X0,sK84_skl),X0)
| relation_dom(sK84_skl) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f4039,plain,
( ~ sQ11_spl
| sQ164_spl ),
inference(split_clause,[status(thm)],[f4012,f4036,f1345]) ).
fof(f4041,definition,
! [X0] :
( sQ165_spl
<=> ( ordinal(ordered_pair(sK43_skl(X0,sK84_skl),sK44_skl(X0,sK84_skl)))
| in(sK43_skl(X0,sK84_skl),X0)
| relation_dom(sK84_skl) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f4044,plain,
( ~ sQ11_spl
| sQ165_spl ),
inference(split_clause,[status(thm)],[f4013,f4041,f1345]) ).
fof(f4053,plain,
( ordinal(sK83_skl(sK84_skl,sK84_skl))
| ordinal(sK83_skl(sK84_skl,sK84_skl))
| sK84_skl = sK84_skl ),
inference(resolution,[status(thm)],[f3332,f967]) ).
fof(f4055,plain,
( ~ sQ98_spl
| ordinal(sK83_skl(sK95_skl(sK84_skl),sK84_skl))
| ordinal(sK83_skl(sK95_skl(sK84_skl),sK84_skl))
| sK84_skl = sK95_skl(sK84_skl) ),
inference(resolution,[status(thm)],[f3332,f2611]) ).
fof(f4071,definition,
( sQ166_spl
<=> ordinal(sK83_skl(sK84_skl,sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f4074,plain,
( sQ166_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f4053,f1244,f4071]) ).
fof(f4081,definition,
( sQ168_spl
<=> sK84_skl = sK95_skl(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f4082,plain,
( ~ sQ168_spl
| sK95_skl(sK84_skl) = sK84_skl ),
inference(component_clause,[status(thm)],[f4081]) ).
fof(f4084,definition,
( sQ169_spl
<=> ordinal(sK83_skl(sK95_skl(sK84_skl),sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f4087,plain,
( ~ sQ98_spl
| sQ169_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f4055,f4081,f4084,f2610]) ).
fof(f4098,plain,
( ~ sQ99_spl
| ~ sQ168_spl
| ordinal(sK84_skl) ),
inference(backward_demodulation,[status(thm)],[f4082,f2615]) ).
fof(f4102,definition,
! [X0] :
( sQ170_spl
<=> ( ~ in(X0,sK84_skl)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f4103,plain,
! [X0] :
( ~ sQ170_spl
| ~ in(X0,sK84_skl)
| ~ in(X0,sK84_skl) ),
inference(component_clause,[status(thm)],[f4102]) ).
fof(f4106,plain,
( ~ sQ99_spl
| ~ sQ168_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f4098,f1272,f4081,f2614]) ).
fof(f4109,plain,
! [X0] :
( ~ sQ170_spl
| ~ in(X0,sK84_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f4103]) ).
fof(f4130,plain,
( ~ sQ170_spl
| empty_set = sK84_skl
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f4109,f1081]) ).
fof(f4136,definition,
! [X0,X1,X2] :
( sQ171_spl
<=> ( X1 != relation_image(sK84_skl,X2)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f4137,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| ~ in(X2,X0)
| X0 != relation_image(sK84_skl,X1) ),
inference(component_clause,[status(thm)],[f4136]) ).
fof(f4141,plain,
( ~ sQ170_spl
| sQ26_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4130,f1345,f1544,f4102]) ).
fof(f4146,plain,
( ~ sQ97_spl
| epsilon_transitive(sK84_skl) ),
inference(resolution,[status(thm)],[f2608,f425]) ).
fof(f4149,plain,
( ~ sQ97_spl
| epsilon_connected(sK84_skl) ),
inference(resolution,[status(thm)],[f2608,f474]) ).
fof(f4174,plain,
( ~ sQ97_spl
| sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4146,f2925]) ).
fof(f4175,plain,
( ~ sQ97_spl
| sQ128_spl ),
inference(contradiction_clause,[status(thm)],[f4174]) ).
fof(f4239,plain,
! [X0] : disjoint(X0,empty_set),
inference(resolution,[status(thm)],[f1149,f1009]) ).
fof(f4282,plain,
! [X0,X1] :
( ~ relation(X0)
| in(apply(X0,X1),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X1,relation_dom(relation_composition(X0,empty_set)))
| ~ function(X0) ),
inference(paramodulation,[status(thm)],[f1089,f927]) ).
fof(f4290,definition,
! [X0,X1] :
( sQ172_spl
<=> ( ~ relation(X0)
| in(apply(X0,X1),empty_set)
| ~ in(X1,relation_dom(relation_composition(X0,empty_set)))
| ~ function(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f4293,plain,
( ~ sQ146_spl
| ~ sQ3_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f4282,f4290,f1257,f3664]) ).
fof(f4299,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| in(sK2_skl(X1,sK84_skl,X0),X1)
| ~ relation(sK84_skl)
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK84_skl ),
inference(resolution,[status(thm)],[f319,f967]) ).
fof(f4322,definition,
! [X0,X1] :
( sQ173_spl
<=> ( ordinal(ordered_pair(sK2_skl(X1,sK84_skl,X0),sK3_skl(X1,sK84_skl,X0)))
| in(sK2_skl(X1,sK84_skl,X0),X1)
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f4325,plain,
( ~ sQ11_spl
| sQ173_spl ),
inference(split_clause,[status(thm)],[f4299,f4322,f1345]) ).
fof(f4487,plain,
( ~ sQ70_spl
| ~ function(empty_set)
| empty_set = relation_dom(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1976,f980]) ).
fof(f4494,definition,
( sQ176_spl
<=> empty_set = relation_dom(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f4497,plain,
( ~ sQ70_spl
| ~ sQ146_spl
| sQ176_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4487,f1257,f4494,f3664,f1975]) ).
fof(f4554,plain,
! [X0] :
( ~ sQ60_spl
| empty_set != set_union2(sK84_skl,X0) ),
inference(resolution,[status(thm)],[f1145,f1880]) ).
fof(f4555,plain,
! [X0,X1] :
( X1 = set_union2(X1,X0)
| ~ subset(X1,X1)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f1145,f2056]) ).
fof(f4564,plain,
! [X0,X1] :
( set_union2(X1,X0) = X1
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f4555,f1225]) ).
fof(f4575,definition,
! [X0] :
( sQ177_spl
<=> ~ in(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f4576,plain,
! [X0] :
( ~ sQ177_spl
| ~ in(X0,empty_set) ),
inference(component_clause,[status(thm)],[f4575]) ).
fof(f4578,definition,
! [X1] :
( sQ178_spl
<=> ~ disjoint(X1,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f4579,plain,
! [X0] :
( ~ sQ178_spl
| ~ disjoint(X0,empty_set) ),
inference(component_clause,[status(thm)],[f4578]) ).
fof(f4589,plain,
( ~ sQ177_spl
| ordinal(sK83_skl(empty_set,sK84_skl))
| sK84_skl = empty_set ),
inference(resolution,[status(thm)],[f4576,f3332]) ).
fof(f4592,plain,
! [X0,X1] :
( ~ sQ177_spl
| sK95_skl(X1) = empty_set
| ~ in(empty_set,X1)
| ~ ordinal(sK95_skl(X1))
| ~ ordinal(empty_set)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f4576,f2311]) ).
fof(f4594,plain,
! [X0] :
( ~ sQ177_spl
| empty_set = singleton(X0)
| X0 = sK23_skl(empty_set,X0) ),
inference(resolution,[status(thm)],[f4576,f407]) ).
fof(f4600,plain,
! [X0,X1] :
( ~ sQ177_spl
| in(empty_set,X0)
| sK20_skl(empty_set,X0,X1) = empty_set
| X0 != set_meet(X1)
| ~ ordinal(empty_set)
| empty_set = X1
| ~ ordinal(sK20_skl(empty_set,X0,X1)) ),
inference(resolution,[status(thm)],[f4576,f2302]) ).
fof(f4604,plain,
! [X0,X1] :
( ~ sQ177_spl
| in(sK2_skl(X1,empty_set,X0),X1)
| ~ relation(empty_set)
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f4576,f319]) ).
fof(f4605,plain,
! [X0] :
( ~ sQ177_spl
| ~ relation(empty_set)
| in(sK43_skl(X0,empty_set),X0)
| relation_dom(empty_set) = X0 ),
inference(resolution,[status(thm)],[f4576,f520]) ).
fof(f4606,plain,
! [X0,X1,X2] :
( ~ sQ177_spl
| ~ relation(empty_set)
| X1 != relation_image(empty_set,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f4576,f355]) ).
fof(f4607,plain,
! [X0] :
( ~ sQ177_spl
| subset(empty_set,X0)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f4576,f483]) ).
fof(f4608,plain,
! [X0,X1] :
( ~ sQ177_spl
| in(sK11_skl(X1,X0,empty_set),X1)
| ~ relation(empty_set)
| relation_image(empty_set,X0) = X1 ),
inference(resolution,[status(thm)],[f4576,f359]) ).
fof(f4610,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ relation(empty_set)
| in(sK14_skl(X1,X0,empty_set),X1)
| relation_inverse_image(empty_set,X0) = X1 ),
inference(resolution,[status(thm)],[f4576,f369]) ).
fof(f4611,plain,
! [X0,X1,X2,X3] :
( ~ sQ177_spl
| relation_rng_restriction(X1,X3) != empty_set
| ~ relation(X3)
| ~ relation(empty_set)
| ~ in(ordered_pair(X2,X0),X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f4576,f337]) ).
fof(f4612,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ in(X1,X0)
| identity_relation(X0) != empty_set
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f4576,f1223]) ).
fof(f4613,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ in(X1,relation_dom(empty_set))
| ~ relation(empty_set)
| ~ function(empty_set)
| X0 != apply(empty_set,X1) ),
inference(resolution,[status(thm)],[f4576,f1167]) ).
fof(f4614,plain,
! [X0] :
( ~ sQ177_spl
| empty_set = X0
| in(empty_set,X0)
| ~ ordinal(X0)
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f4576,f943]) ).
fof(f4615,definition,
! [X0,X1,X2,X3] :
( sQ179_spl
<=> ( relation_rng_restriction(X1,X3) != empty_set
| ~ relation(X3)
| ~ in(ordered_pair(X2,X0),X3)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f4618,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f4611,f4615,f1257,f4575]) ).
fof(f4623,definition,
! [X0,X1,X2] :
( sQ181_spl
<=> ( X1 != relation_image(empty_set,X2)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f4626,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f4606,f4623,f1257,f4575]) ).
fof(f4627,definition,
! [X0] :
( sQ182_spl
<=> ( empty_set = X0
| in(empty_set,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f4630,plain,
( ~ sQ177_spl
| sQ182_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f4614,f2114,f4627,f4575]) ).
fof(f4633,definition,
( sQ183_spl
<=> ordinal(sK83_skl(empty_set,sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f4636,plain,
( ~ sQ177_spl
| sQ183_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f4589,f1544,f4633,f4575]) ).
fof(f4638,definition,
! [X0] :
( sQ184_spl
<=> ( in(sK43_skl(X0,empty_set),X0)
| relation_dom(empty_set) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f4641,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f4605,f4638,f1257,f4575]) ).
fof(f4642,definition,
! [X0,X1] :
( sQ185_spl
<=> ( ~ in(X1,X0)
| identity_relation(X0) != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f4645,plain,
( ~ sQ177_spl
| sQ185_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4612,f1257,f4642,f4575]) ).
fof(f4647,definition,
! [X0,X1] :
( sQ186_spl
<=> ( in(sK2_skl(X1,empty_set,X0),X1)
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f4650,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f4604,f4647,f1257,f4575]) ).
fof(f4651,definition,
! [X0,X1] :
( sQ187_spl
<=> ( in(sK11_skl(X1,X0,empty_set),X1)
| relation_image(empty_set,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f4654,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f4608,f4651,f1257,f4575]) ).
fof(f4655,definition,
! [X0,X1] :
( sQ188_spl
<=> ( in(empty_set,X0)
| sK20_skl(empty_set,X0,X1) = empty_set
| X0 != set_meet(X1)
| empty_set = X1
| ~ ordinal(sK20_skl(empty_set,X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f4658,plain,
( ~ sQ177_spl
| ~ sQ79_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f4600,f4655,f2114,f4575]) ).
fof(f4659,definition,
! [X0,X1] :
( sQ189_spl
<=> ( in(sK14_skl(X1,X0,empty_set),X1)
| relation_inverse_image(empty_set,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f4662,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f4610,f4659,f1257,f4575]) ).
fof(f4663,definition,
! [X0] :
( sQ190_spl
<=> ( subset(empty_set,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f4666,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f4607,f4663,f1257,f4575]) ).
fof(f4671,definition,
! [X0,X1] :
( sQ192_spl
<=> ( sK95_skl(X1) = empty_set
| ~ in(empty_set,X1)
| ~ ordinal(sK95_skl(X1))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f4674,plain,
( ~ sQ177_spl
| ~ sQ79_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f4592,f4671,f2114,f4575]) ).
fof(f4675,definition,
! [X0,X1] :
( sQ193_spl
<=> ( ~ in(X1,relation_dom(empty_set))
| X0 != apply(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f4678,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| ~ sQ146_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f4613,f4675,f3664,f1257,f4575]) ).
fof(f4679,plain,
! [X0] :
( ~ sQ177_spl
| ~ sQ51_spl
| sK23_skl(empty_set,X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f4594,f1760]) ).
fof(f4681,plain,
( ~ sQ178_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4579,f4239]) ).
fof(f4682,plain,
~ sQ178_spl,
inference(contradiction_clause,[status(thm)],[f4681]) ).
fof(f4779,plain,
( ordinal(sK19_skl(sK84_skl))
| relation(sK84_skl) ),
inference(resolution,[status(thm)],[f387,f967]) ).
fof(f4802,definition,
( sQ194_spl
<=> ordinal(sK19_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f4805,plain,
( sQ194_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f4779,f1345,f4802]) ).
fof(f4814,plain,
! [X0] :
( ~ sQ177_spl
| ~ sQ51_spl
| ~ ordinal(empty_set)
| sK23_skl(empty_set,X0) = X0
| ordinal(X0)
| empty_set = singleton(X0) ),
inference(paramodulation,[status(thm)],[f4679,f2353]) ).
fof(f4825,definition,
! [X0] :
( sQ195_spl
<=> ( sK23_skl(empty_set,X0) = X0
| ordinal(X0)
| empty_set = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f4828,plain,
( ~ sQ177_spl
| ~ sQ51_spl
| ~ sQ79_spl
| sQ195_spl ),
inference(split_clause,[status(thm)],[f4814,f4825,f2114,f1759,f4575]) ).
fof(f4882,plain,
! [X0] :
( relation(sK84_skl)
| in(X0,sK84_skl)
| ~ in(X0,sK19_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f1250,f387]) ).
fof(f4900,plain,
! [X0,X1,X2] :
( in(sK2_skl(X1,sK84_skl,X2),X1)
| ~ relation(sK84_skl)
| ~ relation(X2)
| relation_dom_restriction(X2,X1) = sK84_skl
| in(X0,sK84_skl)
| ~ in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X2),sK3_skl(X1,sK84_skl,X2))) ),
inference(resolution,[status(thm)],[f1250,f319]) ).
fof(f4919,plain,
! [X0,X1] :
( ~ relation(sK84_skl)
| ~ relation(X0)
| subset(X0,sK84_skl)
| ~ in(X1,sK84_skl)
| ~ in(ordered_pair(sK38_skl(sK84_skl,X0),sK39_skl(sK84_skl,X0)),X1) ),
inference(resolution,[status(thm)],[f1250,f484]) ).
fof(f4920,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK7_skl(X0,sK84_skl,X1),sK8_skl(X0,sK84_skl,X1)),X1)
| ~ in(sK8_skl(X0,sK84_skl,X1),X0)
| ~ relation(sK84_skl)
| ~ relation(X1)
| relation_rng_restriction(X0,X1) = sK84_skl
| ~ in(X2,sK84_skl)
| ~ in(ordered_pair(sK7_skl(X0,sK84_skl,X1),sK8_skl(X0,sK84_skl,X1)),X2) ),
inference(resolution,[status(thm)],[f1250,f338]) ).
fof(f4923,plain,
! [X0,X1,X2,X3] :
( ~ relation(sK84_skl)
| in(X0,X3)
| sK84_skl != identity_relation(X3)
| ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f1250,f300]) ).
fof(f4924,plain,
! [X0,X1,X2] :
( ~ relation(sK84_skl)
| ~ in(X0,relation_dom(sK84_skl))
| apply(sK84_skl,X0) = X1
| ~ function(sK84_skl)
| ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f1250,f505]) ).
fof(f4949,definition,
! [X0,X1] :
( sQ196_spl
<=> ( ~ in(X1,sK84_skl)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f4950,plain,
! [X0,X1] :
( ~ sQ196_spl
| ~ in(X1,X0)
| ~ in(X0,sK84_skl) ),
inference(component_clause,[status(thm)],[f4949]) ).
fof(f4960,definition,
! [X0,X1,X2] :
( sQ197_spl
<=> ( ~ in(ordered_pair(sK7_skl(X0,sK84_skl,X1),sK8_skl(X0,sK84_skl,X1)),X1)
| ~ in(sK8_skl(X0,sK84_skl,X1),X0)
| ~ relation(X1)
| relation_rng_restriction(X0,X1) = sK84_skl
| ~ in(X2,sK84_skl)
| ~ in(ordered_pair(sK7_skl(X0,sK84_skl,X1),sK8_skl(X0,sK84_skl,X1)),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f4963,plain,
( ~ sQ11_spl
| sQ197_spl ),
inference(split_clause,[status(thm)],[f4920,f4960,f1345]) ).
fof(f4978,definition,
! [X0,X1,X2] :
( sQ200_spl
<=> ( ~ in(X0,relation_dom(sK84_skl))
| apply(sK84_skl,X0) = X1
| ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X0,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f4981,plain,
( ~ sQ11_spl
| ~ sQ68_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f4924,f4978,f1961,f1345]) ).
fof(f4986,definition,
! [X0,X1,X2] :
( sQ201_spl
<=> ( in(sK2_skl(X1,sK84_skl,X2),X1)
| ~ relation(X2)
| relation_dom_restriction(X2,X1) = sK84_skl
| in(X0,sK84_skl)
| ~ in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X2),sK3_skl(X1,sK84_skl,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f4989,plain,
( ~ sQ11_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f4900,f4986,f1345]) ).
fof(f4991,definition,
! [X0,X1,X2,X3] :
( sQ202_spl
<=> ( in(X0,X3)
| sK84_skl != identity_relation(X3)
| ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X0,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f4994,plain,
( ~ sQ11_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f4923,f4991,f1345]) ).
fof(f4997,definition,
! [X0] :
( sQ203_spl
<=> ( in(X0,sK84_skl)
| ~ in(X0,sK19_skl(sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f5000,plain,
( sQ11_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f4882,f4997,f1345]) ).
fof(f5002,definition,
! [X0,X1] :
( sQ204_spl
<=> ( ~ relation(X0)
| subset(X0,sK84_skl)
| ~ in(X1,sK84_skl)
| ~ in(ordered_pair(sK38_skl(sK84_skl,X0),sK39_skl(sK84_skl,X0)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f5005,plain,
( ~ sQ11_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f4919,f5002,f1345]) ).
fof(f5050,plain,
! [X0] : disjoint(empty_set,X0),
inference(resolution,[status(thm)],[f1049,f1149]) ).
fof(f5055,plain,
! [X0] :
( empty_set != empty_set
| disjoint(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f1049,f1149]) ).
fof(f5058,definition,
! [X0] :
( sQ205_spl
<=> disjoint(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f5061,plain,
( ~ sQ2_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f5055,f5058,f1254]) ).
fof(f5062,definition,
! [X0] :
( sQ206_spl
<=> ~ disjoint(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f5063,plain,
! [X0] :
( ~ sQ206_spl
| ~ disjoint(empty_set,X0) ),
inference(component_clause,[status(thm)],[f5062]) ).
fof(f5070,plain,
! [X0] :
( empty_set != empty_set
| ~ in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f1049,f1107]) ).
fof(f5072,plain,
( ~ sQ2_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f5070,f4575,f1254]) ).
fof(f5099,plain,
! [X0,X1,X2] :
( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X1,X0),X2)
| ~ relation(sK84_skl)
| ~ function(sK84_skl)
| X0 = apply(sK84_skl,X1) ),
inference(resolution,[status(thm)],[f1166,f1250]) ).
