%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU241+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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:51 PM UTC 2026
% Result : Theorem 195.68s 25.28s
% Output : CNFRefutation 195.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 504
% Syntax : Number of formulae : 2129 ( 219 unt; 363 def)
% Number of atoms : 7026 ( 839 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 8570 (3673 ~;3582 |; 684 &)
% ( 494 <=>; 136 =>; 0 <=; 1 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 387 ( 385 usr; 362 prp; 0-4 aty)
% Number of functors : 120 ( 120 usr; 10 con; 0-5 aty)
% Number of variables : 3154 (2965 !; 189 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(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(f8,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(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(f13,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(f14,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,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] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,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)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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(f21,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(f22,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,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(f28,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,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(f35,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,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(f38,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(f39,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,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(f44,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( ( in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
=> C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A] : cast_to_subset(A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,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(f48,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(f49,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(f51,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A] :
( being_limit_ordinal(A)
<=> A = union(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,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(f57,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(f58,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f106,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f107,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(f108,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,lemma,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f136,lemma,
! [A] :
( relation(A)
=> ( transitive(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
=> in(ordered_pair(B,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f137,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f140,conjecture,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
inference(negated_conjecture,[status(cth)],[f140]) ).
fof(f145,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f146,lemma,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f147,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f152,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f153,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f154,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(f156,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f162,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f163,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f165,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f166,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f168,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f170,lemma,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f172,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(f173,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f174,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f175,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f177,lemma,
! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f180,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(f181,lemma,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f182,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(f183,lemma,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f184,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f185,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(f186,lemma,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,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(f189,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(f190,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,lemma,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,lemma,
! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,lemma,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,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(f202,lemma,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f208,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(f214,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f215,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(f216,lemma,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f217,lemma,
! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f218,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f221,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(f230,axiom,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f231,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f233,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f234,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f235,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f236,lemma,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f237,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f239,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f240,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(f249,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f253,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(f259,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f267,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f268,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f271,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f274,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f275,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(f276,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f277,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f279,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f280,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f288,lemma,
! [A] : union(powerset(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f289,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(f291,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f292,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f291]) ).
fof(f293,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f294,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f295,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f296,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f295]) ).
fof(f300,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f301,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f302,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f305,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f306,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f307,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f309,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f311,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f312,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f313,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f317,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)],[f13]) ).
fof(f318,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)],[f317]) ).
fof(f319,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)],[f318]) ).
fof(f320,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))],[f319]) ).
fof(f323,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)],[f320]) ).
fof(f325,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X1)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f326,plain,
! [X0,X1] :
( sK0_skl(X1,X0) = sK1_skl(X1,X0)
| in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f327,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f328,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)],[f327]) ).
fof(f329,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f332,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)],[f15]) ).
fof(f333,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)],[f332]) ).
fof(f334,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)],[f333]) ).
fof(f335,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))],[f334]) ).
fof(f338,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X2)
| in(ordered_pair(X3,X4),X1)
| X1 != relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f340,plain,
! [X0,X1,X2] :
( in(sK2_skl(X2,X1,X0),X2)
| in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f341,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK2_skl(X2,X1,X0),sK3_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f342,plain,
! [A] :
( ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f343,definition,
! [A,B,D,E] :
( sP0_prd(E,D,B,A)
<=> ( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f344,plain,
! [A] :
( ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] : sP0_prd(E,D,B,A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(formula_renaming,[status(thm)],[f342,f343]) ).
fof(f345,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] : sP0_prd(E,D,B,A)
| in(D,C) )
& ( ! [E] : ~ sP0_prd(E,D,B,A)
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] : ~ sP0_prd(E,D,B,A)
| in(D,C) )
& ( ? [E] : sP0_prd(E,D,B,A)
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f344]) ).
fof(f346,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] : sP0_prd(E,D,B,A)
| in(D,C) )
& ( ! [E] : ~ sP0_prd(E,D,B,A)
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] : ~ sP0_prd(E,D,B,A)
| in(D,C) )
& ! [D] :
( ? [E] : sP0_prd(E,D,B,A)
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f345]) ).
fof(f347,plain,
! [A] :
( ( ! [B,C] :
( ( ( sP0_prd(sK6_skl(C,B,A),sK5_skl(C,B,A),B,A)
| in(sK5_skl(C,B,A),C) )
& ( ! [E] : ~ sP0_prd(E,sK5_skl(C,B,A),B,A)
| ~ in(sK5_skl(C,B,A),C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] : ~ sP0_prd(E,D,B,A)
| in(D,C) )
& ! [D] :
( sP0_prd(sK4_skl(D,C,B,A),D,B,A)
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(E,sK4_skl(D,C,B,A)),skolemize(D,sK5_skl(C,B,A)),skolemize(E,sK6_skl(C,B,A))],[f346]) ).
fof(f348,plain,
! [X0,X1,X2,X3] :
( sP0_prd(sK4_skl(X3,X1,X2,X0),X3,X2,X0)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f352,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)],[f17]) ).
fof(f353,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)],[f352]) ).
fof(f354,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)],[f353]) ).
fof(f355,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))],[f354]) ).
fof(f358,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X2)
| in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f360,plain,
! [X0,X1,X2] :
( in(sK8_skl(X2,X1,X0),X2)
| in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X1)
| X1 = relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f361,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK7_skl(X2,X1,X0),sK8_skl(X2,X1,X0)),X1)
| X1 = relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f355]) ).
fof(f362,plain,
! [A] :
( ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f363,plain,
! [A] :
( ( ( ~ is_antisymmetric_in(A,relation_field(A))
| antisymmetric(A) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f362]) ).
fof(f364,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f365,plain,
! [X0] :
( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f366,plain,
! [A] :
( ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f367,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| in(D,C) )
& ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| in(D,C) )
& ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f366]) ).
fof(f368,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| in(D,C) )
& ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| in(D,C) )
& ! [D] :
( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f367]) ).
fof(f369,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(apply(A,sK9_skl(C,B,A)),B)
& in(sK9_skl(C,B,A),relation_dom(A)) )
| in(sK9_skl(C,B,A),C) )
& ( ~ in(apply(A,sK9_skl(C,B,A)),B)
| ~ in(sK9_skl(C,B,A),relation_dom(A))
| ~ in(sK9_skl(C,B,A),C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| in(D,C) )
& ! [D] :
( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(D,sK9_skl(C,B,A))],[f368]) ).
fof(f370,plain,
! [X0,X1,X2,X3] :
( in(X3,relation_dom(X0))
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f369]) ).
fof(f371,plain,
! [X0,X1,X2,X3] :
( in(apply(X0,X3),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f369]) ).
fof(f374,plain,
! [X0,X1,X2] :
( in(sK9_skl(X1,X2,X0),relation_dom(X0))
| in(sK9_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f369]) ).
fof(f376,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)],[f20]) ).
fof(f377,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)],[f376]) ).
fof(f378,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)],[f377]) ).
fof(f379,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))],[f378]) ).
fof(f380,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK10_skl(X3,X1,X2,X0),X3),X0)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f381,plain,
! [X0,X1,X2,X3] :
( in(sK10_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f382,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f384,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK12_skl(X1,X2,X0),sK11_skl(X1,X2,X0)),X0)
| in(sK11_skl(X1,X2,X0),X1)
| X1 = relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f386,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)],[f21]) ).
fof(f387,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)],[f386]) ).
fof(f388,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)],[f387]) ).
fof(f389,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))],[f388]) ).
fof(f390,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,sK13_skl(X3,X1,X2,X0)),X0)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f391,plain,
! [X0,X1,X2,X3] :
( in(sK13_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f392,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X0)
| in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f394,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK14_skl(X1,X2,X0),sK15_skl(X1,X2,X0)),X0)
| in(sK14_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f396,plain,
! [A] :
( ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f397,plain,
! [A] :
( ( ( ~ is_transitive_in(A,relation_field(A))
| transitive(A) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f396]) ).
fof(f398,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f399,plain,
! [X0] :
( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f410,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f411,plain,
! [A] :
( relation(A)
<=> ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f412,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)],[f411]) ).
fof(f413,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)],[f412]) ).
fof(f414,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))],[f413]) ).
fof(f416,plain,
! [X0] :
( in(sK19_skl(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[status(thm)],[f414]) ).
fof(f418,plain,
! [A] :
( ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f419,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ! [B] :
( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f419]) ).
fof(f421,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK20_skl(B,A),sK20_skl(B,A)),A)
& in(sK20_skl(B,A),B) )
| is_reflexive_in(A,B) )
& ! [B] :
( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(C,sK20_skl(B,A))],[f420]) ).
fof(f422,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f423,plain,
! [X0,X1] :
( in(sK20_skl(X1,X0),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f425,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)],[f27]) ).
fof(f426,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)],[f425]) ).
fof(f427,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)],[f426]) ).
fof(f428,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(sK22_skl(B,A),D)
| ~ in(D,A) )
| in(sK22_skl(B,A),B) )
& ( ( ~ in(sK22_skl(B,A),sK23_skl(B,A))
& in(sK23_skl(B,A),A) )
| ~ in(sK22_skl(B,A),B) ) )
| B = set_meet(A) )
& ! [B] :
( ( ! [C] :
( ( ~ in(C,sK21_skl(C,B,A))
& in(sK21_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,[sK21_skl,sK22_skl,sK23_skl]),skolemize(D,sK21_skl(C,B,A)),skolemize(C,sK22_skl(B,A)),skolemize(D,sK23_skl(B,A))],[f427]) ).
fof(f430,plain,
! [X0,X1,X2] :
( in(sK21_skl(X2,X1,X0),X0)
| in(X2,X1)
| X1 != set_meet(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f435,plain,
! [X0,X1] :
( X1 = empty_set
| X1 != set_meet(X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f437,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)],[f28]) ).
fof(f438,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)],[f437]) ).
fof(f439,plain,
( ! [A,B] :
( ( ( sK24_skl(B,A) = A
| in(sK24_skl(B,A),B) )
& ( sK24_skl(B,A) != A
| ~ in(sK24_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,[sK24_skl]),skolemize(C,sK24_skl(B,A))],[f438]) ).
fof(f440,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f441,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f444,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f445,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f444]) ).
fof(f446,plain,
( ! [A] :
( in(sK25_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(B,sK25_skl(A))],[f445]) ).
fof(f447,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f446]) ).
fof(f448,plain,
! [X0] :
( in(sK25_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f446]) ).
fof(f449,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)],[f30]) ).
fof(f450,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)],[f449]) ).
fof(f451,plain,
( ! [A,B] :
( ( ( subset(sK26_skl(B,A),A)
| in(sK26_skl(B,A),B) )
& ( ~ subset(sK26_skl(B,A),A)
| ~ in(sK26_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,[sK26_skl]),skolemize(C,sK26_skl(B,A))],[f450]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f451]) ).
fof(f456,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f457,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)],[f456]) ).
fof(f458,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)],[f457]) ).
fof(f459,plain,
( ! [A] :
( ( ~ subset(sK27_skl(A),A)
& in(sK27_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl]),skolemize(B,sK27_skl(A))],[f458]) ).
fof(f460,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ in(X1,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f459]) ).
fof(f461,plain,
! [X0] :
( in(sK27_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f459]) ).
fof(f463,plain,
! [A] :
( ! [B] :
( ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f464,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A = B )
& ( ! [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f463]) ).
fof(f465,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A = B )
& ( ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f464]) ).
fof(f466,plain,
! [A] :
( ! [B] :
( ( ( ( ( in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),B)
| in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),A) )
& ( ~ in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),B)
| ~ in(ordered_pair(sK28_skl(B,A),sK29_skl(B,A)),A) ) )
| A = B )
& ( ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl,sK29_skl]),skolemize(C,sK28_skl(B,A)),skolemize(D,sK29_skl(B,A))],[f465]) ).
fof(f470,plain,
! [X0,X1] :
( in(ordered_pair(sK28_skl(X1,X0),sK29_skl(X1,X0)),X1)
| in(ordered_pair(sK28_skl(X1,X0),sK29_skl(X1,X0)),X0)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f466]) ).
fof(f471,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f472,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(NNF_transformation,[status(thm)],[f471]) ).
fof(f473,plain,
( ! [A] :
( ( ! [B] :
( ~ empty(B)
| element(B,A) )
& ! [B] :
( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ! [A] :
( ( ! [B] :
( ~ in(B,A)
| element(B,A) )
& ! [B] :
( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(miniscoping,[status(thm)],[f472]) ).
fof(f474,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f473]) ).
fof(f478,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)],[f34]) ).
fof(f479,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)],[f478]) ).
fof(f480,plain,
( ! [A,B,C] :
( ( ( sK30_skl(C,B,A) = B
| sK30_skl(C,B,A) = A
| in(sK30_skl(C,B,A),C) )
& ( ( sK30_skl(C,B,A) != B
& sK30_skl(C,B,A) != A )
| ~ in(sK30_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,[sK30_skl]),skolemize(D,sK30_skl(C,B,A))],[f479]) ).
fof(f482,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f480]) ).
fof(f483,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f480]) ).
fof(f487,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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f488,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_union2(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_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f487]) ).
fof(f489,plain,
( ! [A,B,C] :
( ( ( in(sK31_skl(C,B,A),B)
| in(sK31_skl(C,B,A),A)
| in(sK31_skl(C,B,A),C) )
& ( ( ~ in(sK31_skl(C,B,A),B)
& ~ in(sK31_skl(C,B,A),A) )
| ~ in(sK31_skl(C,B,A),C) ) )
| C = set_union2(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_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31_skl]),skolemize(D,sK31_skl(C,B,A))],[f488]) ).
fof(f491,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f489]) ).
fof(f505,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)],[f37]) ).
fof(f506,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)],[f505]) ).
fof(f507,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)],[f506]) ).
fof(f508,plain,
( ! [A] :
( ( ~ in(sK38_skl(A),sK37_skl(A))
& sK37_skl(A) != sK38_skl(A)
& ~ in(sK37_skl(A),sK38_skl(A))
& in(sK38_skl(A),A)
& in(sK37_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,[sK37_skl,sK38_skl]),skolemize(B,sK37_skl(A)),skolemize(C,sK38_skl(A))],[f507]) ).
fof(f509,plain,
! [X0,X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f511,plain,
! [X0] :
( in(sK38_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f515,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)],[f38]) ).
fof(f516,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)],[f515]) ).
fof(f517,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK39_skl(B,A),sK40_skl(B,A)),B)
& in(ordered_pair(sK39_skl(B,A),sK40_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,[sK39_skl,sK40_skl]),skolemize(C,sK39_skl(B,A)),skolemize(D,sK40_skl(B,A))],[f516]) ).
fof(f519,plain,
! [X0,X1] :
( in(ordered_pair(sK39_skl(X1,X0),sK40_skl(X1,X0)),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f517]) ).
fof(f521,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f522,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)],[f521]) ).
fof(f523,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)],[f522]) ).
fof(f524,plain,
( ! [A,B] :
( ( ~ in(sK41_skl(B,A),B)
& in(sK41_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,[sK41_skl]),skolemize(C,sK41_skl(B,A))],[f523]) ).
fof(f525,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f524]) ).
fof(f526,plain,
! [X0,X1] :
( in(sK41_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f524]) ).
fof(f549,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)],[f43]) ).
fof(f550,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)],[f549]) ).
fof(f551,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)],[f550]) ).
fof(f552,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK44_skl(B,A),sK45_skl(B,A)),A)
| in(sK44_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK44_skl(B,A),D),A)
| ~ in(sK44_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,sK43_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl,sK45_skl]),skolemize(D,sK43_skl(C,B,A)),skolemize(C,sK44_skl(B,A)),skolemize(D,sK45_skl(B,A))],[f551]) ).
fof(f553,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK43_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f552]) ).
fof(f554,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f552]) ).
fof(f556,plain,
! [X0,X1] :
( in(ordered_pair(sK44_skl(X1,X0),sK45_skl(X1,X0)),X0)
| in(sK44_skl(X1,X0),X1)
| X1 = relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f552]) ).
fof(f557,plain,
! [A] :
( ! [B] :
( is_antisymmetric_in(A,B)
<=> ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f558,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( C != D
& in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
| is_antisymmetric_in(A,B) )
& ( ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f557]) ).
fof(f559,plain,
! [A] :
( ( ! [B] :
( ? [C,D] :
( C != D
& in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),A)
& in(D,B)
& in(C,B) )
| is_antisymmetric_in(A,B) )
& ! [B] :
( ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f558]) ).
fof(f560,plain,
! [A] :
( ( ! [B] :
( ( sK46_skl(B,A) != sK47_skl(B,A)
& in(ordered_pair(sK47_skl(B,A),sK46_skl(B,A)),A)
& in(ordered_pair(sK46_skl(B,A),sK47_skl(B,A)),A)
& in(sK47_skl(B,A),B)
& in(sK46_skl(B,A),B) )
| is_antisymmetric_in(A,B) )
& ! [B] :
( ! [C,D] :
( C = D
| ~ in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_antisymmetric_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl,sK47_skl]),skolemize(C,sK46_skl(B,A)),skolemize(D,sK47_skl(B,A))],[f559]) ).
fof(f561,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f560]) ).
fof(f564,plain,
! [X0,X1] :
( in(ordered_pair(sK46_skl(X1,X0),sK47_skl(X1,X0)),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f560]) ).
fof(f565,plain,
! [X0,X1] :
( in(ordered_pair(sK47_skl(X1,X0),sK46_skl(X1,X0)),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f560]) ).
fof(f566,plain,
! [X0,X1] :
( sK46_skl(X1,X0) != sK47_skl(X1,X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f560]) ).
fof(f567,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f568,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)],[f46]) ).
fof(f569,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)],[f568]) ).
fof(f570,plain,
( ! [A,B] :
( ( ( ( in(sK50_skl(B,A),A)
& in(sK49_skl(B,A),sK50_skl(B,A)) )
| in(sK49_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK49_skl(B,A),D) )
| ~ in(sK49_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK48_skl(C,B,A),A)
& in(C,sK48_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48_skl,sK49_skl,sK50_skl]),skolemize(D,sK48_skl(C,B,A)),skolemize(C,sK49_skl(B,A)),skolemize(D,sK50_skl(B,A))],[f569]) ).
fof(f572,plain,
! [X0,X1,X2] :
( in(sK48_skl(X2,X0,X1),X1)
| ~ in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f570]) ).
fof(f573,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f570]) ).
fof(f586,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)],[f48]) ).
fof(f587,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)],[f586]) ).
fof(f588,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)],[f587]) ).
fof(f589,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK53_skl(B,A) = apply(A,sK54_skl(B,A))
& in(sK54_skl(B,A),relation_dom(A)) )
| in(sK53_skl(B,A),B) )
& ( ! [D] :
( sK53_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK53_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,sK52_skl(C,B,A))
& in(sK52_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,[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))],[f588]) ).
fof(f590,plain,
! [X0,X1,X2] :
( in(sK52_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f589]) ).
fof(f591,plain,
! [X0,X1,X2] :
( X2 = apply(X0,sK52_skl(X2,X1,X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f589]) ).
fof(f592,plain,
! [X0,X1,X2,X3] :
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f589]) ).
fof(f594,plain,
! [X0,X1] :
( in(sK54_skl(X1,X0),relation_dom(X0))
| in(sK53_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f589]) ).
fof(f596,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)],[f49]) ).
fof(f597,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)],[f596]) ).
fof(f598,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)],[f597]) ).
fof(f599,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK57_skl(B,A),sK56_skl(B,A)),A)
| in(sK56_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK56_skl(B,A)),A)
| ~ in(sK56_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK55_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl,sK57_skl]),skolemize(D,sK55_skl(C,B,A)),skolemize(C,sK56_skl(B,A)),skolemize(D,sK57_skl(B,A))],[f598]) ).
fof(f600,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK55_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f599]) ).
fof(f601,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f599]) ).
fof(f603,plain,
! [X0,X1] :
( in(ordered_pair(sK57_skl(X1,X0),sK56_skl(X1,X0)),X0)
| in(sK56_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f599]) ).
fof(f606,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f607,plain,
! [A] :
( ( A != union(A)
| being_limit_ordinal(A) )
& ( A = union(A)
| ~ being_limit_ordinal(A) ) ),
inference(NNF_transformation,[status(thm)],[f52]) ).
fof(f608,plain,
( ! [A] :
( A != union(A)
| being_limit_ordinal(A) )
& ! [A] :
( A = union(A)
| ~ being_limit_ordinal(A) ) ),
inference(miniscoping,[status(thm)],[f607]) ).
fof(f609,plain,
! [X0] :
( X0 = union(X0)
| ~ being_limit_ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f608]) ).
fof(f610,plain,
! [X0] :
( X0 != union(X0)
| being_limit_ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f608]) ).
fof(f611,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f612,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f611]) ).
fof(f613,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)],[f54]) ).
fof(f614,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)],[f613]) ).
fof(f615,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)],[f614]) ).
fof(f616,plain,
! [A] :
( ! [B] :
( ( ( ( ( in(ordered_pair(sK59_skl(B,A),sK58_skl(B,A)),A)
| in(ordered_pair(sK58_skl(B,A),sK59_skl(B,A)),B) )
& ( ~ in(ordered_pair(sK59_skl(B,A),sK58_skl(B,A)),A)
| ~ in(ordered_pair(sK58_skl(B,A),sK59_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,[sK58_skl,sK59_skl]),skolemize(C,sK58_skl(B,A)),skolemize(D,sK59_skl(B,A))],[f615]) ).
fof(f618,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1)
| X1 != relation_inverse(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f616]) ).
fof(f620,plain,
! [X0,X1] :
( in(ordered_pair(sK59_skl(X1,X0),sK58_skl(X1,X0)),X0)
| in(ordered_pair(sK58_skl(X1,X0),sK59_skl(X1,X0)),X1)
| X1 = relation_inverse(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f616]) ).
fof(f633,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)],[f57]) ).
fof(f634,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)],[f633]) ).
fof(f635,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)],[f634]) ).
fof(f636,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( ( ( in(ordered_pair(sK65_skl(C,B,A),sK64_skl(C,B,A)),B)
& in(ordered_pair(sK63_skl(C,B,A),sK65_skl(C,B,A)),A) )
| in(ordered_pair(sK63_skl(C,B,A),sK64_skl(C,B,A)),C) )
& ( ! [F] :
( ~ in(ordered_pair(F,sK64_skl(C,B,A)),B)
| ~ in(ordered_pair(sK63_skl(C,B,A),F),A) )
| ~ in(ordered_pair(sK63_skl(C,B,A),sK64_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(sK62_skl(E,D,C,B,A),E),B)
& in(ordered_pair(D,sK62_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,[sK62_skl,sK63_skl,sK64_skl,sK65_skl]),skolemize(F,sK62_skl(E,D,C,B,A)),skolemize(D,sK63_skl(C,B,A)),skolemize(E,sK64_skl(C,B,A)),skolemize(F,sK65_skl(C,B,A))],[f635]) ).
fof(f637,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,sK62_skl(X4,X3,X2,X1,X0)),X0)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f636]) ).
fof(f638,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(sK62_skl(X4,X3,X2,X1,X0),X4),X1)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f636]) ).
fof(f639,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0)
| in(ordered_pair(X3,X4),X2)
| X2 != relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f636]) ).
fof(f641,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK63_skl(X2,X1,X0),sK65_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK63_skl(X2,X1,X0),sK64_skl(X2,X1,X0)),X2)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f636]) ).
fof(f642,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK65_skl(X2,X1,X0),sK64_skl(X2,X1,X0)),X1)
| in(ordered_pair(sK63_skl(X2,X1,X0),sK64_skl(X2,X1,X0)),X2)
| X2 = relation_composition(X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f636]) ).
fof(f643,plain,
! [A] :
( ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f644,plain,
! [A] :
( ! [B] :
( ( ? [C,D,E] :
( ~ in(ordered_pair(C,E),A)
& in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
| is_transitive_in(A,B) )
& ( ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f643]) ).
fof(f645,plain,
! [A] :
( ( ! [B] :
( ? [C,E] :
( ~ in(ordered_pair(C,E),A)
& ? [D] :
( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) ) )
| is_transitive_in(A,B) )
& ! [B] :
( ! [C,E] :
( in(ordered_pair(C,E),A)
| ! [D] :
( ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f644]) ).
fof(f646,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK66_skl(B,A),sK67_skl(B,A)),A)
& in(ordered_pair(sK68_skl(B,A),sK67_skl(B,A)),A)
& in(ordered_pair(sK66_skl(B,A),sK68_skl(B,A)),A)
& in(sK67_skl(B,A),B)
& in(sK68_skl(B,A),B)
& in(sK66_skl(B,A),B) )
| is_transitive_in(A,B) )
& ! [B] :
( ! [C,E] :
( in(ordered_pair(C,E),A)
| ! [D] :
( ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl,sK67_skl,sK68_skl]),skolemize(C,sK66_skl(B,A)),skolemize(E,sK67_skl(B,A)),skolemize(D,sK68_skl(B,A))],[f645]) ).
fof(f647,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f646]) ).
fof(f651,plain,
! [X0,X1] :
( in(ordered_pair(sK66_skl(X1,X0),sK68_skl(X1,X0)),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f646]) ).
fof(f662,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)],[f60]) ).
fof(f663,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)],[f662]) ).
fof(f666,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f663]) ).
fof(f669,plain,
! [A] :
( ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f62]) ).
fof(f670,plain,
! [A] :
( ( ( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f669]) ).
fof(f671,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f670]) ).
fof(f676,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f679,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f680,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f679]) ).
fof(f681,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f682,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f681]) ).
fof(f685,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f690,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f691,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f690]) ).
fof(f692,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f691]) ).
fof(f695,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f696,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f695]) ).
fof(f697,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f696]) ).
fof(f698,plain,
! [A] : element(sK70_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70_skl]),skolemize(B,sK70_skl(A))],[f95]) ).
fof(f699,plain,
! [X0] : element(sK70_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f698]) ).
fof(f706,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f707,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f719,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f721,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f722,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f724,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f722]) ).
fof(f727,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f730,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f731,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f733,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f108]) ).
fof(f734,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f733]) ).
fof(f742,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f112]) ).
fof(f744,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f742]) ).
fof(f745,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f742]) ).
fof(f746,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f742]) ).
fof(f790,plain,
! [A] :
( ( reflexive(A)
<=> ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f131]) ).
fof(f791,plain,
! [A] :
( ( ( ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) )
| reflexive(A) )
& ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f790]) ).
fof(f792,plain,
! [A] :
( ( ( ( ~ in(ordered_pair(sK71_skl(A),sK71_skl(A)),A)
& in(sK71_skl(A),relation_field(A)) )
| reflexive(A) )
& ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71_skl]),skolemize(B,sK71_skl(A))],[f791]) ).
fof(f793,plain,
! [X0,X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f792]) ).
fof(f794,plain,
! [X0] :
( in(sK71_skl(X0),relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f792]) ).
fof(f796,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f803,plain,
! [A] :
( ( transitive(A)
<=> ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f136]) ).
fof(f804,plain,
! [A] :
( ( ( ? [B,C,D] :
( ~ in(ordered_pair(B,D),A)
& in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) )
| transitive(A) )
& ( ! [B,C,D] :
( in(ordered_pair(B,D),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f803]) ).
fof(f805,plain,
! [A] :
( ( ( ? [B,D] :
( ~ in(ordered_pair(B,D),A)
& ? [C] :
( in(ordered_pair(C,D),A)
& in(ordered_pair(B,C),A) ) )
| transitive(A) )
& ( ! [B,D] :
( in(ordered_pair(B,D),A)
| ! [C] :
( ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f804]) ).
fof(f806,plain,
! [A] :
( ( ( ( ~ in(ordered_pair(sK72_skl(A),sK73_skl(A)),A)
& in(ordered_pair(sK74_skl(A),sK73_skl(A)),A)
& in(ordered_pair(sK72_skl(A),sK74_skl(A)),A) )
| transitive(A) )
& ( ! [B,D] :
( in(ordered_pair(B,D),A)
| ! [C] :
( ~ in(ordered_pair(C,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72_skl,sK73_skl,sK74_skl]),skolemize(B,sK72_skl(A)),skolemize(D,sK73_skl(A)),skolemize(C,sK74_skl(A))],[f805]) ).
fof(f808,plain,
! [X0] :
( in(ordered_pair(sK72_skl(X0),sK74_skl(X0)),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f806]) ).
fof(f811,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f137]) ).
fof(f812,plain,
( ! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) )
& ! [A,B] :
( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(miniscoping,[status(thm)],[f811]) ).
fof(f813,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f812]) ).
fof(f815,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f816,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f815]) ).
fof(f817,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f816]) ).
fof(f821,plain,
? [A] :
( ( antisymmetric(A)
<~> ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) ) )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f141]) ).
fof(f822,plain,
? [A] :
( ( ? [B,C] :
( B != C
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| antisymmetric(A) )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f821]) ).
fof(f823,plain,
( ( ( sK76_skl != sK77_skl
& in(ordered_pair(sK77_skl,sK76_skl),sK75_skl)
& in(ordered_pair(sK76_skl,sK77_skl),sK75_skl) )
| ~ antisymmetric(sK75_skl) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),sK75_skl)
| ~ in(ordered_pair(B,C),sK75_skl) )
| antisymmetric(sK75_skl) )
& relation(sK75_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75_skl,sK76_skl,sK77_skl]),skolemize(A,sK75_skl),skolemize(B,sK76_skl),skolemize(C,sK77_skl)],[f822]) ).
fof(f824,plain,
relation(sK75_skl),
inference(cnf_transformation,[status(thm)],[f823]) ).
fof(f825,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(X1,X0),sK75_skl)
| ~ in(ordered_pair(X0,X1),sK75_skl)
| antisymmetric(sK75_skl) ),
inference(cnf_transformation,[status(thm)],[f823]) ).
fof(f826,plain,
( in(ordered_pair(sK76_skl,sK77_skl),sK75_skl)
| ~ antisymmetric(sK75_skl) ),
inference(cnf_transformation,[status(thm)],[f823]) ).
fof(f827,plain,
( in(ordered_pair(sK77_skl,sK76_skl),sK75_skl)
| ~ antisymmetric(sK75_skl) ),
inference(cnf_transformation,[status(thm)],[f823]) ).
fof(f828,plain,
( sK76_skl != sK77_skl
| ~ antisymmetric(sK75_skl) ),
inference(cnf_transformation,[status(thm)],[f823]) ).
fof(f839,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f145]) ).
fof(f840,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f839]) ).
fof(f842,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f840]) ).
fof(f843,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f840]) ).
fof(f844,plain,
! [A,B] :
( element(A,powerset(B))
| ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f146]) ).
fof(f845,plain,
! [A,B] :
( element(A,powerset(B))
| ( ~ in(sK78_skl(B,A),B)
& in(sK78_skl(B,A),A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl]),skolemize(C,sK78_skl(B,A))],[f844]) ).
fof(f846,plain,
! [X0,X1] :
( element(X1,powerset(X0))
| in(sK78_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f845]) ).
fof(f848,plain,
! [A,B,C] :
( ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f147]) ).
fof(f849,plain,
! [A,B,C] :
( ( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f848]) ).
fof(f850,plain,
! [C] :
( ( ! [A,B] :
( ~ in(B,A)
| ~ in(B,relation_dom(C))
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& ! [A,B] :
( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f849]) ).
fof(f851,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f850]) ).
fof(f852,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f850]) ).
fof(f853,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f850]) ).
fof(f857,plain,
( ordinal(sK80_skl)
& epsilon_connected(sK80_skl)
& epsilon_transitive(sK80_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80_skl]),skolemize(A,sK80_skl)],[f149]) ).
fof(f858,plain,
epsilon_transitive(sK80_skl),
inference(cnf_transformation,[status(thm)],[f857]) ).
fof(f859,plain,
epsilon_connected(sK80_skl),
inference(cnf_transformation,[status(thm)],[f857]) ).
fof(f861,plain,
( relation(sK81_skl)
& empty(sK81_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81_skl]),skolemize(A,sK81_skl)],[f150]) ).
fof(f862,plain,
empty(sK81_skl),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f868,plain,
empty(sK83_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl]),skolemize(A,sK83_skl)],[f152]) ).
fof(f869,plain,
empty(sK83_skl),
inference(cnf_transformation,[status(thm)],[f868]) ).
fof(f870,plain,
( function(sK84_skl)
& empty(sK84_skl)
& relation(sK84_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84_skl]),skolemize(A,sK84_skl)],[f153]) ).
fof(f872,plain,
empty(sK84_skl),
inference(cnf_transformation,[status(thm)],[f870]) ).
fof(f873,plain,
function(sK84_skl),
inference(cnf_transformation,[status(thm)],[f870]) ).
fof(f874,plain,
( ordinal(sK85_skl)
& epsilon_connected(sK85_skl)
& epsilon_transitive(sK85_skl)
& empty(sK85_skl)
& one_to_one(sK85_skl)
& function(sK85_skl)
& relation(sK85_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85_skl]),skolemize(A,sK85_skl)],[f154]) ).
fof(f875,plain,
relation(sK85_skl),
inference(cnf_transformation,[status(thm)],[f874]) ).
fof(f876,plain,
function(sK85_skl),
inference(cnf_transformation,[status(thm)],[f874]) ).
fof(f878,plain,
empty(sK85_skl),
inference(cnf_transformation,[status(thm)],[f874]) ).
fof(f880,plain,
epsilon_connected(sK85_skl),
inference(cnf_transformation,[status(thm)],[f874]) ).
fof(f885,plain,
! [A] :
( empty(sK87_skl(A))
& element(sK87_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87_skl]),skolemize(B,sK87_skl(A))],[f156]) ).
fof(f886,plain,
! [X0] : element(sK87_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f885]) ).
fof(f887,plain,
! [X0] : empty(sK87_skl(X0)),
inference(cnf_transformation,[status(thm)],[f885]) ).
fof(f894,plain,
( ordinal(sK90_skl)
& epsilon_connected(sK90_skl)
& epsilon_transitive(sK90_skl)
& ~ empty(sK90_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90_skl]),skolemize(A,sK90_skl)],[f159]) ).
fof(f896,plain,
epsilon_transitive(sK90_skl),
inference(cnf_transformation,[status(thm)],[f894]) ).
fof(f897,plain,
epsilon_connected(sK90_skl),
inference(cnf_transformation,[status(thm)],[f894]) ).
fof(f906,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f162]) ).
