%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU293+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 : n010.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 02:20:03 PM UTC 2026
% Result : Theorem 160.09s 22.73s
% Output : CNFRefutation 160.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 582
% Syntax : Number of formulae : 2316 ( 173 unt; 467 def)
% Number of atoms : 8193 (1413 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 9598 (3721 ~;4455 |; 704 &)
% ( 609 <=>; 108 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 497 ( 495 usr; 464 prp; 0-4 aty)
% Number of functors : 127 ( 127 usr; 18 con; 0-4 aty)
% Number of variables : 3106 (2895 !; 211 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,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(f15,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,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(f17,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(f18,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(f19,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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(f21,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(f22,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(f23,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( function(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( B = empty_set
=> ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set ) )
& ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,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(f33,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(f34,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(D,A)
& in(C,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) )
& relation_field(B) = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,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(f48,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(f50,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( ! [D] :
~ ( disjoint(fiber(A,D),C)
& in(D,C) )
& C != empty_set
& subset(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,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(f55,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(f57,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(f58,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [A,B] :
( equipotent(A,B)
<=> ? [C] :
( relation_rng(C) = B
& relation_dom(C) = A
& one_to_one(C)
& function(C)
& relation(C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,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(f62,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(f67,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,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(f73,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,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(f78,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_dom_as_subset(A,B,C),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f122,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f125,axiom,
! [A] :
( empty(A)
=> ( relation(relation_inverse(A))
& empty(relation_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f126,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [A] : ~ empty(succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f135,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(f136,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f139,axiom,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
=> ( function(relation_inverse(A))
& relation(relation_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f140,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(f144,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f152,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f157,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,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(f161,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f165,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f166,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(f168,lemma,
! [A,B] :
( relation(B)
=> ~ ( ! [C] :
( relation(C)
=> ~ well_orders(C,A) )
& equipotent(A,relation_field(B))
& well_ordering(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f171,lemma,
! [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(f173,lemma,
! [A] :
( relation(A)
=> ( connected(A)
<=> ! [B,C] :
~ ( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f176,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(f178,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(f179,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f182,axiom,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f183,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,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(f189,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,axiom,
! [A,B] : equipotent(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f216,axiom,
! [A] :
( ! [B,C,D] :
( ( ordinal(D)
& B = D
& ordinal(C)
& B = C )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ordinal(C)
& D = C
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f238,lemma,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f249,lemma,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f252,lemma,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f253,lemma,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f255,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(f256,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(f258,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f262,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f265,lemma,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f269,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f292,lemma,
! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f293,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f313,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f315,lemma,
! [A] : transitive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f317,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f325,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( B != empty_set
=> ! [E] :
( in(E,relation_inverse_image(D,C))
<=> ( in(apply(D,E),C)
& in(E,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f326,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( B != empty_set
=> ! [E] :
( in(E,relation_inverse_image(D,C))
<=> ( in(apply(D,E),C)
& in(E,A) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f325]) ).
fof(f349,lemma,
! [A] : antisymmetric(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f350,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f354,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f359,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f360,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( in(C,A)
=> ( in(apply(D,C),relation_rng(D))
| B = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f364,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f368,lemma,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f370,lemma,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f371,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f376,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f388,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f389,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f399,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f400,plain,
! [C] :
( relation(C)
| ! [A,B] : ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(miniscoping,[status(thm)],[f399]) ).
fof(f401,plain,
! [X0,X1,X2] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f413,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f417,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)],[f14]) ).
fof(f418,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)],[f417]) ).
fof(f419,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)],[f418]) ).
fof(f420,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))],[f419]) ).
fof(f425,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)],[f420]) ).
fof(f427,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f428,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)],[f427]) ).
fof(f429,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f431,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f432,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)],[f16]) ).
fof(f433,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)],[f432]) ).
fof(f434,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)],[f433]) ).
fof(f435,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))],[f434]) ).
fof(f436,plain,
! [X0,X1,X2,X3,X4] :
( in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f438,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)],[f435]) ).
fof(f441,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)],[f435]) ).
fof(f442,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)],[f17]) ).
fof(f443,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(f444,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)],[f442,f443]) ).
fof(f445,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)],[f444]) ).
fof(f446,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)],[f445]) ).
fof(f447,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))],[f446]) ).
fof(f448,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)],[f447]) ).
fof(f452,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)],[f18]) ).
fof(f453,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)],[f452]) ).
fof(f454,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)],[f453]) ).
fof(f455,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))],[f454]) ).
fof(f456,plain,
! [X0,X1,X2,X3,X4] :
( in(X4,X2)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f455]) ).
fof(f457,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f455]) ).
fof(f458,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)],[f455]) ).
fof(f461,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)],[f455]) ).
fof(f462,plain,
! [A] :
( ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f463,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)],[f462]) ).
fof(f464,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f463]) ).
fof(f466,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)],[f20]) ).
fof(f467,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)],[f466]) ).
fof(f468,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)],[f467]) ).
fof(f469,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))],[f468]) ).
fof(f470,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)],[f469]) ).
fof(f471,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)],[f469]) ).
fof(f472,plain,
! [X0,X1,X2,X3] :
( ~ in(apply(X0,X3),X2)
| ~ in(X3,relation_dom(X0))
| in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f469]) ).
fof(f473,plain,
! [X0,X1,X2] :
( ~ in(apply(X0,sK9_skl(X1,X2,X0)),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)],[f469]) ).
fof(f474,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)],[f469]) ).
fof(f475,plain,
! [X0,X1,X2] :
( in(apply(X0,sK9_skl(X1,X2,X0)),X2)
| in(sK9_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f469]) ).
fof(f476,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)],[f21]) ).
fof(f477,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)],[f476]) ).
fof(f478,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)],[f477]) ).
fof(f479,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))],[f478]) ).
fof(f480,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)],[f479]) ).
fof(f481,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)],[f479]) ).
fof(f482,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)],[f479]) ).
fof(f483,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,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)],[f479]) ).
fof(f484,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)],[f479]) ).
fof(f486,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)],[f22]) ).
fof(f487,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)],[f486]) ).
fof(f488,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)],[f487]) ).
fof(f489,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))],[f488]) ).
fof(f490,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)],[f489]) ).
fof(f491,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)],[f489]) ).
fof(f493,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(sK14_skl(X1,X2,X0),X3),X0)
| ~ in(sK14_skl(X1,X2,X0),X1)
| X1 = relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f489]) ).
fof(f494,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)],[f489]) ).
fof(f496,plain,
! [A] :
( ( connected(A)
<=> is_connected_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f497,plain,
! [A] :
( ( ( ~ is_connected_in(A,relation_field(A))
| connected(A) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f496]) ).
fof(f498,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f497]) ).
fof(f500,plain,
! [A] :
( ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f501,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)],[f500]) ).
fof(f502,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f501]) ).
fof(f504,plain,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ( E = C
| E = B
| E = A ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f505,definition,
! [A,B,C,E] :
( sP1_prd(E,C,B,A)
<=> ( E = C
| E = B
| E = A ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f506,plain,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> sP1_prd(E,C,B,A) ) ),
inference(formula_renaming,[status(thm)],[f504,f505]) ).
fof(f507,plain,
! [A,B,C,D] :
( ( ? [E] :
( ( sP1_prd(E,C,B,A)
| in(E,D) )
& ( ~ sP1_prd(E,C,B,A)
| ~ in(E,D) ) )
| D = unordered_triple(A,B,C) )
& ( ! [E] :
( ( ~ sP1_prd(E,C,B,A)
| in(E,D) )
& ( sP1_prd(E,C,B,A)
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(NNF_transformation,[status(thm)],[f506]) ).
fof(f508,plain,
( ! [A,B,C,D] :
( ? [E] :
( ( sP1_prd(E,C,B,A)
| in(E,D) )
& ( ~ sP1_prd(E,C,B,A)
| ~ in(E,D) ) )
| D = unordered_triple(A,B,C) )
& ! [A,B,C,D] :
( ( ! [E] :
( ~ sP1_prd(E,C,B,A)
| in(E,D) )
& ! [E] :
( sP1_prd(E,C,B,A)
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(miniscoping,[status(thm)],[f507]) ).
fof(f509,plain,
( ! [A,B,C,D] :
( ( ( sP1_prd(sK16_skl(D,C,B,A),C,B,A)
| in(sK16_skl(D,C,B,A),D) )
& ( ~ sP1_prd(sK16_skl(D,C,B,A),C,B,A)
| ~ in(sK16_skl(D,C,B,A),D) ) )
| D = unordered_triple(A,B,C) )
& ! [A,B,C,D] :
( ( ! [E] :
( ~ sP1_prd(E,C,B,A)
| in(E,D) )
& ! [E] :
( sP1_prd(E,C,B,A)
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(E,sK16_skl(D,C,B,A))],[f508]) ).
fof(f511,plain,
! [X0,X1,X2,X3,X4] :
( ~ sP1_prd(X4,X3,X2,X1)
| in(X4,X0)
| X0 != unordered_triple(X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f509]) ).
fof(f514,plain,
! [A] :
( function(A)
<=> ! [B,C,D] :
( C = D
| ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f515,plain,
! [A] :
( ( ? [B,C,D] :
( C != D
& in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
| function(A) )
& ( ! [B,C,D] :
( C = D
| ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) )
| ~ function(A) ) ),
inference(NNF_transformation,[status(thm)],[f514]) ).
fof(f516,plain,
( ! [A] :
( ? [C,D] :
( C != D
& ? [B] :
( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) ) )
| function(A) )
& ! [A] :
( ! [C,D] :
( C = D
| ! [B] :
( ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ function(A) ) ),
inference(miniscoping,[status(thm)],[f515]) ).
fof(f517,plain,
( ! [A] :
( ( sK17_skl(A) != sK18_skl(A)
& in(ordered_pair(sK19_skl(A),sK18_skl(A)),A)
& in(ordered_pair(sK19_skl(A),sK17_skl(A)),A) )
| function(A) )
& ! [A] :
( ! [C,D] :
( C = D
| ! [B] :
( ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) ) )
| ~ function(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(C,sK17_skl(A)),skolemize(D,sK18_skl(A)),skolemize(B,sK19_skl(A))],[f516]) ).
fof(f518,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f517]) ).
fof(f522,plain,
! [A,B,C] :
( ( ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set
| B != empty_set )
& ( ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) )
| ( A != empty_set
& B = empty_set ) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f523,definition,
! [A,B] :
( sP2_prd(B,A)
<=> ( A != empty_set
& B = empty_set ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f524,plain,
! [A,B,C] :
( ( ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set
| B != empty_set )
& ( ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) )
| sP2_prd(B,A) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(formula_renaming,[status(thm)],[f522,f523]) ).
fof(f525,plain,
! [A,B,C] :
( ( ( ( ( C != empty_set
| quasi_total(C,A,B) )
& ( C = empty_set
| ~ quasi_total(C,A,B) ) )
| A = empty_set
| B != empty_set )
& ( ( ( A != relation_dom_as_subset(A,B,C)
| quasi_total(C,A,B) )
& ( A = relation_dom_as_subset(A,B,C)
| ~ quasi_total(C,A,B) ) )
| sP2_prd(B,A) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(NNF_transformation,[status(thm)],[f524]) ).
fof(f526,plain,
! [X0,X1,X2] :
( X1 = relation_dom_as_subset(X1,X2,X0)
| ~ quasi_total(X0,X1,X2)
| sP2_prd(X2,X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f525]) ).
fof(f527,plain,
! [X0,X1,X2] :
( X1 != relation_dom_as_subset(X1,X2,X0)
| quasi_total(X0,X1,X2)
| sP2_prd(X2,X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f525]) ).
fof(f529,plain,
! [X0,X1,X2] :
( X0 != empty_set
| quasi_total(X0,X1,X2)
| X1 = empty_set
| X2 != empty_set
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f525]) ).
fof(f530,plain,
! [A] :
( ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( B = C
| A != ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f531,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( B != C
& A = ordered_pair(C,D) )
| B = pair_first(A) )
& ( ! [C,D] :
( B = C
| A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(NNF_transformation,[status(thm)],[f530]) ).
fof(f532,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( B != C
& ? [D] : A = ordered_pair(C,D) )
| B = pair_first(A) )
& ! [B] :
( ! [C] :
( B = C
| ! [D] : A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f531]) ).
fof(f533,plain,
! [A] :
( ( ! [B] :
( ( B != sK20_skl(B,A)
& A = ordered_pair(sK20_skl(B,A),sK21_skl(B,A)) )
| B = pair_first(A) )
& ! [B] :
( ! [C] :
( B = C
| ! [D] : A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl]),skolemize(C,sK20_skl(B,A)),skolemize(D,sK21_skl(B,A))],[f532]) ).
fof(f535,plain,
! [X0,X1,X2,X3] :
( X0 = ordered_pair(sK20_skl(X3,X0),sK21_skl(X3,X0))
| X3 = pair_first(X0)
| X0 != ordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f533]) ).
fof(f537,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f538,plain,
! [A] :
( relation(A)
<=> ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f539,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)],[f538]) ).
fof(f540,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)],[f539]) ).
fof(f541,plain,
( ! [A] :
( ( ! [C,D] : sK24_skl(A) != ordered_pair(C,D)
& in(sK24_skl(A),A) )
| relation(A) )
& ! [A] :
( ! [B] :
( B = ordered_pair(sK22_skl(B,A),sK23_skl(B,A))
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl,sK23_skl,sK24_skl]),skolemize(C,sK22_skl(B,A)),skolemize(D,sK23_skl(B,A)),skolemize(B,sK24_skl(A))],[f540]) ).
fof(f543,plain,
! [X0] :
( in(sK24_skl(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[status(thm)],[f541]) ).
fof(f545,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)],[f31]) ).
fof(f546,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)],[f545]) ).
fof(f547,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)],[f546]) ).
fof(f548,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK25_skl(B,A),sK25_skl(B,A)),A)
& in(sK25_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,[sK25_skl]),skolemize(C,sK25_skl(B,A))],[f547]) ).
fof(f549,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)],[f548]) ).
fof(f550,plain,
! [X0,X1] :
( in(sK25_skl(X1,X0),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f548]) ).
fof(f556,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)],[f33]) ).
fof(f557,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)],[f556]) ).
fof(f558,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)],[f557]) ).
fof(f559,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(sK27_skl(B,A),D)
| ~ in(D,A) )
| in(sK27_skl(B,A),B) )
& ( ( ~ in(sK27_skl(B,A),sK28_skl(B,A))
& in(sK28_skl(B,A),A) )
| ~ in(sK27_skl(B,A),B) ) )
| B = set_meet(A) )
& ! [B] :
( ( ! [C] :
( ( ~ in(C,sK26_skl(C,B,A))
& in(sK26_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,[sK26_skl,sK27_skl,sK28_skl]),skolemize(D,sK26_skl(C,B,A)),skolemize(C,sK27_skl(B,A)),skolemize(D,sK28_skl(B,A))],[f558]) ).
fof(f561,plain,
! [X0,X1,X2] :
( in(sK26_skl(X2,X1,X0),X0)
| in(X2,X1)
| X1 != set_meet(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f565,plain,
! [X0,X1,X2] :
( in(sK27_skl(X1,X0),X2)
| ~ in(X2,X0)
| in(sK27_skl(X1,X0),X1)
| X1 = set_meet(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f566,plain,
! [X0,X1] :
( X1 = empty_set
| X1 != set_meet(X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f568,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)],[f34]) ).
fof(f569,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)],[f568]) ).
fof(f570,plain,
( ! [A,B] :
( ( ( sK29_skl(B,A) = A
| in(sK29_skl(B,A),B) )
& ( sK29_skl(B,A) != A
| ~ in(sK29_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,[sK29_skl]),skolemize(C,sK29_skl(B,A))],[f569]) ).
fof(f571,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f570]) ).
fof(f574,plain,
! [X0,X1] :
( sK29_skl(X0,X1) = X1
| in(sK29_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f570]) ).
fof(f575,plain,
! [A] :
( ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f576,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ( in(ordered_pair(D,B),A)
& D != B )
| in(D,C) )
& ( ~ in(ordered_pair(D,B),A)
| D = B
| ~ in(D,C) ) )
| C = fiber(A,B) )
& ( ! [D] :
( ( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f575]) ).
fof(f577,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ( in(ordered_pair(D,B),A)
& D != B )
| in(D,C) )
& ( ~ in(ordered_pair(D,B),A)
| D = B
| ~ in(D,C) ) )
| C = fiber(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ! [D] :
( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f576]) ).
fof(f578,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(ordered_pair(sK30_skl(C,B,A),B),A)
& sK30_skl(C,B,A) != B )
| in(sK30_skl(C,B,A),C) )
& ( ~ in(ordered_pair(sK30_skl(C,B,A),B),A)
| sK30_skl(C,B,A) = B
| ~ in(sK30_skl(C,B,A),C) ) )
| C = fiber(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ! [D] :
( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl]),skolemize(D,sK30_skl(C,B,A))],[f577]) ).
fof(f579,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| ~ in(X3,X1)
| X1 != fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f578]) ).
fof(f580,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,X2),X0)
| ~ in(X3,X1)
| X1 != fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f578]) ).
fof(f582,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK30_skl(X1,X2,X0),X2),X0)
| sK30_skl(X1,X2,X0) = X2
| ~ in(sK30_skl(X1,X2,X0),X1)
| X1 = fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f578]) ).
fof(f583,plain,
! [X0,X1,X2] :
( sK30_skl(X1,X2,X0) != X2
| in(sK30_skl(X1,X2,X0),X1)
| X1 = fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f578]) ).
fof(f584,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK30_skl(X1,X2,X0),X2),X0)
| in(sK30_skl(X1,X2,X0),X1)
| X1 = fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f578]) ).
fof(f585,plain,
! [A,B] :
( ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
<=> subset(C,D) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A ) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f586,plain,
! [A,B] :
( ( ( ? [C,D] :
( ( subset(C,D)
| in(ordered_pair(C,D),B) )
& ( ~ subset(C,D)
| ~ in(ordered_pair(C,D),B) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f585]) ).
fof(f587,plain,
! [B] :
( ( ! [A] :
( ? [C,D] :
( ( subset(C,D)
| in(ordered_pair(C,D),B) )
& ( ~ subset(C,D)
| ~ in(ordered_pair(C,D),B) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ! [A] :
( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f586]) ).
fof(f588,plain,
! [B] :
( ( ! [A] :
( ( ( subset(sK31_skl(A,B),sK32_skl(A,B))
| in(ordered_pair(sK31_skl(A,B),sK32_skl(A,B)),B) )
& ( ~ subset(sK31_skl(A,B),sK32_skl(A,B))
| ~ in(ordered_pair(sK31_skl(A,B),sK32_skl(A,B)),B) )
& in(sK32_skl(A,B),A)
& in(sK31_skl(A,B),A) )
| relation_field(B) != A
| B = inclusion_relation(A) )
& ! [A] :
( ( ! [C,D] :
( ( ( ~ subset(C,D)
| in(ordered_pair(C,D),B) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31_skl,sK32_skl]),skolemize(C,sK31_skl(A,B)),skolemize(D,sK32_skl(A,B))],[f587]) ).
fof(f591,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X0 != inclusion_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f588]) ).
fof(f592,plain,
! [X0,X1] :
( in(sK31_skl(X1,X0),X1)
| relation_field(X0) != X1
| X0 = inclusion_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f588]) ).
fof(f596,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f597,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f596]) ).
fof(f598,plain,
( ! [A] :
( in(sK33_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl]),skolemize(B,sK33_skl(A))],[f597]) ).
fof(f599,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f598]) ).
fof(f600,plain,
! [X0] :
( in(sK33_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f598]) ).
fof(f601,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)],[f38]) ).
fof(f602,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)],[f601]) ).
fof(f603,plain,
( ! [A,B] :
( ( ( subset(sK34_skl(B,A),A)
| in(sK34_skl(B,A),B) )
& ( ~ subset(sK34_skl(B,A),A)
| ~ in(sK34_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,[sK34_skl]),skolemize(C,sK34_skl(B,A))],[f602]) ).
fof(f605,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f603]) ).
fof(f607,plain,
! [X0,X1] :
( subset(sK34_skl(X0,X1),X1)
| in(sK34_skl(X0,X1),X0)
| X0 = powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f603]) ).
fof(f608,plain,
! [A] :
( ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( B = D
| A != ordered_pair(C,D) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f609,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( B != D
& A = ordered_pair(C,D) )
| B = pair_second(A) )
& ( ! [C,D] :
( B = D
| A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(NNF_transformation,[status(thm)],[f608]) ).
fof(f610,plain,
! [A] :
( ( ! [B] :
( ? [D] :
( B != D
& ? [C] : A = ordered_pair(C,D) )
| B = pair_second(A) )
& ! [B] :
( ! [D] :
( B = D
| ! [C] : A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f609]) ).
fof(f611,plain,
! [A] :
( ( ! [B] :
( ( B != sK35_skl(B,A)
& A = ordered_pair(sK36_skl(B,A),sK35_skl(B,A)) )
| B = pair_second(A) )
& ! [B] :
( ! [D] :
( B = D
| ! [C] : A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl]),skolemize(D,sK35_skl(B,A)),skolemize(C,sK36_skl(B,A))],[f610]) ).
fof(f613,plain,
! [X0,X1,X2,X3] :
( X0 = ordered_pair(sK36_skl(X3,X0),sK35_skl(X3,X0))
| X3 = pair_second(X0)
| X0 != ordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f611]) ).
fof(f630,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f631,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)],[f630]) ).
fof(f632,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)],[f631]) ).
fof(f633,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f632]) ).
fof(f635,plain,
! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f632]) ).
fof(f682,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)],[f48]) ).
fof(f683,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)],[f682]) ).
fof(f684,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK51_skl(B,A),sK52_skl(B,A)),B)
& in(ordered_pair(sK51_skl(B,A),sK52_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,[sK51_skl,sK52_skl]),skolemize(C,sK51_skl(B,A)),skolemize(D,sK52_skl(B,A))],[f683]) ).
fof(f686,plain,
! [X0,X1] :
( in(ordered_pair(sK51_skl(X1,X0),sK52_skl(X1,X0)),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f695,plain,
! [A] :
( ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f696,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) )
| is_well_founded_in(A,B) )
& ( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f695]) ).
fof(f697,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) )
| is_well_founded_in(A,B) )
& ! [B] :
( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f696]) ).
fof(f698,plain,
! [A] :
( ( ! [B] :
( ( ! [D] :
( ~ disjoint(fiber(A,D),sK55_skl(B,A))
| ~ in(D,sK55_skl(B,A)) )
& sK55_skl(B,A) != empty_set
& subset(sK55_skl(B,A),B) )
| is_well_founded_in(A,B) )
& ! [B] :
( ! [C] :
( ( disjoint(fiber(A,sK54_skl(C,B,A)),C)
& in(sK54_skl(C,B,A),C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54_skl,sK55_skl]),skolemize(D,sK54_skl(C,B,A)),skolemize(C,sK55_skl(B,A))],[f697]) ).
fof(f703,plain,
! [X0,X1,X2] :
( ~ disjoint(fiber(X0,X2),sK55_skl(X1,X0))
| ~ in(X2,sK55_skl(X1,X0))
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f698]) ).
fof(f713,plain,
! [A] :
( ! [B,C] :
( ( ( C = apply(A,B)
<=> C = empty_set )
| in(B,relation_dom(A)) )
& ( ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f714,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f713]) ).
fof(f715,plain,
! [A] :
( ( ! [B] :
( ( ! [C] :
( C != empty_set
| C = apply(A,B) )
& ! [C] :
( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ! [B] :
( ( ! [C] :
( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ! [C] :
( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f714]) ).
fof(f716,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
| X2 != apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f715]) ).
fof(f718,plain,
! [X0,X1,X2] :
( X2 = empty_set
| X2 != apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f715]) ).
fof(f725,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)],[f54]) ).
fof(f726,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)],[f725]) ).
fof(f727,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)],[f726]) ).
fof(f728,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK58_skl(B,A),sK59_skl(B,A)),A)
| in(sK58_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK58_skl(B,A),D),A)
| ~ in(sK58_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,sK57_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57_skl,sK58_skl,sK59_skl]),skolemize(D,sK57_skl(C,B,A)),skolemize(C,sK58_skl(B,A)),skolemize(D,sK59_skl(B,A))],[f727]) ).
fof(f729,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK57_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f728]) ).
fof(f733,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)],[f55]) ).
fof(f734,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)],[f733]) ).
fof(f735,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)],[f734]) ).
fof(f736,plain,
! [A] :
( ( ! [B] :
( ( sK60_skl(B,A) != sK61_skl(B,A)
& in(ordered_pair(sK61_skl(B,A),sK60_skl(B,A)),A)
& in(ordered_pair(sK60_skl(B,A),sK61_skl(B,A)),A)
& in(sK61_skl(B,A),B)
& in(sK60_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,[sK60_skl,sK61_skl]),skolemize(C,sK60_skl(B,A)),skolemize(D,sK61_skl(B,A))],[f735]) ).
fof(f737,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)],[f736]) ).
fof(f744,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)],[f57]) ).
fof(f745,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)],[f744]) ).
fof(f746,plain,
( ! [A,B] :
( ( ( ( in(sK64_skl(B,A),A)
& in(sK63_skl(B,A),sK64_skl(B,A)) )
| in(sK63_skl(B,A),B) )
& ( ! [D] :
( ~ in(D,A)
| ~ in(sK63_skl(B,A),D) )
| ~ in(sK63_skl(B,A),B) ) )
| B = union(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ! [C] :
( ( in(sK62_skl(C,B,A),A)
& in(C,sK62_skl(C,B,A)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62_skl,sK63_skl,sK64_skl]),skolemize(D,sK62_skl(C,B,A)),skolemize(C,sK63_skl(B,A)),skolemize(D,sK64_skl(B,A))],[f745]) ).
fof(f749,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| ~ in(X2,X3)
| in(X2,X0)
| X0 != union(X1) ),
inference(cnf_transformation,[status(thm)],[f746]) ).
fof(f753,plain,
! [A] :
( ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f754,plain,
! [A] :
( ( ( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f753]) ).
fof(f758,plain,
! [X0] :
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f754]) ).
fof(f759,plain,
! [X0] :
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f754]) ).
fof(f761,plain,
! [A,B] :
( ( ! [C] :
( relation_rng(C) != B
| relation_dom(C) != A
| ~ one_to_one(C)
| ~ function(C)
| ~ relation(C) )
| equipotent(A,B) )
& ( ? [C] :
( relation_rng(C) = B
& relation_dom(C) = A
& one_to_one(C)
& function(C)
& relation(C) )
| ~ equipotent(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f59]) ).
fof(f762,plain,
( ! [A,B] :
( ! [C] :
( relation_rng(C) != B
| relation_dom(C) != A
| ~ one_to_one(C)
| ~ function(C)
| ~ relation(C) )
| equipotent(A,B) )
& ! [A,B] :
( ? [C] :
( relation_rng(C) = B
& relation_dom(C) = A
& one_to_one(C)
& function(C)
& relation(C) )
| ~ equipotent(A,B) ) ),
inference(miniscoping,[status(thm)],[f761]) ).
fof(f763,plain,
( ! [A,B] :
( ! [C] :
( relation_rng(C) != B
| relation_dom(C) != A
| ~ one_to_one(C)
| ~ function(C)
| ~ relation(C) )
| equipotent(A,B) )
& ! [A,B] :
( ( relation_rng(sK65_skl(B,A)) = B
& relation_dom(sK65_skl(B,A)) = A
& one_to_one(sK65_skl(B,A))
& function(sK65_skl(B,A))
& relation(sK65_skl(B,A)) )
| ~ equipotent(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(C,sK65_skl(B,A))],[f762]) ).
fof(f764,plain,
! [X0,X1] :
( relation(sK65_skl(X1,X0))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f763]) ).
fof(f766,plain,
! [X0,X1] :
( one_to_one(sK65_skl(X1,X0))
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f763]) ).
fof(f767,plain,
! [X0,X1] :
( relation_dom(sK65_skl(X1,X0)) = X0
| ~ equipotent(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f763]) ).
fof(f769,plain,
! [X0,X1,X2] :
( relation_rng(X2) != X1
| relation_dom(X2) != X0
| ~ one_to_one(X2)
| ~ function(X2)
| ~ relation(X2)
| equipotent(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f763]) ).
fof(f770,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f771,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f770]) ).
fof(f772,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK66_skl(C,B,A),B)
& in(sK66_skl(C,B,A),A) )
| in(sK66_skl(C,B,A),C) )
& ( in(sK66_skl(C,B,A),B)
| ~ in(sK66_skl(C,B,A),A)
| ~ in(sK66_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(D,sK66_skl(C,B,A))],[f771]) ).
fof(f775,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f772]) ).
fof(f779,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)],[f61]) ).
fof(f780,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)],[f779]) ).
fof(f781,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)],[f780]) ).
fof(f782,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK68_skl(B,A) = apply(A,sK69_skl(B,A))
& in(sK69_skl(B,A),relation_dom(A)) )
| in(sK68_skl(B,A),B) )
& ( ! [D] :
( sK68_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK68_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,sK67_skl(C,B,A))
& in(sK67_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,[sK67_skl,sK68_skl,sK69_skl]),skolemize(D,sK67_skl(C,B,A)),skolemize(C,sK68_skl(B,A)),skolemize(D,sK69_skl(B,A))],[f781]) ).
fof(f783,plain,
! [X0,X1,X2] :
( in(sK67_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f782]) ).
fof(f784,plain,
! [X0,X1,X2] :
( X2 = apply(X0,sK67_skl(X2,X1,X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f782]) ).
fof(f785,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)],[f782]) ).
fof(f787,plain,
! [X0,X1] :
( in(sK69_skl(X1,X0),relation_dom(X0))
| in(sK68_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f782]) ).
fof(f788,plain,
! [X0,X1] :
( sK68_skl(X1,X0) = apply(X0,sK69_skl(X1,X0))
| in(sK68_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f782]) ).
fof(f789,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)],[f62]) ).
fof(f790,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)],[f789]) ).
fof(f791,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)],[f790]) ).
fof(f792,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK72_skl(B,A),sK71_skl(B,A)),A)
| in(sK71_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK71_skl(B,A)),A)
| ~ in(sK71_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK70_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70_skl,sK71_skl,sK72_skl]),skolemize(D,sK70_skl(C,B,A)),skolemize(C,sK71_skl(B,A)),skolemize(D,sK72_skl(B,A))],[f791]) ).
fof(f793,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK70_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f792]) ).
fof(f813,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f814,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f813]) ).
fof(f815,plain,
! [A] :
( ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f816,plain,
! [A] :
( ! [B] :
( ( ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) )
| is_connected_in(A,B) )
& ( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f815]) ).
fof(f817,plain,
! [A] :
( ( ! [B] :
( ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) )
| is_connected_in(A,B) )
& ! [B] :
( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f816]) ).
fof(f818,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK74_skl(B,A),sK73_skl(B,A)),A)
& ~ in(ordered_pair(sK73_skl(B,A),sK74_skl(B,A)),A)
& sK73_skl(B,A) != sK74_skl(B,A)
& in(sK74_skl(B,A),B)
& in(sK73_skl(B,A),B) )
| is_connected_in(A,B) )
& ! [B] :
( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73_skl,sK74_skl]),skolemize(C,sK73_skl(B,A)),skolemize(D,sK74_skl(B,A))],[f817]) ).
fof(f819,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f818]) ).
fof(f821,plain,
! [X0,X1] :
( in(sK74_skl(X1,X0),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f818]) ).
fof(f825,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f69]) ).
fof(f826,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f825]) ).
fof(f827,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)],[f70]) ).
fof(f828,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)],[f827]) ).
fof(f829,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)],[f828]) ).
fof(f830,plain,
! [A] :
( ! [B] :
( ( ( ( ( in(ordered_pair(sK76_skl(B,A),sK75_skl(B,A)),A)
| in(ordered_pair(sK75_skl(B,A),sK76_skl(B,A)),B) )
& ( ~ in(ordered_pair(sK76_skl(B,A),sK75_skl(B,A)),A)
| ~ in(ordered_pair(sK75_skl(B,A),sK76_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,[sK75_skl,sK76_skl]),skolemize(C,sK75_skl(B,A)),skolemize(D,sK76_skl(B,A))],[f829]) ).
fof(f831,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)],[f830]) ).
fof(f852,plain,
! [A] :
( ( one_to_one(A)
<=> ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f853,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f852]) ).
fof(f854,plain,
! [A] :
( ( ( ( sK79_skl(A) != sK80_skl(A)
& apply(A,sK79_skl(A)) = apply(A,sK80_skl(A))
& in(sK80_skl(A),relation_dom(A))
& in(sK79_skl(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79_skl,sK80_skl]),skolemize(B,sK79_skl(A)),skolemize(C,sK80_skl(A))],[f853]) ).
fof(f855,plain,
! [X0,X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f854]) ).
fof(f870,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)],[f75]) ).
fof(f871,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)],[f870]) ).
fof(f872,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)],[f871]) ).
fof(f873,plain,
! [A] :
( ( ! [B] :
( ( ~ in(ordered_pair(sK85_skl(B,A),sK86_skl(B,A)),A)
& in(ordered_pair(sK87_skl(B,A),sK86_skl(B,A)),A)
& in(ordered_pair(sK85_skl(B,A),sK87_skl(B,A)),A)
& in(sK86_skl(B,A),B)
& in(sK87_skl(B,A),B)
& in(sK85_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,[sK85_skl,sK86_skl,sK87_skl]),skolemize(C,sK85_skl(B,A)),skolemize(E,sK86_skl(B,A)),skolemize(D,sK87_skl(B,A))],[f872]) ).
fof(f874,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)],[f873]) ).
fof(f894,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f895,plain,
! [X0] :
( function_inverse(X0) = relation_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f894]) ).
fof(f896,plain,
! [A] :
( ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f897,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)],[f896]) ).
fof(f898,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f897]) ).
fof(f900,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f901,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f902,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f901]) ).
fof(f903,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f901]) ).
fof(f910,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f104]) ).
fof(f911,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f910]) ).
fof(f912,plain,
! [A,B,C] :
( element(relation_dom_as_subset(A,B,C),powerset(A))
| ~ relation_of2(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f105]) ).
fof(f913,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X1,X2,X0),powerset(X1))
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f912]) ).
fof(f920,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f933,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f120]) ).
fof(f934,plain,
! [X0,X1,X2] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f933]) ).
fof(f937,plain,
! [A] : element(sK90_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90_skl]),skolemize(B,sK90_skl(A))],[f122]) ).
fof(f938,plain,
! [X0] : element(sK90_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f937]) ).
fof(f939,plain,
! [A,B] : relation_of2_as_subset(sK91_skl(B,A),A,B),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91_skl]),skolemize(C,sK91_skl(B,A))],[f123]) ).
fof(f940,plain,
! [X0,X1] : relation_of2_as_subset(sK91_skl(X0,X1),X1,X0),
inference(cnf_transformation,[status(thm)],[f939]) ).
fof(f944,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f125]) ).
fof(f945,plain,
! [X0] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f944]) ).
fof(f947,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f948,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f957,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f968,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f969,plain,
one_to_one(empty_set),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f973,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f974,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f136]) ).
fof(f975,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f974]) ).
fof(f980,plain,
! [A] :
( ( function(relation_inverse(A))
& relation(relation_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f139]) ).
fof(f982,plain,
! [X0] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f980]) ).
fof(f983,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f140]) ).
fof(f985,plain,
! [X0] :
( epsilon_transitive(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f983]) ).
fof(f986,plain,
! [X0] :
( epsilon_connected(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f983]) ).
fof(f987,plain,
! [X0] :
( ordinal(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f983]) ).
fof(f994,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f144]) ).
fof(f995,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f994]) ).
fof(f997,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f995]) ).
fof(f1012,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f150]) ).
fof(f1013,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1012]) ).
fof(f1017,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f152]) ).
fof(f1019,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1017]) ).
fof(f1029,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f157]) ).
fof(f1030,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1029]) ).
fof(f1035,plain,
! [A] :
( ( reflexive(A)
<=> ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f160]) ).
fof(f1036,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)],[f1035]) ).
fof(f1037,plain,
! [A] :
( ( ( ( ~ in(ordered_pair(sK92_skl(A),sK92_skl(A)),A)
& in(sK92_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,[sK92_skl]),skolemize(B,sK92_skl(A))],[f1036]) ).
fof(f1038,plain,
! [X0,X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1037]) ).
fof(f1041,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f1048,plain,
! [A,B] :
( subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f165]) ).
fof(f1049,plain,
! [B] :
( ! [A] : subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1048]) ).
fof(f1050,plain,
! [X0,X1] :
( subset(relation_dom(relation_rng_restriction(X1,X0)),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1049]) ).
fof(f1051,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)],[f166]) ).
fof(f1052,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)],[f1051]) ).
fof(f1053,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)],[f1052]) ).
fof(f1054,plain,
! [A] :
( ( ( ( ~ in(ordered_pair(sK93_skl(A),sK94_skl(A)),A)
& in(ordered_pair(sK95_skl(A),sK94_skl(A)),A)
& in(ordered_pair(sK93_skl(A),sK95_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,[sK93_skl,sK94_skl,sK95_skl]),skolemize(B,sK93_skl(A)),skolemize(D,sK94_skl(A)),skolemize(C,sK95_skl(A))],[f1053]) ).
fof(f1055,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1054]) ).
fof(f1063,plain,
! [A,B] :
( ? [C] :
( well_orders(C,A)
& relation(C) )
| ~ equipotent(A,relation_field(B))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f168]) ).
fof(f1064,plain,
! [B] :
( ! [A] :
( ? [C] :
( well_orders(C,A)
& relation(C) )
| ~ equipotent(A,relation_field(B))
| ~ well_ordering(B) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1063]) ).
fof(f1065,plain,
! [B] :
( ! [A] :
( ( well_orders(sK96_skl(A,B),A)
& relation(sK96_skl(A,B)) )
| ~ equipotent(A,relation_field(B))
| ~ well_ordering(B) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96_skl]),skolemize(C,sK96_skl(A,B))],[f1064]) ).
fof(f1066,plain,
! [X0,X1] :
( relation(sK96_skl(X1,X0))
| ~ equipotent(X1,relation_field(X0))
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1065]) ).
fof(f1074,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)],[f171]) ).
fof(f1075,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)],[f1074]) ).
fof(f1076,plain,
! [A] :
( ( ( ( sK97_skl(A) != sK98_skl(A)
& in(ordered_pair(sK98_skl(A),sK97_skl(A)),A)
& in(ordered_pair(sK97_skl(A),sK98_skl(A)),A) )
| antisymmetric(A) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97_skl,sK98_skl]),skolemize(B,sK97_skl(A)),skolemize(C,sK98_skl(A))],[f1075]) ).
fof(f1077,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1076]) ).
fof(f1084,plain,
! [A] :
( ( connected(A)
<=> ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f173]) ).
fof(f1085,plain,
! [A] :
( ( ( ? [B,C] :
( ~ in(ordered_pair(C,B),A)
& ~ in(ordered_pair(B,C),A)
& B != C
& in(C,relation_field(A))
& in(B,relation_field(A)) )
| connected(A) )
& ( ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) )
| ~ connected(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f1084]) ).
fof(f1086,plain,
! [A] :
( ( ( ( ~ in(ordered_pair(sK100_skl(A),sK99_skl(A)),A)
& ~ in(ordered_pair(sK99_skl(A),sK100_skl(A)),A)
& sK99_skl(A) != sK100_skl(A)
& in(sK100_skl(A),relation_field(A))
& in(sK99_skl(A),relation_field(A)) )
| connected(A) )
& ( ! [B,C] :
( in(ordered_pair(C,B),A)
| in(ordered_pair(B,C),A)
| B = C
| ~ in(C,relation_field(A))
| ~ in(B,relation_field(A)) )
| ~ connected(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99_skl,sK100_skl]),skolemize(B,sK99_skl(A)),skolemize(C,sK100_skl(A))],[f1085]) ).
fof(f1087,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,X1),X0)
| in(ordered_pair(X1,X2),X0)
| X1 = X2
| ~ in(X2,relation_field(X0))
| ~ in(X1,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1086]) ).
fof(f1100,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)],[f176]) ).
fof(f1101,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)],[f1100]) ).
fof(f1103,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f1101]) ).
fof(f1104,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)],[f1101]) ).
fof(f1109,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)],[f178]) ).
fof(f1110,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)],[f1109]) ).
fof(f1111,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)],[f1110]) ).
fof(f1112,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)],[f1111]) ).
fof(f1113,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)],[f1111]) ).
fof(f1115,plain,
( function(sK102_skl)
& relation(sK102_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102_skl]),skolemize(A,sK102_skl)],[f179]) ).
fof(f1116,plain,
relation(sK102_skl),
inference(cnf_transformation,[status(thm)],[f1115]) ).
fof(f1117,plain,
function(sK102_skl),
inference(cnf_transformation,[status(thm)],[f1115]) ).
fof(f1127,plain,
( empty(sK105_skl)
& one_to_one(sK105_skl)
& function(sK105_skl)
& relation(sK105_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105_skl]),skolemize(A,sK105_skl)],[f182]) ).
fof(f1128,plain,
relation(sK105_skl),
inference(cnf_transformation,[status(thm)],[f1127]) ).
fof(f1129,plain,
function(sK105_skl),
inference(cnf_transformation,[status(thm)],[f1127]) ).
fof(f1132,plain,
( relation(sK106_skl)
& empty(sK106_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106_skl]),skolemize(A,sK106_skl)],[f183]) ).
fof(f1133,plain,
empty(sK106_skl),
inference(cnf_transformation,[status(thm)],[f1132]) ).
fof(f1134,plain,
relation(sK106_skl),
inference(cnf_transformation,[status(thm)],[f1132]) ).
fof(f1141,plain,
( function(sK109_skl)
& empty(sK109_skl)
& relation(sK109_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109_skl]),skolemize(A,sK109_skl)],[f186]) ).
fof(f1142,plain,
relation(sK109_skl),
inference(cnf_transformation,[status(thm)],[f1141]) ).
fof(f1144,plain,
function(sK109_skl),
inference(cnf_transformation,[status(thm)],[f1141]) ).
fof(f1145,plain,
( ordinal(sK110_skl)
& epsilon_connected(sK110_skl)
& epsilon_transitive(sK110_skl)
& empty(sK110_skl)
& one_to_one(sK110_skl)
& function(sK110_skl)
& relation(sK110_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110_skl]),skolemize(A,sK110_skl)],[f187]) ).
fof(f1146,plain,
relation(sK110_skl),
inference(cnf_transformation,[status(thm)],[f1145]) ).
fof(f1147,plain,
function(sK110_skl),
inference(cnf_transformation,[status(thm)],[f1145]) ).
fof(f1157,plain,
( relation(sK112_skl)
& ~ empty(sK112_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112_skl]),skolemize(A,sK112_skl)],[f189]) ).
fof(f1158,plain,
~ empty(sK112_skl),
inference(cnf_transformation,[status(thm)],[f1157]) ).
fof(f1159,plain,
relation(sK112_skl),
inference(cnf_transformation,[status(thm)],[f1157]) ).
fof(f1165,plain,
( one_to_one(sK115_skl)
& function(sK115_skl)
& relation(sK115_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115_skl]),skolemize(A,sK115_skl)],[f192]) ).
fof(f1166,plain,
relation(sK115_skl),
inference(cnf_transformation,[status(thm)],[f1165]) ).
fof(f1167,plain,
function(sK115_skl),
inference(cnf_transformation,[status(thm)],[f1165]) ).
fof(f1168,plain,
one_to_one(sK115_skl),
inference(cnf_transformation,[status(thm)],[f1165]) ).
fof(f1174,plain,
( relation_empty_yielding(sK117_skl)
& relation(sK117_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117_skl]),skolemize(A,sK117_skl)],[f194]) ).
fof(f1175,plain,
relation(sK117_skl),
inference(cnf_transformation,[status(thm)],[f1174]) ).
fof(f1177,plain,
( function(sK118_skl)
& relation_empty_yielding(sK118_skl)
& relation(sK118_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118_skl]),skolemize(A,sK118_skl)],[f195]) ).
fof(f1178,plain,
relation(sK118_skl),
inference(cnf_transformation,[status(thm)],[f1177]) ).
fof(f1180,plain,
function(sK118_skl),
inference(cnf_transformation,[status(thm)],[f1177]) ).
fof(f1181,plain,
! [A,B,C] :
( relation_dom_as_subset(A,B,C) = relation_dom(C)
| ~ relation_of2(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f196]) ).
fof(f1182,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X1,X2,X0) = relation_dom(X0)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1181]) ).
fof(f1191,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f201]) ).
fof(f1192,plain,
( ! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ! [A,B,C] :
( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f1191]) ).
fof(f1193,plain,
! [X0,X1,X2] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1192]) ).
fof(f1208,plain,
! [A] : equipotent(A,A),
inference(miniscoping,[status(thm)],[f206]) ).
fof(f1209,plain,
! [X0] : equipotent(X0,X0),
inference(cnf_transformation,[status(thm)],[f1208]) ).
fof(f1312,plain,
! [A] :
( ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ordinal(C)
& D = C
& in(D,A) ) )
| ? [B,C,D] :
( C != D
& ordinal(D)
& B = D
& ordinal(C)
& B = C ) ),
inference(pre_NNF_transformation,[status(thm)],[f216]) ).
fof(f1313,definition,
! [B,C,D] :
( sP12_prd(D,C,B)
<=> ( C != D
& ordinal(D)
& B = D
& ordinal(C)
& B = C ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f1314,plain,
! [A] :
( ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ordinal(C)
& D = C
& in(D,A) ) )
| ? [B,C,D] : sP12_prd(D,C,B) ),
inference(formula_renaming,[status(thm)],[f1312,f1313]) ).
fof(f1315,plain,
! [A] :
( ? [B] :
! [C] :
( ( ! [D] :
( ~ ordinal(C)
| D != C
| ~ in(D,A) )
| in(C,B) )
& ( ? [D] :
( ordinal(C)
& D = C
& in(D,A) )
| ~ in(C,B) ) )
| ? [B,C,D] : sP12_prd(D,C,B) ),
inference(NNF_transformation,[status(thm)],[f1314]) ).
fof(f1316,plain,
( ! [A] :
? [B] :
( ! [C] :
( ~ ordinal(C)
| ! [D] :
( D != C
| ~ in(D,A) )
| in(C,B) )
& ! [C] :
( ( ordinal(C)
& ? [D] :
( D = C
& in(D,A) ) )
| ~ in(C,B) ) )
| ? [B,C,D] : sP12_prd(D,C,B) ),
inference(miniscoping,[status(thm)],[f1315]) ).
fof(f1317,plain,
( ! [A] :
( ! [C] :
( ~ ordinal(C)
| ! [D] :
( D != C
| ~ in(D,A) )
| in(C,sK169_skl(A)) )
& ! [C] :
( ( ordinal(C)
& sK170_skl(C,A) = C
& in(sK170_skl(C,A),A) )
| ~ in(C,sK169_skl(A)) ) )
| sP12_prd(sK168_skl,sK167_skl,sK166_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166_skl,sK167_skl,sK168_skl,sK169_skl,sK170_skl]),skolemize(B,sK166_skl),skolemize(C,sK167_skl),skolemize(D,sK168_skl),skolemize(B,sK169_skl(A)),skolemize(D,sK170_skl(C,A))],[f1316]) ).
fof(f1318,plain,
! [X0,X1] :
( in(sK170_skl(X0,X1),X1)
| ~ in(X0,sK169_skl(X1))
| sP12_prd(sK168_skl,sK167_skl,sK166_skl) ),
inference(cnf_transformation,[status(thm)],[f1317]) ).
fof(f1319,plain,
! [X0,X1] :
( sK170_skl(X0,X1) = X0
| ~ in(X0,sK169_skl(X1))
| sP12_prd(sK168_skl,sK167_skl,sK166_skl) ),
inference(cnf_transformation,[status(thm)],[f1317]) ).