fof(f5112,definition,
! [X0,X1,X2] :
( sQ208_spl
<=> ( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X1,X0),X2)
| X0 = apply(sK84_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f5115,plain,
( ~ sQ11_spl
| ~ sQ68_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f5099,f5112,f1961,f1345]) ).
fof(f5131,plain,
! [X0,X1,X2] :
( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(sK84_skl)
| in(X0,relation_field(sK84_skl)) ),
inference(resolution,[status(thm)],[f963,f1250]) ).
fof(f5148,definition,
! [X0,X1,X2] :
( sQ209_spl
<=> ( ~ in(X2,sK84_skl)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_field(sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f5151,plain,
( ~ sQ11_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f5131,f5148,f1345]) ).
fof(f5160,plain,
! [X0] :
( ~ relation(X0)
| ~ relation(empty_set)
| relation_image(X0,empty_set) = relation_rng(relation_composition(empty_set,X0)) ),
inference(paramodulation,[status(thm)],[f1090,f891]) ).
fof(f5161,definition,
! [X0] :
( sQ210_spl
<=> ( ~ relation(X0)
| relation_image(X0,empty_set) = relation_rng(relation_composition(empty_set,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f5164,plain,
( ~ sQ3_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f5160,f5161,f1257]) ).
fof(f5232,plain,
! [X0,X1] :
( X1 = empty_set
| ~ relation(empty_set)
| in(X0,empty_set)
| apply(empty_set,X0) != X1
| ~ function(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f506]) ).
fof(f5236,definition,
! [X0,X1] :
( sQ211_spl
<=> ( X1 = empty_set
| in(X0,empty_set)
| apply(empty_set,X0) != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f5239,plain,
( ~ sQ3_spl
| sQ211_spl
| ~ sQ146_spl ),
inference(split_clause,[status(thm)],[f5232,f3664,f5236,f1257]) ).
fof(f5241,plain,
( ~ sQ206_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5063,f5050]) ).
fof(f5242,plain,
~ sQ206_spl,
inference(contradiction_clause,[status(thm)],[f5241]) ).
fof(f5289,plain,
! [X0,X1] :
( ~ in(X1,sK84_skl)
| ~ in(X0,X1)
| ~ empty(sK84_skl) ),
inference(resolution,[status(thm)],[f1139,f1250]) ).
fof(f5306,definition,
( sQ212_spl
<=> empty(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f5309,plain,
( sQ196_spl
| ~ sQ212_spl ),
inference(split_clause,[status(thm)],[f5289,f5306,f4949]) ).
fof(f5320,plain,
! [X0] :
( relation_image(empty_set,X0) = relation_image(empty_set,set_intersection2(empty_set,X0))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f881]) ).
fof(f5322,definition,
! [X0] :
( sQ213_spl
<=> relation_image(empty_set,X0) = relation_image(empty_set,set_intersection2(empty_set,X0)) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f5325,plain,
( sQ213_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5320,f1257,f5322]) ).
fof(f5333,plain,
! [X0,X1] :
( ~ sQ177_spl
| relation_rng_restriction(X1,empty_set) = X0
| in(ordered_pair(sK7_skl(X1,X0,empty_set),sK8_skl(X1,X0,empty_set)),X0)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f340,f4576]) ).
fof(f5335,plain,
! [X0,X1,X2] :
( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)))
| relation_rng_restriction(X1,sK84_skl) = X0
| in(ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)),X0)
| ~ relation(sK84_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f340,f1250]) ).
fof(f5336,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)))
| relation_rng_restriction(X1,sK84_skl) = X0
| in(ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)),X0)
| ~ relation(sK84_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f340,f967]) ).
fof(f5367,definition,
! [X0,X1] :
( sQ214_spl
<=> ( ordinal(ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)))
| relation_rng_restriction(X1,sK84_skl) = X0
| in(ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f5370,plain,
( ~ sQ11_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f5336,f5367,f1345]) ).
fof(f5371,definition,
! [X0,X1] :
( sQ215_spl
<=> ( relation_rng_restriction(X1,empty_set) = X0
| in(ordered_pair(sK7_skl(X1,X0,empty_set),sK8_skl(X1,X0,empty_set)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f5374,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f5333,f5371,f1257,f4575]) ).
fof(f5375,definition,
! [X0,X1,X2] :
( sQ216_spl
<=> ( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)))
| relation_rng_restriction(X1,sK84_skl) = X0
| in(ordered_pair(sK7_skl(X1,X0,sK84_skl),sK8_skl(X1,X0,sK84_skl)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f5378,plain,
( ~ sQ11_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f5335,f5375,f1345]) ).
fof(f5389,plain,
! [X0,X1] :
( ~ sQ55_spl
| ~ subset(sK84_skl,X1)
| subset(X0,X1)
| empty_set != X0 ),
inference(resolution,[status(thm)],[f1812,f917]) ).
fof(f5395,plain,
( ~ sQ55_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f5389,f1579,f1811]) ).
fof(f5469,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ in(X1,X0)
| relation_dom(empty_set) != X0
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f517,f4576]) ).
fof(f5471,plain,
! [X0,X1,X2] :
( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(X1,sK42_skl(X1,X0,sK84_skl)))
| ~ in(X1,X0)
| relation_dom(sK84_skl) != X0
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f517,f1250]) ).
fof(f5472,plain,
! [X0,X1] :
( ordinal(ordered_pair(X1,sK42_skl(X1,X0,sK84_skl)))
| ~ in(X1,X0)
| relation_dom(sK84_skl) != X0
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f517,f967]) ).
fof(f5498,definition,
! [X0,X1,X2] :
( sQ217_spl
<=> ( in(X2,sK84_skl)
| ~ in(X2,ordered_pair(X1,sK42_skl(X1,X0,sK84_skl)))
| ~ in(X1,X0)
| relation_dom(sK84_skl) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f5501,plain,
( sQ217_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5471,f1345,f5498]) ).
fof(f5502,definition,
! [X0,X1] :
( sQ218_spl
<=> ( ordinal(ordered_pair(X1,sK42_skl(X1,X0,sK84_skl)))
| ~ in(X1,X0)
| relation_dom(sK84_skl) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f5505,plain,
( sQ218_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5472,f1345,f5502]) ).
fof(f5509,definition,
! [X0,X1] :
( sQ219_spl
<=> ( ~ in(X1,X0)
| relation_dom(empty_set) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f5512,plain,
( ~ sQ177_spl
| sQ219_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5469,f1257,f5509,f4575]) ).
fof(f5564,plain,
! [X0] :
( ~ sQ196_spl
| relation(sK84_skl)
| ~ in(X0,sK19_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f4950,f387]) ).
fof(f5571,plain,
! [X0,X1] :
( ~ sQ196_spl
| ~ in(X1,sK84_skl)
| ~ in(X0,sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f4950,f1143]) ).
fof(f5579,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| in(X1,X2)
| X2 != set_meet(sK84_skl)
| sK84_skl = empty_set
| ~ in(X0,sK20_skl(X1,X2,sK84_skl)) ),
inference(resolution,[status(thm)],[f4950,f394]) ).
fof(f5581,plain,
! [X0,X1] :
( ~ sQ196_spl
| ~ in(sK21_skl(X1,sK84_skl),X1)
| empty_set = sK84_skl
| set_meet(sK84_skl) = X1
| ~ in(X0,sK22_skl(X1,sK84_skl)) ),
inference(resolution,[status(thm)],[f4950,f396]) ).
fof(f5582,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| relation_rng_restriction(X1,sK84_skl) = X2
| in(ordered_pair(sK7_skl(X1,X2,sK84_skl),sK8_skl(X1,X2,sK84_skl)),X2)
| ~ relation(sK84_skl)
| ~ relation(X2)
| ~ in(X0,ordered_pair(sK7_skl(X1,X2,sK84_skl),sK8_skl(X1,X2,sK84_skl))) ),
inference(resolution,[status(thm)],[f4950,f340]) ).
fof(f5583,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| in(sK2_skl(X1,sK84_skl,X2),X1)
| ~ relation(sK84_skl)
| ~ relation(X2)
| relation_dom_restriction(X2,X1) = sK84_skl
| ~ in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X2),sK3_skl(X1,sK84_skl,X2))) ),
inference(resolution,[status(thm)],[f4950,f319]) ).
fof(f5584,plain,
! [X0,X1] :
( ~ sQ196_spl
| ~ relation(sK84_skl)
| in(sK43_skl(X1,sK84_skl),X1)
| relation_dom(sK84_skl) = X1
| ~ in(X0,ordered_pair(sK43_skl(X1,sK84_skl),sK44_skl(X1,sK84_skl))) ),
inference(resolution,[status(thm)],[f4950,f520]) ).
fof(f5585,plain,
! [X0,X1,X2,X3] :
( ~ sQ196_spl
| ~ relation(sK84_skl)
| X2 != relation_image(sK84_skl,X3)
| ~ in(X1,X2)
| ~ in(X0,ordered_pair(sK10_skl(X1,X2,X3,sK84_skl),X1)) ),
inference(resolution,[status(thm)],[f4950,f355]) ).
fof(f5586,plain,
! [X0,X1] :
( ~ sQ196_spl
| subset(sK84_skl,X1)
| ~ relation(sK84_skl)
| ~ relation(X1)
| ~ in(X0,ordered_pair(sK38_skl(X1,sK84_skl),sK39_skl(X1,sK84_skl))) ),
inference(resolution,[status(thm)],[f4950,f483]) ).
fof(f5587,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| in(sK11_skl(X1,X2,sK84_skl),X1)
| ~ relation(sK84_skl)
| relation_image(sK84_skl,X2) = X1
| ~ in(X0,ordered_pair(sK12_skl(X1,X2,sK84_skl),sK11_skl(X1,X2,sK84_skl))) ),
inference(resolution,[status(thm)],[f4950,f359]) ).
fof(f5588,plain,
! [X0] :
( ~ sQ196_spl
| empty_set = sK84_skl
| ~ relation(sK84_skl)
| ~ in(X0,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f4950,f1081]) ).
fof(f5589,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| ~ relation(sK84_skl)
| in(sK14_skl(X1,X2,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X2) = X1
| ~ in(X0,ordered_pair(sK14_skl(X1,X2,sK84_skl),sK15_skl(X1,X2,sK84_skl))) ),
inference(resolution,[status(thm)],[f4950,f369]) ).
fof(f5590,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| ~ in(X1,X2)
| relation_dom(sK84_skl) != X2
| ~ relation(sK84_skl)
| ~ in(X0,ordered_pair(X1,sK42_skl(X1,X2,sK84_skl))) ),
inference(resolution,[status(thm)],[f4950,f517]) ).
fof(f5591,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ196_spl
| relation_rng_restriction(X3,X4) != sK84_skl
| ~ relation(X4)
| ~ relation(sK84_skl)
| ~ in(ordered_pair(X1,X2),X4)
| ~ in(X2,X3)
| ~ in(X0,ordered_pair(X1,X2)) ),
inference(resolution,[status(thm)],[f4950,f337]) ).
fof(f5592,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| ~ in(X1,X2)
| identity_relation(X2) != sK84_skl
| ~ relation(sK84_skl)
| ~ in(X0,ordered_pair(X1,X1)) ),
inference(resolution,[status(thm)],[f4950,f1223]) ).
fof(f5593,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| ~ in(X1,relation_dom(sK84_skl))
| ~ relation(sK84_skl)
| ~ function(sK84_skl)
| X2 != apply(sK84_skl,X1)
| ~ in(X0,ordered_pair(X1,X2)) ),
inference(resolution,[status(thm)],[f4950,f1167]) ).
fof(f5595,definition,
! [X0,X1,X2] :
( sQ220_spl
<=> ( ~ in(X1,relation_dom(sK84_skl))
| X2 != apply(sK84_skl,X1)
| ~ in(X0,ordered_pair(X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f5598,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| ~ sQ68_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f5593,f5595,f1961,f1345,f4949]) ).
fof(f5600,plain,
( ~ sQ196_spl
| sQ97_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f5571,f2834,f2607,f4949]) ).
fof(f5605,definition,
! [X0,X1,X2] :
( sQ222_spl
<=> ( in(sK2_skl(X1,sK84_skl,X2),X1)
| ~ relation(X2)
| relation_dom_restriction(X2,X1) = sK84_skl
| ~ in(X0,ordered_pair(sK2_skl(X1,sK84_skl,X2),sK3_skl(X1,sK84_skl,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f5608,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f5583,f5605,f1345,f4949]) ).
fof(f5609,definition,
! [X0] :
( sQ223_spl
<=> ~ in(X0,sK19_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f5612,plain,
( ~ sQ196_spl
| sQ11_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f5564,f5609,f1345,f4949]) ).
fof(f5613,definition,
! [X0,X1,X2] :
( sQ224_spl
<=> ( ~ in(X1,X2)
| identity_relation(X2) != sK84_skl
| ~ in(X0,ordered_pair(X1,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f5616,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f5592,f5613,f1345,f4949]) ).
fof(f5625,definition,
! [X0,X1] :
( sQ227_spl
<=> ( subset(sK84_skl,X1)
| ~ relation(X1)
| ~ in(X0,ordered_pair(sK38_skl(X1,sK84_skl),sK39_skl(X1,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f5628,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f5586,f5625,f1345,f4949]) ).
fof(f5629,definition,
! [X0,X1,X2,X3] :
( sQ228_spl
<=> ( X2 != relation_image(sK84_skl,X3)
| ~ in(X1,X2)
| ~ in(X0,ordered_pair(sK10_skl(X1,X2,X3,sK84_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f5632,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f5585,f5629,f1345,f4949]) ).
fof(f5633,definition,
! [X0,X1] :
( sQ229_spl
<=> ( in(sK43_skl(X1,sK84_skl),X1)
| relation_dom(sK84_skl) = X1
| ~ in(X0,ordered_pair(sK43_skl(X1,sK84_skl),sK44_skl(X1,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f5636,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f5584,f5633,f1345,f4949]) ).
fof(f5641,definition,
! [X0,X1,X2] :
( sQ231_spl
<=> ( in(sK14_skl(X1,X2,sK84_skl),X1)
| relation_inverse_image(sK84_skl,X2) = X1
| ~ in(X0,ordered_pair(sK14_skl(X1,X2,sK84_skl),sK15_skl(X1,X2,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f5644,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f5589,f5641,f1345,f4949]) ).
fof(f5645,definition,
! [X0] :
( sQ232_spl
<=> ~ in(X0,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f5648,plain,
( ~ sQ196_spl
| sQ26_spl
| ~ sQ11_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f5588,f5645,f1345,f1544,f4949]) ).
fof(f5649,definition,
! [X0,X1,X2] :
( sQ233_spl
<=> ( ~ in(X1,X2)
| relation_dom(sK84_skl) != X2
| ~ in(X0,ordered_pair(X1,sK42_skl(X1,X2,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f5652,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f5590,f5649,f1345,f4949]) ).
fof(f5657,definition,
! [X0,X1,X2] :
( sQ235_spl
<=> ( in(X1,X2)
| X2 != set_meet(sK84_skl)
| ~ in(X0,sK20_skl(X1,X2,sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f5660,plain,
( ~ sQ196_spl
| sQ26_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f5579,f5657,f1544,f4949]) ).
fof(f5665,definition,
! [X0,X1,X2] :
( sQ237_spl
<=> ( in(sK11_skl(X1,X2,sK84_skl),X1)
| relation_image(sK84_skl,X2) = X1
| ~ in(X0,ordered_pair(sK12_skl(X1,X2,sK84_skl),sK11_skl(X1,X2,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f5668,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f5587,f5665,f1345,f4949]) ).
fof(f5669,definition,
! [X0,X1,X2] :
( sQ238_spl
<=> ( relation_rng_restriction(X1,sK84_skl) = X2
| in(ordered_pair(sK7_skl(X1,X2,sK84_skl),sK8_skl(X1,X2,sK84_skl)),X2)
| ~ relation(X2)
| ~ in(X0,ordered_pair(sK7_skl(X1,X2,sK84_skl),sK8_skl(X1,X2,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f5672,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f5582,f5669,f1345,f4949]) ).
fof(f5673,definition,
! [X0,X1] :
( sQ239_spl
<=> ( ~ in(sK21_skl(X1,sK84_skl),X1)
| set_meet(sK84_skl) = X1
| ~ in(X0,sK22_skl(X1,sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f5676,plain,
( ~ sQ196_spl
| sQ26_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f5581,f5673,f1544,f4949]) ).
fof(f5677,definition,
! [X0,X1,X2,X3,X4] :
( sQ240_spl
<=> ( relation_rng_restriction(X3,X4) != sK84_skl
| ~ relation(X4)
| ~ in(ordered_pair(X1,X2),X4)
| ~ in(X2,X3)
| ~ in(X0,ordered_pair(X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f5680,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f5591,f5677,f1345,f4949]) ).
fof(f5787,plain,
( ~ sQ117_spl
| relation(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f2835,f387]) ).
fof(f5793,plain,
! [X0,X1] :
( ~ sQ117_spl
| sK95_skl(X1) = sK95_skl(sK84_skl)
| ~ in(sK95_skl(sK84_skl),X1)
| ~ ordinal(sK95_skl(X1))
| ~ ordinal(sK95_skl(sK84_skl))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f2835,f2311]) ).
fof(f5801,plain,
! [X0,X1] :
( ~ sQ117_spl
| in(sK95_skl(sK84_skl),X0)
| sK20_skl(sK95_skl(sK84_skl),X0,X1) = sK95_skl(sK84_skl)
| X0 != set_meet(X1)
| ~ ordinal(sK95_skl(sK84_skl))
| empty_set = X1
| ~ ordinal(sK20_skl(sK95_skl(sK84_skl),X0,X1)) ),
inference(resolution,[status(thm)],[f2835,f2302]) ).
fof(f5805,plain,
! [X0,X1] :
( ~ sQ117_spl
| relation_rng_restriction(X1,sK95_skl(sK84_skl)) = X0
| in(ordered_pair(sK7_skl(X1,X0,sK95_skl(sK84_skl)),sK8_skl(X1,X0,sK95_skl(sK84_skl))),X0)
| ~ relation(sK95_skl(sK84_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f2835,f340]) ).
fof(f5806,plain,
! [X0,X1] :
( ~ sQ117_spl
| in(sK2_skl(X1,sK95_skl(sK84_skl),X0),X1)
| ~ relation(sK95_skl(sK84_skl))
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK95_skl(sK84_skl) ),
inference(resolution,[status(thm)],[f2835,f319]) ).
fof(f5807,plain,
! [X0] :
( ~ sQ117_spl
| ~ relation(sK95_skl(sK84_skl))
| in(sK43_skl(X0,sK95_skl(sK84_skl)),X0)
| relation_dom(sK95_skl(sK84_skl)) = X0 ),
inference(resolution,[status(thm)],[f2835,f520]) ).
fof(f5808,plain,
! [X0,X1,X2] :
( ~ sQ117_spl
| ~ relation(sK95_skl(sK84_skl))
| X1 != relation_image(sK95_skl(sK84_skl),X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f2835,f355]) ).
fof(f5809,plain,
! [X0] :
( ~ sQ117_spl
| subset(sK95_skl(sK84_skl),X0)
| ~ relation(sK95_skl(sK84_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f2835,f483]) ).
fof(f5810,plain,
! [X0,X1] :
( ~ sQ117_spl
| in(sK11_skl(X1,X0,sK95_skl(sK84_skl)),X1)
| ~ relation(sK95_skl(sK84_skl))
| relation_image(sK95_skl(sK84_skl),X0) = X1 ),
inference(resolution,[status(thm)],[f2835,f359]) ).
fof(f5811,plain,
( ~ sQ117_spl
| empty_set = sK95_skl(sK84_skl)
| ~ relation(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f2835,f1081]) ).
fof(f5812,plain,
! [X0,X1] :
( ~ sQ117_spl
| ~ relation(sK95_skl(sK84_skl))
| in(sK14_skl(X1,X0,sK95_skl(sK84_skl)),X1)
| relation_inverse_image(sK95_skl(sK84_skl),X0) = X1 ),
inference(resolution,[status(thm)],[f2835,f369]) ).
fof(f5813,plain,
! [X0,X1] :
( ~ sQ117_spl
| ~ in(X1,X0)
| relation_dom(sK95_skl(sK84_skl)) != X0
| ~ relation(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f2835,f517]) ).
fof(f5814,plain,
! [X0,X1,X2,X3] :
( ~ sQ117_spl
| relation_rng_restriction(X1,X3) != sK95_skl(sK84_skl)
| ~ relation(X3)
| ~ relation(sK95_skl(sK84_skl))
| ~ in(ordered_pair(X2,X0),X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f2835,f337]) ).