fof(f907,plain,
! [X0,X1] :
( union_of_subsets(X1,X0) = union(X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f906]) ).
fof(f908,plain,
! [A,B] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f163]) ).
fof(f909,plain,
! [X0,X1] :
( meet_of_subsets(X1,X0) = set_meet(X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f908]) ).
fof(f912,plain,
! [A,B] :
( ( ordinal_subset(A,B)
<=> subset(A,B) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f165]) ).
fof(f913,plain,
! [A,B] :
( ( ( ~ subset(A,B)
| ordinal_subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f912]) ).
fof(f914,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f913]) ).
fof(f915,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f913]) ).
fof(f916,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f166]) ).
fof(f917,plain,
! [A] :
( ordinal_subset(A,A)
| ! [B] : ~ ordinal(B)
| ~ ordinal(A) ),
inference(miniscoping,[status(thm)],[f916]) ).
fof(f918,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f917]) ).
fof(f921,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f168]) ).
fof(f922,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f921]) ).
fof(f928,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f932,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)],[f172]) ).
fof(f933,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)],[f932]) ).
fof(f934,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)],[f933]) ).
fof(f935,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f934]) ).
fof(f936,plain,
! [X0,X1,X2] :
( in(X1,relation_rng(X0))
| ~ in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f934]) ).
fof(f937,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_rng(X0))
| ~ in(X1,X2)
| in(X1,relation_rng(relation_rng_restriction(X2,X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f934]) ).
fof(f938,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f173]) ).
fof(f939,plain,
! [B] :
( ! [A] : subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f938]) ).
fof(f940,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f939]) ).
fof(f941,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f174]) ).
fof(f942,plain,
! [B] :
( ! [A] : subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f941]) ).
fof(f943,plain,
! [X0,X1] :
( subset(relation_rng_restriction(X1,X0),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f942]) ).
fof(f944,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f175]) ).
fof(f945,plain,
! [B] :
( ! [A] : subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f944]) ).
fof(f946,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f945]) ).
fof(f951,plain,
! [A,B] :
( relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f177]) ).
fof(f952,plain,
! [B] :
( ! [A] : relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f951]) ).
fof(f953,plain,
! [X0,X1] :
( relation_rng(relation_rng_restriction(X1,X0)) = set_intersection2(relation_rng(X0),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f952]) ).
fof(f958,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)],[f180]) ).
fof(f959,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)],[f958]) ).
fof(f960,plain,
! [A] :
( ! [C] :
( in(C,sK93_skl(A))
| are_equipotent(C,sK93_skl(A))
| ~ subset(C,sK93_skl(A)) )
& ! [C] :
( in(powerset(C),sK93_skl(A))
| ~ in(C,sK93_skl(A)) )
& ! [D] :
( in(D,sK93_skl(A))
| ! [C] :
( ~ subset(D,C)
| ~ in(C,sK93_skl(A)) ) )
& in(A,sK93_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93_skl]),skolemize(B,sK93_skl(A))],[f959]) ).
fof(f961,plain,
! [X0] : in(X0,sK93_skl(X0)),
inference(cnf_transformation,[status(thm)],[f960]) ).
fof(f962,plain,
! [X0,X1,X2] :
( in(X2,sK93_skl(X1))
| ~ subset(X2,X0)
| ~ in(X0,sK93_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f960]) ).
fof(f965,plain,
! [A,B,C] :
( relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B))
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f181]) ).
fof(f966,plain,
! [C] :
( ! [A,B] : relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B))
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f965]) ).
fof(f967,plain,
! [X0,X1,X2] :
( relation_dom_restriction(relation_rng_restriction(X1,X0),X2) = relation_rng_restriction(X1,relation_dom_restriction(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f966]) ).
fof(f968,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)],[f182]) ).
fof(f969,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)],[f968]) ).
fof(f970,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)],[f969]) ).
fof(f971,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(sK94_skl(B,A,C),B)
& in(ordered_pair(sK94_skl(B,A,C),A),C)
& in(sK94_skl(B,A,C),relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94_skl]),skolemize(D,sK94_skl(B,A,C))],[f970]) ).
fof(f972,plain,
! [X0,X1,X2] :
( in(sK94_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f971]) ).
fof(f973,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK94_skl(X2,X1,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f971]) ).
fof(f976,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f183]) ).
fof(f977,plain,
! [B] :
( ! [A] : subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f976]) ).
fof(f978,plain,
! [X0,X1] :
( subset(relation_image(X0,X1),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f977]) ).
fof(f979,plain,
! [A,B] :
( subset(relation_image(B,relation_inverse_image(B,A)),A)
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f184]) ).
fof(f980,plain,
! [B] :
( ! [A] : subset(relation_image(B,relation_inverse_image(B,A)),A)
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f979]) ).
fof(f981,plain,
! [X0,X1] :
( subset(relation_image(X0,relation_inverse_image(X0,X1)),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f980]) ).
fof(f982,plain,
! [A,B] :
( relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f185]) ).
fof(f983,plain,
! [B] :
( ! [A] : relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f982]) ).
fof(f984,plain,
! [X0,X1] :
( relation_image(X0,X1) = relation_image(X0,set_intersection2(relation_dom(X0),X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f983]) ).
fof(f985,plain,
! [A,B] :
( subset(A,relation_inverse_image(B,relation_image(B,A)))
| ~ subset(A,relation_dom(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f186]) ).
fof(f986,plain,
! [B] :
( ! [A] :
( subset(A,relation_inverse_image(B,relation_image(B,A)))
| ~ subset(A,relation_dom(B)) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f985]) ).
fof(f987,plain,
! [X0,X1] :
( subset(X1,relation_inverse_image(X0,relation_image(X0,X1)))
| ~ subset(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f986]) ).
fof(f988,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f187]) ).
fof(f989,plain,
! [X0] :
( relation_image(X0,relation_dom(X0)) = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f988]) ).
fof(f990,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)],[f188]) ).
fof(f991,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)],[f990]) ).
fof(f992,plain,
! [X0,X1] :
( relation_image(X0,relation_inverse_image(X0,X1)) = X1
| ~ subset(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f991]) ).
fof(f993,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)],[f189]) ).
fof(f994,plain,
! [X0,X1] :
( relation_rng(relation_composition(X0,X1)) = relation_image(X1,relation_rng(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f993]) ).
fof(f995,plain,
! [A,B,C] :
( ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f190]) ).
fof(f996,plain,
! [A,B,C] :
( ( ( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f995]) ).
fof(f997,plain,
! [C] :
( ( ! [A,B] :
( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& ! [A,B] :
( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f996]) ).
fof(f998,plain,
! [C] :
( ( ! [A,B] :
( ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) )
| in(A,relation_inverse_image(C,B)) )
& ! [A,B] :
( ( in(sK95_skl(B,A,C),B)
& in(ordered_pair(A,sK95_skl(B,A,C)),C)
& in(sK95_skl(B,A,C),relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95_skl]),skolemize(D,sK95_skl(B,A,C))],[f997]) ).
fof(f999,plain,
! [X0,X1,X2] :
( in(sK95_skl(X2,X1,X0),relation_rng(X0))
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f998]) ).
fof(f1003,plain,
! [A,B] :
( subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f191]) ).
fof(f1004,plain,
! [B] :
( ! [A] : subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1003]) ).
fof(f1005,plain,
! [X0,X1] :
( subset(relation_inverse_image(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1004]) ).
fof(f1006,plain,
! [A,B] :
( relation_inverse_image(B,A) != empty_set
| ~ subset(A,relation_rng(B))
| A = empty_set
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f192]) ).
fof(f1007,plain,
! [B] :
( ! [A] :
( relation_inverse_image(B,A) != empty_set
| ~ subset(A,relation_rng(B))
| A = empty_set )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1006]) ).
fof(f1008,plain,
! [X0,X1] :
( relation_inverse_image(X0,X1) != empty_set
| ~ subset(X1,relation_rng(X0))
| X1 = empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1007]) ).
fof(f1009,plain,
! [A,B,C] :
( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ subset(A,B)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f193]) ).
fof(f1010,plain,
! [C] :
( ! [A,B] :
( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ subset(A,B) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f1009]) ).
fof(f1011,plain,
! [X0,X1,X2] :
( subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2))
| ~ subset(X1,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1010]) ).
fof(f1015,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f1016,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f197]) ).
fof(f1017,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1016]) ).
fof(f1018,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f198]) ).
fof(f1019,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f1018]) ).
fof(f1020,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1019]) ).
fof(f1021,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f1026,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)],[f201]) ).
fof(f1027,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)],[f1026]) ).
fof(f1028,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)],[f1027]) ).
fof(f1031,plain,
! [X0,X1,X2] :
( ~ in(apply(X1,X2),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| in(X2,relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1028]) ).
fof(f1032,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f202]) ).
fof(f1033,plain,
! [X0,X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f1032]) ).
fof(f1034,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f203]) ).
fof(f1035,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1034]) ).
fof(f1045,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f207]) ).
fof(f1046,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1045]) ).
fof(f1047,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)],[f208]) ).
fof(f1048,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1047]) ).
fof(f1049,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1047]) ).
fof(f1063,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f1064,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)],[f215]) ).
fof(f1065,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)],[f1064]) ).
fof(f1066,plain,
! [X0,X1,X2] :
( in(X1,relation_field(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1065]) ).
fof(f1067,plain,
! [X0,X1,X2] :
( in(X2,relation_field(X0))
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1065]) ).
fof(f1068,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f216]) ).
fof(f1069,plain,
! [A] :
( ordinal(A)
| ( ( ~ subset(sK97_skl(A),A)
| ~ ordinal(sK97_skl(A)) )
& in(sK97_skl(A),A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97_skl]),skolemize(B,sK97_skl(A))],[f1068]) ).
fof(f1070,plain,
! [X0] :
( ordinal(X0)
| in(sK97_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f1069]) ).
fof(f1072,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ordinal_subset(C,D)
| ~ in(D,A)
| ~ ordinal(D) )
& in(C,A)
& ordinal(C) )
| A = empty_set
| ~ subset(A,B)
| ~ ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f217]) ).
fof(f1073,plain,
! [B] :
( ! [A] :
( ? [C] :
( ! [D] :
( ordinal_subset(C,D)
| ~ in(D,A)
| ~ ordinal(D) )
& in(C,A)
& ordinal(C) )
| A = empty_set
| ~ subset(A,B) )
| ~ ordinal(B) ),
inference(miniscoping,[status(thm)],[f1072]) ).
fof(f1074,plain,
! [B] :
( ! [A] :
( ( ! [D] :
( ordinal_subset(sK98_skl(A,B),D)
| ~ in(D,A)
| ~ ordinal(D) )
& in(sK98_skl(A,B),A)
& ordinal(sK98_skl(A,B)) )
| A = empty_set
| ~ subset(A,B) )
| ~ ordinal(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98_skl]),skolemize(C,sK98_skl(A,B))],[f1073]) ).
fof(f1076,plain,
! [X0,X1] :
( in(sK98_skl(X1,X0),X1)
| X1 = empty_set
| ~ subset(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1074]) ).
fof(f1078,plain,
! [A] :
( ! [B] :
( ( in(A,B)
<=> ordinal_subset(succ(A),B) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f218]) ).
fof(f1079,plain,
! [A] :
( ! [B] :
( ( ( ~ ordinal_subset(succ(A),B)
| in(A,B) )
& ( ordinal_subset(succ(A),B)
| ~ in(A,B) ) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f1078]) ).
fof(f1080,plain,
! [X0,X1] :
( ordinal_subset(succ(X0),X1)
| ~ in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1079]) ).
fof(f1081,plain,
! [X0,X1] :
( ~ ordinal_subset(succ(X0),X1)
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1079]) ).
fof(f1088,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)],[f221]) ).
fof(f1089,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)],[f1088]) ).
fof(f1090,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)],[f1089]) ).
fof(f1091,plain,
! [B] :
( ( ! [A] :
( ( apply(B,sK99_skl(A,B)) != sK99_skl(A,B)
& in(sK99_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,[sK99_skl]),skolemize(C,sK99_skl(A,B))],[f1090]) ).
fof(f1093,plain,
! [X0,X1,X2] :
( apply(X0,X2) = X2
| ~ in(X2,X1)
| X0 != identity_relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1091]) ).
fof(f1094,plain,
! [X0,X1] :
( in(sK99_skl(X1,X0),X1)
| relation_dom(X0) != X1
| X0 = identity_relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1091]) ).
fof(f1121,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f1122,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f231]) ).
fof(f1123,plain,
! [A,C] :
( ~ in(C,A)
| ! [B] :
( ~ in(B,C)
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f1122]) ).
fof(f1124,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1123]) ).
fof(f1129,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f233]) ).
fof(f1130,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f1129]) ).
fof(f1131,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ! [A,B] :
( ( in(sK100_skl(B,A),B)
& in(sK100_skl(B,A),A) )
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100_skl]),skolemize(C,sK100_skl(B,A))],[f1130]) ).
fof(f1132,plain,
! [X0,X1] :
( in(sK100_skl(X1,X0),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1131]) ).
fof(f1135,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f234]) ).
fof(f1136,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f1135]) ).
fof(f1137,plain,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f1138,plain,
! [A] :
( ( being_limit_ordinal(A)
<=> ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) ) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f236]) ).
fof(f1139,plain,
! [A] :
( ( ( ? [B] :
( ~ in(succ(B),A)
& in(B,A)
& ordinal(B) )
| being_limit_ordinal(A) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(NNF_transformation,[status(thm)],[f1138]) ).
fof(f1140,plain,
! [A] :
( ( ( ( ~ in(succ(sK101_skl(A)),A)
& in(sK101_skl(A),A)
& ordinal(sK101_skl(A)) )
| being_limit_ordinal(A) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101_skl]),skolemize(B,sK101_skl(A))],[f1139]) ).
fof(f1141,plain,
! [X0,X1] :
( in(succ(X1),X0)
| ~ in(X1,X0)
| ~ ordinal(X1)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1140]) ).
fof(f1145,plain,
! [A] :
( ( ( ~ being_limit_ordinal(A)
| ! [B] :
( A != succ(B)
| ~ ordinal(B) ) )
& ( ? [B] :
( A = succ(B)
& ordinal(B) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f237]) ).
fof(f1146,plain,
! [A] :
( ( ( ~ being_limit_ordinal(A)
| ! [B] :
( A != succ(B)
| ~ ordinal(B) ) )
& ( ( A = succ(sK102_skl(A))
& ordinal(sK102_skl(A)) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102_skl]),skolemize(B,sK102_skl(A))],[f1145]) ).
fof(f1149,plain,
! [X0,X1] :
( ~ being_limit_ordinal(X0)
| X0 != succ(X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1146]) ).
fof(f1154,plain,
! [A] :
( ! [B] :
( subset(relation_dom(relation_composition(A,B)),relation_dom(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f239]) ).
fof(f1155,plain,
! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1154]) ).
fof(f1156,plain,
! [A] :
( ! [B] :
( subset(relation_rng(relation_composition(A,B)),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f240]) ).
fof(f1157,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1156]) ).
fof(f1173,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f1184,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)],[f253]) ).
fof(f1185,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(f1186,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)],[f1184,f1185]) ).
fof(f1187,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)],[f1186]) ).
fof(f1188,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)],[f1187]) ).
fof(f1189,plain,
! [A] :
( ! [B] :
( ( ( ( ( sK107_skl(B,A) != apply(B,sK106_skl(B,A))
| ~ in(sK106_skl(B,A),relation_rng(A)) )
& sK106_skl(B,A) = apply(A,sK107_skl(B,A))
& in(sK107_skl(B,A),relation_dom(A)) )
| ~ sP3_prd(sK105_skl(B,A),sK104_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,[sK104_skl,sK105_skl,sK106_skl,sK107_skl]),skolemize(C,sK104_skl(B,A)),skolemize(D,sK105_skl(B,A)),skolemize(C,sK106_skl(B,A)),skolemize(D,sK107_skl(B,A))],[f1188]) ).
fof(f1194,plain,
! [X0,X1] :
( in(sK107_skl(X1,X0),relation_dom(X0))
| ~ sP3_prd(sK105_skl(X1,X0),sK104_skl(X1,X0),X1,X0)
| relation_dom(X1) != relation_rng(X0)
| X1 = function_inverse(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1189]) ).
fof(f1213,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f1214,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f1241,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f1242,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f268]) ).
fof(f1243,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1242]) ).
fof(f1249,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f271]) ).
fof(f1250,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1249]) ).
fof(f1251,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1249]) ).
fof(f1261,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f274]) ).
fof(f1262,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f1261]) ).
fof(f1263,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1262]) ).
fof(f1264,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f275]) ).
fof(f1265,plain,
! [B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f1264]) ).
fof(f1266,plain,
! [B] :
( ( ! [D] :
( ~ in(D,sK111_skl(B))
| ~ in(D,B) )
& in(sK111_skl(B),B) )
| ! [A] : ~ in(A,B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111_skl]),skolemize(C,sK111_skl(B))],[f1265]) ).
fof(f1267,plain,
! [X0,X1] :
( in(sK111_skl(X1),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1266]) ).
fof(f1269,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f276]) ).
fof(f1270,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f277]) ).
fof(f1271,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)],[f1270]) ).
fof(f1273,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1271]) ).
fof(f1280,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f279]) ).
fof(f1281,plain,
! [B] :
( ! [A] : subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1280]) ).
fof(f1282,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X0,X1),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1281]) ).
fof(f1283,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f280]) ).
fof(f1284,plain,
! [B] :
( ~ empty(B)
| ! [A] :
( A = B
| ~ empty(A) ) ),
inference(miniscoping,[status(thm)],[f1283]) ).
fof(f1285,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1284]) ).
fof(f1308,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f288]) ).
fof(f1309,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)],[f289]) ).
fof(f1310,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)],[f1309]) ).
fof(f1311,plain,
! [A] :
( ! [C] :
( in(C,sK112_skl(A))
| are_equipotent(C,sK112_skl(A))
| ~ subset(C,sK112_skl(A)) )
& ! [C] :
( ( ! [E] :
( in(E,sK113_skl(C,A))
| ~ subset(E,C) )
& in(sK113_skl(C,A),sK112_skl(A)) )
| ~ in(C,sK112_skl(A)) )
& ! [D] :
( in(D,sK112_skl(A))
| ! [C] :
( ~ subset(D,C)
| ~ in(C,sK112_skl(A)) ) )
& in(A,sK112_skl(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112_skl,sK113_skl]),skolemize(B,sK112_skl(A)),skolemize(D,sK113_skl(C,A))],[f1310]) ).
fof(f1312,plain,
! [X0] : in(X0,sK112_skl(X0)),
inference(cnf_transformation,[status(thm)],[f1311]) ).
fof(f1345,definition,
( sQ0_spl
<=> antisymmetric(sK75_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1348,definition,
! [X0,X1] :
( sQ1_spl
<=> ( X0 = X1
| ~ in(ordered_pair(X1,X0),sK75_skl)
| ~ in(ordered_pair(X0,X1),sK75_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1349,plain,
! [X0,X1] :
( ~ sQ1_spl
| X0 = X1
| ~ in(ordered_pair(X1,X0),sK75_skl)
| ~ in(ordered_pair(X0,X1),sK75_skl) ),
inference(component_clause,[status(thm)],[f1348]) ).
fof(f1351,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f825,f1345,f1348]) ).
fof(f1352,definition,
( sQ2_spl
<=> in(ordered_pair(sK76_skl,sK77_skl),sK75_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1353,plain,
( ~ sQ2_spl
| in(ordered_pair(sK76_skl,sK77_skl),sK75_skl) ),
inference(component_clause,[status(thm)],[f1352]) ).
fof(f1355,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f826,f1345,f1352]) ).
fof(f1356,definition,
( sQ3_spl
<=> in(ordered_pair(sK77_skl,sK76_skl),sK75_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1359,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f827,f1345,f1356]) ).
fof(f1360,definition,
( sQ4_spl
<=> sK76_skl = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1363,plain,
( ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f828,f1345,f1360]) ).
fof(f1364,definition,
! [X0] :
( sQ5_spl
<=> ( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1367,definition,
! [X1] :
( sQ6_spl
<=> ~ ordinal(X1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1368,plain,
! [X0] :
( ~ sQ6_spl
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f1367]) ).
fof(f1370,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f918,f1364,f1367]) ).
fof(f1373,plain,
! [X0,X1] :
( ~ in(X1,X0)
| in(ordered_pair(X1,X1),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f323]) ).
fof(f1374,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f329]) ).
fof(f1378,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f338]) ).
fof(f1379,plain,
! [X0,X1,X2] :
( sP0_prd(sK4_skl(X1,relation_image(X0,X2),X2,X0),X1,X2,X0)
| ~ in(X1,relation_image(X0,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f348]) ).
fof(f1383,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f358]) ).
fof(f1384,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f370]) ).
fof(f1385,plain,
! [X0,X1,X2] :
( in(apply(X0,X1),X2)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f371]) ).
fof(f1387,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK10_skl(X1,relation_image(X0,X2),X2,X0),X1),X0)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f380]) ).
fof(f1388,plain,
! [X0,X1,X2] :
( in(sK10_skl(X1,relation_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f381]) ).
fof(f1389,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f382]) ).
fof(f1390,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0)),X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f390]) ).
fof(f1391,plain,
! [X0,X1,X2] :
( in(sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f391]) ).
fof(f1392,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),X0)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f392]) ).
fof(f1396,plain,
! [X0,X1] :
( in(sK21_skl(X1,set_meet(X0),X0),X0)
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(destructive_equality_resolution,[status(thm)],[f430]) ).
fof(f1398,plain,
set_meet(empty_set) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f435]) ).
fof(f1400,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f440]) ).
fof(f1401,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f441]) ).
fof(f1402,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f447]) ).
fof(f1404,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f453]) ).
fof(f1406,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f482]) ).
fof(f1407,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f483]) ).
fof(f1409,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f491]) ).
fof(f1419,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK43_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f553]) ).
fof(f1420,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f554]) ).
fof(f1422,plain,
! [X0,X1] :
( in(sK48_skl(X0,union(X1),X1),X1)
| ~ in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f572]) ).
fof(f1423,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f573]) ).
fof(f1427,plain,
! [X0,X1] :
( in(sK52_skl(X1,relation_rng(X0),X0),relation_dom(X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f590]) ).
fof(f1428,plain,
! [X0,X1] :
( X1 = apply(X0,sK52_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f591]) ).
fof(f1429,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f592]) ).
fof(f1430,plain,
! [X0,X1] :
( in(ordered_pair(sK55_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f600]) ).
fof(f1431,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f601]) ).
fof(f1433,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f618]) ).
fof(f1434,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,sK62_skl(X3,X2,relation_composition(X0,X1),X1,X0)),X0)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f637]) ).
fof(f1435,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(sK62_skl(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f638]) ).
fof(f1436,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X3),X1)
| ~ in(ordered_pair(X2,X4),X0)
| in(ordered_pair(X2,X3),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f639]) ).
fof(f1443,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f1093]) ).
fof(f1444,plain,
! [X0] :
( in(sK99_skl(relation_dom(X0),X0),relation_dom(X0))
| X0 = identity_relation(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f1094]) ).
fof(f1448,plain,
! [X0] :
( ~ being_limit_ordinal(succ(X0))
| ~ ordinal(X0)
| ~ ordinal(succ(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f1149]) ).
fof(f1467,plain,
! [X0] :
( ~ in(X0,X0)
| ~ in(X0,X0) ),
inference(factoring,[status(thm)],[f1124]) ).
fof(f1468,plain,
! [X0] : ~ in(X0,X0),
inference(duplicate_literals_removal,[status(thm)],[f1467]) ).
fof(f1476,plain,
function(sK81_skl),
inference(resolution,[status(thm)],[f862,f296]) ).
fof(f1477,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f301]) ).
fof(f1478,plain,
( one_to_one(sK81_skl)
| ~ function(sK81_skl) ),
inference(resolution,[status(thm)],[f1477,f862]) ).
fof(f1479,plain,
( one_to_one(empty_set)
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f1477,f706]) ).
fof(f1480,definition,
( sQ7_spl
<=> function(sK81_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1482,plain,
( sQ7_spl
| ~ function(sK81_skl) ),
inference(component_clause,[status(thm)],[f1480]) ).
fof(f1483,definition,
( sQ8_spl
<=> one_to_one(sK81_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1486,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1478,f1480,f1483]) ).
fof(f1487,definition,
( sQ9_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1489,plain,
( sQ9_spl
| ~ function(empty_set) ),
inference(component_clause,[status(thm)],[f1487]) ).
fof(f1490,definition,
( sQ10_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1493,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1479,f1487,f1490]) ).
fof(f1494,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1489,f727]) ).
fof(f1495,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1494]) ).
fof(f1496,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(X0,ordered_pair(sK76_skl,sK77_skl))
| ~ in(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f1353,f1124]) ).
fof(f1502,plain,
( ordinal(sK80_skl)
| ~ epsilon_connected(sK80_skl) ),
inference(resolution,[status(thm)],[f307,f858]) ).
fof(f1503,plain,
( ordinal(empty_set)
| ~ epsilon_connected(empty_set) ),
inference(resolution,[status(thm)],[f307,f730]) ).
fof(f1504,definition,
( sQ11_spl
<=> epsilon_connected(sK80_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1506,plain,
( sQ11_spl
| ~ epsilon_connected(sK80_skl) ),
inference(component_clause,[status(thm)],[f1504]) ).
fof(f1507,definition,
( sQ12_spl
<=> ordinal(sK80_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1510,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1502,f1504,f1507]) ).
fof(f1511,definition,
( sQ13_spl
<=> epsilon_connected(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1513,plain,
( sQ13_spl
| ~ epsilon_connected(empty_set) ),
inference(component_clause,[status(thm)],[f1511]) ).
fof(f1514,definition,
( sQ14_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1517,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1503,f1511,f1514]) ).
fof(f1518,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1513,f731]) ).
fof(f1519,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f1518]) ).
fof(f1520,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1506,f859]) ).
fof(f1521,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f1520]) ).
fof(f1522,plain,
epsilon_transitive(sK81_skl),
inference(resolution,[status(thm)],[f309,f862]) ).
fof(f1524,plain,
epsilon_transitive(sK83_skl),
inference(resolution,[status(thm)],[f869,f309]) ).
fof(f1525,plain,
( one_to_one(sK83_skl)
| ~ function(sK83_skl) ),
inference(resolution,[status(thm)],[f869,f1477]) ).
fof(f1527,plain,
function(sK83_skl),
inference(resolution,[status(thm)],[f869,f296]) ).
fof(f1528,definition,
( sQ15_spl
<=> function(sK83_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1530,plain,
( sQ15_spl
| ~ function(sK83_skl) ),
inference(component_clause,[status(thm)],[f1528]) ).
fof(f1531,definition,
( sQ16_spl
<=> one_to_one(sK83_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1534,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1525,f1528,f1531]) ).
fof(f1535,plain,
epsilon_transitive(sK84_skl),
inference(resolution,[status(thm)],[f872,f309]) ).
fof(f1536,plain,
( one_to_one(sK84_skl)
| ~ function(sK84_skl) ),
inference(resolution,[status(thm)],[f872,f1477]) ).
fof(f1539,definition,
( sQ17_spl
<=> function(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f1541,plain,
( sQ17_spl
| ~ function(sK84_skl) ),
inference(component_clause,[status(thm)],[f1539]) ).
fof(f1542,definition,
( sQ18_spl
<=> one_to_one(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f1545,plain,
( sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1536,f1539,f1542]) ).
fof(f1547,plain,
( one_to_one(sK85_skl)
| ~ function(sK85_skl) ),
inference(resolution,[status(thm)],[f878,f1477]) ).
fof(f1550,definition,
( sQ19_spl
<=> function(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f1552,plain,
( sQ19_spl
| ~ function(sK85_skl) ),
inference(component_clause,[status(thm)],[f1550]) ).
fof(f1553,definition,
( sQ20_spl
<=> one_to_one(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1556,plain,
( sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1547,f1550,f1553]) ).
fof(f1557,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1552,f876]) ).
fof(f1558,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f1557]) ).
fof(f1560,definition,
( sQ21_spl
<=> epsilon_connected(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1562,plain,
( sQ21_spl
| ~ epsilon_connected(sK85_skl) ),
inference(component_clause,[status(thm)],[f1560]) ).
fof(f1563,definition,
( sQ22_spl
<=> ordinal(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1570,plain,
epsilon_connected(sK84_skl),
inference(resolution,[status(thm)],[f310,f872]) ).
fof(f1571,plain,
epsilon_connected(sK83_skl),
inference(resolution,[status(thm)],[f310,f869]) ).
fof(f1572,plain,
epsilon_connected(sK81_skl),
inference(resolution,[status(thm)],[f310,f862]) ).
fof(f1583,plain,
( ordinal(sK90_skl)
| ~ epsilon_connected(sK90_skl) ),
inference(resolution,[status(thm)],[f896,f307]) ).
fof(f1584,definition,
( sQ23_spl
<=> epsilon_connected(sK90_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1586,plain,
( sQ23_spl
| ~ epsilon_connected(sK90_skl) ),
inference(component_clause,[status(thm)],[f1584]) ).
fof(f1587,definition,
( sQ24_spl
<=> ordinal(sK90_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1590,plain,
( sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1583,f1584,f1587]) ).
fof(f1601,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1482,f1476]) ).
fof(f1602,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1601]) ).
fof(f1603,plain,
( ordinal(sK81_skl)
| ~ epsilon_connected(sK81_skl) ),
inference(resolution,[status(thm)],[f1522,f307]) ).
fof(f1604,definition,
( sQ25_spl
<=> epsilon_connected(sK81_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f1606,plain,
( sQ25_spl
| ~ epsilon_connected(sK81_skl) ),
inference(component_clause,[status(thm)],[f1604]) ).
fof(f1607,definition,
( sQ26_spl
<=> ordinal(sK81_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1610,plain,
( sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f1603,f1604,f1607]) ).
fof(f1611,plain,
( ordinal(sK83_skl)
| ~ epsilon_connected(sK83_skl) ),
inference(resolution,[status(thm)],[f1524,f307]) ).
fof(f1612,definition,
( sQ27_spl
<=> epsilon_connected(sK83_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1614,plain,
( sQ27_spl
| ~ epsilon_connected(sK83_skl) ),
inference(component_clause,[status(thm)],[f1612]) ).
fof(f1615,definition,
( sQ28_spl
<=> ordinal(sK83_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1618,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1611,f1612,f1615]) ).
fof(f1619,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1530,f1527]) ).
fof(f1620,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1619]) ).
fof(f1621,plain,
( ordinal(sK84_skl)
| ~ epsilon_connected(sK84_skl) ),
inference(resolution,[status(thm)],[f1535,f307]) ).
fof(f1622,definition,
( sQ29_spl
<=> epsilon_connected(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1624,plain,
( sQ29_spl
| ~ epsilon_connected(sK84_skl) ),
inference(component_clause,[status(thm)],[f1622]) ).
fof(f1625,definition,
( sQ30_spl
<=> ordinal(sK84_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1628,plain,
( sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1621,f1622,f1625]) ).
fof(f1629,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1541,f873]) ).
fof(f1630,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f1629]) ).
fof(f1631,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1562,f880]) ).
fof(f1632,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1631]) ).
fof(f1637,plain,
! [X0,X1,X2] :
( ~ in(X2,ordered_pair(X1,X1))
| ~ in(identity_relation(X0),X2)
| ~ in(X1,X0)
| ~ relation(identity_relation(X0)) ),
inference(resolution,[status(thm)],[f1373,f1124]) ).
fof(f1644,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1586,f897]) ).
fof(f1645,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f1644]) ).
fof(f1646,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1606,f1572]) ).
fof(f1647,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f1646]) ).
fof(f1648,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1614,f1571]) ).
fof(f1649,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1648]) ).
fof(f1650,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1624,f1570]) ).
fof(f1651,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1650]) ).
fof(f1652,plain,
! [X0,X1,X2] :
( ~ in(X2,ordered_pair(X0,X0))
| ~ in(identity_relation(X1),X2)
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f1637,f685]) ).
fof(f1657,plain,
! [X0] :
( in(sK0_skl(X0,empty_set),X0)
| empty_set = identity_relation(X0)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f325,f1402]) ).
fof(f1664,definition,
( sQ31_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1666,plain,
( sQ31_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f1664]) ).
fof(f1667,definition,
! [X0] :
( sQ32_spl
<=> ( in(sK0_skl(X0,empty_set),X0)
| empty_set = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1670,plain,
( sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1657,f1664,f1667]) ).
fof(f1685,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1666,f707]) ).
fof(f1686,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1685]) ).
fof(f1696,plain,
! [X0] :
( sK0_skl(X0,empty_set) = sK1_skl(X0,empty_set)
| empty_set = identity_relation(X0)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f326,f1402]) ).
fof(f1703,definition,
! [X0] :
( sQ37_spl
<=> ( sK0_skl(X0,empty_set) = sK1_skl(X0,empty_set)
| empty_set = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1706,plain,
( sQ37_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1696,f1664,f1703]) ).
fof(f1731,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,ordered_pair(X2,X3))
| ~ in(relation_dom_restriction(X0,X1),X4)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1378,f1124]) ).
fof(f1733,plain,
! [X0,X1,X2,X3] :
( ~ in(relation_dom_restriction(X0,X1),ordered_pair(X2,X3))
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1378,f292]) ).
fof(f1741,plain,
! [X0] : ~ in(succ(X0),X0),
inference(resolution,[status(thm)],[f928,f292]) ).
fof(f1746,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f313,f1015]) ).
fof(f1751,plain,
! [X0] : sK87_skl(X0) = empty_set,
inference(resolution,[status(thm)],[f1243,f887]) ).
fof(f1752,plain,
sK85_skl = empty_set,
inference(resolution,[status(thm)],[f1243,f878]) ).
fof(f1762,plain,
! [X0,X1] :
( in(sK2_skl(X1,empty_set,X0),X1)
| empty_set = relation_dom_restriction(X0,X1)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f340,f1402]) ).
fof(f1773,definition,
! [X0,X1] :
( sQ40_spl
<=> ( in(sK2_skl(X1,empty_set,X0),X1)
| empty_set = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1776,plain,
( ~ sQ31_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1762,f1773,f1664]) ).
fof(f1788,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,empty_set,X0),sK3_skl(X1,empty_set,X0)),X0)
| empty_set = relation_dom_restriction(X0,X1)
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f341,f1402]) ).