fof(f1320,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,sK169_skl(X1))
| sP12_prd(sK168_skl,sK167_skl,sK166_skl) ),
inference(cnf_transformation,[status(thm)],[f1317]) ).
fof(f1321,plain,
! [X0,X1,X2] :
( ~ ordinal(X0)
| X2 != X0
| ~ in(X2,X1)
| in(X0,sK169_skl(X1))
| sP12_prd(sK168_skl,sK167_skl,sK166_skl) ),
inference(cnf_transformation,[status(thm)],[f1317]) ).
fof(f1438,plain,
! [A,B,C] :
( ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f238]) ).
fof(f1439,plain,
! [X0,X1,X2] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1438]) ).
fof(f1440,plain,
! [X0,X1,X2] :
( subset(relation_rng(X0),X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1438]) ).
fof(f1478,plain,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,B)
| ~ subset(relation_rng(D),B)
| ~ relation_of2_as_subset(D,C,A) ),
inference(pre_NNF_transformation,[status(thm)],[f249]) ).
fof(f1479,plain,
! [C,D] :
( ! [B] :
( relation_of2_as_subset(D,C,B)
| ~ subset(relation_rng(D),B) )
| ! [A] : ~ relation_of2_as_subset(D,C,A) ),
inference(miniscoping,[status(thm)],[f1478]) ).
fof(f1480,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(relation_rng(X0),X3)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1479]) ).
fof(f1491,plain,
! [A,B] :
( subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f252]) ).
fof(f1492,plain,
! [B] :
( ! [A] : subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1491]) ).
fof(f1493,plain,
! [X0,X1] :
( subset(relation_inverse_image(X0,X1),relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1492]) ).
fof(f1494,plain,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,B)
| ~ subset(A,B)
| ~ relation_of2_as_subset(D,C,A) ),
inference(pre_NNF_transformation,[status(thm)],[f253]) ).
fof(f1495,plain,
! [A,C,D] :
( ! [B] :
( relation_of2_as_subset(D,C,B)
| ~ subset(A,B) )
| ~ relation_of2_as_subset(D,C,A) ),
inference(miniscoping,[status(thm)],[f1494]) ).
fof(f1496,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(X2,X3)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f1495]) ).
fof(f1503,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)],[f255]) ).
fof(f1504,plain,
! [B] :
( ! [A] :
( relation_inverse_image(B,A) != empty_set
| ~ subset(A,relation_rng(B))
| A = empty_set )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f1503]) ).
fof(f1505,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)],[f1504]) ).
fof(f1506,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)],[f256]) ).
fof(f1507,plain,
! [C] :
( ! [A,B] :
( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ subset(A,B) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f1506]) ).
fof(f1508,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)],[f1507]) ).
fof(f1512,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f1522,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f262]) ).
fof(f1528,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f265]) ).
fof(f1543,plain,
! [A,B,C,D] :
( ! [E] :
( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set
| ~ in(C,A)
| ~ function(E)
| ~ relation(E) )
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(pre_NNF_transformation,[status(thm)],[f269]) ).
fof(f1544,plain,
! [A,B,D] :
( ! [E] :
( ! [C] :
( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set
| ~ in(C,A) )
| ~ function(E)
| ~ relation(E) )
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(miniscoping,[status(thm)],[f1543]) ).
fof(f1545,plain,
! [X0,X1,X2,X3,X4] :
( apply(relation_composition(X0,X3),X4) = apply(X3,apply(X0,X4))
| X2 = empty_set
| ~ in(X4,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ relation_of2_as_subset(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f1544]) ).
fof(f1619,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f1620,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f1688,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f313]) ).
fof(f1689,plain,
! [A,C] :
( ~ in(C,A)
| ! [B] :
( ~ in(B,C)
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f1688]) ).
fof(f1690,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1689]) ).
fof(f1695,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f1702,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f317]) ).
fof(f1703,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f1702]) ).
fof(f1727,plain,
? [A,B,C,D] :
( ? [E] :
( in(E,relation_inverse_image(D,C))
<~> ( in(apply(D,E),C)
& in(E,A) ) )
& B != empty_set
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(pre_NNF_transformation,[status(thm)],[f326]) ).
fof(f1728,plain,
? [A,B,C,D] :
( ? [E] :
( ( ~ in(apply(D,E),C)
| ~ in(E,A)
| ~ in(E,relation_inverse_image(D,C)) )
& ( ( in(apply(D,E),C)
& in(E,A) )
| in(E,relation_inverse_image(D,C)) ) )
& B != empty_set
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(NNF_transformation,[status(thm)],[f1727]) ).
fof(f1729,plain,
? [A,B,D] :
( ? [C,E] :
( ( ~ in(apply(D,E),C)
| ~ in(E,A)
| ~ in(E,relation_inverse_image(D,C)) )
& ( ( in(apply(D,E),C)
& in(E,A) )
| in(E,relation_inverse_image(D,C)) ) )
& B != empty_set
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(miniscoping,[status(thm)],[f1728]) ).
fof(f1730,plain,
( ( ~ in(apply(sK214_skl,sK216_skl),sK215_skl)
| ~ in(sK216_skl,sK212_skl)
| ~ in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)) )
& ( ( in(apply(sK214_skl,sK216_skl),sK215_skl)
& in(sK216_skl,sK212_skl) )
| in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)) )
& sK213_skl != empty_set
& relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
& quasi_total(sK214_skl,sK212_skl,sK213_skl)
& function(sK214_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212_skl,sK213_skl,sK214_skl,sK215_skl,sK216_skl]),skolemize(A,sK212_skl),skolemize(B,sK213_skl),skolemize(D,sK214_skl),skolemize(C,sK215_skl),skolemize(E,sK216_skl)],[f1729]) ).
fof(f1731,plain,
function(sK214_skl),
inference(cnf_transformation,[status(thm)],[f1730]) ).
fof(f1732,plain,
quasi_total(sK214_skl,sK212_skl,sK213_skl),
inference(cnf_transformation,[status(thm)],[f1730]) ).
fof(f1733,plain,
relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl),
inference(cnf_transformation,[status(thm)],[f1730]) ).
fof(f1734,plain,
sK213_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f1730]) ).
fof(f1735,plain,
( in(sK216_skl,sK212_skl)
| in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)) ),
inference(cnf_transformation,[status(thm)],[f1730]) ).
fof(f1736,plain,
( in(apply(sK214_skl,sK216_skl),sK215_skl)
| in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)) ),
inference(cnf_transformation,[status(thm)],[f1730]) ).
fof(f1737,plain,
( ~ in(apply(sK214_skl,sK216_skl),sK215_skl)
| ~ in(sK216_skl,sK212_skl)
| ~ in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)) ),
inference(cnf_transformation,[status(thm)],[f1730]) ).
fof(f1807,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[status(thm)],[f349]) ).
fof(f1808,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f350]) ).
fof(f1809,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f350]) ).
fof(f1817,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f354]) ).
fof(f1818,plain,
! [X0] :
( X0 = empty_set
| relation_dom(X0) != empty_set
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1817]) ).
fof(f1837,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f359]) ).
fof(f1838,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f1837]) ).
fof(f1839,plain,
! [A,B,C,D] :
( in(apply(D,C),relation_rng(D))
| B = empty_set
| ~ in(C,A)
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(pre_NNF_transformation,[status(thm)],[f360]) ).
fof(f1840,plain,
! [A,B,D] :
( ! [C] :
( in(apply(D,C),relation_rng(D))
| B = empty_set
| ~ in(C,A) )
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(miniscoping,[status(thm)],[f1839]) ).
fof(f1841,plain,
! [X0,X1,X2,X3] :
( in(apply(X0,X3),relation_rng(X0))
| X2 = empty_set
| ~ in(X3,X1)
| ~ relation_of2_as_subset(X0,X1,X2)
| ~ quasi_total(X0,X1,X2)
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f1840]) ).
fof(f1849,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f364]) ).
fof(f1850,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1849]) ).
fof(f1851,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1849]) ).
fof(f1864,plain,
( ! [A,B] : pair_second(ordered_pair(A,B)) = B
& ! [A,B] : pair_first(ordered_pair(A,B)) = A ),
inference(miniscoping,[status(thm)],[f368]) ).
fof(f1865,plain,
! [X0,X1] : pair_first(ordered_pair(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f1864]) ).
fof(f1866,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1864]) ).
fof(f1872,plain,
! [A] :
( well_ordering(inclusion_relation(A))
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f370]) ).
fof(f1873,plain,
! [X0] :
( well_ordering(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f1872]) ).
fof(f1874,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f1891,plain,
! [A,B,C] :
( ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f376]) ).
fof(f1892,plain,
! [A,B,C] :
( ( ( B != apply(C,A)
| ~ in(A,relation_dom(C))
| in(ordered_pair(A,B),C) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f1891]) ).
fof(f1893,plain,
! [C] :
( ( ! [A,B] :
( B != apply(C,A)
| ~ in(A,relation_dom(C))
| in(ordered_pair(A,B),C) )
& ! [A,B] :
( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f1892]) ).
fof(f1895,plain,
! [X0,X1,X2] :
( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f1893]) ).
fof(f1942,plain,
! [A,B,C,E] :
( ( ( E != C
& E != B
& E != A )
| sP1_prd(E,C,B,A) )
& ( E = C
| E = B
| E = A
| ~ sP1_prd(E,C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f505]) ).
fof(f1943,plain,
( ! [A,B,C,E] :
( ( E != C
& E != B
& E != A )
| sP1_prd(E,C,B,A) )
& ! [A,B,C,E] :
( E = C
| E = B
| E = A
| ~ sP1_prd(E,C,B,A) ) ),
inference(miniscoping,[status(thm)],[f1942]) ).
fof(f1945,plain,
! [X0,X1,X2,X3] :
( X0 != X3
| sP1_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f1943]) ).
fof(f1948,plain,
! [A,B] :
( ( A = empty_set
| B != empty_set
| sP2_prd(B,A) )
& ( ( A != empty_set
& B = empty_set )
| ~ sP2_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f523]) ).
fof(f1949,plain,
( ! [A,B] :
( A = empty_set
| B != empty_set
| sP2_prd(B,A) )
& ! [A,B] :
( ( A != empty_set
& B = empty_set )
| ~ sP2_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f1948]) ).
fof(f1950,plain,
! [X0,X1] :
( X0 = empty_set
| ~ sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1949]) ).
fof(f2057,plain,
! [B,C,D] :
( ( C = D
| ~ ordinal(D)
| B != D
| ~ ordinal(C)
| B != C
| sP12_prd(D,C,B) )
& ( ( C != D
& ordinal(D)
& B = D
& ordinal(C)
& B = C )
| ~ sP12_prd(D,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f1313]) ).
fof(f2058,plain,
( ! [B,C,D] :
( C = D
| ~ ordinal(D)
| B != D
| ~ ordinal(C)
| B != C
| sP12_prd(D,C,B) )
& ! [B,C,D] :
( ( C != D
& ordinal(D)
& B = D
& ordinal(C)
& B = C )
| ~ sP12_prd(D,C,B) ) ),
inference(miniscoping,[status(thm)],[f2057]) ).
fof(f2059,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ sP12_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2058]) ).
fof(f2061,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ sP12_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2058]) ).
fof(f2063,plain,
! [X0,X1,X2] :
( X1 != X0
| ~ sP12_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2058]) ).
fof(f2145,definition,
( sQ2_spl
<=> sP12_prd(sK168_skl,sK167_skl,sK166_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2146,plain,
( ~ sQ2_spl
| sP12_prd(sK168_skl,sK167_skl,sK166_skl) ),
inference(component_clause,[status(thm)],[f2145]) ).
fof(f2148,definition,
! [X0,X1] :
( sQ3_spl
<=> ( in(sK170_skl(X0,X1),X1)
| ~ in(X0,sK169_skl(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f2151,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1318,f2145,f2148]) ).
fof(f2152,definition,
! [X0,X1] :
( sQ4_spl
<=> ( sK170_skl(X0,X1) = X0
| ~ in(X0,sK169_skl(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f2155,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1319,f2145,f2152]) ).
fof(f2156,definition,
! [X0,X1] :
( sQ5_spl
<=> ( ordinal(X0)
| ~ in(X0,sK169_skl(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f2159,plain,
( sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1320,f2145,f2156]) ).
fof(f2160,definition,
! [X0,X1,X2] :
( sQ6_spl
<=> ( ~ ordinal(X0)
| X2 != X0
| ~ in(X2,X1)
| in(X0,sK169_skl(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f2163,plain,
( sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1321,f2145,f2160]) ).
fof(f2164,definition,
( sQ7_spl
<=> in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f2165,plain,
( ~ sQ7_spl
| in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl)) ),
inference(component_clause,[status(thm)],[f2164]) ).
fof(f2167,definition,
( sQ8_spl
<=> in(sK216_skl,sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f2168,plain,
( ~ sQ8_spl
| in(sK216_skl,sK212_skl) ),
inference(component_clause,[status(thm)],[f2167]) ).
fof(f2169,plain,
( sQ8_spl
| ~ in(sK216_skl,sK212_skl) ),
inference(component_clause,[status(thm)],[f2167]) ).
fof(f2170,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1735,f2164,f2167]) ).
fof(f2171,definition,
( sQ9_spl
<=> in(apply(sK214_skl,sK216_skl),sK215_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f2172,plain,
( ~ sQ9_spl
| in(apply(sK214_skl,sK216_skl),sK215_skl) ),
inference(component_clause,[status(thm)],[f2171]) ).
fof(f2174,plain,
( sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1736,f2164,f2171]) ).
fof(f2175,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1737,f2164,f2167,f2171]) ).
fof(f2179,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f429]) ).
fof(f2181,plain,
! [X0,X1,X2,X3] :
( 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)],[f436]) ).
fof(f2182,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f437]) ).
fof(f2183,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)],[f438]) ).
fof(f2184,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)],[f448]) ).
fof(f2186,plain,
! [X0,X1,X2,X3] :
( 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)],[f456]) ).
fof(f2187,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f457]) ).
fof(f2188,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)],[f458]) ).
fof(f2189,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)],[f470]) ).
fof(f2190,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)],[f471]) ).
fof(f2191,plain,
! [X0,X1,X2] :
( ~ in(apply(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)],[f472]) ).
fof(f2192,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)],[f480]) ).
fof(f2193,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)],[f481]) ).
fof(f2194,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)],[f482]) ).
fof(f2195,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)],[f490]) ).
fof(f2196,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)],[f491]) ).
fof(f2199,plain,
! [X0,X1,X2,X3] :
( ~ sP1_prd(X0,X3,X2,X1)
| in(X0,unordered_triple(X1,X2,X3)) ),
inference(destructive_equality_resolution,[status(thm)],[f511]) ).
fof(f2201,plain,
! [X0] :
( quasi_total(empty_set,X0,empty_set)
| X0 = empty_set
| ~ relation_of2_as_subset(empty_set,X0,empty_set) ),
inference(destructive_equality_resolution,[status(thm)],[f529]) ).
fof(f2203,plain,
! [X0,X1,X2] :
( ordered_pair(X1,X2) = ordered_pair(sK20_skl(X0,ordered_pair(X1,X2)),sK21_skl(X0,ordered_pair(X1,X2)))
| X0 = pair_first(ordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f535]) ).
fof(f2206,plain,
! [X0,X1] :
( in(sK26_skl(X1,set_meet(X0),X0),X0)
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(destructive_equality_resolution,[status(thm)],[f561]) ).
fof(f2208,plain,
set_meet(empty_set) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f566]) ).
fof(f2210,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f571]) ).
fof(f2212,plain,
! [X0,X1] :
( ~ in(X1,fiber(X0,X1))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f579]) ).
fof(f2213,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
| ~ in(X1,fiber(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f580]) ).
fof(f2217,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| in(ordered_pair(X1,X2),inclusion_relation(X0))
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f591]) ).
fof(f2218,plain,
! [X0] :
( in(sK31_skl(relation_field(X0),X0),relation_field(X0))
| X0 = inclusion_relation(relation_field(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f592]) ).
fof(f2222,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f599]) ).
fof(f2224,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f605]) ).
fof(f2226,plain,
! [X0,X1,X2] :
( ordered_pair(X1,X2) = ordered_pair(sK36_skl(X0,ordered_pair(X1,X2)),sK35_skl(X0,ordered_pair(X1,X2)))
| X0 = pair_second(ordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f613]) ).
fof(f2239,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f716]) ).
fof(f2240,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f718]) ).
fof(f2242,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK57_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f729]) ).
fof(f2246,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f749]) ).
fof(f2247,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| equipotent(relation_dom(X0),relation_rng(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f769]) ).
fof(f2250,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f775]) ).
fof(f2251,plain,
! [X0,X1] :
( in(sK67_skl(X1,relation_rng(X0),X0),relation_dom(X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f783]) ).
fof(f2252,plain,
! [X0,X1] :
( X1 = apply(X0,sK67_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f784]) ).
fof(f2253,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)],[f785]) ).
fof(f2254,plain,
! [X0,X1] :
( in(ordered_pair(sK70_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f793]) ).
fof(f2256,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)],[f831]) ).
fof(f2303,plain,
! [X0,X1,X2] : sP1_prd(X0,X1,X2,X0),
inference(destructive_equality_resolution,[status(thm)],[f1945]) ).
fof(f2332,plain,
! [X0,X1] : ~ sP12_prd(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f2063]) ).
fof(f2349,plain,
( ~ sQ7_spl
| in(sK216_skl,relation_dom(sK214_skl))
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2165,f2189]) ).
fof(f2351,definition,
( sQ10_spl
<=> relation(sK214_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f2353,plain,
( sQ10_spl
| ~ relation(sK214_skl) ),
inference(component_clause,[status(thm)],[f2351]) ).
fof(f2354,definition,
( sQ11_spl
<=> function(sK214_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f2356,plain,
( sQ11_spl
| ~ function(sK214_skl) ),
inference(component_clause,[status(thm)],[f2354]) ).
fof(f2357,definition,
( sQ12_spl
<=> in(sK216_skl,relation_dom(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f2358,plain,
( ~ sQ12_spl
| in(sK216_skl,relation_dom(sK214_skl)) ),
inference(component_clause,[status(thm)],[f2357]) ).
fof(f2359,plain,
( sQ12_spl
| ~ in(sK216_skl,relation_dom(sK214_skl)) ),
inference(component_clause,[status(thm)],[f2357]) ).
fof(f2360,plain,
( ~ sQ7_spl
| sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2349,f2351,f2354,f2357,f2164]) ).
fof(f2361,plain,
! [X0,X1] :
( in(apply(empty_set,X0),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1))
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f2190,f948]) ).
fof(f2362,definition,
( sQ13_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f2364,plain,
( sQ13_spl
| ~ function(empty_set) ),
inference(component_clause,[status(thm)],[f2362]) ).
fof(f2365,definition,
! [X0,X1] :
( sQ14_spl
<=> ( in(apply(empty_set,X0),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f2368,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2361,f2362,f2365]) ).
fof(f2369,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2364,f968]) ).
fof(f2370,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f2369]) ).
fof(f2371,plain,
! [X0,X1] :
( in(apply(sK102_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK102_skl,X1))
| ~ function(sK102_skl) ),
inference(resolution,[status(thm)],[f1116,f2190]) ).
fof(f2372,definition,
( sQ15_spl
<=> function(sK102_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2373,plain,
( ~ sQ15_spl
| function(sK102_skl) ),
inference(component_clause,[status(thm)],[f2372]) ).
fof(f2374,plain,
( sQ15_spl
| ~ function(sK102_skl) ),
inference(component_clause,[status(thm)],[f2372]) ).
fof(f2375,definition,
! [X0,X1] :
( sQ16_spl
<=> ( in(apply(sK102_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK102_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f2378,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2371,f2372,f2375]) ).
fof(f2380,plain,
! [X0] :
( ~ sQ12_spl
| ~ in(apply(sK214_skl,sK216_skl),X0)
| in(sK216_skl,relation_inverse_image(sK214_skl,X0))
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2358,f2191]) ).
fof(f2382,definition,
! [X0] :
( sQ17_spl
<=> ( ~ in(apply(sK214_skl,sK216_skl),X0)
| in(sK216_skl,relation_inverse_image(sK214_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f2385,plain,
( ~ sQ12_spl
| sQ17_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2380,f2351,f2354,f2382,f2357]) ).
fof(f2386,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2356,f1731]) ).
fof(f2387,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f2386]) ).
fof(f2389,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1117,f2374]) ).
fof(f2390,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f2389]) ).
fof(f2391,plain,
! [X0,X1] :
( in(apply(sK105_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK105_skl,X1))
| ~ function(sK105_skl) ),
inference(resolution,[status(thm)],[f1128,f2190]) ).
fof(f2392,definition,
( sQ18_spl
<=> function(sK105_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f2394,plain,
( sQ18_spl
| ~ function(sK105_skl) ),
inference(component_clause,[status(thm)],[f2392]) ).
fof(f2395,definition,
! [X0,X1] :
( sQ19_spl
<=> ( in(apply(sK105_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK105_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f2398,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f2391,f2392,f2395]) ).
fof(f2400,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2394,f1129]) ).
fof(f2401,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f2400]) ).
fof(f2402,plain,
! [X0,X1] :
( ~ in(apply(empty_set,X0),X1)
| ~ in(X0,empty_set)
| in(X0,relation_inverse_image(empty_set,X1))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f2191]) ).
fof(f2403,definition,
( sQ20_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f2405,plain,
( sQ20_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f2403]) ).
fof(f2406,definition,
! [X0,X1] :
( sQ21_spl
<=> ( ~ in(apply(empty_set,X0),X1)
| ~ in(X0,empty_set)
| in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f2409,plain,
( sQ21_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2402,f2403,f2362,f2406]) ).
fof(f2410,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2405,f948]) ).
fof(f2411,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f2410]) ).
fof(f2415,plain,
subset(relation_dom(sK214_skl),sK212_skl),
inference(resolution,[status(thm)],[f1439,f1733]) ).
fof(f2416,plain,
! [X0] :
( in(ordered_pair(X0,apply(empty_set,X0)),empty_set)
| ~ in(X0,empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f2239]) ).
fof(f2417,definition,
! [X0] :
( sQ22_spl
<=> ( in(ordered_pair(X0,apply(empty_set,X0)),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f2420,plain,
( sQ22_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2416,f2403,f2362,f2417]) ).
fof(f2423,plain,
sK106_skl = empty_set,
inference(resolution,[status(thm)],[f1133,f1838]) ).
fof(f2425,plain,
! [X0,X1] :
( in(apply(sK106_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK106_skl,X1))
| ~ function(sK106_skl) ),
inference(resolution,[status(thm)],[f1134,f2190]) ).
fof(f2426,definition,
( sQ23_spl
<=> function(sK106_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2428,plain,
( sQ23_spl
| ~ function(sK106_skl) ),
inference(component_clause,[status(thm)],[f2426]) ).
fof(f2429,definition,
! [X0,X1] :
( sQ24_spl
<=> ( in(apply(sK106_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK106_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f2432,plain,
( sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2425,f2426,f2429]) ).
fof(f2435,plain,
! [X0,X1] :
( in(apply(sK109_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK109_skl,X1))
| ~ function(sK109_skl) ),
inference(resolution,[status(thm)],[f1142,f2190]) ).
fof(f2436,definition,
( sQ25_spl
<=> function(sK109_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f2438,plain,
( sQ25_spl
| ~ function(sK109_skl) ),
inference(component_clause,[status(thm)],[f2436]) ).
fof(f2439,definition,
! [X0,X1] :
( sQ26_spl
<=> ( in(apply(sK109_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK109_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f2442,plain,
( sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f2435,f2436,f2439]) ).
fof(f2453,plain,
( sQ23_spl
| ~ function(empty_set) ),
inference(forward_demodulation,[status(thm)],[f2423,f2428]) ).
fof(f2454,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2453,f968]) ).
fof(f2455,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f2454]) ).
fof(f2461,plain,
! [X0] :
( apply(sK109_skl,X0) = empty_set
| in(X0,relation_dom(sK109_skl))
| ~ function(sK109_skl) ),
inference(resolution,[status(thm)],[f2240,f1142]) ).
fof(f2462,plain,
! [X0] :
( apply(sK102_skl,X0) = empty_set
| in(X0,relation_dom(sK102_skl))
| ~ function(sK102_skl) ),
inference(resolution,[status(thm)],[f2240,f1116]) ).
fof(f2463,plain,
! [X0] :
( apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set))
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f2240,f948]) ).
fof(f2464,definition,
! [X0] :
( sQ27_spl
<=> ( apply(sK109_skl,X0) = empty_set
| in(X0,relation_dom(sK109_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f2467,plain,
( sQ27_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f2461,f2436,f2464]) ).
fof(f2468,definition,
! [X0] :
( sQ28_spl
<=> ( apply(sK102_skl,X0) = empty_set
| in(X0,relation_dom(sK102_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f2469,plain,
! [X0] :
( ~ sQ28_spl
| apply(sK102_skl,X0) = empty_set
| in(X0,relation_dom(sK102_skl)) ),
inference(component_clause,[status(thm)],[f2468]) ).
fof(f2471,plain,
( sQ28_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2462,f2372,f2468]) ).
fof(f2472,definition,
! [X0] :
( sQ29_spl
<=> ( apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f2473,plain,
! [X0] :
( ~ sQ29_spl
| apply(empty_set,X0) = empty_set
| in(X0,relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f2472]) ).
fof(f2475,plain,
( sQ29_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2463,f2362,f2472]) ).
fof(f2476,plain,
! [X0] :
( ~ sQ29_spl
| apply(empty_set,X0) = empty_set
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1808,f2473]) ).
fof(f2477,plain,
! [X0] :
( ~ sQ29_spl
| apply(empty_set,X0) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f2476,f2222]) ).
fof(f2480,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1144,f2438]) ).
fof(f2481,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f2480]) ).
fof(f2482,plain,
! [X0] :
( apply(sK110_skl,X0) = empty_set
| in(X0,relation_dom(sK110_skl))
| ~ function(sK110_skl) ),
inference(resolution,[status(thm)],[f1146,f2240]) ).
fof(f2483,plain,
! [X0,X1] :
( in(apply(sK110_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK110_skl,X1))
| ~ function(sK110_skl) ),
inference(resolution,[status(thm)],[f1146,f2190]) ).
fof(f2484,definition,
( sQ30_spl
<=> function(sK110_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f2486,plain,
( sQ30_spl
| ~ function(sK110_skl) ),
inference(component_clause,[status(thm)],[f2484]) ).
fof(f2487,definition,
! [X0] :
( sQ31_spl
<=> ( apply(sK110_skl,X0) = empty_set
| in(X0,relation_dom(sK110_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f2490,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2482,f2484,f2487]) ).
fof(f2491,definition,
! [X0,X1] :
( sQ32_spl
<=> ( in(apply(sK110_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK110_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f2494,plain,
( sQ32_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2483,f2484,f2491]) ).
fof(f2508,plain,
! [X0,X1,X2] :
( relation(X0)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[status(thm)],[f934,f401]) ).
fof(f2509,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2486,f1147]) ).
fof(f2510,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f2509]) ).
fof(f2515,plain,
relation(sK214_skl),
inference(resolution,[status(thm)],[f2508,f1733]) ).
fof(f2516,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2515,f2353]) ).
fof(f2517,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f2516]) ).
fof(f2518,plain,
! [X0,X1] :
( relation_rng(X0) = empty_set
| ~ relation_of2_as_subset(X0,X1,empty_set) ),
inference(resolution,[status(thm)],[f1440,f1703]) ).
fof(f2536,plain,
! [X0] :
( apply(sK214_skl,X0) = empty_set
| in(X0,relation_dom(sK214_skl))
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f2515,f2240]) ).
fof(f2537,plain,
! [X0,X1] :
( in(apply(sK214_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK214_skl,X1))
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f2515,f2190]) ).
fof(f2538,definition,
! [X0] :
( sQ36_spl
<=> ( apply(sK214_skl,X0) = empty_set
| in(X0,relation_dom(sK214_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f2541,plain,
( sQ36_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2536,f2354,f2538]) ).
fof(f2542,definition,
! [X0,X1] :
( sQ37_spl
<=> ( in(apply(sK214_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK214_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f2545,plain,
( sQ37_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2537,f2354,f2542]) ).
fof(f2546,plain,
( ~ sQ12_spl
| in(ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)),sK214_skl)
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2358,f2239]) ).
fof(f2549,definition,
( sQ38_spl
<=> in(ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)),sK214_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f2550,plain,
( ~ sQ38_spl
| in(ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)),sK214_skl) ),
inference(component_clause,[status(thm)],[f2549]) ).
fof(f2552,plain,
( ~ sQ12_spl
| sQ38_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2546,f2351,f2354,f2549,f2357]) ).
fof(f2555,plain,
( sK214_skl = empty_set
| relation_dom(sK214_skl) != empty_set ),
inference(resolution,[status(thm)],[f1818,f2515]) ).
fof(f2556,plain,
( sK112_skl = empty_set
| relation_dom(sK112_skl) != empty_set ),
inference(resolution,[status(thm)],[f1818,f1159]) ).
fof(f2559,definition,
( sQ39_spl
<=> relation_dom(sK214_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f2562,definition,
( sQ40_spl
<=> sK214_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f2563,plain,
( ~ sQ40_spl
| sK214_skl = empty_set ),
inference(component_clause,[status(thm)],[f2562]) ).
fof(f2564,plain,
( sQ40_spl
| sK214_skl != empty_set ),
inference(component_clause,[status(thm)],[f2562]) ).
fof(f2565,plain,
( sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f2555,f2559,f2562]) ).
fof(f2566,definition,
( sQ41_spl
<=> relation_dom(sK112_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f2569,definition,
( sQ42_spl
<=> sK112_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f2570,plain,
( ~ sQ42_spl
| sK112_skl = empty_set ),
inference(component_clause,[status(thm)],[f2569]) ).
fof(f2571,plain,
( sQ42_spl
| sK112_skl != empty_set ),
inference(component_clause,[status(thm)],[f2569]) ).
fof(f2572,plain,
( sQ42_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f2556,f2566,f2569]) ).
fof(f2580,definition,
( sQ45_spl
<=> relation_dom(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f2582,plain,
( sQ45_spl
| relation_dom(empty_set) != empty_set ),
inference(component_clause,[status(thm)],[f2580]) ).
fof(f2583,definition,
( sQ46_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f2587,plain,
( sQ45_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f1808,f2582]) ).
fof(f2588,plain,
( sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2587]) ).
fof(f2589,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f2588]) ).
fof(f2590,plain,
! [X0] :
( subset(relation_inverse_image(empty_set,X0),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f1493]) ).
fof(f2591,definition,
! [X0] :
( sQ47_spl
<=> subset(relation_inverse_image(empty_set,X0),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f2592,plain,
! [X0] :
( ~ sQ47_spl
| subset(relation_inverse_image(empty_set,X0),empty_set) ),
inference(component_clause,[status(thm)],[f2591]) ).
fof(f2594,plain,
( sQ47_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2590,f2403,f2591]) ).
fof(f2596,plain,
! [X0] :
( apply(sK115_skl,X0) = empty_set
| in(X0,relation_dom(sK115_skl))
| ~ function(sK115_skl) ),
inference(resolution,[status(thm)],[f1166,f2240]) ).
fof(f2597,plain,
! [X0,X1] :
( in(apply(sK115_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK115_skl,X1))
| ~ function(sK115_skl) ),
inference(resolution,[status(thm)],[f1166,f2190]) ).
fof(f2605,definition,
( sQ50_spl
<=> function(sK115_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f2607,plain,
( sQ50_spl
| ~ function(sK115_skl) ),
inference(component_clause,[status(thm)],[f2605]) ).
fof(f2608,definition,
! [X0] :
( sQ51_spl
<=> ( apply(sK115_skl,X0) = empty_set
| in(X0,relation_dom(sK115_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f2609,plain,
! [X0] :
( ~ sQ51_spl
| apply(sK115_skl,X0) = empty_set
| in(X0,relation_dom(sK115_skl)) ),
inference(component_clause,[status(thm)],[f2608]) ).
fof(f2611,plain,
( sQ51_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2596,f2605,f2608]) ).
fof(f2612,definition,
! [X0,X1] :
( sQ52_spl
<=> ( in(apply(sK115_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK115_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f2615,plain,
( sQ52_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f2597,f2605,f2612]) ).
fof(f2620,plain,
! [X0] :
( in(sK0_skl(X0,empty_set),X0)
| in(ordered_pair(sK0_skl(X0,empty_set),sK1_skl(X0,empty_set)),empty_set)
| empty_set = identity_relation(X0) ),
inference(resolution,[status(thm)],[f425,f948]) ).
fof(f2621,plain,
! [X0] :
( in(sK0_skl(X0,empty_set),X0)
| empty_set = identity_relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2620,f2222]) ).
fof(f2625,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2607,f1167]) ).
fof(f2626,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f2625]) ).
fof(f2627,plain,
! [X0] :
( relation_of2_as_subset(sK214_skl,sK212_skl,X0)
| ~ subset(sK213_skl,X0) ),
inference(resolution,[status(thm)],[f1496,f1733]) ).
fof(f2628,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X1,X2,relation_rng(X0))
| relation_inverse_image(X0,relation_rng(X1)) != empty_set
| relation_rng(X1) = empty_set
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1505,f1440]) ).
fof(f2630,plain,
! [X0] :
( relation_inverse_image(X0,relation_rng(X0)) != empty_set
| relation_rng(X0) = empty_set
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1505,f2179]) ).
fof(f2659,plain,
! [X0] :
( apply(sK118_skl,X0) = empty_set
| in(X0,relation_dom(sK118_skl))
| ~ function(sK118_skl) ),
inference(resolution,[status(thm)],[f1178,f2240]) ).
fof(f2660,plain,
! [X0,X1] :
( in(apply(sK118_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK118_skl,X1))
| ~ function(sK118_skl) ),
inference(resolution,[status(thm)],[f1178,f2190]) ).
fof(f2668,definition,
( sQ61_spl
<=> function(sK118_skl) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f2670,plain,
( sQ61_spl
| ~ function(sK118_skl) ),
inference(component_clause,[status(thm)],[f2668]) ).
fof(f2671,definition,
! [X0] :
( sQ62_spl
<=> ( apply(sK118_skl,X0) = empty_set
| in(X0,relation_dom(sK118_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2674,plain,
( sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f2659,f2668,f2671]) ).
fof(f2675,definition,
! [X0,X1] :
( sQ63_spl
<=> ( in(apply(sK118_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK118_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2678,plain,
( sQ63_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f2660,f2668,f2675]) ).
fof(f2679,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ subset(relation_dom(X0),relation_inverse_image(X0,X1))
| relation_dom(X0) = relation_inverse_image(X0,X1) ),
inference(resolution,[status(thm)],[f431,f1493]) ).
fof(f2684,definition,
( sQ64_spl
<=> sK212_skl = relation_dom(sK214_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2685,plain,
( ~ sQ64_spl
| sK212_skl = relation_dom(sK214_skl) ),
inference(component_clause,[status(thm)],[f2684]) ).
fof(f2686,plain,
( sQ64_spl
| sK212_skl != relation_dom(sK214_skl) ),
inference(component_clause,[status(thm)],[f2684]) ).
fof(f2693,plain,
( ~ sQ12_spl
| ~ sQ64_spl
| in(sK216_skl,sK212_skl) ),
inference(backward_demodulation,[status(thm)],[f2685,f2358]) ).
fof(f2695,plain,
! [X0] :
( ~ sQ64_spl
| subset(relation_inverse_image(sK214_skl,X0),sK212_skl)
| ~ relation(sK214_skl) ),
inference(paramodulation,[status(thm)],[f2685,f1493]) ).
fof(f2696,plain,
! [X0] :
( ~ sQ64_spl
| in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)
| ~ in(X0,sK212_skl)
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(paramodulation,[status(thm)],[f2685,f2239]) ).
fof(f2697,plain,
! [X0,X1] :
( ~ sQ64_spl
| ~ in(apply(sK214_skl,X0),X1)
| ~ in(X0,sK212_skl)
| in(X0,relation_inverse_image(sK214_skl,X1))
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(paramodulation,[status(thm)],[f2685,f2191]) ).
fof(f2698,plain,
( ~ sQ12_spl
| ~ sQ64_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2693,f2169]) ).
fof(f2699,plain,
( ~ sQ12_spl
| ~ sQ64_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f2698]) ).
fof(f2702,plain,
( sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2670,f1180]) ).
fof(f2703,plain,
sQ61_spl,
inference(contradiction_clause,[status(thm)],[f2702]) ).
fof(f2704,plain,
! [X0,X1,X2] :
( ~ subset(relation_inverse_image(X0,X2),relation_inverse_image(X0,X1))
| relation_inverse_image(X0,X2) = relation_inverse_image(X0,X1)
| ~ subset(X1,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1508,f431]) ).
fof(f2705,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| apply(relation_composition(X0,X2),sK216_skl) = apply(X2,apply(X0,sK216_skl))
| X1 = empty_set
| ~ function(X2)
| ~ relation(X2)
| ~ relation_of2_as_subset(X0,sK212_skl,X1)
| ~ quasi_total(X0,sK212_skl,X1)
| ~ function(X0) ),
inference(resolution,[status(thm)],[f1545,f2168]) ).
fof(f2725,plain,
! [X0,X1,X2] :
( in(apply(inclusion_relation(X0),X1),X2)
| ~ in(X1,relation_inverse_image(inclusion_relation(X0),X2))
| ~ function(inclusion_relation(X0)) ),
inference(resolution,[status(thm)],[f900,f2190]) ).
fof(f2742,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,empty_set,X0),sK3_skl(X1,empty_set,X0)),X0)
| in(ordered_pair(sK2_skl(X1,empty_set,X0),sK3_skl(X1,empty_set,X0)),empty_set)
| empty_set = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f441,f948]) ).
fof(f2743,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(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2742,f2222]) ).
fof(f2762,plain,
! [X0] :
( ~ sQ47_spl
| relation_inverse_image(empty_set,X0) = empty_set ),
inference(resolution,[status(thm)],[f2592,f1703]) ).
fof(f2766,plain,
! [X0,X1] :
( ~ sQ47_spl
| subset(relation_inverse_image(empty_set,X0),empty_set)
| ~ subset(X0,X1)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f1508]) ).
fof(f2767,plain,
! [X0,X1] :
( ~ sQ47_spl
| subset(empty_set,relation_inverse_image(empty_set,X1))
| ~ subset(X0,X1)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f1508]) ).
fof(f2768,plain,
( ~ sQ47_spl
| subset(empty_set,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f1493]) ).
fof(f2769,plain,
! [X0] :
( ~ sQ47_spl
| in(X0,relation_dom(empty_set))
| ~ in(X0,empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f2189]) ).
fof(f2770,definition,
! [X0,X1] :
( sQ66_spl
<=> ( subset(relation_inverse_image(empty_set,X0),empty_set)
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2773,plain,
( ~ sQ47_spl
| sQ66_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2766,f2403,f2770,f2591]) ).
fof(f2774,definition,
! [X0,X1] :
( sQ67_spl
<=> ( subset(empty_set,relation_inverse_image(empty_set,X1))
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2777,plain,
( ~ sQ47_spl
| sQ67_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2767,f2403,f2774,f2591]) ).
fof(f2778,definition,
( sQ68_spl
<=> subset(empty_set,relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2781,plain,
( ~ sQ47_spl
| sQ68_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2768,f2403,f2778,f2591]) ).
fof(f2782,definition,
! [X0] :
( sQ69_spl
<=> ( in(X0,relation_dom(empty_set))
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2785,plain,
( ~ sQ47_spl
| sQ69_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2769,f2403,f2362,f2782,f2591]) ).
fof(f2814,plain,
empty_set = identity_relation(empty_set),
inference(resolution,[status(thm)],[f2621,f2222]) ).
fof(f2863,plain,
! [X0,X1] :
( in(ordered_pair(sK7_skl(X1,empty_set,X0),sK8_skl(X1,empty_set,X0)),X0)
| in(ordered_pair(sK7_skl(X1,empty_set,X0),sK8_skl(X1,empty_set,X0)),empty_set)
| empty_set = relation_rng_restriction(X1,X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f461,f948]) ).
fof(f2864,plain,
! [X0,X1] :
( in(ordered_pair(sK7_skl(X1,empty_set,X0),sK8_skl(X1,empty_set,X0)),X0)
| empty_set = relation_rng_restriction(X1,X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2863,f2222]) ).
fof(f2871,definition,
( sQ70_spl
<=> relation_dom(identity_relation(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f2873,plain,
( sQ70_spl
| relation_dom(identity_relation(empty_set)) != empty_set ),
inference(component_clause,[status(thm)],[f2871]) ).
fof(f2888,plain,
! [X0] :
( ~ sQ28_spl
| in(ordered_pair(X0,apply(sK102_skl,X0)),sK102_skl)
| ~ function(sK102_skl)
| ~ relation(sK102_skl)
| apply(sK102_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f2469,f2239]) ).
fof(f2889,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ in(apply(sK102_skl,X0),X1)
| in(X0,relation_inverse_image(sK102_skl,X1))
| ~ function(sK102_skl)
| ~ relation(sK102_skl)
| apply(sK102_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f2469,f2191]) ).
fof(f2933,definition,
! [X0] :
( sQ81_spl
<=> ( in(ordered_pair(X0,apply(sK102_skl,X0)),sK102_skl)
| apply(sK102_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f2936,definition,
( sQ82_spl
<=> relation(sK102_skl) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f2938,plain,
( sQ82_spl
| ~ relation(sK102_skl) ),
inference(component_clause,[status(thm)],[f2936]) ).
fof(f2939,plain,
( ~ sQ28_spl
| ~ sQ15_spl
| ~ sQ82_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f2888,f2933,f2936,f2372,f2468]) ).
fof(f2940,definition,
! [X0,X1] :
( sQ83_spl
<=> ( ~ in(apply(sK102_skl,X0),X1)
| in(X0,relation_inverse_image(sK102_skl,X1))
| apply(sK102_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f2943,plain,
( ~ sQ28_spl
| ~ sQ15_spl
| ~ sQ82_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f2889,f2940,f2936,f2372,f2468]) ).
fof(f2952,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2938,f1116]) ).
fof(f2953,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f2952]) ).
fof(f2968,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK118_skl),relation_dom(sK118_skl))
| in(sK9_skl(X0,X1,sK118_skl),X0)
| X0 = relation_inverse_image(sK118_skl,X1)
| ~ relation(sK118_skl) ),
inference(resolution,[status(thm)],[f474,f1180]) ).
fof(f2969,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK115_skl),relation_dom(sK115_skl))
| in(sK9_skl(X0,X1,sK115_skl),X0)
| X0 = relation_inverse_image(sK115_skl,X1)
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f474,f1167]) ).
fof(f2970,plain,
! [X0,X1] :
( ~ sQ15_spl
| in(sK9_skl(X0,X1,sK102_skl),relation_dom(sK102_skl))
| in(sK9_skl(X0,X1,sK102_skl),X0)
| X0 = relation_inverse_image(sK102_skl,X1)
| ~ relation(sK102_skl) ),
inference(resolution,[status(thm)],[f474,f2373]) ).
fof(f2971,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f474,f968]) ).
fof(f2972,plain,
! [X0,X1] :
( in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f474,f1731]) ).
fof(f2976,definition,
( sQ86_spl
<=> relation(sK118_skl) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f2978,plain,
( sQ86_spl
| ~ relation(sK118_skl) ),
inference(component_clause,[status(thm)],[f2976]) ).
fof(f2979,definition,
! [X0,X1] :
( sQ87_spl
<=> ( in(sK9_skl(X0,X1,sK118_skl),relation_dom(sK118_skl))
| in(sK9_skl(X0,X1,sK118_skl),X0)
| X0 = relation_inverse_image(sK118_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f2982,plain,
( sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f2968,f2976,f2979]) ).
fof(f2983,definition,
( sQ88_spl
<=> relation(sK115_skl) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f2985,plain,
( sQ88_spl
| ~ relation(sK115_skl) ),
inference(component_clause,[status(thm)],[f2983]) ).
fof(f2986,definition,
! [X0,X1] :
( sQ89_spl
<=> ( in(sK9_skl(X0,X1,sK115_skl),relation_dom(sK115_skl))
| in(sK9_skl(X0,X1,sK115_skl),X0)
| X0 = relation_inverse_image(sK115_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f2989,plain,
( sQ89_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f2969,f2983,f2986]) ).
fof(f2990,definition,
! [X0,X1] :
( sQ90_spl
<=> ( in(sK9_skl(X0,X1,sK102_skl),relation_dom(sK102_skl))
| in(sK9_skl(X0,X1,sK102_skl),X0)
| X0 = relation_inverse_image(sK102_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f2993,plain,
( ~ sQ15_spl
| sQ90_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f2970,f2936,f2990,f2372]) ).
fof(f2994,definition,
! [X0,X1] :
( sQ91_spl
<=> ( in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f2995,plain,
! [X0,X1] :
( ~ sQ91_spl
| in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ),
inference(component_clause,[status(thm)],[f2994]) ).
fof(f2997,plain,
( sQ91_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2971,f2403,f2994]) ).
fof(f2998,definition,
! [X0,X1] :
( sQ92_spl
<=> ( in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f2999,plain,
! [X0,X1] :
( ~ sQ92_spl
| in(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl))
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ),
inference(component_clause,[status(thm)],[f2998]) ).
fof(f3001,plain,
( sQ92_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2972,f2351,f2998]) ).
fof(f3003,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ sQ47_spl
| in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = empty_set ),
inference(forward_demodulation,[status(thm)],[f2762,f2995]) ).
fof(f3004,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ sQ47_spl
| in(sK9_skl(X0,X1,empty_set),empty_set)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = empty_set ),
inference(forward_demodulation,[status(thm)],[f1808,f3003]) ).
fof(f3005,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ sQ47_spl
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f3004,f2222]) ).
fof(f3006,plain,
( sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2985,f1166]) ).
fof(f3007,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f3006]) ).
fof(f3008,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2978,f1178]) ).
fof(f3009,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f3008]) ).
fof(f3010,plain,
! [X0,X1] :
( ~ sQ8_spl
| in(apply(X0,sK216_skl),relation_rng(X0))
| X1 = empty_set
| ~ relation_of2_as_subset(X0,sK212_skl,X1)
| ~ quasi_total(X0,sK212_skl,X1)
| ~ function(X0) ),
inference(resolution,[status(thm)],[f2168,f1841]) ).
fof(f3011,plain,
! [X0] :
( ~ sQ8_spl
| ~ in(X0,sK216_skl)
| ~ in(sK212_skl,X0) ),
inference(resolution,[status(thm)],[f2168,f1690]) ).
fof(f3071,plain,
! [X0,X1] :
( in(apply(sK118_skl,sK9_skl(X0,X1,sK118_skl)),X1)
| in(sK9_skl(X0,X1,sK118_skl),X0)
| X0 = relation_inverse_image(sK118_skl,X1)
| ~ relation(sK118_skl) ),
inference(resolution,[status(thm)],[f475,f1180]) ).
fof(f3072,plain,
! [X0,X1] :
( in(apply(sK115_skl,sK9_skl(X0,X1,sK115_skl)),X1)
| in(sK9_skl(X0,X1,sK115_skl),X0)
| X0 = relation_inverse_image(sK115_skl,X1)
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f475,f1167]) ).
fof(f3073,plain,
! [X0,X1] :
( ~ sQ15_spl
| in(apply(sK102_skl,sK9_skl(X0,X1,sK102_skl)),X1)
| in(sK9_skl(X0,X1,sK102_skl),X0)
| X0 = relation_inverse_image(sK102_skl,X1)
| ~ relation(sK102_skl) ),
inference(resolution,[status(thm)],[f475,f2373]) ).
fof(f3074,plain,
! [X0,X1] :
( in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f475,f968]) ).
