%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 08:58:49 AM UTC 2026
% Result : Theorem 39.56s 39.80s
% Output : Proof 39.56s
% 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_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ),
file('theBenchmark.p',d1_mcart_1) ).
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_wellord2,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(D,A)
& in(C,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) )
& relation_field(B) = A ) ) ),
file('theBenchmark.p',d1_wellord2) ).
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_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ),
file('theBenchmark.p',d2_mcart_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_mcart_1,axiom,
$true,
file('theBenchmark.p',dt_k1_mcart_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_wellord2,axiom,
! [A] : relation(inclusion_relation(A)),
file('theBenchmark.p',dt_k1_wellord2) ).
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_mcart_1,axiom,
$true,
file('theBenchmark.p',dt_k2_mcart_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_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_dom_as_subset(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k4_relset_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_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_rng_as_subset(A,B,C),powerset(B)) ),
file('theBenchmark.p',dt_k5_relset_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_k4_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('theBenchmark.p',redefinition_k4_relset_1) ).
fof(redefinition_k5_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_rng_as_subset(A,B,C) = relation_rng(C) ),
file('theBenchmark.p',redefinition_k5_relset_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(s1_ordinal1__e8_6__wellord2,lemma,
! [A] :
( ? [B] :
( in(B,A)
& ordinal(B) )
=> ? [B] :
( ! [C] :
( ordinal(C)
=> ( in(C,A)
=> ordinal_subset(B,C) ) )
& in(B,A)
& ordinal(B) ) ),
file('theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
fof(s1_tarski__e8_6__wellord2__1,axiom,
! [A,B] :
( ordinal(B)
=> ( ! [C,D,E] :
( ( ? [G] :
( in(G,A)
& E = G
& ordinal(G) )
& C = E
& ? [F] :
( in(F,A)
& D = F
& ordinal(F) )
& C = D )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ? [H] :
( in(H,A)
& D = H
& ordinal(H) )
& E = D
& in(E,succ(B)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(s1_xboole_0__e8_6__wellord2__1,lemma,
! [A,B] :
( ordinal(B)
=> ? [C] :
! [D] :
( in(D,C)
<=> ( ? [E] :
( in(E,A)
& D = E
& ordinal(E) )
& in(D,succ(B)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
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,lemma,
! [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_relset_1,lemma,
! [A,B,C] :
( relation_of2_as_subset(C,B,A)
=> ( ! [D] :
~ ( ! [E] : ~ in(ordered_pair(D,E),C)
& in(D,B) )
<=> relation_dom_as_subset(B,A,C) = B ) ),
file('theBenchmark.p',t22_relset_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_relset_1,lemma,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ! [D] :
~ ( ! [E] : ~ in(ordered_pair(E,D),C)
& in(D,B) )
<=> relation_rng_as_subset(A,B,C) = B ) ),
file('theBenchmark.p',t23_relset_1) ).
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_wellord2,lemma,
! [A] : reflexive(inclusion_relation(A)),
file('theBenchmark.p',t2_wellord2) ).
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_wellord2,lemma,
! [A] : transitive(inclusion_relation(A)),
file('theBenchmark.p',t3_wellord2) ).
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_wellord2,lemma,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('theBenchmark.p',t4_wellord2) ).
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(t5_wellord2,lemma,
! [A] : antisymmetric(inclusion_relation(A)),
file('theBenchmark.p',t5_wellord2) ).
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_wellord2,lemma,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('theBenchmark.p',t6_wellord2) ).
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_mcart_1,lemma,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('theBenchmark.p',t7_mcart_1) ).
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_wellord2,conjecture,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('theBenchmark.p',t7_wellord2) ).
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_30,U_25,U_26,U_27,U_28] :
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26)
| ~ sP4(U_29,U_30,U_25,U_26,U_27,U_28) )
& ! [U_29,U_30,U_25,U_26,U_27,U_28] :
( sP3(U_29,U_26,U_27)
| ~ in(ordered_pair(U_29,U_27),U_25)
| ~ sP4(U_29,U_30,U_25,U_26,U_27,U_28) )
& ! [U_29,U_30,U_25,U_26,U_27,U_28] :
( U_25 = identity_relation(U_26)
| sP6(U_25,U_26)
| sP5(U_25,U_26)
| ~ sP7(U_29,U_30,U_25,U_26,U_27,U_28) )
& ! [U_29,U_30,U_25,U_26,U_27,U_28] :
( sP4(U_29,U_30,U_25,U_26,U_27,U_28)
| U_25 != identity_relation(U_26)
| ~ sP7(U_29,U_30,U_25,U_26,U_27,U_28) )
& ! [U_29,U_30,U_25,U_26,U_27,U_28] :
( sP7(U_29,U_30,U_25,U_26,U_27,U_28)
| ~ 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_30,U_25,U_26,U_27,U_28)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_8]) ).
cnf(f_14_10,plain,
( sP4(U_29,U_30,U_25,U_26,U_27,U_28)
| U_25 != identity_relation(U_26)
| ~ sP7(U_29,U_30,U_25,U_26,U_27,U_28) ),
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_30,U_25,U_26,U_27,U_28) ),
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_30,U_25,U_26,U_27,U_28) ),
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_30,U_25,U_26,U_27,U_28) ),
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_47,U_46] :
( ~ in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_45)
| ~ sP12(U_45,U_47,U_46) )
& ! [U_45,U_47,U_46] :
( in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_47)
| ~ sP12(U_45,U_47,U_46) )
& ! [U_45,U_47,U_46] :
( in(sK7(U_47,U_46,U_45),U_46)
| ~ sP12(U_45,U_47,U_46) )
& ! [U_45,U_47,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)
| ~ sP11(U_45,U_47,U_46) )
& ! [U_45,U_47,U_46] :
( in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45)
| ~ sP11(U_45,U_47,U_46) )
& ! [U_47,U_48,U_50,U_46] :
( in(ordered_pair(U_50,U_48),U_47)
| ~ sP9(U_47,U_48,U_50,U_46) )
& ! [U_47,U_48,U_50,U_46] :
( in(U_50,U_46)
| ~ sP9(U_47,U_48,U_50,U_46) )
& ! [U_49,U_45,U_47,U_48,U_51,U_50,U_46] :
( 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_49,U_45,U_47,U_48,U_51,U_50,U_46) )
& ! [U_49,U_45,U_47,U_48,U_51,U_50,U_46] :
( sP9(U_47,U_48,U_50,U_46)
| ~ in(ordered_pair(U_50,U_48),U_45)
| ~ sP10(U_49,U_45,U_47,U_48,U_51,U_50,U_46) )
& ! [U_49,U_45,U_47,U_48,U_51,U_50,U_46] :
( U_45 = relation_dom_restriction(U_47,U_46)
| sP12(U_45,U_47,U_46)
| sP11(U_45,U_47,U_46)
| ~ sP13(U_49,U_45,U_47,U_48,U_51,U_50,U_46) )
& ! [U_49,U_45,U_47,U_48,U_51,U_50,U_46] :
( sP10(U_49,U_45,U_47,U_48,U_51,U_50,U_46)
| U_45 != relation_dom_restriction(U_47,U_46)
| ~ sP13(U_49,U_45,U_47,U_48,U_51,U_50,U_46) )
& ! [U_49,U_45,U_47,U_48,U_51,U_50,U_46] :
( sP13(U_49,U_45,U_47,U_48,U_51,U_50,U_46)
| ~ 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_49,U_45,U_47,U_48,U_51,U_50,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_10,plain,
( sP10(U_49,U_45,U_47,U_48,U_51,U_50,U_46)
| U_45 != relation_dom_restriction(U_47,U_46)
| ~ sP13(U_49,U_45,U_47,U_48,U_51,U_50,U_46) ),
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_47,U_46)
| sP11(U_45,U_47,U_46)
| ~ sP13(U_49,U_45,U_47,U_48,U_51,U_50,U_46) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_12,plain,
( sP9(U_47,U_48,U_50,U_46)
| ~ in(ordered_pair(U_50,U_48),U_45)
| ~ sP10(U_49,U_45,U_47,U_48,U_51,U_50,U_46) ),
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_49,U_45,U_47,U_48,U_51,U_50,U_46) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_14,plain,
( in(U_50,U_46)
| ~ sP9(U_47,U_48,U_50,U_46) ),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_15,plain,
( in(ordered_pair(U_50,U_48),U_47)
| ~ sP9(U_47,U_48,U_50,U_46) ),
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_47,U_46) ),
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_47,U_46) ),
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_47,U_46) ),
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_47,U_46) ),
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_47,U_46) ),
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_70,U_72,U_64] :
( ~ in(sK11(U_64,U_72,U_70),U_70)
| ~ sP17(U_70,U_72,U_64) )
& ! [U_70,U_72,U_64] :
( sK11(U_64,U_72,U_70) = apply(U_64,sK12(U_64,U_72,U_70))
| ~ sP17(U_70,U_72,U_64) )
& ! [U_70,U_72,U_64] :
( in(sK12(U_64,U_72,U_70),U_72)
| ~ sP17(U_70,U_72,U_64) )
& ! [U_70,U_72,U_64] :
( in(sK12(U_64,U_72,U_70),relation_dom(U_64))
| ~ sP17(U_70,U_72,U_64) )
& ! [U_70,U_72,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))
| ~ sP16(U_70,U_72,U_64,U_59) )
& ! [U_70,U_72,U_64,U_59] :
( in(sK10(U_64,U_72,U_70),U_70)
| ~ sP16(U_70,U_72,U_64,U_59) )
& ! [U_65,U_69,U_64,U_71] :
( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
| ~ sP14(U_65,U_69,U_64,U_71) )
& ! [U_65,U_69,U_64,U_71] :
( in(sK9(U_64,U_71,U_69,U_65),U_71)
| ~ sP14(U_65,U_69,U_64,U_71) )
& ! [U_65,U_69,U_64,U_71] :
( in(sK9(U_64,U_71,U_69,U_65),relation_dom(U_64))
| ~ sP14(U_65,U_69,U_64,U_71) )
& ! [U_66,U_65,U_69,U_57,U_64,U_71] :
( 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_66,U_65,U_69,U_57,U_64,U_71) )
& ! [U_66,U_65,U_69,U_57,U_64,U_71] :
( sP14(U_65,U_69,U_64,U_71)
| ~ in(U_65,U_69)
| ~ sP15(U_66,U_65,U_69,U_57,U_64,U_71) )
& ! [U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71] :
( U_70 = relation_image(U_64,U_72)
| sP17(U_70,U_72,U_64)
| sP16(U_70,U_72,U_64,U_59)
| ~ sP18(U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71) )
& ! [U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71] :
( sP15(U_66,U_65,U_69,U_57,U_64,U_71)
| U_69 != relation_image(U_64,U_71)
| ~ sP18(U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71) )
& ! [U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71] :
( sP18(U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71)
| ~ 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_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_10,plain,
( sP15(U_66,U_65,U_69,U_57,U_64,U_71)
| U_69 != relation_image(U_64,U_71)
| ~ sP18(U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_11,plain,
( U_70 = relation_image(U_64,U_72)
| sP17(U_70,U_72,U_64)
| sP16(U_70,U_72,U_64,U_59)
| ~ sP18(U_70,U_66,U_65,U_69,U_57,U_72,U_64,U_59,U_71) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_12,plain,
( sP14(U_65,U_69,U_64,U_71)
| ~ in(U_65,U_69)
| ~ sP15(U_66,U_65,U_69,U_57,U_64,U_71) ),
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_66,U_65,U_69,U_57,U_64,U_71) ),
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_65,U_69,U_64,U_71) ),
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_65,U_69,U_64,U_71) ),
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_65,U_69,U_64,U_71) ),
inference(clausify,[status(thm)],[f_17_8]) ).
cnf(f_17_17,plain,
( in(sK10(U_64,U_72,U_70),U_70)
| ~ sP16(U_70,U_72,U_64,U_59) ),
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_70,U_72,U_64,U_59) ),
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_70,U_72,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_70,U_72,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_70,U_72,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_70,U_72,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_79,U_77,U_78] :
( ~ in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_77)
| ~ sP22(U_79,U_77,U_78) )
& ! [U_79,U_77,U_78] :
( in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_78)
| ~ sP22(U_79,U_77,U_78) )
& ! [U_79,U_77,U_78] :
( in(sK16(U_79,U_78,U_77),U_79)
| ~ sP22(U_79,U_77,U_78) )
& ! [U_79,U_77,U_78] :
( ~ 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_79,U_77,U_78) )
& ! [U_79,U_77,U_78] :
( in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77)
| ~ sP21(U_79,U_77,U_78) )
& ! [U_80,U_79,U_82,U_78] :
( in(ordered_pair(U_82,U_80),U_78)
| ~ sP19(U_80,U_79,U_82,U_78) )
& ! [U_80,U_79,U_82,U_78] :
( in(U_80,U_79)
| ~ sP19(U_80,U_79,U_82,U_78) )
& ! [U_80,U_81,U_79,U_83,U_82,U_77,U_78] :
( 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_79,U_83,U_82,U_77,U_78) )
& ! [U_80,U_81,U_79,U_83,U_82,U_77,U_78] :
( sP19(U_80,U_79,U_82,U_78)
| ~ in(ordered_pair(U_82,U_80),U_77)
| ~ sP20(U_80,U_81,U_79,U_83,U_82,U_77,U_78) )
& ! [U_80,U_81,U_79,U_83,U_82,U_77,U_78] :
( U_77 = relation_rng_restriction(U_79,U_78)
| sP22(U_79,U_77,U_78)
| sP21(U_79,U_77,U_78)
| ~ sP23(U_80,U_81,U_79,U_83,U_82,U_77,U_78) )
& ! [U_80,U_81,U_79,U_83,U_82,U_77,U_78] :
( sP20(U_80,U_81,U_79,U_83,U_82,U_77,U_78)
| U_77 != relation_rng_restriction(U_79,U_78)
| ~ sP23(U_80,U_81,U_79,U_83,U_82,U_77,U_78) )
& ! [U_80,U_81,U_79,U_83,U_82,U_77,U_78] :
( sP23(U_80,U_81,U_79,U_83,U_82,U_77,U_78)
| ~ 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_79,U_83,U_82,U_77,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_10,plain,
( sP20(U_80,U_81,U_79,U_83,U_82,U_77,U_78)
| U_77 != relation_rng_restriction(U_79,U_78)
| ~ sP23(U_80,U_81,U_79,U_83,U_82,U_77,U_78) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_11,plain,
( U_77 = relation_rng_restriction(U_79,U_78)
| sP22(U_79,U_77,U_78)
| sP21(U_79,U_77,U_78)
| ~ sP23(U_80,U_81,U_79,U_83,U_82,U_77,U_78) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_12,plain,
( sP19(U_80,U_79,U_82,U_78)
| ~ in(ordered_pair(U_82,U_80),U_77)
| ~ sP20(U_80,U_81,U_79,U_83,U_82,U_77,U_78) ),
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_79,U_83,U_82,U_77,U_78) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_14,plain,
( in(U_80,U_79)
| ~ sP19(U_80,U_79,U_82,U_78) ),
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_79,U_82,U_78) ),
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_79,U_77,U_78) ),
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_79,U_77,U_78) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_18,plain,
( in(sK16(U_79,U_78,U_77),U_79)
| ~ sP22(U_79,U_77,U_78) ),
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_79,U_77,U_78) ),
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_79,U_77,U_78) ),
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_94,U_100,U_93] :
( in(apply(U_93,U_94),U_100)
| ~ sP25(U_94,U_100,U_93) )
& ! [U_94,U_100,U_93] :
( in(U_94,relation_dom(U_93))
| ~ sP25(U_94,U_100,U_93) )
& ! [U_98,U_95,U_94,U_100,U_93] :
( in(U_95,U_98)
| ~ in(apply(U_93,U_95),U_100)
| ~ in(U_95,relation_dom(U_93))
| ~ sP26(U_98,U_95,U_94,U_100,U_93) )
& ! [U_98,U_95,U_94,U_100,U_93] :
( sP25(U_94,U_100,U_93)
| ~ in(U_94,U_98)
| ~ sP26(U_98,U_95,U_94,U_100,U_93) )
& ! [U_99,U_98,U_95,U_94,U_100,U_101,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_99,U_98,U_95,U_94,U_100,U_101,U_93) )
& ! [U_99,U_98,U_95,U_94,U_100,U_101,U_93] :
( sP26(U_98,U_95,U_94,U_100,U_93)
| U_98 != relation_inverse_image(U_93,U_100)
| ~ sP29(U_99,U_98,U_95,U_94,U_100,U_101,U_93) )
& ! [U_99,U_98,U_95,U_94,U_100,U_101,U_93] :
( sP29(U_99,U_98,U_95,U_94,U_100,U_101,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_99,U_98,U_95,U_94,U_100,U_101,U_93)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_8,plain,
( sP26(U_98,U_95,U_94,U_100,U_93)
| U_98 != relation_inverse_image(U_93,U_100)
| ~ sP29(U_99,U_98,U_95,U_94,U_100,U_101,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_99,U_98,U_95,U_94,U_100,U_101,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_10,plain,
( sP25(U_94,U_100,U_93)
| ~ in(U_94,U_98)
| ~ sP26(U_98,U_95,U_94,U_100,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_98,U_95,U_94,U_100,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_12,plain,
( in(U_94,relation_dom(U_93))
| ~ sP25(U_94,U_100,U_93) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_13,plain,
( in(apply(U_93,U_94),U_100)
| ~ sP25(U_94,U_100,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_116,U_110,U_118] :
( ~ in(sK21(U_110,U_118,U_116),U_116)
| ~ sP33(U_116,U_110,U_118) )
& ! [U_116,U_110,U_118] :
( in(sK22(U_110,U_118,U_116),U_118)
| ~ sP33(U_116,U_110,U_118) )
& ! [U_116,U_110,U_118] :
( in(ordered_pair(sK22(U_110,U_118,U_116),sK21(U_110,U_118,U_116)),U_110)
| ~ sP33(U_116,U_110,U_118) )
& ! [U_116,U_105,U_110,U_118] :
( ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110)
| ~ sP32(U_116,U_105,U_110,U_118) )
& ! [U_116,U_105,U_110,U_118] :
( in(sK20(U_110,U_118,U_116),U_116)
| ~ sP32(U_116,U_105,U_110,U_118) )
& ! [U_111,U_110,U_115,U_117] :
( in(sK19(U_110,U_117,U_115,U_111),U_117)
| ~ sP30(U_111,U_110,U_115,U_117) )
& ! [U_111,U_110,U_115,U_117] :
( in(ordered_pair(sK19(U_110,U_117,U_115,U_111),U_111),U_110)
| ~ sP30(U_111,U_110,U_115,U_117) )
& ! [U_112,U_111,U_103,U_110,U_115,U_117] :
( in(U_112,U_115)
| ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110)
| ~ sP31(U_112,U_111,U_103,U_110,U_115,U_117) )
& ! [U_112,U_111,U_103,U_110,U_115,U_117] :
( sP30(U_111,U_110,U_115,U_117)
| ~ in(U_111,U_115)
| ~ sP31(U_112,U_111,U_103,U_110,U_115,U_117) )
& ! [U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117] :
( U_116 = relation_image(U_110,U_118)
| sP33(U_116,U_110,U_118)
| sP32(U_116,U_105,U_110,U_118)
| ~ sP34(U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117) )
& ! [U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117] :
( sP31(U_112,U_111,U_103,U_110,U_115,U_117)
| U_115 != relation_image(U_110,U_117)
| ~ sP34(U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117) )
& ! [U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117] :
( sP34(U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117)
| ~ 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_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_10,plain,
( sP31(U_112,U_111,U_103,U_110,U_115,U_117)
| U_115 != relation_image(U_110,U_117)
| ~ sP34(U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_11,plain,
( U_116 = relation_image(U_110,U_118)
| sP33(U_116,U_110,U_118)
| sP32(U_116,U_105,U_110,U_118)
| ~ sP34(U_112,U_111,U_116,U_103,U_105,U_110,U_115,U_118,U_117) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_12,plain,
( sP30(U_111,U_110,U_115,U_117)
| ~ in(U_111,U_115)
| ~ sP31(U_112,U_111,U_103,U_110,U_115,U_117) ),
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_112,U_111,U_103,U_110,U_115,U_117) ),
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_111,U_110,U_115,U_117) ),
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_111,U_110,U_115,U_117) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_16,plain,
( in(sK20(U_110,U_118,U_116),U_116)
| ~ sP32(U_116,U_105,U_110,U_118) ),
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_116,U_105,U_110,U_118) ),
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_116,U_110,U_118) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_19,plain,
( in(sK22(U_110,U_118,U_116),U_118)
| ~ sP33(U_116,U_110,U_118) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_20,plain,
( ~ in(sK21(U_110,U_118,U_116),U_116)
| ~ sP33(U_116,U_110,U_118) ),
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_127,U_128,U_132,U_134] :
( in(sK23(U_127,U_134,U_132,U_128),U_134)
| ~ sP35(U_127,U_128,U_132,U_134) )
& ! [U_127,U_128,U_132,U_134] :
( in(ordered_pair(U_128,sK23(U_127,U_134,U_132,U_128)),U_127)
| ~ sP35(U_127,U_128,U_132,U_134) )
& ! [U_127,U_128,U_120,U_132,U_134,U_129] :
( in(U_129,U_132)
| ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127)
| ~ sP36(U_127,U_128,U_120,U_132,U_134,U_129) )
& ! [U_127,U_128,U_120,U_132,U_134,U_129] :
( sP35(U_127,U_128,U_132,U_134)
| ~ in(U_128,U_132)
| ~ sP36(U_127,U_128,U_120,U_132,U_134,U_129) )
& ! [U_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129] :
( 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_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129) )
& ! [U_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129] :
( sP36(U_127,U_128,U_120,U_132,U_134,U_129)
| U_132 != relation_inverse_image(U_127,U_134)
| ~ sP39(U_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129) )
& ! [U_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129] :
( sP39(U_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129)
| ~ 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_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_10,plain,
( sP36(U_127,U_128,U_120,U_132,U_134,U_129)
| U_132 != relation_inverse_image(U_127,U_134)
| ~ sP39(U_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129) ),
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_135,U_127,U_122,U_128,U_120,U_133,U_132,U_134,U_129) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_12,plain,
( sP35(U_127,U_128,U_132,U_134)
| ~ in(U_128,U_132)
| ~ sP36(U_127,U_128,U_120,U_132,U_134,U_129) ),
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_127,U_128,U_120,U_132,U_134,U_129) ),
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_127,U_128,U_132,U_134) ),
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_127,U_128,U_132,U_134) ),
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_155,U_151] :
( ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
| ~ sP45(U_153,U_149,U_155,U_151) )
& ! [U_153,U_149,U_155,U_151] :
( 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_155,U_151) )
& ! [U_153,U_149,U_155,U_151] :
( sK27(U_155,U_153,U_151,U_149) != U_151
| ~ sP44(U_153,U_149,U_155,U_151) )
& ! [U_153,U_149,U_155,U_151] :
( sK27(U_155,U_153,U_151,U_149) != U_153
| ~ sP44(U_153,U_149,U_155,U_151) )
& ! [U_153,U_149,U_155,U_151] :
( sK27(U_155,U_153,U_151,U_149) != U_155
| ~ sP44(U_153,U_149,U_155,U_151) )
& ! [U_153,U_149,U_155,U_151] :
( in(sK27(U_155,U_153,U_151,U_149),U_149)
| ~ sP44(U_153,U_149,U_155,U_151) )
& ! [U_154,U_145,U_152,U_150] :
( U_145 != U_150
| ~ sP42(U_154,U_145,U_152,U_150) )
& ! [U_154,U_145,U_152,U_150] :
( U_145 != U_152
| ~ sP42(U_154,U_145,U_152,U_150) )
& ! [U_154,U_145,U_152,U_150] :
( U_145 != U_154
| ~ sP42(U_154,U_145,U_152,U_150) )
& ! [U_154,U_145,U_148,U_144,U_152,U_150] :
( in(U_145,U_148)
| sP42(U_154,U_145,U_152,U_150)
| ~ sP43(U_154,U_145,U_148,U_144,U_152,U_150) )
& ! [U_154,U_145,U_148,U_144,U_152,U_150] :
( U_144 = U_150
| U_144 = U_152
| U_144 = U_154
| ~ in(U_144,U_148)
| ~ sP43(U_154,U_145,U_148,U_144,U_152,U_150) )
& ! [U_153,U_149,U_155,U_151] :
( U_149 = unordered_triple(U_155,U_153,U_151)
| sP45(U_153,U_149,U_155,U_151)
| sP44(U_153,U_149,U_155,U_151) )
& ! [U_154,U_145,U_148,U_144,U_152,U_150] :
( sP43(U_154,U_145,U_148,U_144,U_152,U_150)
| 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_154,U_145,U_148,U_144,U_152,U_150)
| 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_155,U_151)
| sP44(U_153,U_149,U_155,U_151) ),
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_154,U_145,U_148,U_144,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_10,plain,
( in(U_145,U_148)
| sP42(U_154,U_145,U_152,U_150)
| ~ sP43(U_154,U_145,U_148,U_144,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_11,plain,
( U_145 != U_154
| ~ sP42(U_154,U_145,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_12,plain,
( U_145 != U_152
| ~ sP42(U_154,U_145,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_6]) ).
cnf(f_25_13,plain,
( U_145 != U_150
| ~ sP42(U_154,U_145,U_152,U_150) ),
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_155,U_151) ),
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_155,U_151) ),
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_155,U_151) ),
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_155,U_151) ),
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_155,U_151) ),
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_155,U_151) ),
inference(clausify,[status(thm)],[f_25_6]) ).
fof(f_26_1,plain,
! [A] :
( ! [B] :
( ( B = pair_first(A)
| ? [C,D] :
( B != C
& A = ordered_pair(C,D) ) )
& ( ! [C,D] :
( B = C
| A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[d1_mcart_1]) ).
fof(f_26_2,plain,
! [U_163] :
( ! [U_162] :
( ( U_162 = pair_first(U_163)
| ? [U_161,U_160] :
( U_162 != U_161
& U_163 = ordered_pair(U_161,U_160) ) )
& ( ! [U_159,U_158] :
( U_162 = U_159
| U_163 != ordered_pair(U_159,U_158) )
| U_162 != pair_first(U_163) ) )
| ! [U_157,U_156] : U_163 != ordered_pair(U_157,U_156) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_163] :
( ( ! [U_165] :
( U_165 = pair_first(U_163)
| ? [U_161] :
( ? [U_160] : U_163 = ordered_pair(U_161,U_160)
& U_165 != U_161 ) )
& ! [U_164] :
( ! [U_159] :
( ! [U_158] : U_163 != ordered_pair(U_159,U_158)
| U_164 = U_159 )
| U_164 != pair_first(U_163) ) )
| ! [U_157,U_156] : U_163 != ordered_pair(U_157,U_156) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_163] :
( ( ! [U_165] :
( U_165 = pair_first(U_163)
| ( ? [U_160] : U_163 = ordered_pair(sK29(U_163,U_165),U_160)
& U_165 != sK29(U_163,U_165) ) )
& ! [U_164] :
( ! [U_159] :
( ! [U_158] : U_163 != ordered_pair(U_159,U_158)
| U_164 = U_159 )
| U_164 != pair_first(U_163) ) )
| ! [U_157,U_156] : U_163 != ordered_pair(U_157,U_156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_161,sK29(U_163,U_165))],[f_26_3]) ).
fof(f_26_5,plain,
! [U_163] :
( ( ! [U_165] :
( U_165 = pair_first(U_163)
| ( U_163 = ordered_pair(sK29(U_163,U_165),sK30(U_163,U_165))
& U_165 != sK29(U_163,U_165) ) )
& ! [U_164] :
( ! [U_159] :
( ! [U_158] : U_163 != ordered_pair(U_159,U_158)
| U_164 = U_159 )
| U_164 != pair_first(U_163) ) )
| ! [U_157,U_156] : U_163 != ordered_pair(U_157,U_156) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_160,sK30(U_163,U_165))],[f_26_4]) ).
fof(f_26_6,plain,
( ! [U_165,U_163] :
( U_163 = ordered_pair(sK29(U_163,U_165),sK30(U_163,U_165))
| ~ sP46(U_165,U_163) )
& ! [U_165,U_163] :
( U_165 != sK29(U_163,U_165)
| ~ sP46(U_165,U_163) )
& ! [U_159,U_158,U_164,U_165,U_163] :
( U_165 = pair_first(U_163)
| sP46(U_165,U_163)
| ~ sP47(U_159,U_158,U_164,U_165,U_163) )
& ! [U_159,U_158,U_164,U_165,U_163] :
( U_163 != ordered_pair(U_159,U_158)
| U_164 = U_159
| U_164 != pair_first(U_163)
| ~ sP47(U_159,U_158,U_164,U_165,U_163) )
& ! [U_156,U_159,U_158,U_157,U_164,U_165,U_163] :
( sP47(U_159,U_158,U_164,U_165,U_163)
| U_163 != ordered_pair(U_157,U_156) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46,sP47])],[f_26_5]) ).
cnf(f_26_7,plain,
( sP47(U_159,U_158,U_164,U_165,U_163)
| U_163 != ordered_pair(U_157,U_156) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_8,plain,
( U_163 != ordered_pair(U_159,U_158)
| U_164 = U_159
| U_164 != pair_first(U_163)
| ~ sP47(U_159,U_158,U_164,U_165,U_163) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_9,plain,
( U_165 = pair_first(U_163)
| sP46(U_165,U_163)
| ~ sP47(U_159,U_158,U_164,U_165,U_163) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_10,plain,
( U_165 != sK29(U_163,U_165)
| ~ sP46(U_165,U_163) ),
inference(clausify,[status(thm)],[f_26_6]) ).
cnf(f_26_11,plain,
( U_163 = ordered_pair(sK29(U_163,U_165),sK30(U_163,U_165))
| ~ sP46(U_165,U_163) ),
inference(clausify,[status(thm)],[f_26_6]) ).
fof(f_27_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_27_2,plain,
! [U_166] : succ(U_166) = set_union2(U_166,singleton(U_166)),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_166] : succ(U_166) = set_union2(U_166,singleton(U_166)),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
succ(U_166) = set_union2(U_166,singleton(U_166)),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_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_28_2,plain,
! [U_173] :
( ( relation(U_173)
| ? [U_172] :
( ! [U_171,U_170] : U_172 != ordered_pair(U_171,U_170)
& in(U_172,U_173) ) )
& ( ! [U_169] :
( ? [U_168,U_167] : U_169 = ordered_pair(U_168,U_167)
| ~ in(U_169,U_173) )
| ~ relation(U_173) ) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_175] :
( relation(U_175)
| ? [U_172] :
( ! [U_171,U_170] : U_172 != ordered_pair(U_171,U_170)
& in(U_172,U_175) ) )
& ! [U_174] :
( ! [U_169] :
( ? [U_168,U_167] : U_169 = ordered_pair(U_168,U_167)
| ~ in(U_169,U_174) )
| ~ relation(U_174) ) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_175] :
( relation(U_175)
| ? [U_172] :
( ! [U_171,U_170] : U_172 != ordered_pair(U_171,U_170)
& in(U_172,U_175) ) )
& ! [U_174] :
( ! [U_169] :
( ? [U_167] : U_169 = ordered_pair(sK31(U_174,U_169),U_167)
| ~ in(U_169,U_174) )
| ~ relation(U_174) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_168,sK31(U_174,U_169))],[f_28_3]) ).
fof(f_28_5,plain,
( ! [U_175] :
( relation(U_175)
| ? [U_172] :
( ! [U_171,U_170] : U_172 != ordered_pair(U_171,U_170)
& in(U_172,U_175) ) )
& ! [U_174] :
( ! [U_169] :
( U_169 = ordered_pair(sK31(U_174,U_169),sK32(U_174,U_169))
| ~ in(U_169,U_174) )
| ~ relation(U_174) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_167,sK32(U_174,U_169))],[f_28_4]) ).
fof(f_28_6,plain,
( ! [U_175] :
( relation(U_175)
| ( ! [U_171,U_170] : sK33(U_175) != ordered_pair(U_171,U_170)
& in(sK33(U_175),U_175) ) )
& ! [U_174] :
( ! [U_169] :
( U_169 = ordered_pair(sK31(U_174,U_169),sK32(U_174,U_169))
| ~ in(U_169,U_174) )
| ~ relation(U_174) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_172,sK33(U_175))],[f_28_5]) ).
fof(f_28_7,plain,
( ! [U_171,U_175,U_170] :
( sK33(U_175) != ordered_pair(U_171,U_170)
| ~ sP48(U_171,U_175,U_170) )
& ! [U_171,U_175,U_170] :
( in(sK33(U_175),U_175)
| ~ sP48(U_171,U_175,U_170) )
& ! [U_171,U_175,U_170] :
( relation(U_175)
| sP48(U_171,U_175,U_170) )
& ! [U_174,U_169] :
( U_169 = ordered_pair(sK31(U_174,U_169),sK32(U_174,U_169))
| ~ in(U_169,U_174)
| ~ relation(U_174) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_28_6]) ).
cnf(f_28_8,plain,
( U_169 = ordered_pair(sK31(U_174,U_169),sK32(U_174,U_169))
| ~ in(U_169,U_174)
| ~ relation(U_174) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_9,plain,
( relation(U_175)
| sP48(U_171,U_175,U_170) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_10,plain,
( in(sK33(U_175),U_175)
| ~ sP48(U_171,U_175,U_170) ),
inference(clausify,[status(thm)],[f_28_7]) ).
cnf(f_28_11,plain,
( sK33(U_175) != ordered_pair(U_171,U_170)
| ~ sP48(U_171,U_175,U_170) ),
inference(clausify,[status(thm)],[f_28_7]) ).
fof(f_29_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_29_2,plain,
! [U_179] :
( ! [U_178] :
( ( is_reflexive_in(U_179,U_178)
| ? [U_177] :
( ~ in(ordered_pair(U_177,U_177),U_179)
& in(U_177,U_178) ) )
& ( ! [U_176] :
( in(ordered_pair(U_176,U_176),U_179)
| ~ in(U_176,U_178) )
| ~ is_reflexive_in(U_179,U_178) ) )
| ~ relation(U_179) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_179] :
( ( ! [U_181] :
( is_reflexive_in(U_179,U_181)
| ? [U_177] :
( ~ in(ordered_pair(U_177,U_177),U_179)
& in(U_177,U_181) ) )
& ! [U_180] :
( ! [U_176] :
( in(ordered_pair(U_176,U_176),U_179)
| ~ in(U_176,U_180) )
| ~ is_reflexive_in(U_179,U_180) ) )
| ~ relation(U_179) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_179] :
( ( ! [U_181] :
( is_reflexive_in(U_179,U_181)
| ( ~ in(ordered_pair(sK34(U_179,U_181),sK34(U_179,U_181)),U_179)
& in(sK34(U_179,U_181),U_181) ) )
& ! [U_180] :
( ! [U_176] :
( in(ordered_pair(U_176,U_176),U_179)
| ~ in(U_176,U_180) )
| ~ is_reflexive_in(U_179,U_180) ) )
| ~ relation(U_179) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_177,sK34(U_179,U_181))],[f_29_3]) ).
fof(f_29_5,plain,
( ! [U_179,U_181] :
( ~ in(ordered_pair(sK34(U_179,U_181),sK34(U_179,U_181)),U_179)
| ~ sP49(U_179,U_181) )
& ! [U_179,U_181] :
( in(sK34(U_179,U_181),U_181)
| ~ sP49(U_179,U_181) )
& ! [U_176,U_179,U_181,U_180] :
( is_reflexive_in(U_179,U_181)
| sP49(U_179,U_181)
| ~ sP50(U_176,U_179,U_181,U_180) )
& ! [U_176,U_179,U_181,U_180] :
( in(ordered_pair(U_176,U_176),U_179)
| ~ in(U_176,U_180)
| ~ is_reflexive_in(U_179,U_180)
| ~ sP50(U_176,U_179,U_181,U_180) )
& ! [U_176,U_179,U_181,U_180] :
( sP50(U_176,U_179,U_181,U_180)
| ~ relation(U_179) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50])],[f_29_4]) ).
cnf(f_29_6,plain,
( sP50(U_176,U_179,U_181,U_180)
| ~ relation(U_179) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_7,plain,
( in(ordered_pair(U_176,U_176),U_179)
| ~ in(U_176,U_180)
| ~ is_reflexive_in(U_179,U_180)
| ~ sP50(U_176,U_179,U_181,U_180) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_8,plain,
( is_reflexive_in(U_179,U_181)
| sP49(U_179,U_181)
| ~ sP50(U_176,U_179,U_181,U_180) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_9,plain,
( in(sK34(U_179,U_181),U_181)
| ~ sP49(U_179,U_181) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_10,plain,
( ~ in(ordered_pair(sK34(U_179,U_181),sK34(U_179,U_181)),U_179)
| ~ sP49(U_179,U_181) ),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_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_30_2,plain,
! [U_184,U_183,U_182] :
( ( relation_of2(U_182,U_184,U_183)
| ~ subset(U_182,cartesian_product2(U_184,U_183)) )
& ( subset(U_182,cartesian_product2(U_184,U_183))
| ~ relation_of2(U_182,U_184,U_183) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_190,U_188,U_186] :
( relation_of2(U_186,U_190,U_188)
| ~ subset(U_186,cartesian_product2(U_190,U_188)) )
& ! [U_189,U_187,U_185] :
( subset(U_185,cartesian_product2(U_189,U_187))
| ~ relation_of2(U_185,U_189,U_187) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_186,U_190,U_188] :
( relation_of2(U_186,U_190,U_188)
| ~ subset(U_186,cartesian_product2(U_190,U_188)) )
& ! [U_187,U_189,U_185] :
( subset(U_185,cartesian_product2(U_189,U_187))
| ~ relation_of2(U_185,U_189,U_187) ) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
( subset(U_185,cartesian_product2(U_189,U_187))
| ~ relation_of2(U_185,U_189,U_187) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( relation_of2(U_186,U_190,U_188)
| ~ subset(U_186,cartesian_product2(U_190,U_188)) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_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_31_2,plain,
! [U_198,U_197] :
( ( ( ( U_197 = set_meet(U_198)
| U_197 != empty_set )
& ( U_197 = empty_set
| U_197 != set_meet(U_198) ) )
| U_198 != empty_set )
& ( ( ( U_197 = set_meet(U_198)
| ? [U_196] :
( ( ~ in(U_196,U_197)
& ! [U_195] :
( in(U_196,U_195)
| ~ in(U_195,U_198) ) )
| ( ? [U_194] :
( ~ in(U_196,U_194)
& in(U_194,U_198) )
& in(U_196,U_197) ) ) )
& ( ! [U_193] :
( ( in(U_193,U_197)
| ? [U_192] :
( ~ in(U_193,U_192)
& in(U_192,U_198) ) )
& ( ! [U_191] :
( in(U_193,U_191)
| ~ in(U_191,U_198) )
| ~ in(U_193,U_197) ) )
| U_197 != set_meet(U_198) ) )
| U_198 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_210] :
( ( ! [U_208] :
( U_208 = set_meet(U_210)
| U_208 != empty_set )
& ! [U_207] :
( U_207 = empty_set
| U_207 != set_meet(U_210) ) )
| U_210 != empty_set )
& ! [U_209] :
( ( ! [U_206] :
( U_206 = set_meet(U_209)
| ? [U_202] :
( ~ in(U_202,U_206)
& ! [U_195] :
( in(U_202,U_195)
| ~ in(U_195,U_209) ) )
| ? [U_201] :
( ? [U_194] :
( ~ in(U_201,U_194)
& in(U_194,U_209) )
& in(U_201,U_206) ) )
& ! [U_205] :
( ( ! [U_200] :
( in(U_200,U_205)
| ? [U_192] :
( ~ in(U_200,U_192)
& in(U_192,U_209) ) )
& ! [U_199] :
( ! [U_191] :
( in(U_199,U_191)
| ~ in(U_191,U_209) )
| ~ in(U_199,U_205) ) )
| U_205 != set_meet(U_209) ) )
| U_209 = empty_set ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
( ! [U_210] :
( ( ! [U_208] :
( U_208 = set_meet(U_210)
| U_208 != empty_set )
& ! [U_207] :
( U_207 = empty_set
| U_207 != set_meet(U_210) ) )
| U_210 != empty_set )
& ! [U_209] :
( ( ! [U_206] :
( U_206 = set_meet(U_209)
| ? [U_202] :
( ~ in(U_202,U_206)
& ! [U_195] :
( in(U_202,U_195)
| ~ in(U_195,U_209) ) )
| ? [U_201] :
( ? [U_194] :
( ~ in(U_201,U_194)
& in(U_194,U_209) )
& in(U_201,U_206) ) )
& ! [U_205] :
( ( ! [U_200] :
( in(U_200,U_205)
| ( ~ in(U_200,sK35(U_209,U_205,U_200))
& in(sK35(U_209,U_205,U_200),U_209) ) )
& ! [U_199] :
( ! [U_191] :
( in(U_199,U_191)
| ~ in(U_191,U_209) )
| ~ in(U_199,U_205) ) )
| U_205 != set_meet(U_209) ) )
| U_209 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_192,sK35(U_209,U_205,U_200))],[f_31_3]) ).
fof(f_31_5,plain,
( ! [U_210] :
( ( ! [U_208] :
( U_208 = set_meet(U_210)
| U_208 != empty_set )
& ! [U_207] :
( U_207 = empty_set
| U_207 != set_meet(U_210) ) )
| U_210 != empty_set )
& ! [U_209] :
( ( ! [U_206] :
( U_206 = set_meet(U_209)
| ? [U_202] :
( ~ in(U_202,U_206)
& ! [U_195] :
( in(U_202,U_195)
| ~ in(U_195,U_209) ) )
| ( ? [U_194] :
( ~ in(sK36(U_209,U_206),U_194)
& in(U_194,U_209) )
& in(sK36(U_209,U_206),U_206) ) )
& ! [U_205] :
( ( ! [U_200] :
( in(U_200,U_205)
| ( ~ in(U_200,sK35(U_209,U_205,U_200))
& in(sK35(U_209,U_205,U_200),U_209) ) )
& ! [U_199] :
( ! [U_191] :
( in(U_199,U_191)
| ~ in(U_191,U_209) )
| ~ in(U_199,U_205) ) )
| U_205 != set_meet(U_209) ) )
| U_209 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_201,sK36(U_209,U_206))],[f_31_4]) ).
fof(f_31_6,plain,
( ! [U_210] :
( ( ! [U_208] :
( U_208 = set_meet(U_210)
| U_208 != empty_set )
& ! [U_207] :
( U_207 = empty_set
| U_207 != set_meet(U_210) ) )
| U_210 != empty_set )
& ! [U_209] :
( ( ! [U_206] :
( U_206 = set_meet(U_209)
| ? [U_202] :
( ~ in(U_202,U_206)
& ! [U_195] :
( in(U_202,U_195)
| ~ in(U_195,U_209) ) )
| ( ~ in(sK36(U_209,U_206),sK37(U_209,U_206))
& in(sK37(U_209,U_206),U_209)
& in(sK36(U_209,U_206),U_206) ) )
& ! [U_205] :
( ( ! [U_200] :
( in(U_200,U_205)
| ( ~ in(U_200,sK35(U_209,U_205,U_200))
& in(sK35(U_209,U_205,U_200),U_209) ) )
& ! [U_199] :
( ! [U_191] :
( in(U_199,U_191)
| ~ in(U_191,U_209) )
| ~ in(U_199,U_205) ) )
| U_205 != set_meet(U_209) ) )
| U_209 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_194,sK37(U_209,U_206))],[f_31_5]) ).
fof(f_31_7,plain,
( ! [U_210] :
( ( ! [U_208] :
( U_208 = set_meet(U_210)
| U_208 != empty_set )
& ! [U_207] :
( U_207 = empty_set
| U_207 != set_meet(U_210) ) )
| U_210 != empty_set )
& ! [U_209] :
( ( ! [U_206] :
( U_206 = set_meet(U_209)
| ( ~ in(sK38(U_209,U_206),U_206)
& ! [U_195] :
( in(sK38(U_209,U_206),U_195)
| ~ in(U_195,U_209) ) )
| ( ~ in(sK36(U_209,U_206),sK37(U_209,U_206))
& in(sK37(U_209,U_206),U_209)
& in(sK36(U_209,U_206),U_206) ) )
& ! [U_205] :
( ( ! [U_200] :
( in(U_200,U_205)
| ( ~ in(U_200,sK35(U_209,U_205,U_200))
& in(sK35(U_209,U_205,U_200),U_209) ) )
& ! [U_199] :
( ! [U_191] :
( in(U_199,U_191)
| ~ in(U_191,U_209) )
| ~ in(U_199,U_205) ) )
| U_205 != set_meet(U_209) ) )
| U_209 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_202,sK38(U_209,U_206))],[f_31_6]) ).