fof(f1799,definition,
! [X0,X1] :
( sQ43_spl
<=> ( in(ordered_pair(sK2_skl(X1,empty_set,X0),sK3_skl(X1,empty_set,X0)),X0)
| empty_set = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1802,plain,
( ~ sQ31_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f1788,f1799,f1664]) ).
fof(f1819,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ in(X1,ordered_pair(sK76_skl,sK77_skl))
| ~ in(relation_dom_restriction(sK75_skl,X0),X1)
| ~ in(sK76_skl,X0)
| ~ relation(relation_dom_restriction(sK75_skl,X0))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1731,f1353]) ).
fof(f1828,definition,
( sQ46_spl
<=> relation(sK75_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1830,plain,
( sQ46_spl
| ~ relation(sK75_skl) ),
inference(component_clause,[status(thm)],[f1828]) ).
fof(f1835,definition,
! [X0,X1] :
( sQ48_spl
<=> ( ~ in(X1,ordered_pair(sK76_skl,sK77_skl))
| ~ in(relation_dom_restriction(sK75_skl,X0),X1)
| ~ in(sK76_skl,X0)
| ~ relation(relation_dom_restriction(sK75_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1838,plain,
( ~ sQ2_spl
| sQ48_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1819,f1828,f1835,f1352]) ).
fof(f1840,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1830,f824]) ).
fof(f1841,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f1840]) ).
fof(f1870,plain,
relation_rng(empty_set) = sK85_skl,
inference(backward_demodulation,[status(thm)],[f1752,f1214]) ).
fof(f1871,plain,
relation_dom(empty_set) = sK85_skl,
inference(backward_demodulation,[status(thm)],[f1752,f1213]) ).
fof(f1872,plain,
! [X0] : set_difference(X0,sK85_skl) = X0,
inference(backward_demodulation,[status(thm)],[f1752,f1121]) ).
fof(f1874,plain,
set_meet(empty_set) = sK85_skl,
inference(backward_demodulation,[status(thm)],[f1752,f1398]) ).
fof(f1875,plain,
! [X0] : subset(sK85_skl,X0),
inference(backward_demodulation,[status(thm)],[f1752,f1063]) ).
fof(f1876,plain,
! [X0] : singleton(X0) != sK85_skl,
inference(backward_demodulation,[status(thm)],[f1752,f796]) ).
fof(f1877,plain,
! [X0] : ~ in(X0,sK85_skl),
inference(backward_demodulation,[status(thm)],[f1752,f1402]) ).
fof(f1886,plain,
relation_rng(sK85_skl) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f1752,f1870]) ).
fof(f1887,plain,
relation_dom(sK85_skl) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f1752,f1871]) ).
fof(f1888,plain,
set_meet(sK85_skl) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f1752,f1874]) ).
fof(f1919,plain,
! [X0] : sK87_skl(X0) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f1752,f1751]) ).
fof(f1921,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,sK85_skl,X0),sK3_skl(X1,sK85_skl,X0)),X0)
| sK85_skl = relation_dom_restriction(X0,X1)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1877,f341]) ).
fof(f1922,plain,
! [X0,X1] :
( in(sK2_skl(X1,sK85_skl,X0),X1)
| sK85_skl = relation_dom_restriction(X0,X1)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1877,f340]) ).
fof(f1923,plain,
! [X0] :
( sK0_skl(X0,sK85_skl) = sK1_skl(X0,sK85_skl)
| sK85_skl = identity_relation(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1877,f326]) ).
fof(f1924,plain,
! [X0] :
( in(sK0_skl(X0,sK85_skl),X0)
| sK85_skl = identity_relation(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1877,f325]) ).
fof(f1925,definition,
! [X0,X1] :
( sQ53_spl
<=> ( in(ordered_pair(sK2_skl(X1,sK85_skl,X0),sK3_skl(X1,sK85_skl,X0)),X0)
| sK85_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1928,definition,
( sQ54_spl
<=> relation(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1930,plain,
( sQ54_spl
| ~ relation(sK85_skl) ),
inference(component_clause,[status(thm)],[f1928]) ).
fof(f1931,plain,
( ~ sQ54_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f1921,f1925,f1928]) ).
fof(f1932,definition,
! [X0,X1] :
( sQ55_spl
<=> ( in(sK2_skl(X1,sK85_skl,X0),X1)
| sK85_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1935,plain,
( ~ sQ54_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1922,f1932,f1928]) ).
fof(f1936,definition,
! [X0] :
( sQ56_spl
<=> ( sK0_skl(X0,sK85_skl) = sK1_skl(X0,sK85_skl)
| sK85_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1939,plain,
( sQ56_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1923,f1928,f1936]) ).
fof(f1940,definition,
! [X0] :
( sQ57_spl
<=> ( in(sK0_skl(X0,sK85_skl),X0)
| sK85_skl = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1943,plain,
( sQ57_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1924,f1928,f1940]) ).
fof(f1944,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1930,f875]) ).
fof(f1945,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f1944]) ).
fof(f1964,plain,
! [X0] : set_union2(sK85_skl,X0) = X0,
inference(forward_demodulation,[status(thm)],[f1752,f1746]) ).
fof(f2033,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(unordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f1407,f1124]) ).
fof(f2035,plain,
! [X0,X1] : ~ in(unordered_pair(X0,X1),X1),
inference(resolution,[status(thm)],[f1407,f292]) ).
fof(f2038,plain,
! [X0] :
( powerset(X0) = X0
| ~ being_limit_ordinal(powerset(X0)) ),
inference(paramodulation,[status(thm)],[f1308,f609]) ).
fof(f2058,plain,
! [X0] : set_difference(sK85_skl,X0) = empty_set,
inference(forward_demodulation,[status(thm)],[f1752,f1173]) ).
fof(f2059,plain,
! [X0] : set_difference(sK85_skl,X0) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f1752,f2058]) ).
fof(f2086,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(paramodulation,[status(thm)],[f313,f1269]) ).
fof(f2093,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,ordered_pair(X3,X2))
| ~ in(relation_rng_restriction(X1,X0),X4)
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1)
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1383,f1124]) ).
fof(f2095,plain,
! [X0,X1,X2,X3] :
( ~ in(relation_rng_restriction(X1,X0),ordered_pair(X3,X2))
| ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1)
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1383,f292]) ).
fof(f2110,plain,
! [X0,X1] :
( in(sK8_skl(X1,sK85_skl,X0),X1)
| sK85_skl = relation_rng_restriction(X1,X0)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f360,f1877]) ).
fof(f2129,definition,
! [X0,X1] :
( sQ59_spl
<=> ( in(sK8_skl(X1,sK85_skl,X0),X1)
| sK85_skl = relation_rng_restriction(X1,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f2132,plain,
( ~ sQ54_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f2110,f2129,f1928]) ).
fof(f2180,plain,
! [X0,X1,X2] : ~ in(unordered_pair(unordered_pair(X0,X1),X2),X1),
inference(resolution,[status(thm)],[f2033,f1406]) ).
fof(f2215,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f567,f676]) ).
fof(f2224,plain,
! [X0,X1] :
( in(ordered_pair(sK7_skl(X1,sK85_skl,X0),sK8_skl(X1,sK85_skl,X0)),X0)
| sK85_skl = relation_rng_restriction(X1,X0)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f361,f1877]) ).
fof(f2243,definition,
! [X0,X1] :
( sQ61_spl
<=> ( in(ordered_pair(sK7_skl(X1,sK85_skl,X0),sK8_skl(X1,sK85_skl,X0)),X0)
| sK85_skl = relation_rng_restriction(X1,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f2246,plain,
( ~ sQ54_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f2224,f2243,f1928]) ).
fof(f2319,definition,
( sQ62_spl
<=> empty(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2321,plain,
( sQ62_spl
| ~ empty(sK85_skl) ),
inference(component_clause,[status(thm)],[f2319]) ).
fof(f2348,plain,
! [X0,X1,X2] :
( ~ in(relation_dom(X0),sK9_skl(X1,X2,X0))
| in(sK9_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f374,f292]) ).
fof(f2349,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK85_skl),sK85_skl)
| in(sK9_skl(X0,X1,sK85_skl),X0)
| X0 = relation_inverse_image(sK85_skl,X1)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f374]) ).
fof(f2351,definition,
! [X0,X1] :
( sQ63_spl
<=> ( in(sK9_skl(X0,X1,sK85_skl),sK85_skl)
| in(sK9_skl(X0,X1,sK85_skl),X0)
| X0 = relation_inverse_image(sK85_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2354,plain,
( sQ63_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2349,f1928,f1550,f2351]) ).
fof(f2393,plain,
! [X0] : element(sK85_skl,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f1919,f886]) ).
fof(f2415,plain,
powerset(sK85_skl) = singleton(empty_set),
inference(forward_demodulation,[status(thm)],[f1752,f1021]) ).
fof(f2416,plain,
powerset(sK85_skl) = singleton(sK85_skl),
inference(forward_demodulation,[status(thm)],[f1752,f2415]) ).
fof(f2418,plain,
! [X0] :
( X0 = sK85_skl
| ~ in(X0,powerset(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f2416,f1400]) ).
fof(f2422,plain,
powerset(sK85_skl) != sK85_skl,
inference(paramodulation,[status(thm)],[f2416,f1876]) ).
fof(f2428,plain,
in(sK85_skl,powerset(sK85_skl)),
inference(paramodulation,[status(thm)],[f2416,f1401]) ).
fof(f2430,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1752,f1136]) ).
fof(f2431,plain,
! [X0] :
( X0 = sK85_skl
| ~ subset(X0,sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1752,f2430]) ).
fof(f2466,plain,
! [X0,X1] :
( ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1387,f1877]) ).
fof(f2474,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1387,f1263]) ).
fof(f2475,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,ordered_pair(sK10_skl(X1,relation_image(X0,X2),X2,X0),X1))
| ~ in(X0,X3)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1387,f1124]) ).
fof(f2477,plain,
! [X0,X1,X2] :
( ~ in(X0,ordered_pair(sK10_skl(X1,relation_image(X0,X2),X2,X0),X1))
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1387,f292]) ).
fof(f2488,definition,
! [X0,X1] :
( sQ65_spl
<=> ~ in(X0,relation_image(sK85_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2489,plain,
! [X0,X1] :
( ~ sQ65_spl
| ~ in(X0,relation_image(sK85_skl,X1)) ),
inference(component_clause,[status(thm)],[f2488]) ).
fof(f2491,plain,
( sQ65_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2466,f1928,f2488]) ).
fof(f2492,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| ~ in(X0,relation_image(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2474,f301]) ).
fof(f2502,plain,
! [X0,X1,X2,X3] :
( ~ in(identity_relation(X3),sK10_skl(X1,relation_image(X0,ordered_pair(X2,X2)),ordered_pair(X2,X2),X0))
| ~ in(X2,X3)
| ~ in(X1,relation_image(X0,ordered_pair(X2,X2)))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1388,f1652]) ).
fof(f2505,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,sK10_skl(X1,relation_image(X0,X2),X2,X0))
| ~ in(X2,X3)
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1388,f1124]) ).
fof(f2507,plain,
! [X0,X1,X2] :
( ~ in(X2,sK10_skl(X1,relation_image(X0,X2),X2,X0))
| ~ in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1388,f292]) ).
fof(f2517,plain,
! [X0,X1] :
( ~ in(sK85_skl,sK9_skl(X0,X1,sK85_skl))
| in(sK9_skl(X0,X1,sK85_skl),X0)
| X0 = relation_inverse_image(sK85_skl,X1)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f2348]) ).
fof(f2519,definition,
! [X0,X1] :
( sQ66_spl
<=> ( ~ in(sK85_skl,sK9_skl(X0,X1,sK85_skl))
| in(sK9_skl(X0,X1,sK85_skl),X0)
| X0 = relation_inverse_image(sK85_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2522,plain,
( sQ66_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2517,f1928,f1550,f2519]) ).
fof(f2553,definition,
( sQ67_spl
<=> sK85_skl = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2557,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2321,f878]) ).
fof(f2558,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f2557]) ).
fof(f2607,plain,
! [X0,X1] :
( in(sK11_skl(X0,X1,sK85_skl),X0)
| X0 = relation_image(sK85_skl,X1)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f384,f1877]) ).
fof(f2632,definition,
! [X0,X1] :
( sQ69_spl
<=> ( in(sK11_skl(X0,X1,sK85_skl),X0)
| X0 = relation_image(sK85_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2635,plain,
( sQ69_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2607,f1928,f2632]) ).
fof(f2680,definition,
( sQ70_spl
<=> epsilon_transitive(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f2745,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1390,f1877]) ).
fof(f2757,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,ordered_pair(X1,sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0)))
| ~ in(X0,X3)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1390,f1124]) ).
fof(f2759,plain,
! [X0,X1,X2] :
( ~ in(X0,ordered_pair(X1,sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0)))
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1390,f292]) ).
fof(f2771,definition,
! [X0,X1] :
( sQ72_spl
<=> ~ in(X0,relation_inverse_image(sK85_skl,X1)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f2772,plain,
! [X0,X1] :
( ~ sQ72_spl
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ),
inference(component_clause,[status(thm)],[f2771]) ).
fof(f2774,plain,
( sQ72_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2745,f1928,f2771]) ).
fof(f2791,plain,
! [X0,X1,X2,X3] :
( ~ in(identity_relation(X3),sK13_skl(X1,relation_inverse_image(X0,ordered_pair(X2,X2)),ordered_pair(X2,X2),X0))
| ~ in(X2,X3)
| ~ in(X1,relation_inverse_image(X0,ordered_pair(X2,X2)))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1391,f1652]) ).
fof(f2794,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0))
| ~ in(X2,X3)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1391,f1124]) ).
fof(f2796,plain,
! [X0,X1,X2] :
( ~ in(X2,sK13_skl(X1,relation_inverse_image(X0,X2),X2,X0))
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1391,f292]) ).
fof(f2908,plain,
! [X0,X1] :
( in(sK14_skl(X0,X1,sK85_skl),X0)
| X0 = relation_inverse_image(sK85_skl,X1)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f394,f1877]) ).
fof(f2936,definition,
! [X0,X1] :
( sQ74_spl
<=> ( in(sK14_skl(X0,X1,sK85_skl),X0)
| X0 = relation_inverse_image(sK85_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f2939,plain,
( sQ74_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2908,f1928,f2936]) ).
fof(f2995,plain,
succ(sK85_skl) = singleton(sK85_skl),
inference(paramodulation,[status(thm)],[f1964,f410]) ).
fof(f2999,plain,
! [X0] : subset(X0,succ(X0)),
inference(paramodulation,[status(thm)],[f410,f1269]) ).
fof(f3000,plain,
succ(sK85_skl) = powerset(sK85_skl),
inference(forward_demodulation,[status(thm)],[f2416,f2995]) ).
fof(f3006,plain,
( ordinal(powerset(sK85_skl))
| ~ ordinal(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3000,f746]) ).
fof(f3007,plain,
( epsilon_connected(powerset(sK85_skl))
| ~ ordinal(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3000,f745]) ).
fof(f3008,plain,
( epsilon_transitive(powerset(sK85_skl))
| ~ ordinal(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3000,f744]) ).
fof(f3019,definition,
( sQ75_spl
<=> ordinal(powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f3020,plain,
( ~ sQ75_spl
| ordinal(powerset(sK85_skl)) ),
inference(component_clause,[status(thm)],[f3019]) ).
fof(f3022,plain,
( sQ75_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f3006,f1563,f3019]) ).
fof(f3023,definition,
( sQ76_spl
<=> epsilon_connected(powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f3026,plain,
( sQ76_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f3007,f1563,f3023]) ).
fof(f3027,definition,
( sQ77_spl
<=> epsilon_transitive(powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f3030,plain,
( sQ77_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f3008,f1563,f3027]) ).
fof(f3045,plain,
! [X0,X1,X2] :
( ~ in(X2,sK19_skl(sK13_skl(X0,relation_inverse_image(X1,X2),X2,X1)))
| ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| relation(sK13_skl(X0,relation_inverse_image(X1,X2),X2,X1)) ),
inference(resolution,[status(thm)],[f416,f2794]) ).
fof(f3048,plain,
! [X0,X1,X2] :
( ~ in(X2,sK19_skl(sK10_skl(X0,relation_image(X1,X2),X2,X1)))
| ~ in(X0,relation_image(X1,X2))
| ~ relation(X1)
| relation(sK10_skl(X0,relation_image(X1,X2),X2,X1)) ),
inference(resolution,[status(thm)],[f416,f2505]) ).
fof(f3068,plain,
! [X0,X1] :
( ~ in(X1,sK19_skl(X0))
| ~ in(X0,X1)
| relation(X0) ),
inference(resolution,[status(thm)],[f416,f1124]) ).
fof(f3102,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_inverse_image(X2,sK19_skl(X0)))
| ~ relation(X2)
| ~ in(X0,sK13_skl(X1,relation_inverse_image(X2,sK19_skl(X0)),sK19_skl(X0),X2))
| relation(X0) ),
inference(resolution,[status(thm)],[f3068,f1391]) ).
fof(f3104,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_image(X2,sK19_skl(X0)))
| ~ relation(X2)
| ~ in(X0,sK10_skl(X1,relation_image(X2,sK19_skl(X0)),sK19_skl(X0),X2))
| relation(X0) ),
inference(resolution,[status(thm)],[f3068,f1388]) ).
fof(f3164,plain,
! [X0] :
( in(sK25_skl(X0),X0)
| X0 = sK85_skl ),
inference(forward_demodulation,[status(thm)],[f1752,f448]) ).
fof(f3167,plain,
! [X0] :
( ~ sQ65_spl
| relation_image(sK85_skl,X0) = sK85_skl ),
inference(resolution,[status(thm)],[f3164,f2489]) ).
fof(f3173,plain,
! [X0] :
( ~ sQ72_spl
| relation_inverse_image(sK85_skl,X0) = sK85_skl ),
inference(resolution,[status(thm)],[f3164,f2772]) ).
fof(f3176,plain,
! [X0] :
( sK25_skl(singleton(X0)) = X0
| singleton(X0) = sK85_skl ),
inference(resolution,[status(thm)],[f3164,f1400]) ).
fof(f3192,plain,
! [X0] :
( element(sK25_skl(X0),X0)
| X0 = sK85_skl ),
inference(resolution,[status(thm)],[f3164,f1017]) ).
fof(f3194,plain,
! [X0,X1] :
( ~ in(X1,sK25_skl(X0))
| ~ in(X0,X1)
| X0 = sK85_skl ),
inference(resolution,[status(thm)],[f3164,f1124]) ).
fof(f3196,plain,
! [X0] :
( ~ in(X0,sK25_skl(X0))
| X0 = sK85_skl ),
inference(resolution,[status(thm)],[f3164,f292]) ).
fof(f3197,plain,
! [X0] : sK25_skl(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f3176,f1876]) ).
fof(f3198,plain,
sK25_skl(powerset(sK85_skl)) = sK85_skl,
inference(paramodulation,[status(thm)],[f2416,f3197]) ).
fof(f3202,plain,
! [X0,X1] :
( ~ sQ65_spl
| ~ in(X1,relation_image(sK85_skl,sK19_skl(X0)))
| ~ relation(sK85_skl)
| ~ in(X0,sK10_skl(X1,sK85_skl,sK19_skl(X0),sK85_skl))
| relation(X0) ),
inference(paramodulation,[status(thm)],[f3167,f3104]) ).
fof(f3203,plain,
! [X0,X1,X2] :
( ~ sQ65_spl
| ~ in(identity_relation(X2),sK10_skl(X0,sK85_skl,ordered_pair(X1,X1),sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_image(sK85_skl,ordered_pair(X1,X1)))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f2502]) ).
fof(f3204,plain,
! [X0,X1] :
( ~ sQ65_spl
| ~ in(X1,sK19_skl(sK10_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl)
| relation(sK10_skl(X0,relation_image(sK85_skl,X1),X1,sK85_skl)) ),
inference(paramodulation,[status(thm)],[f3167,f3048]) ).
fof(f3205,plain,
! [X0,X1,X2] :
( ~ sQ65_spl
| ~ in(X2,ordered_pair(sK10_skl(X0,sK85_skl,X1,sK85_skl),X0))
| ~ in(sK85_skl,X2)
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f2475]) ).
fof(f3206,plain,
! [X0,X1,X2] :
( ~ sQ65_spl
| ~ in(X2,sK10_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f2505]) ).
fof(f3207,plain,
! [X0,X1] :
( ~ sQ65_spl
| ~ in(sK85_skl,ordered_pair(sK10_skl(X0,sK85_skl,X1,sK85_skl),X0))
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f2477]) ).
fof(f3208,plain,
! [X0,X1] :
( ~ sQ65_spl
| ~ in(X1,sK10_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f2507]) ).
fof(f3209,plain,
! [X0,X1] :
( ~ sQ65_spl
| in(sK10_skl(X0,sK85_skl,X1,sK85_skl),X1)
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f1388]) ).
fof(f3210,plain,
! [X0,X1] :
( ~ sQ65_spl
| in(ordered_pair(sK10_skl(X0,sK85_skl,X1,sK85_skl),X0),sK85_skl)
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f1387]) ).
fof(f3211,plain,
! [X0,X1] :
( ~ sQ65_spl
| sP0_prd(sK4_skl(X0,sK85_skl,X1,sK85_skl),X0,X1,sK85_skl)
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f1379]) ).
fof(f3212,definition,
! [X0,X1] :
( sQ78_spl
<=> ( ~ in(X1,relation_image(sK85_skl,sK19_skl(X0)))
| ~ in(X0,sK10_skl(X1,sK85_skl,sK19_skl(X0),sK85_skl))
| relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f3215,plain,
( ~ sQ65_spl
| ~ sQ54_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f3202,f3212,f1928,f2488]) ).
fof(f3216,definition,
! [X0,X1,X2] :
( sQ79_spl
<=> ( ~ in(identity_relation(X2),sK10_skl(X0,sK85_skl,ordered_pair(X1,X1),sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_image(sK85_skl,ordered_pair(X1,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f3219,plain,
( ~ sQ65_spl
| sQ79_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3203,f1928,f3216,f2488]) ).
fof(f3220,definition,
! [X0,X1] :
( sQ80_spl
<=> ( ~ in(X1,sK19_skl(sK10_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(X0,relation_image(sK85_skl,X1))
| relation(sK10_skl(X0,relation_image(sK85_skl,X1),X1,sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f3223,plain,
( ~ sQ65_spl
| ~ sQ54_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f3204,f3220,f1928,f2488]) ).
fof(f3224,definition,
! [X0,X1,X2] :
( sQ81_spl
<=> ( ~ in(X2,ordered_pair(sK10_skl(X0,sK85_skl,X1,sK85_skl),X0))
| ~ in(sK85_skl,X2)
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f3227,plain,
( ~ sQ65_spl
| sQ81_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3205,f1928,f3224,f2488]) ).
fof(f3228,definition,
! [X0,X1,X2] :
( sQ82_spl
<=> ( ~ in(X2,sK10_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f3231,plain,
( ~ sQ65_spl
| sQ82_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3206,f1928,f3228,f2488]) ).
fof(f3232,definition,
! [X0,X1] :
( sQ83_spl
<=> ( ~ in(sK85_skl,ordered_pair(sK10_skl(X0,sK85_skl,X1,sK85_skl),X0))
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f3235,plain,
( ~ sQ65_spl
| sQ83_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3207,f1928,f3232,f2488]) ).
fof(f3236,definition,
! [X0,X1] :
( sQ84_spl
<=> ( ~ in(X1,sK10_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f3239,plain,
( ~ sQ65_spl
| sQ84_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3208,f1928,f3236,f2488]) ).
fof(f3240,definition,
! [X0,X1] :
( sQ85_spl
<=> ( in(sK10_skl(X0,sK85_skl,X1,sK85_skl),X1)
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f3243,plain,
( ~ sQ65_spl
| sQ85_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3209,f1928,f3240,f2488]) ).
fof(f3244,definition,
! [X0,X1] :
( sQ86_spl
<=> ( in(ordered_pair(sK10_skl(X0,sK85_skl,X1,sK85_skl),X0),sK85_skl)
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f3247,plain,
( ~ sQ65_spl
| sQ86_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3210,f1928,f3244,f2488]) ).
fof(f3248,definition,
! [X0,X1] :
( sQ87_spl
<=> ( sP0_prd(sK4_skl(X0,sK85_skl,X1,sK85_skl),X0,X1,sK85_skl)
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f3251,plain,
( ~ sQ65_spl
| sQ87_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3211,f1928,f1550,f3248,f2488]) ).
fof(f3266,plain,
! [X0,X1] :
( ~ sQ72_spl
| ~ in(X1,relation_inverse_image(sK85_skl,sK19_skl(X0)))
| ~ relation(sK85_skl)
| ~ in(X0,sK13_skl(X1,sK85_skl,sK19_skl(X0),sK85_skl))
| relation(X0) ),
inference(paramodulation,[status(thm)],[f3173,f3102]) ).
fof(f3267,plain,
! [X0,X1,X2] :
( ~ sQ72_spl
| ~ in(identity_relation(X2),sK13_skl(X0,sK85_skl,ordered_pair(X1,X1),sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_inverse_image(sK85_skl,ordered_pair(X1,X1)))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f2791]) ).
fof(f3268,plain,
! [X0,X1] :
( ~ sQ72_spl
| ~ in(X1,sK19_skl(sK13_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl)
| relation(sK13_skl(X0,relation_inverse_image(sK85_skl,X1),X1,sK85_skl)) ),
inference(paramodulation,[status(thm)],[f3173,f3045]) ).
fof(f3269,plain,
! [X0,X1,X2] :
( ~ sQ72_spl
| ~ in(X2,ordered_pair(X0,sK13_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(sK85_skl,X2)
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f2757]) ).
fof(f3270,plain,
! [X0,X1,X2] :
( ~ sQ72_spl
| ~ in(X2,sK13_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f2794]) ).
fof(f3271,plain,
! [X0,X1] :
( ~ sQ72_spl
| ~ in(sK85_skl,ordered_pair(X0,sK13_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f2759]) ).
fof(f3272,plain,
! [X0,X1] :
( ~ sQ72_spl
| ~ in(X1,sK13_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f2796]) ).
fof(f3273,plain,
! [X0,X1] :
( ~ sQ72_spl
| in(sK13_skl(X0,sK85_skl,X1,sK85_skl),X1)
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f1391]) ).
fof(f3274,plain,
! [X0,X1] :
( ~ sQ72_spl
| in(ordered_pair(X0,sK13_skl(X0,sK85_skl,X1,sK85_skl)),sK85_skl)
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f1390]) ).
fof(f3275,plain,
! [X0,X1] :
( ~ sQ72_spl
| in(apply(sK85_skl,X0),X1)
| ~ in(X0,sK85_skl)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f1385]) ).
fof(f3276,plain,
! [X0] :
( ~ sQ72_spl
| in(X0,relation_dom(sK85_skl))
| ~ in(X0,sK85_skl)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f1384]) ).
fof(f3277,definition,
! [X0,X1] :
( sQ88_spl
<=> ( ~ in(X1,relation_inverse_image(sK85_skl,sK19_skl(X0)))
| ~ in(X0,sK13_skl(X1,sK85_skl,sK19_skl(X0),sK85_skl))
| relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f3280,plain,
( ~ sQ72_spl
| ~ sQ54_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f3266,f3277,f1928,f2771]) ).
fof(f3281,definition,
! [X0,X1,X2] :
( sQ89_spl
<=> ( ~ in(identity_relation(X2),sK13_skl(X0,sK85_skl,ordered_pair(X1,X1),sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_inverse_image(sK85_skl,ordered_pair(X1,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f3284,plain,
( ~ sQ72_spl
| sQ89_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3267,f1928,f3281,f2771]) ).
fof(f3285,definition,
! [X0,X1] :
( sQ90_spl
<=> ( ~ in(X1,sK19_skl(sK13_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| relation(sK13_skl(X0,relation_inverse_image(sK85_skl,X1),X1,sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f3288,plain,
( ~ sQ72_spl
| ~ sQ54_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f3268,f3285,f1928,f2771]) ).
fof(f3289,definition,
! [X0,X1,X2] :
( sQ91_spl
<=> ( ~ in(X2,ordered_pair(X0,sK13_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(sK85_skl,X2)
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f3292,plain,
( ~ sQ72_spl
| sQ91_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3269,f1928,f3289,f2771]) ).
fof(f3293,definition,
! [X0,X1,X2] :
( sQ92_spl
<=> ( ~ in(X2,sK13_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X1,X2)
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f3296,plain,
( ~ sQ72_spl
| sQ92_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3270,f1928,f3293,f2771]) ).
fof(f3297,definition,
! [X0,X1] :
( sQ93_spl
<=> ( ~ in(sK85_skl,ordered_pair(X0,sK13_skl(X0,sK85_skl,X1,sK85_skl)))
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f3300,plain,
( ~ sQ72_spl
| sQ93_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3271,f1928,f3297,f2771]) ).
fof(f3301,definition,
! [X0,X1] :
( sQ94_spl
<=> ( ~ in(X1,sK13_skl(X0,sK85_skl,X1,sK85_skl))
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f3304,plain,
( ~ sQ72_spl
| sQ94_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3272,f1928,f3301,f2771]) ).
fof(f3305,definition,
! [X0,X1] :
( sQ95_spl
<=> ( in(sK13_skl(X0,sK85_skl,X1,sK85_skl),X1)
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f3308,plain,
( ~ sQ72_spl
| sQ95_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3273,f1928,f3305,f2771]) ).
fof(f3309,definition,
! [X0,X1] :
( sQ96_spl
<=> ( in(ordered_pair(X0,sK13_skl(X0,sK85_skl,X1,sK85_skl)),sK85_skl)
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f3312,plain,
( ~ sQ72_spl
| sQ96_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3274,f1928,f3309,f2771]) ).
fof(f3313,definition,
! [X0,X1] :
( sQ97_spl
<=> ( in(apply(sK85_skl,X0),X1)
| ~ in(X0,sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f3316,plain,
( ~ sQ72_spl
| sQ97_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3275,f1928,f1550,f3313,f2771]) ).
fof(f3317,definition,
! [X0] :
( sQ98_spl
<=> ( in(X0,relation_dom(sK85_skl))
| ~ in(X0,sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f3320,plain,
( ~ sQ72_spl
| sQ98_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3276,f1928,f1550,f3317,f2771]) ).
fof(f3331,plain,
( in(sK85_skl,powerset(sK85_skl))
| powerset(sK85_skl) = sK85_skl ),
inference(paramodulation,[status(thm)],[f3198,f3164]) ).
fof(f3332,definition,
( sQ99_spl
<=> powerset(sK85_skl) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f3333,plain,
( ~ sQ99_spl
| powerset(sK85_skl) = sK85_skl ),
inference(component_clause,[status(thm)],[f3332]) ).
fof(f3335,definition,
( sQ100_spl
<=> in(sK85_skl,powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f3338,plain,
( sQ100_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f3331,f3332,f3335]) ).
fof(f3339,plain,
( ~ sQ99_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3333,f2422]) ).
fof(f3340,plain,
~ sQ99_spl,
inference(contradiction_clause,[status(thm)],[f3339]) ).
fof(f3455,plain,
! [X0,X1,X2,X3] :
( ~ in(relation_dom_restriction(X0,X2),ordered_pair(X1,X3))
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1733,f692]) ).
fof(f3456,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,ordered_pair(X1,X3))
| ~ in(relation_dom_restriction(X0,X2),X4)
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1731,f692]) ).
fof(f3460,plain,
! [X0,X1,X2,X3] :
( ~ in(relation_rng_restriction(X2,X0),ordered_pair(X3,X1))
| ~ in(ordered_pair(X3,X1),X0)
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f2095,f697]) ).
fof(f3461,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,ordered_pair(X3,X1))
| ~ in(relation_rng_restriction(X2,X0),X4)
| ~ in(ordered_pair(X3,X1),X0)
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f2093,f697]) ).
fof(f3550,plain,
( ~ in(powerset(sK85_skl),sK85_skl)
| powerset(sK85_skl) = sK85_skl ),
inference(paramodulation,[status(thm)],[f3198,f3196]) ).
fof(f3552,definition,
( sQ101_spl
<=> in(powerset(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f3555,plain,
( ~ sQ101_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f3550,f3332,f3552]) ).
fof(f3576,plain,
! [X0] :
( ~ in(X0,sK85_skl)
| ~ in(powerset(sK85_skl),X0)
| powerset(sK85_skl) = sK85_skl ),
inference(paramodulation,[status(thm)],[f3198,f3194]) ).
fof(f3578,definition,
! [X0] :
( sQ102_spl
<=> ( ~ in(X0,sK85_skl)
| ~ in(powerset(sK85_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f3581,plain,
( sQ102_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f3576,f3332,f3578]) ).
fof(f3648,definition,
! [X0] :
( sQ103_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f3649,plain,
! [X0] :
( ~ sQ103_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f3648]) ).
fof(f3670,definition,
! [X0] :
( sQ104_spl
<=> ~ subset(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f3671,plain,
! [X0] :
( ~ sQ104_spl
| ~ subset(sK85_skl,X0) ),
inference(component_clause,[status(thm)],[f3670]) ).
fof(f3708,definition,
! [X0] :
( sQ105_spl
<=> ~ disjoint(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f3709,plain,
! [X0] :
( ~ sQ105_spl
| ~ disjoint(sK85_skl,X0) ),
inference(component_clause,[status(thm)],[f3708]) ).
fof(f3712,plain,
! [X0] : disjoint(sK85_skl,X0),
inference(resolution,[status(thm)],[f1273,f2059]) ).
fof(f3713,plain,
! [X0] : disjoint(X0,sK85_skl),
inference(resolution,[status(thm)],[f1273,f1872]) ).
fof(f3717,definition,
! [X0] :
( sQ106_spl
<=> disjoint(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f3822,plain,
( element(sK85_skl,powerset(sK85_skl))
| powerset(sK85_skl) = sK85_skl ),
inference(paramodulation,[status(thm)],[f3198,f3192]) ).
fof(f3824,definition,
( sQ107_spl
<=> element(sK85_skl,powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f3827,plain,
( sQ107_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f3822,f3332,f3824]) ).
fof(f3884,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ is_reflexive_in(sK85_skl,X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f422,f1877]) ).