fof(f3075,plain,
! [X0,X1] :
( in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f475,f1731]) ).
fof(f3081,definition,
! [X0,X1] :
( sQ93_spl
<=> ( in(apply(sK118_skl,sK9_skl(X0,X1,sK118_skl)),X1)
| in(sK9_skl(X0,X1,sK118_skl),X0)
| X0 = relation_inverse_image(sK118_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f3084,plain,
( sQ93_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f3071,f2976,f3081]) ).
fof(f3085,definition,
! [X0,X1] :
( sQ94_spl
<=> ( in(apply(sK115_skl,sK9_skl(X0,X1,sK115_skl)),X1)
| in(sK9_skl(X0,X1,sK115_skl),X0)
| X0 = relation_inverse_image(sK115_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f3088,plain,
( sQ94_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f3072,f2983,f3085]) ).
fof(f3089,definition,
! [X0,X1] :
( sQ95_spl
<=> ( in(apply(sK102_skl,sK9_skl(X0,X1,sK102_skl)),X1)
| in(sK9_skl(X0,X1,sK102_skl),X0)
| X0 = relation_inverse_image(sK102_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f3092,plain,
( ~ sQ15_spl
| sQ95_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f3073,f2936,f3089,f2372]) ).
fof(f3093,definition,
! [X0,X1] :
( sQ96_spl
<=> ( in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f3094,plain,
! [X0,X1] :
( ~ sQ96_spl
| in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ),
inference(component_clause,[status(thm)],[f3093]) ).
fof(f3096,plain,
( sQ96_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3074,f2403,f3093]) ).
fof(f3097,definition,
! [X0,X1] :
( sQ97_spl
<=> ( in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X1)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f3100,plain,
( sQ97_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3075,f2351,f3097]) ).
fof(f3102,plain,
! [X0,X1] :
( ~ sQ96_spl
| ~ sQ47_spl
| in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = empty_set ),
inference(forward_demodulation,[status(thm)],[f2762,f3094]) ).
fof(f3103,plain,
! [X0,X1] :
( ~ sQ96_spl
| ~ sQ47_spl
| ~ sQ29_spl
| in(empty_set,X1)
| in(sK9_skl(X0,X1,empty_set),X0)
| X0 = empty_set ),
inference(forward_demodulation,[status(thm)],[f2477,f3102]) ).
fof(f3106,plain,
( ~ sQ8_spl
| empty_set = identity_relation(sK216_skl)
| ~ in(sK212_skl,sK0_skl(sK216_skl,empty_set)) ),
inference(resolution,[status(thm)],[f3011,f2621]) ).
fof(f3107,definition,
( sQ98_spl
<=> in(sK212_skl,sK0_skl(sK216_skl,empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f3110,definition,
( sQ99_spl
<=> empty_set = identity_relation(sK216_skl) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f3111,plain,
( ~ sQ99_spl
| empty_set = identity_relation(sK216_skl) ),
inference(component_clause,[status(thm)],[f3110]) ).
fof(f3113,plain,
( ~ sQ8_spl
| sQ99_spl
| ~ sQ98_spl ),
inference(split_clause,[status(thm)],[f3106,f3107,f3110,f2167]) ).
fof(f3128,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f413,f1522]) ).
fof(f3133,plain,
! [X0] :
( relation_inverse_image(empty_set,X0) != empty_set
| ~ subset(X0,empty_set)
| X0 = empty_set
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1809,f1505]) ).
fof(f3135,definition,
! [X0] :
( sQ100_spl
<=> ( relation_inverse_image(empty_set,X0) != empty_set
| ~ subset(X0,empty_set)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f3138,plain,
( sQ100_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3133,f2403,f3135]) ).
fof(f3151,plain,
! [X0,X1] :
( relation_inverse_image(identity_relation(X0),X1) != empty_set
| ~ subset(X1,X0)
| X1 = empty_set
| ~ relation(identity_relation(X0)) ),
inference(paramodulation,[status(thm)],[f1851,f1505]) ).
fof(f3153,plain,
! [X0,X1] :
( relation_inverse_image(identity_relation(X1),X0) != empty_set
| ~ subset(X0,X1)
| X0 = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f3151,f920]) ).
fof(f3175,plain,
! [X0,X1] :
( in(ordered_pair(sK12_skl(X0,X1,empty_set),sK11_skl(X0,X1,empty_set)),empty_set)
| in(sK11_skl(X0,X1,empty_set),X0)
| X0 = relation_image(empty_set,X1) ),
inference(resolution,[status(thm)],[f484,f948]) ).
fof(f3176,plain,
! [X0,X1] :
( in(sK11_skl(X0,X1,empty_set),X0)
| X0 = relation_image(empty_set,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3175,f2222]) ).
fof(f3177,plain,
! [X0] :
( ~ sQ8_spl
| apply(relation_composition(sK214_skl,X0),sK216_skl) = apply(X0,apply(sK214_skl,sK216_skl))
| sK213_skl = empty_set
| ~ function(X0)
| ~ relation(X0)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f2705,f1732]) ).
fof(f3178,definition,
( sQ102_spl
<=> relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f3180,plain,
( sQ102_spl
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl) ),
inference(component_clause,[status(thm)],[f3178]) ).
fof(f3181,definition,
! [X0] :
( sQ103_spl
<=> ( apply(relation_composition(sK214_skl,X0),sK216_skl) = apply(X0,apply(sK214_skl,sK216_skl))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f3184,definition,
( sQ104_spl
<=> sK213_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f3185,plain,
( ~ sQ104_spl
| sK213_skl = empty_set ),
inference(component_clause,[status(thm)],[f3184]) ).
fof(f3187,plain,
( ~ sQ8_spl
| sQ104_spl
| sQ103_spl
| ~ sQ102_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3177,f2354,f3178,f3181,f3184,f2167]) ).
fof(f3188,plain,
( ~ sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3185,f1734]) ).
fof(f3189,plain,
~ sQ104_spl,
inference(contradiction_clause,[status(thm)],[f3188]) ).
fof(f3190,plain,
( sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3180,f1733]) ).
fof(f3191,plain,
sQ102_spl,
inference(contradiction_clause,[status(thm)],[f3190]) ).
fof(f3224,plain,
! [X0] :
( ~ sQ51_spl
| in(ordered_pair(X0,apply(sK115_skl,X0)),sK115_skl)
| ~ function(sK115_skl)
| ~ relation(sK115_skl)
| apply(sK115_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f2609,f2239]) ).
fof(f3225,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ in(apply(sK115_skl,X0),X1)
| in(X0,relation_inverse_image(sK115_skl,X1))
| ~ function(sK115_skl)
| ~ relation(sK115_skl)
| apply(sK115_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f2609,f2191]) ).
fof(f3273,definition,
! [X0] :
( sQ116_spl
<=> ( in(ordered_pair(X0,apply(sK115_skl,X0)),sK115_skl)
| apply(sK115_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f3276,plain,
( ~ sQ51_spl
| ~ sQ50_spl
| ~ sQ88_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f3224,f3273,f2983,f2605,f2608]) ).
fof(f3277,definition,
! [X0,X1] :
( sQ117_spl
<=> ( ~ in(apply(sK115_skl,X0),X1)
| in(X0,relation_inverse_image(sK115_skl,X1))
| apply(sK115_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f3280,plain,
( ~ sQ51_spl
| ~ sQ50_spl
| ~ sQ88_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f3225,f3277,f2983,f2605,f2608]) ).
fof(f3317,plain,
! [X0,X1] :
( ~ sQ47_spl
| in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f2195]) ).
fof(f3322,definition,
! [X0,X1] :
( sQ121_spl
<=> ( in(ordered_pair(X0,sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f3325,plain,
( ~ sQ47_spl
| sQ121_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3317,f2403,f3322,f2591]) ).
fof(f3329,plain,
! [X0,X1] :
( ~ sQ47_spl
| in(sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f2196]) ).
fof(f3334,definition,
! [X0,X1] :
( sQ123_spl
<=> ( in(sK13_skl(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f3337,plain,
( ~ sQ47_spl
| sQ123_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3329,f2403,f3334,f2591]) ).
fof(f3339,plain,
! [X0] :
( ~ sQ92_spl
| ~ in(apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl)),X0)
| ~ in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))
| relation_dom(sK214_skl) = relation_inverse_image(sK214_skl,X0)
| ~ function(sK214_skl)
| ~ relation(sK214_skl)
| in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))
| relation_dom(sK214_skl) = relation_inverse_image(sK214_skl,X0) ),
inference(resolution,[status(thm)],[f2999,f473]) ).
fof(f3340,plain,
! [X0,X1] :
( ~ sQ92_spl
| in(ordered_pair(sK9_skl(X0,X1,sK214_skl),apply(sK214_skl,sK9_skl(X0,X1,sK214_skl))),sK214_skl)
| ~ function(sK214_skl)
| ~ relation(sK214_skl)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ),
inference(resolution,[status(thm)],[f2999,f2239]) ).
fof(f3341,plain,
! [X0,X1,X2] :
( ~ sQ92_spl
| ~ in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X2)
| in(sK9_skl(X0,X1,sK214_skl),relation_inverse_image(sK214_skl,X2))
| ~ function(sK214_skl)
| ~ relation(sK214_skl)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ),
inference(resolution,[status(thm)],[f2999,f2191]) ).
fof(f3347,definition,
! [X0] :
( sQ124_spl
<=> ( ~ in(apply(sK214_skl,sK9_skl(relation_dom(sK214_skl),X0,sK214_skl)),X0)
| ~ in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))
| relation_dom(sK214_skl) = relation_inverse_image(sK214_skl,X0)
| in(sK9_skl(relation_dom(sK214_skl),X0,sK214_skl),relation_dom(sK214_skl))
| relation_dom(sK214_skl) = relation_inverse_image(sK214_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f3350,plain,
( ~ sQ92_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f3339,f3347,f2351,f2354,f2998]) ).
fof(f3351,definition,
! [X0,X1] :
( sQ125_spl
<=> ( in(ordered_pair(sK9_skl(X0,X1,sK214_skl),apply(sK214_skl,sK9_skl(X0,X1,sK214_skl))),sK214_skl)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f3354,plain,
( ~ sQ92_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f3340,f3351,f2351,f2354,f2998]) ).
fof(f3355,definition,
! [X0,X1,X2] :
( sQ126_spl
<=> ( ~ in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),X2)
| in(sK9_skl(X0,X1,sK214_skl),relation_inverse_image(sK214_skl,X2))
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f3358,plain,
( ~ sQ92_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f3341,f3355,f2351,f2354,f2998]) ).
fof(f3365,plain,
! [X0,X1] :
( ~ relation_of2_as_subset(X0,X1,empty_set)
| relation_inverse_image(empty_set,relation_rng(X0)) != empty_set
| relation_rng(X0) = empty_set
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1809,f2628]) ).
fof(f3374,definition,
! [X0,X1] :
( sQ129_spl
<=> ( ~ relation_of2_as_subset(X0,X1,empty_set)
| relation_inverse_image(empty_set,relation_rng(X0)) != empty_set
| relation_rng(X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f3377,plain,
( sQ129_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3365,f2403,f3374]) ).
fof(f3402,plain,
! [X0,X1] :
( in(ordered_pair(sK14_skl(X0,X1,empty_set),sK15_skl(X0,X1,empty_set)),empty_set)
| in(sK14_skl(X0,X1,empty_set),X0)
| X0 = relation_inverse_image(empty_set,X1) ),
inference(resolution,[status(thm)],[f494,f948]) ).
fof(f3403,plain,
! [X0,X1] :
( ~ sQ47_spl
| in(ordered_pair(sK14_skl(X0,X1,empty_set),sK15_skl(X0,X1,empty_set)),empty_set)
| in(sK14_skl(X0,X1,empty_set),X0)
| X0 = empty_set ),
inference(forward_demodulation,[status(thm)],[f2762,f3402]) ).
fof(f3404,plain,
! [X0,X1] :
( ~ sQ47_spl
| in(sK14_skl(X0,X1,empty_set),X0)
| X0 = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f3403,f2222]) ).
fof(f3480,plain,
( relation_inverse_image(empty_set,relation_rng(empty_set)) != empty_set
| relation_rng(empty_set) = empty_set ),
inference(resolution,[status(thm)],[f2630,f948]) ).
fof(f3519,definition,
( sQ143_spl
<=> relation_rng(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f3522,definition,
( sQ144_spl
<=> relation_inverse_image(empty_set,relation_rng(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f3524,plain,
( sQ144_spl
| relation_inverse_image(empty_set,relation_rng(empty_set)) != empty_set ),
inference(component_clause,[status(thm)],[f3522]) ).
fof(f3525,plain,
( ~ sQ144_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f3480,f3519,f3522]) ).
fof(f3544,definition,
( sQ147_spl
<=> relation(sK112_skl) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f3546,plain,
( sQ147_spl
| ~ relation(sK112_skl) ),
inference(component_clause,[status(thm)],[f3544]) ).
fof(f3555,plain,
( sQ147_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3546,f1159]) ).
fof(f3556,plain,
sQ147_spl,
inference(contradiction_clause,[status(thm)],[f3555]) ).
fof(f3571,definition,
( sQ152_spl
<=> relation(sK117_skl) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f3573,plain,
( sQ152_spl
| ~ relation(sK117_skl) ),
inference(component_clause,[status(thm)],[f3571]) ).
fof(f3582,plain,
( sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3573,f1175]) ).
fof(f3583,plain,
sQ152_spl,
inference(contradiction_clause,[status(thm)],[f3582]) ).
fof(f3628,plain,
! [X0] :
( ~ relation(empty_set)
| ~ subset(empty_set,relation_inverse_image(empty_set,X0))
| relation_dom(empty_set) = relation_inverse_image(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f1808,f2679]) ).
fof(f3629,plain,
! [X0] :
( ~ sQ47_spl
| ~ relation(empty_set)
| ~ subset(relation_dom(empty_set),empty_set)
| relation_dom(empty_set) = relation_inverse_image(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f2762,f2679]) ).
fof(f3634,definition,
! [X0] :
( sQ161_spl
<=> ( ~ subset(empty_set,relation_inverse_image(empty_set,X0))
| relation_dom(empty_set) = relation_inverse_image(empty_set,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f3637,plain,
( ~ sQ20_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f3628,f3634,f2403]) ).
fof(f3638,definition,
! [X0] :
( sQ162_spl
<=> relation_dom(empty_set) = relation_inverse_image(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f3641,definition,
( sQ163_spl
<=> subset(relation_dom(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f3643,plain,
( sQ163_spl
| ~ subset(relation_dom(empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f3641]) ).
fof(f3644,plain,
( ~ sQ47_spl
| ~ sQ20_spl
| ~ sQ163_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f3629,f3638,f3641,f2403,f2591]) ).
fof(f3702,plain,
! [X0,X1,X2] : in(X0,unordered_triple(X0,X1,X2)),
inference(resolution,[status(thm)],[f2199,f2303]) ).
fof(f3721,plain,
! [X0] : set_intersection2(empty_set,X0) = empty_set,
inference(resolution,[status(thm)],[f1512,f1703]) ).
fof(f3777,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ subset(empty_set,relation_inverse_image(empty_set,X0))
| relation_inverse_image(empty_set,X1) = relation_inverse_image(empty_set,X0)
| ~ subset(X0,X1)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f2704]) ).
fof(f3778,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ subset(relation_inverse_image(empty_set,X1),empty_set)
| relation_inverse_image(empty_set,X1) = relation_inverse_image(empty_set,X0)
| ~ subset(X0,X1)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f2704]) ).
fof(f3780,definition,
! [X0,X1] :
( sQ168_spl
<=> ( ~ subset(empty_set,relation_inverse_image(empty_set,X0))
| relation_inverse_image(empty_set,X1) = relation_inverse_image(empty_set,X0)
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f3783,plain,
( ~ sQ47_spl
| sQ168_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3777,f2403,f3780,f2591]) ).
fof(f3784,definition,
! [X0,X1] :
( sQ169_spl
<=> ( ~ subset(relation_inverse_image(empty_set,X1),empty_set)
| relation_inverse_image(empty_set,X1) = relation_inverse_image(empty_set,X0)
| ~ subset(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f3787,plain,
( ~ sQ47_spl
| sQ169_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3778,f2403,f3784,f2591]) ).
fof(f3817,plain,
( sK212_skl = relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl)
| sP2_prd(sK213_skl,sK212_skl)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl) ),
inference(resolution,[status(thm)],[f526,f1732]) ).
fof(f3818,definition,
( sQ170_spl
<=> sP2_prd(sK213_skl,sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f3819,plain,
( ~ sQ170_spl
| sP2_prd(sK213_skl,sK212_skl) ),
inference(component_clause,[status(thm)],[f3818]) ).
fof(f3821,definition,
( sQ171_spl
<=> sK212_skl = relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f3822,plain,
( ~ sQ171_spl
| sK212_skl = relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl) ),
inference(component_clause,[status(thm)],[f3821]) ).
fof(f3824,plain,
( sQ171_spl
| sQ170_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f3817,f3178,f3818,f3821]) ).
fof(f3825,plain,
( ~ sQ170_spl
| sK213_skl = empty_set ),
inference(resolution,[status(thm)],[f3819,f1950]) ).
fof(f3826,plain,
( ~ sQ170_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f3825,f3184,f3818]) ).
fof(f3848,plain,
( sK212_skl != relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl)
| quasi_total(sK214_skl,sK212_skl,sK213_skl)
| sP2_prd(sK213_skl,sK212_skl) ),
inference(resolution,[status(thm)],[f527,f1733]) ).
fof(f3849,definition,
( sQ172_spl
<=> quasi_total(sK214_skl,sK212_skl,sK213_skl) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f3852,plain,
( ~ sQ171_spl
| sQ172_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f3848,f3818,f3849,f3821]) ).
fof(f3855,plain,
! [X0,X1,X2] :
( ordered_pair(X1,X2) = ordered_pair(sK20_skl(X0,ordered_pair(X1,X2)),sK21_skl(X0,ordered_pair(X1,X2)))
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f1865,f2203]) ).
fof(f3866,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| sK21_skl(X3,ordered_pair(X1,X2)) = apply(X0,sK20_skl(X3,ordered_pair(X1,X2)))
| ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f3855,f1895]) ).
fof(f3894,plain,
succ(empty_set) = singleton(empty_set),
inference(paramodulation,[status(thm)],[f3128,f537]) ).
fof(f3898,plain,
! [X0] : subset(X0,succ(X0)),
inference(paramodulation,[status(thm)],[f537,f1874]) ).
fof(f3941,plain,
! [X0] :
( in(ordered_pair(sK2_skl(X0,empty_set,empty_set),sK3_skl(X0,empty_set,empty_set)),empty_set)
| empty_set = relation_dom_restriction(empty_set,X0) ),
inference(resolution,[status(thm)],[f2743,f948]) ).
fof(f3942,plain,
! [X0] : empty_set = relation_dom_restriction(empty_set,X0),
inference(forward_subsumption_resolution,[status(thm)],[f3941,f2222]) ).
fof(f3952,plain,
! [X0] :
( in(ordered_pair(sK24_skl(relation_dom(X0)),apply(X0,sK24_skl(relation_dom(X0)))),X0)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_dom(X0)) ),
inference(resolution,[status(thm)],[f543,f2239]) ).
fof(f3961,plain,
! [X0,X1] :
( in(sK24_skl(relation_inverse_image(X0,X1)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| relation(relation_inverse_image(X0,X1)) ),
inference(resolution,[status(thm)],[f543,f2189]) ).
fof(f3962,plain,
! [X0,X1,X2] :
( in(apply(X1,sK24_skl(X0)),relation_rng(X1))
| X2 = empty_set
| ~ relation_of2_as_subset(X1,X0,X2)
| ~ quasi_total(X1,X0,X2)
| ~ function(X1)
| relation(X0) ),
inference(resolution,[status(thm)],[f543,f1841]) ).
fof(f3965,plain,
! [X0,X1,X2,X3] :
( apply(relation_composition(X1,X3),sK24_skl(X0)) = apply(X3,apply(X1,sK24_skl(X0)))
| X2 = empty_set
| ~ function(X3)
| ~ relation(X3)
| ~ relation_of2_as_subset(X1,X0,X2)
| ~ quasi_total(X1,X0,X2)
| ~ function(X1)
| relation(X0) ),
inference(resolution,[status(thm)],[f543,f1545]) ).
fof(f3975,definition,
( sQ173_spl
<=> sP2_prd(succ(sK213_skl),sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f3976,plain,
( ~ sQ173_spl
| sP2_prd(succ(sK213_skl),sK212_skl) ),
inference(component_clause,[status(thm)],[f3975]) ).
fof(f4008,plain,
! [X0] :
( ~ sQ38_spl
| ~ in(sK216_skl,X0)
| in(apply(sK214_skl,sK216_skl),relation_image(sK214_skl,X0))
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2550,f2194]) ).
fof(f4009,plain,
( ~ sQ38_spl
| apply(sK214_skl,sK216_skl) = apply(sK214_skl,sK216_skl)
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2550,f1895]) ).
fof(f4010,plain,
! [X0] :
( ~ sQ38_spl
| X0 = apply(sK214_skl,sK216_skl)
| ~ in(ordered_pair(sK216_skl,X0),sK214_skl)
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f2550,f518]) ).
fof(f4017,definition,
! [X0] :
( sQ178_spl
<=> ( ~ in(sK216_skl,X0)
| in(apply(sK214_skl,sK216_skl),relation_image(sK214_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f4020,plain,
( ~ sQ38_spl
| sQ178_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4008,f2351,f4017,f2549]) ).
fof(f4021,definition,
( sQ179_spl
<=> apply(sK214_skl,sK216_skl) = apply(sK214_skl,sK216_skl) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f4024,plain,
( ~ sQ38_spl
| sQ179_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4009,f2351,f2354,f4021,f2549]) ).
fof(f4025,definition,
! [X0] :
( sQ180_spl
<=> ( X0 = apply(sK214_skl,sK216_skl)
| ~ in(ordered_pair(sK216_skl,X0),sK214_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f4028,plain,
( ~ sQ38_spl
| sQ180_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4010,f2354,f4025,f2549]) ).
fof(f4051,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_dom_restriction(empty_set,X2))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3942,f2183]) ).
fof(f4052,plain,
! [X0,X1,X2] :
( in(ordered_pair(X0,X1),empty_set)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(empty_set,X2))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3942,f2182]) ).
fof(f4053,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(empty_set,X2))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3942,f2181]) ).
fof(f4054,definition,
! [X0,X1,X2] :
( sQ181_spl
<=> ( ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_dom_restriction(empty_set,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f4057,plain,
( sQ181_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f4051,f2403,f4054]) ).
fof(f4058,definition,
! [X0,X1,X2] :
( sQ182_spl
<=> ( in(ordered_pair(X0,X1),empty_set)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(empty_set,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f4061,plain,
( sQ182_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f4052,f2403,f4058]) ).
fof(f4062,definition,
! [X0,X1,X2] :
( sQ183_spl
<=> ( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(empty_set,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f4065,plain,
( sQ183_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f4053,f2403,f4062]) ).
fof(f4129,plain,
relation(relation_inverse(sK118_skl)),
inference(resolution,[status(thm)],[f911,f1178]) ).
fof(f4130,plain,
relation(relation_inverse(sK117_skl)),
inference(resolution,[status(thm)],[f911,f1175]) ).
fof(f4131,plain,
relation(relation_inverse(sK115_skl)),
inference(resolution,[status(thm)],[f911,f1166]) ).
fof(f4132,plain,
relation(relation_inverse(sK214_skl)),
inference(resolution,[status(thm)],[f911,f2515]) ).
fof(f4133,plain,
relation(relation_inverse(sK112_skl)),
inference(resolution,[status(thm)],[f911,f1159]) ).
fof(f4134,plain,
relation(relation_inverse(sK102_skl)),
inference(resolution,[status(thm)],[f911,f1116]) ).
fof(f4135,plain,
relation(relation_inverse(empty_set)),
inference(resolution,[status(thm)],[f911,f948]) ).
fof(f4235,plain,
! [X0] :
( apply(relation_inverse(sK115_skl),X0) = empty_set
| in(X0,relation_dom(relation_inverse(sK115_skl)))
| ~ function(relation_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f4131,f2240]) ).
fof(f4236,plain,
! [X0,X1] :
( in(apply(relation_inverse(sK115_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK115_skl),X1))
| ~ function(relation_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f4131,f2190]) ).
fof(f4251,definition,
( sQ202_spl
<=> function(relation_inverse(sK115_skl)) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f4252,plain,
( ~ sQ202_spl
| function(relation_inverse(sK115_skl)) ),
inference(component_clause,[status(thm)],[f4251]) ).
fof(f4254,definition,
! [X0] :
( sQ203_spl
<=> ( apply(relation_inverse(sK115_skl),X0) = empty_set
| in(X0,relation_dom(relation_inverse(sK115_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f4257,plain,
( sQ203_spl
| ~ sQ202_spl ),
inference(split_clause,[status(thm)],[f4235,f4251,f4254]) ).
fof(f4258,definition,
! [X0,X1] :
( sQ204_spl
<=> ( in(apply(relation_inverse(sK115_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK115_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f4261,plain,
( sQ204_spl
| ~ sQ202_spl ),
inference(split_clause,[status(thm)],[f4236,f4251,f4258]) ).
fof(f4277,plain,
! [X0,X1] :
( in(ordered_pair(sK26_skl(X1,set_meet(relation_dom(X0)),relation_dom(X0)),apply(X0,sK26_skl(X1,set_meet(relation_dom(X0)),relation_dom(X0)))),X0)
| ~ function(X0)
| ~ relation(X0)
| in(X1,set_meet(relation_dom(X0)))
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f2206,f2239]) ).
fof(f4278,plain,
! [X0,X1,X2] :
( ~ in(apply(X0,sK26_skl(X1,set_meet(relation_dom(X0)),relation_dom(X0))),X2)
| in(sK26_skl(X1,set_meet(relation_dom(X0)),relation_dom(X0)),relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0)
| in(X1,set_meet(relation_dom(X0)))
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f2206,f2191]) ).
fof(f4287,plain,
! [X0,X1,X2] :
( in(sK26_skl(X2,set_meet(relation_inverse_image(X0,X1)),relation_inverse_image(X0,X1)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| in(X2,set_meet(relation_inverse_image(X0,X1)))
| relation_inverse_image(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f2206,f2189]) ).
fof(f4288,plain,
! [X0,X1,X2,X3] :
( in(apply(X2,sK26_skl(X1,set_meet(X0),X0)),relation_rng(X2))
| X3 = empty_set
| ~ relation_of2_as_subset(X2,X0,X3)
| ~ quasi_total(X2,X0,X3)
| ~ function(X2)
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f2206,f1841]) ).
fof(f4289,plain,
! [X0,X1,X2] :
( ~ in(X2,sK26_skl(X1,set_meet(X0),X0))
| ~ in(X0,X2)
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f2206,f1690]) ).
fof(f4291,plain,
! [X0,X1,X2,X3,X4] :
( apply(relation_composition(X2,X4),sK26_skl(X1,set_meet(X0),X0)) = apply(X4,apply(X2,sK26_skl(X1,set_meet(X0),X0)))
| X3 = empty_set
| ~ function(X4)
| ~ relation(X4)
| ~ relation_of2_as_subset(X2,X0,X3)
| ~ quasi_total(X2,X0,X3)
| ~ function(X2)
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f2206,f1545]) ).
fof(f4292,plain,
! [X0,X1] :
( ~ in(X0,sK26_skl(X1,set_meet(X0),X0))
| in(X1,set_meet(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f2206,f389]) ).
fof(f4295,definition,
! [X0] :
( sQ206_spl
<=> in(X0,set_meet(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f4296,plain,
! [X0] :
( ~ sQ206_spl
| in(X0,set_meet(empty_set)) ),
inference(component_clause,[status(thm)],[f4295]) ).
fof(f4299,definition,
! [X0] :
( sQ207_spl
<=> ( in(sK26_skl(X0,empty_set,empty_set),empty_set)
| in(X0,set_meet(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f4300,plain,
! [X0] :
( ~ sQ207_spl
| in(sK26_skl(X0,empty_set,empty_set),empty_set)
| in(X0,set_meet(empty_set)) ),
inference(component_clause,[status(thm)],[f4299]) ).
fof(f4303,plain,
! [X0] :
( ~ sQ207_spl
| in(sK26_skl(X0,empty_set,empty_set),empty_set)
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f2208,f4300]) ).
fof(f4304,plain,
! [X0] :
( ~ sQ207_spl
| in(sK26_skl(X0,empty_set,empty_set),empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[f4303,f2222]) ).
fof(f4305,plain,
! [X0] :
( ~ sQ206_spl
| in(X0,empty_set) ),
inference(forward_demodulation,[status(thm)],[f2208,f4296]) ).
fof(f4306,plain,
( ~ sQ206_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4305,f2222]) ).
fof(f4307,plain,
~ sQ206_spl,
inference(contradiction_clause,[status(thm)],[f4306]) ).
fof(f4322,plain,
( relation_inverse(sK214_skl) = empty_set
| relation_dom(relation_inverse(sK214_skl)) != empty_set ),
inference(resolution,[status(thm)],[f4132,f1818]) ).
fof(f4323,plain,
! [X0] :
( apply(relation_inverse(sK214_skl),X0) = empty_set
| in(X0,relation_dom(relation_inverse(sK214_skl)))
| ~ function(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f4132,f2240]) ).
fof(f4324,plain,
! [X0,X1] :
( in(apply(relation_inverse(sK214_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK214_skl),X1))
| ~ function(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f4132,f2190]) ).
fof(f4332,definition,
( sQ210_spl
<=> relation_dom(relation_inverse(sK214_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f4335,definition,
( sQ211_spl
<=> relation_inverse(sK214_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f4336,plain,
( ~ sQ211_spl
| relation_inverse(sK214_skl) = empty_set ),
inference(component_clause,[status(thm)],[f4335]) ).
fof(f4338,plain,
( sQ211_spl
| ~ sQ210_spl ),
inference(split_clause,[status(thm)],[f4322,f4332,f4335]) ).
fof(f4339,definition,
( sQ212_spl
<=> function(relation_inverse(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f4340,plain,
( ~ sQ212_spl
| function(relation_inverse(sK214_skl)) ),
inference(component_clause,[status(thm)],[f4339]) ).
fof(f4342,definition,
! [X0] :
( sQ213_spl
<=> ( apply(relation_inverse(sK214_skl),X0) = empty_set
| in(X0,relation_dom(relation_inverse(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f4345,plain,
( sQ213_spl
| ~ sQ212_spl ),
inference(split_clause,[status(thm)],[f4323,f4339,f4342]) ).
fof(f4346,definition,
! [X0,X1] :
( sQ214_spl
<=> ( in(apply(relation_inverse(sK214_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK214_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f4349,plain,
( sQ214_spl
| ~ sQ212_spl ),
inference(split_clause,[status(thm)],[f4324,f4339,f4346]) ).
fof(f4367,plain,
( relation_inverse(empty_set) = empty_set
| relation_dom(relation_inverse(empty_set)) != empty_set ),
inference(resolution,[status(thm)],[f4135,f1818]) ).
fof(f4368,plain,
! [X0] :
( apply(relation_inverse(empty_set),X0) = empty_set
| in(X0,relation_dom(relation_inverse(empty_set)))
| ~ function(relation_inverse(empty_set)) ),
inference(resolution,[status(thm)],[f4135,f2240]) ).
fof(f4369,plain,
! [X0,X1] :
( in(apply(relation_inverse(empty_set),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(empty_set),X1))
| ~ function(relation_inverse(empty_set)) ),
inference(resolution,[status(thm)],[f4135,f2190]) ).
fof(f4377,definition,
( sQ217_spl
<=> relation_dom(relation_inverse(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f4379,plain,
( sQ217_spl
| relation_dom(relation_inverse(empty_set)) != empty_set ),
inference(component_clause,[status(thm)],[f4377]) ).
fof(f4380,definition,
( sQ218_spl
<=> relation_inverse(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f4383,plain,
( sQ218_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f4367,f4377,f4380]) ).
fof(f4384,definition,
( sQ219_spl
<=> function(relation_inverse(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f4385,plain,
( ~ sQ219_spl
| function(relation_inverse(empty_set)) ),
inference(component_clause,[status(thm)],[f4384]) ).
fof(f4387,definition,
! [X0] :
( sQ220_spl
<=> ( apply(relation_inverse(empty_set),X0) = empty_set
| in(X0,relation_dom(relation_inverse(empty_set))) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f4390,plain,
( sQ220_spl
| ~ sQ219_spl ),
inference(split_clause,[status(thm)],[f4368,f4384,f4387]) ).
fof(f4391,definition,
! [X0,X1] :
( sQ221_spl
<=> ( in(apply(relation_inverse(empty_set),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(empty_set),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f4394,plain,
( sQ221_spl
| ~ sQ219_spl ),
inference(split_clause,[status(thm)],[f4369,f4384,f4391]) ).
fof(f4422,plain,
( relation_inverse(sK112_skl) = empty_set
| relation_dom(relation_inverse(sK112_skl)) != empty_set ),
inference(resolution,[status(thm)],[f4133,f1818]) ).
fof(f4423,plain,
! [X0] :
( apply(relation_inverse(sK112_skl),X0) = empty_set
| in(X0,relation_dom(relation_inverse(sK112_skl)))
| ~ function(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4133,f2240]) ).
fof(f4424,plain,
! [X0,X1] :
( in(apply(relation_inverse(sK112_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK112_skl),X1))
| ~ function(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4133,f2190]) ).
fof(f4432,definition,
( sQ224_spl
<=> relation_dom(relation_inverse(sK112_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f4435,definition,
( sQ225_spl
<=> relation_inverse(sK112_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f4436,plain,
( ~ sQ225_spl
| relation_inverse(sK112_skl) = empty_set ),
inference(component_clause,[status(thm)],[f4435]) ).
fof(f4438,plain,
( sQ225_spl
| ~ sQ224_spl ),
inference(split_clause,[status(thm)],[f4422,f4432,f4435]) ).
fof(f4439,definition,
( sQ226_spl
<=> function(relation_inverse(sK112_skl)) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f4440,plain,
( ~ sQ226_spl
| function(relation_inverse(sK112_skl)) ),
inference(component_clause,[status(thm)],[f4439]) ).
fof(f4442,definition,
! [X0] :
( sQ227_spl
<=> ( apply(relation_inverse(sK112_skl),X0) = empty_set
| in(X0,relation_dom(relation_inverse(sK112_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f4445,plain,
( sQ227_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f4423,f4439,f4442]) ).
fof(f4446,definition,
! [X0,X1] :
( sQ228_spl
<=> ( in(apply(relation_inverse(sK112_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK112_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f4449,plain,
( sQ228_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f4424,f4439,f4446]) ).
fof(f4513,plain,
! [X0,X1] :
( ~ sQ212_spl
| in(apply(relation_inverse(sK214_skl),sK9_skl(X0,X1,relation_inverse(sK214_skl))),X1)
| in(sK9_skl(X0,X1,relation_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK214_skl),X1)
| ~ relation(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f4340,f475]) ).
fof(f4514,plain,
! [X0,X1] :
( ~ sQ212_spl
| in(sK9_skl(X0,X1,relation_inverse(sK214_skl)),relation_dom(relation_inverse(sK214_skl)))
| in(sK9_skl(X0,X1,relation_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK214_skl),X1)
| ~ relation(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f4340,f474]) ).
fof(f4515,definition,
( sQ237_spl
<=> relation(relation_inverse(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f4517,plain,
( sQ237_spl
| ~ relation(relation_inverse(sK214_skl)) ),
inference(component_clause,[status(thm)],[f4515]) ).
fof(f4518,definition,
! [X0,X1] :
( sQ238_spl
<=> ( in(apply(relation_inverse(sK214_skl),sK9_skl(X0,X1,relation_inverse(sK214_skl))),X1)
| in(sK9_skl(X0,X1,relation_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK214_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f4521,plain,
( ~ sQ212_spl
| sQ238_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f4513,f4515,f4518,f4339]) ).
fof(f4522,definition,
! [X0,X1] :
( sQ239_spl
<=> ( in(sK9_skl(X0,X1,relation_inverse(sK214_skl)),relation_dom(relation_inverse(sK214_skl)))
| in(sK9_skl(X0,X1,relation_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK214_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f4525,plain,
( ~ sQ212_spl
| sQ239_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f4514,f4515,f4522,f4339]) ).
fof(f4526,plain,
relation(relation_inverse(relation_inverse(sK214_skl))),
inference(resolution,[status(thm)],[f4132,f911]) ).
fof(f4555,definition,
( sQ240_spl
<=> relation(relation_inverse(sK118_skl)) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f4557,plain,
( sQ240_spl
| ~ relation(relation_inverse(sK118_skl)) ),
inference(component_clause,[status(thm)],[f4555]) ).
fof(f4601,definition,
( sQ243_spl
<=> relation(relation_inverse(sK117_skl)) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f4603,plain,
( sQ243_spl
| ~ relation(relation_inverse(sK117_skl)) ),
inference(component_clause,[status(thm)],[f4601]) ).
fof(f4636,plain,
! [X0] :
( ~ sQ38_spl
| in(sK27_skl(X0,sK214_skl),ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)))
| in(sK27_skl(X0,sK214_skl),X0)
| X0 = set_meet(sK214_skl)
| sK214_skl = empty_set ),
inference(resolution,[status(thm)],[f565,f2550]) ).
fof(f4639,plain,
! [X0,X1,X2] :
( ~ sQ92_spl
| in(sK9_skl(X1,X2,sK214_skl),X1)
| X1 = relation_inverse_image(sK214_skl,X2)
| in(sK27_skl(X0,relation_dom(sK214_skl)),sK9_skl(X1,X2,sK214_skl))
| in(sK27_skl(X0,relation_dom(sK214_skl)),X0)
| X0 = set_meet(relation_dom(sK214_skl))
| relation_dom(sK214_skl) = empty_set ),
inference(resolution,[status(thm)],[f565,f2999]) ).
fof(f4642,plain,
! [X0] :
( ~ sQ12_spl
| in(sK27_skl(X0,relation_dom(sK214_skl)),sK216_skl)
| in(sK27_skl(X0,relation_dom(sK214_skl)),X0)
| X0 = set_meet(relation_dom(sK214_skl))
| relation_dom(sK214_skl) = empty_set ),
inference(resolution,[status(thm)],[f565,f2358]) ).
fof(f4659,definition,
! [X0] :
( sQ248_spl
<=> ( in(sK27_skl(X0,sK214_skl),ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)))
| in(sK27_skl(X0,sK214_skl),X0)
| X0 = set_meet(sK214_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f4662,plain,
( ~ sQ38_spl
| sQ248_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f4636,f2562,f4659,f2549]) ).
fof(f4667,definition,
! [X0,X1,X2] :
( sQ250_spl
<=> ( in(sK9_skl(X1,X2,sK214_skl),X1)
| X1 = relation_inverse_image(sK214_skl,X2)
| in(sK27_skl(X0,relation_dom(sK214_skl)),sK9_skl(X1,X2,sK214_skl))
| in(sK27_skl(X0,relation_dom(sK214_skl)),X0)
| X0 = set_meet(relation_dom(sK214_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f4670,plain,
( ~ sQ92_spl
| sQ250_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4639,f2559,f4667,f2998]) ).
fof(f4678,definition,
! [X0] :
( sQ253_spl
<=> ( in(sK27_skl(X0,relation_dom(sK214_skl)),sK216_skl)
| in(sK27_skl(X0,relation_dom(sK214_skl)),X0)
| X0 = set_meet(relation_dom(sK214_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f4681,plain,
( ~ sQ12_spl
| sQ253_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4642,f2559,f4678,f2357]) ).
fof(f4700,plain,
! [X0,X1] :
( in(ordered_pair(sK29_skl(relation_dom(X0),X1),apply(X0,sK29_skl(relation_dom(X0),X1))),X0)
| ~ function(X0)
| ~ relation(X0)
| sK29_skl(relation_dom(X0),X1) = X1
| relation_dom(X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f574,f2239]) ).
fof(f4701,plain,
! [X0,X1,X2] :
( ~ in(apply(X0,sK29_skl(relation_dom(X0),X1)),X2)
| in(sK29_skl(relation_dom(X0),X1),relation_inverse_image(X0,X2))
| ~ function(X0)
| ~ relation(X0)
| sK29_skl(relation_dom(X0),X1) = X1
| relation_dom(X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f574,f2191]) ).
fof(f4710,plain,
! [X0,X1,X2] :
( in(sK29_skl(relation_inverse_image(X0,X1),X2),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| sK29_skl(relation_inverse_image(X0,X1),X2) = X2
| relation_inverse_image(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f574,f2189]) ).
fof(f4712,plain,
! [X0,X1,X2,X3] :
( in(apply(X2,sK29_skl(X0,X1)),relation_rng(X2))
| X3 = empty_set
| ~ relation_of2_as_subset(X2,X0,X3)
| ~ quasi_total(X2,X0,X3)
| ~ function(X2)
| sK29_skl(X0,X1) = X1
| X0 = singleton(X1) ),
inference(resolution,[status(thm)],[f574,f1841]) ).
fof(f4715,plain,
! [X0,X1,X2,X3,X4] :
( apply(relation_composition(X2,X4),sK29_skl(X0,X1)) = apply(X4,apply(X2,sK29_skl(X0,X1)))
| X3 = empty_set
| ~ function(X4)
| ~ relation(X4)
| ~ relation_of2_as_subset(X2,X0,X3)
| ~ quasi_total(X2,X0,X3)
| ~ function(X2)
| sK29_skl(X0,X1) = X1
| X0 = singleton(X1) ),
inference(resolution,[status(thm)],[f574,f1545]) ).
fof(f4725,plain,
( ~ sQ38_spl
| ~ sQ40_spl
| in(ordered_pair(sK216_skl,apply(sK214_skl,sK216_skl)),empty_set) ),
inference(backward_demodulation,[status(thm)],[f2563,f2550]) ).
fof(f4762,plain,
( ~ sQ38_spl
| ~ sQ40_spl
| in(ordered_pair(sK216_skl,apply(empty_set,sK216_skl)),empty_set) ),
inference(forward_demodulation,[status(thm)],[f2563,f4725]) ).
fof(f4763,plain,
( ~ sQ38_spl
| ~ sQ40_spl
| ~ sQ29_spl
| in(ordered_pair(sK216_skl,empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f2477,f4762]) ).
fof(f4764,plain,
( ~ sQ38_spl
| ~ sQ40_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4763,f2222]) ).
fof(f4765,plain,
( ~ sQ38_spl
| ~ sQ40_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f4764]) ).
fof(f4807,definition,
( sQ256_spl
<=> quasi_total(empty_set,sK212_skl,sK213_skl) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f4808,plain,
( ~ sQ256_spl
| quasi_total(empty_set,sK212_skl,sK213_skl) ),
inference(component_clause,[status(thm)],[f4807]) ).
fof(f4814,definition,
( sQ258_spl
<=> sK213_skl = relation_rng(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f4815,plain,
( ~ sQ258_spl
| sK213_skl = relation_rng(empty_set) ),
inference(component_clause,[status(thm)],[f4814]) ).
fof(f4824,plain,
( ~ sQ258_spl
| sK213_skl = empty_set ),
inference(forward_demodulation,[status(thm)],[f1809,f4815]) ).
fof(f4825,plain,
( ~ sQ258_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4824,f1734]) ).
fof(f4826,plain,
~ sQ258_spl,
inference(contradiction_clause,[status(thm)],[f4825]) ).
fof(f4864,plain,
! [X0,X1] :
( ~ sQ202_spl
| in(apply(relation_inverse(sK115_skl),sK9_skl(X0,X1,relation_inverse(sK115_skl))),X1)
| in(sK9_skl(X0,X1,relation_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK115_skl),X1)
| ~ relation(relation_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f4252,f475]) ).
fof(f4865,plain,
! [X0,X1] :
( ~ sQ202_spl
| in(sK9_skl(X0,X1,relation_inverse(sK115_skl)),relation_dom(relation_inverse(sK115_skl)))
| in(sK9_skl(X0,X1,relation_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK115_skl),X1)
| ~ relation(relation_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f4252,f474]) ).
fof(f4866,definition,
( sQ260_spl
<=> relation(relation_inverse(sK115_skl)) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f4868,plain,
( sQ260_spl
| ~ relation(relation_inverse(sK115_skl)) ),
inference(component_clause,[status(thm)],[f4866]) ).
fof(f4869,definition,
! [X0,X1] :
( sQ261_spl
<=> ( in(apply(relation_inverse(sK115_skl),sK9_skl(X0,X1,relation_inverse(sK115_skl))),X1)
| in(sK9_skl(X0,X1,relation_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK115_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f4872,plain,
( ~ sQ202_spl
| sQ261_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f4864,f4866,f4869,f4251]) ).
fof(f4873,definition,
! [X0,X1] :
( sQ262_spl
<=> ( in(sK9_skl(X0,X1,relation_inverse(sK115_skl)),relation_dom(relation_inverse(sK115_skl)))
| in(sK9_skl(X0,X1,relation_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK115_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f4876,plain,
( ~ sQ202_spl
| sQ262_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f4865,f4866,f4873,f4251]) ).
fof(f4878,definition,
( sQ263_spl
<=> relation_of2_as_subset(empty_set,sK212_skl,sK213_skl) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f4880,plain,
( sQ263_spl
| ~ relation_of2_as_subset(empty_set,sK212_skl,sK213_skl) ),
inference(component_clause,[status(thm)],[f4878]) ).
fof(f4884,plain,
! [X0] :
( ~ sQ8_spl
| in(sK27_skl(X0,sK212_skl),sK216_skl)
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = set_meet(sK212_skl)
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f2168,f565]) ).
fof(f4890,definition,
( sQ264_spl
<=> sK212_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f4891,plain,
( ~ sQ264_spl
| sK212_skl = empty_set ),
inference(component_clause,[status(thm)],[f4890]) ).
fof(f4892,plain,
( sQ264_spl
| sK212_skl != empty_set ),
inference(component_clause,[status(thm)],[f4890]) ).
fof(f4893,definition,
! [X0] :
( sQ265_spl
<=> ( in(sK27_skl(X0,sK212_skl),sK216_skl)
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = set_meet(sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f4896,plain,
( ~ sQ8_spl
| sQ265_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f4884,f4890,f4893,f2167]) ).
fof(f4943,plain,
( ~ sQ8_spl
| ~ sQ264_spl
| in(sK216_skl,empty_set) ),
inference(backward_demodulation,[status(thm)],[f4891,f2168]) ).
fof(f4947,plain,
( ~ sQ8_spl
| ~ sQ264_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4943,f2222]) ).
fof(f4948,plain,
( ~ sQ8_spl
| ~ sQ264_spl ),
inference(contradiction_clause,[status(thm)],[f4947]) ).
fof(f4965,plain,
! [X0,X1] :
( ~ sQ219_spl
| in(apply(relation_inverse(empty_set),sK9_skl(X0,X1,relation_inverse(empty_set))),X1)
| in(sK9_skl(X0,X1,relation_inverse(empty_set)),X0)
| X0 = relation_inverse_image(relation_inverse(empty_set),X1)
| ~ relation(relation_inverse(empty_set)) ),
inference(resolution,[status(thm)],[f4385,f475]) ).
fof(f4966,plain,
! [X0,X1] :
( ~ sQ219_spl
| in(sK9_skl(X0,X1,relation_inverse(empty_set)),relation_dom(relation_inverse(empty_set)))
| in(sK9_skl(X0,X1,relation_inverse(empty_set)),X0)
| X0 = relation_inverse_image(relation_inverse(empty_set),X1)
| ~ relation(relation_inverse(empty_set)) ),
inference(resolution,[status(thm)],[f4385,f474]) ).
fof(f4967,definition,
( sQ266_spl
<=> relation(relation_inverse(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f4969,plain,
( sQ266_spl
| ~ relation(relation_inverse(empty_set)) ),
inference(component_clause,[status(thm)],[f4967]) ).
