%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU264+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 08:58:46 AM UTC 2026
% Result : Theorem 150.14s 150.45s
% Output : Proof 150.26s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d10_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('theBenchmark.p',d10_relat_1) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d11_relat_1,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('theBenchmark.p',d11_relat_1) ).
fof(d12_funct_1,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('theBenchmark.p',d12_funct_1) ).
fof(d12_relat_1,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('theBenchmark.p',d12_relat_1) ).
fof(d12_relat_2,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> is_antisymmetric_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d12_relat_2) ).
fof(d13_funct_1,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('theBenchmark.p',d13_funct_1) ).
fof(d13_relat_1,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('theBenchmark.p',d13_relat_1) ).
fof(d14_relat_1,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('theBenchmark.p',d14_relat_1) ).
fof(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_relat_2) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_relat_2) ).
fof(d1_enumset1,axiom,
! [A,B,C,D] :
( D = unordered_triple(A,B,C)
<=> ! [E] :
( in(E,D)
<=> ~ ( E != C
& E != B
& E != A ) ) ),
file('theBenchmark.p',d1_enumset1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_relat_1,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('theBenchmark.p',d1_relat_1) ).
fof(d1_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('theBenchmark.p',d1_relat_2) ).
fof(d1_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
<=> subset(C,cartesian_product2(A,B)) ),
file('theBenchmark.p',d1_relset_1) ).
fof(d1_setfam_1,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('theBenchmark.p',d1_setfam_1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('theBenchmark.p',d1_wellord1) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d2_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d2_relat_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('theBenchmark.p',d2_wellord1) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(d3_ordinal1,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('theBenchmark.p',d3_ordinal1) ).
fof(d3_relat_1,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('theBenchmark.p',d3_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_wellord1,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('theBenchmark.p',d3_wellord1) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d4_funct_1,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('theBenchmark.p',d4_funct_1) ).
fof(d4_ordinal1,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',d4_ordinal1) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d4_relat_2,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('theBenchmark.p',d4_relat_2) ).
fof(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('theBenchmark.p',d4_wellord1) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_funct_1,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('theBenchmark.p',d5_funct_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d5_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( well_orders(A,B)
<=> ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) ) ) ),
file('theBenchmark.p',d5_wellord1) ).
fof(d6_ordinal1,axiom,
! [A] :
( being_limit_ordinal(A)
<=> A = union(A) ),
file('theBenchmark.p',d6_ordinal1) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d6_relat_2,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('theBenchmark.p',d6_relat_2) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('theBenchmark.p',d6_wellord1) ).
fof(d7_relat_1,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('theBenchmark.p',d7_relat_1) ).
fof(d7_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
<=> ( ! [D,E] :
( in(ordered_pair(D,E),A)
<=> ( in(ordered_pair(apply(C,D),apply(C,E)),B)
& in(E,relation_field(A))
& in(D,relation_field(A)) ) )
& one_to_one(C)
& relation_rng(C) = relation_field(B)
& relation_dom(C) = relation_field(A) ) ) ) ) ),
file('theBenchmark.p',d7_wellord1) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_funct_1,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('theBenchmark.p',d8_funct_1) ).
fof(d8_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) ) ) ) ) ),
file('theBenchmark.p',d8_relat_1) ).
fof(d8_relat_2,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('theBenchmark.p',d8_relat_2) ).
fof(d8_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('theBenchmark.p',d8_setfam_1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(d9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('theBenchmark.p',d9_funct_1) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d9_relat_2) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k1_enumset1,axiom,
$true,
file('theBenchmark.p',dt_k1_enumset1) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_ordinal1,axiom,
$true,
file('theBenchmark.p',dt_k1_ordinal1) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_setfam_1,axiom,
$true,
file('theBenchmark.p',dt_k1_setfam_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_wellord1,axiom,
$true,
file('theBenchmark.p',dt_k1_wellord1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_subset_1,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('theBenchmark.p',dt_k2_subset_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k3_tarski,axiom,
$true,
file('theBenchmark.p',dt_k3_tarski) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ),
file('theBenchmark.p',dt_k4_relat_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
fof(dt_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : relation_of2(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_1) ).
fof(fc11_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_inverse(A))
& empty(relation_inverse(A)) ) ),
file('theBenchmark.p',fc11_relat_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc13_relat_1,axiom,
! [A,B] :
( ( relation_empty_yielding(A)
& relation(A) )
=> ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc13_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(fc1_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(fc2_ordinal1,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('theBenchmark.p',fc2_ordinal1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_funct_1,axiom,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
=> ( function(relation_inverse(A))
& relation(relation_inverse(A)) ) ),
file('theBenchmark.p',fc3_funct_1) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(fc3_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_difference(A,B)) ),
file('theBenchmark.p',fc3_relat_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(fc4_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) ) ),
file('theBenchmark.p',fc4_ordinal1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc4_subset_1,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ~ empty(cartesian_product2(A,B)) ),
file('theBenchmark.p',fc4_subset_1) ).
fof(fc5_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('theBenchmark.p',fc5_funct_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(l1_wellord1,lemma,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('theBenchmark.p',l1_wellord1) ).
fof(l1_zfmisc_1,lemma,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l23_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',l23_zfmisc_1) ).
fof(l25_zfmisc_1,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,lemma,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l29_wellord1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
file('theBenchmark.p',l29_wellord1) ).
fof(l2_wellord1,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('theBenchmark.p',l2_wellord1) ).
fof(l2_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l32_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',l32_xboole_1) ).
fof(l3_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_wellord1,lemma,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('theBenchmark.p',l3_wellord1) ).
fof(l3_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(l4_wellord1,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('theBenchmark.p',l4_wellord1) ).
fof(l4_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l50_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l55_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(l71_subset_1,lemma,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(l82_funct_1,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('theBenchmark.p',l82_funct_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t106_zfmisc_1,lemma,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t10_ordinal1,lemma,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t10_zfmisc_1,lemma,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t115_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t115_relat_1) ).
fof(t116_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('theBenchmark.p',t116_relat_1) ).
fof(t117_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('theBenchmark.p',t117_relat_1) ).
fof(t118_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('theBenchmark.p',t118_relat_1) ).
fof(t118_zfmisc_1,lemma,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t119_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A) ),
file('theBenchmark.p',t119_relat_1) ).
fof(t119_zfmisc_1,lemma,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t12_relset_1,lemma,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
file('theBenchmark.p',t12_relset_1) ).
fof(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t136_zfmisc_1,lemma,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t136_zfmisc_1) ).
fof(t140_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
file('theBenchmark.p',t140_relat_1) ).
fof(t143_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) ) ) ),
file('theBenchmark.p',t143_relat_1) ).
fof(t144_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_relat_1) ).
fof(t145_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
file('theBenchmark.p',t145_funct_1) ).
fof(t145_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)) ),
file('theBenchmark.p',t145_relat_1) ).
fof(t146_funct_1,lemma,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('theBenchmark.p',t146_funct_1) ).
fof(t146_relat_1,lemma,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_relat_1) ).
fof(t147_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('theBenchmark.p',t147_funct_1) ).
fof(t14_relset_1,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('theBenchmark.p',t14_relset_1) ).
fof(t160_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)) ) ),
file('theBenchmark.p',t160_relat_1) ).
fof(t166_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_inverse_image(C,B))
<=> ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) ) ) ),
file('theBenchmark.p',t166_relat_1) ).
fof(t167_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('theBenchmark.p',t167_relat_1) ).
fof(t16_relset_1,conjecture,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t16_relset_1) ).
fof(t16_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t174_relat_1,lemma,
! [A,B] :
( relation(B)
=> ~ ( relation_inverse_image(B,A) = empty_set
& subset(A,relation_rng(B))
& A != empty_set ) ),
file('theBenchmark.p',t174_relat_1) ).
fof(t178_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('theBenchmark.p',t178_relat_1) ).
fof(t17_wellord1,lemma,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
file('theBenchmark.p',t17_wellord1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t18_wellord1,lemma,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ),
file('theBenchmark.p',t18_wellord1) ).
fof(t19_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_field(relation_restriction(C,B)))
=> ( in(A,B)
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t19_wellord1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t1_zfmisc_1,lemma,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t20_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t20_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( subset(relation_field(relation_restriction(B,A)),A)
& subset(relation_field(relation_restriction(B,A)),relation_field(B)) ) ),
file('theBenchmark.p',t20_wellord1) ).
fof(t21_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_1) ).
fof(t21_ordinal1,lemma,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('theBenchmark.p',t21_ordinal1) ).
fof(t21_relat_1,lemma,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('theBenchmark.p',t21_relat_1) ).
fof(t21_wellord1,lemma,
! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
file('theBenchmark.p',t21_wellord1) ).
fof(t22_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('theBenchmark.p',t22_funct_1) ).
fof(t22_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t22_wellord1) ).
fof(t23_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
fof(t23_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('theBenchmark.p',t23_ordinal1) ).
fof(t23_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( connected(B)
=> connected(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t23_wellord1) ).
fof(t24_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('theBenchmark.p',t24_ordinal1) ).
fof(t24_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t24_wellord1) ).
fof(t25_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('theBenchmark.p',t25_relat_1) ).
fof(t25_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t25_wellord1) ).
fof(t26_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t30_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t31_ordinal1,lemma,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('theBenchmark.p',t31_ordinal1) ).
fof(t31_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( well_founded_relation(B)
=> well_founded_relation(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t31_wellord1) ).
fof(t32_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
file('theBenchmark.p',t32_ordinal1) ).
fof(t32_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t32_wellord1) ).
fof(t33_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t34_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t35_funct_1,lemma,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t38_zfmisc_1,lemma,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t39_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( ( subset(A,relation_field(B))
& well_ordering(B) )
=> relation_field(relation_restriction(B,A)) = A ) ),
file('theBenchmark.p',t39_wellord1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t39_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_ordinal1,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('theBenchmark.p',t3_ordinal1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t41_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('theBenchmark.p',t41_ordinal1) ).
fof(t42_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('theBenchmark.p',t42_ordinal1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t49_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> relation_isomorphism(B,A,function_inverse(C)) ) ) ) ),
file('theBenchmark.p',t49_wellord1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t53_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( well_founded_relation(A)
=> well_founded_relation(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( connected(A)
=> connected(B) )
& ( transitive(A)
=> transitive(B) )
& ( reflexive(A)
=> reflexive(B) ) ) ) ) ) ),
file('theBenchmark.p',t53_wellord1) ).
fof(t54_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t54_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('theBenchmark.p',t54_wellord1) ).
fof(t55_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t57_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t62_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t68_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t70_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t72_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_tarski,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('theBenchmark.p',t7_tarski) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(t8_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('theBenchmark.p',t8_wellord1) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t90_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t94_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
fof(t99_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_0,U_1] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_4_2,plain,
! [U_5] :
( ( epsilon_connected(U_5)
& epsilon_transitive(U_5) )
| ~ ordinal(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_5] :
( epsilon_connected(U_5)
| ~ sP0(U_5) )
& ! [U_5] :
( epsilon_transitive(U_5)
| ~ sP0(U_5) )
& ! [U_5] :
( sP0(U_5)
| ~ ordinal(U_5) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP0(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( epsilon_transitive(U_5)
| ~ sP0(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( epsilon_connected(U_5)
| ~ sP0(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_5_2,plain,
! [U_6] :
( relation(U_6)
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_6] :
( relation(U_6)
| ~ empty(U_6) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( relation(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_6_2,plain,
! [U_9,U_8,U_7] :
( relation(U_7)
| ~ element(U_7,powerset(cartesian_product2(U_9,U_8))) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_7,U_8,U_9] :
( relation(U_7)
| ~ element(U_7,powerset(cartesian_product2(U_9,U_8))) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( relation(U_7)
| ~ element(U_7,powerset(cartesian_product2(U_9,U_8))) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_7_2,plain,
! [U_10] :
( ( one_to_one(U_10)
& function(U_10)
& relation(U_10) )
| ~ function(U_10)
| ~ empty(U_10)
| ~ relation(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_10] :
( one_to_one(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( function(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( relation(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( sP1(U_10)
| ~ function(U_10)
| ~ empty(U_10)
| ~ relation(U_10) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP1(U_10)
| ~ function(U_10)
| ~ empty(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( relation(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( function(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( one_to_one(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_8_2,plain,
! [U_11] :
( ordinal(U_11)
| ~ epsilon_connected(U_11)
| ~ epsilon_transitive(U_11) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_11] :
( ordinal(U_11)
| ~ epsilon_connected(U_11)
| ~ epsilon_transitive(U_11) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( ordinal(U_11)
| ~ epsilon_connected(U_11)
| ~ epsilon_transitive(U_11) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_9_2,plain,
! [U_12] :
( ( ordinal(U_12)
& epsilon_connected(U_12)
& epsilon_transitive(U_12) )
| ~ empty(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_12] :
( ordinal(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( epsilon_connected(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( epsilon_transitive(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( sP2(U_12)
| ~ empty(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP2(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( epsilon_transitive(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( epsilon_connected(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( ordinal(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_10_2,plain,
! [U_14,U_13] : unordered_pair(U_14,U_13) = unordered_pair(U_13,U_14),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_13,U_14] : unordered_pair(U_14,U_13) = unordered_pair(U_13,U_14),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
unordered_pair(U_14,U_13) = unordered_pair(U_13,U_14),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_11_2,plain,
! [U_16,U_15] : set_union2(U_16,U_15) = set_union2(U_15,U_16),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_15,U_16] : set_union2(U_16,U_15) = set_union2(U_15,U_16),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
set_union2(U_16,U_15) = set_union2(U_15,U_16),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_12_2,plain,
! [U_18,U_17] : set_intersection2(U_18,U_17) = set_intersection2(U_17,U_18),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_17,U_18] : set_intersection2(U_18,U_17) = set_intersection2(U_17,U_18),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
set_intersection2(U_18,U_17) = set_intersection2(U_17,U_18),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1]) ).
fof(f_13_2,plain,
! [U_20,U_19] :
( ordinal_subset(U_19,U_20)
| ordinal_subset(U_20,U_19)
| ~ ordinal(U_19)
| ~ ordinal(U_20) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_19,U_20] :
( ordinal_subset(U_19,U_20)
| ordinal_subset(U_20,U_19)
| ~ ordinal(U_19)
| ~ ordinal(U_20) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( ordinal_subset(U_19,U_20)
| ordinal_subset(U_20,U_19)
| ~ ordinal(U_19)
| ~ ordinal(U_20) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& C = D
& in(C,A) )
| ( ( C != D
| ~ in(C,A) )
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| C != D
| ~ in(C,A) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d10_relat_1]) ).
fof(f_14_2,plain,
! [U_26,U_25] :
( ( ( U_25 = identity_relation(U_26)
| ? [U_24,U_23] :
( ( ~ in(ordered_pair(U_24,U_23),U_25)
& U_24 = U_23
& in(U_24,U_26) )
| ( ( U_24 != U_23
| ~ in(U_24,U_26) )
& in(ordered_pair(U_24,U_23),U_25) ) ) )
& ( ! [U_22,U_21] :
( ( in(ordered_pair(U_22,U_21),U_25)
| U_22 != U_21
| ~ in(U_22,U_26) )
& ( ( U_22 = U_21
& in(U_22,U_26) )
| ~ in(ordered_pair(U_22,U_21),U_25) ) )
| U_25 != identity_relation(U_26) ) )
| ~ relation(U_25) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_26,U_25] :
( ( ( U_25 = identity_relation(U_26)
| ? [U_34,U_32] :
( ~ in(ordered_pair(U_34,U_32),U_25)
& U_34 = U_32
& in(U_34,U_26) )
| ? [U_33,U_31] :
( ( U_33 != U_31
| ~ in(U_33,U_26) )
& in(ordered_pair(U_33,U_31),U_25) ) )
& ( ( ! [U_30,U_28] :
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26) )
& ! [U_29,U_27] :
( ( U_29 = U_27
& in(U_29,U_26) )
| ~ in(ordered_pair(U_29,U_27),U_25) ) )
| U_25 != identity_relation(U_26) ) )
| ~ relation(U_25) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
! [U_26,U_25] :
( ( ( U_25 = identity_relation(U_26)
| ? [U_34,U_32] :
( ~ in(ordered_pair(U_34,U_32),U_25)
& U_34 = U_32
& in(U_34,U_26) )
| ? [U_31] :
( ( sK1(U_26,U_25) != U_31
| ~ in(sK1(U_26,U_25),U_26) )
& in(ordered_pair(sK1(U_26,U_25),U_31),U_25) ) )
& ( ( ! [U_30,U_28] :
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26) )
& ! [U_29,U_27] :
( ( U_29 = U_27
& in(U_29,U_26) )
| ~ in(ordered_pair(U_29,U_27),U_25) ) )
| U_25 != identity_relation(U_26) ) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_33,sK1(U_26,U_25))],[f_14_3]) ).
fof(f_14_5,plain,
! [U_26,U_25] :
( ( ( U_25 = identity_relation(U_26)
| ? [U_34,U_32] :
( ~ in(ordered_pair(U_34,U_32),U_25)
& U_34 = U_32
& in(U_34,U_26) )
| ( ( sK1(U_26,U_25) != sK2(U_26,U_25)
| ~ in(sK1(U_26,U_25),U_26) )
& in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25) ) )
& ( ( ! [U_30,U_28] :
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26) )
& ! [U_29,U_27] :
( ( U_29 = U_27
& in(U_29,U_26) )
| ~ in(ordered_pair(U_29,U_27),U_25) ) )
| U_25 != identity_relation(U_26) ) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_31,sK2(U_26,U_25))],[f_14_4]) ).
fof(f_14_6,plain,
! [U_26,U_25] :
( ( ( U_25 = identity_relation(U_26)
| ? [U_32] :
( ~ in(ordered_pair(sK3(U_26,U_25),U_32),U_25)
& sK3(U_26,U_25) = U_32
& in(sK3(U_26,U_25),U_26) )
| ( ( sK1(U_26,U_25) != sK2(U_26,U_25)
| ~ in(sK1(U_26,U_25),U_26) )
& in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25) ) )
& ( ( ! [U_30,U_28] :
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26) )
& ! [U_29,U_27] :
( ( U_29 = U_27
& in(U_29,U_26) )
| ~ in(ordered_pair(U_29,U_27),U_25) ) )
| U_25 != identity_relation(U_26) ) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_34,sK3(U_26,U_25))],[f_14_5]) ).
fof(f_14_7,plain,
! [U_26,U_25] :
( ( ( U_25 = identity_relation(U_26)
| ( ~ in(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_25)
& sK3(U_26,U_25) = sK4(U_26,U_25)
& in(sK3(U_26,U_25),U_26) )
| ( ( sK1(U_26,U_25) != sK2(U_26,U_25)
| ~ in(sK1(U_26,U_25),U_26) )
& in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25) ) )
& ( ( ! [U_30,U_28] :
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26) )
& ! [U_29,U_27] :
( ( U_29 = U_27
& in(U_29,U_26) )
| ~ in(ordered_pair(U_29,U_27),U_25) ) )
| U_25 != identity_relation(U_26) ) )
| ~ relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_32,sK4(U_26,U_25))],[f_14_6]) ).
fof(f_14_8,plain,
( ! [U_25,U_26] :
( ~ in(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_25)
| ~ sP6(U_25,U_26) )
& ! [U_25,U_26] :
( sK3(U_26,U_25) = sK4(U_26,U_25)
| ~ sP6(U_25,U_26) )
& ! [U_25,U_26] :
( in(sK3(U_26,U_25),U_26)
| ~ sP6(U_25,U_26) )
& ! [U_25,U_26] :
( sK1(U_26,U_25) != sK2(U_26,U_25)
| ~ in(sK1(U_26,U_25),U_26)
| ~ sP5(U_25,U_26) )
& ! [U_25,U_26] :
( in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25)
| ~ sP5(U_25,U_26) )
& ! [U_29,U_26,U_27] :
( U_29 = U_27
| ~ sP3(U_29,U_26,U_27) )
& ! [U_29,U_26,U_27] :
( in(U_29,U_26)
| ~ sP3(U_29,U_26,U_27) )
& ! [U_29,U_25,U_26,U_27,U_28,U_30] :
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26)
| ~ sP4(U_29,U_25,U_26,U_27,U_28,U_30) )
& ! [U_29,U_25,U_26,U_27,U_28,U_30] :
( sP3(U_29,U_26,U_27)
| ~ in(ordered_pair(U_29,U_27),U_25)
| ~ sP4(U_29,U_25,U_26,U_27,U_28,U_30) )
& ! [U_29,U_25,U_26,U_27,U_28,U_30] :
( U_25 = identity_relation(U_26)
| sP6(U_25,U_26)
| sP5(U_25,U_26)
| ~ sP7(U_29,U_25,U_26,U_27,U_28,U_30) )
& ! [U_29,U_25,U_26,U_27,U_28,U_30] :
( sP4(U_29,U_25,U_26,U_27,U_28,U_30)
| U_25 != identity_relation(U_26)
| ~ sP7(U_29,U_25,U_26,U_27,U_28,U_30) )
& ! [U_29,U_25,U_26,U_27,U_28,U_30] :
( sP7(U_29,U_25,U_26,U_27,U_28,U_30)
| ~ relation(U_25) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4,sP5,sP6,sP7])],[f_14_7]) ).
cnf(f_14_9,plain,
( sP7(U_29,U_25,U_26,U_27,U_28,U_30)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_10,plain,
( sP4(U_29,U_25,U_26,U_27,U_28,U_30)
| U_25 != identity_relation(U_26)
| ~ sP7(U_29,U_25,U_26,U_27,U_28,U_30) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_11,plain,
( U_25 = identity_relation(U_26)
| sP6(U_25,U_26)
| sP5(U_25,U_26)
| ~ sP7(U_29,U_25,U_26,U_27,U_28,U_30) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_12,plain,
( sP3(U_29,U_26,U_27)
| ~ in(ordered_pair(U_29,U_27),U_25)
| ~ sP4(U_29,U_25,U_26,U_27,U_28,U_30) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_13,plain,
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26)
| ~ sP4(U_29,U_25,U_26,U_27,U_28,U_30) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_14,plain,
( in(U_29,U_26)
| ~ sP3(U_29,U_26,U_27) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_15,plain,
( U_29 = U_27
| ~ sP3(U_29,U_26,U_27) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_16,plain,
( in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25)
| ~ sP5(U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_17,plain,
( sK1(U_26,U_25) != sK2(U_26,U_25)
| ~ in(sK1(U_26,U_25),U_26)
| ~ sP5(U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_18,plain,
( in(sK3(U_26,U_25),U_26)
| ~ sP6(U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_19,plain,
( sK3(U_26,U_25) = sK4(U_26,U_25)
| ~ sP6(U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_20,plain,
( ~ in(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_25)
| ~ sP6(U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_8]) ).
fof(f_15_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_15_2,plain,
! [U_36,U_35] :
( ( U_36 = U_35
| ~ subset(U_35,U_36)
| ~ subset(U_36,U_35) )
& ( ( subset(U_35,U_36)
& subset(U_36,U_35) )
| U_36 != U_35 ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_40,U_38] :
( U_40 = U_38
| ~ subset(U_38,U_40)
| ~ subset(U_40,U_38) )
& ! [U_39,U_37] :
( ( subset(U_37,U_39)
& subset(U_39,U_37) )
| U_39 != U_37 ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_39,U_37] :
( subset(U_37,U_39)
| ~ sP8(U_39,U_37) )
& ! [U_39,U_37] :
( subset(U_39,U_37)
| ~ sP8(U_39,U_37) )
& ! [U_38,U_40] :
( U_40 = U_38
| ~ subset(U_38,U_40)
| ~ subset(U_40,U_38) )
& ! [U_39,U_37] :
( sP8(U_39,U_37)
| U_39 != U_37 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP8(U_39,U_37)
| U_39 != U_37 ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( U_40 = U_38
| ~ subset(U_38,U_40)
| ~ subset(U_40,U_38) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( subset(U_39,U_37)
| ~ sP8(U_39,U_37) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_8,plain,
( subset(U_37,U_39)
| ~ sP8(U_39,U_37) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,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) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( 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(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_16_2,plain,
! [U_47] :
( ! [U_46,U_45] :
( ( ( U_45 = relation_dom_restriction(U_47,U_46)
| ? [U_44,U_43] :
( ( ~ in(ordered_pair(U_44,U_43),U_45)
& in(ordered_pair(U_44,U_43),U_47)
& in(U_44,U_46) )
| ( ( ~ in(ordered_pair(U_44,U_43),U_47)
| ~ in(U_44,U_46) )
& in(ordered_pair(U_44,U_43),U_45) ) ) )
& ( ! [U_42,U_41] :
( ( in(ordered_pair(U_42,U_41),U_45)
| ~ in(ordered_pair(U_42,U_41),U_47)
| ~ in(U_42,U_46) )
& ( ( in(ordered_pair(U_42,U_41),U_47)
& in(U_42,U_46) )
| ~ in(ordered_pair(U_42,U_41),U_45) ) )
| U_45 != relation_dom_restriction(U_47,U_46) ) )
| ~ relation(U_45) )
| ~ relation(U_47) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_47] :
( ! [U_46,U_45] :
( ( ( U_45 = relation_dom_restriction(U_47,U_46)
| ? [U_55,U_53] :
( ~ in(ordered_pair(U_55,U_53),U_45)
& in(ordered_pair(U_55,U_53),U_47)
& in(U_55,U_46) )
| ? [U_54,U_52] :
( ( ~ in(ordered_pair(U_54,U_52),U_47)
| ~ in(U_54,U_46) )
& in(ordered_pair(U_54,U_52),U_45) ) )
& ( ( ! [U_51,U_49] :
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46) )
& ! [U_50,U_48] :
( ( in(ordered_pair(U_50,U_48),U_47)
& in(U_50,U_46) )
| ~ in(ordered_pair(U_50,U_48),U_45) ) )
| U_45 != relation_dom_restriction(U_47,U_46) ) )
| ~ relation(U_45) )
| ~ relation(U_47) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_47] :
( ! [U_46,U_45] :
( ( ( U_45 = relation_dom_restriction(U_47,U_46)
| ? [U_55,U_53] :
( ~ in(ordered_pair(U_55,U_53),U_45)
& in(ordered_pair(U_55,U_53),U_47)
& in(U_55,U_46) )
| ? [U_52] :
( ( ~ in(ordered_pair(sK5(U_47,U_46,U_45),U_52),U_47)
| ~ in(sK5(U_47,U_46,U_45),U_46) )
& in(ordered_pair(sK5(U_47,U_46,U_45),U_52),U_45) ) )
& ( ( ! [U_51,U_49] :
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46) )
& ! [U_50,U_48] :
( ( in(ordered_pair(U_50,U_48),U_47)
& in(U_50,U_46) )
| ~ in(ordered_pair(U_50,U_48),U_45) ) )
| U_45 != relation_dom_restriction(U_47,U_46) ) )
| ~ relation(U_45) )
| ~ relation(U_47) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_54,sK5(U_47,U_46,U_45))],[f_16_3]) ).
fof(f_16_5,plain,
! [U_47] :
( ! [U_46,U_45] :
( ( ( U_45 = relation_dom_restriction(U_47,U_46)
| ? [U_55,U_53] :
( ~ in(ordered_pair(U_55,U_53),U_45)
& in(ordered_pair(U_55,U_53),U_47)
& in(U_55,U_46) )
| ( ( ~ in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_47)
| ~ in(sK5(U_47,U_46,U_45),U_46) )
& in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45) ) )
& ( ( ! [U_51,U_49] :
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46) )
& ! [U_50,U_48] :
( ( in(ordered_pair(U_50,U_48),U_47)
& in(U_50,U_46) )
| ~ in(ordered_pair(U_50,U_48),U_45) ) )
| U_45 != relation_dom_restriction(U_47,U_46) ) )
| ~ relation(U_45) )
| ~ relation(U_47) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_52,sK6(U_47,U_46,U_45))],[f_16_4]) ).
fof(f_16_6,plain,
! [U_47] :
( ! [U_46,U_45] :
( ( ( U_45 = relation_dom_restriction(U_47,U_46)
| ? [U_53] :
( ~ in(ordered_pair(sK7(U_47,U_46,U_45),U_53),U_45)
& in(ordered_pair(sK7(U_47,U_46,U_45),U_53),U_47)
& in(sK7(U_47,U_46,U_45),U_46) )
| ( ( ~ in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_47)
| ~ in(sK5(U_47,U_46,U_45),U_46) )
& in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45) ) )
& ( ( ! [U_51,U_49] :
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46) )
& ! [U_50,U_48] :
( ( in(ordered_pair(U_50,U_48),U_47)
& in(U_50,U_46) )
| ~ in(ordered_pair(U_50,U_48),U_45) ) )
| U_45 != relation_dom_restriction(U_47,U_46) ) )
| ~ relation(U_45) )
| ~ relation(U_47) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_55,sK7(U_47,U_46,U_45))],[f_16_5]) ).
fof(f_16_7,plain,
! [U_47] :
( ! [U_46,U_45] :
( ( ( U_45 = relation_dom_restriction(U_47,U_46)
| ( ~ in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_45)
& in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_47)
& in(sK7(U_47,U_46,U_45),U_46) )
| ( ( ~ in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_47)
| ~ in(sK5(U_47,U_46,U_45),U_46) )
& in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45) ) )
& ( ( ! [U_51,U_49] :
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46) )
& ! [U_50,U_48] :
( ( in(ordered_pair(U_50,U_48),U_47)
& in(U_50,U_46) )
| ~ in(ordered_pair(U_50,U_48),U_45) ) )
| U_45 != relation_dom_restriction(U_47,U_46) ) )
| ~ relation(U_45) )
| ~ relation(U_47) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_53,sK8(U_47,U_46,U_45))],[f_16_6]) ).
fof(f_16_8,plain,
( ! [U_45,U_46,U_47] :
( ~ in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_45)
| ~ sP12(U_45,U_46,U_47) )
& ! [U_45,U_46,U_47] :
( in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_47)
| ~ sP12(U_45,U_46,U_47) )
& ! [U_45,U_46,U_47] :
( in(sK7(U_47,U_46,U_45),U_46)
| ~ sP12(U_45,U_46,U_47) )
& ! [U_45,U_46,U_47] :
( ~ in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_47)
| ~ in(sK5(U_47,U_46,U_45),U_46)
| ~ sP11(U_45,U_46,U_47) )
& ! [U_45,U_46,U_47] :
( in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45)
| ~ sP11(U_45,U_46,U_47) )
& ! [U_50,U_46,U_47,U_48] :
( in(ordered_pair(U_50,U_48),U_47)
| ~ sP9(U_50,U_46,U_47,U_48) )
& ! [U_50,U_46,U_47,U_48] :
( in(U_50,U_46)
| ~ sP9(U_50,U_46,U_47,U_48) )
& ! [U_50,U_45,U_46,U_47,U_51,U_48,U_49] :
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46)
| ~ sP10(U_50,U_45,U_46,U_47,U_51,U_48,U_49) )
& ! [U_50,U_45,U_46,U_47,U_51,U_48,U_49] :
( sP9(U_50,U_46,U_47,U_48)
| ~ in(ordered_pair(U_50,U_48),U_45)
| ~ sP10(U_50,U_45,U_46,U_47,U_51,U_48,U_49) )
& ! [U_50,U_45,U_46,U_47,U_51,U_48,U_49] :
( U_45 = relation_dom_restriction(U_47,U_46)
| sP12(U_45,U_46,U_47)
| sP11(U_45,U_46,U_47)
| ~ sP13(U_50,U_45,U_46,U_47,U_51,U_48,U_49) )
& ! [U_50,U_45,U_46,U_47,U_51,U_48,U_49] :
( sP10(U_50,U_45,U_46,U_47,U_51,U_48,U_49)
| U_45 != relation_dom_restriction(U_47,U_46)
| ~ sP13(U_50,U_45,U_46,U_47,U_51,U_48,U_49) )
& ! [U_50,U_45,U_46,U_47,U_51,U_48,U_49] :
( sP13(U_50,U_45,U_46,U_47,U_51,U_48,U_49)
| ~ relation(U_45)
| ~ relation(U_47) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9,sP10,sP11,sP12,sP13])],[f_16_7]) ).
cnf(f_16_9,plain,
( sP13(U_50,U_45,U_46,U_47,U_51,U_48,U_49)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_10,plain,
( sP10(U_50,U_45,U_46,U_47,U_51,U_48,U_49)
| U_45 != relation_dom_restriction(U_47,U_46)
| ~ sP13(U_50,U_45,U_46,U_47,U_51,U_48,U_49) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_11,plain,
( U_45 = relation_dom_restriction(U_47,U_46)
| sP12(U_45,U_46,U_47)
| sP11(U_45,U_46,U_47)
| ~ sP13(U_50,U_45,U_46,U_47,U_51,U_48,U_49) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_12,plain,
( sP9(U_50,U_46,U_47,U_48)
| ~ in(ordered_pair(U_50,U_48),U_45)
| ~ sP10(U_50,U_45,U_46,U_47,U_51,U_48,U_49) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_13,plain,
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46)
| ~ sP10(U_50,U_45,U_46,U_47,U_51,U_48,U_49) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_14,plain,
( in(U_50,U_46)
| ~ sP9(U_50,U_46,U_47,U_48) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_15,plain,
( in(ordered_pair(U_50,U_48),U_47)
| ~ sP9(U_50,U_46,U_47,U_48) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_16,plain,
( in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45)
| ~ sP11(U_45,U_46,U_47) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_17,plain,
( ~ in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_47)
| ~ in(sK5(U_47,U_46,U_45),U_46)
| ~ sP11(U_45,U_46,U_47) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_18,plain,
( in(sK7(U_47,U_46,U_45),U_46)
| ~ sP12(U_45,U_46,U_47) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_19,plain,
( in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_47)
| ~ sP12(U_45,U_46,U_47) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_20,plain,
( ~ in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_45)
| ~ sP12(U_45,U_46,U_47) ),
inference(clausify,[status(thm)],[f_16_8]) ).
fof(f_17_1,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)) ) )
| ( ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) ) )
& ( ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_funct_1]) ).
fof(f_17_2,plain,
! [U_64] :
( ! [U_63,U_62] :
( ( U_62 = relation_image(U_64,U_63)
| ? [U_61] :
( ( ~ in(U_61,U_62)
& ? [U_60] :
( U_61 = apply(U_64,U_60)
& in(U_60,U_63)
& in(U_60,relation_dom(U_64)) ) )
| ( ! [U_59] :
( U_61 != apply(U_64,U_59)
| ~ in(U_59,U_63)
| ~ in(U_59,relation_dom(U_64)) )
& in(U_61,U_62) ) ) )
& ( ! [U_58] :
( ( in(U_58,U_62)
| ! [U_57] :
( U_58 != apply(U_64,U_57)
| ~ in(U_57,U_63)
| ~ in(U_57,relation_dom(U_64)) ) )
& ( ? [U_56] :
( U_58 = apply(U_64,U_56)
& in(U_56,U_63)
& in(U_56,relation_dom(U_64)) )
| ~ in(U_58,U_62) ) )
| U_62 != relation_image(U_64,U_63) ) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_64] :
( ( ! [U_72,U_70] :
( U_70 = relation_image(U_64,U_72)
| ? [U_68] :
( ~ in(U_68,U_70)
& ? [U_60] :
( U_68 = apply(U_64,U_60)
& in(U_60,U_72)
& in(U_60,relation_dom(U_64)) ) )
| ? [U_67] :
( ! [U_59] :
( U_67 != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64)) )
& in(U_67,U_70) ) )
& ! [U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ! [U_57] :
( U_66 != apply(U_64,U_57)
| ~ in(U_57,U_71)
| ~ in(U_57,relation_dom(U_64)) ) )
& ! [U_65] :
( ? [U_56] :
( U_65 = apply(U_64,U_56)
& in(U_56,U_71)
& in(U_56,relation_dom(U_64)) )
| ~ in(U_65,U_69) ) )
| U_69 != relation_image(U_64,U_71) ) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_64] :
( ( ! [U_72,U_70] :
( U_70 = relation_image(U_64,U_72)
| ? [U_68] :
( ~ in(U_68,U_70)
& ? [U_60] :
( U_68 = apply(U_64,U_60)
& in(U_60,U_72)
& in(U_60,relation_dom(U_64)) ) )
| ? [U_67] :
( ! [U_59] :
( U_67 != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64)) )
& in(U_67,U_70) ) )
& ! [U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ! [U_57] :
( U_66 != apply(U_64,U_57)
| ~ in(U_57,U_71)
| ~ in(U_57,relation_dom(U_64)) ) )
& ! [U_65] :
( ( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
& in(sK9(U_64,U_71,U_69,U_65),U_71)
& in(sK9(U_64,U_71,U_69,U_65),relation_dom(U_64)) )
| ~ in(U_65,U_69) ) )
| U_69 != relation_image(U_64,U_71) ) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_56,sK9(U_64,U_71,U_69,U_65))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_64] :
( ( ! [U_72,U_70] :
( U_70 = relation_image(U_64,U_72)
| ? [U_68] :
( ~ in(U_68,U_70)
& ? [U_60] :
( U_68 = apply(U_64,U_60)
& in(U_60,U_72)
& in(U_60,relation_dom(U_64)) ) )
| ( ! [U_59] :
( sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64)) )
& in(sK10(U_64,U_72,U_70),U_70) ) )
& ! [U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ! [U_57] :
( U_66 != apply(U_64,U_57)
| ~ in(U_57,U_71)
| ~ in(U_57,relation_dom(U_64)) ) )
& ! [U_65] :
( ( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
& in(sK9(U_64,U_71,U_69,U_65),U_71)
& in(sK9(U_64,U_71,U_69,U_65),relation_dom(U_64)) )
| ~ in(U_65,U_69) ) )
| U_69 != relation_image(U_64,U_71) ) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_67,sK10(U_64,U_72,U_70))],[f_17_4]) ).
fof(f_17_6,plain,
! [U_64] :
( ( ! [U_72,U_70] :
( U_70 = relation_image(U_64,U_72)
| ( ~ in(sK11(U_64,U_72,U_70),U_70)
& ? [U_60] :
( sK11(U_64,U_72,U_70) = apply(U_64,U_60)
& in(U_60,U_72)
& in(U_60,relation_dom(U_64)) ) )
| ( ! [U_59] :
( sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64)) )
& in(sK10(U_64,U_72,U_70),U_70) ) )
& ! [U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ! [U_57] :
( U_66 != apply(U_64,U_57)
| ~ in(U_57,U_71)
| ~ in(U_57,relation_dom(U_64)) ) )
& ! [U_65] :
( ( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
& in(sK9(U_64,U_71,U_69,U_65),U_71)
& in(sK9(U_64,U_71,U_69,U_65),relation_dom(U_64)) )
| ~ in(U_65,U_69) ) )
| U_69 != relation_image(U_64,U_71) ) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_68,sK11(U_64,U_72,U_70))],[f_17_5]) ).
fof(f_17_7,plain,
! [U_64] :
( ( ! [U_72,U_70] :
( U_70 = relation_image(U_64,U_72)
| ( ~ in(sK11(U_64,U_72,U_70),U_70)
& sK11(U_64,U_72,U_70) = apply(U_64,sK12(U_64,U_72,U_70))
& in(sK12(U_64,U_72,U_70),U_72)
& in(sK12(U_64,U_72,U_70),relation_dom(U_64)) )
| ( ! [U_59] :
( sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64)) )
& in(sK10(U_64,U_72,U_70),U_70) ) )
& ! [U_71,U_69] :
( ( ! [U_66] :
( in(U_66,U_69)
| ! [U_57] :
( U_66 != apply(U_64,U_57)
| ~ in(U_57,U_71)
| ~ in(U_57,relation_dom(U_64)) ) )
& ! [U_65] :
( ( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
& in(sK9(U_64,U_71,U_69,U_65),U_71)
& in(sK9(U_64,U_71,U_69,U_65),relation_dom(U_64)) )
| ~ in(U_65,U_69) ) )
| U_69 != relation_image(U_64,U_71) ) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_60,sK12(U_64,U_72,U_70))],[f_17_6]) ).
fof(f_17_8,plain,
( ! [U_72,U_70,U_64] :
( ~ in(sK11(U_64,U_72,U_70),U_70)
| ~ sP17(U_72,U_70,U_64) )
& ! [U_72,U_70,U_64] :
( sK11(U_64,U_72,U_70) = apply(U_64,sK12(U_64,U_72,U_70))
| ~ sP17(U_72,U_70,U_64) )
& ! [U_72,U_70,U_64] :
( in(sK12(U_64,U_72,U_70),U_72)
| ~ sP17(U_72,U_70,U_64) )
& ! [U_72,U_70,U_64] :
( in(sK12(U_64,U_72,U_70),relation_dom(U_64))
| ~ sP17(U_72,U_70,U_64) )
& ! [U_72,U_59,U_70,U_64] :
( sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64))
| ~ sP16(U_72,U_59,U_70,U_64) )
& ! [U_72,U_59,U_70,U_64] :
( in(sK10(U_64,U_72,U_70),U_70)
| ~ sP16(U_72,U_59,U_70,U_64) )
& ! [U_69,U_65,U_71,U_64] :
( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
| ~ sP14(U_69,U_65,U_71,U_64) )
& ! [U_69,U_65,U_71,U_64] :
( in(sK9(U_64,U_71,U_69,U_65),U_71)
| ~ sP14(U_69,U_65,U_71,U_64) )
& ! [U_69,U_65,U_71,U_64] :
( in(sK9(U_64,U_71,U_69,U_65),relation_dom(U_64))
| ~ sP14(U_69,U_65,U_71,U_64) )
& ! [U_69,U_57,U_65,U_71,U_64,U_66] :
( in(U_66,U_69)
| U_66 != apply(U_64,U_57)
| ~ in(U_57,U_71)
| ~ in(U_57,relation_dom(U_64))
| ~ sP15(U_69,U_57,U_65,U_71,U_64,U_66) )
& ! [U_69,U_57,U_65,U_71,U_64,U_66] :
( sP14(U_69,U_65,U_71,U_64)
| ~ in(U_65,U_69)
| ~ sP15(U_69,U_57,U_65,U_71,U_64,U_66) )
& ! [U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66] :
( U_70 = relation_image(U_64,U_72)
| sP17(U_72,U_70,U_64)
| sP16(U_72,U_59,U_70,U_64)
| ~ sP18(U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66) )
& ! [U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66] :
( sP15(U_69,U_57,U_65,U_71,U_64,U_66)
| U_69 != relation_image(U_64,U_71)
| ~ sP18(U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66) )
& ! [U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66] :
( sP18(U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66)
| ~ function(U_64)
| ~ relation(U_64) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15,sP16,sP17,sP18])],[f_17_7]) ).
cnf(f_17_9,plain,
( sP18(U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_10,plain,
( sP15(U_69,U_57,U_65,U_71,U_64,U_66)
| U_69 != relation_image(U_64,U_71)
| ~ sP18(U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_11,plain,
( U_70 = relation_image(U_64,U_72)
| sP17(U_72,U_70,U_64)
| sP16(U_72,U_59,U_70,U_64)
| ~ sP18(U_69,U_57,U_65,U_72,U_59,U_70,U_71,U_64,U_66) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_12,plain,
( sP14(U_69,U_65,U_71,U_64)
| ~ in(U_65,U_69)
| ~ sP15(U_69,U_57,U_65,U_71,U_64,U_66) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_13,plain,
( in(U_66,U_69)
| U_66 != apply(U_64,U_57)
| ~ in(U_57,U_71)
| ~ in(U_57,relation_dom(U_64))
| ~ sP15(U_69,U_57,U_65,U_71,U_64,U_66) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_14,plain,
( in(sK9(U_64,U_71,U_69,U_65),relation_dom(U_64))
| ~ sP14(U_69,U_65,U_71,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_15,plain,
( in(sK9(U_64,U_71,U_69,U_65),U_71)
| ~ sP14(U_69,U_65,U_71,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_16,plain,
( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
| ~ sP14(U_69,U_65,U_71,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_17,plain,
( in(sK10(U_64,U_72,U_70),U_70)
| ~ sP16(U_72,U_59,U_70,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_18,plain,
( sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64))
| ~ sP16(U_72,U_59,U_70,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_19,plain,
( in(sK12(U_64,U_72,U_70),relation_dom(U_64))
| ~ sP17(U_72,U_70,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_20,plain,
( in(sK12(U_64,U_72,U_70),U_72)
| ~ sP17(U_72,U_70,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_21,plain,
( sK11(U_64,U_72,U_70) = apply(U_64,sK12(U_64,U_72,U_70))
| ~ sP17(U_72,U_70,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_22,plain,
( ~ in(sK11(U_64,U_72,U_70),U_70)
| ~ sP17(U_72,U_70,U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
fof(f_18_1,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) )
| ( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& ( ( 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(fof_nnf,[status(thm)],[d12_relat_1]) ).
fof(f_18_2,plain,
! [U_79,U_78] :
( ! [U_77] :
( ( ( U_77 = relation_rng_restriction(U_79,U_78)
| ? [U_76,U_75] :
( ( ~ in(ordered_pair(U_76,U_75),U_77)
& in(ordered_pair(U_76,U_75),U_78)
& in(U_75,U_79) )
| ( ( ~ in(ordered_pair(U_76,U_75),U_78)
| ~ in(U_75,U_79) )
& in(ordered_pair(U_76,U_75),U_77) ) ) )
& ( ! [U_74,U_73] :
( ( in(ordered_pair(U_74,U_73),U_77)
| ~ in(ordered_pair(U_74,U_73),U_78)
| ~ in(U_73,U_79) )
& ( ( in(ordered_pair(U_74,U_73),U_78)
& in(U_73,U_79) )
| ~ in(ordered_pair(U_74,U_73),U_77) ) )
| U_77 != relation_rng_restriction(U_79,U_78) ) )
| ~ relation(U_77) )
| ~ relation(U_78) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_79,U_78] :
( ! [U_77] :
( ( ( U_77 = relation_rng_restriction(U_79,U_78)
| ? [U_87,U_85] :
( ~ in(ordered_pair(U_87,U_85),U_77)
& in(ordered_pair(U_87,U_85),U_78)
& in(U_85,U_79) )
| ? [U_86,U_84] :
( ( ~ in(ordered_pair(U_86,U_84),U_78)
| ~ in(U_84,U_79) )
& in(ordered_pair(U_86,U_84),U_77) ) )
& ( ( ! [U_83,U_81] :
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79) )
& ! [U_82,U_80] :
( ( in(ordered_pair(U_82,U_80),U_78)
& in(U_80,U_79) )
| ~ in(ordered_pair(U_82,U_80),U_77) ) )
| U_77 != relation_rng_restriction(U_79,U_78) ) )
| ~ relation(U_77) )
| ~ relation(U_78) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_79,U_78] :
( ! [U_77] :
( ( ( U_77 = relation_rng_restriction(U_79,U_78)
| ? [U_87,U_85] :
( ~ in(ordered_pair(U_87,U_85),U_77)
& in(ordered_pair(U_87,U_85),U_78)
& in(U_85,U_79) )
| ? [U_84] :
( ( ~ in(ordered_pair(sK13(U_79,U_78,U_77),U_84),U_78)
| ~ in(U_84,U_79) )
& in(ordered_pair(sK13(U_79,U_78,U_77),U_84),U_77) ) )
& ( ( ! [U_83,U_81] :
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79) )
& ! [U_82,U_80] :
( ( in(ordered_pair(U_82,U_80),U_78)
& in(U_80,U_79) )
| ~ in(ordered_pair(U_82,U_80),U_77) ) )
| U_77 != relation_rng_restriction(U_79,U_78) ) )
| ~ relation(U_77) )
| ~ relation(U_78) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_86,sK13(U_79,U_78,U_77))],[f_18_3]) ).
fof(f_18_5,plain,
! [U_79,U_78] :
( ! [U_77] :
( ( ( U_77 = relation_rng_restriction(U_79,U_78)
| ? [U_87,U_85] :
( ~ in(ordered_pair(U_87,U_85),U_77)
& in(ordered_pair(U_87,U_85),U_78)
& in(U_85,U_79) )
| ( ( ~ in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_78)
| ~ in(sK14(U_79,U_78,U_77),U_79) )
& in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77) ) )
& ( ( ! [U_83,U_81] :
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79) )
& ! [U_82,U_80] :
( ( in(ordered_pair(U_82,U_80),U_78)
& in(U_80,U_79) )
| ~ in(ordered_pair(U_82,U_80),U_77) ) )
| U_77 != relation_rng_restriction(U_79,U_78) ) )
| ~ relation(U_77) )
| ~ relation(U_78) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_84,sK14(U_79,U_78,U_77))],[f_18_4]) ).
fof(f_18_6,plain,
! [U_79,U_78] :
( ! [U_77] :
( ( ( U_77 = relation_rng_restriction(U_79,U_78)
| ? [U_85] :
( ~ in(ordered_pair(sK15(U_79,U_78,U_77),U_85),U_77)
& in(ordered_pair(sK15(U_79,U_78,U_77),U_85),U_78)
& in(U_85,U_79) )
| ( ( ~ in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_78)
| ~ in(sK14(U_79,U_78,U_77),U_79) )
& in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77) ) )
& ( ( ! [U_83,U_81] :
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79) )
& ! [U_82,U_80] :
( ( in(ordered_pair(U_82,U_80),U_78)
& in(U_80,U_79) )
| ~ in(ordered_pair(U_82,U_80),U_77) ) )
| U_77 != relation_rng_restriction(U_79,U_78) ) )
| ~ relation(U_77) )
| ~ relation(U_78) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_87,sK15(U_79,U_78,U_77))],[f_18_5]) ).
fof(f_18_7,plain,
! [U_79,U_78] :
( ! [U_77] :
( ( ( U_77 = relation_rng_restriction(U_79,U_78)
| ( ~ in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_77)
& in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_78)
& in(sK16(U_79,U_78,U_77),U_79) )
| ( ( ~ in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_78)
| ~ in(sK14(U_79,U_78,U_77),U_79) )
& in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77) ) )
& ( ( ! [U_83,U_81] :
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79) )
& ! [U_82,U_80] :
( ( in(ordered_pair(U_82,U_80),U_78)
& in(U_80,U_79) )
| ~ in(ordered_pair(U_82,U_80),U_77) ) )
| U_77 != relation_rng_restriction(U_79,U_78) ) )
| ~ relation(U_77) )
| ~ relation(U_78) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_85,sK16(U_79,U_78,U_77))],[f_18_6]) ).
fof(f_18_8,plain,
( ! [U_77,U_78,U_79] :
( ~ in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_77)
| ~ sP22(U_77,U_78,U_79) )
& ! [U_77,U_78,U_79] :
( in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_78)
| ~ sP22(U_77,U_78,U_79) )
& ! [U_77,U_78,U_79] :
( in(sK16(U_79,U_78,U_77),U_79)
| ~ sP22(U_77,U_78,U_79) )
& ! [U_77,U_78,U_79] :
( ~ in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_78)
| ~ in(sK14(U_79,U_78,U_77),U_79)
| ~ sP21(U_77,U_78,U_79) )
& ! [U_77,U_78,U_79] :
( in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77)
| ~ sP21(U_77,U_78,U_79) )
& ! [U_80,U_82,U_78,U_79] :
( in(ordered_pair(U_82,U_80),U_78)
| ~ sP19(U_80,U_82,U_78,U_79) )
& ! [U_80,U_82,U_78,U_79] :
( in(U_80,U_79)
| ~ sP19(U_80,U_82,U_78,U_79) )
& ! [U_80,U_81,U_82,U_83,U_77,U_78,U_79] :
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79)
| ~ sP20(U_80,U_81,U_82,U_83,U_77,U_78,U_79) )
& ! [U_80,U_81,U_82,U_83,U_77,U_78,U_79] :
( sP19(U_80,U_82,U_78,U_79)
| ~ in(ordered_pair(U_82,U_80),U_77)
| ~ sP20(U_80,U_81,U_82,U_83,U_77,U_78,U_79) )
& ! [U_80,U_81,U_82,U_83,U_77,U_78,U_79] :
( U_77 = relation_rng_restriction(U_79,U_78)
| sP22(U_77,U_78,U_79)
| sP21(U_77,U_78,U_79)
| ~ sP23(U_80,U_81,U_82,U_83,U_77,U_78,U_79) )
& ! [U_80,U_81,U_82,U_83,U_77,U_78,U_79] :
( sP20(U_80,U_81,U_82,U_83,U_77,U_78,U_79)
| U_77 != relation_rng_restriction(U_79,U_78)
| ~ sP23(U_80,U_81,U_82,U_83,U_77,U_78,U_79) )
& ! [U_80,U_81,U_82,U_83,U_77,U_78,U_79] :
( sP23(U_80,U_81,U_82,U_83,U_77,U_78,U_79)
| ~ relation(U_77)
| ~ relation(U_78) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19,sP20,sP21,sP22,sP23])],[f_18_7]) ).
cnf(f_18_9,plain,
( sP23(U_80,U_81,U_82,U_83,U_77,U_78,U_79)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_10,plain,
( sP20(U_80,U_81,U_82,U_83,U_77,U_78,U_79)
| U_77 != relation_rng_restriction(U_79,U_78)
| ~ sP23(U_80,U_81,U_82,U_83,U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_11,plain,
( U_77 = relation_rng_restriction(U_79,U_78)
| sP22(U_77,U_78,U_79)
| sP21(U_77,U_78,U_79)
| ~ sP23(U_80,U_81,U_82,U_83,U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_12,plain,
( sP19(U_80,U_82,U_78,U_79)
| ~ in(ordered_pair(U_82,U_80),U_77)
| ~ sP20(U_80,U_81,U_82,U_83,U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_13,plain,
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79)
| ~ sP20(U_80,U_81,U_82,U_83,U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_14,plain,
( in(U_80,U_79)
| ~ sP19(U_80,U_82,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_15,plain,
( in(ordered_pair(U_82,U_80),U_78)
| ~ sP19(U_80,U_82,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_16,plain,
( in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77)
| ~ sP21(U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_17,plain,
( ~ in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_78)
| ~ in(sK14(U_79,U_78,U_77),U_79)
| ~ sP21(U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_18,plain,
( in(sK16(U_79,U_78,U_77),U_79)
| ~ sP22(U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_19,plain,
( in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_78)
| ~ sP22(U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_20,plain,
( ~ in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_77)
| ~ sP22(U_77,U_78,U_79) ),
inference(clausify,[status(thm)],[f_18_8]) ).
fof(f_19_1,plain,
! [A] :
( ( ( antisymmetric(A)
| ~ is_antisymmetric_in(A,relation_field(A)) )
& ( is_antisymmetric_in(A,relation_field(A))
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_relat_2]) ).
fof(f_19_2,plain,
! [U_88] :
( ( ( antisymmetric(U_88)
| ~ is_antisymmetric_in(U_88,relation_field(U_88)) )
& ( is_antisymmetric_in(U_88,relation_field(U_88))
| ~ antisymmetric(U_88) ) )
| ~ relation(U_88) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_88] :
( antisymmetric(U_88)
| ~ is_antisymmetric_in(U_88,relation_field(U_88))
| ~ sP24(U_88) )
& ! [U_88] :
( is_antisymmetric_in(U_88,relation_field(U_88))
| ~ antisymmetric(U_88)
| ~ sP24(U_88) )
& ! [U_88] :
( sP24(U_88)
| ~ relation(U_88) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_19_2]) ).
cnf(f_19_4,plain,
( sP24(U_88)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( is_antisymmetric_in(U_88,relation_field(U_88))
| ~ antisymmetric(U_88)
| ~ sP24(U_88) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( antisymmetric(U_88)
| ~ is_antisymmetric_in(U_88,relation_field(U_88))
| ~ sP24(U_88) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ( ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_funct_1]) ).
fof(f_20_2,plain,
! [U_93] :
( ! [U_92,U_91] :
( ( U_91 = relation_inverse_image(U_93,U_92)
| ? [U_90] :
( ( ~ in(U_90,U_91)
& in(apply(U_93,U_90),U_92)
& in(U_90,relation_dom(U_93)) )
| ( ( ~ in(apply(U_93,U_90),U_92)
| ~ in(U_90,relation_dom(U_93)) )
& in(U_90,U_91) ) ) )
& ( ! [U_89] :
( ( in(U_89,U_91)
| ~ in(apply(U_93,U_89),U_92)
| ~ in(U_89,relation_dom(U_93)) )
& ( ( in(apply(U_93,U_89),U_92)
& in(U_89,relation_dom(U_93)) )
| ~ in(U_89,U_91) ) )
| U_91 != relation_inverse_image(U_93,U_92) ) )
| ~ function(U_93)
| ~ relation(U_93) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_93] :
( ( ! [U_101,U_99] :
( U_99 = relation_inverse_image(U_93,U_101)
| ? [U_97] :
( ~ in(U_97,U_99)
& in(apply(U_93,U_97),U_101)
& in(U_97,relation_dom(U_93)) )
| ? [U_96] :
( ( ~ in(apply(U_93,U_96),U_101)
| ~ in(U_96,relation_dom(U_93)) )
& in(U_96,U_99) ) )
& ! [U_100,U_98] :
( ( ! [U_95] :
( in(U_95,U_98)
| ~ in(apply(U_93,U_95),U_100)
| ~ in(U_95,relation_dom(U_93)) )
& ! [U_94] :
( ( in(apply(U_93,U_94),U_100)
& in(U_94,relation_dom(U_93)) )
| ~ in(U_94,U_98) ) )
| U_98 != relation_inverse_image(U_93,U_100) ) )
| ~ function(U_93)
| ~ relation(U_93) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_93] :
( ( ! [U_101,U_99] :
( U_99 = relation_inverse_image(U_93,U_101)
| ? [U_97] :
( ~ in(U_97,U_99)
& in(apply(U_93,U_97),U_101)
& in(U_97,relation_dom(U_93)) )
| ( ( ~ in(apply(U_93,sK17(U_93,U_101,U_99)),U_101)
| ~ in(sK17(U_93,U_101,U_99),relation_dom(U_93)) )
& in(sK17(U_93,U_101,U_99),U_99) ) )
& ! [U_100,U_98] :
( ( ! [U_95] :
( in(U_95,U_98)
| ~ in(apply(U_93,U_95),U_100)
| ~ in(U_95,relation_dom(U_93)) )
& ! [U_94] :
( ( in(apply(U_93,U_94),U_100)
& in(U_94,relation_dom(U_93)) )
| ~ in(U_94,U_98) ) )
| U_98 != relation_inverse_image(U_93,U_100) ) )
| ~ function(U_93)
| ~ relation(U_93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_96,sK17(U_93,U_101,U_99))],[f_20_3]) ).
fof(f_20_5,plain,
! [U_93] :
( ( ! [U_101,U_99] :
( U_99 = relation_inverse_image(U_93,U_101)
| ( ~ in(sK18(U_93,U_101,U_99),U_99)
& in(apply(U_93,sK18(U_93,U_101,U_99)),U_101)
& in(sK18(U_93,U_101,U_99),relation_dom(U_93)) )
| ( ( ~ in(apply(U_93,sK17(U_93,U_101,U_99)),U_101)
| ~ in(sK17(U_93,U_101,U_99),relation_dom(U_93)) )
& in(sK17(U_93,U_101,U_99),U_99) ) )
& ! [U_100,U_98] :
( ( ! [U_95] :
( in(U_95,U_98)
| ~ in(apply(U_93,U_95),U_100)
| ~ in(U_95,relation_dom(U_93)) )
& ! [U_94] :
( ( in(apply(U_93,U_94),U_100)
& in(U_94,relation_dom(U_93)) )
| ~ in(U_94,U_98) ) )
| U_98 != relation_inverse_image(U_93,U_100) ) )
| ~ function(U_93)
| ~ relation(U_93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_97,sK18(U_93,U_101,U_99))],[f_20_4]) ).
fof(f_20_6,plain,
( ! [U_99,U_101,U_93] :
( ~ in(sK18(U_93,U_101,U_99),U_99)
| ~ sP28(U_99,U_101,U_93) )
& ! [U_99,U_101,U_93] :
( in(apply(U_93,sK18(U_93,U_101,U_99)),U_101)
| ~ sP28(U_99,U_101,U_93) )
& ! [U_99,U_101,U_93] :
( in(sK18(U_93,U_101,U_99),relation_dom(U_93))
| ~ sP28(U_99,U_101,U_93) )
& ! [U_99,U_101,U_93] :
( ~ in(apply(U_93,sK17(U_93,U_101,U_99)),U_101)
| ~ in(sK17(U_93,U_101,U_99),relation_dom(U_93))
| ~ sP27(U_99,U_101,U_93) )
& ! [U_99,U_101,U_93] :
( in(sK17(U_93,U_101,U_99),U_99)
| ~ sP27(U_99,U_101,U_93) )
& ! [U_100,U_94,U_93] :
( in(apply(U_93,U_94),U_100)
| ~ sP25(U_100,U_94,U_93) )
& ! [U_100,U_94,U_93] :
( in(U_94,relation_dom(U_93))
| ~ sP25(U_100,U_94,U_93) )
& ! [U_100,U_94,U_95,U_98,U_93] :
( in(U_95,U_98)
| ~ in(apply(U_93,U_95),U_100)
| ~ in(U_95,relation_dom(U_93))
| ~ sP26(U_100,U_94,U_95,U_98,U_93) )
& ! [U_100,U_94,U_95,U_98,U_93] :
( sP25(U_100,U_94,U_93)
| ~ in(U_94,U_98)
| ~ sP26(U_100,U_94,U_95,U_98,U_93) )
& ! [U_100,U_94,U_95,U_99,U_101,U_98,U_93] :
( U_99 = relation_inverse_image(U_93,U_101)
| sP28(U_99,U_101,U_93)
| sP27(U_99,U_101,U_93)
| ~ sP29(U_100,U_94,U_95,U_99,U_101,U_98,U_93) )
& ! [U_100,U_94,U_95,U_99,U_101,U_98,U_93] :
( sP26(U_100,U_94,U_95,U_98,U_93)
| U_98 != relation_inverse_image(U_93,U_100)
| ~ sP29(U_100,U_94,U_95,U_99,U_101,U_98,U_93) )
& ! [U_100,U_94,U_95,U_99,U_101,U_98,U_93] :
( sP29(U_100,U_94,U_95,U_99,U_101,U_98,U_93)
| ~ function(U_93)
| ~ relation(U_93) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26,sP27,sP28,sP29])],[f_20_5]) ).
cnf(f_20_7,plain,
( sP29(U_100,U_94,U_95,U_99,U_101,U_98,U_93)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_8,plain,
( sP26(U_100,U_94,U_95,U_98,U_93)
| U_98 != relation_inverse_image(U_93,U_100)
| ~ sP29(U_100,U_94,U_95,U_99,U_101,U_98,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_9,plain,
( U_99 = relation_inverse_image(U_93,U_101)
| sP28(U_99,U_101,U_93)
| sP27(U_99,U_101,U_93)
| ~ sP29(U_100,U_94,U_95,U_99,U_101,U_98,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_10,plain,
( sP25(U_100,U_94,U_93)
| ~ in(U_94,U_98)
| ~ sP26(U_100,U_94,U_95,U_98,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_11,plain,
( in(U_95,U_98)
| ~ in(apply(U_93,U_95),U_100)
| ~ in(U_95,relation_dom(U_93))
| ~ sP26(U_100,U_94,U_95,U_98,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_12,plain,
( in(U_94,relation_dom(U_93))
| ~ sP25(U_100,U_94,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_13,plain,
( in(apply(U_93,U_94),U_100)
| ~ sP25(U_100,U_94,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_14,plain,
( in(sK17(U_93,U_101,U_99),U_99)
| ~ sP27(U_99,U_101,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_15,plain,
( ~ in(apply(U_93,sK17(U_93,U_101,U_99)),U_101)
| ~ in(sK17(U_93,U_101,U_99),relation_dom(U_93))
| ~ sP27(U_99,U_101,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_16,plain,
( in(sK18(U_93,U_101,U_99),relation_dom(U_93))
| ~ sP28(U_99,U_101,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_17,plain,
( in(apply(U_93,sK18(U_93,U_101,U_99)),U_101)
| ~ sP28(U_99,U_101,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_18,plain,
( ~ in(sK18(U_93,U_101,U_99),U_99)
| ~ sP28(U_99,U_101,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
fof(f_21_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_relat_1]) ).
fof(f_21_2,plain,
! [U_110] :
( ! [U_109,U_108] :
( ( U_108 = relation_image(U_110,U_109)
| ? [U_107] :
( ( ~ in(U_107,U_108)
& ? [U_106] :
( in(U_106,U_109)
& in(ordered_pair(U_106,U_107),U_110) ) )
| ( ! [U_105] :
( ~ in(U_105,U_109)
| ~ in(ordered_pair(U_105,U_107),U_110) )
& in(U_107,U_108) ) ) )
& ( ! [U_104] :
( ( in(U_104,U_108)
| ! [U_103] :
( ~ in(U_103,U_109)
| ~ in(ordered_pair(U_103,U_104),U_110) ) )
& ( ? [U_102] :
( in(U_102,U_109)
& in(ordered_pair(U_102,U_104),U_110) )
| ~ in(U_104,U_108) ) )
| U_108 != relation_image(U_110,U_109) ) )
| ~ relation(U_110) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_110] :
( ( ! [U_118,U_116] :
( U_116 = relation_image(U_110,U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& ? [U_106] :
( in(U_106,U_118)
& in(ordered_pair(U_106,U_114),U_110) ) )
| ? [U_113] :
( ! [U_105] :
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,U_113),U_110) )
& in(U_113,U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ! [U_103] :
( ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110) ) )
& ! [U_111] :
( ? [U_102] :
( in(U_102,U_117)
& in(ordered_pair(U_102,U_111),U_110) )
| ~ in(U_111,U_115) ) )
| U_115 != relation_image(U_110,U_117) ) )
| ~ relation(U_110) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
! [U_110] :
( ( ! [U_118,U_116] :
( U_116 = relation_image(U_110,U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& ? [U_106] :
( in(U_106,U_118)
& in(ordered_pair(U_106,U_114),U_110) ) )
| ? [U_113] :
( ! [U_105] :
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,U_113),U_110) )
& in(U_113,U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ! [U_103] :
( ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110) ) )
& ! [U_111] :
( ( in(sK19(U_110,U_117,U_115,U_111),U_117)
& in(ordered_pair(sK19(U_110,U_117,U_115,U_111),U_111),U_110) )
| ~ in(U_111,U_115) ) )
| U_115 != relation_image(U_110,U_117) ) )
| ~ relation(U_110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_102,sK19(U_110,U_117,U_115,U_111))],[f_21_3]) ).
fof(f_21_5,plain,
! [U_110] :
( ( ! [U_118,U_116] :
( U_116 = relation_image(U_110,U_118)
| ? [U_114] :
( ~ in(U_114,U_116)
& ? [U_106] :
( in(U_106,U_118)
& in(ordered_pair(U_106,U_114),U_110) ) )
| ( ! [U_105] :
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110) )
& in(sK20(U_110,U_118,U_116),U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ! [U_103] :
( ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110) ) )
& ! [U_111] :
( ( in(sK19(U_110,U_117,U_115,U_111),U_117)
& in(ordered_pair(sK19(U_110,U_117,U_115,U_111),U_111),U_110) )
| ~ in(U_111,U_115) ) )
| U_115 != relation_image(U_110,U_117) ) )
| ~ relation(U_110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_113,sK20(U_110,U_118,U_116))],[f_21_4]) ).
fof(f_21_6,plain,
! [U_110] :
( ( ! [U_118,U_116] :
( U_116 = relation_image(U_110,U_118)
| ( ~ in(sK21(U_110,U_118,U_116),U_116)
& ? [U_106] :
( in(U_106,U_118)
& in(ordered_pair(U_106,sK21(U_110,U_118,U_116)),U_110) ) )
| ( ! [U_105] :
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110) )
& in(sK20(U_110,U_118,U_116),U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ! [U_103] :
( ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110) ) )
& ! [U_111] :
( ( in(sK19(U_110,U_117,U_115,U_111),U_117)
& in(ordered_pair(sK19(U_110,U_117,U_115,U_111),U_111),U_110) )
| ~ in(U_111,U_115) ) )
| U_115 != relation_image(U_110,U_117) ) )
| ~ relation(U_110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_114,sK21(U_110,U_118,U_116))],[f_21_5]) ).
fof(f_21_7,plain,
! [U_110] :
( ( ! [U_118,U_116] :
( U_116 = relation_image(U_110,U_118)
| ( ~ in(sK21(U_110,U_118,U_116),U_116)
& in(sK22(U_110,U_118,U_116),U_118)
& in(ordered_pair(sK22(U_110,U_118,U_116),sK21(U_110,U_118,U_116)),U_110) )
| ( ! [U_105] :
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110) )
& in(sK20(U_110,U_118,U_116),U_116) ) )
& ! [U_117,U_115] :
( ( ! [U_112] :
( in(U_112,U_115)
| ! [U_103] :
( ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110) ) )
& ! [U_111] :
( ( in(sK19(U_110,U_117,U_115,U_111),U_117)
& in(ordered_pair(sK19(U_110,U_117,U_115,U_111),U_111),U_110) )
| ~ in(U_111,U_115) ) )
| U_115 != relation_image(U_110,U_117) ) )
| ~ relation(U_110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_106,sK22(U_110,U_118,U_116))],[f_21_6]) ).
fof(f_21_8,plain,
( ! [U_118,U_116,U_110] :
( ~ in(sK21(U_110,U_118,U_116),U_116)
| ~ sP33(U_118,U_116,U_110) )
& ! [U_118,U_116,U_110] :
( in(sK22(U_110,U_118,U_116),U_118)
| ~ sP33(U_118,U_116,U_110) )
& ! [U_118,U_116,U_110] :
( in(ordered_pair(sK22(U_110,U_118,U_116),sK21(U_110,U_118,U_116)),U_110)
| ~ sP33(U_118,U_116,U_110) )
& ! [U_118,U_105,U_116,U_110] :
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110)
| ~ sP32(U_118,U_105,U_116,U_110) )
& ! [U_118,U_105,U_116,U_110] :
( in(sK20(U_110,U_118,U_116),U_116)
| ~ sP32(U_118,U_105,U_116,U_110) )
& ! [U_115,U_117,U_110,U_111] :
( in(sK19(U_110,U_117,U_115,U_111),U_117)
| ~ sP30(U_115,U_117,U_110,U_111) )
& ! [U_115,U_117,U_110,U_111] :
( in(ordered_pair(sK19(U_110,U_117,U_115,U_111),U_111),U_110)
| ~ sP30(U_115,U_117,U_110,U_111) )
& ! [U_115,U_117,U_110,U_112,U_111,U_103] :
( in(U_112,U_115)
| ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110)
| ~ sP31(U_115,U_117,U_110,U_112,U_111,U_103) )
& ! [U_115,U_117,U_110,U_112,U_111,U_103] :
( sP30(U_115,U_117,U_110,U_111)
| ~ in(U_111,U_115)
| ~ sP31(U_115,U_117,U_110,U_112,U_111,U_103) )
& ! [U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103] :
( U_116 = relation_image(U_110,U_118)
| sP33(U_118,U_116,U_110)
| sP32(U_118,U_105,U_116,U_110)
| ~ sP34(U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103) )
& ! [U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103] :
( sP31(U_115,U_117,U_110,U_112,U_111,U_103)
| U_115 != relation_image(U_110,U_117)
| ~ sP34(U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103) )
& ! [U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103] :
( sP34(U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103)
| ~ relation(U_110) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30,sP31,sP32,sP33,sP34])],[f_21_7]) ).
cnf(f_21_9,plain,
( sP34(U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_10,plain,
( sP31(U_115,U_117,U_110,U_112,U_111,U_103)
| U_115 != relation_image(U_110,U_117)
| ~ sP34(U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_11,plain,
( U_116 = relation_image(U_110,U_118)
| sP33(U_118,U_116,U_110)
| sP32(U_118,U_105,U_116,U_110)
| ~ sP34(U_118,U_115,U_117,U_105,U_116,U_110,U_112,U_111,U_103) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_12,plain,
( sP30(U_115,U_117,U_110,U_111)
| ~ in(U_111,U_115)
| ~ sP31(U_115,U_117,U_110,U_112,U_111,U_103) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_13,plain,
( in(U_112,U_115)
| ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110)
| ~ sP31(U_115,U_117,U_110,U_112,U_111,U_103) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_14,plain,
( in(ordered_pair(sK19(U_110,U_117,U_115,U_111),U_111),U_110)
| ~ sP30(U_115,U_117,U_110,U_111) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_15,plain,
( in(sK19(U_110,U_117,U_115,U_111),U_117)
| ~ sP30(U_115,U_117,U_110,U_111) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_16,plain,
( in(sK20(U_110,U_118,U_116),U_116)
| ~ sP32(U_118,U_105,U_116,U_110) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_17,plain,
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110)
| ~ sP32(U_118,U_105,U_116,U_110) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_18,plain,
( in(ordered_pair(sK22(U_110,U_118,U_116),sK21(U_110,U_118,U_116)),U_110)
| ~ sP33(U_118,U_116,U_110) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_19,plain,
( in(sK22(U_110,U_118,U_116),U_118)
| ~ sP33(U_118,U_116,U_110) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_20,plain,
( ~ in(sK21(U_110,U_118,U_116),U_116)
| ~ sP33(U_118,U_116,U_110) ),
inference(clausify,[status(thm)],[f_21_8]) ).
fof(f_22_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_1]) ).
fof(f_22_2,plain,
! [U_127] :
( ! [U_126,U_125] :
( ( U_125 = relation_inverse_image(U_127,U_126)
| ? [U_124] :
( ( ~ in(U_124,U_125)
& ? [U_123] :
( in(U_123,U_126)
& in(ordered_pair(U_124,U_123),U_127) ) )
| ( ! [U_122] :
( ~ in(U_122,U_126)
| ~ in(ordered_pair(U_124,U_122),U_127) )
& in(U_124,U_125) ) ) )
& ( ! [U_121] :
( ( in(U_121,U_125)
| ! [U_120] :
( ~ in(U_120,U_126)
| ~ in(ordered_pair(U_121,U_120),U_127) ) )
& ( ? [U_119] :
( in(U_119,U_126)
& in(ordered_pair(U_121,U_119),U_127) )
| ~ in(U_121,U_125) ) )
| U_125 != relation_inverse_image(U_127,U_126) ) )
| ~ relation(U_127) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_127] :
( ( ! [U_135,U_133] :
( U_133 = relation_inverse_image(U_127,U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& ? [U_123] :
( in(U_123,U_135)
& in(ordered_pair(U_131,U_123),U_127) ) )
| ? [U_130] :
( ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(ordered_pair(U_130,U_122),U_127) )
& in(U_130,U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_120] :
( ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127) ) )
& ! [U_128] :
( ? [U_119] :
( in(U_119,U_134)
& in(ordered_pair(U_128,U_119),U_127) )
| ~ in(U_128,U_132) ) )
| U_132 != relation_inverse_image(U_127,U_134) ) )
| ~ relation(U_127) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_127] :
( ( ! [U_135,U_133] :
( U_133 = relation_inverse_image(U_127,U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& ? [U_123] :
( in(U_123,U_135)
& in(ordered_pair(U_131,U_123),U_127) ) )
| ? [U_130] :
( ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(ordered_pair(U_130,U_122),U_127) )
& in(U_130,U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_120] :
( ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127) ) )
& ! [U_128] :
( ( in(sK23(U_127,U_134,U_132,U_128),U_134)
& in(ordered_pair(U_128,sK23(U_127,U_134,U_132,U_128)),U_127) )
| ~ in(U_128,U_132) ) )
| U_132 != relation_inverse_image(U_127,U_134) ) )
| ~ relation(U_127) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_119,sK23(U_127,U_134,U_132,U_128))],[f_22_3]) ).
fof(f_22_5,plain,
! [U_127] :
( ( ! [U_135,U_133] :
( U_133 = relation_inverse_image(U_127,U_135)
| ? [U_131] :
( ~ in(U_131,U_133)
& ? [U_123] :
( in(U_123,U_135)
& in(ordered_pair(U_131,U_123),U_127) ) )
| ( ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127) )
& in(sK24(U_127,U_135,U_133),U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_120] :
( ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127) ) )
& ! [U_128] :
( ( in(sK23(U_127,U_134,U_132,U_128),U_134)
& in(ordered_pair(U_128,sK23(U_127,U_134,U_132,U_128)),U_127) )
| ~ in(U_128,U_132) ) )
| U_132 != relation_inverse_image(U_127,U_134) ) )
| ~ relation(U_127) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_130,sK24(U_127,U_135,U_133))],[f_22_4]) ).