fof(f_31_8,plain,
( ! [U_207,U_208,U_210] :
( U_208 = set_meet(U_210)
| U_208 != empty_set
| ~ sP56(U_207,U_208,U_210) )
& ! [U_207,U_208,U_210] :
( U_207 = empty_set
| U_207 != set_meet(U_210)
| ~ sP56(U_207,U_208,U_210) )
& ! [U_195,U_206,U_209] :
( ~ in(sK38(U_209,U_206),U_206)
| ~ sP54(U_195,U_206,U_209) )
& ! [U_195,U_206,U_209] :
( in(sK38(U_209,U_206),U_195)
| ~ in(U_195,U_209)
| ~ sP54(U_195,U_206,U_209) )
& ! [U_206,U_209] :
( ~ in(sK36(U_209,U_206),sK37(U_209,U_206))
| ~ sP53(U_206,U_209) )
& ! [U_206,U_209] :
( in(sK37(U_209,U_206),U_209)
| ~ sP53(U_206,U_209) )
& ! [U_206,U_209] :
( in(sK36(U_209,U_206),U_206)
| ~ sP53(U_206,U_209) )
& ! [U_205,U_200,U_209] :
( ~ in(U_200,sK35(U_209,U_205,U_200))
| ~ sP51(U_205,U_200,U_209) )
& ! [U_205,U_200,U_209] :
( in(sK35(U_209,U_205,U_200),U_209)
| ~ sP51(U_205,U_200,U_209) )
& ! [U_191,U_205,U_199,U_200,U_209] :
( in(U_200,U_205)
| sP51(U_205,U_200,U_209)
| ~ sP52(U_191,U_205,U_199,U_200,U_209) )
& ! [U_191,U_205,U_199,U_200,U_209] :
( in(U_199,U_191)
| ~ in(U_191,U_209)
| ~ in(U_199,U_205)
| ~ sP52(U_191,U_205,U_199,U_200,U_209) )
& ! [U_191,U_195,U_205,U_199,U_200,U_206,U_209] :
( U_206 = set_meet(U_209)
| sP54(U_195,U_206,U_209)
| sP53(U_206,U_209)
| ~ sP55(U_191,U_195,U_205,U_199,U_200,U_206,U_209) )
& ! [U_191,U_195,U_205,U_199,U_200,U_206,U_209] :
( sP52(U_191,U_205,U_199,U_200,U_209)
| U_205 != set_meet(U_209)
| ~ sP55(U_191,U_195,U_205,U_199,U_200,U_206,U_209) )
& ! [U_207,U_208,U_210] :
( sP56(U_207,U_208,U_210)
| U_210 != empty_set )
& ! [U_191,U_195,U_205,U_199,U_200,U_206,U_209] :
( sP55(U_191,U_195,U_205,U_199,U_200,U_206,U_209)
| U_209 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51,sP52,sP53,sP54,sP55,sP56])],[f_31_7]) ).
cnf(f_31_9,plain,
( sP55(U_191,U_195,U_205,U_199,U_200,U_206,U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_10,plain,
( sP56(U_207,U_208,U_210)
| U_210 != empty_set ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_11,plain,
( sP52(U_191,U_205,U_199,U_200,U_209)
| U_205 != set_meet(U_209)
| ~ sP55(U_191,U_195,U_205,U_199,U_200,U_206,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_12,plain,
( U_206 = set_meet(U_209)
| sP54(U_195,U_206,U_209)
| sP53(U_206,U_209)
| ~ sP55(U_191,U_195,U_205,U_199,U_200,U_206,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_13,plain,
( in(U_199,U_191)
| ~ in(U_191,U_209)
| ~ in(U_199,U_205)
| ~ sP52(U_191,U_205,U_199,U_200,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_14,plain,
( in(U_200,U_205)
| sP51(U_205,U_200,U_209)
| ~ sP52(U_191,U_205,U_199,U_200,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_15,plain,
( in(sK35(U_209,U_205,U_200),U_209)
| ~ sP51(U_205,U_200,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_16,plain,
( ~ in(U_200,sK35(U_209,U_205,U_200))
| ~ sP51(U_205,U_200,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_17,plain,
( in(sK36(U_209,U_206),U_206)
| ~ sP53(U_206,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_18,plain,
( in(sK37(U_209,U_206),U_209)
| ~ sP53(U_206,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_19,plain,
( ~ in(sK36(U_209,U_206),sK37(U_209,U_206))
| ~ sP53(U_206,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_20,plain,
( in(sK38(U_209,U_206),U_195)
| ~ in(U_195,U_209)
| ~ sP54(U_195,U_206,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_21,plain,
( ~ in(sK38(U_209,U_206),U_206)
| ~ sP54(U_195,U_206,U_209) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_22,plain,
( U_207 = empty_set
| U_207 != set_meet(U_210)
| ~ sP56(U_207,U_208,U_210) ),
inference(clausify,[status(thm)],[f_31_8]) ).
cnf(f_31_23,plain,
( U_208 = set_meet(U_210)
| U_208 != empty_set
| ~ sP56(U_207,U_208,U_210) ),
inference(clausify,[status(thm)],[f_31_8]) ).
fof(f_32_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_32_2,plain,
! [U_214,U_213] :
( ( U_213 = singleton(U_214)
| ? [U_212] :
( ( ~ in(U_212,U_213)
& U_212 = U_214 )
| ( U_212 != U_214
& in(U_212,U_213) ) ) )
& ( ! [U_211] :
( ( in(U_211,U_213)
| U_211 != U_214 )
& ( U_211 = U_214
| ~ in(U_211,U_213) ) )
| U_213 != singleton(U_214) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_222,U_220] :
( U_220 = singleton(U_222)
| ? [U_218] :
( ~ in(U_218,U_220)
& U_218 = U_222 )
| ? [U_217] :
( U_217 != U_222
& in(U_217,U_220) ) )
& ! [U_221,U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| U_216 != U_221 )
& ! [U_215] :
( U_215 = U_221
| ~ in(U_215,U_219) ) )
| U_219 != singleton(U_221) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_222,U_220] :
( U_220 = singleton(U_222)
| ? [U_218] :
( ~ in(U_218,U_220)
& U_218 = U_222 )
| ( sK39(U_222,U_220) != U_222
& in(sK39(U_222,U_220),U_220) ) )
& ! [U_221,U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| U_216 != U_221 )
& ! [U_215] :
( U_215 = U_221
| ~ in(U_215,U_219) ) )
| U_219 != singleton(U_221) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_217,sK39(U_222,U_220))],[f_32_3]) ).
fof(f_32_5,plain,
( ! [U_222,U_220] :
( U_220 = singleton(U_222)
| ( ~ in(sK40(U_222,U_220),U_220)
& sK40(U_222,U_220) = U_222 )
| ( sK39(U_222,U_220) != U_222
& in(sK39(U_222,U_220),U_220) ) )
& ! [U_221,U_219] :
( ( ! [U_216] :
( in(U_216,U_219)
| U_216 != U_221 )
& ! [U_215] :
( U_215 = U_221
| ~ in(U_215,U_219) ) )
| U_219 != singleton(U_221) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_218,sK40(U_222,U_220))],[f_32_4]) ).
fof(f_32_6,plain,
( ! [U_222,U_220] :
( ~ in(sK40(U_222,U_220),U_220)
| ~ sP59(U_222,U_220) )
& ! [U_222,U_220] :
( sK40(U_222,U_220) = U_222
| ~ sP59(U_222,U_220) )
& ! [U_222,U_220] :
( sK39(U_222,U_220) != U_222
| ~ sP58(U_222,U_220) )
& ! [U_222,U_220] :
( in(sK39(U_222,U_220),U_220)
| ~ sP58(U_222,U_220) )
& ! [U_221,U_219,U_216,U_215] :
( in(U_216,U_219)
| U_216 != U_221
| ~ sP57(U_221,U_219,U_216,U_215) )
& ! [U_221,U_219,U_216,U_215] :
( U_215 = U_221
| ~ in(U_215,U_219)
| ~ sP57(U_221,U_219,U_216,U_215) )
& ! [U_222,U_220] :
( U_220 = singleton(U_222)
| sP59(U_222,U_220)
| sP58(U_222,U_220) )
& ! [U_221,U_219,U_216,U_215] :
( sP57(U_221,U_219,U_216,U_215)
| U_219 != singleton(U_221) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57,sP58,sP59])],[f_32_5]) ).
cnf(f_32_7,plain,
( sP57(U_221,U_219,U_216,U_215)
| U_219 != singleton(U_221) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_8,plain,
( U_220 = singleton(U_222)
| sP59(U_222,U_220)
| sP58(U_222,U_220) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_9,plain,
( U_215 = U_221
| ~ in(U_215,U_219)
| ~ sP57(U_221,U_219,U_216,U_215) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_10,plain,
( in(U_216,U_219)
| U_216 != U_221
| ~ sP57(U_221,U_219,U_216,U_215) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_11,plain,
( in(sK39(U_222,U_220),U_220)
| ~ sP58(U_222,U_220) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_12,plain,
( sK39(U_222,U_220) != U_222
| ~ sP58(U_222,U_220) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_13,plain,
( sK40(U_222,U_220) = U_222
| ~ sP59(U_222,U_220) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_14,plain,
( ~ in(sK40(U_222,U_220),U_220)
| ~ sP59(U_222,U_220) ),
inference(clausify,[status(thm)],[f_32_6]) ).
fof(f_33_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_33_2,plain,
! [U_227] :
( ! [U_226,U_225] :
( ( U_225 = fiber(U_227,U_226)
| ? [U_224] :
( ( ~ in(U_224,U_225)
& in(ordered_pair(U_224,U_226),U_227)
& U_224 != U_226 )
| ( ( ~ in(ordered_pair(U_224,U_226),U_227)
| U_224 = U_226 )
& in(U_224,U_225) ) ) )
& ( ! [U_223] :
( ( in(U_223,U_225)
| ~ in(ordered_pair(U_223,U_226),U_227)
| U_223 = U_226 )
& ( ( in(ordered_pair(U_223,U_226),U_227)
& U_223 != U_226 )
| ~ in(U_223,U_225) ) )
| U_225 != fiber(U_227,U_226) ) )
| ~ relation(U_227) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_227] :
( ( ! [U_235,U_233] :
( U_233 = fiber(U_227,U_235)
| ? [U_231] :
( ~ in(U_231,U_233)
& in(ordered_pair(U_231,U_235),U_227)
& U_231 != U_235 )
| ? [U_230] :
( ( ~ in(ordered_pair(U_230,U_235),U_227)
| U_230 = U_235 )
& in(U_230,U_233) ) )
& ! [U_234,U_232] :
( ( ! [U_229] :
( in(U_229,U_232)
| ~ in(ordered_pair(U_229,U_234),U_227)
| U_229 = U_234 )
& ! [U_228] :
( ( in(ordered_pair(U_228,U_234),U_227)
& U_228 != U_234 )
| ~ in(U_228,U_232) ) )
| U_232 != fiber(U_227,U_234) ) )
| ~ relation(U_227) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_227] :
( ( ! [U_235,U_233] :
( U_233 = fiber(U_227,U_235)
| ? [U_231] :
( ~ in(U_231,U_233)
& in(ordered_pair(U_231,U_235),U_227)
& U_231 != U_235 )
| ( ( ~ in(ordered_pair(sK41(U_227,U_235,U_233),U_235),U_227)
| sK41(U_227,U_235,U_233) = U_235 )
& in(sK41(U_227,U_235,U_233),U_233) ) )
& ! [U_234,U_232] :
( ( ! [U_229] :
( in(U_229,U_232)
| ~ in(ordered_pair(U_229,U_234),U_227)
| U_229 = U_234 )
& ! [U_228] :
( ( in(ordered_pair(U_228,U_234),U_227)
& U_228 != U_234 )
| ~ in(U_228,U_232) ) )
| U_232 != fiber(U_227,U_234) ) )
| ~ relation(U_227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_230,sK41(U_227,U_235,U_233))],[f_33_3]) ).
fof(f_33_5,plain,
! [U_227] :
( ( ! [U_235,U_233] :
( U_233 = fiber(U_227,U_235)
| ( ~ in(sK42(U_227,U_235,U_233),U_233)
& in(ordered_pair(sK42(U_227,U_235,U_233),U_235),U_227)
& sK42(U_227,U_235,U_233) != U_235 )
| ( ( ~ in(ordered_pair(sK41(U_227,U_235,U_233),U_235),U_227)
| sK41(U_227,U_235,U_233) = U_235 )
& in(sK41(U_227,U_235,U_233),U_233) ) )
& ! [U_234,U_232] :
( ( ! [U_229] :
( in(U_229,U_232)
| ~ in(ordered_pair(U_229,U_234),U_227)
| U_229 = U_234 )
& ! [U_228] :
( ( in(ordered_pair(U_228,U_234),U_227)
& U_228 != U_234 )
| ~ in(U_228,U_232) ) )
| U_232 != fiber(U_227,U_234) ) )
| ~ relation(U_227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_231,sK42(U_227,U_235,U_233))],[f_33_4]) ).
fof(f_33_6,plain,
( ! [U_235,U_227,U_233] :
( ~ in(sK42(U_227,U_235,U_233),U_233)
| ~ sP63(U_235,U_227,U_233) )
& ! [U_235,U_227,U_233] :
( in(ordered_pair(sK42(U_227,U_235,U_233),U_235),U_227)
| ~ sP63(U_235,U_227,U_233) )
& ! [U_235,U_227,U_233] :
( sK42(U_227,U_235,U_233) != U_235
| ~ sP63(U_235,U_227,U_233) )
& ! [U_235,U_227,U_233] :
( ~ in(ordered_pair(sK41(U_227,U_235,U_233),U_235),U_227)
| sK41(U_227,U_235,U_233) = U_235
| ~ sP62(U_235,U_227,U_233) )
& ! [U_235,U_227,U_233] :
( in(sK41(U_227,U_235,U_233),U_233)
| ~ sP62(U_235,U_227,U_233) )
& ! [U_228,U_227,U_234] :
( in(ordered_pair(U_228,U_234),U_227)
| ~ sP60(U_228,U_227,U_234) )
& ! [U_228,U_227,U_234] :
( U_228 != U_234
| ~ sP60(U_228,U_227,U_234) )
& ! [U_232,U_228,U_229,U_227,U_234] :
( in(U_229,U_232)
| ~ in(ordered_pair(U_229,U_234),U_227)
| U_229 = U_234
| ~ sP61(U_232,U_228,U_229,U_227,U_234) )
& ! [U_232,U_228,U_229,U_227,U_234] :
( sP60(U_228,U_227,U_234)
| ~ in(U_228,U_232)
| ~ sP61(U_232,U_228,U_229,U_227,U_234) )
& ! [U_235,U_232,U_228,U_229,U_227,U_233,U_234] :
( U_233 = fiber(U_227,U_235)
| sP63(U_235,U_227,U_233)
| sP62(U_235,U_227,U_233)
| ~ sP64(U_235,U_232,U_228,U_229,U_227,U_233,U_234) )
& ! [U_235,U_232,U_228,U_229,U_227,U_233,U_234] :
( sP61(U_232,U_228,U_229,U_227,U_234)
| U_232 != fiber(U_227,U_234)
| ~ sP64(U_235,U_232,U_228,U_229,U_227,U_233,U_234) )
& ! [U_235,U_232,U_228,U_229,U_227,U_233,U_234] :
( sP64(U_235,U_232,U_228,U_229,U_227,U_233,U_234)
| ~ relation(U_227) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60,sP61,sP62,sP63,sP64])],[f_33_5]) ).
cnf(f_33_7,plain,
( sP64(U_235,U_232,U_228,U_229,U_227,U_233,U_234)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_8,plain,
( sP61(U_232,U_228,U_229,U_227,U_234)
| U_232 != fiber(U_227,U_234)
| ~ sP64(U_235,U_232,U_228,U_229,U_227,U_233,U_234) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_9,plain,
( U_233 = fiber(U_227,U_235)
| sP63(U_235,U_227,U_233)
| sP62(U_235,U_227,U_233)
| ~ sP64(U_235,U_232,U_228,U_229,U_227,U_233,U_234) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_10,plain,
( sP60(U_228,U_227,U_234)
| ~ in(U_228,U_232)
| ~ sP61(U_232,U_228,U_229,U_227,U_234) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_11,plain,
( in(U_229,U_232)
| ~ in(ordered_pair(U_229,U_234),U_227)
| U_229 = U_234
| ~ sP61(U_232,U_228,U_229,U_227,U_234) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_12,plain,
( U_228 != U_234
| ~ sP60(U_228,U_227,U_234) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_13,plain,
( in(ordered_pair(U_228,U_234),U_227)
| ~ sP60(U_228,U_227,U_234) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_14,plain,
( in(sK41(U_227,U_235,U_233),U_233)
| ~ sP62(U_235,U_227,U_233) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_15,plain,
( ~ in(ordered_pair(sK41(U_227,U_235,U_233),U_235),U_227)
| sK41(U_227,U_235,U_233) = U_235
| ~ sP62(U_235,U_227,U_233) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_16,plain,
( sK42(U_227,U_235,U_233) != U_235
| ~ sP63(U_235,U_227,U_233) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_17,plain,
( in(ordered_pair(sK42(U_227,U_235,U_233),U_235),U_227)
| ~ sP63(U_235,U_227,U_233) ),
inference(clausify,[status(thm)],[f_33_6]) ).
cnf(f_33_18,plain,
( ~ in(sK42(U_227,U_235,U_233),U_233)
| ~ sP63(U_235,U_227,U_233) ),
inference(clausify,[status(thm)],[f_33_6]) ).
fof(f_34_1,plain,
! [A,B] :
( ( ( B = inclusion_relation(A)
| ? [C,D] :
( ( ( ~ in(ordered_pair(C,D),B)
& subset(C,D) )
| ( ~ subset(C,D)
& in(ordered_pair(C,D),B) ) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A )
& ( ( ! [C,D] :
( ( ( in(ordered_pair(C,D),B)
| ~ subset(C,D) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d1_wellord2]) ).
fof(f_34_2,plain,
! [U_241,U_240] :
( ( ( U_240 = inclusion_relation(U_241)
| ? [U_239,U_238] :
( ( ( ~ in(ordered_pair(U_239,U_238),U_240)
& subset(U_239,U_238) )
| ( ~ subset(U_239,U_238)
& in(ordered_pair(U_239,U_238),U_240) ) )
& in(U_238,U_241)
& in(U_239,U_241) )
| relation_field(U_240) != U_241 )
& ( ( ! [U_237,U_236] :
( ( ( in(ordered_pair(U_237,U_236),U_240)
| ~ subset(U_237,U_236) )
& ( subset(U_237,U_236)
| ~ in(ordered_pair(U_237,U_236),U_240) ) )
| ~ in(U_236,U_241)
| ~ in(U_237,U_241) )
& relation_field(U_240) = U_241 )
| U_240 != inclusion_relation(U_241) ) )
| ~ relation(U_240) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_241,U_240] :
( ( ( U_240 = inclusion_relation(U_241)
| ? [U_238] :
( ( ( ~ in(ordered_pair(sK43(U_241,U_240),U_238),U_240)
& subset(sK43(U_241,U_240),U_238) )
| ( ~ subset(sK43(U_241,U_240),U_238)
& in(ordered_pair(sK43(U_241,U_240),U_238),U_240) ) )
& in(U_238,U_241)
& in(sK43(U_241,U_240),U_241) )
| relation_field(U_240) != U_241 )
& ( ( ! [U_237,U_236] :
( ( ( in(ordered_pair(U_237,U_236),U_240)
| ~ subset(U_237,U_236) )
& ( subset(U_237,U_236)
| ~ in(ordered_pair(U_237,U_236),U_240) ) )
| ~ in(U_236,U_241)
| ~ in(U_237,U_241) )
& relation_field(U_240) = U_241 )
| U_240 != inclusion_relation(U_241) ) )
| ~ relation(U_240) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_239,sK43(U_241,U_240))],[f_34_2]) ).
fof(f_34_4,plain,
! [U_241,U_240] :
( ( ( U_240 = inclusion_relation(U_241)
| ( ( ( ~ in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240)
& subset(sK43(U_241,U_240),sK44(U_241,U_240)) )
| ( ~ subset(sK43(U_241,U_240),sK44(U_241,U_240))
& in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240) ) )
& in(sK44(U_241,U_240),U_241)
& in(sK43(U_241,U_240),U_241) )
| relation_field(U_240) != U_241 )
& ( ( ! [U_237,U_236] :
( ( ( in(ordered_pair(U_237,U_236),U_240)
| ~ subset(U_237,U_236) )
& ( subset(U_237,U_236)
| ~ in(ordered_pair(U_237,U_236),U_240) ) )
| ~ in(U_236,U_241)
| ~ in(U_237,U_241) )
& relation_field(U_240) = U_241 )
| U_240 != inclusion_relation(U_241) ) )
| ~ relation(U_240) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_238,sK44(U_241,U_240))],[f_34_3]) ).
fof(f_34_5,plain,
( ! [U_241,U_240] :
( ~ in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240)
| ~ sP68(U_241,U_240) )
& ! [U_241,U_240] :
( subset(sK43(U_241,U_240),sK44(U_241,U_240))
| ~ sP68(U_241,U_240) )
& ! [U_241,U_240] :
( ~ subset(sK43(U_241,U_240),sK44(U_241,U_240))
| ~ sP67(U_241,U_240) )
& ! [U_241,U_240] :
( in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240)
| ~ sP67(U_241,U_240) )
& ! [U_241,U_240] :
( sP68(U_241,U_240)
| sP67(U_241,U_240)
| ~ sP69(U_241,U_240) )
& ! [U_241,U_240] :
( in(sK44(U_241,U_240),U_241)
| ~ sP69(U_241,U_240) )
& ! [U_241,U_240] :
( in(sK43(U_241,U_240),U_241)
| ~ sP69(U_241,U_240) )
& ! [U_236,U_237,U_240] :
( in(ordered_pair(U_237,U_236),U_240)
| ~ subset(U_237,U_236)
| ~ sP65(U_236,U_237,U_240) )
& ! [U_236,U_237,U_240] :
( subset(U_237,U_236)
| ~ in(ordered_pair(U_237,U_236),U_240)
| ~ sP65(U_236,U_237,U_240) )
& ! [U_241,U_236,U_237,U_240] :
( sP65(U_236,U_237,U_240)
| ~ in(U_236,U_241)
| ~ in(U_237,U_241)
| ~ sP66(U_241,U_236,U_237,U_240) )
& ! [U_241,U_236,U_237,U_240] :
( relation_field(U_240) = U_241
| ~ sP66(U_241,U_236,U_237,U_240) )
& ! [U_241,U_236,U_237,U_240] :
( U_240 = inclusion_relation(U_241)
| sP69(U_241,U_240)
| relation_field(U_240) != U_241
| ~ sP70(U_241,U_236,U_237,U_240) )
& ! [U_241,U_236,U_237,U_240] :
( sP66(U_241,U_236,U_237,U_240)
| U_240 != inclusion_relation(U_241)
| ~ sP70(U_241,U_236,U_237,U_240) )
& ! [U_241,U_236,U_237,U_240] :
( sP70(U_241,U_236,U_237,U_240)
| ~ relation(U_240) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65,sP66,sP67,sP68,sP69,sP70])],[f_34_4]) ).
cnf(f_34_6,plain,
( sP70(U_241,U_236,U_237,U_240)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_7,plain,
( sP66(U_241,U_236,U_237,U_240)
| U_240 != inclusion_relation(U_241)
| ~ sP70(U_241,U_236,U_237,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_8,plain,
( U_240 = inclusion_relation(U_241)
| sP69(U_241,U_240)
| relation_field(U_240) != U_241
| ~ sP70(U_241,U_236,U_237,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_9,plain,
( relation_field(U_240) = U_241
| ~ sP66(U_241,U_236,U_237,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_10,plain,
( sP65(U_236,U_237,U_240)
| ~ in(U_236,U_241)
| ~ in(U_237,U_241)
| ~ sP66(U_241,U_236,U_237,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_11,plain,
( subset(U_237,U_236)
| ~ in(ordered_pair(U_237,U_236),U_240)
| ~ sP65(U_236,U_237,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_12,plain,
( in(ordered_pair(U_237,U_236),U_240)
| ~ subset(U_237,U_236)
| ~ sP65(U_236,U_237,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_13,plain,
( in(sK43(U_241,U_240),U_241)
| ~ sP69(U_241,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_14,plain,
( in(sK44(U_241,U_240),U_241)
| ~ sP69(U_241,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_15,plain,
( sP68(U_241,U_240)
| sP67(U_241,U_240)
| ~ sP69(U_241,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_16,plain,
( in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240)
| ~ sP67(U_241,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_17,plain,
( ~ subset(sK43(U_241,U_240),sK44(U_241,U_240))
| ~ sP67(U_241,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_18,plain,
( subset(sK43(U_241,U_240),sK44(U_241,U_240))
| ~ sP68(U_241,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_19,plain,
( ~ in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240)
| ~ sP68(U_241,U_240) ),
inference(clausify,[status(thm)],[f_34_5]) ).
fof(f_35_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_35_2,plain,
! [U_244] :
( ( U_244 = empty_set
| ? [U_243] : in(U_243,U_244) )
& ( ! [U_242] : ~ in(U_242,U_244)
| U_244 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_246] :
( U_246 = empty_set
| ? [U_243] : in(U_243,U_246) )
& ! [U_245] :
( ! [U_242] : ~ in(U_242,U_245)
| U_245 != empty_set ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_246] :
( U_246 = empty_set
| in(sK45(U_246),U_246) )
& ! [U_245] :
( ! [U_242] : ~ in(U_242,U_245)
| U_245 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_243,sK45(U_246))],[f_35_3]) ).
fof(f_35_5,plain,
( ! [U_246] :
( U_246 = empty_set
| in(sK45(U_246),U_246) )
& ! [U_245,U_242] :
( ~ in(U_242,U_245)
| U_245 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_35_4]) ).
cnf(f_35_6,plain,
( ~ in(U_242,U_245)
| U_245 != empty_set ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_7,plain,
( U_246 = empty_set
| in(sK45(U_246),U_246) ),
inference(clausify,[status(thm)],[f_35_5]) ).
fof(f_36_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_36_2,plain,
! [U_250,U_249] :
( ( U_249 = powerset(U_250)
| ? [U_248] :
( ( ~ in(U_248,U_249)
& subset(U_248,U_250) )
| ( ~ subset(U_248,U_250)
& in(U_248,U_249) ) ) )
& ( ! [U_247] :
( ( in(U_247,U_249)
| ~ subset(U_247,U_250) )
& ( subset(U_247,U_250)
| ~ in(U_247,U_249) ) )
| U_249 != powerset(U_250) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_258,U_256] :
( U_256 = powerset(U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& subset(U_254,U_258) )
| ? [U_253] :
( ~ subset(U_253,U_258)
& in(U_253,U_256) ) )
& ! [U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ~ subset(U_252,U_257) )
& ! [U_251] :
( subset(U_251,U_257)
| ~ in(U_251,U_255) ) )
| U_255 != powerset(U_257) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_258,U_256] :
( U_256 = powerset(U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& subset(U_254,U_258) )
| ( ~ subset(sK46(U_258,U_256),U_258)
& in(sK46(U_258,U_256),U_256) ) )
& ! [U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ~ subset(U_252,U_257) )
& ! [U_251] :
( subset(U_251,U_257)
| ~ in(U_251,U_255) ) )
| U_255 != powerset(U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_253,sK46(U_258,U_256))],[f_36_3]) ).
fof(f_36_5,plain,
( ! [U_258,U_256] :
( U_256 = powerset(U_258)
| ( ~ in(sK47(U_258,U_256),U_256)
& subset(sK47(U_258,U_256),U_258) )
| ( ~ subset(sK46(U_258,U_256),U_258)
& in(sK46(U_258,U_256),U_256) ) )
& ! [U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ~ subset(U_252,U_257) )
& ! [U_251] :
( subset(U_251,U_257)
| ~ in(U_251,U_255) ) )
| U_255 != powerset(U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_254,sK47(U_258,U_256))],[f_36_4]) ).
fof(f_36_6,plain,
( ! [U_256,U_258] :
( ~ in(sK47(U_258,U_256),U_256)
| ~ sP73(U_256,U_258) )
& ! [U_256,U_258] :
( subset(sK47(U_258,U_256),U_258)
| ~ sP73(U_256,U_258) )
& ! [U_256,U_258] :
( ~ subset(sK46(U_258,U_256),U_258)
| ~ sP72(U_256,U_258) )
& ! [U_256,U_258] :
( in(sK46(U_258,U_256),U_256)
| ~ sP72(U_256,U_258) )
& ! [U_257,U_252,U_251,U_255] :
( in(U_252,U_255)
| ~ subset(U_252,U_257)
| ~ sP71(U_257,U_252,U_251,U_255) )
& ! [U_257,U_252,U_251,U_255] :
( subset(U_251,U_257)
| ~ in(U_251,U_255)
| ~ sP71(U_257,U_252,U_251,U_255) )
& ! [U_256,U_258] :
( U_256 = powerset(U_258)
| sP73(U_256,U_258)
| sP72(U_256,U_258) )
& ! [U_257,U_252,U_251,U_255] :
( sP71(U_257,U_252,U_251,U_255)
| U_255 != powerset(U_257) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71,sP72,sP73])],[f_36_5]) ).
cnf(f_36_7,plain,
( sP71(U_257,U_252,U_251,U_255)
| U_255 != powerset(U_257) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_8,plain,
( U_256 = powerset(U_258)
| sP73(U_256,U_258)
| sP72(U_256,U_258) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_9,plain,
( subset(U_251,U_257)
| ~ in(U_251,U_255)
| ~ sP71(U_257,U_252,U_251,U_255) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_10,plain,
( in(U_252,U_255)
| ~ subset(U_252,U_257)
| ~ sP71(U_257,U_252,U_251,U_255) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_11,plain,
( in(sK46(U_258,U_256),U_256)
| ~ sP72(U_256,U_258) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_12,plain,
( ~ subset(sK46(U_258,U_256),U_258)
| ~ sP72(U_256,U_258) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_13,plain,
( subset(sK47(U_258,U_256),U_258)
| ~ sP73(U_256,U_258) ),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_14,plain,
( ~ in(sK47(U_258,U_256),U_256)
| ~ sP73(U_256,U_258) ),
inference(clausify,[status(thm)],[f_36_6]) ).
fof(f_37_1,plain,
! [A] :
( ! [B] :
( ( B = pair_second(A)
| ? [C,D] :
( B != D
& A = ordered_pair(C,D) ) )
& ( ! [C,D] :
( B = D
| A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[d2_mcart_1]) ).
fof(f_37_2,plain,
! [U_266] :
( ! [U_265] :
( ( U_265 = pair_second(U_266)
| ? [U_264,U_263] :
( U_265 != U_263
& U_266 = ordered_pair(U_264,U_263) ) )
& ( ! [U_262,U_261] :
( U_265 = U_261
| U_266 != ordered_pair(U_262,U_261) )
| U_265 != pair_second(U_266) ) )
| ! [U_260,U_259] : U_266 != ordered_pair(U_260,U_259) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_266] :
( ( ! [U_268] :
( U_268 = pair_second(U_266)
| ? [U_264,U_263] :
( U_268 != U_263
& U_266 = ordered_pair(U_264,U_263) ) )
& ! [U_267] :
( ! [U_262,U_261] :
( U_267 = U_261
| U_266 != ordered_pair(U_262,U_261) )
| U_267 != pair_second(U_266) ) )
| ! [U_260,U_259] : U_266 != ordered_pair(U_260,U_259) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
! [U_266] :
( ( ! [U_268] :
( U_268 = pair_second(U_266)
| ? [U_263] :
( U_268 != U_263
& U_266 = ordered_pair(sK48(U_266,U_268),U_263) ) )
& ! [U_267] :
( ! [U_262,U_261] :
( U_267 = U_261
| U_266 != ordered_pair(U_262,U_261) )
| U_267 != pair_second(U_266) ) )
| ! [U_260,U_259] : U_266 != ordered_pair(U_260,U_259) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_264,sK48(U_266,U_268))],[f_37_3]) ).
fof(f_37_5,plain,
! [U_266] :
( ( ! [U_268] :
( U_268 = pair_second(U_266)
| ( U_268 != sK49(U_266,U_268)
& U_266 = ordered_pair(sK48(U_266,U_268),sK49(U_266,U_268)) ) )
& ! [U_267] :
( ! [U_262,U_261] :
( U_267 = U_261
| U_266 != ordered_pair(U_262,U_261) )
| U_267 != pair_second(U_266) ) )
| ! [U_260,U_259] : U_266 != ordered_pair(U_260,U_259) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_263,sK49(U_266,U_268))],[f_37_4]) ).
fof(f_37_6,plain,
( ! [U_266,U_268] :
( U_268 != sK49(U_266,U_268)
| ~ sP74(U_266,U_268) )
& ! [U_266,U_268] :
( U_266 = ordered_pair(sK48(U_266,U_268),sK49(U_266,U_268))
| ~ sP74(U_266,U_268) )
& ! [U_266,U_267,U_268,U_261,U_262] :
( U_268 = pair_second(U_266)
| sP74(U_266,U_268)
| ~ sP75(U_266,U_267,U_268,U_261,U_262) )
& ! [U_266,U_267,U_268,U_261,U_262] :
( U_267 = U_261
| U_266 != ordered_pair(U_262,U_261)
| U_267 != pair_second(U_266)
| ~ sP75(U_266,U_267,U_268,U_261,U_262) )
& ! [U_266,U_267,U_268,U_259,U_261,U_260,U_262] :
( sP75(U_266,U_267,U_268,U_261,U_262)
| U_266 != ordered_pair(U_260,U_259) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75])],[f_37_5]) ).
cnf(f_37_7,plain,
( sP75(U_266,U_267,U_268,U_261,U_262)
| U_266 != ordered_pair(U_260,U_259) ),
inference(clausify,[status(thm)],[f_37_6]) ).
cnf(f_37_8,plain,
( U_267 = U_261
| U_266 != ordered_pair(U_262,U_261)
| U_267 != pair_second(U_266)
| ~ sP75(U_266,U_267,U_268,U_261,U_262) ),
inference(clausify,[status(thm)],[f_37_6]) ).
cnf(f_37_9,plain,
( U_268 = pair_second(U_266)
| sP74(U_266,U_268)
| ~ sP75(U_266,U_267,U_268,U_261,U_262) ),
inference(clausify,[status(thm)],[f_37_6]) ).
cnf(f_37_10,plain,
( U_266 = ordered_pair(sK48(U_266,U_268),sK49(U_266,U_268))
| ~ sP74(U_266,U_268) ),
inference(clausify,[status(thm)],[f_37_6]) ).
cnf(f_37_11,plain,
( U_268 != sK49(U_266,U_268)
| ~ sP74(U_266,U_268) ),
inference(clausify,[status(thm)],[f_37_6]) ).
fof(f_38_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_38_2,plain,
! [U_271] :
( ( epsilon_transitive(U_271)
| ? [U_270] :
( ~ subset(U_270,U_271)
& in(U_270,U_271) ) )
& ( ! [U_269] :
( subset(U_269,U_271)
| ~ in(U_269,U_271) )
| ~ epsilon_transitive(U_271) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_273] :
( epsilon_transitive(U_273)
| ? [U_270] :
( ~ subset(U_270,U_273)
& in(U_270,U_273) ) )
& ! [U_272] :
( ! [U_269] :
( subset(U_269,U_272)
| ~ in(U_269,U_272) )
| ~ epsilon_transitive(U_272) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_273] :
( epsilon_transitive(U_273)
| ( ~ subset(sK50(U_273),U_273)
& in(sK50(U_273),U_273) ) )
& ! [U_272] :
( ! [U_269] :
( subset(U_269,U_272)
| ~ in(U_269,U_272) )
| ~ epsilon_transitive(U_272) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_270,sK50(U_273))],[f_38_3]) ).
fof(f_38_5,plain,
( ! [U_273] :
( ~ subset(sK50(U_273),U_273)
| ~ sP76(U_273) )
& ! [U_273] :
( in(sK50(U_273),U_273)
| ~ sP76(U_273) )
& ! [U_273] :
( epsilon_transitive(U_273)
| sP76(U_273) )
& ! [U_269,U_272] :
( subset(U_269,U_272)
| ~ in(U_269,U_272)
| ~ epsilon_transitive(U_272) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_38_4]) ).
cnf(f_38_6,plain,
( subset(U_269,U_272)
| ~ in(U_269,U_272)
| ~ epsilon_transitive(U_272) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_7,plain,
( epsilon_transitive(U_273)
| sP76(U_273) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_8,plain,
( in(sK50(U_273),U_273)
| ~ sP76(U_273) ),
inference(clausify,[status(thm)],[f_38_5]) ).
cnf(f_38_9,plain,
( ~ subset(sK50(U_273),U_273)
| ~ sP76(U_273) ),
inference(clausify,[status(thm)],[f_38_5]) ).
fof(f_39_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_39_2,plain,
! [U_279] :
( ! [U_278] :
( ( ( U_279 = U_278
| ? [U_277,U_276] :
( ( ~ in(ordered_pair(U_277,U_276),U_279)
& in(ordered_pair(U_277,U_276),U_278) )
| ( ~ in(ordered_pair(U_277,U_276),U_278)
& in(ordered_pair(U_277,U_276),U_279) ) ) )
& ( ! [U_275,U_274] :
( ( in(ordered_pair(U_275,U_274),U_279)
| ~ in(ordered_pair(U_275,U_274),U_278) )
& ( in(ordered_pair(U_275,U_274),U_278)
| ~ in(ordered_pair(U_275,U_274),U_279) ) )
| U_279 != U_278 ) )
| ~ relation(U_278) )
| ~ relation(U_279) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_279] :
( ! [U_278] :
( ( ( U_279 = U_278
| ? [U_287,U_285] :
( ~ in(ordered_pair(U_287,U_285),U_279)
& in(ordered_pair(U_287,U_285),U_278) )
| ? [U_286,U_284] :
( ~ in(ordered_pair(U_286,U_284),U_278)
& in(ordered_pair(U_286,U_284),U_279) ) )
& ( ( ! [U_283,U_281] :
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278) )
& ! [U_282,U_280] :
( in(ordered_pair(U_282,U_280),U_278)
| ~ in(ordered_pair(U_282,U_280),U_279) ) )
| U_279 != U_278 ) )
| ~ relation(U_278) )
| ~ relation(U_279) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_279] :
( ! [U_278] :
( ( ( U_279 = U_278
| ? [U_287,U_285] :
( ~ in(ordered_pair(U_287,U_285),U_279)
& in(ordered_pair(U_287,U_285),U_278) )
| ? [U_284] :
( ~ in(ordered_pair(sK51(U_279,U_278),U_284),U_278)
& in(ordered_pair(sK51(U_279,U_278),U_284),U_279) ) )
& ( ( ! [U_283,U_281] :
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278) )
& ! [U_282,U_280] :
( in(ordered_pair(U_282,U_280),U_278)
| ~ in(ordered_pair(U_282,U_280),U_279) ) )
| U_279 != U_278 ) )
| ~ relation(U_278) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_286,sK51(U_279,U_278))],[f_39_3]) ).
fof(f_39_5,plain,
! [U_279] :
( ! [U_278] :
( ( ( U_279 = U_278
| ? [U_287,U_285] :
( ~ in(ordered_pair(U_287,U_285),U_279)
& in(ordered_pair(U_287,U_285),U_278) )
| ( ~ in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_278)
& in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_279) ) )
& ( ( ! [U_283,U_281] :
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278) )
& ! [U_282,U_280] :
( in(ordered_pair(U_282,U_280),U_278)
| ~ in(ordered_pair(U_282,U_280),U_279) ) )
| U_279 != U_278 ) )
| ~ relation(U_278) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_284,sK52(U_279,U_278))],[f_39_4]) ).
fof(f_39_6,plain,
! [U_279] :
( ! [U_278] :
( ( ( U_279 = U_278
| ? [U_285] :
( ~ in(ordered_pair(sK53(U_279,U_278),U_285),U_279)
& in(ordered_pair(sK53(U_279,U_278),U_285),U_278) )
| ( ~ in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_278)
& in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_279) ) )
& ( ( ! [U_283,U_281] :
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278) )
& ! [U_282,U_280] :
( in(ordered_pair(U_282,U_280),U_278)
| ~ in(ordered_pair(U_282,U_280),U_279) ) )
| U_279 != U_278 ) )
| ~ relation(U_278) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_287,sK53(U_279,U_278))],[f_39_5]) ).
fof(f_39_7,plain,
! [U_279] :
( ! [U_278] :
( ( ( U_279 = U_278
| ( ~ in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_279)
& in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_278) )
| ( ~ in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_278)
& in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_279) ) )
& ( ( ! [U_283,U_281] :
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278) )
& ! [U_282,U_280] :
( in(ordered_pair(U_282,U_280),U_278)
| ~ in(ordered_pair(U_282,U_280),U_279) ) )
| U_279 != U_278 ) )
| ~ relation(U_278) )
| ~ relation(U_279) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_285,sK54(U_279,U_278))],[f_39_6]) ).
fof(f_39_8,plain,
( ! [U_278,U_279] :
( ~ in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_279)
| ~ sP79(U_278,U_279) )
& ! [U_278,U_279] :
( in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_278)
| ~ sP79(U_278,U_279) )
& ! [U_278,U_279] :
( ~ in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_278)
| ~ sP78(U_278,U_279) )
& ! [U_278,U_279] :
( in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_279)
| ~ sP78(U_278,U_279) )
& ! [U_278,U_279,U_280,U_281,U_282,U_283] :
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278)
| ~ sP77(U_278,U_279,U_280,U_281,U_282,U_283) )
& ! [U_278,U_279,U_280,U_281,U_282,U_283] :
( in(ordered_pair(U_282,U_280),U_278)
| ~ in(ordered_pair(U_282,U_280),U_279)
| ~ sP77(U_278,U_279,U_280,U_281,U_282,U_283) )
& ! [U_278,U_279,U_280,U_281,U_282,U_283] :
( U_279 = U_278
| sP79(U_278,U_279)
| sP78(U_278,U_279)
| ~ sP80(U_278,U_279,U_280,U_281,U_282,U_283) )
& ! [U_278,U_279,U_280,U_281,U_282,U_283] :
( sP77(U_278,U_279,U_280,U_281,U_282,U_283)
| U_279 != U_278
| ~ sP80(U_278,U_279,U_280,U_281,U_282,U_283) )
& ! [U_278,U_279,U_280,U_281,U_282,U_283] :
( sP80(U_278,U_279,U_280,U_281,U_282,U_283)
| ~ relation(U_278)
| ~ relation(U_279) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77,sP78,sP79,sP80])],[f_39_7]) ).
cnf(f_39_9,plain,
( sP80(U_278,U_279,U_280,U_281,U_282,U_283)
| ~ relation(U_278)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_10,plain,
( sP77(U_278,U_279,U_280,U_281,U_282,U_283)
| U_279 != U_278
| ~ sP80(U_278,U_279,U_280,U_281,U_282,U_283) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_11,plain,
( U_279 = U_278
| sP79(U_278,U_279)
| sP78(U_278,U_279)
| ~ sP80(U_278,U_279,U_280,U_281,U_282,U_283) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_12,plain,
( in(ordered_pair(U_282,U_280),U_278)
| ~ in(ordered_pair(U_282,U_280),U_279)
| ~ sP77(U_278,U_279,U_280,U_281,U_282,U_283) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_13,plain,
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278)
| ~ sP77(U_278,U_279,U_280,U_281,U_282,U_283) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_14,plain,
( in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_279)
| ~ sP78(U_278,U_279) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_15,plain,
( ~ in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_278)
| ~ sP78(U_278,U_279) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_16,plain,
( in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_278)
| ~ sP79(U_278,U_279) ),
inference(clausify,[status(thm)],[f_39_8]) ).
cnf(f_39_17,plain,
( ~ in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_279)
| ~ sP79(U_278,U_279) ),
inference(clausify,[status(thm)],[f_39_8]) ).
fof(f_40_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_40_2,plain,
! [U_289,U_288] :
( ( ( ( element(U_288,U_289)
| ~ empty(U_288) )
& ( empty(U_288)
| ~ element(U_288,U_289) ) )
| ~ empty(U_289) )
& ( ( ( element(U_288,U_289)
| ~ in(U_288,U_289) )
& ( in(U_288,U_289)
| ~ element(U_288,U_289) ) )
| empty(U_289) ) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_297] :
( ( ! [U_295] :
( element(U_295,U_297)
| ~ empty(U_295) )
& ! [U_294] :
( empty(U_294)
| ~ element(U_294,U_297) ) )
| ~ empty(U_297) )
& ! [U_296] :
( ( ! [U_293] :
( element(U_293,U_296)
| ~ in(U_293,U_296) )
& ! [U_292] :
( in(U_292,U_296)
| ~ element(U_292,U_296) ) )
| empty(U_296) ) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_297,U_294,U_295] :
( element(U_295,U_297)
| ~ empty(U_295)
| ~ sP82(U_297,U_294,U_295) )
& ! [U_297,U_294,U_295] :
( empty(U_294)
| ~ element(U_294,U_297)
| ~ sP82(U_297,U_294,U_295) )
& ! [U_296,U_292,U_293] :
( element(U_293,U_296)
| ~ in(U_293,U_296)
| ~ sP81(U_296,U_292,U_293) )
& ! [U_296,U_292,U_293] :
( in(U_292,U_296)
| ~ element(U_292,U_296)
| ~ sP81(U_296,U_292,U_293) )
& ! [U_297,U_294,U_295] :
( sP82(U_297,U_294,U_295)
| ~ empty(U_297) )
& ! [U_296,U_292,U_293] :
( sP81(U_296,U_292,U_293)
| empty(U_296) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81,sP82])],[f_40_3]) ).