fof(f4970,definition,
! [X0,X1] :
( sQ267_spl
<=> ( in(apply(relation_inverse(empty_set),sK9_skl(X0,X1,relation_inverse(empty_set))),X1)
| in(sK9_skl(X0,X1,relation_inverse(empty_set)),X0)
| X0 = relation_inverse_image(relation_inverse(empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f4973,plain,
( ~ sQ219_spl
| sQ267_spl
| ~ sQ266_spl ),
inference(split_clause,[status(thm)],[f4965,f4967,f4970,f4384]) ).
fof(f4974,definition,
! [X0,X1] :
( sQ268_spl
<=> ( in(sK9_skl(X0,X1,relation_inverse(empty_set)),relation_dom(relation_inverse(empty_set)))
| in(sK9_skl(X0,X1,relation_inverse(empty_set)),X0)
| X0 = relation_inverse_image(relation_inverse(empty_set),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f4977,plain,
( ~ sQ219_spl
| sQ268_spl
| ~ sQ266_spl ),
inference(split_clause,[status(thm)],[f4966,f4967,f4974,f4384]) ).
fof(f4992,plain,
( sQ240_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4557,f4129]) ).
fof(f4993,plain,
sQ240_spl,
inference(contradiction_clause,[status(thm)],[f4992]) ).
fof(f5024,plain,
! [X0,X1] :
( ~ sQ226_spl
| in(apply(relation_inverse(sK112_skl),sK9_skl(X0,X1,relation_inverse(sK112_skl))),X1)
| in(sK9_skl(X0,X1,relation_inverse(sK112_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK112_skl),X1)
| ~ relation(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4440,f475]) ).
fof(f5025,plain,
! [X0,X1] :
( ~ sQ226_spl
| in(sK9_skl(X0,X1,relation_inverse(sK112_skl)),relation_dom(relation_inverse(sK112_skl)))
| in(sK9_skl(X0,X1,relation_inverse(sK112_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK112_skl),X1)
| ~ relation(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4440,f474]) ).
fof(f5026,definition,
( sQ269_spl
<=> relation(relation_inverse(sK112_skl)) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f5028,plain,
( sQ269_spl
| ~ relation(relation_inverse(sK112_skl)) ),
inference(component_clause,[status(thm)],[f5026]) ).
fof(f5029,definition,
! [X0,X1] :
( sQ270_spl
<=> ( in(apply(relation_inverse(sK112_skl),sK9_skl(X0,X1,relation_inverse(sK112_skl))),X1)
| in(sK9_skl(X0,X1,relation_inverse(sK112_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK112_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f5032,plain,
( ~ sQ226_spl
| sQ270_spl
| ~ sQ269_spl ),
inference(split_clause,[status(thm)],[f5024,f5026,f5029,f4439]) ).
fof(f5033,definition,
! [X0,X1] :
( sQ271_spl
<=> ( in(sK9_skl(X0,X1,relation_inverse(sK112_skl)),relation_dom(relation_inverse(sK112_skl)))
| in(sK9_skl(X0,X1,relation_inverse(sK112_skl)),X0)
| X0 = relation_inverse_image(relation_inverse(sK112_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f5036,plain,
( ~ sQ226_spl
| sQ271_spl
| ~ sQ269_spl ),
inference(split_clause,[status(thm)],[f5025,f5026,f5033,f4439]) ).
fof(f5060,definition,
( sQ272_spl
<=> relation(relation_inverse(sK102_skl)) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f5062,plain,
( sQ272_spl
| ~ relation(relation_inverse(sK102_skl)) ),
inference(component_clause,[status(thm)],[f5060]) ).
fof(f5092,plain,
( sQ243_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4603,f4130]) ).
fof(f5093,plain,
sQ243_spl,
inference(contradiction_clause,[status(thm)],[f5092]) ).
fof(f5111,plain,
! [X0,X1] :
( sK30_skl(X0,X1,empty_set) != X1
| in(sK30_skl(X0,X1,empty_set),X0)
| X0 = fiber(empty_set,X1) ),
inference(resolution,[status(thm)],[f583,f948]) ).
fof(f5129,plain,
! [X0,X1] :
( in(ordered_pair(sK30_skl(X0,X1,empty_set),X1),empty_set)
| in(sK30_skl(X0,X1,empty_set),X0)
| X0 = fiber(empty_set,X1) ),
inference(resolution,[status(thm)],[f584,f948]) ).
fof(f5130,plain,
! [X0,X1] :
( in(sK30_skl(X0,X1,empty_set),X0)
| X0 = fiber(empty_set,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f5129,f2222]) ).
fof(f5233,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| in(ordered_pair(X0,X2),inclusion_relation(X1))
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2217,f900]) ).
fof(f5235,plain,
! [X0] :
( ~ sQ8_spl
| ~ subset(X0,sK216_skl)
| in(ordered_pair(X0,sK216_skl),inclusion_relation(sK212_skl))
| ~ in(X0,sK212_skl) ),
inference(resolution,[status(thm)],[f5233,f2168]) ).
fof(f5270,plain,
! [X0] :
( in(ordered_pair(sK7_skl(X0,empty_set,empty_set),sK8_skl(X0,empty_set,empty_set)),empty_set)
| empty_set = relation_rng_restriction(X0,empty_set) ),
inference(resolution,[status(thm)],[f2864,f948]) ).
fof(f5271,plain,
! [X0] : empty_set = relation_rng_restriction(X0,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f5270,f2222]) ).
fof(f5272,plain,
( sQ260_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4868,f4131]) ).
fof(f5273,plain,
sQ260_spl,
inference(contradiction_clause,[status(thm)],[f5272]) ).
fof(f5311,definition,
( sQ280_spl
<=> sK216_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f5312,plain,
( ~ sQ280_spl
| sK216_skl = empty_set ),
inference(component_clause,[status(thm)],[f5311]) ).
fof(f5313,plain,
( sQ280_spl
| sK216_skl != empty_set ),
inference(component_clause,[status(thm)],[f5311]) ).
fof(f5317,definition,
( sQ282_spl
<=> sK216_skl = set_meet(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f5318,plain,
( ~ sQ282_spl
| sK216_skl = set_meet(empty_set) ),
inference(component_clause,[status(thm)],[f5317]) ).
fof(f5320,definition,
( sQ283_spl
<=> in(sK28_skl(sK216_skl,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f5321,plain,
( ~ sQ283_spl
| in(sK28_skl(sK216_skl,empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f5320]) ).
fof(f5328,plain,
( ~ sQ283_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5321,f2222]) ).
fof(f5329,plain,
~ sQ283_spl,
inference(contradiction_clause,[status(thm)],[f5328]) ).
fof(f5330,plain,
( ~ sQ282_spl
| sK216_skl = empty_set ),
inference(forward_demodulation,[status(thm)],[f2208,f5318]) ).
fof(f5332,plain,
( ~ sQ8_spl
| ~ sQ280_spl
| in(empty_set,sK212_skl) ),
inference(backward_demodulation,[status(thm)],[f5312,f2168]) ).
fof(f5337,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ280_spl
| in(sK27_skl(X0,sK212_skl),empty_set)
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = set_meet(sK212_skl)
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f5332,f565]) ).
fof(f5343,definition,
! [X0] :
( sQ285_spl
<=> ( in(sK27_skl(X0,sK212_skl),empty_set)
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = set_meet(sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f5344,plain,
! [X0] :
( ~ sQ285_spl
| in(sK27_skl(X0,sK212_skl),empty_set)
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = set_meet(sK212_skl) ),
inference(component_clause,[status(thm)],[f5343]) ).
fof(f5346,plain,
( ~ sQ8_spl
| ~ sQ280_spl
| sQ285_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f5337,f4890,f5343,f5311,f2167]) ).
fof(f5347,plain,
! [X0] :
( ~ sQ285_spl
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = set_meet(sK212_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f5344,f2222]) ).
fof(f5356,plain,
( ~ sQ8_spl
| ~ sQ282_spl
| in(empty_set,sK212_skl) ),
inference(backward_demodulation,[status(thm)],[f5330,f2168]) ).
fof(f5358,plain,
( sQ269_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5028,f4133]) ).
fof(f5359,plain,
sQ269_spl,
inference(contradiction_clause,[status(thm)],[f5358]) ).
fof(f5360,plain,
( sQ272_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5062,f4134]) ).
fof(f5361,plain,
sQ272_spl,
inference(contradiction_clause,[status(thm)],[f5360]) ).
fof(f5368,plain,
! [X0] :
( sK33_skl(singleton(X0)) = X0
| singleton(X0) = empty_set ),
inference(resolution,[status(thm)],[f600,f2210]) ).
fof(f5373,plain,
! [X0] :
( in(ordered_pair(sK33_skl(relation_dom(X0)),apply(X0,sK33_skl(relation_dom(X0)))),X0)
| ~ function(X0)
| ~ relation(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f600,f2239]) ).
fof(f5374,plain,
! [X0,X1] :
( ~ in(apply(X0,sK33_skl(relation_dom(X0))),X1)
| in(sK33_skl(relation_dom(X0)),relation_inverse_image(X0,X1))
| ~ function(X0)
| ~ relation(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f600,f2191]) ).
fof(f5381,plain,
! [X0,X1] :
( in(sK33_skl(relation_inverse_image(X0,X1)),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| relation_inverse_image(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f600,f2189]) ).
fof(f5384,plain,
! [X0,X1,X2] :
( in(apply(X1,sK33_skl(X0)),relation_rng(X1))
| X2 = empty_set
| ~ relation_of2_as_subset(X1,X0,X2)
| ~ quasi_total(X1,X0,X2)
| ~ function(X1)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f600,f1841]) ).
fof(f5385,plain,
! [X0,X1] :
( ~ in(X1,sK33_skl(X0))
| ~ in(X0,X1)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f600,f1690]) ).
fof(f5387,plain,
! [X0,X1,X2,X3] :
( apply(relation_composition(X1,X3),sK33_skl(X0)) = apply(X3,apply(X1,sK33_skl(X0)))
| X2 = empty_set
| ~ function(X3)
| ~ relation(X3)
| ~ relation_of2_as_subset(X1,X0,X2)
| ~ quasi_total(X1,X0,X2)
| ~ function(X1)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f600,f1545]) ).
fof(f5388,plain,
! [X0] :
( ~ in(X0,sK33_skl(X0))
| X0 = empty_set ),
inference(resolution,[status(thm)],[f600,f389]) ).
fof(f5389,plain,
! [X0] : sK33_skl(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f5368,f1041]) ).
fof(f5399,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ282_spl
| in(sK27_skl(X0,sK212_skl),empty_set)
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = set_meet(sK212_skl)
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f5356,f565]) ).
fof(f5405,plain,
( ~ sQ8_spl
| ~ sQ282_spl
| sQ285_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f5399,f4890,f5343,f5317,f2167]) ).
fof(f5449,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ relation(X0)
| in(relation_inverse_image(X0,X1),powerset(relation_inverse_image(X0,X2))) ),
inference(resolution,[status(thm)],[f2224,f1508]) ).
fof(f5450,plain,
! [X0,X1] :
( ~ relation(X0)
| in(relation_inverse_image(X0,X1),powerset(relation_dom(X0))) ),
inference(resolution,[status(thm)],[f2224,f1493]) ).
fof(f5452,plain,
! [X0] : in(empty_set,powerset(X0)),
inference(resolution,[status(thm)],[f2224,f1620]) ).
fof(f5459,plain,
! [X0] :
( sK34_skl(X0,empty_set) = empty_set
| in(sK34_skl(X0,empty_set),X0)
| X0 = powerset(empty_set) ),
inference(resolution,[status(thm)],[f607,f1703]) ).
fof(f5471,definition,
( sQ286_spl
<=> quasi_total(empty_set,sK212_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f5472,plain,
( ~ sQ286_spl
| quasi_total(empty_set,sK212_skl,empty_set) ),
inference(component_clause,[status(thm)],[f5471]) ).
fof(f5473,plain,
( sQ286_spl
| ~ quasi_total(empty_set,sK212_skl,empty_set) ),
inference(component_clause,[status(thm)],[f5471]) ).
fof(f5484,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X1,X2)
| in(ordered_pair(X0,X1),relation_rng_restriction(X2,empty_set))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f5271,f2188]) ).
fof(f5485,plain,
! [X0,X1,X2] :
( in(ordered_pair(X0,X1),empty_set)
| ~ in(ordered_pair(X0,X1),relation_rng_restriction(X2,empty_set))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f5271,f2187]) ).
fof(f5486,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(ordered_pair(X0,X1),relation_rng_restriction(X2,empty_set))
| ~ relation(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f5271,f2186]) ).
fof(f5487,definition,
! [X0,X1,X2] :
( sQ288_spl
<=> ( ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X1,X2)
| in(ordered_pair(X0,X1),relation_rng_restriction(X2,empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f5490,plain,
( sQ288_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5484,f2403,f5487]) ).
fof(f5491,definition,
! [X0,X1,X2] :
( sQ289_spl
<=> ( in(ordered_pair(X0,X1),empty_set)
| ~ in(ordered_pair(X0,X1),relation_rng_restriction(X2,empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f5494,plain,
( sQ289_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5485,f2403,f5491]) ).
fof(f5495,definition,
! [X0,X1,X2] :
( sQ290_spl
<=> ( in(X1,X2)
| ~ in(ordered_pair(X0,X1),relation_rng_restriction(X2,empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f5498,plain,
( sQ290_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5486,f2403,f5495]) ).
fof(f5515,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ sQ47_spl
| ~ in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| ~ in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| X0 = relation_inverse_image(empty_set,X1)
| ~ function(empty_set)
| ~ relation(empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f3005,f473]) ).
fof(f5519,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ sQ47_spl
| sK9_skl(singleton(X0),X1,empty_set) = X0
| singleton(X0) = empty_set ),
inference(resolution,[status(thm)],[f3005,f2210]) ).
fof(f5541,definition,
! [X0,X1] :
( sQ291_spl
<=> ( ~ in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| ~ in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| X0 = relation_inverse_image(empty_set,X1)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f5544,plain,
( ~ sQ91_spl
| ~ sQ47_spl
| ~ sQ13_spl
| ~ sQ20_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f5515,f5541,f2403,f2362,f2591,f2994]) ).
fof(f5545,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ sQ47_spl
| sK9_skl(singleton(X0),X1,empty_set) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f5519,f1041]) ).
fof(f5640,plain,
! [X0,X1,X2] :
( ordered_pair(X2,X1) = ordered_pair(sK36_skl(X0,ordered_pair(X2,X1)),sK35_skl(X0,ordered_pair(X2,X1)))
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f1866,f2226]) ).
fof(f5667,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| sK35_skl(X3,ordered_pair(X1,X2)) = apply(X0,sK36_skl(X3,ordered_pair(X1,X2)))
| ~ in(ordered_pair(X1,X2),X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f5640,f1895]) ).
fof(f5711,definition,
( sQ296_spl
<=> function(relation_inverse(relation_inverse(empty_set))) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f5713,plain,
( sQ296_spl
| ~ function(relation_inverse(relation_inverse(empty_set))) ),
inference(component_clause,[status(thm)],[f5711]) ).
fof(f5747,plain,
! [X0] : relation_rng(sK91_skl(empty_set,X0)) = empty_set,
inference(resolution,[status(thm)],[f940,f2518]) ).
fof(f5752,plain,
! [X0,X1] : relation(sK91_skl(X0,X1)),
inference(resolution,[status(thm)],[f940,f2508]) ).
fof(f5775,plain,
empty(relation_inverse(empty_set)),
inference(resolution,[status(thm)],[f945,f947]) ).
fof(f5781,plain,
relation_inverse(empty_set) = empty_set,
inference(resolution,[status(thm)],[f5775,f1838]) ).
fof(f5822,plain,
( sQ217_spl
| relation_dom(empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f5781,f4379]) ).
fof(f5823,plain,
( sQ217_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f1808,f5822]) ).
fof(f5824,plain,
( sQ217_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5823]) ).
fof(f5825,plain,
sQ217_spl,
inference(contradiction_clause,[status(thm)],[f5824]) ).
fof(f5829,plain,
( sQ266_spl
| ~ relation(empty_set) ),
inference(forward_demodulation,[status(thm)],[f5781,f4969]) ).
fof(f5830,plain,
( sQ266_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5829,f948]) ).
fof(f5831,plain,
sQ266_spl,
inference(contradiction_clause,[status(thm)],[f5830]) ).
fof(f6036,plain,
relation(relation_inverse(sK214_skl)),
inference(resolution,[status(thm)],[f2515,f911]) ).
fof(f6148,plain,
! [X0] :
( empty(X0)
| ~ element(X0,empty_set) ),
inference(resolution,[status(thm)],[f635,f947]) ).
fof(f6151,definition,
( sQ306_spl
<=> in(apply(empty_set,sK216_skl),relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f6152,plain,
( ~ sQ306_spl
| in(apply(empty_set,sK216_skl),relation_rng(empty_set)) ),
inference(component_clause,[status(thm)],[f6151]) ).
fof(f6155,plain,
( ~ sQ306_spl
| ~ sQ29_spl
| in(empty_set,relation_rng(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f2477,f6152]) ).
fof(f6156,plain,
( ~ sQ306_spl
| ~ sQ29_spl
| in(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1809,f6155]) ).
fof(f6157,plain,
( ~ sQ306_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6156,f2222]) ).
fof(f6158,plain,
( ~ sQ306_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f6157]) ).
fof(f6191,plain,
( ~ sQ8_spl
| in(apply(sK214_skl,sK216_skl),relation_rng(sK214_skl))
| sK213_skl = empty_set
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f1732,f3010]) ).
fof(f6193,definition,
( sQ307_spl
<=> in(apply(sK214_skl,sK216_skl),relation_rng(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f6196,plain,
( ~ sQ8_spl
| sQ307_spl
| sQ104_spl
| ~ sQ102_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6191,f2354,f3178,f3184,f6193,f2167]) ).
fof(f6236,plain,
( sQ237_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4517,f6036]) ).
fof(f6237,plain,
sQ237_spl,
inference(contradiction_clause,[status(thm)],[f6236]) ).
fof(f6307,plain,
( ~ sQ286_spl
| sK212_skl = relation_dom_as_subset(sK212_skl,empty_set,empty_set)
| sP2_prd(empty_set,sK212_skl)
| ~ relation_of2_as_subset(empty_set,sK212_skl,empty_set) ),
inference(resolution,[status(thm)],[f5472,f526]) ).
fof(f6308,definition,
( sQ310_spl
<=> relation_of2_as_subset(empty_set,sK212_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f6310,plain,
( sQ310_spl
| ~ relation_of2_as_subset(empty_set,sK212_skl,empty_set) ),
inference(component_clause,[status(thm)],[f6308]) ).
fof(f6313,definition,
( sQ311_spl
<=> sP2_prd(empty_set,sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f6316,definition,
( sQ312_spl
<=> sK212_skl = relation_dom_as_subset(sK212_skl,empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f6319,plain,
( ~ sQ286_spl
| sQ312_spl
| sQ311_spl
| ~ sQ310_spl ),
inference(split_clause,[status(thm)],[f6307,f6308,f6313,f6316,f5471]) ).
fof(f6382,plain,
( sQ296_spl
| ~ function(relation_inverse(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f5781,f5713]) ).
fof(f6383,plain,
( sQ296_spl
| ~ function(empty_set) ),
inference(forward_demodulation,[status(thm)],[f5781,f6382]) ).
fof(f6384,plain,
( sQ296_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6383,f968]) ).
fof(f6385,plain,
sQ296_spl,
inference(contradiction_clause,[status(thm)],[f6384]) ).
fof(f6745,plain,
( ~ sQ8_spl
| ~ sQ256_spl
| in(apply(empty_set,sK216_skl),relation_rng(empty_set))
| sK213_skl = empty_set
| ~ relation_of2_as_subset(empty_set,sK212_skl,sK213_skl)
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f4808,f3010]) ).
fof(f6751,plain,
( ~ sQ8_spl
| ~ sQ256_spl
| sQ306_spl
| sQ104_spl
| ~ sQ263_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6745,f2362,f4878,f3184,f6151,f4807,f2167]) ).
fof(f6761,plain,
empty(sK90_skl(empty_set)),
inference(resolution,[status(thm)],[f6148,f938]) ).
fof(f6772,plain,
sK90_skl(empty_set) = empty_set,
inference(resolution,[status(thm)],[f6761,f1838]) ).
fof(f6775,plain,
element(empty_set,empty_set),
inference(paramodulation,[status(thm)],[f6772,f938]) ).
fof(f6782,plain,
( in(empty_set,empty_set)
| empty(empty_set) ),
inference(resolution,[status(thm)],[f6775,f633]) ).
fof(f6783,definition,
( sQ335_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f6786,definition,
( sQ336_spl
<=> in(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f6787,plain,
( ~ sQ336_spl
| in(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f6786]) ).
fof(f6789,plain,
( sQ336_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f6782,f6783,f6786]) ).
fof(f6790,plain,
( ~ sQ336_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6787,f2222]) ).
fof(f6791,plain,
~ sQ336_spl,
inference(contradiction_clause,[status(thm)],[f6790]) ).
fof(f6794,plain,
sK33_skl(powerset(empty_set)) = empty_set,
inference(paramodulation,[status(thm)],[f1528,f5389]) ).
fof(f6808,plain,
powerset(empty_set) != empty_set,
inference(paramodulation,[status(thm)],[f1528,f1041]) ).
fof(f6947,plain,
! [X0] :
( in(apply(sK214_skl,X0),relation_rng(sK214_skl))
| sK213_skl = empty_set
| ~ in(X0,sK212_skl)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f1841,f1732]) ).
fof(f6949,definition,
! [X0] :
( sQ338_spl
<=> ( in(apply(sK214_skl,X0),relation_rng(sK214_skl))
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f6950,plain,
! [X0] :
( ~ sQ338_spl
| in(apply(sK214_skl,X0),relation_rng(sK214_skl))
| ~ in(X0,sK212_skl) ),
inference(component_clause,[status(thm)],[f6949]) ).
fof(f6952,plain,
( sQ104_spl
| sQ338_spl
| ~ sQ102_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6947,f2354,f3178,f6949,f3184]) ).
fof(f6979,definition,
( sQ339_spl
<=> relation(sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f6980,plain,
( ~ sQ339_spl
| relation(sK212_skl) ),
inference(component_clause,[status(thm)],[f6979]) ).
fof(f7007,definition,
! [X0] :
( sQ347_spl
<=> subset(relation_inverse_image(sK214_skl,X0),sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f7010,plain,
( ~ sQ64_spl
| sQ347_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2695,f2351,f7007,f2684]) ).
fof(f7011,definition,
! [X0] :
( sQ348_spl
<=> ( in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f7014,plain,
( ~ sQ64_spl
| sQ348_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2696,f2351,f2354,f7011,f2684]) ).
fof(f7015,definition,
! [X0,X1] :
( sQ349_spl
<=> ( ~ in(apply(sK214_skl,X0),X1)
| ~ in(X0,sK212_skl)
| in(X0,relation_inverse_image(sK214_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f7018,plain,
( ~ sQ64_spl
| sQ349_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2697,f2351,f2354,f7015,f2684]) ).
fof(f7024,plain,
! [X0,X1] :
( apply(relation_composition(sK214_skl,X0),X1) = apply(X0,apply(sK214_skl,X1))
| sK213_skl = empty_set
| ~ in(X1,sK212_skl)
| ~ function(X0)
| ~ relation(X0)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f1545,f1732]) ).
fof(f7026,definition,
! [X0,X1] :
( sQ350_spl
<=> ( apply(relation_composition(sK214_skl,X0),X1) = apply(X0,apply(sK214_skl,X1))
| ~ in(X1,sK212_skl)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f7027,plain,
! [X0,X1] :
( ~ sQ350_spl
| apply(relation_composition(sK214_skl,X0),X1) = apply(X0,apply(sK214_skl,X1))
| ~ in(X1,sK212_skl)
| ~ function(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f7026]) ).
fof(f7029,plain,
( sQ104_spl
| sQ350_spl
| ~ sQ102_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7024,f2354,f3178,f7026,f3184]) ).
fof(f7202,plain,
! [X0] :
( in(ordered_pair(sK51_skl(empty_set,X0),sK52_skl(empty_set,X0)),X0)
| ~ relation(empty_set)
| ~ relation(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f1703,f686]) ).
fof(f7206,definition,
! [X0] :
( sQ351_spl
<=> ( in(ordered_pair(sK51_skl(empty_set,X0),sK52_skl(empty_set,X0)),X0)
| ~ relation(X0)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f7209,plain,
( ~ sQ20_spl
| sQ351_spl ),
inference(split_clause,[status(thm)],[f7202,f7206,f2403]) ).
fof(f7242,definition,
( sQ352_spl
<=> relation(relation_inverse(relation_inverse(sK214_skl))) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f7244,plain,
( sQ352_spl
| ~ relation(relation_inverse(relation_inverse(sK214_skl))) ),
inference(component_clause,[status(thm)],[f7242]) ).
fof(f7346,plain,
! [X0,X1] :
( ~ sQ96_spl
| ~ sQ47_spl
| ~ sQ29_spl
| ~ in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| ~ in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| X0 = relation_inverse_image(empty_set,X1)
| ~ function(empty_set)
| ~ relation(empty_set)
| in(empty_set,X1)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f3103,f473]) ).
fof(f7376,definition,
! [X0,X1] :
( sQ355_spl
<=> ( ~ in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)
| ~ in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))
| X0 = relation_inverse_image(empty_set,X1)
| in(empty_set,X1)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f7379,plain,
( ~ sQ96_spl
| ~ sQ47_spl
| ~ sQ29_spl
| ~ sQ13_spl
| ~ sQ20_spl
| sQ355_spl ),
inference(split_clause,[status(thm)],[f7346,f7376,f2403,f2362,f2472,f2591,f3093]) ).
fof(f7381,definition,
! [X0] :
( sQ356_spl
<=> in(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f7382,plain,
! [X0] :
( ~ sQ356_spl
| in(empty_set,X0) ),
inference(component_clause,[status(thm)],[f7381]) ).
fof(f7422,plain,
( ~ sQ356_spl
| $false ),
inference(resolution,[status(thm)],[f7382,f2222]) ).
fof(f7446,plain,
~ sQ356_spl,
inference(contradiction_clause,[status(thm)],[f7422]) ).
fof(f7458,plain,
( ~ sQ2_spl
| sK166_skl = sK168_skl ),
inference(resolution,[status(thm)],[f2146,f2061]) ).
fof(f7459,plain,
( ~ sQ2_spl
| sK166_skl = sK167_skl ),
inference(resolution,[status(thm)],[f2146,f2059]) ).
fof(f7551,plain,
( relation_inverse_image(identity_relation(sK212_skl),relation_dom(sK214_skl)) != empty_set
| relation_dom(sK214_skl) = empty_set ),
inference(resolution,[status(thm)],[f3153,f2415]) ).
fof(f7562,plain,
! [X0] :
( relation_inverse_image(identity_relation(X0),empty_set) != empty_set
| empty_set = empty_set ),
inference(resolution,[status(thm)],[f3153,f1620]) ).
fof(f7569,definition,
( sQ357_spl
<=> relation_inverse_image(identity_relation(sK212_skl),relation_dom(sK214_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f7572,plain,
( ~ sQ357_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f7551,f2559,f7569]) ).
fof(f7573,definition,
! [X0] :
( sQ358_spl
<=> relation_inverse_image(identity_relation(X0),empty_set) != empty_set ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f7574,plain,
! [X0] :
( ~ sQ358_spl
| relation_inverse_image(identity_relation(X0),empty_set) != empty_set ),
inference(component_clause,[status(thm)],[f7573]) ).
fof(f7576,plain,
( sQ358_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f7562,f2583,f7573]) ).
fof(f7577,plain,
( ~ sQ2_spl
| sP12_prd(sK166_skl,sK167_skl,sK166_skl) ),
inference(backward_demodulation,[status(thm)],[f7458,f2146]) ).
fof(f7632,plain,
succ(empty_set) = powerset(empty_set),
inference(forward_demodulation,[status(thm)],[f1528,f3894]) ).
fof(f7634,plain,
( ordinal(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f7632,f987]) ).
fof(f7635,plain,
( epsilon_connected(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f7632,f986]) ).
fof(f7636,plain,
( epsilon_transitive(powerset(empty_set))
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f7632,f985]) ).
fof(f7648,definition,
( sQ359_spl
<=> ordinal(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f7650,plain,
( sQ359_spl
| ~ ordinal(empty_set) ),
inference(component_clause,[status(thm)],[f7648]) ).
fof(f7651,definition,
( sQ360_spl
<=> ordinal(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f7654,plain,
( sQ360_spl
| ~ sQ359_spl ),
inference(split_clause,[status(thm)],[f7634,f7648,f7651]) ).
fof(f7655,definition,
( sQ361_spl
<=> epsilon_connected(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f7658,plain,
( sQ361_spl
| ~ sQ359_spl ),
inference(split_clause,[status(thm)],[f7635,f7648,f7655]) ).
fof(f7659,definition,
( sQ362_spl
<=> epsilon_transitive(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f7662,plain,
( sQ362_spl
| ~ sQ359_spl ),
inference(split_clause,[status(thm)],[f7636,f7648,f7659]) ).
fof(f7663,plain,
( sQ359_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7650,f973]) ).
fof(f7664,plain,
sQ359_spl,
inference(contradiction_clause,[status(thm)],[f7663]) ).
fof(f7674,plain,
! [X0] :
( in(ordered_pair(X0,sK57_skl(X0,relation_dom(empty_set),empty_set)),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f2242]) ).
fof(f7679,definition,
! [X0] :
( sQ363_spl
<=> ( in(ordered_pair(X0,sK57_skl(X0,relation_dom(empty_set),empty_set)),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f7682,plain,
( sQ363_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f7674,f2403,f7679]) ).
fof(f7702,plain,
( sQ352_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7244,f4526]) ).
fof(f7703,plain,
sQ352_spl,
inference(contradiction_clause,[status(thm)],[f7702]) ).
fof(f7731,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(X0,X1,empty_set)),empty_set)
| X0 = relation_image(empty_set,X1)
| ~ relation(empty_set)
| X0 = relation_image(empty_set,X1) ),
inference(resolution,[status(thm)],[f3176,f483]) ).
fof(f7742,plain,
! [X0] : empty_set = relation_image(empty_set,X0),
inference(resolution,[status(thm)],[f3176,f2222]) ).
fof(f7762,definition,
! [X0,X1,X2] :
( sQ365_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(X2,sK11_skl(X0,X1,empty_set)),empty_set)
| X0 = relation_image(empty_set,X1)
| X0 = relation_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f7765,plain,
( ~ sQ20_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f7731,f7762,f2403]) ).
fof(f7770,plain,
! [X0,X1] :
( in(sK10_skl(X0,relation_image(empty_set,X1),X1,empty_set),X1)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f7742,f2193]) ).
fof(f7771,plain,
! [X0,X1] :
( in(ordered_pair(sK10_skl(X0,relation_image(empty_set,X1),X1,empty_set),X0),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f7742,f2192]) ).
fof(f7772,plain,
! [X0,X1] :
( sP0_prd(sK4_skl(X0,relation_image(empty_set,X1),X1,empty_set),X0,X1,empty_set)
| ~ in(X0,empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f7742,f2184]) ).
fof(f7773,definition,
! [X0,X1] :
( sQ366_spl
<=> ( in(sK10_skl(X0,relation_image(empty_set,X1),X1,empty_set),X1)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f7776,plain,
( sQ366_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f7770,f2403,f7773]) ).
fof(f7777,definition,
! [X0,X1] :
( sQ367_spl
<=> ( in(ordered_pair(sK10_skl(X0,relation_image(empty_set,X1),X1,empty_set),X0),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f7780,plain,
( sQ367_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f7771,f2403,f7777]) ).
fof(f7781,definition,
! [X0,X1] :
( sQ368_spl
<=> ( sP0_prd(sK4_skl(X0,relation_image(empty_set,X1),X1,empty_set),X0,X1,empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f7784,plain,
( sQ368_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f7772,f2403,f2362,f7781]) ).
fof(f8142,plain,
( ~ sQ8_spl
| ~ subset(sK216_skl,sK216_skl)
| in(ordered_pair(sK216_skl,sK216_skl),inclusion_relation(sK212_skl)) ),
inference(resolution,[status(thm)],[f5235,f2168]) ).
fof(f8144,plain,
( ~ sQ8_spl
| relation(sK212_skl)
| ~ subset(sK24_skl(sK212_skl),sK216_skl)
| in(ordered_pair(sK24_skl(sK212_skl),sK216_skl),inclusion_relation(sK212_skl)) ),
inference(resolution,[status(thm)],[f5235,f543]) ).
fof(f8147,definition,
( sQ389_spl
<=> in(ordered_pair(sK216_skl,sK216_skl),inclusion_relation(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f8150,definition,
( sQ390_spl
<=> subset(sK216_skl,sK216_skl) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f8152,plain,
( sQ390_spl
| ~ subset(sK216_skl,sK216_skl) ),
inference(component_clause,[status(thm)],[f8150]) ).
fof(f8153,plain,
( ~ sQ8_spl
| ~ sQ390_spl
| sQ389_spl ),
inference(split_clause,[status(thm)],[f8142,f8147,f8150,f2167]) ).
fof(f8154,definition,
( sQ391_spl
<=> in(ordered_pair(sK24_skl(sK212_skl),sK216_skl),inclusion_relation(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f8157,definition,
( sQ392_spl
<=> subset(sK24_skl(sK212_skl),sK216_skl) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f8159,plain,
( sQ392_spl
| ~ subset(sK24_skl(sK212_skl),sK216_skl) ),
inference(component_clause,[status(thm)],[f8157]) ).
fof(f8160,plain,
( ~ sQ8_spl
| sQ339_spl
| ~ sQ392_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f8144,f8154,f8157,f6979,f2167]) ).
fof(f8161,plain,
( sQ390_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8152,f2179]) ).
fof(f8162,plain,
sQ390_spl,
inference(contradiction_clause,[status(thm)],[f8161]) ).
fof(f8237,plain,
! [X0] :
( ~ sQ8_spl
| ~ in(X0,sK216_skl)
| in(X0,union(sK212_skl)) ),
inference(resolution,[status(thm)],[f2246,f2168]) ).
fof(f8258,plain,
( sQ392_spl
| in(ordered_pair(sK51_skl(sK216_skl,sK24_skl(sK212_skl)),sK52_skl(sK216_skl,sK24_skl(sK212_skl))),sK24_skl(sK212_skl))
| ~ relation(sK216_skl)
| ~ relation(sK24_skl(sK212_skl)) ),
inference(resolution,[status(thm)],[f8159,f686]) ).
fof(f8259,definition,
( sQ393_spl
<=> relation(sK24_skl(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f8262,definition,
( sQ394_spl
<=> relation(sK216_skl) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f8264,plain,
( sQ394_spl
| ~ relation(sK216_skl) ),
inference(component_clause,[status(thm)],[f8262]) ).
fof(f8265,definition,
( sQ395_spl
<=> in(ordered_pair(sK51_skl(sK216_skl,sK24_skl(sK212_skl)),sK52_skl(sK216_skl,sK24_skl(sK212_skl))),sK24_skl(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f8268,plain,
( sQ392_spl
| sQ395_spl
| ~ sQ394_spl
| ~ sQ393_spl ),
inference(split_clause,[status(thm)],[f8258,f8259,f8262,f8265,f8157]) ).
fof(f8269,plain,
( ~ sQ8_spl
| ~ sQ285_spl
| ~ subset(sK27_skl(sK212_skl,sK212_skl),sK216_skl)
| in(ordered_pair(sK27_skl(sK212_skl,sK212_skl),sK216_skl),inclusion_relation(sK212_skl))
| sK212_skl = set_meet(sK212_skl) ),
inference(resolution,[status(thm)],[f5347,f5235]) ).
fof(f8282,plain,
( ~ sQ285_spl
| empty_set = set_meet(sK212_skl) ),
inference(resolution,[status(thm)],[f5347,f2222]) ).
fof(f8303,definition,
( sQ396_spl
<=> sK212_skl = set_meet(sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f8304,plain,
( ~ sQ396_spl
| sK212_skl = set_meet(sK212_skl) ),
inference(component_clause,[status(thm)],[f8303]) ).
fof(f8306,definition,
( sQ397_spl
<=> in(ordered_pair(sK27_skl(sK212_skl,sK212_skl),sK216_skl),inclusion_relation(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f8309,definition,
( sQ398_spl
<=> subset(sK27_skl(sK212_skl,sK212_skl),sK216_skl) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f8312,plain,
( ~ sQ8_spl
| ~ sQ285_spl
| ~ sQ398_spl
| sQ397_spl
| sQ396_spl ),
inference(split_clause,[status(thm)],[f8269,f8303,f8306,f8309,f5343,f2167]) ).
fof(f8313,plain,
! [X0] :
( ~ sQ285_spl
| in(sK27_skl(X0,sK212_skl),X0)
| X0 = empty_set ),
inference(backward_demodulation,[status(thm)],[f8282,f5347]) ).
fof(f8314,plain,
( ~ sQ396_spl
| ~ sQ285_spl
| sK212_skl = empty_set ),
inference(forward_demodulation,[status(thm)],[f8282,f8304]) ).
fof(f8315,plain,
( ~ sQ396_spl
| ~ sQ285_spl
| sQ264_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8314,f4892]) ).
fof(f8316,plain,
( ~ sQ396_spl
| ~ sQ285_spl
| sQ264_spl ),
inference(contradiction_clause,[status(thm)],[f8315]) ).
fof(f8358,plain,
( ~ sQ2_spl
| sP12_prd(sK166_skl,sK166_skl,sK166_skl) ),
inference(forward_demodulation,[status(thm)],[f7459,f7577]) ).
fof(f8359,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8358,f2332]) ).
fof(f8360,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f8359]) ).
fof(f8423,plain,
! [X0,X1,X2] :
( ~ sQ47_spl
| ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(X0,X1,empty_set),X2),empty_set)
| X0 = relation_inverse_image(empty_set,X1)
| ~ relation(empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f3404,f493]) ).
fof(f8424,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ47_spl
| ~ subset(sK14_skl(sK212_skl,X0,empty_set),sK216_skl)
| in(ordered_pair(sK14_skl(sK212_skl,X0,empty_set),sK216_skl),inclusion_relation(sK212_skl))
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f3404,f5235]) ).
fof(f8458,definition,
! [X0,X1,X2] :
( sQ399_spl
<=> ( ~ in(X2,X1)
| ~ in(ordered_pair(sK14_skl(X0,X1,empty_set),X2),empty_set)
| X0 = relation_inverse_image(empty_set,X1)
| X0 = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f8461,plain,
( ~ sQ47_spl
| ~ sQ20_spl
| sQ399_spl ),
inference(split_clause,[status(thm)],[f8423,f8458,f2403,f2591]) ).
fof(f8462,definition,
! [X0] :
( sQ400_spl
<=> ( ~ subset(sK14_skl(sK212_skl,X0,empty_set),sK216_skl)
| in(ordered_pair(sK14_skl(sK212_skl,X0,empty_set),sK216_skl),inclusion_relation(sK212_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f8465,plain,
( ~ sQ8_spl
| ~ sQ47_spl
| sQ400_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f8424,f4890,f8462,f2591,f2167]) ).
fof(f8586,plain,
! [X0] : relation(sK65_skl(X0,X0)),
inference(resolution,[status(thm)],[f764,f1209]) ).
fof(f8593,plain,
( ~ in(powerset(empty_set),empty_set)
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f6794,f5388]) ).
fof(f8595,definition,
( sQ401_spl
<=> powerset(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f8596,plain,
( ~ sQ401_spl
| powerset(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f8595]) ).
fof(f8598,definition,
( sQ402_spl
<=> in(powerset(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f8601,plain,
( ~ sQ402_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f8593,f8595,f8598]) ).
fof(f8602,plain,
( ~ sQ401_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8596,f6808]) ).
fof(f8603,plain,
~ sQ401_spl,
inference(contradiction_clause,[status(thm)],[f8602]) ).
fof(f8605,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ sQ47_spl
| ~ in(apply(empty_set,sK9_skl(singleton(X0),X1,empty_set)),X1)
| ~ in(sK9_skl(singleton(X0),X1,empty_set),relation_dom(empty_set))
| ~ in(X0,singleton(X0))
| singleton(X0) = relation_inverse_image(empty_set,X1)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f5545,f473]) ).
fof(f8606,definition,
! [X0,X1] :
( sQ403_spl
<=> ( ~ in(apply(empty_set,sK9_skl(singleton(X0),X1,empty_set)),X1)
| ~ in(sK9_skl(singleton(X0),X1,empty_set),relation_dom(empty_set))
| ~ in(X0,singleton(X0))
| singleton(X0) = relation_inverse_image(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f8609,plain,
( ~ sQ91_spl
| ~ sQ47_spl
| sQ403_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f8605,f2403,f2362,f8606,f2591,f2994]) ).
fof(f8727,definition,
! [X0] :
( sQ404_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f8728,plain,
! [X0] :
( ~ sQ404_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f8727]) ).
fof(f8733,plain,
! [X0] : relation_dom(sK65_skl(X0,X0)) = X0,
inference(resolution,[status(thm)],[f767,f1209]) ).
fof(f8815,plain,
( ~ sQ404_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f947,f8728]) ).
fof(f8816,plain,
~ sQ404_spl,
inference(contradiction_clause,[status(thm)],[f8815]) ).
fof(f8826,plain,
( ~ function(sK115_skl)
| ~ relation(sK115_skl)
| equipotent(relation_dom(sK115_skl),relation_rng(sK115_skl)) ),
inference(resolution,[status(thm)],[f2247,f1168]) ).
fof(f8827,plain,
( ~ function(empty_set)
| ~ relation(empty_set)
| equipotent(relation_dom(empty_set),relation_rng(empty_set)) ),
inference(resolution,[status(thm)],[f2247,f969]) ).
fof(f8829,definition,
( sQ413_spl
<=> equipotent(relation_dom(sK115_skl),relation_rng(sK115_skl)) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f8832,plain,
( ~ sQ50_spl
| ~ sQ88_spl
| sQ413_spl ),
inference(split_clause,[status(thm)],[f8826,f8829,f2983,f2605]) ).
fof(f8833,definition,
( sQ414_spl
<=> equipotent(relation_dom(empty_set),relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f8836,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| sQ414_spl ),
inference(split_clause,[status(thm)],[f8827,f8833,f2403,f2362]) ).
fof(f8912,plain,
! [X0] :
( ~ sQ8_spl
| in(sK216_skl,X0)
| in(sK216_skl,set_difference(sK212_skl,X0)) ),
inference(resolution,[status(thm)],[f2250,f2168]) ).
fof(f8979,plain,
( sQ163_spl
| ~ subset(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1808,f3643]) ).
fof(f8980,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8979,f1620]) ).
fof(f8981,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f8980]) ).
fof(f8982,plain,
( sQ144_spl
| ~ sQ47_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f2762,f3524]) ).
fof(f8983,plain,
( sQ144_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f8982]) ).
fof(f8984,plain,
( sQ144_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f8983]) ).
fof(f8990,plain,
( sQ70_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f1850,f2873]) ).
fof(f8991,plain,
( sQ70_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f8990]) ).
fof(f8992,plain,
sQ70_spl,
inference(contradiction_clause,[status(thm)],[f8991]) ).
fof(f9026,plain,
( ~ sQ42_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f2570,f1158]) ).
fof(f9037,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9026,f947]) ).
fof(f9038,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f9037]) ).
fof(f9090,plain,
! [X0] :
( in(sK67_skl(X0,relation_rng(sK118_skl),sK118_skl),relation_dom(sK118_skl))
| ~ in(X0,relation_rng(sK118_skl))
| ~ relation(sK118_skl) ),
inference(resolution,[status(thm)],[f2251,f1180]) ).
fof(f9092,plain,
! [X0] :
( in(sK67_skl(X0,relation_rng(sK214_skl),sK214_skl),relation_dom(sK214_skl))
| ~ in(X0,relation_rng(sK214_skl))
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2251,f1731]) ).
fof(f9093,plain,
! [X0] :
( in(sK67_skl(X0,relation_rng(sK115_skl),sK115_skl),relation_dom(sK115_skl))
| ~ in(X0,relation_rng(sK115_skl))
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f2251,f1167]) ).
fof(f9094,plain,
! [X0] :
( ~ sQ15_spl
| in(sK67_skl(X0,relation_rng(sK102_skl),sK102_skl),relation_dom(sK102_skl))
| ~ in(X0,relation_rng(sK102_skl))
| ~ relation(sK102_skl) ),
inference(resolution,[status(thm)],[f2251,f2373]) ).
fof(f9096,plain,
! [X0] :
( ~ sQ212_spl
| in(sK67_skl(X0,relation_rng(relation_inverse(sK214_skl)),relation_inverse(sK214_skl)),relation_dom(relation_inverse(sK214_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK214_skl)))
| ~ relation(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f2251,f4340]) ).
fof(f9098,plain,
! [X0] :
( ~ sQ202_spl
| in(sK67_skl(X0,relation_rng(relation_inverse(sK115_skl)),relation_inverse(sK115_skl)),relation_dom(relation_inverse(sK115_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK115_skl)))
| ~ relation(relation_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f2251,f4252]) ).
fof(f9103,plain,
! [X0] :
( in(sK67_skl(X0,relation_rng(empty_set),empty_set),relation_dom(empty_set))
| ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f2251,f968]) ).
fof(f9106,definition,
! [X0] :
( sQ417_spl
<=> ( in(sK67_skl(X0,relation_rng(sK118_skl),sK118_skl),relation_dom(sK118_skl))
| ~ in(X0,relation_rng(sK118_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f9109,plain,
( sQ417_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f9090,f2976,f9106]) ).
fof(f9111,definition,
! [X0] :
( sQ418_spl
<=> ( in(sK67_skl(X0,relation_rng(sK214_skl),sK214_skl),relation_dom(sK214_skl))
| ~ in(X0,relation_rng(sK214_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f9114,plain,
( sQ418_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f9092,f2351,f9111]) ).
fof(f9115,definition,
! [X0] :
( sQ419_spl
<=> ( in(sK67_skl(X0,relation_rng(sK115_skl),sK115_skl),relation_dom(sK115_skl))
| ~ in(X0,relation_rng(sK115_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f9118,plain,
( sQ419_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f9093,f2983,f9115]) ).
fof(f9119,definition,
! [X0] :
( sQ420_spl
<=> ( in(sK67_skl(X0,relation_rng(sK102_skl),sK102_skl),relation_dom(sK102_skl))
| ~ in(X0,relation_rng(sK102_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f9122,plain,
( ~ sQ15_spl
| sQ420_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f9094,f2936,f9119,f2372]) ).
fof(f9127,definition,
! [X0] :
( sQ422_spl
<=> ( in(sK67_skl(X0,relation_rng(relation_inverse(sK214_skl)),relation_inverse(sK214_skl)),relation_dom(relation_inverse(sK214_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f9130,plain,
( ~ sQ212_spl
| sQ422_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f9096,f4515,f9127,f4339]) ).
fof(f9135,definition,
! [X0] :
( sQ424_spl
<=> ( in(sK67_skl(X0,relation_rng(relation_inverse(sK115_skl)),relation_inverse(sK115_skl)),relation_dom(relation_inverse(sK115_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK115_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f9138,plain,
( ~ sQ202_spl
| sQ424_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f9098,f4866,f9135,f4251]) ).
fof(f9147,definition,
! [X0] :
( sQ425_spl
<=> ( in(sK67_skl(X0,relation_rng(empty_set),empty_set),relation_dom(empty_set))
| ~ in(X0,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f9150,plain,
( sQ425_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9103,f2403,f9147]) ).