fof(f_22_6,plain,
! [U_127] :
( ( ! [U_135,U_133] :
( U_133 = relation_inverse_image(U_127,U_135)
| ( ~ in(sK25(U_127,U_135,U_133),U_133)
& ? [U_123] :
( in(U_123,U_135)
& in(ordered_pair(sK25(U_127,U_135,U_133),U_123),U_127) ) )
| ( ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127) )
& in(sK24(U_127,U_135,U_133),U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_120] :
( ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127) ) )
& ! [U_128] :
( ( in(sK23(U_127,U_134,U_132,U_128),U_134)
& in(ordered_pair(U_128,sK23(U_127,U_134,U_132,U_128)),U_127) )
| ~ in(U_128,U_132) ) )
| U_132 != relation_inverse_image(U_127,U_134) ) )
| ~ relation(U_127) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_131,sK25(U_127,U_135,U_133))],[f_22_5]) ).
fof(f_22_7,plain,
! [U_127] :
( ( ! [U_135,U_133] :
( U_133 = relation_inverse_image(U_127,U_135)
| ( ~ in(sK25(U_127,U_135,U_133),U_133)
& in(sK26(U_127,U_135,U_133),U_135)
& in(ordered_pair(sK25(U_127,U_135,U_133),sK26(U_127,U_135,U_133)),U_127) )
| ( ! [U_122] :
( ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127) )
& in(sK24(U_127,U_135,U_133),U_133) ) )
& ! [U_134,U_132] :
( ( ! [U_129] :
( in(U_129,U_132)
| ! [U_120] :
( ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127) ) )
& ! [U_128] :
( ( in(sK23(U_127,U_134,U_132,U_128),U_134)
& in(ordered_pair(U_128,sK23(U_127,U_134,U_132,U_128)),U_127) )
| ~ in(U_128,U_132) ) )
| U_132 != relation_inverse_image(U_127,U_134) ) )
| ~ relation(U_127) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_123,sK26(U_127,U_135,U_133))],[f_22_6]) ).
fof(f_22_8,plain,
( ! [U_135,U_127,U_133] :
( ~ in(sK25(U_127,U_135,U_133),U_133)
| ~ sP38(U_135,U_127,U_133) )
& ! [U_135,U_127,U_133] :
( in(sK26(U_127,U_135,U_133),U_135)
| ~ sP38(U_135,U_127,U_133) )
& ! [U_135,U_127,U_133] :
( in(ordered_pair(sK25(U_127,U_135,U_133),sK26(U_127,U_135,U_133)),U_127)
| ~ sP38(U_135,U_127,U_133) )
& ! [U_135,U_127,U_122,U_133] :
( ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127)
| ~ sP37(U_135,U_127,U_122,U_133) )
& ! [U_135,U_127,U_122,U_133] :
( in(sK24(U_127,U_135,U_133),U_133)
| ~ sP37(U_135,U_127,U_122,U_133) )
& ! [U_128,U_127,U_134,U_132] :
( in(sK23(U_127,U_134,U_132,U_128),U_134)
| ~ sP35(U_128,U_127,U_134,U_132) )
& ! [U_128,U_127,U_134,U_132] :
( in(ordered_pair(U_128,sK23(U_127,U_134,U_132,U_128)),U_127)
| ~ sP35(U_128,U_127,U_134,U_132) )
& ! [U_120,U_129,U_128,U_127,U_134,U_132] :
( in(U_129,U_132)
| ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127)
| ~ sP36(U_120,U_129,U_128,U_127,U_134,U_132) )
& ! [U_120,U_129,U_128,U_127,U_134,U_132] :
( sP35(U_128,U_127,U_134,U_132)
| ~ in(U_128,U_132)
| ~ sP36(U_120,U_129,U_128,U_127,U_134,U_132) )
& ! [U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133] :
( U_133 = relation_inverse_image(U_127,U_135)
| sP38(U_135,U_127,U_133)
| sP37(U_135,U_127,U_122,U_133)
| ~ sP39(U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133) )
& ! [U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133] :
( sP36(U_120,U_129,U_128,U_127,U_134,U_132)
| U_132 != relation_inverse_image(U_127,U_134)
| ~ sP39(U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133) )
& ! [U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133] :
( sP39(U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133)
| ~ relation(U_127) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35,sP36,sP37,sP38,sP39])],[f_22_7]) ).
cnf(f_22_9,plain,
( sP39(U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_10,plain,
( sP36(U_120,U_129,U_128,U_127,U_134,U_132)
| U_132 != relation_inverse_image(U_127,U_134)
| ~ sP39(U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_11,plain,
( U_133 = relation_inverse_image(U_127,U_135)
| sP38(U_135,U_127,U_133)
| sP37(U_135,U_127,U_122,U_133)
| ~ sP39(U_120,U_129,U_135,U_128,U_127,U_122,U_134,U_132,U_133) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_12,plain,
( sP35(U_128,U_127,U_134,U_132)
| ~ in(U_128,U_132)
| ~ sP36(U_120,U_129,U_128,U_127,U_134,U_132) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_13,plain,
( in(U_129,U_132)
| ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127)
| ~ sP36(U_120,U_129,U_128,U_127,U_134,U_132) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_14,plain,
( in(ordered_pair(U_128,sK23(U_127,U_134,U_132,U_128)),U_127)
| ~ sP35(U_128,U_127,U_134,U_132) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_15,plain,
( in(sK23(U_127,U_134,U_132,U_128),U_134)
| ~ sP35(U_128,U_127,U_134,U_132) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_16,plain,
( in(sK24(U_127,U_135,U_133),U_133)
| ~ sP37(U_135,U_127,U_122,U_133) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_17,plain,
( ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127)
| ~ sP37(U_135,U_127,U_122,U_133) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_18,plain,
( in(ordered_pair(sK25(U_127,U_135,U_133),sK26(U_127,U_135,U_133)),U_127)
| ~ sP38(U_135,U_127,U_133) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_19,plain,
( in(sK26(U_127,U_135,U_133),U_135)
| ~ sP38(U_135,U_127,U_133) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_20,plain,
( ~ in(sK25(U_127,U_135,U_133),U_133)
| ~ sP38(U_135,U_127,U_133) ),
inference(clausify,[status(thm)],[f_22_8]) ).
fof(f_23_1,plain,
! [A] :
( ( ( connected(A)
| ~ is_connected_in(A,relation_field(A)) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_2]) ).
fof(f_23_2,plain,
! [U_136] :
( ( ( connected(U_136)
| ~ is_connected_in(U_136,relation_field(U_136)) )
& ( is_connected_in(U_136,relation_field(U_136))
| ~ connected(U_136) ) )
| ~ relation(U_136) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_136] :
( connected(U_136)
| ~ is_connected_in(U_136,relation_field(U_136))
| ~ sP40(U_136) )
& ! [U_136] :
( is_connected_in(U_136,relation_field(U_136))
| ~ connected(U_136)
| ~ sP40(U_136) )
& ! [U_136] :
( sP40(U_136)
| ~ relation(U_136) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_23_2]) ).
cnf(f_23_4,plain,
( sP40(U_136)
| ~ relation(U_136) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( is_connected_in(U_136,relation_field(U_136))
| ~ connected(U_136)
| ~ sP40(U_136) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( connected(U_136)
| ~ is_connected_in(U_136,relation_field(U_136))
| ~ sP40(U_136) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( ( ( transitive(A)
| ~ is_transitive_in(A,relation_field(A)) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d16_relat_2]) ).
fof(f_24_2,plain,
! [U_137] :
( ( ( transitive(U_137)
| ~ is_transitive_in(U_137,relation_field(U_137)) )
& ( is_transitive_in(U_137,relation_field(U_137))
| ~ transitive(U_137) ) )
| ~ relation(U_137) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_137] :
( transitive(U_137)
| ~ is_transitive_in(U_137,relation_field(U_137))
| ~ sP41(U_137) )
& ! [U_137] :
( is_transitive_in(U_137,relation_field(U_137))
| ~ transitive(U_137)
| ~ sP41(U_137) )
& ! [U_137] :
( sP41(U_137)
| ~ relation(U_137) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_24_2]) ).
cnf(f_24_4,plain,
( sP41(U_137)
| ~ relation(U_137) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( is_transitive_in(U_137,relation_field(U_137))
| ~ transitive(U_137)
| ~ sP41(U_137) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
( transitive(U_137)
| ~ is_transitive_in(U_137,relation_field(U_137))
| ~ sP41(U_137) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B,C,D] :
( ( D = unordered_triple(A,B,C)
| ? [E] :
( ( ~ in(E,D)
& ( E = C
| E = B
| E = A ) )
| ( E != C
& E != B
& E != A
& in(E,D) ) ) )
& ( ! [E] :
( ( in(E,D)
| ( E != C
& E != B
& E != A ) )
& ( E = C
| E = B
| E = A
| ~ in(E,D) ) )
| D != unordered_triple(A,B,C) ) ),
inference(fof_nnf,[status(thm)],[d1_enumset1]) ).
fof(f_25_2,plain,
! [U_143,U_142,U_141,U_140] :
( ( U_140 = unordered_triple(U_143,U_142,U_141)
| ? [U_139] :
( ( ~ in(U_139,U_140)
& ( U_139 = U_141
| U_139 = U_142
| U_139 = U_143 ) )
| ( U_139 != U_141
& U_139 != U_142
& U_139 != U_143
& in(U_139,U_140) ) ) )
& ( ! [U_138] :
( ( in(U_138,U_140)
| ( U_138 != U_141
& U_138 != U_142
& U_138 != U_143 ) )
& ( U_138 = U_141
| U_138 = U_142
| U_138 = U_143
| ~ in(U_138,U_140) ) )
| U_140 != unordered_triple(U_143,U_142,U_141) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_155,U_153,U_151,U_149] :
( U_149 = unordered_triple(U_155,U_153,U_151)
| ? [U_147] :
( ~ in(U_147,U_149)
& ( U_147 = U_151
| U_147 = U_153
| U_147 = U_155 ) )
| ? [U_146] :
( U_146 != U_151
& U_146 != U_153
& U_146 != U_155
& in(U_146,U_149) ) )
& ! [U_154,U_152,U_150,U_148] :
( ( ! [U_145] :
( in(U_145,U_148)
| ( U_145 != U_150
& U_145 != U_152
& U_145 != U_154 ) )
& ! [U_144] :
( U_144 = U_150
| U_144 = U_152
| U_144 = U_154
| ~ in(U_144,U_148) ) )
| U_148 != unordered_triple(U_154,U_152,U_150) ) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_155,U_153,U_151,U_149] :
( U_149 = unordered_triple(U_155,U_153,U_151)
| ? [U_147] :
( ~ in(U_147,U_149)
& ( U_147 = U_151
| U_147 = U_153
| U_147 = U_155 ) )
| ( sK27(U_155,U_153,U_151,U_149) != U_151
& sK27(U_155,U_153,U_151,U_149) != U_153
& sK27(U_155,U_153,U_151,U_149) != U_155
& in(sK27(U_155,U_153,U_151,U_149),U_149) ) )
& ! [U_154,U_152,U_150,U_148] :
( ( ! [U_145] :
( in(U_145,U_148)
| ( U_145 != U_150
& U_145 != U_152
& U_145 != U_154 ) )
& ! [U_144] :
( U_144 = U_150
| U_144 = U_152
| U_144 = U_154
| ~ in(U_144,U_148) ) )
| U_148 != unordered_triple(U_154,U_152,U_150) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_146,sK27(U_155,U_153,U_151,U_149))],[f_25_3]) ).
fof(f_25_5,plain,
( ! [U_155,U_153,U_151,U_149] :
( U_149 = unordered_triple(U_155,U_153,U_151)
| ( ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
& ( sK28(U_155,U_153,U_151,U_149) = U_151
| sK28(U_155,U_153,U_151,U_149) = U_153
| sK28(U_155,U_153,U_151,U_149) = U_155 ) )
| ( sK27(U_155,U_153,U_151,U_149) != U_151
& sK27(U_155,U_153,U_151,U_149) != U_153
& sK27(U_155,U_153,U_151,U_149) != U_155
& in(sK27(U_155,U_153,U_151,U_149),U_149) ) )
& ! [U_154,U_152,U_150,U_148] :
( ( ! [U_145] :
( in(U_145,U_148)
| ( U_145 != U_150
& U_145 != U_152
& U_145 != U_154 ) )
& ! [U_144] :
( U_144 = U_150
| U_144 = U_152
| U_144 = U_154
| ~ in(U_144,U_148) ) )
| U_148 != unordered_triple(U_154,U_152,U_150) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_147,sK28(U_155,U_153,U_151,U_149))],[f_25_4]) ).
fof(f_25_6,plain,
( ! [U_153,U_149,U_151,U_155] :
( ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
| ~ sP45(U_153,U_149,U_151,U_155) )
& ! [U_153,U_149,U_151,U_155] :
( sK28(U_155,U_153,U_151,U_149) = U_151
| sK28(U_155,U_153,U_151,U_149) = U_153
| sK28(U_155,U_153,U_151,U_149) = U_155
| ~ sP45(U_153,U_149,U_151,U_155) )
& ! [U_153,U_149,U_151,U_155] :
( sK27(U_155,U_153,U_151,U_149) != U_151
| ~ sP44(U_153,U_149,U_151,U_155) )
& ! [U_153,U_149,U_151,U_155] :
( sK27(U_155,U_153,U_151,U_149) != U_153
| ~ sP44(U_153,U_149,U_151,U_155) )
& ! [U_153,U_149,U_151,U_155] :
( sK27(U_155,U_153,U_151,U_149) != U_155
| ~ sP44(U_153,U_149,U_151,U_155) )
& ! [U_153,U_149,U_151,U_155] :
( in(sK27(U_155,U_153,U_151,U_149),U_149)
| ~ sP44(U_153,U_149,U_151,U_155) )
& ! [U_152,U_150,U_145,U_154] :
( U_145 != U_150
| ~ sP42(U_152,U_150,U_145,U_154) )
& ! [U_152,U_150,U_145,U_154] :
( U_145 != U_152
| ~ sP42(U_152,U_150,U_145,U_154) )
& ! [U_152,U_150,U_145,U_154] :
( U_145 != U_154
| ~ sP42(U_152,U_150,U_145,U_154) )
& ! [U_152,U_144,U_148,U_150,U_145,U_154] :
( in(U_145,U_148)
| sP42(U_152,U_150,U_145,U_154)
| ~ sP43(U_152,U_144,U_148,U_150,U_145,U_154) )
& ! [U_152,U_144,U_148,U_150,U_145,U_154] :
( U_144 = U_150
| U_144 = U_152
| U_144 = U_154
| ~ in(U_144,U_148)
| ~ sP43(U_152,U_144,U_148,U_150,U_145,U_154) )
& ! [U_153,U_149,U_151,U_155] :
( U_149 = unordered_triple(U_155,U_153,U_151)
| sP45(U_153,U_149,U_151,U_155)
| sP44(U_153,U_149,U_151,U_155) )
& ! [U_152,U_144,U_148,U_150,U_145,U_154] :
( sP43(U_152,U_144,U_148,U_150,U_145,U_154)
| U_148 != unordered_triple(U_154,U_152,U_150) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42,sP43,sP44,sP45])],[f_25_5]) ).
cnf(f_25_7,plain,
( sP43(U_152,U_144,U_148,U_150,U_145,U_154)
| U_148 != unordered_triple(U_154,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_8,plain,
( U_149 = unordered_triple(U_155,U_153,U_151)
| sP45(U_153,U_149,U_151,U_155)
| sP44(U_153,U_149,U_151,U_155) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_9,plain,
( U_144 = U_150
| U_144 = U_152
| U_144 = U_154
| ~ in(U_144,U_148)
| ~ sP43(U_152,U_144,U_148,U_150,U_145,U_154) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_10,plain,
( in(U_145,U_148)
| sP42(U_152,U_150,U_145,U_154)
| ~ sP43(U_152,U_144,U_148,U_150,U_145,U_154) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_11,plain,
( U_145 != U_154
| ~ sP42(U_152,U_150,U_145,U_154) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_12,plain,
( U_145 != U_152
| ~ sP42(U_152,U_150,U_145,U_154) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_13,plain,
( U_145 != U_150
| ~ sP42(U_152,U_150,U_145,U_154) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_14,plain,
( in(sK27(U_155,U_153,U_151,U_149),U_149)
| ~ sP44(U_153,U_149,U_151,U_155) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_15,plain,
( sK27(U_155,U_153,U_151,U_149) != U_155
| ~ sP44(U_153,U_149,U_151,U_155) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_16,plain,
( sK27(U_155,U_153,U_151,U_149) != U_153
| ~ sP44(U_153,U_149,U_151,U_155) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_17,plain,
( sK27(U_155,U_153,U_151,U_149) != U_151
| ~ sP44(U_153,U_149,U_151,U_155) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_18,plain,
( sK28(U_155,U_153,U_151,U_149) = U_151
| sK28(U_155,U_153,U_151,U_149) = U_153
| sK28(U_155,U_153,U_151,U_149) = U_155
| ~ sP45(U_153,U_149,U_151,U_155) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_19,plain,
( ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
| ~ sP45(U_153,U_149,U_151,U_155) ),
inference(clausify,[status(thm)],[f_25_6]) ).
fof(f_26_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_26_2,plain,
! [U_156] : succ(U_156) = set_union2(U_156,singleton(U_156)),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_156] : succ(U_156) = set_union2(U_156,singleton(U_156)),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
succ(U_156) = set_union2(U_156,singleton(U_156)),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A] :
( ( relation(A)
| ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(fof_nnf,[status(thm)],[d1_relat_1]) ).
fof(f_27_2,plain,
! [U_163] :
( ( relation(U_163)
| ? [U_162] :
( ! [U_161,U_160] : U_162 != ordered_pair(U_161,U_160)
& in(U_162,U_163) ) )
& ( ! [U_159] :
( ? [U_158,U_157] : U_159 = ordered_pair(U_158,U_157)
| ~ in(U_159,U_163) )
| ~ relation(U_163) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_165] :
( relation(U_165)
| ? [U_162] :
( ! [U_161,U_160] : U_162 != ordered_pair(U_161,U_160)
& in(U_162,U_165) ) )
& ! [U_164] :
( ! [U_159] :
( ? [U_158,U_157] : U_159 = ordered_pair(U_158,U_157)
| ~ in(U_159,U_164) )
| ~ relation(U_164) ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_165] :
( relation(U_165)
| ? [U_162] :
( ! [U_161,U_160] : U_162 != ordered_pair(U_161,U_160)
& in(U_162,U_165) ) )
& ! [U_164] :
( ! [U_159] :
( ? [U_157] : U_159 = ordered_pair(sK29(U_164,U_159),U_157)
| ~ in(U_159,U_164) )
| ~ relation(U_164) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_158,sK29(U_164,U_159))],[f_27_3]) ).
fof(f_27_5,plain,
( ! [U_165] :
( relation(U_165)
| ? [U_162] :
( ! [U_161,U_160] : U_162 != ordered_pair(U_161,U_160)
& in(U_162,U_165) ) )
& ! [U_164] :
( ! [U_159] :
( U_159 = ordered_pair(sK29(U_164,U_159),sK30(U_164,U_159))
| ~ in(U_159,U_164) )
| ~ relation(U_164) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_157,sK30(U_164,U_159))],[f_27_4]) ).
fof(f_27_6,plain,
( ! [U_165] :
( relation(U_165)
| ( ! [U_161,U_160] : sK31(U_165) != ordered_pair(U_161,U_160)
& in(sK31(U_165),U_165) ) )
& ! [U_164] :
( ! [U_159] :
( U_159 = ordered_pair(sK29(U_164,U_159),sK30(U_164,U_159))
| ~ in(U_159,U_164) )
| ~ relation(U_164) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_162,sK31(U_165))],[f_27_5]) ).
fof(f_27_7,plain,
( ! [U_165,U_160,U_161] :
( sK31(U_165) != ordered_pair(U_161,U_160)
| ~ sP46(U_165,U_160,U_161) )
& ! [U_165,U_160,U_161] :
( in(sK31(U_165),U_165)
| ~ sP46(U_165,U_160,U_161) )
& ! [U_165,U_160,U_161] :
( relation(U_165)
| sP46(U_165,U_160,U_161) )
& ! [U_164,U_159] :
( U_159 = ordered_pair(sK29(U_164,U_159),sK30(U_164,U_159))
| ~ in(U_159,U_164)
| ~ relation(U_164) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_27_6]) ).
cnf(f_27_8,plain,
( U_159 = ordered_pair(sK29(U_164,U_159),sK30(U_164,U_159))
| ~ in(U_159,U_164)
| ~ relation(U_164) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_9,plain,
( relation(U_165)
| sP46(U_165,U_160,U_161) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_10,plain,
( in(sK31(U_165),U_165)
| ~ sP46(U_165,U_160,U_161) ),
inference(clausify,[status(thm)],[f_27_7]) ).
cnf(f_27_11,plain,
( sK31(U_165) != ordered_pair(U_161,U_160)
| ~ sP46(U_165,U_160,U_161) ),
inference(clausify,[status(thm)],[f_27_7]) ).
fof(f_28_1,plain,
! [A] :
( ! [B] :
( ( is_reflexive_in(A,B)
| ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_relat_2]) ).
fof(f_28_2,plain,
! [U_169] :
( ! [U_168] :
( ( is_reflexive_in(U_169,U_168)
| ? [U_167] :
( ~ in(ordered_pair(U_167,U_167),U_169)
& in(U_167,U_168) ) )
& ( ! [U_166] :
( in(ordered_pair(U_166,U_166),U_169)
| ~ in(U_166,U_168) )
| ~ is_reflexive_in(U_169,U_168) ) )
| ~ relation(U_169) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_169] :
( ( ! [U_171] :
( is_reflexive_in(U_169,U_171)
| ? [U_167] :
( ~ in(ordered_pair(U_167,U_167),U_169)
& in(U_167,U_171) ) )
& ! [U_170] :
( ! [U_166] :
( in(ordered_pair(U_166,U_166),U_169)
| ~ in(U_166,U_170) )
| ~ is_reflexive_in(U_169,U_170) ) )
| ~ relation(U_169) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
! [U_169] :
( ( ! [U_171] :
( is_reflexive_in(U_169,U_171)
| ( ~ in(ordered_pair(sK32(U_169,U_171),sK32(U_169,U_171)),U_169)
& in(sK32(U_169,U_171),U_171) ) )
& ! [U_170] :
( ! [U_166] :
( in(ordered_pair(U_166,U_166),U_169)
| ~ in(U_166,U_170) )
| ~ is_reflexive_in(U_169,U_170) ) )
| ~ relation(U_169) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_167,sK32(U_169,U_171))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_171,U_169] :
( ~ in(ordered_pair(sK32(U_169,U_171),sK32(U_169,U_171)),U_169)
| ~ sP47(U_171,U_169) )
& ! [U_171,U_169] :
( in(sK32(U_169,U_171),U_171)
| ~ sP47(U_171,U_169) )
& ! [U_171,U_170,U_169,U_166] :
( is_reflexive_in(U_169,U_171)
| sP47(U_171,U_169)
| ~ sP48(U_171,U_170,U_169,U_166) )
& ! [U_171,U_170,U_169,U_166] :
( in(ordered_pair(U_166,U_166),U_169)
| ~ in(U_166,U_170)
| ~ is_reflexive_in(U_169,U_170)
| ~ sP48(U_171,U_170,U_169,U_166) )
& ! [U_171,U_170,U_169,U_166] :
( sP48(U_171,U_170,U_169,U_166)
| ~ relation(U_169) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47,sP48])],[f_28_4]) ).
cnf(f_28_6,plain,
( sP48(U_171,U_170,U_169,U_166)
| ~ relation(U_169) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_7,plain,
( in(ordered_pair(U_166,U_166),U_169)
| ~ in(U_166,U_170)
| ~ is_reflexive_in(U_169,U_170)
| ~ sP48(U_171,U_170,U_169,U_166) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_8,plain,
( is_reflexive_in(U_169,U_171)
| sP47(U_171,U_169)
| ~ sP48(U_171,U_170,U_169,U_166) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_9,plain,
( in(sK32(U_169,U_171),U_171)
| ~ sP47(U_171,U_169) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(f_28_10,plain,
( ~ in(ordered_pair(sK32(U_169,U_171),sK32(U_169,U_171)),U_169)
| ~ sP47(U_171,U_169) ),
inference(clausify,[status(thm)],[f_28_5]) ).
fof(f_29_1,plain,
! [A,B,C] :
( ( relation_of2(C,A,B)
| ~ subset(C,cartesian_product2(A,B)) )
& ( subset(C,cartesian_product2(A,B))
| ~ relation_of2(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[d1_relset_1]) ).
fof(f_29_2,plain,
! [U_174,U_173,U_172] :
( ( relation_of2(U_172,U_174,U_173)
| ~ subset(U_172,cartesian_product2(U_174,U_173)) )
& ( subset(U_172,cartesian_product2(U_174,U_173))
| ~ relation_of2(U_172,U_174,U_173) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_180,U_178,U_176] :
( relation_of2(U_176,U_180,U_178)
| ~ subset(U_176,cartesian_product2(U_180,U_178)) )
& ! [U_179,U_177,U_175] :
( subset(U_175,cartesian_product2(U_179,U_177))
| ~ relation_of2(U_175,U_179,U_177) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_176,U_178,U_180] :
( relation_of2(U_176,U_180,U_178)
| ~ subset(U_176,cartesian_product2(U_180,U_178)) )
& ! [U_179,U_177,U_175] :
( subset(U_175,cartesian_product2(U_179,U_177))
| ~ relation_of2(U_175,U_179,U_177) ) ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
( subset(U_175,cartesian_product2(U_179,U_177))
| ~ relation_of2(U_175,U_179,U_177) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( relation_of2(U_176,U_180,U_178)
| ~ subset(U_176,cartesian_product2(U_180,U_178)) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B] :
( ( ( ( B = set_meet(A)
| B != empty_set )
& ( B = empty_set
| B != set_meet(A) ) )
| A != empty_set )
& ( ( ( B = set_meet(A)
| ? [C] :
( ( ~ in(C,B)
& ! [D] :
( in(C,D)
| ~ in(D,A) ) )
| ( ? [D] :
( ~ in(C,D)
& in(D,A) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ? [D] :
( ~ in(C,D)
& in(D,A) ) )
& ( ! [D] :
( in(C,D)
| ~ in(D,A) )
| ~ in(C,B) ) )
| B != set_meet(A) ) )
| A = empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_setfam_1]) ).
fof(f_30_2,plain,
! [U_188,U_187] :
( ( ( ( U_187 = set_meet(U_188)
| U_187 != empty_set )
& ( U_187 = empty_set
| U_187 != set_meet(U_188) ) )
| U_188 != empty_set )
& ( ( ( U_187 = set_meet(U_188)
| ? [U_186] :
( ( ~ in(U_186,U_187)
& ! [U_185] :
( in(U_186,U_185)
| ~ in(U_185,U_188) ) )
| ( ? [U_184] :
( ~ in(U_186,U_184)
& in(U_184,U_188) )
& in(U_186,U_187) ) ) )
& ( ! [U_183] :
( ( in(U_183,U_187)
| ? [U_182] :
( ~ in(U_183,U_182)
& in(U_182,U_188) ) )
& ( ! [U_181] :
( in(U_183,U_181)
| ~ in(U_181,U_188) )
| ~ in(U_183,U_187) ) )
| U_187 != set_meet(U_188) ) )
| U_188 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_200] :
( ( ! [U_198] :
( U_198 = set_meet(U_200)
| U_198 != empty_set )
& ! [U_197] :
( U_197 = empty_set
| U_197 != set_meet(U_200) ) )
| U_200 != empty_set )
& ! [U_199] :
( ( ! [U_196] :
( U_196 = set_meet(U_199)
| ? [U_192] :
( ~ in(U_192,U_196)
& ! [U_185] :
( in(U_192,U_185)
| ~ in(U_185,U_199) ) )
| ? [U_191] :
( ? [U_184] :
( ~ in(U_191,U_184)
& in(U_184,U_199) )
& in(U_191,U_196) ) )
& ! [U_195] :
( ( ! [U_190] :
( in(U_190,U_195)
| ? [U_182] :
( ~ in(U_190,U_182)
& in(U_182,U_199) ) )
& ! [U_189] :
( ! [U_181] :
( in(U_189,U_181)
| ~ in(U_181,U_199) )
| ~ in(U_189,U_195) ) )
| U_195 != set_meet(U_199) ) )
| U_199 = empty_set ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_200] :
( ( ! [U_198] :
( U_198 = set_meet(U_200)
| U_198 != empty_set )
& ! [U_197] :
( U_197 = empty_set
| U_197 != set_meet(U_200) ) )
| U_200 != empty_set )
& ! [U_199] :
( ( ! [U_196] :
( U_196 = set_meet(U_199)
| ? [U_192] :
( ~ in(U_192,U_196)
& ! [U_185] :
( in(U_192,U_185)
| ~ in(U_185,U_199) ) )
| ? [U_191] :
( ? [U_184] :
( ~ in(U_191,U_184)
& in(U_184,U_199) )
& in(U_191,U_196) ) )
& ! [U_195] :
( ( ! [U_190] :
( in(U_190,U_195)
| ( ~ in(U_190,sK33(U_199,U_195,U_190))
& in(sK33(U_199,U_195,U_190),U_199) ) )
& ! [U_189] :
( ! [U_181] :
( in(U_189,U_181)
| ~ in(U_181,U_199) )
| ~ in(U_189,U_195) ) )
| U_195 != set_meet(U_199) ) )
| U_199 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_182,sK33(U_199,U_195,U_190))],[f_30_3]) ).
fof(f_30_5,plain,
( ! [U_200] :
( ( ! [U_198] :
( U_198 = set_meet(U_200)
| U_198 != empty_set )
& ! [U_197] :
( U_197 = empty_set
| U_197 != set_meet(U_200) ) )
| U_200 != empty_set )
& ! [U_199] :
( ( ! [U_196] :
( U_196 = set_meet(U_199)
| ? [U_192] :
( ~ in(U_192,U_196)
& ! [U_185] :
( in(U_192,U_185)
| ~ in(U_185,U_199) ) )
| ( ? [U_184] :
( ~ in(sK34(U_199,U_196),U_184)
& in(U_184,U_199) )
& in(sK34(U_199,U_196),U_196) ) )
& ! [U_195] :
( ( ! [U_190] :
( in(U_190,U_195)
| ( ~ in(U_190,sK33(U_199,U_195,U_190))
& in(sK33(U_199,U_195,U_190),U_199) ) )
& ! [U_189] :
( ! [U_181] :
( in(U_189,U_181)
| ~ in(U_181,U_199) )
| ~ in(U_189,U_195) ) )
| U_195 != set_meet(U_199) ) )
| U_199 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_191,sK34(U_199,U_196))],[f_30_4]) ).
fof(f_30_6,plain,
( ! [U_200] :
( ( ! [U_198] :
( U_198 = set_meet(U_200)
| U_198 != empty_set )
& ! [U_197] :
( U_197 = empty_set
| U_197 != set_meet(U_200) ) )
| U_200 != empty_set )
& ! [U_199] :
( ( ! [U_196] :
( U_196 = set_meet(U_199)
| ? [U_192] :
( ~ in(U_192,U_196)
& ! [U_185] :
( in(U_192,U_185)
| ~ in(U_185,U_199) ) )
| ( ~ in(sK34(U_199,U_196),sK35(U_199,U_196))
& in(sK35(U_199,U_196),U_199)
& in(sK34(U_199,U_196),U_196) ) )
& ! [U_195] :
( ( ! [U_190] :
( in(U_190,U_195)
| ( ~ in(U_190,sK33(U_199,U_195,U_190))
& in(sK33(U_199,U_195,U_190),U_199) ) )
& ! [U_189] :
( ! [U_181] :
( in(U_189,U_181)
| ~ in(U_181,U_199) )
| ~ in(U_189,U_195) ) )
| U_195 != set_meet(U_199) ) )
| U_199 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_184,sK35(U_199,U_196))],[f_30_5]) ).
fof(f_30_7,plain,
( ! [U_200] :
( ( ! [U_198] :
( U_198 = set_meet(U_200)
| U_198 != empty_set )
& ! [U_197] :
( U_197 = empty_set
| U_197 != set_meet(U_200) ) )
| U_200 != empty_set )
& ! [U_199] :
( ( ! [U_196] :
( U_196 = set_meet(U_199)
| ( ~ in(sK36(U_199,U_196),U_196)
& ! [U_185] :
( in(sK36(U_199,U_196),U_185)
| ~ in(U_185,U_199) ) )
| ( ~ in(sK34(U_199,U_196),sK35(U_199,U_196))
& in(sK35(U_199,U_196),U_199)
& in(sK34(U_199,U_196),U_196) ) )
& ! [U_195] :
( ( ! [U_190] :
( in(U_190,U_195)
| ( ~ in(U_190,sK33(U_199,U_195,U_190))
& in(sK33(U_199,U_195,U_190),U_199) ) )
& ! [U_189] :
( ! [U_181] :
( in(U_189,U_181)
| ~ in(U_181,U_199) )
| ~ in(U_189,U_195) ) )
| U_195 != set_meet(U_199) ) )
| U_199 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_192,sK36(U_199,U_196))],[f_30_6]) ).
fof(f_30_8,plain,
( ! [U_198,U_197,U_200] :
( U_198 = set_meet(U_200)
| U_198 != empty_set
| ~ sP54(U_198,U_197,U_200) )
& ! [U_198,U_197,U_200] :
( U_197 = empty_set
| U_197 != set_meet(U_200)
| ~ sP54(U_198,U_197,U_200) )
& ! [U_185,U_196,U_199] :
( ~ in(sK36(U_199,U_196),U_196)
| ~ sP52(U_185,U_196,U_199) )
& ! [U_185,U_196,U_199] :
( in(sK36(U_199,U_196),U_185)
| ~ in(U_185,U_199)
| ~ sP52(U_185,U_196,U_199) )
& ! [U_196,U_199] :
( ~ in(sK34(U_199,U_196),sK35(U_199,U_196))
| ~ sP51(U_196,U_199) )
& ! [U_196,U_199] :
( in(sK35(U_199,U_196),U_199)
| ~ sP51(U_196,U_199) )
& ! [U_196,U_199] :
( in(sK34(U_199,U_196),U_196)
| ~ sP51(U_196,U_199) )
& ! [U_190,U_199,U_195] :
( ~ in(U_190,sK33(U_199,U_195,U_190))
| ~ sP49(U_190,U_199,U_195) )
& ! [U_190,U_199,U_195] :
( in(sK33(U_199,U_195,U_190),U_199)
| ~ sP49(U_190,U_199,U_195) )
& ! [U_189,U_190,U_199,U_195,U_181] :
( in(U_190,U_195)
| sP49(U_190,U_199,U_195)
| ~ sP50(U_189,U_190,U_199,U_195,U_181) )
& ! [U_189,U_190,U_199,U_195,U_181] :
( in(U_189,U_181)
| ~ in(U_181,U_199)
| ~ in(U_189,U_195)
| ~ sP50(U_189,U_190,U_199,U_195,U_181) )
& ! [U_185,U_196,U_189,U_190,U_199,U_195,U_181] :
( U_196 = set_meet(U_199)
| sP52(U_185,U_196,U_199)
| sP51(U_196,U_199)
| ~ sP53(U_185,U_196,U_189,U_190,U_199,U_195,U_181) )
& ! [U_185,U_196,U_189,U_190,U_199,U_195,U_181] :
( sP50(U_189,U_190,U_199,U_195,U_181)
| U_195 != set_meet(U_199)
| ~ sP53(U_185,U_196,U_189,U_190,U_199,U_195,U_181) )
& ! [U_198,U_197,U_200] :
( sP54(U_198,U_197,U_200)
| U_200 != empty_set )
& ! [U_185,U_196,U_189,U_190,U_199,U_195,U_181] :
( sP53(U_185,U_196,U_189,U_190,U_199,U_195,U_181)
| U_199 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50,sP51,sP52,sP53,sP54])],[f_30_7]) ).
cnf(f_30_9,plain,
( sP53(U_185,U_196,U_189,U_190,U_199,U_195,U_181)
| U_199 = empty_set ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_10,plain,
( sP54(U_198,U_197,U_200)
| U_200 != empty_set ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_11,plain,
( sP50(U_189,U_190,U_199,U_195,U_181)
| U_195 != set_meet(U_199)
| ~ sP53(U_185,U_196,U_189,U_190,U_199,U_195,U_181) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_12,plain,
( U_196 = set_meet(U_199)
| sP52(U_185,U_196,U_199)
| sP51(U_196,U_199)
| ~ sP53(U_185,U_196,U_189,U_190,U_199,U_195,U_181) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_13,plain,
( in(U_189,U_181)
| ~ in(U_181,U_199)
| ~ in(U_189,U_195)
| ~ sP50(U_189,U_190,U_199,U_195,U_181) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_14,plain,
( in(U_190,U_195)
| sP49(U_190,U_199,U_195)
| ~ sP50(U_189,U_190,U_199,U_195,U_181) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_15,plain,
( in(sK33(U_199,U_195,U_190),U_199)
| ~ sP49(U_190,U_199,U_195) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_16,plain,
( ~ in(U_190,sK33(U_199,U_195,U_190))
| ~ sP49(U_190,U_199,U_195) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_17,plain,
( in(sK34(U_199,U_196),U_196)
| ~ sP51(U_196,U_199) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_18,plain,
( in(sK35(U_199,U_196),U_199)
| ~ sP51(U_196,U_199) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_19,plain,
( ~ in(sK34(U_199,U_196),sK35(U_199,U_196))
| ~ sP51(U_196,U_199) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_20,plain,
( in(sK36(U_199,U_196),U_185)
| ~ in(U_185,U_199)
| ~ sP52(U_185,U_196,U_199) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_21,plain,
( ~ in(sK36(U_199,U_196),U_196)
| ~ sP52(U_185,U_196,U_199) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_22,plain,
( U_197 = empty_set
| U_197 != set_meet(U_200)
| ~ sP54(U_198,U_197,U_200) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_23,plain,
( U_198 = set_meet(U_200)
| U_198 != empty_set
| ~ sP54(U_198,U_197,U_200) ),
inference(clausify,[status(thm)],[f_30_8]) ).
fof(f_31_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_31_2,plain,
! [U_204,U_203] :
( ( U_203 = singleton(U_204)
| ? [U_202] :
( ( ~ in(U_202,U_203)
& U_202 = U_204 )
| ( U_202 != U_204
& in(U_202,U_203) ) ) )
& ( ! [U_201] :
( ( in(U_201,U_203)
| U_201 != U_204 )
& ( U_201 = U_204
| ~ in(U_201,U_203) ) )
| U_203 != singleton(U_204) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_212,U_210] :
( U_210 = singleton(U_212)
| ? [U_208] :
( ~ in(U_208,U_210)
& U_208 = U_212 )
| ? [U_207] :
( U_207 != U_212
& in(U_207,U_210) ) )
& ! [U_211,U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| U_206 != U_211 )
& ! [U_205] :
( U_205 = U_211
| ~ in(U_205,U_209) ) )
| U_209 != singleton(U_211) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_212,U_210] :
( U_210 = singleton(U_212)
| ? [U_208] :
( ~ in(U_208,U_210)
& U_208 = U_212 )
| ( sK37(U_212,U_210) != U_212
& in(sK37(U_212,U_210),U_210) ) )
& ! [U_211,U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| U_206 != U_211 )
& ! [U_205] :
( U_205 = U_211
| ~ in(U_205,U_209) ) )
| U_209 != singleton(U_211) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_207,sK37(U_212,U_210))],[f_31_3]) ).
fof(f_31_5,plain,
( ! [U_212,U_210] :
( U_210 = singleton(U_212)
| ( ~ in(sK38(U_212,U_210),U_210)
& sK38(U_212,U_210) = U_212 )
| ( sK37(U_212,U_210) != U_212
& in(sK37(U_212,U_210),U_210) ) )
& ! [U_211,U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| U_206 != U_211 )
& ! [U_205] :
( U_205 = U_211
| ~ in(U_205,U_209) ) )
| U_209 != singleton(U_211) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_208,sK38(U_212,U_210))],[f_31_4]) ).
fof(f_31_6,plain,
( ! [U_210,U_212] :
( ~ in(sK38(U_212,U_210),U_210)
| ~ sP57(U_210,U_212) )
& ! [U_210,U_212] :
( sK38(U_212,U_210) = U_212
| ~ sP57(U_210,U_212) )
& ! [U_210,U_212] :
( sK37(U_212,U_210) != U_212
| ~ sP56(U_210,U_212) )
& ! [U_210,U_212] :
( in(sK37(U_212,U_210),U_210)
| ~ sP56(U_210,U_212) )
& ! [U_205,U_206,U_211,U_209] :
( in(U_206,U_209)
| U_206 != U_211
| ~ sP55(U_205,U_206,U_211,U_209) )
& ! [U_205,U_206,U_211,U_209] :
( U_205 = U_211
| ~ in(U_205,U_209)
| ~ sP55(U_205,U_206,U_211,U_209) )
& ! [U_210,U_212] :
( U_210 = singleton(U_212)
| sP57(U_210,U_212)
| sP56(U_210,U_212) )
& ! [U_205,U_206,U_211,U_209] :
( sP55(U_205,U_206,U_211,U_209)
| U_209 != singleton(U_211) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55,sP56,sP57])],[f_31_5]) ).
cnf(f_31_7,plain,
( sP55(U_205,U_206,U_211,U_209)
| U_209 != singleton(U_211) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_8,plain,
( U_210 = singleton(U_212)
| sP57(U_210,U_212)
| sP56(U_210,U_212) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_9,plain,
( U_205 = U_211
| ~ in(U_205,U_209)
| ~ sP55(U_205,U_206,U_211,U_209) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_10,plain,
( in(U_206,U_209)
| U_206 != U_211
| ~ sP55(U_205,U_206,U_211,U_209) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_11,plain,
( in(sK37(U_212,U_210),U_210)
| ~ sP56(U_210,U_212) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_12,plain,
( sK37(U_212,U_210) != U_212
| ~ sP56(U_210,U_212) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_13,plain,
( sK38(U_212,U_210) = U_212
| ~ sP57(U_210,U_212) ),
inference(clausify,[status(thm)],[f_31_6]) ).
cnf(f_31_14,plain,
( ~ in(sK38(U_212,U_210),U_210)
| ~ sP57(U_210,U_212) ),
inference(clausify,[status(thm)],[f_31_6]) ).
fof(f_32_1,plain,
! [A] :
( ! [B,C] :
( ( C = fiber(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(ordered_pair(D,B),A)
& D != B )
| ( ( ~ in(ordered_pair(D,B),A)
| D = B )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(ordered_pair(D,B),A)
| D = B )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_wellord1]) ).
fof(f_32_2,plain,
! [U_217] :
( ! [U_216,U_215] :
( ( U_215 = fiber(U_217,U_216)
| ? [U_214] :
( ( ~ in(U_214,U_215)
& in(ordered_pair(U_214,U_216),U_217)
& U_214 != U_216 )
| ( ( ~ in(ordered_pair(U_214,U_216),U_217)
| U_214 = U_216 )
& in(U_214,U_215) ) ) )
& ( ! [U_213] :
( ( in(U_213,U_215)
| ~ in(ordered_pair(U_213,U_216),U_217)
| U_213 = U_216 )
& ( ( in(ordered_pair(U_213,U_216),U_217)
& U_213 != U_216 )
| ~ in(U_213,U_215) ) )
| U_215 != fiber(U_217,U_216) ) )
| ~ relation(U_217) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_217] :
( ( ! [U_225,U_223] :
( U_223 = fiber(U_217,U_225)
| ? [U_221] :
( ~ in(U_221,U_223)
& in(ordered_pair(U_221,U_225),U_217)
& U_221 != U_225 )
| ? [U_220] :
( ( ~ in(ordered_pair(U_220,U_225),U_217)
| U_220 = U_225 )
& in(U_220,U_223) ) )
& ! [U_224,U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ~ in(ordered_pair(U_219,U_224),U_217)
| U_219 = U_224 )
& ! [U_218] :
( ( in(ordered_pair(U_218,U_224),U_217)
& U_218 != U_224 )
| ~ in(U_218,U_222) ) )
| U_222 != fiber(U_217,U_224) ) )
| ~ relation(U_217) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_217] :
( ( ! [U_225,U_223] :
( U_223 = fiber(U_217,U_225)
| ? [U_221] :
( ~ in(U_221,U_223)
& in(ordered_pair(U_221,U_225),U_217)
& U_221 != U_225 )
| ( ( ~ in(ordered_pair(sK39(U_217,U_225,U_223),U_225),U_217)
| sK39(U_217,U_225,U_223) = U_225 )
& in(sK39(U_217,U_225,U_223),U_223) ) )
& ! [U_224,U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ~ in(ordered_pair(U_219,U_224),U_217)
| U_219 = U_224 )
& ! [U_218] :
( ( in(ordered_pair(U_218,U_224),U_217)
& U_218 != U_224 )
| ~ in(U_218,U_222) ) )
| U_222 != fiber(U_217,U_224) ) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_220,sK39(U_217,U_225,U_223))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_217] :
( ( ! [U_225,U_223] :
( U_223 = fiber(U_217,U_225)
| ( ~ in(sK40(U_217,U_225,U_223),U_223)
& in(ordered_pair(sK40(U_217,U_225,U_223),U_225),U_217)
& sK40(U_217,U_225,U_223) != U_225 )
| ( ( ~ in(ordered_pair(sK39(U_217,U_225,U_223),U_225),U_217)
| sK39(U_217,U_225,U_223) = U_225 )
& in(sK39(U_217,U_225,U_223),U_223) ) )
& ! [U_224,U_222] :
( ( ! [U_219] :
( in(U_219,U_222)
| ~ in(ordered_pair(U_219,U_224),U_217)
| U_219 = U_224 )
& ! [U_218] :
( ( in(ordered_pair(U_218,U_224),U_217)
& U_218 != U_224 )
| ~ in(U_218,U_222) ) )
| U_222 != fiber(U_217,U_224) ) )
| ~ relation(U_217) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_221,sK40(U_217,U_225,U_223))],[f_32_4]) ).
fof(f_32_6,plain,
( ! [U_223,U_225,U_217] :
( ~ in(sK40(U_217,U_225,U_223),U_223)
| ~ sP61(U_223,U_225,U_217) )
& ! [U_223,U_225,U_217] :
( in(ordered_pair(sK40(U_217,U_225,U_223),U_225),U_217)
| ~ sP61(U_223,U_225,U_217) )
& ! [U_223,U_225,U_217] :
( sK40(U_217,U_225,U_223) != U_225
| ~ sP61(U_223,U_225,U_217) )
& ! [U_223,U_225,U_217] :
( ~ in(ordered_pair(sK39(U_217,U_225,U_223),U_225),U_217)
| sK39(U_217,U_225,U_223) = U_225
| ~ sP60(U_223,U_225,U_217) )
& ! [U_223,U_225,U_217] :
( in(sK39(U_217,U_225,U_223),U_223)
| ~ sP60(U_223,U_225,U_217) )
& ! [U_224,U_217,U_218] :
( in(ordered_pair(U_218,U_224),U_217)
| ~ sP58(U_224,U_217,U_218) )
& ! [U_224,U_217,U_218] :
( U_218 != U_224
| ~ sP58(U_224,U_217,U_218) )
& ! [U_224,U_222,U_219,U_217,U_218] :
( in(U_219,U_222)
| ~ in(ordered_pair(U_219,U_224),U_217)
| U_219 = U_224
| ~ sP59(U_224,U_222,U_219,U_217,U_218) )
& ! [U_224,U_222,U_219,U_217,U_218] :
( sP58(U_224,U_217,U_218)
| ~ in(U_218,U_222)
| ~ sP59(U_224,U_222,U_219,U_217,U_218) )
& ! [U_223,U_225,U_224,U_222,U_219,U_217,U_218] :
( U_223 = fiber(U_217,U_225)
| sP61(U_223,U_225,U_217)
| sP60(U_223,U_225,U_217)
| ~ sP62(U_223,U_225,U_224,U_222,U_219,U_217,U_218) )
& ! [U_223,U_225,U_224,U_222,U_219,U_217,U_218] :
( sP59(U_224,U_222,U_219,U_217,U_218)
| U_222 != fiber(U_217,U_224)
| ~ sP62(U_223,U_225,U_224,U_222,U_219,U_217,U_218) )
& ! [U_223,U_225,U_224,U_222,U_219,U_217,U_218] :
( sP62(U_223,U_225,U_224,U_222,U_219,U_217,U_218)
| ~ relation(U_217) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58,sP59,sP60,sP61,sP62])],[f_32_5]) ).
cnf(f_32_7,plain,
( sP62(U_223,U_225,U_224,U_222,U_219,U_217,U_218)
| ~ relation(U_217) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_8,plain,
( sP59(U_224,U_222,U_219,U_217,U_218)
| U_222 != fiber(U_217,U_224)
| ~ sP62(U_223,U_225,U_224,U_222,U_219,U_217,U_218) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_9,plain,
( U_223 = fiber(U_217,U_225)
| sP61(U_223,U_225,U_217)
| sP60(U_223,U_225,U_217)
| ~ sP62(U_223,U_225,U_224,U_222,U_219,U_217,U_218) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_10,plain,
( sP58(U_224,U_217,U_218)
| ~ in(U_218,U_222)
| ~ sP59(U_224,U_222,U_219,U_217,U_218) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_11,plain,
( in(U_219,U_222)
| ~ in(ordered_pair(U_219,U_224),U_217)
| U_219 = U_224
| ~ sP59(U_224,U_222,U_219,U_217,U_218) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_12,plain,
( U_218 != U_224
| ~ sP58(U_224,U_217,U_218) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_13,plain,
( in(ordered_pair(U_218,U_224),U_217)
| ~ sP58(U_224,U_217,U_218) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_14,plain,
( in(sK39(U_217,U_225,U_223),U_223)
| ~ sP60(U_223,U_225,U_217) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_15,plain,
( ~ in(ordered_pair(sK39(U_217,U_225,U_223),U_225),U_217)
| sK39(U_217,U_225,U_223) = U_225
| ~ sP60(U_223,U_225,U_217) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_16,plain,
( sK40(U_217,U_225,U_223) != U_225
| ~ sP61(U_223,U_225,U_217) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_17,plain,
( in(ordered_pair(sK40(U_217,U_225,U_223),U_225),U_217)
| ~ sP61(U_223,U_225,U_217) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_18,plain,
( ~ in(sK40(U_217,U_225,U_223),U_223)
| ~ sP61(U_223,U_225,U_217) ),
inference(clausify,[status(thm)],[f_32_6]) ).
fof(f_33_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_33_2,plain,
! [U_228] :
( ( U_228 = empty_set
| ? [U_227] : in(U_227,U_228) )
& ( ! [U_226] : ~ in(U_226,U_228)
| U_228 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_230] :
( U_230 = empty_set
| ? [U_227] : in(U_227,U_230) )
& ! [U_229] :
( ! [U_226] : ~ in(U_226,U_229)
| U_229 != empty_set ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_230] :
( U_230 = empty_set
| in(sK41(U_230),U_230) )
& ! [U_229] :
( ! [U_226] : ~ in(U_226,U_229)
| U_229 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_227,sK41(U_230))],[f_33_3]) ).
fof(f_33_5,plain,
( ! [U_230] :
( U_230 = empty_set
| in(sK41(U_230),U_230) )
& ! [U_229,U_226] :
( ~ in(U_226,U_229)
| U_229 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_33_4]) ).
cnf(f_33_6,plain,
( ~ in(U_226,U_229)
| U_229 != empty_set ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,plain,
( U_230 = empty_set
| in(sK41(U_230),U_230) ),
inference(clausify,[status(thm)],[f_33_5]) ).
fof(f_34_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_34_2,plain,
! [U_234,U_233] :
( ( U_233 = powerset(U_234)
| ? [U_232] :
( ( ~ in(U_232,U_233)
& subset(U_232,U_234) )
| ( ~ subset(U_232,U_234)
& in(U_232,U_233) ) ) )
& ( ! [U_231] :
( ( in(U_231,U_233)
| ~ subset(U_231,U_234) )
& ( subset(U_231,U_234)
| ~ in(U_231,U_233) ) )
| U_233 != powerset(U_234) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_242,U_240] :
( U_240 = powerset(U_242)
| ? [U_238] :
( ~ in(U_238,U_240)
& subset(U_238,U_242) )
| ? [U_237] :
( ~ subset(U_237,U_242)
& in(U_237,U_240) ) )
& ! [U_241,U_239] :
( ( ! [U_236] :
( in(U_236,U_239)
| ~ subset(U_236,U_241) )
& ! [U_235] :
( subset(U_235,U_241)
| ~ in(U_235,U_239) ) )
| U_239 != powerset(U_241) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_242,U_240] :
( U_240 = powerset(U_242)
| ? [U_238] :
( ~ in(U_238,U_240)
& subset(U_238,U_242) )
| ( ~ subset(sK42(U_242,U_240),U_242)
& in(sK42(U_242,U_240),U_240) ) )
& ! [U_241,U_239] :
( ( ! [U_236] :
( in(U_236,U_239)
| ~ subset(U_236,U_241) )
& ! [U_235] :
( subset(U_235,U_241)
| ~ in(U_235,U_239) ) )
| U_239 != powerset(U_241) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_237,sK42(U_242,U_240))],[f_34_3]) ).
fof(f_34_5,plain,
( ! [U_242,U_240] :
( U_240 = powerset(U_242)
| ( ~ in(sK43(U_242,U_240),U_240)
& subset(sK43(U_242,U_240),U_242) )
| ( ~ subset(sK42(U_242,U_240),U_242)
& in(sK42(U_242,U_240),U_240) ) )
& ! [U_241,U_239] :
( ( ! [U_236] :
( in(U_236,U_239)
| ~ subset(U_236,U_241) )
& ! [U_235] :
( subset(U_235,U_241)
| ~ in(U_235,U_239) ) )
| U_239 != powerset(U_241) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_238,sK43(U_242,U_240))],[f_34_4]) ).
fof(f_34_6,plain,
( ! [U_242,U_240] :
( ~ in(sK43(U_242,U_240),U_240)
| ~ sP65(U_242,U_240) )
& ! [U_242,U_240] :
( subset(sK43(U_242,U_240),U_242)
| ~ sP65(U_242,U_240) )
& ! [U_242,U_240] :
( ~ subset(sK42(U_242,U_240),U_242)
| ~ sP64(U_242,U_240) )
& ! [U_242,U_240] :
( in(sK42(U_242,U_240),U_240)
| ~ sP64(U_242,U_240) )
& ! [U_239,U_235,U_236,U_241] :
( in(U_236,U_239)
| ~ subset(U_236,U_241)
| ~ sP63(U_239,U_235,U_236,U_241) )
& ! [U_239,U_235,U_236,U_241] :
( subset(U_235,U_241)
| ~ in(U_235,U_239)
| ~ sP63(U_239,U_235,U_236,U_241) )
& ! [U_242,U_240] :
( U_240 = powerset(U_242)
| sP65(U_242,U_240)
| sP64(U_242,U_240) )
& ! [U_239,U_235,U_236,U_241] :
( sP63(U_239,U_235,U_236,U_241)
| U_239 != powerset(U_241) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63,sP64,sP65])],[f_34_5]) ).
cnf(f_34_7,plain,
( sP63(U_239,U_235,U_236,U_241)
| U_239 != powerset(U_241) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_8,plain,
( U_240 = powerset(U_242)
| sP65(U_242,U_240)
| sP64(U_242,U_240) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_9,plain,
( subset(U_235,U_241)
| ~ in(U_235,U_239)
| ~ sP63(U_239,U_235,U_236,U_241) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_10,plain,
( in(U_236,U_239)
| ~ subset(U_236,U_241)
| ~ sP63(U_239,U_235,U_236,U_241) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_11,plain,
( in(sK42(U_242,U_240),U_240)
| ~ sP64(U_242,U_240) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_12,plain,
( ~ subset(sK42(U_242,U_240),U_242)
| ~ sP64(U_242,U_240) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_13,plain,
( subset(sK43(U_242,U_240),U_242)
| ~ sP65(U_242,U_240) ),
inference(clausify,[status(thm)],[f_34_6]) ).
cnf(f_34_14,plain,
( ~ in(sK43(U_242,U_240),U_240)
| ~ sP65(U_242,U_240) ),
inference(clausify,[status(thm)],[f_34_6]) ).
fof(f_35_1,plain,
! [A] :
( ( epsilon_transitive(A)
| ? [B] :
( ~ subset(B,A)
& in(B,A) ) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(fof_nnf,[status(thm)],[d2_ordinal1]) ).
fof(f_35_2,plain,
! [U_245] :
( ( epsilon_transitive(U_245)
| ? [U_244] :
( ~ subset(U_244,U_245)
& in(U_244,U_245) ) )
& ( ! [U_243] :
( subset(U_243,U_245)
| ~ in(U_243,U_245) )
| ~ epsilon_transitive(U_245) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_247] :
( epsilon_transitive(U_247)
| ? [U_244] :
( ~ subset(U_244,U_247)
& in(U_244,U_247) ) )
& ! [U_246] :
( ! [U_243] :
( subset(U_243,U_246)
| ~ in(U_243,U_246) )
| ~ epsilon_transitive(U_246) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_247] :
( epsilon_transitive(U_247)
| ( ~ subset(sK44(U_247),U_247)
& in(sK44(U_247),U_247) ) )
& ! [U_246] :
( ! [U_243] :
( subset(U_243,U_246)
| ~ in(U_243,U_246) )
| ~ epsilon_transitive(U_246) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_244,sK44(U_247))],[f_35_3]) ).
fof(f_35_5,plain,
( ! [U_247] :
( ~ subset(sK44(U_247),U_247)
| ~ sP66(U_247) )
& ! [U_247] :
( in(sK44(U_247),U_247)
| ~ sP66(U_247) )
& ! [U_247] :
( epsilon_transitive(U_247)
| sP66(U_247) )
& ! [U_243,U_246] :
( subset(U_243,U_246)
| ~ in(U_243,U_246)
| ~ epsilon_transitive(U_246) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_35_4]) ).
cnf(f_35_6,plain,
( subset(U_243,U_246)
| ~ in(U_243,U_246)
| ~ epsilon_transitive(U_246) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_7,plain,
( epsilon_transitive(U_247)
| sP66(U_247) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_8,plain,
( in(sK44(U_247),U_247)
| ~ sP66(U_247) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_9,plain,
( ~ subset(sK44(U_247),U_247)
| ~ sP66(U_247) ),
inference(clausify,[status(thm)],[f_35_5]) ).
fof(f_36_1,plain,
! [A] :
( ! [B] :
( ( ( A = B
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),A)
& in(ordered_pair(C,D),B) )
| ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_relat_1]) ).
fof(f_36_2,plain,
! [U_253] :
( ! [U_252] :
( ( ( U_253 = U_252
| ? [U_251,U_250] :
( ( ~ in(ordered_pair(U_251,U_250),U_253)
& in(ordered_pair(U_251,U_250),U_252) )
| ( ~ in(ordered_pair(U_251,U_250),U_252)
& in(ordered_pair(U_251,U_250),U_253) ) ) )
& ( ! [U_249,U_248] :
( ( in(ordered_pair(U_249,U_248),U_253)
| ~ in(ordered_pair(U_249,U_248),U_252) )
& ( in(ordered_pair(U_249,U_248),U_252)
| ~ in(ordered_pair(U_249,U_248),U_253) ) )
| U_253 != U_252 ) )
| ~ relation(U_252) )
| ~ relation(U_253) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_253] :
( ! [U_252] :
( ( ( U_253 = U_252
| ? [U_261,U_259] :
( ~ in(ordered_pair(U_261,U_259),U_253)
& in(ordered_pair(U_261,U_259),U_252) )
| ? [U_260,U_258] :
( ~ in(ordered_pair(U_260,U_258),U_252)
& in(ordered_pair(U_260,U_258),U_253) ) )
& ( ( ! [U_257,U_255] :
( in(ordered_pair(U_257,U_255),U_253)
| ~ in(ordered_pair(U_257,U_255),U_252) )
& ! [U_256,U_254] :
( in(ordered_pair(U_256,U_254),U_252)
| ~ in(ordered_pair(U_256,U_254),U_253) ) )
| U_253 != U_252 ) )
| ~ relation(U_252) )
| ~ relation(U_253) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_253] :
( ! [U_252] :
( ( ( U_253 = U_252
| ? [U_261,U_259] :
( ~ in(ordered_pair(U_261,U_259),U_253)
& in(ordered_pair(U_261,U_259),U_252) )
| ? [U_258] :
( ~ in(ordered_pair(sK45(U_253,U_252),U_258),U_252)
& in(ordered_pair(sK45(U_253,U_252),U_258),U_253) ) )
& ( ( ! [U_257,U_255] :
( in(ordered_pair(U_257,U_255),U_253)
| ~ in(ordered_pair(U_257,U_255),U_252) )
& ! [U_256,U_254] :
( in(ordered_pair(U_256,U_254),U_252)
| ~ in(ordered_pair(U_256,U_254),U_253) ) )
| U_253 != U_252 ) )
| ~ relation(U_252) )
| ~ relation(U_253) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_260,sK45(U_253,U_252))],[f_36_3]) ).
fof(f_36_5,plain,
! [U_253] :
( ! [U_252] :
( ( ( U_253 = U_252
| ? [U_261,U_259] :
( ~ in(ordered_pair(U_261,U_259),U_253)
& in(ordered_pair(U_261,U_259),U_252) )
| ( ~ in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_252)
& in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_253) ) )
& ( ( ! [U_257,U_255] :
( in(ordered_pair(U_257,U_255),U_253)
| ~ in(ordered_pair(U_257,U_255),U_252) )
& ! [U_256,U_254] :
( in(ordered_pair(U_256,U_254),U_252)
| ~ in(ordered_pair(U_256,U_254),U_253) ) )
| U_253 != U_252 ) )
| ~ relation(U_252) )
| ~ relation(U_253) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_258,sK46(U_253,U_252))],[f_36_4]) ).
fof(f_36_6,plain,
! [U_253] :
( ! [U_252] :
( ( ( U_253 = U_252
| ? [U_259] :
( ~ in(ordered_pair(sK47(U_253,U_252),U_259),U_253)
& in(ordered_pair(sK47(U_253,U_252),U_259),U_252) )
| ( ~ in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_252)
& in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_253) ) )
& ( ( ! [U_257,U_255] :
( in(ordered_pair(U_257,U_255),U_253)
| ~ in(ordered_pair(U_257,U_255),U_252) )
& ! [U_256,U_254] :
( in(ordered_pair(U_256,U_254),U_252)
| ~ in(ordered_pair(U_256,U_254),U_253) ) )
| U_253 != U_252 ) )
| ~ relation(U_252) )
| ~ relation(U_253) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_261,sK47(U_253,U_252))],[f_36_5]) ).
fof(f_36_7,plain,
! [U_253] :
( ! [U_252] :
( ( ( U_253 = U_252
| ( ~ in(ordered_pair(sK47(U_253,U_252),sK48(U_253,U_252)),U_253)
& in(ordered_pair(sK47(U_253,U_252),sK48(U_253,U_252)),U_252) )
| ( ~ in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_252)
& in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_253) ) )
& ( ( ! [U_257,U_255] :
( in(ordered_pair(U_257,U_255),U_253)
| ~ in(ordered_pair(U_257,U_255),U_252) )
& ! [U_256,U_254] :
( in(ordered_pair(U_256,U_254),U_252)
| ~ in(ordered_pair(U_256,U_254),U_253) ) )
| U_253 != U_252 ) )
| ~ relation(U_252) )
| ~ relation(U_253) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_259,sK48(U_253,U_252))],[f_36_6]) ).
fof(f_36_8,plain,
( ! [U_253,U_252] :
( ~ in(ordered_pair(sK47(U_253,U_252),sK48(U_253,U_252)),U_253)
| ~ sP69(U_253,U_252) )
& ! [U_253,U_252] :
( in(ordered_pair(sK47(U_253,U_252),sK48(U_253,U_252)),U_252)
| ~ sP69(U_253,U_252) )
& ! [U_253,U_252] :
( ~ in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_252)
| ~ sP68(U_253,U_252) )
& ! [U_253,U_252] :
( in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_253)
| ~ sP68(U_253,U_252) )
& ! [U_253,U_252,U_256,U_254,U_255,U_257] :
( in(ordered_pair(U_257,U_255),U_253)
| ~ in(ordered_pair(U_257,U_255),U_252)
| ~ sP67(U_253,U_252,U_256,U_254,U_255,U_257) )
& ! [U_253,U_252,U_256,U_254,U_255,U_257] :
( in(ordered_pair(U_256,U_254),U_252)
| ~ in(ordered_pair(U_256,U_254),U_253)
| ~ sP67(U_253,U_252,U_256,U_254,U_255,U_257) )
& ! [U_253,U_252,U_256,U_254,U_255,U_257] :
( U_253 = U_252
| sP69(U_253,U_252)
| sP68(U_253,U_252)
| ~ sP70(U_253,U_252,U_256,U_254,U_255,U_257) )
& ! [U_253,U_252,U_256,U_254,U_255,U_257] :
( sP67(U_253,U_252,U_256,U_254,U_255,U_257)
| U_253 != U_252
| ~ sP70(U_253,U_252,U_256,U_254,U_255,U_257) )
& ! [U_253,U_252,U_256,U_254,U_255,U_257] :
( sP70(U_253,U_252,U_256,U_254,U_255,U_257)
| ~ relation(U_252)
| ~ relation(U_253) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67,sP68,sP69,sP70])],[f_36_7]) ).
cnf(f_36_9,plain,
( sP70(U_253,U_252,U_256,U_254,U_255,U_257)
| ~ relation(U_252)
| ~ relation(U_253) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_10,plain,
( sP67(U_253,U_252,U_256,U_254,U_255,U_257)
| U_253 != U_252
| ~ sP70(U_253,U_252,U_256,U_254,U_255,U_257) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_11,plain,
( U_253 = U_252
| sP69(U_253,U_252)
| sP68(U_253,U_252)
| ~ sP70(U_253,U_252,U_256,U_254,U_255,U_257) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_12,plain,
( in(ordered_pair(U_256,U_254),U_252)
| ~ in(ordered_pair(U_256,U_254),U_253)
| ~ sP67(U_253,U_252,U_256,U_254,U_255,U_257) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_13,plain,
( in(ordered_pair(U_257,U_255),U_253)
| ~ in(ordered_pair(U_257,U_255),U_252)
| ~ sP67(U_253,U_252,U_256,U_254,U_255,U_257) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_14,plain,
( in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_253)
| ~ sP68(U_253,U_252) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_15,plain,
( ~ in(ordered_pair(sK45(U_253,U_252),sK46(U_253,U_252)),U_252)
| ~ sP68(U_253,U_252) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_16,plain,
( in(ordered_pair(sK47(U_253,U_252),sK48(U_253,U_252)),U_252)
| ~ sP69(U_253,U_252) ),
inference(clausify,[status(thm)],[f_36_8]) ).
cnf(f_36_17,plain,
( ~ in(ordered_pair(sK47(U_253,U_252),sK48(U_253,U_252)),U_253)
| ~ sP69(U_253,U_252) ),
inference(clausify,[status(thm)],[f_36_8]) ).
fof(f_37_1,plain,
! [A,B] :
( ( ( ( element(B,A)
| ~ empty(B) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( element(B,A)
| ~ in(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(fof_nnf,[status(thm)],[d2_subset_1]) ).
fof(f_37_2,plain,
! [U_263,U_262] :
( ( ( ( element(U_262,U_263)
| ~ empty(U_262) )
& ( empty(U_262)
| ~ element(U_262,U_263) ) )
| ~ empty(U_263) )
& ( ( ( element(U_262,U_263)
| ~ in(U_262,U_263) )
& ( in(U_262,U_263)
| ~ element(U_262,U_263) ) )
| empty(U_263) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_271] :
( ( ! [U_269] :
( element(U_269,U_271)
| ~ empty(U_269) )
& ! [U_268] :
( empty(U_268)
| ~ element(U_268,U_271) ) )
| ~ empty(U_271) )
& ! [U_270] :
( ( ! [U_267] :
( element(U_267,U_270)
| ~ in(U_267,U_270) )
& ! [U_266] :
( in(U_266,U_270)
| ~ element(U_266,U_270) ) )
| empty(U_270) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_271,U_268,U_269] :
( element(U_269,U_271)
| ~ empty(U_269)
| ~ sP72(U_271,U_268,U_269) )
& ! [U_271,U_268,U_269] :
( empty(U_268)
| ~ element(U_268,U_271)
| ~ sP72(U_271,U_268,U_269) )
& ! [U_270,U_266,U_267] :
( element(U_267,U_270)
| ~ in(U_267,U_270)
| ~ sP71(U_270,U_266,U_267) )
& ! [U_270,U_266,U_267] :
( in(U_266,U_270)
| ~ element(U_266,U_270)
| ~ sP71(U_270,U_266,U_267) )
& ! [U_271,U_268,U_269] :
( sP72(U_271,U_268,U_269)
| ~ empty(U_271) )
& ! [U_270,U_266,U_267] :
( sP71(U_270,U_266,U_267)
| empty(U_270) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71,sP72])],[f_37_3]) ).
cnf(f_37_5,plain,
( sP71(U_270,U_266,U_267)
| empty(U_270) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
( sP72(U_271,U_268,U_269)
| ~ empty(U_271) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_7,plain,
( in(U_266,U_270)
| ~ element(U_266,U_270)
| ~ sP71(U_270,U_266,U_267) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_8,plain,
( element(U_267,U_270)
| ~ in(U_267,U_270)
| ~ sP71(U_270,U_266,U_267) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_9,plain,
( empty(U_268)
| ~ element(U_268,U_271)
| ~ sP72(U_271,U_268,U_269) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_10,plain,
( element(U_269,U_271)
| ~ empty(U_269)
| ~ sP72(U_271,U_268,U_269) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_38_2,plain,
! [U_276,U_275,U_274] :
( ( U_274 = unordered_pair(U_276,U_275)
| ? [U_273] :
( ( ~ in(U_273,U_274)
& ( U_273 = U_275
| U_273 = U_276 ) )
| ( U_273 != U_275
& U_273 != U_276
& in(U_273,U_274) ) ) )
& ( ! [U_272] :
( ( in(U_272,U_274)
| ( U_272 != U_275
& U_272 != U_276 ) )
& ( U_272 = U_275
| U_272 = U_276
| ~ in(U_272,U_274) ) )
| U_274 != unordered_pair(U_276,U_275) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_286,U_284,U_282] :
( U_282 = unordered_pair(U_286,U_284)
| ? [U_280] :
( ~ in(U_280,U_282)
& ( U_280 = U_284
| U_280 = U_286 ) )
| ? [U_279] :
( U_279 != U_284
& U_279 != U_286
& in(U_279,U_282) ) )
& ! [U_285,U_283,U_281] :
( ( ! [U_278] :
( in(U_278,U_281)
| ( U_278 != U_283
& U_278 != U_285 ) )
& ! [U_277] :
( U_277 = U_283
| U_277 = U_285
| ~ in(U_277,U_281) ) )
| U_281 != unordered_pair(U_285,U_283) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_286,U_284,U_282] :
( U_282 = unordered_pair(U_286,U_284)
| ? [U_280] :
( ~ in(U_280,U_282)
& ( U_280 = U_284
| U_280 = U_286 ) )
| ( sK49(U_286,U_284,U_282) != U_284
& sK49(U_286,U_284,U_282) != U_286
& in(sK49(U_286,U_284,U_282),U_282) ) )
& ! [U_285,U_283,U_281] :
( ( ! [U_278] :
( in(U_278,U_281)
| ( U_278 != U_283
& U_278 != U_285 ) )
& ! [U_277] :
( U_277 = U_283
| U_277 = U_285
| ~ in(U_277,U_281) ) )
| U_281 != unordered_pair(U_285,U_283) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_279,sK49(U_286,U_284,U_282))],[f_38_3]) ).
fof(f_38_5,plain,
( ! [U_286,U_284,U_282] :
( U_282 = unordered_pair(U_286,U_284)
| ( ~ in(sK50(U_286,U_284,U_282),U_282)
& ( sK50(U_286,U_284,U_282) = U_284
| sK50(U_286,U_284,U_282) = U_286 ) )
| ( sK49(U_286,U_284,U_282) != U_284
& sK49(U_286,U_284,U_282) != U_286
& in(sK49(U_286,U_284,U_282),U_282) ) )
& ! [U_285,U_283,U_281] :
( ( ! [U_278] :
( in(U_278,U_281)
| ( U_278 != U_283
& U_278 != U_285 ) )
& ! [U_277] :
( U_277 = U_283
| U_277 = U_285
| ~ in(U_277,U_281) ) )
| U_281 != unordered_pair(U_285,U_283) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_280,sK50(U_286,U_284,U_282))],[f_38_4]) ).
fof(f_38_6,plain,
( ! [U_286,U_284,U_282] :
( ~ in(sK50(U_286,U_284,U_282),U_282)
| ~ sP76(U_286,U_284,U_282) )
& ! [U_286,U_284,U_282] :
( sK50(U_286,U_284,U_282) = U_284
| sK50(U_286,U_284,U_282) = U_286
| ~ sP76(U_286,U_284,U_282) )
& ! [U_286,U_284,U_282] :
( sK49(U_286,U_284,U_282) != U_284
| ~ sP75(U_286,U_284,U_282) )
& ! [U_286,U_284,U_282] :
( sK49(U_286,U_284,U_282) != U_286
| ~ sP75(U_286,U_284,U_282) )
& ! [U_286,U_284,U_282] :
( in(sK49(U_286,U_284,U_282),U_282)
| ~ sP75(U_286,U_284,U_282) )
& ! [U_283,U_285,U_278] :
( U_278 != U_283
| ~ sP73(U_283,U_285,U_278) )
& ! [U_283,U_285,U_278] :
( U_278 != U_285
| ~ sP73(U_283,U_285,U_278) )
& ! [U_283,U_277,U_285,U_281,U_278] :
( in(U_278,U_281)
| sP73(U_283,U_285,U_278)
| ~ sP74(U_283,U_277,U_285,U_281,U_278) )
& ! [U_283,U_277,U_285,U_281,U_278] :
( U_277 = U_283
| U_277 = U_285
| ~ in(U_277,U_281)
| ~ sP74(U_283,U_277,U_285,U_281,U_278) )
& ! [U_286,U_284,U_282] :
( U_282 = unordered_pair(U_286,U_284)
| sP76(U_286,U_284,U_282)
| sP75(U_286,U_284,U_282) )
& ! [U_283,U_277,U_285,U_281,U_278] :
( sP74(U_283,U_277,U_285,U_281,U_278)
| U_281 != unordered_pair(U_285,U_283) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73,sP74,sP75,sP76])],[f_38_5]) ).
cnf(f_38_7,plain,
( sP74(U_283,U_277,U_285,U_281,U_278)
| U_281 != unordered_pair(U_285,U_283) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_8,plain,
( U_282 = unordered_pair(U_286,U_284)
| sP76(U_286,U_284,U_282)
| sP75(U_286,U_284,U_282) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_9,plain,
( U_277 = U_283
| U_277 = U_285
| ~ in(U_277,U_281)
| ~ sP74(U_283,U_277,U_285,U_281,U_278) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_10,plain,
( in(U_278,U_281)
| sP73(U_283,U_285,U_278)
| ~ sP74(U_283,U_277,U_285,U_281,U_278) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_11,plain,
( U_278 != U_285
| ~ sP73(U_283,U_285,U_278) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_12,plain,
( U_278 != U_283
| ~ sP73(U_283,U_285,U_278) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_13,plain,
( in(sK49(U_286,U_284,U_282),U_282)
| ~ sP75(U_286,U_284,U_282) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_14,plain,
( sK49(U_286,U_284,U_282) != U_286
| ~ sP75(U_286,U_284,U_282) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_15,plain,
( sK49(U_286,U_284,U_282) != U_284
| ~ sP75(U_286,U_284,U_282) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_16,plain,
( sK50(U_286,U_284,U_282) = U_284
| sK50(U_286,U_284,U_282) = U_286
| ~ sP76(U_286,U_284,U_282) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_17,plain,
( ~ in(sK50(U_286,U_284,U_282),U_282)
| ~ sP76(U_286,U_284,U_282) ),
inference(clausify,[status(thm)],[f_38_6]) ).
fof(f_39_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ? [B] :
( ! [C] :
( ~ disjoint(fiber(A,C),B)
| ~ in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) )
& ( ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_wellord1]) ).