fof(f3932,definition,
! [X0,X1] :
( sQ109_spl
<=> ( ~ in(X1,X0)
| ~ is_reflexive_in(sK85_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f3933,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ in(X1,X0)
| ~ is_reflexive_in(sK85_skl,X0) ),
inference(component_clause,[status(thm)],[f3932]) ).
fof(f3935,plain,
( sQ109_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f3884,f1928,f3932]) ).
fof(f3953,plain,
! [X0] :
( is_reflexive_in(X0,sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f423,f1877]) ).
fof(f3966,plain,
! [X0,X1] :
( ~ empty(X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f423,f1263]) ).
fof(f4008,plain,
! [X0] :
( ~ sQ109_spl
| ordinal(X0)
| ~ is_reflexive_in(sK85_skl,X0) ),
inference(resolution,[status(thm)],[f3933,f1070]) ).
fof(f4009,plain,
! [X0] :
( ~ sQ109_spl
| epsilon_connected(X0)
| ~ is_reflexive_in(sK85_skl,X0) ),
inference(resolution,[status(thm)],[f3933,f511]) ).
fof(f4011,plain,
! [X0] :
( ~ sQ109_spl
| epsilon_transitive(X0)
| ~ is_reflexive_in(sK85_skl,X0) ),
inference(resolution,[status(thm)],[f3933,f461]) ).
fof(f4012,plain,
! [X0] :
( ~ sQ109_spl
| X0 = sK85_skl
| ~ is_reflexive_in(sK85_skl,X0) ),
inference(resolution,[status(thm)],[f3933,f3164]) ).
fof(f4014,plain,
! [X0] :
( ~ sQ109_spl
| relation(X0)
| ~ is_reflexive_in(sK85_skl,X0) ),
inference(resolution,[status(thm)],[f3933,f416]) ).
fof(f4033,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[f3933,f1407]) ).
fof(f4035,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,sK112_skl(X0)) ),
inference(resolution,[status(thm)],[f3933,f1312]) ).
fof(f4036,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,sK93_skl(X0)) ),
inference(resolution,[status(thm)],[f3933,f961]) ).
fof(f4037,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,succ(X0)) ),
inference(resolution,[status(thm)],[f3933,f928]) ).
fof(f4038,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,singleton(X0)) ),
inference(resolution,[status(thm)],[f3933,f1401]) ).
fof(f4080,plain,
! [X0,X1] :
( in(sK21_skl(X1,set_meet(X0),X0),X0)
| in(X1,set_meet(X0))
| X0 = sK85_skl ),
inference(forward_demodulation,[status(thm)],[f1752,f1396]) ).
fof(f4115,plain,
! [X0,X1] :
( ~ in(X0,sK21_skl(X1,set_meet(X0),X0))
| in(X1,set_meet(X0))
| X0 = sK85_skl ),
inference(resolution,[status(thm)],[f4080,f292]) ).
fof(f4118,definition,
! [X0] :
( sQ111_spl
<=> in(X0,set_meet(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f4119,plain,
! [X0] :
( ~ sQ111_spl
| in(X0,set_meet(sK85_skl)) ),
inference(component_clause,[status(thm)],[f4118]) ).
fof(f4425,definition,
! [X0] :
( sQ114_spl
<=> ~ empty(powerset(X0)) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f4441,definition,
! [X0] :
( sQ115_spl
<=> ( ~ empty(X0)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f4442,plain,
! [X0] :
( ~ sQ115_spl
| ~ empty(X0)
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f4441]) ).
fof(f4444,definition,
! [X1] :
( sQ116_spl
<=> ( empty(X1)
| ~ empty(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f4448,plain,
! [X0] :
( ~ sQ115_spl
| ~ empty(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4442]) ).
fof(f4449,plain,
( ~ sQ115_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f878,f4448]) ).
fof(f4450,plain,
~ sQ115_spl,
inference(contradiction_clause,[status(thm)],[f4449]) ).
fof(f4666,plain,
( subset(sK85_skl,powerset(sK85_skl))
| ~ epsilon_transitive(powerset(sK85_skl)) ),
inference(resolution,[status(thm)],[f460,f2428]) ).
fof(f4689,definition,
( sQ118_spl
<=> subset(sK85_skl,powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f4692,plain,
( sQ118_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f4666,f3027,f4689]) ).
fof(f4823,plain,
! [X0] :
( in(ordered_pair(sK28_skl(sK85_skl,X0),sK29_skl(sK85_skl,X0)),X0)
| X0 = sK85_skl
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f470,f1877]) ).
fof(f4852,definition,
! [X0] :
( sQ121_spl
<=> ( in(ordered_pair(sK28_skl(sK85_skl,X0),sK29_skl(sK85_skl,X0)),X0)
| X0 = sK85_skl
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f4855,plain,
( ~ sQ54_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f4823,f4852,f1928]) ).
fof(f4864,plain,
! [X0] :
( in(sK85_skl,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f474,f2393]) ).
fof(f4865,plain,
! [X0] :
( in(sK70_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f474,f699]) ).
fof(f4872,plain,
! [X0] :
( in(X0,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f474,f2215]) ).
fof(f4873,plain,
! [X0] : in(sK85_skl,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f4864,f719]) ).
fof(f4874,plain,
! [X0] : in(X0,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f4872,f719]) ).
fof(f4985,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,powerset(X0)) ),
inference(resolution,[status(thm)],[f4874,f3933]) ).
fof(f5315,plain,
! [X0,X1] : ~ in(succ(set_union2(X0,X1)),X0),
inference(resolution,[status(thm)],[f1409,f1741]) ).
fof(f5434,plain,
! [X0,X1] : ~ in(succ(set_union2(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f313,f5315]) ).
fof(f5651,plain,
! [X0] : ~ in(succ(succ(X0)),singleton(X0)),
inference(paramodulation,[status(thm)],[f410,f5434]) ).
fof(f5750,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f4865,f3933]) ).
fof(f5754,plain,
! [X0] :
( ~ in(X0,sK70_skl(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f4865,f292]) ).
fof(f5798,definition,
( sQ122_spl
<=> empty(powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f5799,plain,
( ~ sQ122_spl
| empty(powerset(sK85_skl)) ),
inference(component_clause,[status(thm)],[f5798]) ).
fof(f6090,definition,
! [X0] :
( sQ123_spl
<=> ~ disjoint(X0,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f6091,plain,
! [X0] :
( ~ sQ123_spl
| ~ disjoint(X0,sK85_skl) ),
inference(component_clause,[status(thm)],[f6090]) ).
fof(f6109,definition,
! [X0] :
( sQ124_spl
<=> disjoint(X0,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f6119,plain,
! [X0] :
( sK85_skl = X0
| proper_subset(sK85_skl,X0) ),
inference(resolution,[status(thm)],[f666,f1875]) ).
fof(f6120,plain,
! [X0] :
( X0 = succ(X0)
| proper_subset(X0,succ(X0)) ),
inference(resolution,[status(thm)],[f666,f2999]) ).
fof(f6126,plain,
! [X0] :
( ~ proper_subset(X0,sK85_skl)
| sK85_skl = X0 ),
inference(resolution,[status(thm)],[f6119,f294]) ).
fof(f6128,plain,
( sK85_skl = sK85_skl
| sK85_skl = sK85_skl ),
inference(resolution,[status(thm)],[f6126,f6119]) ).
fof(f6129,plain,
sQ67_spl,
inference(split_clause,[status(thm)],[f6128,f2553]) ).
fof(f6137,plain,
! [X0] : in(X0,succ(singleton(X0))),
inference(resolution,[status(thm)],[f813,f2999]) ).
fof(f6138,plain,
! [X0,X1] : in(X0,set_union2(X1,singleton(X0))),
inference(resolution,[status(thm)],[f813,f2086]) ).
fof(f6139,plain,
! [X0,X1] : in(X0,set_union2(singleton(X0),X1)),
inference(resolution,[status(thm)],[f813,f1269]) ).
fof(f6169,plain,
in(sK85_skl,succ(powerset(sK85_skl))),
inference(paramodulation,[status(thm)],[f2416,f6137]) ).
fof(f6195,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(X0,singleton(X1))) ),
inference(resolution,[status(thm)],[f6138,f3933]) ).
fof(f6455,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(singleton(X0),X1)) ),
inference(resolution,[status(thm)],[f6139,f3933]) ).
fof(f6502,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != sK85_skl ),
inference(forward_demodulation,[status(thm)],[f1752,f817]) ).
fof(f6508,definition,
! [X0] :
( sQ125_spl
<=> subset(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f6694,plain,
! [X0] :
( relation_rng_restriction(X0,sK85_skl) = sK85_skl
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f943,f2431]) ).
fof(f6697,definition,
! [X0] :
( sQ126_spl
<=> relation_rng_restriction(X0,sK85_skl) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f6698,plain,
! [X0] :
( ~ sQ126_spl
| relation_rng_restriction(X0,sK85_skl) = sK85_skl ),
inference(component_clause,[status(thm)],[f6697]) ).
fof(f6700,plain,
( sQ126_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6694,f1928,f6697]) ).
fof(f6701,plain,
( ~ sQ126_spl
| subset(sK85_skl,sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f943]) ).
fof(f6702,plain,
! [X0,X1,X2] :
( ~ sQ126_spl
| ~ in(sK85_skl,ordered_pair(X2,X0))
| ~ in(ordered_pair(X2,X0),sK85_skl)
| ~ in(X0,X1)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f3460]) ).
fof(f6704,definition,
( sQ127_spl
<=> subset(sK85_skl,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f6707,plain,
( ~ sQ126_spl
| sQ127_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6701,f1928,f6704,f6697]) ).
fof(f6708,definition,
! [X0,X1,X2] :
( sQ128_spl
<=> ( ~ in(sK85_skl,ordered_pair(X2,X0))
| ~ in(ordered_pair(X2,X0),sK85_skl)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f6711,plain,
( ~ sQ126_spl
| sQ128_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6702,f1928,f6708,f6697]) ).
fof(f6766,definition,
! [X0] :
( sQ129_spl
<=> ~ ordinal(powerset(X0)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f6767,plain,
! [X0] :
( ~ sQ129_spl
| ~ ordinal(powerset(X0)) ),
inference(component_clause,[status(thm)],[f6766]) ).
fof(f6830,plain,
! [X0] :
( subset(sK85_skl,X0)
| ~ relation(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f519,f1877]) ).
fof(f6863,definition,
! [X0] :
( sQ131_spl
<=> ( subset(sK85_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f6866,plain,
( sQ131_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6830,f1928,f6863]) ).
fof(f6916,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(powerset(X0),X1) ),
inference(resolution,[status(thm)],[f525,f4874]) ).
fof(f6921,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(sK112_skl(X0),X1) ),
inference(resolution,[status(thm)],[f525,f1312]) ).
fof(f6922,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(sK93_skl(X0),X1) ),
inference(resolution,[status(thm)],[f525,f961]) ).
fof(f6924,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(succ(X0),X1) ),
inference(resolution,[status(thm)],[f525,f928]) ).
fof(f7122,plain,
! [X0,X1] :
( ~ in(X1,sK111_skl(X1))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f1267,f292]) ).
fof(f7123,plain,
! [X0] :
( relation_dom_restriction(sK85_skl,X0) = sK85_skl
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1282,f2431]) ).
fof(f7126,definition,
! [X0] :
( sQ132_spl
<=> relation_dom_restriction(sK85_skl,X0) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f7127,plain,
! [X0] :
( ~ sQ132_spl
| relation_dom_restriction(sK85_skl,X0) = sK85_skl ),
inference(component_clause,[status(thm)],[f7126]) ).
fof(f7129,plain,
( sQ132_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7123,f1928,f7126]) ).
fof(f7131,plain,
! [X0,X1,X2] :
( ~ sQ132_spl
| ~ in(sK85_skl,ordered_pair(X0,X2))
| ~ in(ordered_pair(X0,X2),sK85_skl)
| ~ in(X0,X1)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f7127,f3455]) ).
fof(f7134,definition,
! [X0,X1,X2] :
( sQ133_spl
<=> ( ~ in(sK85_skl,ordered_pair(X0,X2))
| ~ in(ordered_pair(X0,X2),sK85_skl)
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f7137,plain,
( ~ sQ132_spl
| sQ133_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f7131,f1928,f7134,f7126]) ).
fof(f7192,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f526,f3933]) ).
fof(f7879,plain,
! [X0] :
( ~ in(X0,powerset(sK85_skl))
| sK111_skl(powerset(sK85_skl)) = sK85_skl ),
inference(resolution,[status(thm)],[f2418,f1267]) ).
fof(f7884,plain,
( empty(powerset(sK85_skl))
| sK70_skl(powerset(sK85_skl)) = sK85_skl ),
inference(resolution,[status(thm)],[f2418,f4865]) ).
fof(f7890,plain,
! [X0] :
( in(X0,set_meet(powerset(sK85_skl)))
| powerset(sK85_skl) = sK85_skl
| sK21_skl(X0,set_meet(powerset(sK85_skl)),powerset(sK85_skl)) = sK85_skl ),
inference(resolution,[status(thm)],[f2418,f4080]) ).
fof(f7896,plain,
( powerset(sK85_skl) = sK85_skl
| sK25_skl(powerset(sK85_skl)) = sK85_skl ),
inference(resolution,[status(thm)],[f2418,f3164]) ).
fof(f7918,definition,
( sQ134_spl
<=> sK111_skl(powerset(sK85_skl)) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f7921,definition,
! [X0] :
( sQ135_spl
<=> ~ in(X0,powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f7922,plain,
! [X0] :
( ~ sQ135_spl
| ~ in(X0,powerset(sK85_skl)) ),
inference(component_clause,[status(thm)],[f7921]) ).
fof(f7924,plain,
( sQ135_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f7879,f7918,f7921]) ).
fof(f7927,definition,
( sQ136_spl
<=> sK70_skl(powerset(sK85_skl)) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f7930,plain,
( sQ122_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f7884,f7927,f5798]) ).
fof(f7931,definition,
! [X0] :
( sQ137_spl
<=> ( in(X0,set_meet(powerset(sK85_skl)))
| sK21_skl(X0,set_meet(powerset(sK85_skl)),powerset(sK85_skl)) = sK85_skl ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f7934,plain,
( sQ99_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f7890,f7931,f3332]) ).
fof(f7951,definition,
( sQ142_spl
<=> sK25_skl(powerset(sK85_skl)) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f7954,plain,
( sQ99_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f7896,f7951,f3332]) ).
fof(f8014,plain,
( ~ sQ122_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5799,f719]) ).
fof(f8015,plain,
~ sQ122_spl,
inference(contradiction_clause,[status(thm)],[f8014]) ).
fof(f8028,plain,
( ~ sQ135_spl
| $false ),
inference(resolution,[status(thm)],[f7922,f4873]) ).
fof(f8063,plain,
~ sQ135_spl,
inference(contradiction_clause,[status(thm)],[f8028]) ).
fof(f8068,plain,
! [X0,X1,X2] :
( subset(relation_image(X0,X1),X2)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f2492,f526]) ).
fof(f8074,plain,
! [X0,X1] :
( empty(relation_image(X0,X1))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f2492,f4865]) ).
fof(f8081,plain,
! [X0,X1] :
( ordinal(relation_image(X0,X1))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f2492,f1070]) ).
fof(f8084,plain,
! [X0,X1] :
( epsilon_transitive(relation_image(X0,X1))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f2492,f461]) ).
fof(f8087,plain,
! [X0,X1] :
( relation(relation_image(X0,X1))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f2492,f416]) ).
fof(f8108,definition,
! [X0] :
( sQ158_spl
<=> ~ in(X0,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f8330,definition,
! [X0] :
( sQ161_spl
<=> ~ in(X0,relation_dom(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f8520,definition,
! [X0] :
( sQ162_spl
<=> ( X0 = sK85_skl
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f8852,plain,
! [X0] :
( ~ in(X0,relation_dom(sK85_skl))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1419,f1877]) ).
fof(f8871,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1419,f1263]) ).
fof(f8875,plain,
! [X0,X1,X2] :
( ~ in(X2,ordered_pair(X1,sK43_skl(X1,relation_dom(X0),X0)))
| ~ in(X0,X2)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1419,f1124]) ).
fof(f8877,plain,
! [X0,X1] :
( ~ in(X0,ordered_pair(X1,sK43_skl(X1,relation_dom(X0),X0)))
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1419,f292]) ).
fof(f8878,plain,
! [X0] :
( in(ordered_pair(X0,sK43_skl(X0,sK85_skl,sK85_skl)),sK85_skl)
| ~ in(X0,relation_dom(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1419]) ).
fof(f8892,plain,
( sQ161_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f8852,f1928,f8330]) ).
fof(f8893,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f8871,f301]) ).
fof(f8895,definition,
! [X0] :
( sQ164_spl
<=> ( in(ordered_pair(X0,sK43_skl(X0,sK85_skl,sK85_skl)),sK85_skl)
| ~ in(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f8898,plain,
( sQ164_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f8878,f1928,f8895]) ).
fof(f9139,plain,
! [X0,X1] :
( subset(relation_dom(X0),X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f8893,f526]) ).
fof(f9331,plain,
! [X0] :
( in(sK44_skl(X0,sK85_skl),X0)
| X0 = relation_dom(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f556,f1877]) ).
fof(f9370,definition,
! [X0] :
( sQ166_spl
<=> ( in(sK44_skl(X0,sK85_skl),X0)
| X0 = relation_dom(sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f9373,plain,
( sQ166_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9331,f1928,f9370]) ).
fof(f9687,definition,
( sQ167_spl
<=> succ(sK85_skl) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f9688,plain,
( ~ sQ167_spl
| succ(sK85_skl) = sK85_skl ),
inference(component_clause,[status(thm)],[f9687]) ).
fof(f9690,definition,
( sQ168_spl
<=> subset(powerset(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f9694,plain,
( ~ sQ167_spl
| powerset(sK85_skl) = sK85_skl ),
inference(forward_demodulation,[status(thm)],[f3000,f9688]) ).
fof(f9695,plain,
( ~ sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9694,f2422]) ).
fof(f9696,plain,
~ sQ167_spl,
inference(contradiction_clause,[status(thm)],[f9695]) ).
fof(f9700,definition,
( sQ169_spl
<=> powerset(sK85_skl) = powerset(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f9702,plain,
( sQ169_spl
| powerset(sK85_skl) != powerset(sK85_skl) ),
inference(component_clause,[status(thm)],[f9700]) ).
fof(f9709,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(unordered_pair(X0,X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4033]) ).
fof(f9710,plain,
! [X0] :
( ~ sQ109_spl
| ~ empty(powerset(X0))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4985]) ).
fof(f9711,plain,
! [X0] :
( ~ sQ109_spl
| ~ empty(singleton(X0))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4038]) ).
fof(f9712,plain,
! [X0] :
( ~ sQ109_spl
| ~ empty(succ(X0))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4037]) ).
fof(f9713,plain,
! [X0] :
( ~ sQ109_spl
| ~ empty(sK93_skl(X0))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4036]) ).
fof(f9714,plain,
! [X0] :
( ~ sQ109_spl
| ~ empty(sK112_skl(X0))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4035]) ).
fof(f9715,plain,
! [X0,X1] :
( ~ sQ109_spl
| subset(X0,X1)
| ~ empty(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f7192]) ).
fof(f9716,plain,
! [X0] :
( ~ sQ109_spl
| empty(X0)
| ~ empty(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f5750]) ).
fof(f9717,plain,
! [X0] :
( ~ sQ109_spl
| relation(X0)
| ~ empty(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4014]) ).
fof(f9718,plain,
! [X0] :
( ~ sQ109_spl
| X0 = sK85_skl
| ~ empty(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4012]) ).
fof(f9719,plain,
! [X0] :
( ~ sQ109_spl
| epsilon_transitive(X0)
| ~ empty(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4011]) ).
fof(f9720,plain,
! [X0] :
( ~ sQ109_spl
| epsilon_connected(X0)
| ~ empty(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4009]) ).
fof(f9721,plain,
! [X0] :
( ~ sQ109_spl
| ordinal(X0)
| ~ empty(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f3966,f4008]) ).
fof(f9722,definition,
! [X0,X1] :
( sQ170_spl
<=> ~ empty(unordered_pair(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f9725,plain,
( ~ sQ109_spl
| sQ170_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9709,f1928,f9722,f3932]) ).
fof(f9726,plain,
( ~ sQ109_spl
| sQ114_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9710,f1928,f4425,f3932]) ).
fof(f9727,definition,
! [X0] :
( sQ171_spl
<=> ~ empty(singleton(X0)) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f9730,plain,
( ~ sQ109_spl
| sQ171_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9711,f1928,f9727,f3932]) ).
fof(f9731,definition,
! [X0] :
( sQ172_spl
<=> ~ empty(succ(X0)) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f9734,plain,
( ~ sQ109_spl
| sQ172_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9712,f1928,f9731,f3932]) ).
fof(f9735,definition,
! [X0] :
( sQ173_spl
<=> ~ empty(sK93_skl(X0)) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f9738,plain,
( ~ sQ109_spl
| sQ173_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9713,f1928,f9735,f3932]) ).
fof(f9739,definition,
! [X0] :
( sQ174_spl
<=> ~ empty(sK112_skl(X0)) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f9742,plain,
( ~ sQ109_spl
| sQ174_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9714,f1928,f9739,f3932]) ).
fof(f9743,definition,
! [X0,X1] :
( sQ175_spl
<=> ( subset(X0,X1)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f9746,plain,
( ~ sQ109_spl
| sQ175_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9715,f1928,f9743,f3932]) ).
fof(f9747,plain,
( ~ sQ109_spl
| sQ116_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9716,f1928,f4444,f3932]) ).
fof(f9748,definition,
! [X0] :
( sQ176_spl
<=> ( relation(X0)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f9751,plain,
( ~ sQ109_spl
| sQ176_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9717,f1928,f9748,f3932]) ).
fof(f9752,plain,
( ~ sQ109_spl
| sQ162_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9718,f1928,f8520,f3932]) ).
fof(f9753,definition,
! [X0] :
( sQ177_spl
<=> ( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f9756,plain,
( ~ sQ109_spl
| sQ177_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9719,f1928,f9753,f3932]) ).
fof(f9757,definition,
! [X0] :
( sQ178_spl
<=> ( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f9760,plain,
( ~ sQ109_spl
| sQ178_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9720,f1928,f9757,f3932]) ).
fof(f9761,definition,
! [X0] :
( sQ179_spl
<=> ( ordinal(X0)
| ~ empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f9764,plain,
( ~ sQ109_spl
| sQ179_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f9721,f1928,f9761,f3932]) ).
fof(f9862,plain,
! [X0] :
( ~ sQ1_spl
| sK47_skl(X0,sK75_skl) = sK46_skl(X0,sK75_skl)
| ~ in(ordered_pair(sK47_skl(X0,sK75_skl),sK46_skl(X0,sK75_skl)),sK75_skl)
| is_antisymmetric_in(sK75_skl,X0)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f564,f1349]) ).
fof(f9871,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| is_antisymmetric_in(relation_image(X0,X1),X2)
| ~ relation(relation_image(X0,X1)) ),
inference(resolution,[status(thm)],[f564,f2492]) ).
fof(f9928,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f564,f3933]) ).
fof(f9933,definition,
! [X0] :
( sQ180_spl
<=> ( sK47_skl(X0,sK75_skl) = sK46_skl(X0,sK75_skl)
| ~ in(ordered_pair(sK47_skl(X0,sK75_skl),sK46_skl(X0,sK75_skl)),sK75_skl)
| is_antisymmetric_in(sK75_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f9934,plain,
! [X0] :
( ~ sQ180_spl
| sK47_skl(X0,sK75_skl) = sK46_skl(X0,sK75_skl)
| ~ in(ordered_pair(sK47_skl(X0,sK75_skl),sK46_skl(X0,sK75_skl)),sK75_skl)
| is_antisymmetric_in(sK75_skl,X0) ),
inference(component_clause,[status(thm)],[f9933]) ).
fof(f9936,plain,
( ~ sQ1_spl
| sQ180_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f9862,f1828,f9933,f1348]) ).
fof(f9944,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| is_antisymmetric_in(relation_image(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f9871,f8087]) ).
fof(f9946,definition,
! [X0] :
( sQ181_spl
<=> is_antisymmetric_in(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f9947,plain,
! [X0] :
( ~ sQ181_spl
| is_antisymmetric_in(sK85_skl,X0) ),
inference(component_clause,[status(thm)],[f9946]) ).
fof(f9952,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| is_antisymmetric_in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f9928,f4014]) ).
fof(f10042,plain,
! [X0] :
( ~ sQ180_spl
| is_antisymmetric_in(sK75_skl,X0)
| ~ relation(sK75_skl)
| sK47_skl(X0,sK75_skl) = sK46_skl(X0,sK75_skl)
| is_antisymmetric_in(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f9934,f565]) ).
fof(f10043,definition,
! [X0] :
( sQ183_spl
<=> ( is_antisymmetric_in(sK75_skl,X0)
| sK47_skl(X0,sK75_skl) = sK46_skl(X0,sK75_skl)
| is_antisymmetric_in(sK75_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f10044,plain,
! [X0] :
( ~ sQ183_spl
| is_antisymmetric_in(sK75_skl,X0)
| sK47_skl(X0,sK75_skl) = sK46_skl(X0,sK75_skl)
| is_antisymmetric_in(sK75_skl,X0) ),
inference(component_clause,[status(thm)],[f10043]) ).
fof(f10046,plain,
( ~ sQ180_spl
| ~ sQ46_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f10042,f10043,f1828,f9933]) ).
fof(f10047,plain,
! [X0] :
( ~ sQ183_spl
| sK47_skl(X0,sK75_skl) = sK46_skl(X0,sK75_skl)
| is_antisymmetric_in(sK75_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f10044]) ).
fof(f10144,plain,
! [X0] :
( ~ sQ2_spl
| sK77_skl = sK76_skl
| ~ in(ordered_pair(sK77_skl,sK76_skl),sK75_skl)
| ~ in(sK76_skl,X0)
| ~ in(sK77_skl,X0)
| ~ is_antisymmetric_in(sK75_skl,X0)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1353,f561]) ).
fof(f10145,plain,
( ~ sQ2_spl
| in(sK76_skl,relation_dom(sK75_skl))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1353,f1420]) ).
fof(f10146,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ in(X1,ordered_pair(sK76_skl,sK77_skl))
| ~ in(relation_rng_restriction(X0,sK75_skl),X1)
| ~ in(sK77_skl,X0)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1353,f3461]) ).
fof(f10147,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ in(X1,ordered_pair(sK76_skl,sK77_skl))
| ~ in(relation_dom_restriction(sK75_skl,X0),X1)
| ~ in(sK76_skl,X0)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1353,f3456]) ).
fof(f10148,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK77_skl,X0)
| in(sK76_skl,relation_inverse_image(sK75_skl,X0))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1353,f1392]) ).
fof(f10149,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK76_skl,X0)
| in(sK77_skl,relation_image(sK75_skl,X0))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1353,f1389]) ).
fof(f10151,plain,
! [X0] :
( ~ sQ2_spl
| in(ordered_pair(sK76_skl,sK77_skl),X0)
| ~ subset(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f1353,f525]) ).
fof(f10159,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK75_skl,X0)
| ~ in(X0,ordered_pair(sK76_skl,sK77_skl)) ),
inference(resolution,[status(thm)],[f1353,f1124]) ).
fof(f10161,definition,
! [X0] :
( sQ189_spl
<=> ( ~ in(sK76_skl,X0)
| ~ in(sK77_skl,X0)
| ~ is_antisymmetric_in(sK75_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f10162,plain,
! [X0] :
( ~ sQ189_spl
| ~ in(sK76_skl,X0)
| ~ in(sK77_skl,X0)
| ~ is_antisymmetric_in(sK75_skl,X0) ),
inference(component_clause,[status(thm)],[f10161]) ).
fof(f10164,plain,
( ~ sQ2_spl
| sQ4_spl
| ~ sQ3_spl
| sQ189_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f10144,f1828,f10161,f1356,f1360,f1352]) ).
fof(f10165,definition,
( sQ190_spl
<=> in(sK76_skl,relation_dom(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f10166,plain,
( ~ sQ190_spl
| in(sK76_skl,relation_dom(sK75_skl)) ),
inference(component_clause,[status(thm)],[f10165]) ).
fof(f10168,plain,
( ~ sQ2_spl
| sQ190_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f10145,f1828,f10165,f1352]) ).
fof(f10169,definition,
! [X0,X1] :
( sQ191_spl
<=> ( ~ in(X1,ordered_pair(sK76_skl,sK77_skl))
| ~ in(relation_rng_restriction(X0,sK75_skl),X1)
| ~ in(sK77_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f10172,plain,
( ~ sQ2_spl
| sQ191_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f10146,f1828,f10169,f1352]) ).
fof(f10173,definition,
! [X0,X1] :
( sQ192_spl
<=> ( ~ in(X1,ordered_pair(sK76_skl,sK77_skl))
| ~ in(relation_dom_restriction(sK75_skl,X0),X1)
| ~ in(sK76_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f10176,plain,
( ~ sQ2_spl
| sQ192_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f10147,f1828,f10173,f1352]) ).
fof(f10177,definition,
! [X0] :
( sQ193_spl
<=> ( ~ in(sK77_skl,X0)
| in(sK76_skl,relation_inverse_image(sK75_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f10180,plain,
( ~ sQ2_spl
| sQ193_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f10148,f1828,f10177,f1352]) ).
fof(f10181,definition,
! [X0] :
( sQ194_spl
<=> ( ~ in(sK76_skl,X0)
| in(sK77_skl,relation_image(sK75_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f10184,plain,
( ~ sQ2_spl
| sQ194_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f10149,f1828,f10181,f1352]) ).
fof(f10304,plain,
( ~ sQ181_spl
| antisymmetric(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f9947,f365]) ).
fof(f10305,definition,
( sQ209_spl
<=> antisymmetric(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f10308,plain,
( ~ sQ181_spl
| sQ209_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f10304,f1928,f10305,f9946]) ).
fof(f10310,definition,
( sQ210_spl
<=> empty(sK75_skl) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f10325,plain,
! [X0] :
( ~ sQ190_spl
| in(sK76_skl,X0)
| ~ subset(relation_dom(sK75_skl),X0) ),
inference(resolution,[status(thm)],[f10166,f525]) ).
fof(f10330,plain,
( ~ sQ109_spl
| ~ sQ190_spl
| ~ is_reflexive_in(sK85_skl,relation_dom(sK75_skl)) ),
inference(resolution,[status(thm)],[f10166,f3933]) ).
fof(f10334,plain,
( ~ sQ190_spl
| ~ in(relation_dom(sK75_skl),sK76_skl) ),
inference(resolution,[status(thm)],[f10166,f292]) ).
fof(f10437,plain,
! [X0] : ~ in(X0,union(sK85_skl)),
inference(resolution,[status(thm)],[f1422,f1877]) ).
fof(f10457,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,union(X1)) ),
inference(resolution,[status(thm)],[f1422,f1263]) ).
fof(f10494,plain,
( ~ sQ109_spl
| ~ sQ190_spl
| ~ empty(relation_dom(sK75_skl))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f10330,f3966]) ).
fof(f10495,definition,
( sQ220_spl
<=> empty(relation_dom(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f10498,plain,
( ~ sQ109_spl
| ~ sQ190_spl
| ~ sQ220_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f10494,f1928,f10495,f10165,f3932]) ).
fof(f10543,plain,
epsilon_connected(union(sK85_skl)),
inference(resolution,[status(thm)],[f10437,f511]) ).
fof(f10545,plain,
epsilon_transitive(union(sK85_skl)),
inference(resolution,[status(thm)],[f10437,f461]) ).
fof(f10546,plain,
union(sK85_skl) = sK85_skl,
inference(resolution,[status(thm)],[f10437,f3164]) ).
fof(f10553,plain,
! [X0] :
( is_antisymmetric_in(union(sK85_skl),X0)
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f565]) ).
fof(f10555,plain,
! [X0] :
( in(sK44_skl(X0,union(sK85_skl)),X0)
| X0 = relation_dom(union(sK85_skl))
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f556]) ).
fof(f10556,plain,
! [X0] :
( subset(union(sK85_skl),X0)
| ~ relation(X0)
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f519]) ).
fof(f10557,plain,
! [X0] :
( in(ordered_pair(sK28_skl(union(sK85_skl),X0),sK29_skl(union(sK85_skl),X0)),X0)
| X0 = union(sK85_skl)
| ~ relation(union(sK85_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f10437,f470]) ).
fof(f10558,plain,
! [X0,X1] :
( in(sK14_skl(X0,X1,union(sK85_skl)),X0)
| X0 = relation_inverse_image(union(sK85_skl),X1)
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f394]) ).
fof(f10559,plain,
! [X0,X1] :
( in(sK11_skl(X0,X1,union(sK85_skl)),X0)
| X0 = relation_image(union(sK85_skl),X1)
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f384]) ).
fof(f10560,plain,
! [X0,X1] :
( ~ in(X0,relation_image(union(sK85_skl),X1))
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f1387]) ).
fof(f10561,plain,
! [X0,X1] :
( in(ordered_pair(sK7_skl(X1,union(sK85_skl),X0),sK8_skl(X1,union(sK85_skl),X0)),X0)
| union(sK85_skl) = relation_rng_restriction(X1,X0)
| ~ relation(union(sK85_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f10437,f361]) ).
fof(f10562,plain,
! [X0,X1] :
( in(sK8_skl(X1,union(sK85_skl),X0),X1)
| union(sK85_skl) = relation_rng_restriction(X1,X0)
| ~ relation(union(sK85_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f10437,f360]) ).
fof(f10563,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,union(sK85_skl),X0),sK3_skl(X1,union(sK85_skl),X0)),X0)
| union(sK85_skl) = relation_dom_restriction(X0,X1)
| ~ relation(union(sK85_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f10437,f341]) ).
fof(f10564,plain,
! [X0,X1] :
( in(sK2_skl(X1,union(sK85_skl),X0),X1)
| union(sK85_skl) = relation_dom_restriction(X0,X1)
| ~ relation(union(sK85_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f10437,f340]) ).
fof(f10565,plain,
! [X0] :
( sK0_skl(X0,union(sK85_skl)) = sK1_skl(X0,union(sK85_skl))
| union(sK85_skl) = identity_relation(X0)
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f326]) ).