fof(f9164,plain,
! [X0] :
( X0 = apply(sK118_skl,sK67_skl(X0,relation_rng(sK118_skl),sK118_skl))
| ~ in(X0,relation_rng(sK118_skl))
| ~ relation(sK118_skl) ),
inference(resolution,[status(thm)],[f2252,f1180]) ).
fof(f9166,plain,
! [X0] :
( X0 = apply(sK214_skl,sK67_skl(X0,relation_rng(sK214_skl),sK214_skl))
| ~ in(X0,relation_rng(sK214_skl))
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2252,f1731]) ).
fof(f9167,plain,
! [X0] :
( X0 = apply(sK115_skl,sK67_skl(X0,relation_rng(sK115_skl),sK115_skl))
| ~ in(X0,relation_rng(sK115_skl))
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f2252,f1167]) ).
fof(f9168,plain,
! [X0] :
( ~ sQ15_spl
| X0 = apply(sK102_skl,sK67_skl(X0,relation_rng(sK102_skl),sK102_skl))
| ~ in(X0,relation_rng(sK102_skl))
| ~ relation(sK102_skl) ),
inference(resolution,[status(thm)],[f2252,f2373]) ).
fof(f9170,plain,
! [X0] :
( ~ sQ212_spl
| X0 = apply(relation_inverse(sK214_skl),sK67_skl(X0,relation_rng(relation_inverse(sK214_skl)),relation_inverse(sK214_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK214_skl)))
| ~ relation(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f2252,f4340]) ).
fof(f9172,plain,
! [X0] :
( ~ sQ202_spl
| X0 = apply(relation_inverse(sK115_skl),sK67_skl(X0,relation_rng(relation_inverse(sK115_skl)),relation_inverse(sK115_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK115_skl)))
| ~ relation(relation_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f2252,f4252]) ).
fof(f9177,plain,
! [X0] :
( X0 = apply(empty_set,sK67_skl(X0,relation_rng(empty_set),empty_set))
| ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f2252,f968]) ).
fof(f9180,definition,
! [X0] :
( sQ426_spl
<=> ( X0 = apply(sK118_skl,sK67_skl(X0,relation_rng(sK118_skl),sK118_skl))
| ~ in(X0,relation_rng(sK118_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f9183,plain,
( sQ426_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f9164,f2976,f9180]) ).
fof(f9185,definition,
! [X0] :
( sQ427_spl
<=> ( X0 = apply(sK214_skl,sK67_skl(X0,relation_rng(sK214_skl),sK214_skl))
| ~ in(X0,relation_rng(sK214_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f9188,plain,
( sQ427_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f9166,f2351,f9185]) ).
fof(f9189,definition,
! [X0] :
( sQ428_spl
<=> ( X0 = apply(sK115_skl,sK67_skl(X0,relation_rng(sK115_skl),sK115_skl))
| ~ in(X0,relation_rng(sK115_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f9192,plain,
( sQ428_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f9167,f2983,f9189]) ).
fof(f9193,definition,
! [X0] :
( sQ429_spl
<=> ( X0 = apply(sK102_skl,sK67_skl(X0,relation_rng(sK102_skl),sK102_skl))
| ~ in(X0,relation_rng(sK102_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f9196,plain,
( ~ sQ15_spl
| sQ429_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f9168,f2936,f9193,f2372]) ).
fof(f9201,definition,
! [X0] :
( sQ431_spl
<=> ( X0 = apply(relation_inverse(sK214_skl),sK67_skl(X0,relation_rng(relation_inverse(sK214_skl)),relation_inverse(sK214_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f9204,plain,
( ~ sQ212_spl
| sQ431_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f9170,f4515,f9201,f4339]) ).
fof(f9209,definition,
! [X0] :
( sQ433_spl
<=> ( X0 = apply(relation_inverse(sK115_skl),sK67_skl(X0,relation_rng(relation_inverse(sK115_skl)),relation_inverse(sK115_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK115_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f9212,plain,
( ~ sQ202_spl
| sQ433_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f9172,f4866,f9209,f4251]) ).
fof(f9219,definition,
! [X0] :
( sQ434_spl
<=> ( X0 = apply(empty_set,sK67_skl(X0,relation_rng(empty_set),empty_set))
| ~ in(X0,relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f9222,plain,
( sQ434_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9177,f2403,f9219]) ).
fof(f9305,plain,
! [X0] :
( ~ in(X0,empty_set)
| in(apply(empty_set,X0),relation_rng(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f2253]) ).
fof(f9310,definition,
! [X0] :
( sQ435_spl
<=> ( ~ in(X0,empty_set)
| in(apply(empty_set,X0),relation_rng(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f9313,plain,
( sQ435_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9305,f2403,f2362,f9310]) ).
fof(f9332,plain,
! [X0] :
( in(sK69_skl(X0,empty_set),empty_set)
| in(sK68_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f787]) ).
fof(f9339,definition,
! [X0] :
( sQ436_spl
<=> ( in(sK69_skl(X0,empty_set),empty_set)
| in(sK68_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f9342,plain,
( sQ436_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9332,f2403,f2362,f9339]) ).
fof(f9370,plain,
! [X0] :
( ~ sQ29_spl
| sK68_skl(X0,empty_set) = empty_set
| in(sK68_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2477,f788]) ).
fof(f9371,definition,
! [X0] :
( sQ437_spl
<=> ( sK68_skl(X0,empty_set) = empty_set
| in(sK68_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f9374,plain,
( ~ sQ29_spl
| sQ437_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9370,f2403,f2362,f9371,f2472]) ).
fof(f9392,plain,
! [X0] :
( in(ordered_pair(sK70_skl(X0,relation_rng(empty_set),empty_set),X0),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1809,f2254]) ).
fof(f9410,definition,
! [X0] :
( sQ441_spl
<=> ( in(ordered_pair(sK70_skl(X0,relation_rng(empty_set),empty_set),X0),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f9413,plain,
( sQ441_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9392,f2403,f9410]) ).
fof(f9450,plain,
( ~ sQ99_spl
| relation_rng(empty_set) = sK216_skl ),
inference(paramodulation,[status(thm)],[f3111,f1851]) ).
fof(f9469,plain,
( ~ sQ99_spl
| empty_set = sK216_skl ),
inference(forward_demodulation,[status(thm)],[f1809,f9450]) ).
fof(f9470,plain,
( ~ sQ99_spl
| sQ280_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9469,f5313]) ).
fof(f9471,plain,
( ~ sQ99_spl
| sQ280_spl ),
inference(contradiction_clause,[status(thm)],[f9470]) ).
fof(f9638,plain,
! [X0] :
( ~ sQ226_spl
| X0 = apply(relation_inverse(sK112_skl),sK67_skl(X0,relation_rng(relation_inverse(sK112_skl)),relation_inverse(sK112_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK112_skl)))
| ~ relation(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4440,f2252]) ).
fof(f9639,plain,
! [X0] :
( ~ sQ226_spl
| in(sK67_skl(X0,relation_rng(relation_inverse(sK112_skl)),relation_inverse(sK112_skl)),relation_dom(relation_inverse(sK112_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK112_skl)))
| ~ relation(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4440,f2251]) ).
fof(f9643,definition,
! [X0] :
( sQ451_spl
<=> ( X0 = apply(relation_inverse(sK112_skl),sK67_skl(X0,relation_rng(relation_inverse(sK112_skl)),relation_inverse(sK112_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK112_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f9646,plain,
( ~ sQ226_spl
| sQ451_spl
| ~ sQ269_spl ),
inference(split_clause,[status(thm)],[f9638,f5026,f9643,f4439]) ).
fof(f9647,definition,
! [X0] :
( sQ452_spl
<=> ( in(sK67_skl(X0,relation_rng(relation_inverse(sK112_skl)),relation_inverse(sK112_skl)),relation_dom(relation_inverse(sK112_skl)))
| ~ in(X0,relation_rng(relation_inverse(sK112_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f9650,plain,
( ~ sQ226_spl
| sQ452_spl
| ~ sQ269_spl ),
inference(split_clause,[status(thm)],[f9639,f5026,f9647,f4439]) ).
fof(f9692,plain,
! [X0,X1,X2] :
( ~ sQ29_spl
| X2 = X0
| sK21_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2477,f3866]) ).
fof(f9695,definition,
! [X0,X1,X2] :
( sQ453_spl
<=> ( X2 = X0
| sK21_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f9698,plain,
( ~ sQ29_spl
| sQ453_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9692,f2403,f2362,f9695,f2472]) ).
fof(f9854,plain,
( ~ sQ226_spl
| in(ordered_pair(sK24_skl(relation_dom(relation_inverse(sK112_skl))),apply(relation_inverse(sK112_skl),sK24_skl(relation_dom(relation_inverse(sK112_skl))))),relation_inverse(sK112_skl))
| ~ relation(relation_inverse(sK112_skl))
| relation(relation_dom(relation_inverse(sK112_skl))) ),
inference(resolution,[status(thm)],[f3952,f4440]) ).
fof(f9858,plain,
( ~ sQ212_spl
| in(ordered_pair(sK24_skl(relation_dom(relation_inverse(sK214_skl))),apply(relation_inverse(sK214_skl),sK24_skl(relation_dom(relation_inverse(sK214_skl))))),relation_inverse(sK214_skl))
| ~ relation(relation_inverse(sK214_skl))
| relation(relation_dom(relation_inverse(sK214_skl))) ),
inference(resolution,[status(thm)],[f3952,f4340]) ).
fof(f9865,plain,
( in(ordered_pair(sK24_skl(relation_dom(empty_set)),apply(empty_set,sK24_skl(relation_dom(empty_set)))),empty_set)
| ~ relation(empty_set)
| relation(relation_dom(empty_set)) ),
inference(resolution,[status(thm)],[f3952,f968]) ).
fof(f9888,definition,
( sQ459_spl
<=> relation(relation_dom(relation_inverse(sK112_skl))) ),
introduced(definition,[new_symbols(definition,[sQ459_spl])],[split_symbol_definition]) ).
fof(f9889,plain,
( ~ sQ459_spl
| relation(relation_dom(relation_inverse(sK112_skl))) ),
inference(component_clause,[status(thm)],[f9888]) ).
fof(f9891,definition,
( sQ460_spl
<=> in(ordered_pair(sK24_skl(relation_dom(relation_inverse(sK112_skl))),apply(relation_inverse(sK112_skl),sK24_skl(relation_dom(relation_inverse(sK112_skl))))),relation_inverse(sK112_skl)) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f9894,plain,
( ~ sQ226_spl
| sQ460_spl
| ~ sQ269_spl
| sQ459_spl ),
inference(split_clause,[status(thm)],[f9854,f9888,f5026,f9891,f4439]) ).
fof(f9916,definition,
( sQ467_spl
<=> relation(relation_dom(relation_inverse(sK214_skl))) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f9917,plain,
( ~ sQ467_spl
| relation(relation_dom(relation_inverse(sK214_skl))) ),
inference(component_clause,[status(thm)],[f9916]) ).
fof(f9919,definition,
( sQ468_spl
<=> in(ordered_pair(sK24_skl(relation_dom(relation_inverse(sK214_skl))),apply(relation_inverse(sK214_skl),sK24_skl(relation_dom(relation_inverse(sK214_skl))))),relation_inverse(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f9922,plain,
( ~ sQ212_spl
| sQ468_spl
| ~ sQ237_spl
| sQ467_spl ),
inference(split_clause,[status(thm)],[f9858,f9916,f4515,f9919,f4339]) ).
fof(f9947,definition,
( sQ473_spl
<=> relation(relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f9950,definition,
( sQ474_spl
<=> in(ordered_pair(sK24_skl(relation_dom(empty_set)),apply(empty_set,sK24_skl(relation_dom(empty_set)))),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ474_spl])],[split_symbol_definition]) ).
fof(f9951,plain,
( ~ sQ474_spl
| in(ordered_pair(sK24_skl(relation_dom(empty_set)),apply(empty_set,sK24_skl(relation_dom(empty_set)))),empty_set) ),
inference(component_clause,[status(thm)],[f9950]) ).
fof(f9953,plain,
( sQ474_spl
| ~ sQ20_spl
| sQ473_spl ),
inference(split_clause,[status(thm)],[f9865,f9947,f2403,f9950]) ).
fof(f9955,plain,
( ~ sQ474_spl
| in(ordered_pair(sK24_skl(empty_set),apply(empty_set,sK24_skl(relation_dom(empty_set)))),empty_set) ),
inference(forward_demodulation,[status(thm)],[f1808,f9951]) ).
fof(f9956,plain,
( ~ sQ474_spl
| ~ sQ29_spl
| in(ordered_pair(sK24_skl(empty_set),empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f2477,f9955]) ).
fof(f9957,plain,
( ~ sQ474_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9956,f2222]) ).
fof(f9958,plain,
( ~ sQ474_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f9957]) ).
fof(f9977,definition,
! [X0] :
( sQ475_spl
<=> ( ~ in(empty_set,X0)
| in(sK24_skl(relation_dom(empty_set)),relation_inverse_image(empty_set,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f9978,plain,
! [X0] :
( ~ sQ475_spl
| ~ in(empty_set,X0)
| in(sK24_skl(relation_dom(empty_set)),relation_inverse_image(empty_set,X0)) ),
inference(component_clause,[status(thm)],[f9977]) ).
fof(f9984,definition,
! [X0] :
( sQ476_spl
<=> ( ~ in(apply(empty_set,sK24_skl(empty_set)),X0)
| in(sK24_skl(relation_dom(empty_set)),relation_inverse_image(empty_set,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f9985,plain,
! [X0] :
( ~ sQ476_spl
| ~ in(apply(empty_set,sK24_skl(empty_set)),X0)
| in(sK24_skl(relation_dom(empty_set)),relation_inverse_image(empty_set,X0)) ),
inference(component_clause,[status(thm)],[f9984]) ).
fof(f9994,plain,
! [X0] :
( ~ sQ476_spl
| ~ in(apply(empty_set,sK24_skl(empty_set)),X0)
| in(sK24_skl(empty_set),relation_inverse_image(empty_set,X0)) ),
inference(forward_demodulation,[status(thm)],[f1808,f9985]) ).
fof(f9995,plain,
! [X0] :
( ~ sQ476_spl
| ~ sQ47_spl
| ~ in(apply(empty_set,sK24_skl(empty_set)),X0)
| in(sK24_skl(empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f2762,f9994]) ).
fof(f9996,plain,
! [X0] :
( ~ sQ476_spl
| ~ sQ47_spl
| ~ sQ29_spl
| ~ in(empty_set,X0)
| in(sK24_skl(empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f2477,f9995]) ).
fof(f9997,plain,
! [X0] :
( ~ sQ476_spl
| ~ sQ47_spl
| ~ sQ29_spl
| ~ in(empty_set,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9996,f2222]) ).
fof(f9998,plain,
! [X0] :
( ~ sQ475_spl
| ~ in(empty_set,X0)
| in(sK24_skl(empty_set),relation_inverse_image(empty_set,X0)) ),
inference(forward_demodulation,[status(thm)],[f1808,f9978]) ).
fof(f9999,plain,
! [X0] :
( ~ sQ475_spl
| ~ sQ47_spl
| ~ in(empty_set,X0)
| in(sK24_skl(empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f2762,f9998]) ).
fof(f10000,plain,
! [X0] :
( ~ sQ475_spl
| ~ sQ47_spl
| ~ in(empty_set,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9999,f2222]) ).
fof(f10001,plain,
( ~ sQ476_spl
| ~ sQ47_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5452,f9997]) ).
fof(f10013,plain,
( ~ sQ476_spl
| ~ sQ47_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f10001]) ).
fof(f10014,plain,
( ~ sQ475_spl
| ~ sQ47_spl
| $false ),
inference(resolution,[status(thm)],[f10000,f3702]) ).
fof(f10025,plain,
( ~ sQ475_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f10014]) ).
fof(f10096,plain,
( relation_field(empty_set) = set_union2(empty_set,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f814]) ).
fof(f10100,plain,
( relation_field(empty_set) = set_union2(relation_dom(empty_set),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1809,f814]) ).
fof(f10105,definition,
( sQ483_spl
<=> relation_field(empty_set) = set_union2(empty_set,relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f10106,plain,
( ~ sQ483_spl
| relation_field(empty_set) = set_union2(empty_set,relation_rng(empty_set)) ),
inference(component_clause,[status(thm)],[f10105]) ).
fof(f10108,plain,
( sQ483_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10096,f2403,f10105]) ).
fof(f10116,definition,
( sQ484_spl
<=> relation_field(empty_set) = set_union2(relation_dom(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f10119,plain,
( sQ484_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10100,f2403,f10116]) ).
fof(f10123,plain,
( ~ sQ483_spl
| relation_field(empty_set) = relation_rng(empty_set) ),
inference(forward_demodulation,[status(thm)],[f3128,f10106]) ).
fof(f10124,plain,
( ~ sQ483_spl
| relation_field(empty_set) = empty_set ),
inference(forward_demodulation,[status(thm)],[f1809,f10123]) ).
fof(f10140,plain,
( ~ sQ483_spl
| in(sK31_skl(empty_set,empty_set),relation_field(empty_set))
| empty_set = inclusion_relation(relation_field(empty_set))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f10124,f2218]) ).
fof(f10141,plain,
( ~ sQ483_spl
| is_transitive_in(empty_set,empty_set)
| ~ transitive(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f10124,f502]) ).
fof(f10142,plain,
( ~ sQ483_spl
| is_connected_in(empty_set,empty_set)
| ~ connected(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f10124,f498]) ).
fof(f10143,plain,
( ~ sQ483_spl
| is_antisymmetric_in(empty_set,empty_set)
| ~ antisymmetric(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f10124,f464]) ).
fof(f10144,definition,
( sQ485_spl
<=> empty_set = inclusion_relation(relation_field(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f10145,plain,
( ~ sQ485_spl
| empty_set = inclusion_relation(relation_field(empty_set)) ),
inference(component_clause,[status(thm)],[f10144]) ).
fof(f10160,definition,
( sQ489_spl
<=> in(sK32_skl(relation_field(empty_set),empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f10161,plain,
( ~ sQ489_spl
| in(sK32_skl(relation_field(empty_set),empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f10160]) ).
fof(f10164,definition,
( sQ490_spl
<=> in(sK32_skl(empty_set,empty_set),relation_field(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f10165,plain,
( ~ sQ490_spl
| in(sK32_skl(empty_set,empty_set),relation_field(empty_set)) ),
inference(component_clause,[status(thm)],[f10164]) ).
fof(f10168,definition,
( sQ491_spl
<=> in(sK31_skl(relation_field(empty_set),empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f10169,plain,
( ~ sQ491_spl
| in(sK31_skl(relation_field(empty_set),empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f10168]) ).
fof(f10172,definition,
( sQ492_spl
<=> in(sK31_skl(empty_set,empty_set),relation_field(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f10173,plain,
( ~ sQ492_spl
| in(sK31_skl(empty_set,empty_set),relation_field(empty_set)) ),
inference(component_clause,[status(thm)],[f10172]) ).
fof(f10175,plain,
( ~ sQ483_spl
| sQ492_spl
| sQ485_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10140,f2403,f10144,f10172,f10105]) ).
fof(f10176,definition,
( sQ493_spl
<=> transitive(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f10178,plain,
( sQ493_spl
| ~ transitive(empty_set) ),
inference(component_clause,[status(thm)],[f10176]) ).
fof(f10179,definition,
( sQ494_spl
<=> is_transitive_in(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ494_spl])],[split_symbol_definition]) ).
fof(f10180,plain,
( ~ sQ494_spl
| is_transitive_in(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f10179]) ).
fof(f10182,plain,
( ~ sQ483_spl
| sQ494_spl
| ~ sQ493_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10141,f2403,f10176,f10179,f10105]) ).
fof(f10183,definition,
( sQ495_spl
<=> connected(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f10184,plain,
( ~ sQ495_spl
| connected(empty_set) ),
inference(component_clause,[status(thm)],[f10183]) ).
fof(f10185,plain,
( sQ495_spl
| ~ connected(empty_set) ),
inference(component_clause,[status(thm)],[f10183]) ).
fof(f10186,definition,
( sQ496_spl
<=> is_connected_in(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f10187,plain,
( ~ sQ496_spl
| is_connected_in(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f10186]) ).
fof(f10189,plain,
( ~ sQ483_spl
| sQ496_spl
| ~ sQ495_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10142,f2403,f10183,f10186,f10105]) ).
fof(f10190,definition,
( sQ497_spl
<=> antisymmetric(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition]) ).
fof(f10192,plain,
( sQ497_spl
| ~ antisymmetric(empty_set) ),
inference(component_clause,[status(thm)],[f10190]) ).
fof(f10193,definition,
( sQ498_spl
<=> is_antisymmetric_in(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f10194,plain,
( ~ sQ498_spl
| is_antisymmetric_in(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f10193]) ).
fof(f10196,plain,
( ~ sQ483_spl
| sQ498_spl
| ~ sQ497_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10143,f2403,f10190,f10193,f10105]) ).
fof(f10197,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| empty_set = inclusion_relation(empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10145]) ).
fof(f10198,plain,
( ~ sQ492_spl
| ~ sQ483_spl
| in(sK31_skl(empty_set,empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10173]) ).
fof(f10199,plain,
( ~ sQ492_spl
| ~ sQ483_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10198,f2222]) ).
fof(f10200,plain,
( ~ sQ492_spl
| ~ sQ483_spl ),
inference(contradiction_clause,[status(thm)],[f10199]) ).
fof(f10201,plain,
( ~ sQ491_spl
| ~ sQ483_spl
| in(sK31_skl(empty_set,empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10169]) ).
fof(f10202,plain,
( ~ sQ491_spl
| ~ sQ483_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10201,f2222]) ).
fof(f10203,plain,
( ~ sQ491_spl
| ~ sQ483_spl ),
inference(contradiction_clause,[status(thm)],[f10202]) ).
fof(f10204,plain,
( ~ sQ490_spl
| ~ sQ483_spl
| in(sK32_skl(empty_set,empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10165]) ).
fof(f10205,plain,
( ~ sQ490_spl
| ~ sQ483_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10204,f2222]) ).
fof(f10206,plain,
( ~ sQ490_spl
| ~ sQ483_spl ),
inference(contradiction_clause,[status(thm)],[f10205]) ).
fof(f10207,plain,
( ~ sQ489_spl
| ~ sQ483_spl
| in(sK32_skl(empty_set,empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10161]) ).
fof(f10208,plain,
( ~ sQ489_spl
| ~ sQ483_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10207,f2222]) ).
fof(f10209,plain,
( ~ sQ489_spl
| ~ sQ483_spl ),
inference(contradiction_clause,[status(thm)],[f10208]) ).
fof(f10216,definition,
( sQ499_spl
<=> well_ordering(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f10217,plain,
( ~ sQ499_spl
| well_ordering(empty_set) ),
inference(component_clause,[status(thm)],[f10216]) ).
fof(f10220,definition,
( sQ500_spl
<=> is_transitive_in(empty_set,relation_field(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ500_spl])],[split_symbol_definition]) ).
fof(f10222,plain,
( sQ500_spl
| ~ is_transitive_in(empty_set,relation_field(empty_set)) ),
inference(component_clause,[status(thm)],[f10220]) ).
fof(f10224,plain,
( sQ500_spl
| ~ sQ483_spl
| ~ is_transitive_in(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10222]) ).
fof(f10225,plain,
( sQ495_spl
| ~ well_ordering(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f10185,f758]) ).
fof(f10227,plain,
( sQ495_spl
| ~ sQ499_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10225,f2403,f10216,f10183]) ).
fof(f10228,definition,
( sQ501_spl
<=> is_connected_in(empty_set,relation_field(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f10230,plain,
( sQ501_spl
| ~ is_connected_in(empty_set,relation_field(empty_set)) ),
inference(component_clause,[status(thm)],[f10228]) ).
fof(f10232,plain,
( sQ501_spl
| ~ sQ483_spl
| ~ is_connected_in(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10230]) ).
fof(f10236,definition,
( sQ502_spl
<=> is_antisymmetric_in(empty_set,relation_field(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f10238,plain,
( sQ502_spl
| ~ is_antisymmetric_in(empty_set,relation_field(empty_set)) ),
inference(component_clause,[status(thm)],[f10236]) ).
fof(f10240,plain,
( sQ502_spl
| ~ sQ483_spl
| ~ is_antisymmetric_in(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f10124,f10238]) ).
fof(f10254,plain,
! [X0] :
( ~ sQ47_spl
| in(sK24_skl(empty_set),relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set)
| relation(relation_inverse_image(empty_set,X0)) ),
inference(paramodulation,[status(thm)],[f2762,f3961]) ).
fof(f10256,plain,
! [X0] :
( in(sK24_skl(relation_inverse_image(empty_set,X0)),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set)
| relation(relation_inverse_image(empty_set,X0)) ),
inference(paramodulation,[status(thm)],[f1808,f3961]) ).
fof(f10263,definition,
! [X0] :
( sQ503_spl
<=> relation(relation_inverse_image(empty_set,X0)) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f10266,definition,
( sQ504_spl
<=> in(sK24_skl(empty_set),relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f10267,plain,
( ~ sQ504_spl
| in(sK24_skl(empty_set),relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f10266]) ).
fof(f10269,plain,
( ~ sQ47_spl
| sQ504_spl
| ~ sQ13_spl
| ~ sQ20_spl
| sQ503_spl ),
inference(split_clause,[status(thm)],[f10254,f10263,f2403,f2362,f10266,f2591]) ).
fof(f10271,definition,
! [X0] :
( sQ505_spl
<=> ( in(sK24_skl(relation_inverse_image(empty_set,X0)),empty_set)
| relation(relation_inverse_image(empty_set,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f10274,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| sQ505_spl ),
inference(split_clause,[status(thm)],[f10256,f10271,f2403,f2362]) ).
fof(f10280,plain,
( ~ sQ504_spl
| in(sK24_skl(empty_set),empty_set) ),
inference(forward_demodulation,[status(thm)],[f1808,f10267]) ).
fof(f10281,plain,
( ~ sQ504_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10280,f2222]) ).
fof(f10282,plain,
~ sQ504_spl,
inference(contradiction_clause,[status(thm)],[f10281]) ).
fof(f10285,plain,
( in(apply(sK214_skl,sK24_skl(sK212_skl)),relation_rng(sK214_skl))
| sK213_skl = empty_set
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| relation(sK212_skl) ),
inference(resolution,[status(thm)],[f3962,f1732]) ).
fof(f10287,definition,
( sQ506_spl
<=> in(apply(sK214_skl,sK24_skl(sK212_skl)),relation_rng(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f10290,plain,
( sQ506_spl
| sQ104_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f10285,f6979,f2354,f3178,f3184,f10287]) ).
fof(f10292,definition,
( sQ507_spl
<=> reflexive(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f10293,plain,
( ~ sQ507_spl
| reflexive(empty_set) ),
inference(component_clause,[status(thm)],[f10292]) ).
fof(f10295,definition,
( sQ508_spl
<=> well_founded_relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f10297,plain,
( sQ508_spl
| ~ well_founded_relation(empty_set) ),
inference(component_clause,[status(thm)],[f10295]) ).
fof(f10303,plain,
( ~ sQ339_spl
| sK212_skl = empty_set
| relation_dom(sK212_skl) != empty_set ),
inference(resolution,[status(thm)],[f6980,f1818]) ).
fof(f10307,plain,
( ~ sQ339_spl
| relation(relation_inverse(sK212_skl)) ),
inference(resolution,[status(thm)],[f6980,f911]) ).
fof(f10318,plain,
! [X0,X1] :
( ~ sQ339_spl
| in(apply(sK212_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK212_skl,X1))
| ~ function(sK212_skl) ),
inference(resolution,[status(thm)],[f6980,f2190]) ).
fof(f10319,definition,
( sQ509_spl
<=> relation_dom(sK212_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f10322,plain,
( ~ sQ339_spl
| sQ264_spl
| ~ sQ509_spl ),
inference(split_clause,[status(thm)],[f10303,f10319,f4890,f6979]) ).
fof(f10323,definition,
( sQ510_spl
<=> function(sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f10326,definition,
! [X0,X1] :
( sQ511_spl
<=> ( in(apply(sK212_skl,X0),X1)
| ~ in(X0,relation_inverse_image(sK212_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f10329,plain,
( ~ sQ339_spl
| sQ511_spl
| ~ sQ510_spl ),
inference(split_clause,[status(thm)],[f10318,f10323,f10326,f6979]) ).
fof(f10330,plain,
( sQ508_spl
| ~ well_ordering(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f10297,f759]) ).
fof(f10332,plain,
( sQ508_spl
| ~ sQ499_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10330,f2403,f10216,f10295]) ).
fof(f10350,plain,
( ~ sQ339_spl
| relation_inverse(sK212_skl) = empty_set
| relation_dom(relation_inverse(sK212_skl)) != empty_set ),
inference(resolution,[status(thm)],[f10307,f1818]) ).
fof(f10365,plain,
! [X0,X1] :
( ~ sQ339_spl
| in(apply(relation_inverse(sK212_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK212_skl),X1))
| ~ function(relation_inverse(sK212_skl)) ),
inference(resolution,[status(thm)],[f10307,f2190]) ).
fof(f10366,definition,
( sQ513_spl
<=> relation_dom(relation_inverse(sK212_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f10369,definition,
( sQ514_spl
<=> relation_inverse(sK212_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f10370,plain,
( ~ sQ514_spl
| relation_inverse(sK212_skl) = empty_set ),
inference(component_clause,[status(thm)],[f10369]) ).
fof(f10372,plain,
( ~ sQ339_spl
| sQ514_spl
| ~ sQ513_spl ),
inference(split_clause,[status(thm)],[f10350,f10366,f10369,f6979]) ).
fof(f10373,definition,
( sQ515_spl
<=> function(relation_inverse(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f10375,plain,
( sQ515_spl
| ~ function(relation_inverse(sK212_skl)) ),
inference(component_clause,[status(thm)],[f10373]) ).
fof(f10376,definition,
! [X0,X1] :
( sQ516_spl
<=> ( in(apply(relation_inverse(sK212_skl),X0),X1)
| ~ in(X0,relation_inverse_image(relation_inverse(sK212_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f10379,plain,
( ~ sQ339_spl
| sQ516_spl
| ~ sQ515_spl ),
inference(split_clause,[status(thm)],[f10365,f10373,f10376,f6979]) ).
fof(f10386,definition,
! [X0] :
( sQ517_spl
<=> ~ subset(relation_rng(sK214_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f10387,plain,
! [X0] :
( ~ sQ517_spl
| ~ subset(relation_rng(sK214_skl),X0) ),
inference(component_clause,[status(thm)],[f10386]) ).
fof(f10389,definition,
! [X1] :
( sQ518_spl
<=> ( relation_of2_as_subset(sK214_skl,sK212_skl,X1)
| ~ subset(relation_rng(sK214_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f10394,definition,
( sQ519_spl
<=> subset(relation_dom(sK214_skl),sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f10467,plain,
! [X0,X1] :
( ~ sQ485_spl
| ~ sQ483_spl
| in(apply(inclusion_relation(empty_set),X0),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1))
| ~ function(inclusion_relation(empty_set)) ),
inference(paramodulation,[status(thm)],[f10197,f2725]) ).
fof(f10468,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| antisymmetric(empty_set) ),
inference(paramodulation,[status(thm)],[f10197,f1807]) ).
fof(f10469,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| transitive(empty_set) ),
inference(paramodulation,[status(thm)],[f10197,f1695]) ).
fof(f10470,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| reflexive(empty_set) ),
inference(paramodulation,[status(thm)],[f10197,f1619]) ).
fof(f10473,definition,
( sQ520_spl
<=> function(inclusion_relation(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f10475,plain,
( sQ520_spl
| ~ function(inclusion_relation(empty_set)) ),
inference(component_clause,[status(thm)],[f10473]) ).
fof(f10476,definition,
! [X0,X1] :
( sQ521_spl
<=> ( in(apply(inclusion_relation(empty_set),X0),X1)
| ~ in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f10479,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| sQ521_spl
| ~ sQ520_spl ),
inference(split_clause,[status(thm)],[f10467,f10473,f10476,f10105,f10144]) ).
fof(f10480,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| sQ493_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10469,f10178]) ).
fof(f10481,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| sQ493_spl ),
inference(contradiction_clause,[status(thm)],[f10480]) ).
fof(f10482,plain,
( sQ520_spl
| ~ sQ485_spl
| ~ sQ483_spl
| ~ function(empty_set) ),
inference(forward_demodulation,[status(thm)],[f10197,f10475]) ).
fof(f10483,plain,
( sQ520_spl
| ~ sQ485_spl
| ~ sQ483_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10482,f968]) ).
fof(f10484,plain,
( sQ520_spl
| ~ sQ485_spl
| ~ sQ483_spl ),
inference(contradiction_clause,[status(thm)],[f10483]) ).
fof(f10489,plain,
! [X0] :
( relation_restriction(empty_set,X0) = empty_set
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3721,f826]) ).
fof(f10493,definition,
! [X0] :
( sQ522_spl
<=> relation_restriction(empty_set,X0) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f10496,plain,
( sQ522_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10489,f2403,f10493]) ).
fof(f10500,plain,
( sQ497_spl
| ~ sQ485_spl
| ~ sQ483_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10192,f10468]) ).
fof(f10501,plain,
( sQ497_spl
| ~ sQ485_spl
| ~ sQ483_spl ),
inference(contradiction_clause,[status(thm)],[f10500]) ).
fof(f10502,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| sQ507_spl ),
inference(split_clause,[status(thm)],[f10470,f10292,f10105,f10144]) ).
fof(f10507,plain,
! [X0,X1] :
( ~ sQ498_spl
| X0 = X1
| ~ in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X1,empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f10194,f737]) ).
fof(f10508,definition,
! [X0,X1] :
( sQ523_spl
<=> ( X0 = X1
| ~ in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X1,empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f10511,plain,
( ~ sQ498_spl
| sQ523_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10507,f2403,f10508,f10193]) ).
fof(f10513,plain,
! [X0] :
( apply(relation_composition(sK214_skl,X0),sK24_skl(sK212_skl)) = apply(X0,apply(sK214_skl,sK24_skl(sK212_skl)))
| sK213_skl = empty_set
| ~ function(X0)
| ~ relation(X0)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| relation(sK212_skl) ),
inference(resolution,[status(thm)],[f3965,f1732]) ).
fof(f10515,definition,
! [X0] :
( sQ524_spl
<=> ( apply(relation_composition(sK214_skl,X0),sK24_skl(sK212_skl)) = apply(X0,apply(sK214_skl,sK24_skl(sK212_skl)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f10518,plain,
( sQ104_spl
| sQ524_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f10513,f6979,f2354,f3178,f10515,f3184]) ).
fof(f10521,plain,
! [X0] :
( in(ordered_pair(sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl)),apply(sK214_skl,sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl)))),sK214_skl)
| ~ relation(sK214_skl)
| in(X0,set_meet(relation_dom(sK214_skl)))
| relation_dom(sK214_skl) = empty_set ),
inference(resolution,[status(thm)],[f4277,f1731]) ).
fof(f10524,plain,
! [X0] :
( ~ sQ226_spl
| in(ordered_pair(sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl))),apply(relation_inverse(sK112_skl),sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl))))),relation_inverse(sK112_skl))
| ~ relation(relation_inverse(sK112_skl))
| in(X0,set_meet(relation_dom(relation_inverse(sK112_skl))))
| relation_dom(relation_inverse(sK112_skl)) = empty_set ),
inference(resolution,[status(thm)],[f4277,f4440]) ).
fof(f10528,plain,
! [X0] :
( ~ sQ212_spl
| in(ordered_pair(sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK214_skl))),relation_dom(relation_inverse(sK214_skl))),apply(relation_inverse(sK214_skl),sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK214_skl))),relation_dom(relation_inverse(sK214_skl))))),relation_inverse(sK214_skl))
| ~ relation(relation_inverse(sK214_skl))
| in(X0,set_meet(relation_dom(relation_inverse(sK214_skl))))
| relation_dom(relation_inverse(sK214_skl)) = empty_set ),
inference(resolution,[status(thm)],[f4277,f4340]) ).
fof(f10543,definition,
! [X0] :
( sQ526_spl
<=> ( in(ordered_pair(sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl)),apply(sK214_skl,sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl)))),sK214_skl)
| in(X0,set_meet(relation_dom(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f10546,plain,
( ~ sQ10_spl
| sQ526_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f10521,f2559,f10543,f2351]) ).
fof(f10555,definition,
! [X0] :
( sQ529_spl
<=> ( in(ordered_pair(sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl))),apply(relation_inverse(sK112_skl),sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl))))),relation_inverse(sK112_skl))
| in(X0,set_meet(relation_dom(relation_inverse(sK112_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ529_spl])],[split_symbol_definition]) ).
fof(f10558,plain,
( ~ sQ226_spl
| ~ sQ269_spl
| sQ529_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f10524,f4432,f10555,f5026,f4439]) ).
fof(f10571,definition,
! [X0] :
( sQ533_spl
<=> ( in(ordered_pair(sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK214_skl))),relation_dom(relation_inverse(sK214_skl))),apply(relation_inverse(sK214_skl),sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK214_skl))),relation_dom(relation_inverse(sK214_skl))))),relation_inverse(sK214_skl))
| in(X0,set_meet(relation_dom(relation_inverse(sK214_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f10574,plain,
( ~ sQ212_spl
| ~ sQ237_spl
| sQ533_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f10528,f4332,f10571,f4515,f4339]) ).
fof(f10603,plain,
! [X0,X1] :
( ~ sQ496_spl
| in(ordered_pair(X1,X0),empty_set)
| in(ordered_pair(X0,X1),empty_set)
| X0 = X1
| ~ in(X1,empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f10187,f819]) ).
fof(f10604,definition,
! [X0,X1] :
( sQ537_spl
<=> ( in(ordered_pair(X1,X0),empty_set)
| in(ordered_pair(X0,X1),empty_set)
| X0 = X1
| ~ in(X1,empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f10607,plain,
( ~ sQ496_spl
| sQ537_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10603,f2403,f10604,f10186]) ).
fof(f10612,plain,
( sQ500_spl
| ~ sQ483_spl
| ~ sQ494_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10224,f10180]) ).
fof(f10613,plain,
( sQ500_spl
| ~ sQ483_spl
| ~ sQ494_spl ),
inference(contradiction_clause,[status(thm)],[f10612]) ).
fof(f10615,plain,
( sQ501_spl
| ~ sQ483_spl
| in(sK74_skl(empty_set,empty_set),empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f10232,f821]) ).
fof(f10618,definition,
( sQ538_spl
<=> in(sK74_skl(empty_set,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f10619,plain,
( ~ sQ538_spl
| in(sK74_skl(empty_set,empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f10618]) ).
fof(f10621,plain,
( sQ501_spl
| ~ sQ483_spl
| sQ538_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10615,f2403,f10618,f10105,f10228]) ).
fof(f10622,definition,
( sQ539_spl
<=> in(sK73_skl(empty_set,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ539_spl])],[split_symbol_definition]) ).
fof(f10623,plain,
( ~ sQ539_spl
| in(sK73_skl(empty_set,empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f10622]) ).
fof(f10630,plain,
( ~ sQ538_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10619,f2222]) ).
fof(f10631,plain,
~ sQ538_spl,
inference(contradiction_clause,[status(thm)],[f10630]) ).
fof(f10632,plain,
( ~ sQ539_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10623,f2222]) ).
fof(f10633,plain,
~ sQ539_spl,
inference(contradiction_clause,[status(thm)],[f10632]) ).
fof(f10635,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)],[f2256,f911]) ).
fof(f10638,plain,
! [X0,X1] :
( in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f5781,f10635]) ).
fof(f10639,definition,
! [X0,X1] :
( sQ541_spl
<=> ( in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ541_spl])],[split_symbol_definition]) ).
fof(f10642,plain,
( sQ541_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f10638,f2403,f10639]) ).
fof(f10661,plain,
( sQ515_spl
| ~ sQ514_spl
| ~ function(empty_set) ),
inference(backward_demodulation,[status(thm)],[f10370,f10375]) ).
fof(f10662,plain,
! [X0,X1] :
( ~ sQ514_spl
| in(ordered_pair(X1,X0),sK212_skl)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ relation(sK212_skl) ),
inference(paramodulation,[status(thm)],[f10370,f10635]) ).
fof(f10663,plain,
( sQ515_spl
| ~ sQ514_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10661,f2362,f10369,f10373]) ).
fof(f10664,definition,
! [X0,X1] :
( sQ542_spl
<=> ( in(ordered_pair(X1,X0),sK212_skl)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f10667,plain,
( ~ sQ514_spl
| sQ542_spl
| ~ sQ339_spl ),
inference(split_clause,[status(thm)],[f10662,f6979,f10664,f10369]) ).
fof(f10682,plain,
! [X0,X1] :
( relation_of2_as_subset(sK214_skl,sK212_skl,X1)
| ~ subset(relation_rng(sK214_skl),X1)
| ~ subset(sK213_skl,X0) ),
inference(resolution,[status(thm)],[f2627,f1480]) ).
fof(f10684,plain,
! [X0] :
( subset(relation_dom(sK214_skl),sK212_skl)
| ~ subset(sK213_skl,X0) ),
inference(resolution,[status(thm)],[f2627,f1439]) ).
fof(f10685,definition,
! [X0] :
( sQ544_spl
<=> ~ subset(sK213_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f10686,plain,
! [X0] :
( ~ sQ544_spl
| ~ subset(sK213_skl,X0) ),
inference(component_clause,[status(thm)],[f10685]) ).
fof(f10688,plain,
( sQ518_spl
| sQ544_spl ),
inference(split_clause,[status(thm)],[f10682,f10685,f10389]) ).
fof(f10690,plain,
( sQ519_spl
| sQ544_spl ),
inference(split_clause,[status(thm)],[f10684,f10685,f10394]) ).
fof(f10691,plain,
( ~ sQ544_spl
| $false ),
inference(resolution,[status(thm)],[f10686,f3898]) ).
fof(f10697,plain,
~ sQ544_spl,
inference(contradiction_clause,[status(thm)],[f10691]) ).
fof(f10698,plain,
( sQ502_spl
| ~ sQ483_spl
| ~ sQ498_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10240,f10194]) ).
fof(f10699,plain,
( sQ502_spl
| ~ sQ483_spl
| ~ sQ498_spl ),
inference(contradiction_clause,[status(thm)],[f10698]) ).
fof(f10703,plain,
! [X0,X1] :
( ~ in(apply(sK214_skl,sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl))),X1)
| in(sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X1))
| ~ relation(sK214_skl)
| in(X0,set_meet(relation_dom(sK214_skl)))
| relation_dom(sK214_skl) = empty_set ),
inference(resolution,[status(thm)],[f4278,f1731]) ).
fof(f10706,plain,
! [X0,X1] :
( ~ sQ226_spl
| ~ in(apply(relation_inverse(sK112_skl),sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl)))),X1)
| in(sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl))),relation_inverse_image(relation_inverse(sK112_skl),X1))
| ~ relation(relation_inverse(sK112_skl))
| in(X0,set_meet(relation_dom(relation_inverse(sK112_skl))))
| relation_dom(relation_inverse(sK112_skl)) = empty_set ),
inference(resolution,[status(thm)],[f4278,f4440]) ).
fof(f10723,definition,
! [X0,X1] :
( sQ546_spl
<=> ( ~ in(apply(sK214_skl,sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl))),X1)
| in(sK26_skl(X0,set_meet(relation_dom(sK214_skl)),relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X1))
| in(X0,set_meet(relation_dom(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ546_spl])],[split_symbol_definition]) ).
fof(f10726,plain,
( ~ sQ10_spl
| sQ546_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f10703,f2559,f10723,f2351]) ).
fof(f10735,definition,
! [X0,X1] :
( sQ549_spl
<=> ( ~ in(apply(relation_inverse(sK112_skl),sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl)))),X1)
| in(sK26_skl(X0,set_meet(relation_dom(relation_inverse(sK112_skl))),relation_dom(relation_inverse(sK112_skl))),relation_inverse_image(relation_inverse(sK112_skl),X1))
| in(X0,set_meet(relation_dom(relation_inverse(sK112_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f10738,plain,
( ~ sQ226_spl
| ~ sQ269_spl
| sQ549_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f10706,f4432,f10735,f5026,f4439]) ).
fof(f10775,plain,
! [X0,X1] :
( in(sK26_skl(X1,set_meet(relation_inverse_image(sK118_skl,X0)),relation_inverse_image(sK118_skl,X0)),relation_dom(sK118_skl))
| ~ relation(sK118_skl)
| in(X1,set_meet(relation_inverse_image(sK118_skl,X0)))
| relation_inverse_image(sK118_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f4287,f1180]) ).
fof(f10777,plain,
! [X0,X1] :
( in(sK26_skl(X1,set_meet(relation_inverse_image(sK214_skl,X0)),relation_inverse_image(sK214_skl,X0)),relation_dom(sK214_skl))
| ~ relation(sK214_skl)
| in(X1,set_meet(relation_inverse_image(sK214_skl,X0)))
| relation_inverse_image(sK214_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f4287,f1731]) ).
fof(f10778,plain,
! [X0,X1] :
( in(sK26_skl(X1,set_meet(relation_inverse_image(sK115_skl,X0)),relation_inverse_image(sK115_skl,X0)),relation_dom(sK115_skl))
| ~ relation(sK115_skl)
| in(X1,set_meet(relation_inverse_image(sK115_skl,X0)))
| relation_inverse_image(sK115_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f4287,f1167]) ).
fof(f10779,plain,
! [X0,X1] :
( ~ sQ15_spl
| in(sK26_skl(X1,set_meet(relation_inverse_image(sK102_skl,X0)),relation_inverse_image(sK102_skl,X0)),relation_dom(sK102_skl))
| ~ relation(sK102_skl)
| in(X1,set_meet(relation_inverse_image(sK102_skl,X0)))
| relation_inverse_image(sK102_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f4287,f2373]) ).
fof(f10780,plain,
! [X0,X1] :
( ~ sQ226_spl
| in(sK26_skl(X1,set_meet(relation_inverse_image(relation_inverse(sK112_skl),X0)),relation_inverse_image(relation_inverse(sK112_skl),X0)),relation_dom(relation_inverse(sK112_skl)))
| ~ relation(relation_inverse(sK112_skl))
| in(X1,set_meet(relation_inverse_image(relation_inverse(sK112_skl),X0)))
| relation_inverse_image(relation_inverse(sK112_skl),X0) = empty_set ),
inference(resolution,[status(thm)],[f4287,f4440]) ).
fof(f10784,plain,
! [X0,X1] :
( ~ sQ202_spl
| in(sK26_skl(X1,set_meet(relation_inverse_image(relation_inverse(sK115_skl),X0)),relation_inverse_image(relation_inverse(sK115_skl),X0)),relation_dom(relation_inverse(sK115_skl)))
| ~ relation(relation_inverse(sK115_skl))
| in(X1,set_meet(relation_inverse_image(relation_inverse(sK115_skl),X0)))
| relation_inverse_image(relation_inverse(sK115_skl),X0) = empty_set ),
inference(resolution,[status(thm)],[f4287,f4252]) ).
fof(f10789,plain,
! [X0,X1] :
( in(sK26_skl(X1,set_meet(relation_inverse_image(empty_set,X0)),relation_inverse_image(empty_set,X0)),relation_dom(empty_set))
| ~ relation(empty_set)
| in(X1,set_meet(relation_inverse_image(empty_set,X0)))
| relation_inverse_image(empty_set,X0) = empty_set ),
inference(resolution,[status(thm)],[f4287,f968]) ).
fof(f10792,definition,
! [X0,X1] :
( sQ555_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(sK118_skl,X0)),relation_inverse_image(sK118_skl,X0)),relation_dom(sK118_skl))
| in(X1,set_meet(relation_inverse_image(sK118_skl,X0)))
| relation_inverse_image(sK118_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f10795,plain,
( ~ sQ86_spl
| sQ555_spl ),
inference(split_clause,[status(thm)],[f10775,f10792,f2976]) ).