fof(f_39_2,plain,
! [U_291] :
( ( ( well_founded_relation(U_291)
| ? [U_290] :
( ! [U_289] :
( ~ disjoint(fiber(U_291,U_289),U_290)
| ~ in(U_289,U_290) )
& U_290 != empty_set
& subset(U_290,relation_field(U_291)) ) )
& ( ! [U_288] :
( ? [U_287] :
( disjoint(fiber(U_291,U_287),U_288)
& in(U_287,U_288) )
| U_288 = empty_set
| ~ subset(U_288,relation_field(U_291)) )
| ~ well_founded_relation(U_291) ) )
| ~ relation(U_291) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_291] :
( ( ( well_founded_relation(U_291)
| ? [U_290] :
( ! [U_289] :
( ~ disjoint(fiber(U_291,U_289),U_290)
| ~ in(U_289,U_290) )
& U_290 != empty_set
& subset(U_290,relation_field(U_291)) ) )
& ( ! [U_288] :
( ( disjoint(fiber(U_291,sK51(U_291,U_288)),U_288)
& in(sK51(U_291,U_288),U_288) )
| U_288 = empty_set
| ~ subset(U_288,relation_field(U_291)) )
| ~ well_founded_relation(U_291) ) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_287,sK51(U_291,U_288))],[f_39_2]) ).
fof(f_39_4,plain,
! [U_291] :
( ( ( well_founded_relation(U_291)
| ( ! [U_289] :
( ~ disjoint(fiber(U_291,U_289),sK52(U_291))
| ~ in(U_289,sK52(U_291)) )
& sK52(U_291) != empty_set
& subset(sK52(U_291),relation_field(U_291)) ) )
& ( ! [U_288] :
( ( disjoint(fiber(U_291,sK51(U_291,U_288)),U_288)
& in(sK51(U_291,U_288),U_288) )
| U_288 = empty_set
| ~ subset(U_288,relation_field(U_291)) )
| ~ well_founded_relation(U_291) ) )
| ~ relation(U_291) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_290,sK52(U_291))],[f_39_3]) ).
fof(f_39_5,plain,
( ! [U_291,U_289] :
( ~ disjoint(fiber(U_291,U_289),sK52(U_291))
| ~ in(U_289,sK52(U_291))
| ~ sP78(U_291,U_289) )
& ! [U_291,U_289] :
( sK52(U_291) != empty_set
| ~ sP78(U_291,U_289) )
& ! [U_291,U_289] :
( subset(sK52(U_291),relation_field(U_291))
| ~ sP78(U_291,U_289) )
& ! [U_291,U_288] :
( disjoint(fiber(U_291,sK51(U_291,U_288)),U_288)
| ~ sP77(U_291,U_288) )
& ! [U_291,U_288] :
( in(sK51(U_291,U_288),U_288)
| ~ sP77(U_291,U_288) )
& ! [U_291,U_288,U_289] :
( well_founded_relation(U_291)
| sP78(U_291,U_289)
| ~ sP79(U_291,U_288,U_289) )
& ! [U_291,U_288,U_289] :
( sP77(U_291,U_288)
| U_288 = empty_set
| ~ subset(U_288,relation_field(U_291))
| ~ well_founded_relation(U_291)
| ~ sP79(U_291,U_288,U_289) )
& ! [U_291,U_288,U_289] :
( sP79(U_291,U_288,U_289)
| ~ relation(U_291) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77,sP78,sP79])],[f_39_4]) ).
cnf(f_39_6,plain,
( sP79(U_291,U_288,U_289)
| ~ relation(U_291) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_7,plain,
( sP77(U_291,U_288)
| U_288 = empty_set
| ~ subset(U_288,relation_field(U_291))
| ~ well_founded_relation(U_291)
| ~ sP79(U_291,U_288,U_289) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_8,plain,
( well_founded_relation(U_291)
| sP78(U_291,U_289)
| ~ sP79(U_291,U_288,U_289) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_9,plain,
( in(sK51(U_291,U_288),U_288)
| ~ sP77(U_291,U_288) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_10,plain,
( disjoint(fiber(U_291,sK51(U_291,U_288)),U_288)
| ~ sP77(U_291,U_288) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_11,plain,
( subset(sK52(U_291),relation_field(U_291))
| ~ sP78(U_291,U_289) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_12,plain,
( sK52(U_291) != empty_set
| ~ sP78(U_291,U_289) ),
inference(clausify,[status(thm)],[f_39_5]) ).
cnf(f_39_13,plain,
( ~ disjoint(fiber(U_291,U_289),sK52(U_291))
| ~ in(U_289,sK52(U_291))
| ~ sP78(U_291,U_289) ),
inference(clausify,[status(thm)],[f_39_5]) ).
fof(f_40_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_40_2,plain,
! [U_296,U_295,U_294] :
( ( U_294 = set_union2(U_296,U_295)
| ? [U_293] :
( ( ~ in(U_293,U_294)
& ( in(U_293,U_295)
| in(U_293,U_296) ) )
| ( ~ in(U_293,U_295)
& ~ in(U_293,U_296)
& in(U_293,U_294) ) ) )
& ( ! [U_292] :
( ( in(U_292,U_294)
| ( ~ in(U_292,U_295)
& ~ in(U_292,U_296) ) )
& ( in(U_292,U_295)
| in(U_292,U_296)
| ~ in(U_292,U_294) ) )
| U_294 != set_union2(U_296,U_295) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_306,U_304,U_302] :
( U_302 = set_union2(U_306,U_304)
| ? [U_300] :
( ~ in(U_300,U_302)
& ( in(U_300,U_304)
| in(U_300,U_306) ) )
| ? [U_299] :
( ~ in(U_299,U_304)
& ~ in(U_299,U_306)
& in(U_299,U_302) ) )
& ! [U_305,U_303,U_301] :
( ( ! [U_298] :
( in(U_298,U_301)
| ( ~ in(U_298,U_303)
& ~ in(U_298,U_305) ) )
& ! [U_297] :
( in(U_297,U_303)
| in(U_297,U_305)
| ~ in(U_297,U_301) ) )
| U_301 != set_union2(U_305,U_303) ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_306,U_304,U_302] :
( U_302 = set_union2(U_306,U_304)
| ? [U_300] :
( ~ in(U_300,U_302)
& ( in(U_300,U_304)
| in(U_300,U_306) ) )
| ( ~ in(sK53(U_306,U_304,U_302),U_304)
& ~ in(sK53(U_306,U_304,U_302),U_306)
& in(sK53(U_306,U_304,U_302),U_302) ) )
& ! [U_305,U_303,U_301] :
( ( ! [U_298] :
( in(U_298,U_301)
| ( ~ in(U_298,U_303)
& ~ in(U_298,U_305) ) )
& ! [U_297] :
( in(U_297,U_303)
| in(U_297,U_305)
| ~ in(U_297,U_301) ) )
| U_301 != set_union2(U_305,U_303) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_299,sK53(U_306,U_304,U_302))],[f_40_3]) ).
fof(f_40_5,plain,
( ! [U_306,U_304,U_302] :
( U_302 = set_union2(U_306,U_304)
| ( ~ in(sK54(U_306,U_304,U_302),U_302)
& ( in(sK54(U_306,U_304,U_302),U_304)
| in(sK54(U_306,U_304,U_302),U_306) ) )
| ( ~ in(sK53(U_306,U_304,U_302),U_304)
& ~ in(sK53(U_306,U_304,U_302),U_306)
& in(sK53(U_306,U_304,U_302),U_302) ) )
& ! [U_305,U_303,U_301] :
( ( ! [U_298] :
( in(U_298,U_301)
| ( ~ in(U_298,U_303)
& ~ in(U_298,U_305) ) )
& ! [U_297] :
( in(U_297,U_303)
| in(U_297,U_305)
| ~ in(U_297,U_301) ) )
| U_301 != set_union2(U_305,U_303) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_300,sK54(U_306,U_304,U_302))],[f_40_4]) ).
fof(f_40_6,plain,
( ! [U_304,U_306,U_302] :
( ~ in(sK54(U_306,U_304,U_302),U_302)
| ~ sP83(U_304,U_306,U_302) )
& ! [U_304,U_306,U_302] :
( in(sK54(U_306,U_304,U_302),U_304)
| in(sK54(U_306,U_304,U_302),U_306)
| ~ sP83(U_304,U_306,U_302) )
& ! [U_304,U_306,U_302] :
( ~ in(sK53(U_306,U_304,U_302),U_304)
| ~ sP82(U_304,U_306,U_302) )
& ! [U_304,U_306,U_302] :
( ~ in(sK53(U_306,U_304,U_302),U_306)
| ~ sP82(U_304,U_306,U_302) )
& ! [U_304,U_306,U_302] :
( in(sK53(U_306,U_304,U_302),U_302)
| ~ sP82(U_304,U_306,U_302) )
& ! [U_298,U_303,U_305] :
( ~ in(U_298,U_303)
| ~ sP80(U_298,U_303,U_305) )
& ! [U_298,U_303,U_305] :
( ~ in(U_298,U_305)
| ~ sP80(U_298,U_303,U_305) )
& ! [U_301,U_297,U_298,U_303,U_305] :
( in(U_298,U_301)
| sP80(U_298,U_303,U_305)
| ~ sP81(U_301,U_297,U_298,U_303,U_305) )
& ! [U_301,U_297,U_298,U_303,U_305] :
( in(U_297,U_303)
| in(U_297,U_305)
| ~ in(U_297,U_301)
| ~ sP81(U_301,U_297,U_298,U_303,U_305) )
& ! [U_304,U_306,U_302] :
( U_302 = set_union2(U_306,U_304)
| sP83(U_304,U_306,U_302)
| sP82(U_304,U_306,U_302) )
& ! [U_301,U_297,U_298,U_303,U_305] :
( sP81(U_301,U_297,U_298,U_303,U_305)
| U_301 != set_union2(U_305,U_303) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80,sP81,sP82,sP83])],[f_40_5]) ).
cnf(f_40_7,plain,
( sP81(U_301,U_297,U_298,U_303,U_305)
| U_301 != set_union2(U_305,U_303) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_8,plain,
( U_302 = set_union2(U_306,U_304)
| sP83(U_304,U_306,U_302)
| sP82(U_304,U_306,U_302) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_9,plain,
( in(U_297,U_303)
| in(U_297,U_305)
| ~ in(U_297,U_301)
| ~ sP81(U_301,U_297,U_298,U_303,U_305) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_10,plain,
( in(U_298,U_301)
| sP80(U_298,U_303,U_305)
| ~ sP81(U_301,U_297,U_298,U_303,U_305) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_11,plain,
( ~ in(U_298,U_305)
| ~ sP80(U_298,U_303,U_305) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_12,plain,
( ~ in(U_298,U_303)
| ~ sP80(U_298,U_303,U_305) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_13,plain,
( in(sK53(U_306,U_304,U_302),U_302)
| ~ sP82(U_304,U_306,U_302) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_14,plain,
( ~ in(sK53(U_306,U_304,U_302),U_306)
| ~ sP82(U_304,U_306,U_302) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_15,plain,
( ~ in(sK53(U_306,U_304,U_302),U_304)
| ~ sP82(U_304,U_306,U_302) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_16,plain,
( in(sK54(U_306,U_304,U_302),U_304)
| in(sK54(U_306,U_304,U_302),U_306)
| ~ sP83(U_304,U_306,U_302) ),
inference(clausify,[status(thm)],[f_40_6]) ).
cnf(f_40_17,plain,
( ~ in(sK54(U_306,U_304,U_302),U_302)
| ~ sP83(U_304,U_306,U_302) ),
inference(clausify,[status(thm)],[f_40_6]) ).
fof(f_41_1,plain,
! [A,B,C] :
( ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) ) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_zfmisc_1]) ).
fof(f_41_2,plain,
! [U_319,U_318,U_317] :
( ( U_317 = cartesian_product2(U_319,U_318)
| ? [U_316] :
( ( ~ in(U_316,U_317)
& ? [U_315,U_314] :
( U_316 = ordered_pair(U_315,U_314)
& in(U_314,U_318)
& in(U_315,U_319) ) )
| ( ! [U_313,U_312] :
( U_316 != ordered_pair(U_313,U_312)
| ~ in(U_312,U_318)
| ~ in(U_313,U_319) )
& in(U_316,U_317) ) ) )
& ( ! [U_311] :
( ( in(U_311,U_317)
| ! [U_310,U_309] :
( U_311 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_318)
| ~ in(U_310,U_319) ) )
& ( ? [U_308,U_307] :
( U_311 = ordered_pair(U_308,U_307)
& in(U_307,U_318)
& in(U_308,U_319) )
| ~ in(U_311,U_317) ) )
| U_317 != cartesian_product2(U_319,U_318) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_329,U_327,U_325] :
( U_325 = cartesian_product2(U_329,U_327)
| ? [U_323] :
( ~ in(U_323,U_325)
& ? [U_315] :
( ? [U_314] :
( U_323 = ordered_pair(U_315,U_314)
& in(U_314,U_327) )
& in(U_315,U_329) ) )
| ? [U_322] :
( ! [U_313] :
( ! [U_312] :
( U_322 != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327) )
| ~ in(U_313,U_329) )
& in(U_322,U_325) ) )
& ! [U_328,U_326,U_324] :
( ( ! [U_321] :
( in(U_321,U_324)
| ! [U_310] :
( ! [U_309] :
( U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326) )
| ~ in(U_310,U_328) ) )
& ! [U_320] :
( ? [U_308] :
( ? [U_307] :
( U_320 = ordered_pair(U_308,U_307)
& in(U_307,U_326) )
& in(U_308,U_328) )
| ~ in(U_320,U_324) ) )
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_329,U_327,U_325] :
( U_325 = cartesian_product2(U_329,U_327)
| ? [U_323] :
( ~ in(U_323,U_325)
& ? [U_315] :
( ? [U_314] :
( U_323 = ordered_pair(U_315,U_314)
& in(U_314,U_327) )
& in(U_315,U_329) ) )
| ? [U_322] :
( ! [U_313] :
( ! [U_312] :
( U_322 != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327) )
| ~ in(U_313,U_329) )
& in(U_322,U_325) ) )
& ! [U_328,U_326,U_324] :
( ( ! [U_321] :
( in(U_321,U_324)
| ! [U_310] :
( ! [U_309] :
( U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326) )
| ~ in(U_310,U_328) ) )
& ! [U_320] :
( ( ? [U_307] :
( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),U_307)
& in(U_307,U_326) )
& in(sK55(U_328,U_326,U_324,U_320),U_328) )
| ~ in(U_320,U_324) ) )
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_308,sK55(U_328,U_326,U_324,U_320))],[f_41_3]) ).
fof(f_41_5,plain,
( ! [U_329,U_327,U_325] :
( U_325 = cartesian_product2(U_329,U_327)
| ? [U_323] :
( ~ in(U_323,U_325)
& ? [U_315] :
( ? [U_314] :
( U_323 = ordered_pair(U_315,U_314)
& in(U_314,U_327) )
& in(U_315,U_329) ) )
| ? [U_322] :
( ! [U_313] :
( ! [U_312] :
( U_322 != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327) )
| ~ in(U_313,U_329) )
& in(U_322,U_325) ) )
& ! [U_328,U_326,U_324] :
( ( ! [U_321] :
( in(U_321,U_324)
| ! [U_310] :
( ! [U_309] :
( U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326) )
| ~ in(U_310,U_328) ) )
& ! [U_320] :
( ( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),sK56(U_328,U_326,U_324,U_320))
& in(sK56(U_328,U_326,U_324,U_320),U_326)
& in(sK55(U_328,U_326,U_324,U_320),U_328) )
| ~ in(U_320,U_324) ) )
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_307,sK56(U_328,U_326,U_324,U_320))],[f_41_4]) ).
fof(f_41_6,plain,
( ! [U_329,U_327,U_325] :
( U_325 = cartesian_product2(U_329,U_327)
| ? [U_323] :
( ~ in(U_323,U_325)
& ? [U_315] :
( ? [U_314] :
( U_323 = ordered_pair(U_315,U_314)
& in(U_314,U_327) )
& in(U_315,U_329) ) )
| ( ! [U_313] :
( ! [U_312] :
( sK57(U_329,U_327,U_325) != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327) )
| ~ in(U_313,U_329) )
& in(sK57(U_329,U_327,U_325),U_325) ) )
& ! [U_328,U_326,U_324] :
( ( ! [U_321] :
( in(U_321,U_324)
| ! [U_310] :
( ! [U_309] :
( U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326) )
| ~ in(U_310,U_328) ) )
& ! [U_320] :
( ( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),sK56(U_328,U_326,U_324,U_320))
& in(sK56(U_328,U_326,U_324,U_320),U_326)
& in(sK55(U_328,U_326,U_324,U_320),U_328) )
| ~ in(U_320,U_324) ) )
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_322,sK57(U_329,U_327,U_325))],[f_41_5]) ).
fof(f_41_7,plain,
( ! [U_329,U_327,U_325] :
( U_325 = cartesian_product2(U_329,U_327)
| ( ~ in(sK58(U_329,U_327,U_325),U_325)
& ? [U_315] :
( ? [U_314] :
( sK58(U_329,U_327,U_325) = ordered_pair(U_315,U_314)
& in(U_314,U_327) )
& in(U_315,U_329) ) )
| ( ! [U_313] :
( ! [U_312] :
( sK57(U_329,U_327,U_325) != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327) )
| ~ in(U_313,U_329) )
& in(sK57(U_329,U_327,U_325),U_325) ) )
& ! [U_328,U_326,U_324] :
( ( ! [U_321] :
( in(U_321,U_324)
| ! [U_310] :
( ! [U_309] :
( U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326) )
| ~ in(U_310,U_328) ) )
& ! [U_320] :
( ( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),sK56(U_328,U_326,U_324,U_320))
& in(sK56(U_328,U_326,U_324,U_320),U_326)
& in(sK55(U_328,U_326,U_324,U_320),U_328) )
| ~ in(U_320,U_324) ) )
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_323,sK58(U_329,U_327,U_325))],[f_41_6]) ).
fof(f_41_8,plain,
( ! [U_329,U_327,U_325] :
( U_325 = cartesian_product2(U_329,U_327)
| ( ~ in(sK58(U_329,U_327,U_325),U_325)
& ? [U_314] :
( sK58(U_329,U_327,U_325) = ordered_pair(sK59(U_329,U_327,U_325),U_314)
& in(U_314,U_327) )
& in(sK59(U_329,U_327,U_325),U_329) )
| ( ! [U_313] :
( ! [U_312] :
( sK57(U_329,U_327,U_325) != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327) )
| ~ in(U_313,U_329) )
& in(sK57(U_329,U_327,U_325),U_325) ) )
& ! [U_328,U_326,U_324] :
( ( ! [U_321] :
( in(U_321,U_324)
| ! [U_310] :
( ! [U_309] :
( U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326) )
| ~ in(U_310,U_328) ) )
& ! [U_320] :
( ( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),sK56(U_328,U_326,U_324,U_320))
& in(sK56(U_328,U_326,U_324,U_320),U_326)
& in(sK55(U_328,U_326,U_324,U_320),U_328) )
| ~ in(U_320,U_324) ) )
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_315,sK59(U_329,U_327,U_325))],[f_41_7]) ).
fof(f_41_9,plain,
( ! [U_329,U_327,U_325] :
( U_325 = cartesian_product2(U_329,U_327)
| ( ~ in(sK58(U_329,U_327,U_325),U_325)
& sK58(U_329,U_327,U_325) = ordered_pair(sK59(U_329,U_327,U_325),sK60(U_329,U_327,U_325))
& in(sK60(U_329,U_327,U_325),U_327)
& in(sK59(U_329,U_327,U_325),U_329) )
| ( ! [U_313] :
( ! [U_312] :
( sK57(U_329,U_327,U_325) != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327) )
| ~ in(U_313,U_329) )
& in(sK57(U_329,U_327,U_325),U_325) ) )
& ! [U_328,U_326,U_324] :
( ( ! [U_321] :
( in(U_321,U_324)
| ! [U_310] :
( ! [U_309] :
( U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326) )
| ~ in(U_310,U_328) ) )
& ! [U_320] :
( ( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),sK56(U_328,U_326,U_324,U_320))
& in(sK56(U_328,U_326,U_324,U_320),U_326)
& in(sK55(U_328,U_326,U_324,U_320),U_328) )
| ~ in(U_320,U_324) ) )
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_314,sK60(U_329,U_327,U_325))],[f_41_8]) ).
fof(f_41_10,plain,
( ! [U_325,U_327,U_329] :
( ~ in(sK58(U_329,U_327,U_325),U_325)
| ~ sP87(U_325,U_327,U_329) )
& ! [U_325,U_327,U_329] :
( sK58(U_329,U_327,U_325) = ordered_pair(sK59(U_329,U_327,U_325),sK60(U_329,U_327,U_325))
| ~ sP87(U_325,U_327,U_329) )
& ! [U_325,U_327,U_329] :
( in(sK60(U_329,U_327,U_325),U_327)
| ~ sP87(U_325,U_327,U_329) )
& ! [U_325,U_327,U_329] :
( in(sK59(U_329,U_327,U_325),U_329)
| ~ sP87(U_325,U_327,U_329) )
& ! [U_312,U_313,U_325,U_327,U_329] :
( sK57(U_329,U_327,U_325) != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327)
| ~ in(U_313,U_329)
| ~ sP86(U_312,U_313,U_325,U_327,U_329) )
& ! [U_312,U_313,U_325,U_327,U_329] :
( in(sK57(U_329,U_327,U_325),U_325)
| ~ sP86(U_312,U_313,U_325,U_327,U_329) )
& ! [U_326,U_320,U_324,U_328] :
( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),sK56(U_328,U_326,U_324,U_320))
| ~ sP84(U_326,U_320,U_324,U_328) )
& ! [U_326,U_320,U_324,U_328] :
( in(sK56(U_328,U_326,U_324,U_320),U_326)
| ~ sP84(U_326,U_320,U_324,U_328) )
& ! [U_326,U_320,U_324,U_328] :
( in(sK55(U_328,U_326,U_324,U_320),U_328)
| ~ sP84(U_326,U_320,U_324,U_328) )
& ! [U_326,U_320,U_310,U_321,U_324,U_309,U_328] :
( in(U_321,U_324)
| U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326)
| ~ in(U_310,U_328)
| ~ sP85(U_326,U_320,U_310,U_321,U_324,U_309,U_328) )
& ! [U_326,U_320,U_310,U_321,U_324,U_309,U_328] :
( sP84(U_326,U_320,U_324,U_328)
| ~ in(U_320,U_324)
| ~ sP85(U_326,U_320,U_310,U_321,U_324,U_309,U_328) )
& ! [U_312,U_313,U_325,U_327,U_329] :
( U_325 = cartesian_product2(U_329,U_327)
| sP87(U_325,U_327,U_329)
| sP86(U_312,U_313,U_325,U_327,U_329) )
& ! [U_326,U_320,U_310,U_321,U_324,U_309,U_328] :
( sP85(U_326,U_320,U_310,U_321,U_324,U_309,U_328)
| U_324 != cartesian_product2(U_328,U_326) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84,sP85,sP86,sP87])],[f_41_9]) ).
cnf(f_41_11,plain,
( sP85(U_326,U_320,U_310,U_321,U_324,U_309,U_328)
| U_324 != cartesian_product2(U_328,U_326) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_12,plain,
( U_325 = cartesian_product2(U_329,U_327)
| sP87(U_325,U_327,U_329)
| sP86(U_312,U_313,U_325,U_327,U_329) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_13,plain,
( sP84(U_326,U_320,U_324,U_328)
| ~ in(U_320,U_324)
| ~ sP85(U_326,U_320,U_310,U_321,U_324,U_309,U_328) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_14,plain,
( in(U_321,U_324)
| U_321 != ordered_pair(U_310,U_309)
| ~ in(U_309,U_326)
| ~ in(U_310,U_328)
| ~ sP85(U_326,U_320,U_310,U_321,U_324,U_309,U_328) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_15,plain,
( in(sK55(U_328,U_326,U_324,U_320),U_328)
| ~ sP84(U_326,U_320,U_324,U_328) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_16,plain,
( in(sK56(U_328,U_326,U_324,U_320),U_326)
| ~ sP84(U_326,U_320,U_324,U_328) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_17,plain,
( U_320 = ordered_pair(sK55(U_328,U_326,U_324,U_320),sK56(U_328,U_326,U_324,U_320))
| ~ sP84(U_326,U_320,U_324,U_328) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_18,plain,
( in(sK57(U_329,U_327,U_325),U_325)
| ~ sP86(U_312,U_313,U_325,U_327,U_329) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_19,plain,
( sK57(U_329,U_327,U_325) != ordered_pair(U_313,U_312)
| ~ in(U_312,U_327)
| ~ in(U_313,U_329)
| ~ sP86(U_312,U_313,U_325,U_327,U_329) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_20,plain,
( in(sK59(U_329,U_327,U_325),U_329)
| ~ sP87(U_325,U_327,U_329) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_21,plain,
( in(sK60(U_329,U_327,U_325),U_327)
| ~ sP87(U_325,U_327,U_329) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_22,plain,
( sK58(U_329,U_327,U_325) = ordered_pair(sK59(U_329,U_327,U_325),sK60(U_329,U_327,U_325))
| ~ sP87(U_325,U_327,U_329) ),
inference(clausify,[status(thm)],[f_41_10]) ).
cnf(f_41_23,plain,
( ~ in(sK58(U_329,U_327,U_325),U_325)
| ~ sP87(U_325,U_327,U_329) ),
inference(clausify,[status(thm)],[f_41_10]) ).
fof(f_42_1,plain,
! [A] :
( ( epsilon_connected(A)
| ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(fof_nnf,[status(thm)],[d3_ordinal1]) ).
fof(f_42_2,plain,
! [U_334] :
( ( epsilon_connected(U_334)
| ? [U_333,U_332] :
( ~ in(U_332,U_333)
& U_333 != U_332
& ~ in(U_333,U_332)
& in(U_332,U_334)
& in(U_333,U_334) ) )
& ( ! [U_331,U_330] :
( in(U_330,U_331)
| U_331 = U_330
| in(U_331,U_330)
| ~ in(U_330,U_334)
| ~ in(U_331,U_334) )
| ~ epsilon_connected(U_334) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_336] :
( epsilon_connected(U_336)
| ? [U_333] :
( ? [U_332] :
( ~ in(U_332,U_333)
& U_333 != U_332
& ~ in(U_333,U_332)
& in(U_332,U_336) )
& in(U_333,U_336) ) )
& ! [U_335] :
( ! [U_331] :
( ! [U_330] :
( in(U_330,U_331)
| U_331 = U_330
| in(U_331,U_330)
| ~ in(U_330,U_335) )
| ~ in(U_331,U_335) )
| ~ epsilon_connected(U_335) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_336] :
( epsilon_connected(U_336)
| ( ? [U_332] :
( ~ in(U_332,sK61(U_336))
& sK61(U_336) != U_332
& ~ in(sK61(U_336),U_332)
& in(U_332,U_336) )
& in(sK61(U_336),U_336) ) )
& ! [U_335] :
( ! [U_331] :
( ! [U_330] :
( in(U_330,U_331)
| U_331 = U_330
| in(U_331,U_330)
| ~ in(U_330,U_335) )
| ~ in(U_331,U_335) )
| ~ epsilon_connected(U_335) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_333,sK61(U_336))],[f_42_3]) ).
fof(f_42_5,plain,
( ! [U_336] :
( epsilon_connected(U_336)
| ( ~ in(sK62(U_336),sK61(U_336))
& sK61(U_336) != sK62(U_336)
& ~ in(sK61(U_336),sK62(U_336))
& in(sK62(U_336),U_336)
& in(sK61(U_336),U_336) ) )
& ! [U_335] :
( ! [U_331] :
( ! [U_330] :
( in(U_330,U_331)
| U_331 = U_330
| in(U_331,U_330)
| ~ in(U_330,U_335) )
| ~ in(U_331,U_335) )
| ~ epsilon_connected(U_335) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_332,sK62(U_336))],[f_42_4]) ).
fof(f_42_6,plain,
( ! [U_336] :
( ~ in(sK62(U_336),sK61(U_336))
| ~ sP88(U_336) )
& ! [U_336] :
( sK61(U_336) != sK62(U_336)
| ~ sP88(U_336) )
& ! [U_336] :
( ~ in(sK61(U_336),sK62(U_336))
| ~ sP88(U_336) )
& ! [U_336] :
( in(sK62(U_336),U_336)
| ~ sP88(U_336) )
& ! [U_336] :
( in(sK61(U_336),U_336)
| ~ sP88(U_336) )
& ! [U_336] :
( epsilon_connected(U_336)
| sP88(U_336) )
& ! [U_331,U_335,U_330] :
( in(U_330,U_331)
| U_331 = U_330
| in(U_331,U_330)
| ~ in(U_330,U_335)
| ~ in(U_331,U_335)
| ~ epsilon_connected(U_335) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_42_5]) ).
cnf(f_42_7,plain,
( in(U_330,U_331)
| U_331 = U_330
| in(U_331,U_330)
| ~ in(U_330,U_335)
| ~ in(U_331,U_335)
| ~ epsilon_connected(U_335) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_8,plain,
( epsilon_connected(U_336)
| sP88(U_336) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_9,plain,
( in(sK61(U_336),U_336)
| ~ sP88(U_336) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_10,plain,
( in(sK62(U_336),U_336)
| ~ sP88(U_336) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_11,plain,
( ~ in(sK61(U_336),sK62(U_336))
| ~ sP88(U_336) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_12,plain,
( sK61(U_336) != sK62(U_336)
| ~ sP88(U_336) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_13,plain,
( ~ in(sK62(U_336),sK61(U_336))
| ~ sP88(U_336) ),
inference(clausify,[status(thm)],[f_42_6]) ).
fof(f_43_1,plain,
! [A] :
( ! [B] :
( ( ( subset(A,B)
| ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_relat_1]) ).
fof(f_43_2,plain,
! [U_342] :
( ! [U_341] :
( ( ( subset(U_342,U_341)
| ? [U_340,U_339] :
( ~ in(ordered_pair(U_340,U_339),U_341)
& in(ordered_pair(U_340,U_339),U_342) ) )
& ( ! [U_338,U_337] :
( in(ordered_pair(U_338,U_337),U_341)
| ~ in(ordered_pair(U_338,U_337),U_342) )
| ~ subset(U_342,U_341) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_342] :
( ! [U_341] :
( ( ( subset(U_342,U_341)
| ? [U_339] :
( ~ in(ordered_pair(sK63(U_342,U_341),U_339),U_341)
& in(ordered_pair(sK63(U_342,U_341),U_339),U_342) ) )
& ( ! [U_338,U_337] :
( in(ordered_pair(U_338,U_337),U_341)
| ~ in(ordered_pair(U_338,U_337),U_342) )
| ~ subset(U_342,U_341) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_340,sK63(U_342,U_341))],[f_43_2]) ).
fof(f_43_4,plain,
! [U_342] :
( ! [U_341] :
( ( ( subset(U_342,U_341)
| ( ~ in(ordered_pair(sK63(U_342,U_341),sK64(U_342,U_341)),U_341)
& in(ordered_pair(sK63(U_342,U_341),sK64(U_342,U_341)),U_342) ) )
& ( ! [U_338,U_337] :
( in(ordered_pair(U_338,U_337),U_341)
| ~ in(ordered_pair(U_338,U_337),U_342) )
| ~ subset(U_342,U_341) ) )
| ~ relation(U_341) )
| ~ relation(U_342) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_339,sK64(U_342,U_341))],[f_43_3]) ).
fof(f_43_5,plain,
( ! [U_341,U_342] :
( ~ in(ordered_pair(sK63(U_342,U_341),sK64(U_342,U_341)),U_341)
| ~ sP89(U_341,U_342) )
& ! [U_341,U_342] :
( in(ordered_pair(sK63(U_342,U_341),sK64(U_342,U_341)),U_342)
| ~ sP89(U_341,U_342) )
& ! [U_341,U_342,U_338,U_337] :
( subset(U_342,U_341)
| sP89(U_341,U_342)
| ~ sP90(U_341,U_342,U_338,U_337) )
& ! [U_341,U_342,U_338,U_337] :
( in(ordered_pair(U_338,U_337),U_341)
| ~ in(ordered_pair(U_338,U_337),U_342)
| ~ subset(U_342,U_341)
| ~ sP90(U_341,U_342,U_338,U_337) )
& ! [U_341,U_342,U_338,U_337] :
( sP90(U_341,U_342,U_338,U_337)
| ~ relation(U_341)
| ~ relation(U_342) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89,sP90])],[f_43_4]) ).
cnf(f_43_6,plain,
( sP90(U_341,U_342,U_338,U_337)
| ~ relation(U_341)
| ~ relation(U_342) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_7,plain,
( in(ordered_pair(U_338,U_337),U_341)
| ~ in(ordered_pair(U_338,U_337),U_342)
| ~ subset(U_342,U_341)
| ~ sP90(U_341,U_342,U_338,U_337) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_8,plain,
( subset(U_342,U_341)
| sP89(U_341,U_342)
| ~ sP90(U_341,U_342,U_338,U_337) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_9,plain,
( in(ordered_pair(sK63(U_342,U_341),sK64(U_342,U_341)),U_342)
| ~ sP89(U_341,U_342) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_10,plain,
( ~ in(ordered_pair(sK63(U_342,U_341),sK64(U_342,U_341)),U_341)
| ~ sP89(U_341,U_342) ),
inference(clausify,[status(thm)],[f_43_5]) ).
fof(f_44_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_44_2,plain,
! [U_346,U_345] :
( ( subset(U_346,U_345)
| ? [U_344] :
( ~ in(U_344,U_345)
& in(U_344,U_346) ) )
& ( ! [U_343] :
( in(U_343,U_345)
| ~ in(U_343,U_346) )
| ~ subset(U_346,U_345) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_350,U_348] :
( subset(U_350,U_348)
| ? [U_344] :
( ~ in(U_344,U_348)
& in(U_344,U_350) ) )
& ! [U_349,U_347] :
( ! [U_343] :
( in(U_343,U_347)
| ~ in(U_343,U_349) )
| ~ subset(U_349,U_347) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
( ! [U_350,U_348] :
( subset(U_350,U_348)
| ( ~ in(sK65(U_350,U_348),U_348)
& in(sK65(U_350,U_348),U_350) ) )
& ! [U_349,U_347] :
( ! [U_343] :
( in(U_343,U_347)
| ~ in(U_343,U_349) )
| ~ subset(U_349,U_347) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_344,sK65(U_350,U_348))],[f_44_3]) ).
fof(f_44_5,plain,
( ! [U_350,U_348] :
( ~ in(sK65(U_350,U_348),U_348)
| ~ sP91(U_350,U_348) )
& ! [U_350,U_348] :
( in(sK65(U_350,U_348),U_350)
| ~ sP91(U_350,U_348) )
& ! [U_350,U_348] :
( subset(U_350,U_348)
| sP91(U_350,U_348) )
& ! [U_343,U_349,U_347] :
( in(U_343,U_347)
| ~ in(U_343,U_349)
| ~ subset(U_349,U_347) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_44_4]) ).
cnf(f_44_6,plain,
( in(U_343,U_347)
| ~ in(U_343,U_349)
| ~ subset(U_349,U_347) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_7,plain,
( subset(U_350,U_348)
| sP91(U_350,U_348) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_8,plain,
( in(sK65(U_350,U_348),U_350)
| ~ sP91(U_350,U_348) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_9,plain,
( ~ in(sK65(U_350,U_348),U_348)
| ~ sP91(U_350,U_348) ),
inference(clausify,[status(thm)],[f_44_5]) ).
fof(f_45_1,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) ) )
& ( ! [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(fof_nnf,[status(thm)],[d3_wellord1]) ).
fof(f_45_2,plain,
! [U_356] :
( ! [U_355] :
( ( is_well_founded_in(U_356,U_355)
| ? [U_354] :
( ! [U_353] :
( ~ disjoint(fiber(U_356,U_353),U_354)
| ~ in(U_353,U_354) )
& U_354 != empty_set
& subset(U_354,U_355) ) )
& ( ! [U_352] :
( ? [U_351] :
( disjoint(fiber(U_356,U_351),U_352)
& in(U_351,U_352) )
| U_352 = empty_set
| ~ subset(U_352,U_355) )
| ~ is_well_founded_in(U_356,U_355) ) )
| ~ relation(U_356) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_356] :
( ( ! [U_358] :
( is_well_founded_in(U_356,U_358)
| ? [U_354] :
( ! [U_353] :
( ~ disjoint(fiber(U_356,U_353),U_354)
| ~ in(U_353,U_354) )
& U_354 != empty_set
& subset(U_354,U_358) ) )
& ! [U_357] :
( ! [U_352] :
( ? [U_351] :
( disjoint(fiber(U_356,U_351),U_352)
& in(U_351,U_352) )
| U_352 = empty_set
| ~ subset(U_352,U_357) )
| ~ is_well_founded_in(U_356,U_357) ) )
| ~ relation(U_356) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
! [U_356] :
( ( ! [U_358] :
( is_well_founded_in(U_356,U_358)
| ? [U_354] :
( ! [U_353] :
( ~ disjoint(fiber(U_356,U_353),U_354)
| ~ in(U_353,U_354) )
& U_354 != empty_set
& subset(U_354,U_358) ) )
& ! [U_357] :
( ! [U_352] :
( ( disjoint(fiber(U_356,sK66(U_356,U_357,U_352)),U_352)
& in(sK66(U_356,U_357,U_352),U_352) )
| U_352 = empty_set
| ~ subset(U_352,U_357) )
| ~ is_well_founded_in(U_356,U_357) ) )
| ~ relation(U_356) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_351,sK66(U_356,U_357,U_352))],[f_45_3]) ).
fof(f_45_5,plain,
! [U_356] :
( ( ! [U_358] :
( is_well_founded_in(U_356,U_358)
| ( ! [U_353] :
( ~ disjoint(fiber(U_356,U_353),sK67(U_356,U_358))
| ~ in(U_353,sK67(U_356,U_358)) )
& sK67(U_356,U_358) != empty_set
& subset(sK67(U_356,U_358),U_358) ) )
& ! [U_357] :
( ! [U_352] :
( ( disjoint(fiber(U_356,sK66(U_356,U_357,U_352)),U_352)
& in(sK66(U_356,U_357,U_352),U_352) )
| U_352 = empty_set
| ~ subset(U_352,U_357) )
| ~ is_well_founded_in(U_356,U_357) ) )
| ~ relation(U_356) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_354,sK67(U_356,U_358))],[f_45_4]) ).
fof(f_45_6,plain,
( ! [U_356,U_358,U_353] :
( ~ disjoint(fiber(U_356,U_353),sK67(U_356,U_358))
| ~ in(U_353,sK67(U_356,U_358))
| ~ sP93(U_356,U_358,U_353) )
& ! [U_356,U_358,U_353] :
( sK67(U_356,U_358) != empty_set
| ~ sP93(U_356,U_358,U_353) )
& ! [U_356,U_358,U_353] :
( subset(sK67(U_356,U_358),U_358)
| ~ sP93(U_356,U_358,U_353) )
& ! [U_356,U_357,U_352] :
( disjoint(fiber(U_356,sK66(U_356,U_357,U_352)),U_352)
| ~ sP92(U_356,U_357,U_352) )
& ! [U_356,U_357,U_352] :
( in(sK66(U_356,U_357,U_352),U_352)
| ~ sP92(U_356,U_357,U_352) )
& ! [U_356,U_358,U_357,U_352,U_353] :
( is_well_founded_in(U_356,U_358)
| sP93(U_356,U_358,U_353)
| ~ sP94(U_356,U_358,U_357,U_352,U_353) )
& ! [U_356,U_358,U_357,U_352,U_353] :
( sP92(U_356,U_357,U_352)
| U_352 = empty_set
| ~ subset(U_352,U_357)
| ~ is_well_founded_in(U_356,U_357)
| ~ sP94(U_356,U_358,U_357,U_352,U_353) )
& ! [U_356,U_358,U_357,U_352,U_353] :
( sP94(U_356,U_358,U_357,U_352,U_353)
| ~ relation(U_356) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92,sP93,sP94])],[f_45_5]) ).
cnf(f_45_7,plain,
( sP94(U_356,U_358,U_357,U_352,U_353)
| ~ relation(U_356) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_8,plain,
( sP92(U_356,U_357,U_352)
| U_352 = empty_set
| ~ subset(U_352,U_357)
| ~ is_well_founded_in(U_356,U_357)
| ~ sP94(U_356,U_358,U_357,U_352,U_353) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_9,plain,
( is_well_founded_in(U_356,U_358)
| sP93(U_356,U_358,U_353)
| ~ sP94(U_356,U_358,U_357,U_352,U_353) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_10,plain,
( in(sK66(U_356,U_357,U_352),U_352)
| ~ sP92(U_356,U_357,U_352) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_11,plain,
( disjoint(fiber(U_356,sK66(U_356,U_357,U_352)),U_352)
| ~ sP92(U_356,U_357,U_352) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_12,plain,
( subset(sK67(U_356,U_358),U_358)
| ~ sP93(U_356,U_358,U_353) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_13,plain,
( sK67(U_356,U_358) != empty_set
| ~ sP93(U_356,U_358,U_353) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_14,plain,
( ~ disjoint(fiber(U_356,U_353),sK67(U_356,U_358))
| ~ in(U_353,sK67(U_356,U_358))
| ~ sP93(U_356,U_358,U_353) ),
inference(clausify,[status(thm)],[f_45_6]) ).
fof(f_46_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_46_2,plain,
! [U_363,U_362,U_361] :
( ( U_361 = set_intersection2(U_363,U_362)
| ? [U_360] :
( ( ~ in(U_360,U_361)
& in(U_360,U_362)
& in(U_360,U_363) )
| ( ( ~ in(U_360,U_362)
| ~ in(U_360,U_363) )
& in(U_360,U_361) ) ) )
& ( ! [U_359] :
( ( in(U_359,U_361)
| ~ in(U_359,U_362)
| ~ in(U_359,U_363) )
& ( ( in(U_359,U_362)
& in(U_359,U_363) )
| ~ in(U_359,U_361) ) )
| U_361 != set_intersection2(U_363,U_362) ) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_373,U_371,U_369] :
( U_369 = set_intersection2(U_373,U_371)
| ? [U_367] :
( ~ in(U_367,U_369)
& in(U_367,U_371)
& in(U_367,U_373) )
| ? [U_366] :
( ( ~ in(U_366,U_371)
| ~ in(U_366,U_373) )
& in(U_366,U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ~ in(U_365,U_370)
| ~ in(U_365,U_372) )
& ! [U_364] :
( ( in(U_364,U_370)
& in(U_364,U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != set_intersection2(U_372,U_370) ) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
( ! [U_373,U_371,U_369] :
( U_369 = set_intersection2(U_373,U_371)
| ? [U_367] :
( ~ in(U_367,U_369)
& in(U_367,U_371)
& in(U_367,U_373) )
| ( ( ~ in(sK68(U_373,U_371,U_369),U_371)
| ~ in(sK68(U_373,U_371,U_369),U_373) )
& in(sK68(U_373,U_371,U_369),U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ~ in(U_365,U_370)
| ~ in(U_365,U_372) )
& ! [U_364] :
( ( in(U_364,U_370)
& in(U_364,U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != set_intersection2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_366,sK68(U_373,U_371,U_369))],[f_46_3]) ).
fof(f_46_5,plain,
( ! [U_373,U_371,U_369] :
( U_369 = set_intersection2(U_373,U_371)
| ( ~ in(sK69(U_373,U_371,U_369),U_369)
& in(sK69(U_373,U_371,U_369),U_371)
& in(sK69(U_373,U_371,U_369),U_373) )
| ( ( ~ in(sK68(U_373,U_371,U_369),U_371)
| ~ in(sK68(U_373,U_371,U_369),U_373) )
& in(sK68(U_373,U_371,U_369),U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ~ in(U_365,U_370)
| ~ in(U_365,U_372) )
& ! [U_364] :
( ( in(U_364,U_370)
& in(U_364,U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != set_intersection2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_367,sK69(U_373,U_371,U_369))],[f_46_4]) ).
fof(f_46_6,plain,
( ! [U_373,U_371,U_369] :
( ~ in(sK69(U_373,U_371,U_369),U_369)
| ~ sP98(U_373,U_371,U_369) )
& ! [U_373,U_371,U_369] :
( in(sK69(U_373,U_371,U_369),U_371)
| ~ sP98(U_373,U_371,U_369) )
& ! [U_373,U_371,U_369] :
( in(sK69(U_373,U_371,U_369),U_373)
| ~ sP98(U_373,U_371,U_369) )
& ! [U_373,U_371,U_369] :
( ~ in(sK68(U_373,U_371,U_369),U_371)
| ~ in(sK68(U_373,U_371,U_369),U_373)
| ~ sP97(U_373,U_371,U_369) )
& ! [U_373,U_371,U_369] :
( in(sK68(U_373,U_371,U_369),U_369)
| ~ sP97(U_373,U_371,U_369) )
& ! [U_364,U_370,U_372] :
( in(U_364,U_370)
| ~ sP95(U_364,U_370,U_372) )
& ! [U_364,U_370,U_372] :
( in(U_364,U_372)
| ~ sP95(U_364,U_370,U_372) )
& ! [U_365,U_364,U_370,U_372,U_368] :
( in(U_365,U_368)
| ~ in(U_365,U_370)
| ~ in(U_365,U_372)
| ~ sP96(U_365,U_364,U_370,U_372,U_368) )
& ! [U_365,U_364,U_370,U_372,U_368] :
( sP95(U_364,U_370,U_372)
| ~ in(U_364,U_368)
| ~ sP96(U_365,U_364,U_370,U_372,U_368) )
& ! [U_373,U_371,U_369] :
( U_369 = set_intersection2(U_373,U_371)
| sP98(U_373,U_371,U_369)
| sP97(U_373,U_371,U_369) )
& ! [U_365,U_364,U_370,U_372,U_368] :
( sP96(U_365,U_364,U_370,U_372,U_368)
| U_368 != set_intersection2(U_372,U_370) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95,sP96,sP97,sP98])],[f_46_5]) ).
cnf(f_46_7,plain,
( sP96(U_365,U_364,U_370,U_372,U_368)
| U_368 != set_intersection2(U_372,U_370) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_8,plain,
( U_369 = set_intersection2(U_373,U_371)
| sP98(U_373,U_371,U_369)
| sP97(U_373,U_371,U_369) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_9,plain,
( sP95(U_364,U_370,U_372)
| ~ in(U_364,U_368)
| ~ sP96(U_365,U_364,U_370,U_372,U_368) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_10,plain,
( in(U_365,U_368)
| ~ in(U_365,U_370)
| ~ in(U_365,U_372)
| ~ sP96(U_365,U_364,U_370,U_372,U_368) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_11,plain,
( in(U_364,U_372)
| ~ sP95(U_364,U_370,U_372) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_12,plain,
( in(U_364,U_370)
| ~ sP95(U_364,U_370,U_372) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_13,plain,
( in(sK68(U_373,U_371,U_369),U_369)
| ~ sP97(U_373,U_371,U_369) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_14,plain,
( ~ in(sK68(U_373,U_371,U_369),U_371)
| ~ in(sK68(U_373,U_371,U_369),U_373)
| ~ sP97(U_373,U_371,U_369) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_15,plain,
( in(sK69(U_373,U_371,U_369),U_373)
| ~ sP98(U_373,U_371,U_369) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_16,plain,
( in(sK69(U_373,U_371,U_369),U_371)
| ~ sP98(U_373,U_371,U_369) ),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_17,plain,
( ~ in(sK69(U_373,U_371,U_369),U_369)
| ~ sP98(U_373,U_371,U_369) ),
inference(clausify,[status(thm)],[f_46_6]) ).
fof(f_47_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_47_2,plain,
! [U_376] :
( ! [U_375,U_374] :
( ( ( ( U_374 = apply(U_376,U_375)
| U_374 != empty_set )
& ( U_374 = empty_set
| U_374 != apply(U_376,U_375) ) )
| in(U_375,relation_dom(U_376)) )
& ( ( ( U_374 = apply(U_376,U_375)
| ~ in(ordered_pair(U_375,U_374),U_376) )
& ( in(ordered_pair(U_375,U_374),U_376)
| U_374 != apply(U_376,U_375) ) )
| ~ in(U_375,relation_dom(U_376)) ) )
| ~ function(U_376)
| ~ relation(U_376) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_376] :
( ( ! [U_384] :
( ( ! [U_382] :
( U_382 = apply(U_376,U_384)
| U_382 != empty_set )
& ! [U_381] :
( U_381 = empty_set
| U_381 != apply(U_376,U_384) ) )
| in(U_384,relation_dom(U_376)) )
& ! [U_383] :
( ( ! [U_380] :
( U_380 = apply(U_376,U_383)
| ~ in(ordered_pair(U_383,U_380),U_376) )
& ! [U_379] :
( in(ordered_pair(U_383,U_379),U_376)
| U_379 != apply(U_376,U_383) ) )
| ~ in(U_383,relation_dom(U_376)) ) )
| ~ function(U_376)
| ~ relation(U_376) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
( ! [U_376,U_381,U_382,U_384] :
( U_382 = apply(U_376,U_384)
| U_382 != empty_set
| ~ sP100(U_376,U_381,U_382,U_384) )
& ! [U_376,U_381,U_382,U_384] :
( U_381 = empty_set
| U_381 != apply(U_376,U_384)
| ~ sP100(U_376,U_381,U_382,U_384) )
& ! [U_379,U_376,U_383,U_380] :
( U_380 = apply(U_376,U_383)
| ~ in(ordered_pair(U_383,U_380),U_376)
| ~ sP99(U_379,U_376,U_383,U_380) )
& ! [U_379,U_376,U_383,U_380] :
( in(ordered_pair(U_383,U_379),U_376)
| U_379 != apply(U_376,U_383)
| ~ sP99(U_379,U_376,U_383,U_380) )
& ! [U_379,U_376,U_381,U_383,U_382,U_384,U_380] :
( sP100(U_376,U_381,U_382,U_384)
| in(U_384,relation_dom(U_376))
| ~ sP101(U_379,U_376,U_381,U_383,U_382,U_384,U_380) )
& ! [U_379,U_376,U_381,U_383,U_382,U_384,U_380] :
( sP99(U_379,U_376,U_383,U_380)
| ~ in(U_383,relation_dom(U_376))
| ~ sP101(U_379,U_376,U_381,U_383,U_382,U_384,U_380) )
& ! [U_379,U_376,U_381,U_383,U_382,U_384,U_380] :
( sP101(U_379,U_376,U_381,U_383,U_382,U_384,U_380)
| ~ function(U_376)
| ~ relation(U_376) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99,sP100,sP101])],[f_47_3]) ).
cnf(f_47_5,plain,
( sP101(U_379,U_376,U_381,U_383,U_382,U_384,U_380)
| ~ function(U_376)
| ~ relation(U_376) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_6,plain,
( sP99(U_379,U_376,U_383,U_380)
| ~ in(U_383,relation_dom(U_376))
| ~ sP101(U_379,U_376,U_381,U_383,U_382,U_384,U_380) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_7,plain,
( sP100(U_376,U_381,U_382,U_384)
| in(U_384,relation_dom(U_376))
| ~ sP101(U_379,U_376,U_381,U_383,U_382,U_384,U_380) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_8,plain,
( in(ordered_pair(U_383,U_379),U_376)
| U_379 != apply(U_376,U_383)
| ~ sP99(U_379,U_376,U_383,U_380) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_9,plain,
( U_380 = apply(U_376,U_383)
| ~ in(ordered_pair(U_383,U_380),U_376)
| ~ sP99(U_379,U_376,U_383,U_380) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_10,plain,
( U_381 = empty_set
| U_381 != apply(U_376,U_384)
| ~ sP100(U_376,U_381,U_382,U_384) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_11,plain,
( U_382 = apply(U_376,U_384)
| U_382 != empty_set
| ~ sP100(U_376,U_381,U_382,U_384) ),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
! [A] :
( ( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) )
& ( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[d4_ordinal1]) ).
fof(f_48_2,plain,
! [U_385] :
( ( ordinal(U_385)
| ~ epsilon_connected(U_385)
| ~ epsilon_transitive(U_385) )
& ( ( epsilon_connected(U_385)
& epsilon_transitive(U_385) )
| ~ ordinal(U_385) ) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_387] :
( ordinal(U_387)
| ~ epsilon_connected(U_387)
| ~ epsilon_transitive(U_387) )
& ! [U_386] :
( ( epsilon_connected(U_386)
& epsilon_transitive(U_386) )
| ~ ordinal(U_386) ) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
( ! [U_386] :
( epsilon_connected(U_386)
| ~ sP102(U_386) )
& ! [U_386] :
( epsilon_transitive(U_386)
| ~ sP102(U_386) )
& ! [U_387] :
( ordinal(U_387)
| ~ epsilon_connected(U_387)
| ~ epsilon_transitive(U_387) )
& ! [U_386] :
( sP102(U_386)
| ~ ordinal(U_386) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_48_3]) ).
cnf(f_48_5,plain,
( sP102(U_386)
| ~ ordinal(U_386) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_6,plain,
( ordinal(U_387)
| ~ epsilon_connected(U_387)
| ~ epsilon_transitive(U_387) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_7,plain,
( epsilon_transitive(U_386)
| ~ sP102(U_386) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_8,plain,
( epsilon_connected(U_386)
| ~ sP102(U_386) ),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_1,plain,
! [A] :
( ! [B] :
( ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(C,D),A) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(f_49_2,plain,
! [U_395] :
( ! [U_394] :
( ( U_394 = relation_dom(U_395)
| ? [U_393] :
( ( ~ in(U_393,U_394)
& ? [U_392] : in(ordered_pair(U_393,U_392),U_395) )
| ( ! [U_391] : ~ in(ordered_pair(U_393,U_391),U_395)
& in(U_393,U_394) ) ) )
& ( ! [U_390] :
( ( in(U_390,U_394)
| ! [U_389] : ~ in(ordered_pair(U_390,U_389),U_395) )
& ( ? [U_388] : in(ordered_pair(U_390,U_388),U_395)
| ~ in(U_390,U_394) ) )
| U_394 != relation_dom(U_395) ) )
| ~ relation(U_395) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_395] :
( ( ! [U_401] :
( U_401 = relation_dom(U_395)
| ? [U_399] :
( ~ in(U_399,U_401)
& ? [U_392] : in(ordered_pair(U_399,U_392),U_395) )
| ? [U_398] :
( ! [U_391] : ~ in(ordered_pair(U_398,U_391),U_395)
& in(U_398,U_401) ) )
& ! [U_400] :
( ( ! [U_397] :
( in(U_397,U_400)
| ! [U_389] : ~ in(ordered_pair(U_397,U_389),U_395) )
& ! [U_396] :
( ? [U_388] : in(ordered_pair(U_396,U_388),U_395)
| ~ in(U_396,U_400) ) )
| U_400 != relation_dom(U_395) ) )
| ~ relation(U_395) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
! [U_395] :
( ( ! [U_401] :
( U_401 = relation_dom(U_395)
| ? [U_399] :
( ~ in(U_399,U_401)
& ? [U_392] : in(ordered_pair(U_399,U_392),U_395) )
| ? [U_398] :
( ! [U_391] : ~ in(ordered_pair(U_398,U_391),U_395)
& in(U_398,U_401) ) )
& ! [U_400] :
( ( ! [U_397] :
( in(U_397,U_400)
| ! [U_389] : ~ in(ordered_pair(U_397,U_389),U_395) )
& ! [U_396] :
( in(ordered_pair(U_396,sK70(U_395,U_400,U_396)),U_395)
| ~ in(U_396,U_400) ) )
| U_400 != relation_dom(U_395) ) )
| ~ relation(U_395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_388,sK70(U_395,U_400,U_396))],[f_49_3]) ).
fof(f_49_5,plain,
! [U_395] :
( ( ! [U_401] :
( U_401 = relation_dom(U_395)
| ? [U_399] :
( ~ in(U_399,U_401)
& ? [U_392] : in(ordered_pair(U_399,U_392),U_395) )
| ( ! [U_391] : ~ in(ordered_pair(sK71(U_395,U_401),U_391),U_395)
& in(sK71(U_395,U_401),U_401) ) )
& ! [U_400] :
( ( ! [U_397] :
( in(U_397,U_400)
| ! [U_389] : ~ in(ordered_pair(U_397,U_389),U_395) )
& ! [U_396] :
( in(ordered_pair(U_396,sK70(U_395,U_400,U_396)),U_395)
| ~ in(U_396,U_400) ) )
| U_400 != relation_dom(U_395) ) )
| ~ relation(U_395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_398,sK71(U_395,U_401))],[f_49_4]) ).
fof(f_49_6,plain,
! [U_395] :
( ( ! [U_401] :
( U_401 = relation_dom(U_395)
| ( ~ in(sK72(U_395,U_401),U_401)
& ? [U_392] : in(ordered_pair(sK72(U_395,U_401),U_392),U_395) )
| ( ! [U_391] : ~ in(ordered_pair(sK71(U_395,U_401),U_391),U_395)
& in(sK71(U_395,U_401),U_401) ) )
& ! [U_400] :
( ( ! [U_397] :
( in(U_397,U_400)
| ! [U_389] : ~ in(ordered_pair(U_397,U_389),U_395) )
& ! [U_396] :
( in(ordered_pair(U_396,sK70(U_395,U_400,U_396)),U_395)
| ~ in(U_396,U_400) ) )
| U_400 != relation_dom(U_395) ) )
| ~ relation(U_395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_399,sK72(U_395,U_401))],[f_49_5]) ).
fof(f_49_7,plain,
! [U_395] :
( ( ! [U_401] :
( U_401 = relation_dom(U_395)
| ( ~ in(sK72(U_395,U_401),U_401)
& in(ordered_pair(sK72(U_395,U_401),sK73(U_395,U_401)),U_395) )
| ( ! [U_391] : ~ in(ordered_pair(sK71(U_395,U_401),U_391),U_395)
& in(sK71(U_395,U_401),U_401) ) )
& ! [U_400] :
( ( ! [U_397] :
( in(U_397,U_400)
| ! [U_389] : ~ in(ordered_pair(U_397,U_389),U_395) )
& ! [U_396] :
( in(ordered_pair(U_396,sK70(U_395,U_400,U_396)),U_395)
| ~ in(U_396,U_400) ) )
| U_400 != relation_dom(U_395) ) )
| ~ relation(U_395) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_392,sK73(U_395,U_401))],[f_49_6]) ).
fof(f_49_8,plain,
( ! [U_395,U_401] :
( ~ in(sK72(U_395,U_401),U_401)
| ~ sP105(U_395,U_401) )
& ! [U_395,U_401] :
( in(ordered_pair(sK72(U_395,U_401),sK73(U_395,U_401)),U_395)
| ~ sP105(U_395,U_401) )
& ! [U_395,U_391,U_401] :
( ~ in(ordered_pair(sK71(U_395,U_401),U_391),U_395)
| ~ sP104(U_395,U_391,U_401) )
& ! [U_395,U_391,U_401] :
( in(sK71(U_395,U_401),U_401)
| ~ sP104(U_395,U_391,U_401) )
& ! [U_395,U_389,U_396,U_397,U_400] :
( in(U_397,U_400)
| ~ in(ordered_pair(U_397,U_389),U_395)
| ~ sP103(U_395,U_389,U_396,U_397,U_400) )
& ! [U_395,U_389,U_396,U_397,U_400] :
( in(ordered_pair(U_396,sK70(U_395,U_400,U_396)),U_395)
| ~ in(U_396,U_400)
| ~ sP103(U_395,U_389,U_396,U_397,U_400) )
& ! [U_395,U_389,U_396,U_397,U_391,U_400,U_401] :
( U_401 = relation_dom(U_395)
| sP105(U_395,U_401)
| sP104(U_395,U_391,U_401)
| ~ sP106(U_395,U_389,U_396,U_397,U_391,U_400,U_401) )
& ! [U_395,U_389,U_396,U_397,U_391,U_400,U_401] :
( sP103(U_395,U_389,U_396,U_397,U_400)
| U_400 != relation_dom(U_395)
| ~ sP106(U_395,U_389,U_396,U_397,U_391,U_400,U_401) )
& ! [U_395,U_389,U_396,U_397,U_391,U_400,U_401] :
( sP106(U_395,U_389,U_396,U_397,U_391,U_400,U_401)
| ~ relation(U_395) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103,sP104,sP105,sP106])],[f_49_7]) ).
cnf(f_49_9,plain,
( sP106(U_395,U_389,U_396,U_397,U_391,U_400,U_401)
| ~ relation(U_395) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_10,plain,
( sP103(U_395,U_389,U_396,U_397,U_400)
| U_400 != relation_dom(U_395)
| ~ sP106(U_395,U_389,U_396,U_397,U_391,U_400,U_401) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_11,plain,
( U_401 = relation_dom(U_395)
| sP105(U_395,U_401)
| sP104(U_395,U_391,U_401)
| ~ sP106(U_395,U_389,U_396,U_397,U_391,U_400,U_401) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_12,plain,
( in(ordered_pair(U_396,sK70(U_395,U_400,U_396)),U_395)
| ~ in(U_396,U_400)
| ~ sP103(U_395,U_389,U_396,U_397,U_400) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_13,plain,
( in(U_397,U_400)
| ~ in(ordered_pair(U_397,U_389),U_395)
| ~ sP103(U_395,U_389,U_396,U_397,U_400) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_14,plain,
( in(sK71(U_395,U_401),U_401)
| ~ sP104(U_395,U_391,U_401) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_15,plain,
( ~ in(ordered_pair(sK71(U_395,U_401),U_391),U_395)
| ~ sP104(U_395,U_391,U_401) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_16,plain,
( in(ordered_pair(sK72(U_395,U_401),sK73(U_395,U_401)),U_395)
| ~ sP105(U_395,U_401) ),
inference(clausify,[status(thm)],[f_49_8]) ).
cnf(f_49_17,plain,
( ~ in(sK72(U_395,U_401),U_401)
| ~ sP105(U_395,U_401) ),
inference(clausify,[status(thm)],[f_49_8]) ).
fof(f_50_1,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) ) )
& ( ! [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(fof_nnf,[status(thm)],[d4_relat_2]) ).
fof(f_50_2,plain,
! [U_407] :
( ! [U_406] :
( ( is_antisymmetric_in(U_407,U_406)
| ? [U_405,U_404] :
( U_405 != U_404
& in(ordered_pair(U_404,U_405),U_407)
& in(ordered_pair(U_405,U_404),U_407)
& in(U_404,U_406)
& in(U_405,U_406) ) )
& ( ! [U_403,U_402] :
( U_403 = U_402
| ~ in(ordered_pair(U_402,U_403),U_407)
| ~ in(ordered_pair(U_403,U_402),U_407)
| ~ in(U_402,U_406)
| ~ in(U_403,U_406) )
| ~ is_antisymmetric_in(U_407,U_406) ) )
| ~ relation(U_407) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_407] :
( ( ! [U_409] :
( is_antisymmetric_in(U_407,U_409)
| ? [U_405,U_404] :
( U_405 != U_404
& in(ordered_pair(U_404,U_405),U_407)
& in(ordered_pair(U_405,U_404),U_407)
& in(U_404,U_409)
& in(U_405,U_409) ) )
& ! [U_408] :
( ! [U_403,U_402] :
( U_403 = U_402
| ~ in(ordered_pair(U_402,U_403),U_407)
| ~ in(ordered_pair(U_403,U_402),U_407)
| ~ in(U_402,U_408)
| ~ in(U_403,U_408) )
| ~ is_antisymmetric_in(U_407,U_408) ) )
| ~ relation(U_407) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
! [U_407] :
( ( ! [U_409] :
( is_antisymmetric_in(U_407,U_409)
| ? [U_404] :
( sK74(U_407,U_409) != U_404
& in(ordered_pair(U_404,sK74(U_407,U_409)),U_407)
& in(ordered_pair(sK74(U_407,U_409),U_404),U_407)
& in(U_404,U_409)
& in(sK74(U_407,U_409),U_409) ) )
& ! [U_408] :
( ! [U_403,U_402] :
( U_403 = U_402
| ~ in(ordered_pair(U_402,U_403),U_407)
| ~ in(ordered_pair(U_403,U_402),U_407)
| ~ in(U_402,U_408)
| ~ in(U_403,U_408) )
| ~ is_antisymmetric_in(U_407,U_408) ) )
| ~ relation(U_407) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_405,sK74(U_407,U_409))],[f_50_3]) ).
fof(f_50_5,plain,
! [U_407] :
( ( ! [U_409] :
( is_antisymmetric_in(U_407,U_409)
| ( sK74(U_407,U_409) != sK75(U_407,U_409)
& in(ordered_pair(sK75(U_407,U_409),sK74(U_407,U_409)),U_407)
& in(ordered_pair(sK74(U_407,U_409),sK75(U_407,U_409)),U_407)
& in(sK75(U_407,U_409),U_409)
& in(sK74(U_407,U_409),U_409) ) )
& ! [U_408] :
( ! [U_403,U_402] :
( U_403 = U_402
| ~ in(ordered_pair(U_402,U_403),U_407)
| ~ in(ordered_pair(U_403,U_402),U_407)
| ~ in(U_402,U_408)
| ~ in(U_403,U_408) )
| ~ is_antisymmetric_in(U_407,U_408) ) )
| ~ relation(U_407) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_404,sK75(U_407,U_409))],[f_50_4]) ).
fof(f_50_6,plain,
( ! [U_409,U_407] :
( sK74(U_407,U_409) != sK75(U_407,U_409)
| ~ sP107(U_409,U_407) )
& ! [U_409,U_407] :
( in(ordered_pair(sK75(U_407,U_409),sK74(U_407,U_409)),U_407)
| ~ sP107(U_409,U_407) )
& ! [U_409,U_407] :
( in(ordered_pair(sK74(U_407,U_409),sK75(U_407,U_409)),U_407)
| ~ sP107(U_409,U_407) )
& ! [U_409,U_407] :
( in(sK75(U_407,U_409),U_409)
| ~ sP107(U_409,U_407) )
& ! [U_409,U_407] :
( in(sK74(U_407,U_409),U_409)
| ~ sP107(U_409,U_407) )
& ! [U_409,U_408,U_403,U_402,U_407] :
( is_antisymmetric_in(U_407,U_409)
| sP107(U_409,U_407)
| ~ sP108(U_409,U_408,U_403,U_402,U_407) )
& ! [U_409,U_408,U_403,U_402,U_407] :
( U_403 = U_402
| ~ in(ordered_pair(U_402,U_403),U_407)
| ~ in(ordered_pair(U_403,U_402),U_407)
| ~ in(U_402,U_408)
| ~ in(U_403,U_408)
| ~ is_antisymmetric_in(U_407,U_408)
| ~ sP108(U_409,U_408,U_403,U_402,U_407) )
& ! [U_409,U_408,U_403,U_402,U_407] :
( sP108(U_409,U_408,U_403,U_402,U_407)
| ~ relation(U_407) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107,sP108])],[f_50_5]) ).
cnf(f_50_7,plain,
( sP108(U_409,U_408,U_403,U_402,U_407)
| ~ relation(U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_8,plain,
( U_403 = U_402
| ~ in(ordered_pair(U_402,U_403),U_407)
| ~ in(ordered_pair(U_403,U_402),U_407)
| ~ in(U_402,U_408)
| ~ in(U_403,U_408)
| ~ is_antisymmetric_in(U_407,U_408)
| ~ sP108(U_409,U_408,U_403,U_402,U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_9,plain,
( is_antisymmetric_in(U_407,U_409)
| sP107(U_409,U_407)
| ~ sP108(U_409,U_408,U_403,U_402,U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_10,plain,
( in(sK74(U_407,U_409),U_409)
| ~ sP107(U_409,U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_11,plain,
( in(sK75(U_407,U_409),U_409)
| ~ sP107(U_409,U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_12,plain,
( in(ordered_pair(sK74(U_407,U_409),sK75(U_407,U_409)),U_407)
| ~ sP107(U_409,U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_13,plain,
( in(ordered_pair(sK75(U_407,U_409),sK74(U_407,U_409)),U_407)
| ~ sP107(U_409,U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_14,plain,
( sK74(U_407,U_409) != sK75(U_407,U_409)
| ~ sP107(U_409,U_407) ),
inference(clausify,[status(thm)],[f_50_6]) ).
fof(f_51_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_51_2,plain,
! [U_410] : cast_to_subset(U_410) = U_410,
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_410] : cast_to_subset(U_410) = U_410,
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
cast_to_subset(U_410) = U_410,
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A,B] :
( ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( in(D,A)
& in(C,D) ) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( ~ in(D,A)
| ~ in(C,D) ) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(f_52_2,plain,
! [U_418,U_417] :
( ( U_417 = union(U_418)
| ? [U_416] :
( ( ~ in(U_416,U_417)
& ? [U_415] :
( in(U_415,U_418)
& in(U_416,U_415) ) )
| ( ! [U_414] :
( ~ in(U_414,U_418)
| ~ in(U_416,U_414) )
& in(U_416,U_417) ) ) )
& ( ! [U_413] :
( ( in(U_413,U_417)
| ! [U_412] :
( ~ in(U_412,U_418)
| ~ in(U_413,U_412) ) )
& ( ? [U_411] :
( in(U_411,U_418)
& in(U_413,U_411) )
| ~ in(U_413,U_417) ) )
| U_417 != union(U_418) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_426,U_424] :
( U_424 = union(U_426)
| ? [U_422] :
( ~ in(U_422,U_424)
& ? [U_415] :
( in(U_415,U_426)
& in(U_422,U_415) ) )
| ? [U_421] :
( ! [U_414] :
( ~ in(U_414,U_426)
| ~ in(U_421,U_414) )
& in(U_421,U_424) ) )
& ! [U_425,U_423] :
( ( ! [U_420] :
( in(U_420,U_423)
| ! [U_412] :
( ~ in(U_412,U_425)
| ~ in(U_420,U_412) ) )
& ! [U_419] :
( ? [U_411] :
( in(U_411,U_425)
& in(U_419,U_411) )
| ~ in(U_419,U_423) ) )
| U_423 != union(U_425) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
( ! [U_426,U_424] :
( U_424 = union(U_426)
| ? [U_422] :
( ~ in(U_422,U_424)
& ? [U_415] :
( in(U_415,U_426)
& in(U_422,U_415) ) )
| ? [U_421] :
( ! [U_414] :
( ~ in(U_414,U_426)
| ~ in(U_421,U_414) )
& in(U_421,U_424) ) )
& ! [U_425,U_423] :
( ( ! [U_420] :
( in(U_420,U_423)
| ! [U_412] :
( ~ in(U_412,U_425)
| ~ in(U_420,U_412) ) )
& ! [U_419] :
( ( in(sK76(U_425,U_423,U_419),U_425)
& in(U_419,sK76(U_425,U_423,U_419)) )
| ~ in(U_419,U_423) ) )
| U_423 != union(U_425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_411,sK76(U_425,U_423,U_419))],[f_52_3]) ).
fof(f_52_5,plain,
( ! [U_426,U_424] :
( U_424 = union(U_426)
| ? [U_422] :
( ~ in(U_422,U_424)
& ? [U_415] :
( in(U_415,U_426)
& in(U_422,U_415) ) )
| ( ! [U_414] :
( ~ in(U_414,U_426)
| ~ in(sK77(U_426,U_424),U_414) )
& in(sK77(U_426,U_424),U_424) ) )
& ! [U_425,U_423] :
( ( ! [U_420] :
( in(U_420,U_423)
| ! [U_412] :
( ~ in(U_412,U_425)
| ~ in(U_420,U_412) ) )
& ! [U_419] :
( ( in(sK76(U_425,U_423,U_419),U_425)
& in(U_419,sK76(U_425,U_423,U_419)) )
| ~ in(U_419,U_423) ) )
| U_423 != union(U_425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_421,sK77(U_426,U_424))],[f_52_4]) ).
fof(f_52_6,plain,
( ! [U_426,U_424] :
( U_424 = union(U_426)
| ( ~ in(sK78(U_426,U_424),U_424)
& ? [U_415] :
( in(U_415,U_426)
& in(sK78(U_426,U_424),U_415) ) )
| ( ! [U_414] :
( ~ in(U_414,U_426)
| ~ in(sK77(U_426,U_424),U_414) )
& in(sK77(U_426,U_424),U_424) ) )
& ! [U_425,U_423] :
( ( ! [U_420] :
( in(U_420,U_423)
| ! [U_412] :
( ~ in(U_412,U_425)
| ~ in(U_420,U_412) ) )
& ! [U_419] :
( ( in(sK76(U_425,U_423,U_419),U_425)
& in(U_419,sK76(U_425,U_423,U_419)) )
| ~ in(U_419,U_423) ) )
| U_423 != union(U_425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_422,sK78(U_426,U_424))],[f_52_5]) ).
fof(f_52_7,plain,
( ! [U_426,U_424] :
( U_424 = union(U_426)
| ( ~ in(sK78(U_426,U_424),U_424)
& in(sK79(U_426,U_424),U_426)
& in(sK78(U_426,U_424),sK79(U_426,U_424)) )
| ( ! [U_414] :
( ~ in(U_414,U_426)
| ~ in(sK77(U_426,U_424),U_414) )
& in(sK77(U_426,U_424),U_424) ) )
& ! [U_425,U_423] :
( ( ! [U_420] :
( in(U_420,U_423)
| ! [U_412] :
( ~ in(U_412,U_425)
| ~ in(U_420,U_412) ) )
& ! [U_419] :
( ( in(sK76(U_425,U_423,U_419),U_425)
& in(U_419,sK76(U_425,U_423,U_419)) )
| ~ in(U_419,U_423) ) )
| U_423 != union(U_425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_415,sK79(U_426,U_424))],[f_52_6]) ).
fof(f_52_8,plain,
( ! [U_424,U_426] :
( ~ in(sK78(U_426,U_424),U_424)
| ~ sP112(U_424,U_426) )
& ! [U_424,U_426] :
( in(sK79(U_426,U_424),U_426)
| ~ sP112(U_424,U_426) )
& ! [U_424,U_426] :
( in(sK78(U_426,U_424),sK79(U_426,U_424))
| ~ sP112(U_424,U_426) )
& ! [U_414,U_424,U_426] :
( ~ in(U_414,U_426)
| ~ in(sK77(U_426,U_424),U_414)
| ~ sP111(U_414,U_424,U_426) )
& ! [U_414,U_424,U_426] :
( in(sK77(U_426,U_424),U_424)
| ~ sP111(U_414,U_424,U_426) )
& ! [U_419,U_425,U_423] :
( in(sK76(U_425,U_423,U_419),U_425)
| ~ sP109(U_419,U_425,U_423) )
& ! [U_419,U_425,U_423] :
( in(U_419,sK76(U_425,U_423,U_419))
| ~ sP109(U_419,U_425,U_423) )
& ! [U_420,U_419,U_412,U_425,U_423] :
( in(U_420,U_423)
| ~ in(U_412,U_425)
| ~ in(U_420,U_412)
| ~ sP110(U_420,U_419,U_412,U_425,U_423) )
& ! [U_420,U_419,U_412,U_425,U_423] :
( sP109(U_419,U_425,U_423)
| ~ in(U_419,U_423)
| ~ sP110(U_420,U_419,U_412,U_425,U_423) )
& ! [U_414,U_424,U_426] :
( U_424 = union(U_426)
| sP112(U_424,U_426)
| sP111(U_414,U_424,U_426) )
& ! [U_420,U_419,U_412,U_425,U_423] :
( sP110(U_420,U_419,U_412,U_425,U_423)
| U_423 != union(U_425) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109,sP110,sP111,sP112])],[f_52_7]) ).
cnf(f_52_9,plain,
( sP110(U_420,U_419,U_412,U_425,U_423)
| U_423 != union(U_425) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_10,plain,
( U_424 = union(U_426)
| sP112(U_424,U_426)
| sP111(U_414,U_424,U_426) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_11,plain,
( sP109(U_419,U_425,U_423)
| ~ in(U_419,U_423)
| ~ sP110(U_420,U_419,U_412,U_425,U_423) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_12,plain,
( in(U_420,U_423)
| ~ in(U_412,U_425)
| ~ in(U_420,U_412)
| ~ sP110(U_420,U_419,U_412,U_425,U_423) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_13,plain,
( in(U_419,sK76(U_425,U_423,U_419))
| ~ sP109(U_419,U_425,U_423) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_14,plain,
( in(sK76(U_425,U_423,U_419),U_425)
| ~ sP109(U_419,U_425,U_423) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_15,plain,
( in(sK77(U_426,U_424),U_424)
| ~ sP111(U_414,U_424,U_426) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_16,plain,
( ~ in(U_414,U_426)
| ~ in(sK77(U_426,U_424),U_414)
| ~ sP111(U_414,U_424,U_426) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_17,plain,
( in(sK78(U_426,U_424),sK79(U_426,U_424))
| ~ sP112(U_424,U_426) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_18,plain,
( in(sK79(U_426,U_424),U_426)
| ~ sP112(U_424,U_426) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_19,plain,
( ~ in(sK78(U_426,U_424),U_424)
| ~ sP112(U_424,U_426) ),
inference(clausify,[status(thm)],[f_52_8]) ).