fof(f10566,plain,
! [X0] :
( in(sK0_skl(X0,union(sK85_skl)),X0)
| union(sK85_skl) = identity_relation(X0)
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f325]) ).
fof(f10567,plain,
! [X0] :
( ~ in(X0,relation_dom(union(sK85_skl)))
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f1419]) ).
fof(f10569,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(union(sK85_skl),X1))
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f1390]) ).
fof(f10570,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ is_reflexive_in(union(sK85_skl),X0)
| ~ relation(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10437,f422]) ).
fof(f10573,definition,
( sQ223_spl
<=> union(sK85_skl) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f10576,definition,
! [X0] :
( sQ224_spl
<=> in(X0,set_meet(union(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f10577,plain,
! [X0] :
( ~ sQ224_spl
| in(X0,set_meet(union(sK85_skl))) ),
inference(component_clause,[status(thm)],[f10576]) ).
fof(f10580,definition,
( sQ225_spl
<=> relation(union(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f10582,plain,
( sQ225_spl
| ~ relation(union(sK85_skl)) ),
inference(component_clause,[status(thm)],[f10580]) ).
fof(f10583,definition,
! [X0] :
( sQ226_spl
<=> is_antisymmetric_in(union(sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f10586,plain,
( sQ226_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10553,f10580,f10583]) ).
fof(f10588,definition,
! [X0] :
( sQ227_spl
<=> ( in(sK44_skl(X0,union(sK85_skl)),X0)
| X0 = relation_dom(union(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f10591,plain,
( sQ227_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10555,f10580,f10588]) ).
fof(f10592,definition,
! [X0] :
( sQ228_spl
<=> ( subset(union(sK85_skl),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f10595,plain,
( sQ228_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10556,f10580,f10592]) ).
fof(f10596,definition,
! [X0] :
( sQ229_spl
<=> ( in(ordered_pair(sK28_skl(union(sK85_skl),X0),sK29_skl(union(sK85_skl),X0)),X0)
| X0 = union(sK85_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f10599,plain,
( ~ sQ225_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f10557,f10596,f10580]) ).
fof(f10600,definition,
! [X0,X1] :
( sQ230_spl
<=> ( in(sK14_skl(X0,X1,union(sK85_skl)),X0)
| X0 = relation_inverse_image(union(sK85_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f10603,plain,
( sQ230_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10558,f10580,f10600]) ).
fof(f10604,definition,
! [X0,X1] :
( sQ231_spl
<=> ( in(sK11_skl(X0,X1,union(sK85_skl)),X0)
| X0 = relation_image(union(sK85_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f10607,plain,
( sQ231_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10559,f10580,f10604]) ).
fof(f10608,definition,
! [X0,X1] :
( sQ232_spl
<=> ~ in(X0,relation_image(union(sK85_skl),X1)) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f10611,plain,
( sQ232_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10560,f10580,f10608]) ).
fof(f10612,definition,
! [X0,X1] :
( sQ233_spl
<=> ( in(ordered_pair(sK7_skl(X1,union(sK85_skl),X0),sK8_skl(X1,union(sK85_skl),X0)),X0)
| union(sK85_skl) = relation_rng_restriction(X1,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f10615,plain,
( ~ sQ225_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f10561,f10612,f10580]) ).
fof(f10616,definition,
! [X0,X1] :
( sQ234_spl
<=> ( in(sK8_skl(X1,union(sK85_skl),X0),X1)
| union(sK85_skl) = relation_rng_restriction(X1,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f10619,plain,
( ~ sQ225_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f10562,f10616,f10580]) ).
fof(f10620,definition,
! [X0,X1] :
( sQ235_spl
<=> ( in(ordered_pair(sK2_skl(X1,union(sK85_skl),X0),sK3_skl(X1,union(sK85_skl),X0)),X0)
| union(sK85_skl) = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f10623,plain,
( ~ sQ225_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f10563,f10620,f10580]) ).
fof(f10624,definition,
! [X0,X1] :
( sQ236_spl
<=> ( in(sK2_skl(X1,union(sK85_skl),X0),X1)
| union(sK85_skl) = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f10627,plain,
( ~ sQ225_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f10564,f10624,f10580]) ).
fof(f10628,definition,
! [X0] :
( sQ237_spl
<=> ( sK0_skl(X0,union(sK85_skl)) = sK1_skl(X0,union(sK85_skl))
| union(sK85_skl) = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f10631,plain,
( sQ237_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10565,f10580,f10628]) ).
fof(f10632,definition,
! [X0] :
( sQ238_spl
<=> ( in(sK0_skl(X0,union(sK85_skl)),X0)
| union(sK85_skl) = identity_relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f10635,plain,
( sQ238_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10566,f10580,f10632]) ).
fof(f10636,definition,
! [X0] :
( sQ239_spl
<=> ~ in(X0,relation_dom(union(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f10639,plain,
( sQ239_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10567,f10580,f10636]) ).
fof(f10644,definition,
! [X0,X1] :
( sQ241_spl
<=> ~ in(X0,relation_inverse_image(union(sK85_skl),X1)) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f10647,plain,
( sQ241_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10569,f10580,f10644]) ).
fof(f10648,definition,
! [X0,X1] :
( sQ242_spl
<=> ( ~ in(X1,X0)
| ~ is_reflexive_in(union(sK85_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f10651,plain,
( sQ242_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f10570,f10580,f10648]) ).
fof(f10663,plain,
( ordinal(union(sK85_skl))
| ~ epsilon_connected(union(sK85_skl)) ),
inference(resolution,[status(thm)],[f10545,f307]) ).
fof(f10664,definition,
( sQ243_spl
<=> epsilon_connected(union(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f10666,plain,
( sQ243_spl
| ~ epsilon_connected(union(sK85_skl)) ),
inference(component_clause,[status(thm)],[f10664]) ).
fof(f10667,definition,
( sQ244_spl
<=> ordinal(union(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f10670,plain,
( sQ244_spl
| ~ sQ243_spl ),
inference(split_clause,[status(thm)],[f10663,f10664,f10667]) ).
fof(f10671,plain,
( sQ243_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10666,f10543]) ).
fof(f10672,plain,
sQ243_spl,
inference(contradiction_clause,[status(thm)],[f10671]) ).
fof(f10698,definition,
( sQ245_spl
<=> being_limit_ordinal(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f10704,plain,
( sQ225_spl
| ~ relation(sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f10546,f10582]) ).
fof(f10705,plain,
( sQ225_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10704,f875]) ).
fof(f10706,plain,
sQ225_spl,
inference(contradiction_clause,[status(thm)],[f10705]) ).
fof(f10966,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(union(X0),X1) ),
inference(resolution,[status(thm)],[f1423,f1468]) ).
fof(f11007,definition,
( sQ246_spl
<=> empty(ordered_pair(sK76_skl,sK77_skl)) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f11008,plain,
( ~ sQ246_spl
| empty(ordered_pair(sK76_skl,sK77_skl)) ),
inference(component_clause,[status(thm)],[f11007]) ).
fof(f11014,definition,
( sQ247_spl
<=> empty(ordered_pair(sK77_skl,sK76_skl)) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f11015,plain,
( ~ sQ247_spl
| empty(ordered_pair(sK77_skl,sK76_skl)) ),
inference(component_clause,[status(thm)],[f11014]) ).
fof(f11025,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(X0,ordered_pair(sK76_skl,sK77_skl))
| ~ in(sK75_skl,sK111_skl(ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f1496,f1267]) ).
fof(f11030,plain,
( ~ sQ2_spl
| empty(ordered_pair(sK76_skl,sK77_skl))
| ~ in(sK75_skl,sK70_skl(ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f1496,f4865]) ).
fof(f11035,plain,
! [X0] :
( ~ sQ2_spl
| in(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)))
| ordered_pair(sK76_skl,sK77_skl) = sK85_skl
| ~ in(sK75_skl,sK21_skl(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)),ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f1496,f4080]) ).
fof(f11041,plain,
( ~ sQ2_spl
| ordered_pair(sK76_skl,sK77_skl) = sK85_skl
| ~ in(sK75_skl,sK25_skl(ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f1496,f3164]) ).
fof(f11066,definition,
( sQ248_spl
<=> in(sK75_skl,sK111_skl(ordered_pair(sK76_skl,sK77_skl))) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f11069,definition,
! [X0] :
( sQ249_spl
<=> ~ in(X0,ordered_pair(sK76_skl,sK77_skl)) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f11070,plain,
! [X0] :
( ~ sQ249_spl
| ~ in(X0,ordered_pair(sK76_skl,sK77_skl)) ),
inference(component_clause,[status(thm)],[f11069]) ).
fof(f11072,plain,
( ~ sQ2_spl
| sQ249_spl
| ~ sQ248_spl ),
inference(split_clause,[status(thm)],[f11025,f11066,f11069,f1352]) ).
fof(f11075,definition,
( sQ250_spl
<=> in(sK75_skl,sK70_skl(ordered_pair(sK76_skl,sK77_skl))) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f11078,plain,
( ~ sQ2_spl
| sQ246_spl
| ~ sQ250_spl ),
inference(split_clause,[status(thm)],[f11030,f11075,f11007,f1352]) ).
fof(f11079,definition,
! [X0] :
( sQ251_spl
<=> ( in(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)))
| ~ in(sK75_skl,sK21_skl(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)),ordered_pair(sK76_skl,sK77_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f11082,definition,
( sQ252_spl
<=> ordered_pair(sK76_skl,sK77_skl) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f11083,plain,
( ~ sQ252_spl
| ordered_pair(sK76_skl,sK77_skl) = sK85_skl ),
inference(component_clause,[status(thm)],[f11082]) ).
fof(f11085,plain,
( ~ sQ2_spl
| sQ252_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f11035,f11079,f11082,f1352]) ).
fof(f11108,definition,
( sQ259_spl
<=> in(sK75_skl,sK25_skl(ordered_pair(sK76_skl,sK77_skl))) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f11111,plain,
( ~ sQ2_spl
| sQ252_spl
| ~ sQ259_spl ),
inference(split_clause,[status(thm)],[f11041,f11108,f11082,f1352]) ).
fof(f11179,plain,
( ~ sQ246_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11008,f721]) ).
fof(f11180,plain,
~ sQ246_spl,
inference(contradiction_clause,[status(thm)],[f11179]) ).
fof(f11188,plain,
( ~ sQ252_spl
| ~ empty(sK85_skl) ),
inference(paramodulation,[status(thm)],[f11083,f721]) ).
fof(f11207,plain,
( ~ sQ252_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f11188,f2319,f11082]) ).
fof(f11450,plain,
! [X0,X1] : ~ in(unordered_pair(X0,union(X1)),X1),
inference(resolution,[status(thm)],[f10966,f1407]) ).
fof(f11458,plain,
! [X0,X1] :
( ~ in(X1,powerset(X0))
| ~ in(X0,X1) ),
inference(paramodulation,[status(thm)],[f1308,f10966]) ).
fof(f11569,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(X0)
| ~ relation(sK85_skl)
| is_antisymmetric_in(X0,X1) ),
inference(resolution,[status(thm)],[f9952,f3966]) ).
fof(f11571,definition,
! [X0,X1] :
( sQ277_spl
<=> ( ~ empty(X0)
| is_antisymmetric_in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f11574,plain,
( ~ sQ109_spl
| ~ sQ54_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f11569,f11571,f1928,f3932]) ).
fof(f11587,plain,
! [X0] :
( empty(union(X0))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f10457,f4865]) ).
fof(f11631,plain,
! [X0,X1] :
( X1 = union(X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f11587,f1285]) ).
fof(f12049,plain,
! [X0,X1] : ~ subset(unordered_pair(X0,union(powerset(X1))),X1),
inference(resolution,[status(thm)],[f11450,f1404]) ).
fof(f12056,plain,
! [X0,X1] : ~ subset(unordered_pair(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f1308,f12049]) ).
fof(f12060,plain,
! [X0,X1] : ~ subset(unordered_pair(X0,X1),X0),
inference(paramodulation,[status(thm)],[f312,f12056]) ).
fof(f12177,plain,
! [X0,X1,X2] :
( ~ in(X2,sK52_skl(X1,relation_rng(X0),X0))
| ~ in(relation_dom(X0),X2)
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1427,f1124]) ).
fof(f12179,plain,
! [X0,X1] :
( ~ in(relation_dom(X0),sK52_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1427,f292]) ).
fof(f12180,plain,
! [X0] :
( in(sK52_skl(X0,sK85_skl,sK85_skl),relation_dom(sK85_skl))
| ~ in(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f1427]) ).
fof(f12182,plain,
! [X0] :
( in(sK52_skl(X0,relation_rng(sK85_skl),sK85_skl),sK85_skl)
| ~ in(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1427]) ).
fof(f12185,definition,
! [X0] :
( sQ278_spl
<=> ( in(sK52_skl(X0,sK85_skl,sK85_skl),relation_dom(sK85_skl))
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f12188,plain,
( sQ278_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12180,f1928,f1550,f12185]) ).
fof(f12192,definition,
! [X0] :
( sQ279_spl
<=> ( in(sK52_skl(X0,relation_rng(sK85_skl),sK85_skl),sK85_skl)
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f12195,plain,
( sQ279_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12182,f1928,f1550,f12192]) ).
fof(f12203,plain,
! [X0] :
( X0 = apply(sK85_skl,sK52_skl(X0,sK85_skl,sK85_skl))
| ~ in(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f1428]) ).
fof(f12205,definition,
! [X0] :
( sQ280_spl
<=> ( X0 = apply(sK85_skl,sK52_skl(X0,sK85_skl,sK85_skl))
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f12208,plain,
( sQ280_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12203,f1928,f1550,f12205]) ).
fof(f12252,plain,
! [X0] :
( empty(powerset(X0))
| ~ in(X0,sK70_skl(powerset(X0))) ),
inference(resolution,[status(thm)],[f11458,f4865]) ).
fof(f12290,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f11458,f1404]) ).
fof(f12295,plain,
! [X0] : ~ in(X0,sK70_skl(powerset(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f12252,f719]) ).
fof(f12327,plain,
! [X0] :
( X0 = sK85_skl
| ~ subset(X0,sK25_skl(X0)) ),
inference(resolution,[status(thm)],[f12290,f3164]) ).
fof(f12417,plain,
( powerset(sK85_skl) = sK85_skl
| ~ subset(powerset(sK85_skl),sK85_skl) ),
inference(paramodulation,[status(thm)],[f3198,f12327]) ).
fof(f12420,plain,
( sQ99_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f12417,f9690,f3332]) ).
fof(f12455,plain,
! [X0,X1] :
( ~ in(relation_rng(X0),apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1429,f292]) ).
fof(f12456,plain,
! [X0] :
( ~ in(X0,relation_dom(sK85_skl))
| in(apply(sK85_skl,X0),sK85_skl)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f1429]) ).
fof(f12460,definition,
! [X0] :
( sQ281_spl
<=> ( ~ in(X0,relation_dom(sK85_skl))
| in(apply(sK85_skl,X0),sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f12463,plain,
( sQ281_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12456,f1928,f1550,f12460]) ).
fof(f12482,plain,
! [X0,X1] :
( ~ in(relation_dom(X0),sK54_skl(X1,X0))
| in(sK53_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f594,f292]) ).
fof(f12483,plain,
! [X0] :
( in(sK54_skl(X0,sK85_skl),sK85_skl)
| in(sK53_skl(X0,sK85_skl),X0)
| X0 = relation_rng(sK85_skl)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f594]) ).
fof(f12486,definition,
! [X0] :
( sQ282_spl
<=> ( in(sK54_skl(X0,sK85_skl),sK85_skl)
| in(sK53_skl(X0,sK85_skl),X0)
| X0 = relation_rng(sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f12489,plain,
( sQ282_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12483,f1928,f1550,f12486]) ).
fof(f12538,plain,
! [X0] :
( ~ sQ183_spl
| is_antisymmetric_in(sK75_skl,X0)
| ~ relation(sK75_skl)
| is_antisymmetric_in(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f10047,f566]) ).
fof(f12543,definition,
! [X0] :
( sQ288_spl
<=> ( is_antisymmetric_in(sK75_skl,X0)
| is_antisymmetric_in(sK75_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f12544,plain,
! [X0] :
( ~ sQ288_spl
| is_antisymmetric_in(sK75_skl,X0)
| is_antisymmetric_in(sK75_skl,X0) ),
inference(component_clause,[status(thm)],[f12543]) ).
fof(f12546,plain,
( ~ sQ183_spl
| ~ sQ46_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f12538,f12543,f1828,f10043]) ).
fof(f12554,plain,
! [X0] :
( ~ sQ288_spl
| is_antisymmetric_in(sK75_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f12544]) ).
fof(f12557,plain,
( ~ sQ288_spl
| antisymmetric(sK75_skl)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f12554,f365]) ).
fof(f12558,plain,
( ~ sQ288_spl
| sQ0_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f12557,f1828,f1345,f12543]) ).
fof(f12571,plain,
! [X0] :
( ~ sQ2_spl
| in(ordered_pair(sK76_skl,sK77_skl),X0)
| ~ subset(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f1353,f525]) ).
fof(f12713,plain,
! [X0] :
( ~ in(X0,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1430,f1877]) ).
fof(f12735,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1430,f1263]) ).
fof(f12739,plain,
! [X0,X1,X2] :
( ~ in(X2,ordered_pair(sK55_skl(X1,relation_rng(X0),X0),X1))
| ~ in(X0,X2)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1430,f1124]) ).
fof(f12741,plain,
! [X0,X1] :
( ~ in(X0,ordered_pair(sK55_skl(X1,relation_rng(X0),X0),X1))
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1430,f292]) ).
fof(f12742,plain,
! [X0] :
( in(ordered_pair(sK55_skl(X0,sK85_skl,sK85_skl),X0),sK85_skl)
| ~ in(X0,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f1430]) ).
fof(f12755,definition,
! [X0] :
( sQ290_spl
<=> ~ in(X0,relation_rng(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f12758,plain,
( sQ290_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12713,f1928,f12755]) ).
fof(f12760,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f12735,f301]) ).
fof(f12762,definition,
! [X0] :
( sQ291_spl
<=> ( in(ordered_pair(sK55_skl(X0,sK85_skl,sK85_skl),X0),sK85_skl)
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f12765,plain,
( sQ291_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12742,f1928,f12762]) ).
fof(f12772,plain,
( ~ sQ2_spl
| in(sK77_skl,relation_rng(sK75_skl))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1431,f1353]) ).
fof(f12813,definition,
( sQ293_spl
<=> in(sK77_skl,relation_rng(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f12814,plain,
( ~ sQ293_spl
| in(sK77_skl,relation_rng(sK75_skl)) ),
inference(component_clause,[status(thm)],[f12813]) ).
fof(f12816,plain,
( ~ sQ2_spl
| sQ293_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f12772,f1828,f12813,f1352]) ).
fof(f12883,plain,
( ~ sQ109_spl
| ~ sQ293_spl
| ~ is_reflexive_in(sK85_skl,relation_rng(sK75_skl)) ),
inference(resolution,[status(thm)],[f12814,f3933]) ).
fof(f12958,plain,
! [X0,X1] :
( ~ in(X1,ordered_pair(X0,sK43_skl(X0,sK85_skl,sK85_skl)))
| ~ in(sK85_skl,X1)
| ~ in(X0,relation_dom(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f8875]) ).
fof(f12963,definition,
! [X0,X1] :
( sQ303_spl
<=> ( ~ in(X1,ordered_pair(X0,sK43_skl(X0,sK85_skl,sK85_skl)))
| ~ in(sK85_skl,X1)
| ~ in(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f12966,plain,
( sQ303_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f12958,f1928,f12963]) ).
fof(f13002,plain,
( ~ sQ109_spl
| ~ sQ293_spl
| ~ empty(relation_rng(sK75_skl))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f12883,f3966]) ).
fof(f13003,definition,
( sQ307_spl
<=> empty(relation_rng(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f13006,plain,
( ~ sQ109_spl
| ~ sQ293_spl
| ~ sQ307_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13002,f1928,f13003,f12813,f3932]) ).
fof(f13076,plain,
! [X0] :
( in(sK56_skl(X0,sK85_skl),X0)
| X0 = relation_rng(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f603,f1877]) ).
fof(f13117,definition,
! [X0] :
( sQ308_spl
<=> ( in(sK56_skl(X0,sK85_skl),X0)
| X0 = relation_rng(sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f13120,plain,
( sQ308_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13076,f1928,f13117]) ).
fof(f13172,definition,
! [X0] :
( sQ309_spl
<=> ~ in(sK76_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f13173,plain,
! [X0] :
( ~ sQ309_spl
| ~ in(sK76_skl,X0) ),
inference(component_clause,[status(thm)],[f13172]) ).
fof(f13201,plain,
! [X0] :
( ~ in(sK85_skl,ordered_pair(X0,sK43_skl(X0,sK85_skl,sK85_skl)))
| ~ in(X0,relation_dom(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f8877]) ).
fof(f13203,definition,
! [X0] :
( sQ311_spl
<=> ( ~ in(sK85_skl,ordered_pair(X0,sK43_skl(X0,sK85_skl,sK85_skl)))
| ~ in(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f13206,plain,
( sQ311_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13201,f1928,f13203]) ).
fof(f13650,plain,
! [X0] :
( ~ proper_subset(succ(X0),X0)
| X0 = succ(X0) ),
inference(resolution,[status(thm)],[f6120,f294]) ).
fof(f13651,plain,
( sK85_skl = succ(sK85_skl)
| proper_subset(sK85_skl,powerset(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f3000,f6120]) ).
fof(f13653,definition,
( sQ312_spl
<=> proper_subset(sK85_skl,powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f13656,plain,
( sQ167_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f13651,f13653,f9687]) ).
fof(f13667,plain,
! [X0] : ordered_pair(X0,X0) = unordered_pair(singleton(X0),singleton(X0)),
inference(paramodulation,[status(thm)],[f1241,f606]) ).
fof(f13673,plain,
! [X0,X1] : ~ in(ordered_pair(X0,X1),X1),
inference(paramodulation,[status(thm)],[f606,f2180]) ).
fof(f13680,plain,
! [X0,X1] : ~ subset(ordered_pair(X0,X1),unordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f606,f12060]) ).
fof(f13689,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,ordered_pair(X0,X1)) ),
inference(paramodulation,[status(thm)],[f606,f4033]) ).
fof(f13709,plain,
! [X0,X1] : ~ in(ordered_pair(X0,X1),singleton(X0)),
inference(paramodulation,[status(thm)],[f606,f2035]) ).
fof(f13711,plain,
! [X0,X1] : in(singleton(X0),ordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f606,f1407]) ).
fof(f13712,plain,
! [X0,X1] : in(unordered_pair(X0,X1),ordered_pair(X0,X1)),
inference(paramodulation,[status(thm)],[f606,f1406]) ).
fof(f13715,plain,
! [X0] : ordered_pair(X0,X0) = singleton(singleton(X0)),
inference(forward_demodulation,[status(thm)],[f1241,f13667]) ).
fof(f13718,plain,
( relation_field(sK85_skl) = set_union2(sK85_skl,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f612]) ).
fof(f13720,plain,
( relation_field(sK85_skl) = set_union2(relation_dom(sK85_skl),sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f612]) ).
fof(f13722,definition,
( sQ313_spl
<=> relation_field(sK85_skl) = set_union2(sK85_skl,relation_rng(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f13723,plain,
( ~ sQ313_spl
| relation_field(sK85_skl) = set_union2(sK85_skl,relation_rng(sK85_skl)) ),
inference(component_clause,[status(thm)],[f13722]) ).
fof(f13725,plain,
( sQ313_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13718,f1928,f13722]) ).
fof(f13729,definition,
( sQ314_spl
<=> relation_field(sK85_skl) = set_union2(relation_dom(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f13732,plain,
( sQ314_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13720,f1928,f13729]) ).
fof(f13736,plain,
( ~ sQ313_spl
| relation_field(sK85_skl) = relation_rng(sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1964,f13723]) ).
fof(f13737,plain,
( ~ sQ313_spl
| relation_field(sK85_skl) = sK85_skl ),
inference(forward_demodulation,[status(thm)],[f1886,f13736]) ).
fof(f13812,plain,
! [X0] :
( ~ in(X0,relation_rng(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f13673,f1430]) ).
fof(f13813,plain,
! [X0,X1] :
( ~ in(X0,relation_image(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f13673,f1387]) ).
fof(f13848,plain,
( ~ in(sK85_skl,sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f13812]) ).
fof(f13850,definition,
( sQ317_spl
<=> in(sK85_skl,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f13853,plain,
( ~ sQ317_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13848,f1928,f13850]) ).
fof(f13874,plain,
( ~ sQ313_spl
| is_transitive_in(sK85_skl,sK85_skl)
| ~ transitive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f13737,f398]) ).
fof(f13876,plain,
( ~ sQ313_spl
| is_antisymmetric_in(sK85_skl,sK85_skl)
| ~ antisymmetric(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f13737,f364]) ).
fof(f13877,definition,
( sQ318_spl
<=> transitive(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f13880,definition,
( sQ319_spl
<=> is_transitive_in(sK85_skl,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f13884,plain,
( ~ sQ313_spl
| sQ319_spl
| ~ sQ318_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13874,f1928,f13877,f13880,f13722]) ).
fof(f13885,definition,
( sQ320_spl
<=> is_antisymmetric_in(sK85_skl,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f13889,plain,
( ~ sQ313_spl
| sQ320_spl
| ~ sQ209_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13876,f1928,f10305,f13885,f13722]) ).
fof(f13890,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(ordered_pair(X0,X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f13689,f3966]) ).
fof(f13891,definition,
! [X0,X1] :
( sQ321_spl
<=> ~ empty(ordered_pair(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f13894,plain,
( ~ sQ109_spl
| sQ321_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f13890,f1928,f13891,f3932]) ).
fof(f14032,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),relation_inverse(X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1433,f680]) ).
fof(f14061,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,ordered_pair(X2,X1))
| ~ in(relation_inverse(X0),X3)
| ~ in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f14032,f1124]) ).
fof(f14144,plain,
! [X0] :
( in(ordered_pair(sK59_skl(sK85_skl,X0),sK58_skl(sK85_skl,X0)),X0)
| sK85_skl = relation_inverse(X0)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f620,f1877]) ).
fof(f14185,definition,
! [X0] :
( sQ322_spl
<=> ( in(ordered_pair(sK59_skl(sK85_skl,X0),sK58_skl(sK85_skl,X0)),X0)
| sK85_skl = relation_inverse(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f14188,plain,
( ~ sQ54_spl
| sQ322_spl ),
inference(split_clause,[status(thm)],[f14144,f14185,f1928]) ).
fof(f14347,plain,
! [X0] :
( in(sK85_skl,X0)
| X0 = sK85_skl
| in(X0,sK85_skl)
| ~ in(X0,succ(powerset(sK85_skl)))
| ~ epsilon_connected(succ(powerset(sK85_skl))) ),
inference(resolution,[status(thm)],[f6169,f509]) ).
fof(f14349,plain,
( subset(sK85_skl,succ(powerset(sK85_skl)))
| ~ epsilon_transitive(succ(powerset(sK85_skl))) ),
inference(resolution,[status(thm)],[f6169,f460]) ).
fof(f14355,definition,
( sQ324_spl
<=> ordinal(succ(powerset(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f14359,definition,
( sQ325_spl
<=> epsilon_connected(succ(powerset(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f14361,plain,
( sQ325_spl
| ~ epsilon_connected(succ(powerset(sK85_skl))) ),
inference(component_clause,[status(thm)],[f14359]) ).
fof(f14362,definition,
! [X0] :
( sQ326_spl
<=> ( in(sK85_skl,X0)
| X0 = sK85_skl
| in(X0,sK85_skl)
| ~ in(X0,succ(powerset(sK85_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f14365,plain,
( sQ326_spl
| ~ sQ325_spl ),
inference(split_clause,[status(thm)],[f14347,f14359,f14362]) ).
fof(f14366,definition,
( sQ327_spl
<=> epsilon_transitive(succ(powerset(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f14367,plain,
( ~ sQ327_spl
| epsilon_transitive(succ(powerset(sK85_skl))) ),
inference(component_clause,[status(thm)],[f14366]) ).
fof(f14368,plain,
( sQ327_spl
| ~ epsilon_transitive(succ(powerset(sK85_skl))) ),
inference(component_clause,[status(thm)],[f14366]) ).
fof(f14369,definition,
( sQ328_spl
<=> subset(sK85_skl,succ(powerset(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f14372,plain,
( sQ328_spl
| ~ sQ327_spl ),
inference(split_clause,[status(thm)],[f14349,f14366,f14369]) ).
fof(f14373,plain,
( sQ327_spl
| ~ ordinal(powerset(sK85_skl)) ),
inference(resolution,[status(thm)],[f14368,f744]) ).
fof(f14374,plain,
( sQ327_spl
| ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14373,f3020]) ).
fof(f14375,plain,
( sQ327_spl
| ~ sQ75_spl ),
inference(contradiction_clause,[status(thm)],[f14374]) ).
fof(f14376,plain,
( sQ325_spl
| ~ ordinal(powerset(sK85_skl)) ),
inference(resolution,[status(thm)],[f14361,f745]) ).
fof(f14377,plain,
( sQ325_spl
| ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14376,f3020]) ).
fof(f14378,plain,
( sQ325_spl
| ~ sQ75_spl ),
inference(contradiction_clause,[status(thm)],[f14377]) ).
fof(f14380,plain,
( ~ sQ327_spl
| ordinal(succ(powerset(sK85_skl)))
| ~ epsilon_connected(succ(powerset(sK85_skl))) ),
inference(resolution,[status(thm)],[f14367,f307]) ).
fof(f14381,plain,
( ~ sQ327_spl
| sQ324_spl
| ~ sQ325_spl ),
inference(split_clause,[status(thm)],[f14380,f14359,f14355,f14366]) ).
fof(f14395,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(X0,singleton(X1)))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f6195,f3966]) ).
fof(f14402,definition,
! [X0,X1] :
( sQ331_spl
<=> ~ empty(set_union2(X0,singleton(X1))) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f14405,plain,
( ~ sQ109_spl
| sQ331_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f14395,f1928,f14402,f3932]) ).
fof(f14406,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(singleton(X0),X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f6455,f3966]) ).
fof(f14413,definition,
! [X0,X1] :
( sQ332_spl
<=> ~ empty(set_union2(singleton(X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f14416,plain,
( ~ sQ109_spl
| sQ332_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f14406,f1928,f14413,f3932]) ).
fof(f14422,plain,
! [X0,X1] : in(X0,set_union2(X1,powerset(X0))),
inference(resolution,[status(thm)],[f6916,f2086]) ).
fof(f14423,plain,
! [X0,X1] : in(X0,set_union2(powerset(X0),X1)),
inference(resolution,[status(thm)],[f6916,f1269]) ).
fof(f14491,definition,
( sQ333_spl
<=> in(sK60_skl(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f14492,plain,
( ~ sQ333_spl
| in(sK60_skl(sK85_skl),sK85_skl) ),
inference(component_clause,[status(thm)],[f14491]) ).
fof(f14511,definition,
( sQ334_spl
<=> in(sK61_skl(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f14512,plain,
( ~ sQ334_spl
| in(sK61_skl(sK85_skl),sK85_skl) ),
inference(component_clause,[status(thm)],[f14511]) ).
fof(f14516,plain,
! [X0] :
( ~ sQ190_spl
| ~ empty(sK75_skl)
| in(sK76_skl,X0) ),
inference(resolution,[status(thm)],[f10325,f9139]) ).
fof(f14519,plain,
! [X0] :
( ~ sQ190_spl
| in(sK76_skl,set_union2(X0,relation_dom(sK75_skl))) ),
inference(resolution,[status(thm)],[f10325,f2086]) ).
fof(f14520,plain,
! [X0] :
( ~ sQ190_spl
| in(sK76_skl,set_union2(relation_dom(sK75_skl),X0)) ),
inference(resolution,[status(thm)],[f10325,f1269]) ).
fof(f14523,definition,
! [X0] :
( sQ335_spl
<=> in(sK76_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f14524,plain,
! [X0] :
( ~ sQ335_spl
| in(sK76_skl,X0) ),
inference(component_clause,[status(thm)],[f14523]) ).
fof(f14526,plain,
( ~ sQ190_spl
| ~ sQ210_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f14516,f14523,f10310,f10165]) ).
fof(f14559,plain,
( ~ sQ2_spl
| ~ subset(sK75_skl,singleton(sK76_skl)) ),
inference(resolution,[status(thm)],[f10151,f13709]) ).
fof(f14564,plain,
! [X0,X1] :
( ~ sQ2_spl
| sK77_skl = sK76_skl
| ~ in(ordered_pair(sK77_skl,sK76_skl),X0)
| ~ in(sK76_skl,X1)
| ~ in(sK77_skl,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ~ subset(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f10151,f561]) ).
fof(f14572,plain,
! [X0] :
( ~ sQ2_spl
| ~ empty(X0)
| ~ subset(sK75_skl,relation_rng(X0)) ),
inference(resolution,[status(thm)],[f10151,f12760]) ).
fof(f14586,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(X0,ordered_pair(sK76_skl,sK77_skl))
| ~ subset(sK75_skl,sK111_skl(ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f10151,f7122]) ).
fof(f14598,plain,
( ~ sQ2_spl
| empty(ordered_pair(sK76_skl,sK77_skl))
| ~ subset(sK75_skl,sK70_skl(ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f10151,f5754]) ).
fof(f14609,plain,
! [X0] :
( ~ sQ2_spl
| in(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)))
| ordered_pair(sK76_skl,sK77_skl) = sK85_skl
| ~ subset(sK75_skl,sK21_skl(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)),ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f10151,f4115]) ).
fof(f14624,plain,
( ~ sQ2_spl
| ordered_pair(sK76_skl,sK77_skl) = sK85_skl
| ~ subset(sK75_skl,sK25_skl(ordered_pair(sK76_skl,sK77_skl))) ),
inference(resolution,[status(thm)],[f10151,f3196]) ).
fof(f14697,plain,
! [X0] :
( ~ sQ2_spl
| ~ empty(X0)
| ~ subset(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f10151,f1263]) ).
fof(f14699,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ2_spl
| ~ is_reflexive_in(sK85_skl,X0)
| ~ subset(sK75_skl,X0) ),
inference(resolution,[status(thm)],[f10151,f3933]) ).