fof(f5815,plain,
! [X0,X1] :
( ~ sQ117_spl
| ~ in(X1,X0)
| identity_relation(X0) != sK95_skl(sK84_skl)
| ~ relation(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f2835,f1223]) ).
fof(f5816,plain,
! [X0,X1] :
( ~ sQ117_spl
| ~ in(X1,relation_dom(sK95_skl(sK84_skl)))
| ~ relation(sK95_skl(sK84_skl))
| ~ function(sK95_skl(sK84_skl))
| X0 != apply(sK95_skl(sK84_skl),X1) ),
inference(resolution,[status(thm)],[f2835,f1167]) ).
fof(f5817,plain,
! [X0] :
( ~ sQ117_spl
| sK95_skl(sK84_skl) = X0
| in(sK95_skl(sK84_skl),X0)
| ~ ordinal(X0)
| ~ ordinal(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f2835,f943]) ).
fof(f5818,definition,
! [X0] :
( sQ241_spl
<=> ( sK95_skl(sK84_skl) = X0
| in(sK95_skl(sK84_skl),X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f5821,plain,
( ~ sQ117_spl
| sQ241_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f5817,f2614,f5818,f2834]) ).
fof(f5822,definition,
! [X0,X1] :
( sQ242_spl
<=> ( relation_rng_restriction(X1,sK95_skl(sK84_skl)) = X0
| in(ordered_pair(sK7_skl(X1,X0,sK95_skl(sK84_skl)),sK8_skl(X1,X0,sK95_skl(sK84_skl))),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f5825,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ242_spl ),
inference(split_clause,[status(thm)],[f5805,f5822,f2816,f2834]) ).
fof(f5826,definition,
! [X0] :
( sQ243_spl
<=> ( in(sK43_skl(X0,sK95_skl(sK84_skl)),X0)
| relation_dom(sK95_skl(sK84_skl)) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f5829,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f5807,f5826,f2816,f2834]) ).
fof(f5830,definition,
! [X0,X1] :
( sQ244_spl
<=> ( ~ in(X1,X0)
| relation_dom(sK95_skl(sK84_skl)) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f5833,plain,
( ~ sQ117_spl
| sQ244_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f5813,f2816,f5830,f2834]) ).
fof(f5834,definition,
! [X0,X1,X2] :
( sQ245_spl
<=> ( X1 != relation_image(sK95_skl(sK84_skl),X2)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f5837,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ245_spl ),
inference(split_clause,[status(thm)],[f5808,f5834,f2816,f2834]) ).
fof(f5842,definition,
! [X0,X1] :
( sQ247_spl
<=> ( in(sK2_skl(X1,sK95_skl(sK84_skl),X0),X1)
| ~ relation(X0)
| relation_dom_restriction(X0,X1) = sK95_skl(sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f5845,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f5806,f5842,f2816,f2834]) ).
fof(f5846,plain,
( ~ sQ117_spl
| sQ113_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f5811,f2816,f2819,f2834]) ).
fof(f5847,definition,
! [X0] :
( sQ248_spl
<=> ( subset(sK95_skl(sK84_skl),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f5850,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f5809,f5847,f2816,f2834]) ).
fof(f5851,definition,
! [X0,X1,X2,X3] :
( sQ249_spl
<=> ( relation_rng_restriction(X1,X3) != sK95_skl(sK84_skl)
| ~ relation(X3)
| ~ in(ordered_pair(X2,X0),X3)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f5854,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f5814,f5851,f2816,f2834]) ).
fof(f5855,definition,
! [X0,X1] :
( sQ250_spl
<=> ( in(sK14_skl(X1,X0,sK95_skl(sK84_skl)),X1)
| relation_inverse_image(sK95_skl(sK84_skl),X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f5858,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ250_spl ),
inference(split_clause,[status(thm)],[f5812,f5855,f2816,f2834]) ).
fof(f5859,definition,
! [X0,X1] :
( sQ251_spl
<=> ( in(sK11_skl(X1,X0,sK95_skl(sK84_skl)),X1)
| relation_image(sK95_skl(sK84_skl),X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f5862,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f5810,f5859,f2816,f2834]) ).
fof(f5863,definition,
! [X0,X1] :
( sQ252_spl
<=> ( sK95_skl(X1) = sK95_skl(sK84_skl)
| ~ in(sK95_skl(sK84_skl),X1)
| ~ ordinal(sK95_skl(X1))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f5866,plain,
( ~ sQ117_spl
| ~ sQ99_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f5793,f5863,f2614,f2834]) ).
fof(f5867,definition,
! [X0,X1] :
( sQ253_spl
<=> ( ~ in(X1,X0)
| identity_relation(X0) != sK95_skl(sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f5870,plain,
( ~ sQ117_spl
| sQ253_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f5815,f2816,f5867,f2834]) ).
fof(f5875,plain,
( ~ sQ117_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f5787,f2816,f2834]) ).
fof(f5877,definition,
! [X0,X1] :
( sQ255_spl
<=> ( in(sK95_skl(sK84_skl),X0)
| sK20_skl(sK95_skl(sK84_skl),X0,X1) = sK95_skl(sK84_skl)
| X0 != set_meet(X1)
| empty_set = X1
| ~ ordinal(sK20_skl(sK95_skl(sK84_skl),X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f5880,plain,
( ~ sQ117_spl
| ~ sQ99_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f5801,f5877,f2614,f2834]) ).
fof(f5881,definition,
! [X0,X1] :
( sQ256_spl
<=> ( ~ in(X1,relation_dom(sK95_skl(sK84_skl)))
| X0 != apply(sK95_skl(sK84_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f5884,plain,
( ~ sQ117_spl
| ~ sQ112_spl
| ~ sQ122_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f5816,f5881,f2854,f2816,f2834]) ).
fof(f5887,plain,
( sQ122_spl
| ~ sQ113_spl
| ~ function(empty_set) ),
inference(backward_demodulation,[status(thm)],[f2820,f2856]) ).
fof(f5896,plain,
! [X0] :
( ~ sQ113_spl
| ~ in(X0,sK84_skl)
| ~ in(sK84_skl,empty_set) ),
inference(paramodulation,[status(thm)],[f2820,f2606]) ).
fof(f5897,plain,
! [X0,X1] :
( ~ sQ113_spl
| ~ in(X1,sK84_skl)
| ~ in(sK84_skl,X0)
| ~ in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f2820,f2603]) ).
fof(f5898,plain,
! [X0,X1] :
( ~ sQ113_spl
| sK95_skl(sK84_skl) = X0
| ~ in(X0,sK84_skl)
| ~ ordinal(sK95_skl(sK84_skl))
| ~ ordinal(X0)
| ~ in(X1,sK84_skl)
| in(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f2820,f2311]) ).
fof(f5902,definition,
! [X0] :
( sQ257_spl
<=> ( sK95_skl(sK84_skl) = X0
| ~ in(X0,sK84_skl)
| ~ ordinal(X0)
| in(empty_set,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f5905,plain,
( ~ sQ113_spl
| ~ sQ99_spl
| sQ97_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f5898,f5902,f2607,f2614,f2819]) ).
fof(f5906,definition,
! [X0] :
( sQ258_spl
<=> ( ~ in(sK84_skl,X0)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f5909,plain,
( ~ sQ113_spl
| sQ97_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f5897,f5906,f2607,f2819]) ).
fof(f5910,definition,
( sQ259_spl
<=> in(sK84_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f5913,plain,
( ~ sQ113_spl
| sQ97_spl
| ~ sQ259_spl ),
inference(split_clause,[status(thm)],[f5896,f5910,f2607,f2819]) ).
fof(f5914,plain,
( sQ122_spl
| ~ sQ113_spl
| ~ sQ146_spl ),
inference(split_clause,[status(thm)],[f5887,f3664,f2819,f2854]) ).
fof(f5967,plain,
! [X0,X1] : ~ proper_subset(set_union2(X0,X1),X0),
inference(resolution,[status(thm)],[f1092,f1145]) ).
fof(f6021,plain,
! [X0,X1,X2] :
( ~ one_to_one(empty_set)
| ~ function(X0)
| X1 = apply(X0,X2)
| X0 != function_inverse(empty_set)
| ~ in(X1,empty_set)
| apply(empty_set,X1) != X2
| ~ relation(X0)
| ~ relation(empty_set)
| ~ function(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f1069]) ).
fof(f6028,definition,
! [X0,X1,X2] :
( sQ260_spl
<=> ( ~ function(X0)
| X1 = apply(X0,X2)
| X0 != function_inverse(empty_set)
| ~ in(X1,empty_set)
| apply(empty_set,X1) != X2
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f6031,plain,
( ~ sQ156_spl
| sQ260_spl
| ~ sQ3_spl
| ~ sQ146_spl ),
inference(split_clause,[status(thm)],[f6021,f3664,f1257,f6028,f3705]) ).
fof(f6108,plain,
! [X0] :
( ~ relation(empty_set)
| empty_set = relation_rng(X0)
| ~ function(empty_set)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| function_inverse(X0) != empty_set ),
inference(paramodulation,[status(thm)],[f1089,f1066]) ).
fof(f6111,definition,
! [X0] :
( sQ261_spl
<=> ( empty_set = relation_rng(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| function_inverse(X0) != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f6114,plain,
( ~ sQ3_spl
| ~ sQ146_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f6108,f6111,f3664,f1257]) ).
fof(f6140,plain,
! [X0] :
( ~ sQ177_spl
| in(sK53_skl(X0,empty_set),X0)
| ~ relation(empty_set)
| X0 = relation_rng(empty_set) ),
inference(resolution,[status(thm)],[f557,f4576]) ).
fof(f6142,plain,
! [X0] :
( ordinal(ordered_pair(sK54_skl(X0,sK84_skl),sK53_skl(X0,sK84_skl)))
| in(sK53_skl(X0,sK84_skl),X0)
| ~ relation(sK84_skl)
| X0 = relation_rng(sK84_skl) ),
inference(resolution,[status(thm)],[f557,f967]) ).
fof(f6175,definition,
! [X0] :
( sQ262_spl
<=> ( in(sK53_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f6178,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f6140,f6175,f1257,f4575]) ).
fof(f6179,definition,
! [X0] :
( sQ263_spl
<=> ( ordinal(ordered_pair(sK54_skl(X0,sK84_skl),sK53_skl(X0,sK84_skl)))
| in(sK53_skl(X0,sK84_skl),X0)
| X0 = relation_rng(sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f6182,plain,
( ~ sQ11_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f6142,f6179,f1345]) ).
fof(f6278,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ordinal(sK21_skl(X0,X1))
| ~ ordinal(X2)
| X0 = set_meet(X1)
| in(sK21_skl(X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2784,f411]) ).
fof(f6279,plain,
! [X0,X1] :
( ~ sQ37_spl
| ordinal(sK22_skl(X0,sK84_skl))
| set_meet(sK84_skl) = X0
| ~ in(X1,sK84_skl)
| ordinal(sK21_skl(X0,sK84_skl))
| ~ ordinal(X1)
| X0 = set_meet(sK84_skl) ),
inference(resolution,[status(thm)],[f6278,f1599]) ).
fof(f6316,definition,
! [X1] :
( sQ264_spl
<=> ( ~ in(X1,sK84_skl)
| ~ ordinal(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f6317,plain,
! [X0] :
( ~ sQ264_spl
| ~ in(X0,sK84_skl)
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f6316]) ).
fof(f6319,plain,
( ~ sQ37_spl
| sQ264_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f6279,f3741,f6316,f1598]) ).
fof(f6392,plain,
! [X0] :
( ~ sQ60_spl
| empty_set != set_union2(X0,sK84_skl) ),
inference(paramodulation,[status(thm)],[f294,f4554]) ).
fof(f6393,plain,
! [X0] : X0 = set_union2(empty_set,X0),
inference(paramodulation,[status(thm)],[f294,f912]) ).
fof(f6427,plain,
! [X0] : set_difference(X0,X0) = set_difference(empty_set,X0),
inference(paramodulation,[status(thm)],[f6393,f1025]) ).
fof(f6434,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(forward_demodulation,[status(thm)],[f1049,f6427]) ).
fof(f6473,plain,
! [X0,X1,X2] :
( ~ sQ177_spl
| empty_set = relation_dom(X0)
| ~ ordinal(empty_set)
| ~ relation(X0)
| X2 != apply(X0,empty_set)
| in(X2,relation_rng(X0))
| ~ function(X1)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ relation(X1)
| X1 != function_inverse(X0)
| ~ ordinal(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f2876,f4576]) ).
fof(f6515,plain,
! [X0,X1,X2] :
( X2 = relation_dom(empty_set)
| ~ ordinal(X2)
| ~ relation(empty_set)
| X1 != apply(empty_set,X2)
| in(empty_set,X2)
| in(X1,relation_rng(empty_set))
| ~ function(X0)
| ~ function(empty_set)
| ~ one_to_one(empty_set)
| ~ relation(X0)
| X0 != function_inverse(empty_set)
| ~ ordinal(relation_dom(empty_set)) ),
inference(paramodulation,[status(thm)],[f1089,f2876]) ).
fof(f6519,definition,
( sQ265_spl
<=> ordinal(relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f6522,definition,
! [X1,X2] :
( sQ266_spl
<=> ( X2 = relation_dom(empty_set)
| ~ ordinal(X2)
| X1 != apply(empty_set,X2)
| in(empty_set,X2)
| in(X1,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f6525,plain,
( ~ sQ3_spl
| sQ266_spl
| ~ sQ146_spl
| ~ sQ156_spl
| sQ154_spl
| ~ sQ265_spl ),
inference(split_clause,[status(thm)],[f6515,f6519,f3699,f3705,f3664,f6522,f1257]) ).
fof(f6533,definition,
! [X0,X1,X2] :
( sQ267_spl
<=> ( empty_set = relation_dom(X0)
| ~ relation(X0)
| X2 != apply(X0,empty_set)
| in(X2,relation_rng(X0))
| ~ function(X1)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ relation(X1)
| X1 != function_inverse(X0)
| ~ ordinal(relation_dom(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f6536,plain,
( ~ sQ177_spl
| ~ sQ79_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f6473,f6533,f2114,f4575]) ).
fof(f6641,plain,
! [X0,X1] :
( ~ function(empty_set)
| ~ relation(empty_set)
| empty_set != X1
| in(X0,empty_set)
| apply(empty_set,X0) = X1 ),
inference(paramodulation,[status(thm)],[f1089,f507]) ).
fof(f6644,definition,
! [X0,X1] :
( sQ269_spl
<=> ( empty_set != X1
| in(X0,empty_set)
| apply(empty_set,X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f6647,plain,
( ~ sQ146_spl
| ~ sQ3_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f6641,f6644,f1257,f3664]) ).
fof(f6761,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ relation(X1)
| empty_set = relation_rng_restriction(X0,X1)
| ~ relation(empty_set)
| in(sK8_skl(X0,empty_set,X1),X0) ),
inference(resolution,[status(thm)],[f339,f4576]) ).
fof(f6763,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK7_skl(X0,sK84_skl,X1),sK8_skl(X0,sK84_skl,X1)))
| ~ relation(X1)
| sK84_skl = relation_rng_restriction(X0,X1)
| ~ relation(sK84_skl)
| in(sK8_skl(X0,sK84_skl,X1),X0) ),
inference(resolution,[status(thm)],[f339,f967]) ).
fof(f6801,definition,
! [X0,X1] :
( sQ270_spl
<=> ( ~ relation(X1)
| empty_set = relation_rng_restriction(X0,X1)
| in(sK8_skl(X0,empty_set,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f6804,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f6761,f6801,f1257,f4575]) ).
fof(f6806,definition,
! [X0,X1] :
( sQ271_spl
<=> ( ordinal(ordered_pair(sK7_skl(X0,sK84_skl,X1),sK8_skl(X0,sK84_skl,X1)))
| ~ relation(X1)
| sK84_skl = relation_rng_restriction(X0,X1)
| in(sK8_skl(X0,sK84_skl,X1),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f6809,plain,
( ~ sQ11_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f6763,f6806,f1345]) ).
fof(f6861,plain,
! [X0,X1] :
( ~ sQ177_spl
| empty_set = sK96_skl(X1)
| ~ ordinal(empty_set)
| ~ subset(X0,empty_set)
| ~ ordinal(sK96_skl(X1))
| in(X0,sK96_skl(X1)) ),
inference(resolution,[status(thm)],[f2983,f4576]) ).
fof(f6911,definition,
! [X0,X1] :
( sQ273_spl
<=> ( empty_set = sK96_skl(X1)
| ~ subset(X0,empty_set)
| ~ ordinal(sK96_skl(X1))
| in(X0,sK96_skl(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f6914,plain,
( ~ sQ177_spl
| ~ sQ79_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f6861,f6911,f2114,f4575]) ).
fof(f6941,plain,
( ~ sQ60_spl
| ~ subset(sK84_skl,empty_set) ),
inference(resolution,[status(thm)],[f4564,f6392]) ).
fof(f7118,plain,
! [X0] :
( ~ sQ60_spl
| ~ in(sK84_skl,X0)
| X0 != powerset(empty_set) ),
inference(resolution,[status(thm)],[f416,f6941]) ).
fof(f7192,plain,
! [X0,X1] :
( in(sK48_skl(X0,X1,sK84_skl),X0)
| set_difference(sK84_skl,X1) = X0
| ordinal(sK48_skl(X0,X1,sK84_skl)) ),
inference(resolution,[status(thm)],[f538,f967]) ).
fof(f7243,plain,
( ~ in(sK26_skl(sK84_skl),sK84_skl)
| epsilon_transitive(sK84_skl) ),
inference(resolution,[status(thm)],[f426,f968]) ).
fof(f7248,definition,
( sQ277_spl
<=> in(sK26_skl(sK84_skl),sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f7250,plain,
( sQ277_spl
| ~ in(sK26_skl(sK84_skl),sK84_skl) ),
inference(component_clause,[status(thm)],[f7248]) ).
fof(f7251,plain,
( ~ sQ277_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f7243,f2923,f7248]) ).
fof(f7256,plain,
( sQ277_spl
| epsilon_transitive(sK84_skl) ),
inference(resolution,[status(thm)],[f7250,f425]) ).
fof(f7258,plain,
( sQ277_spl
| sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7256,f2925]) ).
fof(f7259,plain,
( sQ277_spl
| sQ128_spl ),
inference(contradiction_clause,[status(thm)],[f7258]) ).
fof(f7260,plain,
( ~ sQ97_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f4149,f2908,f2607]) ).
fof(f7521,plain,
! [X0,X1] :
( X0 = set_difference(X1,sK84_skl)
| ~ in(sK48_skl(X0,sK84_skl,X1),X1)
| ~ in(sK48_skl(X0,sK84_skl,X1),X0)
| ordinal(sK48_skl(X0,sK84_skl,X1)) ),
inference(resolution,[status(thm)],[f537,f967]) ).
fof(f7577,plain,
! [X0,X1,X2,X3] :
( ~ relation(sK84_skl)
| relation_image(sK84_skl,X3) = X2
| ~ in(sK11_skl(X2,X3,sK84_skl),X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X1,sK11_skl(X2,X3,sK84_skl)),X0)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f358]) ).
fof(f7578,plain,
! [X0,X1,X2,X3] :
( in(X2,relation_image(sK84_skl,X3))
| ~ in(X1,relation_dom(sK84_skl))
| ~ relation(sK84_skl)
| ~ in(X1,X3)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f872]) ).
fof(f7579,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(sK84_skl)
| ~ ordinal(X4)
| ~ in(X2,X3)
| ordinal(ordered_pair(X1,X2))
| ~ relation(X4)
| relation_rng_restriction(X3,sK84_skl) != X4
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f2681]) ).
fof(f7580,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X2,X4)
| ~ relation(sK84_skl)
| relation_rng_restriction(X4,sK84_skl) != X3
| ~ in(X3,ordered_pair(X1,X2))
| ~ relation(X3)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f2682]) ).
fof(f7581,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(X4,X5)
| ~ relation(X4)
| ~ in(X5,ordered_pair(X1,X2))
| ~ relation(sK84_skl)
| ~ in(X2,X3)
| relation_rng_restriction(X3,sK84_skl) != X4
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f2678]) ).
fof(f7582,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(sK84_skl))
| ~ function(sK84_skl)
| ~ relation(sK84_skl)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1250,f1165]) ).
fof(f7610,definition,
! [X0,X1,X2] :
( sQ283_spl
<=> ( in(X1,relation_dom(sK84_skl))
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f7613,plain,
( ~ sQ68_spl
| ~ sQ11_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f7582,f7610,f1345,f1961]) ).