fof(f10797,definition,
! [X0,X1] :
( sQ556_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(sK214_skl,X0)),relation_inverse_image(sK214_skl,X0)),relation_dom(sK214_skl))
| in(X1,set_meet(relation_inverse_image(sK214_skl,X0)))
| relation_inverse_image(sK214_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f10800,plain,
( ~ sQ10_spl
| sQ556_spl ),
inference(split_clause,[status(thm)],[f10777,f10797,f2351]) ).
fof(f10801,definition,
! [X0,X1] :
( sQ557_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(sK115_skl,X0)),relation_inverse_image(sK115_skl,X0)),relation_dom(sK115_skl))
| in(X1,set_meet(relation_inverse_image(sK115_skl,X0)))
| relation_inverse_image(sK115_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ557_spl])],[split_symbol_definition]) ).
fof(f10804,plain,
( ~ sQ88_spl
| sQ557_spl ),
inference(split_clause,[status(thm)],[f10778,f10801,f2983]) ).
fof(f10805,definition,
! [X0,X1] :
( sQ558_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(sK102_skl,X0)),relation_inverse_image(sK102_skl,X0)),relation_dom(sK102_skl))
| in(X1,set_meet(relation_inverse_image(sK102_skl,X0)))
| relation_inverse_image(sK102_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f10808,plain,
( ~ sQ15_spl
| ~ sQ82_spl
| sQ558_spl ),
inference(split_clause,[status(thm)],[f10779,f10805,f2936,f2372]) ).
fof(f10809,definition,
! [X0,X1] :
( sQ559_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(relation_inverse(sK112_skl),X0)),relation_inverse_image(relation_inverse(sK112_skl),X0)),relation_dom(relation_inverse(sK112_skl)))
| in(X1,set_meet(relation_inverse_image(relation_inverse(sK112_skl),X0)))
| relation_inverse_image(relation_inverse(sK112_skl),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f10812,plain,
( ~ sQ226_spl
| ~ sQ269_spl
| sQ559_spl ),
inference(split_clause,[status(thm)],[f10780,f10809,f5026,f4439]) ).
fof(f10825,definition,
! [X0,X1] :
( sQ563_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(relation_inverse(sK115_skl),X0)),relation_inverse_image(relation_inverse(sK115_skl),X0)),relation_dom(relation_inverse(sK115_skl)))
| in(X1,set_meet(relation_inverse_image(relation_inverse(sK115_skl),X0)))
| relation_inverse_image(relation_inverse(sK115_skl),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f10828,plain,
( ~ sQ202_spl
| ~ sQ260_spl
| sQ563_spl ),
inference(split_clause,[status(thm)],[f10784,f10825,f4866,f4251]) ).
fof(f10835,definition,
! [X0,X1] :
( sQ564_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(empty_set,X0)),relation_inverse_image(empty_set,X0)),relation_dom(empty_set))
| in(X1,set_meet(relation_inverse_image(empty_set,X0)))
| relation_inverse_image(empty_set,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f10838,plain,
( ~ sQ20_spl
| sQ564_spl ),
inference(split_clause,[status(thm)],[f10789,f10835,f2403]) ).
fof(f10840,definition,
( sQ565_spl
<=> is_reflexive_in(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f10841,plain,
( ~ sQ565_spl
| is_reflexive_in(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f10840]) ).
fof(f10842,plain,
( sQ565_spl
| ~ is_reflexive_in(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f10840]) ).
fof(f10899,plain,
( ~ sQ517_spl
| $false ),
inference(resolution,[status(thm)],[f10387,f3898]) ).
fof(f10905,plain,
~ sQ517_spl,
inference(contradiction_clause,[status(thm)],[f10899]) ).
fof(f10985,plain,
! [X0] :
( in(apply(sK214_skl,sK26_skl(X0,set_meet(sK212_skl),sK212_skl)),relation_rng(sK214_skl))
| sK213_skl = empty_set
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| in(X0,set_meet(sK212_skl))
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f4288,f1732]) ).
fof(f10987,definition,
! [X0] :
( sQ574_spl
<=> ( in(apply(sK214_skl,sK26_skl(X0,set_meet(sK212_skl),sK212_skl)),relation_rng(sK214_skl))
| in(X0,set_meet(sK212_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f10990,plain,
( sQ104_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ574_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f10985,f4890,f10987,f2354,f3178,f3184]) ).
fof(f11008,plain,
! [X0,X1] :
( ~ sQ285_spl
| ~ in(X1,sK26_skl(X0,empty_set,sK212_skl))
| ~ in(sK212_skl,X1)
| in(X0,set_meet(sK212_skl))
| sK212_skl = empty_set ),
inference(paramodulation,[status(thm)],[f8282,f4289]) ).
fof(f11013,definition,
! [X0,X1] :
( sQ575_spl
<=> ( ~ in(X1,sK26_skl(X0,empty_set,sK212_skl))
| ~ in(sK212_skl,X1)
| in(X0,set_meet(sK212_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f11016,plain,
( ~ sQ285_spl
| sQ575_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f11008,f4890,f11013,f5343]) ).
fof(f11031,plain,
( sQ565_spl
| in(sK25_skl(empty_set,empty_set),empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f10842,f550]) ).
fof(f11037,definition,
( sQ579_spl
<=> in(sK25_skl(empty_set,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ579_spl])],[split_symbol_definition]) ).
fof(f11038,plain,
( ~ sQ579_spl
| in(sK25_skl(empty_set,empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f11037]) ).
fof(f11040,plain,
( sQ565_spl
| sQ579_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f11031,f2403,f11037,f10840]) ).
fof(f11041,plain,
( ~ sQ579_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11038,f2222]) ).
fof(f11042,plain,
~ sQ579_spl,
inference(contradiction_clause,[status(thm)],[f11041]) ).
fof(f11068,plain,
( ~ sQ173_spl
| succ(sK213_skl) = empty_set ),
inference(resolution,[status(thm)],[f3976,f1950]) ).
fof(f11072,plain,
( ~ sQ173_spl
| ~ empty(empty_set) ),
inference(paramodulation,[status(thm)],[f11068,f957]) ).
fof(f11087,plain,
( ~ sQ173_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11072,f947]) ).
fof(f11088,plain,
~ sQ173_spl,
inference(contradiction_clause,[status(thm)],[f11087]) ).
fof(f11090,plain,
! [X0,X1] :
( ~ sQ92_spl
| in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),relation_rng(sK214_skl))
| ~ function(sK214_skl)
| ~ relation(sK214_skl)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ),
inference(resolution,[status(thm)],[f2999,f2253]) ).
fof(f11091,plain,
! [X0,X1] :
( ~ sQ92_spl
| in(ordered_pair(sK9_skl(X0,X1,sK214_skl),sK57_skl(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl),sK214_skl)),sK214_skl)
| ~ relation(sK214_skl)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ),
inference(resolution,[status(thm)],[f2999,f2242]) ).
fof(f11104,definition,
! [X0,X1] :
( sQ580_spl
<=> ( in(apply(sK214_skl,sK9_skl(X0,X1,sK214_skl)),relation_rng(sK214_skl))
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ580_spl])],[split_symbol_definition]) ).
fof(f11107,plain,
( ~ sQ92_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ580_spl ),
inference(split_clause,[status(thm)],[f11090,f11104,f2351,f2354,f2998]) ).
fof(f11108,definition,
! [X0,X1] :
( sQ581_spl
<=> ( in(ordered_pair(sK9_skl(X0,X1,sK214_skl),sK57_skl(sK9_skl(X0,X1,sK214_skl),relation_dom(sK214_skl),sK214_skl)),sK214_skl)
| in(sK9_skl(X0,X1,sK214_skl),X0)
| X0 = relation_inverse_image(sK214_skl,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ581_spl])],[split_symbol_definition]) ).
fof(f11111,plain,
( ~ sQ92_spl
| ~ sQ10_spl
| sQ581_spl ),
inference(split_clause,[status(thm)],[f11091,f11108,f2351,f2998]) ).
fof(f11116,plain,
! [X0] :
( ~ sQ565_spl
| in(ordered_pair(X0,X0),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f10841,f549]) ).
fof(f11117,definition,
! [X0] :
( sQ582_spl
<=> ( in(ordered_pair(X0,X0),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ582_spl])],[split_symbol_definition]) ).
fof(f11120,plain,
( ~ sQ565_spl
| sQ582_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f11116,f2403,f11117,f10840]) ).
fof(f11126,plain,
! [X0,X1] :
( apply(relation_composition(sK214_skl,X1),sK26_skl(X0,set_meet(sK212_skl),sK212_skl)) = apply(X1,apply(sK214_skl,sK26_skl(X0,set_meet(sK212_skl),sK212_skl)))
| sK213_skl = empty_set
| ~ function(X1)
| ~ relation(X1)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| in(X0,set_meet(sK212_skl))
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f4291,f1732]) ).
fof(f11128,definition,
! [X0,X1] :
( sQ583_spl
<=> ( apply(relation_composition(sK214_skl,X1),sK26_skl(X0,set_meet(sK212_skl),sK212_skl)) = apply(X1,apply(sK214_skl,sK26_skl(X0,set_meet(sK212_skl),sK212_skl)))
| ~ function(X1)
| ~ relation(X1)
| in(X0,set_meet(sK212_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ583_spl])],[split_symbol_definition]) ).
fof(f11131,plain,
( sQ104_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ583_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f11126,f4890,f11128,f2354,f3178,f3184]) ).
fof(f11268,plain,
! [X0] :
( ~ sQ285_spl
| ~ in(sK212_skl,sK26_skl(X0,empty_set,sK212_skl))
| in(X0,set_meet(sK212_skl))
| sK212_skl = empty_set ),
inference(paramodulation,[status(thm)],[f8282,f4292]) ).
fof(f11270,definition,
! [X0] :
( sQ589_spl
<=> ( ~ in(sK212_skl,sK26_skl(X0,empty_set,sK212_skl))
| in(X0,set_meet(sK212_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ589_spl])],[split_symbol_definition]) ).
fof(f11273,plain,
( ~ sQ285_spl
| sQ589_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f11268,f4890,f11270,f5343]) ).
fof(f11282,plain,
( ~ sQ8_spl
| ~ sQ280_spl
| ~ subset(empty_set,sK216_skl)
| in(ordered_pair(empty_set,sK216_skl),inclusion_relation(sK212_skl)) ),
inference(resolution,[status(thm)],[f5332,f5235]) ).
fof(f11292,definition,
( sQ591_spl
<=> in(ordered_pair(empty_set,sK216_skl),inclusion_relation(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ591_spl])],[split_symbol_definition]) ).
fof(f11295,definition,
( sQ592_spl
<=> subset(empty_set,sK216_skl) ),
introduced(definition,[new_symbols(definition,[sQ592_spl])],[split_symbol_definition]) ).
fof(f11297,plain,
( sQ592_spl
| ~ subset(empty_set,sK216_skl) ),
inference(component_clause,[status(thm)],[f11295]) ).
fof(f11298,plain,
( ~ sQ8_spl
| ~ sQ280_spl
| ~ sQ592_spl
| sQ591_spl ),
inference(split_clause,[status(thm)],[f11282,f11292,f11295,f5311,f2167]) ).
fof(f11299,plain,
( sQ592_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11297,f1620]) ).
fof(f11300,plain,
sQ592_spl,
inference(contradiction_clause,[status(thm)],[f11299]) ).
fof(f11326,plain,
( sQ394_spl
| ~ sQ280_spl
| ~ relation(empty_set) ),
inference(backward_demodulation,[status(thm)],[f5312,f8264]) ).
fof(f11352,plain,
( sQ394_spl
| ~ sQ280_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f11326,f2403,f5311,f8262]) ).
fof(f11401,plain,
! [X0,X1] :
( X0 = X1
| apply(sK115_skl,X0) != apply(sK115_skl,X1)
| ~ in(X1,relation_dom(sK115_skl))
| ~ in(X0,relation_dom(sK115_skl))
| ~ function(sK115_skl)
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f855,f1168]) ).
fof(f11402,plain,
! [X0,X1] :
( X0 = X1
| apply(empty_set,X0) != apply(empty_set,X1)
| ~ in(X1,relation_dom(empty_set))
| ~ in(X0,relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f855,f969]) ).
fof(f11404,definition,
! [X0,X1] :
( sQ593_spl
<=> ( X0 = X1
| apply(sK115_skl,X0) != apply(sK115_skl,X1)
| ~ in(X1,relation_dom(sK115_skl))
| ~ in(X0,relation_dom(sK115_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ593_spl])],[split_symbol_definition]) ).
fof(f11407,plain,
( sQ593_spl
| ~ sQ50_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f11401,f2983,f2605,f11404]) ).
fof(f11408,definition,
! [X0,X1] :
( sQ594_spl
<=> ( X0 = X1
| apply(empty_set,X0) != apply(empty_set,X1)
| ~ in(X1,relation_dom(empty_set))
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ594_spl])],[split_symbol_definition]) ).
fof(f11411,plain,
( sQ594_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f11402,f2403,f2362,f11408]) ).
fof(f11498,plain,
( ~ sQ207_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4304,f2222]) ).
fof(f11499,plain,
~ sQ207_spl,
inference(contradiction_clause,[status(thm)],[f11498]) ).
fof(f11526,plain,
! [X0] :
( in(ordered_pair(sK29_skl(relation_dom(sK118_skl),X0),apply(sK118_skl,sK29_skl(relation_dom(sK118_skl),X0))),sK118_skl)
| ~ relation(sK118_skl)
| sK29_skl(relation_dom(sK118_skl),X0) = X0
| relation_dom(sK118_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4700,f1180]) ).
fof(f11528,plain,
! [X0] :
( in(ordered_pair(sK29_skl(relation_dom(sK214_skl),X0),apply(sK214_skl,sK29_skl(relation_dom(sK214_skl),X0))),sK214_skl)
| ~ relation(sK214_skl)
| sK29_skl(relation_dom(sK214_skl),X0) = X0
| relation_dom(sK214_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4700,f1731]) ).
fof(f11529,plain,
! [X0] :
( in(ordered_pair(sK29_skl(relation_dom(sK115_skl),X0),apply(sK115_skl,sK29_skl(relation_dom(sK115_skl),X0))),sK115_skl)
| ~ relation(sK115_skl)
| sK29_skl(relation_dom(sK115_skl),X0) = X0
| relation_dom(sK115_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4700,f1167]) ).
fof(f11530,plain,
! [X0] :
( ~ sQ15_spl
| in(ordered_pair(sK29_skl(relation_dom(sK102_skl),X0),apply(sK102_skl,sK29_skl(relation_dom(sK102_skl),X0))),sK102_skl)
| ~ relation(sK102_skl)
| sK29_skl(relation_dom(sK102_skl),X0) = X0
| relation_dom(sK102_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4700,f2373]) ).
fof(f11535,plain,
! [X0] :
( in(ordered_pair(sK29_skl(relation_dom(empty_set),X0),apply(empty_set,sK29_skl(relation_dom(empty_set),X0))),empty_set)
| ~ relation(empty_set)
| sK29_skl(relation_dom(empty_set),X0) = X0
| relation_dom(empty_set) = singleton(X0) ),
inference(resolution,[status(thm)],[f4700,f968]) ).
fof(f11538,definition,
! [X0] :
( sQ595_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(sK118_skl),X0),apply(sK118_skl,sK29_skl(relation_dom(sK118_skl),X0))),sK118_skl)
| sK29_skl(relation_dom(sK118_skl),X0) = X0
| relation_dom(sK118_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ595_spl])],[split_symbol_definition]) ).
fof(f11541,plain,
( ~ sQ86_spl
| sQ595_spl ),
inference(split_clause,[status(thm)],[f11526,f11538,f2976]) ).
fof(f11543,definition,
! [X0] :
( sQ596_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(sK214_skl),X0),apply(sK214_skl,sK29_skl(relation_dom(sK214_skl),X0))),sK214_skl)
| sK29_skl(relation_dom(sK214_skl),X0) = X0
| relation_dom(sK214_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ596_spl])],[split_symbol_definition]) ).
fof(f11546,plain,
( ~ sQ10_spl
| sQ596_spl ),
inference(split_clause,[status(thm)],[f11528,f11543,f2351]) ).
fof(f11547,definition,
! [X0] :
( sQ597_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(sK115_skl),X0),apply(sK115_skl,sK29_skl(relation_dom(sK115_skl),X0))),sK115_skl)
| sK29_skl(relation_dom(sK115_skl),X0) = X0
| relation_dom(sK115_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f11550,plain,
( ~ sQ88_spl
| sQ597_spl ),
inference(split_clause,[status(thm)],[f11529,f11547,f2983]) ).
fof(f11551,definition,
! [X0] :
( sQ598_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(sK102_skl),X0),apply(sK102_skl,sK29_skl(relation_dom(sK102_skl),X0))),sK102_skl)
| sK29_skl(relation_dom(sK102_skl),X0) = X0
| relation_dom(sK102_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ598_spl])],[split_symbol_definition]) ).
fof(f11554,plain,
( ~ sQ15_spl
| ~ sQ82_spl
| sQ598_spl ),
inference(split_clause,[status(thm)],[f11530,f11551,f2936,f2372]) ).
fof(f11567,definition,
! [X0] :
( sQ599_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(empty_set),X0),apply(empty_set,sK29_skl(relation_dom(empty_set),X0))),empty_set)
| sK29_skl(relation_dom(empty_set),X0) = X0
| relation_dom(empty_set) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ599_spl])],[split_symbol_definition]) ).
fof(f11570,plain,
( ~ sQ20_spl
| sQ599_spl ),
inference(split_clause,[status(thm)],[f11535,f11567,f2403]) ).
fof(f11573,plain,
! [X0,X1] :
( ~ in(apply(sK118_skl,sK29_skl(relation_dom(sK118_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK118_skl),X0),relation_inverse_image(sK118_skl,X1))
| ~ relation(sK118_skl)
| sK29_skl(relation_dom(sK118_skl),X0) = X0
| relation_dom(sK118_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4701,f1180]) ).
fof(f11575,plain,
! [X0,X1] :
( ~ in(apply(sK214_skl,sK29_skl(relation_dom(sK214_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK214_skl),X0),relation_inverse_image(sK214_skl,X1))
| ~ relation(sK214_skl)
| sK29_skl(relation_dom(sK214_skl),X0) = X0
| relation_dom(sK214_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4701,f1731]) ).
fof(f11576,plain,
! [X0,X1] :
( ~ in(apply(sK115_skl,sK29_skl(relation_dom(sK115_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK115_skl),X0),relation_inverse_image(sK115_skl,X1))
| ~ relation(sK115_skl)
| sK29_skl(relation_dom(sK115_skl),X0) = X0
| relation_dom(sK115_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4701,f1167]) ).
fof(f11577,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ in(apply(sK102_skl,sK29_skl(relation_dom(sK102_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK102_skl),X0),relation_inverse_image(sK102_skl,X1))
| ~ relation(sK102_skl)
| sK29_skl(relation_dom(sK102_skl),X0) = X0
| relation_dom(sK102_skl) = singleton(X0) ),
inference(resolution,[status(thm)],[f4701,f2373]) ).
fof(f11582,plain,
! [X0,X1] :
( ~ in(apply(empty_set,sK29_skl(relation_dom(empty_set),X0)),X1)
| in(sK29_skl(relation_dom(empty_set),X0),relation_inverse_image(empty_set,X1))
| ~ relation(empty_set)
| sK29_skl(relation_dom(empty_set),X0) = X0
| relation_dom(empty_set) = singleton(X0) ),
inference(resolution,[status(thm)],[f4701,f968]) ).
fof(f11585,definition,
! [X0,X1] :
( sQ600_spl
<=> ( ~ in(apply(sK118_skl,sK29_skl(relation_dom(sK118_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK118_skl),X0),relation_inverse_image(sK118_skl,X1))
| sK29_skl(relation_dom(sK118_skl),X0) = X0
| relation_dom(sK118_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition]) ).
fof(f11588,plain,
( ~ sQ86_spl
| sQ600_spl ),
inference(split_clause,[status(thm)],[f11573,f11585,f2976]) ).
fof(f11590,definition,
! [X0,X1] :
( sQ601_spl
<=> ( ~ in(apply(sK214_skl,sK29_skl(relation_dom(sK214_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK214_skl),X0),relation_inverse_image(sK214_skl,X1))
| sK29_skl(relation_dom(sK214_skl),X0) = X0
| relation_dom(sK214_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ601_spl])],[split_symbol_definition]) ).
fof(f11593,plain,
( ~ sQ10_spl
| sQ601_spl ),
inference(split_clause,[status(thm)],[f11575,f11590,f2351]) ).
fof(f11594,definition,
! [X0,X1] :
( sQ602_spl
<=> ( ~ in(apply(sK115_skl,sK29_skl(relation_dom(sK115_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK115_skl),X0),relation_inverse_image(sK115_skl,X1))
| sK29_skl(relation_dom(sK115_skl),X0) = X0
| relation_dom(sK115_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ602_spl])],[split_symbol_definition]) ).
fof(f11597,plain,
( ~ sQ88_spl
| sQ602_spl ),
inference(split_clause,[status(thm)],[f11576,f11594,f2983]) ).
fof(f11598,definition,
! [X0,X1] :
( sQ603_spl
<=> ( ~ in(apply(sK102_skl,sK29_skl(relation_dom(sK102_skl),X0)),X1)
| in(sK29_skl(relation_dom(sK102_skl),X0),relation_inverse_image(sK102_skl,X1))
| sK29_skl(relation_dom(sK102_skl),X0) = X0
| relation_dom(sK102_skl) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ603_spl])],[split_symbol_definition]) ).
fof(f11601,plain,
( ~ sQ15_spl
| ~ sQ82_spl
| sQ603_spl ),
inference(split_clause,[status(thm)],[f11577,f11598,f2936,f2372]) ).
fof(f11614,definition,
! [X0,X1] :
( sQ604_spl
<=> ( ~ in(apply(empty_set,sK29_skl(relation_dom(empty_set),X0)),X1)
| in(sK29_skl(relation_dom(empty_set),X0),relation_inverse_image(empty_set,X1))
| sK29_skl(relation_dom(empty_set),X0) = X0
| relation_dom(empty_set) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ604_spl])],[split_symbol_definition]) ).
fof(f11617,plain,
( ~ sQ20_spl
| sQ604_spl ),
inference(split_clause,[status(thm)],[f11582,f11614,f2403]) ).
fof(f11625,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| well_ordering(empty_set)
| ~ ordinal(empty_set) ),
inference(paramodulation,[status(thm)],[f10197,f1873]) ).
fof(f11626,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| sQ499_spl
| ~ sQ359_spl ),
inference(split_clause,[status(thm)],[f11625,f7648,f10216,f10105,f10144]) ).
fof(f11908,plain,
! [X0,X1] :
( in(sK29_skl(relation_inverse_image(sK118_skl,X0),X1),relation_dom(sK118_skl))
| ~ relation(sK118_skl)
| sK29_skl(relation_inverse_image(sK118_skl,X0),X1) = X1
| relation_inverse_image(sK118_skl,X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f4710,f1180]) ).
fof(f11910,plain,
! [X0,X1] :
( in(sK29_skl(relation_inverse_image(sK214_skl,X0),X1),relation_dom(sK214_skl))
| ~ relation(sK214_skl)
| sK29_skl(relation_inverse_image(sK214_skl,X0),X1) = X1
| relation_inverse_image(sK214_skl,X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f4710,f1731]) ).
fof(f11911,plain,
! [X0,X1] :
( in(sK29_skl(relation_inverse_image(sK115_skl,X0),X1),relation_dom(sK115_skl))
| ~ relation(sK115_skl)
| sK29_skl(relation_inverse_image(sK115_skl,X0),X1) = X1
| relation_inverse_image(sK115_skl,X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f4710,f1167]) ).
fof(f11912,plain,
! [X0,X1] :
( ~ sQ15_spl
| in(sK29_skl(relation_inverse_image(sK102_skl,X0),X1),relation_dom(sK102_skl))
| ~ relation(sK102_skl)
| sK29_skl(relation_inverse_image(sK102_skl,X0),X1) = X1
| relation_inverse_image(sK102_skl,X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f4710,f2373]) ).
fof(f11917,plain,
! [X0,X1] :
( in(sK29_skl(relation_inverse_image(empty_set,X0),X1),relation_dom(empty_set))
| ~ relation(empty_set)
| sK29_skl(relation_inverse_image(empty_set,X0),X1) = X1
| relation_inverse_image(empty_set,X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f4710,f968]) ).
fof(f11920,definition,
! [X0,X1] :
( sQ611_spl
<=> ( in(sK29_skl(relation_inverse_image(sK118_skl,X0),X1),relation_dom(sK118_skl))
| sK29_skl(relation_inverse_image(sK118_skl,X0),X1) = X1
| relation_inverse_image(sK118_skl,X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ611_spl])],[split_symbol_definition]) ).
fof(f11923,plain,
( ~ sQ86_spl
| sQ611_spl ),
inference(split_clause,[status(thm)],[f11908,f11920,f2976]) ).
fof(f11925,definition,
! [X0,X1] :
( sQ612_spl
<=> ( in(sK29_skl(relation_inverse_image(sK214_skl,X0),X1),relation_dom(sK214_skl))
| sK29_skl(relation_inverse_image(sK214_skl,X0),X1) = X1
| relation_inverse_image(sK214_skl,X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f11928,plain,
( ~ sQ10_spl
| sQ612_spl ),
inference(split_clause,[status(thm)],[f11910,f11925,f2351]) ).
fof(f11929,definition,
! [X0,X1] :
( sQ613_spl
<=> ( in(sK29_skl(relation_inverse_image(sK115_skl,X0),X1),relation_dom(sK115_skl))
| sK29_skl(relation_inverse_image(sK115_skl,X0),X1) = X1
| relation_inverse_image(sK115_skl,X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ613_spl])],[split_symbol_definition]) ).
fof(f11932,plain,
( ~ sQ88_spl
| sQ613_spl ),
inference(split_clause,[status(thm)],[f11911,f11929,f2983]) ).
fof(f11933,definition,
! [X0,X1] :
( sQ614_spl
<=> ( in(sK29_skl(relation_inverse_image(sK102_skl,X0),X1),relation_dom(sK102_skl))
| sK29_skl(relation_inverse_image(sK102_skl,X0),X1) = X1
| relation_inverse_image(sK102_skl,X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f11936,plain,
( ~ sQ15_spl
| ~ sQ82_spl
| sQ614_spl ),
inference(split_clause,[status(thm)],[f11912,f11933,f2936,f2372]) ).
fof(f11943,definition,
! [X0,X1] :
( sQ615_spl
<=> ( in(sK29_skl(relation_inverse_image(empty_set,X0),X1),relation_dom(empty_set))
| sK29_skl(relation_inverse_image(empty_set,X0),X1) = X1
| relation_inverse_image(empty_set,X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f11946,plain,
( ~ sQ20_spl
| sQ615_spl ),
inference(split_clause,[status(thm)],[f11917,f11943,f2403]) ).
fof(f11950,plain,
! [X0] :
( in(apply(sK214_skl,sK29_skl(sK212_skl,X0)),relation_rng(sK214_skl))
| sK213_skl = empty_set
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| sK29_skl(sK212_skl,X0) = X0
| sK212_skl = singleton(X0) ),
inference(resolution,[status(thm)],[f4712,f1732]) ).
fof(f11952,definition,
! [X0] :
( sQ616_spl
<=> ( in(apply(sK214_skl,sK29_skl(sK212_skl,X0)),relation_rng(sK214_skl))
| sK29_skl(sK212_skl,X0) = X0
| sK212_skl = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ616_spl])],[split_symbol_definition]) ).
fof(f11955,plain,
( sQ104_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ616_spl ),
inference(split_clause,[status(thm)],[f11950,f11952,f2354,f3178,f3184]) ).
fof(f11968,plain,
! [X0,X1,X2] :
( ~ sQ494_spl
| in(ordered_pair(X0,X2),empty_set)
| ~ in(ordered_pair(X1,X2),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X2,empty_set)
| ~ in(X1,empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f874,f10180]) ).
fof(f11971,definition,
! [X0,X1,X2] :
( sQ617_spl
<=> ( in(ordered_pair(X0,X2),empty_set)
| ~ in(ordered_pair(X1,X2),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ in(X2,empty_set)
| ~ in(X1,empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ617_spl])],[split_symbol_definition]) ).
fof(f11974,plain,
( ~ sQ494_spl
| sQ617_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f11968,f2403,f11971,f10179]) ).
fof(f12034,definition,
( sQ623_spl
<=> relation_inverse_image(identity_relation(empty_set),sK42_skl(empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ623_spl])],[split_symbol_definition]) ).
fof(f12036,plain,
( sQ623_spl
| relation_inverse_image(identity_relation(empty_set),sK42_skl(empty_set)) != empty_set ),
inference(component_clause,[status(thm)],[f12034]) ).
fof(f12039,definition,
( sQ624_spl
<=> subset(empty_set,sK42_skl(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ624_spl])],[split_symbol_definition]) ).
fof(f12041,plain,
( sQ624_spl
| ~ subset(empty_set,sK42_skl(empty_set)) ),
inference(component_clause,[status(thm)],[f12039]) ).
fof(f12043,plain,
( sQ624_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12041,f1620]) ).
fof(f12044,plain,
sQ624_spl,
inference(contradiction_clause,[status(thm)],[f12043]) ).
fof(f12045,plain,
( sQ623_spl
| relation_inverse_image(empty_set,sK42_skl(empty_set)) != empty_set ),
inference(forward_demodulation,[status(thm)],[f2814,f12036]) ).
fof(f12046,plain,
( sQ623_spl
| ~ sQ47_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f2762,f12045]) ).
fof(f12047,plain,
( sQ623_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f12046]) ).
fof(f12048,plain,
( sQ623_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f12047]) ).
fof(f12099,plain,
! [X0,X1] :
( apply(relation_composition(sK214_skl,X1),sK29_skl(sK212_skl,X0)) = apply(X1,apply(sK214_skl,sK29_skl(sK212_skl,X0)))
| sK213_skl = empty_set
| ~ function(X1)
| ~ relation(X1)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| sK29_skl(sK212_skl,X0) = X0
| sK212_skl = singleton(X0) ),
inference(resolution,[status(thm)],[f4715,f1732]) ).
fof(f12101,definition,
! [X0,X1] :
( sQ626_spl
<=> ( apply(relation_composition(sK214_skl,X1),sK29_skl(sK212_skl,X0)) = apply(X1,apply(sK214_skl,sK29_skl(sK212_skl,X0)))
| ~ function(X1)
| ~ relation(X1)
| sK29_skl(sK212_skl,X0) = X0
| sK212_skl = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ626_spl])],[split_symbol_definition]) ).
fof(f12104,plain,
( sQ104_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ626_spl ),
inference(split_clause,[status(thm)],[f12099,f12101,f2354,f3178,f3184]) ).
fof(f12200,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| in(sK20_skl(X2,ordered_pair(X0,X1)),relation_dom(sK115_skl))
| X2 = X0
| sK21_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),sK115_skl)
| ~ function(sK115_skl)
| ~ relation(sK115_skl) ),
inference(paramodulation,[status(thm)],[f2609,f3866]) ).
fof(f12201,plain,
! [X0] :
( ~ sQ51_spl
| in(sK69_skl(X0,sK115_skl),relation_dom(sK115_skl))
| sK68_skl(X0,sK115_skl) = empty_set
| in(sK68_skl(X0,sK115_skl),X0)
| X0 = relation_rng(sK115_skl)
| ~ function(sK115_skl)
| ~ relation(sK115_skl) ),
inference(paramodulation,[status(thm)],[f2609,f788]) ).
fof(f12209,definition,
! [X0,X1,X2] :
( sQ629_spl
<=> ( in(sK20_skl(X2,ordered_pair(X0,X1)),relation_dom(sK115_skl))
| X2 = X0
| sK21_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),sK115_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ629_spl])],[split_symbol_definition]) ).
fof(f12212,plain,
( ~ sQ51_spl
| sQ629_spl
| ~ sQ50_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f12200,f2983,f2605,f12209,f2608]) ).
fof(f12213,definition,
! [X0] :
( sQ630_spl
<=> ( in(sK69_skl(X0,sK115_skl),relation_dom(sK115_skl))
| sK68_skl(X0,sK115_skl) = empty_set
| in(sK68_skl(X0,sK115_skl),X0)
| X0 = relation_rng(sK115_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ630_spl])],[split_symbol_definition]) ).
fof(f12216,plain,
( ~ sQ51_spl
| sQ630_spl
| ~ sQ50_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f12201,f2983,f2605,f12213,f2608]) ).
fof(f12252,plain,
! [X0,X1,X2] :
( ~ sQ28_spl
| in(sK20_skl(X2,ordered_pair(X0,X1)),relation_dom(sK102_skl))
| X2 = X0
| sK21_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),sK102_skl)
| ~ function(sK102_skl)
| ~ relation(sK102_skl) ),
inference(paramodulation,[status(thm)],[f2469,f3866]) ).
fof(f12253,plain,
! [X0] :
( ~ sQ28_spl
| in(sK69_skl(X0,sK102_skl),relation_dom(sK102_skl))
| sK68_skl(X0,sK102_skl) = empty_set
| in(sK68_skl(X0,sK102_skl),X0)
| X0 = relation_rng(sK102_skl)
| ~ function(sK102_skl)
| ~ relation(sK102_skl) ),
inference(paramodulation,[status(thm)],[f2469,f788]) ).
fof(f12261,definition,
! [X0,X1,X2] :
( sQ634_spl
<=> ( in(sK20_skl(X2,ordered_pair(X0,X1)),relation_dom(sK102_skl))
| X2 = X0
| sK21_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),sK102_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ634_spl])],[split_symbol_definition]) ).
fof(f12264,plain,
( ~ sQ28_spl
| sQ634_spl
| ~ sQ15_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f12252,f2936,f2372,f12261,f2468]) ).
fof(f12265,definition,
! [X0] :
( sQ635_spl
<=> ( in(sK69_skl(X0,sK102_skl),relation_dom(sK102_skl))
| sK68_skl(X0,sK102_skl) = empty_set
| in(sK68_skl(X0,sK102_skl),X0)
| X0 = relation_rng(sK102_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ635_spl])],[split_symbol_definition]) ).
fof(f12268,plain,
( ~ sQ28_spl
| sQ635_spl
| ~ sQ15_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f12253,f2936,f2372,f12265,f2468]) ).
fof(f12293,plain,
relation_inverse(relation_inverse(sK112_skl)) = sK112_skl,
inference(resolution,[status(thm)],[f1030,f1159]) ).
fof(f12299,plain,
relation_inverse(relation_inverse(sK214_skl)) = sK214_skl,
inference(resolution,[status(thm)],[f1030,f2515]) ).
fof(f12301,plain,
relation_inverse(relation_inverse(sK102_skl)) = sK102_skl,
inference(resolution,[status(thm)],[f1030,f1116]) ).
fof(f12302,plain,
relation_inverse(relation_inverse(sK115_skl)) = sK115_skl,
inference(resolution,[status(thm)],[f1030,f1166]) ).
fof(f12328,plain,
( ~ sQ225_spl
| relation_inverse(empty_set) = sK112_skl ),
inference(forward_demodulation,[status(thm)],[f4436,f12293]) ).
fof(f12329,plain,
( ~ sQ225_spl
| empty_set = sK112_skl ),
inference(forward_demodulation,[status(thm)],[f5781,f12328]) ).
fof(f12330,plain,
( ~ sQ225_spl
| sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12329,f2571]) ).
fof(f12331,plain,
( ~ sQ225_spl
| sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f12330]) ).
fof(f12336,plain,
( ~ sQ211_spl
| relation_inverse(empty_set) = sK214_skl ),
inference(forward_demodulation,[status(thm)],[f4336,f12299]) ).
fof(f12337,plain,
( ~ sQ211_spl
| empty_set = sK214_skl ),
inference(forward_demodulation,[status(thm)],[f5781,f12336]) ).
fof(f12338,plain,
( ~ sQ211_spl
| sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12337,f2564]) ).
fof(f12339,plain,
( ~ sQ211_spl
| sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f12338]) ).
fof(f13309,plain,
( function_inverse(sK115_skl) = relation_inverse(sK115_skl)
| ~ function(sK115_skl)
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f895,f1168]) ).
fof(f13310,plain,
( function_inverse(empty_set) = relation_inverse(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f895,f969]) ).
fof(f13315,definition,
( sQ636_spl
<=> function_inverse(sK115_skl) = relation_inverse(sK115_skl) ),
introduced(definition,[new_symbols(definition,[sQ636_spl])],[split_symbol_definition]) ).
fof(f13316,plain,
( ~ sQ636_spl
| function_inverse(sK115_skl) = relation_inverse(sK115_skl) ),
inference(component_clause,[status(thm)],[f13315]) ).
fof(f13318,plain,
( sQ636_spl
| ~ sQ50_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13309,f2983,f2605,f13315]) ).
fof(f13319,definition,
( sQ637_spl
<=> function_inverse(empty_set) = relation_inverse(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f13322,plain,
( sQ637_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f13310,f2403,f2362,f13319]) ).
fof(f13327,plain,
( ~ sQ507_spl
| is_reflexive_in(empty_set,relation_field(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f898,f10293]) ).
fof(f13330,definition,
( sQ638_spl
<=> is_reflexive_in(empty_set,relation_field(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ638_spl])],[split_symbol_definition]) ).
fof(f13333,plain,
( ~ sQ507_spl
| sQ638_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f13327,f2403,f13330,f10292]) ).
fof(f13352,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK30_skl(X0,X1,empty_set),X1),empty_set)
| sK30_skl(X0,X1,empty_set) = X1
| X0 = fiber(empty_set,X1)
| ~ relation(empty_set)
| sK30_skl(X0,X1,empty_set) != X1
| X0 = fiber(empty_set,X1) ),
inference(resolution,[status(thm)],[f5111,f582]) ).
fof(f13395,definition,
! [X0,X1] :
( sQ639_spl
<=> ( ~ in(ordered_pair(sK30_skl(X0,X1,empty_set),X1),empty_set)
| sK30_skl(X0,X1,empty_set) = X1
| X0 = fiber(empty_set,X1)
| sK30_skl(X0,X1,empty_set) != X1
| X0 = fiber(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ639_spl])],[split_symbol_definition]) ).
fof(f13398,plain,
( ~ sQ20_spl
| sQ639_spl ),
inference(split_clause,[status(thm)],[f13352,f13395,f2403]) ).
fof(f13399,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK30_skl(X0,X1,empty_set),X1),empty_set)
| sK30_skl(X0,X1,empty_set) = X1
| X0 = fiber(empty_set,X1)
| ~ relation(empty_set)
| X0 = fiber(empty_set,X1) ),
inference(resolution,[status(thm)],[f5130,f582]) ).
fof(f13418,plain,
! [X0] : empty_set = fiber(empty_set,X0),
inference(resolution,[status(thm)],[f5130,f2222]) ).
fof(f13442,definition,
! [X0,X1] :
( sQ640_spl
<=> ( ~ in(ordered_pair(sK30_skl(X0,X1,empty_set),X1),empty_set)
| sK30_skl(X0,X1,empty_set) = X1
| X0 = fiber(empty_set,X1)
| X0 = fiber(empty_set,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ640_spl])],[split_symbol_definition]) ).
fof(f13445,plain,
( ~ sQ20_spl
| sQ640_spl ),
inference(split_clause,[status(thm)],[f13399,f13442,f2403]) ).
fof(f13517,plain,
( relation(function_inverse(sK214_skl))
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f902,f1731]) ).
fof(f13518,plain,
( relation(function_inverse(sK115_skl))
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f902,f1167]) ).
fof(f13519,plain,
( ~ sQ15_spl
| relation(function_inverse(sK102_skl))
| ~ relation(sK102_skl) ),
inference(resolution,[status(thm)],[f902,f2373]) ).
fof(f13524,plain,
( relation(function_inverse(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f902,f968]) ).
fof(f13528,definition,
( sQ641_spl
<=> relation(function_inverse(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ641_spl])],[split_symbol_definition]) ).
fof(f13529,plain,
( ~ sQ641_spl
| relation(function_inverse(sK214_skl)) ),
inference(component_clause,[status(thm)],[f13528]) ).
fof(f13531,plain,
( sQ641_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f13517,f2351,f13528]) ).
fof(f13532,definition,
( sQ642_spl
<=> relation(function_inverse(sK115_skl)) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f13533,plain,
( ~ sQ642_spl
| relation(function_inverse(sK115_skl)) ),
inference(component_clause,[status(thm)],[f13532]) ).
fof(f13535,plain,
( sQ642_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13518,f2983,f13532]) ).
fof(f13536,definition,
( sQ643_spl
<=> relation(function_inverse(sK102_skl)) ),
introduced(definition,[new_symbols(definition,[sQ643_spl])],[split_symbol_definition]) ).
fof(f13537,plain,
( ~ sQ643_spl
| relation(function_inverse(sK102_skl)) ),
inference(component_clause,[status(thm)],[f13536]) ).
fof(f13539,plain,
( ~ sQ15_spl
| sQ643_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f13519,f2936,f13536,f2372]) ).
fof(f13544,definition,
( sQ644_spl
<=> relation(function_inverse(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ644_spl])],[split_symbol_definition]) ).
fof(f13547,plain,
( sQ644_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f13524,f2403,f13544]) ).
fof(f13549,plain,
( function(function_inverse(sK214_skl))
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f903,f1731]) ).
fof(f13550,plain,
( function(function_inverse(sK115_skl))
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f903,f1167]) ).
fof(f13551,plain,
( ~ sQ15_spl
| function(function_inverse(sK102_skl))
| ~ relation(sK102_skl) ),
inference(resolution,[status(thm)],[f903,f2373]) ).
fof(f13556,plain,
( function(function_inverse(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f903,f968]) ).
fof(f13560,definition,
( sQ645_spl
<=> function(function_inverse(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ645_spl])],[split_symbol_definition]) ).
fof(f13561,plain,
( ~ sQ645_spl
| function(function_inverse(sK214_skl)) ),
inference(component_clause,[status(thm)],[f13560]) ).
fof(f13563,plain,
( sQ645_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f13549,f2351,f13560]) ).
fof(f13564,definition,
( sQ646_spl
<=> function(function_inverse(sK115_skl)) ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f13565,plain,
( ~ sQ646_spl
| function(function_inverse(sK115_skl)) ),
inference(component_clause,[status(thm)],[f13564]) ).
fof(f13567,plain,
( sQ646_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f13550,f2983,f13564]) ).
fof(f13568,definition,
( sQ647_spl
<=> function(function_inverse(sK102_skl)) ),
introduced(definition,[new_symbols(definition,[sQ647_spl])],[split_symbol_definition]) ).
fof(f13569,plain,
( ~ sQ647_spl
| function(function_inverse(sK102_skl)) ),
inference(component_clause,[status(thm)],[f13568]) ).
fof(f13571,plain,
( ~ sQ15_spl
| sQ647_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f13551,f2936,f13568,f2372]) ).
fof(f13576,definition,
( sQ648_spl
<=> function(function_inverse(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f13579,plain,
( sQ648_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f13556,f2403,f13576]) ).
fof(f13609,plain,
! [X0,X1] :
( ~ sQ641_spl
| in(apply(function_inverse(sK214_skl),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(sK214_skl),X1))
| ~ function(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13529,f2190]) ).
fof(f13617,definition,
! [X0,X1] :
( sQ651_spl
<=> ( in(apply(function_inverse(sK214_skl),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(sK214_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f13620,plain,
( ~ sQ641_spl
| sQ651_spl
| ~ sQ645_spl ),
inference(split_clause,[status(thm)],[f13609,f13560,f13617,f13528]) ).
fof(f13665,plain,
! [X0,X1] :
( ~ sQ643_spl
| in(apply(function_inverse(sK102_skl),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(sK102_skl),X1))
| ~ function(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13537,f2190]) ).
fof(f13673,definition,
! [X0,X1] :
( sQ654_spl
<=> ( in(apply(function_inverse(sK102_skl),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(sK102_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ654_spl])],[split_symbol_definition]) ).
fof(f13676,plain,
( ~ sQ643_spl
| sQ654_spl
| ~ sQ647_spl ),
inference(split_clause,[status(thm)],[f13665,f13568,f13673,f13536]) ).
fof(f13756,plain,
! [X0,X1] :
( ~ sQ642_spl
| in(apply(function_inverse(sK115_skl),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(sK115_skl),X1))
| ~ function(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13533,f2190]) ).
fof(f13764,definition,
! [X0,X1] :
( sQ659_spl
<=> ( in(apply(function_inverse(sK115_skl),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(sK115_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ659_spl])],[split_symbol_definition]) ).
fof(f13767,plain,
( ~ sQ642_spl
| sQ659_spl
| ~ sQ646_spl ),
inference(split_clause,[status(thm)],[f13756,f13564,f13764,f13532]) ).
fof(f13768,plain,
( ~ sQ647_spl
| function(function_inverse(function_inverse(sK102_skl)))
| ~ relation(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13569,f903]) ).
fof(f13769,plain,
( ~ sQ647_spl
| relation(function_inverse(function_inverse(sK102_skl)))
| ~ relation(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13569,f902]) ).
fof(f13770,plain,
! [X0,X1] :
( ~ sQ647_spl
| in(sK29_skl(relation_inverse_image(function_inverse(sK102_skl),X0),X1),relation_dom(function_inverse(sK102_skl)))
| ~ relation(function_inverse(sK102_skl))
| sK29_skl(relation_inverse_image(function_inverse(sK102_skl),X0),X1) = X1
| relation_inverse_image(function_inverse(sK102_skl),X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f13569,f4710]) ).
fof(f13771,plain,
! [X0,X1] :
( ~ sQ647_spl
| ~ in(apply(function_inverse(sK102_skl),sK29_skl(relation_dom(function_inverse(sK102_skl)),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(sK102_skl)),X0),relation_inverse_image(function_inverse(sK102_skl),X1))
| ~ relation(function_inverse(sK102_skl))
| sK29_skl(relation_dom(function_inverse(sK102_skl)),X0) = X0
| relation_dom(function_inverse(sK102_skl)) = singleton(X0) ),
inference(resolution,[status(thm)],[f13569,f4701]) ).
fof(f13772,plain,
! [X0] :
( ~ sQ647_spl
| in(ordered_pair(sK29_skl(relation_dom(function_inverse(sK102_skl)),X0),apply(function_inverse(sK102_skl),sK29_skl(relation_dom(function_inverse(sK102_skl)),X0))),function_inverse(sK102_skl))
| ~ relation(function_inverse(sK102_skl))
| sK29_skl(relation_dom(function_inverse(sK102_skl)),X0) = X0
| relation_dom(function_inverse(sK102_skl)) = singleton(X0) ),
inference(resolution,[status(thm)],[f13569,f4700]) ).
fof(f13773,plain,
! [X0,X1] :
( ~ sQ647_spl
| in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(sK102_skl),X0)),relation_inverse_image(function_inverse(sK102_skl),X0)),relation_dom(function_inverse(sK102_skl)))
| ~ relation(function_inverse(sK102_skl))
| in(X1,set_meet(relation_inverse_image(function_inverse(sK102_skl),X0)))
| relation_inverse_image(function_inverse(sK102_skl),X0) = empty_set ),
inference(resolution,[status(thm)],[f13569,f4287]) ).
fof(f13777,plain,
! [X0] :
( ~ sQ647_spl
| X0 = apply(function_inverse(sK102_skl),sK67_skl(X0,relation_rng(function_inverse(sK102_skl)),function_inverse(sK102_skl)))
| ~ in(X0,relation_rng(function_inverse(sK102_skl)))
| ~ relation(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13569,f2252]) ).
fof(f13778,plain,
! [X0] :
( ~ sQ647_spl
| in(sK67_skl(X0,relation_rng(function_inverse(sK102_skl)),function_inverse(sK102_skl)),relation_dom(function_inverse(sK102_skl)))
| ~ in(X0,relation_rng(function_inverse(sK102_skl)))
| ~ relation(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13569,f2251]) ).