fof(f14707,definition,
! [X0,X1] :
( sQ341_spl
<=> ( ~ in(ordered_pair(sK77_skl,sK76_skl),X0)
| ~ in(sK76_skl,X1)
| ~ in(sK77_skl,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ~ subset(sK75_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f14710,plain,
( ~ sQ2_spl
| sQ4_spl
| sQ341_spl ),
inference(split_clause,[status(thm)],[f14564,f14707,f1360,f1352]) ).
fof(f14719,definition,
( sQ344_spl
<=> subset(sK75_skl,sK111_skl(ordered_pair(sK76_skl,sK77_skl))) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f14722,plain,
( ~ sQ2_spl
| sQ249_spl
| ~ sQ344_spl ),
inference(split_clause,[status(thm)],[f14586,f14719,f11069,f1352]) ).
fof(f14723,definition,
( sQ345_spl
<=> subset(sK75_skl,sK70_skl(ordered_pair(sK76_skl,sK77_skl))) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f14726,plain,
( ~ sQ2_spl
| sQ246_spl
| ~ sQ345_spl ),
inference(split_clause,[status(thm)],[f14598,f14723,f11007,f1352]) ).
fof(f14727,definition,
! [X0] :
( sQ346_spl
<=> ( in(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)))
| ~ subset(sK75_skl,sK21_skl(X0,set_meet(ordered_pair(sK76_skl,sK77_skl)),ordered_pair(sK76_skl,sK77_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f14730,plain,
( ~ sQ2_spl
| sQ252_spl
| sQ346_spl ),
inference(split_clause,[status(thm)],[f14609,f14727,f11082,f1352]) ).
fof(f14747,definition,
( sQ351_spl
<=> subset(sK75_skl,sK25_skl(ordered_pair(sK76_skl,sK77_skl))) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f14750,plain,
( ~ sQ2_spl
| sQ252_spl
| ~ sQ351_spl ),
inference(split_clause,[status(thm)],[f14624,f14747,f11082,f1352]) ).
fof(f15001,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(X0,powerset(X1))) ),
inference(resolution,[status(thm)],[f14422,f3933]) ).
fof(f15049,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(powerset(X0),X1)) ),
inference(resolution,[status(thm)],[f14423,f3933]) ).
fof(f15059,plain,
( ~ sQ249_spl
| $false ),
inference(resolution,[status(thm)],[f11070,f13711]) ).
fof(f15112,plain,
~ sQ249_spl,
inference(contradiction_clause,[status(thm)],[f15059]) ).
fof(f15128,plain,
! [X0,X1] : in(X0,set_union2(X1,sK112_skl(X0))),
inference(resolution,[status(thm)],[f6921,f2086]) ).
fof(f15129,plain,
! [X0,X1] : in(X0,set_union2(sK112_skl(X0),X1)),
inference(resolution,[status(thm)],[f6921,f1269]) ).
fof(f15240,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),relation_composition(sK85_skl,X0))
| ~ relation(relation_composition(sK85_skl,X0))
| ~ relation(X0)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f1434,f1877]) ).
fof(f15283,definition,
! [X0,X1,X2] :
( sQ385_spl
<=> ( ~ in(ordered_pair(X1,X2),relation_composition(sK85_skl,X0))
| ~ relation(relation_composition(sK85_skl,X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f15286,plain,
( sQ385_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f15240,f1928,f15283]) ).
fof(f15556,plain,
( ~ sQ105_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3709,f3712]) ).
fof(f15557,plain,
~ sQ105_spl,
inference(contradiction_clause,[status(thm)],[f15556]) ).
fof(f15558,plain,
( ~ sQ123_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6091,f3713]) ).
fof(f15559,plain,
~ sQ123_spl,
inference(contradiction_clause,[status(thm)],[f15558]) ).
fof(f15716,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),relation_composition(X0,sK85_skl))
| ~ relation(relation_composition(X0,sK85_skl))
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1435,f1877]) ).
fof(f15759,definition,
! [X0,X1,X2] :
( sQ416_spl
<=> ( ~ in(ordered_pair(X1,X2),relation_composition(X0,sK85_skl))
| ~ relation(relation_composition(X0,sK85_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f15762,plain,
( ~ sQ54_spl
| sQ416_spl ),
inference(split_clause,[status(thm)],[f15716,f15759,f1928]) ).
fof(f15795,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(X5,ordered_pair(X2,X4))
| ~ in(relation_composition(X0,X1),X5)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1436,f1124]) ).
fof(f15997,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(X0,sK112_skl(X1))) ),
inference(resolution,[status(thm)],[f15128,f3933]) ).
fof(f16054,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(sK112_skl(X0),X1)) ),
inference(resolution,[status(thm)],[f15129,f3933]) ).
fof(f16170,plain,
! [X0,X1] :
( in(ordered_pair(sK63_skl(sK85_skl,X1,X0),sK65_skl(sK85_skl,X1,X0)),X0)
| sK85_skl = relation_composition(X0,X1)
| ~ relation(sK85_skl)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f641,f1877]) ).
fof(f16212,definition,
! [X0,X1] :
( sQ417_spl
<=> ( in(ordered_pair(sK63_skl(sK85_skl,X1,X0),sK65_skl(sK85_skl,X1,X0)),X0)
| sK85_skl = relation_composition(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f16215,plain,
( ~ sQ54_spl
| sQ417_spl ),
inference(split_clause,[status(thm)],[f16170,f16212,f1928]) ).
fof(f16274,plain,
! [X0,X1] :
( in(ordered_pair(sK65_skl(sK85_skl,X1,X0),sK64_skl(sK85_skl,X1,X0)),X1)
| sK85_skl = relation_composition(X0,X1)
| ~ relation(sK85_skl)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f642,f1877]) ).
fof(f16316,definition,
! [X0,X1] :
( sQ418_spl
<=> ( in(ordered_pair(sK65_skl(sK85_skl,X1,X0),sK64_skl(sK85_skl,X1,X0)),X1)
| sK85_skl = relation_composition(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f16319,plain,
( ~ sQ54_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f16274,f16316,f1928]) ).
fof(f16325,plain,
! [X0,X1] :
( ~ sQ2_spl
| in(ordered_pair(X1,sK77_skl),sK75_skl)
| ~ in(ordered_pair(X1,sK76_skl),sK75_skl)
| ~ in(sK77_skl,X0)
| ~ in(sK76_skl,X0)
| ~ in(X1,X0)
| ~ is_transitive_in(sK75_skl,X0)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f647,f1353]) ).
fof(f16379,definition,
! [X0,X1] :
( sQ419_spl
<=> ( in(ordered_pair(X1,sK77_skl),sK75_skl)
| ~ in(ordered_pair(X1,sK76_skl),sK75_skl)
| ~ in(sK77_skl,X0)
| ~ in(sK76_skl,X0)
| ~ in(X1,X0)
| ~ is_transitive_in(sK75_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f16380,plain,
! [X0,X1] :
( ~ sQ419_spl
| in(ordered_pair(X1,sK77_skl),sK75_skl)
| ~ in(ordered_pair(X1,sK76_skl),sK75_skl)
| ~ in(sK77_skl,X0)
| ~ in(sK76_skl,X0)
| ~ in(X1,X0)
| ~ is_transitive_in(sK75_skl,X0) ),
inference(component_clause,[status(thm)],[f16379]) ).
fof(f16382,plain,
( ~ sQ2_spl
| sQ419_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f16325,f1828,f16379,f1352]) ).
fof(f16412,plain,
( ~ sQ2_spl
| ~ empty(sK85_skl)
| ~ subset(sK75_skl,sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f14572]) ).
fof(f16415,definition,
( sQ421_spl
<=> subset(sK75_skl,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f16418,plain,
( ~ sQ2_spl
| ~ sQ62_spl
| ~ sQ421_spl ),
inference(split_clause,[status(thm)],[f16412,f16415,f2319,f1352]) ).
fof(f16693,plain,
! [X0,X1] : in(X0,set_union2(X1,sK93_skl(X0))),
inference(resolution,[status(thm)],[f6922,f2086]) ).
fof(f16694,plain,
! [X0,X1] : in(X0,set_union2(sK93_skl(X0),X1)),
inference(resolution,[status(thm)],[f6922,f1269]) ).
fof(f16785,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(X0,sK93_skl(X1))) ),
inference(resolution,[status(thm)],[f16693,f3933]) ).
fof(f16843,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(sK93_skl(X0),X1)) ),
inference(resolution,[status(thm)],[f16694,f3933]) ).
fof(f17107,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ2_spl
| ~ is_reflexive_in(sK85_skl,set_union2(X0,sK75_skl)) ),
inference(resolution,[status(thm)],[f14699,f2086]) ).
fof(f17108,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ2_spl
| ~ is_reflexive_in(sK85_skl,set_union2(sK75_skl,X0)) ),
inference(resolution,[status(thm)],[f14699,f1269]) ).
fof(f17111,definition,
! [X0] :
( sQ425_spl
<=> ~ is_reflexive_in(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f17112,plain,
! [X0] :
( ~ sQ425_spl
| ~ is_reflexive_in(sK85_skl,X0) ),
inference(component_clause,[status(thm)],[f17111]) ).
fof(f17115,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ2_spl
| ~ empty(set_union2(X0,sK75_skl))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f17107,f3966]) ).
fof(f17120,definition,
! [X0] :
( sQ426_spl
<=> ~ empty(set_union2(X0,sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f17123,plain,
( ~ sQ109_spl
| ~ sQ2_spl
| sQ426_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f17115,f1928,f17120,f1352,f3932]) ).
fof(f17124,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ2_spl
| ~ empty(set_union2(sK75_skl,X0))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f17108,f3966]) ).
fof(f17130,definition,
! [X0] :
( sQ427_spl
<=> ~ empty(set_union2(sK75_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f17133,plain,
( ~ sQ109_spl
| ~ sQ2_spl
| sQ427_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f17124,f1928,f17130,f1352,f3932]) ).
fof(f17193,plain,
! [X0,X1] : in(X0,set_union2(X1,succ(X0))),
inference(resolution,[status(thm)],[f6924,f2086]) ).
fof(f17194,plain,
! [X0,X1] : in(X0,set_union2(succ(X0),X1)),
inference(resolution,[status(thm)],[f6924,f1269]) ).
fof(f17289,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(X0,succ(X1))) ),
inference(resolution,[status(thm)],[f17193,f3933]) ).
fof(f17329,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| is_transitive_in(relation_image(X0,X1),X2)
| ~ relation(relation_image(X0,X1)) ),
inference(resolution,[status(thm)],[f651,f2492]) ).
fof(f17388,plain,
! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f651,f1263]) ).
fof(f17390,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f651,f3933]) ).
fof(f17407,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| is_transitive_in(relation_image(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f17329,f8087]) ).
fof(f17409,definition,
! [X0] :
( sQ428_spl
<=> is_transitive_in(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f17418,plain,
! [X0,X1] :
( ~ empty(X0)
| is_transitive_in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f17388,f301]) ).
fof(f17419,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| is_transitive_in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f17390,f4014]) ).
fof(f17639,definition,
! [X0] :
( sQ432_spl
<=> ~ in(X0,ordered_pair(sK77_skl,sK76_skl)) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f17640,plain,
! [X0] :
( ~ sQ432_spl
| ~ in(X0,ordered_pair(sK77_skl,sK76_skl)) ),
inference(component_clause,[status(thm)],[f17639]) ).
fof(f17652,definition,
( sQ435_spl
<=> ordered_pair(sK77_skl,sK76_skl) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f17653,plain,
( ~ sQ435_spl
| ordered_pair(sK77_skl,sK76_skl) = sK85_skl ),
inference(component_clause,[status(thm)],[f17652]) ).
fof(f17781,plain,
( ~ sQ247_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11015,f721]) ).
fof(f17782,plain,
~ sQ247_spl,
inference(contradiction_clause,[status(thm)],[f17781]) ).
fof(f17788,plain,
( ~ sQ435_spl
| ~ subset(sK85_skl,unordered_pair(sK77_skl,sK76_skl)) ),
inference(paramodulation,[status(thm)],[f17653,f13680]) ).
fof(f17818,plain,
( ~ sQ435_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17788,f1875]) ).
fof(f17819,plain,
~ sQ435_spl,
inference(contradiction_clause,[status(thm)],[f17818]) ).
fof(f17932,plain,
! [X0] :
( transitive(X0)
| ~ relation(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f17418,f399]) ).
fof(f17933,plain,
! [X0] :
( transitive(X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17932,f301]) ).
fof(f17936,plain,
! [X0,X1] :
( ~ empty(X0)
| transitive(relation_image(X0,X1)) ),
inference(resolution,[status(thm)],[f17933,f8074]) ).
fof(f17995,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,set_union2(succ(X0),X1)) ),
inference(resolution,[status(thm)],[f17194,f3933]) ).
fof(f18388,plain,
( ~ sQ432_spl
| $false ),
inference(resolution,[status(thm)],[f17640,f13711]) ).
fof(f18447,plain,
~ sQ432_spl,
inference(contradiction_clause,[status(thm)],[f18388]) ).
fof(f18511,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(X0)
| ~ relation(sK85_skl)
| is_transitive_in(X0,X1) ),
inference(resolution,[status(thm)],[f17419,f3966]) ).
fof(f18513,definition,
! [X0,X1] :
( sQ515_spl
<=> ( ~ empty(X0)
| is_transitive_in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f18516,plain,
( ~ sQ109_spl
| ~ sQ54_spl
| sQ515_spl ),
inference(split_clause,[status(thm)],[f18511,f18513,f1928,f3932]) ).
fof(f18888,definition,
( sQ516_spl
<=> subset(sK75_skl,powerset(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f19056,plain,
! [X0] :
( ~ sQ109_spl
| is_transitive_in(relation_field(sK85_skl),X0)
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f17419]) ).
fof(f19057,plain,
! [X0] :
( ~ sQ109_spl
| is_antisymmetric_in(relation_field(sK85_skl),X0)
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f9952]) ).
fof(f19058,plain,
! [X0] :
( ~ sQ109_spl
| subset(relation_field(sK85_skl),X0)
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f7192]) ).
fof(f19059,plain,
( ~ sQ109_spl
| empty(relation_field(sK85_skl))
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f5750]) ).
fof(f19060,plain,
( ~ sQ109_spl
| relation(relation_field(sK85_skl))
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f4014]) ).
fof(f19061,plain,
( ~ sQ109_spl
| relation_field(sK85_skl) = sK85_skl
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f4012]) ).
fof(f19062,plain,
( ~ sQ109_spl
| epsilon_transitive(relation_field(sK85_skl))
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f4011]) ).
fof(f19063,plain,
( ~ sQ109_spl
| epsilon_connected(relation_field(sK85_skl))
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f4009]) ).
fof(f19064,plain,
( ~ sQ109_spl
| ordinal(relation_field(sK85_skl))
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f671,f4008]) ).
fof(f19067,definition,
( sQ540_spl
<=> reflexive(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f19070,definition,
! [X0] :
( sQ541_spl
<=> is_transitive_in(relation_field(sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ541_spl])],[split_symbol_definition]) ).
fof(f19073,plain,
( ~ sQ109_spl
| sQ541_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19056,f1928,f19067,f19070,f3932]) ).
fof(f19074,definition,
! [X0] :
( sQ542_spl
<=> is_antisymmetric_in(relation_field(sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f19077,plain,
( ~ sQ109_spl
| sQ542_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19057,f1928,f19067,f19074,f3932]) ).
fof(f19078,definition,
! [X0] :
( sQ543_spl
<=> subset(relation_field(sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ543_spl])],[split_symbol_definition]) ).
fof(f19081,plain,
( ~ sQ109_spl
| sQ543_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19058,f1928,f19067,f19078,f3932]) ).
fof(f19082,definition,
( sQ544_spl
<=> empty(relation_field(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f19085,plain,
( ~ sQ109_spl
| sQ544_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19059,f1928,f19067,f19082,f3932]) ).
fof(f19086,definition,
( sQ545_spl
<=> relation(relation_field(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f19089,plain,
( ~ sQ109_spl
| sQ545_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19060,f1928,f19067,f19086,f3932]) ).
fof(f19090,definition,
( sQ546_spl
<=> relation_field(sK85_skl) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ546_spl])],[split_symbol_definition]) ).
fof(f19093,plain,
( ~ sQ109_spl
| sQ546_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19061,f1928,f19067,f19090,f3932]) ).
fof(f19094,definition,
( sQ547_spl
<=> epsilon_transitive(relation_field(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ547_spl])],[split_symbol_definition]) ).
fof(f19097,plain,
( ~ sQ109_spl
| sQ547_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19062,f1928,f19067,f19094,f3932]) ).
fof(f19098,definition,
( sQ548_spl
<=> epsilon_connected(relation_field(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f19101,plain,
( ~ sQ109_spl
| sQ548_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19063,f1928,f19067,f19098,f3932]) ).
fof(f19102,definition,
( sQ549_spl
<=> ordinal(relation_field(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f19105,plain,
( ~ sQ109_spl
| sQ549_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19064,f1928,f19067,f19102,f3932]) ).
fof(f19106,definition,
( sQ550_spl
<=> is_reflexive_in(sK85_skl,sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f19107,plain,
( ~ sQ550_spl
| is_reflexive_in(sK85_skl,sK85_skl) ),
inference(component_clause,[status(thm)],[f19106]) ).
fof(f19108,plain,
( sQ550_spl
| ~ is_reflexive_in(sK85_skl,sK85_skl) ),
inference(component_clause,[status(thm)],[f19106]) ).
fof(f19245,plain,
( sQ550_spl
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f19108,f3953]) ).
fof(f19247,plain,
( sQ550_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19245,f1928,f19106]) ).
fof(f19285,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ empty(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f11631,f610]) ).
fof(f19289,plain,
! [X0] :
( being_limit_ordinal(X0)
| ~ empty(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f19285]) ).
fof(f19293,plain,
! [X0,X1] :
( ~ empty(X0)
| being_limit_ordinal(relation_image(X0,X1)) ),
inference(resolution,[status(thm)],[f19289,f8074]) ).
fof(f19369,plain,
( ~ sQ2_spl
| ordered_pair(sK76_skl,sK77_skl) = sK85_skl
| ~ subset(sK75_skl,powerset(sK85_skl)) ),
inference(resolution,[status(thm)],[f12571,f2418]) ).
fof(f19486,plain,
( ~ sQ2_spl
| sQ252_spl
| ~ sQ516_spl ),
inference(split_clause,[status(thm)],[f19369,f18888,f11082,f1352]) ).
fof(f19622,plain,
( ~ proper_subset(powerset(sK85_skl),sK85_skl)
| sK85_skl = succ(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3000,f13650]) ).
fof(f19624,definition,
( sQ555_spl
<=> proper_subset(powerset(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f19627,plain,
( ~ sQ555_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f19622,f9687,f19624]) ).
fof(f19820,plain,
! [X0,X1] : in(unordered_pair(X0,X1),ordered_pair(X1,X0)),
inference(paramodulation,[status(thm)],[f312,f13712]) ).
fof(f19831,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(X0,powerset(X1)))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f15001,f3966]) ).
fof(f19836,definition,
! [X0,X1] :
( sQ556_spl
<=> ~ empty(set_union2(X0,powerset(X1))) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f19839,plain,
( ~ sQ109_spl
| sQ556_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19831,f1928,f19836,f3932]) ).
fof(f19845,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(powerset(X0),X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f15049,f3966]) ).
fof(f19851,definition,
! [X0,X1] :
( sQ557_spl
<=> ~ empty(set_union2(powerset(X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ557_spl])],[split_symbol_definition]) ).
fof(f19854,plain,
( ~ sQ109_spl
| sQ557_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19845,f1928,f19851,f3932]) ).
fof(f19860,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(X0,sK112_skl(X1)))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f15997,f3966]) ).
fof(f19865,definition,
! [X0,X1] :
( sQ558_spl
<=> ~ empty(set_union2(X0,sK112_skl(X1))) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f19868,plain,
( ~ sQ109_spl
| sQ558_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19860,f1928,f19865,f3932]) ).
fof(f19874,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(sK112_skl(X0),X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f16054,f3966]) ).
fof(f19880,definition,
! [X0,X1] :
( sQ559_spl
<=> ~ empty(set_union2(sK112_skl(X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f19883,plain,
( ~ sQ109_spl
| sQ559_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f19874,f1928,f19880,f3932]) ).
fof(f19912,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ190_spl
| ~ is_reflexive_in(sK85_skl,set_union2(X0,relation_dom(sK75_skl))) ),
inference(resolution,[status(thm)],[f14519,f3933]) ).
fof(f20085,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(X0,sK93_skl(X1)))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f16785,f3966]) ).
fof(f20090,definition,
! [X0,X1] :
( sQ561_spl
<=> ~ empty(set_union2(X0,sK93_skl(X1))) ),
introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition]) ).
fof(f20093,plain,
( ~ sQ109_spl
| sQ561_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f20085,f1928,f20090,f3932]) ).
fof(f20099,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(sK93_skl(X0),X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f16843,f3966]) ).
fof(f20105,definition,
! [X0,X1] :
( sQ562_spl
<=> ~ empty(set_union2(sK93_skl(X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f20108,plain,
( ~ sQ109_spl
| sQ562_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f20099,f1928,f20105,f3932]) ).
fof(f20119,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(X0,succ(X1)))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f17289,f3966]) ).
fof(f20125,definition,
! [X0,X1] :
( sQ563_spl
<=> ~ empty(set_union2(X0,succ(X1))) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f20128,plain,
( ~ sQ109_spl
| sQ563_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f20119,f1928,f20125,f3932]) ).
fof(f20154,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ190_spl
| ~ is_reflexive_in(sK85_skl,set_union2(relation_dom(sK75_skl),X0)) ),
inference(resolution,[status(thm)],[f14520,f3933]) ).
fof(f20274,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(set_union2(succ(X0),X1))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f17995,f3966]) ).
fof(f20281,definition,
! [X0,X1] :
( sQ566_spl
<=> ~ empty(set_union2(succ(X0),X1)) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f20284,plain,
( ~ sQ109_spl
| sQ566_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f20274,f1928,f20281,f3932]) ).
fof(f20345,plain,
! [X0] :
( relation(X0)
| ~ relation(X0)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1964,f734]) ).
fof(f20351,definition,
! [X0] :
( sQ568_spl
<=> ( relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f20354,plain,
( sQ568_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f20345,f1928,f20351]) ).
fof(f20786,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ190_spl
| ~ empty(set_union2(X0,relation_dom(sK75_skl)))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f19912,f3966]) ).
fof(f20791,definition,
! [X0] :
( sQ570_spl
<=> ~ empty(set_union2(X0,relation_dom(sK75_skl))) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f20794,plain,
( ~ sQ109_spl
| ~ sQ190_spl
| sQ570_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f20786,f1928,f20791,f10165,f3932]) ).
fof(f21488,plain,
! [X0,X1] :
( in(singleton(singleton(X1)),X0)
| ~ in(X1,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f13715,f793]) ).
fof(f21592,plain,
! [X0] :
( ~ in(X0,relation_field(sK85_skl))
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f21488,f1877]) ).
fof(f21674,definition,
! [X0] :
( sQ637_spl
<=> ~ in(X0,relation_field(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f21677,plain,
( sQ637_spl
| ~ sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f21592,f1928,f19067,f21674]) ).
fof(f21708,plain,
( ~ sQ313_spl
| in(sK71_skl(sK85_skl),sK85_skl)
| reflexive(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f13737,f794]) ).
fof(f21710,definition,
( sQ642_spl
<=> in(sK71_skl(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f21711,plain,
( ~ sQ642_spl
| in(sK71_skl(sK85_skl),sK85_skl) ),
inference(component_clause,[status(thm)],[f21710]) ).
fof(f21713,plain,
( ~ sQ313_spl
| sQ642_spl
| sQ540_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f21708,f1928,f19067,f21710,f13722]) ).
fof(f21855,plain,
! [X0,X1] :
( ~ in(X1,sK52_skl(X0,sK85_skl,sK85_skl))
| ~ in(relation_dom(sK85_skl),X1)
| ~ in(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f12177]) ).
fof(f21859,definition,
! [X0,X1] :
( sQ645_spl
<=> ( ~ in(X1,sK52_skl(X0,sK85_skl,sK85_skl))
| ~ in(relation_dom(sK85_skl),X1)
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ645_spl])],[split_symbol_definition]) ).
fof(f21862,plain,
( sQ645_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f21855,f1928,f1550,f21859]) ).
fof(f22242,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| transitive(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f808,f3933]) ).
fof(f22278,plain,
! [X0] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| transitive(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f22242,f4014]) ).
fof(f22334,plain,
! [X0] :
( ~ in(sK85_skl,sK52_skl(X0,relation_rng(sK85_skl),sK85_skl))
| ~ in(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f12179]) ).
fof(f22336,plain,
! [X0] :
( ~ in(relation_dom(sK85_skl),sK52_skl(X0,sK85_skl,sK85_skl))
| ~ in(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f12179]) ).
fof(f22338,definition,
! [X0] :
( sQ655_spl
<=> ( ~ in(sK85_skl,sK52_skl(X0,relation_rng(sK85_skl),sK85_skl))
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ655_spl])],[split_symbol_definition]) ).
fof(f22341,plain,
( sQ655_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f22334,f1928,f1550,f22338]) ).
fof(f22345,definition,
! [X0] :
( sQ656_spl
<=> ( ~ in(relation_dom(sK85_skl),sK52_skl(X0,sK85_skl,sK85_skl))
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ656_spl])],[split_symbol_definition]) ).
fof(f22348,plain,
( sQ656_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f22336,f1928,f1550,f22345]) ).
fof(f22357,plain,
( ~ sQ109_spl
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl)
| transitive(relation_field(sK85_skl)) ),
inference(resolution,[status(thm)],[f22278,f671]) ).
fof(f22359,plain,
! [X0] :
( ~ sQ109_spl
| ~ empty(X0)
| ~ relation(sK85_skl)
| transitive(X0) ),
inference(resolution,[status(thm)],[f22278,f3966]) ).
fof(f22360,definition,
( sQ657_spl
<=> transitive(relation_field(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ657_spl])],[split_symbol_definition]) ).
fof(f22363,plain,
( ~ sQ109_spl
| ~ sQ540_spl
| ~ sQ54_spl
| sQ657_spl ),
inference(split_clause,[status(thm)],[f22357,f22360,f1928,f19067,f3932]) ).
fof(f22365,definition,
! [X0] :
( sQ658_spl
<=> ( ~ empty(X0)
| transitive(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ658_spl])],[split_symbol_definition]) ).
fof(f22368,plain,
( ~ sQ109_spl
| ~ sQ54_spl
| sQ658_spl ),
inference(split_clause,[status(thm)],[f22359,f22365,f1928,f3932]) ).
fof(f22997,plain,
! [X0,X1,X2] :
( ~ empty(X0)
| disjoint(relation_image(X0,X1),X2) ),
inference(resolution,[status(thm)],[f1132,f2492]) ).
fof(f23062,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ is_reflexive_in(sK85_skl,X0)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[f1132,f3933]) ).
fof(f23240,plain,
! [X0] :
( ~ sQ109_spl
| ~ sQ190_spl
| ~ empty(set_union2(relation_dom(sK75_skl),X0))
| ~ relation(sK85_skl) ),
inference(resolution,[status(thm)],[f20154,f3966]) ).
fof(f23247,definition,
! [X0] :
( sQ663_spl
<=> ~ empty(set_union2(relation_dom(sK75_skl),X0)) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f23250,plain,
( ~ sQ109_spl
| ~ sQ190_spl
| sQ663_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f23240,f1928,f23247,f10165,f3932]) ).
fof(f23282,plain,
! [X0] :
( ~ in(sK85_skl,apply(sK85_skl,X0))
| ~ in(X0,relation_dom(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f12455]) ).
fof(f23284,definition,
! [X0] :
( sQ664_spl
<=> ( ~ in(sK85_skl,apply(sK85_skl,X0))
| ~ in(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ664_spl])],[split_symbol_definition]) ).
fof(f23287,plain,
( sQ664_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f23282,f1928,f1550,f23284]) ).
fof(f23375,plain,
! [X0] :
( ~ sQ109_spl
| ~ reflexive(sK85_skl)
| ~ relation(sK85_skl)
| disjoint(relation_field(sK85_skl),X0) ),
inference(resolution,[status(thm)],[f23062,f671]) ).
fof(f23377,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ empty(X0)
| ~ relation(sK85_skl)
| disjoint(X0,X1) ),
inference(resolution,[status(thm)],[f23062,f3966]) ).
fof(f23378,definition,
! [X0] :
( sQ665_spl
<=> disjoint(relation_field(sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f23381,plain,
( ~ sQ109_spl
| ~ sQ540_spl
| ~ sQ54_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f23375,f23378,f1928,f19067,f3932]) ).
fof(f23383,definition,
! [X0,X1] :
( sQ666_spl
<=> ( ~ empty(X0)
| disjoint(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ666_spl])],[split_symbol_definition]) ).
fof(f23386,plain,
( ~ sQ109_spl
| ~ sQ54_spl
| sQ666_spl ),
inference(split_clause,[status(thm)],[f23377,f23383,f1928,f3932]) ).
fof(f23408,plain,
! [X0,X1,X2] :
( disjoint(X1,relation_image(X0,X2))
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f22997,f922]) ).
fof(f23467,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f843,f842]) ).
fof(f23493,definition,
! [X0,X1] :
( sQ667_spl
<=> ~ in(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ667_spl])],[split_symbol_definition]) ).
fof(f23494,plain,
! [X0,X1] :
( ~ sQ667_spl
| ~ in(X0,X1) ),
inference(component_clause,[status(thm)],[f23493]) ).
fof(f23496,definition,
! [X2,X3] :
( sQ668_spl
<=> ( in(X2,X3)
| ~ in(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ668_spl])],[split_symbol_definition]) ).
fof(f23499,plain,
( sQ668_spl
| sQ667_spl ),
inference(split_clause,[status(thm)],[f23467,f23493,f23496]) ).
fof(f23580,plain,
! [X0,X1] :
( ~ empty(X0)
| element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f846,f1263]) ).
fof(f23607,plain,
! [X0] :
( ~ in(sK85_skl,sK54_skl(X0,sK85_skl))
| in(sK53_skl(X0,sK85_skl),X0)
| X0 = relation_rng(sK85_skl)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f12482]) ).
fof(f23609,definition,
! [X0] :
( sQ669_spl
<=> ( ~ in(sK85_skl,sK54_skl(X0,sK85_skl))
| in(sK53_skl(X0,sK85_skl),X0)
| X0 = relation_rng(sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ669_spl])],[split_symbol_definition]) ).
fof(f23612,plain,
( sQ669_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f23607,f1928,f1550,f23609]) ).
fof(f23664,plain,
( ~ sQ667_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19820,f23494]) ).
fof(f23763,plain,
~ sQ667_spl,
inference(contradiction_clause,[status(thm)],[f23664]) ).
fof(f23768,plain,
! [X0] :
( ~ sQ132_spl
| in(X0,relation_dom(sK85_skl))
| ~ in(X0,relation_dom(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f7127,f851]) ).
fof(f23769,definition,
! [X0] :
( sQ670_spl
<=> ( in(X0,relation_dom(sK85_skl))
| ~ in(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f23772,plain,
( ~ sQ132_spl
| sQ670_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f23768,f1928,f1550,f23769,f7126]) ).
fof(f23773,plain,
! [X0,X1] :
( ~ sQ132_spl
| in(X0,X1)
| ~ in(X0,relation_dom(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f7127,f852]) ).
fof(f23774,definition,
! [X0,X1] :
( sQ671_spl
<=> ( in(X0,X1)
| ~ in(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f23777,plain,
( ~ sQ132_spl
| sQ671_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f23773,f1928,f1550,f23774,f7126]) ).
fof(f23875,plain,
! [X0,X1] :
( ~ sQ132_spl
| ~ in(X0,X1)
| ~ in(X0,relation_dom(sK85_skl))
| in(X0,relation_dom(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f7127,f853]) ).
fof(f23876,definition,
! [X0,X1] :
( sQ672_spl
<=> ( ~ in(X0,X1)
| ~ in(X0,relation_dom(sK85_skl))
| in(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f23879,plain,
( ~ sQ132_spl
| sQ672_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f23875,f1928,f1550,f23876,f7126]) ).
fof(f23893,plain,
! [X0] : union_of_subsets(X0,sK85_skl) = union(sK85_skl),
inference(resolution,[status(thm)],[f907,f2393]) ).
fof(f23899,plain,
! [X0] : union_of_subsets(X0,sK85_skl) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f10546,f23893]) ).
fof(f23914,plain,
! [X0] : meet_of_subsets(X0,sK85_skl) = set_meet(sK85_skl),
inference(resolution,[status(thm)],[f909,f2393]) ).
fof(f23920,plain,
! [X0] : meet_of_subsets(X0,sK85_skl) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f1888,f23914]) ).
fof(f23942,plain,
! [X0,X1] :
( ~ in(X1,ordered_pair(sK55_skl(X0,sK85_skl,sK85_skl),X0))
| ~ in(sK85_skl,X1)
| ~ in(X0,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f12739]) ).
fof(f23944,definition,
! [X0,X1] :
( sQ673_spl
<=> ( ~ in(X1,ordered_pair(sK55_skl(X0,sK85_skl,sK85_skl),X0))
| ~ in(sK85_skl,X1)
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ673_spl])],[split_symbol_definition]) ).
fof(f23947,plain,
( sQ673_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f23942,f1928,f23944]) ).
fof(f23991,plain,
! [X0] :
( ordinal_subset(sK85_skl,X0)
| ~ ordinal(X0)
| ~ ordinal(sK85_skl) ),
inference(resolution,[status(thm)],[f915,f1875]) ).
fof(f24002,definition,
! [X0] :
( sQ674_spl
<=> ( ordinal_subset(sK85_skl,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f24003,plain,
! [X0] :
( ~ sQ674_spl
| ordinal_subset(sK85_skl,X0)
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f24002]) ).
fof(f24005,plain,
( sQ674_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f23991,f1563,f24002]) ).
fof(f24061,plain,
! [X0] :
( ~ in(sK85_skl,ordered_pair(sK55_skl(X0,sK85_skl,sK85_skl),X0))
| ~ in(X0,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f12741]) ).
fof(f24067,definition,
! [X0] :
( sQ676_spl
<=> ( ~ in(sK85_skl,ordered_pair(sK55_skl(X0,sK85_skl,sK85_skl),X0))
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ676_spl])],[split_symbol_definition]) ).