fof(f_53_1,plain,
! [A] :
( ( ( well_ordering(A)
| ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_wellord1]) ).
fof(f_53_2,plain,
! [U_427] :
( ( ( well_ordering(U_427)
| ~ well_founded_relation(U_427)
| ~ connected(U_427)
| ~ antisymmetric(U_427)
| ~ transitive(U_427)
| ~ reflexive(U_427) )
& ( ( well_founded_relation(U_427)
& connected(U_427)
& antisymmetric(U_427)
& transitive(U_427)
& reflexive(U_427) )
| ~ well_ordering(U_427) ) )
| ~ relation(U_427) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ! [U_427] :
( well_founded_relation(U_427)
| ~ sP113(U_427) )
& ! [U_427] :
( connected(U_427)
| ~ sP113(U_427) )
& ! [U_427] :
( antisymmetric(U_427)
| ~ sP113(U_427) )
& ! [U_427] :
( transitive(U_427)
| ~ sP113(U_427) )
& ! [U_427] :
( reflexive(U_427)
| ~ sP113(U_427) )
& ! [U_427] :
( well_ordering(U_427)
| ~ well_founded_relation(U_427)
| ~ connected(U_427)
| ~ antisymmetric(U_427)
| ~ transitive(U_427)
| ~ reflexive(U_427)
| ~ sP114(U_427) )
& ! [U_427] :
( sP113(U_427)
| ~ well_ordering(U_427)
| ~ sP114(U_427) )
& ! [U_427] :
( sP114(U_427)
| ~ relation(U_427) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113,sP114])],[f_53_2]) ).
cnf(f_53_4,plain,
( sP114(U_427)
| ~ relation(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_5,plain,
( sP113(U_427)
| ~ well_ordering(U_427)
| ~ sP114(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_6,plain,
( well_ordering(U_427)
| ~ well_founded_relation(U_427)
| ~ connected(U_427)
| ~ antisymmetric(U_427)
| ~ transitive(U_427)
| ~ reflexive(U_427)
| ~ sP114(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_7,plain,
( reflexive(U_427)
| ~ sP113(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_8,plain,
( transitive(U_427)
| ~ sP113(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_9,plain,
( antisymmetric(U_427)
| ~ sP113(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_10,plain,
( connected(U_427)
| ~ sP113(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
cnf(f_53_11,plain,
( well_founded_relation(U_427)
| ~ sP113(U_427) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [A,B,C] :
( ( C = set_difference(A,B)
| ? [D] :
( ( ~ in(D,C)
& ~ in(D,B)
& in(D,A) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| in(D,B)
| ~ in(D,A) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_54_2,plain,
! [U_432,U_431,U_430] :
( ( U_430 = set_difference(U_432,U_431)
| ? [U_429] :
( ( ~ in(U_429,U_430)
& ~ in(U_429,U_431)
& in(U_429,U_432) )
| ( ( in(U_429,U_431)
| ~ in(U_429,U_432) )
& in(U_429,U_430) ) ) )
& ( ! [U_428] :
( ( in(U_428,U_430)
| in(U_428,U_431)
| ~ in(U_428,U_432) )
& ( ( ~ in(U_428,U_431)
& in(U_428,U_432) )
| ~ in(U_428,U_430) ) )
| U_430 != set_difference(U_432,U_431) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_442,U_440,U_438] :
( U_438 = set_difference(U_442,U_440)
| ? [U_436] :
( ~ in(U_436,U_438)
& ~ in(U_436,U_440)
& in(U_436,U_442) )
| ? [U_435] :
( ( in(U_435,U_440)
| ~ in(U_435,U_442) )
& in(U_435,U_438) ) )
& ! [U_441,U_439,U_437] :
( ( ! [U_434] :
( in(U_434,U_437)
| in(U_434,U_439)
| ~ in(U_434,U_441) )
& ! [U_433] :
( ( ~ in(U_433,U_439)
& in(U_433,U_441) )
| ~ in(U_433,U_437) ) )
| U_437 != set_difference(U_441,U_439) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
( ! [U_442,U_440,U_438] :
( U_438 = set_difference(U_442,U_440)
| ? [U_436] :
( ~ in(U_436,U_438)
& ~ in(U_436,U_440)
& in(U_436,U_442) )
| ( ( in(sK80(U_442,U_440,U_438),U_440)
| ~ in(sK80(U_442,U_440,U_438),U_442) )
& in(sK80(U_442,U_440,U_438),U_438) ) )
& ! [U_441,U_439,U_437] :
( ( ! [U_434] :
( in(U_434,U_437)
| in(U_434,U_439)
| ~ in(U_434,U_441) )
& ! [U_433] :
( ( ~ in(U_433,U_439)
& in(U_433,U_441) )
| ~ in(U_433,U_437) ) )
| U_437 != set_difference(U_441,U_439) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_435,sK80(U_442,U_440,U_438))],[f_54_3]) ).
fof(f_54_5,plain,
( ! [U_442,U_440,U_438] :
( U_438 = set_difference(U_442,U_440)
| ( ~ in(sK81(U_442,U_440,U_438),U_438)
& ~ in(sK81(U_442,U_440,U_438),U_440)
& in(sK81(U_442,U_440,U_438),U_442) )
| ( ( in(sK80(U_442,U_440,U_438),U_440)
| ~ in(sK80(U_442,U_440,U_438),U_442) )
& in(sK80(U_442,U_440,U_438),U_438) ) )
& ! [U_441,U_439,U_437] :
( ( ! [U_434] :
( in(U_434,U_437)
| in(U_434,U_439)
| ~ in(U_434,U_441) )
& ! [U_433] :
( ( ~ in(U_433,U_439)
& in(U_433,U_441) )
| ~ in(U_433,U_437) ) )
| U_437 != set_difference(U_441,U_439) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_436,sK81(U_442,U_440,U_438))],[f_54_4]) ).
fof(f_54_6,plain,
( ! [U_442,U_438,U_440] :
( ~ in(sK81(U_442,U_440,U_438),U_438)
| ~ sP118(U_442,U_438,U_440) )
& ! [U_442,U_438,U_440] :
( ~ in(sK81(U_442,U_440,U_438),U_440)
| ~ sP118(U_442,U_438,U_440) )
& ! [U_442,U_438,U_440] :
( in(sK81(U_442,U_440,U_438),U_442)
| ~ sP118(U_442,U_438,U_440) )
& ! [U_442,U_438,U_440] :
( in(sK80(U_442,U_440,U_438),U_440)
| ~ in(sK80(U_442,U_440,U_438),U_442)
| ~ sP117(U_442,U_438,U_440) )
& ! [U_442,U_438,U_440] :
( in(sK80(U_442,U_440,U_438),U_438)
| ~ sP117(U_442,U_438,U_440) )
& ! [U_433,U_441,U_439] :
( ~ in(U_433,U_439)
| ~ sP115(U_433,U_441,U_439) )
& ! [U_433,U_441,U_439] :
( in(U_433,U_441)
| ~ sP115(U_433,U_441,U_439) )
& ! [U_433,U_434,U_441,U_437,U_439] :
( in(U_434,U_437)
| in(U_434,U_439)
| ~ in(U_434,U_441)
| ~ sP116(U_433,U_434,U_441,U_437,U_439) )
& ! [U_433,U_434,U_441,U_437,U_439] :
( sP115(U_433,U_441,U_439)
| ~ in(U_433,U_437)
| ~ sP116(U_433,U_434,U_441,U_437,U_439) )
& ! [U_442,U_438,U_440] :
( U_438 = set_difference(U_442,U_440)
| sP118(U_442,U_438,U_440)
| sP117(U_442,U_438,U_440) )
& ! [U_433,U_434,U_441,U_437,U_439] :
( sP116(U_433,U_434,U_441,U_437,U_439)
| U_437 != set_difference(U_441,U_439) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115,sP116,sP117,sP118])],[f_54_5]) ).
cnf(f_54_7,plain,
( sP116(U_433,U_434,U_441,U_437,U_439)
| U_437 != set_difference(U_441,U_439) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_8,plain,
( U_438 = set_difference(U_442,U_440)
| sP118(U_442,U_438,U_440)
| sP117(U_442,U_438,U_440) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_9,plain,
( sP115(U_433,U_441,U_439)
| ~ in(U_433,U_437)
| ~ sP116(U_433,U_434,U_441,U_437,U_439) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_10,plain,
( in(U_434,U_437)
| in(U_434,U_439)
| ~ in(U_434,U_441)
| ~ sP116(U_433,U_434,U_441,U_437,U_439) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_11,plain,
( in(U_433,U_441)
| ~ sP115(U_433,U_441,U_439) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_12,plain,
( ~ in(U_433,U_439)
| ~ sP115(U_433,U_441,U_439) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_13,plain,
( in(sK80(U_442,U_440,U_438),U_438)
| ~ sP117(U_442,U_438,U_440) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_14,plain,
( in(sK80(U_442,U_440,U_438),U_440)
| ~ in(sK80(U_442,U_440,U_438),U_442)
| ~ sP117(U_442,U_438,U_440) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_15,plain,
( in(sK81(U_442,U_440,U_438),U_442)
| ~ sP118(U_442,U_438,U_440) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_16,plain,
( ~ in(sK81(U_442,U_440,U_438),U_440)
| ~ sP118(U_442,U_438,U_440) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_17,plain,
( ~ in(sK81(U_442,U_440,U_438),U_438)
| ~ sP118(U_442,U_438,U_440) ),
inference(clausify,[status(thm)],[f_54_6]) ).
fof(f_55_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) ) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_funct_1]) ).
fof(f_55_2,plain,
! [U_450] :
( ! [U_449] :
( ( U_449 = relation_rng(U_450)
| ? [U_448] :
( ( ~ in(U_448,U_449)
& ? [U_447] :
( U_448 = apply(U_450,U_447)
& in(U_447,relation_dom(U_450)) ) )
| ( ! [U_446] :
( U_448 != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450)) )
& in(U_448,U_449) ) ) )
& ( ! [U_445] :
( ( in(U_445,U_449)
| ! [U_444] :
( U_445 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450)) ) )
& ( ? [U_443] :
( U_445 = apply(U_450,U_443)
& in(U_443,relation_dom(U_450)) )
| ~ in(U_445,U_449) ) )
| U_449 != relation_rng(U_450) ) )
| ~ function(U_450)
| ~ relation(U_450) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_450] :
( ( ! [U_456] :
( U_456 = relation_rng(U_450)
| ? [U_454] :
( ~ in(U_454,U_456)
& ? [U_447] :
( U_454 = apply(U_450,U_447)
& in(U_447,relation_dom(U_450)) ) )
| ? [U_453] :
( ! [U_446] :
( U_453 != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450)) )
& in(U_453,U_456) ) )
& ! [U_455] :
( ( ! [U_452] :
( in(U_452,U_455)
| ! [U_444] :
( U_452 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450)) ) )
& ! [U_451] :
( ? [U_443] :
( U_451 = apply(U_450,U_443)
& in(U_443,relation_dom(U_450)) )
| ~ in(U_451,U_455) ) )
| U_455 != relation_rng(U_450) ) )
| ~ function(U_450)
| ~ relation(U_450) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
! [U_450] :
( ( ! [U_456] :
( U_456 = relation_rng(U_450)
| ? [U_454] :
( ~ in(U_454,U_456)
& ? [U_447] :
( U_454 = apply(U_450,U_447)
& in(U_447,relation_dom(U_450)) ) )
| ? [U_453] :
( ! [U_446] :
( U_453 != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450)) )
& in(U_453,U_456) ) )
& ! [U_455] :
( ( ! [U_452] :
( in(U_452,U_455)
| ! [U_444] :
( U_452 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450)) ) )
& ! [U_451] :
( ( U_451 = apply(U_450,sK82(U_450,U_455,U_451))
& in(sK82(U_450,U_455,U_451),relation_dom(U_450)) )
| ~ in(U_451,U_455) ) )
| U_455 != relation_rng(U_450) ) )
| ~ function(U_450)
| ~ relation(U_450) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_443,sK82(U_450,U_455,U_451))],[f_55_3]) ).
fof(f_55_5,plain,
! [U_450] :
( ( ! [U_456] :
( U_456 = relation_rng(U_450)
| ? [U_454] :
( ~ in(U_454,U_456)
& ? [U_447] :
( U_454 = apply(U_450,U_447)
& in(U_447,relation_dom(U_450)) ) )
| ( ! [U_446] :
( sK83(U_450,U_456) != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450)) )
& in(sK83(U_450,U_456),U_456) ) )
& ! [U_455] :
( ( ! [U_452] :
( in(U_452,U_455)
| ! [U_444] :
( U_452 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450)) ) )
& ! [U_451] :
( ( U_451 = apply(U_450,sK82(U_450,U_455,U_451))
& in(sK82(U_450,U_455,U_451),relation_dom(U_450)) )
| ~ in(U_451,U_455) ) )
| U_455 != relation_rng(U_450) ) )
| ~ function(U_450)
| ~ relation(U_450) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_453,sK83(U_450,U_456))],[f_55_4]) ).
fof(f_55_6,plain,
! [U_450] :
( ( ! [U_456] :
( U_456 = relation_rng(U_450)
| ( ~ in(sK84(U_450,U_456),U_456)
& ? [U_447] :
( sK84(U_450,U_456) = apply(U_450,U_447)
& in(U_447,relation_dom(U_450)) ) )
| ( ! [U_446] :
( sK83(U_450,U_456) != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450)) )
& in(sK83(U_450,U_456),U_456) ) )
& ! [U_455] :
( ( ! [U_452] :
( in(U_452,U_455)
| ! [U_444] :
( U_452 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450)) ) )
& ! [U_451] :
( ( U_451 = apply(U_450,sK82(U_450,U_455,U_451))
& in(sK82(U_450,U_455,U_451),relation_dom(U_450)) )
| ~ in(U_451,U_455) ) )
| U_455 != relation_rng(U_450) ) )
| ~ function(U_450)
| ~ relation(U_450) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_454,sK84(U_450,U_456))],[f_55_5]) ).
fof(f_55_7,plain,
! [U_450] :
( ( ! [U_456] :
( U_456 = relation_rng(U_450)
| ( ~ in(sK84(U_450,U_456),U_456)
& sK84(U_450,U_456) = apply(U_450,sK85(U_450,U_456))
& in(sK85(U_450,U_456),relation_dom(U_450)) )
| ( ! [U_446] :
( sK83(U_450,U_456) != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450)) )
& in(sK83(U_450,U_456),U_456) ) )
& ! [U_455] :
( ( ! [U_452] :
( in(U_452,U_455)
| ! [U_444] :
( U_452 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450)) ) )
& ! [U_451] :
( ( U_451 = apply(U_450,sK82(U_450,U_455,U_451))
& in(sK82(U_450,U_455,U_451),relation_dom(U_450)) )
| ~ in(U_451,U_455) ) )
| U_455 != relation_rng(U_450) ) )
| ~ function(U_450)
| ~ relation(U_450) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_447,sK85(U_450,U_456))],[f_55_6]) ).
fof(f_55_8,plain,
( ! [U_456,U_450] :
( ~ in(sK84(U_450,U_456),U_456)
| ~ sP122(U_456,U_450) )
& ! [U_456,U_450] :
( sK84(U_450,U_456) = apply(U_450,sK85(U_450,U_456))
| ~ sP122(U_456,U_450) )
& ! [U_456,U_450] :
( in(sK85(U_450,U_456),relation_dom(U_450))
| ~ sP122(U_456,U_450) )
& ! [U_456,U_450,U_446] :
( sK83(U_450,U_456) != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450))
| ~ sP121(U_456,U_450,U_446) )
& ! [U_456,U_450,U_446] :
( in(sK83(U_450,U_456),U_456)
| ~ sP121(U_456,U_450,U_446) )
& ! [U_451,U_450,U_455] :
( U_451 = apply(U_450,sK82(U_450,U_455,U_451))
| ~ sP119(U_451,U_450,U_455) )
& ! [U_451,U_450,U_455] :
( in(sK82(U_450,U_455,U_451),relation_dom(U_450))
| ~ sP119(U_451,U_450,U_455) )
& ! [U_451,U_450,U_452,U_444,U_455] :
( in(U_452,U_455)
| U_452 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450))
| ~ sP120(U_451,U_450,U_452,U_444,U_455) )
& ! [U_451,U_450,U_452,U_444,U_455] :
( sP119(U_451,U_450,U_455)
| ~ in(U_451,U_455)
| ~ sP120(U_451,U_450,U_452,U_444,U_455) )
& ! [U_451,U_456,U_450,U_446,U_452,U_444,U_455] :
( U_456 = relation_rng(U_450)
| sP122(U_456,U_450)
| sP121(U_456,U_450,U_446)
| ~ sP123(U_451,U_456,U_450,U_446,U_452,U_444,U_455) )
& ! [U_451,U_456,U_450,U_446,U_452,U_444,U_455] :
( sP120(U_451,U_450,U_452,U_444,U_455)
| U_455 != relation_rng(U_450)
| ~ sP123(U_451,U_456,U_450,U_446,U_452,U_444,U_455) )
& ! [U_451,U_456,U_450,U_446,U_452,U_444,U_455] :
( sP123(U_451,U_456,U_450,U_446,U_452,U_444,U_455)
| ~ function(U_450)
| ~ relation(U_450) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119,sP120,sP121,sP122,sP123])],[f_55_7]) ).
cnf(f_55_9,plain,
( sP123(U_451,U_456,U_450,U_446,U_452,U_444,U_455)
| ~ function(U_450)
| ~ relation(U_450) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_10,plain,
( sP120(U_451,U_450,U_452,U_444,U_455)
| U_455 != relation_rng(U_450)
| ~ sP123(U_451,U_456,U_450,U_446,U_452,U_444,U_455) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_11,plain,
( U_456 = relation_rng(U_450)
| sP122(U_456,U_450)
| sP121(U_456,U_450,U_446)
| ~ sP123(U_451,U_456,U_450,U_446,U_452,U_444,U_455) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_12,plain,
( sP119(U_451,U_450,U_455)
| ~ in(U_451,U_455)
| ~ sP120(U_451,U_450,U_452,U_444,U_455) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_13,plain,
( in(U_452,U_455)
| U_452 != apply(U_450,U_444)
| ~ in(U_444,relation_dom(U_450))
| ~ sP120(U_451,U_450,U_452,U_444,U_455) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_14,plain,
( in(sK82(U_450,U_455,U_451),relation_dom(U_450))
| ~ sP119(U_451,U_450,U_455) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_15,plain,
( U_451 = apply(U_450,sK82(U_450,U_455,U_451))
| ~ sP119(U_451,U_450,U_455) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_16,plain,
( in(sK83(U_450,U_456),U_456)
| ~ sP121(U_456,U_450,U_446) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_17,plain,
( sK83(U_450,U_456) != apply(U_450,U_446)
| ~ in(U_446,relation_dom(U_450))
| ~ sP121(U_456,U_450,U_446) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_18,plain,
( in(sK85(U_450,U_456),relation_dom(U_450))
| ~ sP122(U_456,U_450) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_19,plain,
( sK84(U_450,U_456) = apply(U_450,sK85(U_450,U_456))
| ~ sP122(U_456,U_450) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_20,plain,
( ~ in(sK84(U_450,U_456),U_456)
| ~ sP122(U_456,U_450) ),
inference(clausify,[status(thm)],[f_55_8]) ).
fof(f_56_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(D,C),A) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(f_56_2,plain,
! [U_464] :
( ! [U_463] :
( ( U_463 = relation_rng(U_464)
| ? [U_462] :
( ( ~ in(U_462,U_463)
& ? [U_461] : in(ordered_pair(U_461,U_462),U_464) )
| ( ! [U_460] : ~ in(ordered_pair(U_460,U_462),U_464)
& in(U_462,U_463) ) ) )
& ( ! [U_459] :
( ( in(U_459,U_463)
| ! [U_458] : ~ in(ordered_pair(U_458,U_459),U_464) )
& ( ? [U_457] : in(ordered_pair(U_457,U_459),U_464)
| ~ in(U_459,U_463) ) )
| U_463 != relation_rng(U_464) ) )
| ~ relation(U_464) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_464] :
( ( ! [U_470] :
( U_470 = relation_rng(U_464)
| ? [U_468] :
( ~ in(U_468,U_470)
& ? [U_461] : in(ordered_pair(U_461,U_468),U_464) )
| ? [U_467] :
( ! [U_460] : ~ in(ordered_pair(U_460,U_467),U_464)
& in(U_467,U_470) ) )
& ! [U_469] :
( ( ! [U_466] :
( in(U_466,U_469)
| ! [U_458] : ~ in(ordered_pair(U_458,U_466),U_464) )
& ! [U_465] :
( ? [U_457] : in(ordered_pair(U_457,U_465),U_464)
| ~ in(U_465,U_469) ) )
| U_469 != relation_rng(U_464) ) )
| ~ relation(U_464) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
! [U_464] :
( ( ! [U_470] :
( U_470 = relation_rng(U_464)
| ? [U_468] :
( ~ in(U_468,U_470)
& ? [U_461] : in(ordered_pair(U_461,U_468),U_464) )
| ? [U_467] :
( ! [U_460] : ~ in(ordered_pair(U_460,U_467),U_464)
& in(U_467,U_470) ) )
& ! [U_469] :
( ( ! [U_466] :
( in(U_466,U_469)
| ! [U_458] : ~ in(ordered_pair(U_458,U_466),U_464) )
& ! [U_465] :
( in(ordered_pair(sK86(U_464,U_469,U_465),U_465),U_464)
| ~ in(U_465,U_469) ) )
| U_469 != relation_rng(U_464) ) )
| ~ relation(U_464) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_457,sK86(U_464,U_469,U_465))],[f_56_3]) ).
fof(f_56_5,plain,
! [U_464] :
( ( ! [U_470] :
( U_470 = relation_rng(U_464)
| ? [U_468] :
( ~ in(U_468,U_470)
& ? [U_461] : in(ordered_pair(U_461,U_468),U_464) )
| ( ! [U_460] : ~ in(ordered_pair(U_460,sK87(U_464,U_470)),U_464)
& in(sK87(U_464,U_470),U_470) ) )
& ! [U_469] :
( ( ! [U_466] :
( in(U_466,U_469)
| ! [U_458] : ~ in(ordered_pair(U_458,U_466),U_464) )
& ! [U_465] :
( in(ordered_pair(sK86(U_464,U_469,U_465),U_465),U_464)
| ~ in(U_465,U_469) ) )
| U_469 != relation_rng(U_464) ) )
| ~ relation(U_464) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_467,sK87(U_464,U_470))],[f_56_4]) ).
fof(f_56_6,plain,
! [U_464] :
( ( ! [U_470] :
( U_470 = relation_rng(U_464)
| ( ~ in(sK88(U_464,U_470),U_470)
& ? [U_461] : in(ordered_pair(U_461,sK88(U_464,U_470)),U_464) )
| ( ! [U_460] : ~ in(ordered_pair(U_460,sK87(U_464,U_470)),U_464)
& in(sK87(U_464,U_470),U_470) ) )
& ! [U_469] :
( ( ! [U_466] :
( in(U_466,U_469)
| ! [U_458] : ~ in(ordered_pair(U_458,U_466),U_464) )
& ! [U_465] :
( in(ordered_pair(sK86(U_464,U_469,U_465),U_465),U_464)
| ~ in(U_465,U_469) ) )
| U_469 != relation_rng(U_464) ) )
| ~ relation(U_464) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_468,sK88(U_464,U_470))],[f_56_5]) ).
fof(f_56_7,plain,
! [U_464] :
( ( ! [U_470] :
( U_470 = relation_rng(U_464)
| ( ~ in(sK88(U_464,U_470),U_470)
& in(ordered_pair(sK89(U_464,U_470),sK88(U_464,U_470)),U_464) )
| ( ! [U_460] : ~ in(ordered_pair(U_460,sK87(U_464,U_470)),U_464)
& in(sK87(U_464,U_470),U_470) ) )
& ! [U_469] :
( ( ! [U_466] :
( in(U_466,U_469)
| ! [U_458] : ~ in(ordered_pair(U_458,U_466),U_464) )
& ! [U_465] :
( in(ordered_pair(sK86(U_464,U_469,U_465),U_465),U_464)
| ~ in(U_465,U_469) ) )
| U_469 != relation_rng(U_464) ) )
| ~ relation(U_464) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_461,sK89(U_464,U_470))],[f_56_6]) ).
fof(f_56_8,plain,
( ! [U_464,U_470] :
( ~ in(sK88(U_464,U_470),U_470)
| ~ sP126(U_464,U_470) )
& ! [U_464,U_470] :
( in(ordered_pair(sK89(U_464,U_470),sK88(U_464,U_470)),U_464)
| ~ sP126(U_464,U_470) )
& ! [U_464,U_470,U_460] :
( ~ in(ordered_pair(U_460,sK87(U_464,U_470)),U_464)
| ~ sP125(U_464,U_470,U_460) )
& ! [U_464,U_470,U_460] :
( in(sK87(U_464,U_470),U_470)
| ~ sP125(U_464,U_470,U_460) )
& ! [U_464,U_458,U_465,U_466,U_469] :
( in(U_466,U_469)
| ~ in(ordered_pair(U_458,U_466),U_464)
| ~ sP124(U_464,U_458,U_465,U_466,U_469) )
& ! [U_464,U_458,U_465,U_466,U_469] :
( in(ordered_pair(sK86(U_464,U_469,U_465),U_465),U_464)
| ~ in(U_465,U_469)
| ~ sP124(U_464,U_458,U_465,U_466,U_469) )
& ! [U_464,U_458,U_465,U_466,U_469,U_470,U_460] :
( U_470 = relation_rng(U_464)
| sP126(U_464,U_470)
| sP125(U_464,U_470,U_460)
| ~ sP127(U_464,U_458,U_465,U_466,U_469,U_470,U_460) )
& ! [U_464,U_458,U_465,U_466,U_469,U_470,U_460] :
( sP124(U_464,U_458,U_465,U_466,U_469)
| U_469 != relation_rng(U_464)
| ~ sP127(U_464,U_458,U_465,U_466,U_469,U_470,U_460) )
& ! [U_464,U_458,U_465,U_466,U_469,U_470,U_460] :
( sP127(U_464,U_458,U_465,U_466,U_469,U_470,U_460)
| ~ relation(U_464) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124,sP125,sP126,sP127])],[f_56_7]) ).
cnf(f_56_9,plain,
( sP127(U_464,U_458,U_465,U_466,U_469,U_470,U_460)
| ~ relation(U_464) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_10,plain,
( sP124(U_464,U_458,U_465,U_466,U_469)
| U_469 != relation_rng(U_464)
| ~ sP127(U_464,U_458,U_465,U_466,U_469,U_470,U_460) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_11,plain,
( U_470 = relation_rng(U_464)
| sP126(U_464,U_470)
| sP125(U_464,U_470,U_460)
| ~ sP127(U_464,U_458,U_465,U_466,U_469,U_470,U_460) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_12,plain,
( in(ordered_pair(sK86(U_464,U_469,U_465),U_465),U_464)
| ~ in(U_465,U_469)
| ~ sP124(U_464,U_458,U_465,U_466,U_469) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_13,plain,
( in(U_466,U_469)
| ~ in(ordered_pair(U_458,U_466),U_464)
| ~ sP124(U_464,U_458,U_465,U_466,U_469) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_14,plain,
( in(sK87(U_464,U_470),U_470)
| ~ sP125(U_464,U_470,U_460) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_15,plain,
( ~ in(ordered_pair(U_460,sK87(U_464,U_470)),U_464)
| ~ sP125(U_464,U_470,U_460) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_16,plain,
( in(ordered_pair(sK89(U_464,U_470),sK88(U_464,U_470)),U_464)
| ~ sP126(U_464,U_470) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_17,plain,
( ~ in(sK88(U_464,U_470),U_470)
| ~ sP126(U_464,U_470) ),
inference(clausify,[status(thm)],[f_56_8]) ).
fof(f_57_1,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[d5_subset_1]) ).
fof(f_57_2,plain,
! [U_472,U_471] :
( subset_complement(U_472,U_471) = set_difference(U_472,U_471)
| ~ element(U_471,powerset(U_472)) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_472,U_471] :
( subset_complement(U_472,U_471) = set_difference(U_472,U_471)
| ~ element(U_471,powerset(U_472)) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( subset_complement(U_472,U_471) = set_difference(U_472,U_471)
| ~ element(U_471,powerset(U_472)) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_58_2,plain,
! [U_474,U_473] : ordered_pair(U_474,U_473) = unordered_pair(unordered_pair(U_474,U_473),singleton(U_474)),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_474,U_473] : ordered_pair(U_474,U_473) = unordered_pair(unordered_pair(U_474,U_473),singleton(U_474)),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
ordered_pair(U_474,U_473) = unordered_pair(unordered_pair(U_474,U_473),singleton(U_474)),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A] :
( ! [B] :
( ( well_orders(A,B)
| ~ is_well_founded_in(A,B)
| ~ is_connected_in(A,B)
| ~ is_antisymmetric_in(A,B)
| ~ is_transitive_in(A,B)
| ~ is_reflexive_in(A,B) )
& ( ( is_well_founded_in(A,B)
& is_connected_in(A,B)
& is_antisymmetric_in(A,B)
& is_transitive_in(A,B)
& is_reflexive_in(A,B) )
| ~ well_orders(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_wellord1]) ).
fof(f_59_2,plain,
! [U_476] :
( ! [U_475] :
( ( well_orders(U_476,U_475)
| ~ is_well_founded_in(U_476,U_475)
| ~ is_connected_in(U_476,U_475)
| ~ is_antisymmetric_in(U_476,U_475)
| ~ is_transitive_in(U_476,U_475)
| ~ is_reflexive_in(U_476,U_475) )
& ( ( is_well_founded_in(U_476,U_475)
& is_connected_in(U_476,U_475)
& is_antisymmetric_in(U_476,U_475)
& is_transitive_in(U_476,U_475)
& is_reflexive_in(U_476,U_475) )
| ~ well_orders(U_476,U_475) ) )
| ~ relation(U_476) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_476] :
( ( ! [U_478] :
( well_orders(U_476,U_478)
| ~ is_well_founded_in(U_476,U_478)
| ~ is_connected_in(U_476,U_478)
| ~ is_antisymmetric_in(U_476,U_478)
| ~ is_transitive_in(U_476,U_478)
| ~ is_reflexive_in(U_476,U_478) )
& ! [U_477] :
( ( is_well_founded_in(U_476,U_477)
& is_connected_in(U_476,U_477)
& is_antisymmetric_in(U_476,U_477)
& is_transitive_in(U_476,U_477)
& is_reflexive_in(U_476,U_477) )
| ~ well_orders(U_476,U_477) ) )
| ~ relation(U_476) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
( ! [U_477,U_476] :
( is_well_founded_in(U_476,U_477)
| ~ sP128(U_477,U_476) )
& ! [U_477,U_476] :
( is_connected_in(U_476,U_477)
| ~ sP128(U_477,U_476) )
& ! [U_477,U_476] :
( is_antisymmetric_in(U_476,U_477)
| ~ sP128(U_477,U_476) )
& ! [U_477,U_476] :
( is_transitive_in(U_476,U_477)
| ~ sP128(U_477,U_476) )
& ! [U_477,U_476] :
( is_reflexive_in(U_476,U_477)
| ~ sP128(U_477,U_476) )
& ! [U_477,U_476,U_478] :
( well_orders(U_476,U_478)
| ~ is_well_founded_in(U_476,U_478)
| ~ is_connected_in(U_476,U_478)
| ~ is_antisymmetric_in(U_476,U_478)
| ~ is_transitive_in(U_476,U_478)
| ~ is_reflexive_in(U_476,U_478)
| ~ sP129(U_477,U_476,U_478) )
& ! [U_477,U_476,U_478] :
( sP128(U_477,U_476)
| ~ well_orders(U_476,U_477)
| ~ sP129(U_477,U_476,U_478) )
& ! [U_477,U_476,U_478] :
( sP129(U_477,U_476,U_478)
| ~ relation(U_476) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128,sP129])],[f_59_3]) ).
cnf(f_59_5,plain,
( sP129(U_477,U_476,U_478)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_6,plain,
( sP128(U_477,U_476)
| ~ well_orders(U_476,U_477)
| ~ sP129(U_477,U_476,U_478) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_7,plain,
( well_orders(U_476,U_478)
| ~ is_well_founded_in(U_476,U_478)
| ~ is_connected_in(U_476,U_478)
| ~ is_antisymmetric_in(U_476,U_478)
| ~ is_transitive_in(U_476,U_478)
| ~ is_reflexive_in(U_476,U_478)
| ~ sP129(U_477,U_476,U_478) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_8,plain,
( is_reflexive_in(U_476,U_477)
| ~ sP128(U_477,U_476) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_9,plain,
( is_transitive_in(U_476,U_477)
| ~ sP128(U_477,U_476) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_10,plain,
( is_antisymmetric_in(U_476,U_477)
| ~ sP128(U_477,U_476) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_11,plain,
( is_connected_in(U_476,U_477)
| ~ sP128(U_477,U_476) ),
inference(clausify,[status(thm)],[f_59_4]) ).
cnf(f_59_12,plain,
( is_well_founded_in(U_476,U_477)
| ~ sP128(U_477,U_476) ),
inference(clausify,[status(thm)],[f_59_4]) ).
fof(f_60_1,plain,
! [A] :
( ( being_limit_ordinal(A)
| A != union(A) )
& ( A = union(A)
| ~ being_limit_ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[d6_ordinal1]) ).
fof(f_60_2,plain,
! [U_479] :
( ( being_limit_ordinal(U_479)
| U_479 != union(U_479) )
& ( U_479 = union(U_479)
| ~ being_limit_ordinal(U_479) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( ! [U_481] :
( being_limit_ordinal(U_481)
| U_481 != union(U_481) )
& ! [U_480] :
( U_480 = union(U_480)
| ~ being_limit_ordinal(U_480) ) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
fof(f_60_4,plain,
( ! [U_481] :
( being_limit_ordinal(U_481)
| U_481 != union(U_481) )
& ! [U_480] :
( U_480 = union(U_480)
| ~ being_limit_ordinal(U_480) ) ),
inference(definitional_conversion,[status(esa)],[f_60_3]) ).
cnf(f_60_5,plain,
( U_480 = union(U_480)
| ~ being_limit_ordinal(U_480) ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_6,plain,
( being_limit_ordinal(U_481)
| U_481 != union(U_481) ),
inference(clausify,[status(thm)],[f_60_4]) ).
fof(f_61_1,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_1]) ).
fof(f_61_2,plain,
! [U_482] :
( relation_field(U_482) = set_union2(relation_dom(U_482),relation_rng(U_482))
| ~ relation(U_482) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_482] :
( relation_field(U_482) = set_union2(relation_dom(U_482),relation_rng(U_482))
| ~ relation(U_482) ),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
( relation_field(U_482) = set_union2(relation_dom(U_482),relation_rng(U_482))
| ~ relation(U_482) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,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) ) )
& ( ! [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(fof_nnf,[status(thm)],[d6_relat_2]) ).
fof(f_62_2,plain,
! [U_488] :
( ! [U_487] :
( ( is_connected_in(U_488,U_487)
| ? [U_486,U_485] :
( ~ in(ordered_pair(U_485,U_486),U_488)
& ~ in(ordered_pair(U_486,U_485),U_488)
& U_486 != U_485
& in(U_485,U_487)
& in(U_486,U_487) ) )
& ( ! [U_484,U_483] :
( in(ordered_pair(U_483,U_484),U_488)
| in(ordered_pair(U_484,U_483),U_488)
| U_484 = U_483
| ~ in(U_483,U_487)
| ~ in(U_484,U_487) )
| ~ is_connected_in(U_488,U_487) ) )
| ~ relation(U_488) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_488] :
( ( ! [U_490] :
( is_connected_in(U_488,U_490)
| ? [U_486] :
( ? [U_485] :
( ~ in(ordered_pair(U_485,U_486),U_488)
& ~ in(ordered_pair(U_486,U_485),U_488)
& U_486 != U_485
& in(U_485,U_490) )
& in(U_486,U_490) ) )
& ! [U_489] :
( ! [U_484] :
( ! [U_483] :
( in(ordered_pair(U_483,U_484),U_488)
| in(ordered_pair(U_484,U_483),U_488)
| U_484 = U_483
| ~ in(U_483,U_489) )
| ~ in(U_484,U_489) )
| ~ is_connected_in(U_488,U_489) ) )
| ~ relation(U_488) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
fof(f_62_4,plain,
! [U_488] :
( ( ! [U_490] :
( is_connected_in(U_488,U_490)
| ( ? [U_485] :
( ~ in(ordered_pair(U_485,sK90(U_488,U_490)),U_488)
& ~ in(ordered_pair(sK90(U_488,U_490),U_485),U_488)
& sK90(U_488,U_490) != U_485
& in(U_485,U_490) )
& in(sK90(U_488,U_490),U_490) ) )
& ! [U_489] :
( ! [U_484] :
( ! [U_483] :
( in(ordered_pair(U_483,U_484),U_488)
| in(ordered_pair(U_484,U_483),U_488)
| U_484 = U_483
| ~ in(U_483,U_489) )
| ~ in(U_484,U_489) )
| ~ is_connected_in(U_488,U_489) ) )
| ~ relation(U_488) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_486,sK90(U_488,U_490))],[f_62_3]) ).
fof(f_62_5,plain,
! [U_488] :
( ( ! [U_490] :
( is_connected_in(U_488,U_490)
| ( ~ in(ordered_pair(sK91(U_488,U_490),sK90(U_488,U_490)),U_488)
& ~ in(ordered_pair(sK90(U_488,U_490),sK91(U_488,U_490)),U_488)
& sK90(U_488,U_490) != sK91(U_488,U_490)
& in(sK91(U_488,U_490),U_490)
& in(sK90(U_488,U_490),U_490) ) )
& ! [U_489] :
( ! [U_484] :
( ! [U_483] :
( in(ordered_pair(U_483,U_484),U_488)
| in(ordered_pair(U_484,U_483),U_488)
| U_484 = U_483
| ~ in(U_483,U_489) )
| ~ in(U_484,U_489) )
| ~ is_connected_in(U_488,U_489) ) )
| ~ relation(U_488) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_485,sK91(U_488,U_490))],[f_62_4]) ).
fof(f_62_6,plain,
( ! [U_490,U_488] :
( ~ in(ordered_pair(sK91(U_488,U_490),sK90(U_488,U_490)),U_488)
| ~ sP130(U_490,U_488) )
& ! [U_490,U_488] :
( ~ in(ordered_pair(sK90(U_488,U_490),sK91(U_488,U_490)),U_488)
| ~ sP130(U_490,U_488) )
& ! [U_490,U_488] :
( sK90(U_488,U_490) != sK91(U_488,U_490)
| ~ sP130(U_490,U_488) )
& ! [U_490,U_488] :
( in(sK91(U_488,U_490),U_490)
| ~ sP130(U_490,U_488) )
& ! [U_490,U_488] :
( in(sK90(U_488,U_490),U_490)
| ~ sP130(U_490,U_488) )
& ! [U_489,U_490,U_483,U_484,U_488] :
( is_connected_in(U_488,U_490)
| sP130(U_490,U_488)
| ~ sP131(U_489,U_490,U_483,U_484,U_488) )
& ! [U_489,U_490,U_483,U_484,U_488] :
( in(ordered_pair(U_483,U_484),U_488)
| in(ordered_pair(U_484,U_483),U_488)
| U_484 = U_483
| ~ in(U_483,U_489)
| ~ in(U_484,U_489)
| ~ is_connected_in(U_488,U_489)
| ~ sP131(U_489,U_490,U_483,U_484,U_488) )
& ! [U_489,U_490,U_483,U_484,U_488] :
( sP131(U_489,U_490,U_483,U_484,U_488)
| ~ relation(U_488) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130,sP131])],[f_62_5]) ).
cnf(f_62_7,plain,
( sP131(U_489,U_490,U_483,U_484,U_488)
| ~ relation(U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
cnf(f_62_8,plain,
( in(ordered_pair(U_483,U_484),U_488)
| in(ordered_pair(U_484,U_483),U_488)
| U_484 = U_483
| ~ in(U_483,U_489)
| ~ in(U_484,U_489)
| ~ is_connected_in(U_488,U_489)
| ~ sP131(U_489,U_490,U_483,U_484,U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
cnf(f_62_9,plain,
( is_connected_in(U_488,U_490)
| sP130(U_490,U_488)
| ~ sP131(U_489,U_490,U_483,U_484,U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
cnf(f_62_10,plain,
( in(sK90(U_488,U_490),U_490)
| ~ sP130(U_490,U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
cnf(f_62_11,plain,
( in(sK91(U_488,U_490),U_490)
| ~ sP130(U_490,U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
cnf(f_62_12,plain,
( sK90(U_488,U_490) != sK91(U_488,U_490)
| ~ sP130(U_490,U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
cnf(f_62_13,plain,
( ~ in(ordered_pair(sK90(U_488,U_490),sK91(U_488,U_490)),U_488)
| ~ sP130(U_490,U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
cnf(f_62_14,plain,
( ~ in(ordered_pair(sK91(U_488,U_490),sK90(U_488,U_490)),U_488)
| ~ sP130(U_490,U_488) ),
inference(clausify,[status(thm)],[f_62_6]) ).
fof(f_63_1,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_wellord1]) ).
fof(f_63_2,plain,
! [U_492] :
( ! [U_491] : relation_restriction(U_492,U_491) = set_intersection2(U_492,cartesian_product2(U_491,U_491))
| ~ relation(U_492) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_491,U_492] :
( relation_restriction(U_492,U_491) = set_intersection2(U_492,cartesian_product2(U_491,U_491))
| ~ relation(U_492) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( relation_restriction(U_492,U_491) = set_intersection2(U_492,cartesian_product2(U_491,U_491))
| ~ relation(U_492) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [A] :
( ! [B] :
( ( ( B = relation_inverse(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(D,C),A) )
| ( ~ in(ordered_pair(D,C),A)
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(D,C),A) )
& ( in(ordered_pair(D,C),A)
| ~ in(ordered_pair(C,D),B) ) )
| B != relation_inverse(A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d7_relat_1]) ).
fof(f_64_2,plain,
! [U_498] :
( ! [U_497] :
( ( ( U_497 = relation_inverse(U_498)
| ? [U_496,U_495] :
( ( ~ in(ordered_pair(U_496,U_495),U_497)
& in(ordered_pair(U_495,U_496),U_498) )
| ( ~ in(ordered_pair(U_495,U_496),U_498)
& in(ordered_pair(U_496,U_495),U_497) ) ) )
& ( ! [U_494,U_493] :
( ( in(ordered_pair(U_494,U_493),U_497)
| ~ in(ordered_pair(U_493,U_494),U_498) )
& ( in(ordered_pair(U_493,U_494),U_498)
| ~ in(ordered_pair(U_494,U_493),U_497) ) )
| U_497 != relation_inverse(U_498) ) )
| ~ relation(U_497) )
| ~ relation(U_498) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_498] :
( ! [U_497] :
( ( ( U_497 = relation_inverse(U_498)
| ? [U_506,U_504] :
( ~ in(ordered_pair(U_506,U_504),U_497)
& in(ordered_pair(U_504,U_506),U_498) )
| ? [U_505,U_503] :
( ~ in(ordered_pair(U_503,U_505),U_498)
& in(ordered_pair(U_505,U_503),U_497) ) )
& ( ( ! [U_502,U_500] :
( in(ordered_pair(U_502,U_500),U_497)
| ~ in(ordered_pair(U_500,U_502),U_498) )
& ! [U_501,U_499] :
( in(ordered_pair(U_499,U_501),U_498)
| ~ in(ordered_pair(U_501,U_499),U_497) ) )
| U_497 != relation_inverse(U_498) ) )
| ~ relation(U_497) )
| ~ relation(U_498) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
fof(f_64_4,plain,
! [U_498] :
( ! [U_497] :
( ( ( U_497 = relation_inverse(U_498)
| ? [U_506,U_504] :
( ~ in(ordered_pair(U_506,U_504),U_497)
& in(ordered_pair(U_504,U_506),U_498) )
| ? [U_503] :
( ~ in(ordered_pair(U_503,sK92(U_498,U_497)),U_498)
& in(ordered_pair(sK92(U_498,U_497),U_503),U_497) ) )
& ( ( ! [U_502,U_500] :
( in(ordered_pair(U_502,U_500),U_497)
| ~ in(ordered_pair(U_500,U_502),U_498) )
& ! [U_501,U_499] :
( in(ordered_pair(U_499,U_501),U_498)
| ~ in(ordered_pair(U_501,U_499),U_497) ) )
| U_497 != relation_inverse(U_498) ) )
| ~ relation(U_497) )
| ~ relation(U_498) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_505,sK92(U_498,U_497))],[f_64_3]) ).
fof(f_64_5,plain,
! [U_498] :
( ! [U_497] :
( ( ( U_497 = relation_inverse(U_498)
| ? [U_506,U_504] :
( ~ in(ordered_pair(U_506,U_504),U_497)
& in(ordered_pair(U_504,U_506),U_498) )
| ( ~ in(ordered_pair(sK93(U_498,U_497),sK92(U_498,U_497)),U_498)
& in(ordered_pair(sK92(U_498,U_497),sK93(U_498,U_497)),U_497) ) )
& ( ( ! [U_502,U_500] :
( in(ordered_pair(U_502,U_500),U_497)
| ~ in(ordered_pair(U_500,U_502),U_498) )
& ! [U_501,U_499] :
( in(ordered_pair(U_499,U_501),U_498)
| ~ in(ordered_pair(U_501,U_499),U_497) ) )
| U_497 != relation_inverse(U_498) ) )
| ~ relation(U_497) )
| ~ relation(U_498) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_503,sK93(U_498,U_497))],[f_64_4]) ).
fof(f_64_6,plain,
! [U_498] :
( ! [U_497] :
( ( ( U_497 = relation_inverse(U_498)
| ? [U_504] :
( ~ in(ordered_pair(sK94(U_498,U_497),U_504),U_497)
& in(ordered_pair(U_504,sK94(U_498,U_497)),U_498) )
| ( ~ in(ordered_pair(sK93(U_498,U_497),sK92(U_498,U_497)),U_498)
& in(ordered_pair(sK92(U_498,U_497),sK93(U_498,U_497)),U_497) ) )
& ( ( ! [U_502,U_500] :
( in(ordered_pair(U_502,U_500),U_497)
| ~ in(ordered_pair(U_500,U_502),U_498) )
& ! [U_501,U_499] :
( in(ordered_pair(U_499,U_501),U_498)
| ~ in(ordered_pair(U_501,U_499),U_497) ) )
| U_497 != relation_inverse(U_498) ) )
| ~ relation(U_497) )
| ~ relation(U_498) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_506,sK94(U_498,U_497))],[f_64_5]) ).
fof(f_64_7,plain,
! [U_498] :
( ! [U_497] :
( ( ( U_497 = relation_inverse(U_498)
| ( ~ in(ordered_pair(sK94(U_498,U_497),sK95(U_498,U_497)),U_497)
& in(ordered_pair(sK95(U_498,U_497),sK94(U_498,U_497)),U_498) )
| ( ~ in(ordered_pair(sK93(U_498,U_497),sK92(U_498,U_497)),U_498)
& in(ordered_pair(sK92(U_498,U_497),sK93(U_498,U_497)),U_497) ) )
& ( ( ! [U_502,U_500] :
( in(ordered_pair(U_502,U_500),U_497)
| ~ in(ordered_pair(U_500,U_502),U_498) )
& ! [U_501,U_499] :
( in(ordered_pair(U_499,U_501),U_498)
| ~ in(ordered_pair(U_501,U_499),U_497) ) )
| U_497 != relation_inverse(U_498) ) )
| ~ relation(U_497) )
| ~ relation(U_498) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_504,sK95(U_498,U_497))],[f_64_6]) ).
fof(f_64_8,plain,
( ! [U_498,U_497] :
( ~ in(ordered_pair(sK94(U_498,U_497),sK95(U_498,U_497)),U_497)
| ~ sP134(U_498,U_497) )
& ! [U_498,U_497] :
( in(ordered_pair(sK95(U_498,U_497),sK94(U_498,U_497)),U_498)
| ~ sP134(U_498,U_497) )
& ! [U_498,U_497] :
( ~ in(ordered_pair(sK93(U_498,U_497),sK92(U_498,U_497)),U_498)
| ~ sP133(U_498,U_497) )
& ! [U_498,U_497] :
( in(ordered_pair(sK92(U_498,U_497),sK93(U_498,U_497)),U_497)
| ~ sP133(U_498,U_497) )
& ! [U_498,U_497,U_502,U_500,U_499,U_501] :
( in(ordered_pair(U_502,U_500),U_497)
| ~ in(ordered_pair(U_500,U_502),U_498)
| ~ sP132(U_498,U_497,U_502,U_500,U_499,U_501) )
& ! [U_498,U_497,U_502,U_500,U_499,U_501] :
( in(ordered_pair(U_499,U_501),U_498)
| ~ in(ordered_pair(U_501,U_499),U_497)
| ~ sP132(U_498,U_497,U_502,U_500,U_499,U_501) )
& ! [U_498,U_497,U_502,U_500,U_499,U_501] :
( U_497 = relation_inverse(U_498)
| sP134(U_498,U_497)
| sP133(U_498,U_497)
| ~ sP135(U_498,U_497,U_502,U_500,U_499,U_501) )
& ! [U_498,U_497,U_502,U_500,U_499,U_501] :
( sP132(U_498,U_497,U_502,U_500,U_499,U_501)
| U_497 != relation_inverse(U_498)
| ~ sP135(U_498,U_497,U_502,U_500,U_499,U_501) )
& ! [U_498,U_497,U_502,U_500,U_499,U_501] :
( sP135(U_498,U_497,U_502,U_500,U_499,U_501)
| ~ relation(U_497)
| ~ relation(U_498) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132,sP133,sP134,sP135])],[f_64_7]) ).
cnf(f_64_9,plain,
( sP135(U_498,U_497,U_502,U_500,U_499,U_501)
| ~ relation(U_497)
| ~ relation(U_498) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_10,plain,
( sP132(U_498,U_497,U_502,U_500,U_499,U_501)
| U_497 != relation_inverse(U_498)
| ~ sP135(U_498,U_497,U_502,U_500,U_499,U_501) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_11,plain,
( U_497 = relation_inverse(U_498)
| sP134(U_498,U_497)
| sP133(U_498,U_497)
| ~ sP135(U_498,U_497,U_502,U_500,U_499,U_501) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_12,plain,
( in(ordered_pair(U_499,U_501),U_498)
| ~ in(ordered_pair(U_501,U_499),U_497)
| ~ sP132(U_498,U_497,U_502,U_500,U_499,U_501) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_13,plain,
( in(ordered_pair(U_502,U_500),U_497)
| ~ in(ordered_pair(U_500,U_502),U_498)
| ~ sP132(U_498,U_497,U_502,U_500,U_499,U_501) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_14,plain,
( in(ordered_pair(sK92(U_498,U_497),sK93(U_498,U_497)),U_497)
| ~ sP133(U_498,U_497) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_15,plain,
( ~ in(ordered_pair(sK93(U_498,U_497),sK92(U_498,U_497)),U_498)
| ~ sP133(U_498,U_497) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_16,plain,
( in(ordered_pair(sK95(U_498,U_497),sK94(U_498,U_497)),U_498)
| ~ sP134(U_498,U_497) ),
inference(clausify,[status(thm)],[f_64_8]) ).
cnf(f_64_17,plain,
( ~ in(ordered_pair(sK94(U_498,U_497),sK95(U_498,U_497)),U_497)
| ~ sP134(U_498,U_497) ),
inference(clausify,[status(thm)],[f_64_8]) ).
fof(f_65_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( relation_isomorphism(A,B,C)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),A)
& in(ordered_pair(apply(C,D),apply(C,E)),B)
& in(E,relation_field(A))
& in(D,relation_field(A)) )
| ( ( ~ in(ordered_pair(apply(C,D),apply(C,E)),B)
| ~ in(E,relation_field(A))
| ~ in(D,relation_field(A)) )
& in(ordered_pair(D,E),A) ) )
| ~ one_to_one(C)
| relation_rng(C) != relation_field(B)
| relation_dom(C) != relation_field(A) )
& ( ( ! [D,E] :
( ( in(ordered_pair(D,E),A)
| ~ in(ordered_pair(apply(C,D),apply(C,E)),B)
| ~ in(E,relation_field(A))
| ~ in(D,relation_field(A)) )
& ( ( in(ordered_pair(apply(C,D),apply(C,E)),B)
& in(E,relation_field(A))
& in(D,relation_field(A)) )
| ~ in(ordered_pair(D,E),A) ) )
& one_to_one(C)
& relation_rng(C) = relation_field(B)
& relation_dom(C) = relation_field(A) )
| ~ relation_isomorphism(A,B,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d7_wellord1]) ).
fof(f_65_2,plain,
! [U_513] :
( ! [U_512] :
( ! [U_511] :
( ( ( relation_isomorphism(U_513,U_512,U_511)
| ? [U_510,U_509] :
( ( ~ in(ordered_pair(U_510,U_509),U_513)
& in(ordered_pair(apply(U_511,U_510),apply(U_511,U_509)),U_512)
& in(U_509,relation_field(U_513))
& in(U_510,relation_field(U_513)) )
| ( ( ~ in(ordered_pair(apply(U_511,U_510),apply(U_511,U_509)),U_512)
| ~ in(U_509,relation_field(U_513))
| ~ in(U_510,relation_field(U_513)) )
& in(ordered_pair(U_510,U_509),U_513) ) )
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513) )
& ( ( ! [U_508,U_507] :
( ( in(ordered_pair(U_508,U_507),U_513)
| ~ in(ordered_pair(apply(U_511,U_508),apply(U_511,U_507)),U_512)
| ~ in(U_507,relation_field(U_513))
| ~ in(U_508,relation_field(U_513)) )
& ( ( in(ordered_pair(apply(U_511,U_508),apply(U_511,U_507)),U_512)
& in(U_507,relation_field(U_513))
& in(U_508,relation_field(U_513)) )
| ~ in(ordered_pair(U_508,U_507),U_513) ) )
& one_to_one(U_511)
& relation_rng(U_511) = relation_field(U_512)
& relation_dom(U_511) = relation_field(U_513) )
| ~ relation_isomorphism(U_513,U_512,U_511) ) )
| ~ function(U_511)
| ~ relation(U_511) )
| ~ relation(U_512) )
| ~ relation(U_513) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_513] :
( ! [U_512] :
( ! [U_511] :
( ( ( relation_isomorphism(U_513,U_512,U_511)
| ? [U_521,U_519] :
( ~ in(ordered_pair(U_521,U_519),U_513)
& in(ordered_pair(apply(U_511,U_521),apply(U_511,U_519)),U_512)
& in(U_519,relation_field(U_513))
& in(U_521,relation_field(U_513)) )
| ? [U_520,U_518] :
( ( ~ in(ordered_pair(apply(U_511,U_520),apply(U_511,U_518)),U_512)
| ~ in(U_518,relation_field(U_513))
| ~ in(U_520,relation_field(U_513)) )
& in(ordered_pair(U_520,U_518),U_513) )
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513) )
& ( ( ! [U_517,U_515] :
( in(ordered_pair(U_517,U_515),U_513)
| ~ in(ordered_pair(apply(U_511,U_517),apply(U_511,U_515)),U_512)
| ~ in(U_515,relation_field(U_513))
| ~ in(U_517,relation_field(U_513)) )
& ! [U_516,U_514] :
( ( in(ordered_pair(apply(U_511,U_516),apply(U_511,U_514)),U_512)
& in(U_514,relation_field(U_513))
& in(U_516,relation_field(U_513)) )
| ~ in(ordered_pair(U_516,U_514),U_513) )
& one_to_one(U_511)
& relation_rng(U_511) = relation_field(U_512)
& relation_dom(U_511) = relation_field(U_513) )
| ~ relation_isomorphism(U_513,U_512,U_511) ) )
| ~ function(U_511)
| ~ relation(U_511) )
| ~ relation(U_512) )
| ~ relation(U_513) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
fof(f_65_4,plain,
! [U_513] :
( ! [U_512] :
( ! [U_511] :
( ( ( relation_isomorphism(U_513,U_512,U_511)
| ? [U_521,U_519] :
( ~ in(ordered_pair(U_521,U_519),U_513)
& in(ordered_pair(apply(U_511,U_521),apply(U_511,U_519)),U_512)
& in(U_519,relation_field(U_513))
& in(U_521,relation_field(U_513)) )
| ? [U_518] :
( ( ~ in(ordered_pair(apply(U_511,sK96(U_513,U_512,U_511)),apply(U_511,U_518)),U_512)
| ~ in(U_518,relation_field(U_513))
| ~ in(sK96(U_513,U_512,U_511),relation_field(U_513)) )
& in(ordered_pair(sK96(U_513,U_512,U_511),U_518),U_513) )
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513) )
& ( ( ! [U_517,U_515] :
( in(ordered_pair(U_517,U_515),U_513)
| ~ in(ordered_pair(apply(U_511,U_517),apply(U_511,U_515)),U_512)
| ~ in(U_515,relation_field(U_513))
| ~ in(U_517,relation_field(U_513)) )
& ! [U_516,U_514] :
( ( in(ordered_pair(apply(U_511,U_516),apply(U_511,U_514)),U_512)
& in(U_514,relation_field(U_513))
& in(U_516,relation_field(U_513)) )
| ~ in(ordered_pair(U_516,U_514),U_513) )
& one_to_one(U_511)
& relation_rng(U_511) = relation_field(U_512)
& relation_dom(U_511) = relation_field(U_513) )
| ~ relation_isomorphism(U_513,U_512,U_511) ) )
| ~ function(U_511)
| ~ relation(U_511) )
| ~ relation(U_512) )
| ~ relation(U_513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_520,sK96(U_513,U_512,U_511))],[f_65_3]) ).
fof(f_65_5,plain,
! [U_513] :
( ! [U_512] :
( ! [U_511] :
( ( ( relation_isomorphism(U_513,U_512,U_511)
| ? [U_521,U_519] :
( ~ in(ordered_pair(U_521,U_519),U_513)
& in(ordered_pair(apply(U_511,U_521),apply(U_511,U_519)),U_512)
& in(U_519,relation_field(U_513))
& in(U_521,relation_field(U_513)) )
| ( ( ~ in(ordered_pair(apply(U_511,sK96(U_513,U_512,U_511)),apply(U_511,sK97(U_513,U_512,U_511))),U_512)
| ~ in(sK97(U_513,U_512,U_511),relation_field(U_513))
| ~ in(sK96(U_513,U_512,U_511),relation_field(U_513)) )
& in(ordered_pair(sK96(U_513,U_512,U_511),sK97(U_513,U_512,U_511)),U_513) )
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513) )
& ( ( ! [U_517,U_515] :
( in(ordered_pair(U_517,U_515),U_513)
| ~ in(ordered_pair(apply(U_511,U_517),apply(U_511,U_515)),U_512)
| ~ in(U_515,relation_field(U_513))
| ~ in(U_517,relation_field(U_513)) )
& ! [U_516,U_514] :
( ( in(ordered_pair(apply(U_511,U_516),apply(U_511,U_514)),U_512)
& in(U_514,relation_field(U_513))
& in(U_516,relation_field(U_513)) )
| ~ in(ordered_pair(U_516,U_514),U_513) )
& one_to_one(U_511)
& relation_rng(U_511) = relation_field(U_512)
& relation_dom(U_511) = relation_field(U_513) )
| ~ relation_isomorphism(U_513,U_512,U_511) ) )
| ~ function(U_511)
| ~ relation(U_511) )
| ~ relation(U_512) )
| ~ relation(U_513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_518,sK97(U_513,U_512,U_511))],[f_65_4]) ).
fof(f_65_6,plain,
! [U_513] :
( ! [U_512] :
( ! [U_511] :
( ( ( relation_isomorphism(U_513,U_512,U_511)
| ? [U_519] :
( ~ in(ordered_pair(sK98(U_513,U_512,U_511),U_519),U_513)
& in(ordered_pair(apply(U_511,sK98(U_513,U_512,U_511)),apply(U_511,U_519)),U_512)
& in(U_519,relation_field(U_513))
& in(sK98(U_513,U_512,U_511),relation_field(U_513)) )
| ( ( ~ in(ordered_pair(apply(U_511,sK96(U_513,U_512,U_511)),apply(U_511,sK97(U_513,U_512,U_511))),U_512)
| ~ in(sK97(U_513,U_512,U_511),relation_field(U_513))
| ~ in(sK96(U_513,U_512,U_511),relation_field(U_513)) )
& in(ordered_pair(sK96(U_513,U_512,U_511),sK97(U_513,U_512,U_511)),U_513) )
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513) )
& ( ( ! [U_517,U_515] :
( in(ordered_pair(U_517,U_515),U_513)
| ~ in(ordered_pair(apply(U_511,U_517),apply(U_511,U_515)),U_512)
| ~ in(U_515,relation_field(U_513))
| ~ in(U_517,relation_field(U_513)) )
& ! [U_516,U_514] :
( ( in(ordered_pair(apply(U_511,U_516),apply(U_511,U_514)),U_512)
& in(U_514,relation_field(U_513))
& in(U_516,relation_field(U_513)) )
| ~ in(ordered_pair(U_516,U_514),U_513) )
& one_to_one(U_511)
& relation_rng(U_511) = relation_field(U_512)
& relation_dom(U_511) = relation_field(U_513) )
| ~ relation_isomorphism(U_513,U_512,U_511) ) )
| ~ function(U_511)
| ~ relation(U_511) )
| ~ relation(U_512) )
| ~ relation(U_513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_521,sK98(U_513,U_512,U_511))],[f_65_5]) ).
fof(f_65_7,plain,
! [U_513] :
( ! [U_512] :
( ! [U_511] :
( ( ( relation_isomorphism(U_513,U_512,U_511)
| ( ~ in(ordered_pair(sK98(U_513,U_512,U_511),sK99(U_513,U_512,U_511)),U_513)
& in(ordered_pair(apply(U_511,sK98(U_513,U_512,U_511)),apply(U_511,sK99(U_513,U_512,U_511))),U_512)
& in(sK99(U_513,U_512,U_511),relation_field(U_513))
& in(sK98(U_513,U_512,U_511),relation_field(U_513)) )
| ( ( ~ in(ordered_pair(apply(U_511,sK96(U_513,U_512,U_511)),apply(U_511,sK97(U_513,U_512,U_511))),U_512)
| ~ in(sK97(U_513,U_512,U_511),relation_field(U_513))
| ~ in(sK96(U_513,U_512,U_511),relation_field(U_513)) )
& in(ordered_pair(sK96(U_513,U_512,U_511),sK97(U_513,U_512,U_511)),U_513) )
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513) )
& ( ( ! [U_517,U_515] :
( in(ordered_pair(U_517,U_515),U_513)
| ~ in(ordered_pair(apply(U_511,U_517),apply(U_511,U_515)),U_512)
| ~ in(U_515,relation_field(U_513))
| ~ in(U_517,relation_field(U_513)) )
& ! [U_516,U_514] :
( ( in(ordered_pair(apply(U_511,U_516),apply(U_511,U_514)),U_512)
& in(U_514,relation_field(U_513))
& in(U_516,relation_field(U_513)) )
| ~ in(ordered_pair(U_516,U_514),U_513) )
& one_to_one(U_511)
& relation_rng(U_511) = relation_field(U_512)
& relation_dom(U_511) = relation_field(U_513) )
| ~ relation_isomorphism(U_513,U_512,U_511) ) )
| ~ function(U_511)
| ~ relation(U_511) )
| ~ relation(U_512) )
| ~ relation(U_513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_519,sK99(U_513,U_512,U_511))],[f_65_6]) ).
fof(f_65_8,plain,
( ! [U_511,U_512,U_513] :
( ~ in(ordered_pair(sK98(U_513,U_512,U_511),sK99(U_513,U_512,U_511)),U_513)
| ~ sP139(U_511,U_512,U_513) )
& ! [U_511,U_512,U_513] :
( in(ordered_pair(apply(U_511,sK98(U_513,U_512,U_511)),apply(U_511,sK99(U_513,U_512,U_511))),U_512)
| ~ sP139(U_511,U_512,U_513) )
& ! [U_511,U_512,U_513] :
( in(sK99(U_513,U_512,U_511),relation_field(U_513))
| ~ sP139(U_511,U_512,U_513) )
& ! [U_511,U_512,U_513] :
( in(sK98(U_513,U_512,U_511),relation_field(U_513))
| ~ sP139(U_511,U_512,U_513) )
& ! [U_511,U_512,U_513] :
( ~ in(ordered_pair(apply(U_511,sK96(U_513,U_512,U_511)),apply(U_511,sK97(U_513,U_512,U_511))),U_512)
| ~ in(sK97(U_513,U_512,U_511),relation_field(U_513))
| ~ in(sK96(U_513,U_512,U_511),relation_field(U_513))
| ~ sP138(U_511,U_512,U_513) )
& ! [U_511,U_512,U_513] :
( in(ordered_pair(sK96(U_513,U_512,U_511),sK97(U_513,U_512,U_511)),U_513)
| ~ sP138(U_511,U_512,U_513) )
& ! [U_511,U_514,U_512,U_516,U_513] :
( in(ordered_pair(apply(U_511,U_516),apply(U_511,U_514)),U_512)
| ~ sP136(U_511,U_514,U_512,U_516,U_513) )
& ! [U_511,U_514,U_512,U_516,U_513] :
( in(U_514,relation_field(U_513))
| ~ sP136(U_511,U_514,U_512,U_516,U_513) )
& ! [U_511,U_514,U_512,U_516,U_513] :
( in(U_516,relation_field(U_513))
| ~ sP136(U_511,U_514,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( in(ordered_pair(U_517,U_515),U_513)
| ~ in(ordered_pair(apply(U_511,U_517),apply(U_511,U_515)),U_512)
| ~ in(U_515,relation_field(U_513))
| ~ in(U_517,relation_field(U_513))
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( sP136(U_511,U_514,U_512,U_516,U_513)
| ~ in(ordered_pair(U_516,U_514),U_513)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( one_to_one(U_511)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( relation_rng(U_511) = relation_field(U_512)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( relation_dom(U_511) = relation_field(U_513)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( relation_isomorphism(U_513,U_512,U_511)
| sP139(U_511,U_512,U_513)
| sP138(U_511,U_512,U_513)
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513)
| ~ sP140(U_511,U_514,U_515,U_517,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513)
| ~ relation_isomorphism(U_513,U_512,U_511)
| ~ sP140(U_511,U_514,U_515,U_517,U_512,U_516,U_513) )
& ! [U_511,U_514,U_515,U_517,U_512,U_516,U_513] :
( sP140(U_511,U_514,U_515,U_517,U_512,U_516,U_513)
| ~ function(U_511)
| ~ relation(U_511)
| ~ relation(U_512)
| ~ relation(U_513) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136,sP137,sP138,sP139,sP140])],[f_65_7]) ).
cnf(f_65_9,plain,
( sP140(U_511,U_514,U_515,U_517,U_512,U_516,U_513)
| ~ function(U_511)
| ~ relation(U_511)
| ~ relation(U_512)
| ~ relation(U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_10,plain,
( sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513)
| ~ relation_isomorphism(U_513,U_512,U_511)
| ~ sP140(U_511,U_514,U_515,U_517,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_11,plain,
( relation_isomorphism(U_513,U_512,U_511)
| sP139(U_511,U_512,U_513)
| sP138(U_511,U_512,U_513)
| ~ one_to_one(U_511)
| relation_rng(U_511) != relation_field(U_512)
| relation_dom(U_511) != relation_field(U_513)
| ~ sP140(U_511,U_514,U_515,U_517,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_12,plain,
( relation_dom(U_511) = relation_field(U_513)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_13,plain,
( relation_rng(U_511) = relation_field(U_512)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_14,plain,
( one_to_one(U_511)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_15,plain,
( sP136(U_511,U_514,U_512,U_516,U_513)
| ~ in(ordered_pair(U_516,U_514),U_513)
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_16,plain,
( in(ordered_pair(U_517,U_515),U_513)
| ~ in(ordered_pair(apply(U_511,U_517),apply(U_511,U_515)),U_512)
| ~ in(U_515,relation_field(U_513))
| ~ in(U_517,relation_field(U_513))
| ~ sP137(U_511,U_514,U_515,U_517,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_17,plain,
( in(U_516,relation_field(U_513))
| ~ sP136(U_511,U_514,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_18,plain,
( in(U_514,relation_field(U_513))
| ~ sP136(U_511,U_514,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_19,plain,
( in(ordered_pair(apply(U_511,U_516),apply(U_511,U_514)),U_512)
| ~ sP136(U_511,U_514,U_512,U_516,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_20,plain,
( in(ordered_pair(sK96(U_513,U_512,U_511),sK97(U_513,U_512,U_511)),U_513)
| ~ sP138(U_511,U_512,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_21,plain,
( ~ in(ordered_pair(apply(U_511,sK96(U_513,U_512,U_511)),apply(U_511,sK97(U_513,U_512,U_511))),U_512)
| ~ in(sK97(U_513,U_512,U_511),relation_field(U_513))
| ~ in(sK96(U_513,U_512,U_511),relation_field(U_513))
| ~ sP138(U_511,U_512,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_22,plain,
( in(sK98(U_513,U_512,U_511),relation_field(U_513))
| ~ sP139(U_511,U_512,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_23,plain,
( in(sK99(U_513,U_512,U_511),relation_field(U_513))
| ~ sP139(U_511,U_512,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_24,plain,
( in(ordered_pair(apply(U_511,sK98(U_513,U_512,U_511)),apply(U_511,sK99(U_513,U_512,U_511))),U_512)
| ~ sP139(U_511,U_512,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_25,plain,
( ~ in(ordered_pair(sK98(U_513,U_512,U_511),sK99(U_513,U_512,U_511)),U_513)
| ~ sP139(U_511,U_512,U_513) ),
inference(clausify,[status(thm)],[f_65_8]) ).
fof(f_66_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_intersection2(A,B) != empty_set )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[d7_xboole_0]) ).
fof(f_66_2,plain,
! [U_523,U_522] :
( ( disjoint(U_523,U_522)
| set_intersection2(U_523,U_522) != empty_set )
& ( set_intersection2(U_523,U_522) = empty_set
| ~ disjoint(U_523,U_522) ) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_527,U_525] :
( disjoint(U_527,U_525)
| set_intersection2(U_527,U_525) != empty_set )
& ! [U_526,U_524] :
( set_intersection2(U_526,U_524) = empty_set
| ~ disjoint(U_526,U_524) ) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
( ! [U_525,U_527] :
( disjoint(U_527,U_525)
| set_intersection2(U_527,U_525) != empty_set )
& ! [U_526,U_524] :
( set_intersection2(U_526,U_524) = empty_set
| ~ disjoint(U_526,U_524) ) ),
inference(definitional_conversion,[status(esa)],[f_66_3]) ).
cnf(f_66_5,plain,
( set_intersection2(U_526,U_524) = empty_set
| ~ disjoint(U_526,U_524) ),
inference(clausify,[status(thm)],[f_66_4]) ).
cnf(f_66_6,plain,
( disjoint(U_527,U_525)
| set_intersection2(U_527,U_525) != empty_set ),
inference(clausify,[status(thm)],[f_66_4]) ).
fof(f_67_1,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)) ) )
& ( ! [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(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(f_67_2,plain,
! [U_532] :
( ( ( one_to_one(U_532)
| ? [U_531,U_530] :
( U_531 != U_530
& apply(U_532,U_531) = apply(U_532,U_530)
& in(U_530,relation_dom(U_532))
& in(U_531,relation_dom(U_532)) ) )
& ( ! [U_529,U_528] :
( U_529 = U_528
| apply(U_532,U_529) != apply(U_532,U_528)
| ~ in(U_528,relation_dom(U_532))
| ~ in(U_529,relation_dom(U_532)) )
| ~ one_to_one(U_532) ) )
| ~ function(U_532)
| ~ relation(U_532) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_532] :
( ( ( one_to_one(U_532)
| ? [U_530] :
( sK100(U_532) != U_530
& apply(U_532,sK100(U_532)) = apply(U_532,U_530)
& in(U_530,relation_dom(U_532))
& in(sK100(U_532),relation_dom(U_532)) ) )
& ( ! [U_529,U_528] :
( U_529 = U_528
| apply(U_532,U_529) != apply(U_532,U_528)
| ~ in(U_528,relation_dom(U_532))
| ~ in(U_529,relation_dom(U_532)) )
| ~ one_to_one(U_532) ) )
| ~ function(U_532)
| ~ relation(U_532) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_531,sK100(U_532))],[f_67_2]) ).
fof(f_67_4,plain,
! [U_532] :
( ( ( one_to_one(U_532)
| ( sK100(U_532) != sK101(U_532)
& apply(U_532,sK100(U_532)) = apply(U_532,sK101(U_532))
& in(sK101(U_532),relation_dom(U_532))
& in(sK100(U_532),relation_dom(U_532)) ) )
& ( ! [U_529,U_528] :
( U_529 = U_528
| apply(U_532,U_529) != apply(U_532,U_528)
| ~ in(U_528,relation_dom(U_532))
| ~ in(U_529,relation_dom(U_532)) )
| ~ one_to_one(U_532) ) )
| ~ function(U_532)
| ~ relation(U_532) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_530,sK101(U_532))],[f_67_3]) ).
fof(f_67_5,plain,
( ! [U_532] :
( sK100(U_532) != sK101(U_532)
| ~ sP141(U_532) )
& ! [U_532] :
( apply(U_532,sK100(U_532)) = apply(U_532,sK101(U_532))
| ~ sP141(U_532) )
& ! [U_532] :
( in(sK101(U_532),relation_dom(U_532))
| ~ sP141(U_532) )
& ! [U_532] :
( in(sK100(U_532),relation_dom(U_532))
| ~ sP141(U_532) )
& ! [U_528,U_532,U_529] :
( one_to_one(U_532)
| sP141(U_532)
| ~ sP142(U_528,U_532,U_529) )
& ! [U_528,U_532,U_529] :
( U_529 = U_528
| apply(U_532,U_529) != apply(U_532,U_528)
| ~ in(U_528,relation_dom(U_532))
| ~ in(U_529,relation_dom(U_532))
| ~ one_to_one(U_532)
| ~ sP142(U_528,U_532,U_529) )
& ! [U_528,U_532,U_529] :
( sP142(U_528,U_532,U_529)
| ~ function(U_532)
| ~ relation(U_532) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141,sP142])],[f_67_4]) ).
cnf(f_67_6,plain,
( sP142(U_528,U_532,U_529)
| ~ function(U_532)
| ~ relation(U_532) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_7,plain,
( U_529 = U_528
| apply(U_532,U_529) != apply(U_532,U_528)
| ~ in(U_528,relation_dom(U_532))
| ~ in(U_529,relation_dom(U_532))
| ~ one_to_one(U_532)
| ~ sP142(U_528,U_532,U_529) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_8,plain,
( one_to_one(U_532)
| sP141(U_532)
| ~ sP142(U_528,U_532,U_529) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_9,plain,
( in(sK100(U_532),relation_dom(U_532))
| ~ sP141(U_532) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_10,plain,
( in(sK101(U_532),relation_dom(U_532))
| ~ sP141(U_532) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_11,plain,
( apply(U_532,sK100(U_532)) = apply(U_532,sK101(U_532))
| ~ sP141(U_532) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_12,plain,
( sK100(U_532) != sK101(U_532)
| ~ sP141(U_532) ),
inference(clausify,[status(thm)],[f_67_5]) ).
fof(f_68_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( C = relation_composition(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) ) )
| ( ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(F,E),B)
| ~ in(ordered_pair(D,F),A) ) )
& ( ? [F] :
( in(ordered_pair(F,E),B)
& in(ordered_pair(D,F),A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_composition(A,B) ) )
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_relat_1]) ).