fof(f7615,definition,
! [X0,X1,X2,X3] :
( sQ284_spl
<=> ( relation_image(sK84_skl,X3) = X2
| ~ in(sK11_skl(X2,X3,sK84_skl),X2)
| ~ in(X1,X3)
| ~ in(ordered_pair(X1,sK11_skl(X2,X3,sK84_skl)),X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f7618,plain,
( ~ sQ11_spl
| sQ284_spl ),
inference(split_clause,[status(thm)],[f7577,f7615,f1345]) ).
fof(f7619,definition,
! [X0,X1,X2,X3,X4] :
( sQ285_spl
<=> ( ~ in(X2,X4)
| relation_rng_restriction(X4,sK84_skl) != X3
| ~ in(X3,ordered_pair(X1,X2))
| ~ relation(X3)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f7622,plain,
( ~ sQ11_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f7580,f7619,f1345]) ).
fof(f7623,definition,
! [X0,X1,X2,X3] :
( sQ286_spl
<=> ( in(X2,relation_image(sK84_skl,X3))
| ~ in(X1,relation_dom(sK84_skl))
| ~ in(X1,X3)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f7626,plain,
( ~ sQ11_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f7578,f7623,f1345]) ).
fof(f7628,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ287_spl
<=> ( ~ in(X4,X5)
| ~ relation(X4)
| ~ in(X5,ordered_pair(X1,X2))
| ~ in(X2,X3)
| relation_rng_restriction(X3,sK84_skl) != X4
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f7631,plain,
( ~ sQ11_spl
| sQ287_spl ),
inference(split_clause,[status(thm)],[f7581,f7628,f1345]) ).
fof(f7645,definition,
! [X0,X1,X2,X3,X4] :
( sQ288_spl
<=> ( ~ ordinal(X4)
| ~ in(X2,X3)
| ordinal(ordered_pair(X1,X2))
| ~ relation(X4)
| relation_rng_restriction(X3,sK84_skl) != X4
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f7648,plain,
( ~ sQ11_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f7579,f7645,f1345]) ).
fof(f7778,plain,
( ordinal(sK24_skl(sK84_skl))
| sK84_skl = empty_set ),
inference(resolution,[status(thm)],[f412,f967]) ).
fof(f7810,definition,
( sQ290_spl
<=> ordinal(sK24_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f7813,plain,
( sQ290_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f7778,f1544,f7810]) ).
fof(f7915,plain,
( ~ sQ98_spl
| sK95_skl(sK84_skl) = empty_set
| ordinal(sK24_skl(sK95_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f2611,f412]) ).
fof(f7920,plain,
! [X0,X1] :
( ~ sQ98_spl
| sK95_skl(sK84_skl) = sK96_skl(X0)
| ~ ordinal(sK95_skl(sK84_skl))
| ~ subset(X1,sK95_skl(sK84_skl))
| ~ ordinal(sK96_skl(X0))
| in(X1,sK96_skl(X0))
| ordinal(sK96_skl(X0)) ),
inference(resolution,[status(thm)],[f2611,f2983]) ).
fof(f7921,plain,
! [X0,X1,X2] :
( ~ sQ98_spl
| sK95_skl(sK84_skl) = relation_dom(X0)
| ~ ordinal(sK95_skl(sK84_skl))
| ~ relation(X0)
| X2 != apply(X0,sK95_skl(sK84_skl))
| in(X2,relation_rng(X0))
| ~ function(X1)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ relation(X1)
| X1 != function_inverse(X0)
| ~ ordinal(relation_dom(X0))
| ordinal(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f2611,f2876]) ).
fof(f7928,plain,
( ~ sQ98_spl
| relation(sK95_skl(sK84_skl))
| ordinal(sK19_skl(sK95_skl(sK84_skl))) ),
inference(resolution,[status(thm)],[f2611,f387]) ).
fof(f7935,plain,
! [X0,X1] :
( ~ sQ98_spl
| sK95_skl(X0) = sK95_skl(sK84_skl)
| ~ in(sK95_skl(sK84_skl),X0)
| ~ ordinal(sK95_skl(X0))
| ~ ordinal(sK95_skl(sK84_skl))
| ~ in(X1,X0)
| ordinal(sK95_skl(X0)) ),
inference(resolution,[status(thm)],[f2611,f2311]) ).
fof(f7943,plain,
! [X0,X1] :
( ~ sQ98_spl
| in(sK95_skl(sK84_skl),X0)
| sK20_skl(sK95_skl(sK84_skl),X0,X1) = sK95_skl(sK84_skl)
| X0 != set_meet(X1)
| ~ ordinal(sK95_skl(sK84_skl))
| empty_set = X1
| ~ ordinal(sK20_skl(sK95_skl(sK84_skl),X0,X1))
| ordinal(sK20_skl(sK95_skl(sK84_skl),X0,X1)) ),
inference(resolution,[status(thm)],[f2611,f2302]) ).
fof(f7947,plain,
! [X0] :
( ~ sQ98_spl
| in(sK53_skl(X0,sK95_skl(sK84_skl)),X0)
| ~ relation(sK95_skl(sK84_skl))
| X0 = relation_rng(sK95_skl(sK84_skl))
| ordinal(ordered_pair(sK54_skl(X0,sK95_skl(sK84_skl)),sK53_skl(X0,sK95_skl(sK84_skl)))) ),
inference(resolution,[status(thm)],[f2611,f557]) ).
fof(f7948,plain,
! [X0,X1] :
( ~ sQ98_spl
| ~ relation(X1)
| sK95_skl(sK84_skl) = relation_rng_restriction(X0,X1)
| ~ relation(sK95_skl(sK84_skl))
| in(sK8_skl(X0,sK95_skl(sK84_skl),X1),X0)
| ordinal(ordered_pair(sK7_skl(X0,sK95_skl(sK84_skl),X1),sK8_skl(X0,sK95_skl(sK84_skl),X1))) ),
inference(resolution,[status(thm)],[f2611,f339]) ).
fof(f7949,plain,
! [X0,X1] :
( ~ sQ98_spl
| relation_rng_restriction(X0,sK95_skl(sK84_skl)) = X1
| in(ordered_pair(sK7_skl(X0,X1,sK95_skl(sK84_skl)),sK8_skl(X0,X1,sK95_skl(sK84_skl))),X1)
| ~ relation(sK95_skl(sK84_skl))
| ~ relation(X1)
| ordinal(ordered_pair(sK7_skl(X0,X1,sK95_skl(sK84_skl)),sK8_skl(X0,X1,sK95_skl(sK84_skl)))) ),
inference(resolution,[status(thm)],[f2611,f340]) ).
fof(f7950,plain,
! [X0,X1] :
( ~ sQ98_spl
| in(sK2_skl(X0,sK95_skl(sK84_skl),X1),X0)
| ~ relation(sK95_skl(sK84_skl))
| ~ relation(X1)
| relation_dom_restriction(X1,X0) = sK95_skl(sK84_skl)
| ordinal(ordered_pair(sK2_skl(X0,sK95_skl(sK84_skl),X1),sK3_skl(X0,sK95_skl(sK84_skl),X1))) ),
inference(resolution,[status(thm)],[f2611,f319]) ).
fof(f7957,plain,
! [X0,X1] :
( ~ sQ98_spl
| ~ in(X0,X1)
| relation_dom(sK95_skl(sK84_skl)) != X1
| ~ relation(sK95_skl(sK84_skl))
| ordinal(ordered_pair(X0,sK42_skl(X0,X1,sK95_skl(sK84_skl)))) ),
inference(resolution,[status(thm)],[f2611,f517]) ).
fof(f7962,definition,
( sQ291_spl
<=> ordinal(sK19_skl(sK95_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f7965,plain,
( ~ sQ98_spl
| sQ112_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f7928,f7962,f2816,f2610]) ).
fof(f7966,definition,
! [X0,X1] :
( sQ292_spl
<=> ( sK95_skl(X0) = sK95_skl(sK84_skl)
| ~ in(sK95_skl(sK84_skl),X0)
| ~ ordinal(sK95_skl(X0))
| ~ in(X1,X0)
| ordinal(sK95_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f7969,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ292_spl ),
inference(split_clause,[status(thm)],[f7935,f7966,f2614,f2610]) ).
fof(f7971,definition,
! [X0,X1] :
( sQ293_spl
<=> ( in(sK95_skl(sK84_skl),X0)
| sK20_skl(sK95_skl(sK84_skl),X0,X1) = sK95_skl(sK84_skl)
| X0 != set_meet(X1)
| empty_set = X1
| ~ ordinal(sK20_skl(sK95_skl(sK84_skl),X0,X1))
| ordinal(sK20_skl(sK95_skl(sK84_skl),X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f7974,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f7943,f7971,f2614,f2610]) ).
fof(f7975,definition,
( sQ294_spl
<=> ordinal(sK24_skl(sK95_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f7978,plain,
( ~ sQ98_spl
| sQ113_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f7915,f7975,f2819,f2610]) ).
fof(f7981,definition,
! [X0] :
( sQ295_spl
<=> ( in(sK53_skl(X0,sK95_skl(sK84_skl)),X0)
| X0 = relation_rng(sK95_skl(sK84_skl))
| ordinal(ordered_pair(sK54_skl(X0,sK95_skl(sK84_skl)),sK53_skl(X0,sK95_skl(sK84_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f7984,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f7947,f7981,f2816,f2610]) ).
fof(f7991,definition,
! [X0,X1] :
( sQ296_spl
<=> ( relation_rng_restriction(X0,sK95_skl(sK84_skl)) = X1
| in(ordered_pair(sK7_skl(X0,X1,sK95_skl(sK84_skl)),sK8_skl(X0,X1,sK95_skl(sK84_skl))),X1)
| ~ relation(X1)
| ordinal(ordered_pair(sK7_skl(X0,X1,sK95_skl(sK84_skl)),sK8_skl(X0,X1,sK95_skl(sK84_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f7994,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f7949,f7991,f2816,f2610]) ).
fof(f7995,definition,
! [X0,X1] :
( sQ297_spl
<=> ( sK95_skl(sK84_skl) = sK96_skl(X0)
| ~ subset(X1,sK95_skl(sK84_skl))
| ~ ordinal(sK96_skl(X0))
| in(X1,sK96_skl(X0))
| ordinal(sK96_skl(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f7998,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f7920,f7995,f2614,f2610]) ).
fof(f8007,definition,
! [X0,X1] :
( sQ298_spl
<=> ( in(sK2_skl(X0,sK95_skl(sK84_skl),X1),X0)
| ~ relation(X1)
| relation_dom_restriction(X1,X0) = sK95_skl(sK84_skl)
| ordinal(ordered_pair(sK2_skl(X0,sK95_skl(sK84_skl),X1),sK3_skl(X0,sK95_skl(sK84_skl),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f8010,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f7950,f8007,f2816,f2610]) ).
fof(f8013,definition,
! [X0,X1] :
( sQ299_spl
<=> ( ~ relation(X1)
| sK95_skl(sK84_skl) = relation_rng_restriction(X0,X1)
| in(sK8_skl(X0,sK95_skl(sK84_skl),X1),X0)
| ordinal(ordered_pair(sK7_skl(X0,sK95_skl(sK84_skl),X1),sK8_skl(X0,sK95_skl(sK84_skl),X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f8016,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f7948,f8013,f2816,f2610]) ).
fof(f8017,definition,
! [X0,X1] :
( sQ300_spl
<=> ( ~ in(X0,X1)
| relation_dom(sK95_skl(sK84_skl)) != X1
| ordinal(ordered_pair(X0,sK42_skl(X0,X1,sK95_skl(sK84_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f8020,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ300_spl ),
inference(split_clause,[status(thm)],[f7957,f8017,f2816,f2610]) ).
fof(f8023,definition,
! [X0,X1,X2] :
( sQ301_spl
<=> ( sK95_skl(sK84_skl) = relation_dom(X0)
| ~ relation(X0)
| X2 != apply(X0,sK95_skl(sK84_skl))
| in(X2,relation_rng(X0))
| ~ function(X1)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ relation(X1)
| X1 != function_inverse(X0)
| ~ ordinal(relation_dom(X0))
| ordinal(relation_dom(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f8026,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f7921,f8023,f2614,f2610]) ).
fof(f8111,plain,
! [X0] :
( ~ sQ177_spl
| X0 = empty_set
| ~ ordinal(empty_set)
| ~ ordinal(X0)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f3279,f4576]) ).
fof(f8122,plain,
! [X0] :
( ~ sQ98_spl
| ordinal(X0)
| X0 = sK95_skl(sK84_skl)
| ~ ordinal(sK95_skl(sK84_skl))
| ~ ordinal(X0)
| X0 != empty_set ),
inference(resolution,[status(thm)],[f3279,f2611]) ).
fof(f8160,definition,
! [X0] :
( sQ302_spl
<=> ( ordinal(X0)
| X0 = sK95_skl(sK84_skl)
| ~ ordinal(X0)
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f8163,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f8122,f8160,f2614,f2610]) ).
fof(f8172,definition,
! [X0] :
( sQ304_spl
<=> ( X0 = empty_set
| ~ ordinal(X0)
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f8175,plain,
( ~ sQ177_spl
| ~ sQ79_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f8111,f8172,f2114,f4575]) ).
fof(f8218,plain,
! [X0] :
( ~ sQ177_spl
| empty_set = identity_relation(X0)
| ~ relation(empty_set)
| sK0_skl(X0,empty_set) = sK1_skl(X0,empty_set) ),
inference(resolution,[status(thm)],[f305,f4576]) ).
fof(f8220,plain,
! [X0] :
( ordinal(ordered_pair(sK0_skl(X0,sK84_skl),sK1_skl(X0,sK84_skl)))
| sK84_skl = identity_relation(X0)
| ~ relation(sK84_skl)
| sK0_skl(X0,sK84_skl) = sK1_skl(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f305,f967]) ).
fof(f8228,plain,
! [X0] :
( ~ sQ98_spl
| ordinal(ordered_pair(sK0_skl(X0,sK95_skl(sK84_skl)),sK1_skl(X0,sK95_skl(sK84_skl))))
| sK95_skl(sK84_skl) = identity_relation(X0)
| ~ relation(sK95_skl(sK84_skl))
| sK0_skl(X0,sK95_skl(sK84_skl)) = sK1_skl(X0,sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f305,f2611]) ).
fof(f8255,definition,
! [X0] :
( sQ308_spl
<=> ( empty_set = identity_relation(X0)
| sK0_skl(X0,empty_set) = sK1_skl(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f8258,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ308_spl ),
inference(split_clause,[status(thm)],[f8218,f8255,f1257,f4575]) ).
fof(f8266,definition,
! [X0] :
( sQ309_spl
<=> ( ordinal(ordered_pair(sK0_skl(X0,sK95_skl(sK84_skl)),sK1_skl(X0,sK95_skl(sK84_skl))))
| sK95_skl(sK84_skl) = identity_relation(X0)
| sK0_skl(X0,sK95_skl(sK84_skl)) = sK1_skl(X0,sK95_skl(sK84_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f8269,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ309_spl ),
inference(split_clause,[status(thm)],[f8228,f8266,f2816,f2610]) ).
fof(f8270,definition,
! [X0] :
( sQ310_spl
<=> ( ordinal(ordered_pair(sK0_skl(X0,sK84_skl),sK1_skl(X0,sK84_skl)))
| sK84_skl = identity_relation(X0)
| sK0_skl(X0,sK84_skl) = sK1_skl(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f8273,plain,
( ~ sQ11_spl
| sQ310_spl ),
inference(split_clause,[status(thm)],[f8220,f8270,f1345]) ).
fof(f8279,plain,
! [X0] :
( disjoint(X0,empty_set)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f952,f574]) ).
fof(f8282,definition,
! [X0] :
( sQ311_spl
<=> disjoint(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f8285,plain,
( sQ311_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f8279,f1254,f8282]) ).
fof(f8341,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X2,X3),X4)
| ~ in(X4,sK84_skl)
| ~ in(X2,X1)
| ~ relation(sK84_skl)
| ~ relation(X0)
| in(ordered_pair(X2,X3),X0)
| X0 != relation_dom_restriction(sK84_skl,X1) ),
inference(resolution,[status(thm)],[f317,f1250]) ).
fof(f8369,definition,
! [X0,X1,X2,X3,X4] :
( sQ312_spl
<=> ( ~ in(ordered_pair(X2,X3),X4)
| ~ in(X4,sK84_skl)
| ~ in(X2,X1)
| ~ relation(X0)
| in(ordered_pair(X2,X3),X0)
| X0 != relation_dom_restriction(sK84_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f8372,plain,
( ~ sQ11_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f8341,f8369,f1345]) ).
fof(f8599,plain,
! [X0] :
( ~ relation(empty_set)
| subset(relation_image(empty_set,X0),empty_set) ),
inference(paramodulation,[status(thm)],[f1090,f875]) ).
fof(f8600,definition,
! [X0] :
( sQ315_spl
<=> subset(relation_image(empty_set,X0),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f8603,plain,
( ~ sQ3_spl
| sQ315_spl ),
inference(split_clause,[status(thm)],[f8599,f8600,f1257]) ).
fof(f8702,plain,
! [X0] :
( ~ sQ60_spl
| ~ in(sK84_skl,X0)
| ~ in(X0,sK84_skl)
| sK84_skl != powerset(empty_set) ),
inference(resolution,[status(thm)],[f7118,f1250]) ).
fof(f8717,definition,
( sQ316_spl
<=> sK84_skl = powerset(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f8720,plain,
( ~ sQ60_spl
| sQ40_spl
| ~ sQ316_spl ),
inference(split_clause,[status(thm)],[f8702,f8717,f1661,f1879]) ).
fof(f8741,plain,
! [X0,X1] :
( ~ sQ177_spl
| empty_set = set_intersection2(X0,X1)
| ~ ordinal(set_intersection2(X0,X1))
| ~ disjoint(X0,X1)
| ~ ordinal(empty_set) ),
inference(resolution,[status(thm)],[f3483,f4576]) ).
fof(f8752,plain,
! [X0,X1] :
( ~ sQ98_spl
| ordinal(set_intersection2(X0,X1))
| sK95_skl(sK84_skl) = set_intersection2(X0,X1)
| ~ ordinal(set_intersection2(X0,X1))
| ~ disjoint(X0,X1)
| ~ ordinal(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f3483,f2611]) ).
fof(f8796,definition,
! [X0,X1] :
( sQ320_spl
<=> ( ordinal(set_intersection2(X0,X1))
| sK95_skl(sK84_skl) = set_intersection2(X0,X1)
| ~ ordinal(set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f8799,plain,
( ~ sQ98_spl
| sQ320_spl
| ~ sQ99_spl ),
inference(split_clause,[status(thm)],[f8752,f2614,f8796,f2610]) ).
fof(f8813,definition,
! [X0,X1] :
( sQ322_spl
<=> ( empty_set = set_intersection2(X0,X1)
| ~ ordinal(set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f8816,plain,
( ~ sQ177_spl
| sQ322_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f8741,f2114,f8813,f4575]) ).
fof(f8842,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X0,sK84_skl),sK1_skl(X0,sK84_skl)),X1)
| ~ in(X1,sK84_skl)
| ~ in(sK0_skl(X0,sK84_skl),X0)
| sK0_skl(X0,sK84_skl) != sK1_skl(X0,sK84_skl)
| ~ relation(sK84_skl)
| identity_relation(X0) = sK84_skl ),
inference(resolution,[status(thm)],[f303,f1250]) ).
fof(f8850,definition,
! [X0,X1] :
( sQ323_spl
<=> ( ~ in(ordered_pair(sK0_skl(X0,sK84_skl),sK1_skl(X0,sK84_skl)),X1)
| ~ in(X1,sK84_skl)
| ~ in(sK0_skl(X0,sK84_skl),X0)
| sK0_skl(X0,sK84_skl) != sK1_skl(X0,sK84_skl)
| identity_relation(X0) = sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f8853,plain,
( ~ sQ11_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f8842,f8850,f1345]) ).
fof(f8930,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK55_skl(sK84_skl,X0),sK56_skl(sK84_skl,X0)),X1)
| ~ in(X1,sK84_skl)
| ~ relation(X0)
| ~ relation(sK84_skl)
| ~ in(ordered_pair(sK56_skl(sK84_skl,X0),sK55_skl(sK84_skl,X0)),X0)
| sK84_skl = relation_inverse(X0) ),
inference(resolution,[status(thm)],[f569,f1250]) ).
fof(f8938,definition,
! [X0,X1] :
( sQ325_spl
<=> ( ~ in(ordered_pair(sK55_skl(sK84_skl,X0),sK56_skl(sK84_skl,X0)),X1)
| ~ in(X1,sK84_skl)
| ~ relation(X0)
| ~ in(ordered_pair(sK56_skl(sK84_skl,X0),sK55_skl(sK84_skl,X0)),X0)
| sK84_skl = relation_inverse(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f8941,plain,
( ~ sQ11_spl
| sQ325_spl ),
inference(split_clause,[status(thm)],[f8930,f8938,f1345]) ).