cnf(f_40_5,plain,
( sP81(U_296,U_292,U_293)
| empty(U_296) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
( sP82(U_297,U_294,U_295)
| ~ empty(U_297) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
( in(U_292,U_296)
| ~ element(U_292,U_296)
| ~ sP81(U_296,U_292,U_293) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_8,plain,
( element(U_293,U_296)
| ~ in(U_293,U_296)
| ~ sP81(U_296,U_292,U_293) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_9,plain,
( empty(U_294)
| ~ element(U_294,U_297)
| ~ sP82(U_297,U_294,U_295) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_10,plain,
( element(U_295,U_297)
| ~ empty(U_295)
| ~ sP82(U_297,U_294,U_295) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_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_41_2,plain,
! [U_302,U_301,U_300] :
( ( U_300 = unordered_pair(U_302,U_301)
| ? [U_299] :
( ( ~ in(U_299,U_300)
& ( U_299 = U_301
| U_299 = U_302 ) )
| ( U_299 != U_301
& U_299 != U_302
& in(U_299,U_300) ) ) )
& ( ! [U_298] :
( ( in(U_298,U_300)
| ( U_298 != U_301
& U_298 != U_302 ) )
& ( U_298 = U_301
| U_298 = U_302
| ~ in(U_298,U_300) ) )
| U_300 != unordered_pair(U_302,U_301) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_312,U_310,U_308] :
( U_308 = unordered_pair(U_312,U_310)
| ? [U_306] :
( ~ in(U_306,U_308)
& ( U_306 = U_310
| U_306 = U_312 ) )
| ? [U_305] :
( U_305 != U_310
& U_305 != U_312
& in(U_305,U_308) ) )
& ! [U_311,U_309,U_307] :
( ( ! [U_304] :
( in(U_304,U_307)
| ( U_304 != U_309
& U_304 != U_311 ) )
& ! [U_303] :
( U_303 = U_309
| U_303 = U_311
| ~ in(U_303,U_307) ) )
| U_307 != unordered_pair(U_311,U_309) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_312,U_310,U_308] :
( U_308 = unordered_pair(U_312,U_310)
| ? [U_306] :
( ~ in(U_306,U_308)
& ( U_306 = U_310
| U_306 = U_312 ) )
| ( sK55(U_312,U_310,U_308) != U_310
& sK55(U_312,U_310,U_308) != U_312
& in(sK55(U_312,U_310,U_308),U_308) ) )
& ! [U_311,U_309,U_307] :
( ( ! [U_304] :
( in(U_304,U_307)
| ( U_304 != U_309
& U_304 != U_311 ) )
& ! [U_303] :
( U_303 = U_309
| U_303 = U_311
| ~ in(U_303,U_307) ) )
| U_307 != unordered_pair(U_311,U_309) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_305,sK55(U_312,U_310,U_308))],[f_41_3]) ).
fof(f_41_5,plain,
( ! [U_312,U_310,U_308] :
( U_308 = unordered_pair(U_312,U_310)
| ( ~ in(sK56(U_312,U_310,U_308),U_308)
& ( sK56(U_312,U_310,U_308) = U_310
| sK56(U_312,U_310,U_308) = U_312 ) )
| ( sK55(U_312,U_310,U_308) != U_310
& sK55(U_312,U_310,U_308) != U_312
& in(sK55(U_312,U_310,U_308),U_308) ) )
& ! [U_311,U_309,U_307] :
( ( ! [U_304] :
( in(U_304,U_307)
| ( U_304 != U_309
& U_304 != U_311 ) )
& ! [U_303] :
( U_303 = U_309
| U_303 = U_311
| ~ in(U_303,U_307) ) )
| U_307 != unordered_pair(U_311,U_309) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_306,sK56(U_312,U_310,U_308))],[f_41_4]) ).
fof(f_41_6,plain,
( ! [U_312,U_308,U_310] :
( ~ in(sK56(U_312,U_310,U_308),U_308)
| ~ sP86(U_312,U_308,U_310) )
& ! [U_312,U_308,U_310] :
( sK56(U_312,U_310,U_308) = U_310
| sK56(U_312,U_310,U_308) = U_312
| ~ sP86(U_312,U_308,U_310) )
& ! [U_312,U_308,U_310] :
( sK55(U_312,U_310,U_308) != U_310
| ~ sP85(U_312,U_308,U_310) )
& ! [U_312,U_308,U_310] :
( sK55(U_312,U_310,U_308) != U_312
| ~ sP85(U_312,U_308,U_310) )
& ! [U_312,U_308,U_310] :
( in(sK55(U_312,U_310,U_308),U_308)
| ~ sP85(U_312,U_308,U_310) )
& ! [U_311,U_309,U_304] :
( U_304 != U_309
| ~ sP83(U_311,U_309,U_304) )
& ! [U_311,U_309,U_304] :
( U_304 != U_311
| ~ sP83(U_311,U_309,U_304) )
& ! [U_311,U_309,U_303,U_307,U_304] :
( in(U_304,U_307)
| sP83(U_311,U_309,U_304)
| ~ sP84(U_311,U_309,U_303,U_307,U_304) )
& ! [U_311,U_309,U_303,U_307,U_304] :
( U_303 = U_309
| U_303 = U_311
| ~ in(U_303,U_307)
| ~ sP84(U_311,U_309,U_303,U_307,U_304) )
& ! [U_312,U_308,U_310] :
( U_308 = unordered_pair(U_312,U_310)
| sP86(U_312,U_308,U_310)
| sP85(U_312,U_308,U_310) )
& ! [U_311,U_309,U_303,U_307,U_304] :
( sP84(U_311,U_309,U_303,U_307,U_304)
| U_307 != unordered_pair(U_311,U_309) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83,sP84,sP85,sP86])],[f_41_5]) ).
cnf(f_41_7,plain,
( sP84(U_311,U_309,U_303,U_307,U_304)
| U_307 != unordered_pair(U_311,U_309) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_8,plain,
( U_308 = unordered_pair(U_312,U_310)
| sP86(U_312,U_308,U_310)
| sP85(U_312,U_308,U_310) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_9,plain,
( U_303 = U_309
| U_303 = U_311
| ~ in(U_303,U_307)
| ~ sP84(U_311,U_309,U_303,U_307,U_304) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_10,plain,
( in(U_304,U_307)
| sP83(U_311,U_309,U_304)
| ~ sP84(U_311,U_309,U_303,U_307,U_304) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_11,plain,
( U_304 != U_311
| ~ sP83(U_311,U_309,U_304) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_12,plain,
( U_304 != U_309
| ~ sP83(U_311,U_309,U_304) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_13,plain,
( in(sK55(U_312,U_310,U_308),U_308)
| ~ sP85(U_312,U_308,U_310) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_14,plain,
( sK55(U_312,U_310,U_308) != U_312
| ~ sP85(U_312,U_308,U_310) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_15,plain,
( sK55(U_312,U_310,U_308) != U_310
| ~ sP85(U_312,U_308,U_310) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_16,plain,
( sK56(U_312,U_310,U_308) = U_310
| sK56(U_312,U_310,U_308) = U_312
| ~ sP86(U_312,U_308,U_310) ),
inference(clausify,[status(thm)],[f_41_6]) ).
cnf(f_41_17,plain,
( ~ in(sK56(U_312,U_310,U_308),U_308)
| ~ sP86(U_312,U_308,U_310) ),
inference(clausify,[status(thm)],[f_41_6]) ).
fof(f_42_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_42_2,plain,
! [U_317] :
( ( ( well_founded_relation(U_317)
| ? [U_316] :
( ! [U_315] :
( ~ disjoint(fiber(U_317,U_315),U_316)
| ~ in(U_315,U_316) )
& U_316 != empty_set
& subset(U_316,relation_field(U_317)) ) )
& ( ! [U_314] :
( ? [U_313] :
( disjoint(fiber(U_317,U_313),U_314)
& in(U_313,U_314) )
| U_314 = empty_set
| ~ subset(U_314,relation_field(U_317)) )
| ~ well_founded_relation(U_317) ) )
| ~ relation(U_317) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_317] :
( ( ( well_founded_relation(U_317)
| ? [U_316] :
( ! [U_315] :
( ~ disjoint(fiber(U_317,U_315),U_316)
| ~ in(U_315,U_316) )
& U_316 != empty_set
& subset(U_316,relation_field(U_317)) ) )
& ( ! [U_314] :
( ( disjoint(fiber(U_317,sK57(U_317,U_314)),U_314)
& in(sK57(U_317,U_314),U_314) )
| U_314 = empty_set
| ~ subset(U_314,relation_field(U_317)) )
| ~ well_founded_relation(U_317) ) )
| ~ relation(U_317) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_313,sK57(U_317,U_314))],[f_42_2]) ).
fof(f_42_4,plain,
! [U_317] :
( ( ( well_founded_relation(U_317)
| ( ! [U_315] :
( ~ disjoint(fiber(U_317,U_315),sK58(U_317))
| ~ in(U_315,sK58(U_317)) )
& sK58(U_317) != empty_set
& subset(sK58(U_317),relation_field(U_317)) ) )
& ( ! [U_314] :
( ( disjoint(fiber(U_317,sK57(U_317,U_314)),U_314)
& in(sK57(U_317,U_314),U_314) )
| U_314 = empty_set
| ~ subset(U_314,relation_field(U_317)) )
| ~ well_founded_relation(U_317) ) )
| ~ relation(U_317) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_316,sK58(U_317))],[f_42_3]) ).
fof(f_42_5,plain,
( ! [U_315,U_317] :
( ~ disjoint(fiber(U_317,U_315),sK58(U_317))
| ~ in(U_315,sK58(U_317))
| ~ sP88(U_315,U_317) )
& ! [U_315,U_317] :
( sK58(U_317) != empty_set
| ~ sP88(U_315,U_317) )
& ! [U_315,U_317] :
( subset(sK58(U_317),relation_field(U_317))
| ~ sP88(U_315,U_317) )
& ! [U_317,U_314] :
( disjoint(fiber(U_317,sK57(U_317,U_314)),U_314)
| ~ sP87(U_317,U_314) )
& ! [U_317,U_314] :
( in(sK57(U_317,U_314),U_314)
| ~ sP87(U_317,U_314) )
& ! [U_315,U_317,U_314] :
( well_founded_relation(U_317)
| sP88(U_315,U_317)
| ~ sP89(U_315,U_317,U_314) )
& ! [U_315,U_317,U_314] :
( sP87(U_317,U_314)
| U_314 = empty_set
| ~ subset(U_314,relation_field(U_317))
| ~ well_founded_relation(U_317)
| ~ sP89(U_315,U_317,U_314) )
& ! [U_315,U_317,U_314] :
( sP89(U_315,U_317,U_314)
| ~ relation(U_317) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87,sP88,sP89])],[f_42_4]) ).
cnf(f_42_6,plain,
( sP89(U_315,U_317,U_314)
| ~ relation(U_317) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_7,plain,
( sP87(U_317,U_314)
| U_314 = empty_set
| ~ subset(U_314,relation_field(U_317))
| ~ well_founded_relation(U_317)
| ~ sP89(U_315,U_317,U_314) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_8,plain,
( well_founded_relation(U_317)
| sP88(U_315,U_317)
| ~ sP89(U_315,U_317,U_314) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_9,plain,
( in(sK57(U_317,U_314),U_314)
| ~ sP87(U_317,U_314) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_10,plain,
( disjoint(fiber(U_317,sK57(U_317,U_314)),U_314)
| ~ sP87(U_317,U_314) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_11,plain,
( subset(sK58(U_317),relation_field(U_317))
| ~ sP88(U_315,U_317) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_12,plain,
( sK58(U_317) != empty_set
| ~ sP88(U_315,U_317) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_13,plain,
( ~ disjoint(fiber(U_317,U_315),sK58(U_317))
| ~ in(U_315,sK58(U_317))
| ~ sP88(U_315,U_317) ),
inference(clausify,[status(thm)],[f_42_5]) ).
fof(f_43_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_43_2,plain,
! [U_322,U_321,U_320] :
( ( U_320 = set_union2(U_322,U_321)
| ? [U_319] :
( ( ~ in(U_319,U_320)
& ( in(U_319,U_321)
| in(U_319,U_322) ) )
| ( ~ in(U_319,U_321)
& ~ in(U_319,U_322)
& in(U_319,U_320) ) ) )
& ( ! [U_318] :
( ( in(U_318,U_320)
| ( ~ in(U_318,U_321)
& ~ in(U_318,U_322) ) )
& ( in(U_318,U_321)
| in(U_318,U_322)
| ~ in(U_318,U_320) ) )
| U_320 != set_union2(U_322,U_321) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_332,U_330,U_328] :
( U_328 = set_union2(U_332,U_330)
| ? [U_326] :
( ~ in(U_326,U_328)
& ( in(U_326,U_330)
| in(U_326,U_332) ) )
| ? [U_325] :
( ~ in(U_325,U_330)
& ~ in(U_325,U_332)
& in(U_325,U_328) ) )
& ! [U_331,U_329,U_327] :
( ( ! [U_324] :
( in(U_324,U_327)
| ( ~ in(U_324,U_329)
& ~ in(U_324,U_331) ) )
& ! [U_323] :
( in(U_323,U_329)
| in(U_323,U_331)
| ~ in(U_323,U_327) ) )
| U_327 != set_union2(U_331,U_329) ) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
( ! [U_332,U_330,U_328] :
( U_328 = set_union2(U_332,U_330)
| ? [U_326] :
( ~ in(U_326,U_328)
& ( in(U_326,U_330)
| in(U_326,U_332) ) )
| ( ~ in(sK59(U_332,U_330,U_328),U_330)
& ~ in(sK59(U_332,U_330,U_328),U_332)
& in(sK59(U_332,U_330,U_328),U_328) ) )
& ! [U_331,U_329,U_327] :
( ( ! [U_324] :
( in(U_324,U_327)
| ( ~ in(U_324,U_329)
& ~ in(U_324,U_331) ) )
& ! [U_323] :
( in(U_323,U_329)
| in(U_323,U_331)
| ~ in(U_323,U_327) ) )
| U_327 != set_union2(U_331,U_329) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_325,sK59(U_332,U_330,U_328))],[f_43_3]) ).
fof(f_43_5,plain,
( ! [U_332,U_330,U_328] :
( U_328 = set_union2(U_332,U_330)
| ( ~ in(sK60(U_332,U_330,U_328),U_328)
& ( in(sK60(U_332,U_330,U_328),U_330)
| in(sK60(U_332,U_330,U_328),U_332) ) )
| ( ~ in(sK59(U_332,U_330,U_328),U_330)
& ~ in(sK59(U_332,U_330,U_328),U_332)
& in(sK59(U_332,U_330,U_328),U_328) ) )
& ! [U_331,U_329,U_327] :
( ( ! [U_324] :
( in(U_324,U_327)
| ( ~ in(U_324,U_329)
& ~ in(U_324,U_331) ) )
& ! [U_323] :
( in(U_323,U_329)
| in(U_323,U_331)
| ~ in(U_323,U_327) ) )
| U_327 != set_union2(U_331,U_329) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_326,sK60(U_332,U_330,U_328))],[f_43_4]) ).
fof(f_43_6,plain,
( ! [U_330,U_332,U_328] :
( ~ in(sK60(U_332,U_330,U_328),U_328)
| ~ sP93(U_330,U_332,U_328) )
& ! [U_330,U_332,U_328] :
( in(sK60(U_332,U_330,U_328),U_330)
| in(sK60(U_332,U_330,U_328),U_332)
| ~ sP93(U_330,U_332,U_328) )
& ! [U_330,U_332,U_328] :
( ~ in(sK59(U_332,U_330,U_328),U_330)
| ~ sP92(U_330,U_332,U_328) )
& ! [U_330,U_332,U_328] :
( ~ in(sK59(U_332,U_330,U_328),U_332)
| ~ sP92(U_330,U_332,U_328) )
& ! [U_330,U_332,U_328] :
( in(sK59(U_332,U_330,U_328),U_328)
| ~ sP92(U_330,U_332,U_328) )
& ! [U_324,U_331,U_329] :
( ~ in(U_324,U_329)
| ~ sP90(U_324,U_331,U_329) )
& ! [U_324,U_331,U_329] :
( ~ in(U_324,U_331)
| ~ sP90(U_324,U_331,U_329) )
& ! [U_323,U_324,U_331,U_329,U_327] :
( in(U_324,U_327)
| sP90(U_324,U_331,U_329)
| ~ sP91(U_323,U_324,U_331,U_329,U_327) )
& ! [U_323,U_324,U_331,U_329,U_327] :
( in(U_323,U_329)
| in(U_323,U_331)
| ~ in(U_323,U_327)
| ~ sP91(U_323,U_324,U_331,U_329,U_327) )
& ! [U_330,U_332,U_328] :
( U_328 = set_union2(U_332,U_330)
| sP93(U_330,U_332,U_328)
| sP92(U_330,U_332,U_328) )
& ! [U_323,U_324,U_331,U_329,U_327] :
( sP91(U_323,U_324,U_331,U_329,U_327)
| U_327 != set_union2(U_331,U_329) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90,sP91,sP92,sP93])],[f_43_5]) ).
cnf(f_43_7,plain,
( sP91(U_323,U_324,U_331,U_329,U_327)
| U_327 != set_union2(U_331,U_329) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_8,plain,
( U_328 = set_union2(U_332,U_330)
| sP93(U_330,U_332,U_328)
| sP92(U_330,U_332,U_328) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_9,plain,
( in(U_323,U_329)
| in(U_323,U_331)
| ~ in(U_323,U_327)
| ~ sP91(U_323,U_324,U_331,U_329,U_327) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_10,plain,
( in(U_324,U_327)
| sP90(U_324,U_331,U_329)
| ~ sP91(U_323,U_324,U_331,U_329,U_327) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_11,plain,
( ~ in(U_324,U_331)
| ~ sP90(U_324,U_331,U_329) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_12,plain,
( ~ in(U_324,U_329)
| ~ sP90(U_324,U_331,U_329) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_13,plain,
( in(sK59(U_332,U_330,U_328),U_328)
| ~ sP92(U_330,U_332,U_328) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_14,plain,
( ~ in(sK59(U_332,U_330,U_328),U_332)
| ~ sP92(U_330,U_332,U_328) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_15,plain,
( ~ in(sK59(U_332,U_330,U_328),U_330)
| ~ sP92(U_330,U_332,U_328) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_16,plain,
( in(sK60(U_332,U_330,U_328),U_330)
| in(sK60(U_332,U_330,U_328),U_332)
| ~ sP93(U_330,U_332,U_328) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_17,plain,
( ~ in(sK60(U_332,U_330,U_328),U_328)
| ~ sP93(U_330,U_332,U_328) ),
inference(clausify,[status(thm)],[f_43_6]) ).
fof(f_44_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_44_2,plain,
! [U_345,U_344,U_343] :
( ( U_343 = cartesian_product2(U_345,U_344)
| ? [U_342] :
( ( ~ in(U_342,U_343)
& ? [U_341,U_340] :
( U_342 = ordered_pair(U_341,U_340)
& in(U_340,U_344)
& in(U_341,U_345) ) )
| ( ! [U_339,U_338] :
( U_342 != ordered_pair(U_339,U_338)
| ~ in(U_338,U_344)
| ~ in(U_339,U_345) )
& in(U_342,U_343) ) ) )
& ( ! [U_337] :
( ( in(U_337,U_343)
| ! [U_336,U_335] :
( U_337 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_344)
| ~ in(U_336,U_345) ) )
& ( ? [U_334,U_333] :
( U_337 = ordered_pair(U_334,U_333)
& in(U_333,U_344)
& in(U_334,U_345) )
| ~ in(U_337,U_343) ) )
| U_343 != cartesian_product2(U_345,U_344) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_355,U_353,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| ? [U_349] :
( ~ in(U_349,U_351)
& ? [U_341] :
( ? [U_340] :
( U_349 = ordered_pair(U_341,U_340)
& in(U_340,U_353) )
& in(U_341,U_355) ) )
| ? [U_348] :
( ! [U_339] :
( ! [U_338] :
( U_348 != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353) )
| ~ in(U_339,U_355) )
& in(U_348,U_351) ) )
& ! [U_354,U_352,U_350] :
( ( ! [U_347] :
( in(U_347,U_350)
| ! [U_336] :
( ! [U_335] :
( U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352) )
| ~ in(U_336,U_354) ) )
& ! [U_346] :
( ? [U_334] :
( ? [U_333] :
( U_346 = ordered_pair(U_334,U_333)
& in(U_333,U_352) )
& in(U_334,U_354) )
| ~ in(U_346,U_350) ) )
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
( ! [U_355,U_353,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| ? [U_349] :
( ~ in(U_349,U_351)
& ? [U_341] :
( ? [U_340] :
( U_349 = ordered_pair(U_341,U_340)
& in(U_340,U_353) )
& in(U_341,U_355) ) )
| ? [U_348] :
( ! [U_339] :
( ! [U_338] :
( U_348 != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353) )
| ~ in(U_339,U_355) )
& in(U_348,U_351) ) )
& ! [U_354,U_352,U_350] :
( ( ! [U_347] :
( in(U_347,U_350)
| ! [U_336] :
( ! [U_335] :
( U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352) )
| ~ in(U_336,U_354) ) )
& ! [U_346] :
( ( ? [U_333] :
( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),U_333)
& in(U_333,U_352) )
& in(sK61(U_354,U_352,U_350,U_346),U_354) )
| ~ in(U_346,U_350) ) )
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_334,sK61(U_354,U_352,U_350,U_346))],[f_44_3]) ).
fof(f_44_5,plain,
( ! [U_355,U_353,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| ? [U_349] :
( ~ in(U_349,U_351)
& ? [U_341] :
( ? [U_340] :
( U_349 = ordered_pair(U_341,U_340)
& in(U_340,U_353) )
& in(U_341,U_355) ) )
| ? [U_348] :
( ! [U_339] :
( ! [U_338] :
( U_348 != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353) )
| ~ in(U_339,U_355) )
& in(U_348,U_351) ) )
& ! [U_354,U_352,U_350] :
( ( ! [U_347] :
( in(U_347,U_350)
| ! [U_336] :
( ! [U_335] :
( U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352) )
| ~ in(U_336,U_354) ) )
& ! [U_346] :
( ( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
& in(sK62(U_354,U_352,U_350,U_346),U_352)
& in(sK61(U_354,U_352,U_350,U_346),U_354) )
| ~ in(U_346,U_350) ) )
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_333,sK62(U_354,U_352,U_350,U_346))],[f_44_4]) ).
fof(f_44_6,plain,
( ! [U_355,U_353,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| ? [U_349] :
( ~ in(U_349,U_351)
& ? [U_341] :
( ? [U_340] :
( U_349 = ordered_pair(U_341,U_340)
& in(U_340,U_353) )
& in(U_341,U_355) ) )
| ( ! [U_339] :
( ! [U_338] :
( sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353) )
| ~ in(U_339,U_355) )
& in(sK63(U_355,U_353,U_351),U_351) ) )
& ! [U_354,U_352,U_350] :
( ( ! [U_347] :
( in(U_347,U_350)
| ! [U_336] :
( ! [U_335] :
( U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352) )
| ~ in(U_336,U_354) ) )
& ! [U_346] :
( ( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
& in(sK62(U_354,U_352,U_350,U_346),U_352)
& in(sK61(U_354,U_352,U_350,U_346),U_354) )
| ~ in(U_346,U_350) ) )
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_348,sK63(U_355,U_353,U_351))],[f_44_5]) ).
fof(f_44_7,plain,
( ! [U_355,U_353,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| ( ~ in(sK64(U_355,U_353,U_351),U_351)
& ? [U_341] :
( ? [U_340] :
( sK64(U_355,U_353,U_351) = ordered_pair(U_341,U_340)
& in(U_340,U_353) )
& in(U_341,U_355) ) )
| ( ! [U_339] :
( ! [U_338] :
( sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353) )
| ~ in(U_339,U_355) )
& in(sK63(U_355,U_353,U_351),U_351) ) )
& ! [U_354,U_352,U_350] :
( ( ! [U_347] :
( in(U_347,U_350)
| ! [U_336] :
( ! [U_335] :
( U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352) )
| ~ in(U_336,U_354) ) )
& ! [U_346] :
( ( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
& in(sK62(U_354,U_352,U_350,U_346),U_352)
& in(sK61(U_354,U_352,U_350,U_346),U_354) )
| ~ in(U_346,U_350) ) )
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_349,sK64(U_355,U_353,U_351))],[f_44_6]) ).
fof(f_44_8,plain,
( ! [U_355,U_353,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| ( ~ in(sK64(U_355,U_353,U_351),U_351)
& ? [U_340] :
( sK64(U_355,U_353,U_351) = ordered_pair(sK65(U_355,U_353,U_351),U_340)
& in(U_340,U_353) )
& in(sK65(U_355,U_353,U_351),U_355) )
| ( ! [U_339] :
( ! [U_338] :
( sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353) )
| ~ in(U_339,U_355) )
& in(sK63(U_355,U_353,U_351),U_351) ) )
& ! [U_354,U_352,U_350] :
( ( ! [U_347] :
( in(U_347,U_350)
| ! [U_336] :
( ! [U_335] :
( U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352) )
| ~ in(U_336,U_354) ) )
& ! [U_346] :
( ( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
& in(sK62(U_354,U_352,U_350,U_346),U_352)
& in(sK61(U_354,U_352,U_350,U_346),U_354) )
| ~ in(U_346,U_350) ) )
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_341,sK65(U_355,U_353,U_351))],[f_44_7]) ).
fof(f_44_9,plain,
( ! [U_355,U_353,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| ( ~ in(sK64(U_355,U_353,U_351),U_351)
& sK64(U_355,U_353,U_351) = ordered_pair(sK65(U_355,U_353,U_351),sK66(U_355,U_353,U_351))
& in(sK66(U_355,U_353,U_351),U_353)
& in(sK65(U_355,U_353,U_351),U_355) )
| ( ! [U_339] :
( ! [U_338] :
( sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353) )
| ~ in(U_339,U_355) )
& in(sK63(U_355,U_353,U_351),U_351) ) )
& ! [U_354,U_352,U_350] :
( ( ! [U_347] :
( in(U_347,U_350)
| ! [U_336] :
( ! [U_335] :
( U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352) )
| ~ in(U_336,U_354) ) )
& ! [U_346] :
( ( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
& in(sK62(U_354,U_352,U_350,U_346),U_352)
& in(sK61(U_354,U_352,U_350,U_346),U_354) )
| ~ in(U_346,U_350) ) )
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_340,sK66(U_355,U_353,U_351))],[f_44_8]) ).
fof(f_44_10,plain,
( ! [U_355,U_353,U_351] :
( ~ in(sK64(U_355,U_353,U_351),U_351)
| ~ sP97(U_355,U_353,U_351) )
& ! [U_355,U_353,U_351] :
( sK64(U_355,U_353,U_351) = ordered_pair(sK65(U_355,U_353,U_351),sK66(U_355,U_353,U_351))
| ~ sP97(U_355,U_353,U_351) )
& ! [U_355,U_353,U_351] :
( in(sK66(U_355,U_353,U_351),U_353)
| ~ sP97(U_355,U_353,U_351) )
& ! [U_355,U_353,U_351] :
( in(sK65(U_355,U_353,U_351),U_355)
| ~ sP97(U_355,U_353,U_351) )
& ! [U_355,U_353,U_339,U_338,U_351] :
( sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353)
| ~ in(U_339,U_355)
| ~ sP96(U_355,U_353,U_339,U_338,U_351) )
& ! [U_355,U_353,U_339,U_338,U_351] :
( in(sK63(U_355,U_353,U_351),U_351)
| ~ sP96(U_355,U_353,U_339,U_338,U_351) )
& ! [U_346,U_352,U_350,U_354] :
( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
| ~ sP94(U_346,U_352,U_350,U_354) )
& ! [U_346,U_352,U_350,U_354] :
( in(sK62(U_354,U_352,U_350,U_346),U_352)
| ~ sP94(U_346,U_352,U_350,U_354) )
& ! [U_346,U_352,U_350,U_354] :
( in(sK61(U_354,U_352,U_350,U_346),U_354)
| ~ sP94(U_346,U_352,U_350,U_354) )
& ! [U_336,U_347,U_346,U_335,U_352,U_350,U_354] :
( in(U_347,U_350)
| U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352)
| ~ in(U_336,U_354)
| ~ sP95(U_336,U_347,U_346,U_335,U_352,U_350,U_354) )
& ! [U_336,U_347,U_346,U_335,U_352,U_350,U_354] :
( sP94(U_346,U_352,U_350,U_354)
| ~ in(U_346,U_350)
| ~ sP95(U_336,U_347,U_346,U_335,U_352,U_350,U_354) )
& ! [U_355,U_353,U_339,U_338,U_351] :
( U_351 = cartesian_product2(U_355,U_353)
| sP97(U_355,U_353,U_351)
| sP96(U_355,U_353,U_339,U_338,U_351) )
& ! [U_336,U_347,U_346,U_335,U_352,U_350,U_354] :
( sP95(U_336,U_347,U_346,U_335,U_352,U_350,U_354)
| U_350 != cartesian_product2(U_354,U_352) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94,sP95,sP96,sP97])],[f_44_9]) ).
cnf(f_44_11,plain,
( sP95(U_336,U_347,U_346,U_335,U_352,U_350,U_354)
| U_350 != cartesian_product2(U_354,U_352) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_12,plain,
( U_351 = cartesian_product2(U_355,U_353)
| sP97(U_355,U_353,U_351)
| sP96(U_355,U_353,U_339,U_338,U_351) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_13,plain,
( sP94(U_346,U_352,U_350,U_354)
| ~ in(U_346,U_350)
| ~ sP95(U_336,U_347,U_346,U_335,U_352,U_350,U_354) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_14,plain,
( in(U_347,U_350)
| U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352)
| ~ in(U_336,U_354)
| ~ sP95(U_336,U_347,U_346,U_335,U_352,U_350,U_354) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_15,plain,
( in(sK61(U_354,U_352,U_350,U_346),U_354)
| ~ sP94(U_346,U_352,U_350,U_354) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_16,plain,
( in(sK62(U_354,U_352,U_350,U_346),U_352)
| ~ sP94(U_346,U_352,U_350,U_354) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_17,plain,
( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
| ~ sP94(U_346,U_352,U_350,U_354) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_18,plain,
( in(sK63(U_355,U_353,U_351),U_351)
| ~ sP96(U_355,U_353,U_339,U_338,U_351) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_19,plain,
( sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353)
| ~ in(U_339,U_355)
| ~ sP96(U_355,U_353,U_339,U_338,U_351) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_20,plain,
( in(sK65(U_355,U_353,U_351),U_355)
| ~ sP97(U_355,U_353,U_351) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_21,plain,
( in(sK66(U_355,U_353,U_351),U_353)
| ~ sP97(U_355,U_353,U_351) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_22,plain,
( sK64(U_355,U_353,U_351) = ordered_pair(sK65(U_355,U_353,U_351),sK66(U_355,U_353,U_351))
| ~ sP97(U_355,U_353,U_351) ),
inference(clausify,[status(thm)],[f_44_10]) ).
cnf(f_44_23,plain,
( ~ in(sK64(U_355,U_353,U_351),U_351)
| ~ sP97(U_355,U_353,U_351) ),
inference(clausify,[status(thm)],[f_44_10]) ).
fof(f_45_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_45_2,plain,
! [U_360] :
( ( epsilon_connected(U_360)
| ? [U_359,U_358] :
( ~ in(U_358,U_359)
& U_359 != U_358
& ~ in(U_359,U_358)
& in(U_358,U_360)
& in(U_359,U_360) ) )
& ( ! [U_357,U_356] :
( in(U_356,U_357)
| U_357 = U_356
| in(U_357,U_356)
| ~ in(U_356,U_360)
| ~ in(U_357,U_360) )
| ~ epsilon_connected(U_360) ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_362] :
( epsilon_connected(U_362)
| ? [U_359] :
( ? [U_358] :
( ~ in(U_358,U_359)
& U_359 != U_358
& ~ in(U_359,U_358)
& in(U_358,U_362) )
& in(U_359,U_362) ) )
& ! [U_361] :
( ! [U_357] :
( ! [U_356] :
( in(U_356,U_357)
| U_357 = U_356
| in(U_357,U_356)
| ~ in(U_356,U_361) )
| ~ in(U_357,U_361) )
| ~ epsilon_connected(U_361) ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_362] :
( epsilon_connected(U_362)
| ( ? [U_358] :
( ~ in(U_358,sK67(U_362))
& sK67(U_362) != U_358
& ~ in(sK67(U_362),U_358)
& in(U_358,U_362) )
& in(sK67(U_362),U_362) ) )
& ! [U_361] :
( ! [U_357] :
( ! [U_356] :
( in(U_356,U_357)
| U_357 = U_356
| in(U_357,U_356)
| ~ in(U_356,U_361) )
| ~ in(U_357,U_361) )
| ~ epsilon_connected(U_361) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_359,sK67(U_362))],[f_45_3]) ).
fof(f_45_5,plain,
( ! [U_362] :
( epsilon_connected(U_362)
| ( ~ in(sK68(U_362),sK67(U_362))
& sK67(U_362) != sK68(U_362)
& ~ in(sK67(U_362),sK68(U_362))
& in(sK68(U_362),U_362)
& in(sK67(U_362),U_362) ) )
& ! [U_361] :
( ! [U_357] :
( ! [U_356] :
( in(U_356,U_357)
| U_357 = U_356
| in(U_357,U_356)
| ~ in(U_356,U_361) )
| ~ in(U_357,U_361) )
| ~ epsilon_connected(U_361) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_358,sK68(U_362))],[f_45_4]) ).
fof(f_45_6,plain,
( ! [U_362] :
( ~ in(sK68(U_362),sK67(U_362))
| ~ sP98(U_362) )
& ! [U_362] :
( sK67(U_362) != sK68(U_362)
| ~ sP98(U_362) )
& ! [U_362] :
( ~ in(sK67(U_362),sK68(U_362))
| ~ sP98(U_362) )
& ! [U_362] :
( in(sK68(U_362),U_362)
| ~ sP98(U_362) )
& ! [U_362] :
( in(sK67(U_362),U_362)
| ~ sP98(U_362) )
& ! [U_362] :
( epsilon_connected(U_362)
| sP98(U_362) )
& ! [U_356,U_357,U_361] :
( in(U_356,U_357)
| U_357 = U_356
| in(U_357,U_356)
| ~ in(U_356,U_361)
| ~ in(U_357,U_361)
| ~ epsilon_connected(U_361) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_45_5]) ).
cnf(f_45_7,plain,
( in(U_356,U_357)
| U_357 = U_356
| in(U_357,U_356)
| ~ in(U_356,U_361)
| ~ in(U_357,U_361)
| ~ epsilon_connected(U_361) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_8,plain,
( epsilon_connected(U_362)
| sP98(U_362) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_9,plain,
( in(sK67(U_362),U_362)
| ~ sP98(U_362) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_10,plain,
( in(sK68(U_362),U_362)
| ~ sP98(U_362) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_11,plain,
( ~ in(sK67(U_362),sK68(U_362))
| ~ sP98(U_362) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_12,plain,
( sK67(U_362) != sK68(U_362)
| ~ sP98(U_362) ),
inference(clausify,[status(thm)],[f_45_6]) ).
cnf(f_45_13,plain,
( ~ in(sK68(U_362),sK67(U_362))
| ~ sP98(U_362) ),
inference(clausify,[status(thm)],[f_45_6]) ).
fof(f_46_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_46_2,plain,
! [U_368] :
( ! [U_367] :
( ( ( subset(U_368,U_367)
| ? [U_366,U_365] :
( ~ in(ordered_pair(U_366,U_365),U_367)
& in(ordered_pair(U_366,U_365),U_368) ) )
& ( ! [U_364,U_363] :
( in(ordered_pair(U_364,U_363),U_367)
| ~ in(ordered_pair(U_364,U_363),U_368) )
| ~ subset(U_368,U_367) ) )
| ~ relation(U_367) )
| ~ relation(U_368) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_368] :
( ! [U_367] :
( ( ( subset(U_368,U_367)
| ? [U_365] :
( ~ in(ordered_pair(sK69(U_368,U_367),U_365),U_367)
& in(ordered_pair(sK69(U_368,U_367),U_365),U_368) ) )
& ( ! [U_364,U_363] :
( in(ordered_pair(U_364,U_363),U_367)
| ~ in(ordered_pair(U_364,U_363),U_368) )
| ~ subset(U_368,U_367) ) )
| ~ relation(U_367) )
| ~ relation(U_368) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_366,sK69(U_368,U_367))],[f_46_2]) ).
fof(f_46_4,plain,
! [U_368] :
( ! [U_367] :
( ( ( subset(U_368,U_367)
| ( ~ in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_367)
& in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_368) ) )
& ( ! [U_364,U_363] :
( in(ordered_pair(U_364,U_363),U_367)
| ~ in(ordered_pair(U_364,U_363),U_368) )
| ~ subset(U_368,U_367) ) )
| ~ relation(U_367) )
| ~ relation(U_368) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_365,sK70(U_368,U_367))],[f_46_3]) ).
fof(f_46_5,plain,
( ! [U_367,U_368] :
( ~ in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_367)
| ~ sP99(U_367,U_368) )
& ! [U_367,U_368] :
( in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_368)
| ~ sP99(U_367,U_368) )
& ! [U_367,U_368,U_364,U_363] :
( subset(U_368,U_367)
| sP99(U_367,U_368)
| ~ sP100(U_367,U_368,U_364,U_363) )
& ! [U_367,U_368,U_364,U_363] :
( in(ordered_pair(U_364,U_363),U_367)
| ~ in(ordered_pair(U_364,U_363),U_368)
| ~ subset(U_368,U_367)
| ~ sP100(U_367,U_368,U_364,U_363) )
& ! [U_367,U_368,U_364,U_363] :
( sP100(U_367,U_368,U_364,U_363)
| ~ relation(U_367)
| ~ relation(U_368) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99,sP100])],[f_46_4]) ).
cnf(f_46_6,plain,
( sP100(U_367,U_368,U_364,U_363)
| ~ relation(U_367)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_7,plain,
( in(ordered_pair(U_364,U_363),U_367)
| ~ in(ordered_pair(U_364,U_363),U_368)
| ~ subset(U_368,U_367)
| ~ sP100(U_367,U_368,U_364,U_363) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_8,plain,
( subset(U_368,U_367)
| sP99(U_367,U_368)
| ~ sP100(U_367,U_368,U_364,U_363) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_9,plain,
( in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_368)
| ~ sP99(U_367,U_368) ),
inference(clausify,[status(thm)],[f_46_5]) ).
cnf(f_46_10,plain,
( ~ in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_367)
| ~ sP99(U_367,U_368) ),
inference(clausify,[status(thm)],[f_46_5]) ).
fof(f_47_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_47_2,plain,
! [U_372,U_371] :
( ( subset(U_372,U_371)
| ? [U_370] :
( ~ in(U_370,U_371)
& in(U_370,U_372) ) )
& ( ! [U_369] :
( in(U_369,U_371)
| ~ in(U_369,U_372) )
| ~ subset(U_372,U_371) ) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( ! [U_376,U_374] :
( subset(U_376,U_374)
| ? [U_370] :
( ~ in(U_370,U_374)
& in(U_370,U_376) ) )
& ! [U_375,U_373] :
( ! [U_369] :
( in(U_369,U_373)
| ~ in(U_369,U_375) )
| ~ subset(U_375,U_373) ) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
( ! [U_376,U_374] :
( subset(U_376,U_374)
| ( ~ in(sK71(U_376,U_374),U_374)
& in(sK71(U_376,U_374),U_376) ) )
& ! [U_375,U_373] :
( ! [U_369] :
( in(U_369,U_373)
| ~ in(U_369,U_375) )
| ~ subset(U_375,U_373) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_370,sK71(U_376,U_374))],[f_47_3]) ).
fof(f_47_5,plain,
( ! [U_376,U_374] :
( ~ in(sK71(U_376,U_374),U_374)
| ~ sP101(U_376,U_374) )
& ! [U_376,U_374] :
( in(sK71(U_376,U_374),U_376)
| ~ sP101(U_376,U_374) )
& ! [U_376,U_374] :
( subset(U_376,U_374)
| sP101(U_376,U_374) )
& ! [U_373,U_375,U_369] :
( in(U_369,U_373)
| ~ in(U_369,U_375)
| ~ subset(U_375,U_373) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_47_4]) ).
cnf(f_47_6,plain,
( in(U_369,U_373)
| ~ in(U_369,U_375)
| ~ subset(U_375,U_373) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_7,plain,
( subset(U_376,U_374)
| sP101(U_376,U_374) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_8,plain,
( in(sK71(U_376,U_374),U_376)
| ~ sP101(U_376,U_374) ),
inference(clausify,[status(thm)],[f_47_5]) ).
cnf(f_47_9,plain,
( ~ in(sK71(U_376,U_374),U_374)
| ~ sP101(U_376,U_374) ),
inference(clausify,[status(thm)],[f_47_5]) ).
fof(f_48_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_48_2,plain,
! [U_382] :
( ! [U_381] :
( ( is_well_founded_in(U_382,U_381)
| ? [U_380] :
( ! [U_379] :
( ~ disjoint(fiber(U_382,U_379),U_380)
| ~ in(U_379,U_380) )
& U_380 != empty_set
& subset(U_380,U_381) ) )
& ( ! [U_378] :
( ? [U_377] :
( disjoint(fiber(U_382,U_377),U_378)
& in(U_377,U_378) )
| U_378 = empty_set
| ~ subset(U_378,U_381) )
| ~ is_well_founded_in(U_382,U_381) ) )
| ~ relation(U_382) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_382] :
( ( ! [U_384] :
( is_well_founded_in(U_382,U_384)
| ? [U_380] :
( ! [U_379] :
( ~ disjoint(fiber(U_382,U_379),U_380)
| ~ in(U_379,U_380) )
& U_380 != empty_set
& subset(U_380,U_384) ) )
& ! [U_383] :
( ! [U_378] :
( ? [U_377] :
( disjoint(fiber(U_382,U_377),U_378)
& in(U_377,U_378) )
| U_378 = empty_set
| ~ subset(U_378,U_383) )
| ~ is_well_founded_in(U_382,U_383) ) )
| ~ relation(U_382) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
! [U_382] :
( ( ! [U_384] :
( is_well_founded_in(U_382,U_384)
| ? [U_380] :
( ! [U_379] :
( ~ disjoint(fiber(U_382,U_379),U_380)
| ~ in(U_379,U_380) )
& U_380 != empty_set
& subset(U_380,U_384) ) )
& ! [U_383] :
( ! [U_378] :
( ( disjoint(fiber(U_382,sK72(U_382,U_383,U_378)),U_378)
& in(sK72(U_382,U_383,U_378),U_378) )
| U_378 = empty_set
| ~ subset(U_378,U_383) )
| ~ is_well_founded_in(U_382,U_383) ) )
| ~ relation(U_382) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_377,sK72(U_382,U_383,U_378))],[f_48_3]) ).
fof(f_48_5,plain,
! [U_382] :
( ( ! [U_384] :
( is_well_founded_in(U_382,U_384)
| ( ! [U_379] :
( ~ disjoint(fiber(U_382,U_379),sK73(U_382,U_384))
| ~ in(U_379,sK73(U_382,U_384)) )
& sK73(U_382,U_384) != empty_set
& subset(sK73(U_382,U_384),U_384) ) )
& ! [U_383] :
( ! [U_378] :
( ( disjoint(fiber(U_382,sK72(U_382,U_383,U_378)),U_378)
& in(sK72(U_382,U_383,U_378),U_378) )
| U_378 = empty_set
| ~ subset(U_378,U_383) )
| ~ is_well_founded_in(U_382,U_383) ) )
| ~ relation(U_382) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_380,sK73(U_382,U_384))],[f_48_4]) ).
fof(f_48_6,plain,
( ! [U_379,U_382,U_384] :
( ~ disjoint(fiber(U_382,U_379),sK73(U_382,U_384))
| ~ in(U_379,sK73(U_382,U_384))
| ~ sP103(U_379,U_382,U_384) )
& ! [U_379,U_382,U_384] :
( sK73(U_382,U_384) != empty_set
| ~ sP103(U_379,U_382,U_384) )
& ! [U_379,U_382,U_384] :
( subset(sK73(U_382,U_384),U_384)
| ~ sP103(U_379,U_382,U_384) )
& ! [U_378,U_382,U_383] :
( disjoint(fiber(U_382,sK72(U_382,U_383,U_378)),U_378)
| ~ sP102(U_378,U_382,U_383) )
& ! [U_378,U_382,U_383] :
( in(sK72(U_382,U_383,U_378),U_378)
| ~ sP102(U_378,U_382,U_383) )
& ! [U_378,U_379,U_382,U_383,U_384] :
( is_well_founded_in(U_382,U_384)
| sP103(U_379,U_382,U_384)
| ~ sP104(U_378,U_379,U_382,U_383,U_384) )
& ! [U_378,U_379,U_382,U_383,U_384] :
( sP102(U_378,U_382,U_383)
| U_378 = empty_set
| ~ subset(U_378,U_383)
| ~ is_well_founded_in(U_382,U_383)
| ~ sP104(U_378,U_379,U_382,U_383,U_384) )
& ! [U_378,U_379,U_382,U_383,U_384] :
( sP104(U_378,U_379,U_382,U_383,U_384)
| ~ relation(U_382) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102,sP103,sP104])],[f_48_5]) ).
cnf(f_48_7,plain,
( sP104(U_378,U_379,U_382,U_383,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_48_6]) ).
cnf(f_48_8,plain,
( sP102(U_378,U_382,U_383)
| U_378 = empty_set
| ~ subset(U_378,U_383)
| ~ is_well_founded_in(U_382,U_383)
| ~ sP104(U_378,U_379,U_382,U_383,U_384) ),
inference(clausify,[status(thm)],[f_48_6]) ).
cnf(f_48_9,plain,
( is_well_founded_in(U_382,U_384)
| sP103(U_379,U_382,U_384)
| ~ sP104(U_378,U_379,U_382,U_383,U_384) ),
inference(clausify,[status(thm)],[f_48_6]) ).
cnf(f_48_10,plain,
( in(sK72(U_382,U_383,U_378),U_378)
| ~ sP102(U_378,U_382,U_383) ),
inference(clausify,[status(thm)],[f_48_6]) ).
cnf(f_48_11,plain,
( disjoint(fiber(U_382,sK72(U_382,U_383,U_378)),U_378)
| ~ sP102(U_378,U_382,U_383) ),
inference(clausify,[status(thm)],[f_48_6]) ).
cnf(f_48_12,plain,
( subset(sK73(U_382,U_384),U_384)
| ~ sP103(U_379,U_382,U_384) ),
inference(clausify,[status(thm)],[f_48_6]) ).
cnf(f_48_13,plain,
( sK73(U_382,U_384) != empty_set
| ~ sP103(U_379,U_382,U_384) ),
inference(clausify,[status(thm)],[f_48_6]) ).