fof(f24070,plain,
( sQ676_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24061,f1928,f24067]) ).
fof(f24212,plain,
! [X0] :
( ~ sQ674_spl
| subset(sK85_skl,X0)
| ~ ordinal(X0)
| ~ ordinal(sK85_skl)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f24003,f914]) ).
fof(f24213,definition,
! [X0] :
( sQ678_spl
<=> ( subset(sK85_skl,X0)
| ~ ordinal(X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f24216,plain,
( ~ sQ674_spl
| ~ sQ22_spl
| sQ678_spl ),
inference(split_clause,[status(thm)],[f24212,f24213,f1563,f24002]) ).
fof(f24218,plain,
! [X0,X1] :
( meet_of_subsets(X1,X0) = set_meet(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f23580,f909]) ).
fof(f24219,plain,
! [X0,X1] :
( union_of_subsets(X1,X0) = union(X0)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f23580,f907]) ).
fof(f24310,plain,
! [X0,X1] :
( ~ sQ126_spl
| in(X0,X1)
| ~ in(X0,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f935]) ).
fof(f24311,definition,
! [X0,X1] :
( sQ679_spl
<=> ( in(X0,X1)
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f24314,plain,
( ~ sQ126_spl
| sQ679_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24310,f1928,f24311,f6697]) ).
fof(f24317,plain,
! [X0] :
( ~ sQ126_spl
| in(X0,relation_rng(sK85_skl))
| ~ in(X0,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f936]) ).
fof(f24318,definition,
! [X0] :
( sQ680_spl
<=> ( in(X0,relation_rng(sK85_skl))
| ~ in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f24321,plain,
( ~ sQ126_spl
| sQ680_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24317,f1928,f24318,f6697]) ).
fof(f24574,plain,
! [X0,X1] :
( ~ sQ126_spl
| ~ in(X0,relation_rng(sK85_skl))
| ~ in(X0,X1)
| in(X0,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f937]) ).
fof(f24575,definition,
! [X0,X1] :
( sQ682_spl
<=> ( ~ in(X0,relation_rng(sK85_skl))
| ~ in(X0,X1)
| in(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ682_spl])],[split_symbol_definition]) ).
fof(f24578,plain,
( ~ sQ126_spl
| sQ682_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24574,f1928,f24575,f6697]) ).
fof(f24585,plain,
! [X0] :
( ~ sQ126_spl
| subset(relation_rng(sK85_skl),X0)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f940]) ).
fof(f24586,definition,
! [X0] :
( sQ683_spl
<=> subset(relation_rng(sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ683_spl])],[split_symbol_definition]) ).
fof(f24589,plain,
( ~ sQ126_spl
| sQ683_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24585,f1928,f24586,f6697]) ).
fof(f24595,plain,
( ~ sQ126_spl
| subset(relation_rng(sK85_skl),relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f946]) ).
fof(f24596,plain,
! [X0] :
( subset(relation_rng(relation_rng_restriction(X0,sK85_skl)),sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f946]) ).
fof(f24598,definition,
( sQ684_spl
<=> subset(relation_rng(sK85_skl),relation_rng(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ684_spl])],[split_symbol_definition]) ).
fof(f24601,plain,
( ~ sQ126_spl
| sQ684_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24595,f1928,f24598,f6697]) ).
fof(f24602,definition,
! [X0] :
( sQ685_spl
<=> subset(relation_rng(relation_rng_restriction(X0,sK85_skl)),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ685_spl])],[split_symbol_definition]) ).
fof(f24605,plain,
( sQ685_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24596,f1928,f24602]) ).
fof(f24967,plain,
! [X0] :
( relation_rng(relation_rng_restriction(X0,sK85_skl)) = set_intersection2(sK85_skl,X0)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f953]) ).
fof(f24969,definition,
! [X0] :
( sQ689_spl
<=> relation_rng(relation_rng_restriction(X0,sK85_skl)) = set_intersection2(sK85_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ689_spl])],[split_symbol_definition]) ).
fof(f24972,plain,
( sQ689_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f24967,f1928,f24969]) ).
fof(f25005,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(X0,ordered_pair(sK77_skl,sK76_skl))
| ~ in(relation_inverse(sK75_skl),X0)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f14061,f1353]) ).
fof(f25025,definition,
! [X0] :
( sQ690_spl
<=> ( ~ in(X0,ordered_pair(sK77_skl,sK76_skl))
| ~ in(relation_inverse(sK75_skl),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ690_spl])],[split_symbol_definition]) ).
fof(f25028,plain,
( ~ sQ2_spl
| sQ690_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f25005,f1828,f25025,f1352]) ).
fof(f25318,plain,
! [X0,X1] :
( in(X0,sK93_skl(X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f962,f961]) ).
fof(f25371,plain,
! [X0,X1] :
( ~ sQ126_spl
| relation_dom_restriction(sK85_skl,X0) = relation_rng_restriction(X1,relation_dom_restriction(sK85_skl,X0))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f6698,f967]) ).
fof(f25372,definition,
! [X0,X1] :
( sQ692_spl
<=> relation_dom_restriction(sK85_skl,X0) = relation_rng_restriction(X1,relation_dom_restriction(sK85_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ692_spl])],[split_symbol_definition]) ).
fof(f25375,plain,
( ~ sQ126_spl
| sQ692_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f25371,f1928,f25372,f6697]) ).
fof(f25389,plain,
! [X0,X1] :
( in(sK94_skl(X1,X0,sK85_skl),sK85_skl)
| ~ in(X0,relation_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f972]) ).
fof(f25394,definition,
! [X0,X1] :
( sQ693_spl
<=> ( in(sK94_skl(X1,X0,sK85_skl),sK85_skl)
| ~ in(X0,relation_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ693_spl])],[split_symbol_definition]) ).
fof(f25397,plain,
( sQ693_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f25389,f1928,f25394]) ).
fof(f25432,plain,
! [X0,X1] :
( ~ sQ419_spl
| in(ordered_pair(sK94_skl(X0,sK76_skl,sK75_skl),sK77_skl),sK75_skl)
| ~ in(sK77_skl,X1)
| ~ in(sK76_skl,X1)
| ~ in(sK94_skl(X0,sK76_skl,sK75_skl),X1)
| ~ is_transitive_in(sK75_skl,X1)
| ~ in(sK76_skl,relation_image(sK75_skl,X0))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f973,f16380]) ).
fof(f25464,definition,
! [X0,X1] :
( sQ701_spl
<=> ( in(ordered_pair(sK94_skl(X0,sK76_skl,sK75_skl),sK77_skl),sK75_skl)
| ~ in(sK77_skl,X1)
| ~ in(sK76_skl,X1)
| ~ in(sK94_skl(X0,sK76_skl,sK75_skl),X1)
| ~ is_transitive_in(sK75_skl,X1)
| ~ in(sK76_skl,relation_image(sK75_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ701_spl])],[split_symbol_definition]) ).
fof(f25467,plain,
( ~ sQ419_spl
| sQ701_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f25432,f1828,f25464,f16379]) ).
fof(f26128,plain,
( ~ sQ65_spl
| subset(sK85_skl,relation_rng(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f978]) ).
fof(f26129,plain,
! [X0] :
( subset(relation_image(sK85_skl,X0),sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f978]) ).
fof(f26130,plain,
! [X0,X1] :
( subset(relation_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f1251,f978]) ).
fof(f26131,definition,
( sQ708_spl
<=> subset(sK85_skl,relation_rng(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ708_spl])],[split_symbol_definition]) ).
fof(f26134,plain,
( ~ sQ65_spl
| sQ708_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26128,f1928,f26131,f2488]) ).
fof(f26135,definition,
! [X0] :
( sQ709_spl
<=> subset(relation_image(sK85_skl,X0),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ709_spl])],[split_symbol_definition]) ).
fof(f26138,plain,
( sQ709_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26129,f1928,f26135]) ).
fof(f26139,plain,
! [X0,X1] : subset(relation_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[f26130,f685]) ).
fof(f26150,plain,
! [X0] :
( ~ sQ72_spl
| subset(relation_image(sK85_skl,sK85_skl),X0)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f981]) ).
fof(f26152,definition,
! [X0] :
( sQ710_spl
<=> subset(relation_image(sK85_skl,sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ710_spl])],[split_symbol_definition]) ).
fof(f26155,plain,
( ~ sQ72_spl
| sQ710_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26150,f1928,f1550,f26152,f2771]) ).
fof(f26157,plain,
! [X0] :
( ~ sQ65_spl
| relation_image(sK85_skl,X0) = sK85_skl
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f984]) ).
fof(f26162,plain,
! [X0] :
( relation_image(sK85_skl,X0) = relation_image(sK85_skl,set_intersection2(sK85_skl,X0))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f984]) ).
fof(f26164,definition,
! [X0] :
( sQ711_spl
<=> relation_image(sK85_skl,X0) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ711_spl])],[split_symbol_definition]) ).
fof(f26167,plain,
( ~ sQ65_spl
| sQ711_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26157,f1928,f26164,f2488]) ).
fof(f26168,definition,
! [X0] :
( sQ712_spl
<=> relation_image(sK85_skl,X0) = relation_image(sK85_skl,set_intersection2(sK85_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ712_spl])],[split_symbol_definition]) ).
fof(f26171,plain,
( sQ712_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26162,f1928,f26168]) ).
fof(f26391,plain,
! [X0] : relation_image(identity_relation(sK85_skl),X0) = sK85_skl,
inference(resolution,[status(thm)],[f26139,f2431]) ).
fof(f26397,plain,
! [X0] :
( relation_image(identity_relation(sK85_skl),X0) = sK85_skl
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f984]) ).
fof(f26399,plain,
( subset(sK85_skl,relation_rng(identity_relation(sK85_skl)))
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f978]) ).
fof(f26400,plain,
! [X0] :
( disjoint(X0,sK85_skl)
| ~ empty(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f23408]) ).
fof(f26401,plain,
! [X0] :
( ~ empty(identity_relation(sK85_skl))
| disjoint(sK85_skl,X0) ),
inference(paramodulation,[status(thm)],[f26391,f22997]) ).
fof(f26403,plain,
! [X0] :
( ~ empty(identity_relation(sK85_skl))
| is_transitive_in(sK85_skl,X0) ),
inference(paramodulation,[status(thm)],[f26391,f17407]) ).
fof(f26404,plain,
( ~ empty(identity_relation(sK85_skl))
| being_limit_ordinal(sK85_skl) ),
inference(paramodulation,[status(thm)],[f26391,f19293]) ).
fof(f26405,plain,
! [X0] :
( ~ empty(identity_relation(sK85_skl))
| is_antisymmetric_in(sK85_skl,X0) ),
inference(paramodulation,[status(thm)],[f26391,f9944]) ).
fof(f26406,plain,
! [X0] :
( subset(sK85_skl,X0)
| ~ empty(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f8068]) ).
fof(f26407,plain,
( ~ empty(identity_relation(sK85_skl))
| transitive(sK85_skl) ),
inference(paramodulation,[status(thm)],[f26391,f17936]) ).
fof(f26413,plain,
( epsilon_transitive(sK85_skl)
| ~ empty(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f8084]) ).
fof(f26415,plain,
( ordinal(sK85_skl)
| ~ empty(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f8081]) ).
fof(f26417,definition,
( sQ715_spl
<=> relation(identity_relation(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ715_spl])],[split_symbol_definition]) ).
fof(f26419,plain,
( sQ715_spl
| ~ relation(identity_relation(sK85_skl)) ),
inference(component_clause,[status(thm)],[f26417]) ).
fof(f26420,definition,
! [X0] :
( sQ716_spl
<=> relation_image(identity_relation(sK85_skl),X0) = sK85_skl ),
introduced(definition,[new_symbols(definition,[sQ716_spl])],[split_symbol_definition]) ).
fof(f26423,plain,
( sQ716_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f26397,f26417,f26420]) ).
fof(f26424,definition,
( sQ717_spl
<=> function(identity_relation(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ717_spl])],[split_symbol_definition]) ).
fof(f26426,plain,
( sQ717_spl
| ~ function(identity_relation(sK85_skl)) ),
inference(component_clause,[status(thm)],[f26424]) ).
fof(f26428,definition,
( sQ718_spl
<=> subset(sK85_skl,relation_rng(identity_relation(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f26431,plain,
( sQ718_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f26399,f26417,f26428]) ).
fof(f26432,definition,
( sQ719_spl
<=> empty(identity_relation(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ719_spl])],[split_symbol_definition]) ).
fof(f26434,plain,
( sQ719_spl
| ~ empty(identity_relation(sK85_skl)) ),
inference(component_clause,[status(thm)],[f26432]) ).
fof(f26435,plain,
( sQ124_spl
| ~ sQ719_spl ),
inference(split_clause,[status(thm)],[f26400,f26432,f6109]) ).
fof(f26436,plain,
( ~ sQ719_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f26401,f3717,f26432]) ).
fof(f26438,plain,
( ~ sQ719_spl
| sQ428_spl ),
inference(split_clause,[status(thm)],[f26403,f17409,f26432]) ).
fof(f26439,plain,
( ~ sQ719_spl
| sQ245_spl ),
inference(split_clause,[status(thm)],[f26404,f10698,f26432]) ).
fof(f26440,plain,
( ~ sQ719_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f26405,f9946,f26432]) ).
fof(f26441,plain,
( sQ125_spl
| ~ sQ719_spl ),
inference(split_clause,[status(thm)],[f26406,f26432,f6508]) ).
fof(f26442,plain,
( ~ sQ719_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f26407,f13877,f26432]) ).
fof(f26448,plain,
( sQ70_spl
| ~ sQ719_spl ),
inference(split_clause,[status(thm)],[f26413,f26432,f2680]) ).
fof(f26450,plain,
( sQ22_spl
| ~ sQ719_spl ),
inference(split_clause,[status(thm)],[f26415,f26432,f1563]) ).
fof(f26452,plain,
( sQ715_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26419,f685]) ).
fof(f26453,plain,
sQ715_spl,
inference(contradiction_clause,[status(thm)],[f26452]) ).
fof(f26584,plain,
! [X0] :
( ~ sQ72_spl
| subset(X0,sK85_skl)
| ~ subset(X0,relation_dom(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f987]) ).
fof(f26585,plain,
! [X0] :
( subset(X0,relation_inverse_image(identity_relation(sK85_skl),sK85_skl))
| ~ subset(X0,relation_dom(identity_relation(sK85_skl)))
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f987]) ).
fof(f26586,plain,
! [X0] :
( ~ sQ65_spl
| subset(X0,relation_inverse_image(sK85_skl,sK85_skl))
| ~ subset(X0,relation_dom(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f987]) ).
fof(f26587,definition,
! [X0] :
( sQ720_spl
<=> ( subset(X0,sK85_skl)
| ~ subset(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ720_spl])],[split_symbol_definition]) ).
fof(f26590,plain,
( ~ sQ72_spl
| sQ720_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26584,f1928,f26587,f2771]) ).
fof(f26591,definition,
! [X0] :
( sQ721_spl
<=> ( subset(X0,relation_inverse_image(identity_relation(sK85_skl),sK85_skl))
| ~ subset(X0,relation_dom(identity_relation(sK85_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ721_spl])],[split_symbol_definition]) ).
fof(f26594,plain,
( sQ721_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f26585,f26417,f26591]) ).
fof(f26595,definition,
! [X0] :
( sQ722_spl
<=> ( subset(X0,relation_inverse_image(sK85_skl,sK85_skl))
| ~ subset(X0,relation_dom(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ722_spl])],[split_symbol_definition]) ).
fof(f26598,plain,
( ~ sQ65_spl
| sQ722_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26586,f1928,f26595,f2488]) ).
fof(f26601,plain,
( sK85_skl = relation_rng(identity_relation(sK85_skl))
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f989]) ).
fof(f26602,plain,
( ~ sQ65_spl
| sK85_skl = relation_rng(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f989]) ).
fof(f26603,plain,
( relation_image(sK85_skl,sK85_skl) = relation_rng(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f989]) ).
fof(f26605,definition,
( sQ723_spl
<=> sK85_skl = relation_rng(identity_relation(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ723_spl])],[split_symbol_definition]) ).
fof(f26608,plain,
( sQ723_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f26601,f26417,f26605]) ).
fof(f26609,definition,
( sQ724_spl
<=> sK85_skl = relation_rng(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ724_spl])],[split_symbol_definition]) ).
fof(f26612,plain,
( ~ sQ65_spl
| sQ724_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26602,f1928,f26609,f2488]) ).
fof(f26613,definition,
( sQ725_spl
<=> relation_image(sK85_skl,sK85_skl) = relation_rng(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ725_spl])],[split_symbol_definition]) ).
fof(f26616,plain,
( sQ725_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26603,f1928,f26613]) ).
fof(f26621,plain,
! [X0] :
( ~ sQ65_spl
| sK85_skl = X0
| ~ subset(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3167,f992]) ).
fof(f26622,plain,
! [X0] :
( ~ sQ72_spl
| relation_image(sK85_skl,sK85_skl) = X0
| ~ subset(X0,relation_rng(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f992]) ).
fof(f26623,definition,
! [X0] :
( sQ726_spl
<=> ( sK85_skl = X0
| ~ subset(X0,relation_rng(identity_relation(sK85_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ726_spl])],[split_symbol_definition]) ).
fof(f26627,definition,
! [X0] :
( sQ727_spl
<=> ( sK85_skl = X0
| ~ subset(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ727_spl])],[split_symbol_definition]) ).
fof(f26630,plain,
( ~ sQ65_spl
| sQ727_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26621,f1928,f1550,f26627,f2488]) ).
fof(f26631,definition,
! [X0] :
( sQ728_spl
<=> ( relation_image(sK85_skl,sK85_skl) = X0
| ~ subset(X0,relation_rng(sK85_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ728_spl])],[split_symbol_definition]) ).
fof(f26634,plain,
( ~ sQ72_spl
| sQ728_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26622,f1928,f1550,f26631,f2771]) ).
fof(f26635,plain,
( sQ717_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26426,f724]) ).
fof(f26636,plain,
sQ717_spl,
inference(contradiction_clause,[status(thm)],[f26635]) ).
fof(f26823,plain,
! [X0] :
( relation_rng(relation_composition(X0,identity_relation(sK85_skl))) = sK85_skl
| ~ relation(identity_relation(sK85_skl))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f26391,f994]) ).
fof(f26825,plain,
! [X0] :
( ~ sQ65_spl
| relation_rng(relation_composition(X0,sK85_skl)) = sK85_skl
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3167,f994]) ).
fof(f26826,plain,
! [X0] :
( relation_rng(relation_composition(sK85_skl,X0)) = relation_image(X0,sK85_skl)
| ~ relation(X0)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f994]) ).
fof(f26828,definition,
! [X0] :
( sQ730_spl
<=> ( relation_rng(relation_composition(X0,identity_relation(sK85_skl))) = sK85_skl
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ730_spl])],[split_symbol_definition]) ).
fof(f26831,plain,
( ~ sQ715_spl
| sQ730_spl ),
inference(split_clause,[status(thm)],[f26823,f26828,f26417]) ).
fof(f26833,definition,
! [X0] :
( sQ731_spl
<=> ( relation_rng(relation_composition(X0,sK85_skl)) = sK85_skl
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ731_spl])],[split_symbol_definition]) ).
fof(f26836,plain,
( ~ sQ65_spl
| ~ sQ54_spl
| sQ731_spl ),
inference(split_clause,[status(thm)],[f26825,f26833,f1928,f2488]) ).
fof(f26837,definition,
! [X0] :
( sQ732_spl
<=> ( relation_rng(relation_composition(sK85_skl,X0)) = relation_image(X0,sK85_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ732_spl])],[split_symbol_definition]) ).
fof(f26840,plain,
( sQ732_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26826,f1928,f26837]) ).
fof(f26853,plain,
! [X0,X1] :
( in(sK95_skl(X1,X0,sK85_skl),sK85_skl)
| ~ in(X0,relation_inverse_image(sK85_skl,X1))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f999]) ).
fof(f26858,definition,
! [X0,X1] :
( sQ733_spl
<=> ( in(sK95_skl(X1,X0,sK85_skl),sK85_skl)
| ~ in(X0,relation_inverse_image(sK85_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ733_spl])],[split_symbol_definition]) ).
fof(f26861,plain,
( sQ733_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f26853,f1928,f26858]) ).
fof(f27115,plain,
( ~ sQ72_spl
| subset(sK85_skl,relation_dom(sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f1005]) ).
fof(f27116,plain,
! [X0] :
( subset(relation_inverse_image(sK85_skl,X0),sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1005]) ).
fof(f27117,plain,
! [X0,X1] :
( subset(relation_inverse_image(identity_relation(X0),X1),X0)
| ~ relation(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f1250,f1005]) ).
fof(f27118,definition,
( sQ736_spl
<=> subset(sK85_skl,relation_dom(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ736_spl])],[split_symbol_definition]) ).
fof(f27121,plain,
( ~ sQ72_spl
| sQ736_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f27115,f1928,f27118,f2771]) ).
fof(f27122,definition,
! [X0] :
( sQ737_spl
<=> subset(relation_inverse_image(sK85_skl,X0),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ737_spl])],[split_symbol_definition]) ).
fof(f27125,plain,
( sQ737_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f27116,f1928,f27122]) ).
fof(f27126,plain,
! [X0,X1] : subset(relation_inverse_image(identity_relation(X0),X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[f27117,f685]) ).
fof(f27201,plain,
! [X0] : relation_inverse_image(identity_relation(sK85_skl),X0) = sK85_skl,
inference(resolution,[status(thm)],[f27126,f2431]) ).
fof(f27207,plain,
! [X0] :
( subset(X0,sK85_skl)
| ~ subset(X0,relation_dom(identity_relation(sK85_skl)))
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f27201,f987]) ).
fof(f27208,plain,
( subset(sK85_skl,relation_dom(identity_relation(sK85_skl)))
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f27201,f1005]) ).
fof(f27209,plain,
! [X0] :
( relation_image(identity_relation(sK85_skl),sK85_skl) = X0
| ~ subset(X0,relation_rng(identity_relation(sK85_skl)))
| ~ function(identity_relation(sK85_skl))
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f27201,f992]) ).
fof(f27210,plain,
! [X0] :
( subset(relation_image(identity_relation(sK85_skl),sK85_skl),X0)
| ~ function(identity_relation(sK85_skl))
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f27201,f981]) ).
fof(f27228,definition,
! [X0] :
( sQ740_spl
<=> ( subset(X0,sK85_skl)
| ~ subset(X0,relation_dom(identity_relation(sK85_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ740_spl])],[split_symbol_definition]) ).
fof(f27231,plain,
( sQ740_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27207,f26417,f27228]) ).
fof(f27232,definition,
( sQ741_spl
<=> subset(sK85_skl,relation_dom(identity_relation(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ741_spl])],[split_symbol_definition]) ).
fof(f27235,plain,
( sQ741_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27208,f26417,f27232]) ).
fof(f27236,definition,
! [X0] :
( sQ742_spl
<=> ( relation_image(identity_relation(sK85_skl),sK85_skl) = X0
| ~ subset(X0,relation_rng(identity_relation(sK85_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ742_spl])],[split_symbol_definition]) ).
fof(f27239,plain,
( sQ742_spl
| ~ sQ717_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27209,f26417,f26424,f27236]) ).
fof(f27240,definition,
! [X0] :
( sQ743_spl
<=> subset(relation_image(identity_relation(sK85_skl),sK85_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ743_spl])],[split_symbol_definition]) ).
fof(f27243,plain,
( sQ743_spl
| ~ sQ717_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27210,f26417,f26424,f27240]) ).
fof(f27365,plain,
! [X0,X1] :
( relation_inverse_image(X0,X1) != empty_set
| ~ subset(X1,relation_rng(X0))
| X1 = sK85_skl
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1752,f1008]) ).
fof(f27366,plain,
! [X0,X1] :
( relation_inverse_image(X0,X1) != sK85_skl
| ~ subset(X1,relation_rng(X0))
| X1 = sK85_skl
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1752,f27365]) ).
fof(f27367,plain,
! [X0] :
( ~ subset(X0,relation_rng(identity_relation(sK85_skl)))
| X0 = sK85_skl
| ~ relation(identity_relation(sK85_skl)) ),
inference(resolution,[status(thm)],[f27366,f27201]) ).
fof(f27372,plain,
( sQ726_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27367,f26417,f26623]) ).
fof(f27381,plain,
! [X0,X1] :
( subset(sK85_skl,relation_inverse_image(identity_relation(sK85_skl),X1))
| ~ subset(X0,X1)
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f27201,f1011]) ).
fof(f27382,plain,
! [X0,X1] :
( ~ sQ72_spl
| subset(sK85_skl,relation_inverse_image(sK85_skl,X1))
| ~ subset(X0,X1)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f1011]) ).
fof(f27383,plain,
! [X0,X1] :
( subset(relation_inverse_image(identity_relation(sK85_skl),X0),sK85_skl)
| ~ subset(X0,X1)
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f27201,f1011]) ).
fof(f27384,plain,
! [X0,X1] :
( ~ sQ72_spl
| subset(relation_inverse_image(sK85_skl,X0),sK85_skl)
| ~ subset(X0,X1)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3173,f1011]) ).
fof(f27385,definition,
! [X0,X1] :
( sQ744_spl
<=> ( subset(sK85_skl,relation_inverse_image(identity_relation(sK85_skl),X1))
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ744_spl])],[split_symbol_definition]) ).
fof(f27388,plain,
( sQ744_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27381,f26417,f27385]) ).
fof(f27389,definition,
! [X0,X1] :
( sQ745_spl
<=> ( subset(sK85_skl,relation_inverse_image(sK85_skl,X1))
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ745_spl])],[split_symbol_definition]) ).
fof(f27392,plain,
( ~ sQ72_spl
| sQ745_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f27382,f1928,f27389,f2771]) ).
fof(f27393,definition,
! [X0,X1] :
( sQ746_spl
<=> ( subset(relation_inverse_image(identity_relation(sK85_skl),X0),sK85_skl)
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ746_spl])],[split_symbol_definition]) ).
fof(f27396,plain,
( sQ746_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27383,f26417,f27393]) ).
fof(f27397,definition,
! [X0,X1] :
( sQ747_spl
<=> ( subset(relation_inverse_image(sK85_skl,X0),sK85_skl)
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ747_spl])],[split_symbol_definition]) ).
fof(f27400,plain,
( ~ sQ72_spl
| sQ747_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f27384,f1928,f27397,f2771]) ).
fof(f27533,definition,
! [X0] :
( sQ748_spl
<=> in(sK77_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ748_spl])],[split_symbol_definition]) ).
fof(f27534,plain,
! [X0] :
( ~ sQ748_spl
| in(sK77_skl,X0) ),
inference(component_clause,[status(thm)],[f27533]) ).
fof(f27556,plain,
( ~ in(identity_relation(sK85_skl),sK85_skl)
| ~ relation(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f26391,f13813]) ).
fof(f27561,definition,
( sQ749_spl
<=> in(identity_relation(sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ749_spl])],[split_symbol_definition]) ).
fof(f27564,plain,
( ~ sQ749_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f27556,f26417,f27561]) ).
fof(f27600,plain,
! [X0] :
( ~ empty(identity_relation(sK85_skl))
| ~ in(X0,sK85_skl) ),
inference(paramodulation,[status(thm)],[f26391,f2492]) ).
fof(f27606,plain,
( ~ sQ719_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f27600,f8108,f26432]) ).
fof(f27822,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ subset(X0,sK85_skl) ),
inference(resolution,[status(thm)],[f1020,f1875]) ).
fof(f27968,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(X5,ordered_pair(X2,X4))
| ~ in(relation_composition(X0,X1),X5)
| ~ in(ordered_pair(X3,X4),X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f15795,f682]) ).
fof(f27970,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ in(X2,ordered_pair(X1,sK77_skl))
| ~ in(relation_composition(X0,sK75_skl),X2)
| ~ in(ordered_pair(X1,sK76_skl),X0)
| ~ relation(sK75_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f27968,f1353]) ).
fof(f28005,definition,
! [X0,X1,X2] :
( sQ754_spl
<=> ( ~ in(X2,ordered_pair(X1,sK77_skl))
| ~ in(relation_composition(X0,sK75_skl),X2)
| ~ in(ordered_pair(X1,sK76_skl),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ754_spl])],[split_symbol_definition]) ).
fof(f28008,plain,
( ~ sQ2_spl
| ~ sQ46_spl
| sQ754_spl ),
inference(split_clause,[status(thm)],[f27970,f28005,f1828,f1352]) ).
fof(f28024,plain,
! [X0,X1] :
( ~ relation(sK85_skl)
| subset(relation_dom_restriction(sK85_skl,X0),X1) ),
inference(resolution,[status(thm)],[f27822,f1282]) ).
fof(f28025,plain,
! [X0,X1] :
( ~ relation(sK85_skl)
| subset(relation_rng_restriction(X0,sK85_skl),X1) ),
inference(resolution,[status(thm)],[f27822,f943]) ).
fof(f28040,definition,
! [X0,X1] :
( sQ757_spl
<=> subset(relation_dom_restriction(sK85_skl,X0),X1) ),
introduced(definition,[new_symbols(definition,[sQ757_spl])],[split_symbol_definition]) ).
fof(f28043,plain,
( ~ sQ54_spl
| sQ757_spl ),
inference(split_clause,[status(thm)],[f28024,f28040,f1928]) ).
fof(f28044,definition,
! [X0,X1] :
( sQ758_spl
<=> subset(relation_rng_restriction(X0,sK85_skl),X1) ),
introduced(definition,[new_symbols(definition,[sQ758_spl])],[split_symbol_definition]) ).
fof(f28047,plain,
( ~ sQ54_spl
| sQ758_spl ),
inference(split_clause,[status(thm)],[f28025,f28044,f1928]) ).
fof(f28513,plain,
! [X0,X1] :
( ~ in(apply(X0,X1),sK85_skl)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_dom(relation_composition(X0,sK85_skl)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1031]) ).
fof(f28516,definition,
! [X0,X1] :
( sQ759_spl
<=> ( ~ in(apply(X0,X1),sK85_skl)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_dom(relation_composition(X0,sK85_skl)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ759_spl])],[split_symbol_definition]) ).
fof(f28519,plain,
( sQ759_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f28513,f1928,f1550,f28516]) ).
fof(f28574,plain,
( sK85_skl = set_meet(sK85_skl)
| ~ empty(sK85_skl) ),
inference(paramodulation,[status(thm)],[f23920,f24218]) ).
fof(f28575,definition,
( sQ760_spl
<=> sK85_skl = set_meet(sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ760_spl])],[split_symbol_definition]) ).
fof(f28578,plain,
( sQ760_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f28574,f2319,f28575]) ).
fof(f28580,plain,
( sK85_skl = union(sK85_skl)
| ~ empty(sK85_skl) ),
inference(paramodulation,[status(thm)],[f23899,f24219]) ).
fof(f28581,plain,
( sQ223_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f28580,f2319,f10573]) ).
fof(f28826,plain,
! [X0] :
( sK85_skl = X0
| in(sK85_skl,X0)
| ~ ordinal(X0)
| ~ epsilon_transitive(sK85_skl) ),
inference(resolution,[status(thm)],[f1033,f6119]) ).
fof(f28830,definition,
! [X0] :
( sQ761_spl
<=> ( sK85_skl = X0
| in(sK85_skl,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ761_spl])],[split_symbol_definition]) ).
fof(f28833,plain,
( sQ761_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f28826,f2680,f28830]) ).
fof(f28835,plain,
( ~ sQ109_spl
| ~ sQ2_spl
| ~ is_reflexive_in(sK85_skl,cartesian_product2(relation_dom(sK75_skl),relation_rng(sK75_skl)))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1035,f14699]) ).
fof(f28836,plain,
( ~ sQ2_spl
| ~ empty(cartesian_product2(relation_dom(sK75_skl),relation_rng(sK75_skl)))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1035,f14697]) ).
fof(f28851,plain,
( subset(sK85_skl,cartesian_product2(sK85_skl,relation_rng(sK85_skl)))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1035]) ).
fof(f28853,plain,
( subset(sK85_skl,cartesian_product2(relation_dom(sK85_skl),sK85_skl))
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f1035]) ).
fof(f28855,definition,
( sQ762_spl
<=> is_reflexive_in(sK85_skl,cartesian_product2(relation_dom(sK75_skl),relation_rng(sK75_skl))) ),
introduced(definition,[new_symbols(definition,[sQ762_spl])],[split_symbol_definition]) ).
fof(f28858,plain,
( ~ sQ109_spl
| ~ sQ2_spl
| ~ sQ762_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f28835,f1828,f28855,f1352,f3932]) ).
fof(f28859,definition,
( sQ763_spl
<=> empty(cartesian_product2(relation_dom(sK75_skl),relation_rng(sK75_skl))) ),
introduced(definition,[new_symbols(definition,[sQ763_spl])],[split_symbol_definition]) ).
fof(f28862,plain,
( ~ sQ2_spl
| ~ sQ763_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f28836,f1828,f28859,f1352]) ).
fof(f28870,definition,
( sQ766_spl
<=> subset(sK85_skl,cartesian_product2(sK85_skl,relation_rng(sK85_skl))) ),
introduced(definition,[new_symbols(definition,[sQ766_spl])],[split_symbol_definition]) ).
fof(f28873,plain,
( sQ766_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f28851,f1928,f28870]) ).
fof(f28876,definition,
( sQ767_spl
<=> subset(sK85_skl,cartesian_product2(relation_dom(sK85_skl),sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ767_spl])],[split_symbol_definition]) ).
fof(f28879,plain,
( sQ767_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f28853,f1928,f28876]) ).
fof(f29180,plain,
! [X0] :
( X0 = sK85_skl
| powerset(sK85_skl) = X0
| in(powerset(sK85_skl),X0)
| ~ ordinal(X0)
| ~ ordinal(powerset(sK85_skl)) ),
inference(resolution,[status(thm)],[f1046,f2418]) ).
fof(f29292,definition,
( sQ785_spl
<=> singleton(sK76_skl) = sK75_skl ),
introduced(definition,[new_symbols(definition,[sQ785_spl])],[split_symbol_definition]) ).
fof(f29293,plain,
( ~ sQ785_spl
| singleton(sK76_skl) = sK75_skl ),
inference(component_clause,[status(thm)],[f29292]) ).
fof(f29348,definition,
( sQ800_spl
<=> sK76_skl = singleton(relation_dom(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ800_spl])],[split_symbol_definition]) ).