fof(f8956,plain,
( set_difference(sK84_skl,sK84_skl) = sK84_skl
| ordinal(sK48_skl(sK84_skl,sK84_skl,sK84_skl))
| sK84_skl = set_difference(sK84_skl,sK84_skl)
| ~ in(sK48_skl(sK84_skl,sK84_skl,sK84_skl),sK84_skl)
| ordinal(sK48_skl(sK84_skl,sK84_skl,sK84_skl)) ),
inference(resolution,[status(thm)],[f7521,f7192]) ).
fof(f8972,definition,
( sQ326_spl
<=> ordinal(sK48_skl(sK84_skl,sK84_skl,sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f8975,definition,
( sQ327_spl
<=> in(sK48_skl(sK84_skl,sK84_skl,sK84_skl),sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f8978,definition,
( sQ328_spl
<=> sK84_skl = set_difference(sK84_skl,sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f8979,plain,
( ~ sQ328_spl
| sK84_skl = set_difference(sK84_skl,sK84_skl) ),
inference(component_clause,[status(thm)],[f8978]) ).
fof(f8981,plain,
( sQ328_spl
| ~ sQ327_spl
| sQ326_spl ),
inference(split_clause,[status(thm)],[f8956,f8972,f8975,f8978]) ).
fof(f8982,plain,
( ~ sQ328_spl
| sK84_skl = empty_set ),
inference(forward_demodulation,[status(thm)],[f6434,f8979]) ).
fof(f8983,plain,
( ~ sQ328_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8982,f1546]) ).
fof(f8984,plain,
( ~ sQ328_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f8983]) ).
fof(f9024,plain,
! [X0] :
( ~ in(X0,sK84_skl)
| X0 = sK84_skl
| proper_subset(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f605,f968]) ).
fof(f9046,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ in(X1,X0)
| relation_rng(empty_set) != X0
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f554,f4576]) ).
fof(f9048,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK52_skl(X1,X0,sK84_skl),X1))
| ~ in(X1,X0)
| relation_rng(sK84_skl) != X0
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f554,f967]) ).
fof(f9056,plain,
! [X0,X1] :
( ~ sQ98_spl
| ordinal(ordered_pair(sK52_skl(X1,X0,sK95_skl(sK84_skl)),X1))
| ~ in(X1,X0)
| relation_rng(sK95_skl(sK84_skl)) != X0
| ~ relation(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f554,f2611]) ).
fof(f9082,definition,
! [X0,X1] :
( sQ329_spl
<=> ( ~ in(X1,X0)
| relation_rng(empty_set) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f9085,plain,
( ~ sQ177_spl
| sQ329_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f9046,f1257,f9082,f4575]) ).
fof(f9089,definition,
! [X0,X1] :
( sQ330_spl
<=> ( ordinal(ordered_pair(sK52_skl(X1,X0,sK84_skl),X1))
| ~ in(X1,X0)
| relation_rng(sK84_skl) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f9092,plain,
( sQ330_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9048,f1345,f9089]) ).
fof(f9096,definition,
! [X0,X1] :
( sQ331_spl
<=> ( ordinal(ordered_pair(sK52_skl(X1,X0,sK95_skl(sK84_skl)),X1))
| ~ in(X1,X0)
| relation_rng(sK95_skl(sK84_skl)) != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f9099,plain,
( ~ sQ98_spl
| sQ331_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f9056,f2816,f9096,f2610]) ).
fof(f9320,plain,
! [X0,X1] :
( ~ sQ171_spl
| ~ relation(sK84_skl)
| ~ in(X0,relation_image(sK84_skl,X1)) ),
inference(resolution,[status(thm)],[f4137,f881]) ).
fof(f9327,plain,
! [X0,X1,X2] :
( ~ sQ171_spl
| X1 != empty_set
| relation_image(sK84_skl,X2) != empty_set
| ~ in(X0,set_meet(X1)) ),
inference(resolution,[status(thm)],[f4137,f400]) ).
fof(f9333,plain,
! [X0,X1] :
( ~ sQ171_spl
| ~ function(sK84_skl)
| ~ subset(X1,relation_rng(sK84_skl))
| ~ relation(sK84_skl)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f4137,f889]) ).
fof(f9334,plain,
! [X0,X1] :
( ~ sQ171_spl
| ~ relation(sK84_skl)
| ~ relation(X1)
| ~ in(X0,relation_rng(relation_composition(X1,sK84_skl))) ),
inference(resolution,[status(thm)],[f4137,f891]) ).
fof(f9335,plain,
! [X0,X1] :
( ~ sQ171_spl
| ~ relation(sK84_skl)
| ~ in(X0,relation_image(sK84_skl,set_intersection2(relation_dom(sK84_skl),X1))) ),
inference(resolution,[status(thm)],[f4137,f881]) ).
fof(f9347,definition,
! [X0,X1] :
( sQ335_spl
<=> ~ in(X0,relation_image(sK84_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f9350,plain,
( ~ sQ171_spl
| ~ sQ11_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f9320,f9347,f1345,f4136]) ).
fof(f9353,definition,
! [X0,X1] :
( sQ336_spl
<=> ~ in(X0,relation_image(sK84_skl,set_intersection2(relation_dom(sK84_skl),X1))) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f9356,plain,
( ~ sQ171_spl
| ~ sQ11_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f9335,f9353,f1345,f4136]) ).
fof(f9357,definition,
! [X0,X1] :
( sQ337_spl
<=> ( X1 != empty_set
| ~ in(X0,set_meet(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f9360,definition,
! [X2] :
( sQ338_spl
<=> relation_image(sK84_skl,X2) != empty_set ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f9361,plain,
! [X0] :
( ~ sQ338_spl
| empty_set != relation_image(sK84_skl,X0) ),
inference(component_clause,[status(thm)],[f9360]) ).
fof(f9363,plain,
( ~ sQ171_spl
| sQ338_spl
| sQ337_spl ),
inference(split_clause,[status(thm)],[f9327,f9357,f9360,f4136]) ).
fof(f9364,definition,
! [X0,X1] :
( sQ339_spl
<=> ( ~ subset(X1,relation_rng(sK84_skl))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f9367,plain,
( ~ sQ171_spl
| ~ sQ68_spl
| ~ sQ11_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f9333,f9364,f1345,f1961,f4136]) ).
fof(f9369,definition,
! [X0,X1] :
( sQ340_spl
<=> ( ~ relation(X1)
| ~ in(X0,relation_rng(relation_composition(X1,sK84_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f9372,plain,
( ~ sQ171_spl
| ~ sQ11_spl
| sQ340_spl ),
inference(split_clause,[status(thm)],[f9334,f9369,f1345,f4136]) ).
fof(f9438,plain,
! [X0,X1] :
( ~ sQ177_spl
| X1 = empty_set
| X0 = empty_set
| ~ ordinal(empty_set)
| singleton(X1) != X0
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f3558,f4576]) ).
fof(f9449,plain,
! [X0,X1] :
( ~ sQ98_spl
| ordinal(X0)
| X1 = sK95_skl(sK84_skl)
| X0 = sK95_skl(sK84_skl)
| ~ ordinal(sK95_skl(sK84_skl))
| singleton(X1) != X0
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f3558,f2611]) ).
fof(f9507,definition,
! [X0,X1] :
( sQ344_spl
<=> ( X1 = empty_set
| X0 = empty_set
| singleton(X1) != X0
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f9510,plain,
( ~ sQ177_spl
| ~ sQ79_spl
| sQ344_spl ),
inference(split_clause,[status(thm)],[f9438,f9507,f2114,f4575]) ).
fof(f9530,definition,
! [X0,X1] :
( sQ346_spl
<=> ( ordinal(X0)
| X1 = sK95_skl(sK84_skl)
| X0 = sK95_skl(sK84_skl)
| singleton(X1) != X0
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f9533,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ346_spl ),
inference(split_clause,[status(thm)],[f9449,f9530,f2614,f2610]) ).
fof(f9550,plain,
! [X0,X1] :
( ~ subset(X0,empty_set)
| ~ relation(empty_set)
| ~ relation(X0)
| ~ subset(empty_set,X1)
| subset(relation_dom(X0),X1) ),
inference(paramodulation,[status(thm)],[f1089,f3599]) ).
fof(f9554,definition,
! [X0,X1] :
( sQ348_spl
<=> ( ~ subset(X0,empty_set)
| ~ relation(X0)
| ~ subset(empty_set,X1)
| subset(relation_dom(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f9557,plain,
( ~ sQ3_spl
| sQ348_spl ),
inference(split_clause,[status(thm)],[f9550,f9554,f1257]) ).
fof(f9562,definition,
! [X0] :
( sQ349_spl
<=> ( sK84_skl = X0
| X0 != empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f9563,plain,
! [X0] :
( ~ sQ349_spl
| empty_set != X0
| X0 = sK84_skl ),
inference(component_clause,[status(thm)],[f9562]) ).
fof(f9582,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ in(X0,relation_image(empty_set,X1))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f870,f4576]) ).
fof(f9584,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK81_skl(X1,X0,sK84_skl),X0))
| ~ in(X0,relation_image(sK84_skl,X1))
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f870,f967]) ).
fof(f9592,plain,
! [X0,X1] :
( ~ sQ98_spl
| ordinal(ordered_pair(sK81_skl(X1,X0,sK95_skl(sK84_skl)),X0))
| ~ in(X0,relation_image(sK95_skl(sK84_skl),X1))
| ~ relation(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f870,f2611]) ).
fof(f9618,definition,
! [X0,X1] :
( sQ350_spl
<=> ~ in(X0,relation_image(empty_set,X1)) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f9621,plain,
( ~ sQ177_spl
| sQ350_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f9582,f1257,f9618,f4575]) ).
fof(f9625,definition,
! [X0,X1] :
( sQ351_spl
<=> ( ordinal(ordered_pair(sK81_skl(X1,X0,sK84_skl),X0))
| ~ in(X0,relation_image(sK84_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f9628,plain,
( sQ351_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9584,f1345,f9625]) ).
fof(f9636,definition,
! [X0,X1] :
( sQ352_spl
<=> ( ordinal(ordered_pair(sK81_skl(X1,X0,sK95_skl(sK84_skl)),X0))
| ~ in(X0,relation_image(sK95_skl(sK84_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f9639,plain,
( ~ sQ98_spl
| sQ352_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f9592,f2816,f9636,f2610]) ).
fof(f9654,plain,
! [X0,X1] :
( ~ relation(empty_set)
| ~ function(empty_set)
| relation_rng(empty_set) != X1
| ~ in(X0,X1)
| in(sK49_skl(X0,X1,empty_set),empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f544]) ).
fof(f9658,definition,
! [X0,X1] :
( sQ353_spl
<=> ( relation_rng(empty_set) != X1
| ~ in(X0,X1)
| in(sK49_skl(X0,X1,empty_set),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f9661,plain,
( ~ sQ3_spl
| ~ sQ146_spl
| sQ353_spl ),
inference(split_clause,[status(thm)],[f9654,f9658,f3664,f1257]) ).
fof(f9685,plain,
( sQ26_spl
| ~ sQ349_spl
| empty_set != empty_set ),
inference(resolution,[status(thm)],[f9563,f1546]) ).
fof(f9697,plain,
( sQ26_spl
| ~ sQ349_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f9685]) ).
fof(f9698,plain,
( sQ26_spl
| ~ sQ349_spl ),
inference(contradiction_clause,[status(thm)],[f9697]) ).
fof(f9699,plain,
( ~ sQ338_spl
| ~ function(sK84_skl)
| ~ subset(empty_set,relation_rng(sK84_skl))
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f9361,f889]) ).
fof(f9700,definition,
( sQ355_spl
<=> subset(empty_set,relation_rng(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f9702,plain,
( sQ355_spl
| ~ subset(empty_set,relation_rng(sK84_skl)) ),
inference(component_clause,[status(thm)],[f9700]) ).
fof(f9703,plain,
( ~ sQ338_spl
| ~ sQ68_spl
| ~ sQ355_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9699,f1345,f9700,f1961,f9360]) ).
fof(f9704,plain,
( sQ355_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9702,f960]) ).
fof(f9705,plain,
sQ355_spl,
inference(contradiction_clause,[status(thm)],[f9704]) ).
fof(f9796,plain,
! [X0] :
( ~ subset(X0,empty_set)
| ~ subset(empty_set,relation_dom(X0))
| relation_dom(X0) = relation_dom(empty_set)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1089,f3601]) ).
fof(f9798,plain,
! [X0] :
( ~ subset(empty_set,X0)
| ~ subset(relation_dom(X0),empty_set)
| relation_dom(empty_set) = relation_dom(X0)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f3601]) ).
fof(f9802,definition,
! [X0] :
( sQ357_spl
<=> ( ~ subset(empty_set,X0)
| ~ subset(relation_dom(X0),empty_set)
| relation_dom(empty_set) = relation_dom(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f9805,plain,
( sQ357_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f9798,f1257,f9802]) ).
fof(f9809,definition,
! [X0] :
( sQ358_spl
<=> ( ~ subset(X0,empty_set)
| ~ subset(empty_set,relation_dom(X0))
| relation_dom(X0) = relation_dom(empty_set)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f9812,plain,
( ~ sQ3_spl
| sQ358_spl ),
inference(split_clause,[status(thm)],[f9796,f9809,f1257]) ).
fof(f9866,plain,
! [X0,X1] :
( ~ subset(X1,empty_set)
| ~ subset(empty_set,X0)
| ~ relation(empty_set)
| subset(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1089,f3597]) ).
fof(f9868,definition,
! [X0,X1] :
( sQ364_spl
<=> ( ~ subset(X1,empty_set)
| ~ subset(empty_set,X0)
| subset(X1,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f9871,plain,
( ~ sQ3_spl
| sQ364_spl ),
inference(split_clause,[status(thm)],[f9866,f9868,f1257]) ).
fof(f9963,plain,
! [X0,X1] :
( ~ in(sK84_skl,X1)
| ~ in(X1,sK84_skl)
| X0 != union(sK84_skl)
| in(sK84_skl,X0) ),
inference(resolution,[status(thm)],[f527,f1250]) ).
fof(f10069,definition,
! [X0] :
( sQ365_spl
<=> ( X0 != union(sK84_skl)
| in(sK84_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f10072,plain,
( sQ40_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f9963,f10069,f1661]) ).
fof(f10139,plain,
! [X0] :
( ~ sQ177_spl
| empty_set != singleton(X0) ),
inference(resolution,[status(thm)],[f1228,f4576]) ).
fof(f10191,plain,
( ~ sQ177_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f10139,f1759,f4575]) ).
fof(f10210,plain,
! [X0] :
( subset(relation_rng(relation_composition(X0,empty_set)),empty_set)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1090,f1033]) ).
fof(f10212,definition,
! [X0] :
( sQ366_spl
<=> ( subset(relation_rng(relation_composition(X0,empty_set)),empty_set)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f10215,plain,
( sQ366_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f10210,f1257,f10212]) ).
fof(f10312,plain,
! [X0,X1] :
( ~ in(X0,empty_set)
| ~ relation(empty_set)
| ~ relation(X1)
| ~ subset(empty_set,X1)
| in(X0,relation_dom(X1)) ),
inference(paramodulation,[status(thm)],[f1089,f3600]) ).
fof(f10319,definition,
! [X0,X1] :
( sQ367_spl
<=> ( ~ in(X0,empty_set)
| ~ relation(X1)
| ~ subset(empty_set,X1)
| in(X0,relation_dom(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f10322,plain,
( ~ sQ3_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f10312,f10319,f1257]) ).
fof(f10363,plain,
! [X0] : ~ proper_subset(succ(X0),X0),
inference(paramodulation,[status(thm)],[f381,f5967]) ).
fof(f10380,plain,
( sK84_skl = succ(sK84_skl)
| ~ in(succ(sK84_skl),sK84_skl) ),
inference(resolution,[status(thm)],[f10363,f9024]) ).
fof(f10381,definition,
( sQ368_spl
<=> in(succ(sK84_skl),sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f10384,definition,
( sQ369_spl
<=> sK84_skl = succ(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f10385,plain,
( ~ sQ369_spl
| succ(sK84_skl) = sK84_skl ),
inference(component_clause,[status(thm)],[f10384]) ).
fof(f10387,plain,
( sQ369_spl
| ~ sQ368_spl ),
inference(split_clause,[status(thm)],[f10380,f10381,f10384]) ).
fof(f10419,plain,
( ~ sQ369_spl
| in(sK84_skl,sK84_skl) ),
inference(paramodulation,[status(thm)],[f10385,f825]) ).
fof(f10422,plain,
( ~ sQ369_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10419,f1241,f10384]) ).
fof(f10424,plain,
( ~ relation(empty_set)
| relation_image(empty_set,empty_set) = relation_rng(empty_set) ),
inference(paramodulation,[status(thm)],[f1089,f886]) ).
fof(f10428,definition,
( sQ370_spl
<=> relation_image(empty_set,empty_set) = relation_rng(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f10431,plain,
( ~ sQ3_spl
| sQ370_spl ),
inference(split_clause,[status(thm)],[f10424,f10428,f1257]) ).
fof(f10448,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ relation(X1)
| empty_set = relation_composition(X0,X1)
| ~ relation(empty_set)
| in(ordered_pair(sK60_skl(empty_set,X1,X0),sK62_skl(empty_set,X1,X0)),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f591,f4576]) ).
fof(f10450,plain,
! [X0,X1] :
( ordinal(ordered_pair(sK60_skl(sK84_skl,X1,X0),sK61_skl(sK84_skl,X1,X0)))
| ~ relation(X1)
| sK84_skl = relation_composition(X0,X1)
| ~ relation(sK84_skl)
| in(ordered_pair(sK60_skl(sK84_skl,X1,X0),sK62_skl(sK84_skl,X1,X0)),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f591,f967]) ).
fof(f10459,plain,
! [X0,X1] :
( ~ sQ98_spl
| ordinal(ordered_pair(sK60_skl(sK95_skl(sK84_skl),X1,X0),sK61_skl(sK95_skl(sK84_skl),X1,X0)))
| ~ relation(X1)
| sK95_skl(sK84_skl) = relation_composition(X0,X1)
| ~ relation(sK95_skl(sK84_skl))
| in(ordered_pair(sK60_skl(sK95_skl(sK84_skl),X1,X0),sK62_skl(sK95_skl(sK84_skl),X1,X0)),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f591,f2611]) ).
fof(f10487,definition,
! [X0,X1] :
( sQ371_spl
<=> ( ~ relation(X1)
| empty_set = relation_composition(X0,X1)
| in(ordered_pair(sK60_skl(empty_set,X1,X0),sK62_skl(empty_set,X1,X0)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f10490,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ371_spl ),
inference(split_clause,[status(thm)],[f10448,f10487,f1257,f4575]) ).
fof(f10491,definition,
! [X0,X1] :
( sQ372_spl
<=> ( ordinal(ordered_pair(sK60_skl(sK95_skl(sK84_skl),X1,X0),sK61_skl(sK95_skl(sK84_skl),X1,X0)))
| ~ relation(X1)
| sK95_skl(sK84_skl) = relation_composition(X0,X1)
| in(ordered_pair(sK60_skl(sK95_skl(sK84_skl),X1,X0),sK62_skl(sK95_skl(sK84_skl),X1,X0)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f10494,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ372_spl ),
inference(split_clause,[status(thm)],[f10459,f10491,f2816,f2610]) ).
fof(f10498,definition,
! [X0,X1] :
( sQ373_spl
<=> ( ordinal(ordered_pair(sK60_skl(sK84_skl,X1,X0),sK61_skl(sK84_skl,X1,X0)))
| ~ relation(X1)
| sK84_skl = relation_composition(X0,X1)
| in(ordered_pair(sK60_skl(sK84_skl,X1,X0),sK62_skl(sK84_skl,X1,X0)),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f10499,plain,
! [X0,X1] :
( ~ sQ373_spl
| ~ relation(X0)
| in(ordered_pair(sK60_skl(sK84_skl,X1,X0),sK62_skl(sK84_skl,X1,X0)),X0)
| ~ relation(X1)
| ordinal(ordered_pair(sK60_skl(sK84_skl,X1,X0),sK61_skl(sK84_skl,X1,X0)))
| relation_composition(X0,X1) = sK84_skl ),
inference(component_clause,[status(thm)],[f10498]) ).
fof(f10501,plain,
( ~ sQ11_spl
| sQ373_spl ),
inference(split_clause,[status(thm)],[f10450,f10498,f1345]) ).