cnf(f_48_14,plain,
( ~ disjoint(fiber(U_382,U_379),sK73(U_382,U_384))
| ~ in(U_379,sK73(U_382,U_384))
| ~ sP103(U_379,U_382,U_384) ),
inference(clausify,[status(thm)],[f_48_6]) ).
fof(f_49_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_49_2,plain,
! [U_389,U_388,U_387] :
( ( U_387 = set_intersection2(U_389,U_388)
| ? [U_386] :
( ( ~ in(U_386,U_387)
& in(U_386,U_388)
& in(U_386,U_389) )
| ( ( ~ in(U_386,U_388)
| ~ in(U_386,U_389) )
& in(U_386,U_387) ) ) )
& ( ! [U_385] :
( ( in(U_385,U_387)
| ~ in(U_385,U_388)
| ~ in(U_385,U_389) )
& ( ( in(U_385,U_388)
& in(U_385,U_389) )
| ~ in(U_385,U_387) ) )
| U_387 != set_intersection2(U_389,U_388) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_399,U_397,U_395] :
( U_395 = set_intersection2(U_399,U_397)
| ? [U_393] :
( ~ in(U_393,U_395)
& in(U_393,U_397)
& in(U_393,U_399) )
| ? [U_392] :
( ( ~ in(U_392,U_397)
| ~ in(U_392,U_399) )
& in(U_392,U_395) ) )
& ! [U_398,U_396,U_394] :
( ( ! [U_391] :
( in(U_391,U_394)
| ~ in(U_391,U_396)
| ~ in(U_391,U_398) )
& ! [U_390] :
( ( in(U_390,U_396)
& in(U_390,U_398) )
| ~ in(U_390,U_394) ) )
| U_394 != set_intersection2(U_398,U_396) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_399,U_397,U_395] :
( U_395 = set_intersection2(U_399,U_397)
| ? [U_393] :
( ~ in(U_393,U_395)
& in(U_393,U_397)
& in(U_393,U_399) )
| ( ( ~ in(sK74(U_399,U_397,U_395),U_397)
| ~ in(sK74(U_399,U_397,U_395),U_399) )
& in(sK74(U_399,U_397,U_395),U_395) ) )
& ! [U_398,U_396,U_394] :
( ( ! [U_391] :
( in(U_391,U_394)
| ~ in(U_391,U_396)
| ~ in(U_391,U_398) )
& ! [U_390] :
( ( in(U_390,U_396)
& in(U_390,U_398) )
| ~ in(U_390,U_394) ) )
| U_394 != set_intersection2(U_398,U_396) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_392,sK74(U_399,U_397,U_395))],[f_49_3]) ).
fof(f_49_5,plain,
( ! [U_399,U_397,U_395] :
( U_395 = set_intersection2(U_399,U_397)
| ( ~ in(sK75(U_399,U_397,U_395),U_395)
& in(sK75(U_399,U_397,U_395),U_397)
& in(sK75(U_399,U_397,U_395),U_399) )
| ( ( ~ in(sK74(U_399,U_397,U_395),U_397)
| ~ in(sK74(U_399,U_397,U_395),U_399) )
& in(sK74(U_399,U_397,U_395),U_395) ) )
& ! [U_398,U_396,U_394] :
( ( ! [U_391] :
( in(U_391,U_394)
| ~ in(U_391,U_396)
| ~ in(U_391,U_398) )
& ! [U_390] :
( ( in(U_390,U_396)
& in(U_390,U_398) )
| ~ in(U_390,U_394) ) )
| U_394 != set_intersection2(U_398,U_396) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_393,sK75(U_399,U_397,U_395))],[f_49_4]) ).
fof(f_49_6,plain,
( ! [U_397,U_399,U_395] :
( ~ in(sK75(U_399,U_397,U_395),U_395)
| ~ sP108(U_397,U_399,U_395) )
& ! [U_397,U_399,U_395] :
( in(sK75(U_399,U_397,U_395),U_397)
| ~ sP108(U_397,U_399,U_395) )
& ! [U_397,U_399,U_395] :
( in(sK75(U_399,U_397,U_395),U_399)
| ~ sP108(U_397,U_399,U_395) )
& ! [U_397,U_399,U_395] :
( ~ in(sK74(U_399,U_397,U_395),U_397)
| ~ in(sK74(U_399,U_397,U_395),U_399)
| ~ sP107(U_397,U_399,U_395) )
& ! [U_397,U_399,U_395] :
( in(sK74(U_399,U_397,U_395),U_395)
| ~ sP107(U_397,U_399,U_395) )
& ! [U_390,U_396,U_398] :
( in(U_390,U_396)
| ~ sP105(U_390,U_396,U_398) )
& ! [U_390,U_396,U_398] :
( in(U_390,U_398)
| ~ sP105(U_390,U_396,U_398) )
& ! [U_390,U_394,U_391,U_396,U_398] :
( in(U_391,U_394)
| ~ in(U_391,U_396)
| ~ in(U_391,U_398)
| ~ sP106(U_390,U_394,U_391,U_396,U_398) )
& ! [U_390,U_394,U_391,U_396,U_398] :
( sP105(U_390,U_396,U_398)
| ~ in(U_390,U_394)
| ~ sP106(U_390,U_394,U_391,U_396,U_398) )
& ! [U_397,U_399,U_395] :
( U_395 = set_intersection2(U_399,U_397)
| sP108(U_397,U_399,U_395)
| sP107(U_397,U_399,U_395) )
& ! [U_390,U_394,U_391,U_396,U_398] :
( sP106(U_390,U_394,U_391,U_396,U_398)
| U_394 != set_intersection2(U_398,U_396) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105,sP106,sP107,sP108])],[f_49_5]) ).
cnf(f_49_7,plain,
( sP106(U_390,U_394,U_391,U_396,U_398)
| U_394 != set_intersection2(U_398,U_396) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_8,plain,
( U_395 = set_intersection2(U_399,U_397)
| sP108(U_397,U_399,U_395)
| sP107(U_397,U_399,U_395) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_9,plain,
( sP105(U_390,U_396,U_398)
| ~ in(U_390,U_394)
| ~ sP106(U_390,U_394,U_391,U_396,U_398) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_10,plain,
( in(U_391,U_394)
| ~ in(U_391,U_396)
| ~ in(U_391,U_398)
| ~ sP106(U_390,U_394,U_391,U_396,U_398) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_11,plain,
( in(U_390,U_398)
| ~ sP105(U_390,U_396,U_398) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_12,plain,
( in(U_390,U_396)
| ~ sP105(U_390,U_396,U_398) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_13,plain,
( in(sK74(U_399,U_397,U_395),U_395)
| ~ sP107(U_397,U_399,U_395) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_14,plain,
( ~ in(sK74(U_399,U_397,U_395),U_397)
| ~ in(sK74(U_399,U_397,U_395),U_399)
| ~ sP107(U_397,U_399,U_395) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_15,plain,
( in(sK75(U_399,U_397,U_395),U_399)
| ~ sP108(U_397,U_399,U_395) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_16,plain,
( in(sK75(U_399,U_397,U_395),U_397)
| ~ sP108(U_397,U_399,U_395) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_17,plain,
( ~ in(sK75(U_399,U_397,U_395),U_395)
| ~ sP108(U_397,U_399,U_395) ),
inference(clausify,[status(thm)],[f_49_6]) ).
fof(f_50_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_50_2,plain,
! [U_402] :
( ! [U_401,U_400] :
( ( ( ( U_400 = apply(U_402,U_401)
| U_400 != empty_set )
& ( U_400 = empty_set
| U_400 != apply(U_402,U_401) ) )
| in(U_401,relation_dom(U_402)) )
& ( ( ( U_400 = apply(U_402,U_401)
| ~ in(ordered_pair(U_401,U_400),U_402) )
& ( in(ordered_pair(U_401,U_400),U_402)
| U_400 != apply(U_402,U_401) ) )
| ~ in(U_401,relation_dom(U_402)) ) )
| ~ function(U_402)
| ~ relation(U_402) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_402] :
( ( ! [U_410] :
( ( ! [U_408] :
( U_408 = apply(U_402,U_410)
| U_408 != empty_set )
& ! [U_407] :
( U_407 = empty_set
| U_407 != apply(U_402,U_410) ) )
| in(U_410,relation_dom(U_402)) )
& ! [U_409] :
( ( ! [U_406] :
( U_406 = apply(U_402,U_409)
| ~ in(ordered_pair(U_409,U_406),U_402) )
& ! [U_405] :
( in(ordered_pair(U_409,U_405),U_402)
| U_405 != apply(U_402,U_409) ) )
| ~ in(U_409,relation_dom(U_402)) ) )
| ~ function(U_402)
| ~ relation(U_402) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
( ! [U_408,U_407,U_410,U_402] :
( U_408 = apply(U_402,U_410)
| U_408 != empty_set
| ~ sP110(U_408,U_407,U_410,U_402) )
& ! [U_408,U_407,U_410,U_402] :
( U_407 = empty_set
| U_407 != apply(U_402,U_410)
| ~ sP110(U_408,U_407,U_410,U_402) )
& ! [U_409,U_405,U_406,U_402] :
( U_406 = apply(U_402,U_409)
| ~ in(ordered_pair(U_409,U_406),U_402)
| ~ sP109(U_409,U_405,U_406,U_402) )
& ! [U_409,U_405,U_406,U_402] :
( in(ordered_pair(U_409,U_405),U_402)
| U_405 != apply(U_402,U_409)
| ~ sP109(U_409,U_405,U_406,U_402) )
& ! [U_409,U_405,U_408,U_407,U_406,U_410,U_402] :
( sP110(U_408,U_407,U_410,U_402)
| in(U_410,relation_dom(U_402))
| ~ sP111(U_409,U_405,U_408,U_407,U_406,U_410,U_402) )
& ! [U_409,U_405,U_408,U_407,U_406,U_410,U_402] :
( sP109(U_409,U_405,U_406,U_402)
| ~ in(U_409,relation_dom(U_402))
| ~ sP111(U_409,U_405,U_408,U_407,U_406,U_410,U_402) )
& ! [U_409,U_405,U_408,U_407,U_406,U_410,U_402] :
( sP111(U_409,U_405,U_408,U_407,U_406,U_410,U_402)
| ~ function(U_402)
| ~ relation(U_402) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109,sP110,sP111])],[f_50_3]) ).
cnf(f_50_5,plain,
( sP111(U_409,U_405,U_408,U_407,U_406,U_410,U_402)
| ~ function(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_6,plain,
( sP109(U_409,U_405,U_406,U_402)
| ~ in(U_409,relation_dom(U_402))
| ~ sP111(U_409,U_405,U_408,U_407,U_406,U_410,U_402) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_7,plain,
( sP110(U_408,U_407,U_410,U_402)
| in(U_410,relation_dom(U_402))
| ~ sP111(U_409,U_405,U_408,U_407,U_406,U_410,U_402) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_8,plain,
( in(ordered_pair(U_409,U_405),U_402)
| U_405 != apply(U_402,U_409)
| ~ sP109(U_409,U_405,U_406,U_402) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_9,plain,
( U_406 = apply(U_402,U_409)
| ~ in(ordered_pair(U_409,U_406),U_402)
| ~ sP109(U_409,U_405,U_406,U_402) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_10,plain,
( U_407 = empty_set
| U_407 != apply(U_402,U_410)
| ~ sP110(U_408,U_407,U_410,U_402) ),
inference(clausify,[status(thm)],[f_50_4]) ).
cnf(f_50_11,plain,
( U_408 = apply(U_402,U_410)
| U_408 != empty_set
| ~ sP110(U_408,U_407,U_410,U_402) ),
inference(clausify,[status(thm)],[f_50_4]) ).
fof(f_51_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_51_2,plain,
! [U_411] :
( ( ordinal(U_411)
| ~ epsilon_connected(U_411)
| ~ epsilon_transitive(U_411) )
& ( ( epsilon_connected(U_411)
& epsilon_transitive(U_411) )
| ~ ordinal(U_411) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_413] :
( ordinal(U_413)
| ~ epsilon_connected(U_413)
| ~ epsilon_transitive(U_413) )
& ! [U_412] :
( ( epsilon_connected(U_412)
& epsilon_transitive(U_412) )
| ~ ordinal(U_412) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_412] :
( epsilon_connected(U_412)
| ~ sP112(U_412) )
& ! [U_412] :
( epsilon_transitive(U_412)
| ~ sP112(U_412) )
& ! [U_413] :
( ordinal(U_413)
| ~ epsilon_connected(U_413)
| ~ epsilon_transitive(U_413) )
& ! [U_412] :
( sP112(U_412)
| ~ ordinal(U_412) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_51_3]) ).
cnf(f_51_5,plain,
( sP112(U_412)
| ~ ordinal(U_412) ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,plain,
( ordinal(U_413)
| ~ epsilon_connected(U_413)
| ~ epsilon_transitive(U_413) ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_7,plain,
( epsilon_transitive(U_412)
| ~ sP112(U_412) ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_8,plain,
( epsilon_connected(U_412)
| ~ sP112(U_412) ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_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_52_2,plain,
! [U_421] :
( ! [U_420] :
( ( U_420 = relation_dom(U_421)
| ? [U_419] :
( ( ~ in(U_419,U_420)
& ? [U_418] : in(ordered_pair(U_419,U_418),U_421) )
| ( ! [U_417] : ~ in(ordered_pair(U_419,U_417),U_421)
& in(U_419,U_420) ) ) )
& ( ! [U_416] :
( ( in(U_416,U_420)
| ! [U_415] : ~ in(ordered_pair(U_416,U_415),U_421) )
& ( ? [U_414] : in(ordered_pair(U_416,U_414),U_421)
| ~ in(U_416,U_420) ) )
| U_420 != relation_dom(U_421) ) )
| ~ relation(U_421) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_421] :
( ( ! [U_427] :
( U_427 = relation_dom(U_421)
| ? [U_425] :
( ~ in(U_425,U_427)
& ? [U_418] : in(ordered_pair(U_425,U_418),U_421) )
| ? [U_424] :
( ! [U_417] : ~ in(ordered_pair(U_424,U_417),U_421)
& in(U_424,U_427) ) )
& ! [U_426] :
( ( ! [U_423] :
( in(U_423,U_426)
| ! [U_415] : ~ in(ordered_pair(U_423,U_415),U_421) )
& ! [U_422] :
( ? [U_414] : in(ordered_pair(U_422,U_414),U_421)
| ~ in(U_422,U_426) ) )
| U_426 != relation_dom(U_421) ) )
| ~ relation(U_421) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
! [U_421] :
( ( ! [U_427] :
( U_427 = relation_dom(U_421)
| ? [U_425] :
( ~ in(U_425,U_427)
& ? [U_418] : in(ordered_pair(U_425,U_418),U_421) )
| ? [U_424] :
( ! [U_417] : ~ in(ordered_pair(U_424,U_417),U_421)
& in(U_424,U_427) ) )
& ! [U_426] :
( ( ! [U_423] :
( in(U_423,U_426)
| ! [U_415] : ~ in(ordered_pair(U_423,U_415),U_421) )
& ! [U_422] :
( in(ordered_pair(U_422,sK76(U_421,U_426,U_422)),U_421)
| ~ in(U_422,U_426) ) )
| U_426 != relation_dom(U_421) ) )
| ~ relation(U_421) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_414,sK76(U_421,U_426,U_422))],[f_52_3]) ).
fof(f_52_5,plain,
! [U_421] :
( ( ! [U_427] :
( U_427 = relation_dom(U_421)
| ? [U_425] :
( ~ in(U_425,U_427)
& ? [U_418] : in(ordered_pair(U_425,U_418),U_421) )
| ( ! [U_417] : ~ in(ordered_pair(sK77(U_421,U_427),U_417),U_421)
& in(sK77(U_421,U_427),U_427) ) )
& ! [U_426] :
( ( ! [U_423] :
( in(U_423,U_426)
| ! [U_415] : ~ in(ordered_pair(U_423,U_415),U_421) )
& ! [U_422] :
( in(ordered_pair(U_422,sK76(U_421,U_426,U_422)),U_421)
| ~ in(U_422,U_426) ) )
| U_426 != relation_dom(U_421) ) )
| ~ relation(U_421) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_424,sK77(U_421,U_427))],[f_52_4]) ).
fof(f_52_6,plain,
! [U_421] :
( ( ! [U_427] :
( U_427 = relation_dom(U_421)
| ( ~ in(sK78(U_421,U_427),U_427)
& ? [U_418] : in(ordered_pair(sK78(U_421,U_427),U_418),U_421) )
| ( ! [U_417] : ~ in(ordered_pair(sK77(U_421,U_427),U_417),U_421)
& in(sK77(U_421,U_427),U_427) ) )
& ! [U_426] :
( ( ! [U_423] :
( in(U_423,U_426)
| ! [U_415] : ~ in(ordered_pair(U_423,U_415),U_421) )
& ! [U_422] :
( in(ordered_pair(U_422,sK76(U_421,U_426,U_422)),U_421)
| ~ in(U_422,U_426) ) )
| U_426 != relation_dom(U_421) ) )
| ~ relation(U_421) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_425,sK78(U_421,U_427))],[f_52_5]) ).
fof(f_52_7,plain,
! [U_421] :
( ( ! [U_427] :
( U_427 = relation_dom(U_421)
| ( ~ in(sK78(U_421,U_427),U_427)
& in(ordered_pair(sK78(U_421,U_427),sK79(U_421,U_427)),U_421) )
| ( ! [U_417] : ~ in(ordered_pair(sK77(U_421,U_427),U_417),U_421)
& in(sK77(U_421,U_427),U_427) ) )
& ! [U_426] :
( ( ! [U_423] :
( in(U_423,U_426)
| ! [U_415] : ~ in(ordered_pair(U_423,U_415),U_421) )
& ! [U_422] :
( in(ordered_pair(U_422,sK76(U_421,U_426,U_422)),U_421)
| ~ in(U_422,U_426) ) )
| U_426 != relation_dom(U_421) ) )
| ~ relation(U_421) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_418,sK79(U_421,U_427))],[f_52_6]) ).
fof(f_52_8,plain,
( ! [U_427,U_421] :
( ~ in(sK78(U_421,U_427),U_427)
| ~ sP115(U_427,U_421) )
& ! [U_427,U_421] :
( in(ordered_pair(sK78(U_421,U_427),sK79(U_421,U_427)),U_421)
| ~ sP115(U_427,U_421) )
& ! [U_427,U_417,U_421] :
( ~ in(ordered_pair(sK77(U_421,U_427),U_417),U_421)
| ~ sP114(U_427,U_417,U_421) )
& ! [U_427,U_417,U_421] :
( in(sK77(U_421,U_427),U_427)
| ~ sP114(U_427,U_417,U_421) )
& ! [U_422,U_423,U_426,U_421,U_415] :
( in(U_423,U_426)
| ~ in(ordered_pair(U_423,U_415),U_421)
| ~ sP113(U_422,U_423,U_426,U_421,U_415) )
& ! [U_422,U_423,U_426,U_421,U_415] :
( in(ordered_pair(U_422,sK76(U_421,U_426,U_422)),U_421)
| ~ in(U_422,U_426)
| ~ sP113(U_422,U_423,U_426,U_421,U_415) )
& ! [U_422,U_423,U_427,U_417,U_426,U_421,U_415] :
( U_427 = relation_dom(U_421)
| sP115(U_427,U_421)
| sP114(U_427,U_417,U_421)
| ~ sP116(U_422,U_423,U_427,U_417,U_426,U_421,U_415) )
& ! [U_422,U_423,U_427,U_417,U_426,U_421,U_415] :
( sP113(U_422,U_423,U_426,U_421,U_415)
| U_426 != relation_dom(U_421)
| ~ sP116(U_422,U_423,U_427,U_417,U_426,U_421,U_415) )
& ! [U_422,U_423,U_427,U_417,U_426,U_421,U_415] :
( sP116(U_422,U_423,U_427,U_417,U_426,U_421,U_415)
| ~ relation(U_421) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113,sP114,sP115,sP116])],[f_52_7]) ).
cnf(f_52_9,plain,
( sP116(U_422,U_423,U_427,U_417,U_426,U_421,U_415)
| ~ relation(U_421) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_10,plain,
( sP113(U_422,U_423,U_426,U_421,U_415)
| U_426 != relation_dom(U_421)
| ~ sP116(U_422,U_423,U_427,U_417,U_426,U_421,U_415) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_11,plain,
( U_427 = relation_dom(U_421)
| sP115(U_427,U_421)
| sP114(U_427,U_417,U_421)
| ~ sP116(U_422,U_423,U_427,U_417,U_426,U_421,U_415) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_12,plain,
( in(ordered_pair(U_422,sK76(U_421,U_426,U_422)),U_421)
| ~ in(U_422,U_426)
| ~ sP113(U_422,U_423,U_426,U_421,U_415) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_13,plain,
( in(U_423,U_426)
| ~ in(ordered_pair(U_423,U_415),U_421)
| ~ sP113(U_422,U_423,U_426,U_421,U_415) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_14,plain,
( in(sK77(U_421,U_427),U_427)
| ~ sP114(U_427,U_417,U_421) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_15,plain,
( ~ in(ordered_pair(sK77(U_421,U_427),U_417),U_421)
| ~ sP114(U_427,U_417,U_421) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_16,plain,
( in(ordered_pair(sK78(U_421,U_427),sK79(U_421,U_427)),U_421)
| ~ sP115(U_427,U_421) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_17,plain,
( ~ in(sK78(U_421,U_427),U_427)
| ~ sP115(U_427,U_421) ),
inference(clausify,[status(thm)],[f_52_8]) ).
fof(f_53_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_53_2,plain,
! [U_433] :
( ! [U_432] :
( ( is_antisymmetric_in(U_433,U_432)
| ? [U_431,U_430] :
( U_431 != U_430
& in(ordered_pair(U_430,U_431),U_433)
& in(ordered_pair(U_431,U_430),U_433)
& in(U_430,U_432)
& in(U_431,U_432) ) )
& ( ! [U_429,U_428] :
( U_429 = U_428
| ~ in(ordered_pair(U_428,U_429),U_433)
| ~ in(ordered_pair(U_429,U_428),U_433)
| ~ in(U_428,U_432)
| ~ in(U_429,U_432) )
| ~ is_antisymmetric_in(U_433,U_432) ) )
| ~ relation(U_433) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_433] :
( ( ! [U_435] :
( is_antisymmetric_in(U_433,U_435)
| ? [U_431,U_430] :
( U_431 != U_430
& in(ordered_pair(U_430,U_431),U_433)
& in(ordered_pair(U_431,U_430),U_433)
& in(U_430,U_435)
& in(U_431,U_435) ) )
& ! [U_434] :
( ! [U_429,U_428] :
( U_429 = U_428
| ~ in(ordered_pair(U_428,U_429),U_433)
| ~ in(ordered_pair(U_429,U_428),U_433)
| ~ in(U_428,U_434)
| ~ in(U_429,U_434) )
| ~ is_antisymmetric_in(U_433,U_434) ) )
| ~ relation(U_433) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
! [U_433] :
( ( ! [U_435] :
( is_antisymmetric_in(U_433,U_435)
| ? [U_430] :
( sK80(U_433,U_435) != U_430
& in(ordered_pair(U_430,sK80(U_433,U_435)),U_433)
& in(ordered_pair(sK80(U_433,U_435),U_430),U_433)
& in(U_430,U_435)
& in(sK80(U_433,U_435),U_435) ) )
& ! [U_434] :
( ! [U_429,U_428] :
( U_429 = U_428
| ~ in(ordered_pair(U_428,U_429),U_433)
| ~ in(ordered_pair(U_429,U_428),U_433)
| ~ in(U_428,U_434)
| ~ in(U_429,U_434) )
| ~ is_antisymmetric_in(U_433,U_434) ) )
| ~ relation(U_433) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_431,sK80(U_433,U_435))],[f_53_3]) ).
fof(f_53_5,plain,
! [U_433] :
( ( ! [U_435] :
( is_antisymmetric_in(U_433,U_435)
| ( sK80(U_433,U_435) != sK81(U_433,U_435)
& in(ordered_pair(sK81(U_433,U_435),sK80(U_433,U_435)),U_433)
& in(ordered_pair(sK80(U_433,U_435),sK81(U_433,U_435)),U_433)
& in(sK81(U_433,U_435),U_435)
& in(sK80(U_433,U_435),U_435) ) )
& ! [U_434] :
( ! [U_429,U_428] :
( U_429 = U_428
| ~ in(ordered_pair(U_428,U_429),U_433)
| ~ in(ordered_pair(U_429,U_428),U_433)
| ~ in(U_428,U_434)
| ~ in(U_429,U_434) )
| ~ is_antisymmetric_in(U_433,U_434) ) )
| ~ relation(U_433) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_430,sK81(U_433,U_435))],[f_53_4]) ).
fof(f_53_6,plain,
( ! [U_435,U_433] :
( sK80(U_433,U_435) != sK81(U_433,U_435)
| ~ sP117(U_435,U_433) )
& ! [U_435,U_433] :
( in(ordered_pair(sK81(U_433,U_435),sK80(U_433,U_435)),U_433)
| ~ sP117(U_435,U_433) )
& ! [U_435,U_433] :
( in(ordered_pair(sK80(U_433,U_435),sK81(U_433,U_435)),U_433)
| ~ sP117(U_435,U_433) )
& ! [U_435,U_433] :
( in(sK81(U_433,U_435),U_435)
| ~ sP117(U_435,U_433) )
& ! [U_435,U_433] :
( in(sK80(U_433,U_435),U_435)
| ~ sP117(U_435,U_433) )
& ! [U_434,U_435,U_433,U_429,U_428] :
( is_antisymmetric_in(U_433,U_435)
| sP117(U_435,U_433)
| ~ sP118(U_434,U_435,U_433,U_429,U_428) )
& ! [U_434,U_435,U_433,U_429,U_428] :
( U_429 = U_428
| ~ in(ordered_pair(U_428,U_429),U_433)
| ~ in(ordered_pair(U_429,U_428),U_433)
| ~ in(U_428,U_434)
| ~ in(U_429,U_434)
| ~ is_antisymmetric_in(U_433,U_434)
| ~ sP118(U_434,U_435,U_433,U_429,U_428) )
& ! [U_434,U_435,U_433,U_429,U_428] :
( sP118(U_434,U_435,U_433,U_429,U_428)
| ~ relation(U_433) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117,sP118])],[f_53_5]) ).
cnf(f_53_7,plain,
( sP118(U_434,U_435,U_433,U_429,U_428)
| ~ relation(U_433) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_8,plain,
( U_429 = U_428
| ~ in(ordered_pair(U_428,U_429),U_433)
| ~ in(ordered_pair(U_429,U_428),U_433)
| ~ in(U_428,U_434)
| ~ in(U_429,U_434)
| ~ is_antisymmetric_in(U_433,U_434)
| ~ sP118(U_434,U_435,U_433,U_429,U_428) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_9,plain,
( is_antisymmetric_in(U_433,U_435)
| sP117(U_435,U_433)
| ~ sP118(U_434,U_435,U_433,U_429,U_428) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_10,plain,
( in(sK80(U_433,U_435),U_435)
| ~ sP117(U_435,U_433) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_11,plain,
( in(sK81(U_433,U_435),U_435)
| ~ sP117(U_435,U_433) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_12,plain,
( in(ordered_pair(sK80(U_433,U_435),sK81(U_433,U_435)),U_433)
| ~ sP117(U_435,U_433) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_13,plain,
( in(ordered_pair(sK81(U_433,U_435),sK80(U_433,U_435)),U_433)
| ~ sP117(U_435,U_433) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_14,plain,
( sK80(U_433,U_435) != sK81(U_433,U_435)
| ~ sP117(U_435,U_433) ),
inference(clausify,[status(thm)],[f_53_6]) ).
fof(f_54_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_54_2,plain,
! [U_436] : cast_to_subset(U_436) = U_436,
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_436] : cast_to_subset(U_436) = U_436,
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
cast_to_subset(U_436) = U_436,
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_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_55_2,plain,
! [U_444,U_443] :
( ( U_443 = union(U_444)
| ? [U_442] :
( ( ~ in(U_442,U_443)
& ? [U_441] :
( in(U_441,U_444)
& in(U_442,U_441) ) )
| ( ! [U_440] :
( ~ in(U_440,U_444)
| ~ in(U_442,U_440) )
& in(U_442,U_443) ) ) )
& ( ! [U_439] :
( ( in(U_439,U_443)
| ! [U_438] :
( ~ in(U_438,U_444)
| ~ in(U_439,U_438) ) )
& ( ? [U_437] :
( in(U_437,U_444)
& in(U_439,U_437) )
| ~ in(U_439,U_443) ) )
| U_443 != union(U_444) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_452,U_450] :
( U_450 = union(U_452)
| ? [U_448] :
( ~ in(U_448,U_450)
& ? [U_441] :
( in(U_441,U_452)
& in(U_448,U_441) ) )
| ? [U_447] :
( ! [U_440] :
( ~ in(U_440,U_452)
| ~ in(U_447,U_440) )
& in(U_447,U_450) ) )
& ! [U_451,U_449] :
( ( ! [U_446] :
( in(U_446,U_449)
| ! [U_438] :
( ~ in(U_438,U_451)
| ~ in(U_446,U_438) ) )
& ! [U_445] :
( ? [U_437] :
( in(U_437,U_451)
& in(U_445,U_437) )
| ~ in(U_445,U_449) ) )
| U_449 != union(U_451) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
( ! [U_452,U_450] :
( U_450 = union(U_452)
| ? [U_448] :
( ~ in(U_448,U_450)
& ? [U_441] :
( in(U_441,U_452)
& in(U_448,U_441) ) )
| ? [U_447] :
( ! [U_440] :
( ~ in(U_440,U_452)
| ~ in(U_447,U_440) )
& in(U_447,U_450) ) )
& ! [U_451,U_449] :
( ( ! [U_446] :
( in(U_446,U_449)
| ! [U_438] :
( ~ in(U_438,U_451)
| ~ in(U_446,U_438) ) )
& ! [U_445] :
( ( in(sK82(U_451,U_449,U_445),U_451)
& in(U_445,sK82(U_451,U_449,U_445)) )
| ~ in(U_445,U_449) ) )
| U_449 != union(U_451) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_437,sK82(U_451,U_449,U_445))],[f_55_3]) ).
fof(f_55_5,plain,
( ! [U_452,U_450] :
( U_450 = union(U_452)
| ? [U_448] :
( ~ in(U_448,U_450)
& ? [U_441] :
( in(U_441,U_452)
& in(U_448,U_441) ) )
| ( ! [U_440] :
( ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440) )
& in(sK83(U_452,U_450),U_450) ) )
& ! [U_451,U_449] :
( ( ! [U_446] :
( in(U_446,U_449)
| ! [U_438] :
( ~ in(U_438,U_451)
| ~ in(U_446,U_438) ) )
& ! [U_445] :
( ( in(sK82(U_451,U_449,U_445),U_451)
& in(U_445,sK82(U_451,U_449,U_445)) )
| ~ in(U_445,U_449) ) )
| U_449 != union(U_451) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_447,sK83(U_452,U_450))],[f_55_4]) ).
fof(f_55_6,plain,
( ! [U_452,U_450] :
( U_450 = union(U_452)
| ( ~ in(sK84(U_452,U_450),U_450)
& ? [U_441] :
( in(U_441,U_452)
& in(sK84(U_452,U_450),U_441) ) )
| ( ! [U_440] :
( ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440) )
& in(sK83(U_452,U_450),U_450) ) )
& ! [U_451,U_449] :
( ( ! [U_446] :
( in(U_446,U_449)
| ! [U_438] :
( ~ in(U_438,U_451)
| ~ in(U_446,U_438) ) )
& ! [U_445] :
( ( in(sK82(U_451,U_449,U_445),U_451)
& in(U_445,sK82(U_451,U_449,U_445)) )
| ~ in(U_445,U_449) ) )
| U_449 != union(U_451) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_448,sK84(U_452,U_450))],[f_55_5]) ).
fof(f_55_7,plain,
( ! [U_452,U_450] :
( U_450 = union(U_452)
| ( ~ in(sK84(U_452,U_450),U_450)
& in(sK85(U_452,U_450),U_452)
& in(sK84(U_452,U_450),sK85(U_452,U_450)) )
| ( ! [U_440] :
( ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440) )
& in(sK83(U_452,U_450),U_450) ) )
& ! [U_451,U_449] :
( ( ! [U_446] :
( in(U_446,U_449)
| ! [U_438] :
( ~ in(U_438,U_451)
| ~ in(U_446,U_438) ) )
& ! [U_445] :
( ( in(sK82(U_451,U_449,U_445),U_451)
& in(U_445,sK82(U_451,U_449,U_445)) )
| ~ in(U_445,U_449) ) )
| U_449 != union(U_451) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_441,sK85(U_452,U_450))],[f_55_6]) ).
fof(f_55_8,plain,
( ! [U_450,U_452] :
( ~ in(sK84(U_452,U_450),U_450)
| ~ sP122(U_450,U_452) )
& ! [U_450,U_452] :
( in(sK85(U_452,U_450),U_452)
| ~ sP122(U_450,U_452) )
& ! [U_450,U_452] :
( in(sK84(U_452,U_450),sK85(U_452,U_450))
| ~ sP122(U_450,U_452) )
& ! [U_440,U_450,U_452] :
( ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440)
| ~ sP121(U_440,U_450,U_452) )
& ! [U_440,U_450,U_452] :
( in(sK83(U_452,U_450),U_450)
| ~ sP121(U_440,U_450,U_452) )
& ! [U_445,U_449,U_451] :
( in(sK82(U_451,U_449,U_445),U_451)
| ~ sP119(U_445,U_449,U_451) )
& ! [U_445,U_449,U_451] :
( in(U_445,sK82(U_451,U_449,U_445))
| ~ sP119(U_445,U_449,U_451) )
& ! [U_446,U_445,U_438,U_449,U_451] :
( in(U_446,U_449)
| ~ in(U_438,U_451)
| ~ in(U_446,U_438)
| ~ sP120(U_446,U_445,U_438,U_449,U_451) )
& ! [U_446,U_445,U_438,U_449,U_451] :
( sP119(U_445,U_449,U_451)
| ~ in(U_445,U_449)
| ~ sP120(U_446,U_445,U_438,U_449,U_451) )
& ! [U_440,U_450,U_452] :
( U_450 = union(U_452)
| sP122(U_450,U_452)
| sP121(U_440,U_450,U_452) )
& ! [U_446,U_445,U_438,U_449,U_451] :
( sP120(U_446,U_445,U_438,U_449,U_451)
| U_449 != union(U_451) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119,sP120,sP121,sP122])],[f_55_7]) ).
cnf(f_55_9,plain,
( sP120(U_446,U_445,U_438,U_449,U_451)
| U_449 != union(U_451) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_10,plain,
( U_450 = union(U_452)
| sP122(U_450,U_452)
| sP121(U_440,U_450,U_452) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_11,plain,
( sP119(U_445,U_449,U_451)
| ~ in(U_445,U_449)
| ~ sP120(U_446,U_445,U_438,U_449,U_451) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_12,plain,
( in(U_446,U_449)
| ~ in(U_438,U_451)
| ~ in(U_446,U_438)
| ~ sP120(U_446,U_445,U_438,U_449,U_451) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_13,plain,
( in(U_445,sK82(U_451,U_449,U_445))
| ~ sP119(U_445,U_449,U_451) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_14,plain,
( in(sK82(U_451,U_449,U_445),U_451)
| ~ sP119(U_445,U_449,U_451) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_15,plain,
( in(sK83(U_452,U_450),U_450)
| ~ sP121(U_440,U_450,U_452) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_16,plain,
( ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440)
| ~ sP121(U_440,U_450,U_452) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_17,plain,
( in(sK84(U_452,U_450),sK85(U_452,U_450))
| ~ sP122(U_450,U_452) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_18,plain,
( in(sK85(U_452,U_450),U_452)
| ~ sP122(U_450,U_452) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_19,plain,
( ~ in(sK84(U_452,U_450),U_450)
| ~ sP122(U_450,U_452) ),
inference(clausify,[status(thm)],[f_55_8]) ).
fof(f_56_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_56_2,plain,
! [U_453] :
( ( ( well_ordering(U_453)
| ~ well_founded_relation(U_453)
| ~ connected(U_453)
| ~ antisymmetric(U_453)
| ~ transitive(U_453)
| ~ reflexive(U_453) )
& ( ( well_founded_relation(U_453)
& connected(U_453)
& antisymmetric(U_453)
& transitive(U_453)
& reflexive(U_453) )
| ~ well_ordering(U_453) ) )
| ~ relation(U_453) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_453] :
( well_founded_relation(U_453)
| ~ sP123(U_453) )
& ! [U_453] :
( connected(U_453)
| ~ sP123(U_453) )
& ! [U_453] :
( antisymmetric(U_453)
| ~ sP123(U_453) )
& ! [U_453] :
( transitive(U_453)
| ~ sP123(U_453) )
& ! [U_453] :
( reflexive(U_453)
| ~ sP123(U_453) )
& ! [U_453] :
( well_ordering(U_453)
| ~ well_founded_relation(U_453)
| ~ connected(U_453)
| ~ antisymmetric(U_453)
| ~ transitive(U_453)
| ~ reflexive(U_453)
| ~ sP124(U_453) )
& ! [U_453] :
( sP123(U_453)
| ~ well_ordering(U_453)
| ~ sP124(U_453) )
& ! [U_453] :
( sP124(U_453)
| ~ relation(U_453) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123,sP124])],[f_56_2]) ).
cnf(f_56_4,plain,
( sP124(U_453)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( sP123(U_453)
| ~ well_ordering(U_453)
| ~ sP124(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_6,plain,
( well_ordering(U_453)
| ~ well_founded_relation(U_453)
| ~ connected(U_453)
| ~ antisymmetric(U_453)
| ~ transitive(U_453)
| ~ reflexive(U_453)
| ~ sP124(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_7,plain,
( reflexive(U_453)
| ~ sP123(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_8,plain,
( transitive(U_453)
| ~ sP123(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_9,plain,
( antisymmetric(U_453)
| ~ sP123(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_10,plain,
( connected(U_453)
| ~ sP123(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_11,plain,
( well_founded_relation(U_453)
| ~ sP123(U_453) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_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_57_2,plain,
! [U_458,U_457,U_456] :
( ( U_456 = set_difference(U_458,U_457)
| ? [U_455] :
( ( ~ in(U_455,U_456)
& ~ in(U_455,U_457)
& in(U_455,U_458) )
| ( ( in(U_455,U_457)
| ~ in(U_455,U_458) )
& in(U_455,U_456) ) ) )
& ( ! [U_454] :
( ( in(U_454,U_456)
| in(U_454,U_457)
| ~ in(U_454,U_458) )
& ( ( ~ in(U_454,U_457)
& in(U_454,U_458) )
| ~ in(U_454,U_456) ) )
| U_456 != set_difference(U_458,U_457) ) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_468,U_466,U_464] :
( U_464 = set_difference(U_468,U_466)
| ? [U_462] :
( ~ in(U_462,U_464)
& ~ in(U_462,U_466)
& in(U_462,U_468) )
| ? [U_461] :
( ( in(U_461,U_466)
| ~ in(U_461,U_468) )
& in(U_461,U_464) ) )
& ! [U_467,U_465,U_463] :
( ( ! [U_460] :
( in(U_460,U_463)
| in(U_460,U_465)
| ~ in(U_460,U_467) )
& ! [U_459] :
( ( ~ in(U_459,U_465)
& in(U_459,U_467) )
| ~ in(U_459,U_463) ) )
| U_463 != set_difference(U_467,U_465) ) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
( ! [U_468,U_466,U_464] :
( U_464 = set_difference(U_468,U_466)
| ? [U_462] :
( ~ in(U_462,U_464)
& ~ in(U_462,U_466)
& in(U_462,U_468) )
| ( ( in(sK86(U_468,U_466,U_464),U_466)
| ~ in(sK86(U_468,U_466,U_464),U_468) )
& in(sK86(U_468,U_466,U_464),U_464) ) )
& ! [U_467,U_465,U_463] :
( ( ! [U_460] :
( in(U_460,U_463)
| in(U_460,U_465)
| ~ in(U_460,U_467) )
& ! [U_459] :
( ( ~ in(U_459,U_465)
& in(U_459,U_467) )
| ~ in(U_459,U_463) ) )
| U_463 != set_difference(U_467,U_465) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_461,sK86(U_468,U_466,U_464))],[f_57_3]) ).
fof(f_57_5,plain,
( ! [U_468,U_466,U_464] :
( U_464 = set_difference(U_468,U_466)
| ( ~ in(sK87(U_468,U_466,U_464),U_464)
& ~ in(sK87(U_468,U_466,U_464),U_466)
& in(sK87(U_468,U_466,U_464),U_468) )
| ( ( in(sK86(U_468,U_466,U_464),U_466)
| ~ in(sK86(U_468,U_466,U_464),U_468) )
& in(sK86(U_468,U_466,U_464),U_464) ) )
& ! [U_467,U_465,U_463] :
( ( ! [U_460] :
( in(U_460,U_463)
| in(U_460,U_465)
| ~ in(U_460,U_467) )
& ! [U_459] :
( ( ~ in(U_459,U_465)
& in(U_459,U_467) )
| ~ in(U_459,U_463) ) )
| U_463 != set_difference(U_467,U_465) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_462,sK87(U_468,U_466,U_464))],[f_57_4]) ).
fof(f_57_6,plain,
( ! [U_466,U_468,U_464] :
( ~ in(sK87(U_468,U_466,U_464),U_464)
| ~ sP128(U_466,U_468,U_464) )
& ! [U_466,U_468,U_464] :
( ~ in(sK87(U_468,U_466,U_464),U_466)
| ~ sP128(U_466,U_468,U_464) )
& ! [U_466,U_468,U_464] :
( in(sK87(U_468,U_466,U_464),U_468)
| ~ sP128(U_466,U_468,U_464) )
& ! [U_466,U_468,U_464] :
( in(sK86(U_468,U_466,U_464),U_466)
| ~ in(sK86(U_468,U_466,U_464),U_468)
| ~ sP127(U_466,U_468,U_464) )
& ! [U_466,U_468,U_464] :
( in(sK86(U_468,U_466,U_464),U_464)
| ~ sP127(U_466,U_468,U_464) )
& ! [U_459,U_467,U_465] :
( ~ in(U_459,U_465)
| ~ sP125(U_459,U_467,U_465) )
& ! [U_459,U_467,U_465] :
( in(U_459,U_467)
| ~ sP125(U_459,U_467,U_465) )
& ! [U_459,U_467,U_460,U_465,U_463] :
( in(U_460,U_463)
| in(U_460,U_465)
| ~ in(U_460,U_467)
| ~ sP126(U_459,U_467,U_460,U_465,U_463) )
& ! [U_459,U_467,U_460,U_465,U_463] :
( sP125(U_459,U_467,U_465)
| ~ in(U_459,U_463)
| ~ sP126(U_459,U_467,U_460,U_465,U_463) )
& ! [U_466,U_468,U_464] :
( U_464 = set_difference(U_468,U_466)
| sP128(U_466,U_468,U_464)
| sP127(U_466,U_468,U_464) )
& ! [U_459,U_467,U_460,U_465,U_463] :
( sP126(U_459,U_467,U_460,U_465,U_463)
| U_463 != set_difference(U_467,U_465) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125,sP126,sP127,sP128])],[f_57_5]) ).
cnf(f_57_7,plain,
( sP126(U_459,U_467,U_460,U_465,U_463)
| U_463 != set_difference(U_467,U_465) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_8,plain,
( U_464 = set_difference(U_468,U_466)
| sP128(U_466,U_468,U_464)
| sP127(U_466,U_468,U_464) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_9,plain,
( sP125(U_459,U_467,U_465)
| ~ in(U_459,U_463)
| ~ sP126(U_459,U_467,U_460,U_465,U_463) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_10,plain,
( in(U_460,U_463)
| in(U_460,U_465)
| ~ in(U_460,U_467)
| ~ sP126(U_459,U_467,U_460,U_465,U_463) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_11,plain,
( in(U_459,U_467)
| ~ sP125(U_459,U_467,U_465) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_12,plain,
( ~ in(U_459,U_465)
| ~ sP125(U_459,U_467,U_465) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_13,plain,
( in(sK86(U_468,U_466,U_464),U_464)
| ~ sP127(U_466,U_468,U_464) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_14,plain,
( in(sK86(U_468,U_466,U_464),U_466)
| ~ in(sK86(U_468,U_466,U_464),U_468)
| ~ sP127(U_466,U_468,U_464) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_15,plain,
( in(sK87(U_468,U_466,U_464),U_468)
| ~ sP128(U_466,U_468,U_464) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_16,plain,
( ~ in(sK87(U_468,U_466,U_464),U_466)
| ~ sP128(U_466,U_468,U_464) ),
inference(clausify,[status(thm)],[f_57_6]) ).
cnf(f_57_17,plain,
( ~ in(sK87(U_468,U_466,U_464),U_464)
| ~ sP128(U_466,U_468,U_464) ),
inference(clausify,[status(thm)],[f_57_6]) ).