fof(f13779,plain,
! [X0] :
( ~ sQ647_spl
| apply(function_inverse(sK102_skl),X0) = empty_set
| in(X0,relation_dom(function_inverse(sK102_skl)))
| ~ relation(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13569,f2240]) ).
fof(f13780,plain,
! [X0,X1] :
( ~ sQ647_spl
| in(apply(function_inverse(sK102_skl),sK9_skl(X0,X1,function_inverse(sK102_skl))),X1)
| in(sK9_skl(X0,X1,function_inverse(sK102_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK102_skl),X1)
| ~ relation(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13569,f475]) ).
fof(f13781,plain,
! [X0,X1] :
( ~ sQ647_spl
| in(sK9_skl(X0,X1,function_inverse(sK102_skl)),relation_dom(function_inverse(sK102_skl)))
| in(sK9_skl(X0,X1,function_inverse(sK102_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK102_skl),X1)
| ~ relation(function_inverse(sK102_skl)) ),
inference(resolution,[status(thm)],[f13569,f474]) ).
fof(f13782,definition,
( sQ660_spl
<=> function(function_inverse(function_inverse(sK102_skl))) ),
introduced(definition,[new_symbols(definition,[sQ660_spl])],[split_symbol_definition]) ).
fof(f13785,plain,
( ~ sQ647_spl
| sQ660_spl
| ~ sQ643_spl ),
inference(split_clause,[status(thm)],[f13768,f13536,f13782,f13568]) ).
fof(f13786,definition,
( sQ661_spl
<=> relation(function_inverse(function_inverse(sK102_skl))) ),
introduced(definition,[new_symbols(definition,[sQ661_spl])],[split_symbol_definition]) ).
fof(f13789,plain,
( ~ sQ647_spl
| sQ661_spl
| ~ sQ643_spl ),
inference(split_clause,[status(thm)],[f13769,f13536,f13786,f13568]) ).
fof(f13790,definition,
! [X0,X1] :
( sQ662_spl
<=> ( in(sK29_skl(relation_inverse_image(function_inverse(sK102_skl),X0),X1),relation_dom(function_inverse(sK102_skl)))
| sK29_skl(relation_inverse_image(function_inverse(sK102_skl),X0),X1) = X1
| relation_inverse_image(function_inverse(sK102_skl),X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ662_spl])],[split_symbol_definition]) ).
fof(f13793,plain,
( ~ sQ647_spl
| ~ sQ643_spl
| sQ662_spl ),
inference(split_clause,[status(thm)],[f13770,f13790,f13536,f13568]) ).
fof(f13794,definition,
! [X0,X1] :
( sQ663_spl
<=> ( ~ in(apply(function_inverse(sK102_skl),sK29_skl(relation_dom(function_inverse(sK102_skl)),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(sK102_skl)),X0),relation_inverse_image(function_inverse(sK102_skl),X1))
| sK29_skl(relation_dom(function_inverse(sK102_skl)),X0) = X0
| relation_dom(function_inverse(sK102_skl)) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f13797,plain,
( ~ sQ647_spl
| ~ sQ643_spl
| sQ663_spl ),
inference(split_clause,[status(thm)],[f13771,f13794,f13536,f13568]) ).
fof(f13798,definition,
! [X0] :
( sQ664_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(function_inverse(sK102_skl)),X0),apply(function_inverse(sK102_skl),sK29_skl(relation_dom(function_inverse(sK102_skl)),X0))),function_inverse(sK102_skl))
| sK29_skl(relation_dom(function_inverse(sK102_skl)),X0) = X0
| relation_dom(function_inverse(sK102_skl)) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ664_spl])],[split_symbol_definition]) ).
fof(f13801,plain,
( ~ sQ647_spl
| ~ sQ643_spl
| sQ664_spl ),
inference(split_clause,[status(thm)],[f13772,f13798,f13536,f13568]) ).
fof(f13802,definition,
! [X0,X1] :
( sQ665_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(sK102_skl),X0)),relation_inverse_image(function_inverse(sK102_skl),X0)),relation_dom(function_inverse(sK102_skl)))
| in(X1,set_meet(relation_inverse_image(function_inverse(sK102_skl),X0)))
| relation_inverse_image(function_inverse(sK102_skl),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f13805,plain,
( ~ sQ647_spl
| ~ sQ643_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f13773,f13802,f13536,f13568]) ).
fof(f13821,definition,
! [X0] :
( sQ670_spl
<=> ( X0 = apply(function_inverse(sK102_skl),sK67_skl(X0,relation_rng(function_inverse(sK102_skl)),function_inverse(sK102_skl)))
| ~ in(X0,relation_rng(function_inverse(sK102_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f13824,plain,
( ~ sQ647_spl
| sQ670_spl
| ~ sQ643_spl ),
inference(split_clause,[status(thm)],[f13777,f13536,f13821,f13568]) ).
fof(f13825,definition,
! [X0] :
( sQ671_spl
<=> ( in(sK67_skl(X0,relation_rng(function_inverse(sK102_skl)),function_inverse(sK102_skl)),relation_dom(function_inverse(sK102_skl)))
| ~ in(X0,relation_rng(function_inverse(sK102_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f13828,plain,
( ~ sQ647_spl
| sQ671_spl
| ~ sQ643_spl ),
inference(split_clause,[status(thm)],[f13778,f13536,f13825,f13568]) ).
fof(f13829,definition,
! [X0] :
( sQ672_spl
<=> ( apply(function_inverse(sK102_skl),X0) = empty_set
| in(X0,relation_dom(function_inverse(sK102_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f13832,plain,
( ~ sQ647_spl
| sQ672_spl
| ~ sQ643_spl ),
inference(split_clause,[status(thm)],[f13779,f13536,f13829,f13568]) ).
fof(f13833,definition,
! [X0,X1] :
( sQ673_spl
<=> ( in(apply(function_inverse(sK102_skl),sK9_skl(X0,X1,function_inverse(sK102_skl))),X1)
| in(sK9_skl(X0,X1,function_inverse(sK102_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK102_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ673_spl])],[split_symbol_definition]) ).
fof(f13836,plain,
( ~ sQ647_spl
| sQ673_spl
| ~ sQ643_spl ),
inference(split_clause,[status(thm)],[f13780,f13536,f13833,f13568]) ).
fof(f13837,definition,
! [X0,X1] :
( sQ674_spl
<=> ( in(sK9_skl(X0,X1,function_inverse(sK102_skl)),relation_dom(function_inverse(sK102_skl)))
| in(sK9_skl(X0,X1,function_inverse(sK102_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK102_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f13840,plain,
( ~ sQ647_spl
| sQ674_spl
| ~ sQ643_spl ),
inference(split_clause,[status(thm)],[f13781,f13536,f13837,f13568]) ).
fof(f13842,plain,
( ~ sQ645_spl
| function(function_inverse(function_inverse(sK214_skl)))
| ~ relation(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13561,f903]) ).
fof(f13843,plain,
( ~ sQ645_spl
| relation(function_inverse(function_inverse(sK214_skl)))
| ~ relation(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13561,f902]) ).
fof(f13844,plain,
! [X0,X1] :
( ~ sQ645_spl
| in(sK29_skl(relation_inverse_image(function_inverse(sK214_skl),X0),X1),relation_dom(function_inverse(sK214_skl)))
| ~ relation(function_inverse(sK214_skl))
| sK29_skl(relation_inverse_image(function_inverse(sK214_skl),X0),X1) = X1
| relation_inverse_image(function_inverse(sK214_skl),X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f13561,f4710]) ).
fof(f13845,plain,
! [X0,X1] :
( ~ sQ645_spl
| ~ in(apply(function_inverse(sK214_skl),sK29_skl(relation_dom(function_inverse(sK214_skl)),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(sK214_skl)),X0),relation_inverse_image(function_inverse(sK214_skl),X1))
| ~ relation(function_inverse(sK214_skl))
| sK29_skl(relation_dom(function_inverse(sK214_skl)),X0) = X0
| relation_dom(function_inverse(sK214_skl)) = singleton(X0) ),
inference(resolution,[status(thm)],[f13561,f4701]) ).
fof(f13846,plain,
! [X0] :
( ~ sQ645_spl
| in(ordered_pair(sK29_skl(relation_dom(function_inverse(sK214_skl)),X0),apply(function_inverse(sK214_skl),sK29_skl(relation_dom(function_inverse(sK214_skl)),X0))),function_inverse(sK214_skl))
| ~ relation(function_inverse(sK214_skl))
| sK29_skl(relation_dom(function_inverse(sK214_skl)),X0) = X0
| relation_dom(function_inverse(sK214_skl)) = singleton(X0) ),
inference(resolution,[status(thm)],[f13561,f4700]) ).
fof(f13847,plain,
! [X0,X1] :
( ~ sQ645_spl
| in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(sK214_skl),X0)),relation_inverse_image(function_inverse(sK214_skl),X0)),relation_dom(function_inverse(sK214_skl)))
| ~ relation(function_inverse(sK214_skl))
| in(X1,set_meet(relation_inverse_image(function_inverse(sK214_skl),X0)))
| relation_inverse_image(function_inverse(sK214_skl),X0) = empty_set ),
inference(resolution,[status(thm)],[f13561,f4287]) ).
fof(f13851,plain,
! [X0] :
( ~ sQ645_spl
| X0 = apply(function_inverse(sK214_skl),sK67_skl(X0,relation_rng(function_inverse(sK214_skl)),function_inverse(sK214_skl)))
| ~ in(X0,relation_rng(function_inverse(sK214_skl)))
| ~ relation(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13561,f2252]) ).
fof(f13852,plain,
! [X0] :
( ~ sQ645_spl
| in(sK67_skl(X0,relation_rng(function_inverse(sK214_skl)),function_inverse(sK214_skl)),relation_dom(function_inverse(sK214_skl)))
| ~ in(X0,relation_rng(function_inverse(sK214_skl)))
| ~ relation(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13561,f2251]) ).
fof(f13853,plain,
! [X0] :
( ~ sQ645_spl
| apply(function_inverse(sK214_skl),X0) = empty_set
| in(X0,relation_dom(function_inverse(sK214_skl)))
| ~ relation(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13561,f2240]) ).
fof(f13854,plain,
! [X0,X1] :
( ~ sQ645_spl
| in(apply(function_inverse(sK214_skl),sK9_skl(X0,X1,function_inverse(sK214_skl))),X1)
| in(sK9_skl(X0,X1,function_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK214_skl),X1)
| ~ relation(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13561,f475]) ).
fof(f13855,plain,
! [X0,X1] :
( ~ sQ645_spl
| in(sK9_skl(X0,X1,function_inverse(sK214_skl)),relation_dom(function_inverse(sK214_skl)))
| in(sK9_skl(X0,X1,function_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK214_skl),X1)
| ~ relation(function_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f13561,f474]) ).
fof(f13856,definition,
( sQ675_spl
<=> function(function_inverse(function_inverse(sK214_skl))) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f13859,plain,
( ~ sQ645_spl
| sQ675_spl
| ~ sQ641_spl ),
inference(split_clause,[status(thm)],[f13842,f13528,f13856,f13560]) ).
fof(f13860,definition,
( sQ676_spl
<=> relation(function_inverse(function_inverse(sK214_skl))) ),
introduced(definition,[new_symbols(definition,[sQ676_spl])],[split_symbol_definition]) ).
fof(f13863,plain,
( ~ sQ645_spl
| sQ676_spl
| ~ sQ641_spl ),
inference(split_clause,[status(thm)],[f13843,f13528,f13860,f13560]) ).
fof(f13864,definition,
! [X0,X1] :
( sQ677_spl
<=> ( in(sK29_skl(relation_inverse_image(function_inverse(sK214_skl),X0),X1),relation_dom(function_inverse(sK214_skl)))
| sK29_skl(relation_inverse_image(function_inverse(sK214_skl),X0),X1) = X1
| relation_inverse_image(function_inverse(sK214_skl),X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ677_spl])],[split_symbol_definition]) ).
fof(f13867,plain,
( ~ sQ645_spl
| ~ sQ641_spl
| sQ677_spl ),
inference(split_clause,[status(thm)],[f13844,f13864,f13528,f13560]) ).
fof(f13868,definition,
! [X0,X1] :
( sQ678_spl
<=> ( ~ in(apply(function_inverse(sK214_skl),sK29_skl(relation_dom(function_inverse(sK214_skl)),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(sK214_skl)),X0),relation_inverse_image(function_inverse(sK214_skl),X1))
| sK29_skl(relation_dom(function_inverse(sK214_skl)),X0) = X0
| relation_dom(function_inverse(sK214_skl)) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f13871,plain,
( ~ sQ645_spl
| ~ sQ641_spl
| sQ678_spl ),
inference(split_clause,[status(thm)],[f13845,f13868,f13528,f13560]) ).
fof(f13872,definition,
! [X0] :
( sQ679_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(function_inverse(sK214_skl)),X0),apply(function_inverse(sK214_skl),sK29_skl(relation_dom(function_inverse(sK214_skl)),X0))),function_inverse(sK214_skl))
| sK29_skl(relation_dom(function_inverse(sK214_skl)),X0) = X0
| relation_dom(function_inverse(sK214_skl)) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f13875,plain,
( ~ sQ645_spl
| ~ sQ641_spl
| sQ679_spl ),
inference(split_clause,[status(thm)],[f13846,f13872,f13528,f13560]) ).
fof(f13876,definition,
! [X0,X1] :
( sQ680_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(sK214_skl),X0)),relation_inverse_image(function_inverse(sK214_skl),X0)),relation_dom(function_inverse(sK214_skl)))
| in(X1,set_meet(relation_inverse_image(function_inverse(sK214_skl),X0)))
| relation_inverse_image(function_inverse(sK214_skl),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f13879,plain,
( ~ sQ645_spl
| ~ sQ641_spl
| sQ680_spl ),
inference(split_clause,[status(thm)],[f13847,f13876,f13528,f13560]) ).
fof(f13895,definition,
! [X0] :
( sQ685_spl
<=> ( X0 = apply(function_inverse(sK214_skl),sK67_skl(X0,relation_rng(function_inverse(sK214_skl)),function_inverse(sK214_skl)))
| ~ in(X0,relation_rng(function_inverse(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ685_spl])],[split_symbol_definition]) ).
fof(f13898,plain,
( ~ sQ645_spl
| sQ685_spl
| ~ sQ641_spl ),
inference(split_clause,[status(thm)],[f13851,f13528,f13895,f13560]) ).
fof(f13899,definition,
! [X0] :
( sQ686_spl
<=> ( in(sK67_skl(X0,relation_rng(function_inverse(sK214_skl)),function_inverse(sK214_skl)),relation_dom(function_inverse(sK214_skl)))
| ~ in(X0,relation_rng(function_inverse(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ686_spl])],[split_symbol_definition]) ).
fof(f13902,plain,
( ~ sQ645_spl
| sQ686_spl
| ~ sQ641_spl ),
inference(split_clause,[status(thm)],[f13852,f13528,f13899,f13560]) ).
fof(f13903,definition,
! [X0] :
( sQ687_spl
<=> ( apply(function_inverse(sK214_skl),X0) = empty_set
| in(X0,relation_dom(function_inverse(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ687_spl])],[split_symbol_definition]) ).
fof(f13906,plain,
( ~ sQ645_spl
| sQ687_spl
| ~ sQ641_spl ),
inference(split_clause,[status(thm)],[f13853,f13528,f13903,f13560]) ).
fof(f13907,definition,
! [X0,X1] :
( sQ688_spl
<=> ( in(apply(function_inverse(sK214_skl),sK9_skl(X0,X1,function_inverse(sK214_skl))),X1)
| in(sK9_skl(X0,X1,function_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK214_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ688_spl])],[split_symbol_definition]) ).
fof(f13910,plain,
( ~ sQ645_spl
| sQ688_spl
| ~ sQ641_spl ),
inference(split_clause,[status(thm)],[f13854,f13528,f13907,f13560]) ).
fof(f13911,definition,
! [X0,X1] :
( sQ689_spl
<=> ( in(sK9_skl(X0,X1,function_inverse(sK214_skl)),relation_dom(function_inverse(sK214_skl)))
| in(sK9_skl(X0,X1,function_inverse(sK214_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK214_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ689_spl])],[split_symbol_definition]) ).
fof(f13914,plain,
( ~ sQ645_spl
| sQ689_spl
| ~ sQ641_spl ),
inference(split_clause,[status(thm)],[f13855,f13528,f13911,f13560]) ).
fof(f13915,plain,
( ~ sQ646_spl
| function(function_inverse(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13565,f903]) ).
fof(f13916,plain,
( ~ sQ646_spl
| relation(function_inverse(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13565,f902]) ).
fof(f13917,plain,
! [X0,X1] :
( ~ sQ646_spl
| in(sK29_skl(relation_inverse_image(function_inverse(sK115_skl),X0),X1),relation_dom(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl))
| sK29_skl(relation_inverse_image(function_inverse(sK115_skl),X0),X1) = X1
| relation_inverse_image(function_inverse(sK115_skl),X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f13565,f4710]) ).
fof(f13918,plain,
! [X0,X1] :
( ~ sQ646_spl
| ~ in(apply(function_inverse(sK115_skl),sK29_skl(relation_dom(function_inverse(sK115_skl)),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(sK115_skl)),X0),relation_inverse_image(function_inverse(sK115_skl),X1))
| ~ relation(function_inverse(sK115_skl))
| sK29_skl(relation_dom(function_inverse(sK115_skl)),X0) = X0
| relation_dom(function_inverse(sK115_skl)) = singleton(X0) ),
inference(resolution,[status(thm)],[f13565,f4701]) ).
fof(f13919,plain,
! [X0] :
( ~ sQ646_spl
| in(ordered_pair(sK29_skl(relation_dom(function_inverse(sK115_skl)),X0),apply(function_inverse(sK115_skl),sK29_skl(relation_dom(function_inverse(sK115_skl)),X0))),function_inverse(sK115_skl))
| ~ relation(function_inverse(sK115_skl))
| sK29_skl(relation_dom(function_inverse(sK115_skl)),X0) = X0
| relation_dom(function_inverse(sK115_skl)) = singleton(X0) ),
inference(resolution,[status(thm)],[f13565,f4700]) ).
fof(f13920,plain,
! [X0,X1] :
( ~ sQ646_spl
| in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(sK115_skl),X0)),relation_inverse_image(function_inverse(sK115_skl),X0)),relation_dom(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl))
| in(X1,set_meet(relation_inverse_image(function_inverse(sK115_skl),X0)))
| relation_inverse_image(function_inverse(sK115_skl),X0) = empty_set ),
inference(resolution,[status(thm)],[f13565,f4287]) ).
fof(f13924,plain,
! [X0] :
( ~ sQ646_spl
| X0 = apply(function_inverse(sK115_skl),sK67_skl(X0,relation_rng(function_inverse(sK115_skl)),function_inverse(sK115_skl)))
| ~ in(X0,relation_rng(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13565,f2252]) ).
fof(f13925,plain,
! [X0] :
( ~ sQ646_spl
| in(sK67_skl(X0,relation_rng(function_inverse(sK115_skl)),function_inverse(sK115_skl)),relation_dom(function_inverse(sK115_skl)))
| ~ in(X0,relation_rng(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13565,f2251]) ).
fof(f13926,plain,
! [X0] :
( ~ sQ646_spl
| apply(function_inverse(sK115_skl),X0) = empty_set
| in(X0,relation_dom(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13565,f2240]) ).
fof(f13927,plain,
! [X0,X1] :
( ~ sQ646_spl
| in(apply(function_inverse(sK115_skl),sK9_skl(X0,X1,function_inverse(sK115_skl))),X1)
| in(sK9_skl(X0,X1,function_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK115_skl),X1)
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13565,f475]) ).
fof(f13928,plain,
! [X0,X1] :
( ~ sQ646_spl
| in(sK9_skl(X0,X1,function_inverse(sK115_skl)),relation_dom(function_inverse(sK115_skl)))
| in(sK9_skl(X0,X1,function_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK115_skl),X1)
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f13565,f474]) ).
fof(f13929,definition,
( sQ690_spl
<=> function(function_inverse(function_inverse(sK115_skl))) ),
introduced(definition,[new_symbols(definition,[sQ690_spl])],[split_symbol_definition]) ).
fof(f13930,plain,
( ~ sQ690_spl
| function(function_inverse(function_inverse(sK115_skl))) ),
inference(component_clause,[status(thm)],[f13929]) ).
fof(f13932,plain,
( ~ sQ646_spl
| sQ690_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f13915,f13532,f13929,f13564]) ).
fof(f13933,definition,
( sQ691_spl
<=> relation(function_inverse(function_inverse(sK115_skl))) ),
introduced(definition,[new_symbols(definition,[sQ691_spl])],[split_symbol_definition]) ).
fof(f13934,plain,
( ~ sQ691_spl
| relation(function_inverse(function_inverse(sK115_skl))) ),
inference(component_clause,[status(thm)],[f13933]) ).
fof(f13936,plain,
( ~ sQ646_spl
| sQ691_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f13916,f13532,f13933,f13564]) ).
fof(f13937,definition,
! [X0,X1] :
( sQ692_spl
<=> ( in(sK29_skl(relation_inverse_image(function_inverse(sK115_skl),X0),X1),relation_dom(function_inverse(sK115_skl)))
| sK29_skl(relation_inverse_image(function_inverse(sK115_skl),X0),X1) = X1
| relation_inverse_image(function_inverse(sK115_skl),X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ692_spl])],[split_symbol_definition]) ).
fof(f13940,plain,
( ~ sQ646_spl
| ~ sQ642_spl
| sQ692_spl ),
inference(split_clause,[status(thm)],[f13917,f13937,f13532,f13564]) ).
fof(f13941,definition,
! [X0,X1] :
( sQ693_spl
<=> ( ~ in(apply(function_inverse(sK115_skl),sK29_skl(relation_dom(function_inverse(sK115_skl)),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(sK115_skl)),X0),relation_inverse_image(function_inverse(sK115_skl),X1))
| sK29_skl(relation_dom(function_inverse(sK115_skl)),X0) = X0
| relation_dom(function_inverse(sK115_skl)) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ693_spl])],[split_symbol_definition]) ).
fof(f13944,plain,
( ~ sQ646_spl
| ~ sQ642_spl
| sQ693_spl ),
inference(split_clause,[status(thm)],[f13918,f13941,f13532,f13564]) ).
fof(f13945,definition,
! [X0] :
( sQ694_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(function_inverse(sK115_skl)),X0),apply(function_inverse(sK115_skl),sK29_skl(relation_dom(function_inverse(sK115_skl)),X0))),function_inverse(sK115_skl))
| sK29_skl(relation_dom(function_inverse(sK115_skl)),X0) = X0
| relation_dom(function_inverse(sK115_skl)) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ694_spl])],[split_symbol_definition]) ).
fof(f13948,plain,
( ~ sQ646_spl
| ~ sQ642_spl
| sQ694_spl ),
inference(split_clause,[status(thm)],[f13919,f13945,f13532,f13564]) ).
fof(f13949,definition,
! [X0,X1] :
( sQ695_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(sK115_skl),X0)),relation_inverse_image(function_inverse(sK115_skl),X0)),relation_dom(function_inverse(sK115_skl)))
| in(X1,set_meet(relation_inverse_image(function_inverse(sK115_skl),X0)))
| relation_inverse_image(function_inverse(sK115_skl),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ695_spl])],[split_symbol_definition]) ).
fof(f13952,plain,
( ~ sQ646_spl
| ~ sQ642_spl
| sQ695_spl ),
inference(split_clause,[status(thm)],[f13920,f13949,f13532,f13564]) ).
fof(f13968,definition,
! [X0] :
( sQ700_spl
<=> ( X0 = apply(function_inverse(sK115_skl),sK67_skl(X0,relation_rng(function_inverse(sK115_skl)),function_inverse(sK115_skl)))
| ~ in(X0,relation_rng(function_inverse(sK115_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ700_spl])],[split_symbol_definition]) ).
fof(f13971,plain,
( ~ sQ646_spl
| sQ700_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f13924,f13532,f13968,f13564]) ).
fof(f13972,definition,
! [X0] :
( sQ701_spl
<=> ( in(sK67_skl(X0,relation_rng(function_inverse(sK115_skl)),function_inverse(sK115_skl)),relation_dom(function_inverse(sK115_skl)))
| ~ in(X0,relation_rng(function_inverse(sK115_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ701_spl])],[split_symbol_definition]) ).
fof(f13975,plain,
( ~ sQ646_spl
| sQ701_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f13925,f13532,f13972,f13564]) ).
fof(f13976,definition,
! [X0] :
( sQ702_spl
<=> ( apply(function_inverse(sK115_skl),X0) = empty_set
| in(X0,relation_dom(function_inverse(sK115_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ702_spl])],[split_symbol_definition]) ).
fof(f13979,plain,
( ~ sQ646_spl
| sQ702_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f13926,f13532,f13976,f13564]) ).
fof(f13980,definition,
! [X0,X1] :
( sQ703_spl
<=> ( in(apply(function_inverse(sK115_skl),sK9_skl(X0,X1,function_inverse(sK115_skl))),X1)
| in(sK9_skl(X0,X1,function_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK115_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ703_spl])],[split_symbol_definition]) ).
fof(f13983,plain,
( ~ sQ646_spl
| sQ703_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f13927,f13532,f13980,f13564]) ).
fof(f13984,definition,
! [X0,X1] :
( sQ704_spl
<=> ( in(sK9_skl(X0,X1,function_inverse(sK115_skl)),relation_dom(function_inverse(sK115_skl)))
| in(sK9_skl(X0,X1,function_inverse(sK115_skl)),X0)
| X0 = relation_inverse_image(function_inverse(sK115_skl),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ704_spl])],[split_symbol_definition]) ).
fof(f13987,plain,
( ~ sQ646_spl
| sQ704_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f13928,f13532,f13984,f13564]) ).
fof(f13997,plain,
( ~ sQ171_spl
| element(sK212_skl,powerset(sK212_skl))
| ~ relation_of2(sK214_skl,sK212_skl,sK213_skl) ),
inference(paramodulation,[status(thm)],[f3822,f913]) ).
fof(f13998,definition,
( sQ705_spl
<=> relation_of2(sK214_skl,sK212_skl,sK213_skl) ),
introduced(definition,[new_symbols(definition,[sQ705_spl])],[split_symbol_definition]) ).
fof(f13999,plain,
( ~ sQ705_spl
| relation_of2(sK214_skl,sK212_skl,sK213_skl) ),
inference(component_clause,[status(thm)],[f13998]) ).
fof(f14000,plain,
( sQ705_spl
| ~ relation_of2(sK214_skl,sK212_skl,sK213_skl) ),
inference(component_clause,[status(thm)],[f13998]) ).
fof(f14001,definition,
( sQ706_spl
<=> element(sK212_skl,powerset(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ706_spl])],[split_symbol_definition]) ).
fof(f14004,plain,
( ~ sQ171_spl
| sQ706_spl
| ~ sQ705_spl ),
inference(split_clause,[status(thm)],[f13997,f13998,f14001,f3821]) ).
fof(f14040,plain,
! [X0,X1] :
( in(ordered_pair(X1,X0),relation_inverse(sK214_skl))
| ~ in(ordered_pair(X0,X1),sK214_skl)
| ~ relation(relation_inverse(sK214_skl)) ),
inference(paramodulation,[status(thm)],[f12299,f10635]) ).
fof(f14041,definition,
! [X0,X1] :
( sQ707_spl
<=> ( in(ordered_pair(X1,X0),relation_inverse(sK214_skl))
| ~ in(ordered_pair(X0,X1),sK214_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ707_spl])],[split_symbol_definition]) ).
fof(f14044,plain,
( sQ707_spl
| ~ sQ237_spl ),
inference(split_clause,[status(thm)],[f14040,f4515,f14041]) ).
fof(f14050,plain,
! [X0,X1] :
( ~ disjoint(empty_set,sK55_skl(X0,empty_set))
| ~ in(X1,sK55_skl(X0,empty_set))
| is_well_founded_in(empty_set,X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f13418,f703]) ).
fof(f14052,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),empty_set)
| ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f13418,f2213]) ).
fof(f14053,plain,
! [X0] :
( ~ in(X0,empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f13418,f2212]) ).
fof(f14054,definition,
! [X0,X1] :
( sQ708_spl
<=> ( ~ disjoint(empty_set,sK55_skl(X0,empty_set))
| ~ in(X1,sK55_skl(X0,empty_set))
| is_well_founded_in(empty_set,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ708_spl])],[split_symbol_definition]) ).
fof(f14057,plain,
( sQ708_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f14050,f2403,f14054]) ).
fof(f14065,definition,
! [X0,X1] :
( sQ711_spl
<=> ( in(ordered_pair(X0,X1),empty_set)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ711_spl])],[split_symbol_definition]) ).
fof(f14068,plain,
( sQ711_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f14052,f2403,f14065]) ).
fof(f14069,definition,
! [X0] :
( sQ712_spl
<=> ~ in(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ712_spl])],[split_symbol_definition]) ).
fof(f14072,plain,
( sQ712_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f14053,f2403,f14069]) ).
fof(f14268,plain,
( ~ sQ467_spl
| relation_dom(relation_inverse(sK214_skl)) = empty_set
| relation_dom(relation_dom(relation_inverse(sK214_skl))) != empty_set ),
inference(resolution,[status(thm)],[f9917,f1818]) ).
fof(f14283,plain,
! [X0,X1] :
( ~ sQ467_spl
| in(apply(relation_dom(relation_inverse(sK214_skl)),X0),X1)
| ~ in(X0,relation_inverse_image(relation_dom(relation_inverse(sK214_skl)),X1))
| ~ function(relation_dom(relation_inverse(sK214_skl))) ),
inference(resolution,[status(thm)],[f9917,f2190]) ).
fof(f14284,definition,
( sQ714_spl
<=> relation_dom(relation_dom(relation_inverse(sK214_skl))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ714_spl])],[split_symbol_definition]) ).
fof(f14287,plain,
( ~ sQ467_spl
| sQ210_spl
| ~ sQ714_spl ),
inference(split_clause,[status(thm)],[f14268,f14284,f4332,f9916]) ).
fof(f14288,definition,
( sQ715_spl
<=> function(relation_dom(relation_inverse(sK214_skl))) ),
introduced(definition,[new_symbols(definition,[sQ715_spl])],[split_symbol_definition]) ).
fof(f14291,definition,
! [X0,X1] :
( sQ716_spl
<=> ( in(apply(relation_dom(relation_inverse(sK214_skl)),X0),X1)
| ~ in(X0,relation_inverse_image(relation_dom(relation_inverse(sK214_skl)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ716_spl])],[split_symbol_definition]) ).
fof(f14294,plain,
( ~ sQ467_spl
| sQ716_spl
| ~ sQ715_spl ),
inference(split_clause,[status(thm)],[f14283,f14288,f14291,f9916]) ).
fof(f14322,plain,
( ~ sQ459_spl
| relation_dom(relation_inverse(sK112_skl)) = empty_set
| relation_dom(relation_dom(relation_inverse(sK112_skl))) != empty_set ),
inference(resolution,[status(thm)],[f9889,f1818]) ).
fof(f14337,plain,
! [X0,X1] :
( ~ sQ459_spl
| in(apply(relation_dom(relation_inverse(sK112_skl)),X0),X1)
| ~ in(X0,relation_inverse_image(relation_dom(relation_inverse(sK112_skl)),X1))
| ~ function(relation_dom(relation_inverse(sK112_skl))) ),
inference(resolution,[status(thm)],[f9889,f2190]) ).
fof(f14338,definition,
( sQ718_spl
<=> relation_dom(relation_dom(relation_inverse(sK112_skl))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f14341,plain,
( ~ sQ459_spl
| sQ224_spl
| ~ sQ718_spl ),
inference(split_clause,[status(thm)],[f14322,f14338,f4432,f9888]) ).
fof(f14342,definition,
( sQ719_spl
<=> function(relation_dom(relation_inverse(sK112_skl))) ),
introduced(definition,[new_symbols(definition,[sQ719_spl])],[split_symbol_definition]) ).
fof(f14345,definition,
! [X0,X1] :
( sQ720_spl
<=> ( in(apply(relation_dom(relation_inverse(sK112_skl)),X0),X1)
| ~ in(X0,relation_inverse_image(relation_dom(relation_inverse(sK112_skl)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ720_spl])],[split_symbol_definition]) ).
fof(f14348,plain,
( ~ sQ459_spl
| sQ720_spl
| ~ sQ719_spl ),
inference(split_clause,[status(thm)],[f14337,f14342,f14345,f9888]) ).
fof(f14415,plain,
! [X0,X1] :
( in(ordered_pair(X1,X0),relation_inverse(sK102_skl))
| ~ in(ordered_pair(X0,X1),sK102_skl)
| ~ relation(relation_inverse(sK102_skl)) ),
inference(paramodulation,[status(thm)],[f12301,f10635]) ).
fof(f14416,definition,
! [X0,X1] :
( sQ726_spl
<=> ( in(ordered_pair(X1,X0),relation_inverse(sK102_skl))
| ~ in(ordered_pair(X0,X1),sK102_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ726_spl])],[split_symbol_definition]) ).
fof(f14419,plain,
( sQ726_spl
| ~ sQ272_spl ),
inference(split_clause,[status(thm)],[f14415,f5060,f14416]) ).
fof(f14422,plain,
! [X0,X1] :
( in(ordered_pair(X1,X0),relation_inverse(sK115_skl))
| ~ in(ordered_pair(X0,X1),sK115_skl)
| ~ relation(relation_inverse(sK115_skl)) ),
inference(paramodulation,[status(thm)],[f12302,f10635]) ).
fof(f14423,definition,
! [X0,X1] :
( sQ727_spl
<=> ( in(ordered_pair(X1,X0),relation_inverse(sK115_skl))
| ~ in(ordered_pair(X0,X1),sK115_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ727_spl])],[split_symbol_definition]) ).
fof(f14426,plain,
( sQ727_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f14422,f4866,f14423]) ).
fof(f14428,plain,
! [X0,X1] :
( in(ordered_pair(X1,X0),relation_inverse(sK112_skl))
| ~ in(ordered_pair(X0,X1),sK112_skl)
| ~ relation(relation_inverse(sK112_skl)) ),
inference(paramodulation,[status(thm)],[f12293,f10635]) ).
fof(f14429,definition,
! [X0,X1] :
( sQ728_spl
<=> ( in(ordered_pair(X1,X0),relation_inverse(sK112_skl))
| ~ in(ordered_pair(X0,X1),sK112_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ728_spl])],[split_symbol_definition]) ).
fof(f14432,plain,
( sQ728_spl
| ~ sQ269_spl ),
inference(split_clause,[status(thm)],[f14428,f5026,f14429]) ).
fof(f14897,plain,
( in(ordered_pair(sK33_skl(relation_dom(sK214_skl)),apply(sK214_skl,sK33_skl(relation_dom(sK214_skl)))),sK214_skl)
| ~ relation(sK214_skl)
| relation_dom(sK214_skl) = empty_set ),
inference(resolution,[status(thm)],[f5373,f1731]) ).
fof(f14917,definition,
( sQ743_spl
<=> in(ordered_pair(sK33_skl(relation_dom(sK214_skl)),apply(sK214_skl,sK33_skl(relation_dom(sK214_skl)))),sK214_skl) ),
introduced(definition,[new_symbols(definition,[sQ743_spl])],[split_symbol_definition]) ).
fof(f14920,plain,
( sQ743_spl
| ~ sQ10_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f14897,f2559,f2351,f14917]) ).
fof(f14950,plain,
! [X0] :
( ~ in(apply(sK214_skl,sK33_skl(relation_dom(sK214_skl))),X0)
| in(sK33_skl(relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X0))
| ~ relation(sK214_skl)
| relation_dom(sK214_skl) = empty_set ),
inference(resolution,[status(thm)],[f5374,f1731]) ).
fof(f14970,definition,
! [X0] :
( sQ748_spl
<=> ( ~ in(apply(sK214_skl,sK33_skl(relation_dom(sK214_skl))),X0)
| in(sK33_skl(relation_dom(sK214_skl)),relation_inverse_image(sK214_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ748_spl])],[split_symbol_definition]) ).
fof(f14973,plain,
( sQ748_spl
| ~ sQ10_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f14950,f2559,f2351,f14970]) ).
fof(f14998,plain,
( ~ sQ690_spl
| function(function_inverse(function_inverse(function_inverse(sK115_skl))))
| ~ relation(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13930,f903]) ).
fof(f14999,plain,
( ~ sQ690_spl
| relation(function_inverse(function_inverse(function_inverse(sK115_skl))))
| ~ relation(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13930,f902]) ).
fof(f15000,plain,
! [X0,X1] :
( ~ sQ690_spl
| in(sK29_skl(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0),X1),relation_dom(function_inverse(function_inverse(sK115_skl))))
| ~ relation(function_inverse(function_inverse(sK115_skl)))
| sK29_skl(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0),X1) = X1
| relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f13930,f4710]) ).
fof(f15001,plain,
! [X0,X1] :
( ~ sQ690_spl
| ~ in(apply(function_inverse(function_inverse(sK115_skl)),sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0),relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1))
| ~ relation(function_inverse(function_inverse(sK115_skl)))
| sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0) = X0
| relation_dom(function_inverse(function_inverse(sK115_skl))) = singleton(X0) ),
inference(resolution,[status(thm)],[f13930,f4701]) ).
fof(f15002,plain,
! [X0] :
( ~ sQ690_spl
| in(ordered_pair(sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0),apply(function_inverse(function_inverse(sK115_skl)),sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0))),function_inverse(function_inverse(sK115_skl)))
| ~ relation(function_inverse(function_inverse(sK115_skl)))
| sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0) = X0
| relation_dom(function_inverse(function_inverse(sK115_skl))) = singleton(X0) ),
inference(resolution,[status(thm)],[f13930,f4700]) ).
fof(f15003,plain,
! [X0,X1] :
( ~ sQ690_spl
| in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0)),relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0)),relation_dom(function_inverse(function_inverse(sK115_skl))))
| ~ relation(function_inverse(function_inverse(sK115_skl)))
| in(X1,set_meet(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0)))
| relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0) = empty_set ),
inference(resolution,[status(thm)],[f13930,f4287]) ).
fof(f15007,plain,
! [X0] :
( ~ sQ690_spl
| X0 = apply(function_inverse(function_inverse(sK115_skl)),sK67_skl(X0,relation_rng(function_inverse(function_inverse(sK115_skl))),function_inverse(function_inverse(sK115_skl))))
| ~ in(X0,relation_rng(function_inverse(function_inverse(sK115_skl))))
| ~ relation(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13930,f2252]) ).
fof(f15008,plain,
! [X0] :
( ~ sQ690_spl
| in(sK67_skl(X0,relation_rng(function_inverse(function_inverse(sK115_skl))),function_inverse(function_inverse(sK115_skl))),relation_dom(function_inverse(function_inverse(sK115_skl))))
| ~ in(X0,relation_rng(function_inverse(function_inverse(sK115_skl))))
| ~ relation(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13930,f2251]) ).
fof(f15009,plain,
! [X0] :
( ~ sQ690_spl
| apply(function_inverse(function_inverse(sK115_skl)),X0) = empty_set
| in(X0,relation_dom(function_inverse(function_inverse(sK115_skl))))
| ~ relation(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13930,f2240]) ).
fof(f15010,plain,
! [X0,X1] :
( ~ sQ690_spl
| in(apply(function_inverse(function_inverse(sK115_skl)),sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl)))),X1)
| in(sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl))),X0)
| X0 = relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1)
| ~ relation(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13930,f475]) ).
fof(f15011,plain,
! [X0,X1] :
( ~ sQ690_spl
| in(sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl))),relation_dom(function_inverse(function_inverse(sK115_skl))))
| in(sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl))),X0)
| X0 = relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1)
| ~ relation(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13930,f474]) ).
fof(f15023,definition,
( sQ755_spl
<=> function(function_inverse(function_inverse(function_inverse(sK115_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ755_spl])],[split_symbol_definition]) ).
fof(f15026,plain,
( ~ sQ690_spl
| sQ755_spl
| ~ sQ691_spl ),
inference(split_clause,[status(thm)],[f14998,f13933,f15023,f13929]) ).
fof(f15027,definition,
( sQ756_spl
<=> relation(function_inverse(function_inverse(function_inverse(sK115_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ756_spl])],[split_symbol_definition]) ).
fof(f15030,plain,
( ~ sQ690_spl
| sQ756_spl
| ~ sQ691_spl ),
inference(split_clause,[status(thm)],[f14999,f13933,f15027,f13929]) ).
fof(f15031,definition,
! [X0,X1] :
( sQ757_spl
<=> ( in(sK29_skl(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0),X1),relation_dom(function_inverse(function_inverse(sK115_skl))))
| sK29_skl(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0),X1) = X1
| relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0) = singleton(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ757_spl])],[split_symbol_definition]) ).
fof(f15034,plain,
( ~ sQ690_spl
| ~ sQ691_spl
| sQ757_spl ),
inference(split_clause,[status(thm)],[f15000,f15031,f13933,f13929]) ).
fof(f15035,definition,
! [X0,X1] :
( sQ758_spl
<=> ( ~ in(apply(function_inverse(function_inverse(sK115_skl)),sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0)),X1)
| in(sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0),relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1))
| sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0) = X0
| relation_dom(function_inverse(function_inverse(sK115_skl))) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ758_spl])],[split_symbol_definition]) ).
fof(f15038,plain,
( ~ sQ690_spl
| ~ sQ691_spl
| sQ758_spl ),
inference(split_clause,[status(thm)],[f15001,f15035,f13933,f13929]) ).
fof(f15039,definition,
! [X0] :
( sQ759_spl
<=> ( in(ordered_pair(sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0),apply(function_inverse(function_inverse(sK115_skl)),sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0))),function_inverse(function_inverse(sK115_skl)))
| sK29_skl(relation_dom(function_inverse(function_inverse(sK115_skl))),X0) = X0
| relation_dom(function_inverse(function_inverse(sK115_skl))) = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ759_spl])],[split_symbol_definition]) ).
fof(f15042,plain,
( ~ sQ690_spl
| ~ sQ691_spl
| sQ759_spl ),
inference(split_clause,[status(thm)],[f15002,f15039,f13933,f13929]) ).
fof(f15043,definition,
! [X0,X1] :
( sQ760_spl
<=> ( in(sK26_skl(X1,set_meet(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0)),relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0)),relation_dom(function_inverse(function_inverse(sK115_skl))))
| in(X1,set_meet(relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0)))
| relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ760_spl])],[split_symbol_definition]) ).
fof(f15046,plain,
( ~ sQ690_spl
| ~ sQ691_spl
| sQ760_spl ),
inference(split_clause,[status(thm)],[f15003,f15043,f13933,f13929]) ).
fof(f15062,definition,
! [X0] :
( sQ765_spl
<=> ( X0 = apply(function_inverse(function_inverse(sK115_skl)),sK67_skl(X0,relation_rng(function_inverse(function_inverse(sK115_skl))),function_inverse(function_inverse(sK115_skl))))
| ~ in(X0,relation_rng(function_inverse(function_inverse(sK115_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ765_spl])],[split_symbol_definition]) ).
fof(f15065,plain,
( ~ sQ690_spl
| sQ765_spl
| ~ sQ691_spl ),
inference(split_clause,[status(thm)],[f15007,f13933,f15062,f13929]) ).
fof(f15066,definition,
! [X0] :
( sQ766_spl
<=> ( in(sK67_skl(X0,relation_rng(function_inverse(function_inverse(sK115_skl))),function_inverse(function_inverse(sK115_skl))),relation_dom(function_inverse(function_inverse(sK115_skl))))
| ~ in(X0,relation_rng(function_inverse(function_inverse(sK115_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ766_spl])],[split_symbol_definition]) ).
fof(f15069,plain,
( ~ sQ690_spl
| sQ766_spl
| ~ sQ691_spl ),
inference(split_clause,[status(thm)],[f15008,f13933,f15066,f13929]) ).
fof(f15070,definition,
! [X0] :
( sQ767_spl
<=> ( apply(function_inverse(function_inverse(sK115_skl)),X0) = empty_set
| in(X0,relation_dom(function_inverse(function_inverse(sK115_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ767_spl])],[split_symbol_definition]) ).
fof(f15073,plain,
( ~ sQ690_spl
| sQ767_spl
| ~ sQ691_spl ),
inference(split_clause,[status(thm)],[f15009,f13933,f15070,f13929]) ).
fof(f15074,definition,
! [X0,X1] :
( sQ768_spl
<=> ( in(apply(function_inverse(function_inverse(sK115_skl)),sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl)))),X1)
| in(sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl))),X0)
| X0 = relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ768_spl])],[split_symbol_definition]) ).
fof(f15077,plain,
( ~ sQ690_spl
| sQ768_spl
| ~ sQ691_spl ),
inference(split_clause,[status(thm)],[f15010,f13933,f15074,f13929]) ).
fof(f15078,definition,
! [X0,X1] :
( sQ769_spl
<=> ( in(sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl))),relation_dom(function_inverse(function_inverse(sK115_skl))))
| in(sK9_skl(X0,X1,function_inverse(function_inverse(sK115_skl))),X0)
| X0 = relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ769_spl])],[split_symbol_definition]) ).
fof(f15081,plain,
( ~ sQ690_spl
| sQ769_spl
| ~ sQ691_spl ),
inference(split_clause,[status(thm)],[f15011,f13933,f15078,f13929]) ).
fof(f15111,plain,
! [X0,X1] :
( ~ sQ691_spl
| in(apply(function_inverse(function_inverse(sK115_skl)),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1))
| ~ function(function_inverse(function_inverse(sK115_skl))) ),
inference(resolution,[status(thm)],[f13934,f2190]) ).
fof(f15116,definition,
! [X0,X1] :
( sQ771_spl
<=> ( in(apply(function_inverse(function_inverse(sK115_skl)),X0),X1)
| ~ in(X0,relation_inverse_image(function_inverse(function_inverse(sK115_skl)),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ771_spl])],[split_symbol_definition]) ).
fof(f15119,plain,
( ~ sQ691_spl
| sQ771_spl
| ~ sQ690_spl ),
inference(split_clause,[status(thm)],[f15111,f13929,f15116,f13933]) ).
fof(f15120,plain,
( ~ sQ636_spl
| relation_inverse(function_inverse(sK115_skl)) = sK115_skl ),
inference(backward_demodulation,[status(thm)],[f13316,f12302]) ).
fof(f15128,plain,
! [X0,X1] :
( ~ sQ636_spl
| in(ordered_pair(X1,X0),sK115_skl)
| ~ in(ordered_pair(X0,X1),function_inverse(sK115_skl))
| ~ relation(sK115_skl) ),
inference(paramodulation,[status(thm)],[f13316,f10635]) ).
fof(f15131,definition,
! [X0,X1] :
( sQ772_spl
<=> ( in(ordered_pair(X1,X0),sK115_skl)
| ~ in(ordered_pair(X0,X1),function_inverse(sK115_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ772_spl])],[split_symbol_definition]) ).
fof(f15134,plain,
( ~ sQ636_spl
| sQ772_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15128,f2983,f15131,f13315]) ).
fof(f15318,plain,
! [X0] :
( relation(X0)
| ~ relation(X0)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3128,f975]) ).
fof(f15324,definition,
! [X0] :
( sQ773_spl
<=> ( relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ773_spl])],[split_symbol_definition]) ).
fof(f15327,plain,
( sQ773_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f15318,f2403,f15324]) ).
fof(f15330,plain,
( function(relation_inverse(sK115_skl))
| ~ function(sK115_skl)
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f982,f1168]) ).
fof(f15331,plain,
( function(relation_inverse(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f982,f969]) ).
fof(f15336,plain,
( sQ202_spl
| ~ sQ50_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15330,f2983,f2605,f4251]) ).