fof(f10633,plain,
! [X0,X1,X2] :
( ~ sQ177_spl
| ~ relation(empty_set)
| ~ in(X2,X1)
| relation_inverse_image(empty_set,X0) != X1 ),
inference(resolution,[status(thm)],[f365,f4576]) ).
fof(f10635,plain,
! [X0,X1,X2] :
( ordinal(ordered_pair(X2,sK13_skl(X2,X1,X0,sK84_skl)))
| ~ relation(sK84_skl)
| ~ in(X2,X1)
| relation_inverse_image(sK84_skl,X0) != X1 ),
inference(resolution,[status(thm)],[f365,f967]) ).
fof(f10644,plain,
! [X0,X1,X2] :
( ~ sQ98_spl
| ordinal(ordered_pair(X2,sK13_skl(X2,X1,X0,sK95_skl(sK84_skl))))
| ~ relation(sK95_skl(sK84_skl))
| ~ in(X2,X1)
| relation_inverse_image(sK95_skl(sK84_skl),X0) != X1 ),
inference(resolution,[status(thm)],[f365,f2611]) ).
fof(f10676,definition,
! [X0,X1,X2] :
( sQ375_spl
<=> ( ordinal(ordered_pair(X2,sK13_skl(X2,X1,X0,sK95_skl(sK84_skl))))
| ~ in(X2,X1)
| relation_inverse_image(sK95_skl(sK84_skl),X0) != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f10679,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f10644,f10676,f2816,f2610]) ).
fof(f10682,definition,
! [X0,X1,X2] :
( sQ376_spl
<=> ( ordinal(ordered_pair(X2,sK13_skl(X2,X1,X0,sK84_skl)))
| ~ in(X2,X1)
| relation_inverse_image(sK84_skl,X0) != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f10685,plain,
( ~ sQ11_spl
| sQ376_spl ),
inference(split_clause,[status(thm)],[f10635,f10682,f1345]) ).
fof(f10687,definition,
! [X0,X1,X2] :
( sQ377_spl
<=> ( ~ in(X2,X1)
| relation_inverse_image(empty_set,X0) != X1 ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f10690,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ377_spl ),
inference(split_clause,[status(thm)],[f10633,f10687,f1257,f4575]) ).
fof(f10719,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ177_spl
| ~ in(ordered_pair(X4,X1),X0)
| ~ relation(X3)
| empty_set != relation_composition(X0,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f589,f4576]) ).
fof(f10722,plain,
! [X0,X1,X2,X3,X4] :
( ordinal(ordered_pair(X4,X2))
| ~ in(ordered_pair(X4,X1),X0)
| ~ relation(X3)
| sK84_skl != relation_composition(X0,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(X0)
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f589,f967]) ).
fof(f10731,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ98_spl
| ordinal(ordered_pair(X4,X2))
| ~ in(ordered_pair(X4,X1),X0)
| ~ relation(X3)
| sK95_skl(sK84_skl) != relation_composition(X0,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(X0)
| ~ relation(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f589,f2611]) ).
fof(f10793,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(ordered_pair(X4,X1),X5)
| ~ in(X5,sK84_skl)
| ~ relation(X3)
| in(ordered_pair(X4,X2),X0)
| X0 != relation_composition(sK84_skl,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(sK84_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f589,f1250]) ).
fof(f10828,definition,
! [X0,X1,X2,X3,X4] :
( sQ378_spl
<=> ( ordinal(ordered_pair(X4,X2))
| ~ in(ordered_pair(X4,X1),X0)
| ~ relation(X3)
| sK84_skl != relation_composition(X0,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f10829,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ378_spl
| ~ relation(X4)
| ~ in(ordered_pair(X3,X2),X0)
| sK84_skl != relation_composition(X4,X0)
| ~ in(ordered_pair(X1,X3),X4)
| ordinal(ordered_pair(X1,X2))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f10828]) ).
fof(f10831,plain,
( sQ378_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10722,f1345,f10828]) ).
fof(f10836,definition,
! [X0,X1,X2,X3,X4] :
( sQ379_spl
<=> ( ordinal(ordered_pair(X4,X2))
| ~ in(ordered_pair(X4,X1),X0)
| ~ relation(X3)
| sK95_skl(sK84_skl) != relation_composition(X0,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f10839,plain,
( ~ sQ98_spl
| sQ379_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f10731,f2816,f10836,f2610]) ).
fof(f10840,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ380_spl
<=> ( ~ in(ordered_pair(X4,X1),X5)
| ~ in(X5,sK84_skl)
| ~ relation(X3)
| in(ordered_pair(X4,X2),X0)
| X0 != relation_composition(sK84_skl,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f10843,plain,
( ~ sQ11_spl
| sQ380_spl ),
inference(split_clause,[status(thm)],[f10793,f10840,f1345]) ).
fof(f10845,definition,
! [X0,X1,X2,X3,X4] :
( sQ381_spl
<=> ( ~ in(ordered_pair(X4,X1),X0)
| ~ relation(X3)
| empty_set != relation_composition(X0,X3)
| ~ in(ordered_pair(X1,X2),X3)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f10848,plain,
( ~ sQ177_spl
| sQ381_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f10719,f1257,f10845,f4575]) ).
fof(f10875,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,sK53_skl(X0,sK84_skl)),X1)
| ~ in(X1,sK84_skl)
| ~ relation(sK84_skl)
| ~ in(sK53_skl(X0,sK84_skl),X0)
| relation_rng(sK84_skl) = X0 ),
inference(resolution,[status(thm)],[f556,f1250]) ).
fof(f10891,definition,
! [X0,X1,X2] :
( sQ382_spl
<=> ( ~ in(ordered_pair(X2,sK53_skl(X0,sK84_skl)),X1)
| ~ in(X1,sK84_skl)
| ~ in(sK53_skl(X0,sK84_skl),X0)
| relation_rng(sK84_skl) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f10894,plain,
( ~ sQ11_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f10875,f10891,f1345]) ).
fof(f11023,plain,
! [X0] :
( ~ relation(empty_set)
| subset(relation_rng(relation_rng_restriction(X0,empty_set)),empty_set) ),
inference(paramodulation,[status(thm)],[f1090,f843]) ).
fof(f11024,definition,
! [X0] :
( sQ386_spl
<=> subset(relation_rng(relation_rng_restriction(X0,empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f11027,plain,
( ~ sQ3_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f11023,f11024,f1257]) ).
fof(f11032,plain,
! [X0] :
( ~ relation(empty_set)
| relation_rng(empty_set) = relation_rng(relation_dom_restriction(empty_set,X0))
| ~ subset(empty_set,relation_rng(relation_dom_restriction(empty_set,X0))) ),
inference(paramodulation,[status(thm)],[f1090,f3612]) ).
fof(f11033,definition,
! [X0] :
( sQ387_spl
<=> ( relation_rng(empty_set) = relation_rng(relation_dom_restriction(empty_set,X0))
| ~ subset(empty_set,relation_rng(relation_dom_restriction(empty_set,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f11036,plain,
( ~ sQ3_spl
| sQ387_spl ),
inference(split_clause,[status(thm)],[f11032,f11033,f1257]) ).
fof(f11262,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X0,empty_set),X1)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f840,f2752]) ).
fof(f11263,plain,
! [X0] :
( relation_rng_restriction(X0,empty_set) = empty_set
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f840,f2756]) ).
fof(f11272,definition,
! [X0] :
( sQ389_spl
<=> relation_rng_restriction(X0,empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f11273,plain,
! [X0] :
( ~ sQ389_spl
| empty_set = relation_rng_restriction(X0,empty_set) ),
inference(component_clause,[status(thm)],[f11272]) ).
fof(f11275,plain,
( sQ389_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f11263,f1257,f11272]) ).
fof(f11276,definition,
! [X0,X1] :
( sQ390_spl
<=> subset(relation_rng_restriction(X0,empty_set),X1) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f11279,plain,
( sQ390_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f11262,f1257,f11276]) ).
fof(f11280,plain,
( ~ sQ389_spl
| subset(empty_set,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f11273,f840]) ).
fof(f11281,plain,
( ~ sQ389_spl
| ~ relation(empty_set)
| subset(relation_rng(empty_set),relation_rng(empty_set)) ),
inference(paramodulation,[status(thm)],[f11273,f843]) ).
fof(f11282,plain,
! [X0] :
( ~ sQ389_spl
| subset(relation_rng(empty_set),X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f11273,f837]) ).
fof(f11283,plain,
! [X0] :
( ~ sQ389_spl
| ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set)
| in(X0,relation_rng(empty_set)) ),
inference(paramodulation,[status(thm)],[f11273,f833]) ).
fof(f11284,definition,
( sQ391_spl
<=> subset(relation_rng(empty_set),relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f11287,plain,
( ~ sQ389_spl
| ~ sQ3_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f11281,f11284,f1257,f11272]) ).
fof(f11288,definition,
! [X0] :
( sQ392_spl
<=> ( ~ in(X0,relation_rng(empty_set))
| in(X0,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f11291,plain,
( ~ sQ389_spl
| ~ sQ3_spl
| sQ392_spl ),
inference(split_clause,[status(thm)],[f11283,f11288,f1257,f11272]) ).
fof(f11292,definition,
( sQ393_spl
<=> subset(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f11295,plain,
( ~ sQ389_spl
| sQ393_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f11280,f1257,f11292,f11272]) ).
fof(f11296,definition,
! [X0] :
( sQ394_spl
<=> subset(relation_rng(empty_set),X0) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f11299,plain,
( ~ sQ389_spl
| sQ394_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f11282,f1257,f11296,f11272]) ).
fof(f11338,plain,
! [X0,X1,X2] :
( ~ sQ177_spl
| ~ relation(empty_set)
| relation_inverse(empty_set) != X2
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f567,f4576]) ).
fof(f11341,plain,
! [X0,X1,X2] :
( ordinal(ordered_pair(X1,X0))
| ~ relation(sK84_skl)
| relation_inverse(sK84_skl) != X2
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f567,f967]) ).
fof(f11350,plain,
! [X0,X1,X2] :
( ~ sQ98_spl
| ordinal(ordered_pair(X1,X0))
| ~ relation(sK95_skl(sK84_skl))
| relation_inverse(sK95_skl(sK84_skl)) != X2
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f567,f2611]) ).
fof(f11394,definition,
! [X0,X1,X2] :
( sQ395_spl
<=> ( relation_inverse(empty_set) != X2
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f11397,plain,
( ~ sQ177_spl
| ~ sQ3_spl
| sQ395_spl ),
inference(split_clause,[status(thm)],[f11338,f11394,f1257,f4575]) ).
fof(f11400,definition,
! [X0,X1,X2] :
( sQ396_spl
<=> ( ordinal(ordered_pair(X1,X0))
| relation_inverse(sK95_skl(sK84_skl)) != X2
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f11403,plain,
( ~ sQ98_spl
| ~ sQ112_spl
| sQ396_spl ),
inference(split_clause,[status(thm)],[f11350,f11400,f2816,f2610]) ).
fof(f11412,definition,
! [X0,X1,X2] :
( sQ397_spl
<=> ( ordinal(ordered_pair(X1,X0))
| relation_inverse(sK84_skl) != X2
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f11413,plain,
! [X0,X1,X2] :
( ~ sQ397_spl
| ~ in(ordered_pair(X2,X1),X0)
| relation_inverse(sK84_skl) != X0
| ordinal(ordered_pair(X1,X2))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f11412]) ).
fof(f11415,plain,
( ~ sQ11_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f11341,f11412,f1345]) ).
fof(f11504,plain,
! [X0] :
( ~ sQ177_spl
| ~ sQ373_spl
| ~ relation(empty_set)
| ~ relation(X0)
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,empty_set),sK61_skl(sK84_skl,X0,empty_set)))
| relation_composition(empty_set,X0) = sK84_skl ),
inference(resolution,[status(thm)],[f10499,f4576]) ).
fof(f11506,plain,
! [X0] :
( ~ sQ373_spl
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK84_skl),sK62_skl(sK84_skl,X0,sK84_skl)))
| ~ relation(sK84_skl)
| ~ relation(X0)
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK84_skl),sK61_skl(sK84_skl,X0,sK84_skl)))
| relation_composition(sK84_skl,X0) = sK84_skl ),
inference(resolution,[status(thm)],[f10499,f967]) ).
fof(f11515,plain,
! [X0] :
( ~ sQ98_spl
| ~ sQ373_spl
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK95_skl(sK84_skl)),sK62_skl(sK84_skl,X0,sK95_skl(sK84_skl))))
| ~ relation(sK95_skl(sK84_skl))
| ~ relation(X0)
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK95_skl(sK84_skl)),sK61_skl(sK84_skl,X0,sK95_skl(sK84_skl))))
| relation_composition(sK95_skl(sK84_skl),X0) = sK84_skl ),
inference(resolution,[status(thm)],[f10499,f2611]) ).
fof(f11544,definition,
! [X0] :
( sQ399_spl
<=> ( ~ relation(X0)
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,empty_set),sK61_skl(sK84_skl,X0,empty_set)))
| relation_composition(empty_set,X0) = sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f11547,plain,
( ~ sQ177_spl
| ~ sQ373_spl
| ~ sQ3_spl
| sQ399_spl ),
inference(split_clause,[status(thm)],[f11504,f11544,f1257,f10498,f4575]) ).
fof(f11549,definition,
! [X0] :
( sQ400_spl
<=> ( ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK95_skl(sK84_skl)),sK62_skl(sK84_skl,X0,sK95_skl(sK84_skl))))
| ~ relation(X0)
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK95_skl(sK84_skl)),sK61_skl(sK84_skl,X0,sK95_skl(sK84_skl))))
| relation_composition(sK95_skl(sK84_skl),X0) = sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f11552,plain,
( ~ sQ98_spl
| ~ sQ373_spl
| ~ sQ112_spl
| sQ400_spl ),
inference(split_clause,[status(thm)],[f11515,f11549,f2816,f10498,f2610]) ).
fof(f11556,definition,
! [X0] :
( sQ401_spl
<=> ( ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK84_skl),sK62_skl(sK84_skl,X0,sK84_skl)))
| ~ relation(X0)
| ordinal(ordered_pair(sK60_skl(sK84_skl,X0,sK84_skl),sK61_skl(sK84_skl,X0,sK84_skl)))
| relation_composition(sK84_skl,X0) = sK84_skl ) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f11559,plain,
( ~ sQ373_spl
| ~ sQ11_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f11506,f11556,f1345,f10498]) ).
fof(f11633,plain,
! [X0,X1,X2,X3] :
( X3 != set_meet(X1)
| in(X2,X0)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f393,f411]) ).
fof(f11794,plain,
! [X0,X1,X2] :
( ~ in(sK84_skl,X1)
| ~ in(X2,X0)
| ordinal(X2)
| X0 != set_meet(X1) ),
inference(resolution,[status(thm)],[f11633,f967]) ).
fof(f11958,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X3),X2)
| ~ in(X2,sK84_skl)
| relation_dom(sK84_skl) != X1
| in(X0,X1)
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f518,f1250]) ).
fof(f11984,definition,
! [X0,X1,X2,X3] :
( sQ402_spl
<=> ( ~ in(ordered_pair(X0,X3),X2)
| ~ in(X2,sK84_skl)
| relation_dom(sK84_skl) != X1
| in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f11987,plain,
( sQ402_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f11958,f1345,f11984]) ).
fof(f12024,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X2,X3),X4)
| ~ in(X4,sK84_skl)
| in(X3,X0)
| ~ in(X2,X1)
| X0 != relation_image(sK84_skl,X1)
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f357,f1250]) ).
fof(f12062,definition,
! [X0,X1,X2,X3,X4] :
( sQ403_spl
<=> ( ~ in(ordered_pair(X2,X3),X4)
| ~ in(X4,sK84_skl)
| in(X3,X0)
| ~ in(X2,X1)
| X0 != relation_image(sK84_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f12065,plain,
( sQ403_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f12024,f1345,f12062]) ).
fof(f12090,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ378_spl
| ~ in(ordered_pair(X2,X1),X4)
| ~ in(X4,sK84_skl)
| ~ relation(X3)
| sK84_skl != relation_composition(X3,sK84_skl)
| ~ in(ordered_pair(X0,X2),X3)
| ordinal(ordered_pair(X0,X1))
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f10829,f1250]) ).
fof(f12115,definition,
! [X0,X1,X2,X3,X4] :
( sQ404_spl
<=> ( ~ in(ordered_pair(X2,X1),X4)
| ~ in(X4,sK84_skl)
| ~ relation(X3)
| sK84_skl != relation_composition(X3,sK84_skl)
| ~ in(ordered_pair(X0,X2),X3)
| ordinal(ordered_pair(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f12118,plain,
( ~ sQ378_spl
| sQ404_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f12090,f1345,f12115,f10828]) ).
fof(f12200,plain,
! [X0,X1] :
( ~ sQ389_spl
| ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set)
| in(X0,X1) ),
inference(paramodulation,[status(thm)],[f11273,f832]) ).
fof(f12201,definition,
! [X0,X1] :
( sQ405_spl
<=> ( ~ in(X0,relation_rng(empty_set))
| in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f12204,plain,
( ~ sQ389_spl
| ~ sQ3_spl
| sQ405_spl ),
inference(split_clause,[status(thm)],[f12200,f12201,f1257,f11272]) ).
fof(f12249,plain,
! [X0,X1,X2] :
( ~ sQ397_spl
| ~ in(ordered_pair(X1,X0),X2)
| ~ in(X2,sK84_skl)
| relation_inverse(sK84_skl) != sK84_skl
| ordinal(ordered_pair(X0,X1))
| ~ relation(sK84_skl) ),
inference(resolution,[status(thm)],[f11413,f1250]) ).
fof(f12278,definition,
! [X0,X1,X2] :
( sQ406_spl
<=> ( ~ in(ordered_pair(X1,X0),X2)
| ~ in(X2,sK84_skl)
| ordinal(ordered_pair(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f12281,definition,
( sQ407_spl
<=> relation_inverse(sK84_skl) = sK84_skl ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f12284,plain,
( ~ sQ397_spl
| ~ sQ407_spl
| sQ406_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f12249,f1345,f12278,f12281,f11412]) ).
fof(f12365,plain,
! [X0] :
( ~ in(sK84_skl,X0)
| ~ in(X0,sK84_skl)
| ordinal(sK84_skl)
| sK84_skl != set_meet(sK84_skl) ),
inference(resolution,[status(thm)],[f11794,f1250]) ).
fof(f12367,plain,
! [X0] :
( ordinal(sK84_skl)
| unordered_pair(sK84_skl,X0) != set_meet(unordered_pair(sK84_skl,X0)) ),
inference(resolution,[status(thm)],[f11794,f2027]) ).
fof(f12369,plain,
! [X0] :
( ordinal(sK84_skl)
| unordered_pair(X0,sK84_skl) != set_meet(unordered_pair(X0,sK84_skl)) ),
inference(resolution,[status(thm)],[f11794,f2034]) ).
fof(f12371,plain,
! [X0,X1] :
( ~ in(sK84_skl,X1)
| ~ relation(X0)
| ~ in(sK84_skl,relation_dom(X0))
| ordinal(sK84_skl)
| relation_dom(relation_dom_restriction(X0,X1)) != set_meet(relation_dom(relation_dom_restriction(X0,X1))) ),
inference(resolution,[status(thm)],[f11794,f1155]) ).
fof(f12373,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| empty_set != X1
| apply(X0,sK84_skl) = X1
| ordinal(sK84_skl)
| relation_dom(X0) != set_meet(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f11794,f507]) ).
fof(f12375,plain,
! [X0,X1] :
( X1 = empty_set
| ~ relation(X0)
| apply(X0,sK84_skl) != X1
| ~ function(X0)
| ordinal(sK84_skl)
| relation_dom(X0) != set_meet(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f11794,f506]) ).
fof(f12377,plain,
! [X0,X1] :
( ~ subset(sK84_skl,X0)
| ~ in(X0,sK96_skl(X1))
| ordinal(sK84_skl)
| sK97_skl(X0,X1) != set_meet(sK97_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f11794,f1191]) ).
fof(f12379,plain,
( ordinal(sK84_skl)
| singleton(sK84_skl) != set_meet(singleton(sK84_skl)) ),
inference(resolution,[status(thm)],[f11794,f2062]) ).
fof(f12381,plain,
! [X0,X1] :
( in(sK84_skl,X1)
| X0 = empty_set
| ~ element(sK84_skl,X0)
| ~ element(X1,powerset(X0))
| ordinal(sK84_skl)
| subset_complement(X0,X1) != set_meet(subset_complement(X0,X1)) ),
inference(resolution,[status(thm)],[f11794,f1059]) ).