fof(f_68_2,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ? [U_540,U_539] :
( ( ~ in(ordered_pair(U_540,U_539),U_541)
& ? [U_538] :
( in(ordered_pair(U_538,U_539),U_542)
& in(ordered_pair(U_540,U_538),U_543) ) )
| ( ! [U_537] :
( ~ in(ordered_pair(U_537,U_539),U_542)
| ~ in(ordered_pair(U_540,U_537),U_543) )
& in(ordered_pair(U_540,U_539),U_541) ) ) )
& ( ! [U_536,U_535] :
( ( in(ordered_pair(U_536,U_535),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_535),U_542)
| ~ in(ordered_pair(U_536,U_534),U_543) ) )
& ( ? [U_533] :
( in(ordered_pair(U_533,U_535),U_542)
& in(ordered_pair(U_536,U_533),U_543) )
| ~ in(ordered_pair(U_536,U_535),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ? [U_551,U_549] :
( ~ in(ordered_pair(U_551,U_549),U_541)
& ? [U_538] :
( in(ordered_pair(U_538,U_549),U_542)
& in(ordered_pair(U_551,U_538),U_543) ) )
| ? [U_550,U_548] :
( ! [U_537] :
( ~ in(ordered_pair(U_537,U_548),U_542)
| ~ in(ordered_pair(U_550,U_537),U_543) )
& in(ordered_pair(U_550,U_548),U_541) ) )
& ( ( ! [U_547,U_545] :
( in(ordered_pair(U_547,U_545),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543) ) )
& ! [U_546,U_544] :
( ? [U_533] :
( in(ordered_pair(U_533,U_544),U_542)
& in(ordered_pair(U_546,U_533),U_543) )
| ~ in(ordered_pair(U_546,U_544),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ? [U_551,U_549] :
( ~ in(ordered_pair(U_551,U_549),U_541)
& ? [U_538] :
( in(ordered_pair(U_538,U_549),U_542)
& in(ordered_pair(U_551,U_538),U_543) ) )
| ? [U_550,U_548] :
( ! [U_537] :
( ~ in(ordered_pair(U_537,U_548),U_542)
| ~ in(ordered_pair(U_550,U_537),U_543) )
& in(ordered_pair(U_550,U_548),U_541) ) )
& ( ( ! [U_547,U_545] :
( in(ordered_pair(U_547,U_545),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543) ) )
& ! [U_546,U_544] :
( ( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
& in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543) )
| ~ in(ordered_pair(U_546,U_544),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_533,sK102(U_543,U_542,U_541,U_546,U_544))],[f_68_3]) ).
fof(f_68_5,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ? [U_551,U_549] :
( ~ in(ordered_pair(U_551,U_549),U_541)
& ? [U_538] :
( in(ordered_pair(U_538,U_549),U_542)
& in(ordered_pair(U_551,U_538),U_543) ) )
| ? [U_548] :
( ! [U_537] :
( ~ in(ordered_pair(U_537,U_548),U_542)
| ~ in(ordered_pair(sK103(U_543,U_542,U_541),U_537),U_543) )
& in(ordered_pair(sK103(U_543,U_542,U_541),U_548),U_541) ) )
& ( ( ! [U_547,U_545] :
( in(ordered_pair(U_547,U_545),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543) ) )
& ! [U_546,U_544] :
( ( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
& in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543) )
| ~ in(ordered_pair(U_546,U_544),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_550,sK103(U_543,U_542,U_541))],[f_68_4]) ).
fof(f_68_6,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ? [U_551,U_549] :
( ~ in(ordered_pair(U_551,U_549),U_541)
& ? [U_538] :
( in(ordered_pair(U_538,U_549),U_542)
& in(ordered_pair(U_551,U_538),U_543) ) )
| ( ! [U_537] :
( ~ in(ordered_pair(U_537,sK104(U_543,U_542,U_541)),U_542)
| ~ in(ordered_pair(sK103(U_543,U_542,U_541),U_537),U_543) )
& in(ordered_pair(sK103(U_543,U_542,U_541),sK104(U_543,U_542,U_541)),U_541) ) )
& ( ( ! [U_547,U_545] :
( in(ordered_pair(U_547,U_545),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543) ) )
& ! [U_546,U_544] :
( ( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
& in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543) )
| ~ in(ordered_pair(U_546,U_544),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_548,sK104(U_543,U_542,U_541))],[f_68_5]) ).
fof(f_68_7,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ? [U_549] :
( ~ in(ordered_pair(sK105(U_543,U_542,U_541),U_549),U_541)
& ? [U_538] :
( in(ordered_pair(U_538,U_549),U_542)
& in(ordered_pair(sK105(U_543,U_542,U_541),U_538),U_543) ) )
| ( ! [U_537] :
( ~ in(ordered_pair(U_537,sK104(U_543,U_542,U_541)),U_542)
| ~ in(ordered_pair(sK103(U_543,U_542,U_541),U_537),U_543) )
& in(ordered_pair(sK103(U_543,U_542,U_541),sK104(U_543,U_542,U_541)),U_541) ) )
& ( ( ! [U_547,U_545] :
( in(ordered_pair(U_547,U_545),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543) ) )
& ! [U_546,U_544] :
( ( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
& in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543) )
| ~ in(ordered_pair(U_546,U_544),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_551,sK105(U_543,U_542,U_541))],[f_68_6]) ).
fof(f_68_8,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ( ~ in(ordered_pair(sK105(U_543,U_542,U_541),sK106(U_543,U_542,U_541)),U_541)
& ? [U_538] :
( in(ordered_pair(U_538,sK106(U_543,U_542,U_541)),U_542)
& in(ordered_pair(sK105(U_543,U_542,U_541),U_538),U_543) ) )
| ( ! [U_537] :
( ~ in(ordered_pair(U_537,sK104(U_543,U_542,U_541)),U_542)
| ~ in(ordered_pair(sK103(U_543,U_542,U_541),U_537),U_543) )
& in(ordered_pair(sK103(U_543,U_542,U_541),sK104(U_543,U_542,U_541)),U_541) ) )
& ( ( ! [U_547,U_545] :
( in(ordered_pair(U_547,U_545),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543) ) )
& ! [U_546,U_544] :
( ( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
& in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543) )
| ~ in(ordered_pair(U_546,U_544),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_549,sK106(U_543,U_542,U_541))],[f_68_7]) ).
fof(f_68_9,plain,
! [U_543] :
( ! [U_542] :
( ! [U_541] :
( ( ( U_541 = relation_composition(U_543,U_542)
| ( ~ in(ordered_pair(sK105(U_543,U_542,U_541),sK106(U_543,U_542,U_541)),U_541)
& in(ordered_pair(sK107(U_543,U_542,U_541),sK106(U_543,U_542,U_541)),U_542)
& in(ordered_pair(sK105(U_543,U_542,U_541),sK107(U_543,U_542,U_541)),U_543) )
| ( ! [U_537] :
( ~ in(ordered_pair(U_537,sK104(U_543,U_542,U_541)),U_542)
| ~ in(ordered_pair(sK103(U_543,U_542,U_541),U_537),U_543) )
& in(ordered_pair(sK103(U_543,U_542,U_541),sK104(U_543,U_542,U_541)),U_541) ) )
& ( ( ! [U_547,U_545] :
( in(ordered_pair(U_547,U_545),U_541)
| ! [U_534] :
( ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543) ) )
& ! [U_546,U_544] :
( ( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
& in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543) )
| ~ in(ordered_pair(U_546,U_544),U_541) ) )
| U_541 != relation_composition(U_543,U_542) ) )
| ~ relation(U_541) )
| ~ relation(U_542) )
| ~ relation(U_543) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_538,sK107(U_543,U_542,U_541))],[f_68_8]) ).
fof(f_68_10,plain,
( ! [U_542,U_541,U_543] :
( ~ in(ordered_pair(sK105(U_543,U_542,U_541),sK106(U_543,U_542,U_541)),U_541)
| ~ sP146(U_542,U_541,U_543) )
& ! [U_542,U_541,U_543] :
( in(ordered_pair(sK107(U_543,U_542,U_541),sK106(U_543,U_542,U_541)),U_542)
| ~ sP146(U_542,U_541,U_543) )
& ! [U_542,U_541,U_543] :
( in(ordered_pair(sK105(U_543,U_542,U_541),sK107(U_543,U_542,U_541)),U_543)
| ~ sP146(U_542,U_541,U_543) )
& ! [U_542,U_541,U_537,U_543] :
( ~ in(ordered_pair(U_537,sK104(U_543,U_542,U_541)),U_542)
| ~ in(ordered_pair(sK103(U_543,U_542,U_541),U_537),U_543)
| ~ sP145(U_542,U_541,U_537,U_543) )
& ! [U_542,U_541,U_537,U_543] :
( in(ordered_pair(sK103(U_543,U_542,U_541),sK104(U_543,U_542,U_541)),U_541)
| ~ sP145(U_542,U_541,U_537,U_543) )
& ! [U_546,U_542,U_541,U_544,U_543] :
( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
| ~ sP143(U_546,U_542,U_541,U_544,U_543) )
& ! [U_546,U_542,U_541,U_544,U_543] :
( in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543)
| ~ sP143(U_546,U_542,U_541,U_544,U_543) )
& ! [U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547] :
( in(ordered_pair(U_547,U_545),U_541)
| ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543)
| ~ sP144(U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547) )
& ! [U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547] :
( sP143(U_546,U_542,U_541,U_544,U_543)
| ~ in(ordered_pair(U_546,U_544),U_541)
| ~ sP144(U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547) )
& ! [U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547] :
( U_541 = relation_composition(U_543,U_542)
| sP146(U_542,U_541,U_543)
| sP145(U_542,U_541,U_537,U_543)
| ~ sP147(U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547) )
& ! [U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547] :
( sP144(U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547)
| U_541 != relation_composition(U_543,U_542)
| ~ sP147(U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547) )
& ! [U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547] :
( sP147(U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547)
| ~ relation(U_541)
| ~ relation(U_542)
| ~ relation(U_543) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143,sP144,sP145,sP146,sP147])],[f_68_9]) ).
cnf(f_68_11,plain,
( sP147(U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547)
| ~ relation(U_541)
| ~ relation(U_542)
| ~ relation(U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_12,plain,
( sP144(U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547)
| U_541 != relation_composition(U_543,U_542)
| ~ sP147(U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_13,plain,
( U_541 = relation_composition(U_543,U_542)
| sP146(U_542,U_541,U_543)
| sP145(U_542,U_541,U_537,U_543)
| ~ sP147(U_534,U_546,U_542,U_541,U_537,U_544,U_545,U_543,U_547) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_14,plain,
( sP143(U_546,U_542,U_541,U_544,U_543)
| ~ in(ordered_pair(U_546,U_544),U_541)
| ~ sP144(U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_15,plain,
( in(ordered_pair(U_547,U_545),U_541)
| ~ in(ordered_pair(U_534,U_545),U_542)
| ~ in(ordered_pair(U_547,U_534),U_543)
| ~ sP144(U_534,U_546,U_542,U_541,U_544,U_545,U_543,U_547) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_16,plain,
( in(ordered_pair(U_546,sK102(U_543,U_542,U_541,U_546,U_544)),U_543)
| ~ sP143(U_546,U_542,U_541,U_544,U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_17,plain,
( in(ordered_pair(sK102(U_543,U_542,U_541,U_546,U_544),U_544),U_542)
| ~ sP143(U_546,U_542,U_541,U_544,U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_18,plain,
( in(ordered_pair(sK103(U_543,U_542,U_541),sK104(U_543,U_542,U_541)),U_541)
| ~ sP145(U_542,U_541,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_19,plain,
( ~ in(ordered_pair(U_537,sK104(U_543,U_542,U_541)),U_542)
| ~ in(ordered_pair(sK103(U_543,U_542,U_541),U_537),U_543)
| ~ sP145(U_542,U_541,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_20,plain,
( in(ordered_pair(sK105(U_543,U_542,U_541),sK107(U_543,U_542,U_541)),U_543)
| ~ sP146(U_542,U_541,U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_21,plain,
( in(ordered_pair(sK107(U_543,U_542,U_541),sK106(U_543,U_542,U_541)),U_542)
| ~ sP146(U_542,U_541,U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
cnf(f_68_22,plain,
( ~ in(ordered_pair(sK105(U_543,U_542,U_541),sK106(U_543,U_542,U_541)),U_541)
| ~ sP146(U_542,U_541,U_543) ),
inference(clausify,[status(thm)],[f_68_10]) ).
fof(f_69_1,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) ) )
& ( ! [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(fof_nnf,[status(thm)],[d8_relat_2]) ).
fof(f_69_2,plain,
! [U_559] :
( ! [U_558] :
( ( is_transitive_in(U_559,U_558)
| ? [U_557,U_556,U_555] :
( ~ in(ordered_pair(U_557,U_555),U_559)
& in(ordered_pair(U_556,U_555),U_559)
& in(ordered_pair(U_557,U_556),U_559)
& in(U_555,U_558)
& in(U_556,U_558)
& in(U_557,U_558) ) )
& ( ! [U_554,U_553,U_552] :
( in(ordered_pair(U_554,U_552),U_559)
| ~ in(ordered_pair(U_553,U_552),U_559)
| ~ in(ordered_pair(U_554,U_553),U_559)
| ~ in(U_552,U_558)
| ~ in(U_553,U_558)
| ~ in(U_554,U_558) )
| ~ is_transitive_in(U_559,U_558) ) )
| ~ relation(U_559) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_559] :
( ( ! [U_561] :
( is_transitive_in(U_559,U_561)
| ? [U_557,U_556,U_555] :
( ~ in(ordered_pair(U_557,U_555),U_559)
& in(ordered_pair(U_556,U_555),U_559)
& in(ordered_pair(U_557,U_556),U_559)
& in(U_555,U_561)
& in(U_556,U_561)
& in(U_557,U_561) ) )
& ! [U_560] :
( ! [U_554,U_553,U_552] :
( in(ordered_pair(U_554,U_552),U_559)
| ~ in(ordered_pair(U_553,U_552),U_559)
| ~ in(ordered_pair(U_554,U_553),U_559)
| ~ in(U_552,U_560)
| ~ in(U_553,U_560)
| ~ in(U_554,U_560) )
| ~ is_transitive_in(U_559,U_560) ) )
| ~ relation(U_559) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
! [U_559] :
( ( ! [U_561] :
( is_transitive_in(U_559,U_561)
| ? [U_556,U_555] :
( ~ in(ordered_pair(sK108(U_559,U_561),U_555),U_559)
& in(ordered_pair(U_556,U_555),U_559)
& in(ordered_pair(sK108(U_559,U_561),U_556),U_559)
& in(U_555,U_561)
& in(U_556,U_561)
& in(sK108(U_559,U_561),U_561) ) )
& ! [U_560] :
( ! [U_554,U_553,U_552] :
( in(ordered_pair(U_554,U_552),U_559)
| ~ in(ordered_pair(U_553,U_552),U_559)
| ~ in(ordered_pair(U_554,U_553),U_559)
| ~ in(U_552,U_560)
| ~ in(U_553,U_560)
| ~ in(U_554,U_560) )
| ~ is_transitive_in(U_559,U_560) ) )
| ~ relation(U_559) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_557,sK108(U_559,U_561))],[f_69_3]) ).
fof(f_69_5,plain,
! [U_559] :
( ( ! [U_561] :
( is_transitive_in(U_559,U_561)
| ? [U_555] :
( ~ in(ordered_pair(sK108(U_559,U_561),U_555),U_559)
& in(ordered_pair(sK109(U_559,U_561),U_555),U_559)
& in(ordered_pair(sK108(U_559,U_561),sK109(U_559,U_561)),U_559)
& in(U_555,U_561)
& in(sK109(U_559,U_561),U_561)
& in(sK108(U_559,U_561),U_561) ) )
& ! [U_560] :
( ! [U_554,U_553,U_552] :
( in(ordered_pair(U_554,U_552),U_559)
| ~ in(ordered_pair(U_553,U_552),U_559)
| ~ in(ordered_pair(U_554,U_553),U_559)
| ~ in(U_552,U_560)
| ~ in(U_553,U_560)
| ~ in(U_554,U_560) )
| ~ is_transitive_in(U_559,U_560) ) )
| ~ relation(U_559) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_556,sK109(U_559,U_561))],[f_69_4]) ).
fof(f_69_6,plain,
! [U_559] :
( ( ! [U_561] :
( is_transitive_in(U_559,U_561)
| ( ~ in(ordered_pair(sK108(U_559,U_561),sK110(U_559,U_561)),U_559)
& in(ordered_pair(sK109(U_559,U_561),sK110(U_559,U_561)),U_559)
& in(ordered_pair(sK108(U_559,U_561),sK109(U_559,U_561)),U_559)
& in(sK110(U_559,U_561),U_561)
& in(sK109(U_559,U_561),U_561)
& in(sK108(U_559,U_561),U_561) ) )
& ! [U_560] :
( ! [U_554,U_553,U_552] :
( in(ordered_pair(U_554,U_552),U_559)
| ~ in(ordered_pair(U_553,U_552),U_559)
| ~ in(ordered_pair(U_554,U_553),U_559)
| ~ in(U_552,U_560)
| ~ in(U_553,U_560)
| ~ in(U_554,U_560) )
| ~ is_transitive_in(U_559,U_560) ) )
| ~ relation(U_559) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_555,sK110(U_559,U_561))],[f_69_5]) ).
fof(f_69_7,plain,
( ! [U_561,U_559] :
( ~ in(ordered_pair(sK108(U_559,U_561),sK110(U_559,U_561)),U_559)
| ~ sP148(U_561,U_559) )
& ! [U_561,U_559] :
( in(ordered_pair(sK109(U_559,U_561),sK110(U_559,U_561)),U_559)
| ~ sP148(U_561,U_559) )
& ! [U_561,U_559] :
( in(ordered_pair(sK108(U_559,U_561),sK109(U_559,U_561)),U_559)
| ~ sP148(U_561,U_559) )
& ! [U_561,U_559] :
( in(sK110(U_559,U_561),U_561)
| ~ sP148(U_561,U_559) )
& ! [U_561,U_559] :
( in(sK109(U_559,U_561),U_561)
| ~ sP148(U_561,U_559) )
& ! [U_561,U_559] :
( in(sK108(U_559,U_561),U_561)
| ~ sP148(U_561,U_559) )
& ! [U_552,U_560,U_554,U_561,U_553,U_559] :
( is_transitive_in(U_559,U_561)
| sP148(U_561,U_559)
| ~ sP149(U_552,U_560,U_554,U_561,U_553,U_559) )
& ! [U_552,U_560,U_554,U_561,U_553,U_559] :
( in(ordered_pair(U_554,U_552),U_559)
| ~ in(ordered_pair(U_553,U_552),U_559)
| ~ in(ordered_pair(U_554,U_553),U_559)
| ~ in(U_552,U_560)
| ~ in(U_553,U_560)
| ~ in(U_554,U_560)
| ~ is_transitive_in(U_559,U_560)
| ~ sP149(U_552,U_560,U_554,U_561,U_553,U_559) )
& ! [U_552,U_560,U_554,U_561,U_553,U_559] :
( sP149(U_552,U_560,U_554,U_561,U_553,U_559)
| ~ relation(U_559) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148,sP149])],[f_69_6]) ).
cnf(f_69_8,plain,
( sP149(U_552,U_560,U_554,U_561,U_553,U_559)
| ~ relation(U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_9,plain,
( in(ordered_pair(U_554,U_552),U_559)
| ~ in(ordered_pair(U_553,U_552),U_559)
| ~ in(ordered_pair(U_554,U_553),U_559)
| ~ in(U_552,U_560)
| ~ in(U_553,U_560)
| ~ in(U_554,U_560)
| ~ is_transitive_in(U_559,U_560)
| ~ sP149(U_552,U_560,U_554,U_561,U_553,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_10,plain,
( is_transitive_in(U_559,U_561)
| sP148(U_561,U_559)
| ~ sP149(U_552,U_560,U_554,U_561,U_553,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_11,plain,
( in(sK108(U_559,U_561),U_561)
| ~ sP148(U_561,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_12,plain,
( in(sK109(U_559,U_561),U_561)
| ~ sP148(U_561,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_13,plain,
( in(sK110(U_559,U_561),U_561)
| ~ sP148(U_561,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_14,plain,
( in(ordered_pair(sK108(U_559,U_561),sK109(U_559,U_561)),U_559)
| ~ sP148(U_561,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_15,plain,
( in(ordered_pair(sK109(U_559,U_561),sK110(U_559,U_561)),U_559)
| ~ sP148(U_561,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
cnf(f_69_16,plain,
( ~ in(ordered_pair(sK108(U_559,U_561),sK110(U_559,U_561)),U_559)
| ~ sP148(U_561,U_559) ),
inference(clausify,[status(thm)],[f_69_7]) ).
fof(f_70_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = complements_of_subsets(A,B)
| ? [D] :
( ( ( ~ in(D,C)
& in(subset_complement(A,D),B) )
| ( ~ in(subset_complement(A,D),B)
& in(D,C) ) )
& element(D,powerset(A)) ) )
& ( ! [D] :
( ( ( in(D,C)
| ~ in(subset_complement(A,D),B) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[d8_setfam_1]) ).
fof(f_70_2,plain,
! [U_566,U_565] :
( ! [U_564] :
( ( ( U_564 = complements_of_subsets(U_566,U_565)
| ? [U_563] :
( ( ( ~ in(U_563,U_564)
& in(subset_complement(U_566,U_563),U_565) )
| ( ~ in(subset_complement(U_566,U_563),U_565)
& in(U_563,U_564) ) )
& element(U_563,powerset(U_566)) ) )
& ( ! [U_562] :
( ( ( in(U_562,U_564)
| ~ in(subset_complement(U_566,U_562),U_565) )
& ( in(subset_complement(U_566,U_562),U_565)
| ~ in(U_562,U_564) ) )
| ~ element(U_562,powerset(U_566)) )
| U_564 != complements_of_subsets(U_566,U_565) ) )
| ~ element(U_564,powerset(powerset(U_566))) )
| ~ element(U_565,powerset(powerset(U_566))) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_566,U_565] :
( ! [U_564] :
( ( ( U_564 = complements_of_subsets(U_566,U_565)
| ( ( ( ~ in(sK111(U_566,U_565,U_564),U_564)
& in(subset_complement(U_566,sK111(U_566,U_565,U_564)),U_565) )
| ( ~ in(subset_complement(U_566,sK111(U_566,U_565,U_564)),U_565)
& in(sK111(U_566,U_565,U_564),U_564) ) )
& element(sK111(U_566,U_565,U_564),powerset(U_566)) ) )
& ( ! [U_562] :
( ( ( in(U_562,U_564)
| ~ in(subset_complement(U_566,U_562),U_565) )
& ( in(subset_complement(U_566,U_562),U_565)
| ~ in(U_562,U_564) ) )
| ~ element(U_562,powerset(U_566)) )
| U_564 != complements_of_subsets(U_566,U_565) ) )
| ~ element(U_564,powerset(powerset(U_566))) )
| ~ element(U_565,powerset(powerset(U_566))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_563,sK111(U_566,U_565,U_564))],[f_70_2]) ).
fof(f_70_4,plain,
( ! [U_565,U_564,U_566] :
( ~ in(sK111(U_566,U_565,U_564),U_564)
| ~ sP152(U_565,U_564,U_566) )
& ! [U_565,U_564,U_566] :
( in(subset_complement(U_566,sK111(U_566,U_565,U_564)),U_565)
| ~ sP152(U_565,U_564,U_566) )
& ! [U_565,U_564,U_566] :
( ~ in(subset_complement(U_566,sK111(U_566,U_565,U_564)),U_565)
| ~ sP151(U_565,U_564,U_566) )
& ! [U_565,U_564,U_566] :
( in(sK111(U_566,U_565,U_564),U_564)
| ~ sP151(U_565,U_564,U_566) )
& ! [U_565,U_564,U_566] :
( sP152(U_565,U_564,U_566)
| sP151(U_565,U_564,U_566)
| ~ sP153(U_565,U_564,U_566) )
& ! [U_565,U_564,U_566] :
( element(sK111(U_566,U_565,U_564),powerset(U_566))
| ~ sP153(U_565,U_564,U_566) )
& ! [U_565,U_562,U_564,U_566] :
( in(U_562,U_564)
| ~ in(subset_complement(U_566,U_562),U_565)
| ~ sP150(U_565,U_562,U_564,U_566) )
& ! [U_565,U_562,U_564,U_566] :
( in(subset_complement(U_566,U_562),U_565)
| ~ in(U_562,U_564)
| ~ sP150(U_565,U_562,U_564,U_566) )
& ! [U_565,U_562,U_564,U_566] :
( U_564 = complements_of_subsets(U_566,U_565)
| sP153(U_565,U_564,U_566)
| ~ sP154(U_565,U_562,U_564,U_566) )
& ! [U_565,U_562,U_564,U_566] :
( sP150(U_565,U_562,U_564,U_566)
| ~ element(U_562,powerset(U_566))
| U_564 != complements_of_subsets(U_566,U_565)
| ~ sP154(U_565,U_562,U_564,U_566) )
& ! [U_565,U_562,U_564,U_566] :
( sP154(U_565,U_562,U_564,U_566)
| ~ element(U_564,powerset(powerset(U_566)))
| ~ element(U_565,powerset(powerset(U_566))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150,sP151,sP152,sP153,sP154])],[f_70_3]) ).
cnf(f_70_5,plain,
( sP154(U_565,U_562,U_564,U_566)
| ~ element(U_564,powerset(powerset(U_566)))
| ~ element(U_565,powerset(powerset(U_566))) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_6,plain,
( sP150(U_565,U_562,U_564,U_566)
| ~ element(U_562,powerset(U_566))
| U_564 != complements_of_subsets(U_566,U_565)
| ~ sP154(U_565,U_562,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_7,plain,
( U_564 = complements_of_subsets(U_566,U_565)
| sP153(U_565,U_564,U_566)
| ~ sP154(U_565,U_562,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_8,plain,
( in(subset_complement(U_566,U_562),U_565)
| ~ in(U_562,U_564)
| ~ sP150(U_565,U_562,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_9,plain,
( in(U_562,U_564)
| ~ in(subset_complement(U_566,U_562),U_565)
| ~ sP150(U_565,U_562,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_10,plain,
( element(sK111(U_566,U_565,U_564),powerset(U_566))
| ~ sP153(U_565,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_11,plain,
( sP152(U_565,U_564,U_566)
| sP151(U_565,U_564,U_566)
| ~ sP153(U_565,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_12,plain,
( in(sK111(U_566,U_565,U_564),U_564)
| ~ sP151(U_565,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_13,plain,
( ~ in(subset_complement(U_566,sK111(U_566,U_565,U_564)),U_565)
| ~ sP151(U_565,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_14,plain,
( in(subset_complement(U_566,sK111(U_566,U_565,U_564)),U_565)
| ~ sP152(U_565,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_15,plain,
( ~ in(sK111(U_566,U_565,U_564),U_564)
| ~ sP152(U_565,U_564,U_566) ),
inference(clausify,[status(thm)],[f_70_4]) ).
fof(f_71_1,plain,
! [A,B] :
( ( proper_subset(A,B)
| A = B
| ~ subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d8_xboole_0]) ).
fof(f_71_2,plain,
! [U_568,U_567] :
( ( proper_subset(U_568,U_567)
| U_568 = U_567
| ~ subset(U_568,U_567) )
& ( ( U_568 != U_567
& subset(U_568,U_567) )
| ~ proper_subset(U_568,U_567) ) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
( ! [U_572,U_570] :
( proper_subset(U_572,U_570)
| U_572 = U_570
| ~ subset(U_572,U_570) )
& ! [U_571,U_569] :
( ( U_571 != U_569
& subset(U_571,U_569) )
| ~ proper_subset(U_571,U_569) ) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
( ! [U_571,U_569] :
( U_571 != U_569
| ~ sP155(U_571,U_569) )
& ! [U_571,U_569] :
( subset(U_571,U_569)
| ~ sP155(U_571,U_569) )
& ! [U_572,U_570] :
( proper_subset(U_572,U_570)
| U_572 = U_570
| ~ subset(U_572,U_570) )
& ! [U_571,U_569] :
( sP155(U_571,U_569)
| ~ proper_subset(U_571,U_569) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_71_3]) ).
cnf(f_71_5,plain,
( sP155(U_571,U_569)
| ~ proper_subset(U_571,U_569) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_6,plain,
( proper_subset(U_572,U_570)
| U_572 = U_570
| ~ subset(U_572,U_570) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_7,plain,
( subset(U_571,U_569)
| ~ sP155(U_571,U_569) ),
inference(clausify,[status(thm)],[f_71_4]) ).
cnf(f_71_8,plain,
( U_571 != U_569
| ~ sP155(U_571,U_569) ),
inference(clausify,[status(thm)],[f_71_4]) ).
fof(f_72_1,plain,
! [A] :
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_funct_1]) ).
fof(f_72_2,plain,
! [U_573] :
( function_inverse(U_573) = relation_inverse(U_573)
| ~ one_to_one(U_573)
| ~ function(U_573)
| ~ relation(U_573) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_573] :
( function_inverse(U_573) = relation_inverse(U_573)
| ~ one_to_one(U_573)
| ~ function(U_573)
| ~ relation(U_573) ),
inference(definitional_conversion,[status(esa)],[f_72_2]) ).
cnf(f_72_4,plain,
( function_inverse(U_573) = relation_inverse(U_573)
| ~ one_to_one(U_573)
| ~ function(U_573)
| ~ relation(U_573) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
! [A] :
( ( ( reflexive(A)
| ~ is_reflexive_in(A,relation_field(A)) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d9_relat_2]) ).
fof(f_73_2,plain,
! [U_574] :
( ( ( reflexive(U_574)
| ~ is_reflexive_in(U_574,relation_field(U_574)) )
& ( is_reflexive_in(U_574,relation_field(U_574))
| ~ reflexive(U_574) ) )
| ~ relation(U_574) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_574] :
( reflexive(U_574)
| ~ is_reflexive_in(U_574,relation_field(U_574))
| ~ sP156(U_574) )
& ! [U_574] :
( is_reflexive_in(U_574,relation_field(U_574))
| ~ reflexive(U_574)
| ~ sP156(U_574) )
& ! [U_574] :
( sP156(U_574)
| ~ relation(U_574) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156])],[f_73_2]) ).
cnf(f_73_4,plain,
( sP156(U_574)
| ~ relation(U_574) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_5,plain,
( is_reflexive_in(U_574,relation_field(U_574))
| ~ reflexive(U_574)
| ~ sP156(U_574) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_6,plain,
( reflexive(U_574)
| ~ is_reflexive_in(U_574,relation_field(U_574))
| ~ sP156(U_574) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
fof(f_74_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_74_1]) ).
cnf(f_74_3,plain,
$true,
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
fof(f_75_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_75_1]) ).
cnf(f_75_3,plain,
$true,
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
fof(f_76_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_76_1]) ).
cnf(f_76_3,plain,
$true,
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
fof(f_77_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_77_1]) ).
cnf(f_77_3,plain,
$true,
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_78_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_78_1]) ).
cnf(f_78_3,plain,
$true,
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
fof(f_79_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_79_1]) ).
cnf(f_79_3,plain,
$true,
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_80_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_80_1]) ).
cnf(f_80_3,plain,
$true,
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
fof(f_81_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_81_1]) ).
cnf(f_81_3,plain,
$true,
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_82_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_82_1]) ).
cnf(f_82_3,plain,
$true,
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_83_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_83_1]) ).
cnf(f_83_3,plain,
$true,
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_84_2,plain,
! [U_575] :
( ( function(function_inverse(U_575))
& relation(function_inverse(U_575)) )
| ~ function(U_575)
| ~ relation(U_575) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_575] :
( function(function_inverse(U_575))
| ~ sP157(U_575) )
& ! [U_575] :
( relation(function_inverse(U_575))
| ~ sP157(U_575) )
& ! [U_575] :
( sP157(U_575)
| ~ function(U_575)
| ~ relation(U_575) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157])],[f_84_2]) ).
cnf(f_84_4,plain,
( sP157(U_575)
| ~ function(U_575)
| ~ relation(U_575) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_5,plain,
( relation(function_inverse(U_575))
| ~ sP157(U_575) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_6,plain,
( function(function_inverse(U_575))
| ~ sP157(U_575) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
fof(f_85_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_85_1]) ).
cnf(f_85_3,plain,
$true,
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_86_2,plain,
! [U_576] : element(cast_to_subset(U_576),powerset(U_576)),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_576] : element(cast_to_subset(U_576),powerset(U_576)),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
element(cast_to_subset(U_576),powerset(U_576)),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_87_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_87_1]) ).
cnf(f_87_3,plain,
$true,
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_88_2,plain,
! [U_578,U_577] :
( relation(relation_restriction(U_578,U_577))
| ~ relation(U_578) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_578] :
( ! [U_577] : relation(relation_restriction(U_578,U_577))
| ~ relation(U_578) ),
inference(miniscope,[status(thm)],[f_88_2]) ).
fof(f_88_4,plain,
! [U_578,U_577] :
( relation(relation_restriction(U_578,U_577))
| ~ relation(U_578) ),
inference(definitional_conversion,[status(esa)],[f_88_3]) ).
cnf(f_88_5,plain,
( relation(relation_restriction(U_578,U_577))
| ~ relation(U_578) ),
inference(clausify,[status(thm)],[f_88_4]) ).
fof(f_89_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_89_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_89_1]) ).
cnf(f_89_3,plain,
$true,
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_90_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_90_1]) ).
cnf(f_90_3,plain,
$true,
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_91_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_91_1]) ).
cnf(f_91_3,plain,
$true,
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_92_2,plain,
! [U_580,U_579] :
( element(subset_complement(U_580,U_579),powerset(U_580))
| ~ element(U_579,powerset(U_580)) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_579,U_580] :
( element(subset_complement(U_580,U_579),powerset(U_580))
| ~ element(U_579,powerset(U_580)) ),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
( element(subset_complement(U_580,U_579),powerset(U_580))
| ~ element(U_579,powerset(U_580)) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_93_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_93_1]) ).
cnf(f_93_3,plain,
$true,
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_94_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_94_1]) ).
cnf(f_94_3,plain,
$true,
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_95_2,plain,
! [U_581] :
( relation(relation_inverse(U_581))
| ~ relation(U_581) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_581] :
( relation(relation_inverse(U_581))
| ~ relation(U_581) ),
inference(definitional_conversion,[status(esa)],[f_95_2]) ).
cnf(f_95_4,plain,
( relation(relation_inverse(U_581))
| ~ relation(U_581) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_96_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_96_1]) ).
cnf(f_96_3,plain,
$true,
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_97_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_97_1]) ).
cnf(f_97_3,plain,
$true,
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_98_2,plain,
! [U_583,U_582] :
( relation(relation_composition(U_583,U_582))
| ~ relation(U_582)
| ~ relation(U_583) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_582,U_583] :
( relation(relation_composition(U_583,U_582))
| ~ relation(U_582)
| ~ relation(U_583) ),
inference(definitional_conversion,[status(esa)],[f_98_2]) ).
cnf(f_98_4,plain,
( relation(relation_composition(U_583,U_582))
| ~ relation(U_582)
| ~ relation(U_583) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
! [A,B] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k5_setfam_1]) ).
fof(f_99_2,plain,
! [U_585,U_584] :
( element(union_of_subsets(U_585,U_584),powerset(U_585))
| ~ element(U_584,powerset(powerset(U_585))) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_585,U_584] :
( element(union_of_subsets(U_585,U_584),powerset(U_585))
| ~ element(U_584,powerset(powerset(U_585))) ),
inference(definitional_conversion,[status(esa)],[f_99_2]) ).
cnf(f_99_4,plain,
( element(union_of_subsets(U_585,U_584),powerset(U_585))
| ~ element(U_584,powerset(powerset(U_585))) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_100_2,plain,
! [U_586] : relation(identity_relation(U_586)),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_586] : relation(identity_relation(U_586)),
inference(definitional_conversion,[status(esa)],[f_100_2]) ).
cnf(f_100_4,plain,
relation(identity_relation(U_586)),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [A,B] :
( element(meet_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k6_setfam_1]) ).
fof(f_101_2,plain,
! [U_588,U_587] :
( element(meet_of_subsets(U_588,U_587),powerset(U_588))
| ~ element(U_587,powerset(powerset(U_588))) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_587,U_588] :
( element(meet_of_subsets(U_588,U_587),powerset(U_588))
| ~ element(U_587,powerset(powerset(U_588))) ),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
( element(meet_of_subsets(U_588,U_587),powerset(U_588))
| ~ element(U_587,powerset(powerset(U_588))) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_1,plain,
! [A,B,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k6_subset_1]) ).
fof(f_102_2,plain,
! [U_591,U_590,U_589] :
( element(subset_difference(U_591,U_590,U_589),powerset(U_591))
| ~ element(U_589,powerset(U_591))
| ~ element(U_590,powerset(U_591)) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_590,U_589,U_591] :
( element(subset_difference(U_591,U_590,U_589),powerset(U_591))
| ~ element(U_589,powerset(U_591))
| ~ element(U_590,powerset(U_591)) ),
inference(definitional_conversion,[status(esa)],[f_102_2]) ).
cnf(f_102_4,plain,
( element(subset_difference(U_591,U_590,U_589),powerset(U_591))
| ~ element(U_589,powerset(U_591))
| ~ element(U_590,powerset(U_591)) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_103_2,plain,
! [U_593,U_592] :
( relation(relation_dom_restriction(U_593,U_592))
| ~ relation(U_593) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_593] :
( ! [U_592] : relation(relation_dom_restriction(U_593,U_592))
| ~ relation(U_593) ),
inference(miniscope,[status(thm)],[f_103_2]) ).
fof(f_103_4,plain,
! [U_593,U_592] :
( relation(relation_dom_restriction(U_593,U_592))
| ~ relation(U_593) ),
inference(definitional_conversion,[status(esa)],[f_103_3]) ).
cnf(f_103_5,plain,
( relation(relation_dom_restriction(U_593,U_592))
| ~ relation(U_593) ),
inference(clausify,[status(thm)],[f_103_4]) ).
fof(f_104_1,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k7_setfam_1]) ).
fof(f_104_2,plain,
! [U_595,U_594] :
( element(complements_of_subsets(U_595,U_594),powerset(powerset(U_595)))
| ~ element(U_594,powerset(powerset(U_595))) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_594,U_595] :
( element(complements_of_subsets(U_595,U_594),powerset(powerset(U_595)))
| ~ element(U_594,powerset(powerset(U_595))) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( element(complements_of_subsets(U_595,U_594),powerset(powerset(U_595)))
| ~ element(U_594,powerset(powerset(U_595))) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_105_2,plain,
! [U_597,U_596] :
( relation(relation_rng_restriction(U_597,U_596))
| ~ relation(U_596) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_596,U_597] :
( relation(relation_rng_restriction(U_597,U_596))
| ~ relation(U_596) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( relation(relation_rng_restriction(U_597,U_596))
| ~ relation(U_596) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
fof(f_106_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_106_1]) ).
cnf(f_106_3,plain,
$true,
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_107_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_107_1]) ).
cnf(f_107_3,plain,
$true,
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_108_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_108_1]) ).
cnf(f_108_3,plain,
$true,
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_109_2,plain,
! [U_600,U_599,U_598] :
( element(U_598,powerset(cartesian_product2(U_600,U_599)))
| ~ relation_of2_as_subset(U_598,U_600,U_599) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_598,U_599,U_600] :
( element(U_598,powerset(cartesian_product2(U_600,U_599)))
| ~ relation_of2_as_subset(U_598,U_600,U_599) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( element(U_598,powerset(cartesian_product2(U_600,U_599)))
| ~ relation_of2_as_subset(U_598,U_600,U_599) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_110_2,plain,
! [U_603,U_602] :
? [U_601] : relation_of2(U_601,U_603,U_602),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_603,U_602] : relation_of2(sK112(U_603,U_602),U_603,U_602),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_601,sK112(U_603,U_602))],[f_110_2]) ).
fof(f_110_4,plain,
! [U_602,U_603] : relation_of2(sK112(U_603,U_602),U_603,U_602),
inference(definitional_conversion,[status(esa)],[f_110_3]) ).
cnf(f_110_5,plain,
relation_of2(sK112(U_603,U_602),U_603,U_602),
inference(clausify,[status(thm)],[f_110_4]) ).
fof(f_111_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_111_2,plain,
! [U_605] :
? [U_604] : element(U_604,U_605),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_605] : element(sK113(U_605),U_605),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_604,sK113(U_605))],[f_111_2]) ).
fof(f_111_4,plain,
! [U_605] : element(sK113(U_605),U_605),
inference(definitional_conversion,[status(esa)],[f_111_3]) ).
cnf(f_111_5,plain,
element(sK113(U_605),U_605),
inference(clausify,[status(thm)],[f_111_4]) ).
fof(f_112_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_112_2,plain,
! [U_608,U_607] :
? [U_606] : relation_of2_as_subset(U_606,U_608,U_607),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_608,U_607] : relation_of2_as_subset(sK114(U_608,U_607),U_608,U_607),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_606,sK114(U_608,U_607))],[f_112_2]) ).
fof(f_112_4,plain,
! [U_607,U_608] : relation_of2_as_subset(sK114(U_608,U_607),U_608,U_607),
inference(definitional_conversion,[status(esa)],[f_112_3]) ).
cnf(f_112_5,plain,
relation_of2_as_subset(sK114(U_608,U_607),U_608,U_607),
inference(clausify,[status(thm)],[f_112_4]) ).
fof(f_113_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_113_2,plain,
! [U_610,U_609] :
( ( relation(relation_composition(U_609,U_610))
& empty(relation_composition(U_609,U_610)) )
| ~ relation(U_609)
| ~ empty(U_610) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_609,U_610] :
( relation(relation_composition(U_609,U_610))
| ~ sP158(U_609,U_610) )
& ! [U_609,U_610] :
( empty(relation_composition(U_609,U_610))
| ~ sP158(U_609,U_610) )
& ! [U_609,U_610] :
( sP158(U_609,U_610)
| ~ relation(U_609)
| ~ empty(U_610) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158])],[f_113_2]) ).
cnf(f_113_4,plain,
( sP158(U_609,U_610)
| ~ relation(U_609)
| ~ empty(U_610) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
( empty(relation_composition(U_609,U_610))
| ~ sP158(U_609,U_610) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_6,plain,
( relation(relation_composition(U_609,U_610))
| ~ sP158(U_609,U_610) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_114_2,plain,
! [U_611] :
( ( relation(relation_inverse(U_611))
& empty(relation_inverse(U_611)) )
| ~ empty(U_611) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( ! [U_611] :
( relation(relation_inverse(U_611))
| ~ sP159(U_611) )
& ! [U_611] :
( empty(relation_inverse(U_611))
| ~ sP159(U_611) )
& ! [U_611] :
( sP159(U_611)
| ~ empty(U_611) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_114_2]) ).
cnf(f_114_4,plain,
( sP159(U_611)
| ~ empty(U_611) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_5,plain,
( empty(relation_inverse(U_611))
| ~ sP159(U_611) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_6,plain,
( relation(relation_inverse(U_611))
| ~ sP159(U_611) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_115_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_115_1]) ).
cnf(f_115_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_115_2]) ).
cnf(f_115_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_115_2]) ).
cnf(f_115_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [A,B] :
( ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ relation_empty_yielding(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc13_relat_1]) ).
fof(f_116_2,plain,
! [U_613,U_612] :
( ( relation_empty_yielding(relation_dom_restriction(U_613,U_612))
& relation(relation_dom_restriction(U_613,U_612)) )
| ~ relation_empty_yielding(U_613)
| ~ relation(U_613) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_613] :
( ( ! [U_615] : relation_empty_yielding(relation_dom_restriction(U_613,U_615))
& ! [U_614] : relation(relation_dom_restriction(U_613,U_614)) )
| ~ relation_empty_yielding(U_613)
| ~ relation(U_613) ),
inference(miniscope,[status(thm)],[f_116_2]) ).
fof(f_116_4,plain,
( ! [U_613,U_615,U_614] :
( relation_empty_yielding(relation_dom_restriction(U_613,U_615))
| ~ sP160(U_613,U_615,U_614) )
& ! [U_613,U_615,U_614] :
( relation(relation_dom_restriction(U_613,U_614))
| ~ sP160(U_613,U_615,U_614) )
& ! [U_613,U_615,U_614] :
( sP160(U_613,U_615,U_614)
| ~ relation_empty_yielding(U_613)
| ~ relation(U_613) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_116_3]) ).
cnf(f_116_5,plain,
( sP160(U_613,U_615,U_614)
| ~ relation_empty_yielding(U_613)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_6,plain,
( relation(relation_dom_restriction(U_613,U_614))
| ~ sP160(U_613,U_615,U_614) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_7,plain,
( relation_empty_yielding(relation_dom_restriction(U_613,U_615))
| ~ sP160(U_613,U_615,U_614) ),
inference(clausify,[status(thm)],[f_116_4]) ).
fof(f_117_1,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_funct_1]) ).
fof(f_117_2,plain,
! [U_617,U_616] :
( ( function(relation_composition(U_617,U_616))
& relation(relation_composition(U_617,U_616)) )
| ~ function(U_616)
| ~ relation(U_616)
| ~ function(U_617)
| ~ relation(U_617) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_617,U_616] :
( function(relation_composition(U_617,U_616))
| ~ sP161(U_617,U_616) )
& ! [U_617,U_616] :
( relation(relation_composition(U_617,U_616))
| ~ sP161(U_617,U_616) )
& ! [U_617,U_616] :
( sP161(U_617,U_616)
| ~ function(U_616)
| ~ relation(U_616)
| ~ function(U_617)
| ~ relation(U_617) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_117_2]) ).
cnf(f_117_4,plain,
( sP161(U_617,U_616)
| ~ function(U_616)
| ~ relation(U_616)
| ~ function(U_617)
| ~ relation(U_617) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_5,plain,
( relation(relation_composition(U_617,U_616))
| ~ sP161(U_617,U_616) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_6,plain,
( function(relation_composition(U_617,U_616))
| ~ sP161(U_617,U_616) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_118_2,plain,
! [U_618] : ~ empty(succ(U_618)),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_618] : ~ empty(succ(U_618)),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
~ empty(succ(U_618)),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_119_2,plain,
! [U_620,U_619] :
( relation(set_intersection2(U_620,U_619))
| ~ relation(U_619)
| ~ relation(U_620) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_619,U_620] :
( relation(set_intersection2(U_620,U_619))
| ~ relation(U_619)
| ~ relation(U_620) ),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
( relation(set_intersection2(U_620,U_619))
| ~ relation(U_619)
| ~ relation(U_620) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_120_2,plain,
! [U_621] : ~ empty(powerset(U_621)),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_621] : ~ empty(powerset(U_621)),
inference(definitional_conversion,[status(esa)],[f_120_2]) ).
cnf(f_120_4,plain,
~ empty(powerset(U_621)),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_121_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_121_1]) ).
cnf(f_121_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_122_2,plain,
! [U_623,U_622] : ~ empty(ordered_pair(U_623,U_622)),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_622,U_623] : ~ empty(ordered_pair(U_623,U_622)),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
~ empty(ordered_pair(U_623,U_622)),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_123_2,plain,
! [U_624] :
( function(identity_relation(U_624))
& relation(identity_relation(U_624)) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_626] : function(identity_relation(U_626))
& ! [U_625] : relation(identity_relation(U_625)) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
fof(f_123_4,plain,
( ! [U_626] : function(identity_relation(U_626))
& ! [U_625] : relation(identity_relation(U_625)) ),
inference(definitional_conversion,[status(esa)],[f_123_3]) ).
cnf(f_123_5,plain,
relation(identity_relation(U_625)),
inference(clausify,[status(thm)],[f_123_4]) ).
cnf(f_123_6,plain,
function(identity_relation(U_626)),
inference(clausify,[status(thm)],[f_123_4]) ).
fof(f_124_1,plain,
( 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) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
fof(f_124_2,plain,
( 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) ),
inference(definitional_conversion,[status(esa)],[f_124_1]) ).
cnf(f_124_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
cnf(f_124_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_125_2,plain,
! [U_628,U_627] :
( relation(set_union2(U_628,U_627))
| ~ relation(U_627)
| ~ relation(U_628) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_627,U_628] :
( relation(set_union2(U_628,U_627))
| ~ relation(U_627)
| ~ relation(U_628) ),
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
( relation(set_union2(U_628,U_627))
| ~ relation(U_627)
| ~ relation(U_628) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_126_2,plain,
! [U_629] : ~ empty(singleton(U_629)),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_629] : ~ empty(singleton(U_629)),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
~ empty(singleton(U_629)),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_127_2,plain,
! [U_631,U_630] :
( ~ empty(set_union2(U_631,U_630))
| empty(U_631) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_631] :
( ! [U_630] : ~ empty(set_union2(U_631,U_630))
| empty(U_631) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
fof(f_127_4,plain,
! [U_630,U_631] :
( ~ empty(set_union2(U_631,U_630))
| empty(U_631) ),
inference(definitional_conversion,[status(esa)],[f_127_3]) ).
cnf(f_127_5,plain,
( ~ empty(set_union2(U_631,U_630))
| empty(U_631) ),
inference(clausify,[status(thm)],[f_127_4]) ).
fof(f_128_1,plain,
! [A] :
( ( function(relation_inverse(A))
& relation(relation_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_funct_1]) ).
fof(f_128_2,plain,
! [U_632] :
( ( function(relation_inverse(U_632))
& relation(relation_inverse(U_632)) )
| ~ one_to_one(U_632)
| ~ function(U_632)
| ~ relation(U_632) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_632] :
( function(relation_inverse(U_632))
| ~ sP162(U_632) )
& ! [U_632] :
( relation(relation_inverse(U_632))
| ~ sP162(U_632) )
& ! [U_632] :
( sP162(U_632)
| ~ one_to_one(U_632)
| ~ function(U_632)
| ~ relation(U_632) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_128_2]) ).
cnf(f_128_4,plain,
( sP162(U_632)
| ~ one_to_one(U_632)
| ~ function(U_632)
| ~ relation(U_632) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( relation(relation_inverse(U_632))
| ~ sP162(U_632) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_6,plain,
( function(relation_inverse(U_632))
| ~ sP162(U_632) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc3_ordinal1]) ).
fof(f_129_2,plain,
! [U_633] :
( ( ordinal(succ(U_633))
& epsilon_connected(succ(U_633))
& epsilon_transitive(succ(U_633))
& ~ empty(succ(U_633)) )
| ~ ordinal(U_633) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_633] :
( ordinal(succ(U_633))
| ~ sP163(U_633) )
& ! [U_633] :
( epsilon_connected(succ(U_633))
| ~ sP163(U_633) )
& ! [U_633] :
( epsilon_transitive(succ(U_633))
| ~ sP163(U_633) )
& ! [U_633] :
( ~ empty(succ(U_633))
| ~ sP163(U_633) )
& ! [U_633] :
( sP163(U_633)
| ~ ordinal(U_633) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_129_2]) ).
cnf(f_129_4,plain,
( sP163(U_633)
| ~ ordinal(U_633) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_5,plain,
( ~ empty(succ(U_633))
| ~ sP163(U_633) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_6,plain,
( epsilon_transitive(succ(U_633))
| ~ sP163(U_633) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_7,plain,
( epsilon_connected(succ(U_633))
| ~ sP163(U_633) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_8,plain,
( ordinal(succ(U_633))
| ~ sP163(U_633) ),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_130_2,plain,
! [U_635,U_634] :
( relation(set_difference(U_635,U_634))
| ~ relation(U_634)
| ~ relation(U_635) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_635,U_634] :
( relation(set_difference(U_635,U_634))
| ~ relation(U_634)
| ~ relation(U_635) ),
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
( relation(set_difference(U_635,U_634))
| ~ relation(U_634)
| ~ relation(U_635) ),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_131_2,plain,
! [U_637,U_636] : ~ empty(unordered_pair(U_637,U_636)),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_636,U_637] : ~ empty(unordered_pair(U_637,U_636)),
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
~ empty(unordered_pair(U_637,U_636)),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_132_2,plain,
! [U_639,U_638] :
( ~ empty(set_union2(U_638,U_639))
| empty(U_639) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_639] :
( ! [U_638] : ~ empty(set_union2(U_638,U_639))
| empty(U_639) ),
inference(miniscope,[status(thm)],[f_132_2]) ).
fof(f_132_4,plain,
! [U_638,U_639] :
( ~ empty(set_union2(U_638,U_639))
| empty(U_639) ),
inference(definitional_conversion,[status(esa)],[f_132_3]) ).
cnf(f_132_5,plain,
( ~ empty(set_union2(U_638,U_639))
| empty(U_639) ),
inference(clausify,[status(thm)],[f_132_4]) ).
fof(f_133_1,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_133_2,plain,
! [U_641,U_640] :
( ( function(relation_dom_restriction(U_641,U_640))
& relation(relation_dom_restriction(U_641,U_640)) )
| ~ function(U_641)
| ~ relation(U_641) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_641] :
( ( ! [U_643] : function(relation_dom_restriction(U_641,U_643))
& ! [U_642] : relation(relation_dom_restriction(U_641,U_642)) )
| ~ function(U_641)
| ~ relation(U_641) ),
inference(miniscope,[status(thm)],[f_133_2]) ).
fof(f_133_4,plain,
( ! [U_641,U_642,U_643] :
( function(relation_dom_restriction(U_641,U_643))
| ~ sP164(U_641,U_642,U_643) )
& ! [U_641,U_642,U_643] :
( relation(relation_dom_restriction(U_641,U_642))
| ~ sP164(U_641,U_642,U_643) )
& ! [U_641,U_642,U_643] :
( sP164(U_641,U_642,U_643)
| ~ function(U_641)
| ~ relation(U_641) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_133_3]) ).
cnf(f_133_5,plain,
( sP164(U_641,U_642,U_643)
| ~ function(U_641)
| ~ relation(U_641) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_6,plain,
( relation(relation_dom_restriction(U_641,U_642))
| ~ sP164(U_641,U_642,U_643) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_7,plain,
( function(relation_dom_restriction(U_641,U_643))
| ~ sP164(U_641,U_642,U_643) ),
inference(clausify,[status(thm)],[f_133_4]) ).
fof(f_134_1,plain,
! [A] :
( ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc4_ordinal1]) ).
fof(f_134_2,plain,
! [U_644] :
( ( ordinal(union(U_644))
& epsilon_connected(union(U_644))
& epsilon_transitive(union(U_644)) )
| ~ ordinal(U_644) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
( ! [U_644] :
( ordinal(union(U_644))
| ~ sP165(U_644) )
& ! [U_644] :
( epsilon_connected(union(U_644))
| ~ sP165(U_644) )
& ! [U_644] :
( epsilon_transitive(union(U_644))
| ~ sP165(U_644) )
& ! [U_644] :
( sP165(U_644)
| ~ ordinal(U_644) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_134_2]) ).
cnf(f_134_4,plain,
( sP165(U_644)
| ~ ordinal(U_644) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_5,plain,
( epsilon_transitive(union(U_644))
| ~ sP165(U_644) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_6,plain,
( epsilon_connected(union(U_644))
| ~ sP165(U_644) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_7,plain,
( ordinal(union(U_644))
| ~ sP165(U_644) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_135_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_135_1]) ).
cnf(f_135_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_136_2,plain,
! [U_646,U_645] :
( ~ empty(cartesian_product2(U_646,U_645))
| empty(U_645)
| empty(U_646) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_645,U_646] :
( ~ empty(cartesian_product2(U_646,U_645))
| empty(U_645)
| empty(U_646) ),
inference(definitional_conversion,[status(esa)],[f_136_2]) ).
cnf(f_136_4,plain,
( ~ empty(cartesian_product2(U_646,U_645))
| empty(U_645)
| empty(U_646) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[fc5_funct_1]) ).
fof(f_137_2,plain,
! [U_648,U_647] :
( ( function(relation_rng_restriction(U_648,U_647))
& relation(relation_rng_restriction(U_648,U_647)) )
| ~ function(U_647)
| ~ relation(U_647) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
( ! [U_648,U_647] :
( function(relation_rng_restriction(U_648,U_647))
| ~ sP166(U_648,U_647) )
& ! [U_648,U_647] :
( relation(relation_rng_restriction(U_648,U_647))
| ~ sP166(U_648,U_647) )
& ! [U_648,U_647] :
( sP166(U_648,U_647)
| ~ function(U_647)
| ~ relation(U_647) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_137_2]) ).
cnf(f_137_4,plain,
( sP166(U_648,U_647)
| ~ function(U_647)
| ~ relation(U_647) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_5,plain,
( relation(relation_rng_restriction(U_648,U_647))
| ~ sP166(U_648,U_647) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_6,plain,
( function(relation_rng_restriction(U_648,U_647))
| ~ sP166(U_648,U_647) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_138_2,plain,
! [U_649] :
( ~ empty(relation_dom(U_649))
| ~ relation(U_649)
| empty(U_649) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_649] :
( ~ empty(relation_dom(U_649))
| ~ relation(U_649)
| empty(U_649) ),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
( ~ empty(relation_dom(U_649))
| ~ relation(U_649)
| empty(U_649) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_139_2,plain,
! [U_650] :
( ~ empty(relation_rng(U_650))
| ~ relation(U_650)
| empty(U_650) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_650] :
( ~ empty(relation_rng(U_650))
| ~ relation(U_650)
| empty(U_650) ),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
( ~ empty(relation_rng(U_650))
| ~ relation(U_650)
| empty(U_650) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_140_2,plain,
! [U_651] :
( ( relation(relation_dom(U_651))
& empty(relation_dom(U_651)) )
| ~ empty(U_651) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_651] :
( relation(relation_dom(U_651))
| ~ sP167(U_651) )
& ! [U_651] :
( empty(relation_dom(U_651))
| ~ sP167(U_651) )
& ! [U_651] :
( sP167(U_651)
| ~ empty(U_651) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_140_2]) ).
cnf(f_140_4,plain,
( sP167(U_651)
| ~ empty(U_651) ),
inference(clausify,[status(thm)],[f_140_3]) ).
cnf(f_140_5,plain,
( empty(relation_dom(U_651))
| ~ sP167(U_651) ),
inference(clausify,[status(thm)],[f_140_3]) ).
cnf(f_140_6,plain,
( relation(relation_dom(U_651))
| ~ sP167(U_651) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_141_2,plain,
! [U_652] :
( ( relation(relation_rng(U_652))
& empty(relation_rng(U_652)) )
| ~ empty(U_652) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( ! [U_652] :
( relation(relation_rng(U_652))
| ~ sP168(U_652) )
& ! [U_652] :
( empty(relation_rng(U_652))
| ~ sP168(U_652) )
& ! [U_652] :
( sP168(U_652)
| ~ empty(U_652) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168])],[f_141_2]) ).
cnf(f_141_4,plain,
( sP168(U_652)
| ~ empty(U_652) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_5,plain,
( empty(relation_rng(U_652))
| ~ sP168(U_652) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_6,plain,
( relation(relation_rng(U_652))
| ~ sP168(U_652) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_142_2,plain,
! [U_654,U_653] :
( ( relation(relation_composition(U_654,U_653))
& empty(relation_composition(U_654,U_653)) )
| ~ relation(U_653)
| ~ empty(U_654) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_654,U_653] :
( relation(relation_composition(U_654,U_653))
| ~ sP169(U_654,U_653) )
& ! [U_654,U_653] :
( empty(relation_composition(U_654,U_653))
| ~ sP169(U_654,U_653) )
& ! [U_654,U_653] :
( sP169(U_654,U_653)
| ~ relation(U_653)
| ~ empty(U_654) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_142_2]) ).
cnf(f_142_4,plain,
( sP169(U_654,U_653)
| ~ relation(U_653)
| ~ empty(U_654) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( empty(relation_composition(U_654,U_653))
| ~ sP169(U_654,U_653) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_6,plain,
( relation(relation_composition(U_654,U_653))
| ~ sP169(U_654,U_653) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_143_2,plain,
! [U_656,U_655] : set_union2(U_656,U_656) = U_656,
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_656] : set_union2(U_656,U_656) = U_656,
inference(miniscope,[status(thm)],[f_143_2]) ).
fof(f_143_4,plain,
! [U_656] : set_union2(U_656,U_656) = U_656,
inference(definitional_conversion,[status(esa)],[f_143_3]) ).
cnf(f_143_5,plain,
set_union2(U_656,U_656) = U_656,
inference(clausify,[status(thm)],[f_143_4]) ).
fof(f_144_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_144_2,plain,
! [U_658,U_657] : set_intersection2(U_658,U_658) = U_658,
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_658] : set_intersection2(U_658,U_658) = U_658,
inference(miniscope,[status(thm)],[f_144_2]) ).
fof(f_144_4,plain,
! [U_658] : set_intersection2(U_658,U_658) = U_658,
inference(definitional_conversion,[status(esa)],[f_144_3]) ).
cnf(f_144_5,plain,
set_intersection2(U_658,U_658) = U_658,
inference(clausify,[status(thm)],[f_144_4]) ).
fof(f_145_1,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1]) ).
fof(f_145_2,plain,
! [U_660,U_659] :
( subset_complement(U_660,subset_complement(U_660,U_659)) = U_659
| ~ element(U_659,powerset(U_660)) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_659,U_660] :
( subset_complement(U_660,subset_complement(U_660,U_659)) = U_659
| ~ element(U_659,powerset(U_660)) ),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
( subset_complement(U_660,subset_complement(U_660,U_659)) = U_659
| ~ element(U_659,powerset(U_660)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_146_2,plain,
! [U_661] :
( relation_inverse(relation_inverse(U_661)) = U_661
| ~ relation(U_661) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_661] :
( relation_inverse(relation_inverse(U_661)) = U_661
| ~ relation(U_661) ),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
( relation_inverse(relation_inverse(U_661)) = U_661
| ~ relation(U_661) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [A,B] :
( complements_of_subsets(A,complements_of_subsets(A,B)) = B
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1]) ).
fof(f_147_2,plain,
! [U_663,U_662] :
( complements_of_subsets(U_663,complements_of_subsets(U_663,U_662)) = U_662
| ~ element(U_662,powerset(powerset(U_663))) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_662,U_663] :
( complements_of_subsets(U_663,complements_of_subsets(U_663,U_662)) = U_662
| ~ element(U_662,powerset(powerset(U_663))) ),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
( complements_of_subsets(U_663,complements_of_subsets(U_663,U_662)) = U_662
| ~ element(U_662,powerset(powerset(U_663))) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_148_2,plain,
! [U_665,U_664] : ~ proper_subset(U_665,U_665),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_665] : ~ proper_subset(U_665,U_665),
inference(miniscope,[status(thm)],[f_148_2]) ).
fof(f_148_4,plain,
! [U_665] : ~ proper_subset(U_665,U_665),
inference(definitional_conversion,[status(esa)],[f_148_3]) ).
cnf(f_148_5,plain,
~ proper_subset(U_665,U_665),
inference(clausify,[status(thm)],[f_148_4]) ).
fof(f_149_1,plain,
! [A] :
( ( ( reflexive(A)
| ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) ) )
& ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l1_wellord1]) ).
fof(f_149_2,plain,
! [U_668] :
( ( ( reflexive(U_668)
| ? [U_667] :
( ~ in(ordered_pair(U_667,U_667),U_668)
& in(U_667,relation_field(U_668)) ) )
& ( ! [U_666] :
( in(ordered_pair(U_666,U_666),U_668)
| ~ in(U_666,relation_field(U_668)) )
| ~ reflexive(U_668) ) )
| ~ relation(U_668) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_668] :
( ( ( reflexive(U_668)
| ( ~ in(ordered_pair(sK115(U_668),sK115(U_668)),U_668)
& in(sK115(U_668),relation_field(U_668)) ) )
& ( ! [U_666] :
( in(ordered_pair(U_666,U_666),U_668)
| ~ in(U_666,relation_field(U_668)) )
| ~ reflexive(U_668) ) )
| ~ relation(U_668) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_667,sK115(U_668))],[f_149_2]) ).
fof(f_149_4,plain,
( ! [U_668] :
( ~ in(ordered_pair(sK115(U_668),sK115(U_668)),U_668)
| ~ sP170(U_668) )
& ! [U_668] :
( in(sK115(U_668),relation_field(U_668))
| ~ sP170(U_668) )
& ! [U_666,U_668] :
( reflexive(U_668)
| sP170(U_668)
| ~ sP171(U_666,U_668) )
& ! [U_666,U_668] :
( in(ordered_pair(U_666,U_666),U_668)
| ~ in(U_666,relation_field(U_668))
| ~ reflexive(U_668)
| ~ sP171(U_666,U_668) )
& ! [U_666,U_668] :
( sP171(U_666,U_668)
| ~ relation(U_668) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170,sP171])],[f_149_3]) ).
cnf(f_149_5,plain,
( sP171(U_666,U_668)
| ~ relation(U_668) ),
inference(clausify,[status(thm)],[f_149_4]) ).
cnf(f_149_6,plain,
( in(ordered_pair(U_666,U_666),U_668)
| ~ in(U_666,relation_field(U_668))
| ~ reflexive(U_668)
| ~ sP171(U_666,U_668) ),
inference(clausify,[status(thm)],[f_149_4]) ).
cnf(f_149_7,plain,
( reflexive(U_668)
| sP170(U_668)
| ~ sP171(U_666,U_668) ),
inference(clausify,[status(thm)],[f_149_4]) ).
cnf(f_149_8,plain,
( in(sK115(U_668),relation_field(U_668))
| ~ sP170(U_668) ),
inference(clausify,[status(thm)],[f_149_4]) ).
cnf(f_149_9,plain,
( ~ in(ordered_pair(sK115(U_668),sK115(U_668)),U_668)
| ~ sP170(U_668) ),
inference(clausify,[status(thm)],[f_149_4]) ).
fof(f_150_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_150_2,plain,
! [U_669] : singleton(U_669) != empty_set,
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_669] : singleton(U_669) != empty_set,
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
singleton(U_669) != empty_set,
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_151_2,plain,
! [U_671,U_670] :
( set_union2(singleton(U_671),U_670) = U_670
| ~ in(U_671,U_670) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_670,U_671] :
( set_union2(singleton(U_671),U_670) = U_670
| ~ in(U_671,U_670) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( set_union2(singleton(U_671),U_670) = U_670
| ~ in(U_671,U_670) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_152_2,plain,
! [U_673,U_672] :
( ~ in(U_673,U_672)
| ~ disjoint(singleton(U_673),U_672) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_673,U_672] :
( ~ in(U_673,U_672)
| ~ disjoint(singleton(U_673),U_672) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( ~ in(U_673,U_672)
| ~ disjoint(singleton(U_673),U_672) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_153_2,plain,
! [U_675,U_674] :
( disjoint(singleton(U_675),U_674)
| in(U_675,U_674) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_675,U_674] :
( disjoint(singleton(U_675),U_674)
| in(U_675,U_674) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( disjoint(singleton(U_675),U_674)
| in(U_675,U_674) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [A,B] :
( subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[l29_wellord1]) ).
fof(f_154_2,plain,
! [U_677,U_676] :
( subset(relation_dom(relation_rng_restriction(U_677,U_676)),relation_dom(U_676))
| ~ relation(U_676) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_676,U_677] :
( subset(relation_dom(relation_rng_restriction(U_677,U_676)),relation_dom(U_676))
| ~ relation(U_676) ),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
( subset(relation_dom(relation_rng_restriction(U_677,U_676)),relation_dom(U_676))
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_1,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) ) )
& ( ! [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(fof_nnf,[status(thm)],[l2_wellord1]) ).
fof(f_155_2,plain,
! [U_684] :
( ( ( transitive(U_684)
| ? [U_683,U_682,U_681] :
( ~ in(ordered_pair(U_683,U_681),U_684)
& in(ordered_pair(U_682,U_681),U_684)
& in(ordered_pair(U_683,U_682),U_684) ) )
& ( ! [U_680,U_679,U_678] :
( in(ordered_pair(U_680,U_678),U_684)
| ~ in(ordered_pair(U_679,U_678),U_684)
| ~ in(ordered_pair(U_680,U_679),U_684) )
| ~ transitive(U_684) ) )
| ~ relation(U_684) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_684] :
( ( ( transitive(U_684)
| ? [U_682,U_681] :
( ~ in(ordered_pair(sK116(U_684),U_681),U_684)
& in(ordered_pair(U_682,U_681),U_684)
& in(ordered_pair(sK116(U_684),U_682),U_684) ) )
& ( ! [U_680,U_679,U_678] :
( in(ordered_pair(U_680,U_678),U_684)
| ~ in(ordered_pair(U_679,U_678),U_684)
| ~ in(ordered_pair(U_680,U_679),U_684) )
| ~ transitive(U_684) ) )
| ~ relation(U_684) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_683,sK116(U_684))],[f_155_2]) ).
fof(f_155_4,plain,
! [U_684] :
( ( ( transitive(U_684)
| ? [U_681] :
( ~ in(ordered_pair(sK116(U_684),U_681),U_684)
& in(ordered_pair(sK117(U_684),U_681),U_684)
& in(ordered_pair(sK116(U_684),sK117(U_684)),U_684) ) )
& ( ! [U_680,U_679,U_678] :
( in(ordered_pair(U_680,U_678),U_684)
| ~ in(ordered_pair(U_679,U_678),U_684)
| ~ in(ordered_pair(U_680,U_679),U_684) )
| ~ transitive(U_684) ) )
| ~ relation(U_684) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_682,sK117(U_684))],[f_155_3]) ).
fof(f_155_5,plain,
! [U_684] :
( ( ( transitive(U_684)
| ( ~ in(ordered_pair(sK116(U_684),sK118(U_684)),U_684)
& in(ordered_pair(sK117(U_684),sK118(U_684)),U_684)
& in(ordered_pair(sK116(U_684),sK117(U_684)),U_684) ) )
& ( ! [U_680,U_679,U_678] :
( in(ordered_pair(U_680,U_678),U_684)
| ~ in(ordered_pair(U_679,U_678),U_684)
| ~ in(ordered_pair(U_680,U_679),U_684) )
| ~ transitive(U_684) ) )
| ~ relation(U_684) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_681,sK118(U_684))],[f_155_4]) ).
fof(f_155_6,plain,
( ! [U_684] :
( ~ in(ordered_pair(sK116(U_684),sK118(U_684)),U_684)
| ~ sP172(U_684) )
& ! [U_684] :
( in(ordered_pair(sK117(U_684),sK118(U_684)),U_684)
| ~ sP172(U_684) )
& ! [U_684] :
( in(ordered_pair(sK116(U_684),sK117(U_684)),U_684)
| ~ sP172(U_684) )
& ! [U_678,U_679,U_680,U_684] :
( transitive(U_684)
| sP172(U_684)
| ~ sP173(U_678,U_679,U_680,U_684) )
& ! [U_678,U_679,U_680,U_684] :
( in(ordered_pair(U_680,U_678),U_684)
| ~ in(ordered_pair(U_679,U_678),U_684)
| ~ in(ordered_pair(U_680,U_679),U_684)
| ~ transitive(U_684)
| ~ sP173(U_678,U_679,U_680,U_684) )
& ! [U_678,U_679,U_680,U_684] :
( sP173(U_678,U_679,U_680,U_684)
| ~ relation(U_684) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172,sP173])],[f_155_5]) ).
cnf(f_155_7,plain,
( sP173(U_678,U_679,U_680,U_684)
| ~ relation(U_684) ),
inference(clausify,[status(thm)],[f_155_6]) ).
cnf(f_155_8,plain,
( in(ordered_pair(U_680,U_678),U_684)
| ~ in(ordered_pair(U_679,U_678),U_684)
| ~ in(ordered_pair(U_680,U_679),U_684)
| ~ transitive(U_684)
| ~ sP173(U_678,U_679,U_680,U_684) ),
inference(clausify,[status(thm)],[f_155_6]) ).
cnf(f_155_9,plain,
( transitive(U_684)
| sP172(U_684)
| ~ sP173(U_678,U_679,U_680,U_684) ),
inference(clausify,[status(thm)],[f_155_6]) ).
cnf(f_155_10,plain,
( in(ordered_pair(sK116(U_684),sK117(U_684)),U_684)
| ~ sP172(U_684) ),
inference(clausify,[status(thm)],[f_155_6]) ).
cnf(f_155_11,plain,
( in(ordered_pair(sK117(U_684),sK118(U_684)),U_684)
| ~ sP172(U_684) ),
inference(clausify,[status(thm)],[f_155_6]) ).
cnf(f_155_12,plain,
( ~ in(ordered_pair(sK116(U_684),sK118(U_684)),U_684)
| ~ sP172(U_684) ),
inference(clausify,[status(thm)],[f_155_6]) ).
fof(f_156_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[l2_zfmisc_1]) ).
fof(f_156_2,plain,
! [U_686,U_685] :
( ( subset(singleton(U_686),U_685)
| ~ in(U_686,U_685) )
& ( in(U_686,U_685)
| ~ subset(singleton(U_686),U_685) ) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ! [U_690,U_688] :
( subset(singleton(U_690),U_688)
| ~ in(U_690,U_688) )
& ! [U_689,U_687] :
( in(U_689,U_687)
| ~ subset(singleton(U_689),U_687) ) ),
inference(miniscope,[status(thm)],[f_156_2]) ).
fof(f_156_4,plain,
( ! [U_690,U_688] :
( subset(singleton(U_690),U_688)
| ~ in(U_690,U_688) )
& ! [U_689,U_687] :
( in(U_689,U_687)
| ~ subset(singleton(U_689),U_687) ) ),
inference(definitional_conversion,[status(esa)],[f_156_3]) ).
cnf(f_156_5,plain,
( in(U_689,U_687)
| ~ subset(singleton(U_689),U_687) ),
inference(clausify,[status(thm)],[f_156_4]) ).
cnf(f_156_6,plain,
( subset(singleton(U_690),U_688)
| ~ in(U_690,U_688) ),
inference(clausify,[status(thm)],[f_156_4]) ).
fof(f_157_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[l32_xboole_1]) ).
fof(f_157_2,plain,
! [U_692,U_691] :
( ( set_difference(U_692,U_691) = empty_set
| ~ subset(U_692,U_691) )
& ( subset(U_692,U_691)
| set_difference(U_692,U_691) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_696,U_694] :
( set_difference(U_696,U_694) = empty_set
| ~ subset(U_696,U_694) )
& ! [U_695,U_693] :
( subset(U_695,U_693)
| set_difference(U_695,U_693) != empty_set ) ),
inference(miniscope,[status(thm)],[f_157_2]) ).
fof(f_157_4,plain,
( ! [U_694,U_696] :
( set_difference(U_696,U_694) = empty_set
| ~ subset(U_696,U_694) )
& ! [U_695,U_693] :
( subset(U_695,U_693)
| set_difference(U_695,U_693) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_157_3]) ).
cnf(f_157_5,plain,
( subset(U_695,U_693)
| set_difference(U_695,U_693) != empty_set ),
inference(clausify,[status(thm)],[f_157_4]) ).
cnf(f_157_6,plain,
( set_difference(U_696,U_694) = empty_set
| ~ subset(U_696,U_694) ),
inference(clausify,[status(thm)],[f_157_4]) ).
fof(f_158_1,plain,
! [A,B] :
( ! [C] :
( in(C,A)
| ~ in(C,B) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[l3_subset_1]) ).
fof(f_158_2,plain,
! [U_699,U_698] :
( ! [U_697] :
( in(U_697,U_699)
| ~ in(U_697,U_698) )
| ~ element(U_698,powerset(U_699)) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_698,U_699,U_697] :
( in(U_697,U_699)
| ~ in(U_697,U_698)
| ~ element(U_698,powerset(U_699)) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( in(U_697,U_699)
| ~ in(U_697,U_698)
| ~ element(U_698,powerset(U_699)) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [A] :
( ( ( antisymmetric(A)
| ? [B,C] :
( B != C
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) ) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l3_wellord1]) ).
fof(f_159_2,plain,
! [U_704] :
( ( ( antisymmetric(U_704)
| ? [U_703,U_702] :
( U_703 != U_702
& in(ordered_pair(U_702,U_703),U_704)
& in(ordered_pair(U_703,U_702),U_704) ) )
& ( ! [U_701,U_700] :
( U_701 = U_700
| ~ in(ordered_pair(U_700,U_701),U_704)
| ~ in(ordered_pair(U_701,U_700),U_704) )
| ~ antisymmetric(U_704) ) )
| ~ relation(U_704) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_704] :
( ( ( antisymmetric(U_704)
| ? [U_702] :
( sK119(U_704) != U_702
& in(ordered_pair(U_702,sK119(U_704)),U_704)
& in(ordered_pair(sK119(U_704),U_702),U_704) ) )
& ( ! [U_701,U_700] :
( U_701 = U_700
| ~ in(ordered_pair(U_700,U_701),U_704)
| ~ in(ordered_pair(U_701,U_700),U_704) )
| ~ antisymmetric(U_704) ) )
| ~ relation(U_704) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_703,sK119(U_704))],[f_159_2]) ).