fof(f_58_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_58_2,plain,
! [U_476] :
( ! [U_475] :
( ( U_475 = relation_rng(U_476)
| ? [U_474] :
( ( ~ in(U_474,U_475)
& ? [U_473] :
( U_474 = apply(U_476,U_473)
& in(U_473,relation_dom(U_476)) ) )
| ( ! [U_472] :
( U_474 != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476)) )
& in(U_474,U_475) ) ) )
& ( ! [U_471] :
( ( in(U_471,U_475)
| ! [U_470] :
( U_471 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476)) ) )
& ( ? [U_469] :
( U_471 = apply(U_476,U_469)
& in(U_469,relation_dom(U_476)) )
| ~ in(U_471,U_475) ) )
| U_475 != relation_rng(U_476) ) )
| ~ function(U_476)
| ~ relation(U_476) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_476] :
( ( ! [U_482] :
( U_482 = relation_rng(U_476)
| ? [U_480] :
( ~ in(U_480,U_482)
& ? [U_473] :
( U_480 = apply(U_476,U_473)
& in(U_473,relation_dom(U_476)) ) )
| ? [U_479] :
( ! [U_472] :
( U_479 != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476)) )
& in(U_479,U_482) ) )
& ! [U_481] :
( ( ! [U_478] :
( in(U_478,U_481)
| ! [U_470] :
( U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476)) ) )
& ! [U_477] :
( ? [U_469] :
( U_477 = apply(U_476,U_469)
& in(U_469,relation_dom(U_476)) )
| ~ in(U_477,U_481) ) )
| U_481 != relation_rng(U_476) ) )
| ~ function(U_476)
| ~ relation(U_476) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
fof(f_58_4,plain,
! [U_476] :
( ( ! [U_482] :
( U_482 = relation_rng(U_476)
| ? [U_480] :
( ~ in(U_480,U_482)
& ? [U_473] :
( U_480 = apply(U_476,U_473)
& in(U_473,relation_dom(U_476)) ) )
| ? [U_479] :
( ! [U_472] :
( U_479 != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476)) )
& in(U_479,U_482) ) )
& ! [U_481] :
( ( ! [U_478] :
( in(U_478,U_481)
| ! [U_470] :
( U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476)) ) )
& ! [U_477] :
( ( U_477 = apply(U_476,sK88(U_476,U_481,U_477))
& in(sK88(U_476,U_481,U_477),relation_dom(U_476)) )
| ~ in(U_477,U_481) ) )
| U_481 != relation_rng(U_476) ) )
| ~ function(U_476)
| ~ relation(U_476) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_469,sK88(U_476,U_481,U_477))],[f_58_3]) ).
fof(f_58_5,plain,
! [U_476] :
( ( ! [U_482] :
( U_482 = relation_rng(U_476)
| ? [U_480] :
( ~ in(U_480,U_482)
& ? [U_473] :
( U_480 = apply(U_476,U_473)
& in(U_473,relation_dom(U_476)) ) )
| ( ! [U_472] :
( sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476)) )
& in(sK89(U_476,U_482),U_482) ) )
& ! [U_481] :
( ( ! [U_478] :
( in(U_478,U_481)
| ! [U_470] :
( U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476)) ) )
& ! [U_477] :
( ( U_477 = apply(U_476,sK88(U_476,U_481,U_477))
& in(sK88(U_476,U_481,U_477),relation_dom(U_476)) )
| ~ in(U_477,U_481) ) )
| U_481 != relation_rng(U_476) ) )
| ~ function(U_476)
| ~ relation(U_476) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_479,sK89(U_476,U_482))],[f_58_4]) ).
fof(f_58_6,plain,
! [U_476] :
( ( ! [U_482] :
( U_482 = relation_rng(U_476)
| ( ~ in(sK90(U_476,U_482),U_482)
& ? [U_473] :
( sK90(U_476,U_482) = apply(U_476,U_473)
& in(U_473,relation_dom(U_476)) ) )
| ( ! [U_472] :
( sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476)) )
& in(sK89(U_476,U_482),U_482) ) )
& ! [U_481] :
( ( ! [U_478] :
( in(U_478,U_481)
| ! [U_470] :
( U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476)) ) )
& ! [U_477] :
( ( U_477 = apply(U_476,sK88(U_476,U_481,U_477))
& in(sK88(U_476,U_481,U_477),relation_dom(U_476)) )
| ~ in(U_477,U_481) ) )
| U_481 != relation_rng(U_476) ) )
| ~ function(U_476)
| ~ relation(U_476) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_480,sK90(U_476,U_482))],[f_58_5]) ).
fof(f_58_7,plain,
! [U_476] :
( ( ! [U_482] :
( U_482 = relation_rng(U_476)
| ( ~ in(sK90(U_476,U_482),U_482)
& sK90(U_476,U_482) = apply(U_476,sK91(U_476,U_482))
& in(sK91(U_476,U_482),relation_dom(U_476)) )
| ( ! [U_472] :
( sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476)) )
& in(sK89(U_476,U_482),U_482) ) )
& ! [U_481] :
( ( ! [U_478] :
( in(U_478,U_481)
| ! [U_470] :
( U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476)) ) )
& ! [U_477] :
( ( U_477 = apply(U_476,sK88(U_476,U_481,U_477))
& in(sK88(U_476,U_481,U_477),relation_dom(U_476)) )
| ~ in(U_477,U_481) ) )
| U_481 != relation_rng(U_476) ) )
| ~ function(U_476)
| ~ relation(U_476) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_473,sK91(U_476,U_482))],[f_58_6]) ).
fof(f_58_8,plain,
( ! [U_476,U_482] :
( ~ in(sK90(U_476,U_482),U_482)
| ~ sP132(U_476,U_482) )
& ! [U_476,U_482] :
( sK90(U_476,U_482) = apply(U_476,sK91(U_476,U_482))
| ~ sP132(U_476,U_482) )
& ! [U_476,U_482] :
( in(sK91(U_476,U_482),relation_dom(U_476))
| ~ sP132(U_476,U_482) )
& ! [U_472,U_476,U_482] :
( sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476))
| ~ sP131(U_472,U_476,U_482) )
& ! [U_472,U_476,U_482] :
( in(sK89(U_476,U_482),U_482)
| ~ sP131(U_472,U_476,U_482) )
& ! [U_477,U_476,U_481] :
( U_477 = apply(U_476,sK88(U_476,U_481,U_477))
| ~ sP129(U_477,U_476,U_481) )
& ! [U_477,U_476,U_481] :
( in(sK88(U_476,U_481,U_477),relation_dom(U_476))
| ~ sP129(U_477,U_476,U_481) )
& ! [U_477,U_478,U_470,U_476,U_481] :
( in(U_478,U_481)
| U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476))
| ~ sP130(U_477,U_478,U_470,U_476,U_481) )
& ! [U_477,U_478,U_470,U_476,U_481] :
( sP129(U_477,U_476,U_481)
| ~ in(U_477,U_481)
| ~ sP130(U_477,U_478,U_470,U_476,U_481) )
& ! [U_472,U_477,U_478,U_470,U_476,U_481,U_482] :
( U_482 = relation_rng(U_476)
| sP132(U_476,U_482)
| sP131(U_472,U_476,U_482)
| ~ sP133(U_472,U_477,U_478,U_470,U_476,U_481,U_482) )
& ! [U_472,U_477,U_478,U_470,U_476,U_481,U_482] :
( sP130(U_477,U_478,U_470,U_476,U_481)
| U_481 != relation_rng(U_476)
| ~ sP133(U_472,U_477,U_478,U_470,U_476,U_481,U_482) )
& ! [U_472,U_477,U_478,U_470,U_476,U_481,U_482] :
( sP133(U_472,U_477,U_478,U_470,U_476,U_481,U_482)
| ~ function(U_476)
| ~ relation(U_476) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129,sP130,sP131,sP132,sP133])],[f_58_7]) ).
cnf(f_58_9,plain,
( sP133(U_472,U_477,U_478,U_470,U_476,U_481,U_482)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_10,plain,
( sP130(U_477,U_478,U_470,U_476,U_481)
| U_481 != relation_rng(U_476)
| ~ sP133(U_472,U_477,U_478,U_470,U_476,U_481,U_482) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_11,plain,
( U_482 = relation_rng(U_476)
| sP132(U_476,U_482)
| sP131(U_472,U_476,U_482)
| ~ sP133(U_472,U_477,U_478,U_470,U_476,U_481,U_482) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_12,plain,
( sP129(U_477,U_476,U_481)
| ~ in(U_477,U_481)
| ~ sP130(U_477,U_478,U_470,U_476,U_481) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_13,plain,
( in(U_478,U_481)
| U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476))
| ~ sP130(U_477,U_478,U_470,U_476,U_481) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_14,plain,
( in(sK88(U_476,U_481,U_477),relation_dom(U_476))
| ~ sP129(U_477,U_476,U_481) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_15,plain,
( U_477 = apply(U_476,sK88(U_476,U_481,U_477))
| ~ sP129(U_477,U_476,U_481) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_16,plain,
( in(sK89(U_476,U_482),U_482)
| ~ sP131(U_472,U_476,U_482) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_17,plain,
( sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476))
| ~ sP131(U_472,U_476,U_482) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_18,plain,
( in(sK91(U_476,U_482),relation_dom(U_476))
| ~ sP132(U_476,U_482) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_19,plain,
( sK90(U_476,U_482) = apply(U_476,sK91(U_476,U_482))
| ~ sP132(U_476,U_482) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_20,plain,
( ~ in(sK90(U_476,U_482),U_482)
| ~ sP132(U_476,U_482) ),
inference(clausify,[status(thm)],[f_58_8]) ).
fof(f_59_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_59_2,plain,
! [U_490] :
( ! [U_489] :
( ( U_489 = relation_rng(U_490)
| ? [U_488] :
( ( ~ in(U_488,U_489)
& ? [U_487] : in(ordered_pair(U_487,U_488),U_490) )
| ( ! [U_486] : ~ in(ordered_pair(U_486,U_488),U_490)
& in(U_488,U_489) ) ) )
& ( ! [U_485] :
( ( in(U_485,U_489)
| ! [U_484] : ~ in(ordered_pair(U_484,U_485),U_490) )
& ( ? [U_483] : in(ordered_pair(U_483,U_485),U_490)
| ~ in(U_485,U_489) ) )
| U_489 != relation_rng(U_490) ) )
| ~ relation(U_490) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_490] :
( ( ! [U_496] :
( U_496 = relation_rng(U_490)
| ? [U_494] :
( ~ in(U_494,U_496)
& ? [U_487] : in(ordered_pair(U_487,U_494),U_490) )
| ? [U_493] :
( ! [U_486] : ~ in(ordered_pair(U_486,U_493),U_490)
& in(U_493,U_496) ) )
& ! [U_495] :
( ( ! [U_492] :
( in(U_492,U_495)
| ! [U_484] : ~ in(ordered_pair(U_484,U_492),U_490) )
& ! [U_491] :
( ? [U_483] : in(ordered_pair(U_483,U_491),U_490)
| ~ in(U_491,U_495) ) )
| U_495 != relation_rng(U_490) ) )
| ~ relation(U_490) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
! [U_490] :
( ( ! [U_496] :
( U_496 = relation_rng(U_490)
| ? [U_494] :
( ~ in(U_494,U_496)
& ? [U_487] : in(ordered_pair(U_487,U_494),U_490) )
| ? [U_493] :
( ! [U_486] : ~ in(ordered_pair(U_486,U_493),U_490)
& in(U_493,U_496) ) )
& ! [U_495] :
( ( ! [U_492] :
( in(U_492,U_495)
| ! [U_484] : ~ in(ordered_pair(U_484,U_492),U_490) )
& ! [U_491] :
( in(ordered_pair(sK92(U_490,U_495,U_491),U_491),U_490)
| ~ in(U_491,U_495) ) )
| U_495 != relation_rng(U_490) ) )
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_483,sK92(U_490,U_495,U_491))],[f_59_3]) ).
fof(f_59_5,plain,
! [U_490] :
( ( ! [U_496] :
( U_496 = relation_rng(U_490)
| ? [U_494] :
( ~ in(U_494,U_496)
& ? [U_487] : in(ordered_pair(U_487,U_494),U_490) )
| ( ! [U_486] : ~ in(ordered_pair(U_486,sK93(U_490,U_496)),U_490)
& in(sK93(U_490,U_496),U_496) ) )
& ! [U_495] :
( ( ! [U_492] :
( in(U_492,U_495)
| ! [U_484] : ~ in(ordered_pair(U_484,U_492),U_490) )
& ! [U_491] :
( in(ordered_pair(sK92(U_490,U_495,U_491),U_491),U_490)
| ~ in(U_491,U_495) ) )
| U_495 != relation_rng(U_490) ) )
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_493,sK93(U_490,U_496))],[f_59_4]) ).
fof(f_59_6,plain,
! [U_490] :
( ( ! [U_496] :
( U_496 = relation_rng(U_490)
| ( ~ in(sK94(U_490,U_496),U_496)
& ? [U_487] : in(ordered_pair(U_487,sK94(U_490,U_496)),U_490) )
| ( ! [U_486] : ~ in(ordered_pair(U_486,sK93(U_490,U_496)),U_490)
& in(sK93(U_490,U_496),U_496) ) )
& ! [U_495] :
( ( ! [U_492] :
( in(U_492,U_495)
| ! [U_484] : ~ in(ordered_pair(U_484,U_492),U_490) )
& ! [U_491] :
( in(ordered_pair(sK92(U_490,U_495,U_491),U_491),U_490)
| ~ in(U_491,U_495) ) )
| U_495 != relation_rng(U_490) ) )
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_494,sK94(U_490,U_496))],[f_59_5]) ).
fof(f_59_7,plain,
! [U_490] :
( ( ! [U_496] :
( U_496 = relation_rng(U_490)
| ( ~ in(sK94(U_490,U_496),U_496)
& in(ordered_pair(sK95(U_490,U_496),sK94(U_490,U_496)),U_490) )
| ( ! [U_486] : ~ in(ordered_pair(U_486,sK93(U_490,U_496)),U_490)
& in(sK93(U_490,U_496),U_496) ) )
& ! [U_495] :
( ( ! [U_492] :
( in(U_492,U_495)
| ! [U_484] : ~ in(ordered_pair(U_484,U_492),U_490) )
& ! [U_491] :
( in(ordered_pair(sK92(U_490,U_495,U_491),U_491),U_490)
| ~ in(U_491,U_495) ) )
| U_495 != relation_rng(U_490) ) )
| ~ relation(U_490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_487,sK95(U_490,U_496))],[f_59_6]) ).
fof(f_59_8,plain,
( ! [U_490,U_496] :
( ~ in(sK94(U_490,U_496),U_496)
| ~ sP136(U_490,U_496) )
& ! [U_490,U_496] :
( in(ordered_pair(sK95(U_490,U_496),sK94(U_490,U_496)),U_490)
| ~ sP136(U_490,U_496) )
& ! [U_490,U_496,U_486] :
( ~ in(ordered_pair(U_486,sK93(U_490,U_496)),U_490)
| ~ sP135(U_490,U_496,U_486) )
& ! [U_490,U_496,U_486] :
( in(sK93(U_490,U_496),U_496)
| ~ sP135(U_490,U_496,U_486) )
& ! [U_492,U_490,U_495,U_491,U_484] :
( in(U_492,U_495)
| ~ in(ordered_pair(U_484,U_492),U_490)
| ~ sP134(U_492,U_490,U_495,U_491,U_484) )
& ! [U_492,U_490,U_495,U_491,U_484] :
( in(ordered_pair(sK92(U_490,U_495,U_491),U_491),U_490)
| ~ in(U_491,U_495)
| ~ sP134(U_492,U_490,U_495,U_491,U_484) )
& ! [U_492,U_490,U_495,U_496,U_491,U_486,U_484] :
( U_496 = relation_rng(U_490)
| sP136(U_490,U_496)
| sP135(U_490,U_496,U_486)
| ~ sP137(U_492,U_490,U_495,U_496,U_491,U_486,U_484) )
& ! [U_492,U_490,U_495,U_496,U_491,U_486,U_484] :
( sP134(U_492,U_490,U_495,U_491,U_484)
| U_495 != relation_rng(U_490)
| ~ sP137(U_492,U_490,U_495,U_496,U_491,U_486,U_484) )
& ! [U_492,U_490,U_495,U_496,U_491,U_486,U_484] :
( sP137(U_492,U_490,U_495,U_496,U_491,U_486,U_484)
| ~ relation(U_490) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134,sP135,sP136,sP137])],[f_59_7]) ).
cnf(f_59_9,plain,
( sP137(U_492,U_490,U_495,U_496,U_491,U_486,U_484)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_10,plain,
( sP134(U_492,U_490,U_495,U_491,U_484)
| U_495 != relation_rng(U_490)
| ~ sP137(U_492,U_490,U_495,U_496,U_491,U_486,U_484) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_11,plain,
( U_496 = relation_rng(U_490)
| sP136(U_490,U_496)
| sP135(U_490,U_496,U_486)
| ~ sP137(U_492,U_490,U_495,U_496,U_491,U_486,U_484) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_12,plain,
( in(ordered_pair(sK92(U_490,U_495,U_491),U_491),U_490)
| ~ in(U_491,U_495)
| ~ sP134(U_492,U_490,U_495,U_491,U_484) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_13,plain,
( in(U_492,U_495)
| ~ in(ordered_pair(U_484,U_492),U_490)
| ~ sP134(U_492,U_490,U_495,U_491,U_484) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_14,plain,
( in(sK93(U_490,U_496),U_496)
| ~ sP135(U_490,U_496,U_486) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_15,plain,
( ~ in(ordered_pair(U_486,sK93(U_490,U_496)),U_490)
| ~ sP135(U_490,U_496,U_486) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_16,plain,
( in(ordered_pair(sK95(U_490,U_496),sK94(U_490,U_496)),U_490)
| ~ sP136(U_490,U_496) ),
inference(clausify,[status(thm)],[f_59_8]) ).
cnf(f_59_17,plain,
( ~ in(sK94(U_490,U_496),U_496)
| ~ sP136(U_490,U_496) ),
inference(clausify,[status(thm)],[f_59_8]) ).
fof(f_60_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_60_2,plain,
! [U_498,U_497] :
( subset_complement(U_498,U_497) = set_difference(U_498,U_497)
| ~ element(U_497,powerset(U_498)) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_498,U_497] :
( subset_complement(U_498,U_497) = set_difference(U_498,U_497)
| ~ element(U_497,powerset(U_498)) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( subset_complement(U_498,U_497) = set_difference(U_498,U_497)
| ~ element(U_497,powerset(U_498)) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_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_61_2,plain,
! [U_500,U_499] : ordered_pair(U_500,U_499) = unordered_pair(unordered_pair(U_500,U_499),singleton(U_500)),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_500,U_499] : ordered_pair(U_500,U_499) = unordered_pair(unordered_pair(U_500,U_499),singleton(U_500)),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
ordered_pair(U_500,U_499) = unordered_pair(unordered_pair(U_500,U_499),singleton(U_500)),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_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_62_2,plain,
! [U_502] :
( ! [U_501] :
( ( well_orders(U_502,U_501)
| ~ is_well_founded_in(U_502,U_501)
| ~ is_connected_in(U_502,U_501)
| ~ is_antisymmetric_in(U_502,U_501)
| ~ is_transitive_in(U_502,U_501)
| ~ is_reflexive_in(U_502,U_501) )
& ( ( is_well_founded_in(U_502,U_501)
& is_connected_in(U_502,U_501)
& is_antisymmetric_in(U_502,U_501)
& is_transitive_in(U_502,U_501)
& is_reflexive_in(U_502,U_501) )
| ~ well_orders(U_502,U_501) ) )
| ~ relation(U_502) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_502] :
( ( ! [U_504] :
( well_orders(U_502,U_504)
| ~ is_well_founded_in(U_502,U_504)
| ~ is_connected_in(U_502,U_504)
| ~ is_antisymmetric_in(U_502,U_504)
| ~ is_transitive_in(U_502,U_504)
| ~ is_reflexive_in(U_502,U_504) )
& ! [U_503] :
( ( is_well_founded_in(U_502,U_503)
& is_connected_in(U_502,U_503)
& is_antisymmetric_in(U_502,U_503)
& is_transitive_in(U_502,U_503)
& is_reflexive_in(U_502,U_503) )
| ~ well_orders(U_502,U_503) ) )
| ~ relation(U_502) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
fof(f_62_4,plain,
( ! [U_503,U_502] :
( is_well_founded_in(U_502,U_503)
| ~ sP138(U_503,U_502) )
& ! [U_503,U_502] :
( is_connected_in(U_502,U_503)
| ~ sP138(U_503,U_502) )
& ! [U_503,U_502] :
( is_antisymmetric_in(U_502,U_503)
| ~ sP138(U_503,U_502) )
& ! [U_503,U_502] :
( is_transitive_in(U_502,U_503)
| ~ sP138(U_503,U_502) )
& ! [U_503,U_502] :
( is_reflexive_in(U_502,U_503)
| ~ sP138(U_503,U_502) )
& ! [U_503,U_504,U_502] :
( well_orders(U_502,U_504)
| ~ is_well_founded_in(U_502,U_504)
| ~ is_connected_in(U_502,U_504)
| ~ is_antisymmetric_in(U_502,U_504)
| ~ is_transitive_in(U_502,U_504)
| ~ is_reflexive_in(U_502,U_504)
| ~ sP139(U_503,U_504,U_502) )
& ! [U_503,U_504,U_502] :
( sP138(U_503,U_502)
| ~ well_orders(U_502,U_503)
| ~ sP139(U_503,U_504,U_502) )
& ! [U_503,U_504,U_502] :
( sP139(U_503,U_504,U_502)
| ~ relation(U_502) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138,sP139])],[f_62_3]) ).
cnf(f_62_5,plain,
( sP139(U_503,U_504,U_502)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_6,plain,
( sP138(U_503,U_502)
| ~ well_orders(U_502,U_503)
| ~ sP139(U_503,U_504,U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_7,plain,
( well_orders(U_502,U_504)
| ~ is_well_founded_in(U_502,U_504)
| ~ is_connected_in(U_502,U_504)
| ~ is_antisymmetric_in(U_502,U_504)
| ~ is_transitive_in(U_502,U_504)
| ~ is_reflexive_in(U_502,U_504)
| ~ sP139(U_503,U_504,U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_8,plain,
( is_reflexive_in(U_502,U_503)
| ~ sP138(U_503,U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_9,plain,
( is_transitive_in(U_502,U_503)
| ~ sP138(U_503,U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_10,plain,
( is_antisymmetric_in(U_502,U_503)
| ~ sP138(U_503,U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_11,plain,
( is_connected_in(U_502,U_503)
| ~ sP138(U_503,U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
cnf(f_62_12,plain,
( is_well_founded_in(U_502,U_503)
| ~ sP138(U_503,U_502) ),
inference(clausify,[status(thm)],[f_62_4]) ).
fof(f_63_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_63_2,plain,
! [U_505] :
( ( being_limit_ordinal(U_505)
| U_505 != union(U_505) )
& ( U_505 = union(U_505)
| ~ being_limit_ordinal(U_505) ) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ! [U_507] :
( being_limit_ordinal(U_507)
| U_507 != union(U_507) )
& ! [U_506] :
( U_506 = union(U_506)
| ~ being_limit_ordinal(U_506) ) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
fof(f_63_4,plain,
( ! [U_507] :
( being_limit_ordinal(U_507)
| U_507 != union(U_507) )
& ! [U_506] :
( U_506 = union(U_506)
| ~ being_limit_ordinal(U_506) ) ),
inference(definitional_conversion,[status(esa)],[f_63_3]) ).
cnf(f_63_5,plain,
( U_506 = union(U_506)
| ~ being_limit_ordinal(U_506) ),
inference(clausify,[status(thm)],[f_63_4]) ).
cnf(f_63_6,plain,
( being_limit_ordinal(U_507)
| U_507 != union(U_507) ),
inference(clausify,[status(thm)],[f_63_4]) ).
fof(f_64_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_64_2,plain,
! [U_508] :
( relation_field(U_508) = set_union2(relation_dom(U_508),relation_rng(U_508))
| ~ relation(U_508) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_508] :
( relation_field(U_508) = set_union2(relation_dom(U_508),relation_rng(U_508))
| ~ relation(U_508) ),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
( relation_field(U_508) = set_union2(relation_dom(U_508),relation_rng(U_508))
| ~ relation(U_508) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_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_65_2,plain,
! [U_514] :
( ! [U_513] :
( ( is_connected_in(U_514,U_513)
| ? [U_512,U_511] :
( ~ in(ordered_pair(U_511,U_512),U_514)
& ~ in(ordered_pair(U_512,U_511),U_514)
& U_512 != U_511
& in(U_511,U_513)
& in(U_512,U_513) ) )
& ( ! [U_510,U_509] :
( in(ordered_pair(U_509,U_510),U_514)
| in(ordered_pair(U_510,U_509),U_514)
| U_510 = U_509
| ~ in(U_509,U_513)
| ~ in(U_510,U_513) )
| ~ is_connected_in(U_514,U_513) ) )
| ~ relation(U_514) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_514] :
( ( ! [U_516] :
( is_connected_in(U_514,U_516)
| ? [U_512] :
( ? [U_511] :
( ~ in(ordered_pair(U_511,U_512),U_514)
& ~ in(ordered_pair(U_512,U_511),U_514)
& U_512 != U_511
& in(U_511,U_516) )
& in(U_512,U_516) ) )
& ! [U_515] :
( ! [U_510] :
( ! [U_509] :
( in(ordered_pair(U_509,U_510),U_514)
| in(ordered_pair(U_510,U_509),U_514)
| U_510 = U_509
| ~ in(U_509,U_515) )
| ~ in(U_510,U_515) )
| ~ is_connected_in(U_514,U_515) ) )
| ~ relation(U_514) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
fof(f_65_4,plain,
! [U_514] :
( ( ! [U_516] :
( is_connected_in(U_514,U_516)
| ( ? [U_511] :
( ~ in(ordered_pair(U_511,sK96(U_514,U_516)),U_514)
& ~ in(ordered_pair(sK96(U_514,U_516),U_511),U_514)
& sK96(U_514,U_516) != U_511
& in(U_511,U_516) )
& in(sK96(U_514,U_516),U_516) ) )
& ! [U_515] :
( ! [U_510] :
( ! [U_509] :
( in(ordered_pair(U_509,U_510),U_514)
| in(ordered_pair(U_510,U_509),U_514)
| U_510 = U_509
| ~ in(U_509,U_515) )
| ~ in(U_510,U_515) )
| ~ is_connected_in(U_514,U_515) ) )
| ~ relation(U_514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_512,sK96(U_514,U_516))],[f_65_3]) ).
fof(f_65_5,plain,
! [U_514] :
( ( ! [U_516] :
( is_connected_in(U_514,U_516)
| ( ~ in(ordered_pair(sK97(U_514,U_516),sK96(U_514,U_516)),U_514)
& ~ in(ordered_pair(sK96(U_514,U_516),sK97(U_514,U_516)),U_514)
& sK96(U_514,U_516) != sK97(U_514,U_516)
& in(sK97(U_514,U_516),U_516)
& in(sK96(U_514,U_516),U_516) ) )
& ! [U_515] :
( ! [U_510] :
( ! [U_509] :
( in(ordered_pair(U_509,U_510),U_514)
| in(ordered_pair(U_510,U_509),U_514)
| U_510 = U_509
| ~ in(U_509,U_515) )
| ~ in(U_510,U_515) )
| ~ is_connected_in(U_514,U_515) ) )
| ~ relation(U_514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_511,sK97(U_514,U_516))],[f_65_4]) ).
fof(f_65_6,plain,
( ! [U_516,U_514] :
( ~ in(ordered_pair(sK97(U_514,U_516),sK96(U_514,U_516)),U_514)
| ~ sP140(U_516,U_514) )
& ! [U_516,U_514] :
( ~ in(ordered_pair(sK96(U_514,U_516),sK97(U_514,U_516)),U_514)
| ~ sP140(U_516,U_514) )
& ! [U_516,U_514] :
( sK96(U_514,U_516) != sK97(U_514,U_516)
| ~ sP140(U_516,U_514) )
& ! [U_516,U_514] :
( in(sK97(U_514,U_516),U_516)
| ~ sP140(U_516,U_514) )
& ! [U_516,U_514] :
( in(sK96(U_514,U_516),U_516)
| ~ sP140(U_516,U_514) )
& ! [U_515,U_516,U_509,U_514,U_510] :
( is_connected_in(U_514,U_516)
| sP140(U_516,U_514)
| ~ sP141(U_515,U_516,U_509,U_514,U_510) )
& ! [U_515,U_516,U_509,U_514,U_510] :
( in(ordered_pair(U_509,U_510),U_514)
| in(ordered_pair(U_510,U_509),U_514)
| U_510 = U_509
| ~ in(U_509,U_515)
| ~ in(U_510,U_515)
| ~ is_connected_in(U_514,U_515)
| ~ sP141(U_515,U_516,U_509,U_514,U_510) )
& ! [U_515,U_516,U_509,U_514,U_510] :
( sP141(U_515,U_516,U_509,U_514,U_510)
| ~ relation(U_514) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140,sP141])],[f_65_5]) ).
cnf(f_65_7,plain,
( sP141(U_515,U_516,U_509,U_514,U_510)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_65_6]) ).
cnf(f_65_8,plain,
( in(ordered_pair(U_509,U_510),U_514)
| in(ordered_pair(U_510,U_509),U_514)
| U_510 = U_509
| ~ in(U_509,U_515)
| ~ in(U_510,U_515)
| ~ is_connected_in(U_514,U_515)
| ~ sP141(U_515,U_516,U_509,U_514,U_510) ),
inference(clausify,[status(thm)],[f_65_6]) ).
cnf(f_65_9,plain,
( is_connected_in(U_514,U_516)
| sP140(U_516,U_514)
| ~ sP141(U_515,U_516,U_509,U_514,U_510) ),
inference(clausify,[status(thm)],[f_65_6]) ).
cnf(f_65_10,plain,
( in(sK96(U_514,U_516),U_516)
| ~ sP140(U_516,U_514) ),
inference(clausify,[status(thm)],[f_65_6]) ).
cnf(f_65_11,plain,
( in(sK97(U_514,U_516),U_516)
| ~ sP140(U_516,U_514) ),
inference(clausify,[status(thm)],[f_65_6]) ).
cnf(f_65_12,plain,
( sK96(U_514,U_516) != sK97(U_514,U_516)
| ~ sP140(U_516,U_514) ),
inference(clausify,[status(thm)],[f_65_6]) ).
cnf(f_65_13,plain,
( ~ in(ordered_pair(sK96(U_514,U_516),sK97(U_514,U_516)),U_514)
| ~ sP140(U_516,U_514) ),
inference(clausify,[status(thm)],[f_65_6]) ).
cnf(f_65_14,plain,
( ~ in(ordered_pair(sK97(U_514,U_516),sK96(U_514,U_516)),U_514)
| ~ sP140(U_516,U_514) ),
inference(clausify,[status(thm)],[f_65_6]) ).
fof(f_66_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_66_2,plain,
! [U_518] :
( ! [U_517] : relation_restriction(U_518,U_517) = set_intersection2(U_518,cartesian_product2(U_517,U_517))
| ~ relation(U_518) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_518,U_517] :
( relation_restriction(U_518,U_517) = set_intersection2(U_518,cartesian_product2(U_517,U_517))
| ~ relation(U_518) ),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
( relation_restriction(U_518,U_517) = set_intersection2(U_518,cartesian_product2(U_517,U_517))
| ~ relation(U_518) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_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_67_2,plain,
! [U_524] :
( ! [U_523] :
( ( ( U_523 = relation_inverse(U_524)
| ? [U_522,U_521] :
( ( ~ in(ordered_pair(U_522,U_521),U_523)
& in(ordered_pair(U_521,U_522),U_524) )
| ( ~ in(ordered_pair(U_521,U_522),U_524)
& in(ordered_pair(U_522,U_521),U_523) ) ) )
& ( ! [U_520,U_519] :
( ( in(ordered_pair(U_520,U_519),U_523)
| ~ in(ordered_pair(U_519,U_520),U_524) )
& ( in(ordered_pair(U_519,U_520),U_524)
| ~ in(ordered_pair(U_520,U_519),U_523) ) )
| U_523 != relation_inverse(U_524) ) )
| ~ relation(U_523) )
| ~ relation(U_524) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_524] :
( ! [U_523] :
( ( ( U_523 = relation_inverse(U_524)
| ? [U_532,U_530] :
( ~ in(ordered_pair(U_532,U_530),U_523)
& in(ordered_pair(U_530,U_532),U_524) )
| ? [U_531,U_529] :
( ~ in(ordered_pair(U_529,U_531),U_524)
& in(ordered_pair(U_531,U_529),U_523) ) )
& ( ( ! [U_528,U_526] :
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524) )
& ! [U_527,U_525] :
( in(ordered_pair(U_525,U_527),U_524)
| ~ in(ordered_pair(U_527,U_525),U_523) ) )
| U_523 != relation_inverse(U_524) ) )
| ~ relation(U_523) )
| ~ relation(U_524) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
! [U_524] :
( ! [U_523] :
( ( ( U_523 = relation_inverse(U_524)
| ? [U_532,U_530] :
( ~ in(ordered_pair(U_532,U_530),U_523)
& in(ordered_pair(U_530,U_532),U_524) )
| ? [U_529] :
( ~ in(ordered_pair(U_529,sK98(U_524,U_523)),U_524)
& in(ordered_pair(sK98(U_524,U_523),U_529),U_523) ) )
& ( ( ! [U_528,U_526] :
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524) )
& ! [U_527,U_525] :
( in(ordered_pair(U_525,U_527),U_524)
| ~ in(ordered_pair(U_527,U_525),U_523) ) )
| U_523 != relation_inverse(U_524) ) )
| ~ relation(U_523) )
| ~ relation(U_524) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_531,sK98(U_524,U_523))],[f_67_3]) ).
fof(f_67_5,plain,
! [U_524] :
( ! [U_523] :
( ( ( U_523 = relation_inverse(U_524)
| ? [U_532,U_530] :
( ~ in(ordered_pair(U_532,U_530),U_523)
& in(ordered_pair(U_530,U_532),U_524) )
| ( ~ in(ordered_pair(sK99(U_524,U_523),sK98(U_524,U_523)),U_524)
& in(ordered_pair(sK98(U_524,U_523),sK99(U_524,U_523)),U_523) ) )
& ( ( ! [U_528,U_526] :
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524) )
& ! [U_527,U_525] :
( in(ordered_pair(U_525,U_527),U_524)
| ~ in(ordered_pair(U_527,U_525),U_523) ) )
| U_523 != relation_inverse(U_524) ) )
| ~ relation(U_523) )
| ~ relation(U_524) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_529,sK99(U_524,U_523))],[f_67_4]) ).
fof(f_67_6,plain,
! [U_524] :
( ! [U_523] :
( ( ( U_523 = relation_inverse(U_524)
| ? [U_530] :
( ~ in(ordered_pair(sK100(U_524,U_523),U_530),U_523)
& in(ordered_pair(U_530,sK100(U_524,U_523)),U_524) )
| ( ~ in(ordered_pair(sK99(U_524,U_523),sK98(U_524,U_523)),U_524)
& in(ordered_pair(sK98(U_524,U_523),sK99(U_524,U_523)),U_523) ) )
& ( ( ! [U_528,U_526] :
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524) )
& ! [U_527,U_525] :
( in(ordered_pair(U_525,U_527),U_524)
| ~ in(ordered_pair(U_527,U_525),U_523) ) )
| U_523 != relation_inverse(U_524) ) )
| ~ relation(U_523) )
| ~ relation(U_524) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_532,sK100(U_524,U_523))],[f_67_5]) ).
fof(f_67_7,plain,
! [U_524] :
( ! [U_523] :
( ( ( U_523 = relation_inverse(U_524)
| ( ~ in(ordered_pair(sK100(U_524,U_523),sK101(U_524,U_523)),U_523)
& in(ordered_pair(sK101(U_524,U_523),sK100(U_524,U_523)),U_524) )
| ( ~ in(ordered_pair(sK99(U_524,U_523),sK98(U_524,U_523)),U_524)
& in(ordered_pair(sK98(U_524,U_523),sK99(U_524,U_523)),U_523) ) )
& ( ( ! [U_528,U_526] :
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524) )
& ! [U_527,U_525] :
( in(ordered_pair(U_525,U_527),U_524)
| ~ in(ordered_pair(U_527,U_525),U_523) ) )
| U_523 != relation_inverse(U_524) ) )
| ~ relation(U_523) )
| ~ relation(U_524) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_530,sK101(U_524,U_523))],[f_67_6]) ).
fof(f_67_8,plain,
( ! [U_523,U_524] :
( ~ in(ordered_pair(sK100(U_524,U_523),sK101(U_524,U_523)),U_523)
| ~ sP144(U_523,U_524) )
& ! [U_523,U_524] :
( in(ordered_pair(sK101(U_524,U_523),sK100(U_524,U_523)),U_524)
| ~ sP144(U_523,U_524) )
& ! [U_523,U_524] :
( ~ in(ordered_pair(sK99(U_524,U_523),sK98(U_524,U_523)),U_524)
| ~ sP143(U_523,U_524) )
& ! [U_523,U_524] :
( in(ordered_pair(sK98(U_524,U_523),sK99(U_524,U_523)),U_523)
| ~ sP143(U_523,U_524) )
& ! [U_527,U_523,U_524,U_526,U_528,U_525] :
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524)
| ~ sP142(U_527,U_523,U_524,U_526,U_528,U_525) )
& ! [U_527,U_523,U_524,U_526,U_528,U_525] :
( in(ordered_pair(U_525,U_527),U_524)
| ~ in(ordered_pair(U_527,U_525),U_523)
| ~ sP142(U_527,U_523,U_524,U_526,U_528,U_525) )
& ! [U_527,U_523,U_524,U_526,U_528,U_525] :
( U_523 = relation_inverse(U_524)
| sP144(U_523,U_524)
| sP143(U_523,U_524)
| ~ sP145(U_527,U_523,U_524,U_526,U_528,U_525) )
& ! [U_527,U_523,U_524,U_526,U_528,U_525] :
( sP142(U_527,U_523,U_524,U_526,U_528,U_525)
| U_523 != relation_inverse(U_524)
| ~ sP145(U_527,U_523,U_524,U_526,U_528,U_525) )
& ! [U_527,U_523,U_524,U_526,U_528,U_525] :
( sP145(U_527,U_523,U_524,U_526,U_528,U_525)
| ~ relation(U_523)
| ~ relation(U_524) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142,sP143,sP144,sP145])],[f_67_7]) ).
cnf(f_67_9,plain,
( sP145(U_527,U_523,U_524,U_526,U_528,U_525)
| ~ relation(U_523)
| ~ relation(U_524) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_10,plain,
( sP142(U_527,U_523,U_524,U_526,U_528,U_525)
| U_523 != relation_inverse(U_524)
| ~ sP145(U_527,U_523,U_524,U_526,U_528,U_525) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_11,plain,
( U_523 = relation_inverse(U_524)
| sP144(U_523,U_524)
| sP143(U_523,U_524)
| ~ sP145(U_527,U_523,U_524,U_526,U_528,U_525) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_12,plain,
( in(ordered_pair(U_525,U_527),U_524)
| ~ in(ordered_pair(U_527,U_525),U_523)
| ~ sP142(U_527,U_523,U_524,U_526,U_528,U_525) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_13,plain,
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524)
| ~ sP142(U_527,U_523,U_524,U_526,U_528,U_525) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_14,plain,
( in(ordered_pair(sK98(U_524,U_523),sK99(U_524,U_523)),U_523)
| ~ sP143(U_523,U_524) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_15,plain,
( ~ in(ordered_pair(sK99(U_524,U_523),sK98(U_524,U_523)),U_524)
| ~ sP143(U_523,U_524) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_16,plain,
( in(ordered_pair(sK101(U_524,U_523),sK100(U_524,U_523)),U_524)
| ~ sP144(U_523,U_524) ),
inference(clausify,[status(thm)],[f_67_8]) ).
cnf(f_67_17,plain,
( ~ in(ordered_pair(sK100(U_524,U_523),sK101(U_524,U_523)),U_523)
| ~ sP144(U_523,U_524) ),
inference(clausify,[status(thm)],[f_67_8]) ).
fof(f_68_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_68_2,plain,
! [U_539] :
( ! [U_538] :
( ! [U_537] :
( ( ( relation_isomorphism(U_539,U_538,U_537)
| ? [U_536,U_535] :
( ( ~ in(ordered_pair(U_536,U_535),U_539)
& in(ordered_pair(apply(U_537,U_536),apply(U_537,U_535)),U_538)
& in(U_535,relation_field(U_539))
& in(U_536,relation_field(U_539)) )
| ( ( ~ in(ordered_pair(apply(U_537,U_536),apply(U_537,U_535)),U_538)
| ~ in(U_535,relation_field(U_539))
| ~ in(U_536,relation_field(U_539)) )
& in(ordered_pair(U_536,U_535),U_539) ) )
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539) )
& ( ( ! [U_534,U_533] :
( ( in(ordered_pair(U_534,U_533),U_539)
| ~ in(ordered_pair(apply(U_537,U_534),apply(U_537,U_533)),U_538)
| ~ in(U_533,relation_field(U_539))
| ~ in(U_534,relation_field(U_539)) )
& ( ( in(ordered_pair(apply(U_537,U_534),apply(U_537,U_533)),U_538)
& in(U_533,relation_field(U_539))
& in(U_534,relation_field(U_539)) )
| ~ in(ordered_pair(U_534,U_533),U_539) ) )
& one_to_one(U_537)
& relation_rng(U_537) = relation_field(U_538)
& relation_dom(U_537) = relation_field(U_539) )
| ~ relation_isomorphism(U_539,U_538,U_537) ) )
| ~ function(U_537)
| ~ relation(U_537) )
| ~ relation(U_538) )
| ~ relation(U_539) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_539] :
( ! [U_538] :
( ! [U_537] :
( ( ( relation_isomorphism(U_539,U_538,U_537)
| ? [U_547,U_545] :
( ~ in(ordered_pair(U_547,U_545),U_539)
& in(ordered_pair(apply(U_537,U_547),apply(U_537,U_545)),U_538)
& in(U_545,relation_field(U_539))
& in(U_547,relation_field(U_539)) )
| ? [U_546,U_544] :
( ( ~ in(ordered_pair(apply(U_537,U_546),apply(U_537,U_544)),U_538)
| ~ in(U_544,relation_field(U_539))
| ~ in(U_546,relation_field(U_539)) )
& in(ordered_pair(U_546,U_544),U_539) )
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539) )
& ( ( ! [U_543,U_541] :
( in(ordered_pair(U_543,U_541),U_539)
| ~ in(ordered_pair(apply(U_537,U_543),apply(U_537,U_541)),U_538)
| ~ in(U_541,relation_field(U_539))
| ~ in(U_543,relation_field(U_539)) )
& ! [U_542,U_540] :
( ( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
& in(U_540,relation_field(U_539))
& in(U_542,relation_field(U_539)) )
| ~ in(ordered_pair(U_542,U_540),U_539) )
& one_to_one(U_537)
& relation_rng(U_537) = relation_field(U_538)
& relation_dom(U_537) = relation_field(U_539) )
| ~ relation_isomorphism(U_539,U_538,U_537) ) )
| ~ function(U_537)
| ~ relation(U_537) )
| ~ relation(U_538) )
| ~ relation(U_539) ),
inference(miniscope,[status(thm)],[f_68_2]) ).
fof(f_68_4,plain,
! [U_539] :
( ! [U_538] :
( ! [U_537] :
( ( ( relation_isomorphism(U_539,U_538,U_537)
| ? [U_547,U_545] :
( ~ in(ordered_pair(U_547,U_545),U_539)
& in(ordered_pair(apply(U_537,U_547),apply(U_537,U_545)),U_538)
& in(U_545,relation_field(U_539))
& in(U_547,relation_field(U_539)) )
| ? [U_544] :
( ( ~ in(ordered_pair(apply(U_537,sK102(U_539,U_538,U_537)),apply(U_537,U_544)),U_538)
| ~ in(U_544,relation_field(U_539))
| ~ in(sK102(U_539,U_538,U_537),relation_field(U_539)) )
& in(ordered_pair(sK102(U_539,U_538,U_537),U_544),U_539) )
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539) )
& ( ( ! [U_543,U_541] :
( in(ordered_pair(U_543,U_541),U_539)
| ~ in(ordered_pair(apply(U_537,U_543),apply(U_537,U_541)),U_538)
| ~ in(U_541,relation_field(U_539))
| ~ in(U_543,relation_field(U_539)) )
& ! [U_542,U_540] :
( ( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
& in(U_540,relation_field(U_539))
& in(U_542,relation_field(U_539)) )
| ~ in(ordered_pair(U_542,U_540),U_539) )
& one_to_one(U_537)
& relation_rng(U_537) = relation_field(U_538)
& relation_dom(U_537) = relation_field(U_539) )
| ~ relation_isomorphism(U_539,U_538,U_537) ) )
| ~ function(U_537)
| ~ relation(U_537) )
| ~ relation(U_538) )
| ~ relation(U_539) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_546,sK102(U_539,U_538,U_537))],[f_68_3]) ).
fof(f_68_5,plain,
! [U_539] :
( ! [U_538] :
( ! [U_537] :
( ( ( relation_isomorphism(U_539,U_538,U_537)
| ? [U_547,U_545] :
( ~ in(ordered_pair(U_547,U_545),U_539)
& in(ordered_pair(apply(U_537,U_547),apply(U_537,U_545)),U_538)
& in(U_545,relation_field(U_539))
& in(U_547,relation_field(U_539)) )
| ( ( ~ in(ordered_pair(apply(U_537,sK102(U_539,U_538,U_537)),apply(U_537,sK103(U_539,U_538,U_537))),U_538)
| ~ in(sK103(U_539,U_538,U_537),relation_field(U_539))
| ~ in(sK102(U_539,U_538,U_537),relation_field(U_539)) )
& in(ordered_pair(sK102(U_539,U_538,U_537),sK103(U_539,U_538,U_537)),U_539) )
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539) )
& ( ( ! [U_543,U_541] :
( in(ordered_pair(U_543,U_541),U_539)
| ~ in(ordered_pair(apply(U_537,U_543),apply(U_537,U_541)),U_538)
| ~ in(U_541,relation_field(U_539))
| ~ in(U_543,relation_field(U_539)) )
& ! [U_542,U_540] :
( ( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
& in(U_540,relation_field(U_539))
& in(U_542,relation_field(U_539)) )
| ~ in(ordered_pair(U_542,U_540),U_539) )
& one_to_one(U_537)
& relation_rng(U_537) = relation_field(U_538)
& relation_dom(U_537) = relation_field(U_539) )
| ~ relation_isomorphism(U_539,U_538,U_537) ) )
| ~ function(U_537)
| ~ relation(U_537) )
| ~ relation(U_538) )
| ~ relation(U_539) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_544,sK103(U_539,U_538,U_537))],[f_68_4]) ).