fof(f12383,plain,
( ordinal(sK84_skl)
| succ(sK84_skl) != set_meet(succ(sK84_skl)) ),
inference(resolution,[status(thm)],[f11794,f825]) ).
fof(f12385,plain,
( ordinal(sK84_skl)
| sK96_skl(sK84_skl) != set_meet(sK96_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f11794,f1188]) ).
fof(f12387,plain,
( ordinal(sK84_skl)
| sK80_skl(sK84_skl) != set_meet(sK80_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f11794,f858]) ).
fof(f12393,plain,
! [X0,X1,X2] :
( X2 != set_meet(X1)
| ~ in(sK84_skl,X2)
| ~ in(X0,X1)
| ordinal(sK84_skl)
| X0 != set_meet(X0) ),
inference(resolution,[status(thm)],[f11794,f11633]) ).
fof(f12395,plain,
! [X0] :
( X0 != singleton(sK84_skl)
| ordinal(sK84_skl)
| X0 != set_meet(X0) ),
inference(resolution,[status(thm)],[f11794,f1228]) ).
fof(f12404,plain,
! [X0,X1,X2] :
( ~ in(sK84_skl,X2)
| ~ in(X2,sK84_skl)
| ~ in(X1,X0)
| ordinal(X1)
| X0 != set_meet(sK84_skl) ),
inference(resolution,[status(thm)],[f11794,f1250]) ).
fof(f12423,plain,
! [X0] :
( ~ in(sK84_skl,X0)
| ordinal(sK84_skl)
| X0 != set_meet(X0) ),
inference(factoring,[status(thm)],[f11794]) ).
fof(f12429,definition,
! [X0] :
( sQ409_spl
<=> ( X0 != singleton(sK84_skl)
| X0 != set_meet(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f12432,plain,
( sQ4_spl
| sQ409_spl ),
inference(split_clause,[status(thm)],[f12395,f12429,f1272]) ).
fof(f12433,definition,
( sQ410_spl
<=> sK96_skl(sK84_skl) = set_meet(sK96_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f12436,plain,
( sQ4_spl
| ~ sQ410_spl ),
inference(split_clause,[status(thm)],[f12385,f12433,f1272]) ).
fof(f12445,definition,
! [X0,X1] :
( sQ413_spl
<=> ( ~ function(X0)
| ~ relation(X0)
| empty_set != X1
| apply(X0,sK84_skl) = X1
| relation_dom(X0) != set_meet(relation_dom(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f12448,plain,
( sQ4_spl
| sQ413_spl ),
inference(split_clause,[status(thm)],[f12373,f12445,f1272]) ).
fof(f12453,definition,
! [X0,X1] :
( sQ415_spl
<=> ( ~ in(X1,X0)
| ordinal(X1)
| X0 != set_meet(sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f12456,plain,
( sQ40_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f12404,f12453,f1661]) ).
fof(f12457,definition,
! [X0] :
( sQ416_spl
<=> unordered_pair(sK84_skl,X0) != set_meet(unordered_pair(sK84_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f12460,plain,
( sQ4_spl
| sQ416_spl ),
inference(split_clause,[status(thm)],[f12367,f12457,f1272]) ).
fof(f12461,definition,
! [X0,X1] :
( sQ417_spl
<=> ( X1 = empty_set
| ~ relation(X0)
| apply(X0,sK84_skl) != X1
| ~ function(X0)
| relation_dom(X0) != set_meet(relation_dom(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f12464,plain,
( sQ4_spl
| sQ417_spl ),
inference(split_clause,[status(thm)],[f12375,f12461,f1272]) ).
fof(f12470,definition,
! [X0,X1] :
( sQ419_spl
<=> ( ~ subset(sK84_skl,X0)
| ~ in(X0,sK96_skl(X1))
| sK97_skl(X0,X1) != set_meet(sK97_skl(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f12473,plain,
( sQ4_spl
| sQ419_spl ),
inference(split_clause,[status(thm)],[f12377,f12470,f1272]) ).
fof(f12474,definition,
! [X0,X1,X2] :
( sQ420_spl
<=> ( X2 != set_meet(X1)
| ~ in(sK84_skl,X2)
| ~ in(X0,X1)
| X0 != set_meet(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f12477,plain,
( sQ4_spl
| sQ420_spl ),
inference(split_clause,[status(thm)],[f12393,f12474,f1272]) ).
fof(f12478,definition,
! [X0] :
( sQ421_spl
<=> unordered_pair(X0,sK84_skl) != set_meet(unordered_pair(X0,sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f12481,plain,
( sQ4_spl
| sQ421_spl ),
inference(split_clause,[status(thm)],[f12369,f12478,f1272]) ).
fof(f12487,definition,
( sQ423_spl
<=> succ(sK84_skl) = set_meet(succ(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f12490,plain,
( sQ4_spl
| ~ sQ423_spl ),
inference(split_clause,[status(thm)],[f12383,f12487,f1272]) ).
fof(f12492,definition,
! [X0] :
( sQ424_spl
<=> ( ~ in(sK84_skl,X0)
| X0 != set_meet(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f12495,plain,
( sQ4_spl
| sQ424_spl ),
inference(split_clause,[status(thm)],[f12423,f12492,f1272]) ).
fof(f12500,definition,
( sQ426_spl
<=> sK80_skl(sK84_skl) = set_meet(sK80_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f12503,plain,
( sQ4_spl
| ~ sQ426_spl ),
inference(split_clause,[status(thm)],[f12387,f12500,f1272]) ).
fof(f12504,definition,
! [X0,X1] :
( sQ427_spl
<=> ( ~ in(sK84_skl,X1)
| ~ relation(X0)
| ~ in(sK84_skl,relation_dom(X0))
| relation_dom(relation_dom_restriction(X0,X1)) != set_meet(relation_dom(relation_dom_restriction(X0,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f12507,plain,
( sQ4_spl
| sQ427_spl ),
inference(split_clause,[status(thm)],[f12371,f12504,f1272]) ).
fof(f12508,definition,
! [X0,X1] :
( sQ428_spl
<=> ( in(sK84_skl,X1)
| X0 = empty_set
| ~ element(sK84_skl,X0)
| ~ element(X1,powerset(X0))
| subset_complement(X0,X1) != set_meet(subset_complement(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f12511,plain,
( sQ4_spl
| sQ428_spl ),
inference(split_clause,[status(thm)],[f12381,f12508,f1272]) ).
fof(f12529,definition,
( sQ433_spl
<=> singleton(sK84_skl) = set_meet(singleton(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f12532,plain,
( sQ4_spl
| ~ sQ433_spl ),
inference(split_clause,[status(thm)],[f12379,f12529,f1272]) ).
fof(f12543,plain,
( sQ40_spl
| sQ4_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f12365,f1668,f1272,f1661]) ).
fof(f12562,plain,
! [X0,X1,X2] :
( subset(X1,X2)
| ~ subset(X1,X0)
| ~ subset(sK84_skl,empty_set)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1318,f2752]) ).
fof(f12563,plain,
! [X0,X1] :
( X1 = empty_set
| ~ subset(X1,X0)
| ~ subset(sK84_skl,empty_set)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1318,f2756]) ).
fof(f12565,plain,
! [X0,X1] :
( subset(sK84_skl,X1)
| ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X0)
| ~ subset(sK84_skl,X1)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1318,f1318]) ).
fof(f12592,plain,
! [X0,X1] :
( ~ subset(sK84_skl,X1)
| X1 != empty_set
| subset(sK84_skl,singleton(X0))
| ~ in(singleton(X0),sK84_skl) ),
inference(resolution,[status(thm)],[f1318,f1539]) ).
fof(f12593,plain,
! [X0,X1,X2,X3] :
( ~ subset(sK84_skl,X3)
| X3 != empty_set
| ~ subset(X1,X0)
| subset(X1,singleton(X2))
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1318,f1539]) ).
fof(f12619,plain,
! [X0,X1] :
( ~ subset(sK84_skl,X1)
| subset(empty_set,X1)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1318,f960]) ).
fof(f12639,plain,
( sQ60_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f12593,f1567,f1879]) ).
fof(f12641,definition,
! [X1] :
( sQ436_spl
<=> ( ~ subset(sK84_skl,X1)
| subset(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f12644,plain,
( sQ436_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f12619,f2607,f12641]) ).
fof(f12652,definition,
! [X0,X1,X2] :
( sQ437_spl
<=> ( subset(X1,X2)
| ~ subset(X1,X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f12655,definition,
( sQ438_spl
<=> subset(sK84_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f12658,plain,
( ~ sQ438_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f12562,f12652,f12655]) ).
fof(f12661,plain,
( sQ60_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f12592,f1571,f1879]) ).
fof(f12665,definition,
! [X1] :
( sQ439_spl
<=> ( subset(sK84_skl,X1)
| ~ in(X1,sK84_skl)
| ~ subset(sK84_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f12668,plain,
( sQ439_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f12565,f1321,f12665]) ).
fof(f12681,definition,
! [X0,X1] :
( sQ441_spl
<=> ( X1 = empty_set
| ~ subset(X1,X0)
| ~ in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f12684,plain,
( ~ sQ438_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f12563,f12681,f12655]) ).
fof(f12685,plain,
! [X0] :
( ~ sQ60_spl
| ~ subset(sK84_skl,X0)
| ~ subset(sK84_skl,empty_set)
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f6941,f1318]) ).
fof(f12688,plain,
( ~ sQ60_spl
| ~ sQ438_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f12685,f1321,f12655,f1879]) ).
fof(f12698,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK43_skl(X0,sK84_skl),X2),X1)
| ~ in(X1,sK84_skl)
| ~ relation(sK84_skl)
| relation_dom(sK84_skl) = X0
| ~ in(sK43_skl(X0,sK84_skl),X0) ),
inference(resolution,[status(thm)],[f519,f1250]) ).
fof(f12711,definition,
! [X0,X1,X2] :
( sQ442_spl
<=> ( ~ in(ordered_pair(sK43_skl(X0,sK84_skl),X2),X1)
| ~ in(X1,sK84_skl)
| relation_dom(sK84_skl) = X0
| ~ in(sK43_skl(X0,sK84_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f12714,plain,
( ~ sQ11_spl
| sQ442_spl ),
inference(split_clause,[status(thm)],[f12698,f12711,f1345]) ).
fof(f12730,plain,
( ordinal(sK37_skl(sK84_skl))
| epsilon_connected(sK84_skl) ),
inference(resolution,[status(thm)],[f475,f967]) ).
fof(f12739,plain,
( ~ sQ98_spl
| ordinal(sK37_skl(sK95_skl(sK84_skl)))
| epsilon_connected(sK95_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f475,f2611]) ).
fof(f12769,definition,
( sQ443_spl
<=> ordinal(sK37_skl(sK84_skl)) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f12770,plain,
( ~ sQ443_spl
| ordinal(sK37_skl(sK84_skl)) ),
inference(component_clause,[status(thm)],[f12769]) ).
fof(f12772,plain,
( sQ443_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f12730,f2908,f12769]) ).
fof(f12773,definition,
( sQ444_spl
<=> ordinal(sK37_skl(sK95_skl(sK84_skl))) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f12776,plain,
( ~ sQ98_spl
| sQ444_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f12739,f2915,f12773,f2610]) ).
fof(f12781,plain,
! [X0,X1] :
( sK84_skl = empty_set
| ~ subset(X1,sK24_skl(sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f412]) ).
fof(f12795,plain,
! [X0,X1] :
( relation(sK84_skl)
| ~ subset(X1,sK19_skl(sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f387]) ).
fof(f12807,plain,
! [X0,X1,X2] :
( ~ in(X2,sK84_skl)
| ~ subset(X1,sK95_skl(sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f1143]) ).
fof(f12815,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| X3 != set_meet(sK84_skl)
| sK84_skl = empty_set
| ~ subset(X1,sK20_skl(X2,X3,sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f394]) ).
fof(f12818,plain,
! [X0,X1,X2] :
( ~ in(sK21_skl(X2,sK84_skl),X2)
| empty_set = sK84_skl
| set_meet(sK84_skl) = X2
| ~ subset(X1,sK22_skl(X2,sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f396]) ).
fof(f12819,plain,
! [X0,X1,X2,X3] :
( ~ relation(X2)
| sK84_skl = relation_composition(X3,X2)
| ~ relation(sK84_skl)
| in(ordered_pair(sK60_skl(sK84_skl,X2,X3),sK62_skl(sK84_skl,X2,X3)),X3)
| ~ relation(X3)
| ~ subset(X1,ordered_pair(sK60_skl(sK84_skl,X2,X3),sK61_skl(sK84_skl,X2,X3)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f591]) ).
fof(f12820,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,relation_image(sK84_skl,X2))
| ~ relation(sK84_skl)
| ~ subset(X1,ordered_pair(sK81_skl(X2,X3,sK84_skl),X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f870]) ).
fof(f12821,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| relation_rng(sK84_skl) != X3
| ~ relation(sK84_skl)
| ~ subset(X1,ordered_pair(sK52_skl(X2,X3,sK84_skl),X2))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f554]) ).
fof(f12822,plain,
! [X0,X1,X2] :
( sK84_skl = identity_relation(X2)
| ~ relation(sK84_skl)
| sK0_skl(X2,sK84_skl) = sK1_skl(X2,sK84_skl)
| ~ subset(X1,ordered_pair(sK0_skl(X2,sK84_skl),sK1_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f305]) ).
fof(f12823,plain,
! [X0,X1,X2] :
( in(sK53_skl(X2,sK84_skl),X2)
| ~ relation(sK84_skl)
| X2 = relation_rng(sK84_skl)
| ~ subset(X1,ordered_pair(sK54_skl(X2,sK84_skl),sK53_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f557]) ).
fof(f12824,plain,
! [X0,X1,X2,X3] :
( ~ relation(X3)
| sK84_skl = relation_rng_restriction(X2,X3)
| ~ relation(sK84_skl)
| in(sK8_skl(X2,sK84_skl,X3),X2)
| ~ subset(X1,ordered_pair(sK7_skl(X2,sK84_skl,X3),sK8_skl(X2,sK84_skl,X3)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f339]) ).
fof(f12825,plain,
! [X0,X1,X2,X3] :
( relation_rng_restriction(X2,sK84_skl) = X3
| in(ordered_pair(sK7_skl(X2,X3,sK84_skl),sK8_skl(X2,X3,sK84_skl)),X3)
| ~ relation(sK84_skl)
| ~ relation(X3)
| ~ subset(X1,ordered_pair(sK7_skl(X2,X3,sK84_skl),sK8_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f340]) ).
fof(f12826,plain,
! [X0,X1,X2,X3] :
( in(sK2_skl(X2,sK84_skl,X3),X2)
| ~ relation(sK84_skl)
| ~ relation(X3)
| relation_dom_restriction(X3,X2) = sK84_skl
| ~ subset(X1,ordered_pair(sK2_skl(X2,sK84_skl,X3),sK3_skl(X2,sK84_skl,X3)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f319]) ).
fof(f12827,plain,
! [X0,X1,X2] :
( ~ relation(sK84_skl)
| in(sK43_skl(X2,sK84_skl),X2)
| relation_dom(sK84_skl) = X2
| ~ subset(X1,ordered_pair(sK43_skl(X2,sK84_skl),sK44_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f520]) ).
fof(f12828,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(sK84_skl)
| X3 != relation_image(sK84_skl,X4)
| ~ in(X2,X3)
| ~ subset(X1,ordered_pair(sK10_skl(X2,X3,X4,sK84_skl),X2))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f355]) ).
fof(f12829,plain,
! [X0,X1,X2] :
( subset(sK84_skl,X2)
| ~ relation(sK84_skl)
| ~ relation(X2)
| ~ subset(X1,ordered_pair(sK38_skl(X2,sK84_skl),sK39_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f483]) ).
fof(f12830,plain,
! [X0,X1,X2,X3] :
( in(sK11_skl(X2,X3,sK84_skl),X2)
| ~ relation(sK84_skl)
| relation_image(sK84_skl,X3) = X2
| ~ subset(X1,ordered_pair(sK12_skl(X2,X3,sK84_skl),sK11_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f359]) ).
fof(f12831,plain,
! [X0,X1] :
( empty_set = sK84_skl
| ~ relation(sK84_skl)
| ~ subset(X1,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f1081]) ).
fof(f12832,plain,
! [X0,X1,X2,X3] :
( ~ relation(sK84_skl)
| in(sK14_skl(X2,X3,sK84_skl),X2)
| relation_inverse_image(sK84_skl,X3) = X2
| ~ subset(X1,ordered_pair(sK14_skl(X2,X3,sK84_skl),sK15_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f369]) ).
fof(f12833,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(sK84_skl)
| ~ in(X2,X3)
| relation_inverse_image(sK84_skl,X4) != X3
| ~ subset(X1,ordered_pair(X2,sK13_skl(X2,X3,X4,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f365]) ).
fof(f12834,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| relation_dom(sK84_skl) != X3
| ~ relation(sK84_skl)
| ~ subset(X1,ordered_pair(X2,sK42_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f517]) ).
fof(f12835,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(sK84_skl)
| relation_inverse(sK84_skl) != X4
| ~ relation(X4)
| ~ in(ordered_pair(X3,X2),X4)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f567]) ).
fof(f12836,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ in(ordered_pair(X2,X5),X4)
| ~ relation(X6)
| sK84_skl != relation_composition(X4,X6)
| ~ in(ordered_pair(X5,X3),X6)
| ~ relation(X4)
| ~ relation(sK84_skl)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f589]) ).
fof(f12837,plain,
! [X0,X1,X2,X3,X4,X5] :
( relation_rng_restriction(X4,X5) != sK84_skl
| ~ relation(X5)
| ~ relation(sK84_skl)
| ~ in(ordered_pair(X2,X3),X5)
| ~ in(X3,X4)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f337]) ).
fof(f12838,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| identity_relation(X3) != sK84_skl
| ~ relation(sK84_skl)
| ~ subset(X1,ordered_pair(X2,X2))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f1223]) ).
fof(f12839,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,relation_dom(sK84_skl))
| ~ relation(sK84_skl)
| ~ function(sK84_skl)
| X3 != apply(sK84_skl,X2)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f1167]) ).
fof(f12861,plain,
! [X0,X1] :
( ~ in(X1,sK84_skl)
| ~ in(X0,empty_set)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f960]) ).
fof(f12872,plain,
! [X0,X1,X2,X3] :
( ~ subset(X1,X3)
| X3 != empty_set
| ~ in(singleton(X2),sK84_skl)
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f1539]) ).
fof(f12874,plain,
! [X0,X1,X2,X3] :
( ~ subset(X1,X3)
| ~ subset(sK84_skl,X2)
| ~ in(X3,sK84_skl)
| ~ in(X2,sK84_skl)
| ~ in(X0,X1)
| in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f1319,f1318]) ).
fof(f12879,definition,
! [X0,X1] :
( sQ445_spl
<=> ( ~ subset(X1,sK95_skl(sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f12882,plain,
( sQ97_spl
| sQ445_spl ),
inference(split_clause,[status(thm)],[f12807,f12879,f2607]) ).
fof(f12883,definition,
! [X0,X1,X2,X3,X4] :
( sQ446_spl
<=> ( X3 != relation_image(sK84_skl,X4)
| ~ in(X2,X3)
| ~ subset(X1,ordered_pair(sK10_skl(X2,X3,X4,sK84_skl),X2))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f12886,plain,
( ~ sQ11_spl
| sQ446_spl ),
inference(split_clause,[status(thm)],[f12828,f12883,f1345]) ).
fof(f12887,definition,
! [X0,X1] :
( sQ447_spl
<=> ( ~ subset(X1,ordered_pair(sK92_skl(sK84_skl),sK93_skl(sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f12890,plain,
( sQ26_spl
| ~ sQ11_spl
| sQ447_spl ),
inference(split_clause,[status(thm)],[f12831,f12887,f1345,f1544]) ).
fof(f12891,definition,
! [X0,X1,X2,X3] :
( sQ448_spl
<=> ( ~ in(X2,X3)
| identity_relation(X3) != sK84_skl
| ~ subset(X1,ordered_pair(X2,X2))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f12894,plain,
( ~ sQ11_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f12838,f12891,f1345]) ).
fof(f12899,definition,
! [X0,X1,X2,X3,X4] :
( sQ450_spl
<=> ( relation_inverse(sK84_skl) != X4
| ~ relation(X4)
| ~ in(ordered_pair(X3,X2),X4)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f12902,plain,
( ~ sQ11_spl
| sQ450_spl ),
inference(split_clause,[status(thm)],[f12835,f12899,f1345]) ).