fof(f_159_4,plain,
! [U_704] :
( ( ( antisymmetric(U_704)
| ( sK119(U_704) != sK120(U_704)
& in(ordered_pair(sK120(U_704),sK119(U_704)),U_704)
& in(ordered_pair(sK119(U_704),sK120(U_704)),U_704) ) )
& ( ! [U_701,U_700] :
( U_701 = U_700
| ~ in(ordered_pair(U_700,U_701),U_704)
| ~ in(ordered_pair(U_701,U_700),U_704) )
| ~ antisymmetric(U_704) ) )
| ~ relation(U_704) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_702,sK120(U_704))],[f_159_3]) ).
fof(f_159_5,plain,
( ! [U_704] :
( sK119(U_704) != sK120(U_704)
| ~ sP174(U_704) )
& ! [U_704] :
( in(ordered_pair(sK120(U_704),sK119(U_704)),U_704)
| ~ sP174(U_704) )
& ! [U_704] :
( in(ordered_pair(sK119(U_704),sK120(U_704)),U_704)
| ~ sP174(U_704) )
& ! [U_700,U_701,U_704] :
( antisymmetric(U_704)
| sP174(U_704)
| ~ sP175(U_700,U_701,U_704) )
& ! [U_700,U_701,U_704] :
( U_701 = U_700
| ~ in(ordered_pair(U_700,U_701),U_704)
| ~ in(ordered_pair(U_701,U_700),U_704)
| ~ antisymmetric(U_704)
| ~ sP175(U_700,U_701,U_704) )
& ! [U_700,U_701,U_704] :
( sP175(U_700,U_701,U_704)
| ~ relation(U_704) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174,sP175])],[f_159_4]) ).
cnf(f_159_6,plain,
( sP175(U_700,U_701,U_704)
| ~ relation(U_704) ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_7,plain,
( U_701 = U_700
| ~ in(ordered_pair(U_700,U_701),U_704)
| ~ in(ordered_pair(U_701,U_700),U_704)
| ~ antisymmetric(U_704)
| ~ sP175(U_700,U_701,U_704) ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_8,plain,
( antisymmetric(U_704)
| sP174(U_704)
| ~ sP175(U_700,U_701,U_704) ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_9,plain,
( in(ordered_pair(sK119(U_704),sK120(U_704)),U_704)
| ~ sP174(U_704) ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_10,plain,
( in(ordered_pair(sK120(U_704),sK119(U_704)),U_704)
| ~ sP174(U_704) ),
inference(clausify,[status(thm)],[f_159_5]) ).
cnf(f_159_11,plain,
( sK119(U_704) != sK120(U_704)
| ~ sP174(U_704) ),
inference(clausify,[status(thm)],[f_159_5]) ).
fof(f_160_1,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[l3_zfmisc_1]) ).
fof(f_160_2,plain,
! [U_707,U_706,U_705] :
( subset(U_707,set_difference(U_706,singleton(U_705)))
| in(U_705,U_707)
| ~ subset(U_707,U_706) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_707,U_706] :
( ! [U_705] :
( subset(U_707,set_difference(U_706,singleton(U_705)))
| in(U_705,U_707) )
| ~ subset(U_707,U_706) ),
inference(miniscope,[status(thm)],[f_160_2]) ).
fof(f_160_4,plain,
! [U_707,U_706,U_705] :
( subset(U_707,set_difference(U_706,singleton(U_705)))
| in(U_705,U_707)
| ~ subset(U_707,U_706) ),
inference(definitional_conversion,[status(esa)],[f_160_3]) ).
cnf(f_160_5,plain,
( subset(U_707,set_difference(U_706,singleton(U_705)))
| in(U_705,U_707)
| ~ subset(U_707,U_706) ),
inference(clausify,[status(thm)],[f_160_4]) ).
fof(f_161_1,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)) ) )
& ( ! [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(fof_nnf,[status(thm)],[l4_wellord1]) ).
fof(f_161_2,plain,
! [U_712] :
( ( ( connected(U_712)
| ? [U_711,U_710] :
( ~ in(ordered_pair(U_710,U_711),U_712)
& ~ in(ordered_pair(U_711,U_710),U_712)
& U_711 != U_710
& in(U_710,relation_field(U_712))
& in(U_711,relation_field(U_712)) ) )
& ( ! [U_709,U_708] :
( in(ordered_pair(U_708,U_709),U_712)
| in(ordered_pair(U_709,U_708),U_712)
| U_709 = U_708
| ~ in(U_708,relation_field(U_712))
| ~ in(U_709,relation_field(U_712)) )
| ~ connected(U_712) ) )
| ~ relation(U_712) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_712] :
( ( ( connected(U_712)
| ? [U_711] :
( ? [U_710] :
( ~ in(ordered_pair(U_710,U_711),U_712)
& ~ in(ordered_pair(U_711,U_710),U_712)
& U_711 != U_710
& in(U_710,relation_field(U_712)) )
& in(U_711,relation_field(U_712)) ) )
& ( ! [U_709] :
( ! [U_708] :
( in(ordered_pair(U_708,U_709),U_712)
| in(ordered_pair(U_709,U_708),U_712)
| U_709 = U_708
| ~ in(U_708,relation_field(U_712)) )
| ~ in(U_709,relation_field(U_712)) )
| ~ connected(U_712) ) )
| ~ relation(U_712) ),
inference(miniscope,[status(thm)],[f_161_2]) ).
fof(f_161_4,plain,
! [U_712] :
( ( ( connected(U_712)
| ( ? [U_710] :
( ~ in(ordered_pair(U_710,sK121(U_712)),U_712)
& ~ in(ordered_pair(sK121(U_712),U_710),U_712)
& sK121(U_712) != U_710
& in(U_710,relation_field(U_712)) )
& in(sK121(U_712),relation_field(U_712)) ) )
& ( ! [U_709] :
( ! [U_708] :
( in(ordered_pair(U_708,U_709),U_712)
| in(ordered_pair(U_709,U_708),U_712)
| U_709 = U_708
| ~ in(U_708,relation_field(U_712)) )
| ~ in(U_709,relation_field(U_712)) )
| ~ connected(U_712) ) )
| ~ relation(U_712) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_711,sK121(U_712))],[f_161_3]) ).
fof(f_161_5,plain,
! [U_712] :
( ( ( connected(U_712)
| ( ~ in(ordered_pair(sK122(U_712),sK121(U_712)),U_712)
& ~ in(ordered_pair(sK121(U_712),sK122(U_712)),U_712)
& sK121(U_712) != sK122(U_712)
& in(sK122(U_712),relation_field(U_712))
& in(sK121(U_712),relation_field(U_712)) ) )
& ( ! [U_709] :
( ! [U_708] :
( in(ordered_pair(U_708,U_709),U_712)
| in(ordered_pair(U_709,U_708),U_712)
| U_709 = U_708
| ~ in(U_708,relation_field(U_712)) )
| ~ in(U_709,relation_field(U_712)) )
| ~ connected(U_712) ) )
| ~ relation(U_712) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_710,sK122(U_712))],[f_161_4]) ).
fof(f_161_6,plain,
( ! [U_712] :
( ~ in(ordered_pair(sK122(U_712),sK121(U_712)),U_712)
| ~ sP176(U_712) )
& ! [U_712] :
( ~ in(ordered_pair(sK121(U_712),sK122(U_712)),U_712)
| ~ sP176(U_712) )
& ! [U_712] :
( sK121(U_712) != sK122(U_712)
| ~ sP176(U_712) )
& ! [U_712] :
( in(sK122(U_712),relation_field(U_712))
| ~ sP176(U_712) )
& ! [U_712] :
( in(sK121(U_712),relation_field(U_712))
| ~ sP176(U_712) )
& ! [U_712,U_708,U_709] :
( connected(U_712)
| sP176(U_712)
| ~ sP177(U_712,U_708,U_709) )
& ! [U_712,U_708,U_709] :
( in(ordered_pair(U_708,U_709),U_712)
| in(ordered_pair(U_709,U_708),U_712)
| U_709 = U_708
| ~ in(U_708,relation_field(U_712))
| ~ in(U_709,relation_field(U_712))
| ~ connected(U_712)
| ~ sP177(U_712,U_708,U_709) )
& ! [U_712,U_708,U_709] :
( sP177(U_712,U_708,U_709)
| ~ relation(U_712) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176,sP177])],[f_161_5]) ).
cnf(f_161_7,plain,
( sP177(U_712,U_708,U_709)
| ~ relation(U_712) ),
inference(clausify,[status(thm)],[f_161_6]) ).
cnf(f_161_8,plain,
( in(ordered_pair(U_708,U_709),U_712)
| in(ordered_pair(U_709,U_708),U_712)
| U_709 = U_708
| ~ in(U_708,relation_field(U_712))
| ~ in(U_709,relation_field(U_712))
| ~ connected(U_712)
| ~ sP177(U_712,U_708,U_709) ),
inference(clausify,[status(thm)],[f_161_6]) ).
cnf(f_161_9,plain,
( connected(U_712)
| sP176(U_712)
| ~ sP177(U_712,U_708,U_709) ),
inference(clausify,[status(thm)],[f_161_6]) ).
cnf(f_161_10,plain,
( in(sK121(U_712),relation_field(U_712))
| ~ sP176(U_712) ),
inference(clausify,[status(thm)],[f_161_6]) ).
cnf(f_161_11,plain,
( in(sK122(U_712),relation_field(U_712))
| ~ sP176(U_712) ),
inference(clausify,[status(thm)],[f_161_6]) ).
cnf(f_161_12,plain,
( sK121(U_712) != sK122(U_712)
| ~ sP176(U_712) ),
inference(clausify,[status(thm)],[f_161_6]) ).
cnf(f_161_13,plain,
( ~ in(ordered_pair(sK121(U_712),sK122(U_712)),U_712)
| ~ sP176(U_712) ),
inference(clausify,[status(thm)],[f_161_6]) ).
cnf(f_161_14,plain,
( ~ in(ordered_pair(sK122(U_712),sK121(U_712)),U_712)
| ~ sP176(U_712) ),
inference(clausify,[status(thm)],[f_161_6]) ).
fof(f_162_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[l4_zfmisc_1]) ).
fof(f_162_2,plain,
! [U_714,U_713] :
( ( subset(U_714,singleton(U_713))
| ( U_714 != singleton(U_713)
& U_714 != empty_set ) )
& ( U_714 = singleton(U_713)
| U_714 = empty_set
| ~ subset(U_714,singleton(U_713)) ) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
( ! [U_718,U_716] :
( subset(U_718,singleton(U_716))
| ( U_718 != singleton(U_716)
& U_718 != empty_set ) )
& ! [U_717,U_715] :
( U_717 = singleton(U_715)
| U_717 = empty_set
| ~ subset(U_717,singleton(U_715)) ) ),
inference(miniscope,[status(thm)],[f_162_2]) ).
fof(f_162_4,plain,
( ! [U_718,U_716] :
( U_718 != singleton(U_716)
| ~ sP178(U_718,U_716) )
& ! [U_718,U_716] :
( U_718 != empty_set
| ~ sP178(U_718,U_716) )
& ! [U_718,U_716] :
( subset(U_718,singleton(U_716))
| sP178(U_718,U_716) )
& ! [U_717,U_715] :
( U_717 = singleton(U_715)
| U_717 = empty_set
| ~ subset(U_717,singleton(U_715)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_162_3]) ).
cnf(f_162_5,plain,
( U_717 = singleton(U_715)
| U_717 = empty_set
| ~ subset(U_717,singleton(U_715)) ),
inference(clausify,[status(thm)],[f_162_4]) ).
cnf(f_162_6,plain,
( subset(U_718,singleton(U_716))
| sP178(U_718,U_716) ),
inference(clausify,[status(thm)],[f_162_4]) ).
cnf(f_162_7,plain,
( U_718 != empty_set
| ~ sP178(U_718,U_716) ),
inference(clausify,[status(thm)],[f_162_4]) ).
cnf(f_162_8,plain,
( U_718 != singleton(U_716)
| ~ sP178(U_718,U_716) ),
inference(clausify,[status(thm)],[f_162_4]) ).
fof(f_163_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_163_2,plain,
! [U_720,U_719] :
( subset(U_720,union(U_719))
| ~ in(U_720,U_719) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_720,U_719] :
( subset(U_720,union(U_719))
| ~ in(U_720,U_719) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( subset(U_720,union(U_719))
| ~ in(U_720,U_719) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[l55_zfmisc_1]) ).
fof(f_164_2,plain,
! [U_724,U_723,U_722,U_721] :
( ( in(ordered_pair(U_724,U_723),cartesian_product2(U_722,U_721))
| ~ in(U_723,U_721)
| ~ in(U_724,U_722) )
& ( ( in(U_723,U_721)
& in(U_724,U_722) )
| ~ in(ordered_pair(U_724,U_723),cartesian_product2(U_722,U_721)) ) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
( ! [U_732,U_730,U_728,U_726] :
( in(ordered_pair(U_732,U_730),cartesian_product2(U_728,U_726))
| ~ in(U_730,U_726)
| ~ in(U_732,U_728) )
& ! [U_731,U_729,U_727,U_725] :
( ( in(U_729,U_725)
& in(U_731,U_727) )
| ~ in(ordered_pair(U_731,U_729),cartesian_product2(U_727,U_725)) ) ),
inference(miniscope,[status(thm)],[f_164_2]) ).
fof(f_164_4,plain,
( ! [U_725,U_727,U_731,U_729] :
( in(U_729,U_725)
| ~ sP179(U_725,U_727,U_731,U_729) )
& ! [U_725,U_727,U_731,U_729] :
( in(U_731,U_727)
| ~ sP179(U_725,U_727,U_731,U_729) )
& ! [U_732,U_728,U_730,U_726] :
( in(ordered_pair(U_732,U_730),cartesian_product2(U_728,U_726))
| ~ in(U_730,U_726)
| ~ in(U_732,U_728) )
& ! [U_725,U_727,U_731,U_729] :
( sP179(U_725,U_727,U_731,U_729)
| ~ in(ordered_pair(U_731,U_729),cartesian_product2(U_727,U_725)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_164_3]) ).
cnf(f_164_5,plain,
( sP179(U_725,U_727,U_731,U_729)
| ~ in(ordered_pair(U_731,U_729),cartesian_product2(U_727,U_725)) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_6,plain,
( in(ordered_pair(U_732,U_730),cartesian_product2(U_728,U_726))
| ~ in(U_730,U_726)
| ~ in(U_732,U_728) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_7,plain,
( in(U_731,U_727)
| ~ sP179(U_725,U_727,U_731,U_729) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_8,plain,
( in(U_729,U_725)
| ~ sP179(U_725,U_727,U_731,U_729) ),
inference(clausify,[status(thm)],[f_164_4]) ).
fof(f_165_1,plain,
! [A,B] :
( element(A,powerset(B))
| ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(fof_nnf,[status(thm)],[l71_subset_1]) ).
fof(f_165_2,plain,
! [U_735,U_734] :
( element(U_735,powerset(U_734))
| ? [U_733] :
( ~ in(U_733,U_734)
& in(U_733,U_735) ) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_735,U_734] :
( element(U_735,powerset(U_734))
| ( ~ in(sK123(U_735,U_734),U_734)
& in(sK123(U_735,U_734),U_735) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_733,sK123(U_735,U_734))],[f_165_2]) ).
fof(f_165_4,plain,
( ! [U_735,U_734] :
( ~ in(sK123(U_735,U_734),U_734)
| ~ sP180(U_735,U_734) )
& ! [U_735,U_734] :
( in(sK123(U_735,U_734),U_735)
| ~ sP180(U_735,U_734) )
& ! [U_735,U_734] :
( element(U_735,powerset(U_734))
| sP180(U_735,U_734) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_165_3]) ).
cnf(f_165_5,plain,
( element(U_735,powerset(U_734))
| sP180(U_735,U_734) ),
inference(clausify,[status(thm)],[f_165_4]) ).
cnf(f_165_6,plain,
( in(sK123(U_735,U_734),U_735)
| ~ sP180(U_735,U_734) ),
inference(clausify,[status(thm)],[f_165_4]) ).
cnf(f_165_7,plain,
( ~ in(sK123(U_735,U_734),U_734)
| ~ sP180(U_735,U_734) ),
inference(clausify,[status(thm)],[f_165_4]) ).
fof(f_166_1,plain,
! [A,B,C] :
( ( ( in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ in(B,A)
| ~ in(B,relation_dom(C)) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[l82_funct_1]) ).
fof(f_166_2,plain,
! [U_738,U_737,U_736] :
( ( ( in(U_737,relation_dom(relation_dom_restriction(U_736,U_738)))
| ~ in(U_737,U_738)
| ~ in(U_737,relation_dom(U_736)) )
& ( ( in(U_737,U_738)
& in(U_737,relation_dom(U_736)) )
| ~ in(U_737,relation_dom(relation_dom_restriction(U_736,U_738))) ) )
| ~ function(U_736)
| ~ relation(U_736) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
( ! [U_736,U_737,U_738] :
( in(U_737,U_738)
| ~ sP181(U_736,U_737,U_738) )
& ! [U_736,U_737,U_738] :
( in(U_737,relation_dom(U_736))
| ~ sP181(U_736,U_737,U_738) )
& ! [U_736,U_737,U_738] :
( in(U_737,relation_dom(relation_dom_restriction(U_736,U_738)))
| ~ in(U_737,U_738)
| ~ in(U_737,relation_dom(U_736))
| ~ sP182(U_736,U_737,U_738) )
& ! [U_736,U_737,U_738] :
( sP181(U_736,U_737,U_738)
| ~ in(U_737,relation_dom(relation_dom_restriction(U_736,U_738)))
| ~ sP182(U_736,U_737,U_738) )
& ! [U_736,U_737,U_738] :
( sP182(U_736,U_737,U_738)
| ~ function(U_736)
| ~ relation(U_736) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181,sP182])],[f_166_2]) ).
cnf(f_166_4,plain,
( sP182(U_736,U_737,U_738)
| ~ function(U_736)
| ~ relation(U_736) ),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_5,plain,
( sP181(U_736,U_737,U_738)
| ~ in(U_737,relation_dom(relation_dom_restriction(U_736,U_738)))
| ~ sP182(U_736,U_737,U_738) ),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_6,plain,
( in(U_737,relation_dom(relation_dom_restriction(U_736,U_738)))
| ~ in(U_737,U_738)
| ~ in(U_737,relation_dom(U_736))
| ~ sP182(U_736,U_737,U_738) ),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_7,plain,
( in(U_737,relation_dom(U_736))
| ~ sP181(U_736,U_737,U_738) ),
inference(clausify,[status(thm)],[f_166_3]) ).
cnf(f_166_8,plain,
( in(U_737,U_738)
| ~ sP181(U_736,U_737,U_738) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_167_2,plain,
? [U_739] :
( function(U_739)
& relation(U_739) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
( function(sK124)
& relation(sK124) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_739,sK124)],[f_167_2]) ).
fof(f_167_4,plain,
( function(sK124)
& relation(sK124) ),
inference(definitional_conversion,[status(esa)],[f_167_3]) ).
cnf(f_167_5,plain,
relation(sK124),
inference(clausify,[status(thm)],[f_167_4]) ).
cnf(f_167_6,plain,
function(sK124),
inference(clausify,[status(thm)],[f_167_4]) ).
fof(f_168_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_168_2,plain,
? [U_740] :
( ordinal(U_740)
& epsilon_connected(U_740)
& epsilon_transitive(U_740) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
( ordinal(sK125)
& epsilon_connected(sK125)
& epsilon_transitive(sK125) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_740,sK125)],[f_168_2]) ).
fof(f_168_4,plain,
( ordinal(sK125)
& epsilon_connected(sK125)
& epsilon_transitive(sK125) ),
inference(definitional_conversion,[status(esa)],[f_168_3]) ).
cnf(f_168_5,plain,
epsilon_transitive(sK125),
inference(clausify,[status(thm)],[f_168_4]) ).
cnf(f_168_6,plain,
epsilon_connected(sK125),
inference(clausify,[status(thm)],[f_168_4]) ).
cnf(f_168_7,plain,
ordinal(sK125),
inference(clausify,[status(thm)],[f_168_4]) ).
fof(f_169_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_169_2,plain,
? [U_741] :
( relation(U_741)
& empty(U_741) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
( relation(sK126)
& empty(sK126) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_741,sK126)],[f_169_2]) ).
fof(f_169_4,plain,
( relation(sK126)
& empty(sK126) ),
inference(definitional_conversion,[status(esa)],[f_169_3]) ).
cnf(f_169_5,plain,
empty(sK126),
inference(clausify,[status(thm)],[f_169_4]) ).
cnf(f_169_6,plain,
relation(sK126),
inference(clausify,[status(thm)],[f_169_4]) ).
fof(f_170_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_170_2,plain,
! [U_743] :
( ? [U_742] :
( ~ empty(U_742)
& element(U_742,powerset(U_743)) )
| empty(U_743) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_743] :
( ( ~ empty(sK127(U_743))
& element(sK127(U_743),powerset(U_743)) )
| empty(U_743) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_742,sK127(U_743))],[f_170_2]) ).
fof(f_170_4,plain,
( ! [U_743] :
( ~ empty(sK127(U_743))
| ~ sP183(U_743) )
& ! [U_743] :
( element(sK127(U_743),powerset(U_743))
| ~ sP183(U_743) )
& ! [U_743] :
( sP183(U_743)
| empty(U_743) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_170_3]) ).
cnf(f_170_5,plain,
( sP183(U_743)
| empty(U_743) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_6,plain,
( element(sK127(U_743),powerset(U_743))
| ~ sP183(U_743) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_7,plain,
( ~ empty(sK127(U_743))
| ~ sP183(U_743) ),
inference(clausify,[status(thm)],[f_170_4]) ).
fof(f_171_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_171_2,plain,
? [U_744] : empty(U_744),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
empty(sK128),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_744,sK128)],[f_171_2]) ).
fof(f_171_4,plain,
empty(sK128),
inference(definitional_conversion,[status(esa)],[f_171_3]) ).
cnf(f_171_5,plain,
empty(sK128),
inference(clausify,[status(thm)],[f_171_4]) ).
fof(f_172_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_172_2,plain,
? [U_745] :
( function(U_745)
& empty(U_745)
& relation(U_745) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( function(sK129)
& empty(sK129)
& relation(sK129) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_745,sK129)],[f_172_2]) ).
fof(f_172_4,plain,
( function(sK129)
& empty(sK129)
& relation(sK129) ),
inference(definitional_conversion,[status(esa)],[f_172_3]) ).
cnf(f_172_5,plain,
relation(sK129),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_6,plain,
empty(sK129),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_7,plain,
function(sK129),
inference(clausify,[status(thm)],[f_172_4]) ).
fof(f_173_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal1]) ).
fof(f_173_2,plain,
? [U_746] :
( ordinal(U_746)
& epsilon_connected(U_746)
& epsilon_transitive(U_746)
& empty(U_746)
& one_to_one(U_746)
& function(U_746)
& relation(U_746) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
( ordinal(sK130)
& epsilon_connected(sK130)
& epsilon_transitive(sK130)
& empty(sK130)
& one_to_one(sK130)
& function(sK130)
& relation(sK130) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_746,sK130)],[f_173_2]) ).
fof(f_173_4,plain,
( ordinal(sK130)
& epsilon_connected(sK130)
& epsilon_transitive(sK130)
& empty(sK130)
& one_to_one(sK130)
& function(sK130)
& relation(sK130) ),
inference(definitional_conversion,[status(esa)],[f_173_3]) ).
cnf(f_173_5,plain,
relation(sK130),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_6,plain,
function(sK130),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_7,plain,
one_to_one(sK130),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_8,plain,
empty(sK130),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_9,plain,
epsilon_transitive(sK130),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_10,plain,
epsilon_connected(sK130),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_11,plain,
ordinal(sK130),
inference(clausify,[status(thm)],[f_173_4]) ).
fof(f_174_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_174_2,plain,
? [U_747] :
( relation(U_747)
& ~ empty(U_747) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
( relation(sK131)
& ~ empty(sK131) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_747,sK131)],[f_174_2]) ).
fof(f_174_4,plain,
( relation(sK131)
& ~ empty(sK131) ),
inference(definitional_conversion,[status(esa)],[f_174_3]) ).
cnf(f_174_5,plain,
~ empty(sK131),
inference(clausify,[status(thm)],[f_174_4]) ).
cnf(f_174_6,plain,
relation(sK131),
inference(clausify,[status(thm)],[f_174_4]) ).
fof(f_175_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_175_2,plain,
! [U_749] :
? [U_748] :
( empty(U_748)
& element(U_748,powerset(U_749)) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_749] :
( empty(sK132(U_749))
& element(sK132(U_749),powerset(U_749)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_748,sK132(U_749))],[f_175_2]) ).
fof(f_175_4,plain,
( ! [U_749] : empty(sK132(U_749))
& ! [U_749] : element(sK132(U_749),powerset(U_749)) ),
inference(definitional_conversion,[status(esa)],[f_175_3]) ).
cnf(f_175_5,plain,
element(sK132(U_749),powerset(U_749)),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_6,plain,
empty(sK132(U_749)),
inference(clausify,[status(thm)],[f_175_4]) ).
fof(f_176_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_176_2,plain,
? [U_750] : ~ empty(U_750),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
~ empty(sK133),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_750,sK133)],[f_176_2]) ).
fof(f_176_4,plain,
~ empty(sK133),
inference(definitional_conversion,[status(esa)],[f_176_3]) ).
cnf(f_176_5,plain,
~ empty(sK133),
inference(clausify,[status(thm)],[f_176_4]) ).
fof(f_177_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_177_2,plain,
? [U_751] :
( one_to_one(U_751)
& function(U_751)
& relation(U_751) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
( one_to_one(sK134)
& function(sK134)
& relation(sK134) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_751,sK134)],[f_177_2]) ).
fof(f_177_4,plain,
( one_to_one(sK134)
& function(sK134)
& relation(sK134) ),
inference(definitional_conversion,[status(esa)],[f_177_3]) ).
cnf(f_177_5,plain,
relation(sK134),
inference(clausify,[status(thm)],[f_177_4]) ).
cnf(f_177_6,plain,
function(sK134),
inference(clausify,[status(thm)],[f_177_4]) ).
cnf(f_177_7,plain,
one_to_one(sK134),
inference(clausify,[status(thm)],[f_177_4]) ).
fof(f_178_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_178_2,plain,
? [U_752] :
( ordinal(U_752)
& epsilon_connected(U_752)
& epsilon_transitive(U_752)
& ~ empty(U_752) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
( ordinal(sK135)
& epsilon_connected(sK135)
& epsilon_transitive(sK135)
& ~ empty(sK135) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_752,sK135)],[f_178_2]) ).
fof(f_178_4,plain,
( ordinal(sK135)
& epsilon_connected(sK135)
& epsilon_transitive(sK135)
& ~ empty(sK135) ),
inference(definitional_conversion,[status(esa)],[f_178_3]) ).
cnf(f_178_5,plain,
~ empty(sK135),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_6,plain,
epsilon_transitive(sK135),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_7,plain,
epsilon_connected(sK135),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_8,plain,
ordinal(sK135),
inference(clausify,[status(thm)],[f_178_4]) ).
fof(f_179_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_179_2,plain,
? [U_753] :
( relation_empty_yielding(U_753)
& relation(U_753) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
( relation_empty_yielding(sK136)
& relation(sK136) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_753,sK136)],[f_179_2]) ).
fof(f_179_4,plain,
( relation_empty_yielding(sK136)
& relation(sK136) ),
inference(definitional_conversion,[status(esa)],[f_179_3]) ).
cnf(f_179_5,plain,
relation(sK136),
inference(clausify,[status(thm)],[f_179_4]) ).
cnf(f_179_6,plain,
relation_empty_yielding(sK136),
inference(clausify,[status(thm)],[f_179_4]) ).
fof(f_180_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_180_2,plain,
? [U_754] :
( function(U_754)
& relation_empty_yielding(U_754)
& relation(U_754) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( function(sK137)
& relation_empty_yielding(sK137)
& relation(sK137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_754,sK137)],[f_180_2]) ).
fof(f_180_4,plain,
( function(sK137)
& relation_empty_yielding(sK137)
& relation(sK137) ),
inference(definitional_conversion,[status(esa)],[f_180_3]) ).
cnf(f_180_5,plain,
relation(sK137),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_6,plain,
relation_empty_yielding(sK137),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_7,plain,
function(sK137),
inference(clausify,[status(thm)],[f_180_4]) ).
fof(f_181_1,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1]) ).
fof(f_181_2,plain,
! [U_756,U_755] :
( union_of_subsets(U_756,U_755) = union(U_755)
| ~ element(U_755,powerset(powerset(U_756))) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_755,U_756] :
( union_of_subsets(U_756,U_755) = union(U_755)
| ~ element(U_755,powerset(powerset(U_756))) ),
inference(definitional_conversion,[status(esa)],[f_181_2]) ).
cnf(f_181_4,plain,
( union_of_subsets(U_756,U_755) = union(U_755)
| ~ element(U_755,powerset(powerset(U_756))) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [A,B] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1]) ).
fof(f_182_2,plain,
! [U_758,U_757] :
( meet_of_subsets(U_758,U_757) = set_meet(U_757)
| ~ element(U_757,powerset(powerset(U_758))) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_757,U_758] :
( meet_of_subsets(U_758,U_757) = set_meet(U_757)
| ~ element(U_757,powerset(powerset(U_758))) ),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,plain,
( meet_of_subsets(U_758,U_757) = set_meet(U_757)
| ~ element(U_757,powerset(powerset(U_758))) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1]) ).
fof(f_183_2,plain,
! [U_761,U_760,U_759] :
( subset_difference(U_761,U_760,U_759) = set_difference(U_760,U_759)
| ~ element(U_759,powerset(U_761))
| ~ element(U_760,powerset(U_761)) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_759,U_760,U_761] :
( subset_difference(U_761,U_760,U_759) = set_difference(U_760,U_759)
| ~ element(U_759,powerset(U_761))
| ~ element(U_760,powerset(U_761)) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( subset_difference(U_761,U_760,U_759) = set_difference(U_760,U_759)
| ~ element(U_759,powerset(U_761))
| ~ element(U_760,powerset(U_761)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_184_2,plain,
! [U_764,U_763,U_762] :
( ( relation_of2_as_subset(U_762,U_764,U_763)
| ~ relation_of2(U_762,U_764,U_763) )
& ( relation_of2(U_762,U_764,U_763)
| ~ relation_of2_as_subset(U_762,U_764,U_763) ) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
( ! [U_770,U_768,U_766] :
( relation_of2_as_subset(U_766,U_770,U_768)
| ~ relation_of2(U_766,U_770,U_768) )
& ! [U_769,U_767,U_765] :
( relation_of2(U_765,U_769,U_767)
| ~ relation_of2_as_subset(U_765,U_769,U_767) ) ),
inference(miniscope,[status(thm)],[f_184_2]) ).
fof(f_184_4,plain,
( ! [U_770,U_768,U_766] :
( relation_of2_as_subset(U_766,U_770,U_768)
| ~ relation_of2(U_766,U_770,U_768) )
& ! [U_769,U_765,U_767] :
( relation_of2(U_765,U_769,U_767)
| ~ relation_of2_as_subset(U_765,U_769,U_767) ) ),
inference(definitional_conversion,[status(esa)],[f_184_3]) ).
cnf(f_184_5,plain,
( relation_of2(U_765,U_769,U_767)
| ~ relation_of2_as_subset(U_765,U_769,U_767) ),
inference(clausify,[status(thm)],[f_184_4]) ).
cnf(f_184_6,plain,
( relation_of2_as_subset(U_766,U_770,U_768)
| ~ relation_of2(U_766,U_770,U_768) ),
inference(clausify,[status(thm)],[f_184_4]) ).
fof(f_185_1,plain,
! [A,B] :
( ( ( ordinal_subset(A,B)
| ~ subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1]) ).
fof(f_185_2,plain,
! [U_772,U_771] :
( ( ( ordinal_subset(U_772,U_771)
| ~ subset(U_772,U_771) )
& ( subset(U_772,U_771)
| ~ ordinal_subset(U_772,U_771) ) )
| ~ ordinal(U_771)
| ~ ordinal(U_772) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( ! [U_771,U_772] :
( ordinal_subset(U_772,U_771)
| ~ subset(U_772,U_771)
| ~ sP184(U_771,U_772) )
& ! [U_771,U_772] :
( subset(U_772,U_771)
| ~ ordinal_subset(U_772,U_771)
| ~ sP184(U_771,U_772) )
& ! [U_771,U_772] :
( sP184(U_771,U_772)
| ~ ordinal(U_771)
| ~ ordinal(U_772) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_185_2]) ).
cnf(f_185_4,plain,
( sP184(U_771,U_772)
| ~ ordinal(U_771)
| ~ ordinal(U_772) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_5,plain,
( subset(U_772,U_771)
| ~ ordinal_subset(U_772,U_771)
| ~ sP184(U_771,U_772) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_6,plain,
( ordinal_subset(U_772,U_771)
| ~ subset(U_772,U_771)
| ~ sP184(U_771,U_772) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_186_2,plain,
! [U_774,U_773] :
( ordinal_subset(U_774,U_774)
| ~ ordinal(U_773)
| ~ ordinal(U_774) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_774] :
( ! [U_773] : ~ ordinal(U_773)
| ~ ordinal(U_774)
| ordinal_subset(U_774,U_774) ),
inference(miniscope,[status(thm)],[f_186_2]) ).
fof(f_186_4,plain,
! [U_773,U_774] :
( ~ ordinal(U_773)
| ~ ordinal(U_774)
| ordinal_subset(U_774,U_774) ),
inference(definitional_conversion,[status(esa)],[f_186_3]) ).
cnf(f_186_5,plain,
( ~ ordinal(U_773)
| ~ ordinal(U_774)
| ordinal_subset(U_774,U_774) ),
inference(clausify,[status(thm)],[f_186_4]) ).
fof(f_187_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_187_2,plain,
! [U_776,U_775] : subset(U_776,U_776),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_776] : subset(U_776,U_776),
inference(miniscope,[status(thm)],[f_187_2]) ).
fof(f_187_4,plain,
! [U_776] : subset(U_776,U_776),
inference(definitional_conversion,[status(esa)],[f_187_3]) ).
cnf(f_187_5,plain,
subset(U_776,U_776),
inference(clausify,[status(thm)],[f_187_4]) ).
fof(f_188_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_188_2,plain,
! [U_778,U_777] :
( disjoint(U_777,U_778)
| ~ disjoint(U_778,U_777) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_777,U_778] :
( disjoint(U_777,U_778)
| ~ disjoint(U_778,U_777) ),
inference(definitional_conversion,[status(esa)],[f_188_2]) ).
cnf(f_188_4,plain,
( disjoint(U_777,U_778)
| ~ disjoint(U_778,U_777) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[t106_zfmisc_1]) ).
fof(f_189_2,plain,
! [U_782,U_781,U_780,U_779] :
( ( in(ordered_pair(U_782,U_781),cartesian_product2(U_780,U_779))
| ~ in(U_781,U_779)
| ~ in(U_782,U_780) )
& ( ( in(U_781,U_779)
& in(U_782,U_780) )
| ~ in(ordered_pair(U_782,U_781),cartesian_product2(U_780,U_779)) ) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( ! [U_790,U_788,U_786,U_784] :
( in(ordered_pair(U_790,U_788),cartesian_product2(U_786,U_784))
| ~ in(U_788,U_784)
| ~ in(U_790,U_786) )
& ! [U_789,U_787,U_785,U_783] :
( ( in(U_787,U_783)
& in(U_789,U_785) )
| ~ in(ordered_pair(U_789,U_787),cartesian_product2(U_785,U_783)) ) ),
inference(miniscope,[status(thm)],[f_189_2]) ).
fof(f_189_4,plain,
( ! [U_789,U_783,U_785,U_787] :
( in(U_787,U_783)
| ~ sP185(U_789,U_783,U_785,U_787) )
& ! [U_789,U_783,U_785,U_787] :
( in(U_789,U_785)
| ~ sP185(U_789,U_783,U_785,U_787) )
& ! [U_786,U_790,U_784,U_788] :
( in(ordered_pair(U_790,U_788),cartesian_product2(U_786,U_784))
| ~ in(U_788,U_784)
| ~ in(U_790,U_786) )
& ! [U_789,U_783,U_785,U_787] :
( sP185(U_789,U_783,U_785,U_787)
| ~ in(ordered_pair(U_789,U_787),cartesian_product2(U_785,U_783)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_189_3]) ).
cnf(f_189_5,plain,
( sP185(U_789,U_783,U_785,U_787)
| ~ in(ordered_pair(U_789,U_787),cartesian_product2(U_785,U_783)) ),
inference(clausify,[status(thm)],[f_189_4]) ).
cnf(f_189_6,plain,
( in(ordered_pair(U_790,U_788),cartesian_product2(U_786,U_784))
| ~ in(U_788,U_784)
| ~ in(U_790,U_786) ),
inference(clausify,[status(thm)],[f_189_4]) ).
cnf(f_189_7,plain,
( in(U_789,U_785)
| ~ sP185(U_789,U_783,U_785,U_787) ),
inference(clausify,[status(thm)],[f_189_4]) ).
cnf(f_189_8,plain,
( in(U_787,U_783)
| ~ sP185(U_789,U_783,U_785,U_787) ),
inference(clausify,[status(thm)],[f_189_4]) ).
fof(f_190_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_190_2,plain,
! [U_791] : in(U_791,succ(U_791)),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_791] : in(U_791,succ(U_791)),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
in(U_791,succ(U_791)),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[t10_zfmisc_1]) ).
fof(f_191_2,plain,
! [U_795,U_794,U_793,U_792] :
( U_795 = U_792
| U_795 = U_793
| unordered_pair(U_795,U_794) != unordered_pair(U_793,U_792) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_795,U_794,U_793] :
( ! [U_792] :
( U_795 = U_792
| unordered_pair(U_795,U_794) != unordered_pair(U_793,U_792) )
| U_795 = U_793 ),
inference(miniscope,[status(thm)],[f_191_2]) ).
fof(f_191_4,plain,
! [U_793,U_792,U_794,U_795] :
( U_795 = U_792
| unordered_pair(U_795,U_794) != unordered_pair(U_793,U_792)
| U_795 = U_793 ),
inference(definitional_conversion,[status(esa)],[f_191_3]) ).
cnf(f_191_5,plain,
( U_795 = U_792
| unordered_pair(U_795,U_794) != unordered_pair(U_793,U_792)
| U_795 = U_793 ),
inference(clausify,[status(thm)],[f_191_4]) ).
fof(f_192_1,plain,
! [A,B,C] :
( ( ( in(A,relation_rng(relation_rng_restriction(B,C)))
| ~ in(A,relation_rng(C))
| ~ in(A,B) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t115_relat_1]) ).
fof(f_192_2,plain,
! [U_798,U_797,U_796] :
( ( ( in(U_798,relation_rng(relation_rng_restriction(U_797,U_796)))
| ~ in(U_798,relation_rng(U_796))
| ~ in(U_798,U_797) )
& ( ( in(U_798,relation_rng(U_796))
& in(U_798,U_797) )
| ~ in(U_798,relation_rng(relation_rng_restriction(U_797,U_796))) ) )
| ~ relation(U_796) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
( ! [U_796,U_797,U_798] :
( in(U_798,relation_rng(U_796))
| ~ sP186(U_796,U_797,U_798) )
& ! [U_796,U_797,U_798] :
( in(U_798,U_797)
| ~ sP186(U_796,U_797,U_798) )
& ! [U_796,U_797,U_798] :
( in(U_798,relation_rng(relation_rng_restriction(U_797,U_796)))
| ~ in(U_798,relation_rng(U_796))
| ~ in(U_798,U_797)
| ~ sP187(U_796,U_797,U_798) )
& ! [U_796,U_797,U_798] :
( sP186(U_796,U_797,U_798)
| ~ in(U_798,relation_rng(relation_rng_restriction(U_797,U_796)))
| ~ sP187(U_796,U_797,U_798) )
& ! [U_796,U_797,U_798] :
( sP187(U_796,U_797,U_798)
| ~ relation(U_796) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186,sP187])],[f_192_2]) ).
cnf(f_192_4,plain,
( sP187(U_796,U_797,U_798)
| ~ relation(U_796) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
( sP186(U_796,U_797,U_798)
| ~ in(U_798,relation_rng(relation_rng_restriction(U_797,U_796)))
| ~ sP187(U_796,U_797,U_798) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_6,plain,
( in(U_798,relation_rng(relation_rng_restriction(U_797,U_796)))
| ~ in(U_798,relation_rng(U_796))
| ~ in(U_798,U_797)
| ~ sP187(U_796,U_797,U_798) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_7,plain,
( in(U_798,U_797)
| ~ sP186(U_796,U_797,U_798) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_8,plain,
( in(U_798,relation_rng(U_796))
| ~ sP186(U_796,U_797,U_798) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t116_relat_1]) ).
fof(f_193_2,plain,
! [U_800,U_799] :
( subset(relation_rng(relation_rng_restriction(U_800,U_799)),U_800)
| ~ relation(U_799) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_800,U_799] :
( subset(relation_rng(relation_rng_restriction(U_800,U_799)),U_800)
| ~ relation(U_799) ),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
( subset(relation_rng(relation_rng_restriction(U_800,U_799)),U_800)
| ~ relation(U_799) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_194_2,plain,
! [U_802,U_801] :
( subset(relation_rng_restriction(U_802,U_801),U_801)
| ~ relation(U_801) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_801,U_802] :
( subset(relation_rng_restriction(U_802,U_801),U_801)
| ~ relation(U_801) ),
inference(definitional_conversion,[status(esa)],[f_194_2]) ).
cnf(f_194_4,plain,
( subset(relation_rng_restriction(U_802,U_801),U_801)
| ~ relation(U_801) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t118_relat_1]) ).
fof(f_195_2,plain,
! [U_804,U_803] :
( subset(relation_rng(relation_rng_restriction(U_804,U_803)),relation_rng(U_803))
| ~ relation(U_803) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_803,U_804] :
( subset(relation_rng(relation_rng_restriction(U_804,U_803)),relation_rng(U_803))
| ~ relation(U_803) ),
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
( subset(relation_rng(relation_rng_restriction(U_804,U_803)),relation_rng(U_803))
| ~ relation(U_803) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [A,B,C] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t118_zfmisc_1]) ).
fof(f_196_2,plain,
! [U_807,U_806,U_805] :
( ( subset(cartesian_product2(U_805,U_807),cartesian_product2(U_805,U_806))
& subset(cartesian_product2(U_807,U_805),cartesian_product2(U_806,U_805)) )
| ~ subset(U_807,U_806) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
! [U_807,U_806] :
( ( ! [U_809] : subset(cartesian_product2(U_809,U_807),cartesian_product2(U_809,U_806))
& ! [U_808] : subset(cartesian_product2(U_807,U_808),cartesian_product2(U_806,U_808)) )
| ~ subset(U_807,U_806) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
fof(f_196_4,plain,
( ! [U_806,U_807,U_808,U_809] :
( subset(cartesian_product2(U_809,U_807),cartesian_product2(U_809,U_806))
| ~ sP188(U_806,U_807,U_808,U_809) )
& ! [U_806,U_807,U_808,U_809] :
( subset(cartesian_product2(U_807,U_808),cartesian_product2(U_806,U_808))
| ~ sP188(U_806,U_807,U_808,U_809) )
& ! [U_806,U_807,U_808,U_809] :
( sP188(U_806,U_807,U_808,U_809)
| ~ subset(U_807,U_806) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_196_3]) ).
cnf(f_196_5,plain,
( sP188(U_806,U_807,U_808,U_809)
| ~ subset(U_807,U_806) ),
inference(clausify,[status(thm)],[f_196_4]) ).
cnf(f_196_6,plain,
( subset(cartesian_product2(U_807,U_808),cartesian_product2(U_806,U_808))
| ~ sP188(U_806,U_807,U_808,U_809) ),
inference(clausify,[status(thm)],[f_196_4]) ).
cnf(f_196_7,plain,
( subset(cartesian_product2(U_809,U_807),cartesian_product2(U_809,U_806))
| ~ sP188(U_806,U_807,U_808,U_809) ),
inference(clausify,[status(thm)],[f_196_4]) ).
fof(f_197_1,plain,
! [A,B] :
( relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t119_relat_1]) ).
fof(f_197_2,plain,
! [U_811,U_810] :
( relation_rng(relation_rng_restriction(U_811,U_810)) = set_intersection2(relation_rng(U_810),U_811)
| ~ relation(U_810) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_810,U_811] :
( relation_rng(relation_rng_restriction(U_811,U_810)) = set_intersection2(relation_rng(U_810),U_811)
| ~ relation(U_810) ),
inference(definitional_conversion,[status(esa)],[f_197_2]) ).
cnf(f_197_4,plain,
( relation_rng(relation_rng_restriction(U_811,U_810)) = set_intersection2(relation_rng(U_810),U_811)
| ~ relation(U_810) ),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_1,plain,
! [A,B,C,D] :
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t119_zfmisc_1]) ).
fof(f_198_2,plain,
! [U_815,U_814,U_813,U_812] :
( subset(cartesian_product2(U_815,U_813),cartesian_product2(U_814,U_812))
| ~ subset(U_813,U_812)
| ~ subset(U_815,U_814) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_812,U_813,U_814,U_815] :
( subset(cartesian_product2(U_815,U_813),cartesian_product2(U_814,U_812))
| ~ subset(U_813,U_812)
| ~ subset(U_815,U_814) ),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
( subset(cartesian_product2(U_815,U_813),cartesian_product2(U_814,U_812))
| ~ subset(U_813,U_812)
| ~ subset(U_815,U_814) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [A,B,C] :
( ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[t12_relset_1]) ).
fof(f_199_2,plain,
! [U_818,U_817,U_816] :
( ( subset(relation_rng(U_816),U_817)
& subset(relation_dom(U_816),U_818) )
| ~ relation_of2_as_subset(U_816,U_818,U_817) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
( ! [U_817,U_816,U_818] :
( subset(relation_rng(U_816),U_817)
| ~ sP189(U_817,U_816,U_818) )
& ! [U_817,U_816,U_818] :
( subset(relation_dom(U_816),U_818)
| ~ sP189(U_817,U_816,U_818) )
& ! [U_817,U_816,U_818] :
( sP189(U_817,U_816,U_818)
| ~ relation_of2_as_subset(U_816,U_818,U_817) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_199_2]) ).
cnf(f_199_4,plain,
( sP189(U_817,U_816,U_818)
| ~ relation_of2_as_subset(U_816,U_818,U_817) ),
inference(clausify,[status(thm)],[f_199_3]) ).
cnf(f_199_5,plain,
( subset(relation_dom(U_816),U_818)
| ~ sP189(U_817,U_816,U_818) ),
inference(clausify,[status(thm)],[f_199_3]) ).
cnf(f_199_6,plain,
( subset(relation_rng(U_816),U_817)
| ~ sP189(U_817,U_816,U_818) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_200_2,plain,
! [U_820,U_819] :
( set_union2(U_820,U_819) = U_819
| ~ subset(U_820,U_819) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_820,U_819] :
( set_union2(U_820,U_819) = U_819
| ~ subset(U_820,U_819) ),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
( set_union2(U_820,U_819) = U_819
| ~ subset(U_820,U_819) ),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_1,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( in(powerset(C),B)
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t136_zfmisc_1]) ).
fof(f_201_2,plain,
! [U_826] :
? [U_825] :
( ! [U_824] :
( in(U_824,U_825)
| are_equipotent(U_824,U_825)
| ~ subset(U_824,U_825) )
& ! [U_823] :
( in(powerset(U_823),U_825)
| ~ in(U_823,U_825) )
& ! [U_822,U_821] :
( in(U_821,U_825)
| ~ subset(U_821,U_822)
| ~ in(U_822,U_825) )
& in(U_826,U_825) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_826] :
( ! [U_824] :
( in(U_824,sK138(U_826))
| are_equipotent(U_824,sK138(U_826))
| ~ subset(U_824,sK138(U_826)) )
& ! [U_823] :
( in(powerset(U_823),sK138(U_826))
| ~ in(U_823,sK138(U_826)) )
& ! [U_822,U_821] :
( in(U_821,sK138(U_826))
| ~ subset(U_821,U_822)
| ~ in(U_822,sK138(U_826)) )
& in(U_826,sK138(U_826)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_825,sK138(U_826))],[f_201_2]) ).
fof(f_201_4,plain,
( ! [U_824,U_826] :
( in(U_824,sK138(U_826))
| are_equipotent(U_824,sK138(U_826))
| ~ subset(U_824,sK138(U_826)) )
& ! [U_823,U_826] :
( in(powerset(U_823),sK138(U_826))
| ~ in(U_823,sK138(U_826)) )
& ! [U_822,U_821,U_826] :
( in(U_821,sK138(U_826))
| ~ subset(U_821,U_822)
| ~ in(U_822,sK138(U_826)) )
& ! [U_826] : in(U_826,sK138(U_826)) ),
inference(definitional_conversion,[status(esa)],[f_201_3]) ).
cnf(f_201_5,plain,
in(U_826,sK138(U_826)),
inference(clausify,[status(thm)],[f_201_4]) ).
cnf(f_201_6,plain,
( in(U_821,sK138(U_826))
| ~ subset(U_821,U_822)
| ~ in(U_822,sK138(U_826)) ),
inference(clausify,[status(thm)],[f_201_4]) ).
cnf(f_201_7,plain,
( in(powerset(U_823),sK138(U_826))
| ~ in(U_823,sK138(U_826)) ),
inference(clausify,[status(thm)],[f_201_4]) ).
cnf(f_201_8,plain,
( in(U_824,sK138(U_826))
| are_equipotent(U_824,sK138(U_826))
| ~ subset(U_824,sK138(U_826)) ),
inference(clausify,[status(thm)],[f_201_4]) ).
fof(f_202_1,plain,
! [A,B,C] :
( relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t140_relat_1]) ).
fof(f_202_2,plain,
! [U_829,U_828,U_827] :
( relation_dom_restriction(relation_rng_restriction(U_829,U_827),U_828) = relation_rng_restriction(U_829,relation_dom_restriction(U_827,U_828))
| ~ relation(U_827) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_827,U_828,U_829] :
( relation_dom_restriction(relation_rng_restriction(U_829,U_827),U_828) = relation_rng_restriction(U_829,relation_dom_restriction(U_827,U_828))
| ~ relation(U_827) ),
inference(definitional_conversion,[status(esa)],[f_202_2]) ).
cnf(f_202_4,plain,
( relation_dom_restriction(relation_rng_restriction(U_829,U_827),U_828) = relation_rng_restriction(U_829,relation_dom_restriction(U_827,U_828))
| ~ relation(U_827) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_1,plain,
! [A,B,C] :
( ( ( in(A,relation_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(D,A),C)
| ~ in(D,relation_dom(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(D,A),C)
& in(D,relation_dom(C)) )
| ~ in(A,relation_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t143_relat_1]) ).
fof(f_203_2,plain,
! [U_834,U_833,U_832] :
( ( ( in(U_834,relation_image(U_832,U_833))
| ! [U_831] :
( ~ in(U_831,U_833)
| ~ in(ordered_pair(U_831,U_834),U_832)
| ~ in(U_831,relation_dom(U_832)) ) )
& ( ? [U_830] :
( in(U_830,U_833)
& in(ordered_pair(U_830,U_834),U_832)
& in(U_830,relation_dom(U_832)) )
| ~ in(U_834,relation_image(U_832,U_833)) ) )
| ~ relation(U_832) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_834,U_833,U_832] :
( ( ( in(U_834,relation_image(U_832,U_833))
| ! [U_831] :
( ~ in(U_831,U_833)
| ~ in(ordered_pair(U_831,U_834),U_832)
| ~ in(U_831,relation_dom(U_832)) ) )
& ( ( in(sK139(U_834,U_833,U_832),U_833)
& in(ordered_pair(sK139(U_834,U_833,U_832),U_834),U_832)
& in(sK139(U_834,U_833,U_832),relation_dom(U_832)) )
| ~ in(U_834,relation_image(U_832,U_833)) ) )
| ~ relation(U_832) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_830,sK139(U_834,U_833,U_832))],[f_203_2]) ).
fof(f_203_4,plain,
( ! [U_832,U_833,U_834] :
( in(sK139(U_834,U_833,U_832),U_833)
| ~ sP190(U_832,U_833,U_834) )
& ! [U_832,U_833,U_834] :
( in(ordered_pair(sK139(U_834,U_833,U_832),U_834),U_832)
| ~ sP190(U_832,U_833,U_834) )
& ! [U_832,U_833,U_834] :
( in(sK139(U_834,U_833,U_832),relation_dom(U_832))
| ~ sP190(U_832,U_833,U_834) )
& ! [U_831,U_832,U_833,U_834] :
( in(U_834,relation_image(U_832,U_833))
| ~ in(U_831,U_833)
| ~ in(ordered_pair(U_831,U_834),U_832)
| ~ in(U_831,relation_dom(U_832))
| ~ sP191(U_831,U_832,U_833,U_834) )
& ! [U_831,U_832,U_833,U_834] :
( sP190(U_832,U_833,U_834)
| ~ in(U_834,relation_image(U_832,U_833))
| ~ sP191(U_831,U_832,U_833,U_834) )
& ! [U_831,U_832,U_833,U_834] :
( sP191(U_831,U_832,U_833,U_834)
| ~ relation(U_832) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190,sP191])],[f_203_3]) ).
cnf(f_203_5,plain,
( sP191(U_831,U_832,U_833,U_834)
| ~ relation(U_832) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_6,plain,
( sP190(U_832,U_833,U_834)
| ~ in(U_834,relation_image(U_832,U_833))
| ~ sP191(U_831,U_832,U_833,U_834) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_7,plain,
( in(U_834,relation_image(U_832,U_833))
| ~ in(U_831,U_833)
| ~ in(ordered_pair(U_831,U_834),U_832)
| ~ in(U_831,relation_dom(U_832))
| ~ sP191(U_831,U_832,U_833,U_834) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_8,plain,
( in(sK139(U_834,U_833,U_832),relation_dom(U_832))
| ~ sP190(U_832,U_833,U_834) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_9,plain,
( in(ordered_pair(sK139(U_834,U_833,U_832),U_834),U_832)
| ~ sP190(U_832,U_833,U_834) ),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_10,plain,
( in(sK139(U_834,U_833,U_832),U_833)
| ~ sP190(U_832,U_833,U_834) ),
inference(clausify,[status(thm)],[f_203_4]) ).
fof(f_204_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_204_2,plain,
! [U_836,U_835] :
( subset(relation_image(U_835,U_836),relation_rng(U_835))
| ~ relation(U_835) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_836,U_835] :
( subset(relation_image(U_835,U_836),relation_rng(U_835))
| ~ relation(U_835) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( subset(relation_image(U_835,U_836),relation_rng(U_835))
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_1,plain,
! [A,B] :
( subset(relation_image(B,relation_inverse_image(B,A)),A)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_funct_1]) ).
fof(f_205_2,plain,
! [U_838,U_837] :
( subset(relation_image(U_837,relation_inverse_image(U_837,U_838)),U_838)
| ~ function(U_837)
| ~ relation(U_837) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_837,U_838] :
( subset(relation_image(U_837,relation_inverse_image(U_837,U_838)),U_838)
| ~ function(U_837)
| ~ relation(U_837) ),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
( subset(relation_image(U_837,relation_inverse_image(U_837,U_838)),U_838)
| ~ function(U_837)
| ~ relation(U_837) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_1,plain,
! [A,B] :
( relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t145_relat_1]) ).
fof(f_206_2,plain,
! [U_840,U_839] :
( relation_image(U_839,U_840) = relation_image(U_839,set_intersection2(relation_dom(U_839),U_840))
| ~ relation(U_839) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_839,U_840] :
( relation_image(U_839,U_840) = relation_image(U_839,set_intersection2(relation_dom(U_839),U_840))
| ~ relation(U_839) ),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
( relation_image(U_839,U_840) = relation_image(U_839,set_intersection2(relation_dom(U_839),U_840))
| ~ relation(U_839) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
! [A,B] :
( subset(A,relation_inverse_image(B,relation_image(B,A)))
| ~ subset(A,relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t146_funct_1]) ).
fof(f_207_2,plain,
! [U_842,U_841] :
( subset(U_842,relation_inverse_image(U_841,relation_image(U_841,U_842)))
| ~ subset(U_842,relation_dom(U_841))
| ~ relation(U_841) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_842,U_841] :
( subset(U_842,relation_inverse_image(U_841,relation_image(U_841,U_842)))
| ~ subset(U_842,relation_dom(U_841))
| ~ relation(U_841) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( subset(U_842,relation_inverse_image(U_841,relation_image(U_841,U_842)))
| ~ subset(U_842,relation_dom(U_841))
| ~ relation(U_841) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_208_2,plain,
! [U_843] :
( relation_image(U_843,relation_dom(U_843)) = relation_rng(U_843)
| ~ relation(U_843) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_843] :
( relation_image(U_843,relation_dom(U_843)) = relation_rng(U_843)
| ~ relation(U_843) ),
inference(definitional_conversion,[status(esa)],[f_208_2]) ).
cnf(f_208_4,plain,
( relation_image(U_843,relation_dom(U_843)) = relation_rng(U_843)
| ~ relation(U_843) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_1,plain,
! [A,B] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B))
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t147_funct_1]) ).
fof(f_209_2,plain,
! [U_845,U_844] :
( relation_image(U_844,relation_inverse_image(U_844,U_845)) = U_845
| ~ subset(U_845,relation_rng(U_844))
| ~ function(U_844)
| ~ relation(U_844) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_844,U_845] :
( relation_image(U_844,relation_inverse_image(U_844,U_845)) = U_845
| ~ subset(U_845,relation_rng(U_844))
| ~ function(U_844)
| ~ relation(U_844) ),
inference(definitional_conversion,[status(esa)],[f_209_2]) ).
cnf(f_209_4,plain,
( relation_image(U_844,relation_inverse_image(U_844,U_845)) = U_845
| ~ subset(U_845,relation_rng(U_844))
| ~ function(U_844)
| ~ relation(U_844) ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_1,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(fof_nnf,[status(thm)],[t14_relset_1]) ).
fof(f_210_2,plain,
! [U_849,U_848,U_847,U_846] :
( relation_of2_as_subset(U_846,U_847,U_848)
| ~ subset(relation_rng(U_846),U_848)
| ~ relation_of2_as_subset(U_846,U_847,U_849) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_846,U_847,U_848,U_849] :
( relation_of2_as_subset(U_846,U_847,U_848)
| ~ subset(relation_rng(U_846),U_848)
| ~ relation_of2_as_subset(U_846,U_847,U_849) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( relation_of2_as_subset(U_846,U_847,U_848)
| ~ subset(relation_rng(U_846),U_848)
| ~ relation_of2_as_subset(U_846,U_847,U_849) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t160_relat_1]) ).
fof(f_211_2,plain,
! [U_851] :
( ! [U_850] :
( relation_rng(relation_composition(U_851,U_850)) = relation_image(U_850,relation_rng(U_851))
| ~ relation(U_850) )
| ~ relation(U_851) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_850,U_851] :
( relation_rng(relation_composition(U_851,U_850)) = relation_image(U_850,relation_rng(U_851))
| ~ relation(U_850)
| ~ relation(U_851) ),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
( relation_rng(relation_composition(U_851,U_850)) = relation_image(U_850,relation_rng(U_851))
| ~ relation(U_850)
| ~ relation(U_851) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_1,plain,
! [A,B,C] :
( ( ( in(A,relation_inverse_image(C,B))
| ! [D] :
( ~ in(D,B)
| ~ in(ordered_pair(A,D),C)
| ~ in(D,relation_rng(C)) ) )
& ( ? [D] :
( in(D,B)
& in(ordered_pair(A,D),C)
& in(D,relation_rng(C)) )
| ~ in(A,relation_inverse_image(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t166_relat_1]) ).
fof(f_212_2,plain,
! [U_856,U_855,U_854] :
( ( ( in(U_856,relation_inverse_image(U_854,U_855))
| ! [U_853] :
( ~ in(U_853,U_855)
| ~ in(ordered_pair(U_856,U_853),U_854)
| ~ in(U_853,relation_rng(U_854)) ) )
& ( ? [U_852] :
( in(U_852,U_855)
& in(ordered_pair(U_856,U_852),U_854)
& in(U_852,relation_rng(U_854)) )
| ~ in(U_856,relation_inverse_image(U_854,U_855)) ) )
| ~ relation(U_854) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_856,U_855,U_854] :
( ( ( in(U_856,relation_inverse_image(U_854,U_855))
| ! [U_853] :
( ~ in(U_853,U_855)
| ~ in(ordered_pair(U_856,U_853),U_854)
| ~ in(U_853,relation_rng(U_854)) ) )
& ( ( in(sK140(U_856,U_855,U_854),U_855)
& in(ordered_pair(U_856,sK140(U_856,U_855,U_854)),U_854)
& in(sK140(U_856,U_855,U_854),relation_rng(U_854)) )
| ~ in(U_856,relation_inverse_image(U_854,U_855)) ) )
| ~ relation(U_854) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_852,sK140(U_856,U_855,U_854))],[f_212_2]) ).
fof(f_212_4,plain,
( ! [U_854,U_855,U_856] :
( in(sK140(U_856,U_855,U_854),U_855)
| ~ sP192(U_854,U_855,U_856) )
& ! [U_854,U_855,U_856] :
( in(ordered_pair(U_856,sK140(U_856,U_855,U_854)),U_854)
| ~ sP192(U_854,U_855,U_856) )
& ! [U_854,U_855,U_856] :
( in(sK140(U_856,U_855,U_854),relation_rng(U_854))
| ~ sP192(U_854,U_855,U_856) )
& ! [U_853,U_854,U_855,U_856] :
( in(U_856,relation_inverse_image(U_854,U_855))
| ~ in(U_853,U_855)
| ~ in(ordered_pair(U_856,U_853),U_854)
| ~ in(U_853,relation_rng(U_854))
| ~ sP193(U_853,U_854,U_855,U_856) )
& ! [U_853,U_854,U_855,U_856] :
( sP192(U_854,U_855,U_856)
| ~ in(U_856,relation_inverse_image(U_854,U_855))
| ~ sP193(U_853,U_854,U_855,U_856) )
& ! [U_853,U_854,U_855,U_856] :
( sP193(U_853,U_854,U_855,U_856)
| ~ relation(U_854) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192,sP193])],[f_212_3]) ).
cnf(f_212_5,plain,
( sP193(U_853,U_854,U_855,U_856)
| ~ relation(U_854) ),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_6,plain,
( sP192(U_854,U_855,U_856)
| ~ in(U_856,relation_inverse_image(U_854,U_855))
| ~ sP193(U_853,U_854,U_855,U_856) ),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_7,plain,
( in(U_856,relation_inverse_image(U_854,U_855))
| ~ in(U_853,U_855)
| ~ in(ordered_pair(U_856,U_853),U_854)
| ~ in(U_853,relation_rng(U_854))
| ~ sP193(U_853,U_854,U_855,U_856) ),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_8,plain,
( in(sK140(U_856,U_855,U_854),relation_rng(U_854))
| ~ sP192(U_854,U_855,U_856) ),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_9,plain,
( in(ordered_pair(U_856,sK140(U_856,U_855,U_854)),U_854)
| ~ sP192(U_854,U_855,U_856) ),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_10,plain,
( in(sK140(U_856,U_855,U_854),U_855)
| ~ sP192(U_854,U_855,U_856) ),
inference(clausify,[status(thm)],[f_212_4]) ).
fof(f_213_1,plain,
! [A,B] :
( subset(relation_inverse_image(B,A),relation_dom(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t167_relat_1]) ).
fof(f_213_2,plain,
! [U_858,U_857] :
( subset(relation_inverse_image(U_857,U_858),relation_dom(U_857))
| ~ relation(U_857) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_857,U_858] :
( subset(relation_inverse_image(U_857,U_858),relation_dom(U_857))
| ~ relation(U_857) ),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
( subset(relation_inverse_image(U_857,U_858),relation_dom(U_857))
| ~ relation(U_857) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_1,negated_conjecture,
~ ! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
inference(negate,[status(cth)],[t16_relset_1]) ).
fof(f_214_2,negated_conjecture,
? [A,B,C,D] :
( ~ relation_of2_as_subset(D,C,B)
& subset(A,B)
& relation_of2_as_subset(D,C,A) ),
inference(fof_nnf,[status(thm)],[f_214_1]) ).
fof(f_214_3,negated_conjecture,
? [U_862,U_861,U_860,U_859] :
( ~ relation_of2_as_subset(U_859,U_860,U_861)
& subset(U_862,U_861)
& relation_of2_as_subset(U_859,U_860,U_862) ),
inference(variable_rename,[status(thm)],[f_214_2]) ).
fof(f_214_4,negated_conjecture,
? [U_861,U_860,U_859] :
( ~ relation_of2_as_subset(U_859,U_860,U_861)
& subset(sK141,U_861)
& relation_of2_as_subset(U_859,U_860,sK141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_862,sK141)],[f_214_3]) ).
fof(f_214_5,negated_conjecture,
? [U_860,U_859] :
( ~ relation_of2_as_subset(U_859,U_860,sK142)
& subset(sK141,sK142)
& relation_of2_as_subset(U_859,U_860,sK141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_861,sK142)],[f_214_4]) ).
fof(f_214_6,negated_conjecture,
? [U_859] :
( ~ relation_of2_as_subset(U_859,sK143,sK142)
& subset(sK141,sK142)
& relation_of2_as_subset(U_859,sK143,sK141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_860,sK143)],[f_214_5]) ).
fof(f_214_7,negated_conjecture,
( ~ relation_of2_as_subset(sK144,sK143,sK142)
& subset(sK141,sK142)
& relation_of2_as_subset(sK144,sK143,sK141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_859,sK144)],[f_214_6]) ).
fof(f_214_8,negated_conjecture,
( ~ relation_of2_as_subset(sK144,sK143,sK142)
& subset(sK141,sK142)
& relation_of2_as_subset(sK144,sK143,sK141) ),
inference(definitional_conversion,[status(esa)],[f_214_7]) ).
cnf(f_214_9,negated_conjecture,
relation_of2_as_subset(sK144,sK143,sK141),
inference(clausify,[status(thm)],[f_214_8]) ).
cnf(f_214_10,negated_conjecture,
subset(sK141,sK142),
inference(clausify,[status(thm)],[f_214_8]) ).
cnf(f_214_11,negated_conjecture,
~ relation_of2_as_subset(sK144,sK143,sK142),
inference(clausify,[status(thm)],[f_214_8]) ).
fof(f_215_1,plain,
! [A,B,C] :
( ( ( in(A,relation_restriction(C,B))
| ~ in(A,cartesian_product2(B,B))
| ~ in(A,C) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t16_wellord1]) ).
fof(f_215_2,plain,
! [U_865,U_864,U_863] :
( ( ( in(U_865,relation_restriction(U_863,U_864))
| ~ in(U_865,cartesian_product2(U_864,U_864))
| ~ in(U_865,U_863) )
& ( ( in(U_865,cartesian_product2(U_864,U_864))
& in(U_865,U_863) )
| ~ in(U_865,relation_restriction(U_863,U_864)) ) )
| ~ relation(U_863) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
( ! [U_863,U_864,U_865] :
( in(U_865,cartesian_product2(U_864,U_864))
| ~ sP194(U_863,U_864,U_865) )
& ! [U_863,U_864,U_865] :
( in(U_865,U_863)
| ~ sP194(U_863,U_864,U_865) )
& ! [U_863,U_864,U_865] :
( in(U_865,relation_restriction(U_863,U_864))
| ~ in(U_865,cartesian_product2(U_864,U_864))
| ~ in(U_865,U_863)
| ~ sP195(U_863,U_864,U_865) )
& ! [U_863,U_864,U_865] :
( sP194(U_863,U_864,U_865)
| ~ in(U_865,relation_restriction(U_863,U_864))
| ~ sP195(U_863,U_864,U_865) )
& ! [U_863,U_864,U_865] :
( sP195(U_863,U_864,U_865)
| ~ relation(U_863) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194,sP195])],[f_215_2]) ).
cnf(f_215_4,plain,
( sP195(U_863,U_864,U_865)
| ~ relation(U_863) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_5,plain,
( sP194(U_863,U_864,U_865)
| ~ in(U_865,relation_restriction(U_863,U_864))
| ~ sP195(U_863,U_864,U_865) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_6,plain,
( in(U_865,relation_restriction(U_863,U_864))
| ~ in(U_865,cartesian_product2(U_864,U_864))
| ~ in(U_865,U_863)
| ~ sP195(U_863,U_864,U_865) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_7,plain,
( in(U_865,U_863)
| ~ sP194(U_863,U_864,U_865) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_8,plain,
( in(U_865,cartesian_product2(U_864,U_864))
| ~ sP194(U_863,U_864,U_865) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_1,plain,
! [A,B] :
( relation_inverse_image(B,A) != empty_set
| ~ subset(A,relation_rng(B))
| A = empty_set
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t174_relat_1]) ).
fof(f_216_2,plain,
! [U_867,U_866] :
( relation_inverse_image(U_866,U_867) != empty_set
| ~ subset(U_867,relation_rng(U_866))
| U_867 = empty_set
| ~ relation(U_866) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_866,U_867] :
( relation_inverse_image(U_866,U_867) != empty_set
| ~ subset(U_867,relation_rng(U_866))
| U_867 = empty_set
| ~ relation(U_866) ),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
( relation_inverse_image(U_866,U_867) != empty_set
| ~ subset(U_867,relation_rng(U_866))
| U_867 = empty_set
| ~ relation(U_866) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [A,B,C] :
( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
| ~ subset(A,B)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t178_relat_1]) ).
fof(f_217_2,plain,
! [U_870,U_869,U_868] :
( subset(relation_inverse_image(U_868,U_870),relation_inverse_image(U_868,U_869))
| ~ subset(U_870,U_869)
| ~ relation(U_868) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_868,U_869,U_870] :
( subset(relation_inverse_image(U_868,U_870),relation_inverse_image(U_868,U_869))
| ~ subset(U_870,U_869)
| ~ relation(U_868) ),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
( subset(relation_inverse_image(U_868,U_870),relation_inverse_image(U_868,U_869))
| ~ subset(U_870,U_869)
| ~ relation(U_868) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_1,plain,
! [A,B] :
( relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t17_wellord1]) ).
fof(f_218_2,plain,
! [U_872,U_871] :
( relation_restriction(U_871,U_872) = relation_dom_restriction(relation_rng_restriction(U_872,U_871),U_872)
| ~ relation(U_871) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_872,U_871] :
( relation_restriction(U_871,U_872) = relation_dom_restriction(relation_rng_restriction(U_872,U_871),U_872)
| ~ relation(U_871) ),
inference(definitional_conversion,[status(esa)],[f_218_2]) ).
cnf(f_218_4,plain,
( relation_restriction(U_871,U_872) = relation_dom_restriction(relation_rng_restriction(U_872,U_871),U_872)
| ~ relation(U_871) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_219_2,plain,
! [U_874,U_873] : subset(set_intersection2(U_874,U_873),U_874),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_873,U_874] : subset(set_intersection2(U_874,U_873),U_874),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
subset(set_intersection2(U_874,U_873),U_874),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_1,plain,
! [A,B] :
( relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t18_wellord1]) ).
fof(f_220_2,plain,
! [U_876,U_875] :
( relation_restriction(U_875,U_876) = relation_rng_restriction(U_876,relation_dom_restriction(U_875,U_876))
| ~ relation(U_875) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_875,U_876] :
( relation_restriction(U_875,U_876) = relation_rng_restriction(U_876,relation_dom_restriction(U_875,U_876))
| ~ relation(U_875) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( relation_restriction(U_875,U_876) = relation_rng_restriction(U_876,relation_dom_restriction(U_875,U_876))
| ~ relation(U_875) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [A,B,C] :
( ( in(A,B)
& in(A,relation_field(C)) )
| ~ in(A,relation_field(relation_restriction(C,B)))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t19_wellord1]) ).
fof(f_221_2,plain,
! [U_879,U_878,U_877] :
( ( in(U_879,U_878)
& in(U_879,relation_field(U_877)) )
| ~ in(U_879,relation_field(relation_restriction(U_877,U_878)))
| ~ relation(U_877) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
( ! [U_877,U_878,U_879] :
( in(U_879,U_878)
| ~ sP196(U_877,U_878,U_879) )
& ! [U_877,U_878,U_879] :
( in(U_879,relation_field(U_877))
| ~ sP196(U_877,U_878,U_879) )
& ! [U_877,U_878,U_879] :
( sP196(U_877,U_878,U_879)
| ~ in(U_879,relation_field(relation_restriction(U_877,U_878)))
| ~ relation(U_877) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_221_2]) ).
cnf(f_221_4,plain,
( sP196(U_877,U_878,U_879)
| ~ in(U_879,relation_field(relation_restriction(U_877,U_878)))
| ~ relation(U_877) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_5,plain,
( in(U_879,relation_field(U_877))
| ~ sP196(U_877,U_878,U_879) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_6,plain,
( in(U_879,U_878)
| ~ sP196(U_877,U_878,U_879) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t19_xboole_1]) ).
fof(f_222_2,plain,
! [U_882,U_881,U_880] :
( subset(U_882,set_intersection2(U_881,U_880))
| ~ subset(U_882,U_880)
| ~ subset(U_882,U_881) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_882,U_880,U_881] :
( subset(U_882,set_intersection2(U_881,U_880))
| ~ subset(U_882,U_880)
| ~ subset(U_882,U_881) ),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
( subset(U_882,set_intersection2(U_881,U_880))
| ~ subset(U_882,U_880)
| ~ subset(U_882,U_881) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_223_2,plain,
! [U_883] : set_union2(U_883,empty_set) = U_883,
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_883] : set_union2(U_883,empty_set) = U_883,
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
set_union2(U_883,empty_set) = U_883,
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_224_2,plain,
! [U_885,U_884] :
( element(U_885,U_884)
| ~ in(U_885,U_884) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_884,U_885] :
( element(U_885,U_884)
| ~ in(U_885,U_884) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( element(U_885,U_884)
| ~ in(U_885,U_884) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_225_2,plain,
! [U_888,U_887,U_886] :
( subset(U_888,U_886)
| ~ subset(U_887,U_886)
| ~ subset(U_888,U_887) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_887,U_886,U_888] :
( subset(U_888,U_886)
| ~ subset(U_887,U_886)
| ~ subset(U_888,U_887) ),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
( subset(U_888,U_886)
| ~ subset(U_887,U_886)
| ~ subset(U_888,U_887) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_226_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_226_1]) ).
cnf(f_226_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_1,plain,
! [A,B,C] :
( ( in(B,relation_rng(C))
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t20_relat_1]) ).
fof(f_227_2,plain,
! [U_891,U_890,U_889] :
( ( in(U_890,relation_rng(U_889))
& in(U_891,relation_dom(U_889)) )
| ~ in(ordered_pair(U_891,U_890),U_889)
| ~ relation(U_889) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
( ! [U_889,U_890,U_891] :
( in(U_890,relation_rng(U_889))
| ~ sP197(U_889,U_890,U_891) )
& ! [U_889,U_890,U_891] :
( in(U_891,relation_dom(U_889))
| ~ sP197(U_889,U_890,U_891) )
& ! [U_889,U_890,U_891] :
( sP197(U_889,U_890,U_891)
| ~ in(ordered_pair(U_891,U_890),U_889)
| ~ relation(U_889) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_227_2]) ).
cnf(f_227_4,plain,
( sP197(U_889,U_890,U_891)
| ~ in(ordered_pair(U_891,U_890),U_889)
| ~ relation(U_889) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_5,plain,
( in(U_891,relation_dom(U_889))
| ~ sP197(U_889,U_890,U_891) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_6,plain,
( in(U_890,relation_rng(U_889))
| ~ sP197(U_889,U_890,U_891) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_1,plain,
! [A,B] :
( ( subset(relation_field(relation_restriction(B,A)),A)
& subset(relation_field(relation_restriction(B,A)),relation_field(B)) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t20_wellord1]) ).