fof(f_68_6,plain,
! [U_539] :
( ! [U_538] :
( ! [U_537] :
( ( ( relation_isomorphism(U_539,U_538,U_537)
| ? [U_545] :
( ~ in(ordered_pair(sK104(U_539,U_538,U_537),U_545),U_539)
& in(ordered_pair(apply(U_537,sK104(U_539,U_538,U_537)),apply(U_537,U_545)),U_538)
& in(U_545,relation_field(U_539))
& in(sK104(U_539,U_538,U_537),relation_field(U_539)) )
| ( ( ~ in(ordered_pair(apply(U_537,sK102(U_539,U_538,U_537)),apply(U_537,sK103(U_539,U_538,U_537))),U_538)
| ~ in(sK103(U_539,U_538,U_537),relation_field(U_539))
| ~ in(sK102(U_539,U_538,U_537),relation_field(U_539)) )
& in(ordered_pair(sK102(U_539,U_538,U_537),sK103(U_539,U_538,U_537)),U_539) )
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539) )
& ( ( ! [U_543,U_541] :
( in(ordered_pair(U_543,U_541),U_539)
| ~ in(ordered_pair(apply(U_537,U_543),apply(U_537,U_541)),U_538)
| ~ in(U_541,relation_field(U_539))
| ~ in(U_543,relation_field(U_539)) )
& ! [U_542,U_540] :
( ( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
& in(U_540,relation_field(U_539))
& in(U_542,relation_field(U_539)) )
| ~ in(ordered_pair(U_542,U_540),U_539) )
& one_to_one(U_537)
& relation_rng(U_537) = relation_field(U_538)
& relation_dom(U_537) = relation_field(U_539) )
| ~ relation_isomorphism(U_539,U_538,U_537) ) )
| ~ function(U_537)
| ~ relation(U_537) )
| ~ relation(U_538) )
| ~ relation(U_539) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_547,sK104(U_539,U_538,U_537))],[f_68_5]) ).
fof(f_68_7,plain,
! [U_539] :
( ! [U_538] :
( ! [U_537] :
( ( ( relation_isomorphism(U_539,U_538,U_537)
| ( ~ in(ordered_pair(sK104(U_539,U_538,U_537),sK105(U_539,U_538,U_537)),U_539)
& in(ordered_pair(apply(U_537,sK104(U_539,U_538,U_537)),apply(U_537,sK105(U_539,U_538,U_537))),U_538)
& in(sK105(U_539,U_538,U_537),relation_field(U_539))
& in(sK104(U_539,U_538,U_537),relation_field(U_539)) )
| ( ( ~ in(ordered_pair(apply(U_537,sK102(U_539,U_538,U_537)),apply(U_537,sK103(U_539,U_538,U_537))),U_538)
| ~ in(sK103(U_539,U_538,U_537),relation_field(U_539))
| ~ in(sK102(U_539,U_538,U_537),relation_field(U_539)) )
& in(ordered_pair(sK102(U_539,U_538,U_537),sK103(U_539,U_538,U_537)),U_539) )
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539) )
& ( ( ! [U_543,U_541] :
( in(ordered_pair(U_543,U_541),U_539)
| ~ in(ordered_pair(apply(U_537,U_543),apply(U_537,U_541)),U_538)
| ~ in(U_541,relation_field(U_539))
| ~ in(U_543,relation_field(U_539)) )
& ! [U_542,U_540] :
( ( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
& in(U_540,relation_field(U_539))
& in(U_542,relation_field(U_539)) )
| ~ in(ordered_pair(U_542,U_540),U_539) )
& one_to_one(U_537)
& relation_rng(U_537) = relation_field(U_538)
& relation_dom(U_537) = relation_field(U_539) )
| ~ relation_isomorphism(U_539,U_538,U_537) ) )
| ~ function(U_537)
| ~ relation(U_537) )
| ~ relation(U_538) )
| ~ relation(U_539) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_545,sK105(U_539,U_538,U_537))],[f_68_6]) ).
fof(f_68_8,plain,
( ! [U_538,U_539,U_537] :
( ~ in(ordered_pair(sK104(U_539,U_538,U_537),sK105(U_539,U_538,U_537)),U_539)
| ~ sP149(U_538,U_539,U_537) )
& ! [U_538,U_539,U_537] :
( in(ordered_pair(apply(U_537,sK104(U_539,U_538,U_537)),apply(U_537,sK105(U_539,U_538,U_537))),U_538)
| ~ sP149(U_538,U_539,U_537) )
& ! [U_538,U_539,U_537] :
( in(sK105(U_539,U_538,U_537),relation_field(U_539))
| ~ sP149(U_538,U_539,U_537) )
& ! [U_538,U_539,U_537] :
( in(sK104(U_539,U_538,U_537),relation_field(U_539))
| ~ sP149(U_538,U_539,U_537) )
& ! [U_538,U_539,U_537] :
( ~ in(ordered_pair(apply(U_537,sK102(U_539,U_538,U_537)),apply(U_537,sK103(U_539,U_538,U_537))),U_538)
| ~ in(sK103(U_539,U_538,U_537),relation_field(U_539))
| ~ in(sK102(U_539,U_538,U_537),relation_field(U_539))
| ~ sP148(U_538,U_539,U_537) )
& ! [U_538,U_539,U_537] :
( in(ordered_pair(sK102(U_539,U_538,U_537),sK103(U_539,U_538,U_537)),U_539)
| ~ sP148(U_538,U_539,U_537) )
& ! [U_542,U_540,U_538,U_539,U_537] :
( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
| ~ sP146(U_542,U_540,U_538,U_539,U_537) )
& ! [U_542,U_540,U_538,U_539,U_537] :
( in(U_540,relation_field(U_539))
| ~ sP146(U_542,U_540,U_538,U_539,U_537) )
& ! [U_542,U_540,U_538,U_539,U_537] :
( in(U_542,relation_field(U_539))
| ~ sP146(U_542,U_540,U_538,U_539,U_537) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( in(ordered_pair(U_543,U_541),U_539)
| ~ in(ordered_pair(apply(U_537,U_543),apply(U_537,U_541)),U_538)
| ~ in(U_541,relation_field(U_539))
| ~ in(U_543,relation_field(U_539))
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( sP146(U_542,U_540,U_538,U_539,U_537)
| ~ in(ordered_pair(U_542,U_540),U_539)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( one_to_one(U_537)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( relation_rng(U_537) = relation_field(U_538)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( relation_dom(U_537) = relation_field(U_539)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( relation_isomorphism(U_539,U_538,U_537)
| sP149(U_538,U_539,U_537)
| sP148(U_538,U_539,U_537)
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539)
| ~ sP150(U_542,U_541,U_540,U_538,U_539,U_537,U_543) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543)
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ sP150(U_542,U_541,U_540,U_538,U_539,U_537,U_543) )
& ! [U_542,U_541,U_540,U_538,U_539,U_537,U_543] :
( sP150(U_542,U_541,U_540,U_538,U_539,U_537,U_543)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146,sP147,sP148,sP149,sP150])],[f_68_7]) ).
cnf(f_68_9,plain,
( sP150(U_542,U_541,U_540,U_538,U_539,U_537,U_543)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_10,plain,
( sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543)
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ sP150(U_542,U_541,U_540,U_538,U_539,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_11,plain,
( relation_isomorphism(U_539,U_538,U_537)
| sP149(U_538,U_539,U_537)
| sP148(U_538,U_539,U_537)
| ~ one_to_one(U_537)
| relation_rng(U_537) != relation_field(U_538)
| relation_dom(U_537) != relation_field(U_539)
| ~ sP150(U_542,U_541,U_540,U_538,U_539,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_12,plain,
( relation_dom(U_537) = relation_field(U_539)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_13,plain,
( relation_rng(U_537) = relation_field(U_538)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_14,plain,
( one_to_one(U_537)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_15,plain,
( sP146(U_542,U_540,U_538,U_539,U_537)
| ~ in(ordered_pair(U_542,U_540),U_539)
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_16,plain,
( in(ordered_pair(U_543,U_541),U_539)
| ~ in(ordered_pair(apply(U_537,U_543),apply(U_537,U_541)),U_538)
| ~ in(U_541,relation_field(U_539))
| ~ in(U_543,relation_field(U_539))
| ~ sP147(U_542,U_541,U_540,U_538,U_539,U_537,U_543) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_17,plain,
( in(U_542,relation_field(U_539))
| ~ sP146(U_542,U_540,U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_18,plain,
( in(U_540,relation_field(U_539))
| ~ sP146(U_542,U_540,U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_19,plain,
( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
| ~ sP146(U_542,U_540,U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_20,plain,
( in(ordered_pair(sK102(U_539,U_538,U_537),sK103(U_539,U_538,U_537)),U_539)
| ~ sP148(U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_21,plain,
( ~ in(ordered_pair(apply(U_537,sK102(U_539,U_538,U_537)),apply(U_537,sK103(U_539,U_538,U_537))),U_538)
| ~ in(sK103(U_539,U_538,U_537),relation_field(U_539))
| ~ in(sK102(U_539,U_538,U_537),relation_field(U_539))
| ~ sP148(U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_22,plain,
( in(sK104(U_539,U_538,U_537),relation_field(U_539))
| ~ sP149(U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_23,plain,
( in(sK105(U_539,U_538,U_537),relation_field(U_539))
| ~ sP149(U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_24,plain,
( in(ordered_pair(apply(U_537,sK104(U_539,U_538,U_537)),apply(U_537,sK105(U_539,U_538,U_537))),U_538)
| ~ sP149(U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
cnf(f_68_25,plain,
( ~ in(ordered_pair(sK104(U_539,U_538,U_537),sK105(U_539,U_538,U_537)),U_539)
| ~ sP149(U_538,U_539,U_537) ),
inference(clausify,[status(thm)],[f_68_8]) ).
fof(f_69_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_69_2,plain,
! [U_549,U_548] :
( ( disjoint(U_549,U_548)
| set_intersection2(U_549,U_548) != empty_set )
& ( set_intersection2(U_549,U_548) = empty_set
| ~ disjoint(U_549,U_548) ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ! [U_553,U_551] :
( disjoint(U_553,U_551)
| set_intersection2(U_553,U_551) != empty_set )
& ! [U_552,U_550] :
( set_intersection2(U_552,U_550) = empty_set
| ~ disjoint(U_552,U_550) ) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
( ! [U_553,U_551] :
( disjoint(U_553,U_551)
| set_intersection2(U_553,U_551) != empty_set )
& ! [U_552,U_550] :
( set_intersection2(U_552,U_550) = empty_set
| ~ disjoint(U_552,U_550) ) ),
inference(definitional_conversion,[status(esa)],[f_69_3]) ).
cnf(f_69_5,plain,
( set_intersection2(U_552,U_550) = empty_set
| ~ disjoint(U_552,U_550) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_6,plain,
( disjoint(U_553,U_551)
| set_intersection2(U_553,U_551) != empty_set ),
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_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_70_2,plain,
! [U_558] :
( ( ( one_to_one(U_558)
| ? [U_557,U_556] :
( U_557 != U_556
& apply(U_558,U_557) = apply(U_558,U_556)
& in(U_556,relation_dom(U_558))
& in(U_557,relation_dom(U_558)) ) )
& ( ! [U_555,U_554] :
( U_555 = U_554
| apply(U_558,U_555) != apply(U_558,U_554)
| ~ in(U_554,relation_dom(U_558))
| ~ in(U_555,relation_dom(U_558)) )
| ~ one_to_one(U_558) ) )
| ~ function(U_558)
| ~ relation(U_558) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_558] :
( ( ( one_to_one(U_558)
| ? [U_556] :
( sK106(U_558) != U_556
& apply(U_558,sK106(U_558)) = apply(U_558,U_556)
& in(U_556,relation_dom(U_558))
& in(sK106(U_558),relation_dom(U_558)) ) )
& ( ! [U_555,U_554] :
( U_555 = U_554
| apply(U_558,U_555) != apply(U_558,U_554)
| ~ in(U_554,relation_dom(U_558))
| ~ in(U_555,relation_dom(U_558)) )
| ~ one_to_one(U_558) ) )
| ~ function(U_558)
| ~ relation(U_558) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_557,sK106(U_558))],[f_70_2]) ).
fof(f_70_4,plain,
! [U_558] :
( ( ( one_to_one(U_558)
| ( sK106(U_558) != sK107(U_558)
& apply(U_558,sK106(U_558)) = apply(U_558,sK107(U_558))
& in(sK107(U_558),relation_dom(U_558))
& in(sK106(U_558),relation_dom(U_558)) ) )
& ( ! [U_555,U_554] :
( U_555 = U_554
| apply(U_558,U_555) != apply(U_558,U_554)
| ~ in(U_554,relation_dom(U_558))
| ~ in(U_555,relation_dom(U_558)) )
| ~ one_to_one(U_558) ) )
| ~ function(U_558)
| ~ relation(U_558) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_556,sK107(U_558))],[f_70_3]) ).
fof(f_70_5,plain,
( ! [U_558] :
( sK106(U_558) != sK107(U_558)
| ~ sP151(U_558) )
& ! [U_558] :
( apply(U_558,sK106(U_558)) = apply(U_558,sK107(U_558))
| ~ sP151(U_558) )
& ! [U_558] :
( in(sK107(U_558),relation_dom(U_558))
| ~ sP151(U_558) )
& ! [U_558] :
( in(sK106(U_558),relation_dom(U_558))
| ~ sP151(U_558) )
& ! [U_558,U_555,U_554] :
( one_to_one(U_558)
| sP151(U_558)
| ~ sP152(U_558,U_555,U_554) )
& ! [U_558,U_555,U_554] :
( U_555 = U_554
| apply(U_558,U_555) != apply(U_558,U_554)
| ~ in(U_554,relation_dom(U_558))
| ~ in(U_555,relation_dom(U_558))
| ~ one_to_one(U_558)
| ~ sP152(U_558,U_555,U_554) )
& ! [U_558,U_555,U_554] :
( sP152(U_558,U_555,U_554)
| ~ function(U_558)
| ~ relation(U_558) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151,sP152])],[f_70_4]) ).
cnf(f_70_6,plain,
( sP152(U_558,U_555,U_554)
| ~ function(U_558)
| ~ relation(U_558) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_7,plain,
( U_555 = U_554
| apply(U_558,U_555) != apply(U_558,U_554)
| ~ in(U_554,relation_dom(U_558))
| ~ in(U_555,relation_dom(U_558))
| ~ one_to_one(U_558)
| ~ sP152(U_558,U_555,U_554) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_8,plain,
( one_to_one(U_558)
| sP151(U_558)
| ~ sP152(U_558,U_555,U_554) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_9,plain,
( in(sK106(U_558),relation_dom(U_558))
| ~ sP151(U_558) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_10,plain,
( in(sK107(U_558),relation_dom(U_558))
| ~ sP151(U_558) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_11,plain,
( apply(U_558,sK106(U_558)) = apply(U_558,sK107(U_558))
| ~ sP151(U_558) ),
inference(clausify,[status(thm)],[f_70_5]) ).
cnf(f_70_12,plain,
( sK106(U_558) != sK107(U_558)
| ~ sP151(U_558) ),
inference(clausify,[status(thm)],[f_70_5]) ).
fof(f_71_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_71_2,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ? [U_566,U_565] :
( ( ~ in(ordered_pair(U_566,U_565),U_567)
& ? [U_564] :
( in(ordered_pair(U_564,U_565),U_568)
& in(ordered_pair(U_566,U_564),U_569) ) )
| ( ! [U_563] :
( ~ in(ordered_pair(U_563,U_565),U_568)
| ~ in(ordered_pair(U_566,U_563),U_569) )
& in(ordered_pair(U_566,U_565),U_567) ) ) )
& ( ! [U_562,U_561] :
( ( in(ordered_pair(U_562,U_561),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_561),U_568)
| ~ in(ordered_pair(U_562,U_560),U_569) ) )
& ( ? [U_559] :
( in(ordered_pair(U_559,U_561),U_568)
& in(ordered_pair(U_562,U_559),U_569) )
| ~ in(ordered_pair(U_562,U_561),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ? [U_577,U_575] :
( ~ in(ordered_pair(U_577,U_575),U_567)
& ? [U_564] :
( in(ordered_pair(U_564,U_575),U_568)
& in(ordered_pair(U_577,U_564),U_569) ) )
| ? [U_576,U_574] :
( ! [U_563] :
( ~ in(ordered_pair(U_563,U_574),U_568)
| ~ in(ordered_pair(U_576,U_563),U_569) )
& in(ordered_pair(U_576,U_574),U_567) ) )
& ( ( ! [U_573,U_571] :
( in(ordered_pair(U_573,U_571),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569) ) )
& ! [U_572,U_570] :
( ? [U_559] :
( in(ordered_pair(U_559,U_570),U_568)
& in(ordered_pair(U_572,U_559),U_569) )
| ~ in(ordered_pair(U_572,U_570),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ? [U_577,U_575] :
( ~ in(ordered_pair(U_577,U_575),U_567)
& ? [U_564] :
( in(ordered_pair(U_564,U_575),U_568)
& in(ordered_pair(U_577,U_564),U_569) ) )
| ? [U_576,U_574] :
( ! [U_563] :
( ~ in(ordered_pair(U_563,U_574),U_568)
| ~ in(ordered_pair(U_576,U_563),U_569) )
& in(ordered_pair(U_576,U_574),U_567) ) )
& ( ( ! [U_573,U_571] :
( in(ordered_pair(U_573,U_571),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569) ) )
& ! [U_572,U_570] :
( ( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
& in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569) )
| ~ in(ordered_pair(U_572,U_570),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_559,sK108(U_569,U_568,U_567,U_572,U_570))],[f_71_3]) ).
fof(f_71_5,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ? [U_577,U_575] :
( ~ in(ordered_pair(U_577,U_575),U_567)
& ? [U_564] :
( in(ordered_pair(U_564,U_575),U_568)
& in(ordered_pair(U_577,U_564),U_569) ) )
| ? [U_574] :
( ! [U_563] :
( ~ in(ordered_pair(U_563,U_574),U_568)
| ~ in(ordered_pair(sK109(U_569,U_568,U_567),U_563),U_569) )
& in(ordered_pair(sK109(U_569,U_568,U_567),U_574),U_567) ) )
& ( ( ! [U_573,U_571] :
( in(ordered_pair(U_573,U_571),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569) ) )
& ! [U_572,U_570] :
( ( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
& in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569) )
| ~ in(ordered_pair(U_572,U_570),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_576,sK109(U_569,U_568,U_567))],[f_71_4]) ).
fof(f_71_6,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ? [U_577,U_575] :
( ~ in(ordered_pair(U_577,U_575),U_567)
& ? [U_564] :
( in(ordered_pair(U_564,U_575),U_568)
& in(ordered_pair(U_577,U_564),U_569) ) )
| ( ! [U_563] :
( ~ in(ordered_pair(U_563,sK110(U_569,U_568,U_567)),U_568)
| ~ in(ordered_pair(sK109(U_569,U_568,U_567),U_563),U_569) )
& in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567) ) )
& ( ( ! [U_573,U_571] :
( in(ordered_pair(U_573,U_571),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569) ) )
& ! [U_572,U_570] :
( ( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
& in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569) )
| ~ in(ordered_pair(U_572,U_570),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_574,sK110(U_569,U_568,U_567))],[f_71_5]) ).
fof(f_71_7,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ? [U_575] :
( ~ in(ordered_pair(sK111(U_569,U_568,U_567),U_575),U_567)
& ? [U_564] :
( in(ordered_pair(U_564,U_575),U_568)
& in(ordered_pair(sK111(U_569,U_568,U_567),U_564),U_569) ) )
| ( ! [U_563] :
( ~ in(ordered_pair(U_563,sK110(U_569,U_568,U_567)),U_568)
| ~ in(ordered_pair(sK109(U_569,U_568,U_567),U_563),U_569) )
& in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567) ) )
& ( ( ! [U_573,U_571] :
( in(ordered_pair(U_573,U_571),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569) ) )
& ! [U_572,U_570] :
( ( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
& in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569) )
| ~ in(ordered_pair(U_572,U_570),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_577,sK111(U_569,U_568,U_567))],[f_71_6]) ).
fof(f_71_8,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ( ~ in(ordered_pair(sK111(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_567)
& ? [U_564] :
( in(ordered_pair(U_564,sK112(U_569,U_568,U_567)),U_568)
& in(ordered_pair(sK111(U_569,U_568,U_567),U_564),U_569) ) )
| ( ! [U_563] :
( ~ in(ordered_pair(U_563,sK110(U_569,U_568,U_567)),U_568)
| ~ in(ordered_pair(sK109(U_569,U_568,U_567),U_563),U_569) )
& in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567) ) )
& ( ( ! [U_573,U_571] :
( in(ordered_pair(U_573,U_571),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569) ) )
& ! [U_572,U_570] :
( ( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
& in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569) )
| ~ in(ordered_pair(U_572,U_570),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_575,sK112(U_569,U_568,U_567))],[f_71_7]) ).
fof(f_71_9,plain,
! [U_569] :
( ! [U_568] :
( ! [U_567] :
( ( ( U_567 = relation_composition(U_569,U_568)
| ( ~ in(ordered_pair(sK111(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_567)
& in(ordered_pair(sK113(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_568)
& in(ordered_pair(sK111(U_569,U_568,U_567),sK113(U_569,U_568,U_567)),U_569) )
| ( ! [U_563] :
( ~ in(ordered_pair(U_563,sK110(U_569,U_568,U_567)),U_568)
| ~ in(ordered_pair(sK109(U_569,U_568,U_567),U_563),U_569) )
& in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567) ) )
& ( ( ! [U_573,U_571] :
( in(ordered_pair(U_573,U_571),U_567)
| ! [U_560] :
( ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569) ) )
& ! [U_572,U_570] :
( ( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
& in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569) )
| ~ in(ordered_pair(U_572,U_570),U_567) ) )
| U_567 != relation_composition(U_569,U_568) ) )
| ~ relation(U_567) )
| ~ relation(U_568) )
| ~ relation(U_569) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_564,sK113(U_569,U_568,U_567))],[f_71_8]) ).
fof(f_71_10,plain,
( ! [U_567,U_569,U_568] :
( ~ in(ordered_pair(sK111(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_567)
| ~ sP156(U_567,U_569,U_568) )
& ! [U_567,U_569,U_568] :
( in(ordered_pair(sK113(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_568)
| ~ sP156(U_567,U_569,U_568) )
& ! [U_567,U_569,U_568] :
( in(ordered_pair(sK111(U_569,U_568,U_567),sK113(U_569,U_568,U_567)),U_569)
| ~ sP156(U_567,U_569,U_568) )
& ! [U_567,U_563,U_569,U_568] :
( ~ in(ordered_pair(U_563,sK110(U_569,U_568,U_567)),U_568)
| ~ in(ordered_pair(sK109(U_569,U_568,U_567),U_563),U_569)
| ~ sP155(U_567,U_563,U_569,U_568) )
& ! [U_567,U_563,U_569,U_568] :
( in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567)
| ~ sP155(U_567,U_563,U_569,U_568) )
& ! [U_567,U_569,U_568,U_570,U_572] :
( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
| ~ sP153(U_567,U_569,U_568,U_570,U_572) )
& ! [U_567,U_569,U_568,U_570,U_572] :
( in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569)
| ~ sP153(U_567,U_569,U_568,U_570,U_572) )
& ! [U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572] :
( in(ordered_pair(U_573,U_571),U_567)
| ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569)
| ~ sP154(U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572) )
& ! [U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572] :
( sP153(U_567,U_569,U_568,U_570,U_572)
| ~ in(ordered_pair(U_572,U_570),U_567)
| ~ sP154(U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572) )
& ! [U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572] :
( U_567 = relation_composition(U_569,U_568)
| sP156(U_567,U_569,U_568)
| sP155(U_567,U_563,U_569,U_568)
| ~ sP157(U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572) )
& ! [U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572] :
( sP154(U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572)
| U_567 != relation_composition(U_569,U_568)
| ~ sP157(U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572) )
& ! [U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572] :
( sP157(U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153,sP154,sP155,sP156,sP157])],[f_71_9]) ).
cnf(f_71_11,plain,
( sP157(U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_12,plain,
( sP154(U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572)
| U_567 != relation_composition(U_569,U_568)
| ~ sP157(U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_13,plain,
( U_567 = relation_composition(U_569,U_568)
| sP156(U_567,U_569,U_568)
| sP155(U_567,U_563,U_569,U_568)
| ~ sP157(U_567,U_560,U_563,U_569,U_568,U_573,U_570,U_571,U_572) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_14,plain,
( sP153(U_567,U_569,U_568,U_570,U_572)
| ~ in(ordered_pair(U_572,U_570),U_567)
| ~ sP154(U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_15,plain,
( in(ordered_pair(U_573,U_571),U_567)
| ~ in(ordered_pair(U_560,U_571),U_568)
| ~ in(ordered_pair(U_573,U_560),U_569)
| ~ sP154(U_567,U_560,U_569,U_568,U_573,U_570,U_571,U_572) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_16,plain,
( in(ordered_pair(U_572,sK108(U_569,U_568,U_567,U_572,U_570)),U_569)
| ~ sP153(U_567,U_569,U_568,U_570,U_572) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_17,plain,
( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
| ~ sP153(U_567,U_569,U_568,U_570,U_572) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_18,plain,
( in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567)
| ~ sP155(U_567,U_563,U_569,U_568) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_19,plain,
( ~ in(ordered_pair(U_563,sK110(U_569,U_568,U_567)),U_568)
| ~ in(ordered_pair(sK109(U_569,U_568,U_567),U_563),U_569)
| ~ sP155(U_567,U_563,U_569,U_568) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_20,plain,
( in(ordered_pair(sK111(U_569,U_568,U_567),sK113(U_569,U_568,U_567)),U_569)
| ~ sP156(U_567,U_569,U_568) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_21,plain,
( in(ordered_pair(sK113(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_568)
| ~ sP156(U_567,U_569,U_568) ),
inference(clausify,[status(thm)],[f_71_10]) ).
cnf(f_71_22,plain,
( ~ in(ordered_pair(sK111(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_567)
| ~ sP156(U_567,U_569,U_568) ),
inference(clausify,[status(thm)],[f_71_10]) ).
fof(f_72_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_72_2,plain,
! [U_585] :
( ! [U_584] :
( ( is_transitive_in(U_585,U_584)
| ? [U_583,U_582,U_581] :
( ~ in(ordered_pair(U_583,U_581),U_585)
& in(ordered_pair(U_582,U_581),U_585)
& in(ordered_pair(U_583,U_582),U_585)
& in(U_581,U_584)
& in(U_582,U_584)
& in(U_583,U_584) ) )
& ( ! [U_580,U_579,U_578] :
( in(ordered_pair(U_580,U_578),U_585)
| ~ in(ordered_pair(U_579,U_578),U_585)
| ~ in(ordered_pair(U_580,U_579),U_585)
| ~ in(U_578,U_584)
| ~ in(U_579,U_584)
| ~ in(U_580,U_584) )
| ~ is_transitive_in(U_585,U_584) ) )
| ~ relation(U_585) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_585] :
( ( ! [U_587] :
( is_transitive_in(U_585,U_587)
| ? [U_583,U_582,U_581] :
( ~ in(ordered_pair(U_583,U_581),U_585)
& in(ordered_pair(U_582,U_581),U_585)
& in(ordered_pair(U_583,U_582),U_585)
& in(U_581,U_587)
& in(U_582,U_587)
& in(U_583,U_587) ) )
& ! [U_586] :
( ! [U_580,U_579,U_578] :
( in(ordered_pair(U_580,U_578),U_585)
| ~ in(ordered_pair(U_579,U_578),U_585)
| ~ in(ordered_pair(U_580,U_579),U_585)
| ~ in(U_578,U_586)
| ~ in(U_579,U_586)
| ~ in(U_580,U_586) )
| ~ is_transitive_in(U_585,U_586) ) )
| ~ relation(U_585) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
! [U_585] :
( ( ! [U_587] :
( is_transitive_in(U_585,U_587)
| ? [U_582,U_581] :
( ~ in(ordered_pair(sK114(U_585,U_587),U_581),U_585)
& in(ordered_pair(U_582,U_581),U_585)
& in(ordered_pair(sK114(U_585,U_587),U_582),U_585)
& in(U_581,U_587)
& in(U_582,U_587)
& in(sK114(U_585,U_587),U_587) ) )
& ! [U_586] :
( ! [U_580,U_579,U_578] :
( in(ordered_pair(U_580,U_578),U_585)
| ~ in(ordered_pair(U_579,U_578),U_585)
| ~ in(ordered_pair(U_580,U_579),U_585)
| ~ in(U_578,U_586)
| ~ in(U_579,U_586)
| ~ in(U_580,U_586) )
| ~ is_transitive_in(U_585,U_586) ) )
| ~ relation(U_585) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_583,sK114(U_585,U_587))],[f_72_3]) ).
fof(f_72_5,plain,
! [U_585] :
( ( ! [U_587] :
( is_transitive_in(U_585,U_587)
| ? [U_581] :
( ~ in(ordered_pair(sK114(U_585,U_587),U_581),U_585)
& in(ordered_pair(sK115(U_585,U_587),U_581),U_585)
& in(ordered_pair(sK114(U_585,U_587),sK115(U_585,U_587)),U_585)
& in(U_581,U_587)
& in(sK115(U_585,U_587),U_587)
& in(sK114(U_585,U_587),U_587) ) )
& ! [U_586] :
( ! [U_580,U_579,U_578] :
( in(ordered_pair(U_580,U_578),U_585)
| ~ in(ordered_pair(U_579,U_578),U_585)
| ~ in(ordered_pair(U_580,U_579),U_585)
| ~ in(U_578,U_586)
| ~ in(U_579,U_586)
| ~ in(U_580,U_586) )
| ~ is_transitive_in(U_585,U_586) ) )
| ~ relation(U_585) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_582,sK115(U_585,U_587))],[f_72_4]) ).
fof(f_72_6,plain,
! [U_585] :
( ( ! [U_587] :
( is_transitive_in(U_585,U_587)
| ( ~ in(ordered_pair(sK114(U_585,U_587),sK116(U_585,U_587)),U_585)
& in(ordered_pair(sK115(U_585,U_587),sK116(U_585,U_587)),U_585)
& in(ordered_pair(sK114(U_585,U_587),sK115(U_585,U_587)),U_585)
& in(sK116(U_585,U_587),U_587)
& in(sK115(U_585,U_587),U_587)
& in(sK114(U_585,U_587),U_587) ) )
& ! [U_586] :
( ! [U_580,U_579,U_578] :
( in(ordered_pair(U_580,U_578),U_585)
| ~ in(ordered_pair(U_579,U_578),U_585)
| ~ in(ordered_pair(U_580,U_579),U_585)
| ~ in(U_578,U_586)
| ~ in(U_579,U_586)
| ~ in(U_580,U_586) )
| ~ is_transitive_in(U_585,U_586) ) )
| ~ relation(U_585) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_581,sK116(U_585,U_587))],[f_72_5]) ).
fof(f_72_7,plain,
( ! [U_585,U_587] :
( ~ in(ordered_pair(sK114(U_585,U_587),sK116(U_585,U_587)),U_585)
| ~ sP158(U_585,U_587) )
& ! [U_585,U_587] :
( in(ordered_pair(sK115(U_585,U_587),sK116(U_585,U_587)),U_585)
| ~ sP158(U_585,U_587) )
& ! [U_585,U_587] :
( in(ordered_pair(sK114(U_585,U_587),sK115(U_585,U_587)),U_585)
| ~ sP158(U_585,U_587) )
& ! [U_585,U_587] :
( in(sK116(U_585,U_587),U_587)
| ~ sP158(U_585,U_587) )
& ! [U_585,U_587] :
( in(sK115(U_585,U_587),U_587)
| ~ sP158(U_585,U_587) )
& ! [U_585,U_587] :
( in(sK114(U_585,U_587),U_587)
| ~ sP158(U_585,U_587) )
& ! [U_585,U_587,U_586,U_578,U_579,U_580] :
( is_transitive_in(U_585,U_587)
| sP158(U_585,U_587)
| ~ sP159(U_585,U_587,U_586,U_578,U_579,U_580) )
& ! [U_585,U_587,U_586,U_578,U_579,U_580] :
( in(ordered_pair(U_580,U_578),U_585)
| ~ in(ordered_pair(U_579,U_578),U_585)
| ~ in(ordered_pair(U_580,U_579),U_585)
| ~ in(U_578,U_586)
| ~ in(U_579,U_586)
| ~ in(U_580,U_586)
| ~ is_transitive_in(U_585,U_586)
| ~ sP159(U_585,U_587,U_586,U_578,U_579,U_580) )
& ! [U_585,U_587,U_586,U_578,U_579,U_580] :
( sP159(U_585,U_587,U_586,U_578,U_579,U_580)
| ~ relation(U_585) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158,sP159])],[f_72_6]) ).
cnf(f_72_8,plain,
( sP159(U_585,U_587,U_586,U_578,U_579,U_580)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_9,plain,
( in(ordered_pair(U_580,U_578),U_585)
| ~ in(ordered_pair(U_579,U_578),U_585)
| ~ in(ordered_pair(U_580,U_579),U_585)
| ~ in(U_578,U_586)
| ~ in(U_579,U_586)
| ~ in(U_580,U_586)
| ~ is_transitive_in(U_585,U_586)
| ~ sP159(U_585,U_587,U_586,U_578,U_579,U_580) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_10,plain,
( is_transitive_in(U_585,U_587)
| sP158(U_585,U_587)
| ~ sP159(U_585,U_587,U_586,U_578,U_579,U_580) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_11,plain,
( in(sK114(U_585,U_587),U_587)
| ~ sP158(U_585,U_587) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_12,plain,
( in(sK115(U_585,U_587),U_587)
| ~ sP158(U_585,U_587) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_13,plain,
( in(sK116(U_585,U_587),U_587)
| ~ sP158(U_585,U_587) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_14,plain,
( in(ordered_pair(sK114(U_585,U_587),sK115(U_585,U_587)),U_585)
| ~ sP158(U_585,U_587) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_15,plain,
( in(ordered_pair(sK115(U_585,U_587),sK116(U_585,U_587)),U_585)
| ~ sP158(U_585,U_587) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_16,plain,
( ~ in(ordered_pair(sK114(U_585,U_587),sK116(U_585,U_587)),U_585)
| ~ sP158(U_585,U_587) ),
inference(clausify,[status(thm)],[f_72_7]) ).
fof(f_73_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_73_2,plain,
! [U_592,U_591] :
( ! [U_590] :
( ( ( U_590 = complements_of_subsets(U_592,U_591)
| ? [U_589] :
( ( ( ~ in(U_589,U_590)
& in(subset_complement(U_592,U_589),U_591) )
| ( ~ in(subset_complement(U_592,U_589),U_591)
& in(U_589,U_590) ) )
& element(U_589,powerset(U_592)) ) )
& ( ! [U_588] :
( ( ( in(U_588,U_590)
| ~ in(subset_complement(U_592,U_588),U_591) )
& ( in(subset_complement(U_592,U_588),U_591)
| ~ in(U_588,U_590) ) )
| ~ element(U_588,powerset(U_592)) )
| U_590 != complements_of_subsets(U_592,U_591) ) )
| ~ element(U_590,powerset(powerset(U_592))) )
| ~ element(U_591,powerset(powerset(U_592))) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_592,U_591] :
( ! [U_590] :
( ( ( U_590 = complements_of_subsets(U_592,U_591)
| ( ( ( ~ in(sK117(U_592,U_591,U_590),U_590)
& in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591) )
| ( ~ in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591)
& in(sK117(U_592,U_591,U_590),U_590) ) )
& element(sK117(U_592,U_591,U_590),powerset(U_592)) ) )
& ( ! [U_588] :
( ( ( in(U_588,U_590)
| ~ in(subset_complement(U_592,U_588),U_591) )
& ( in(subset_complement(U_592,U_588),U_591)
| ~ in(U_588,U_590) ) )
| ~ element(U_588,powerset(U_592)) )
| U_590 != complements_of_subsets(U_592,U_591) ) )
| ~ element(U_590,powerset(powerset(U_592))) )
| ~ element(U_591,powerset(powerset(U_592))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_589,sK117(U_592,U_591,U_590))],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_591,U_592,U_590] :
( ~ in(sK117(U_592,U_591,U_590),U_590)
| ~ sP162(U_591,U_592,U_590) )
& ! [U_591,U_592,U_590] :
( in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591)
| ~ sP162(U_591,U_592,U_590) )
& ! [U_591,U_592,U_590] :
( ~ in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591)
| ~ sP161(U_591,U_592,U_590) )
& ! [U_591,U_592,U_590] :
( in(sK117(U_592,U_591,U_590),U_590)
| ~ sP161(U_591,U_592,U_590) )
& ! [U_591,U_592,U_590] :
( sP162(U_591,U_592,U_590)
| sP161(U_591,U_592,U_590)
| ~ sP163(U_591,U_592,U_590) )
& ! [U_591,U_592,U_590] :
( element(sK117(U_592,U_591,U_590),powerset(U_592))
| ~ sP163(U_591,U_592,U_590) )
& ! [U_591,U_588,U_592,U_590] :
( in(U_588,U_590)
| ~ in(subset_complement(U_592,U_588),U_591)
| ~ sP160(U_591,U_588,U_592,U_590) )
& ! [U_591,U_588,U_592,U_590] :
( in(subset_complement(U_592,U_588),U_591)
| ~ in(U_588,U_590)
| ~ sP160(U_591,U_588,U_592,U_590) )
& ! [U_591,U_588,U_592,U_590] :
( U_590 = complements_of_subsets(U_592,U_591)
| sP163(U_591,U_592,U_590)
| ~ sP164(U_591,U_588,U_592,U_590) )
& ! [U_591,U_588,U_592,U_590] :
( sP160(U_591,U_588,U_592,U_590)
| ~ element(U_588,powerset(U_592))
| U_590 != complements_of_subsets(U_592,U_591)
| ~ sP164(U_591,U_588,U_592,U_590) )
& ! [U_591,U_588,U_592,U_590] :
( sP164(U_591,U_588,U_592,U_590)
| ~ element(U_590,powerset(powerset(U_592)))
| ~ element(U_591,powerset(powerset(U_592))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160,sP161,sP162,sP163,sP164])],[f_73_3]) ).
cnf(f_73_5,plain,
( sP164(U_591,U_588,U_592,U_590)
| ~ element(U_590,powerset(powerset(U_592)))
| ~ element(U_591,powerset(powerset(U_592))) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_6,plain,
( sP160(U_591,U_588,U_592,U_590)
| ~ element(U_588,powerset(U_592))
| U_590 != complements_of_subsets(U_592,U_591)
| ~ sP164(U_591,U_588,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_7,plain,
( U_590 = complements_of_subsets(U_592,U_591)
| sP163(U_591,U_592,U_590)
| ~ sP164(U_591,U_588,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_8,plain,
( in(subset_complement(U_592,U_588),U_591)
| ~ in(U_588,U_590)
| ~ sP160(U_591,U_588,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_9,plain,
( in(U_588,U_590)
| ~ in(subset_complement(U_592,U_588),U_591)
| ~ sP160(U_591,U_588,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_10,plain,
( element(sK117(U_592,U_591,U_590),powerset(U_592))
| ~ sP163(U_591,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_11,plain,
( sP162(U_591,U_592,U_590)
| sP161(U_591,U_592,U_590)
| ~ sP163(U_591,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_12,plain,
( in(sK117(U_592,U_591,U_590),U_590)
| ~ sP161(U_591,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_13,plain,
( ~ in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591)
| ~ sP161(U_591,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_14,plain,
( in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591)
| ~ sP162(U_591,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_15,plain,
( ~ in(sK117(U_592,U_591,U_590),U_590)
| ~ sP162(U_591,U_592,U_590) ),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_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_74_2,plain,
! [U_594,U_593] :
( ( proper_subset(U_594,U_593)
| U_594 = U_593
| ~ subset(U_594,U_593) )
& ( ( U_594 != U_593
& subset(U_594,U_593) )
| ~ proper_subset(U_594,U_593) ) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
( ! [U_598,U_596] :
( proper_subset(U_598,U_596)
| U_598 = U_596
| ~ subset(U_598,U_596) )
& ! [U_597,U_595] :
( ( U_597 != U_595
& subset(U_597,U_595) )
| ~ proper_subset(U_597,U_595) ) ),
inference(miniscope,[status(thm)],[f_74_2]) ).
fof(f_74_4,plain,
( ! [U_597,U_595] :
( U_597 != U_595
| ~ sP165(U_597,U_595) )
& ! [U_597,U_595] :
( subset(U_597,U_595)
| ~ sP165(U_597,U_595) )
& ! [U_596,U_598] :
( proper_subset(U_598,U_596)
| U_598 = U_596
| ~ subset(U_598,U_596) )
& ! [U_597,U_595] :
( sP165(U_597,U_595)
| ~ proper_subset(U_597,U_595) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_74_3]) ).
cnf(f_74_5,plain,
( sP165(U_597,U_595)
| ~ proper_subset(U_597,U_595) ),
inference(clausify,[status(thm)],[f_74_4]) ).
cnf(f_74_6,plain,
( proper_subset(U_598,U_596)
| U_598 = U_596
| ~ subset(U_598,U_596) ),
inference(clausify,[status(thm)],[f_74_4]) ).
cnf(f_74_7,plain,
( subset(U_597,U_595)
| ~ sP165(U_597,U_595) ),
inference(clausify,[status(thm)],[f_74_4]) ).
cnf(f_74_8,plain,
( U_597 != U_595
| ~ sP165(U_597,U_595) ),
inference(clausify,[status(thm)],[f_74_4]) ).
fof(f_75_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_75_2,plain,
! [U_599] :
( function_inverse(U_599) = relation_inverse(U_599)
| ~ one_to_one(U_599)
| ~ function(U_599)
| ~ relation(U_599) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_599] :
( function_inverse(U_599) = relation_inverse(U_599)
| ~ one_to_one(U_599)
| ~ function(U_599)
| ~ relation(U_599) ),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
( function_inverse(U_599) = relation_inverse(U_599)
| ~ one_to_one(U_599)
| ~ function(U_599)
| ~ relation(U_599) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_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_76_2,plain,
! [U_600] :
( ( ( reflexive(U_600)
| ~ is_reflexive_in(U_600,relation_field(U_600)) )
& ( is_reflexive_in(U_600,relation_field(U_600))
| ~ reflexive(U_600) ) )
| ~ relation(U_600) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_600] :
( reflexive(U_600)
| ~ is_reflexive_in(U_600,relation_field(U_600))
| ~ sP166(U_600) )
& ! [U_600] :
( is_reflexive_in(U_600,relation_field(U_600))
| ~ reflexive(U_600)
| ~ sP166(U_600) )
& ! [U_600] :
( sP166(U_600)
| ~ relation(U_600) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_76_2]) ).
cnf(f_76_4,plain,
( sP166(U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_5,plain,
( is_reflexive_in(U_600,relation_field(U_600))
| ~ reflexive(U_600)
| ~ sP166(U_600) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_6,plain,
( reflexive(U_600)
| ~ is_reflexive_in(U_600,relation_field(U_600))
| ~ sP166(U_600) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
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_enumset1]) ).
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_funct_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_mcart_1]) ).
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_ordinal1]) ).
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_relat_1]) ).
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_setfam_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,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_84_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_84_1]) ).
cnf(f_84_3,plain,
$true,
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
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] : relation(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k1_wellord2]) ).
fof(f_86_2,plain,
! [U_601] : relation(inclusion_relation(U_601)),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_601] : relation(inclusion_relation(U_601)),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
relation(inclusion_relation(U_601)),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_88_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_88_1]) ).
cnf(f_88_3,plain,
$true,
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_602] :
( ( function(function_inverse(U_602))
& relation(function_inverse(U_602)) )
| ~ function(U_602)
| ~ relation(U_602) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_602] :
( function(function_inverse(U_602))
| ~ sP167(U_602) )
& ! [U_602] :
( relation(function_inverse(U_602))
| ~ sP167(U_602) )
& ! [U_602] :
( sP167(U_602)
| ~ function(U_602)
| ~ relation(U_602) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_89_2]) ).
cnf(f_89_4,plain,
( sP167(U_602)
| ~ function(U_602)
| ~ relation(U_602) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_5,plain,
( relation(function_inverse(U_602))
| ~ sP167(U_602) ),
inference(clausify,[status(thm)],[f_89_3]) ).
cnf(f_89_6,plain,
( function(function_inverse(U_602))
| ~ sP167(U_602) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_mcart_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_k2_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] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_92_2,plain,
! [U_603] : element(cast_to_subset(U_603),powerset(U_603)),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_603] : element(cast_to_subset(U_603),powerset(U_603)),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
element(cast_to_subset(U_603),powerset(U_603)),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_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,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_94_2,plain,
! [U_605,U_604] :
( relation(relation_restriction(U_605,U_604))
| ~ relation(U_605) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_605] :
( ! [U_604] : relation(relation_restriction(U_605,U_604))
| ~ relation(U_605) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
fof(f_94_4,plain,
! [U_604,U_605] :
( relation(relation_restriction(U_605,U_604))
| ~ relation(U_605) ),
inference(definitional_conversion,[status(esa)],[f_94_3]) ).
cnf(f_94_5,plain,
( relation(relation_restriction(U_605,U_604))
| ~ relation(U_605) ),
inference(clausify,[status(thm)],[f_94_4]) ).
fof(f_95_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_95_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_95_1]) ).
cnf(f_95_3,plain,
$true,
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
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_k3_relat_1]) ).