fof(f29349,plain,
( ~ sQ800_spl
| sK76_skl = singleton(relation_dom(sK75_skl)) ),
inference(component_clause,[status(thm)],[f29348]) ).
fof(f29366,definition,
( sQ805_spl
<=> sK76_skl = sK93_skl(relation_dom(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ805_spl])],[split_symbol_definition]) ).
fof(f29367,plain,
( ~ sQ805_spl
| sK76_skl = sK93_skl(relation_dom(sK75_skl)) ),
inference(component_clause,[status(thm)],[f29366]) ).
fof(f29376,definition,
( sQ808_spl
<=> sK76_skl = sK112_skl(relation_dom(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ808_spl])],[split_symbol_definition]) ).
fof(f29377,plain,
( ~ sQ808_spl
| sK76_skl = sK112_skl(relation_dom(sK75_skl)) ),
inference(component_clause,[status(thm)],[f29376]) ).
fof(f29386,definition,
( sQ811_spl
<=> sK76_skl = powerset(relation_dom(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ811_spl])],[split_symbol_definition]) ).
fof(f29387,plain,
( ~ sQ811_spl
| sK76_skl = powerset(relation_dom(sK75_skl)) ),
inference(component_clause,[status(thm)],[f29386]) ).
fof(f29594,definition,
! [X0] :
( sQ872_spl
<=> ( X0 = sK85_skl
| powerset(sK85_skl) = X0
| in(powerset(sK85_skl),X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ872_spl])],[split_symbol_definition]) ).
fof(f29597,plain,
( sQ872_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f29180,f3019,f29594]) ).
fof(f29622,plain,
! [X0] :
( subset(sK85_skl,relation_dom(X0))
| ~ subset(sK85_skl,X0)
| ~ relation(X0)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1048]) ).
fof(f29624,plain,
! [X0] :
( subset(relation_dom(X0),sK85_skl)
| ~ subset(X0,sK85_skl)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1887,f1048]) ).
fof(f29630,definition,
! [X0] :
( sQ876_spl
<=> ( subset(sK85_skl,relation_dom(X0))
| ~ subset(sK85_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ876_spl])],[split_symbol_definition]) ).
fof(f29633,plain,
( sQ876_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f29622,f1928,f29630]) ).
fof(f29635,definition,
! [X0] :
( sQ877_spl
<=> ( subset(relation_dom(X0),sK85_skl)
| ~ subset(X0,sK85_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ877_spl])],[split_symbol_definition]) ).
fof(f29638,plain,
( ~ sQ54_spl
| sQ877_spl ),
inference(split_clause,[status(thm)],[f29624,f29635,f1928]) ).
fof(f29805,plain,
( ~ sQ103_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f878,f3649]) ).
fof(f29806,plain,
~ sQ103_spl,
inference(contradiction_clause,[status(thm)],[f29805]) ).
fof(f29807,plain,
( ~ sQ190_spl
| ~ sQ309_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f14520,f13173]) ).
fof(f29846,plain,
( ~ sQ190_spl
| ~ sQ309_spl ),
inference(contradiction_clause,[status(thm)],[f29807]) ).
fof(f29867,plain,
( ~ sQ748_spl
| $false ),
inference(resolution,[status(thm)],[f27534,f12295]) ).
fof(f29907,plain,
~ sQ748_spl,
inference(contradiction_clause,[status(thm)],[f29867]) ).
fof(f29928,plain,
( ~ sQ335_spl
| $false ),
inference(resolution,[status(thm)],[f14524,f12295]) ).
fof(f29968,plain,
~ sQ335_spl,
inference(contradiction_clause,[status(thm)],[f29928]) ).
fof(f29974,plain,
! [X0] :
( subset(sK85_skl,relation_rng(X0))
| ~ subset(sK85_skl,X0)
| ~ relation(X0)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1886,f1049]) ).
fof(f29976,plain,
! [X0] :
( subset(relation_rng(X0),sK85_skl)
| ~ subset(X0,sK85_skl)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1886,f1049]) ).
fof(f29978,definition,
! [X0] :
( sQ882_spl
<=> ( subset(sK85_skl,relation_rng(X0))
| ~ subset(sK85_skl,X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ882_spl])],[split_symbol_definition]) ).
fof(f29981,plain,
( sQ882_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f29974,f1928,f29978]) ).
fof(f29983,definition,
! [X0] :
( sQ883_spl
<=> ( subset(relation_rng(X0),sK85_skl)
| ~ subset(X0,sK85_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ883_spl])],[split_symbol_definition]) ).
fof(f29986,plain,
( ~ sQ54_spl
| sQ883_spl ),
inference(split_clause,[status(thm)],[f29976,f29983,f1928]) ).
fof(f30224,definition,
( sQ884_spl
<=> sK77_skl = succ(sK77_skl) ),
introduced(definition,[new_symbols(definition,[sQ884_spl])],[split_symbol_definition]) ).
fof(f30225,plain,
( ~ sQ884_spl
| sK77_skl = succ(sK77_skl) ),
inference(component_clause,[status(thm)],[f30224]) ).
fof(f30501,definition,
( sQ888_spl
<=> being_limit_ordinal(powerset(sK77_skl)) ),
introduced(definition,[new_symbols(definition,[sQ888_spl])],[split_symbol_definition]) ).
fof(f30502,plain,
( ~ sQ888_spl
| being_limit_ordinal(powerset(sK77_skl)) ),
inference(component_clause,[status(thm)],[f30501]) ).
fof(f30508,definition,
( sQ890_spl
<=> powerset(sK77_skl) = sK77_skl ),
introduced(definition,[new_symbols(definition,[sQ890_spl])],[split_symbol_definition]) ).
fof(f30509,plain,
( ~ sQ890_spl
| powerset(sK77_skl) = sK77_skl ),
inference(component_clause,[status(thm)],[f30508]) ).
fof(f30695,definition,
( sQ892_spl
<=> sK76_skl = succ(sK76_skl) ),
introduced(definition,[new_symbols(definition,[sQ892_spl])],[split_symbol_definition]) ).
fof(f30696,plain,
( ~ sQ892_spl
| sK76_skl = succ(sK76_skl) ),
inference(component_clause,[status(thm)],[f30695]) ).
fof(f30965,definition,
( sQ893_spl
<=> being_limit_ordinal(powerset(sK76_skl)) ),
introduced(definition,[new_symbols(definition,[sQ893_spl])],[split_symbol_definition]) ).
fof(f30966,plain,
( ~ sQ893_spl
| being_limit_ordinal(powerset(sK76_skl)) ),
inference(component_clause,[status(thm)],[f30965]) ).
fof(f30972,definition,
( sQ895_spl
<=> powerset(sK76_skl) = sK76_skl ),
introduced(definition,[new_symbols(definition,[sQ895_spl])],[split_symbol_definition]) ).
fof(f30973,plain,
( ~ sQ895_spl
| powerset(sK76_skl) = sK76_skl ),
inference(component_clause,[status(thm)],[f30972]) ).
fof(f30987,plain,
( ~ sQ2_spl
| in(sK76_skl,relation_field(sK75_skl))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1066,f1353]) ).
fof(f31026,definition,
( sQ896_spl
<=> in(sK77_skl,relation_field(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ896_spl])],[split_symbol_definition]) ).
fof(f31030,definition,
( sQ897_spl
<=> in(sK76_skl,relation_field(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ897_spl])],[split_symbol_definition]) ).
fof(f31031,plain,
( ~ sQ897_spl
| in(sK76_skl,relation_field(sK75_skl)) ),
inference(component_clause,[status(thm)],[f31030]) ).
fof(f31033,plain,
( ~ sQ2_spl
| sQ897_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f30987,f1828,f31030,f1352]) ).
fof(f31037,plain,
( ~ sQ2_spl
| in(sK77_skl,relation_field(sK75_skl))
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f1067,f1353]) ).
fof(f31077,plain,
( ~ sQ2_spl
| sQ896_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f31037,f1828,f31026,f1352]) ).
fof(f31194,plain,
( ~ sQ884_spl
| ~ in(succ(sK77_skl),singleton(sK77_skl)) ),
inference(paramodulation,[status(thm)],[f30225,f5651]) ).
fof(f31267,plain,
( ~ sQ884_spl
| ~ in(sK77_skl,singleton(sK77_skl)) ),
inference(forward_demodulation,[status(thm)],[f30225,f31194]) ).
fof(f31268,plain,
( ~ sQ884_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31267,f1401]) ).
fof(f31269,plain,
~ sQ884_spl,
inference(contradiction_clause,[status(thm)],[f31268]) ).
fof(f31314,plain,
( ~ sQ890_spl
| in(sK77_skl,sK77_skl) ),
inference(paramodulation,[status(thm)],[f30509,f4874]) ).
fof(f31422,plain,
( ~ sQ888_spl
| powerset(sK77_skl) = sK77_skl ),
inference(resolution,[status(thm)],[f30502,f2038]) ).
fof(f31423,plain,
( ~ sQ888_spl
| sQ890_spl ),
inference(split_clause,[status(thm)],[f31422,f30508,f30501]) ).
fof(f31441,plain,
( ~ sQ892_spl
| ~ in(succ(sK76_skl),singleton(sK76_skl)) ),
inference(paramodulation,[status(thm)],[f30696,f5651]) ).
fof(f31514,plain,
( ~ sQ892_spl
| ~ in(sK76_skl,singleton(sK76_skl)) ),
inference(forward_demodulation,[status(thm)],[f30696,f31441]) ).
fof(f31515,plain,
( ~ sQ892_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31514,f1401]) ).
fof(f31516,plain,
~ sQ892_spl,
inference(contradiction_clause,[status(thm)],[f31515]) ).
fof(f31589,plain,
( ~ sQ895_spl
| in(sK76_skl,sK76_skl) ),
inference(paramodulation,[status(thm)],[f30973,f4874]) ).
fof(f31697,plain,
( ~ sQ893_spl
| powerset(sK76_skl) = sK76_skl ),
inference(resolution,[status(thm)],[f30966,f2038]) ).
fof(f31698,plain,
( ~ sQ893_spl
| sQ895_spl ),
inference(split_clause,[status(thm)],[f31697,f30972,f30965]) ).
fof(f31704,plain,
! [X0,X1] :
( in(sK98_skl(X1,X0),X1)
| X1 = sK85_skl
| ~ subset(X1,X0)
| ~ ordinal(X0) ),
inference(forward_demodulation,[status(thm)],[f1752,f1076]) ).
fof(f31706,plain,
! [X0] :
( sK98_skl(powerset(sK85_skl),X0) = sK85_skl
| powerset(sK85_skl) = sK85_skl
| ~ subset(powerset(sK85_skl),X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f31704,f2418]) ).
fof(f31716,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK75_skl,sK98_skl(ordered_pair(sK76_skl,sK77_skl),X0))
| ordered_pair(sK76_skl,sK77_skl) = sK85_skl
| ~ subset(ordered_pair(sK76_skl,sK77_skl),X0)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f31704,f10159]) ).
fof(f31737,definition,
! [X0] :
( sQ900_spl
<=> ( sK98_skl(powerset(sK85_skl),X0) = sK85_skl
| ~ subset(powerset(sK85_skl),X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ900_spl])],[split_symbol_definition]) ).
fof(f31740,plain,
( sQ99_spl
| sQ900_spl ),
inference(split_clause,[status(thm)],[f31706,f31737,f3332]) ).
fof(f31745,definition,
! [X0] :
( sQ901_spl
<=> ( ~ in(sK75_skl,sK98_skl(ordered_pair(sK76_skl,sK77_skl),X0))
| ~ subset(ordered_pair(sK76_skl,sK77_skl),X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ901_spl])],[split_symbol_definition]) ).
fof(f31748,plain,
( ~ sQ2_spl
| sQ252_spl
| sQ901_spl ),
inference(split_clause,[status(thm)],[f31716,f31745,f11082,f1352]) ).
fof(f31749,definition,
! [X0] :
( sQ902_spl
<=> ( ~ subset(sK85_skl,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ902_spl])],[split_symbol_definition]) ).
fof(f31750,plain,
! [X0] :
( ~ sQ902_spl
| ~ subset(sK85_skl,X0)
| ~ ordinal(X0) ),
inference(component_clause,[status(thm)],[f31749]) ).
fof(f31753,plain,
! [X0] :
( ~ sQ902_spl
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f31750,f1875]) ).
fof(f31872,plain,
! [X0] :
( ~ sQ902_spl
| ~ empty(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f311,f31753]) ).
fof(f31890,plain,
( ~ sQ902_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f31872,f3648,f31749]) ).
fof(f31903,plain,
! [X0] :
( ordinal_subset(powerset(sK85_skl),X0)
| ~ in(sK85_skl,X0)
| ~ ordinal(X0)
| ~ ordinal(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3000,f1080]) ).
fof(f31904,definition,
! [X0] :
( sQ908_spl
<=> ( ordinal_subset(powerset(sK85_skl),X0)
| ~ in(sK85_skl,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ908_spl])],[split_symbol_definition]) ).
fof(f31907,plain,
( sQ908_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f31903,f1563,f31904]) ).
fof(f31909,plain,
! [X0] :
( ~ ordinal_subset(powerset(sK85_skl),X0)
| in(sK85_skl,X0)
| ~ ordinal(X0)
| ~ ordinal(sK85_skl) ),
inference(paramodulation,[status(thm)],[f3000,f1081]) ).
fof(f31910,definition,
! [X0] :
( sQ909_spl
<=> ( ~ ordinal_subset(powerset(sK85_skl),X0)
| in(sK85_skl,X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ909_spl])],[split_symbol_definition]) ).
fof(f31913,plain,
( sQ909_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f31909,f1563,f31910]) ).
fof(f32298,plain,
! [X0,X1] :
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1443,f685]) ).
fof(f32572,plain,
( ~ sQ890_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31314,f1468]) ).
fof(f32573,plain,
~ sQ890_spl,
inference(contradiction_clause,[status(thm)],[f32572]) ).
fof(f32722,plain,
( in(sK99_skl(sK85_skl,sK85_skl),relation_dom(sK85_skl))
| sK85_skl = identity_relation(relation_dom(sK85_skl))
| ~ function(sK85_skl)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1444]) ).
fof(f32730,definition,
( sQ927_spl
<=> sK85_skl = identity_relation(relation_dom(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ927_spl])],[split_symbol_definition]) ).
fof(f32731,plain,
( ~ sQ927_spl
| sK85_skl = identity_relation(relation_dom(sK85_skl)) ),
inference(component_clause,[status(thm)],[f32730]) ).
fof(f32733,definition,
( sQ928_spl
<=> in(sK99_skl(sK85_skl,sK85_skl),relation_dom(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ928_spl])],[split_symbol_definition]) ).
fof(f32734,plain,
( ~ sQ928_spl
| in(sK99_skl(sK85_skl,sK85_skl),relation_dom(sK85_skl)) ),
inference(component_clause,[status(thm)],[f32733]) ).
fof(f32736,plain,
( sQ928_spl
| sQ927_spl
| ~ sQ19_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f32722,f1928,f1550,f32730,f32733]) ).
fof(f32737,definition,
( sQ929_spl
<=> in(sK99_skl(relation_dom(sK85_skl),sK85_skl),sK85_skl) ),
introduced(definition,[new_symbols(definition,[sQ929_spl])],[split_symbol_definition]) ).
fof(f32738,plain,
( ~ sQ929_spl
| in(sK99_skl(relation_dom(sK85_skl),sK85_skl),sK85_skl) ),
inference(component_clause,[status(thm)],[f32737]) ).
fof(f32741,plain,
( ~ sQ927_spl
| sK85_skl = identity_relation(sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1887,f32731]) ).
fof(f32742,plain,
( ~ sQ929_spl
| in(sK99_skl(sK85_skl,sK85_skl),sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1887,f32738]) ).
fof(f32743,plain,
( ~ sQ929_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f32742,f1877]) ).
fof(f32744,plain,
~ sQ929_spl,
inference(contradiction_clause,[status(thm)],[f32743]) ).
fof(f32745,plain,
( ~ sQ928_spl
| in(sK99_skl(sK85_skl,sK85_skl),sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1887,f32734]) ).
fof(f32746,plain,
( ~ sQ928_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f32745,f1877]) ).
fof(f32747,plain,
~ sQ928_spl,
inference(contradiction_clause,[status(thm)],[f32746]) ).
fof(f33033,plain,
( sQ719_spl
| ~ sQ927_spl
| ~ empty(sK85_skl) ),
inference(backward_demodulation,[status(thm)],[f32741,f26434]) ).
fof(f33036,plain,
! [X0] :
( ~ sQ927_spl
| apply(sK85_skl,X0) = X0
| ~ in(X0,sK85_skl)
| ~ function(identity_relation(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f32741,f32298]) ).
fof(f33048,plain,
( sQ719_spl
| ~ sQ927_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f33033,f2319,f32730,f26432]) ).
fof(f33049,definition,
! [X0] :
( sQ942_spl
<=> ( apply(sK85_skl,X0) = X0
| ~ in(X0,sK85_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ942_spl])],[split_symbol_definition]) ).
fof(f33052,plain,
( ~ sQ927_spl
| sQ942_spl
| ~ sQ717_spl ),
inference(split_clause,[status(thm)],[f33036,f26424,f33049,f32730]) ).
fof(f33566,plain,
( ~ sQ895_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f31589,f1468]) ).
fof(f33567,plain,
~ sQ895_spl,
inference(contradiction_clause,[status(thm)],[f33566]) ).
fof(f33675,plain,
! [X0] : set_difference(X0,X0) = set_difference(sK85_skl,X0),
inference(paramodulation,[status(thm)],[f1964,f1137]) ).
fof(f33698,plain,
! [X0] : set_difference(X0,X0) = sK85_skl,
inference(forward_demodulation,[status(thm)],[f2059,f33675]) ).
fof(f33803,plain,
! [X0] :
( ~ in(X0,sK85_skl)
| ~ ordinal(X0)
| ~ being_limit_ordinal(sK85_skl)
| ~ ordinal(sK85_skl) ),
inference(resolution,[status(thm)],[f1141,f1877]) ).
fof(f33816,plain,
! [X0] :
( in(powerset(sK85_skl),X0)
| ~ in(sK85_skl,X0)
| ~ ordinal(sK85_skl)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(paramodulation,[status(thm)],[f3000,f1141]) ).
fof(f33845,definition,
! [X0] :
( sQ970_spl
<=> ( ~ in(X0,sK85_skl)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ970_spl])],[split_symbol_definition]) ).
fof(f33848,plain,
( sQ970_spl
| ~ sQ245_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f33803,f1563,f10698,f33845]) ).
fof(f33854,definition,
! [X0] :
( sQ972_spl
<=> ( in(powerset(sK85_skl),X0)
| ~ in(sK85_skl,X0)
| ~ being_limit_ordinal(X0)
| ~ ordinal(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ972_spl])],[split_symbol_definition]) ).
fof(f33857,plain,
( ~ sQ22_spl
| sQ972_spl ),
inference(split_clause,[status(thm)],[f33816,f33854,f1563]) ).
fof(f34059,plain,
( ~ sQ811_spl
| in(relation_dom(sK75_skl),sK76_skl) ),
inference(paramodulation,[status(thm)],[f29387,f4874]) ).
fof(f34164,plain,
( ~ sQ811_spl
| ~ sQ190_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34059,f10334]) ).
fof(f34165,plain,
( ~ sQ811_spl
| ~ sQ190_spl ),
inference(contradiction_clause,[status(thm)],[f34164]) ).
fof(f34190,plain,
( ~ sQ808_spl
| in(relation_dom(sK75_skl),sK76_skl) ),
inference(paramodulation,[status(thm)],[f29377,f1312]) ).
fof(f34207,plain,
( ~ sQ808_spl
| ~ sQ190_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34190,f10334]) ).
fof(f34208,plain,
( ~ sQ808_spl
| ~ sQ190_spl ),
inference(contradiction_clause,[status(thm)],[f34207]) ).
fof(f34255,plain,
! [X0] :
( subset(X0,X0)
| sK85_skl != sK85_skl ),
inference(paramodulation,[status(thm)],[f33698,f6502]) ).
fof(f34264,definition,
! [X0] :
( sQ981_spl
<=> ( ~ relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ981_spl])],[split_symbol_definition]) ).
fof(f34265,plain,
! [X0] :
( ~ sQ981_spl
| ~ relation(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f34264]) ).
fof(f34272,definition,
! [X0] :
( sQ983_spl
<=> subset(X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ983_spl])],[split_symbol_definition]) ).
fof(f34275,plain,
( sQ983_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f34255,f2553,f34272]) ).
fof(f34277,plain,
! [X0] :
( ~ sQ981_spl
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f34265]) ).
fof(f34278,plain,
! [X0] :
( ~ sQ981_spl
| ~ empty(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f301,f34277]) ).
fof(f34294,plain,
( ~ sQ981_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f34278,f3648,f34264]) ).
fof(f34378,plain,
( ~ sQ805_spl
| in(relation_dom(sK75_skl),sK76_skl) ),
inference(paramodulation,[status(thm)],[f29367,f961]) ).
fof(f34403,plain,
( ~ sQ805_spl
| ~ sQ190_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34378,f10334]) ).
fof(f34404,plain,
( ~ sQ805_spl
| ~ sQ190_spl ),
inference(contradiction_clause,[status(thm)],[f34403]) ).
fof(f34536,plain,
( ~ sQ800_spl
| in(relation_dom(sK75_skl),sK76_skl) ),
inference(paramodulation,[status(thm)],[f29349,f1401]) ).
fof(f34567,plain,
( ~ sQ800_spl
| ~ sQ190_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34536,f10334]) ).
fof(f34568,plain,
( ~ sQ800_spl
| ~ sQ190_spl ),
inference(contradiction_clause,[status(thm)],[f34567]) ).
fof(f34741,definition,
( sQ1013_spl
<=> in(sK85_skl,sK93_skl(sK77_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1013_spl])],[split_symbol_definition]) ).
fof(f34743,plain,
( sQ1013_spl
| ~ in(sK85_skl,sK93_skl(sK77_skl)) ),
inference(component_clause,[status(thm)],[f34741]) ).
fof(f34750,definition,
( sQ1015_spl
<=> in(sK85_skl,powerset(sK77_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1015_spl])],[split_symbol_definition]) ).
fof(f34752,plain,
( sQ1015_spl
| ~ in(sK85_skl,powerset(sK77_skl)) ),
inference(component_clause,[status(thm)],[f34750]) ).
fof(f34754,plain,
( sQ1015_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f34752,f4873]) ).
fof(f34755,plain,
sQ1015_spl,
inference(contradiction_clause,[status(thm)],[f34754]) ).
fof(f34808,plain,
( ~ being_limit_ordinal(succ(sK85_skl))
| ~ ordinal(sK85_skl)
| ~ ordinal(powerset(sK85_skl)) ),
inference(paramodulation,[status(thm)],[f3000,f1448]) ).
fof(f34817,definition,
( sQ1018_spl
<=> being_limit_ordinal(succ(sK85_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1018_spl])],[split_symbol_definition]) ).
fof(f34820,plain,
( ~ sQ1018_spl
| ~ sQ22_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f34808,f3019,f1563,f34817]) ).
fof(f35079,plain,
! [X0] :
( subset(relation_dom(relation_composition(sK85_skl,X0)),sK85_skl)
| ~ relation(X0)
| ~ relation(sK85_skl) ),
inference(paramodulation,[status(thm)],[f1887,f1155]) ).
fof(f35081,definition,
! [X0] :
( sQ1021_spl
<=> ( subset(relation_dom(relation_composition(sK85_skl,X0)),sK85_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1021_spl])],[split_symbol_definition]) ).
fof(f35084,plain,
( sQ1021_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f35079,f1928,f35081]) ).
fof(f35089,plain,
! [X0] :
( subset(relation_rng(relation_composition(X0,sK85_skl)),sK85_skl)
| ~ relation(sK85_skl)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1886,f1157]) ).
fof(f35091,definition,
! [X0] :
( sQ1022_spl
<=> ( subset(relation_rng(relation_composition(X0,sK85_skl)),sK85_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1022_spl])],[split_symbol_definition]) ).
fof(f35094,plain,
( ~ sQ54_spl
| sQ1022_spl ),
inference(split_clause,[status(thm)],[f35089,f35091,f1928]) ).
fof(f35117,plain,
( ~ sQ189_spl
| ~ sQ897_spl
| ~ in(sK77_skl,relation_field(sK75_skl))
| ~ is_antisymmetric_in(sK75_skl,relation_field(sK75_skl)) ),
inference(resolution,[status(thm)],[f31031,f10162]) ).
fof(f35126,definition,
( sQ1023_spl
<=> is_antisymmetric_in(sK75_skl,relation_field(sK75_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1023_spl])],[split_symbol_definition]) ).
fof(f35128,plain,
( sQ1023_spl
| ~ is_antisymmetric_in(sK75_skl,relation_field(sK75_skl)) ),
inference(component_clause,[status(thm)],[f35126]) ).
fof(f35129,plain,
( ~ sQ189_spl
| ~ sQ897_spl
| ~ sQ896_spl
| ~ sQ1023_spl ),
inference(split_clause,[status(thm)],[f35117,f35126,f31026,f31030,f10161]) ).
fof(f35132,plain,
( ~ sQ642_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f21711,f1877]) ).
fof(f35133,plain,
~ sQ642_spl,
inference(contradiction_clause,[status(thm)],[f35132]) ).
fof(f35136,plain,
( ~ sQ334_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14512,f1877]) ).
fof(f35137,plain,
~ sQ334_spl,
inference(contradiction_clause,[status(thm)],[f35136]) ).
fof(f35138,plain,
( ~ sQ333_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14492,f1877]) ).
fof(f35139,plain,
~ sQ333_spl,
inference(contradiction_clause,[status(thm)],[f35138]) ).
fof(f35141,plain,
! [X0] :
( ~ sQ224_spl
| in(X0,set_meet(sK85_skl)) ),
inference(forward_demodulation,[status(thm)],[f10546,f10577]) ).
fof(f35142,plain,
! [X0] :
( ~ sQ224_spl
| in(X0,sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1888,f35141]) ).
fof(f35143,plain,
( ~ sQ224_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35142,f1877]) ).
fof(f35144,plain,
~ sQ224_spl,
inference(contradiction_clause,[status(thm)],[f35143]) ).
fof(f35145,plain,
( sQ169_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f9702]) ).
fof(f35146,plain,
sQ169_spl,
inference(contradiction_clause,[status(thm)],[f35145]) ).
fof(f35155,plain,
! [X0] :
( ~ sQ111_spl
| in(X0,sK85_skl) ),
inference(forward_demodulation,[status(thm)],[f1888,f4119]) ).
fof(f35156,plain,
( ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35155,f1877]) ).
fof(f35157,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f35156]) ).
fof(f35158,plain,
( ~ sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3671,f1875]) ).
fof(f35159,plain,
~ sQ104_spl,
inference(contradiction_clause,[status(thm)],[f35158]) ).
fof(f35160,plain,
( ~ sQ550_spl
| ~ sQ425_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19107,f17112]) ).
fof(f35161,plain,
( ~ sQ550_spl
| ~ sQ425_spl ),
inference(contradiction_clause,[status(thm)],[f35160]) ).
fof(f35247,plain,
( ~ sQ2_spl
| ~ sQ785_spl
| ~ subset(sK75_skl,sK75_skl) ),
inference(backward_demodulation,[status(thm)],[f29293,f14559]) ).
fof(f35317,plain,
( ~ sQ2_spl
| ~ sQ785_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35247,f1374]) ).
fof(f35318,plain,
( ~ sQ2_spl
| ~ sQ785_spl ),
inference(contradiction_clause,[status(thm)],[f35317]) ).
fof(f35331,plain,
! [X0] :
( ~ sQ6_spl
| ~ empty(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f311,f1368]) ).
fof(f35341,plain,
( ~ sQ6_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f35331,f3648,f1367]) ).
fof(f35383,plain,
( ~ sQ75_spl
| ~ sQ129_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3020,f6767]) ).
fof(f35384,plain,
( ~ sQ75_spl
| ~ sQ129_spl ),
inference(contradiction_clause,[status(thm)],[f35383]) ).
fof(f35636,definition,
! [X0] :
( sQ1029_spl
<=> sK85_skl = X0 ),
introduced(definition,[new_symbols(definition,[sQ1029_spl])],[split_symbol_definition]) ).
fof(f35637,plain,
! [X0] :
( ~ sQ1029_spl
| sK85_skl = X0 ),
inference(component_clause,[status(thm)],[f35636]) ).
fof(f35647,plain,
( ~ sQ1029_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2422,f35637]) ).
fof(f35708,plain,
~ sQ1029_spl,
inference(contradiction_clause,[status(thm)],[f35647]) ).
fof(f36399,plain,
! [X0] :
( in(sK107_skl(sK85_skl,X0),relation_dom(X0))
| ~ sP3_prd(sK105_skl(sK85_skl,X0),sK104_skl(sK85_skl,X0),sK85_skl,X0)
| sK85_skl != relation_rng(X0)
| sK85_skl = function_inverse(X0)
| ~ function(sK85_skl)
| ~ relation(sK85_skl)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f1887,f1194]) ).
fof(f36405,definition,
! [X0] :
( sQ1037_spl
<=> ( in(sK107_skl(sK85_skl,X0),relation_dom(X0))
| ~ sP3_prd(sK105_skl(sK85_skl,X0),sK104_skl(sK85_skl,X0),sK85_skl,X0)
| sK85_skl != relation_rng(X0)
| sK85_skl = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1037_spl])],[split_symbol_definition]) ).
fof(f36408,plain,
( ~ sQ19_spl
| ~ sQ54_spl
| sQ1037_spl ),
inference(split_clause,[status(thm)],[f36399,f36405,f1928,f1550]) ).
fof(f36417,plain,
( sQ1013_spl
| ~ subset(sK85_skl,sK77_skl) ),
inference(resolution,[status(thm)],[f34743,f25318]) ).
fof(f36418,plain,
( sQ1013_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f36417,f1875]) ).
fof(f36419,plain,
sQ1013_spl,
inference(contradiction_clause,[status(thm)],[f36418]) ).
fof(f36634,plain,
( sQ1023_spl
| ~ antisymmetric(sK75_skl)
| ~ relation(sK75_skl) ),
inference(resolution,[status(thm)],[f35128,f364]) ).
fof(f36636,plain,
( sQ1023_spl
| ~ sQ0_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f36634,f1828,f1345,f35126]) ).
fof(f36637,plain,
$false,
inference(sat_refutation,[status(thm)],[f1351,f1355,f1359,f1363,f1370,f1486,f1493,f1495,f1510,f1517,f1519,f1521,f1534,f1545,f1556,f1558,f1590,f1602,f1610,f1618,f1620,f1628,f1630,f1632,f1645,f1647,f1649,f1651,f1670,f1686,f1706,f1776,f1802,f1838,f1841,f1931,f1935,f1939,f1943,f1945,f2132,f2246,f2354,f2491,f2522,f2558,f2635,f2774,f2939,f3022,f3026,f3030,f3215,f3219,f3223,f3227,f3231,f3235,f3239,f3243,f3247,f3251,f3280,f3284,f3288,f3292,f3296,f3300,f3304,f3308,f3312,f3316,f3320,f3338,f3340,f3555,f3581,f3827,f3935,f4450,f4692,f4855,f6129,f6700,f6707,f6711,f6866,f7129,f7137,f7924,f7930,f7934,f7954,f8015,f8063,f8892,f8898,f9373,f9696,f9725,f9726,f9730,f9734,f9738,f9742,f9746,f9747,f9751,f9752,f9756,f9760,f9764,f9936,f10046,f10164,f10168,f10172,f10176,f10180,f10184,f10308,f10498,f10586,f10591,f10595,f10599,f10603,f10607,f10611,f10615,f10619,f10623,f10627,f10631,f10635,f10639,f10647,f10651,f10670,f10672,f10706,f11072,f11078,f11085,f11111,f11180,f11207,f11574,f12188,f12195,f12208,f12420,f12463,f12489,f12546,f12558,f12758,f12765,f12816,f12966,f13006,f13120,f13206,f13656,f13725,f13732,f13853,f13884,f13889,f13894,f14188,f14365,f14372,f14375,f14378,f14381,f14405,f14416,f14526,f14710,f14722,f14726,f14730,f14750,f15112,f15286,f15557,f15559,f15762,f16215,f16319,f16382,f16418,f17123,f17133,f17782,f17819,f18447,f18516,f19073,f19077,f19081,f19085,f19089,f19093,f19097,f19101,f19105,f19247,f19486,f19627,f19839,f19854,f19868,f19883,f20093,f20108,f20128,f20284,f20354,f20794,f21677,f21713,f21862,f22341,f22348,f22363,f22368,f23250,f23287,f23381,f23386,f23499,f23612,f23763,f23772,f23777,f23879,f23947,f24005,f24070,f24216,f24314,f24321,f24578,f24589,f24601,f24605,f24972,f25028,f25375,f25397,f25467,f26134,f26138,f26155,f26167,f26171,f26423,f26431,f26435,f26436,f26438,f26439,f26440,f26441,f26442,f26448,f26450,f26453,f26590,f26594,f26598,f26608,f26612,f26616,f26630,f26634,f26636,f26831,f26836,f26840,f26861,f27121,f27125,f27231,f27235,f27239,f27243,f27372,f27388,f27392,f27396,f27400,f27564,f27606,f28008,f28043,f28047,f28519,f28578,f28581,f28833,f28858,f28862,f28873,f28879,f29597,f29633,f29638,f29806,f29846,f29907,f29968,f29981,f29986,f31033,f31077,f31269,f31423,f31516,f31698,f31740,f31748,f31890,f31907,f31913,f32573,f32736,f32744,f32747,f33048,f33052,f33567,f33848,f33857,f34165,f34208,f34275,f34294,f34404,f34568,f34755,f34820,f35084,f35094,f35129,f35133,f35137,f35139,f35144,f35146,f35157,f35159,f35161,f35318,f35341,f35384,f35708,f36408,f36419,f36636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU241+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43 % Computer : n026.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Mon Sep 21 06:05:22 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.14/0.46 % Drodi V4.1.1
% 195.68/25.28 % Refutation found
% 195.68/25.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 195.68/25.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.21/25.37 % Elapsed time: 24.925418 seconds
% 6.21/25.37 % CPU time: 196.450023 seconds
% 6.21/25.37 % Total memory used: 502.435 MB
% 6.21/25.37 % Net memory used: 427.932 MB
%------------------------------------------------------------------------------