fof(f_228_2,plain,
! [U_893,U_892] :
( ( subset(relation_field(relation_restriction(U_892,U_893)),U_893)
& subset(relation_field(relation_restriction(U_892,U_893)),relation_field(U_892)) )
| ~ relation(U_892) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
( ! [U_893,U_892] :
( subset(relation_field(relation_restriction(U_892,U_893)),U_893)
| ~ sP198(U_893,U_892) )
& ! [U_893,U_892] :
( subset(relation_field(relation_restriction(U_892,U_893)),relation_field(U_892))
| ~ sP198(U_893,U_892) )
& ! [U_893,U_892] :
( sP198(U_893,U_892)
| ~ relation(U_892) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_228_2]) ).
cnf(f_228_4,plain,
( sP198(U_893,U_892)
| ~ relation(U_892) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_5,plain,
( subset(relation_field(relation_restriction(U_892,U_893)),relation_field(U_892))
| ~ sP198(U_893,U_892) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_6,plain,
( subset(relation_field(relation_restriction(U_892,U_893)),U_893)
| ~ sP198(U_893,U_892) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [A,B] :
( ! [C] :
( ( ( in(A,relation_dom(relation_composition(C,B)))
| ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C)) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t21_funct_1]) ).
fof(f_229_2,plain,
! [U_896,U_895] :
( ! [U_894] :
( ( ( in(U_896,relation_dom(relation_composition(U_894,U_895)))
| ~ in(apply(U_894,U_896),relation_dom(U_895))
| ~ in(U_896,relation_dom(U_894)) )
& ( ( in(apply(U_894,U_896),relation_dom(U_895))
& in(U_896,relation_dom(U_894)) )
| ~ in(U_896,relation_dom(relation_composition(U_894,U_895))) ) )
| ~ function(U_894)
| ~ relation(U_894) )
| ~ function(U_895)
| ~ relation(U_895) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
( ! [U_894,U_895,U_896] :
( in(apply(U_894,U_896),relation_dom(U_895))
| ~ sP199(U_894,U_895,U_896) )
& ! [U_894,U_895,U_896] :
( in(U_896,relation_dom(U_894))
| ~ sP199(U_894,U_895,U_896) )
& ! [U_894,U_895,U_896] :
( in(U_896,relation_dom(relation_composition(U_894,U_895)))
| ~ in(apply(U_894,U_896),relation_dom(U_895))
| ~ in(U_896,relation_dom(U_894))
| ~ sP200(U_894,U_895,U_896) )
& ! [U_894,U_895,U_896] :
( sP199(U_894,U_895,U_896)
| ~ in(U_896,relation_dom(relation_composition(U_894,U_895)))
| ~ sP200(U_894,U_895,U_896) )
& ! [U_894,U_895,U_896] :
( sP200(U_894,U_895,U_896)
| ~ function(U_894)
| ~ relation(U_894)
| ~ function(U_895)
| ~ relation(U_895) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199,sP200])],[f_229_2]) ).
cnf(f_229_4,plain,
( sP200(U_894,U_895,U_896)
| ~ function(U_894)
| ~ relation(U_894)
| ~ function(U_895)
| ~ relation(U_895) ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_5,plain,
( sP199(U_894,U_895,U_896)
| ~ in(U_896,relation_dom(relation_composition(U_894,U_895)))
| ~ sP200(U_894,U_895,U_896) ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_6,plain,
( in(U_896,relation_dom(relation_composition(U_894,U_895)))
| ~ in(apply(U_894,U_896),relation_dom(U_895))
| ~ in(U_896,relation_dom(U_894))
| ~ sP200(U_894,U_895,U_896) ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_7,plain,
( in(U_896,relation_dom(U_894))
| ~ sP199(U_894,U_895,U_896) ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_8,plain,
( in(apply(U_894,U_896),relation_dom(U_895))
| ~ sP199(U_894,U_895,U_896) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[t21_ordinal1]) ).
fof(f_230_2,plain,
! [U_898] :
( ! [U_897] :
( in(U_898,U_897)
| ~ proper_subset(U_898,U_897)
| ~ ordinal(U_897) )
| ~ epsilon_transitive(U_898) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_898,U_897] :
( in(U_898,U_897)
| ~ proper_subset(U_898,U_897)
| ~ ordinal(U_897)
| ~ epsilon_transitive(U_898) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( in(U_898,U_897)
| ~ proper_subset(U_898,U_897)
| ~ ordinal(U_897)
| ~ epsilon_transitive(U_898) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t21_relat_1]) ).
fof(f_231_2,plain,
! [U_899] :
( subset(U_899,cartesian_product2(relation_dom(U_899),relation_rng(U_899)))
| ~ relation(U_899) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_899] :
( subset(U_899,cartesian_product2(relation_dom(U_899),relation_rng(U_899)))
| ~ relation(U_899) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( subset(U_899,cartesian_product2(relation_dom(U_899),relation_rng(U_899)))
| ~ relation(U_899) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
! [A,B,C] :
( subset(fiber(relation_restriction(C,A),B),fiber(C,B))
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t21_wellord1]) ).
fof(f_232_2,plain,
! [U_902,U_901,U_900] :
( subset(fiber(relation_restriction(U_900,U_902),U_901),fiber(U_900,U_901))
| ~ relation(U_900) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_901,U_900,U_902] :
( subset(fiber(relation_restriction(U_900,U_902),U_901),fiber(U_900,U_901))
| ~ relation(U_900) ),
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
( subset(fiber(relation_restriction(U_900,U_902),U_901),fiber(U_900,U_901))
| ~ relation(U_900) ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B)))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_funct_1]) ).
fof(f_233_2,plain,
! [U_905,U_904] :
( ! [U_903] :
( apply(relation_composition(U_903,U_904),U_905) = apply(U_904,apply(U_903,U_905))
| ~ in(U_905,relation_dom(relation_composition(U_903,U_904)))
| ~ function(U_903)
| ~ relation(U_903) )
| ~ function(U_904)
| ~ relation(U_904) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_903,U_904,U_905] :
( apply(relation_composition(U_903,U_904),U_905) = apply(U_904,apply(U_903,U_905))
| ~ in(U_905,relation_dom(relation_composition(U_903,U_904)))
| ~ function(U_903)
| ~ relation(U_903)
| ~ function(U_904)
| ~ relation(U_904) ),
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
( apply(relation_composition(U_903,U_904),U_905) = apply(U_904,apply(U_903,U_905))
| ~ in(U_905,relation_dom(relation_composition(U_903,U_904)))
| ~ function(U_903)
| ~ relation(U_903)
| ~ function(U_904)
| ~ relation(U_904) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_234_2,plain,
! [U_907,U_906] :
( reflexive(relation_restriction(U_906,U_907))
| ~ reflexive(U_906)
| ~ relation(U_906) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_906,U_907] :
( reflexive(relation_restriction(U_906,U_907))
| ~ reflexive(U_906)
| ~ relation(U_906) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( reflexive(relation_restriction(U_906,U_907))
| ~ reflexive(U_906)
| ~ relation(U_906) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_funct_1]) ).
fof(f_235_2,plain,
! [U_910,U_909] :
( ! [U_908] :
( apply(relation_composition(U_909,U_908),U_910) = apply(U_908,apply(U_909,U_910))
| ~ in(U_910,relation_dom(U_909))
| ~ function(U_908)
| ~ relation(U_908) )
| ~ function(U_909)
| ~ relation(U_909) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_908,U_909,U_910] :
( apply(relation_composition(U_909,U_908),U_910) = apply(U_908,apply(U_909,U_910))
| ~ in(U_910,relation_dom(U_909))
| ~ function(U_908)
| ~ relation(U_908)
| ~ function(U_909)
| ~ relation(U_909) ),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
( apply(relation_composition(U_909,U_908),U_910) = apply(U_908,apply(U_909,U_910))
| ~ in(U_910,relation_dom(U_909))
| ~ function(U_908)
| ~ relation(U_908)
| ~ function(U_909)
| ~ relation(U_909) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_236_2,plain,
! [U_912,U_911] :
( ordinal(U_912)
| ~ in(U_912,U_911)
| ~ ordinal(U_911) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_912,U_911] :
( ordinal(U_912)
| ~ in(U_912,U_911)
| ~ ordinal(U_911) ),
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
( ordinal(U_912)
| ~ in(U_912,U_911)
| ~ ordinal(U_911) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_237_2,plain,
! [U_914,U_913] :
( connected(relation_restriction(U_913,U_914))
| ~ connected(U_913)
| ~ relation(U_913) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_914,U_913] :
( connected(relation_restriction(U_913,U_914))
| ~ connected(U_913)
| ~ relation(U_913) ),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
( connected(relation_restriction(U_913,U_914))
| ~ connected(U_913)
| ~ relation(U_913) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t24_ordinal1]) ).
fof(f_238_2,plain,
! [U_916] :
( ! [U_915] :
( in(U_915,U_916)
| U_916 = U_915
| in(U_916,U_915)
| ~ ordinal(U_915) )
| ~ ordinal(U_916) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_916,U_915] :
( in(U_915,U_916)
| U_916 = U_915
| in(U_916,U_915)
| ~ ordinal(U_915)
| ~ ordinal(U_916) ),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
( in(U_915,U_916)
| U_916 = U_915
| in(U_916,U_915)
| ~ ordinal(U_915)
| ~ ordinal(U_916) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_239_2,plain,
! [U_918,U_917] :
( transitive(relation_restriction(U_917,U_918))
| ~ transitive(U_917)
| ~ relation(U_917) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_918,U_917] :
( transitive(relation_restriction(U_917,U_918))
| ~ transitive(U_917)
| ~ relation(U_917) ),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
( transitive(relation_restriction(U_917,U_918))
| ~ transitive(U_917)
| ~ relation(U_917) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
! [A] :
( ! [B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t25_relat_1]) ).
fof(f_240_2,plain,
! [U_920] :
( ! [U_919] :
( ( subset(relation_rng(U_920),relation_rng(U_919))
& subset(relation_dom(U_920),relation_dom(U_919)) )
| ~ subset(U_920,U_919)
| ~ relation(U_919) )
| ~ relation(U_920) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
( ! [U_920,U_919] :
( subset(relation_rng(U_920),relation_rng(U_919))
| ~ sP201(U_920,U_919) )
& ! [U_920,U_919] :
( subset(relation_dom(U_920),relation_dom(U_919))
| ~ sP201(U_920,U_919) )
& ! [U_920,U_919] :
( sP201(U_920,U_919)
| ~ subset(U_920,U_919)
| ~ relation(U_919)
| ~ relation(U_920) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_240_2]) ).
cnf(f_240_4,plain,
( sP201(U_920,U_919)
| ~ subset(U_920,U_919)
| ~ relation(U_919)
| ~ relation(U_920) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_5,plain,
( subset(relation_dom(U_920),relation_dom(U_919))
| ~ sP201(U_920,U_919) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_6,plain,
( subset(relation_rng(U_920),relation_rng(U_919))
| ~ sP201(U_920,U_919) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_241_2,plain,
! [U_922,U_921] :
( antisymmetric(relation_restriction(U_921,U_922))
| ~ antisymmetric(U_921)
| ~ relation(U_921) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
! [U_922,U_921] :
( antisymmetric(relation_restriction(U_921,U_922))
| ~ antisymmetric(U_921)
| ~ relation(U_921) ),
inference(definitional_conversion,[status(esa)],[f_241_2]) ).
cnf(f_241_4,plain,
( antisymmetric(relation_restriction(U_921,U_922))
| ~ antisymmetric(U_921)
| ~ relation(U_921) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
! [A,B,C] :
( subset(set_intersection2(A,C),set_intersection2(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t26_xboole_1]) ).
fof(f_242_2,plain,
! [U_925,U_924,U_923] :
( subset(set_intersection2(U_925,U_923),set_intersection2(U_924,U_923))
| ~ subset(U_925,U_924) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_925,U_924] :
( ! [U_923] : subset(set_intersection2(U_925,U_923),set_intersection2(U_924,U_923))
| ~ subset(U_925,U_924) ),
inference(miniscope,[status(thm)],[f_242_2]) ).
fof(f_242_4,plain,
! [U_923,U_924,U_925] :
( subset(set_intersection2(U_925,U_923),set_intersection2(U_924,U_923))
| ~ subset(U_925,U_924) ),
inference(definitional_conversion,[status(esa)],[f_242_3]) ).
cnf(f_242_5,plain,
( subset(set_intersection2(U_925,U_923),set_intersection2(U_924,U_923))
| ~ subset(U_925,U_924) ),
inference(clausify,[status(thm)],[f_242_4]) ).
fof(f_243_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_243_2,plain,
! [U_927,U_926] :
( set_intersection2(U_927,U_926) = U_927
| ~ subset(U_927,U_926) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_926,U_927] :
( set_intersection2(U_927,U_926) = U_927
| ~ subset(U_927,U_926) ),
inference(definitional_conversion,[status(esa)],[f_243_2]) ).
cnf(f_243_4,plain,
( set_intersection2(U_927,U_926) = U_927
| ~ subset(U_927,U_926) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_244_2,plain,
! [U_928] : set_intersection2(U_928,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_928] : set_intersection2(U_928,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_244_2]) ).
cnf(f_244_4,plain,
set_intersection2(U_928,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_245_2,plain,
! [U_930,U_929] :
( in(U_930,U_929)
| empty(U_929)
| ~ element(U_930,U_929) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_930,U_929] :
( in(U_930,U_929)
| empty(U_929)
| ~ element(U_930,U_929) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( in(U_930,U_929)
| empty(U_929)
| ~ element(U_930,U_929) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_246_2,plain,
! [U_933,U_932] :
( U_933 = U_932
| ? [U_931] :
( ( ~ in(U_931,U_933)
& in(U_931,U_932) )
| ( ~ in(U_931,U_932)
& in(U_931,U_933) ) ) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_933,U_932] :
( U_933 = U_932
| ? [U_935] :
( ~ in(U_935,U_933)
& in(U_935,U_932) )
| ? [U_934] :
( ~ in(U_934,U_932)
& in(U_934,U_933) ) ),
inference(miniscope,[status(thm)],[f_246_2]) ).
fof(f_246_4,plain,
! [U_933,U_932] :
( U_933 = U_932
| ? [U_935] :
( ~ in(U_935,U_933)
& in(U_935,U_932) )
| ( ~ in(sK145(U_933,U_932),U_932)
& in(sK145(U_933,U_932),U_933) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_934,sK145(U_933,U_932))],[f_246_3]) ).
fof(f_246_5,plain,
! [U_933,U_932] :
( U_933 = U_932
| ( ~ in(sK146(U_933,U_932),U_933)
& in(sK146(U_933,U_932),U_932) )
| ( ~ in(sK145(U_933,U_932),U_932)
& in(sK145(U_933,U_932),U_933) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_935,sK146(U_933,U_932))],[f_246_4]) ).
fof(f_246_6,plain,
( ! [U_932,U_933] :
( ~ in(sK146(U_933,U_932),U_933)
| ~ sP203(U_932,U_933) )
& ! [U_932,U_933] :
( in(sK146(U_933,U_932),U_932)
| ~ sP203(U_932,U_933) )
& ! [U_932,U_933] :
( ~ in(sK145(U_933,U_932),U_932)
| ~ sP202(U_932,U_933) )
& ! [U_932,U_933] :
( in(sK145(U_933,U_932),U_933)
| ~ sP202(U_932,U_933) )
& ! [U_932,U_933] :
( U_933 = U_932
| sP203(U_932,U_933)
| sP202(U_932,U_933) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202,sP203])],[f_246_5]) ).
cnf(f_246_7,plain,
( U_933 = U_932
| sP203(U_932,U_933)
| sP202(U_932,U_933) ),
inference(clausify,[status(thm)],[f_246_6]) ).
cnf(f_246_8,plain,
( in(sK145(U_933,U_932),U_933)
| ~ sP202(U_932,U_933) ),
inference(clausify,[status(thm)],[f_246_6]) ).
cnf(f_246_9,plain,
( ~ in(sK145(U_933,U_932),U_932)
| ~ sP202(U_932,U_933) ),
inference(clausify,[status(thm)],[f_246_6]) ).
cnf(f_246_10,plain,
( in(sK146(U_933,U_932),U_932)
| ~ sP203(U_932,U_933) ),
inference(clausify,[status(thm)],[f_246_6]) ).
cnf(f_246_11,plain,
( ~ in(sK146(U_933,U_932),U_933)
| ~ sP203(U_932,U_933) ),
inference(clausify,[status(thm)],[f_246_6]) ).
fof(f_247_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_247_2,plain,
! [U_936] : subset(empty_set,U_936),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_936] : subset(empty_set,U_936),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
subset(empty_set,U_936),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [A,B,C] :
( ( in(B,relation_field(C))
& in(A,relation_field(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t30_relat_1]) ).
fof(f_248_2,plain,
! [U_939,U_938,U_937] :
( ( in(U_938,relation_field(U_937))
& in(U_939,relation_field(U_937)) )
| ~ in(ordered_pair(U_939,U_938),U_937)
| ~ relation(U_937) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
( ! [U_939,U_937,U_938] :
( in(U_938,relation_field(U_937))
| ~ sP204(U_939,U_937,U_938) )
& ! [U_939,U_937,U_938] :
( in(U_939,relation_field(U_937))
| ~ sP204(U_939,U_937,U_938) )
& ! [U_939,U_937,U_938] :
( sP204(U_939,U_937,U_938)
| ~ in(ordered_pair(U_939,U_938),U_937)
| ~ relation(U_937) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_248_2]) ).
cnf(f_248_4,plain,
( sP204(U_939,U_937,U_938)
| ~ in(ordered_pair(U_939,U_938),U_937)
| ~ relation(U_937) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_5,plain,
( in(U_939,relation_field(U_937))
| ~ sP204(U_939,U_937,U_938) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_6,plain,
( in(U_938,relation_field(U_937))
| ~ sP204(U_939,U_937,U_938) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_249_2,plain,
! [U_941] :
( ordinal(U_941)
| ? [U_940] :
( ( ~ subset(U_940,U_941)
| ~ ordinal(U_940) )
& in(U_940,U_941) ) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_941] :
( ordinal(U_941)
| ( ( ~ subset(sK147(U_941),U_941)
| ~ ordinal(sK147(U_941)) )
& in(sK147(U_941),U_941) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_940,sK147(U_941))],[f_249_2]) ).
fof(f_249_4,plain,
( ! [U_941] :
( ~ subset(sK147(U_941),U_941)
| ~ ordinal(sK147(U_941))
| ~ sP205(U_941) )
& ! [U_941] :
( in(sK147(U_941),U_941)
| ~ sP205(U_941) )
& ! [U_941] :
( ordinal(U_941)
| sP205(U_941) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_249_3]) ).
cnf(f_249_5,plain,
( ordinal(U_941)
| sP205(U_941) ),
inference(clausify,[status(thm)],[f_249_4]) ).
cnf(f_249_6,plain,
( in(sK147(U_941),U_941)
| ~ sP205(U_941) ),
inference(clausify,[status(thm)],[f_249_4]) ).
cnf(f_249_7,plain,
( ~ subset(sK147(U_941),U_941)
| ~ ordinal(sK147(U_941))
| ~ sP205(U_941) ),
inference(clausify,[status(thm)],[f_249_4]) ).
fof(f_250_1,plain,
! [A,B] :
( well_founded_relation(relation_restriction(B,A))
| ~ well_founded_relation(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t31_wellord1]) ).
fof(f_250_2,plain,
! [U_943,U_942] :
( well_founded_relation(relation_restriction(U_942,U_943))
| ~ well_founded_relation(U_942)
| ~ relation(U_942) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_943,U_942] :
( well_founded_relation(relation_restriction(U_942,U_943))
| ~ well_founded_relation(U_942)
| ~ relation(U_942) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( well_founded_relation(relation_restriction(U_942,U_943))
| ~ well_founded_relation(U_942)
| ~ relation(U_942) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ordinal_subset(C,D)
| ~ in(D,A)
| ~ ordinal(D) )
& in(C,A)
& ordinal(C) )
| A = empty_set
| ~ subset(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t32_ordinal1]) ).
fof(f_251_2,plain,
! [U_947,U_946] :
( ? [U_945] :
( ! [U_944] :
( ordinal_subset(U_945,U_944)
| ~ in(U_944,U_947)
| ~ ordinal(U_944) )
& in(U_945,U_947)
& ordinal(U_945) )
| U_947 = empty_set
| ~ subset(U_947,U_946)
| ~ ordinal(U_946) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_947,U_946] :
( ( ! [U_944] :
( ordinal_subset(sK148(U_947,U_946),U_944)
| ~ in(U_944,U_947)
| ~ ordinal(U_944) )
& in(sK148(U_947,U_946),U_947)
& ordinal(sK148(U_947,U_946)) )
| U_947 = empty_set
| ~ subset(U_947,U_946)
| ~ ordinal(U_946) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_945,sK148(U_947,U_946))],[f_251_2]) ).
fof(f_251_4,plain,
( ! [U_946,U_944,U_947] :
( ordinal_subset(sK148(U_947,U_946),U_944)
| ~ in(U_944,U_947)
| ~ ordinal(U_944)
| ~ sP206(U_946,U_944,U_947) )
& ! [U_946,U_944,U_947] :
( in(sK148(U_947,U_946),U_947)
| ~ sP206(U_946,U_944,U_947) )
& ! [U_946,U_944,U_947] :
( ordinal(sK148(U_947,U_946))
| ~ sP206(U_946,U_944,U_947) )
& ! [U_946,U_944,U_947] :
( sP206(U_946,U_944,U_947)
| U_947 = empty_set
| ~ subset(U_947,U_946)
| ~ ordinal(U_946) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_251_3]) ).
cnf(f_251_5,plain,
( sP206(U_946,U_944,U_947)
| U_947 = empty_set
| ~ subset(U_947,U_946)
| ~ ordinal(U_946) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_6,plain,
( ordinal(sK148(U_947,U_946))
| ~ sP206(U_946,U_944,U_947) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_7,plain,
( in(sK148(U_947,U_946),U_947)
| ~ sP206(U_946,U_944,U_947) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_8,plain,
( ordinal_subset(sK148(U_947,U_946),U_944)
| ~ in(U_944,U_947)
| ~ ordinal(U_944)
| ~ sP206(U_946,U_944,U_947) ),
inference(clausify,[status(thm)],[f_251_4]) ).
fof(f_252_1,plain,
! [A,B] :
( well_ordering(relation_restriction(B,A))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t32_wellord1]) ).
fof(f_252_2,plain,
! [U_949,U_948] :
( well_ordering(relation_restriction(U_948,U_949))
| ~ well_ordering(U_948)
| ~ relation(U_948) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_949,U_948] :
( well_ordering(relation_restriction(U_948,U_949))
| ~ well_ordering(U_948)
| ~ relation(U_948) ),
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
( well_ordering(relation_restriction(U_948,U_949))
| ~ well_ordering(U_948)
| ~ relation(U_948) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_1,plain,
! [A] :
( ! [B] :
( ( ( in(A,B)
| ~ ordinal_subset(succ(A),B) )
& ( ordinal_subset(succ(A),B)
| ~ in(A,B) ) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t33_ordinal1]) ).
fof(f_253_2,plain,
! [U_951] :
( ! [U_950] :
( ( ( in(U_951,U_950)
| ~ ordinal_subset(succ(U_951),U_950) )
& ( ordinal_subset(succ(U_951),U_950)
| ~ in(U_951,U_950) ) )
| ~ ordinal(U_950) )
| ~ ordinal(U_951) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_951,U_950] :
( in(U_951,U_950)
| ~ ordinal_subset(succ(U_951),U_950)
| ~ sP207(U_951,U_950) )
& ! [U_951,U_950] :
( ordinal_subset(succ(U_951),U_950)
| ~ in(U_951,U_950)
| ~ sP207(U_951,U_950) )
& ! [U_951,U_950] :
( sP207(U_951,U_950)
| ~ ordinal(U_950)
| ~ ordinal(U_951) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_253_2]) ).
cnf(f_253_4,plain,
( sP207(U_951,U_950)
| ~ ordinal(U_950)
| ~ ordinal(U_951) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
( ordinal_subset(succ(U_951),U_950)
| ~ in(U_951,U_950)
| ~ sP207(U_951,U_950) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_6,plain,
( in(U_951,U_950)
| ~ ordinal_subset(succ(U_951),U_950)
| ~ sP207(U_951,U_950) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [A,B,C] :
( subset(set_difference(A,C),set_difference(B,C))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t33_xboole_1]) ).
fof(f_254_2,plain,
! [U_954,U_953,U_952] :
( subset(set_difference(U_954,U_952),set_difference(U_953,U_952))
| ~ subset(U_954,U_953) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_954,U_953] :
( ! [U_952] : subset(set_difference(U_954,U_952),set_difference(U_953,U_952))
| ~ subset(U_954,U_953) ),
inference(miniscope,[status(thm)],[f_254_2]) ).
fof(f_254_4,plain,
! [U_953,U_952,U_954] :
( subset(set_difference(U_954,U_952),set_difference(U_953,U_952))
| ~ subset(U_954,U_953) ),
inference(definitional_conversion,[status(esa)],[f_254_3]) ).
cnf(f_254_5,plain,
( subset(set_difference(U_954,U_952),set_difference(U_953,U_952))
| ~ subset(U_954,U_953) ),
inference(clausify,[status(thm)],[f_254_4]) ).
fof(f_255_1,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[t33_zfmisc_1]) ).
fof(f_255_2,plain,
! [U_958,U_957,U_956,U_955] :
( ( U_957 = U_955
& U_958 = U_956 )
| ordered_pair(U_958,U_957) != ordered_pair(U_956,U_955) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
( ! [U_957,U_958,U_955,U_956] :
( U_957 = U_955
| ~ sP208(U_957,U_958,U_955,U_956) )
& ! [U_957,U_958,U_955,U_956] :
( U_958 = U_956
| ~ sP208(U_957,U_958,U_955,U_956) )
& ! [U_957,U_958,U_955,U_956] :
( sP208(U_957,U_958,U_955,U_956)
| ordered_pair(U_958,U_957) != ordered_pair(U_956,U_955) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_255_2]) ).
cnf(f_255_4,plain,
( sP208(U_957,U_958,U_955,U_956)
| ordered_pair(U_958,U_957) != ordered_pair(U_956,U_955) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_5,plain,
( U_958 = U_956
| ~ sP208(U_957,U_958,U_955,U_956) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_6,plain,
( U_957 = U_955
| ~ sP208(U_957,U_958,U_955,U_956) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t34_funct_1]) ).
fof(f_256_2,plain,
! [U_962,U_961] :
( ( ( U_961 = identity_relation(U_962)
| ? [U_960] :
( apply(U_961,U_960) != U_960
& in(U_960,U_962) )
| relation_dom(U_961) != U_962 )
& ( ( ! [U_959] :
( apply(U_961,U_959) = U_959
| ~ in(U_959,U_962) )
& relation_dom(U_961) = U_962 )
| U_961 != identity_relation(U_962) ) )
| ~ function(U_961)
| ~ relation(U_961) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_962,U_961] :
( ( ( U_961 = identity_relation(U_962)
| ( apply(U_961,sK149(U_962,U_961)) != sK149(U_962,U_961)
& in(sK149(U_962,U_961),U_962) )
| relation_dom(U_961) != U_962 )
& ( ( ! [U_959] :
( apply(U_961,U_959) = U_959
| ~ in(U_959,U_962) )
& relation_dom(U_961) = U_962 )
| U_961 != identity_relation(U_962) ) )
| ~ function(U_961)
| ~ relation(U_961) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_960,sK149(U_962,U_961))],[f_256_2]) ).
fof(f_256_4,plain,
( ! [U_961,U_962] :
( apply(U_961,sK149(U_962,U_961)) != sK149(U_962,U_961)
| ~ sP210(U_961,U_962) )
& ! [U_961,U_962] :
( in(sK149(U_962,U_961),U_962)
| ~ sP210(U_961,U_962) )
& ! [U_961,U_959,U_962] :
( apply(U_961,U_959) = U_959
| ~ in(U_959,U_962)
| ~ sP209(U_961,U_959,U_962) )
& ! [U_961,U_959,U_962] :
( relation_dom(U_961) = U_962
| ~ sP209(U_961,U_959,U_962) )
& ! [U_961,U_959,U_962] :
( U_961 = identity_relation(U_962)
| sP210(U_961,U_962)
| relation_dom(U_961) != U_962
| ~ sP211(U_961,U_959,U_962) )
& ! [U_961,U_959,U_962] :
( sP209(U_961,U_959,U_962)
| U_961 != identity_relation(U_962)
| ~ sP211(U_961,U_959,U_962) )
& ! [U_961,U_959,U_962] :
( sP211(U_961,U_959,U_962)
| ~ function(U_961)
| ~ relation(U_961) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209,sP210,sP211])],[f_256_3]) ).
cnf(f_256_5,plain,
( sP211(U_961,U_959,U_962)
| ~ function(U_961)
| ~ relation(U_961) ),
inference(clausify,[status(thm)],[f_256_4]) ).
cnf(f_256_6,plain,
( sP209(U_961,U_959,U_962)
| U_961 != identity_relation(U_962)
| ~ sP211(U_961,U_959,U_962) ),
inference(clausify,[status(thm)],[f_256_4]) ).
cnf(f_256_7,plain,
( U_961 = identity_relation(U_962)
| sP210(U_961,U_962)
| relation_dom(U_961) != U_962
| ~ sP211(U_961,U_959,U_962) ),
inference(clausify,[status(thm)],[f_256_4]) ).
cnf(f_256_8,plain,
( relation_dom(U_961) = U_962
| ~ sP209(U_961,U_959,U_962) ),
inference(clausify,[status(thm)],[f_256_4]) ).
cnf(f_256_9,plain,
( apply(U_961,U_959) = U_959
| ~ in(U_959,U_962)
| ~ sP209(U_961,U_959,U_962) ),
inference(clausify,[status(thm)],[f_256_4]) ).
cnf(f_256_10,plain,
( in(sK149(U_962,U_961),U_962)
| ~ sP210(U_961,U_962) ),
inference(clausify,[status(thm)],[f_256_4]) ).
cnf(f_256_11,plain,
( apply(U_961,sK149(U_962,U_961)) != sK149(U_962,U_961)
| ~ sP210(U_961,U_962) ),
inference(clausify,[status(thm)],[f_256_4]) ).
fof(f_257_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_257_2,plain,
! [U_964,U_963] :
( apply(identity_relation(U_964),U_963) = U_963
| ~ in(U_963,U_964) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_963,U_964] :
( apply(identity_relation(U_964),U_963) = U_963
| ~ in(U_963,U_964) ),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
( apply(identity_relation(U_964),U_963) = U_963
| ~ in(U_963,U_964) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_258_2,plain,
! [U_966,U_965] : subset(set_difference(U_966,U_965),U_966),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_965,U_966] : subset(set_difference(U_966,U_965),U_966),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
subset(set_difference(U_966,U_965),U_966),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t37_relat_1]) ).
fof(f_259_2,plain,
! [U_967] :
( ( relation_dom(U_967) = relation_rng(relation_inverse(U_967))
& relation_rng(U_967) = relation_dom(relation_inverse(U_967)) )
| ~ relation(U_967) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
( ! [U_967] :
( relation_dom(U_967) = relation_rng(relation_inverse(U_967))
| ~ sP212(U_967) )
& ! [U_967] :
( relation_rng(U_967) = relation_dom(relation_inverse(U_967))
| ~ sP212(U_967) )
& ! [U_967] :
( sP212(U_967)
| ~ relation(U_967) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_259_2]) ).
cnf(f_259_4,plain,
( sP212(U_967)
| ~ relation(U_967) ),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_5,plain,
( relation_rng(U_967) = relation_dom(relation_inverse(U_967))
| ~ sP212(U_967) ),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_6,plain,
( relation_dom(U_967) = relation_rng(relation_inverse(U_967))
| ~ sP212(U_967) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_260_2,plain,
! [U_969,U_968] :
( ( set_difference(U_969,U_968) = empty_set
| ~ subset(U_969,U_968) )
& ( subset(U_969,U_968)
| set_difference(U_969,U_968) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_973,U_971] :
( set_difference(U_973,U_971) = empty_set
| ~ subset(U_973,U_971) )
& ! [U_972,U_970] :
( subset(U_972,U_970)
| set_difference(U_972,U_970) != empty_set ) ),
inference(miniscope,[status(thm)],[f_260_2]) ).
fof(f_260_4,plain,
( ! [U_973,U_971] :
( set_difference(U_973,U_971) = empty_set
| ~ subset(U_973,U_971) )
& ! [U_970,U_972] :
( subset(U_972,U_970)
| set_difference(U_972,U_970) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_260_3]) ).
cnf(f_260_5,plain,
( subset(U_972,U_970)
| set_difference(U_972,U_970) != empty_set ),
inference(clausify,[status(thm)],[f_260_4]) ).
cnf(f_260_6,plain,
( set_difference(U_973,U_971) = empty_set
| ~ subset(U_973,U_971) ),
inference(clausify,[status(thm)],[f_260_4]) ).
fof(f_261_1,plain,
! [A,B] :
( ( subset(singleton(A),B)
| ~ in(A,B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[t37_zfmisc_1]) ).
fof(f_261_2,plain,
! [U_975,U_974] :
( ( subset(singleton(U_975),U_974)
| ~ in(U_975,U_974) )
& ( in(U_975,U_974)
| ~ subset(singleton(U_975),U_974) ) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( ! [U_979,U_977] :
( subset(singleton(U_979),U_977)
| ~ in(U_979,U_977) )
& ! [U_978,U_976] :
( in(U_978,U_976)
| ~ subset(singleton(U_978),U_976) ) ),
inference(miniscope,[status(thm)],[f_261_2]) ).
fof(f_261_4,plain,
( ! [U_977,U_979] :
( subset(singleton(U_979),U_977)
| ~ in(U_979,U_977) )
& ! [U_976,U_978] :
( in(U_978,U_976)
| ~ subset(singleton(U_978),U_976) ) ),
inference(definitional_conversion,[status(esa)],[f_261_3]) ).
cnf(f_261_5,plain,
( in(U_978,U_976)
| ~ subset(singleton(U_978),U_976) ),
inference(clausify,[status(thm)],[f_261_4]) ).
cnf(f_261_6,plain,
( subset(singleton(U_979),U_977)
| ~ in(U_979,U_977) ),
inference(clausify,[status(thm)],[f_261_4]) ).
fof(f_262_1,plain,
! [A,B,C] :
( ( subset(unordered_pair(A,B),C)
| ~ in(B,C)
| ~ in(A,C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(fof_nnf,[status(thm)],[t38_zfmisc_1]) ).
fof(f_262_2,plain,
! [U_982,U_981,U_980] :
( ( subset(unordered_pair(U_982,U_981),U_980)
| ~ in(U_981,U_980)
| ~ in(U_982,U_980) )
& ( ( in(U_981,U_980)
& in(U_982,U_980) )
| ~ subset(unordered_pair(U_982,U_981),U_980) ) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
( ! [U_988,U_986,U_984] :
( subset(unordered_pair(U_988,U_986),U_984)
| ~ in(U_986,U_984)
| ~ in(U_988,U_984) )
& ! [U_987,U_985,U_983] :
( ( in(U_985,U_983)
& in(U_987,U_983) )
| ~ subset(unordered_pair(U_987,U_985),U_983) ) ),
inference(miniscope,[status(thm)],[f_262_2]) ).
fof(f_262_4,plain,
( ! [U_987,U_983,U_985] :
( in(U_985,U_983)
| ~ sP213(U_987,U_983,U_985) )
& ! [U_987,U_983,U_985] :
( in(U_987,U_983)
| ~ sP213(U_987,U_983,U_985) )
& ! [U_988,U_986,U_984] :
( subset(unordered_pair(U_988,U_986),U_984)
| ~ in(U_986,U_984)
| ~ in(U_988,U_984) )
& ! [U_987,U_983,U_985] :
( sP213(U_987,U_983,U_985)
| ~ subset(unordered_pair(U_987,U_985),U_983) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_262_3]) ).
cnf(f_262_5,plain,
( sP213(U_987,U_983,U_985)
| ~ subset(unordered_pair(U_987,U_985),U_983) ),
inference(clausify,[status(thm)],[f_262_4]) ).
cnf(f_262_6,plain,
( subset(unordered_pair(U_988,U_986),U_984)
| ~ in(U_986,U_984)
| ~ in(U_988,U_984) ),
inference(clausify,[status(thm)],[f_262_4]) ).
cnf(f_262_7,plain,
( in(U_987,U_983)
| ~ sP213(U_987,U_983,U_985) ),
inference(clausify,[status(thm)],[f_262_4]) ).
cnf(f_262_8,plain,
( in(U_985,U_983)
| ~ sP213(U_987,U_983,U_985) ),
inference(clausify,[status(thm)],[f_262_4]) ).
fof(f_263_1,plain,
! [A,B] :
( relation_field(relation_restriction(B,A)) = A
| ~ subset(A,relation_field(B))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t39_wellord1]) ).
fof(f_263_2,plain,
! [U_990,U_989] :
( relation_field(relation_restriction(U_989,U_990)) = U_990
| ~ subset(U_990,relation_field(U_989))
| ~ well_ordering(U_989)
| ~ relation(U_989) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_989,U_990] :
( relation_field(relation_restriction(U_989,U_990)) = U_990
| ~ subset(U_990,relation_field(U_989))
| ~ well_ordering(U_989)
| ~ relation(U_989) ),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
( relation_field(relation_restriction(U_989,U_990)) = U_990
| ~ subset(U_990,relation_field(U_989))
| ~ well_ordering(U_989)
| ~ relation(U_989) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(fof_nnf,[status(thm)],[t39_xboole_1]) ).
fof(f_264_2,plain,
! [U_992,U_991] : set_union2(U_992,set_difference(U_991,U_992)) = set_union2(U_992,U_991),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_991,U_992] : set_union2(U_992,set_difference(U_991,U_992)) = set_union2(U_992,U_991),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
set_union2(U_992,set_difference(U_991,U_992)) = set_union2(U_992,U_991),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[t39_zfmisc_1]) ).
fof(f_265_2,plain,
! [U_994,U_993] :
( ( subset(U_994,singleton(U_993))
| ( U_994 != singleton(U_993)
& U_994 != empty_set ) )
& ( U_994 = singleton(U_993)
| U_994 = empty_set
| ~ subset(U_994,singleton(U_993)) ) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
( ! [U_998,U_996] :
( subset(U_998,singleton(U_996))
| ( U_998 != singleton(U_996)
& U_998 != empty_set ) )
& ! [U_997,U_995] :
( U_997 = singleton(U_995)
| U_997 = empty_set
| ~ subset(U_997,singleton(U_995)) ) ),
inference(miniscope,[status(thm)],[f_265_2]) ).
fof(f_265_4,plain,
( ! [U_996,U_998] :
( U_998 != singleton(U_996)
| ~ sP214(U_996,U_998) )
& ! [U_996,U_998] :
( U_998 != empty_set
| ~ sP214(U_996,U_998) )
& ! [U_996,U_998] :
( subset(U_998,singleton(U_996))
| sP214(U_996,U_998) )
& ! [U_997,U_995] :
( U_997 = singleton(U_995)
| U_997 = empty_set
| ~ subset(U_997,singleton(U_995)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_265_3]) ).
cnf(f_265_5,plain,
( U_997 = singleton(U_995)
| U_997 = empty_set
| ~ subset(U_997,singleton(U_995)) ),
inference(clausify,[status(thm)],[f_265_4]) ).
cnf(f_265_6,plain,
( subset(U_998,singleton(U_996))
| sP214(U_996,U_998) ),
inference(clausify,[status(thm)],[f_265_4]) ).
cnf(f_265_7,plain,
( U_998 != empty_set
| ~ sP214(U_996,U_998) ),
inference(clausify,[status(thm)],[f_265_4]) ).
cnf(f_265_8,plain,
( U_998 != singleton(U_996)
| ~ sP214(U_996,U_998) ),
inference(clausify,[status(thm)],[f_265_4]) ).
fof(f_266_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_266_2,plain,
! [U_999] : set_difference(U_999,empty_set) = U_999,
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_999] : set_difference(U_999,empty_set) = U_999,
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
set_difference(U_999,empty_set) = U_999,
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_267_2,plain,
! [U_1002,U_1001,U_1000] :
( ~ in(U_1000,U_1002)
| ~ in(U_1001,U_1000)
| ~ in(U_1002,U_1001) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_1002,U_1001] :
( ! [U_1000] :
( ~ in(U_1000,U_1002)
| ~ in(U_1001,U_1000) )
| ~ in(U_1002,U_1001) ),
inference(miniscope,[status(thm)],[f_267_2]) ).
fof(f_267_4,plain,
! [U_1001,U_1000,U_1002] :
( ~ in(U_1000,U_1002)
| ~ in(U_1001,U_1000)
| ~ in(U_1002,U_1001) ),
inference(definitional_conversion,[status(esa)],[f_267_3]) ).
cnf(f_267_5,plain,
( ~ in(U_1000,U_1002)
| ~ in(U_1001,U_1000)
| ~ in(U_1002,U_1001) ),
inference(clausify,[status(thm)],[f_267_4]) ).
fof(f_268_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_268_2,plain,
! [U_1004,U_1003] :
( ( element(U_1004,powerset(U_1003))
| ~ subset(U_1004,U_1003) )
& ( subset(U_1004,U_1003)
| ~ element(U_1004,powerset(U_1003)) ) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
( ! [U_1008,U_1006] :
( element(U_1008,powerset(U_1006))
| ~ subset(U_1008,U_1006) )
& ! [U_1007,U_1005] :
( subset(U_1007,U_1005)
| ~ element(U_1007,powerset(U_1005)) ) ),
inference(miniscope,[status(thm)],[f_268_2]) ).
fof(f_268_4,plain,
( ! [U_1008,U_1006] :
( element(U_1008,powerset(U_1006))
| ~ subset(U_1008,U_1006) )
& ! [U_1007,U_1005] :
( subset(U_1007,U_1005)
| ~ element(U_1007,powerset(U_1005)) ) ),
inference(definitional_conversion,[status(esa)],[f_268_3]) ).
cnf(f_268_5,plain,
( subset(U_1007,U_1005)
| ~ element(U_1007,powerset(U_1005)) ),
inference(clausify,[status(thm)],[f_268_4]) ).
cnf(f_268_6,plain,
( element(U_1008,powerset(U_1006))
| ~ subset(U_1008,U_1006) ),
inference(clausify,[status(thm)],[f_268_4]) ).
fof(f_269_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(f_269_2,plain,
! [U_1012,U_1011] :
( ( ~ disjoint(U_1012,U_1011)
| ! [U_1010] :
( ~ in(U_1010,U_1011)
| ~ in(U_1010,U_1012) ) )
& ( ? [U_1009] :
( in(U_1009,U_1011)
& in(U_1009,U_1012) )
| disjoint(U_1012,U_1011) ) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_1016,U_1014] :
( ~ disjoint(U_1016,U_1014)
| ! [U_1010] :
( ~ in(U_1010,U_1014)
| ~ in(U_1010,U_1016) ) )
& ! [U_1015,U_1013] :
( ? [U_1009] :
( in(U_1009,U_1013)
& in(U_1009,U_1015) )
| disjoint(U_1015,U_1013) ) ),
inference(miniscope,[status(thm)],[f_269_2]) ).
fof(f_269_4,plain,
( ! [U_1016,U_1014] :
( ~ disjoint(U_1016,U_1014)
| ! [U_1010] :
( ~ in(U_1010,U_1014)
| ~ in(U_1010,U_1016) ) )
& ! [U_1015,U_1013] :
( ( in(sK150(U_1015,U_1013),U_1013)
& in(sK150(U_1015,U_1013),U_1015) )
| disjoint(U_1015,U_1013) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_1009,sK150(U_1015,U_1013))],[f_269_3]) ).
fof(f_269_5,plain,
( ! [U_1013,U_1015] :
( in(sK150(U_1015,U_1013),U_1013)
| ~ sP215(U_1013,U_1015) )
& ! [U_1013,U_1015] :
( in(sK150(U_1015,U_1013),U_1015)
| ~ sP215(U_1013,U_1015) )
& ! [U_1010,U_1016,U_1014] :
( ~ disjoint(U_1016,U_1014)
| ~ in(U_1010,U_1014)
| ~ in(U_1010,U_1016) )
& ! [U_1013,U_1015] :
( sP215(U_1013,U_1015)
| disjoint(U_1015,U_1013) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_269_4]) ).
cnf(f_269_6,plain,
( sP215(U_1013,U_1015)
| disjoint(U_1015,U_1013) ),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_7,plain,
( ~ disjoint(U_1016,U_1014)
| ~ in(U_1010,U_1014)
| ~ in(U_1010,U_1016) ),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_8,plain,
( in(sK150(U_1015,U_1013),U_1015)
| ~ sP215(U_1013,U_1015) ),
inference(clausify,[status(thm)],[f_269_5]) ).
cnf(f_269_9,plain,
( in(sK150(U_1015,U_1013),U_1013)
| ~ sP215(U_1013,U_1015) ),
inference(clausify,[status(thm)],[f_269_5]) ).
fof(f_270_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_270_2,plain,
! [U_1017] :
( U_1017 = empty_set
| ~ subset(U_1017,empty_set) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_1017] :
( U_1017 = empty_set
| ~ subset(U_1017,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
( U_1017 = empty_set
| ~ subset(U_1017,empty_set) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(fof_nnf,[status(thm)],[t40_xboole_1]) ).
fof(f_271_2,plain,
! [U_1019,U_1018] : set_difference(set_union2(U_1019,U_1018),U_1018) = set_difference(U_1019,U_1018),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_1019,U_1018] : set_difference(set_union2(U_1019,U_1018),U_1018) = set_difference(U_1019,U_1018),
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
set_difference(set_union2(U_1019,U_1018),U_1018) = set_difference(U_1019,U_1018),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [A] :
( ( ( being_limit_ordinal(A)
| ? [B] :
( ~ in(succ(B),A)
& in(B,A)
& ordinal(B) ) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t41_ordinal1]) ).
fof(f_272_2,plain,
! [U_1022] :
( ( ( being_limit_ordinal(U_1022)
| ? [U_1021] :
( ~ in(succ(U_1021),U_1022)
& in(U_1021,U_1022)
& ordinal(U_1021) ) )
& ( ! [U_1020] :
( in(succ(U_1020),U_1022)
| ~ in(U_1020,U_1022)
| ~ ordinal(U_1020) )
| ~ being_limit_ordinal(U_1022) ) )
| ~ ordinal(U_1022) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_1022] :
( ( ( being_limit_ordinal(U_1022)
| ( ~ in(succ(sK151(U_1022)),U_1022)
& in(sK151(U_1022),U_1022)
& ordinal(sK151(U_1022)) ) )
& ( ! [U_1020] :
( in(succ(U_1020),U_1022)
| ~ in(U_1020,U_1022)
| ~ ordinal(U_1020) )
| ~ being_limit_ordinal(U_1022) ) )
| ~ ordinal(U_1022) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_1021,sK151(U_1022))],[f_272_2]) ).
fof(f_272_4,plain,
( ! [U_1022] :
( ~ in(succ(sK151(U_1022)),U_1022)
| ~ sP216(U_1022) )
& ! [U_1022] :
( in(sK151(U_1022),U_1022)
| ~ sP216(U_1022) )
& ! [U_1022] :
( ordinal(sK151(U_1022))
| ~ sP216(U_1022) )
& ! [U_1022,U_1020] :
( being_limit_ordinal(U_1022)
| sP216(U_1022)
| ~ sP217(U_1022,U_1020) )
& ! [U_1022,U_1020] :
( in(succ(U_1020),U_1022)
| ~ in(U_1020,U_1022)
| ~ ordinal(U_1020)
| ~ being_limit_ordinal(U_1022)
| ~ sP217(U_1022,U_1020) )
& ! [U_1022,U_1020] :
( sP217(U_1022,U_1020)
| ~ ordinal(U_1022) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216,sP217])],[f_272_3]) ).
cnf(f_272_5,plain,
( sP217(U_1022,U_1020)
| ~ ordinal(U_1022) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_6,plain,
( in(succ(U_1020),U_1022)
| ~ in(U_1020,U_1022)
| ~ ordinal(U_1020)
| ~ being_limit_ordinal(U_1022)
| ~ sP217(U_1022,U_1020) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_7,plain,
( being_limit_ordinal(U_1022)
| sP216(U_1022)
| ~ sP217(U_1022,U_1020) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_8,plain,
( ordinal(sK151(U_1022))
| ~ sP216(U_1022) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_9,plain,
( in(sK151(U_1022),U_1022)
| ~ sP216(U_1022) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_10,plain,
( ~ in(succ(sK151(U_1022)),U_1022)
| ~ sP216(U_1022) ),
inference(clausify,[status(thm)],[f_272_4]) ).
fof(f_273_1,plain,
! [A] :
( ( ( ~ being_limit_ordinal(A)
| ! [B] :
( A != succ(B)
| ~ ordinal(B) ) )
& ( ? [B] :
( A = succ(B)
& ordinal(B) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t42_ordinal1]) ).
fof(f_273_2,plain,
! [U_1025] :
( ( ( ~ being_limit_ordinal(U_1025)
| ! [U_1024] :
( U_1025 != succ(U_1024)
| ~ ordinal(U_1024) ) )
& ( ? [U_1023] :
( U_1025 = succ(U_1023)
& ordinal(U_1023) )
| being_limit_ordinal(U_1025) ) )
| ~ ordinal(U_1025) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_1025] :
( ( ( ~ being_limit_ordinal(U_1025)
| ! [U_1024] :
( U_1025 != succ(U_1024)
| ~ ordinal(U_1024) ) )
& ( ( U_1025 = succ(sK152(U_1025))
& ordinal(sK152(U_1025)) )
| being_limit_ordinal(U_1025) ) )
| ~ ordinal(U_1025) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_1023,sK152(U_1025))],[f_273_2]) ).
fof(f_273_4,plain,
( ! [U_1025] :
( U_1025 = succ(sK152(U_1025))
| ~ sP218(U_1025) )
& ! [U_1025] :
( ordinal(sK152(U_1025))
| ~ sP218(U_1025) )
& ! [U_1024,U_1025] :
( ~ being_limit_ordinal(U_1025)
| U_1025 != succ(U_1024)
| ~ ordinal(U_1024)
| ~ sP219(U_1024,U_1025) )
& ! [U_1024,U_1025] :
( sP218(U_1025)
| being_limit_ordinal(U_1025)
| ~ sP219(U_1024,U_1025) )
& ! [U_1024,U_1025] :
( sP219(U_1024,U_1025)
| ~ ordinal(U_1025) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218,sP219])],[f_273_3]) ).
cnf(f_273_5,plain,
( sP219(U_1024,U_1025)
| ~ ordinal(U_1025) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_6,plain,
( sP218(U_1025)
| being_limit_ordinal(U_1025)
| ~ sP219(U_1024,U_1025) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_7,plain,
( ~ being_limit_ordinal(U_1025)
| U_1025 != succ(U_1024)
| ~ ordinal(U_1024)
| ~ sP219(U_1024,U_1025) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_8,plain,
( ordinal(sK152(U_1025))
| ~ sP218(U_1025) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_9,plain,
( U_1025 = succ(sK152(U_1025))
| ~ sP218(U_1025) ),
inference(clausify,[status(thm)],[f_273_4]) ).
fof(f_274_1,plain,
! [A,B] :
( ! [C] :
( ( ( disjoint(B,C)
| ~ subset(B,subset_complement(A,C)) )
& ( subset(B,subset_complement(A,C))
| ~ disjoint(B,C) ) )
| ~ element(C,powerset(A)) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t43_subset_1]) ).
fof(f_274_2,plain,
! [U_1028,U_1027] :
( ! [U_1026] :
( ( ( disjoint(U_1027,U_1026)
| ~ subset(U_1027,subset_complement(U_1028,U_1026)) )
& ( subset(U_1027,subset_complement(U_1028,U_1026))
| ~ disjoint(U_1027,U_1026) ) )
| ~ element(U_1026,powerset(U_1028)) )
| ~ element(U_1027,powerset(U_1028)) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
( ! [U_1027,U_1026,U_1028] :
( disjoint(U_1027,U_1026)
| ~ subset(U_1027,subset_complement(U_1028,U_1026))
| ~ sP220(U_1027,U_1026,U_1028) )
& ! [U_1027,U_1026,U_1028] :
( subset(U_1027,subset_complement(U_1028,U_1026))
| ~ disjoint(U_1027,U_1026)
| ~ sP220(U_1027,U_1026,U_1028) )
& ! [U_1027,U_1026,U_1028] :
( sP220(U_1027,U_1026,U_1028)
| ~ element(U_1026,powerset(U_1028))
| ~ element(U_1027,powerset(U_1028)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_274_2]) ).
cnf(f_274_4,plain,
( sP220(U_1027,U_1026,U_1028)
| ~ element(U_1026,powerset(U_1028))
| ~ element(U_1027,powerset(U_1028)) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( subset(U_1027,subset_complement(U_1028,U_1026))
| ~ disjoint(U_1027,U_1026)
| ~ sP220(U_1027,U_1026,U_1028) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_6,plain,
( disjoint(U_1027,U_1026)
| ~ subset(U_1027,subset_complement(U_1028,U_1026))
| ~ sP220(U_1027,U_1026,U_1028) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [A] :
( ! [B] :
( subset(relation_dom(relation_composition(A,B)),relation_dom(A))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t44_relat_1]) ).
fof(f_275_2,plain,
! [U_1030] :
( ! [U_1029] :
( subset(relation_dom(relation_composition(U_1030,U_1029)),relation_dom(U_1030))
| ~ relation(U_1029) )
| ~ relation(U_1030) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_1029,U_1030] :
( subset(relation_dom(relation_composition(U_1030,U_1029)),relation_dom(U_1030))
| ~ relation(U_1029)
| ~ relation(U_1030) ),
inference(definitional_conversion,[status(esa)],[f_275_2]) ).
cnf(f_275_4,plain,
( subset(relation_dom(relation_composition(U_1030,U_1029)),relation_dom(U_1030))
| ~ relation(U_1029)
| ~ relation(U_1030) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [A] :
( ! [B] :
( subset(relation_rng(relation_composition(A,B)),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t45_relat_1]) ).
fof(f_276_2,plain,
! [U_1032] :
( ! [U_1031] :
( subset(relation_rng(relation_composition(U_1032,U_1031)),relation_rng(U_1031))
| ~ relation(U_1031) )
| ~ relation(U_1032) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_1031,U_1032] :
( subset(relation_rng(relation_composition(U_1032,U_1031)),relation_rng(U_1031))
| ~ relation(U_1031)
| ~ relation(U_1032) ),
inference(definitional_conversion,[status(esa)],[f_276_2]) ).
cnf(f_276_4,plain,
( subset(relation_rng(relation_composition(U_1032,U_1031)),relation_rng(U_1031))
| ~ relation(U_1031)
| ~ relation(U_1032) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [A,B] :
( B = set_union2(A,set_difference(B,A))
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t45_xboole_1]) ).
fof(f_277_2,plain,
! [U_1034,U_1033] :
( U_1033 = set_union2(U_1034,set_difference(U_1033,U_1034))
| ~ subset(U_1034,U_1033) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_1033,U_1034] :
( U_1033 = set_union2(U_1034,set_difference(U_1033,U_1034))
| ~ subset(U_1034,U_1033) ),
inference(definitional_conversion,[status(esa)],[f_277_2]) ).
cnf(f_277_4,plain,
( U_1033 = set_union2(U_1034,set_difference(U_1033,U_1034))
| ~ subset(U_1034,U_1033) ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [A] :
( ! [B] :
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t46_relat_1]) ).
fof(f_278_2,plain,
! [U_1036] :
( ! [U_1035] :
( relation_dom(relation_composition(U_1036,U_1035)) = relation_dom(U_1036)
| ~ subset(relation_rng(U_1036),relation_dom(U_1035))
| ~ relation(U_1035) )
| ~ relation(U_1036) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_1035,U_1036] :
( relation_dom(relation_composition(U_1036,U_1035)) = relation_dom(U_1036)
| ~ subset(relation_rng(U_1036),relation_dom(U_1035))
| ~ relation(U_1035)
| ~ relation(U_1036) ),
inference(definitional_conversion,[status(esa)],[f_278_2]) ).
cnf(f_278_4,plain,
( relation_dom(relation_composition(U_1036,U_1035)) = relation_dom(U_1036)
| ~ subset(relation_rng(U_1036),relation_dom(U_1035))
| ~ relation(U_1035)
| ~ relation(U_1036) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_1,plain,
! [A,B] :
( complements_of_subsets(A,B) != empty_set
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t46_setfam_1]) ).
fof(f_279_2,plain,
! [U_1038,U_1037] :
( complements_of_subsets(U_1038,U_1037) != empty_set
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1037,U_1038] :
( complements_of_subsets(U_1038,U_1037) != empty_set
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) ),
inference(definitional_conversion,[status(esa)],[f_279_2]) ).
cnf(f_279_4,plain,
( complements_of_subsets(U_1038,U_1037) != empty_set
| U_1037 = empty_set
| ~ element(U_1037,powerset(powerset(U_1038))) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_280_2,plain,
! [U_1040,U_1039] :
( set_union2(singleton(U_1040),U_1039) = U_1039
| ~ in(U_1040,U_1039) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_1040,U_1039] :
( set_union2(singleton(U_1040),U_1039) = U_1039
| ~ in(U_1040,U_1039) ),
inference(definitional_conversion,[status(esa)],[f_280_2]) ).
cnf(f_280_4,plain,
( set_union2(singleton(U_1040),U_1039) = U_1039
| ~ in(U_1040,U_1039) ),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_1,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(B,A)) = relation_rng(A)
| ~ subset(relation_dom(A),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t47_relat_1]) ).
fof(f_281_2,plain,
! [U_1042] :
( ! [U_1041] :
( relation_rng(relation_composition(U_1041,U_1042)) = relation_rng(U_1042)
| ~ subset(relation_dom(U_1042),relation_rng(U_1041))
| ~ relation(U_1041) )
| ~ relation(U_1042) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_1041,U_1042] :
( relation_rng(relation_composition(U_1041,U_1042)) = relation_rng(U_1042)
| ~ subset(relation_dom(U_1042),relation_rng(U_1041))
| ~ relation(U_1041)
| ~ relation(U_1042) ),
inference(definitional_conversion,[status(esa)],[f_281_2]) ).
cnf(f_281_4,plain,
( relation_rng(relation_composition(U_1041,U_1042)) = relation_rng(U_1042)
| ~ subset(relation_dom(U_1042),relation_rng(U_1041))
| ~ relation(U_1041)
| ~ relation(U_1042) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_1,plain,
! [A,B] :
( subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t47_setfam_1]) ).
fof(f_282_2,plain,
! [U_1044,U_1043] :
( subset_difference(U_1044,cast_to_subset(U_1044),union_of_subsets(U_1044,U_1043)) = meet_of_subsets(U_1044,complements_of_subsets(U_1044,U_1043))
| U_1043 = empty_set
| ~ element(U_1043,powerset(powerset(U_1044))) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_1043,U_1044] :
( subset_difference(U_1044,cast_to_subset(U_1044),union_of_subsets(U_1044,U_1043)) = meet_of_subsets(U_1044,complements_of_subsets(U_1044,U_1043))
| U_1043 = empty_set
| ~ element(U_1043,powerset(powerset(U_1044))) ),
inference(definitional_conversion,[status(esa)],[f_282_2]) ).
cnf(f_282_4,plain,
( subset_difference(U_1044,cast_to_subset(U_1044),union_of_subsets(U_1044,U_1043)) = meet_of_subsets(U_1044,complements_of_subsets(U_1044,U_1043))
| U_1043 = empty_set
| ~ element(U_1043,powerset(powerset(U_1044))) ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_1,plain,
! [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t48_setfam_1]) ).
fof(f_283_2,plain,
! [U_1046,U_1045] :
( union_of_subsets(U_1046,complements_of_subsets(U_1046,U_1045)) = subset_difference(U_1046,cast_to_subset(U_1046),meet_of_subsets(U_1046,U_1045))
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1045,U_1046] :
( union_of_subsets(U_1046,complements_of_subsets(U_1046,U_1045)) = subset_difference(U_1046,cast_to_subset(U_1046),meet_of_subsets(U_1046,U_1045))
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) ),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
( union_of_subsets(U_1046,complements_of_subsets(U_1046,U_1045)) = subset_difference(U_1046,cast_to_subset(U_1046),meet_of_subsets(U_1046,U_1045))
| U_1045 = empty_set
| ~ element(U_1045,powerset(powerset(U_1046))) ),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_1,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(fof_nnf,[status(thm)],[t48_xboole_1]) ).
fof(f_284_2,plain,
! [U_1048,U_1047] : set_difference(U_1048,set_difference(U_1048,U_1047)) = set_intersection2(U_1048,U_1047),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_1047,U_1048] : set_difference(U_1048,set_difference(U_1048,U_1047)) = set_intersection2(U_1048,U_1047),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
set_difference(U_1048,set_difference(U_1048,U_1047)) = set_intersection2(U_1048,U_1047),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( relation_isomorphism(B,A,function_inverse(C))
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t49_wellord1]) ).
fof(f_285_2,plain,
! [U_1051] :
( ! [U_1050] :
( ! [U_1049] :
( relation_isomorphism(U_1050,U_1051,function_inverse(U_1049))
| ~ relation_isomorphism(U_1051,U_1050,U_1049)
| ~ function(U_1049)
| ~ relation(U_1049) )
| ~ relation(U_1050) )
| ~ relation(U_1051) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1049,U_1050,U_1051] :
( relation_isomorphism(U_1050,U_1051,function_inverse(U_1049))
| ~ relation_isomorphism(U_1051,U_1050,U_1049)
| ~ function(U_1049)
| ~ relation(U_1049)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(definitional_conversion,[status(esa)],[f_285_2]) ).
cnf(f_285_4,plain,
( relation_isomorphism(U_1050,U_1051,function_inverse(U_1049))
| ~ relation_isomorphism(U_1051,U_1050,U_1049)
| ~ function(U_1049)
| ~ relation(U_1049)
| ~ relation(U_1050)
| ~ relation(U_1051) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_286_2,plain,
! [U_1052] : set_difference(empty_set,U_1052) = empty_set,
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1052] : set_difference(empty_set,U_1052) = empty_set,
inference(definitional_conversion,[status(esa)],[f_286_2]) ).
cnf(f_286_4,plain,
set_difference(empty_set,U_1052) = empty_set,
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_287_2,plain,
! [U_1055,U_1054,U_1053] :
( element(U_1055,U_1053)
| ~ element(U_1054,powerset(U_1053))
| ~ in(U_1055,U_1054) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_1055,U_1054,U_1053] :
( element(U_1055,U_1053)
| ~ element(U_1054,powerset(U_1053))
| ~ in(U_1055,U_1054) ),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
( element(U_1055,U_1053)
| ~ element(U_1054,powerset(U_1053))
| ~ in(U_1055,U_1054) ),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(f_288_2,plain,
! [U_1059,U_1058] :
( ( ~ disjoint(U_1059,U_1058)
| ! [U_1057] : ~ in(U_1057,set_intersection2(U_1059,U_1058)) )
& ( ? [U_1056] : in(U_1056,set_intersection2(U_1059,U_1058))
| disjoint(U_1059,U_1058) ) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
( ! [U_1063,U_1061] :
( ~ disjoint(U_1063,U_1061)
| ! [U_1057] : ~ in(U_1057,set_intersection2(U_1063,U_1061)) )
& ! [U_1062,U_1060] :
( ? [U_1056] : in(U_1056,set_intersection2(U_1062,U_1060))
| disjoint(U_1062,U_1060) ) ),
inference(miniscope,[status(thm)],[f_288_2]) ).
fof(f_288_4,plain,
( ! [U_1063,U_1061] :
( ~ disjoint(U_1063,U_1061)
| ! [U_1057] : ~ in(U_1057,set_intersection2(U_1063,U_1061)) )
& ! [U_1062,U_1060] :
( in(sK153(U_1062,U_1060),set_intersection2(U_1062,U_1060))
| disjoint(U_1062,U_1060) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_1056,sK153(U_1062,U_1060))],[f_288_3]) ).
fof(f_288_5,plain,
( ! [U_1061,U_1057,U_1063] :
( ~ disjoint(U_1063,U_1061)
| ~ in(U_1057,set_intersection2(U_1063,U_1061)) )
& ! [U_1060,U_1062] :
( in(sK153(U_1062,U_1060),set_intersection2(U_1062,U_1060))
| disjoint(U_1062,U_1060) ) ),
inference(definitional_conversion,[status(esa)],[f_288_4]) ).
cnf(f_288_6,plain,
( in(sK153(U_1062,U_1060),set_intersection2(U_1062,U_1060))
| disjoint(U_1062,U_1060) ),
inference(clausify,[status(thm)],[f_288_5]) ).
cnf(f_288_7,plain,
( ~ disjoint(U_1063,U_1061)
| ~ in(U_1057,set_intersection2(U_1063,U_1061)) ),
inference(clausify,[status(thm)],[f_288_5]) ).
fof(f_289_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( in(C,subset_complement(A,B))
| in(C,B)
| ~ element(C,A) )
| ~ element(B,powerset(A)) )
| A = empty_set ),
inference(fof_nnf,[status(thm)],[t50_subset_1]) ).
fof(f_289_2,plain,
! [U_1066] :
( ! [U_1065] :
( ! [U_1064] :
( in(U_1064,subset_complement(U_1066,U_1065))
| in(U_1064,U_1065)
| ~ element(U_1064,U_1066) )
| ~ element(U_1065,powerset(U_1066)) )
| U_1066 = empty_set ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_1065,U_1064,U_1066] :
( in(U_1064,subset_complement(U_1066,U_1065))
| in(U_1064,U_1065)
| ~ element(U_1064,U_1066)
| ~ element(U_1065,powerset(U_1066))
| U_1066 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_289_2]) ).
cnf(f_289_4,plain,
( in(U_1064,subset_complement(U_1066,U_1065))
| in(U_1064,U_1065)
| ~ element(U_1064,U_1066)
| ~ element(U_1065,powerset(U_1066))
| U_1066 = empty_set ),
inference(clausify,[status(thm)],[f_289_3]) ).
fof(f_290_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( well_founded_relation(B)
| ~ well_founded_relation(A) )
& ( antisymmetric(B)
| ~ antisymmetric(A) )
& ( connected(B)
| ~ connected(A) )
& ( transitive(B)
| ~ transitive(A) )
& ( reflexive(B)
| ~ reflexive(A) ) )
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t53_wellord1]) ).
fof(f_290_2,plain,
! [U_1069] :
( ! [U_1068] :
( ! [U_1067] :
( ( ( well_founded_relation(U_1068)
| ~ well_founded_relation(U_1069) )
& ( antisymmetric(U_1068)
| ~ antisymmetric(U_1069) )
& ( connected(U_1068)
| ~ connected(U_1069) )
& ( transitive(U_1068)
| ~ transitive(U_1069) )
& ( reflexive(U_1068)
| ~ reflexive(U_1069) ) )
| ~ relation_isomorphism(U_1069,U_1068,U_1067)
| ~ function(U_1067)
| ~ relation(U_1067) )
| ~ relation(U_1068) )
| ~ relation(U_1069) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
( ! [U_1069,U_1068] :
( well_founded_relation(U_1068)
| ~ well_founded_relation(U_1069)
| ~ sP221(U_1069,U_1068) )
& ! [U_1069,U_1068] :
( antisymmetric(U_1068)
| ~ antisymmetric(U_1069)
| ~ sP221(U_1069,U_1068) )
& ! [U_1069,U_1068] :
( connected(U_1068)
| ~ connected(U_1069)
| ~ sP221(U_1069,U_1068) )
& ! [U_1069,U_1068] :
( transitive(U_1068)
| ~ transitive(U_1069)
| ~ sP221(U_1069,U_1068) )
& ! [U_1069,U_1068] :
( reflexive(U_1068)
| ~ reflexive(U_1069)
| ~ sP221(U_1069,U_1068) )
& ! [U_1067,U_1069,U_1068] :
( sP221(U_1069,U_1068)
| ~ relation_isomorphism(U_1069,U_1068,U_1067)
| ~ function(U_1067)
| ~ relation(U_1067)
| ~ relation(U_1068)
| ~ relation(U_1069) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_290_2]) ).
cnf(f_290_4,plain,
( sP221(U_1069,U_1068)
| ~ relation_isomorphism(U_1069,U_1068,U_1067)
| ~ function(U_1067)
| ~ relation(U_1067)
| ~ relation(U_1068)
| ~ relation(U_1069) ),
inference(clausify,[status(thm)],[f_290_3]) ).
cnf(f_290_5,plain,
( reflexive(U_1068)
| ~ reflexive(U_1069)
| ~ sP221(U_1069,U_1068) ),
inference(clausify,[status(thm)],[f_290_3]) ).
cnf(f_290_6,plain,
( transitive(U_1068)
| ~ transitive(U_1069)
| ~ sP221(U_1069,U_1068) ),
inference(clausify,[status(thm)],[f_290_3]) ).
cnf(f_290_7,plain,
( connected(U_1068)
| ~ connected(U_1069)
| ~ sP221(U_1069,U_1068) ),
inference(clausify,[status(thm)],[f_290_3]) ).
cnf(f_290_8,plain,
( antisymmetric(U_1068)
| ~ antisymmetric(U_1069)
| ~ sP221(U_1069,U_1068) ),
inference(clausify,[status(thm)],[f_290_3]) ).
cnf(f_290_9,plain,
( well_founded_relation(U_1068)
| ~ well_founded_relation(U_1069)
| ~ sP221(U_1069,U_1068) ),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_1,plain,
! [A] :
( ! [B] :
( ( ( B = function_inverse(A)
| ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) ) )
| relation_dom(B) != relation_rng(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t54_funct_1]) ).
fof(f_291_2,plain,
! [U_1075] :
( ! [U_1074] :
( ( ( U_1074 = function_inverse(U_1075)
| ? [U_1073,U_1072] :
( ( ( U_1072 != apply(U_1074,U_1073)
| ~ in(U_1073,relation_rng(U_1075)) )
& U_1073 = apply(U_1075,U_1072)
& in(U_1072,relation_dom(U_1075)) )
| ( ( U_1073 != apply(U_1075,U_1072)
| ~ in(U_1072,relation_dom(U_1075)) )
& U_1072 = apply(U_1074,U_1073)
& in(U_1073,relation_rng(U_1075)) ) )
| relation_dom(U_1074) != relation_rng(U_1075) )
& ( ( ! [U_1071,U_1070] :
( ( ( U_1070 = apply(U_1074,U_1071)
& in(U_1071,relation_rng(U_1075)) )
| U_1071 != apply(U_1075,U_1070)
| ~ in(U_1070,relation_dom(U_1075)) )
& ( ( U_1071 = apply(U_1075,U_1070)
& in(U_1070,relation_dom(U_1075)) )
| U_1070 != apply(U_1074,U_1071)
| ~ in(U_1071,relation_rng(U_1075)) ) )
& relation_dom(U_1074) = relation_rng(U_1075) )
| U_1074 != function_inverse(U_1075) ) )
| ~ function(U_1074)
| ~ relation(U_1074) )
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_1075] :
( ! [U_1074] :
( ( ( U_1074 = function_inverse(U_1075)
| ? [U_1083,U_1081] :
( ( U_1081 != apply(U_1074,U_1083)
| ~ in(U_1083,relation_rng(U_1075)) )
& U_1083 = apply(U_1075,U_1081)
& in(U_1081,relation_dom(U_1075)) )
| ? [U_1082,U_1080] :
( ( U_1082 != apply(U_1075,U_1080)
| ~ in(U_1080,relation_dom(U_1075)) )
& U_1080 = apply(U_1074,U_1082)
& in(U_1082,relation_rng(U_1075)) )
| relation_dom(U_1074) != relation_rng(U_1075) )
& ( ( ! [U_1079,U_1077] :
( ( U_1077 = apply(U_1074,U_1079)
& in(U_1079,relation_rng(U_1075)) )
| U_1079 != apply(U_1075,U_1077)
| ~ in(U_1077,relation_dom(U_1075)) )
& ! [U_1078,U_1076] :
( ( U_1078 = apply(U_1075,U_1076)
& in(U_1076,relation_dom(U_1075)) )
| U_1076 != apply(U_1074,U_1078)
| ~ in(U_1078,relation_rng(U_1075)) )
& relation_dom(U_1074) = relation_rng(U_1075) )
| U_1074 != function_inverse(U_1075) ) )
| ~ function(U_1074)
| ~ relation(U_1074) )
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ),
inference(miniscope,[status(thm)],[f_291_2]) ).
fof(f_291_4,plain,
! [U_1075] :
( ! [U_1074] :
( ( ( U_1074 = function_inverse(U_1075)
| ? [U_1083,U_1081] :
( ( U_1081 != apply(U_1074,U_1083)
| ~ in(U_1083,relation_rng(U_1075)) )
& U_1083 = apply(U_1075,U_1081)
& in(U_1081,relation_dom(U_1075)) )
| ? [U_1080] :
( ( sK154(U_1075,U_1074) != apply(U_1075,U_1080)
| ~ in(U_1080,relation_dom(U_1075)) )
& U_1080 = apply(U_1074,sK154(U_1075,U_1074))
& in(sK154(U_1075,U_1074),relation_rng(U_1075)) )
| relation_dom(U_1074) != relation_rng(U_1075) )
& ( ( ! [U_1079,U_1077] :
( ( U_1077 = apply(U_1074,U_1079)
& in(U_1079,relation_rng(U_1075)) )
| U_1079 != apply(U_1075,U_1077)
| ~ in(U_1077,relation_dom(U_1075)) )
& ! [U_1078,U_1076] :
( ( U_1078 = apply(U_1075,U_1076)
& in(U_1076,relation_dom(U_1075)) )
| U_1076 != apply(U_1074,U_1078)
| ~ in(U_1078,relation_rng(U_1075)) )
& relation_dom(U_1074) = relation_rng(U_1075) )
| U_1074 != function_inverse(U_1075) ) )
| ~ function(U_1074)
| ~ relation(U_1074) )
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_1082,sK154(U_1075,U_1074))],[f_291_3]) ).
fof(f_291_5,plain,
! [U_1075] :
( ! [U_1074] :
( ( ( U_1074 = function_inverse(U_1075)
| ? [U_1083,U_1081] :
( ( U_1081 != apply(U_1074,U_1083)
| ~ in(U_1083,relation_rng(U_1075)) )
& U_1083 = apply(U_1075,U_1081)
& in(U_1081,relation_dom(U_1075)) )
| ( ( sK154(U_1075,U_1074) != apply(U_1075,sK155(U_1075,U_1074))
| ~ in(sK155(U_1075,U_1074),relation_dom(U_1075)) )
& sK155(U_1075,U_1074) = apply(U_1074,sK154(U_1075,U_1074))
& in(sK154(U_1075,U_1074),relation_rng(U_1075)) )
| relation_dom(U_1074) != relation_rng(U_1075) )
& ( ( ! [U_1079,U_1077] :
( ( U_1077 = apply(U_1074,U_1079)
& in(U_1079,relation_rng(U_1075)) )
| U_1079 != apply(U_1075,U_1077)
| ~ in(U_1077,relation_dom(U_1075)) )
& ! [U_1078,U_1076] :
( ( U_1078 = apply(U_1075,U_1076)
& in(U_1076,relation_dom(U_1075)) )
| U_1076 != apply(U_1074,U_1078)
| ~ in(U_1078,relation_rng(U_1075)) )
& relation_dom(U_1074) = relation_rng(U_1075) )
| U_1074 != function_inverse(U_1075) ) )
| ~ function(U_1074)
| ~ relation(U_1074) )
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_1080,sK155(U_1075,U_1074))],[f_291_4]) ).
fof(f_291_6,plain,
! [U_1075] :
( ! [U_1074] :
( ( ( U_1074 = function_inverse(U_1075)
| ? [U_1081] :
( ( U_1081 != apply(U_1074,sK156(U_1075,U_1074))
| ~ in(sK156(U_1075,U_1074),relation_rng(U_1075)) )
& sK156(U_1075,U_1074) = apply(U_1075,U_1081)
& in(U_1081,relation_dom(U_1075)) )
| ( ( sK154(U_1075,U_1074) != apply(U_1075,sK155(U_1075,U_1074))
| ~ in(sK155(U_1075,U_1074),relation_dom(U_1075)) )
& sK155(U_1075,U_1074) = apply(U_1074,sK154(U_1075,U_1074))
& in(sK154(U_1075,U_1074),relation_rng(U_1075)) )
| relation_dom(U_1074) != relation_rng(U_1075) )
& ( ( ! [U_1079,U_1077] :
( ( U_1077 = apply(U_1074,U_1079)
& in(U_1079,relation_rng(U_1075)) )
| U_1079 != apply(U_1075,U_1077)
| ~ in(U_1077,relation_dom(U_1075)) )
& ! [U_1078,U_1076] :
( ( U_1078 = apply(U_1075,U_1076)
& in(U_1076,relation_dom(U_1075)) )
| U_1076 != apply(U_1074,U_1078)
| ~ in(U_1078,relation_rng(U_1075)) )
& relation_dom(U_1074) = relation_rng(U_1075) )
| U_1074 != function_inverse(U_1075) ) )
| ~ function(U_1074)
| ~ relation(U_1074) )
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_1083,sK156(U_1075,U_1074))],[f_291_5]) ).