fof(f15337,plain,
( sQ219_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f15331,f2403,f2362,f4384]) ).
fof(f15385,plain,
! [X0] :
( ~ sQ646_spl
| in(sK33_skl(relation_inverse_image(function_inverse(sK115_skl),X0)),relation_dom(function_inverse(sK115_skl)))
| ~ relation(function_inverse(sK115_skl))
| relation_inverse_image(function_inverse(sK115_skl),X0) = empty_set ),
inference(resolution,[status(thm)],[f5381,f13565]) ).
fof(f15389,plain,
! [X0] :
( in(sK33_skl(relation_inverse_image(sK214_skl,X0)),relation_dom(sK214_skl))
| ~ relation(sK214_skl)
| relation_inverse_image(sK214_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f5381,f1731]) ).
fof(f15390,plain,
! [X0] :
( in(sK33_skl(relation_inverse_image(sK115_skl,X0)),relation_dom(sK115_skl))
| ~ relation(sK115_skl)
| relation_inverse_image(sK115_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f5381,f1167]) ).
fof(f15391,plain,
! [X0] :
( ~ sQ15_spl
| in(sK33_skl(relation_inverse_image(sK102_skl,X0)),relation_dom(sK102_skl))
| ~ relation(sK102_skl)
| relation_inverse_image(sK102_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f5381,f2373]) ).
fof(f15396,plain,
! [X0] :
( in(sK33_skl(relation_inverse_image(empty_set,X0)),relation_dom(empty_set))
| ~ relation(empty_set)
| relation_inverse_image(empty_set,X0) = empty_set ),
inference(resolution,[status(thm)],[f5381,f968]) ).
fof(f15402,definition,
! [X0] :
( sQ776_spl
<=> ( in(sK33_skl(relation_inverse_image(function_inverse(sK115_skl),X0)),relation_dom(function_inverse(sK115_skl)))
| relation_inverse_image(function_inverse(sK115_skl),X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition]) ).
fof(f15405,plain,
( ~ sQ646_spl
| ~ sQ642_spl
| sQ776_spl ),
inference(split_clause,[status(thm)],[f15385,f15402,f13532,f13564]) ).
fof(f15409,definition,
! [X0] :
( sQ777_spl
<=> ( in(sK33_skl(relation_inverse_image(sK214_skl,X0)),relation_dom(sK214_skl))
| relation_inverse_image(sK214_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ777_spl])],[split_symbol_definition]) ).
fof(f15412,plain,
( ~ sQ10_spl
| sQ777_spl ),
inference(split_clause,[status(thm)],[f15389,f15409,f2351]) ).
fof(f15413,definition,
! [X0] :
( sQ778_spl
<=> ( in(sK33_skl(relation_inverse_image(sK115_skl,X0)),relation_dom(sK115_skl))
| relation_inverse_image(sK115_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ778_spl])],[split_symbol_definition]) ).
fof(f15416,plain,
( ~ sQ88_spl
| sQ778_spl ),
inference(split_clause,[status(thm)],[f15390,f15413,f2983]) ).
fof(f15417,definition,
! [X0] :
( sQ779_spl
<=> ( in(sK33_skl(relation_inverse_image(sK102_skl,X0)),relation_dom(sK102_skl))
| relation_inverse_image(sK102_skl,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ779_spl])],[split_symbol_definition]) ).
fof(f15420,plain,
( ~ sQ15_spl
| ~ sQ82_spl
| sQ779_spl ),
inference(split_clause,[status(thm)],[f15391,f15417,f2936,f2372]) ).
fof(f15427,definition,
! [X0] :
( sQ780_spl
<=> ( in(sK33_skl(relation_inverse_image(empty_set,X0)),relation_dom(empty_set))
| relation_inverse_image(empty_set,X0) = empty_set ) ),
introduced(definition,[new_symbols(definition,[sQ780_spl])],[split_symbol_definition]) ).
fof(f15430,plain,
( ~ sQ20_spl
| sQ780_spl ),
inference(split_clause,[status(thm)],[f15396,f15427,f2403]) ).
fof(f15432,plain,
( in(apply(sK214_skl,sK33_skl(sK212_skl)),relation_rng(sK214_skl))
| sK213_skl = empty_set
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f5384,f1732]) ).
fof(f15434,definition,
( sQ781_spl
<=> in(apply(sK214_skl,sK33_skl(sK212_skl)),relation_rng(sK214_skl)) ),
introduced(definition,[new_symbols(definition,[sQ781_spl])],[split_symbol_definition]) ).
fof(f15437,plain,
( sQ781_spl
| sQ104_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f15432,f4890,f2354,f3178,f3184,f15434]) ).
fof(f15438,plain,
! [X0,X1] :
( ~ sQ636_spl
| in(ordered_pair(X1,X0),function_inverse(sK115_skl))
| ~ in(ordered_pair(X0,X1),sK115_skl)
| ~ relation(function_inverse(sK115_skl)) ),
inference(paramodulation,[status(thm)],[f15120,f10635]) ).
fof(f15439,definition,
! [X0,X1] :
( sQ782_spl
<=> ( in(ordered_pair(X1,X0),function_inverse(sK115_skl))
| ~ in(ordered_pair(X0,X1),sK115_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ782_spl])],[split_symbol_definition]) ).
fof(f15442,plain,
( ~ sQ636_spl
| sQ782_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f15438,f13532,f15439,f13315]) ).
fof(f15488,plain,
! [X0] :
( ~ sQ646_spl
| function(relation_dom_restriction(function_inverse(sK115_skl),X0))
| ~ relation(function_inverse(sK115_skl)) ),
inference(resolution,[status(thm)],[f997,f13565]) ).
fof(f15492,plain,
! [X0] :
( function(relation_dom_restriction(sK214_skl,X0))
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f997,f1731]) ).
fof(f15493,plain,
! [X0] :
( function(relation_dom_restriction(sK115_skl,X0))
| ~ relation(sK115_skl) ),
inference(resolution,[status(thm)],[f997,f1167]) ).
fof(f15494,plain,
! [X0] :
( ~ sQ15_spl
| function(relation_dom_restriction(sK102_skl,X0))
| ~ relation(sK102_skl) ),
inference(resolution,[status(thm)],[f997,f2373]) ).
fof(f15499,plain,
! [X0] :
( function(relation_dom_restriction(empty_set,X0))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f997,f968]) ).
fof(f15505,definition,
! [X0] :
( sQ783_spl
<=> function(relation_dom_restriction(function_inverse(sK115_skl),X0)) ),
introduced(definition,[new_symbols(definition,[sQ783_spl])],[split_symbol_definition]) ).
fof(f15508,plain,
( ~ sQ646_spl
| sQ783_spl
| ~ sQ642_spl ),
inference(split_clause,[status(thm)],[f15488,f13532,f15505,f13564]) ).
fof(f15512,definition,
! [X0] :
( sQ784_spl
<=> function(relation_dom_restriction(sK214_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ784_spl])],[split_symbol_definition]) ).
fof(f15515,plain,
( sQ784_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f15492,f2351,f15512]) ).
fof(f15516,definition,
! [X0] :
( sQ785_spl
<=> function(relation_dom_restriction(sK115_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ785_spl])],[split_symbol_definition]) ).
fof(f15519,plain,
( sQ785_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f15493,f2983,f15516]) ).
fof(f15520,definition,
! [X0] :
( sQ786_spl
<=> function(relation_dom_restriction(sK102_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition]) ).
fof(f15523,plain,
( ~ sQ15_spl
| sQ786_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f15494,f2936,f15520,f2372]) ).
fof(f15528,definition,
! [X0] :
( sQ787_spl
<=> function(relation_dom_restriction(empty_set,X0)) ),
introduced(definition,[new_symbols(definition,[sQ787_spl])],[split_symbol_definition]) ).
fof(f15531,plain,
( sQ787_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f15499,f2403,f15528]) ).
fof(f15613,plain,
! [X0] :
( ~ in(X0,empty_set)
| ~ in(powerset(empty_set),X0)
| powerset(empty_set) = empty_set ),
inference(paramodulation,[status(thm)],[f6794,f5385]) ).
fof(f15617,definition,
! [X0] :
( sQ788_spl
<=> ( ~ in(X0,empty_set)
| ~ in(powerset(empty_set),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ788_spl])],[split_symbol_definition]) ).
fof(f15620,plain,
( sQ788_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f15613,f8595,f15617]) ).
fof(f15778,plain,
( ~ sQ358_spl
| relation_inverse_image(empty_set,empty_set) != empty_set ),
inference(paramodulation,[status(thm)],[f2814,f7574]) ).
fof(f15779,plain,
( ~ sQ358_spl
| ~ sQ47_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f2762,f15778]) ).
fof(f15780,plain,
( ~ sQ358_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f15779]) ).
fof(f15781,plain,
( ~ sQ358_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f15780]) ).
fof(f15789,plain,
! [X0] :
( apply(relation_composition(sK214_skl,X0),sK33_skl(sK212_skl)) = apply(X0,apply(sK214_skl,sK33_skl(sK212_skl)))
| sK213_skl = empty_set
| ~ function(X0)
| ~ relation(X0)
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl)
| ~ function(sK214_skl)
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f5387,f1732]) ).
fof(f15791,definition,
! [X0] :
( sQ789_spl
<=> ( apply(relation_composition(sK214_skl,X0),sK33_skl(sK212_skl)) = apply(X0,apply(sK214_skl,sK33_skl(sK212_skl)))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ789_spl])],[split_symbol_definition]) ).
fof(f15794,plain,
( sQ104_spl
| sQ789_spl
| ~ sQ102_spl
| ~ sQ11_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f15789,f4890,f2354,f3178,f15791,f3184]) ).
fof(f15805,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ subset(X1,X0)
| ~ relation(empty_set)
| in(empty_set,powerset(relation_inverse_image(empty_set,X0))) ),
inference(paramodulation,[status(thm)],[f2762,f5449]) ).
fof(f15806,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ subset(X0,X1)
| ~ relation(empty_set)
| in(relation_inverse_image(empty_set,X0),powerset(empty_set)) ),
inference(paramodulation,[status(thm)],[f2762,f5449]) ).
fof(f15808,definition,
! [X0,X1] :
( sQ790_spl
<=> ( ~ subset(X1,X0)
| in(empty_set,powerset(relation_inverse_image(empty_set,X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ790_spl])],[split_symbol_definition]) ).
fof(f15811,plain,
( ~ sQ47_spl
| ~ sQ20_spl
| sQ790_spl ),
inference(split_clause,[status(thm)],[f15805,f15808,f2403,f2591]) ).
fof(f15812,definition,
! [X0,X1] :
( sQ791_spl
<=> ( ~ subset(X0,X1)
| in(relation_inverse_image(empty_set,X0),powerset(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ791_spl])],[split_symbol_definition]) ).
fof(f15815,plain,
( ~ sQ47_spl
| ~ sQ20_spl
| sQ791_spl ),
inference(split_clause,[status(thm)],[f15806,f15812,f2403,f2591]) ).
fof(f15881,plain,
! [X0] :
( ~ empty(empty_set)
| ~ relation(sK91_skl(empty_set,X0))
| empty(sK91_skl(empty_set,X0)) ),
inference(paramodulation,[status(thm)],[f5747,f1013]) ).
fof(f15885,definition,
! [X0] :
( sQ792_spl
<=> ( ~ relation(sK91_skl(empty_set,X0))
| empty(sK91_skl(empty_set,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ792_spl])],[split_symbol_definition]) ).
fof(f15886,plain,
! [X0] :
( ~ sQ792_spl
| ~ relation(sK91_skl(empty_set,X0))
| empty(sK91_skl(empty_set,X0)) ),
inference(component_clause,[status(thm)],[f15885]) ).
fof(f15888,plain,
( ~ sQ335_spl
| sQ792_spl ),
inference(split_clause,[status(thm)],[f15881,f15885,f6783]) ).
fof(f15892,plain,
! [X0] :
( ~ sQ792_spl
| empty(sK91_skl(empty_set,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f15886,f5752]) ).
fof(f15932,plain,
! [X0] :
( ~ sQ792_spl
| sK91_skl(empty_set,X0) = empty_set ),
inference(resolution,[status(thm)],[f15892,f1838]) ).
fof(f15985,plain,
( ~ sQ47_spl
| ~ relation(empty_set)
| in(empty_set,powerset(relation_dom(empty_set))) ),
inference(paramodulation,[status(thm)],[f2762,f5450]) ).
fof(f15987,plain,
! [X0] :
( ~ relation(empty_set)
| in(relation_inverse_image(empty_set,X0),powerset(empty_set)) ),
inference(paramodulation,[status(thm)],[f1808,f5450]) ).
fof(f15991,definition,
( sQ793_spl
<=> in(empty_set,powerset(relation_dom(empty_set))) ),
introduced(definition,[new_symbols(definition,[sQ793_spl])],[split_symbol_definition]) ).
fof(f15994,plain,
( ~ sQ47_spl
| ~ sQ20_spl
| sQ793_spl ),
inference(split_clause,[status(thm)],[f15985,f15991,f2403,f2591]) ).
fof(f15996,definition,
! [X0] :
( sQ794_spl
<=> in(relation_inverse_image(empty_set,X0),powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ794_spl])],[split_symbol_definition]) ).
fof(f15999,plain,
( ~ sQ20_spl
| sQ794_spl ),
inference(split_clause,[status(thm)],[f15987,f15996,f2403]) ).
fof(f16017,plain,
! [X0] :
( ~ sQ792_spl
| relation_of2_as_subset(empty_set,X0,empty_set) ),
inference(paramodulation,[status(thm)],[f15932,f940]) ).
fof(f16020,plain,
( sQ310_spl
| ~ sQ792_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6310,f16017]) ).
fof(f16021,plain,
! [X0] :
( ~ sQ792_spl
| quasi_total(empty_set,X0,empty_set)
| X0 = empty_set ),
inference(backward_subsumption_resolution,[status(thm)],[f2201,f16017]) ).
fof(f16025,plain,
! [X0,X1] :
( ~ sQ792_spl
| relation_of2_as_subset(empty_set,X1,X0)
| ~ subset(empty_set,X0) ),
inference(resolution,[status(thm)],[f16017,f1496]) ).
fof(f16029,plain,
( sQ310_spl
| ~ sQ792_spl ),
inference(contradiction_clause,[status(thm)],[f16020]) ).
fof(f16031,definition,
( sQ795_spl
<=> subset(empty_set,relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ795_spl])],[split_symbol_definition]) ).
fof(f16033,plain,
( sQ795_spl
| ~ subset(empty_set,relation_rng(empty_set)) ),
inference(component_clause,[status(thm)],[f16031]) ).
fof(f16035,plain,
! [X0,X1] :
( ~ sQ792_spl
| relation_of2_as_subset(empty_set,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f16025,f1620]) ).
fof(f16039,plain,
( sQ795_spl
| ~ subset(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1809,f16033]) ).
fof(f16040,plain,
( sQ795_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16039,f1620]) ).
fof(f16041,plain,
sQ795_spl,
inference(contradiction_clause,[status(thm)],[f16040]) ).
fof(f16043,plain,
( sQ263_spl
| ~ sQ792_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4880,f16035]) ).
fof(f16051,plain,
( sQ263_spl
| ~ sQ792_spl ),
inference(contradiction_clause,[status(thm)],[f16043]) ).
fof(f16106,plain,
! [X0] :
( ~ sQ338_spl
| in(ordered_pair(sK70_skl(apply(sK214_skl,X0),relation_rng(sK214_skl),sK214_skl),apply(sK214_skl,X0)),sK214_skl)
| ~ relation(sK214_skl)
| ~ in(X0,sK212_skl) ),
inference(resolution,[status(thm)],[f6950,f2254]) ).
fof(f16123,definition,
! [X0] :
( sQ798_spl
<=> ( in(ordered_pair(sK70_skl(apply(sK214_skl,X0),relation_rng(sK214_skl),sK214_skl),apply(sK214_skl,X0)),sK214_skl)
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ798_spl])],[split_symbol_definition]) ).
fof(f16126,plain,
( ~ sQ338_spl
| ~ sQ10_spl
| sQ798_spl ),
inference(split_clause,[status(thm)],[f16106,f16123,f2351,f6949]) ).
fof(f16138,definition,
! [X0] :
( sQ799_spl
<=> ( ~ relation(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ799_spl])],[split_symbol_definition]) ).
fof(f16139,plain,
! [X0] :
( ~ sQ799_spl
| ~ relation(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f16138]) ).
fof(f16142,plain,
! [X0] :
( ~ sQ799_spl
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f16139]) ).
fof(f16143,plain,
! [X0] :
( ~ sQ799_spl
| ~ empty(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1019,f16142]) ).
fof(f16188,plain,
( ~ sQ799_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f16143,f8727,f16138]) ).
fof(f16195,plain,
( sQ286_spl
| ~ sQ792_spl
| sK212_skl = empty_set ),
inference(resolution,[status(thm)],[f16021,f5473]) ).
fof(f16207,plain,
( sQ286_spl
| ~ sQ792_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f16195,f4890,f15885,f5471]) ).
fof(f16209,definition,
( sQ800_spl
<=> relation_of2_as_subset(empty_set,sK215_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ800_spl])],[split_symbol_definition]) ).
fof(f16211,plain,
( sQ800_spl
| ~ relation_of2_as_subset(empty_set,sK215_skl,empty_set) ),
inference(component_clause,[status(thm)],[f16209]) ).
fof(f16212,definition,
( sQ801_spl
<=> in(apply(empty_set,apply(sK214_skl,sK216_skl)),relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ801_spl])],[split_symbol_definition]) ).
fof(f16213,plain,
( ~ sQ801_spl
| in(apply(empty_set,apply(sK214_skl,sK216_skl)),relation_rng(empty_set)) ),
inference(component_clause,[status(thm)],[f16212]) ).
fof(f16273,plain,
( ~ sQ801_spl
| ~ sQ29_spl
| in(empty_set,relation_rng(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f2477,f16213]) ).
fof(f16274,plain,
( ~ sQ801_spl
| ~ sQ29_spl
| in(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1809,f16273]) ).
fof(f16275,plain,
( ~ sQ801_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16274,f2222]) ).
fof(f16276,plain,
( ~ sQ801_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f16275]) ).
fof(f16277,plain,
( sQ800_spl
| ~ sQ792_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16211,f16035]) ).
fof(f16278,plain,
( sQ800_spl
| ~ sQ792_spl ),
inference(contradiction_clause,[status(thm)],[f16277]) ).
fof(f16380,plain,
! [X0] :
( ~ sQ507_spl
| in(ordered_pair(X0,X0),empty_set)
| ~ in(X0,relation_field(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1038,f10293]) ).
fof(f16382,definition,
! [X0] :
( sQ810_spl
<=> ( in(ordered_pair(X0,X0),empty_set)
| ~ in(X0,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ810_spl])],[split_symbol_definition]) ).
fof(f16385,plain,
( ~ sQ507_spl
| sQ810_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f16380,f2403,f16382,f10292]) ).
fof(f16475,plain,
! [X0] :
( ~ sQ350_spl
| apply(relation_composition(sK214_skl,empty_set),X0) = apply(empty_set,apply(sK214_skl,X0))
| ~ in(X0,sK212_skl)
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f7027,f948]) ).
fof(f16476,plain,
! [X0] :
( ~ sQ350_spl
| apply(relation_composition(sK214_skl,sK102_skl),X0) = apply(sK102_skl,apply(sK214_skl,X0))
| ~ in(X0,sK212_skl)
| ~ function(sK102_skl) ),
inference(resolution,[status(thm)],[f7027,f1116]) ).
fof(f16477,plain,
! [X0] :
( ~ sQ350_spl
| apply(relation_composition(sK214_skl,sK214_skl),X0) = apply(sK214_skl,apply(sK214_skl,X0))
| ~ in(X0,sK212_skl)
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f7027,f2515]) ).
fof(f16479,definition,
! [X0] :
( sQ811_spl
<=> ( apply(relation_composition(sK214_skl,empty_set),X0) = apply(empty_set,apply(sK214_skl,X0))
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ811_spl])],[split_symbol_definition]) ).
fof(f16482,plain,
( ~ sQ350_spl
| sQ811_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f16475,f2362,f16479,f7026]) ).
fof(f16483,definition,
! [X0] :
( sQ812_spl
<=> ( apply(relation_composition(sK214_skl,sK102_skl),X0) = apply(sK102_skl,apply(sK214_skl,X0))
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ812_spl])],[split_symbol_definition]) ).
fof(f16486,plain,
( ~ sQ350_spl
| sQ812_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f16476,f2372,f16483,f7026]) ).
fof(f16487,definition,
! [X0] :
( sQ813_spl
<=> ( apply(relation_composition(sK214_skl,sK214_skl),X0) = apply(sK214_skl,apply(sK214_skl,X0))
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ813_spl])],[split_symbol_definition]) ).
fof(f16490,plain,
( ~ sQ350_spl
| sQ813_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f16477,f2354,f16487,f7026]) ).
fof(f16498,plain,
! [X0,X1] :
( X1 = apply(empty_set,X0)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f1895,f948]) ).
fof(f16499,plain,
! [X0,X1] :
( X1 = apply(sK102_skl,X0)
| ~ in(ordered_pair(X0,X1),sK102_skl)
| ~ function(sK102_skl) ),
inference(resolution,[status(thm)],[f1895,f1116]) ).
fof(f16500,plain,
! [X0,X1] :
( X1 = apply(sK214_skl,X0)
| ~ in(ordered_pair(X0,X1),sK214_skl)
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f1895,f2515]) ).
fof(f16502,definition,
! [X0,X1] :
( sQ815_spl
<=> ( X1 = apply(empty_set,X0)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ815_spl])],[split_symbol_definition]) ).
fof(f16505,plain,
( sQ815_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f16498,f2362,f16502]) ).
fof(f16506,definition,
! [X0,X1] :
( sQ816_spl
<=> ( X1 = apply(sK102_skl,X0)
| ~ in(ordered_pair(X0,X1),sK102_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ816_spl])],[split_symbol_definition]) ).
fof(f16509,plain,
( sQ816_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f16499,f2372,f16506]) ).
fof(f16510,definition,
! [X0,X1] :
( sQ817_spl
<=> ( X1 = apply(sK214_skl,X0)
| ~ in(ordered_pair(X0,X1),sK214_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ817_spl])],[split_symbol_definition]) ).
fof(f16513,plain,
( sQ817_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f16500,f2354,f16510]) ).
fof(f16552,plain,
! [X0,X1,X2] :
( ~ sQ485_spl
| ~ sQ483_spl
| in(ordered_pair(X0,X2),empty_set)
| ~ in(ordered_pair(X1,X2),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1055,f10469]) ).
fof(f16554,definition,
! [X0,X1,X2] :
( sQ819_spl
<=> ( in(ordered_pair(X0,X2),empty_set)
| ~ in(ordered_pair(X1,X2),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ819_spl])],[split_symbol_definition]) ).
fof(f16557,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| sQ819_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f16552,f2403,f16554,f10105,f10144]) ).
fof(f16561,plain,
! [X0,X1] :
( X1 = apply(relation_inverse(sK214_skl),X0)
| ~ in(ordered_pair(X0,X1),relation_inverse(sK214_skl))
| ~ function(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f6036,f1895]) ).
fof(f16562,plain,
! [X0] :
( ~ sQ350_spl
| apply(relation_composition(sK214_skl,relation_inverse(sK214_skl)),X0) = apply(relation_inverse(sK214_skl),apply(sK214_skl,X0))
| ~ in(X0,sK212_skl)
| ~ function(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f6036,f7027]) ).
fof(f16564,definition,
! [X0,X1] :
( sQ820_spl
<=> ( X1 = apply(relation_inverse(sK214_skl),X0)
| ~ in(ordered_pair(X0,X1),relation_inverse(sK214_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ820_spl])],[split_symbol_definition]) ).
fof(f16567,plain,
( sQ820_spl
| ~ sQ212_spl ),
inference(split_clause,[status(thm)],[f16561,f4339,f16564]) ).
fof(f16568,definition,
! [X0] :
( sQ821_spl
<=> ( apply(relation_composition(sK214_skl,relation_inverse(sK214_skl)),X0) = apply(relation_inverse(sK214_skl),apply(sK214_skl,X0))
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ821_spl])],[split_symbol_definition]) ).
fof(f16571,plain,
( ~ sQ350_spl
| sQ821_spl
| ~ sQ212_spl ),
inference(split_clause,[status(thm)],[f16562,f4339,f16568,f7026]) ).
fof(f16607,plain,
! [X0] :
( in(ordered_pair(X0,apply(relation_inverse(sK214_skl),X0)),relation_inverse(sK214_skl))
| ~ in(X0,relation_dom(relation_inverse(sK214_skl)))
| ~ function(relation_inverse(sK214_skl)) ),
inference(resolution,[status(thm)],[f2239,f6036]) ).
fof(f16612,plain,
! [X0] :
( in(ordered_pair(X0,apply(empty_set,X0)),empty_set)
| ~ in(X0,relation_dom(empty_set))
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f2239,f948]) ).
fof(f16613,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK102_skl,X0)),sK102_skl)
| ~ in(X0,relation_dom(sK102_skl))
| ~ function(sK102_skl) ),
inference(resolution,[status(thm)],[f2239,f1116]) ).
fof(f16614,plain,
! [X0] :
( in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)
| ~ in(X0,relation_dom(sK214_skl))
| ~ function(sK214_skl) ),
inference(resolution,[status(thm)],[f2239,f2515]) ).
fof(f16616,definition,
! [X0] :
( sQ823_spl
<=> ( in(ordered_pair(X0,apply(relation_inverse(sK214_skl),X0)),relation_inverse(sK214_skl))
| ~ in(X0,relation_dom(relation_inverse(sK214_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ823_spl])],[split_symbol_definition]) ).
fof(f16619,plain,
( sQ823_spl
| ~ sQ212_spl ),
inference(split_clause,[status(thm)],[f16607,f4339,f16616]) ).
fof(f16622,definition,
! [X0] :
( sQ824_spl
<=> ( in(ordered_pair(X0,apply(empty_set,X0)),empty_set)
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ824_spl])],[split_symbol_definition]) ).
fof(f16625,plain,
( sQ824_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f16612,f2362,f16622]) ).
fof(f16626,definition,
! [X0] :
( sQ825_spl
<=> ( in(ordered_pair(X0,apply(sK102_skl,X0)),sK102_skl)
| ~ in(X0,relation_dom(sK102_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ825_spl])],[split_symbol_definition]) ).
fof(f16629,plain,
( sQ825_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f16613,f2372,f16626]) ).
fof(f16630,definition,
! [X0] :
( sQ826_spl
<=> ( in(ordered_pair(X0,apply(sK214_skl,X0)),sK214_skl)
| ~ in(X0,relation_dom(sK214_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ826_spl])],[split_symbol_definition]) ).
fof(f16633,plain,
( sQ826_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f16614,f2354,f16630]) ).
fof(f16648,plain,
! [X0] :
( in(ordered_pair(X0,apply(relation_inverse(sK112_skl),X0)),relation_inverse(sK112_skl))
| ~ in(X0,relation_dom(relation_inverse(sK112_skl)))
| ~ function(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4133,f2239]) ).
fof(f16649,plain,
! [X0,X1] :
( X1 = apply(relation_inverse(sK112_skl),X0)
| ~ in(ordered_pair(X0,X1),relation_inverse(sK112_skl))
| ~ function(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4133,f1895]) ).
fof(f16650,plain,
! [X0] :
( ~ sQ350_spl
| apply(relation_composition(sK214_skl,relation_inverse(sK112_skl)),X0) = apply(relation_inverse(sK112_skl),apply(sK214_skl,X0))
| ~ in(X0,sK212_skl)
| ~ function(relation_inverse(sK112_skl)) ),
inference(resolution,[status(thm)],[f4133,f7027]) ).
fof(f16652,definition,
! [X0] :
( sQ828_spl
<=> ( in(ordered_pair(X0,apply(relation_inverse(sK112_skl),X0)),relation_inverse(sK112_skl))
| ~ in(X0,relation_dom(relation_inverse(sK112_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ828_spl])],[split_symbol_definition]) ).
fof(f16655,plain,
( sQ828_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f16648,f4439,f16652]) ).
fof(f16656,definition,
! [X0,X1] :
( sQ829_spl
<=> ( X1 = apply(relation_inverse(sK112_skl),X0)
| ~ in(ordered_pair(X0,X1),relation_inverse(sK112_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ829_spl])],[split_symbol_definition]) ).
fof(f16659,plain,
( sQ829_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f16649,f4439,f16656]) ).
fof(f16660,definition,
! [X0] :
( sQ830_spl
<=> ( apply(relation_composition(sK214_skl,relation_inverse(sK112_skl)),X0) = apply(relation_inverse(sK112_skl),apply(sK214_skl,X0))
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ830_spl])],[split_symbol_definition]) ).
fof(f16663,plain,
( ~ sQ350_spl
| sQ830_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f16650,f4439,f16660,f7026]) ).
fof(f16793,plain,
! [X0] :
( ~ sQ499_spl
| relation(sK96_skl(X0,empty_set))
| ~ equipotent(X0,relation_field(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1066,f10217]) ).
fof(f16796,definition,
! [X0] :
( sQ835_spl
<=> ( relation(sK96_skl(X0,empty_set))
| ~ equipotent(X0,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ835_spl])],[split_symbol_definition]) ).
fof(f16799,plain,
( ~ sQ499_spl
| sQ835_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f16793,f2403,f16796,f10216]) ).
fof(f16838,plain,
! [X0] :
( sK65_skl(X0,X0) = empty_set
| relation_dom(sK65_skl(X0,X0)) != empty_set ),
inference(resolution,[status(thm)],[f1818,f8586]) ).
fof(f16851,plain,
! [X0] :
( sK65_skl(X0,X0) = empty_set
| X0 != empty_set ),
inference(forward_demodulation,[status(thm)],[f8733,f16838]) ).
fof(f16852,plain,
sK65_skl(empty_set,empty_set) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f16851]) ).
fof(f16868,plain,
! [X0] :
( subset(relation_dom(relation_rng_restriction(X0,empty_set)),empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f1808,f1050]) ).
fof(f16872,definition,
! [X0] :
( sQ836_spl
<=> subset(relation_dom(relation_rng_restriction(X0,empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ836_spl])],[split_symbol_definition]) ).
fof(f16875,plain,
( sQ836_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f16868,f2403,f16872]) ).
fof(f17012,plain,
! [X0,X1] :
( ~ sQ485_spl
| ~ sQ483_spl
| X0 = X1
| ~ in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1077,f10468]) ).
fof(f17014,definition,
! [X0,X1] :
( sQ837_spl
<=> ( X0 = X1
| ~ in(ordered_pair(X1,X0),empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ837_spl])],[split_symbol_definition]) ).
fof(f17017,plain,
( ~ sQ485_spl
| ~ sQ483_spl
| sQ837_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17012,f2403,f17014,f10105,f10144]) ).
fof(f17030,plain,
( ~ sQ8_spl
| ~ sQ285_spl
| in(sK27_skl(sK216_skl,sK212_skl),union(sK212_skl))
| sK216_skl = empty_set ),
inference(resolution,[status(thm)],[f8313,f8237]) ).
fof(f17063,definition,
( sQ839_spl
<=> in(sK27_skl(sK216_skl,sK212_skl),union(sK212_skl)) ),
introduced(definition,[new_symbols(definition,[sQ839_spl])],[split_symbol_definition]) ).
fof(f17066,plain,
( ~ sQ8_spl
| ~ sQ285_spl
| sQ839_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f17030,f5311,f17063,f5343,f2167]) ).
fof(f17178,plain,
! [X0,X1] :
( ~ sQ495_spl
| in(ordered_pair(X1,X0),empty_set)
| in(ordered_pair(X0,X1),empty_set)
| X0 = X1
| ~ in(X1,relation_field(empty_set))
| ~ in(X0,relation_field(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f1087,f10184]) ).
fof(f17182,definition,
! [X0,X1] :
( sQ843_spl
<=> ( in(ordered_pair(X1,X0),empty_set)
| in(ordered_pair(X0,X1),empty_set)
| X0 = X1
| ~ in(X1,relation_field(empty_set))
| ~ in(X0,relation_field(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ843_spl])],[split_symbol_definition]) ).
fof(f17185,plain,
( ~ sQ495_spl
| sQ843_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17178,f2403,f17182,f10183]) ).
fof(f17192,plain,
! [X0,X1] :
( ~ sQ47_spl
| in(apply(empty_set,X0),X1)
| ~ in(X0,empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2762,f2190]) ).
fof(f17197,definition,
! [X0,X1] :
( sQ844_spl
<=> ( in(apply(empty_set,X0),X1)
| ~ in(X0,empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ844_spl])],[split_symbol_definition]) ).
fof(f17200,plain,
( ~ sQ47_spl
| sQ844_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17192,f2403,f2362,f17197,f2591]) ).
fof(f17225,definition,
! [X0] :
( sQ845_spl
<=> ( in(apply(empty_set,X0),relation_rng(empty_set))
| ~ in(X0,sK212_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ845_spl])],[split_symbol_definition]) ).
fof(f17226,plain,
! [X0] :
( ~ sQ845_spl
| in(apply(empty_set,X0),relation_rng(empty_set))
| ~ in(X0,sK212_skl) ),
inference(component_clause,[status(thm)],[f17225]) ).
fof(f17232,plain,
! [X0] :
( ~ sQ845_spl
| ~ sQ29_spl
| in(empty_set,relation_rng(empty_set))
| ~ in(X0,sK212_skl) ),
inference(forward_demodulation,[status(thm)],[f2477,f17226]) ).
fof(f17233,plain,
! [X0] :
( ~ sQ845_spl
| ~ sQ29_spl
| in(empty_set,empty_set)
| ~ in(X0,sK212_skl) ),
inference(forward_demodulation,[status(thm)],[f1809,f17232]) ).
fof(f17234,plain,
! [X0] :
( ~ sQ845_spl
| ~ sQ29_spl
| ~ in(X0,sK212_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f17233,f2222]) ).
fof(f17235,plain,
( ~ sQ8_spl
| ~ sQ280_spl
| ~ sQ845_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5332,f17234]) ).
fof(f17248,plain,
( ~ sQ8_spl
| ~ sQ280_spl
| ~ sQ845_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f17235]) ).
fof(f17359,definition,
! [X0] :
( sQ846_spl
<=> empty_set = singleton(X0) ),
introduced(definition,[new_symbols(definition,[sQ846_spl])],[split_symbol_definition]) ).
fof(f17360,plain,
! [X0] :
( ~ sQ846_spl
| empty_set = singleton(X0) ),
inference(component_clause,[status(thm)],[f17359]) ).
fof(f17364,plain,
( ~ sQ846_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17360,f1041]) ).
fof(f17365,plain,
~ sQ846_spl,
inference(contradiction_clause,[status(thm)],[f17364]) ).
fof(f17382,definition,
( sQ847_spl
<=> in(apply(sK214_skl,sK216_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ847_spl])],[split_symbol_definition]) ).
fof(f17383,plain,
( ~ sQ847_spl
| in(apply(sK214_skl,sK216_skl),empty_set) ),
inference(component_clause,[status(thm)],[f17382]) ).
fof(f17387,plain,
( subset(relation_dom(empty_set),relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f5271,f1050]) ).
fof(f17388,definition,
( sQ848_spl
<=> subset(relation_dom(empty_set),relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ848_spl])],[split_symbol_definition]) ).
fof(f17391,plain,
( sQ848_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17387,f2403,f17388]) ).
fof(f17409,plain,
( sK34_skl(empty_set,empty_set) = empty_set
| empty_set = powerset(empty_set) ),
inference(resolution,[status(thm)],[f5459,f2222]) ).
fof(f17428,definition,
( sQ849_spl
<=> sK34_skl(empty_set,empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ849_spl])],[split_symbol_definition]) ).
fof(f17431,plain,
( sQ849_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f17409,f8595,f17428]) ).
fof(f17432,plain,
! [X0,X1,X2] :
( ~ sQ29_spl
| X2 = X1
| sK35_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2477,f5667]) ).
fof(f17435,definition,
! [X0,X1,X2] :
( sQ850_spl
<=> ( X2 = X1
| sK35_skl(X2,ordered_pair(X0,X1)) = empty_set
| ~ in(ordered_pair(X0,X1),empty_set) ) ),
introduced(definition,[new_symbols(definition,[sQ850_spl])],[split_symbol_definition]) ).
fof(f17438,plain,
( ~ sQ29_spl
| sQ850_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17432,f2403,f2362,f17435,f2472]) ).
fof(f17536,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f1104,f1103]) ).
fof(f17558,definition,
! [X0,X1] :
( sQ852_spl
<=> ~ in(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ852_spl])],[split_symbol_definition]) ).
fof(f17559,plain,
! [X0,X1] :
( ~ sQ852_spl
| ~ in(X0,X1) ),
inference(component_clause,[status(thm)],[f17558]) ).
fof(f17561,definition,
! [X2,X3] :
( sQ853_spl
<=> ( in(X2,X3)
| ~ in(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ853_spl])],[split_symbol_definition]) ).
fof(f17564,plain,
( sQ853_spl
| sQ852_spl ),
inference(split_clause,[status(thm)],[f17536,f17558,f17561]) ).
fof(f17637,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ852_spl
| in(sK216_skl,set_difference(sK212_skl,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f8912,f17559]) ).
fof(f17693,plain,
( ~ sQ8_spl
| ~ sQ852_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17637,f17559]) ).
fof(f17694,plain,
( ~ sQ8_spl
| ~ sQ852_spl ),
inference(contradiction_clause,[status(thm)],[f17693]) ).
fof(f17697,plain,
! [X0] :
( in(X0,relation_dom(empty_set))
| ~ in(X0,relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3942,f1112]) ).
fof(f17698,definition,
! [X0] :
( sQ854_spl
<=> ( in(X0,relation_dom(empty_set))
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ854_spl])],[split_symbol_definition]) ).
fof(f17701,plain,
( sQ854_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17697,f2403,f2362,f17698]) ).
fof(f17702,plain,
! [X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(empty_set))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f3942,f1113]) ).
fof(f17703,definition,
! [X0,X1] :
( sQ855_spl
<=> ( in(X0,X1)
| ~ in(X0,relation_dom(empty_set)) ) ),
introduced(definition,[new_symbols(definition,[sQ855_spl])],[split_symbol_definition]) ).
fof(f17706,plain,
( sQ855_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17702,f2403,f2362,f17703]) ).
fof(f17711,plain,
! [X0,X1] :
( ~ sQ29_spl
| ~ in(empty_set,X1)
| ~ in(X0,relation_dom(empty_set))
| in(X0,relation_inverse_image(empty_set,X1))
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(paramodulation,[status(thm)],[f2477,f2191]) ).
fof(f17712,definition,
! [X0,X1] :
( sQ856_spl
<=> ( ~ in(empty_set,X1)
| ~ in(X0,relation_dom(empty_set))
| in(X0,relation_inverse_image(empty_set,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ856_spl])],[split_symbol_definition]) ).
fof(f17715,plain,
( ~ sQ29_spl
| sQ856_spl
| ~ sQ13_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f17711,f2403,f2362,f17712,f2472]) ).
fof(f17749,plain,
( ~ sQ9_spl
| ~ in(sK216_skl,relation_dom(sK214_skl))
| in(sK216_skl,relation_inverse_image(sK214_skl,sK215_skl))
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2172,f2191]) ).
fof(f17751,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| sQ7_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f17749,f2351,f2354,f2164,f2357,f2171]) ).
fof(f17834,plain,
( sQ705_spl
| ~ relation_of2_as_subset(sK214_skl,sK212_skl,sK213_skl) ),
inference(resolution,[status(thm)],[f1193,f14000]) ).
fof(f17838,plain,
( sQ705_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f17834,f3178,f13998]) ).
fof(f18898,plain,
( one_to_one(empty_set)
| ~ equipotent(empty_set,empty_set) ),
inference(paramodulation,[status(thm)],[f16852,f766]) ).
fof(f18900,definition,
( sQ857_spl
<=> equipotent(empty_set,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ857_spl])],[split_symbol_definition]) ).
fof(f18902,plain,
( sQ857_spl
| ~ equipotent(empty_set,empty_set) ),
inference(component_clause,[status(thm)],[f18900]) ).
fof(f18903,definition,
( sQ858_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ858_spl])],[split_symbol_definition]) ).
fof(f18906,plain,
( sQ858_spl
| ~ sQ857_spl ),
inference(split_clause,[status(thm)],[f18898,f18900,f18903]) ).
fof(f18908,plain,
( sQ857_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18902,f1209]) ).
fof(f18909,plain,
sQ857_spl,
inference(contradiction_clause,[status(thm)],[f18908]) ).
fof(f19042,plain,
( ~ sQ705_spl
| relation_dom_as_subset(sK212_skl,sK213_skl,sK214_skl) = relation_dom(sK214_skl) ),
inference(resolution,[status(thm)],[f13999,f1182]) ).
fof(f19044,plain,
( ~ sQ705_spl
| ~ sQ171_spl
| sK212_skl = relation_dom(sK214_skl) ),
inference(forward_demodulation,[status(thm)],[f3822,f19042]) ).
fof(f19045,plain,
( ~ sQ705_spl
| ~ sQ171_spl
| sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19044,f2686]) ).
fof(f19046,plain,
( ~ sQ705_spl
| ~ sQ171_spl
| sQ64_spl ),
inference(contradiction_clause,[status(thm)],[f19045]) ).
fof(f19048,plain,
( sQ12_spl
| ~ sQ705_spl
| ~ sQ171_spl
| ~ in(sK216_skl,sK212_skl) ),
inference(backward_demodulation,[status(thm)],[f19044,f2359]) ).
fof(f19056,plain,
! [X0] :
( ~ sQ705_spl
| ~ sQ171_spl
| subset(relation_dom(relation_rng_restriction(X0,sK214_skl)),sK212_skl)
| ~ relation(sK214_skl) ),
inference(paramodulation,[status(thm)],[f19044,f1050]) ).
fof(f19057,plain,
( sQ12_spl
| ~ sQ705_spl
| ~ sQ171_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f19048,f2167,f3821,f13998,f2357]) ).
fof(f19060,definition,
! [X0] :
( sQ866_spl
<=> subset(relation_dom(relation_rng_restriction(X0,sK214_skl)),sK212_skl) ),
introduced(definition,[new_symbols(definition,[sQ866_spl])],[split_symbol_definition]) ).
fof(f19063,plain,
( ~ sQ705_spl
| ~ sQ171_spl
| sQ866_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f19056,f2351,f19060,f3821,f13998]) ).
fof(f19092,plain,
( ~ sQ847_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17383,f2222]) ).
fof(f19093,plain,
~ sQ847_spl,
inference(contradiction_clause,[status(thm)],[f19092]) ).
fof(f19095,plain,
( ~ sQ7_spl
| in(apply(sK214_skl,sK216_skl),sK215_skl)
| ~ function(sK214_skl)
| ~ relation(sK214_skl) ),
inference(resolution,[status(thm)],[f2165,f2190]) ).
fof(f19101,plain,
( ~ sQ7_spl
| sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f19095,f2351,f2354,f2171,f2164]) ).
fof(f19102,plain,
$false,
inference(sat_refutation,[status(thm)],[f2151,f2155,f2159,f2163,f2170,f2174,f2175,f2360,f2368,f2370,f2378,f2385,f2387,f2390,f2398,f2401,f2409,f2411,f2420,f2432,f2442,f2455,f2467,f2471,f2475,f2481,f2490,f2494,f2510,f2517,f2541,f2545,f2552,f2565,f2572,f2589,f2594,f2611,f2615,f2626,f2674,f2678,f2699,f2703,f2773,f2777,f2781,f2785,f2939,f2943,f2953,f2982,f2989,f2993,f2997,f3001,f3007,f3009,f3084,f3088,f3092,f3096,f3100,f3113,f3138,f3187,f3189,f3191,f3276,f3280,f3325,f3337,f3350,f3354,f3358,f3377,f3525,f3556,f3583,f3637,f3644,f3783,f3787,f3824,f3826,f3852,f4020,f4024,f4028,f4057,f4061,f4065,f4257,f4261,f4307,f4338,f4345,f4349,f4383,f4390,f4394,f4438,f4445,f4449,f4521,f4525,f4662,f4670,f4681,f4765,f4826,f4872,f4876,f4896,f4948,f4973,f4977,f4993,f5032,f5036,f5093,f5273,f5329,f5346,f5359,f5361,f5405,f5490,f5494,f5498,f5544,f5825,f5831,f6158,f6196,f6237,f6319,f6385,f6751,f6789,f6791,f6952,f7010,f7014,f7018,f7029,f7209,f7379,f7446,f7572,f7576,f7654,f7658,f7662,f7664,f7682,f7703,f7765,f7776,f7780,f7784,f8153,f8160,f8162,f8268,f8312,f8316,f8360,f8461,f8465,f8601,f8603,f8609,f8816,f8832,f8836,f8981,f8984,f8992,f9038,f9109,f9114,f9118,f9122,f9130,f9138,f9150,f9183,f9188,f9192,f9196,f9204,f9212,f9222,f9313,f9342,f9374,f9413,f9471,f9646,f9650,f9698,f9894,f9922,f9953,f9958,f10013,f10025,f10108,f10119,f10175,f10182,f10189,f10196,f10200,f10203,f10206,f10209,f10227,f10269,f10274,f10282,f10290,f10322,f10329,f10332,f10372,f10379,f10479,f10481,f10484,f10496,f10501,f10502,f10511,f10518,f10546,f10558,f10574,f10607,f10613,f10621,f10631,f10633,f10642,f10663,f10667,f10688,f10690,f10697,f10699,f10726,f10738,f10795,f10800,f10804,f10808,f10812,f10828,f10838,f10905,f10990,f11016,f11040,f11042,f11088,f11107,f11111,f11120,f11131,f11273,f11298,f11300,f11352,f11407,f11411,f11499,f11541,f11546,f11550,f11554,f11570,f11588,f11593,f11597,f11601,f11617,f11626,f11923,f11928,f11932,f11936,f11946,f11955,f11974,f12044,f12048,f12104,f12212,f12216,f12264,f12268,f12331,f12339,f13318,f13322,f13333,f13398,f13445,f13531,f13535,f13539,f13547,f13563,f13567,f13571,f13579,f13620,f13676,f13767,f13785,f13789,f13793,f13797,f13801,f13805,f13824,f13828,f13832,f13836,f13840,f13859,f13863,f13867,f13871,f13875,f13879,f13898,f13902,f13906,f13910,f13914,f13932,f13936,f13940,f13944,f13948,f13952,f13971,f13975,f13979,f13983,f13987,f14004,f14044,f14057,f14068,f14072,f14287,f14294,f14341,f14348,f14419,f14426,f14432,f14920,f14973,f15026,f15030,f15034,f15038,f15042,f15046,f15065,f15069,f15073,f15077,f15081,f15119,f15134,f15327,f15336,f15337,f15405,f15412,f15416,f15420,f15430,f15437,f15442,f15508,f15515,f15519,f15523,f15531,f15620,f15781,f15794,f15811,f15815,f15888,f15994,f15999,f16029,f16041,f16051,f16126,f16188,f16207,f16276,f16278,f16385,f16482,f16486,f16490,f16505,f16509,f16513,f16557,f16567,f16571,f16619,f16625,f16629,f16633,f16655,f16659,f16663,f16799,f16875,f17017,f17066,f17185,f17200,f17248,f17365,f17391,f17431,f17438,f17564,f17694,f17701,f17706,f17715,f17751,f17838,f18906,f18909,f19046,f19057,f19063,f19093,f19101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU293+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 06:08:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 160.09/22.73 % Refutation found
% 160.09/22.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 160.09/22.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 160.09/22.79 % Elapsed time: 22.408814 seconds
% 160.09/22.79 % CPU time: 177.305323 seconds
% 160.09/22.79 % Total memory used: 603.316 MB
% 160.09/22.79 % Net memory used: 518.591 MB
%------------------------------------------------------------------------------