fof(f12903,definition,
! [X0,X1,X2,X3] :
( sQ451_spl
<=> ( in(sK11_skl(X2,X3,sK84_skl),X2)
| relation_image(sK84_skl,X3) = X2
| ~ subset(X1,ordered_pair(sK12_skl(X2,X3,sK84_skl),sK11_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f12906,plain,
( ~ sQ11_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f12830,f12903,f1345]) ).
fof(f12911,definition,
! [X0,X1,X2,X3] :
( sQ453_spl
<=> ( ~ relation(X2)
| sK84_skl = relation_composition(X3,X2)
| in(ordered_pair(sK60_skl(sK84_skl,X2,X3),sK62_skl(sK84_skl,X2,X3)),X3)
| ~ relation(X3)
| ~ subset(X1,ordered_pair(sK60_skl(sK84_skl,X2,X3),sK61_skl(sK84_skl,X2,X3)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f12914,plain,
( ~ sQ11_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f12819,f12911,f1345]) ).
fof(f12915,definition,
! [X0,X1,X2,X3] :
( sQ454_spl
<=> ( ~ in(X3,relation_image(sK84_skl,X2))
| ~ subset(X1,ordered_pair(sK81_skl(X2,X3,sK84_skl),X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f12918,plain,
( ~ sQ11_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f12820,f12915,f1345]) ).
fof(f12919,definition,
! [X0,X1] :
( sQ455_spl
<=> ( ~ subset(X1,sK24_skl(sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f12922,plain,
( sQ26_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f12781,f12919,f1544]) ).
fof(f12923,definition,
! [X0,X1,X2] :
( sQ456_spl
<=> ( in(sK53_skl(X2,sK84_skl),X2)
| X2 = relation_rng(sK84_skl)
| ~ subset(X1,ordered_pair(sK54_skl(X2,sK84_skl),sK53_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f12926,plain,
( ~ sQ11_spl
| sQ456_spl ),
inference(split_clause,[status(thm)],[f12823,f12923,f1345]) ).
fof(f12927,definition,
! [X0,X1,X2,X3] :
( sQ457_spl
<=> ( in(sK2_skl(X2,sK84_skl,X3),X2)
| ~ relation(X3)
| relation_dom_restriction(X3,X2) = sK84_skl
| ~ subset(X1,ordered_pair(sK2_skl(X2,sK84_skl,X3),sK3_skl(X2,sK84_skl,X3)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f12930,plain,
( ~ sQ11_spl
| sQ457_spl ),
inference(split_clause,[status(thm)],[f12826,f12927,f1345]) ).
fof(f12931,definition,
! [X0,X1,X2,X3] :
( sQ458_spl
<=> ( ~ in(X2,relation_dom(sK84_skl))
| X3 != apply(sK84_skl,X2)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f12934,plain,
( ~ sQ11_spl
| ~ sQ68_spl
| sQ458_spl ),
inference(split_clause,[status(thm)],[f12839,f12931,f1961,f1345]) ).
fof(f12939,definition,
! [X0] :
( sQ460_spl
<=> ( ~ in(X0,empty_set)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f12942,plain,
( sQ97_spl
| sQ460_spl ),
inference(split_clause,[status(thm)],[f12861,f12939,f2607]) ).
fof(f12956,definition,
! [X0,X1,X2] :
( sQ464_spl
<=> ( in(sK43_skl(X2,sK84_skl),X2)
| relation_dom(sK84_skl) = X2
| ~ subset(X1,ordered_pair(sK43_skl(X2,sK84_skl),sK44_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f12959,plain,
( ~ sQ11_spl
| sQ464_spl ),
inference(split_clause,[status(thm)],[f12827,f12956,f1345]) ).
fof(f12960,definition,
! [X0,X1,X2] :
( sQ465_spl
<=> ( sK84_skl = identity_relation(X2)
| sK0_skl(X2,sK84_skl) = sK1_skl(X2,sK84_skl)
| ~ subset(X1,ordered_pair(sK0_skl(X2,sK84_skl),sK1_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f12963,plain,
( ~ sQ11_spl
| sQ465_spl ),
inference(split_clause,[status(thm)],[f12822,f12960,f1345]) ).
fof(f12964,definition,
! [X0,X1,X2,X3] :
( sQ466_spl
<=> ( ~ relation(X3)
| sK84_skl = relation_rng_restriction(X2,X3)
| in(sK8_skl(X2,sK84_skl,X3),X2)
| ~ subset(X1,ordered_pair(sK7_skl(X2,sK84_skl,X3),sK8_skl(X2,sK84_skl,X3)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f12967,plain,
( ~ sQ11_spl
| sQ466_spl ),
inference(split_clause,[status(thm)],[f12824,f12964,f1345]) ).
fof(f12972,definition,
! [X0,X1,X2,X3] :
( sQ468_spl
<=> ( in(sK14_skl(X2,X3,sK84_skl),X2)
| relation_inverse_image(sK84_skl,X3) = X2
| ~ subset(X1,ordered_pair(sK14_skl(X2,X3,sK84_skl),sK15_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f12975,plain,
( ~ sQ11_spl
| sQ468_spl ),
inference(split_clause,[status(thm)],[f12832,f12972,f1345]) ).
fof(f12992,definition,
! [X0,X1,X2] :
( sQ473_spl
<=> ( subset(sK84_skl,X2)
| ~ relation(X2)
| ~ subset(X1,ordered_pair(sK38_skl(X2,sK84_skl),sK39_skl(X2,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f12995,plain,
( ~ sQ11_spl
| sQ473_spl ),
inference(split_clause,[status(thm)],[f12829,f12992,f1345]) ).
fof(f13001,plain,
( sQ9_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f12874,f1471,f1321]) ).
fof(f13002,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ475_spl
<=> ( relation_rng_restriction(X4,X5) != sK84_skl
| ~ relation(X5)
| ~ in(ordered_pair(X2,X3),X5)
| ~ in(X3,X4)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f13005,plain,
( ~ sQ11_spl
| sQ475_spl ),
inference(split_clause,[status(thm)],[f12837,f13002,f1345]) ).
fof(f13006,definition,
! [X0,X1,X2,X3] :
( sQ476_spl
<=> ( ~ in(X2,X3)
| relation_rng(sK84_skl) != X3
| ~ subset(X1,ordered_pair(sK52_skl(X2,X3,sK84_skl),X2))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f13009,plain,
( ~ sQ11_spl
| sQ476_spl ),
inference(split_clause,[status(thm)],[f12821,f13006,f1345]) ).
fof(f13010,definition,
! [X0,X1,X3] :
( sQ477_spl
<=> ( ~ subset(X1,X3)
| X3 != empty_set
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f13013,plain,
( sQ30_spl
| sQ477_spl ),
inference(split_clause,[status(thm)],[f12872,f13010,f1558]) ).
fof(f13014,definition,
! [X0,X1,X2,X3,X4] :
( sQ478_spl
<=> ( ~ in(X2,X3)
| relation_inverse_image(sK84_skl,X4) != X3
| ~ subset(X1,ordered_pair(X2,sK13_skl(X2,X3,X4,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f13017,plain,
( ~ sQ11_spl
| sQ478_spl ),
inference(split_clause,[status(thm)],[f12833,f13014,f1345]) ).
fof(f13018,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ479_spl
<=> ( ~ in(ordered_pair(X2,X5),X4)
| ~ relation(X6)
| sK84_skl != relation_composition(X4,X6)
| ~ in(ordered_pair(X5,X3),X6)
| ~ relation(X4)
| ~ subset(X1,ordered_pair(X2,X3))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ479_spl])],[split_symbol_definition]) ).
fof(f13021,plain,
( ~ sQ11_spl
| sQ479_spl ),
inference(split_clause,[status(thm)],[f12836,f13018,f1345]) ).
fof(f13023,definition,
! [X0,X1,X2] :
( sQ480_spl
<=> ( ~ in(sK21_skl(X2,sK84_skl),X2)
| set_meet(sK84_skl) = X2
| ~ subset(X1,sK22_skl(X2,sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f13026,plain,
( sQ26_spl
| sQ480_spl ),
inference(split_clause,[status(thm)],[f12818,f13023,f1544]) ).
fof(f13028,definition,
! [X0,X1] :
( sQ481_spl
<=> ( ~ subset(X1,sK19_skl(sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f13031,plain,
( sQ11_spl
| sQ481_spl ),
inference(split_clause,[status(thm)],[f12795,f13028,f1345]) ).
fof(f13032,definition,
! [X0,X1,X2,X3] :
( sQ482_spl
<=> ( in(X2,X3)
| X3 != set_meet(sK84_skl)
| ~ subset(X1,sK20_skl(X2,X3,sK84_skl))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f13035,plain,
( sQ26_spl
| sQ482_spl ),
inference(split_clause,[status(thm)],[f12815,f13032,f1544]) ).
fof(f13036,definition,
! [X0,X1,X2,X3] :
( sQ483_spl
<=> ( relation_rng_restriction(X2,sK84_skl) = X3
| in(ordered_pair(sK7_skl(X2,X3,sK84_skl),sK8_skl(X2,X3,sK84_skl)),X3)
| ~ relation(X3)
| ~ subset(X1,ordered_pair(sK7_skl(X2,X3,sK84_skl),sK8_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f13039,plain,
( ~ sQ11_spl
| sQ483_spl ),
inference(split_clause,[status(thm)],[f12825,f13036,f1345]) ).
fof(f13040,definition,
! [X0,X1,X2,X3] :
( sQ484_spl
<=> ( ~ in(X2,X3)
| relation_dom(sK84_skl) != X3
| ~ subset(X1,ordered_pair(X2,sK42_skl(X2,X3,sK84_skl)))
| ~ in(X0,X1)
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f13043,plain,
( ~ sQ11_spl
| sQ484_spl ),
inference(split_clause,[status(thm)],[f12834,f13040,f1345]) ).
fof(f13085,plain,
! [X0,X1,X2] :
( ~ sQ38_spl
| ~ in(X2,sK84_skl)
| ordinal(sK21_skl(X0,sK84_skl))
| ~ ordinal(X2)
| X0 = set_meet(sK84_skl)
| ~ in(X1,sK22_skl(X0,sK84_skl))
| in(X1,sK84_skl)
| X0 = set_meet(sK84_skl) ),
inference(resolution,[status(thm)],[f1603,f6278]) ).
fof(f13088,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ in(sK21_skl(sK84_skl,sK84_skl),X1)
| ~ in(X1,sK84_skl)
| ~ in(X0,sK22_skl(sK84_skl,sK84_skl))
| in(X0,sK84_skl)
| sK84_skl = set_meet(sK84_skl) ),
inference(resolution,[status(thm)],[f1603,f1250]) ).
fof(f13100,definition,
! [X0,X1] :
( sQ487_spl
<=> ( set_meet(sK84_skl) = X0
| ordinal(sK21_skl(X0,sK84_skl))
| ~ in(X1,sK22_skl(X0,sK84_skl))
| in(X1,sK84_skl)
| X0 = set_meet(sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f13104,definition,
! [X0] :
( sQ488_spl
<=> ( ~ in(X0,sK22_skl(sK84_skl,sK84_skl))
| in(X0,sK84_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f13107,plain,
( ~ sQ38_spl
| sQ41_spl
| sQ488_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f13088,f1668,f13104,f1665,f1602]) ).
fof(f13110,plain,
( ~ sQ38_spl
| sQ264_spl
| sQ487_spl ),
inference(split_clause,[status(thm)],[f13085,f13100,f6316,f1602]) ).
fof(f13111,plain,
! [X0] :
( ~ sQ264_spl
| ~ in(X0,sK84_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6317,f967]) ).
fof(f13126,plain,
! [X0,X1] :
( X0 != empty_set
| X1 != empty_set
| X1 = empty_set
| empty_set != X0 ),
inference(resolution,[status(thm)],[f399,f400]) ).
fof(f13152,definition,
! [X0] :
( sQ490_spl
<=> ( X0 != empty_set
| empty_set != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f13153,plain,
! [X0] :
( ~ sQ490_spl
| X0 != empty_set
| empty_set != X0 ),
inference(component_clause,[status(thm)],[f13152]) ).
fof(f13155,definition,
! [X1] :
( sQ491_spl
<=> ( X1 != empty_set
| X1 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f13158,plain,
( sQ491_spl
| sQ490_spl ),
inference(split_clause,[status(thm)],[f13126,f13152,f13155]) ).
fof(f13159,plain,
! [X0] :
( ~ sQ490_spl
| X0 != empty_set ),
inference(duplicate_literals_removal,[status(thm)],[f13153]) ).
fof(f13206,plain,
( ~ sQ490_spl
| $false ),
inference(resolution,[status(thm)],[f13159,f1009]) ).
fof(f13220,plain,
~ sQ490_spl,
inference(contradiction_clause,[status(thm)],[f13206]) ).
fof(f13298,plain,
( ~ sQ264_spl
| relation(sK84_skl) ),
inference(resolution,[status(thm)],[f13111,f387]) ).
fof(f13310,plain,
! [X0] :
( ~ sQ264_spl
| ~ in(X0,sK84_skl) ),
inference(resolution,[status(thm)],[f13111,f1143]) ).
fof(f13386,plain,
( ~ sQ264_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f13310,f2607,f6316]) ).
fof(f13407,plain,
( ~ sQ264_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13298,f1347]) ).
fof(f13408,plain,
( ~ sQ264_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f13407]) ).
fof(f13954,plain,
! [X0,X1] :
( in(X1,relation_dom(relation_composition(X0,empty_set)))
| ~ in(apply(X0,X1),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0) ),
inference(paramodulation,[status(thm)],[f1089,f928]) ).
fof(f13990,definition,
! [X0,X1] :
( sQ508_spl
<=> ( in(X1,relation_dom(relation_composition(X0,empty_set)))
| ~ in(apply(X0,X1),empty_set)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f13993,plain,
( ~ sQ146_spl
| ~ sQ3_spl
| sQ508_spl ),
inference(split_clause,[status(thm)],[f13954,f13990,f1257,f3664]) ).
fof(f14042,plain,
! [X0,X1] :
( ~ sQ177_spl
| ~ ordinal(empty_set)
| ~ function(X1)
| ~ function(X0)
| ~ ordinal(relation_dom(relation_composition(X1,X0)))
| in(empty_set,relation_dom(X1))
| ~ relation(X1)
| relation_dom(relation_composition(X1,X0)) = empty_set
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f3914,f4576]) ).
fof(f14053,plain,
! [X0,X1] :
( ~ sQ98_spl
| ordinal(relation_dom(relation_composition(X1,X0)))
| ~ ordinal(sK95_skl(sK84_skl))
| ~ function(X1)
| ~ function(X0)
| ~ ordinal(relation_dom(relation_composition(X1,X0)))
| in(sK95_skl(sK84_skl),relation_dom(X1))
| ~ relation(X1)
| relation_dom(relation_composition(X1,X0)) = sK95_skl(sK84_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f3914,f2611]) ).
fof(f14094,definition,
! [X0,X1] :
( sQ509_spl
<=> ( ordinal(relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ function(X0)
| ~ ordinal(relation_dom(relation_composition(X1,X0)))
| in(sK95_skl(sK84_skl),relation_dom(X1))
| ~ relation(X1)
| relation_dom(relation_composition(X1,X0)) = sK95_skl(sK84_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f14097,plain,
( ~ sQ98_spl
| ~ sQ99_spl
| sQ509_spl ),
inference(split_clause,[status(thm)],[f14053,f14094,f2614,f2610]) ).
fof(f14109,definition,
! [X0,X1] :
( sQ511_spl
<=> ( ~ function(X1)
| ~ function(X0)
| ~ ordinal(relation_dom(relation_composition(X1,X0)))
| in(empty_set,relation_dom(X1))
| ~ relation(X1)
| relation_dom(relation_composition(X1,X0)) = empty_set
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f14112,plain,
( ~ sQ177_spl
| ~ sQ79_spl
| sQ511_spl ),
inference(split_clause,[status(thm)],[f14042,f14109,f2114,f4575]) ).
fof(f14120,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(sK36_skl(X0))
| ~ ordinal(sK37_skl(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3964,f477]) ).
fof(f14121,plain,
( ~ sQ443_spl
| epsilon_connected(sK84_skl)
| ~ ordinal(sK36_skl(sK84_skl)) ),
inference(resolution,[status(thm)],[f14120,f12770]) ).
fof(f14123,plain,
( ~ sQ443_spl
| sQ124_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f14121,f2911,f2908,f12769]) ).
fof(f14124,plain,
( ~ sQ33_spl
| ~ sQ9_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f1606,f1558,f1321,f1571]) ).
fof(f14125,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1273,f969]) ).
fof(f14126,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f14125]) ).
fof(f14127,plain,
$false,
inference(sat_refutation,[status(thm)],[f1261,f1325,f1326,f1331,f1348,f1352,f1371,f1372,f1381,f1451,f1505,f1513,f1515,f1521,f1561,f1582,f1586,f1588,f1601,f1605,f1621,f1674,f1697,f1699,f1724,f1737,f1783,f1787,f1814,f1827,f1830,f1882,f1886,f1887,f1888,f1910,f1914,f1964,f1969,f1981,f2089,f2093,f2101,f2105,f2109,f2117,f2119,f2157,f2161,f2206,f2211,f2240,f2244,f2284,f2296,f2388,f2392,f2396,f2476,f2486,f2492,f2613,f2617,f2622,f2652,f2694,f2696,f2720,f2736,f2794,f2822,f2826,f2830,f2837,f2841,f2845,f2849,f2857,f2861,f2914,f2921,f2926,f2963,f2967,f2991,f3002,f3006,f3096,f3146,f3157,f3232,f3240,f3246,f3248,f3356,f3619,f3621,f3670,f3675,f3683,f3687,f3689,f3694,f3698,f3708,f3710,f3713,f3810,f3815,f3947,f3953,f3961,f4034,f4039,f4044,f4074,f4087,f4106,f4141,f4175,f4293,f4325,f4497,f4618,f4626,f4630,f4636,f4641,f4645,f4650,f4654,f4658,f4662,f4666,f4674,f4678,f4682,f4805,f4828,f4963,f4981,f4989,f4994,f5000,f5005,f5061,f5072,f5115,f5151,f5164,f5239,f5242,f5309,f5325,f5370,f5374,f5378,f5395,f5501,f5505,f5512,f5598,f5600,f5608,f5612,f5616,f5628,f5632,f5636,f5644,f5648,f5652,f5660,f5668,f5672,f5676,f5680,f5821,f5825,f5829,f5833,f5837,f5845,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5875,f5880,f5884,f5905,f5909,f5913,f5914,f6031,f6114,f6178,f6182,f6319,f6525,f6536,f6647,f6804,f6809,f6914,f7251,f7259,f7260,f7613,f7618,f7622,f7626,f7631,f7648,f7813,f7965,f7969,f7974,f7978,f7984,f7994,f7998,f8010,f8016,f8020,f8026,f8163,f8175,f8258,f8269,f8273,f8285,f8372,f8603,f8720,f8799,f8816,f8853,f8941,f8981,f8984,f9085,f9092,f9099,f9350,f9356,f9363,f9367,f9372,f9510,f9533,f9557,f9621,f9628,f9639,f9661,f9698,f9703,f9705,f9805,f9812,f9871,f10072,f10191,f10215,f10322,f10387,f10422,f10431,f10490,f10494,f10501,f10679,f10685,f10690,f10831,f10839,f10843,f10848,f10894,f11027,f11036,f11275,f11279,f11287,f11291,f11295,f11299,f11397,f11403,f11415,f11547,f11552,f11559,f11987,f12065,f12118,f12204,f12284,f12432,f12436,f12448,f12456,f12460,f12464,f12473,f12477,f12481,f12490,f12495,f12503,f12507,f12511,f12532,f12543,f12639,f12644,f12658,f12661,f12668,f12684,f12688,f12714,f12772,f12776,f12882,f12886,f12890,f12894,f12902,f12906,f12914,f12918,f12922,f12926,f12930,f12934,f12942,f12959,f12963,f12967,f12975,f12995,f13001,f13005,f13009,f13013,f13017,f13021,f13026,f13031,f13035,f13039,f13043,f13107,f13110,f13158,f13220,f13386,f13408,f13993,f14097,f14112,f14123,f14124,f14126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU234+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:03:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 143.89/18.66 % Refutation found
% 143.89/18.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 143.89/18.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 130.32/18.72 % Elapsed time: 18.335946 seconds
% 130.32/18.72 % CPU time: 144.459803 seconds
% 130.32/18.72 % Total memory used: 402.351 MB
% 130.32/18.72 % Net memory used: 343.833 MB
%------------------------------------------------------------------------------