fof(f_291_7,plain,
! [U_1075] :
( ! [U_1074] :
( ( ( U_1074 = function_inverse(U_1075)
| ( ( sK157(U_1075,U_1074) != apply(U_1074,sK156(U_1075,U_1074))
| ~ in(sK156(U_1075,U_1074),relation_rng(U_1075)) )
& sK156(U_1075,U_1074) = apply(U_1075,sK157(U_1075,U_1074))
& in(sK157(U_1075,U_1074),relation_dom(U_1075)) )
| ( ( sK154(U_1075,U_1074) != apply(U_1075,sK155(U_1075,U_1074))
| ~ in(sK155(U_1075,U_1074),relation_dom(U_1075)) )
& sK155(U_1075,U_1074) = apply(U_1074,sK154(U_1075,U_1074))
& in(sK154(U_1075,U_1074),relation_rng(U_1075)) )
| relation_dom(U_1074) != relation_rng(U_1075) )
& ( ( ! [U_1079,U_1077] :
( ( U_1077 = apply(U_1074,U_1079)
& in(U_1079,relation_rng(U_1075)) )
| U_1079 != apply(U_1075,U_1077)
| ~ in(U_1077,relation_dom(U_1075)) )
& ! [U_1078,U_1076] :
( ( U_1078 = apply(U_1075,U_1076)
& in(U_1076,relation_dom(U_1075)) )
| U_1076 != apply(U_1074,U_1078)
| ~ in(U_1078,relation_rng(U_1075)) )
& relation_dom(U_1074) = relation_rng(U_1075) )
| U_1074 != function_inverse(U_1075) ) )
| ~ function(U_1074)
| ~ relation(U_1074) )
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_1081,sK157(U_1075,U_1074))],[f_291_6]) ).
fof(f_291_8,plain,
( ! [U_1074,U_1075] :
( sK157(U_1075,U_1074) != apply(U_1074,sK156(U_1075,U_1074))
| ~ in(sK156(U_1075,U_1074),relation_rng(U_1075))
| ~ sP226(U_1074,U_1075) )
& ! [U_1074,U_1075] :
( sK156(U_1075,U_1074) = apply(U_1075,sK157(U_1075,U_1074))
| ~ sP226(U_1074,U_1075) )
& ! [U_1074,U_1075] :
( in(sK157(U_1075,U_1074),relation_dom(U_1075))
| ~ sP226(U_1074,U_1075) )
& ! [U_1074,U_1075] :
( sK154(U_1075,U_1074) != apply(U_1075,sK155(U_1075,U_1074))
| ~ in(sK155(U_1075,U_1074),relation_dom(U_1075))
| ~ sP225(U_1074,U_1075) )
& ! [U_1074,U_1075] :
( sK155(U_1075,U_1074) = apply(U_1074,sK154(U_1075,U_1074))
| ~ sP225(U_1074,U_1075) )
& ! [U_1074,U_1075] :
( in(sK154(U_1075,U_1074),relation_rng(U_1075))
| ~ sP225(U_1074,U_1075) )
& ! [U_1074,U_1075,U_1077,U_1079] :
( U_1077 = apply(U_1074,U_1079)
| ~ sP223(U_1074,U_1075,U_1077,U_1079) )
& ! [U_1074,U_1075,U_1077,U_1079] :
( in(U_1079,relation_rng(U_1075))
| ~ sP223(U_1074,U_1075,U_1077,U_1079) )
& ! [U_1075,U_1078,U_1076] :
( U_1078 = apply(U_1075,U_1076)
| ~ sP222(U_1075,U_1078,U_1076) )
& ! [U_1075,U_1078,U_1076] :
( in(U_1076,relation_dom(U_1075))
| ~ sP222(U_1075,U_1078,U_1076) )
& ! [U_1074,U_1075,U_1078,U_1076,U_1077,U_1079] :
( sP223(U_1074,U_1075,U_1077,U_1079)
| U_1079 != apply(U_1075,U_1077)
| ~ in(U_1077,relation_dom(U_1075))
| ~ sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) )
& ! [U_1074,U_1075,U_1078,U_1076,U_1077,U_1079] :
( sP222(U_1075,U_1078,U_1076)
| U_1076 != apply(U_1074,U_1078)
| ~ in(U_1078,relation_rng(U_1075))
| ~ sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) )
& ! [U_1074,U_1075,U_1078,U_1076,U_1077,U_1079] :
( relation_dom(U_1074) = relation_rng(U_1075)
| ~ sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) )
& ! [U_1074,U_1075,U_1078,U_1076,U_1077,U_1079] :
( U_1074 = function_inverse(U_1075)
| sP226(U_1074,U_1075)
| sP225(U_1074,U_1075)
| relation_dom(U_1074) != relation_rng(U_1075)
| ~ sP227(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) )
& ! [U_1074,U_1075,U_1078,U_1076,U_1077,U_1079] :
( sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079)
| U_1074 != function_inverse(U_1075)
| ~ sP227(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) )
& ! [U_1074,U_1075,U_1078,U_1076,U_1077,U_1079] :
( sP227(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079)
| ~ function(U_1074)
| ~ relation(U_1074)
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222,sP223,sP224,sP225,sP226,sP227])],[f_291_7]) ).
cnf(f_291_9,plain,
( sP227(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079)
| ~ function(U_1074)
| ~ relation(U_1074)
| ~ one_to_one(U_1075)
| ~ function(U_1075)
| ~ relation(U_1075) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_10,plain,
( sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079)
| U_1074 != function_inverse(U_1075)
| ~ sP227(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_11,plain,
( U_1074 = function_inverse(U_1075)
| sP226(U_1074,U_1075)
| sP225(U_1074,U_1075)
| relation_dom(U_1074) != relation_rng(U_1075)
| ~ sP227(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_12,plain,
( relation_dom(U_1074) = relation_rng(U_1075)
| ~ sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_13,plain,
( sP222(U_1075,U_1078,U_1076)
| U_1076 != apply(U_1074,U_1078)
| ~ in(U_1078,relation_rng(U_1075))
| ~ sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_14,plain,
( sP223(U_1074,U_1075,U_1077,U_1079)
| U_1079 != apply(U_1075,U_1077)
| ~ in(U_1077,relation_dom(U_1075))
| ~ sP224(U_1074,U_1075,U_1078,U_1076,U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_15,plain,
( in(U_1076,relation_dom(U_1075))
| ~ sP222(U_1075,U_1078,U_1076) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_16,plain,
( U_1078 = apply(U_1075,U_1076)
| ~ sP222(U_1075,U_1078,U_1076) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_17,plain,
( in(U_1079,relation_rng(U_1075))
| ~ sP223(U_1074,U_1075,U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_18,plain,
( U_1077 = apply(U_1074,U_1079)
| ~ sP223(U_1074,U_1075,U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_19,plain,
( in(sK154(U_1075,U_1074),relation_rng(U_1075))
| ~ sP225(U_1074,U_1075) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_20,plain,
( sK155(U_1075,U_1074) = apply(U_1074,sK154(U_1075,U_1074))
| ~ sP225(U_1074,U_1075) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_21,plain,
( sK154(U_1075,U_1074) != apply(U_1075,sK155(U_1075,U_1074))
| ~ in(sK155(U_1075,U_1074),relation_dom(U_1075))
| ~ sP225(U_1074,U_1075) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_22,plain,
( in(sK157(U_1075,U_1074),relation_dom(U_1075))
| ~ sP226(U_1074,U_1075) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_23,plain,
( sK156(U_1075,U_1074) = apply(U_1075,sK157(U_1075,U_1074))
| ~ sP226(U_1074,U_1075) ),
inference(clausify,[status(thm)],[f_291_8]) ).
cnf(f_291_24,plain,
( sK157(U_1075,U_1074) != apply(U_1074,sK156(U_1075,U_1074))
| ~ in(sK156(U_1075,U_1074),relation_rng(U_1075))
| ~ sP226(U_1074,U_1075) ),
inference(clausify,[status(thm)],[f_291_8]) ).
fof(f_292_1,plain,
! [A,B,C] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t54_subset_1]) ).
fof(f_292_2,plain,
! [U_1086,U_1085,U_1084] :
( ~ in(U_1085,U_1084)
| ~ in(U_1085,subset_complement(U_1086,U_1084))
| ~ element(U_1084,powerset(U_1086)) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1085,U_1086,U_1084] :
( ~ in(U_1085,U_1084)
| ~ in(U_1085,subset_complement(U_1086,U_1084))
| ~ element(U_1084,powerset(U_1086)) ),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
( ~ in(U_1085,U_1084)
| ~ in(U_1085,subset_complement(U_1086,U_1084))
| ~ element(U_1084,powerset(U_1086)) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( well_ordering(B)
| ~ relation_isomorphism(A,B,C)
| ~ well_ordering(A)
| ~ function(C)
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t54_wellord1]) ).
fof(f_293_2,plain,
! [U_1089] :
( ! [U_1088] :
( ! [U_1087] :
( well_ordering(U_1088)
| ~ relation_isomorphism(U_1089,U_1088,U_1087)
| ~ well_ordering(U_1089)
| ~ function(U_1087)
| ~ relation(U_1087) )
| ~ relation(U_1088) )
| ~ relation(U_1089) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_1089,U_1087,U_1088] :
( well_ordering(U_1088)
| ~ relation_isomorphism(U_1089,U_1088,U_1087)
| ~ well_ordering(U_1089)
| ~ function(U_1087)
| ~ relation(U_1087)
| ~ relation(U_1088)
| ~ relation(U_1089) ),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
( well_ordering(U_1088)
| ~ relation_isomorphism(U_1089,U_1088,U_1087)
| ~ well_ordering(U_1089)
| ~ function(U_1087)
| ~ relation(U_1087)
| ~ relation(U_1088)
| ~ relation(U_1089) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_1,plain,
! [A] :
( ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t55_funct_1]) ).
fof(f_294_2,plain,
! [U_1090] :
( ( relation_dom(U_1090) = relation_rng(function_inverse(U_1090))
& relation_rng(U_1090) = relation_dom(function_inverse(U_1090)) )
| ~ one_to_one(U_1090)
| ~ function(U_1090)
| ~ relation(U_1090) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
( ! [U_1090] :
( relation_dom(U_1090) = relation_rng(function_inverse(U_1090))
| ~ sP228(U_1090) )
& ! [U_1090] :
( relation_rng(U_1090) = relation_dom(function_inverse(U_1090))
| ~ sP228(U_1090) )
& ! [U_1090] :
( sP228(U_1090)
| ~ one_to_one(U_1090)
| ~ function(U_1090)
| ~ relation(U_1090) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_294_2]) ).
cnf(f_294_4,plain,
( sP228(U_1090)
| ~ one_to_one(U_1090)
| ~ function(U_1090)
| ~ relation(U_1090) ),
inference(clausify,[status(thm)],[f_294_3]) ).
cnf(f_294_5,plain,
( relation_rng(U_1090) = relation_dom(function_inverse(U_1090))
| ~ sP228(U_1090) ),
inference(clausify,[status(thm)],[f_294_3]) ).
cnf(f_294_6,plain,
( relation_dom(U_1090) = relation_rng(function_inverse(U_1090))
| ~ sP228(U_1090) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_1,plain,
! [A] :
( A = empty_set
| ? [B,C] : in(ordered_pair(B,C),A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t56_relat_1]) ).
fof(f_295_2,plain,
! [U_1093] :
( U_1093 = empty_set
| ? [U_1092,U_1091] : in(ordered_pair(U_1092,U_1091),U_1093)
| ~ relation(U_1093) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1093] :
( U_1093 = empty_set
| ? [U_1091] : in(ordered_pair(sK158(U_1093),U_1091),U_1093)
| ~ relation(U_1093) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_1092,sK158(U_1093))],[f_295_2]) ).
fof(f_295_4,plain,
! [U_1093] :
( U_1093 = empty_set
| in(ordered_pair(sK158(U_1093),sK159(U_1093)),U_1093)
| ~ relation(U_1093) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_1091,sK159(U_1093))],[f_295_3]) ).
fof(f_295_5,plain,
! [U_1093] :
( U_1093 = empty_set
| in(ordered_pair(sK158(U_1093),sK159(U_1093)),U_1093)
| ~ relation(U_1093) ),
inference(definitional_conversion,[status(esa)],[f_295_4]) ).
cnf(f_295_6,plain,
( U_1093 = empty_set
| in(ordered_pair(sK158(U_1093),sK159(U_1093)),U_1093)
| ~ relation(U_1093) ),
inference(clausify,[status(thm)],[f_295_5]) ).
fof(f_296_1,plain,
! [A,B] :
( ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) )
| ~ in(A,relation_rng(B))
| ~ one_to_one(B)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t57_funct_1]) ).
fof(f_296_2,plain,
! [U_1095,U_1094] :
( ( U_1095 = apply(relation_composition(function_inverse(U_1094),U_1094),U_1095)
& U_1095 = apply(U_1094,apply(function_inverse(U_1094),U_1095)) )
| ~ in(U_1095,relation_rng(U_1094))
| ~ one_to_one(U_1094)
| ~ function(U_1094)
| ~ relation(U_1094) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
( ! [U_1094,U_1095] :
( U_1095 = apply(relation_composition(function_inverse(U_1094),U_1094),U_1095)
| ~ sP229(U_1094,U_1095) )
& ! [U_1094,U_1095] :
( U_1095 = apply(U_1094,apply(function_inverse(U_1094),U_1095))
| ~ sP229(U_1094,U_1095) )
& ! [U_1094,U_1095] :
( sP229(U_1094,U_1095)
| ~ in(U_1095,relation_rng(U_1094))
| ~ one_to_one(U_1094)
| ~ function(U_1094)
| ~ relation(U_1094) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_296_2]) ).
cnf(f_296_4,plain,
( sP229(U_1094,U_1095)
| ~ in(U_1095,relation_rng(U_1094))
| ~ one_to_one(U_1094)
| ~ function(U_1094)
| ~ relation(U_1094) ),
inference(clausify,[status(thm)],[f_296_3]) ).
cnf(f_296_5,plain,
( U_1095 = apply(U_1094,apply(function_inverse(U_1094),U_1095))
| ~ sP229(U_1094,U_1095) ),
inference(clausify,[status(thm)],[f_296_3]) ).
cnf(f_296_6,plain,
( U_1095 = apply(relation_composition(function_inverse(U_1094),U_1094),U_1095)
| ~ sP229(U_1094,U_1095) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_297_2,plain,
! [U_1098,U_1097,U_1096] :
( ~ empty(U_1096)
| ~ element(U_1097,powerset(U_1096))
| ~ in(U_1098,U_1097) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_1098,U_1097] :
( ! [U_1096] :
( ~ empty(U_1096)
| ~ element(U_1097,powerset(U_1096)) )
| ~ in(U_1098,U_1097) ),
inference(miniscope,[status(thm)],[f_297_2]) ).
fof(f_297_4,plain,
! [U_1096,U_1097,U_1098] :
( ~ empty(U_1096)
| ~ element(U_1097,powerset(U_1096))
| ~ in(U_1098,U_1097) ),
inference(definitional_conversion,[status(esa)],[f_297_3]) ).
cnf(f_297_5,plain,
( ~ empty(U_1096)
| ~ element(U_1097,powerset(U_1096))
| ~ in(U_1098,U_1097) ),
inference(clausify,[status(thm)],[f_297_4]) ).
fof(f_298_1,plain,
! [A] :
( ( ( well_founded_relation(A)
| ~ is_well_founded_in(A,relation_field(A)) )
& ( is_well_founded_in(A,relation_field(A))
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t5_wellord1]) ).
fof(f_298_2,plain,
! [U_1099] :
( ( ( well_founded_relation(U_1099)
| ~ is_well_founded_in(U_1099,relation_field(U_1099)) )
& ( is_well_founded_in(U_1099,relation_field(U_1099))
| ~ well_founded_relation(U_1099) ) )
| ~ relation(U_1099) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
( ! [U_1099] :
( well_founded_relation(U_1099)
| ~ is_well_founded_in(U_1099,relation_field(U_1099))
| ~ sP230(U_1099) )
& ! [U_1099] :
( is_well_founded_in(U_1099,relation_field(U_1099))
| ~ well_founded_relation(U_1099)
| ~ sP230(U_1099) )
& ! [U_1099] :
( sP230(U_1099)
| ~ relation(U_1099) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_298_2]) ).
cnf(f_298_4,plain,
( sP230(U_1099)
| ~ relation(U_1099) ),
inference(clausify,[status(thm)],[f_298_3]) ).
cnf(f_298_5,plain,
( is_well_founded_in(U_1099,relation_field(U_1099))
| ~ well_founded_relation(U_1099)
| ~ sP230(U_1099) ),
inference(clausify,[status(thm)],[f_298_3]) ).
cnf(f_298_6,plain,
( well_founded_relation(U_1099)
| ~ is_well_founded_in(U_1099,relation_field(U_1099))
| ~ sP230(U_1099) ),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
fof(f_299_2,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(definitional_conversion,[status(esa)],[f_299_1]) ).
cnf(f_299_3,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_299_2]) ).
cnf(f_299_4,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_300_2,plain,
! [U_1101,U_1100] :
( ~ proper_subset(U_1100,U_1101)
| ~ subset(U_1101,U_1100) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1100,U_1101] :
( ~ proper_subset(U_1100,U_1101)
| ~ subset(U_1101,U_1100) ),
inference(definitional_conversion,[status(esa)],[f_300_2]) ).
cnf(f_300_4,plain,
( ~ proper_subset(U_1100,U_1101)
| ~ subset(U_1101,U_1100) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_1,plain,
! [A] :
( one_to_one(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t62_funct_1]) ).
fof(f_301_2,plain,
! [U_1102] :
( one_to_one(function_inverse(U_1102))
| ~ one_to_one(U_1102)
| ~ function(U_1102)
| ~ relation(U_1102) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_1102] :
( one_to_one(function_inverse(U_1102))
| ~ one_to_one(U_1102)
| ~ function(U_1102)
| ~ relation(U_1102) ),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
( one_to_one(function_inverse(U_1102))
| ~ one_to_one(U_1102)
| ~ function(U_1102)
| ~ relation(U_1102) ),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_302_2,plain,
! [U_1105,U_1104,U_1103] :
( disjoint(U_1105,U_1103)
| ~ disjoint(U_1104,U_1103)
| ~ subset(U_1105,U_1104) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_1103,U_1105,U_1104] :
( disjoint(U_1105,U_1103)
| ~ disjoint(U_1104,U_1103)
| ~ subset(U_1105,U_1104) ),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
( disjoint(U_1105,U_1103)
| ~ disjoint(U_1104,U_1103)
| ~ subset(U_1105,U_1104) ),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_1,plain,
! [A] :
( A = empty_set
| ( relation_rng(A) != empty_set
& relation_dom(A) != empty_set )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t64_relat_1]) ).
fof(f_303_2,plain,
! [U_1106] :
( U_1106 = empty_set
| ( relation_rng(U_1106) != empty_set
& relation_dom(U_1106) != empty_set )
| ~ relation(U_1106) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
( ! [U_1106] :
( relation_rng(U_1106) != empty_set
| ~ sP231(U_1106) )
& ! [U_1106] :
( relation_dom(U_1106) != empty_set
| ~ sP231(U_1106) )
& ! [U_1106] :
( U_1106 = empty_set
| sP231(U_1106)
| ~ relation(U_1106) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_303_2]) ).
cnf(f_303_4,plain,
( U_1106 = empty_set
| sP231(U_1106)
| ~ relation(U_1106) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_5,plain,
( relation_dom(U_1106) != empty_set
| ~ sP231(U_1106) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_6,plain,
( relation_rng(U_1106) != empty_set
| ~ sP231(U_1106) ),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_1,plain,
! [A] :
( ( ( relation_dom(A) = empty_set
| relation_rng(A) != empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) != empty_set ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t65_relat_1]) ).
fof(f_304_2,plain,
! [U_1107] :
( ( ( relation_dom(U_1107) = empty_set
| relation_rng(U_1107) != empty_set )
& ( relation_rng(U_1107) = empty_set
| relation_dom(U_1107) != empty_set ) )
| ~ relation(U_1107) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
( ! [U_1107] :
( relation_dom(U_1107) = empty_set
| relation_rng(U_1107) != empty_set
| ~ sP232(U_1107) )
& ! [U_1107] :
( relation_rng(U_1107) = empty_set
| relation_dom(U_1107) != empty_set
| ~ sP232(U_1107) )
& ! [U_1107] :
( sP232(U_1107)
| ~ relation(U_1107) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_304_2]) ).
cnf(f_304_4,plain,
( sP232(U_1107)
| ~ relation(U_1107) ),
inference(clausify,[status(thm)],[f_304_3]) ).
cnf(f_304_5,plain,
( relation_rng(U_1107) = empty_set
| relation_dom(U_1107) != empty_set
| ~ sP232(U_1107) ),
inference(clausify,[status(thm)],[f_304_3]) ).
cnf(f_304_6,plain,
( relation_dom(U_1107) = empty_set
| relation_rng(U_1107) != empty_set
| ~ sP232(U_1107) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_1,plain,
! [A,B] :
( ( set_difference(A,singleton(B)) = A
| in(B,A) )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(fof_nnf,[status(thm)],[t65_zfmisc_1]) ).
fof(f_305_2,plain,
! [U_1109,U_1108] :
( ( set_difference(U_1109,singleton(U_1108)) = U_1109
| in(U_1108,U_1109) )
& ( ~ in(U_1108,U_1109)
| set_difference(U_1109,singleton(U_1108)) != U_1109 ) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
( ! [U_1113,U_1111] :
( set_difference(U_1113,singleton(U_1111)) = U_1113
| in(U_1111,U_1113) )
& ! [U_1112,U_1110] :
( ~ in(U_1110,U_1112)
| set_difference(U_1112,singleton(U_1110)) != U_1112 ) ),
inference(miniscope,[status(thm)],[f_305_2]) ).
fof(f_305_4,plain,
( ! [U_1111,U_1113] :
( set_difference(U_1113,singleton(U_1111)) = U_1113
| in(U_1111,U_1113) )
& ! [U_1112,U_1110] :
( ~ in(U_1110,U_1112)
| set_difference(U_1112,singleton(U_1110)) != U_1112 ) ),
inference(definitional_conversion,[status(esa)],[f_305_3]) ).
cnf(f_305_5,plain,
( ~ in(U_1110,U_1112)
| set_difference(U_1112,singleton(U_1110)) != U_1112 ),
inference(clausify,[status(thm)],[f_305_4]) ).
cnf(f_305_6,plain,
( set_difference(U_1113,singleton(U_1111)) = U_1113
| in(U_1111,U_1113) ),
inference(clausify,[status(thm)],[f_305_4]) ).
fof(f_306_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_dom_restriction(C,A)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t68_funct_1]) ).
fof(f_306_2,plain,
! [U_1118,U_1117] :
( ! [U_1116] :
( ( ( U_1117 = relation_dom_restriction(U_1116,U_1118)
| ? [U_1115] :
( apply(U_1117,U_1115) != apply(U_1116,U_1115)
& in(U_1115,relation_dom(U_1117)) )
| relation_dom(U_1117) != set_intersection2(relation_dom(U_1116),U_1118) )
& ( ( ! [U_1114] :
( apply(U_1117,U_1114) = apply(U_1116,U_1114)
| ~ in(U_1114,relation_dom(U_1117)) )
& relation_dom(U_1117) = set_intersection2(relation_dom(U_1116),U_1118) )
| U_1117 != relation_dom_restriction(U_1116,U_1118) ) )
| ~ function(U_1116)
| ~ relation(U_1116) )
| ~ function(U_1117)
| ~ relation(U_1117) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_1118,U_1117] :
( ! [U_1116] :
( ( ( U_1117 = relation_dom_restriction(U_1116,U_1118)
| ( apply(U_1117,sK160(U_1118,U_1117,U_1116)) != apply(U_1116,sK160(U_1118,U_1117,U_1116))
& in(sK160(U_1118,U_1117,U_1116),relation_dom(U_1117)) )
| relation_dom(U_1117) != set_intersection2(relation_dom(U_1116),U_1118) )
& ( ( ! [U_1114] :
( apply(U_1117,U_1114) = apply(U_1116,U_1114)
| ~ in(U_1114,relation_dom(U_1117)) )
& relation_dom(U_1117) = set_intersection2(relation_dom(U_1116),U_1118) )
| U_1117 != relation_dom_restriction(U_1116,U_1118) ) )
| ~ function(U_1116)
| ~ relation(U_1116) )
| ~ function(U_1117)
| ~ relation(U_1117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_1115,sK160(U_1118,U_1117,U_1116))],[f_306_2]) ).
fof(f_306_4,plain,
( ! [U_1117,U_1118,U_1116] :
( apply(U_1117,sK160(U_1118,U_1117,U_1116)) != apply(U_1116,sK160(U_1118,U_1117,U_1116))
| ~ sP234(U_1117,U_1118,U_1116) )
& ! [U_1117,U_1118,U_1116] :
( in(sK160(U_1118,U_1117,U_1116),relation_dom(U_1117))
| ~ sP234(U_1117,U_1118,U_1116) )
& ! [U_1114,U_1117,U_1118,U_1116] :
( apply(U_1117,U_1114) = apply(U_1116,U_1114)
| ~ in(U_1114,relation_dom(U_1117))
| ~ sP233(U_1114,U_1117,U_1118,U_1116) )
& ! [U_1114,U_1117,U_1118,U_1116] :
( relation_dom(U_1117) = set_intersection2(relation_dom(U_1116),U_1118)
| ~ sP233(U_1114,U_1117,U_1118,U_1116) )
& ! [U_1114,U_1117,U_1118,U_1116] :
( U_1117 = relation_dom_restriction(U_1116,U_1118)
| sP234(U_1117,U_1118,U_1116)
| relation_dom(U_1117) != set_intersection2(relation_dom(U_1116),U_1118)
| ~ sP235(U_1114,U_1117,U_1118,U_1116) )
& ! [U_1114,U_1117,U_1118,U_1116] :
( sP233(U_1114,U_1117,U_1118,U_1116)
| U_1117 != relation_dom_restriction(U_1116,U_1118)
| ~ sP235(U_1114,U_1117,U_1118,U_1116) )
& ! [U_1114,U_1117,U_1118,U_1116] :
( sP235(U_1114,U_1117,U_1118,U_1116)
| ~ function(U_1116)
| ~ relation(U_1116)
| ~ function(U_1117)
| ~ relation(U_1117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233,sP234,sP235])],[f_306_3]) ).
cnf(f_306_5,plain,
( sP235(U_1114,U_1117,U_1118,U_1116)
| ~ function(U_1116)
| ~ relation(U_1116)
| ~ function(U_1117)
| ~ relation(U_1117) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_6,plain,
( sP233(U_1114,U_1117,U_1118,U_1116)
| U_1117 != relation_dom_restriction(U_1116,U_1118)
| ~ sP235(U_1114,U_1117,U_1118,U_1116) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_7,plain,
( U_1117 = relation_dom_restriction(U_1116,U_1118)
| sP234(U_1117,U_1118,U_1116)
| relation_dom(U_1117) != set_intersection2(relation_dom(U_1116),U_1118)
| ~ sP235(U_1114,U_1117,U_1118,U_1116) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_8,plain,
( relation_dom(U_1117) = set_intersection2(relation_dom(U_1116),U_1118)
| ~ sP233(U_1114,U_1117,U_1118,U_1116) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_9,plain,
( apply(U_1117,U_1114) = apply(U_1116,U_1114)
| ~ in(U_1114,relation_dom(U_1117))
| ~ sP233(U_1114,U_1117,U_1118,U_1116) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_10,plain,
( in(sK160(U_1118,U_1117,U_1116),relation_dom(U_1117))
| ~ sP234(U_1117,U_1118,U_1116) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_11,plain,
( apply(U_1117,sK160(U_1118,U_1117,U_1116)) != apply(U_1116,sK160(U_1118,U_1117,U_1116))
| ~ sP234(U_1117,U_1118,U_1116) ),
inference(clausify,[status(thm)],[f_306_4]) ).
fof(f_307_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_307_2,plain,
! [U_1119] : unordered_pair(U_1119,U_1119) = singleton(U_1119),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_1119] : unordered_pair(U_1119,U_1119) = singleton(U_1119),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
unordered_pair(U_1119,U_1119) = singleton(U_1119),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_308_2,plain,
! [U_1120] :
( U_1120 = empty_set
| ~ empty(U_1120) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
! [U_1120] :
( U_1120 = empty_set
| ~ empty(U_1120) ),
inference(definitional_conversion,[status(esa)],[f_308_2]) ).
cnf(f_308_4,plain,
( U_1120 = empty_set
| ~ empty(U_1120) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_309_2,plain,
! [U_1122,U_1121] :
( U_1122 = U_1121
| ~ subset(singleton(U_1122),singleton(U_1121)) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_1121,U_1122] :
( U_1122 = U_1121
| ~ subset(singleton(U_1122),singleton(U_1121)) ),
inference(definitional_conversion,[status(esa)],[f_309_2]) ).
cnf(f_309_4,plain,
( U_1122 = U_1121
| ~ subset(singleton(U_1122),singleton(U_1121)) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t70_funct_1]) ).
fof(f_310_2,plain,
! [U_1125,U_1124,U_1123] :
( apply(relation_dom_restriction(U_1123,U_1125),U_1124) = apply(U_1123,U_1124)
| ~ in(U_1124,relation_dom(relation_dom_restriction(U_1123,U_1125)))
| ~ function(U_1123)
| ~ relation(U_1123) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_1125,U_1123,U_1124] :
( apply(relation_dom_restriction(U_1123,U_1125),U_1124) = apply(U_1123,U_1124)
| ~ in(U_1124,relation_dom(relation_dom_restriction(U_1123,U_1125)))
| ~ function(U_1123)
| ~ relation(U_1123) ),
inference(definitional_conversion,[status(esa)],[f_310_2]) ).
cnf(f_310_4,plain,
( apply(relation_dom_restriction(U_1123,U_1125),U_1124) = apply(U_1123,U_1124)
| ~ in(U_1124,relation_dom(relation_dom_restriction(U_1123,U_1125)))
| ~ function(U_1123)
| ~ relation(U_1123) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_1,plain,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
inference(fof_nnf,[status(thm)],[t71_relat_1]) ).
fof(f_311_2,plain,
! [U_1126] :
( relation_rng(identity_relation(U_1126)) = U_1126
& relation_dom(identity_relation(U_1126)) = U_1126 ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
( ! [U_1128] : relation_rng(identity_relation(U_1128)) = U_1128
& ! [U_1127] : relation_dom(identity_relation(U_1127)) = U_1127 ),
inference(miniscope,[status(thm)],[f_311_2]) ).
fof(f_311_4,plain,
( ! [U_1128] : relation_rng(identity_relation(U_1128)) = U_1128
& ! [U_1127] : relation_dom(identity_relation(U_1127)) = U_1127 ),
inference(definitional_conversion,[status(esa)],[f_311_3]) ).
cnf(f_311_5,plain,
relation_dom(identity_relation(U_1127)) = U_1127,
inference(clausify,[status(thm)],[f_311_4]) ).
cnf(f_311_6,plain,
relation_rng(identity_relation(U_1128)) = U_1128,
inference(clausify,[status(thm)],[f_311_4]) ).
fof(f_312_1,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,A)
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t72_funct_1]) ).
fof(f_312_2,plain,
! [U_1131,U_1130,U_1129] :
( apply(relation_dom_restriction(U_1129,U_1131),U_1130) = apply(U_1129,U_1130)
| ~ in(U_1130,U_1131)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_1131,U_1129,U_1130] :
( apply(relation_dom_restriction(U_1129,U_1131),U_1130) = apply(U_1129,U_1130)
| ~ in(U_1130,U_1131)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(definitional_conversion,[status(esa)],[f_312_2]) ).
cnf(f_312_4,plain,
( apply(relation_dom_restriction(U_1129,U_1131),U_1130) = apply(U_1129,U_1130)
| ~ in(U_1130,U_1131)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [A,B,C,D] :
( ( ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
| ~ in(ordered_pair(A,B),D)
| ~ in(A,C) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
| ~ relation(D) ),
inference(fof_nnf,[status(thm)],[t74_relat_1]) ).
fof(f_313_2,plain,
! [U_1135,U_1134,U_1133,U_1132] :
( ( ( in(ordered_pair(U_1135,U_1134),relation_composition(identity_relation(U_1133),U_1132))
| ~ in(ordered_pair(U_1135,U_1134),U_1132)
| ~ in(U_1135,U_1133) )
& ( ( in(ordered_pair(U_1135,U_1134),U_1132)
& in(U_1135,U_1133) )
| ~ in(ordered_pair(U_1135,U_1134),relation_composition(identity_relation(U_1133),U_1132)) ) )
| ~ relation(U_1132) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
( ! [U_1134,U_1135,U_1132,U_1133] :
( in(ordered_pair(U_1135,U_1134),U_1132)
| ~ sP236(U_1134,U_1135,U_1132,U_1133) )
& ! [U_1134,U_1135,U_1132,U_1133] :
( in(U_1135,U_1133)
| ~ sP236(U_1134,U_1135,U_1132,U_1133) )
& ! [U_1134,U_1135,U_1132,U_1133] :
( in(ordered_pair(U_1135,U_1134),relation_composition(identity_relation(U_1133),U_1132))
| ~ in(ordered_pair(U_1135,U_1134),U_1132)
| ~ in(U_1135,U_1133)
| ~ sP237(U_1134,U_1135,U_1132,U_1133) )
& ! [U_1134,U_1135,U_1132,U_1133] :
( sP236(U_1134,U_1135,U_1132,U_1133)
| ~ in(ordered_pair(U_1135,U_1134),relation_composition(identity_relation(U_1133),U_1132))
| ~ sP237(U_1134,U_1135,U_1132,U_1133) )
& ! [U_1134,U_1135,U_1132,U_1133] :
( sP237(U_1134,U_1135,U_1132,U_1133)
| ~ relation(U_1132) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236,sP237])],[f_313_2]) ).
cnf(f_313_4,plain,
( sP237(U_1134,U_1135,U_1132,U_1133)
| ~ relation(U_1132) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_5,plain,
( sP236(U_1134,U_1135,U_1132,U_1133)
| ~ in(ordered_pair(U_1135,U_1134),relation_composition(identity_relation(U_1133),U_1132))
| ~ sP237(U_1134,U_1135,U_1132,U_1133) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_6,plain,
( in(ordered_pair(U_1135,U_1134),relation_composition(identity_relation(U_1133),U_1132))
| ~ in(ordered_pair(U_1135,U_1134),U_1132)
| ~ in(U_1135,U_1133)
| ~ sP237(U_1134,U_1135,U_1132,U_1133) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_7,plain,
( in(U_1135,U_1133)
| ~ sP236(U_1134,U_1135,U_1132,U_1133) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_8,plain,
( in(ordered_pair(U_1135,U_1134),U_1132)
| ~ sP236(U_1134,U_1135,U_1132,U_1133) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_314_2,plain,
! [U_1137,U_1136] :
( ~ empty(U_1136)
| ~ in(U_1137,U_1136) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
! [U_1136,U_1137] :
( ~ empty(U_1136)
| ~ in(U_1137,U_1136) ),
inference(definitional_conversion,[status(esa)],[f_314_2]) ).
cnf(f_314_4,plain,
( ~ empty(U_1136)
| ~ in(U_1137,U_1136) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_tarski]) ).
fof(f_315_2,plain,
! [U_1141,U_1140] :
( ? [U_1139] :
( ! [U_1138] :
( ~ in(U_1138,U_1139)
| ~ in(U_1138,U_1140) )
& in(U_1139,U_1140) )
| ~ in(U_1141,U_1140) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
! [U_1141,U_1140] :
( ( ! [U_1138] :
( ~ in(U_1138,sK161(U_1141,U_1140))
| ~ in(U_1138,U_1140) )
& in(sK161(U_1141,U_1140),U_1140) )
| ~ in(U_1141,U_1140) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_1139,sK161(U_1141,U_1140))],[f_315_2]) ).
fof(f_315_4,plain,
( ! [U_1140,U_1141,U_1138] :
( ~ in(U_1138,sK161(U_1141,U_1140))
| ~ in(U_1138,U_1140)
| ~ sP238(U_1140,U_1141,U_1138) )
& ! [U_1140,U_1141,U_1138] :
( in(sK161(U_1141,U_1140),U_1140)
| ~ sP238(U_1140,U_1141,U_1138) )
& ! [U_1140,U_1141,U_1138] :
( sP238(U_1140,U_1141,U_1138)
| ~ in(U_1141,U_1140) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238])],[f_315_3]) ).
cnf(f_315_5,plain,
( sP238(U_1140,U_1141,U_1138)
| ~ in(U_1141,U_1140) ),
inference(clausify,[status(thm)],[f_315_4]) ).
cnf(f_315_6,plain,
( in(sK161(U_1141,U_1140),U_1140)
| ~ sP238(U_1140,U_1141,U_1138) ),
inference(clausify,[status(thm)],[f_315_4]) ).
cnf(f_315_7,plain,
( ~ in(U_1138,sK161(U_1141,U_1140))
| ~ in(U_1138,U_1140)
| ~ sP238(U_1140,U_1141,U_1138) ),
inference(clausify,[status(thm)],[f_315_4]) ).
fof(f_316_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_316_2,plain,
! [U_1143,U_1142] : subset(U_1143,set_union2(U_1143,U_1142)),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
! [U_1142,U_1143] : subset(U_1143,set_union2(U_1143,U_1142)),
inference(definitional_conversion,[status(esa)],[f_316_2]) ).
cnf(f_316_4,plain,
subset(U_1143,set_union2(U_1143,U_1142)),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_difference(A,B) != A )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t83_xboole_1]) ).
fof(f_317_2,plain,
! [U_1145,U_1144] :
( ( disjoint(U_1145,U_1144)
| set_difference(U_1145,U_1144) != U_1145 )
& ( set_difference(U_1145,U_1144) = U_1145
| ~ disjoint(U_1145,U_1144) ) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
( ! [U_1149,U_1147] :
( disjoint(U_1149,U_1147)
| set_difference(U_1149,U_1147) != U_1149 )
& ! [U_1148,U_1146] :
( set_difference(U_1148,U_1146) = U_1148
| ~ disjoint(U_1148,U_1146) ) ),
inference(miniscope,[status(thm)],[f_317_2]) ).
fof(f_317_4,plain,
( ! [U_1149,U_1147] :
( disjoint(U_1149,U_1147)
| set_difference(U_1149,U_1147) != U_1149 )
& ! [U_1148,U_1146] :
( set_difference(U_1148,U_1146) = U_1148
| ~ disjoint(U_1148,U_1146) ) ),
inference(definitional_conversion,[status(esa)],[f_317_3]) ).
cnf(f_317_5,plain,
( set_difference(U_1148,U_1146) = U_1148
| ~ disjoint(U_1148,U_1146) ),
inference(clausify,[status(thm)],[f_317_4]) ).
cnf(f_317_6,plain,
( disjoint(U_1149,U_1147)
| set_difference(U_1149,U_1147) != U_1149 ),
inference(clausify,[status(thm)],[f_317_4]) ).
fof(f_318_1,plain,
! [A,B,C] :
( ( ( in(A,relation_dom(relation_dom_restriction(C,B)))
| ~ in(A,relation_dom(C))
| ~ in(A,B) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t86_relat_1]) ).
fof(f_318_2,plain,
! [U_1152,U_1151,U_1150] :
( ( ( in(U_1152,relation_dom(relation_dom_restriction(U_1150,U_1151)))
| ~ in(U_1152,relation_dom(U_1150))
| ~ in(U_1152,U_1151) )
& ( ( in(U_1152,relation_dom(U_1150))
& in(U_1152,U_1151) )
| ~ in(U_1152,relation_dom(relation_dom_restriction(U_1150,U_1151))) ) )
| ~ relation(U_1150) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
( ! [U_1150,U_1151,U_1152] :
( in(U_1152,relation_dom(U_1150))
| ~ sP239(U_1150,U_1151,U_1152) )
& ! [U_1150,U_1151,U_1152] :
( in(U_1152,U_1151)
| ~ sP239(U_1150,U_1151,U_1152) )
& ! [U_1150,U_1151,U_1152] :
( in(U_1152,relation_dom(relation_dom_restriction(U_1150,U_1151)))
| ~ in(U_1152,relation_dom(U_1150))
| ~ in(U_1152,U_1151)
| ~ sP240(U_1150,U_1151,U_1152) )
& ! [U_1150,U_1151,U_1152] :
( sP239(U_1150,U_1151,U_1152)
| ~ in(U_1152,relation_dom(relation_dom_restriction(U_1150,U_1151)))
| ~ sP240(U_1150,U_1151,U_1152) )
& ! [U_1150,U_1151,U_1152] :
( sP240(U_1150,U_1151,U_1152)
| ~ relation(U_1150) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239,sP240])],[f_318_2]) ).
cnf(f_318_4,plain,
( sP240(U_1150,U_1151,U_1152)
| ~ relation(U_1150) ),
inference(clausify,[status(thm)],[f_318_3]) ).
cnf(f_318_5,plain,
( sP239(U_1150,U_1151,U_1152)
| ~ in(U_1152,relation_dom(relation_dom_restriction(U_1150,U_1151)))
| ~ sP240(U_1150,U_1151,U_1152) ),
inference(clausify,[status(thm)],[f_318_3]) ).
cnf(f_318_6,plain,
( in(U_1152,relation_dom(relation_dom_restriction(U_1150,U_1151)))
| ~ in(U_1152,relation_dom(U_1150))
| ~ in(U_1152,U_1151)
| ~ sP240(U_1150,U_1151,U_1152) ),
inference(clausify,[status(thm)],[f_318_3]) ).
cnf(f_318_7,plain,
( in(U_1152,U_1151)
| ~ sP239(U_1150,U_1151,U_1152) ),
inference(clausify,[status(thm)],[f_318_3]) ).
cnf(f_318_8,plain,
( in(U_1152,relation_dom(U_1150))
| ~ sP239(U_1150,U_1151,U_1152) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_319_2,plain,
! [U_1154,U_1153] :
( subset(relation_dom_restriction(U_1153,U_1154),U_1153)
| ~ relation(U_1153) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_1153,U_1154] :
( subset(relation_dom_restriction(U_1153,U_1154),U_1153)
| ~ relation(U_1153) ),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
( subset(relation_dom_restriction(U_1153,U_1154),U_1153)
| ~ relation(U_1153) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_320_2,plain,
! [U_1156,U_1155] :
( ~ empty(U_1155)
| U_1156 = U_1155
| ~ empty(U_1156) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1156] :
( ! [U_1155] :
( ~ empty(U_1155)
| U_1156 = U_1155 )
| ~ empty(U_1156) ),
inference(miniscope,[status(thm)],[f_320_2]) ).
fof(f_320_4,plain,
! [U_1155,U_1156] :
( ~ empty(U_1155)
| U_1156 = U_1155
| ~ empty(U_1156) ),
inference(definitional_conversion,[status(esa)],[f_320_3]) ).
cnf(f_320_5,plain,
( ~ empty(U_1155)
| U_1156 = U_1155
| ~ empty(U_1156) ),
inference(clausify,[status(thm)],[f_320_4]) ).
fof(f_321_1,plain,
! [A,B,C] :
( ( ( in(ordered_pair(A,B),C)
| B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t8_funct_1]) ).
fof(f_321_2,plain,
! [U_1159,U_1158,U_1157] :
( ( ( in(ordered_pair(U_1159,U_1158),U_1157)
| U_1158 != apply(U_1157,U_1159)
| ~ in(U_1159,relation_dom(U_1157)) )
& ( ( U_1158 = apply(U_1157,U_1159)
& in(U_1159,relation_dom(U_1157)) )
| ~ in(ordered_pair(U_1159,U_1158),U_1157) ) )
| ~ function(U_1157)
| ~ relation(U_1157) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
( ! [U_1158,U_1159,U_1157] :
( U_1158 = apply(U_1157,U_1159)
| ~ sP241(U_1158,U_1159,U_1157) )
& ! [U_1158,U_1159,U_1157] :
( in(U_1159,relation_dom(U_1157))
| ~ sP241(U_1158,U_1159,U_1157) )
& ! [U_1158,U_1159,U_1157] :
( in(ordered_pair(U_1159,U_1158),U_1157)
| U_1158 != apply(U_1157,U_1159)
| ~ in(U_1159,relation_dom(U_1157))
| ~ sP242(U_1158,U_1159,U_1157) )
& ! [U_1158,U_1159,U_1157] :
( sP241(U_1158,U_1159,U_1157)
| ~ in(ordered_pair(U_1159,U_1158),U_1157)
| ~ sP242(U_1158,U_1159,U_1157) )
& ! [U_1158,U_1159,U_1157] :
( sP242(U_1158,U_1159,U_1157)
| ~ function(U_1157)
| ~ relation(U_1157) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241,sP242])],[f_321_2]) ).
cnf(f_321_4,plain,
( sP242(U_1158,U_1159,U_1157)
| ~ function(U_1157)
| ~ relation(U_1157) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_5,plain,
( sP241(U_1158,U_1159,U_1157)
| ~ in(ordered_pair(U_1159,U_1158),U_1157)
| ~ sP242(U_1158,U_1159,U_1157) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_6,plain,
( in(ordered_pair(U_1159,U_1158),U_1157)
| U_1158 != apply(U_1157,U_1159)
| ~ in(U_1159,relation_dom(U_1157))
| ~ sP242(U_1158,U_1159,U_1157) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_7,plain,
( in(U_1159,relation_dom(U_1157))
| ~ sP241(U_1158,U_1159,U_1157) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_8,plain,
( U_1158 = apply(U_1157,U_1159)
| ~ sP241(U_1158,U_1159,U_1157) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [A] :
( ( ( well_orders(A,relation_field(A))
| ~ well_ordering(A) )
& ( well_ordering(A)
| ~ well_orders(A,relation_field(A)) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t8_wellord1]) ).
fof(f_322_2,plain,
! [U_1160] :
( ( ( well_orders(U_1160,relation_field(U_1160))
| ~ well_ordering(U_1160) )
& ( well_ordering(U_1160)
| ~ well_orders(U_1160,relation_field(U_1160)) ) )
| ~ relation(U_1160) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
( ! [U_1160] :
( well_orders(U_1160,relation_field(U_1160))
| ~ well_ordering(U_1160)
| ~ sP243(U_1160) )
& ! [U_1160] :
( well_ordering(U_1160)
| ~ well_orders(U_1160,relation_field(U_1160))
| ~ sP243(U_1160) )
& ! [U_1160] :
( sP243(U_1160)
| ~ relation(U_1160) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243])],[f_322_2]) ).
cnf(f_322_4,plain,
( sP243(U_1160)
| ~ relation(U_1160) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_5,plain,
( well_ordering(U_1160)
| ~ well_orders(U_1160,relation_field(U_1160))
| ~ sP243(U_1160) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_6,plain,
( well_orders(U_1160,relation_field(U_1160))
| ~ well_ordering(U_1160)
| ~ sP243(U_1160) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_1,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1]) ).
fof(f_323_2,plain,
! [U_1163,U_1162,U_1161] :
( subset(set_union2(U_1163,U_1161),U_1162)
| ~ subset(U_1161,U_1162)
| ~ subset(U_1163,U_1162) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
! [U_1161,U_1163,U_1162] :
( subset(set_union2(U_1163,U_1161),U_1162)
| ~ subset(U_1161,U_1162)
| ~ subset(U_1163,U_1162) ),
inference(definitional_conversion,[status(esa)],[f_323_2]) ).
cnf(f_323_4,plain,
( subset(set_union2(U_1163,U_1161),U_1162)
| ~ subset(U_1161,U_1162)
| ~ subset(U_1163,U_1162) ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_324_2,plain,
! [U_1166,U_1165,U_1164] :
( U_1166 = U_1165
| singleton(U_1166) != unordered_pair(U_1165,U_1164) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
! [U_1166,U_1165] :
( ! [U_1164] : singleton(U_1166) != unordered_pair(U_1165,U_1164)
| U_1166 = U_1165 ),
inference(miniscope,[status(thm)],[f_324_2]) ).
fof(f_324_4,plain,
! [U_1164,U_1166,U_1165] :
( singleton(U_1166) != unordered_pair(U_1165,U_1164)
| U_1166 = U_1165 ),
inference(definitional_conversion,[status(esa)],[f_324_3]) ).
cnf(f_324_5,plain,
( singleton(U_1166) != unordered_pair(U_1165,U_1164)
| U_1166 = U_1165 ),
inference(clausify,[status(thm)],[f_324_4]) ).
fof(f_325_1,plain,
! [A,B] :
( relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t90_relat_1]) ).
fof(f_325_2,plain,
! [U_1168,U_1167] :
( relation_dom(relation_dom_restriction(U_1167,U_1168)) = set_intersection2(relation_dom(U_1167),U_1168)
| ~ relation(U_1167) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1167,U_1168] :
( relation_dom(relation_dom_restriction(U_1167,U_1168)) = set_intersection2(relation_dom(U_1167),U_1168)
| ~ relation(U_1167) ),
inference(definitional_conversion,[status(esa)],[f_325_2]) ).
cnf(f_325_4,plain,
( relation_dom(relation_dom_restriction(U_1167,U_1168)) = set_intersection2(relation_dom(U_1167),U_1168)
| ~ relation(U_1167) ),
inference(clausify,[status(thm)],[f_325_3]) ).
fof(f_326_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_326_2,plain,
! [U_1170,U_1169] :
( subset(U_1170,union(U_1169))
| ~ in(U_1170,U_1169) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1169,U_1170] :
( subset(U_1170,union(U_1169))
| ~ in(U_1170,U_1169) ),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
( subset(U_1170,union(U_1169))
| ~ in(U_1170,U_1169) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_1,plain,
! [A,B] :
( relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t94_relat_1]) ).
fof(f_327_2,plain,
! [U_1172,U_1171] :
( relation_dom_restriction(U_1171,U_1172) = relation_composition(identity_relation(U_1172),U_1171)
| ~ relation(U_1171) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1171,U_1172] :
( relation_dom_restriction(U_1171,U_1172) = relation_composition(identity_relation(U_1172),U_1171)
| ~ relation(U_1171) ),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
( relation_dom_restriction(U_1171,U_1172) = relation_composition(identity_relation(U_1172),U_1171)
| ~ relation(U_1171) ),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_1,plain,
! [A,B] :
( subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t99_relat_1]) ).
fof(f_328_2,plain,
! [U_1174,U_1173] :
( subset(relation_rng(relation_dom_restriction(U_1173,U_1174)),relation_rng(U_1173))
| ~ relation(U_1173) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
! [U_1173,U_1174] :
( subset(relation_rng(relation_dom_restriction(U_1173,U_1174)),relation_rng(U_1173))
| ~ relation(U_1173) ),
inference(definitional_conversion,[status(esa)],[f_328_2]) ).
cnf(f_328_4,plain,
( subset(relation_rng(relation_dom_restriction(U_1173,U_1174)),relation_rng(U_1173))
| ~ relation(U_1173) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_329_2,plain,
! [U_1175] : union(powerset(U_1175)) = U_1175,
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
! [U_1175] : union(powerset(U_1175)) = U_1175,
inference(definitional_conversion,[status(esa)],[f_329_2]) ).
cnf(f_329_4,plain,
union(powerset(U_1175)) = U_1175,
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_1,plain,
! [A] :
? [B] :
( ! [C] :
( in(C,B)
| are_equipotent(C,B)
| ~ subset(C,B) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(E,D)
| ~ subset(E,C) )
& in(D,B) )
| ~ in(C,B) )
& ! [C,D] :
( in(D,B)
| ~ subset(D,C)
| ~ in(C,B) )
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t9_tarski]) ).
fof(f_330_2,plain,
! [U_1183] :
? [U_1182] :
( ! [U_1181] :
( in(U_1181,U_1182)
| are_equipotent(U_1181,U_1182)
| ~ subset(U_1181,U_1182) )
& ! [U_1180] :
( ? [U_1179] :
( ! [U_1178] :
( in(U_1178,U_1179)
| ~ subset(U_1178,U_1180) )
& in(U_1179,U_1182) )
| ~ in(U_1180,U_1182) )
& ! [U_1177,U_1176] :
( in(U_1176,U_1182)
| ~ subset(U_1176,U_1177)
| ~ in(U_1177,U_1182) )
& in(U_1183,U_1182) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_1183] :
( ! [U_1181] :
( in(U_1181,sK162(U_1183))
| are_equipotent(U_1181,sK162(U_1183))
| ~ subset(U_1181,sK162(U_1183)) )
& ! [U_1180] :
( ? [U_1179] :
( ! [U_1178] :
( in(U_1178,U_1179)
| ~ subset(U_1178,U_1180) )
& in(U_1179,sK162(U_1183)) )
| ~ in(U_1180,sK162(U_1183)) )
& ! [U_1177,U_1176] :
( in(U_1176,sK162(U_1183))
| ~ subset(U_1176,U_1177)
| ~ in(U_1177,sK162(U_1183)) )
& in(U_1183,sK162(U_1183)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_1182,sK162(U_1183))],[f_330_2]) ).
fof(f_330_4,plain,
! [U_1183] :
( ! [U_1181] :
( in(U_1181,sK162(U_1183))
| are_equipotent(U_1181,sK162(U_1183))
| ~ subset(U_1181,sK162(U_1183)) )
& ! [U_1180] :
( ( ! [U_1178] :
( in(U_1178,sK163(U_1183,U_1180))
| ~ subset(U_1178,U_1180) )
& in(sK163(U_1183,U_1180),sK162(U_1183)) )
| ~ in(U_1180,sK162(U_1183)) )
& ! [U_1177,U_1176] :
( in(U_1176,sK162(U_1183))
| ~ subset(U_1176,U_1177)
| ~ in(U_1177,sK162(U_1183)) )
& in(U_1183,sK162(U_1183)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_1179,sK163(U_1183,U_1180))],[f_330_3]) ).
fof(f_330_5,plain,
( ! [U_1178,U_1180,U_1183] :
( in(U_1178,sK163(U_1183,U_1180))
| ~ subset(U_1178,U_1180)
| ~ sP244(U_1178,U_1180,U_1183) )
& ! [U_1178,U_1180,U_1183] :
( in(sK163(U_1183,U_1180),sK162(U_1183))
| ~ sP244(U_1178,U_1180,U_1183) )
& ! [U_1181,U_1183] :
( in(U_1181,sK162(U_1183))
| are_equipotent(U_1181,sK162(U_1183))
| ~ subset(U_1181,sK162(U_1183)) )
& ! [U_1178,U_1180,U_1183] :
( sP244(U_1178,U_1180,U_1183)
| ~ in(U_1180,sK162(U_1183)) )
& ! [U_1177,U_1176,U_1183] :
( in(U_1176,sK162(U_1183))
| ~ subset(U_1176,U_1177)
| ~ in(U_1177,sK162(U_1183)) )
& ! [U_1183] : in(U_1183,sK162(U_1183)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_330_4]) ).
cnf(f_330_6,plain,
in(U_1183,sK162(U_1183)),
inference(clausify,[status(thm)],[f_330_5]) ).
cnf(f_330_7,plain,
( in(U_1176,sK162(U_1183))
| ~ subset(U_1176,U_1177)
| ~ in(U_1177,sK162(U_1183)) ),
inference(clausify,[status(thm)],[f_330_5]) ).
cnf(f_330_8,plain,
( sP244(U_1178,U_1180,U_1183)
| ~ in(U_1180,sK162(U_1183)) ),
inference(clausify,[status(thm)],[f_330_5]) ).
cnf(f_330_9,plain,
( in(U_1181,sK162(U_1183))
| are_equipotent(U_1181,sK162(U_1183))
| ~ subset(U_1181,sK162(U_1183)) ),
inference(clausify,[status(thm)],[f_330_5]) ).
cnf(f_330_10,plain,
( in(sK163(U_1183,U_1180),sK162(U_1183))
| ~ sP244(U_1178,U_1180,U_1183) ),
inference(clausify,[status(thm)],[f_330_5]) ).
cnf(f_330_11,plain,
( in(U_1178,sK163(U_1183,U_1180))
| ~ subset(U_1178,U_1180)
| ~ sP244(U_1178,U_1180,U_1183) ),
inference(clausify,[status(thm)],[f_330_5]) ).
fof(f_331_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_331_2,plain,
! [U_1186,U_1185,U_1184] :
( U_1185 = U_1184
| singleton(U_1186) != unordered_pair(U_1185,U_1184) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1185,U_1184,U_1186] :
( U_1185 = U_1184
| singleton(U_1186) != unordered_pair(U_1185,U_1184) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( U_1185 = U_1184
| singleton(U_1186) != unordered_pair(U_1185,U_1184) ),
inference(clausify,[status(thm)],[f_331_3]) ).
cnf(f_74_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_74_3]) ).
cnf(f_75_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_75_3]) ).
cnf(f_76_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_76_3]) ).
cnf(f_77_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_77_3]) ).
cnf(f_78_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_78_3]) ).
cnf(f_79_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_79_3]) ).
cnf(f_80_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_80_3]) ).
cnf(f_81_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_81_3]) ).
cnf(f_82_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_82_3]) ).
cnf(f_83_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_83_3]) ).
cnf(f_85_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_85_3]) ).
cnf(f_87_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_87_3]) ).
cnf(f_89_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_89_3]) ).
cnf(f_90_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_90_3]) ).
cnf(f_91_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_91_3]) ).
cnf(f_93_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_93_3]) ).
cnf(f_94_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_94_3]) ).
cnf(f_96_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_96_3]) ).
cnf(f_97_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_97_3]) ).
cnf(f_106_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_106_3]) ).
cnf(f_107_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_3]) ).
cnf(f_108_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_108_3]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( relation_image(Eq_x_0,Eq_x_1) = relation_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( relation_rng_restriction(Eq_x_0,Eq_x_1) = relation_rng_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( relation_inverse_image(Eq_x_0,Eq_x_1) = relation_inverse_image(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( unordered_triple(Eq_x_0,Eq_x_1,Eq_x_2) = unordered_triple(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( fiber(Eq_x_0,Eq_x_1) = fiber(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( cast_to_subset(Eq_x_0) = cast_to_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( subset_complement(Eq_x_0,Eq_x_1) = subset_complement(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( relation_restriction(Eq_x_0,Eq_x_1) = relation_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( complements_of_subsets(Eq_x_0,Eq_x_1) = complements_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( union_of_subsets(Eq_x_0,Eq_x_1) = union_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( meet_of_subsets(Eq_x_0,Eq_x_1) = meet_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( subset_difference(Eq_x_0,Eq_x_1,Eq_x_2) = subset_difference(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2) = sK33(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK41(Eq_x_0) = sK41(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK44(Eq_x_0) = sK44(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK45(Eq_x_0,Eq_x_1) = sK45(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK46(Eq_x_0,Eq_x_1) = sK46(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK49(Eq_x_0,Eq_x_1,Eq_x_2) = sK49(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK52(Eq_x_0) = sK52(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK61(Eq_x_0) = sK61(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK62(Eq_x_0) = sK62(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK64(Eq_x_0,Eq_x_1) = sK64(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( sK65(Eq_x_0,Eq_x_1) = sK65(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK67(Eq_x_0,Eq_x_1) = sK67(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_104,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_105,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_107,axiom,
( sK72(Eq_x_0,Eq_x_1) = sK72(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK73(Eq_x_0,Eq_x_1) = sK73(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK74(Eq_x_0,Eq_x_1) = sK74(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK78(Eq_x_0,Eq_x_1) = sK78(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_114,axiom,
( sK79(Eq_x_0,Eq_x_1) = sK79(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_115,axiom,
( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK81(Eq_x_0,Eq_x_1,Eq_x_2) = sK81(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( sK82(Eq_x_0,Eq_x_1,Eq_x_2) = sK82(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,axiom,
( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_120,axiom,
( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_121,axiom,
( sK86(Eq_x_0,Eq_x_1,Eq_x_2) = sK86(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,axiom,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( sK88(Eq_x_0,Eq_x_1) = sK88(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( sK89(Eq_x_0,Eq_x_1) = sK89(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( sK90(Eq_x_0,Eq_x_1) = sK90(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( sK91(Eq_x_0,Eq_x_1) = sK91(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK93(Eq_x_0,Eq_x_1) = sK93(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,axiom,
( sK94(Eq_x_0,Eq_x_1) = sK94(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_130,axiom,
( sK95(Eq_x_0,Eq_x_1) = sK95(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_131,axiom,
( sK96(Eq_x_0,Eq_x_1,Eq_x_2) = sK96(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( sK97(Eq_x_0,Eq_x_1,Eq_x_2) = sK97(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_133,axiom,
( sK98(Eq_x_0,Eq_x_1,Eq_x_2) = sK98(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_134,axiom,
( sK99(Eq_x_0,Eq_x_1,Eq_x_2) = sK99(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_135,axiom,
( sK100(Eq_x_0) = sK100(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_136,axiom,
( sK101(Eq_x_0) = sK101(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK102(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK102(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK103(Eq_x_0,Eq_x_1,Eq_x_2) = sK103(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK104(Eq_x_0,Eq_x_1,Eq_x_2) = sK104(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK105(Eq_x_0,Eq_x_1,Eq_x_2) = sK105(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK106(Eq_x_0,Eq_x_1,Eq_x_2) = sK106(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( sK108(Eq_x_0,Eq_x_1) = sK108(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( sK109(Eq_x_0,Eq_x_1) = sK109(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( sK110(Eq_x_0,Eq_x_1) = sK110(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK111(Eq_x_0,Eq_x_1,Eq_x_2) = sK111(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK112(Eq_x_0,Eq_x_1) = sK112(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK113(Eq_x_0) = sK113(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_149,axiom,
( sK114(Eq_x_0,Eq_x_1) = sK114(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,axiom,
( sK115(Eq_x_0) = sK115(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_151,axiom,
( sK116(Eq_x_0) = sK116(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_152,axiom,
( sK117(Eq_x_0) = sK117(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_153,axiom,
( sK118(Eq_x_0) = sK118(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_154,axiom,
( sK119(Eq_x_0) = sK119(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_155,axiom,
( sK120(Eq_x_0) = sK120(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,axiom,
( sK121(Eq_x_0) = sK121(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_157,axiom,
( sK122(Eq_x_0) = sK122(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( sK123(Eq_x_0,Eq_x_1) = sK123(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( sK127(Eq_x_0) = sK127(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_160,axiom,
( sK132(Eq_x_0) = sK132(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_161,axiom,
( sK138(Eq_x_0) = sK138(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_162,axiom,
( sK139(Eq_x_0,Eq_x_1,Eq_x_2) = sK139(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_163,axiom,
( sK140(Eq_x_0,Eq_x_1,Eq_x_2) = sK140(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_164,axiom,
( sK145(Eq_x_0,Eq_x_1) = sK145(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( sK146(Eq_x_0,Eq_x_1) = sK146(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_166,axiom,
( sK147(Eq_x_0) = sK147(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_167,axiom,
( sK148(Eq_x_0,Eq_x_1) = sK148(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_168,axiom,
( sK149(Eq_x_0,Eq_x_1) = sK149(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_169,axiom,
( sK150(Eq_x_0,Eq_x_1) = sK150(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_170,axiom,
( sK151(Eq_x_0) = sK151(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,axiom,
( sK152(Eq_x_0) = sK152(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_172,axiom,
( sK153(Eq_x_0,Eq_x_1) = sK153(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_173,axiom,
( sK154(Eq_x_0,Eq_x_1) = sK154(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_174,axiom,
( sK155(Eq_x_0,Eq_x_1) = sK155(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_175,axiom,
( sK156(Eq_x_0,Eq_x_1) = sK156(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_176,axiom,
( sK157(Eq_x_0,Eq_x_1) = sK157(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_177,axiom,
( sK158(Eq_x_0) = sK158(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_178,axiom,
( sK159(Eq_x_0) = sK159(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_179,axiom,
( sK160(Eq_x_0,Eq_x_1,Eq_x_2) = sK160(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_180,axiom,
( sK161(Eq_x_0,Eq_x_1) = sK161(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_181,axiom,
( sK162(Eq_x_0) = sK162(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_182,axiom,
( sK163(Eq_x_0,Eq_x_1) = sK163(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_183,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_184,axiom,
( proper_subset(Eq_y_0,Eq_y_1)
| ~ proper_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_187,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( ordinal_subset(Eq_y_0,Eq_y_1)
| ~ ordinal_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( is_antisymmetric_in(Eq_y_0,Eq_y_1)
| ~ is_antisymmetric_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_197,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_198,axiom,
( is_connected_in(Eq_y_0,Eq_y_1)
| ~ is_connected_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( is_transitive_in(Eq_y_0,Eq_y_1)
| ~ is_transitive_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( is_reflexive_in(Eq_y_0,Eq_y_1)
| ~ is_reflexive_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( relation_of2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( well_founded_relation(Eq_y_0)
| ~ well_founded_relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_205,axiom,
( is_well_founded_in(Eq_y_0,Eq_y_1)
| ~ is_well_founded_in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_206,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_207,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_208,axiom,
( well_orders(Eq_y_0,Eq_y_1)
| ~ well_orders(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_209,axiom,
( being_limit_ordinal(Eq_y_0)
| ~ being_limit_ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_210,axiom,
( relation_isomorphism(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_isomorphism(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,axiom,
( relation_of2_as_subset(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2_as_subset(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_212,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_214,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_217,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_218,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_220,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_221,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_224,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_225,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_226,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_227,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_228,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_229,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_230,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_231,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_232,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_233,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_234,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_235,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_236,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_237,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_238,axiom,
( sP24(Eq_y_0)
| ~ sP24(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_239,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_240,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_241,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_242,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_243,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_244,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_245,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_246,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_247,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_248,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_249,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_250,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_251,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_252,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_253,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_254,axiom,
( sP40(Eq_y_0)
| ~ sP40(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_255,axiom,
( sP41(Eq_y_0)
| ~ sP41(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_256,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_257,axiom,
( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_258,axiom,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_259,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_260,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_261,axiom,
( sP47(Eq_y_0,Eq_y_1)
| ~ sP47(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_262,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_263,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_264,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_265,axiom,
( sP51(Eq_y_0,Eq_y_1)
| ~ sP51(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_266,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_267,axiom,
( sP53(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP53(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_268,axiom,
( sP54(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_269,axiom,
( sP55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_270,axiom,
( sP56(Eq_y_0,Eq_y_1)
| ~ sP56(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_271,axiom,
( sP57(Eq_y_0,Eq_y_1)
| ~ sP57(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_272,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_273,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_274,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_275,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_276,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_277,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_278,axiom,
( sP64(Eq_y_0,Eq_y_1)
| ~ sP64(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_279,axiom,
( sP65(Eq_y_0,Eq_y_1)
| ~ sP65(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_280,axiom,
( sP66(Eq_y_0)
| ~ sP66(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_281,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_282,axiom,
( sP68(Eq_y_0,Eq_y_1)
| ~ sP68(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_283,axiom,
( sP69(Eq_y_0,Eq_y_1)
| ~ sP69(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_284,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_285,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_286,axiom,
( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_287,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_288,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_289,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_290,axiom,
( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_291,axiom,
( sP77(Eq_y_0,Eq_y_1)
| ~ sP77(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_292,axiom,
( sP78(Eq_y_0,Eq_y_1)
| ~ sP78(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_293,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_294,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_295,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_296,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_297,axiom,
( sP83(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_298,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_299,axiom,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_300,axiom,
( sP86(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP86(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_301,axiom,
( sP87(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_302,axiom,
( sP88(Eq_y_0)
| ~ sP88(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_303,axiom,
( sP89(Eq_y_0,Eq_y_1)
| ~ sP89(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_304,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_305,axiom,
( sP91(Eq_y_0,Eq_y_1)
| ~ sP91(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_306,axiom,
( sP92(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP92(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_307,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_308,axiom,
( sP94(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_309,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_310,axiom,
( sP96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_311,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_312,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_313,axiom,
( sP99(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_314,axiom,
( sP100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_315,axiom,
( sP101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_316,axiom,
( sP102(Eq_y_0)
| ~ sP102(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_317,axiom,
( sP103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_318,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_319,axiom,
( sP105(Eq_y_0,Eq_y_1)
| ~ sP105(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_320,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_321,axiom,
( sP107(Eq_y_0,Eq_y_1)
| ~ sP107(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_322,axiom,
( sP108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_323,axiom,
( sP109(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP109(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_324,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_325,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_326,axiom,
( sP112(Eq_y_0,Eq_y_1)
| ~ sP112(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_327,axiom,
( sP113(Eq_y_0)
| ~ sP113(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_328,axiom,
( sP114(Eq_y_0)
| ~ sP114(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_329,axiom,
( sP115(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_330,axiom,
( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_331,axiom,
( sP117(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_332,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_333,axiom,
( sP119(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_334,axiom,
( sP120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_335,axiom,
( sP121(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP121(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_336,axiom,
( sP122(Eq_y_0,Eq_y_1)
| ~ sP122(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_337,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_338,axiom,
( sP124(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP124(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_339,axiom,
( sP125(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_340,axiom,
( sP126(Eq_y_0,Eq_y_1)
| ~ sP126(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_341,axiom,
( sP127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_342,axiom,
( sP128(Eq_y_0,Eq_y_1)
| ~ sP128(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_343,axiom,
( sP129(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP129(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_344,axiom,
( sP130(Eq_y_0,Eq_y_1)
| ~ sP130(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_345,axiom,
( sP131(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_346,axiom,
( sP132(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_347,axiom,
( sP133(Eq_y_0,Eq_y_1)
| ~ sP133(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_348,axiom,
( sP134(Eq_y_0,Eq_y_1)
| ~ sP134(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_349,axiom,
( sP135(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_350,axiom,
( sP136(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP136(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_351,axiom,
( sP137(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP137(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_352,axiom,
( sP138(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_353,axiom,
( sP139(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP139(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_354,axiom,
( sP140(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP140(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_355,axiom,
( sP141(Eq_y_0)
| ~ sP141(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_356,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_357,axiom,
( sP143(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_358,axiom,
( sP144(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_359,axiom,
( sP145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_360,axiom,
( sP146(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP146(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_361,axiom,
( sP147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_362,axiom,
( sP148(Eq_y_0,Eq_y_1)
| ~ sP148(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_363,axiom,
( sP149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_364,axiom,
( sP150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_365,axiom,
( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_366,axiom,
( sP152(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP152(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_367,axiom,
( sP153(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP153(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_368,axiom,
( sP154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_369,axiom,
( sP155(Eq_y_0,Eq_y_1)
| ~ sP155(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_370,axiom,
( sP156(Eq_y_0)
| ~ sP156(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_371,axiom,
( sP157(Eq_y_0)
| ~ sP157(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_372,axiom,
( sP158(Eq_y_0,Eq_y_1)
| ~ sP158(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_373,axiom,
( sP159(Eq_y_0)
| ~ sP159(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_374,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_375,axiom,
( sP161(Eq_y_0,Eq_y_1)
| ~ sP161(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_376,axiom,
( sP162(Eq_y_0)
| ~ sP162(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_377,axiom,
( sP163(Eq_y_0)
| ~ sP163(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_378,axiom,
( sP164(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP164(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_379,axiom,
( sP165(Eq_y_0)
| ~ sP165(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_380,axiom,
( sP166(Eq_y_0,Eq_y_1)
| ~ sP166(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_381,axiom,
( sP167(Eq_y_0)
| ~ sP167(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_382,axiom,
( sP168(Eq_y_0)
| ~ sP168(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_383,axiom,
( sP169(Eq_y_0,Eq_y_1)
| ~ sP169(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_384,axiom,
( sP170(Eq_y_0)
| ~ sP170(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_385,axiom,
( sP171(Eq_y_0,Eq_y_1)
| ~ sP171(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_386,axiom,
( sP172(Eq_y_0)
| ~ sP172(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_387,axiom,
( sP173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_388,axiom,
( sP174(Eq_y_0)
| ~ sP174(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_389,axiom,
( sP175(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP175(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_390,axiom,
( sP176(Eq_y_0)
| ~ sP176(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_391,axiom,
( sP177(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP177(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_392,axiom,
( sP178(Eq_y_0,Eq_y_1)
| ~ sP178(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_393,axiom,
( sP179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_394,axiom,
( sP180(Eq_y_0,Eq_y_1)
| ~ sP180(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_395,axiom,
( sP181(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP181(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_396,axiom,
( sP182(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP182(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_397,axiom,
( sP183(Eq_y_0)
| ~ sP183(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_398,axiom,
( sP184(Eq_y_0,Eq_y_1)
| ~ sP184(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_399,axiom,
( sP185(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP185(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_400,axiom,
( sP186(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP186(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_401,axiom,
( sP187(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP187(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_402,axiom,
( sP188(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP188(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_403,axiom,
( sP189(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP189(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_404,axiom,
( sP190(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP190(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_405,axiom,
( sP191(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_406,axiom,
( sP192(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP192(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_407,axiom,
( sP193(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP193(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_408,axiom,
( sP194(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP194(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_409,axiom,
( sP195(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP195(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_410,axiom,
( sP196(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP196(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_411,axiom,
( sP197(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP197(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_412,axiom,
( sP198(Eq_y_0,Eq_y_1)
| ~ sP198(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_413,axiom,
( sP199(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP199(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_414,axiom,
( sP200(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP200(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_415,axiom,
( sP201(Eq_y_0,Eq_y_1)
| ~ sP201(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_416,axiom,
( sP202(Eq_y_0,Eq_y_1)
| ~ sP202(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_417,axiom,
( sP203(Eq_y_0,Eq_y_1)
| ~ sP203(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_418,axiom,
( sP204(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP204(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_419,axiom,
( sP205(Eq_y_0)
| ~ sP205(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_420,axiom,
( sP206(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP206(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_421,axiom,
( sP207(Eq_y_0,Eq_y_1)
| ~ sP207(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_422,axiom,
( sP208(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_423,axiom,
( sP209(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP209(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_424,axiom,
( sP210(Eq_y_0,Eq_y_1)
| ~ sP210(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_425,axiom,
( sP211(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_426,axiom,
( sP212(Eq_y_0)
| ~ sP212(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_427,axiom,
( sP213(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP213(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_428,axiom,
( sP214(Eq_y_0,Eq_y_1)
| ~ sP214(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_429,axiom,
( sP215(Eq_y_0,Eq_y_1)
| ~ sP215(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_430,axiom,
( sP216(Eq_y_0)
| ~ sP216(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_431,axiom,
( sP217(Eq_y_0,Eq_y_1)
| ~ sP217(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_432,axiom,
( sP218(Eq_y_0)
| ~ sP218(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_433,axiom,
( sP219(Eq_y_0,Eq_y_1)
| ~ sP219(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_434,axiom,
( sP220(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP220(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_435,axiom,
( sP221(Eq_y_0,Eq_y_1)
| ~ sP221(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_436,axiom,
( sP222(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_437,axiom,
( sP223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_438,axiom,
( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_439,axiom,
( sP225(Eq_y_0,Eq_y_1)
| ~ sP225(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_440,axiom,
( sP226(Eq_y_0,Eq_y_1)
| ~ sP226(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_441,axiom,
( sP227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_442,axiom,
( sP228(Eq_y_0)
| ~ sP228(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_443,axiom,
( sP229(Eq_y_0,Eq_y_1)
| ~ sP229(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_444,axiom,
( sP230(Eq_y_0)
| ~ sP230(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_445,axiom,
( sP231(Eq_y_0)
| ~ sP231(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_446,axiom,
( sP232(Eq_y_0)
| ~ sP232(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_447,axiom,
( sP233(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_448,axiom,
( sP234(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP234(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_449,axiom,
( sP235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_450,axiom,
( sP236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_451,axiom,
( sP237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_452,axiom,
( sP238(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP238(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_453,axiom,
( sP239(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP239(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_454,axiom,
( sP240(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP240(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_455,axiom,
( sP241(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP241(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_456,axiom,
( sP242(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP242(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_457,axiom,
( sP243(Eq_y_0)
| ~ sP243(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_458,axiom,
( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU264+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:44:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 150.14/150.45 % SZS status Theorem for theBenchmark
% 150.14/150.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------