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] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_98_2,plain,
! [U_607,U_606] :
( element(subset_complement(U_607,U_606),powerset(U_607))
| ~ element(U_606,powerset(U_607)) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_607,U_606] :
( element(subset_complement(U_607,U_606),powerset(U_607))
| ~ element(U_606,powerset(U_607)) ),
inference(definitional_conversion,[status(esa)],[f_98_2]) ).
cnf(f_98_4,plain,
( element(subset_complement(U_607,U_606),powerset(U_607))
| ~ element(U_606,powerset(U_607)) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_99_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_99_1]) ).
cnf(f_99_3,plain,
$true,
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_100_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_100_1]) ).
cnf(f_100_3,plain,
$true,
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_101_2,plain,
! [U_608] :
( relation(relation_inverse(U_608))
| ~ relation(U_608) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_608] :
( relation(relation_inverse(U_608))
| ~ relation(U_608) ),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
( relation(relation_inverse(U_608))
| ~ relation(U_608) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_1,plain,
! [A,B,C] :
( element(relation_dom_as_subset(A,B,C),powerset(A))
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_k4_relset_1]) ).
fof(f_102_2,plain,
! [U_611,U_610,U_609] :
( element(relation_dom_as_subset(U_611,U_610,U_609),powerset(U_611))
| ~ relation_of2(U_609,U_611,U_610) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_610,U_609,U_611] :
( element(relation_dom_as_subset(U_611,U_610,U_609),powerset(U_611))
| ~ relation_of2(U_609,U_611,U_610) ),
inference(definitional_conversion,[status(esa)],[f_102_2]) ).
cnf(f_102_4,plain,
( element(relation_dom_as_subset(U_611,U_610,U_609),powerset(U_611))
| ~ relation_of2(U_609,U_611,U_610) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_103_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_103_1]) ).
cnf(f_103_3,plain,
$true,
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_104_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_104_1]) ).
cnf(f_104_3,plain,
$true,
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_105_2,plain,
! [U_613,U_612] :
( relation(relation_composition(U_613,U_612))
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_612,U_613] :
( relation(relation_composition(U_613,U_612))
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( relation(relation_composition(U_613,U_612))
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [A,B,C] :
( element(relation_rng_as_subset(A,B,C),powerset(B))
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_k5_relset_1]) ).
fof(f_106_2,plain,
! [U_616,U_615,U_614] :
( element(relation_rng_as_subset(U_616,U_615,U_614),powerset(U_615))
| ~ relation_of2(U_614,U_616,U_615) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_616,U_614,U_615] :
( element(relation_rng_as_subset(U_616,U_615,U_614),powerset(U_615))
| ~ relation_of2(U_614,U_616,U_615) ),
inference(definitional_conversion,[status(esa)],[f_106_2]) ).
cnf(f_106_4,plain,
( element(relation_rng_as_subset(U_616,U_615,U_614),powerset(U_615))
| ~ relation_of2(U_614,U_616,U_615) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_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_107_2,plain,
! [U_618,U_617] :
( element(union_of_subsets(U_618,U_617),powerset(U_618))
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_617,U_618] :
( element(union_of_subsets(U_618,U_617),powerset(U_618))
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( element(union_of_subsets(U_618,U_617),powerset(U_618))
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_108_2,plain,
! [U_619] : relation(identity_relation(U_619)),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_619] : relation(identity_relation(U_619)),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
relation(identity_relation(U_619)),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_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_109_2,plain,
! [U_621,U_620] :
( element(meet_of_subsets(U_621,U_620),powerset(U_621))
| ~ element(U_620,powerset(powerset(U_621))) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_620,U_621] :
( element(meet_of_subsets(U_621,U_620),powerset(U_621))
| ~ element(U_620,powerset(powerset(U_621))) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( element(meet_of_subsets(U_621,U_620),powerset(U_621))
| ~ element(U_620,powerset(powerset(U_621))) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_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_110_2,plain,
! [U_624,U_623,U_622] :
( element(subset_difference(U_624,U_623,U_622),powerset(U_624))
| ~ element(U_622,powerset(U_624))
| ~ element(U_623,powerset(U_624)) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_623,U_622,U_624] :
( element(subset_difference(U_624,U_623,U_622),powerset(U_624))
| ~ element(U_622,powerset(U_624))
| ~ element(U_623,powerset(U_624)) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( element(subset_difference(U_624,U_623,U_622),powerset(U_624))
| ~ element(U_622,powerset(U_624))
| ~ element(U_623,powerset(U_624)) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_111_2,plain,
! [U_626,U_625] :
( relation(relation_dom_restriction(U_626,U_625))
| ~ relation(U_626) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_626] :
( ! [U_625] : relation(relation_dom_restriction(U_626,U_625))
| ~ relation(U_626) ),
inference(miniscope,[status(thm)],[f_111_2]) ).
fof(f_111_4,plain,
! [U_626,U_625] :
( relation(relation_dom_restriction(U_626,U_625))
| ~ relation(U_626) ),
inference(definitional_conversion,[status(esa)],[f_111_3]) ).
cnf(f_111_5,plain,
( relation(relation_dom_restriction(U_626,U_625))
| ~ relation(U_626) ),
inference(clausify,[status(thm)],[f_111_4]) ).
fof(f_112_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_112_2,plain,
! [U_628,U_627] :
( element(complements_of_subsets(U_628,U_627),powerset(powerset(U_628)))
| ~ element(U_627,powerset(powerset(U_628))) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_627,U_628] :
( element(complements_of_subsets(U_628,U_627),powerset(powerset(U_628)))
| ~ element(U_627,powerset(powerset(U_628))) ),
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
( element(complements_of_subsets(U_628,U_627),powerset(powerset(U_628)))
| ~ element(U_627,powerset(powerset(U_628))) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_113_2,plain,
! [U_630,U_629] :
( relation(relation_rng_restriction(U_630,U_629))
| ~ relation(U_629) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_629,U_630] :
( relation(relation_rng_restriction(U_630,U_629))
| ~ relation(U_629) ),
inference(definitional_conversion,[status(esa)],[f_113_2]) ).
cnf(f_113_4,plain,
( relation(relation_rng_restriction(U_630,U_629))
| ~ relation(U_629) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
fof(f_114_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_114_1]) ).
cnf(f_114_3,plain,
$true,
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_115_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_115_1]) ).
cnf(f_115_3,plain,
$true,
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_116_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_116_1]) ).
cnf(f_116_3,plain,
$true,
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_633,U_632,U_631] :
( element(U_631,powerset(cartesian_product2(U_633,U_632)))
| ~ relation_of2_as_subset(U_631,U_633,U_632) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_631,U_632,U_633] :
( element(U_631,powerset(cartesian_product2(U_633,U_632)))
| ~ relation_of2_as_subset(U_631,U_633,U_632) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( element(U_631,powerset(cartesian_product2(U_633,U_632)))
| ~ relation_of2_as_subset(U_631,U_633,U_632) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_118_2,plain,
! [U_636,U_635] :
? [U_634] : relation_of2(U_634,U_636,U_635),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_636,U_635] : relation_of2(sK118(U_636,U_635),U_636,U_635),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_634,sK118(U_636,U_635))],[f_118_2]) ).
fof(f_118_4,plain,
! [U_635,U_636] : relation_of2(sK118(U_636,U_635),U_636,U_635),
inference(definitional_conversion,[status(esa)],[f_118_3]) ).
cnf(f_118_5,plain,
relation_of2(sK118(U_636,U_635),U_636,U_635),
inference(clausify,[status(thm)],[f_118_4]) ).
fof(f_119_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_119_2,plain,
! [U_638] :
? [U_637] : element(U_637,U_638),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_638] : element(sK119(U_638),U_638),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_637,sK119(U_638))],[f_119_2]) ).
fof(f_119_4,plain,
! [U_638] : element(sK119(U_638),U_638),
inference(definitional_conversion,[status(esa)],[f_119_3]) ).
cnf(f_119_5,plain,
element(sK119(U_638),U_638),
inference(clausify,[status(thm)],[f_119_4]) ).
fof(f_120_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_120_2,plain,
! [U_641,U_640] :
? [U_639] : relation_of2_as_subset(U_639,U_641,U_640),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_641,U_640] : relation_of2_as_subset(sK120(U_641,U_640),U_641,U_640),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_639,sK120(U_641,U_640))],[f_120_2]) ).
fof(f_120_4,plain,
! [U_640,U_641] : relation_of2_as_subset(sK120(U_641,U_640),U_641,U_640),
inference(definitional_conversion,[status(esa)],[f_120_3]) ).
cnf(f_120_5,plain,
relation_of2_as_subset(sK120(U_641,U_640),U_641,U_640),
inference(clausify,[status(thm)],[f_120_4]) ).
fof(f_121_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_121_2,plain,
! [U_643,U_642] :
( ( relation(relation_composition(U_642,U_643))
& empty(relation_composition(U_642,U_643)) )
| ~ relation(U_642)
| ~ empty(U_643) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
( ! [U_642,U_643] :
( relation(relation_composition(U_642,U_643))
| ~ sP168(U_642,U_643) )
& ! [U_642,U_643] :
( empty(relation_composition(U_642,U_643))
| ~ sP168(U_642,U_643) )
& ! [U_642,U_643] :
( sP168(U_642,U_643)
| ~ relation(U_642)
| ~ empty(U_643) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168])],[f_121_2]) ).
cnf(f_121_4,plain,
( sP168(U_642,U_643)
| ~ relation(U_642)
| ~ empty(U_643) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_5,plain,
( empty(relation_composition(U_642,U_643))
| ~ sP168(U_642,U_643) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_6,plain,
( relation(relation_composition(U_642,U_643))
| ~ sP168(U_642,U_643) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_122_2,plain,
! [U_644] :
( ( relation(relation_inverse(U_644))
& empty(relation_inverse(U_644)) )
| ~ empty(U_644) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_644] :
( relation(relation_inverse(U_644))
| ~ sP169(U_644) )
& ! [U_644] :
( empty(relation_inverse(U_644))
| ~ sP169(U_644) )
& ! [U_644] :
( sP169(U_644)
| ~ empty(U_644) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_122_2]) ).
cnf(f_122_4,plain,
( sP169(U_644)
| ~ empty(U_644) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_5,plain,
( empty(relation_inverse(U_644))
| ~ sP169(U_644) ),
inference(clausify,[status(thm)],[f_122_3]) ).
cnf(f_122_6,plain,
( relation(relation_inverse(U_644))
| ~ sP169(U_644) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_123_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_123_1]) ).
cnf(f_123_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_123_2]) ).
cnf(f_123_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_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_124_2,plain,
! [U_646,U_645] :
( ( relation_empty_yielding(relation_dom_restriction(U_646,U_645))
& relation(relation_dom_restriction(U_646,U_645)) )
| ~ relation_empty_yielding(U_646)
| ~ relation(U_646) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_646] :
( ( ! [U_648] : relation_empty_yielding(relation_dom_restriction(U_646,U_648))
& ! [U_647] : relation(relation_dom_restriction(U_646,U_647)) )
| ~ relation_empty_yielding(U_646)
| ~ relation(U_646) ),
inference(miniscope,[status(thm)],[f_124_2]) ).
fof(f_124_4,plain,
( ! [U_646,U_648,U_647] :
( relation_empty_yielding(relation_dom_restriction(U_646,U_648))
| ~ sP170(U_646,U_648,U_647) )
& ! [U_646,U_648,U_647] :
( relation(relation_dom_restriction(U_646,U_647))
| ~ sP170(U_646,U_648,U_647) )
& ! [U_646,U_648,U_647] :
( sP170(U_646,U_648,U_647)
| ~ relation_empty_yielding(U_646)
| ~ relation(U_646) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_124_3]) ).
cnf(f_124_5,plain,
( sP170(U_646,U_648,U_647)
| ~ relation_empty_yielding(U_646)
| ~ relation(U_646) ),
inference(clausify,[status(thm)],[f_124_4]) ).
cnf(f_124_6,plain,
( relation(relation_dom_restriction(U_646,U_647))
| ~ sP170(U_646,U_648,U_647) ),
inference(clausify,[status(thm)],[f_124_4]) ).
cnf(f_124_7,plain,
( relation_empty_yielding(relation_dom_restriction(U_646,U_648))
| ~ sP170(U_646,U_648,U_647) ),
inference(clausify,[status(thm)],[f_124_4]) ).
fof(f_125_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_125_2,plain,
! [U_650,U_649] :
( ( function(relation_composition(U_650,U_649))
& relation(relation_composition(U_650,U_649)) )
| ~ function(U_649)
| ~ relation(U_649)
| ~ function(U_650)
| ~ relation(U_650) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_650,U_649] :
( function(relation_composition(U_650,U_649))
| ~ sP171(U_650,U_649) )
& ! [U_650,U_649] :
( relation(relation_composition(U_650,U_649))
| ~ sP171(U_650,U_649) )
& ! [U_650,U_649] :
( sP171(U_650,U_649)
| ~ function(U_649)
| ~ relation(U_649)
| ~ function(U_650)
| ~ relation(U_650) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171])],[f_125_2]) ).
cnf(f_125_4,plain,
( sP171(U_650,U_649)
| ~ function(U_649)
| ~ relation(U_649)
| ~ function(U_650)
| ~ relation(U_650) ),
inference(clausify,[status(thm)],[f_125_3]) ).
cnf(f_125_5,plain,
( relation(relation_composition(U_650,U_649))
| ~ sP171(U_650,U_649) ),
inference(clausify,[status(thm)],[f_125_3]) ).
cnf(f_125_6,plain,
( function(relation_composition(U_650,U_649))
| ~ sP171(U_650,U_649) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_126_2,plain,
! [U_651] : ~ empty(succ(U_651)),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_651] : ~ empty(succ(U_651)),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
~ empty(succ(U_651)),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_127_2,plain,
! [U_653,U_652] :
( relation(set_intersection2(U_653,U_652))
| ~ relation(U_652)
| ~ relation(U_653) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_652,U_653] :
( relation(set_intersection2(U_653,U_652))
| ~ relation(U_652)
| ~ relation(U_653) ),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
( relation(set_intersection2(U_653,U_652))
| ~ relation(U_652)
| ~ relation(U_653) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_128_2,plain,
! [U_654] : ~ empty(powerset(U_654)),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_654] : ~ empty(powerset(U_654)),
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
~ empty(powerset(U_654)),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_129_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_129_1]) ).
cnf(f_129_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_130_2,plain,
! [U_656,U_655] : ~ empty(ordered_pair(U_656,U_655)),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_656,U_655] : ~ empty(ordered_pair(U_656,U_655)),
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
~ empty(ordered_pair(U_656,U_655)),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_131_2,plain,
! [U_657] :
( function(identity_relation(U_657))
& relation(identity_relation(U_657)) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
( ! [U_659] : function(identity_relation(U_659))
& ! [U_658] : relation(identity_relation(U_658)) ),
inference(miniscope,[status(thm)],[f_131_2]) ).
fof(f_131_4,plain,
( ! [U_659] : function(identity_relation(U_659))
& ! [U_658] : relation(identity_relation(U_658)) ),
inference(definitional_conversion,[status(esa)],[f_131_3]) ).
cnf(f_131_5,plain,
relation(identity_relation(U_658)),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_6,plain,
function(identity_relation(U_659)),
inference(clausify,[status(thm)],[f_131_4]) ).
fof(f_132_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_132_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_132_1]) ).
cnf(f_132_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
cnf(f_132_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_133_2,plain,
! [U_661,U_660] :
( relation(set_union2(U_661,U_660))
| ~ relation(U_660)
| ~ relation(U_661) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_661,U_660] :
( relation(set_union2(U_661,U_660))
| ~ relation(U_660)
| ~ relation(U_661) ),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
( relation(set_union2(U_661,U_660))
| ~ relation(U_660)
| ~ relation(U_661) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_134_2,plain,
! [U_662] : ~ empty(singleton(U_662)),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_662] : ~ empty(singleton(U_662)),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
~ empty(singleton(U_662)),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_135_2,plain,
! [U_664,U_663] :
( ~ empty(set_union2(U_664,U_663))
| empty(U_664) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_664] :
( ! [U_663] : ~ empty(set_union2(U_664,U_663))
| empty(U_664) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
fof(f_135_4,plain,
! [U_663,U_664] :
( ~ empty(set_union2(U_664,U_663))
| empty(U_664) ),
inference(definitional_conversion,[status(esa)],[f_135_3]) ).
cnf(f_135_5,plain,
( ~ empty(set_union2(U_664,U_663))
| empty(U_664) ),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_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_136_2,plain,
! [U_665] :
( ( function(relation_inverse(U_665))
& relation(relation_inverse(U_665)) )
| ~ one_to_one(U_665)
| ~ function(U_665)
| ~ relation(U_665) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_665] :
( function(relation_inverse(U_665))
| ~ sP172(U_665) )
& ! [U_665] :
( relation(relation_inverse(U_665))
| ~ sP172(U_665) )
& ! [U_665] :
( sP172(U_665)
| ~ one_to_one(U_665)
| ~ function(U_665)
| ~ relation(U_665) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_136_2]) ).
cnf(f_136_4,plain,
( sP172(U_665)
| ~ one_to_one(U_665)
| ~ function(U_665)
| ~ relation(U_665) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_5,plain,
( relation(relation_inverse(U_665))
| ~ sP172(U_665) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_6,plain,
( function(relation_inverse(U_665))
| ~ sP172(U_665) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_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_137_2,plain,
! [U_666] :
( ( ordinal(succ(U_666))
& epsilon_connected(succ(U_666))
& epsilon_transitive(succ(U_666))
& ~ empty(succ(U_666)) )
| ~ ordinal(U_666) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
( ! [U_666] :
( ordinal(succ(U_666))
| ~ sP173(U_666) )
& ! [U_666] :
( epsilon_connected(succ(U_666))
| ~ sP173(U_666) )
& ! [U_666] :
( epsilon_transitive(succ(U_666))
| ~ sP173(U_666) )
& ! [U_666] :
( ~ empty(succ(U_666))
| ~ sP173(U_666) )
& ! [U_666] :
( sP173(U_666)
| ~ ordinal(U_666) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_137_2]) ).
cnf(f_137_4,plain,
( sP173(U_666)
| ~ ordinal(U_666) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_5,plain,
( ~ empty(succ(U_666))
| ~ sP173(U_666) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_6,plain,
( epsilon_transitive(succ(U_666))
| ~ sP173(U_666) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_7,plain,
( epsilon_connected(succ(U_666))
| ~ sP173(U_666) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_8,plain,
( ordinal(succ(U_666))
| ~ sP173(U_666) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_138_2,plain,
! [U_668,U_667] :
( relation(set_difference(U_668,U_667))
| ~ relation(U_667)
| ~ relation(U_668) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_668,U_667] :
( relation(set_difference(U_668,U_667))
| ~ relation(U_667)
| ~ relation(U_668) ),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
( relation(set_difference(U_668,U_667))
| ~ relation(U_667)
| ~ relation(U_668) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_139_2,plain,
! [U_670,U_669] : ~ empty(unordered_pair(U_670,U_669)),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_670,U_669] : ~ empty(unordered_pair(U_670,U_669)),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
~ empty(unordered_pair(U_670,U_669)),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_140_2,plain,
! [U_672,U_671] :
( ~ empty(set_union2(U_671,U_672))
| empty(U_672) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_672] :
( ! [U_671] : ~ empty(set_union2(U_671,U_672))
| empty(U_672) ),
inference(miniscope,[status(thm)],[f_140_2]) ).
fof(f_140_4,plain,
! [U_671,U_672] :
( ~ empty(set_union2(U_671,U_672))
| empty(U_672) ),
inference(definitional_conversion,[status(esa)],[f_140_3]) ).
cnf(f_140_5,plain,
( ~ empty(set_union2(U_671,U_672))
| empty(U_672) ),
inference(clausify,[status(thm)],[f_140_4]) ).
fof(f_141_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_141_2,plain,
! [U_674,U_673] :
( ( function(relation_dom_restriction(U_674,U_673))
& relation(relation_dom_restriction(U_674,U_673)) )
| ~ function(U_674)
| ~ relation(U_674) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_674] :
( ( ! [U_676] : function(relation_dom_restriction(U_674,U_676))
& ! [U_675] : relation(relation_dom_restriction(U_674,U_675)) )
| ~ function(U_674)
| ~ relation(U_674) ),
inference(miniscope,[status(thm)],[f_141_2]) ).
fof(f_141_4,plain,
( ! [U_674,U_675,U_676] :
( function(relation_dom_restriction(U_674,U_676))
| ~ sP174(U_674,U_675,U_676) )
& ! [U_674,U_675,U_676] :
( relation(relation_dom_restriction(U_674,U_675))
| ~ sP174(U_674,U_675,U_676) )
& ! [U_674,U_675,U_676] :
( sP174(U_674,U_675,U_676)
| ~ function(U_674)
| ~ relation(U_674) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_141_3]) ).
cnf(f_141_5,plain,
( sP174(U_674,U_675,U_676)
| ~ function(U_674)
| ~ relation(U_674) ),
inference(clausify,[status(thm)],[f_141_4]) ).
cnf(f_141_6,plain,
( relation(relation_dom_restriction(U_674,U_675))
| ~ sP174(U_674,U_675,U_676) ),
inference(clausify,[status(thm)],[f_141_4]) ).
cnf(f_141_7,plain,
( function(relation_dom_restriction(U_674,U_676))
| ~ sP174(U_674,U_675,U_676) ),
inference(clausify,[status(thm)],[f_141_4]) ).
fof(f_142_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_142_2,plain,
! [U_677] :
( ( ordinal(union(U_677))
& epsilon_connected(union(U_677))
& epsilon_transitive(union(U_677)) )
| ~ ordinal(U_677) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_677] :
( ordinal(union(U_677))
| ~ sP175(U_677) )
& ! [U_677] :
( epsilon_connected(union(U_677))
| ~ sP175(U_677) )
& ! [U_677] :
( epsilon_transitive(union(U_677))
| ~ sP175(U_677) )
& ! [U_677] :
( sP175(U_677)
| ~ ordinal(U_677) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_142_2]) ).
cnf(f_142_4,plain,
( sP175(U_677)
| ~ ordinal(U_677) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( epsilon_transitive(union(U_677))
| ~ sP175(U_677) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_6,plain,
( epsilon_connected(union(U_677))
| ~ sP175(U_677) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_7,plain,
( ordinal(union(U_677))
| ~ sP175(U_677) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_143_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_143_1]) ).
cnf(f_143_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_144_2,plain,
! [U_679,U_678] :
( ~ empty(cartesian_product2(U_679,U_678))
| empty(U_678)
| empty(U_679) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_678,U_679] :
( ~ empty(cartesian_product2(U_679,U_678))
| empty(U_678)
| empty(U_679) ),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
( ~ empty(cartesian_product2(U_679,U_678))
| empty(U_678)
| empty(U_679) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_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_145_2,plain,
! [U_681,U_680] :
( ( function(relation_rng_restriction(U_681,U_680))
& relation(relation_rng_restriction(U_681,U_680)) )
| ~ function(U_680)
| ~ relation(U_680) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
( ! [U_681,U_680] :
( function(relation_rng_restriction(U_681,U_680))
| ~ sP176(U_681,U_680) )
& ! [U_681,U_680] :
( relation(relation_rng_restriction(U_681,U_680))
| ~ sP176(U_681,U_680) )
& ! [U_681,U_680] :
( sP176(U_681,U_680)
| ~ function(U_680)
| ~ relation(U_680) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_145_2]) ).
cnf(f_145_4,plain,
( sP176(U_681,U_680)
| ~ function(U_680)
| ~ relation(U_680) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_5,plain,
( relation(relation_rng_restriction(U_681,U_680))
| ~ sP176(U_681,U_680) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_6,plain,
( function(relation_rng_restriction(U_681,U_680))
| ~ sP176(U_681,U_680) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_146_2,plain,
! [U_682] :
( ~ empty(relation_dom(U_682))
| ~ relation(U_682)
| empty(U_682) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_682] :
( ~ empty(relation_dom(U_682))
| ~ relation(U_682)
| empty(U_682) ),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
( ~ empty(relation_dom(U_682))
| ~ relation(U_682)
| empty(U_682) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_147_2,plain,
! [U_683] :
( ~ empty(relation_rng(U_683))
| ~ relation(U_683)
| empty(U_683) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_683] :
( ~ empty(relation_rng(U_683))
| ~ relation(U_683)
| empty(U_683) ),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
( ~ empty(relation_rng(U_683))
| ~ relation(U_683)
| empty(U_683) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_148_2,plain,
! [U_684] :
( ( relation(relation_dom(U_684))
& empty(relation_dom(U_684)) )
| ~ empty(U_684) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
( ! [U_684] :
( relation(relation_dom(U_684))
| ~ sP177(U_684) )
& ! [U_684] :
( empty(relation_dom(U_684))
| ~ sP177(U_684) )
& ! [U_684] :
( sP177(U_684)
| ~ empty(U_684) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_148_2]) ).
cnf(f_148_4,plain,
( sP177(U_684)
| ~ empty(U_684) ),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_5,plain,
( empty(relation_dom(U_684))
| ~ sP177(U_684) ),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_6,plain,
( relation(relation_dom(U_684))
| ~ sP177(U_684) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_149_2,plain,
! [U_685] :
( ( relation(relation_rng(U_685))
& empty(relation_rng(U_685)) )
| ~ empty(U_685) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
( ! [U_685] :
( relation(relation_rng(U_685))
| ~ sP178(U_685) )
& ! [U_685] :
( empty(relation_rng(U_685))
| ~ sP178(U_685) )
& ! [U_685] :
( sP178(U_685)
| ~ empty(U_685) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_149_2]) ).
cnf(f_149_4,plain,
( sP178(U_685)
| ~ empty(U_685) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_5,plain,
( empty(relation_rng(U_685))
| ~ sP178(U_685) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_6,plain,
( relation(relation_rng(U_685))
| ~ sP178(U_685) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_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_150_2,plain,
! [U_687,U_686] :
( ( relation(relation_composition(U_687,U_686))
& empty(relation_composition(U_687,U_686)) )
| ~ relation(U_686)
| ~ empty(U_687) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
( ! [U_687,U_686] :
( relation(relation_composition(U_687,U_686))
| ~ sP179(U_687,U_686) )
& ! [U_687,U_686] :
( empty(relation_composition(U_687,U_686))
| ~ sP179(U_687,U_686) )
& ! [U_687,U_686] :
( sP179(U_687,U_686)
| ~ relation(U_686)
| ~ empty(U_687) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_150_2]) ).
cnf(f_150_4,plain,
( sP179(U_687,U_686)
| ~ relation(U_686)
| ~ empty(U_687) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( empty(relation_composition(U_687,U_686))
| ~ sP179(U_687,U_686) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_6,plain,
( relation(relation_composition(U_687,U_686))
| ~ sP179(U_687,U_686) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_151_2,plain,
! [U_689,U_688] : set_union2(U_689,U_689) = U_689,
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_689] : set_union2(U_689,U_689) = U_689,
inference(miniscope,[status(thm)],[f_151_2]) ).
fof(f_151_4,plain,
! [U_689] : set_union2(U_689,U_689) = U_689,
inference(definitional_conversion,[status(esa)],[f_151_3]) ).
cnf(f_151_5,plain,
set_union2(U_689,U_689) = U_689,
inference(clausify,[status(thm)],[f_151_4]) ).
fof(f_152_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_152_2,plain,
! [U_691,U_690] : set_intersection2(U_691,U_691) = U_691,
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_691] : set_intersection2(U_691,U_691) = U_691,
inference(miniscope,[status(thm)],[f_152_2]) ).
fof(f_152_4,plain,
! [U_691] : set_intersection2(U_691,U_691) = U_691,
inference(definitional_conversion,[status(esa)],[f_152_3]) ).
cnf(f_152_5,plain,
set_intersection2(U_691,U_691) = U_691,
inference(clausify,[status(thm)],[f_152_4]) ).
fof(f_153_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_153_2,plain,
! [U_693,U_692] :
( subset_complement(U_693,subset_complement(U_693,U_692)) = U_692
| ~ element(U_692,powerset(U_693)) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_692,U_693] :
( subset_complement(U_693,subset_complement(U_693,U_692)) = U_692
| ~ element(U_692,powerset(U_693)) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( subset_complement(U_693,subset_complement(U_693,U_692)) = U_692
| ~ element(U_692,powerset(U_693)) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_154_2,plain,
! [U_694] :
( relation_inverse(relation_inverse(U_694)) = U_694
| ~ relation(U_694) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_694] :
( relation_inverse(relation_inverse(U_694)) = U_694
| ~ relation(U_694) ),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
( relation_inverse(relation_inverse(U_694)) = U_694
| ~ relation(U_694) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_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_155_2,plain,
! [U_696,U_695] :
( complements_of_subsets(U_696,complements_of_subsets(U_696,U_695)) = U_695
| ~ element(U_695,powerset(powerset(U_696))) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_695,U_696] :
( complements_of_subsets(U_696,complements_of_subsets(U_696,U_695)) = U_695
| ~ element(U_695,powerset(powerset(U_696))) ),
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
( complements_of_subsets(U_696,complements_of_subsets(U_696,U_695)) = U_695
| ~ element(U_695,powerset(powerset(U_696))) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_156_2,plain,
! [U_698,U_697] : ~ proper_subset(U_698,U_698),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_698] : ~ proper_subset(U_698,U_698),
inference(miniscope,[status(thm)],[f_156_2]) ).
fof(f_156_4,plain,
! [U_698] : ~ proper_subset(U_698,U_698),
inference(definitional_conversion,[status(esa)],[f_156_3]) ).
cnf(f_156_5,plain,
~ proper_subset(U_698,U_698),
inference(clausify,[status(thm)],[f_156_4]) ).
fof(f_157_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_157_2,plain,
! [U_701] :
( ( ( reflexive(U_701)
| ? [U_700] :
( ~ in(ordered_pair(U_700,U_700),U_701)
& in(U_700,relation_field(U_701)) ) )
& ( ! [U_699] :
( in(ordered_pair(U_699,U_699),U_701)
| ~ in(U_699,relation_field(U_701)) )
| ~ reflexive(U_701) ) )
| ~ relation(U_701) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
! [U_701] :
( ( ( reflexive(U_701)
| ( ~ in(ordered_pair(sK121(U_701),sK121(U_701)),U_701)
& in(sK121(U_701),relation_field(U_701)) ) )
& ( ! [U_699] :
( in(ordered_pair(U_699,U_699),U_701)
| ~ in(U_699,relation_field(U_701)) )
| ~ reflexive(U_701) ) )
| ~ relation(U_701) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_700,sK121(U_701))],[f_157_2]) ).
fof(f_157_4,plain,
( ! [U_701] :
( ~ in(ordered_pair(sK121(U_701),sK121(U_701)),U_701)
| ~ sP180(U_701) )
& ! [U_701] :
( in(sK121(U_701),relation_field(U_701))
| ~ sP180(U_701) )
& ! [U_699,U_701] :
( reflexive(U_701)
| sP180(U_701)
| ~ sP181(U_699,U_701) )
& ! [U_699,U_701] :
( in(ordered_pair(U_699,U_699),U_701)
| ~ in(U_699,relation_field(U_701))
| ~ reflexive(U_701)
| ~ sP181(U_699,U_701) )
& ! [U_699,U_701] :
( sP181(U_699,U_701)
| ~ relation(U_701) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180,sP181])],[f_157_3]) ).
cnf(f_157_5,plain,
( sP181(U_699,U_701)
| ~ relation(U_701) ),
inference(clausify,[status(thm)],[f_157_4]) ).
cnf(f_157_6,plain,
( in(ordered_pair(U_699,U_699),U_701)
| ~ in(U_699,relation_field(U_701))
| ~ reflexive(U_701)
| ~ sP181(U_699,U_701) ),
inference(clausify,[status(thm)],[f_157_4]) ).
cnf(f_157_7,plain,
( reflexive(U_701)
| sP180(U_701)
| ~ sP181(U_699,U_701) ),
inference(clausify,[status(thm)],[f_157_4]) ).
cnf(f_157_8,plain,
( in(sK121(U_701),relation_field(U_701))
| ~ sP180(U_701) ),
inference(clausify,[status(thm)],[f_157_4]) ).
cnf(f_157_9,plain,
( ~ in(ordered_pair(sK121(U_701),sK121(U_701)),U_701)
| ~ sP180(U_701) ),
inference(clausify,[status(thm)],[f_157_4]) ).
fof(f_158_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_158_2,plain,
! [U_702] : singleton(U_702) != empty_set,
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_702] : singleton(U_702) != empty_set,
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
singleton(U_702) != empty_set,
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_159_2,plain,
! [U_704,U_703] :
( set_union2(singleton(U_704),U_703) = U_703
| ~ in(U_704,U_703) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_703,U_704] :
( set_union2(singleton(U_704),U_703) = U_703
| ~ in(U_704,U_703) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( set_union2(singleton(U_704),U_703) = U_703
| ~ in(U_704,U_703) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_160_2,plain,
! [U_706,U_705] :
( ~ in(U_706,U_705)
| ~ disjoint(singleton(U_706),U_705) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_706,U_705] :
( ~ in(U_706,U_705)
| ~ disjoint(singleton(U_706),U_705) ),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
( ~ in(U_706,U_705)
| ~ disjoint(singleton(U_706),U_705) ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_161_2,plain,
! [U_708,U_707] :
( disjoint(singleton(U_708),U_707)
| in(U_708,U_707) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_708,U_707] :
( disjoint(singleton(U_708),U_707)
| in(U_708,U_707) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( disjoint(singleton(U_708),U_707)
| in(U_708,U_707) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_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_162_2,plain,
! [U_710,U_709] :
( subset(relation_dom(relation_rng_restriction(U_710,U_709)),relation_dom(U_709))
| ~ relation(U_709) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_709,U_710] :
( subset(relation_dom(relation_rng_restriction(U_710,U_709)),relation_dom(U_709))
| ~ relation(U_709) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( subset(relation_dom(relation_rng_restriction(U_710,U_709)),relation_dom(U_709))
| ~ relation(U_709) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_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_163_2,plain,
! [U_717] :
( ( ( transitive(U_717)
| ? [U_716,U_715,U_714] :
( ~ in(ordered_pair(U_716,U_714),U_717)
& in(ordered_pair(U_715,U_714),U_717)
& in(ordered_pair(U_716,U_715),U_717) ) )
& ( ! [U_713,U_712,U_711] :
( in(ordered_pair(U_713,U_711),U_717)
| ~ in(ordered_pair(U_712,U_711),U_717)
| ~ in(ordered_pair(U_713,U_712),U_717) )
| ~ transitive(U_717) ) )
| ~ relation(U_717) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_717] :
( ( ( transitive(U_717)
| ? [U_715,U_714] :
( ~ in(ordered_pair(sK122(U_717),U_714),U_717)
& in(ordered_pair(U_715,U_714),U_717)
& in(ordered_pair(sK122(U_717),U_715),U_717) ) )
& ( ! [U_713,U_712,U_711] :
( in(ordered_pair(U_713,U_711),U_717)
| ~ in(ordered_pair(U_712,U_711),U_717)
| ~ in(ordered_pair(U_713,U_712),U_717) )
| ~ transitive(U_717) ) )
| ~ relation(U_717) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_716,sK122(U_717))],[f_163_2]) ).
fof(f_163_4,plain,
! [U_717] :
( ( ( transitive(U_717)
| ? [U_714] :
( ~ in(ordered_pair(sK122(U_717),U_714),U_717)
& in(ordered_pair(sK123(U_717),U_714),U_717)
& in(ordered_pair(sK122(U_717),sK123(U_717)),U_717) ) )
& ( ! [U_713,U_712,U_711] :
( in(ordered_pair(U_713,U_711),U_717)
| ~ in(ordered_pair(U_712,U_711),U_717)
| ~ in(ordered_pair(U_713,U_712),U_717) )
| ~ transitive(U_717) ) )
| ~ relation(U_717) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_715,sK123(U_717))],[f_163_3]) ).
fof(f_163_5,plain,
! [U_717] :
( ( ( transitive(U_717)
| ( ~ in(ordered_pair(sK122(U_717),sK124(U_717)),U_717)
& in(ordered_pair(sK123(U_717),sK124(U_717)),U_717)
& in(ordered_pair(sK122(U_717),sK123(U_717)),U_717) ) )
& ( ! [U_713,U_712,U_711] :
( in(ordered_pair(U_713,U_711),U_717)
| ~ in(ordered_pair(U_712,U_711),U_717)
| ~ in(ordered_pair(U_713,U_712),U_717) )
| ~ transitive(U_717) ) )
| ~ relation(U_717) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_714,sK124(U_717))],[f_163_4]) ).
fof(f_163_6,plain,
( ! [U_717] :
( ~ in(ordered_pair(sK122(U_717),sK124(U_717)),U_717)
| ~ sP182(U_717) )
& ! [U_717] :
( in(ordered_pair(sK123(U_717),sK124(U_717)),U_717)
| ~ sP182(U_717) )
& ! [U_717] :
( in(ordered_pair(sK122(U_717),sK123(U_717)),U_717)
| ~ sP182(U_717) )
& ! [U_711,U_712,U_713,U_717] :
( transitive(U_717)
| sP182(U_717)
| ~ sP183(U_711,U_712,U_713,U_717) )
& ! [U_711,U_712,U_713,U_717] :
( in(ordered_pair(U_713,U_711),U_717)
| ~ in(ordered_pair(U_712,U_711),U_717)
| ~ in(ordered_pair(U_713,U_712),U_717)
| ~ transitive(U_717)
| ~ sP183(U_711,U_712,U_713,U_717) )
& ! [U_711,U_712,U_713,U_717] :
( sP183(U_711,U_712,U_713,U_717)
| ~ relation(U_717) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182,sP183])],[f_163_5]) ).
cnf(f_163_7,plain,
( sP183(U_711,U_712,U_713,U_717)
| ~ relation(U_717) ),
inference(clausify,[status(thm)],[f_163_6]) ).
cnf(f_163_8,plain,
( in(ordered_pair(U_713,U_711),U_717)
| ~ in(ordered_pair(U_712,U_711),U_717)
| ~ in(ordered_pair(U_713,U_712),U_717)
| ~ transitive(U_717)
| ~ sP183(U_711,U_712,U_713,U_717) ),
inference(clausify,[status(thm)],[f_163_6]) ).
cnf(f_163_9,plain,
( transitive(U_717)
| sP182(U_717)
| ~ sP183(U_711,U_712,U_713,U_717) ),
inference(clausify,[status(thm)],[f_163_6]) ).
cnf(f_163_10,plain,
( in(ordered_pair(sK122(U_717),sK123(U_717)),U_717)
| ~ sP182(U_717) ),
inference(clausify,[status(thm)],[f_163_6]) ).
cnf(f_163_11,plain,
( in(ordered_pair(sK123(U_717),sK124(U_717)),U_717)
| ~ sP182(U_717) ),
inference(clausify,[status(thm)],[f_163_6]) ).
cnf(f_163_12,plain,
( ~ in(ordered_pair(sK122(U_717),sK124(U_717)),U_717)
| ~ sP182(U_717) ),
inference(clausify,[status(thm)],[f_163_6]) ).
fof(f_164_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_164_2,plain,
! [U_719,U_718] :
( ( subset(singleton(U_719),U_718)
| ~ in(U_719,U_718) )
& ( in(U_719,U_718)
| ~ subset(singleton(U_719),U_718) ) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
( ! [U_723,U_721] :
( subset(singleton(U_723),U_721)
| ~ in(U_723,U_721) )
& ! [U_722,U_720] :
( in(U_722,U_720)
| ~ subset(singleton(U_722),U_720) ) ),
inference(miniscope,[status(thm)],[f_164_2]) ).
fof(f_164_4,plain,
( ! [U_723,U_721] :
( subset(singleton(U_723),U_721)
| ~ in(U_723,U_721) )
& ! [U_722,U_720] :
( in(U_722,U_720)
| ~ subset(singleton(U_722),U_720) ) ),
inference(definitional_conversion,[status(esa)],[f_164_3]) ).
cnf(f_164_5,plain,
( in(U_722,U_720)
| ~ subset(singleton(U_722),U_720) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_6,plain,
( subset(singleton(U_723),U_721)
| ~ in(U_723,U_721) ),
inference(clausify,[status(thm)],[f_164_4]) ).
fof(f_165_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_165_2,plain,
! [U_725,U_724] :
( ( set_difference(U_725,U_724) = empty_set
| ~ subset(U_725,U_724) )
& ( subset(U_725,U_724)
| set_difference(U_725,U_724) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( ! [U_729,U_727] :
( set_difference(U_729,U_727) = empty_set
| ~ subset(U_729,U_727) )
& ! [U_728,U_726] :
( subset(U_728,U_726)
| set_difference(U_728,U_726) != empty_set ) ),
inference(miniscope,[status(thm)],[f_165_2]) ).
fof(f_165_4,plain,
( ! [U_727,U_729] :
( set_difference(U_729,U_727) = empty_set
| ~ subset(U_729,U_727) )
& ! [U_728,U_726] :
( subset(U_728,U_726)
| set_difference(U_728,U_726) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_165_3]) ).
cnf(f_165_5,plain,
( subset(U_728,U_726)
| set_difference(U_728,U_726) != empty_set ),
inference(clausify,[status(thm)],[f_165_4]) ).
cnf(f_165_6,plain,
( set_difference(U_729,U_727) = empty_set
| ~ subset(U_729,U_727) ),
inference(clausify,[status(thm)],[f_165_4]) ).
fof(f_166_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_166_2,plain,
! [U_732,U_731] :
( ! [U_730] :
( in(U_730,U_732)
| ~ in(U_730,U_731) )
| ~ element(U_731,powerset(U_732)) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_731,U_732,U_730] :
( in(U_730,U_732)
| ~ in(U_730,U_731)
| ~ element(U_731,powerset(U_732)) ),
inference(definitional_conversion,[status(esa)],[f_166_2]) ).
cnf(f_166_4,plain,
( in(U_730,U_732)
| ~ in(U_730,U_731)
| ~ element(U_731,powerset(U_732)) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_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_167_2,plain,
! [U_737] :
( ( ( antisymmetric(U_737)
| ? [U_736,U_735] :
( U_736 != U_735
& in(ordered_pair(U_735,U_736),U_737)
& in(ordered_pair(U_736,U_735),U_737) ) )
& ( ! [U_734,U_733] :
( U_734 = U_733
| ~ in(ordered_pair(U_733,U_734),U_737)
| ~ in(ordered_pair(U_734,U_733),U_737) )
| ~ antisymmetric(U_737) ) )
| ~ relation(U_737) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_737] :
( ( ( antisymmetric(U_737)
| ? [U_735] :
( sK125(U_737) != U_735
& in(ordered_pair(U_735,sK125(U_737)),U_737)
& in(ordered_pair(sK125(U_737),U_735),U_737) ) )
& ( ! [U_734,U_733] :
( U_734 = U_733
| ~ in(ordered_pair(U_733,U_734),U_737)
| ~ in(ordered_pair(U_734,U_733),U_737) )
| ~ antisymmetric(U_737) ) )
| ~ relation(U_737) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_736,sK125(U_737))],[f_167_2]) ).
fof(f_167_4,plain,
! [U_737] :
( ( ( antisymmetric(U_737)
| ( sK125(U_737) != sK126(U_737)
& in(ordered_pair(sK126(U_737),sK125(U_737)),U_737)
& in(ordered_pair(sK125(U_737),sK126(U_737)),U_737) ) )
& ( ! [U_734,U_733] :
( U_734 = U_733
| ~ in(ordered_pair(U_733,U_734),U_737)
| ~ in(ordered_pair(U_734,U_733),U_737) )
| ~ antisymmetric(U_737) ) )
| ~ relation(U_737) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_735,sK126(U_737))],[f_167_3]) ).
fof(f_167_5,plain,
( ! [U_737] :
( sK125(U_737) != sK126(U_737)
| ~ sP184(U_737) )
& ! [U_737] :
( in(ordered_pair(sK126(U_737),sK125(U_737)),U_737)
| ~ sP184(U_737) )
& ! [U_737] :
( in(ordered_pair(sK125(U_737),sK126(U_737)),U_737)
| ~ sP184(U_737) )
& ! [U_733,U_734,U_737] :
( antisymmetric(U_737)
| sP184(U_737)
| ~ sP185(U_733,U_734,U_737) )
& ! [U_733,U_734,U_737] :
( U_734 = U_733
| ~ in(ordered_pair(U_733,U_734),U_737)
| ~ in(ordered_pair(U_734,U_733),U_737)
| ~ antisymmetric(U_737)
| ~ sP185(U_733,U_734,U_737) )
& ! [U_733,U_734,U_737] :
( sP185(U_733,U_734,U_737)
| ~ relation(U_737) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184,sP185])],[f_167_4]) ).
cnf(f_167_6,plain,
( sP185(U_733,U_734,U_737)
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_167_5]) ).
cnf(f_167_7,plain,
( U_734 = U_733
| ~ in(ordered_pair(U_733,U_734),U_737)
| ~ in(ordered_pair(U_734,U_733),U_737)
| ~ antisymmetric(U_737)
| ~ sP185(U_733,U_734,U_737) ),
inference(clausify,[status(thm)],[f_167_5]) ).
cnf(f_167_8,plain,
( antisymmetric(U_737)
| sP184(U_737)
| ~ sP185(U_733,U_734,U_737) ),
inference(clausify,[status(thm)],[f_167_5]) ).
cnf(f_167_9,plain,
( in(ordered_pair(sK125(U_737),sK126(U_737)),U_737)
| ~ sP184(U_737) ),
inference(clausify,[status(thm)],[f_167_5]) ).
cnf(f_167_10,plain,
( in(ordered_pair(sK126(U_737),sK125(U_737)),U_737)
| ~ sP184(U_737) ),
inference(clausify,[status(thm)],[f_167_5]) ).
cnf(f_167_11,plain,
( sK125(U_737) != sK126(U_737)
| ~ sP184(U_737) ),
inference(clausify,[status(thm)],[f_167_5]) ).
fof(f_168_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_168_2,plain,
! [U_740,U_739,U_738] :
( subset(U_740,set_difference(U_739,singleton(U_738)))
| in(U_738,U_740)
| ~ subset(U_740,U_739) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_740,U_739] :
( ! [U_738] :
( subset(U_740,set_difference(U_739,singleton(U_738)))
| in(U_738,U_740) )
| ~ subset(U_740,U_739) ),
inference(miniscope,[status(thm)],[f_168_2]) ).
fof(f_168_4,plain,
! [U_740,U_739,U_738] :
( subset(U_740,set_difference(U_739,singleton(U_738)))
| in(U_738,U_740)
| ~ subset(U_740,U_739) ),
inference(definitional_conversion,[status(esa)],[f_168_3]) ).
cnf(f_168_5,plain,
( subset(U_740,set_difference(U_739,singleton(U_738)))
| in(U_738,U_740)
| ~ subset(U_740,U_739) ),
inference(clausify,[status(thm)],[f_168_4]) ).
fof(f_169_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_169_2,plain,
! [U_745] :
( ( ( connected(U_745)
| ? [U_744,U_743] :
( ~ in(ordered_pair(U_743,U_744),U_745)
& ~ in(ordered_pair(U_744,U_743),U_745)
& U_744 != U_743
& in(U_743,relation_field(U_745))
& in(U_744,relation_field(U_745)) ) )
& ( ! [U_742,U_741] :
( in(ordered_pair(U_741,U_742),U_745)
| in(ordered_pair(U_742,U_741),U_745)
| U_742 = U_741
| ~ in(U_741,relation_field(U_745))
| ~ in(U_742,relation_field(U_745)) )
| ~ connected(U_745) ) )
| ~ relation(U_745) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_745] :
( ( ( connected(U_745)
| ? [U_744] :
( ? [U_743] :
( ~ in(ordered_pair(U_743,U_744),U_745)
& ~ in(ordered_pair(U_744,U_743),U_745)
& U_744 != U_743
& in(U_743,relation_field(U_745)) )
& in(U_744,relation_field(U_745)) ) )
& ( ! [U_742] :
( ! [U_741] :
( in(ordered_pair(U_741,U_742),U_745)
| in(ordered_pair(U_742,U_741),U_745)
| U_742 = U_741
| ~ in(U_741,relation_field(U_745)) )
| ~ in(U_742,relation_field(U_745)) )
| ~ connected(U_745) ) )
| ~ relation(U_745) ),
inference(miniscope,[status(thm)],[f_169_2]) ).
fof(f_169_4,plain,
! [U_745] :
( ( ( connected(U_745)
| ( ? [U_743] :
( ~ in(ordered_pair(U_743,sK127(U_745)),U_745)
& ~ in(ordered_pair(sK127(U_745),U_743),U_745)
& sK127(U_745) != U_743
& in(U_743,relation_field(U_745)) )
& in(sK127(U_745),relation_field(U_745)) ) )
& ( ! [U_742] :
( ! [U_741] :
( in(ordered_pair(U_741,U_742),U_745)
| in(ordered_pair(U_742,U_741),U_745)
| U_742 = U_741
| ~ in(U_741,relation_field(U_745)) )
| ~ in(U_742,relation_field(U_745)) )
| ~ connected(U_745) ) )
| ~ relation(U_745) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_744,sK127(U_745))],[f_169_3]) ).
fof(f_169_5,plain,
! [U_745] :
( ( ( connected(U_745)
| ( ~ in(ordered_pair(sK128(U_745),sK127(U_745)),U_745)
& ~ in(ordered_pair(sK127(U_745),sK128(U_745)),U_745)
& sK127(U_745) != sK128(U_745)
& in(sK128(U_745),relation_field(U_745))
& in(sK127(U_745),relation_field(U_745)) ) )
& ( ! [U_742] :
( ! [U_741] :
( in(ordered_pair(U_741,U_742),U_745)
| in(ordered_pair(U_742,U_741),U_745)
| U_742 = U_741
| ~ in(U_741,relation_field(U_745)) )
| ~ in(U_742,relation_field(U_745)) )
| ~ connected(U_745) ) )
| ~ relation(U_745) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_743,sK128(U_745))],[f_169_4]) ).
fof(f_169_6,plain,
( ! [U_745] :
( ~ in(ordered_pair(sK128(U_745),sK127(U_745)),U_745)
| ~ sP186(U_745) )
& ! [U_745] :
( ~ in(ordered_pair(sK127(U_745),sK128(U_745)),U_745)
| ~ sP186(U_745) )
& ! [U_745] :
( sK127(U_745) != sK128(U_745)
| ~ sP186(U_745) )
& ! [U_745] :
( in(sK128(U_745),relation_field(U_745))
| ~ sP186(U_745) )
& ! [U_745] :
( in(sK127(U_745),relation_field(U_745))
| ~ sP186(U_745) )
& ! [U_741,U_745,U_742] :
( connected(U_745)
| sP186(U_745)
| ~ sP187(U_741,U_745,U_742) )
& ! [U_741,U_745,U_742] :
( in(ordered_pair(U_741,U_742),U_745)
| in(ordered_pair(U_742,U_741),U_745)
| U_742 = U_741
| ~ in(U_741,relation_field(U_745))
| ~ in(U_742,relation_field(U_745))
| ~ connected(U_745)
| ~ sP187(U_741,U_745,U_742) )
& ! [U_741,U_745,U_742] :
( sP187(U_741,U_745,U_742)
| ~ relation(U_745) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186,sP187])],[f_169_5]) ).
cnf(f_169_7,plain,
( sP187(U_741,U_745,U_742)
| ~ relation(U_745) ),
inference(clausify,[status(thm)],[f_169_6]) ).
cnf(f_169_8,plain,
( in(ordered_pair(U_741,U_742),U_745)
| in(ordered_pair(U_742,U_741),U_745)
| U_742 = U_741
| ~ in(U_741,relation_field(U_745))
| ~ in(U_742,relation_field(U_745))
| ~ connected(U_745)
| ~ sP187(U_741,U_745,U_742) ),
inference(clausify,[status(thm)],[f_169_6]) ).
cnf(f_169_9,plain,
( connected(U_745)
| sP186(U_745)
| ~ sP187(U_741,U_745,U_742) ),
inference(clausify,[status(thm)],[f_169_6]) ).
cnf(f_169_10,plain,
( in(sK127(U_745),relation_field(U_745))
| ~ sP186(U_745) ),
inference(clausify,[status(thm)],[f_169_6]) ).
cnf(f_169_11,plain,
( in(sK128(U_745),relation_field(U_745))
| ~ sP186(U_745) ),
inference(clausify,[status(thm)],[f_169_6]) ).
cnf(f_169_12,plain,
( sK127(U_745) != sK128(U_745)
| ~ sP186(U_745) ),
inference(clausify,[status(thm)],[f_169_6]) ).
cnf(f_169_13,plain,
( ~ in(ordered_pair(sK127(U_745),sK128(U_745)),U_745)
| ~ sP186(U_745) ),
inference(clausify,[status(thm)],[f_169_6]) ).
cnf(f_169_14,plain,
( ~ in(ordered_pair(sK128(U_745),sK127(U_745)),U_745)
| ~ sP186(U_745) ),
inference(clausify,[status(thm)],[f_169_6]) ).
fof(f_170_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_170_2,plain,
! [U_747,U_746] :
( ( subset(U_747,singleton(U_746))
| ( U_747 != singleton(U_746)
& U_747 != empty_set ) )
& ( U_747 = singleton(U_746)
| U_747 = empty_set
| ~ subset(U_747,singleton(U_746)) ) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
( ! [U_751,U_749] :
( subset(U_751,singleton(U_749))
| ( U_751 != singleton(U_749)
& U_751 != empty_set ) )
& ! [U_750,U_748] :
( U_750 = singleton(U_748)
| U_750 = empty_set
| ~ subset(U_750,singleton(U_748)) ) ),
inference(miniscope,[status(thm)],[f_170_2]) ).
fof(f_170_4,plain,
( ! [U_751,U_749] :
( U_751 != singleton(U_749)
| ~ sP188(U_751,U_749) )
& ! [U_751,U_749] :
( U_751 != empty_set
| ~ sP188(U_751,U_749) )
& ! [U_751,U_749] :
( subset(U_751,singleton(U_749))
| sP188(U_751,U_749) )
& ! [U_750,U_748] :
( U_750 = singleton(U_748)
| U_750 = empty_set
| ~ subset(U_750,singleton(U_748)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_170_3]) ).
cnf(f_170_5,plain,
( U_750 = singleton(U_748)
| U_750 = empty_set
| ~ subset(U_750,singleton(U_748)) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_6,plain,
( subset(U_751,singleton(U_749))
| sP188(U_751,U_749) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_7,plain,
( U_751 != empty_set
| ~ sP188(U_751,U_749) ),
inference(clausify,[status(thm)],[f_170_4]) ).
cnf(f_170_8,plain,
( U_751 != singleton(U_749)
| ~ sP188(U_751,U_749) ),
inference(clausify,[status(thm)],[f_170_4]) ).
fof(f_171_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_171_2,plain,
! [U_753,U_752] :
( subset(U_753,union(U_752))
| ~ in(U_753,U_752) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_752,U_753] :
( subset(U_753,union(U_752))
| ~ in(U_753,U_752) ),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
( subset(U_753,union(U_752))
| ~ in(U_753,U_752) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_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_172_2,plain,
! [U_757,U_756,U_755,U_754] :
( ( in(ordered_pair(U_757,U_756),cartesian_product2(U_755,U_754))
| ~ in(U_756,U_754)
| ~ in(U_757,U_755) )
& ( ( in(U_756,U_754)
& in(U_757,U_755) )
| ~ in(ordered_pair(U_757,U_756),cartesian_product2(U_755,U_754)) ) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( ! [U_765,U_763,U_761,U_759] :
( in(ordered_pair(U_765,U_763),cartesian_product2(U_761,U_759))
| ~ in(U_763,U_759)
| ~ in(U_765,U_761) )
& ! [U_764,U_762,U_760,U_758] :
( ( in(U_762,U_758)
& in(U_764,U_760) )
| ~ in(ordered_pair(U_764,U_762),cartesian_product2(U_760,U_758)) ) ),
inference(miniscope,[status(thm)],[f_172_2]) ).
fof(f_172_4,plain,
( ! [U_760,U_762,U_758,U_764] :
( in(U_762,U_758)
| ~ sP189(U_760,U_762,U_758,U_764) )
& ! [U_760,U_762,U_758,U_764] :
( in(U_764,U_760)
| ~ sP189(U_760,U_762,U_758,U_764) )
& ! [U_763,U_761,U_759,U_765] :
( in(ordered_pair(U_765,U_763),cartesian_product2(U_761,U_759))
| ~ in(U_763,U_759)
| ~ in(U_765,U_761) )
& ! [U_760,U_762,U_758,U_764] :
( sP189(U_760,U_762,U_758,U_764)
| ~ in(ordered_pair(U_764,U_762),cartesian_product2(U_760,U_758)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_172_3]) ).
cnf(f_172_5,plain,
( sP189(U_760,U_762,U_758,U_764)
| ~ in(ordered_pair(U_764,U_762),cartesian_product2(U_760,U_758)) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_6,plain,
( in(ordered_pair(U_765,U_763),cartesian_product2(U_761,U_759))
| ~ in(U_763,U_759)
| ~ in(U_765,U_761) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_7,plain,
( in(U_764,U_760)
| ~ sP189(U_760,U_762,U_758,U_764) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_8,plain,
( in(U_762,U_758)
| ~ sP189(U_760,U_762,U_758,U_764) ),
inference(clausify,[status(thm)],[f_172_4]) ).
fof(f_173_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_173_2,plain,
! [U_768,U_767] :
( element(U_768,powerset(U_767))
| ? [U_766] :
( ~ in(U_766,U_767)
& in(U_766,U_768) ) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_768,U_767] :
( element(U_768,powerset(U_767))
| ( ~ in(sK129(U_768,U_767),U_767)
& in(sK129(U_768,U_767),U_768) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_766,sK129(U_768,U_767))],[f_173_2]) ).
fof(f_173_4,plain,
( ! [U_768,U_767] :
( ~ in(sK129(U_768,U_767),U_767)
| ~ sP190(U_768,U_767) )
& ! [U_768,U_767] :
( in(sK129(U_768,U_767),U_768)
| ~ sP190(U_768,U_767) )
& ! [U_768,U_767] :
( element(U_768,powerset(U_767))
| sP190(U_768,U_767) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_173_3]) ).
cnf(f_173_5,plain,
( element(U_768,powerset(U_767))
| sP190(U_768,U_767) ),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_6,plain,
( in(sK129(U_768,U_767),U_768)
| ~ sP190(U_768,U_767) ),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_7,plain,
( ~ in(sK129(U_768,U_767),U_767)
| ~ sP190(U_768,U_767) ),
inference(clausify,[status(thm)],[f_173_4]) ).
fof(f_174_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_174_2,plain,
! [U_771,U_770,U_769] :
( ( ( in(U_770,relation_dom(relation_dom_restriction(U_769,U_771)))
| ~ in(U_770,U_771)
| ~ in(U_770,relation_dom(U_769)) )
& ( ( in(U_770,U_771)
& in(U_770,relation_dom(U_769)) )
| ~ in(U_770,relation_dom(relation_dom_restriction(U_769,U_771))) ) )
| ~ function(U_769)
| ~ relation(U_769) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
( ! [U_769,U_770,U_771] :
( in(U_770,U_771)
| ~ sP191(U_769,U_770,U_771) )
& ! [U_769,U_770,U_771] :
( in(U_770,relation_dom(U_769))
| ~ sP191(U_769,U_770,U_771) )
& ! [U_769,U_770,U_771] :
( in(U_770,relation_dom(relation_dom_restriction(U_769,U_771)))
| ~ in(U_770,U_771)
| ~ in(U_770,relation_dom(U_769))
| ~ sP192(U_769,U_770,U_771) )
& ! [U_769,U_770,U_771] :
( sP191(U_769,U_770,U_771)
| ~ in(U_770,relation_dom(relation_dom_restriction(U_769,U_771)))
| ~ sP192(U_769,U_770,U_771) )
& ! [U_769,U_770,U_771] :
( sP192(U_769,U_770,U_771)
| ~ function(U_769)
| ~ relation(U_769) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191,sP192])],[f_174_2]) ).
cnf(f_174_4,plain,
( sP192(U_769,U_770,U_771)
| ~ function(U_769)
| ~ relation(U_769) ),
inference(clausify,[status(thm)],[f_174_3]) ).
cnf(f_174_5,plain,
( sP191(U_769,U_770,U_771)
| ~ in(U_770,relation_dom(relation_dom_restriction(U_769,U_771)))
| ~ sP192(U_769,U_770,U_771) ),
inference(clausify,[status(thm)],[f_174_3]) ).
cnf(f_174_6,plain,
( in(U_770,relation_dom(relation_dom_restriction(U_769,U_771)))
| ~ in(U_770,U_771)
| ~ in(U_770,relation_dom(U_769))
| ~ sP192(U_769,U_770,U_771) ),
inference(clausify,[status(thm)],[f_174_3]) ).
cnf(f_174_7,plain,
( in(U_770,relation_dom(U_769))
| ~ sP191(U_769,U_770,U_771) ),
inference(clausify,[status(thm)],[f_174_3]) ).
cnf(f_174_8,plain,
( in(U_770,U_771)
| ~ sP191(U_769,U_770,U_771) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_175_2,plain,
? [U_772] :
( function(U_772)
& relation(U_772) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
( function(sK130)
& relation(sK130) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_772,sK130)],[f_175_2]) ).
fof(f_175_4,plain,
( function(sK130)
& relation(sK130) ),
inference(definitional_conversion,[status(esa)],[f_175_3]) ).
cnf(f_175_5,plain,
relation(sK130),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_6,plain,
function(sK130),
inference(clausify,[status(thm)],[f_175_4]) ).
fof(f_176_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_176_2,plain,
? [U_773] :
( ordinal(U_773)
& epsilon_connected(U_773)
& epsilon_transitive(U_773) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
( ordinal(sK131)
& epsilon_connected(sK131)
& epsilon_transitive(sK131) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_773,sK131)],[f_176_2]) ).
fof(f_176_4,plain,
( ordinal(sK131)
& epsilon_connected(sK131)
& epsilon_transitive(sK131) ),
inference(definitional_conversion,[status(esa)],[f_176_3]) ).
cnf(f_176_5,plain,
epsilon_transitive(sK131),
inference(clausify,[status(thm)],[f_176_4]) ).
cnf(f_176_6,plain,
epsilon_connected(sK131),
inference(clausify,[status(thm)],[f_176_4]) ).
cnf(f_176_7,plain,
ordinal(sK131),
inference(clausify,[status(thm)],[f_176_4]) ).
fof(f_177_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_177_2,plain,
? [U_774] :
( relation(U_774)
& empty(U_774) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
( relation(sK132)
& empty(sK132) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_774,sK132)],[f_177_2]) ).
fof(f_177_4,plain,
( relation(sK132)
& empty(sK132) ),
inference(definitional_conversion,[status(esa)],[f_177_3]) ).
cnf(f_177_5,plain,
empty(sK132),
inference(clausify,[status(thm)],[f_177_4]) ).
cnf(f_177_6,plain,
relation(sK132),
inference(clausify,[status(thm)],[f_177_4]) ).
fof(f_178_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_178_2,plain,
! [U_776] :
( ? [U_775] :
( ~ empty(U_775)
& element(U_775,powerset(U_776)) )
| empty(U_776) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_776] :
( ( ~ empty(sK133(U_776))
& element(sK133(U_776),powerset(U_776)) )
| empty(U_776) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_775,sK133(U_776))],[f_178_2]) ).
fof(f_178_4,plain,
( ! [U_776] :
( ~ empty(sK133(U_776))
| ~ sP193(U_776) )
& ! [U_776] :
( element(sK133(U_776),powerset(U_776))
| ~ sP193(U_776) )
& ! [U_776] :
( sP193(U_776)
| empty(U_776) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193])],[f_178_3]) ).
cnf(f_178_5,plain,
( sP193(U_776)
| empty(U_776) ),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_6,plain,
( element(sK133(U_776),powerset(U_776))
| ~ sP193(U_776) ),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_7,plain,
( ~ empty(sK133(U_776))
| ~ sP193(U_776) ),
inference(clausify,[status(thm)],[f_178_4]) ).
fof(f_179_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_179_2,plain,
? [U_777] : empty(U_777),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
empty(sK134),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_777,sK134)],[f_179_2]) ).
fof(f_179_4,plain,
empty(sK134),
inference(definitional_conversion,[status(esa)],[f_179_3]) ).
cnf(f_179_5,plain,
empty(sK134),
inference(clausify,[status(thm)],[f_179_4]) ).
fof(f_180_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_180_2,plain,
? [U_778] :
( function(U_778)
& empty(U_778)
& relation(U_778) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( function(sK135)
& empty(sK135)
& relation(sK135) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_778,sK135)],[f_180_2]) ).
fof(f_180_4,plain,
( function(sK135)
& empty(sK135)
& relation(sK135) ),
inference(definitional_conversion,[status(esa)],[f_180_3]) ).
cnf(f_180_5,plain,
relation(sK135),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_6,plain,
empty(sK135),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_7,plain,
function(sK135),
inference(clausify,[status(thm)],[f_180_4]) ).
fof(f_181_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_181_2,plain,
? [U_779] :
( ordinal(U_779)
& epsilon_connected(U_779)
& epsilon_transitive(U_779)
& empty(U_779)
& one_to_one(U_779)
& function(U_779)
& relation(U_779) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ordinal(sK136)
& epsilon_connected(sK136)
& epsilon_transitive(sK136)
& empty(sK136)
& one_to_one(sK136)
& function(sK136)
& relation(sK136) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_779,sK136)],[f_181_2]) ).
fof(f_181_4,plain,
( ordinal(sK136)
& epsilon_connected(sK136)
& epsilon_transitive(sK136)
& empty(sK136)
& one_to_one(sK136)
& function(sK136)
& relation(sK136) ),
inference(definitional_conversion,[status(esa)],[f_181_3]) ).
cnf(f_181_5,plain,
relation(sK136),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_6,plain,
function(sK136),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_7,plain,
one_to_one(sK136),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_8,plain,
empty(sK136),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_9,plain,
epsilon_transitive(sK136),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_10,plain,
epsilon_connected(sK136),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_11,plain,
ordinal(sK136),
inference(clausify,[status(thm)],[f_181_4]) ).
fof(f_182_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_182_2,plain,
? [U_780] :
( relation(U_780)
& ~ empty(U_780) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( relation(sK137)
& ~ empty(sK137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_780,sK137)],[f_182_2]) ).
fof(f_182_4,plain,
( relation(sK137)
& ~ empty(sK137) ),
inference(definitional_conversion,[status(esa)],[f_182_3]) ).
cnf(f_182_5,plain,
~ empty(sK137),
inference(clausify,[status(thm)],[f_182_4]) ).
cnf(f_182_6,plain,
relation(sK137),
inference(clausify,[status(thm)],[f_182_4]) ).
fof(f_183_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_183_2,plain,
! [U_782] :
? [U_781] :
( empty(U_781)
& element(U_781,powerset(U_782)) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_782] :
( empty(sK138(U_782))
& element(sK138(U_782),powerset(U_782)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_781,sK138(U_782))],[f_183_2]) ).
fof(f_183_4,plain,
( ! [U_782] : empty(sK138(U_782))
& ! [U_782] : element(sK138(U_782),powerset(U_782)) ),
inference(definitional_conversion,[status(esa)],[f_183_3]) ).
cnf(f_183_5,plain,
element(sK138(U_782),powerset(U_782)),
inference(clausify,[status(thm)],[f_183_4]) ).
cnf(f_183_6,plain,
empty(sK138(U_782)),
inference(clausify,[status(thm)],[f_183_4]) ).
fof(f_184_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_184_2,plain,
? [U_783] : ~ empty(U_783),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
~ empty(sK139),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_783,sK139)],[f_184_2]) ).
fof(f_184_4,plain,
~ empty(sK139),
inference(definitional_conversion,[status(esa)],[f_184_3]) ).
cnf(f_184_5,plain,
~ empty(sK139),
inference(clausify,[status(thm)],[f_184_4]) ).
fof(f_185_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_185_2,plain,
? [U_784] :
( one_to_one(U_784)
& function(U_784)
& relation(U_784) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( one_to_one(sK140)
& function(sK140)
& relation(sK140) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_784,sK140)],[f_185_2]) ).
fof(f_185_4,plain,
( one_to_one(sK140)
& function(sK140)
& relation(sK140) ),
inference(definitional_conversion,[status(esa)],[f_185_3]) ).
cnf(f_185_5,plain,
relation(sK140),
inference(clausify,[status(thm)],[f_185_4]) ).
cnf(f_185_6,plain,
function(sK140),
inference(clausify,[status(thm)],[f_185_4]) ).
cnf(f_185_7,plain,
one_to_one(sK140),
inference(clausify,[status(thm)],[f_185_4]) ).
fof(f_186_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_186_2,plain,
? [U_785] :
( ordinal(U_785)
& epsilon_connected(U_785)
& epsilon_transitive(U_785)
& ~ empty(U_785) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
( ordinal(sK141)
& epsilon_connected(sK141)
& epsilon_transitive(sK141)
& ~ empty(sK141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_785,sK141)],[f_186_2]) ).
fof(f_186_4,plain,
( ordinal(sK141)
& epsilon_connected(sK141)
& epsilon_transitive(sK141)
& ~ empty(sK141) ),
inference(definitional_conversion,[status(esa)],[f_186_3]) ).
cnf(f_186_5,plain,
~ empty(sK141),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_6,plain,
epsilon_transitive(sK141),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_7,plain,
epsilon_connected(sK141),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_8,plain,
ordinal(sK141),
inference(clausify,[status(thm)],[f_186_4]) ).
fof(f_187_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_187_2,plain,
? [U_786] :
( relation_empty_yielding(U_786)
& relation(U_786) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
( relation_empty_yielding(sK142)
& relation(sK142) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_786,sK142)],[f_187_2]) ).
fof(f_187_4,plain,
( relation_empty_yielding(sK142)
& relation(sK142) ),
inference(definitional_conversion,[status(esa)],[f_187_3]) ).
cnf(f_187_5,plain,
relation(sK142),
inference(clausify,[status(thm)],[f_187_4]) ).
cnf(f_187_6,plain,
relation_empty_yielding(sK142),
inference(clausify,[status(thm)],[f_187_4]) ).
fof(f_188_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_188_2,plain,
? [U_787] :
( function(U_787)
& relation_empty_yielding(U_787)
& relation(U_787) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
( function(sK143)
& relation_empty_yielding(sK143)
& relation(sK143) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_787,sK143)],[f_188_2]) ).
fof(f_188_4,plain,
( function(sK143)
& relation_empty_yielding(sK143)
& relation(sK143) ),
inference(definitional_conversion,[status(esa)],[f_188_3]) ).
cnf(f_188_5,plain,
relation(sK143),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_6,plain,
relation_empty_yielding(sK143),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_7,plain,
function(sK143),
inference(clausify,[status(thm)],[f_188_4]) ).
fof(f_189_1,plain,
! [A,B,C] :
( relation_dom_as_subset(A,B,C) = relation_dom(C)
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1]) ).
fof(f_189_2,plain,
! [U_790,U_789,U_788] :
( relation_dom_as_subset(U_790,U_789,U_788) = relation_dom(U_788)
| ~ relation_of2(U_788,U_790,U_789) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_788,U_789,U_790] :
( relation_dom_as_subset(U_790,U_789,U_788) = relation_dom(U_788)
| ~ relation_of2(U_788,U_790,U_789) ),
inference(definitional_conversion,[status(esa)],[f_189_2]) ).
cnf(f_189_4,plain,
( relation_dom_as_subset(U_790,U_789,U_788) = relation_dom(U_788)
| ~ relation_of2(U_788,U_790,U_789) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [A,B,C] :
( relation_rng_as_subset(A,B,C) = relation_rng(C)
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_relset_1]) ).
fof(f_190_2,plain,
! [U_793,U_792,U_791] :
( relation_rng_as_subset(U_793,U_792,U_791) = relation_rng(U_791)
| ~ relation_of2(U_791,U_793,U_792) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_791,U_792,U_793] :
( relation_rng_as_subset(U_793,U_792,U_791) = relation_rng(U_791)
| ~ relation_of2(U_791,U_793,U_792) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( relation_rng_as_subset(U_793,U_792,U_791) = relation_rng(U_791)
| ~ relation_of2(U_791,U_793,U_792) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_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_191_2,plain,
! [U_795,U_794] :
( union_of_subsets(U_795,U_794) = union(U_794)
| ~ element(U_794,powerset(powerset(U_795))) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_794,U_795] :
( union_of_subsets(U_795,U_794) = union(U_794)
| ~ element(U_794,powerset(powerset(U_795))) ),
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
( union_of_subsets(U_795,U_794) = union(U_794)
| ~ element(U_794,powerset(powerset(U_795))) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_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_192_2,plain,
! [U_797,U_796] :
( meet_of_subsets(U_797,U_796) = set_meet(U_796)
| ~ element(U_796,powerset(powerset(U_797))) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_796,U_797] :
( meet_of_subsets(U_797,U_796) = set_meet(U_796)
| ~ element(U_796,powerset(powerset(U_797))) ),
inference(definitional_conversion,[status(esa)],[f_192_2]) ).
cnf(f_192_4,plain,
( meet_of_subsets(U_797,U_796) = set_meet(U_796)
| ~ element(U_796,powerset(powerset(U_797))) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_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_193_2,plain,
! [U_800,U_799,U_798] :
( subset_difference(U_800,U_799,U_798) = set_difference(U_799,U_798)
| ~ element(U_798,powerset(U_800))
| ~ element(U_799,powerset(U_800)) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_798,U_799,U_800] :
( subset_difference(U_800,U_799,U_798) = set_difference(U_799,U_798)
| ~ element(U_798,powerset(U_800))
| ~ element(U_799,powerset(U_800)) ),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
( subset_difference(U_800,U_799,U_798) = set_difference(U_799,U_798)
| ~ element(U_798,powerset(U_800))
| ~ element(U_799,powerset(U_800)) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_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_194_2,plain,
! [U_803,U_802,U_801] :
( ( relation_of2_as_subset(U_801,U_803,U_802)
| ~ relation_of2(U_801,U_803,U_802) )
& ( relation_of2(U_801,U_803,U_802)
| ~ relation_of2_as_subset(U_801,U_803,U_802) ) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ! [U_809,U_807,U_805] :
( relation_of2_as_subset(U_805,U_809,U_807)
| ~ relation_of2(U_805,U_809,U_807) )
& ! [U_808,U_806,U_804] :
( relation_of2(U_804,U_808,U_806)
| ~ relation_of2_as_subset(U_804,U_808,U_806) ) ),
inference(miniscope,[status(thm)],[f_194_2]) ).
fof(f_194_4,plain,
( ! [U_809,U_807,U_805] :
( relation_of2_as_subset(U_805,U_809,U_807)
| ~ relation_of2(U_805,U_809,U_807) )
& ! [U_808,U_804,U_806] :
( relation_of2(U_804,U_808,U_806)
| ~ relation_of2_as_subset(U_804,U_808,U_806) ) ),
inference(definitional_conversion,[status(esa)],[f_194_3]) ).
cnf(f_194_5,plain,
( relation_of2(U_804,U_808,U_806)
| ~ relation_of2_as_subset(U_804,U_808,U_806) ),
inference(clausify,[status(thm)],[f_194_4]) ).
cnf(f_194_6,plain,
( relation_of2_as_subset(U_805,U_809,U_807)
| ~ relation_of2(U_805,U_809,U_807) ),
inference(clausify,[status(thm)],[f_194_4]) ).
fof(f_195_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_195_2,plain,
! [U_811,U_810] :
( ( ( ordinal_subset(U_811,U_810)
| ~ subset(U_811,U_810) )
& ( subset(U_811,U_810)
| ~ ordinal_subset(U_811,U_810) ) )
| ~ ordinal(U_810)
| ~ ordinal(U_811) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
( ! [U_810,U_811] :
( ordinal_subset(U_811,U_810)
| ~ subset(U_811,U_810)
| ~ sP194(U_810,U_811) )
& ! [U_810,U_811] :
( subset(U_811,U_810)
| ~ ordinal_subset(U_811,U_810)
| ~ sP194(U_810,U_811) )
& ! [U_810,U_811] :
( sP194(U_810,U_811)
| ~ ordinal(U_810)
| ~ ordinal(U_811) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194])],[f_195_2]) ).
cnf(f_195_4,plain,
( sP194(U_810,U_811)
| ~ ordinal(U_810)
| ~ ordinal(U_811) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_5,plain,
( subset(U_811,U_810)
| ~ ordinal_subset(U_811,U_810)
| ~ sP194(U_810,U_811) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_6,plain,
( ordinal_subset(U_811,U_810)
| ~ subset(U_811,U_810)
| ~ sP194(U_810,U_811) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_196_2,plain,
! [U_813,U_812] :
( ordinal_subset(U_813,U_813)
| ~ ordinal(U_812)
| ~ ordinal(U_813) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
! [U_813] :
( ! [U_812] : ~ ordinal(U_812)
| ~ ordinal(U_813)
| ordinal_subset(U_813,U_813) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
fof(f_196_4,plain,
! [U_812,U_813] :
( ~ ordinal(U_812)
| ~ ordinal(U_813)
| ordinal_subset(U_813,U_813) ),
inference(definitional_conversion,[status(esa)],[f_196_3]) ).
cnf(f_196_5,plain,
( ~ ordinal(U_812)
| ~ ordinal(U_813)
| ordinal_subset(U_813,U_813) ),
inference(clausify,[status(thm)],[f_196_4]) ).
fof(f_197_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_197_2,plain,
! [U_815,U_814] : subset(U_815,U_815),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_815] : subset(U_815,U_815),
inference(miniscope,[status(thm)],[f_197_2]) ).
fof(f_197_4,plain,
! [U_815] : subset(U_815,U_815),
inference(definitional_conversion,[status(esa)],[f_197_3]) ).
cnf(f_197_5,plain,
subset(U_815,U_815),
inference(clausify,[status(thm)],[f_197_4]) ).
fof(f_198_1,plain,
! [A] :
( ? [B] :
( ! [C] :
( ordinal_subset(B,C)
| ~ in(C,A)
| ~ ordinal(C) )
& in(B,A)
& ordinal(B) )
| ! [B] :
( ~ in(B,A)
| ~ ordinal(B) ) ),
inference(fof_nnf,[status(thm)],[s1_ordinal1__e8_6__wellord2]) ).
fof(f_198_2,plain,
! [U_819] :
( ? [U_818] :
( ! [U_817] :
( ordinal_subset(U_818,U_817)
| ~ in(U_817,U_819)
| ~ ordinal(U_817) )
& in(U_818,U_819)
& ordinal(U_818) )
| ! [U_816] :
( ~ in(U_816,U_819)
| ~ ordinal(U_816) ) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_819] :
( ( ! [U_817] :
( ordinal_subset(sK144(U_819),U_817)
| ~ in(U_817,U_819)
| ~ ordinal(U_817) )
& in(sK144(U_819),U_819)
& ordinal(sK144(U_819)) )
| ! [U_816] :
( ~ in(U_816,U_819)
| ~ ordinal(U_816) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_818,sK144(U_819))],[f_198_2]) ).
fof(f_198_4,plain,
( ! [U_817,U_819] :
( ordinal_subset(sK144(U_819),U_817)
| ~ in(U_817,U_819)
| ~ ordinal(U_817)
| ~ sP195(U_817,U_819) )
& ! [U_817,U_819] :
( in(sK144(U_819),U_819)
| ~ sP195(U_817,U_819) )
& ! [U_817,U_819] :
( ordinal(sK144(U_819))
| ~ sP195(U_817,U_819) )
& ! [U_816,U_817,U_819] :
( sP195(U_817,U_819)
| ~ in(U_816,U_819)
| ~ ordinal(U_816) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_198_3]) ).
cnf(f_198_5,plain,
( sP195(U_817,U_819)
| ~ in(U_816,U_819)
| ~ ordinal(U_816) ),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_6,plain,
( ordinal(sK144(U_819))
| ~ sP195(U_817,U_819) ),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_7,plain,
( in(sK144(U_819),U_819)
| ~ sP195(U_817,U_819) ),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_8,plain,
( ordinal_subset(sK144(U_819),U_817)
| ~ in(U_817,U_819)
| ~ ordinal(U_817)
| ~ sP195(U_817,U_819) ),
inference(clausify,[status(thm)],[f_198_4]) ).
fof(f_199_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ! [H] :
( ~ in(H,A)
| D != H
| ~ ordinal(H) )
| E != D
| ~ in(E,succ(B)) ) )
& ( ? [E] :
( ? [H] :
( in(H,A)
& D = H
& ordinal(H) )
& E = D
& in(E,succ(B)) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ? [G] :
( in(G,A)
& E = G
& ordinal(G) )
& C = E
& ? [F] :
( in(F,A)
& D = F
& ordinal(F) )
& C = D )
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e8_6__wellord2__1]) ).
fof(f_199_2,plain,
! [U_832,U_831] :
( ? [U_830] :
! [U_829] :
( ( in(U_829,U_830)
| ! [U_828] :
( ! [U_827] :
( ~ in(U_827,U_832)
| U_829 != U_827
| ~ ordinal(U_827) )
| U_828 != U_829
| ~ in(U_828,succ(U_831)) ) )
& ( ? [U_826] :
( ? [U_825] :
( in(U_825,U_832)
& U_829 = U_825
& ordinal(U_825) )
& U_826 = U_829
& in(U_826,succ(U_831)) )
| ~ in(U_829,U_830) ) )
| ? [U_824,U_823,U_822] :
( U_823 != U_822
& ? [U_821] :
( in(U_821,U_832)
& U_822 = U_821
& ordinal(U_821) )
& U_824 = U_822
& ? [U_820] :
( in(U_820,U_832)
& U_823 = U_820
& ordinal(U_820) )
& U_824 = U_823 )
| ~ ordinal(U_831) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_832,U_831] :
( ? [U_830] :
( ! [U_834] :
( in(U_834,U_830)
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& ? [U_825] :
( in(U_825,U_832)
& U_833 = U_825
& ordinal(U_825) ) )
| ~ in(U_833,U_830) ) )
| ? [U_824,U_823,U_822] :
( U_823 != U_822
& ? [U_821] :
( in(U_821,U_832)
& U_822 = U_821
& ordinal(U_821) )
& U_824 = U_822
& ? [U_820] :
( in(U_820,U_832)
& U_823 = U_820
& ordinal(U_820) )
& U_824 = U_823 )
| ~ ordinal(U_831) ),
inference(miniscope,[status(thm)],[f_199_2]) ).
fof(f_199_4,plain,
! [U_832,U_831] :
( ? [U_830] :
( ! [U_834] :
( in(U_834,U_830)
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& ? [U_825] :
( in(U_825,U_832)
& U_833 = U_825
& ordinal(U_825) ) )
| ~ in(U_833,U_830) ) )
| ? [U_823,U_822] :
( U_823 != U_822
& ? [U_821] :
( in(U_821,U_832)
& U_822 = U_821
& ordinal(U_821) )
& sK145(U_832,U_831) = U_822
& ? [U_820] :
( in(U_820,U_832)
& U_823 = U_820
& ordinal(U_820) )
& sK145(U_832,U_831) = U_823 )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_824,sK145(U_832,U_831))],[f_199_3]) ).
fof(f_199_5,plain,
! [U_832,U_831] :
( ? [U_830] :
( ! [U_834] :
( in(U_834,U_830)
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& ? [U_825] :
( in(U_825,U_832)
& U_833 = U_825
& ordinal(U_825) ) )
| ~ in(U_833,U_830) ) )
| ? [U_822] :
( sK146(U_832,U_831) != U_822
& ? [U_821] :
( in(U_821,U_832)
& U_822 = U_821
& ordinal(U_821) )
& sK145(U_832,U_831) = U_822
& ? [U_820] :
( in(U_820,U_832)
& sK146(U_832,U_831) = U_820
& ordinal(U_820) )
& sK145(U_832,U_831) = sK146(U_832,U_831) )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_823,sK146(U_832,U_831))],[f_199_4]) ).
fof(f_199_6,plain,
! [U_832,U_831] :
( ? [U_830] :
( ! [U_834] :
( in(U_834,U_830)
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& ? [U_825] :
( in(U_825,U_832)
& U_833 = U_825
& ordinal(U_825) ) )
| ~ in(U_833,U_830) ) )
| ( sK146(U_832,U_831) != sK147(U_832,U_831)
& ? [U_821] :
( in(U_821,U_832)
& sK147(U_832,U_831) = U_821
& ordinal(U_821) )
& sK145(U_832,U_831) = sK147(U_832,U_831)
& ? [U_820] :
( in(U_820,U_832)
& sK146(U_832,U_831) = U_820
& ordinal(U_820) )
& sK145(U_832,U_831) = sK146(U_832,U_831) )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_822,sK147(U_832,U_831))],[f_199_5]) ).
fof(f_199_7,plain,
! [U_832,U_831] :
( ? [U_830] :
( ! [U_834] :
( in(U_834,U_830)
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& ? [U_825] :
( in(U_825,U_832)
& U_833 = U_825
& ordinal(U_825) ) )
| ~ in(U_833,U_830) ) )
| ( sK146(U_832,U_831) != sK147(U_832,U_831)
& ? [U_821] :
( in(U_821,U_832)
& sK147(U_832,U_831) = U_821
& ordinal(U_821) )
& sK145(U_832,U_831) = sK147(U_832,U_831)
& in(sK148(U_832,U_831),U_832)
& sK146(U_832,U_831) = sK148(U_832,U_831)
& ordinal(sK148(U_832,U_831))
& sK145(U_832,U_831) = sK146(U_832,U_831) )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_820,sK148(U_832,U_831))],[f_199_6]) ).
fof(f_199_8,plain,
! [U_832,U_831] :
( ? [U_830] :
( ! [U_834] :
( in(U_834,U_830)
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& ? [U_825] :
( in(U_825,U_832)
& U_833 = U_825
& ordinal(U_825) ) )
| ~ in(U_833,U_830) ) )
| ( sK146(U_832,U_831) != sK147(U_832,U_831)
& in(sK149(U_832,U_831),U_832)
& sK147(U_832,U_831) = sK149(U_832,U_831)
& ordinal(sK149(U_832,U_831))
& sK145(U_832,U_831) = sK147(U_832,U_831)
& in(sK148(U_832,U_831),U_832)
& sK146(U_832,U_831) = sK148(U_832,U_831)
& ordinal(sK148(U_832,U_831))
& sK145(U_832,U_831) = sK146(U_832,U_831) )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_821,sK149(U_832,U_831))],[f_199_7]) ).
fof(f_199_9,plain,
! [U_832,U_831] :
( ( ! [U_834] :
( in(U_834,sK150(U_832,U_831))
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& ? [U_825] :
( in(U_825,U_832)
& U_833 = U_825
& ordinal(U_825) ) )
| ~ in(U_833,sK150(U_832,U_831)) ) )
| ( sK146(U_832,U_831) != sK147(U_832,U_831)
& in(sK149(U_832,U_831),U_832)
& sK147(U_832,U_831) = sK149(U_832,U_831)
& ordinal(sK149(U_832,U_831))
& sK145(U_832,U_831) = sK147(U_832,U_831)
& in(sK148(U_832,U_831),U_832)
& sK146(U_832,U_831) = sK148(U_832,U_831)
& ordinal(sK148(U_832,U_831))
& sK145(U_832,U_831) = sK146(U_832,U_831) )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_830,sK150(U_832,U_831))],[f_199_8]) ).
fof(f_199_10,plain,
! [U_832,U_831] :
( ( ! [U_834] :
( in(U_834,sK150(U_832,U_831))
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( ? [U_826] :
( U_826 = U_833
& in(U_826,succ(U_831)) )
& in(sK151(U_832,U_831,U_833),U_832)
& U_833 = sK151(U_832,U_831,U_833)
& ordinal(sK151(U_832,U_831,U_833)) )
| ~ in(U_833,sK150(U_832,U_831)) ) )
| ( sK146(U_832,U_831) != sK147(U_832,U_831)
& in(sK149(U_832,U_831),U_832)
& sK147(U_832,U_831) = sK149(U_832,U_831)
& ordinal(sK149(U_832,U_831))
& sK145(U_832,U_831) = sK147(U_832,U_831)
& in(sK148(U_832,U_831),U_832)
& sK146(U_832,U_831) = sK148(U_832,U_831)
& ordinal(sK148(U_832,U_831))
& sK145(U_832,U_831) = sK146(U_832,U_831) )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_825,sK151(U_832,U_831,U_833))],[f_199_9]) ).
fof(f_199_11,plain,
! [U_832,U_831] :
( ( ! [U_834] :
( in(U_834,sK150(U_832,U_831))
| ! [U_828] :
( U_828 != U_834
| ~ in(U_828,succ(U_831)) )
| ! [U_827] :
( ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827) ) )
& ! [U_833] :
( ( sK152(U_832,U_831,U_833) = U_833
& in(sK152(U_832,U_831,U_833),succ(U_831))
& in(sK151(U_832,U_831,U_833),U_832)
& U_833 = sK151(U_832,U_831,U_833)
& ordinal(sK151(U_832,U_831,U_833)) )
| ~ in(U_833,sK150(U_832,U_831)) ) )
| ( sK146(U_832,U_831) != sK147(U_832,U_831)
& in(sK149(U_832,U_831),U_832)
& sK147(U_832,U_831) = sK149(U_832,U_831)
& ordinal(sK149(U_832,U_831))
& sK145(U_832,U_831) = sK147(U_832,U_831)
& in(sK148(U_832,U_831),U_832)
& sK146(U_832,U_831) = sK148(U_832,U_831)
& ordinal(sK148(U_832,U_831))
& sK145(U_832,U_831) = sK146(U_832,U_831) )
| ~ ordinal(U_831) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_826,sK152(U_832,U_831,U_833))],[f_199_10]) ).
fof(f_199_12,plain,
( ! [U_833,U_831,U_832] :
( sK152(U_832,U_831,U_833) = U_833
| ~ sP197(U_833,U_831,U_832) )
& ! [U_833,U_831,U_832] :
( in(sK152(U_832,U_831,U_833),succ(U_831))
| ~ sP197(U_833,U_831,U_832) )
& ! [U_833,U_831,U_832] :
( in(sK151(U_832,U_831,U_833),U_832)
| ~ sP197(U_833,U_831,U_832) )
& ! [U_833,U_831,U_832] :
( U_833 = sK151(U_832,U_831,U_833)
| ~ sP197(U_833,U_831,U_832) )
& ! [U_833,U_831,U_832] :
( ordinal(sK151(U_832,U_831,U_833))
| ~ sP197(U_833,U_831,U_832) )
& ! [U_833,U_827,U_828,U_831,U_832,U_834] :
( in(U_834,sK150(U_832,U_831))
| U_828 != U_834
| ~ in(U_828,succ(U_831))
| ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827)
| ~ sP198(U_833,U_827,U_828,U_831,U_832,U_834) )
& ! [U_833,U_827,U_828,U_831,U_832,U_834] :
( sP197(U_833,U_831,U_832)
| ~ in(U_833,sK150(U_832,U_831))
| ~ sP198(U_833,U_827,U_828,U_831,U_832,U_834) )
& ! [U_831,U_832] :
( sK146(U_832,U_831) != sK147(U_832,U_831)
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( in(sK149(U_832,U_831),U_832)
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( sK147(U_832,U_831) = sK149(U_832,U_831)
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( ordinal(sK149(U_832,U_831))
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( sK145(U_832,U_831) = sK147(U_832,U_831)
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( in(sK148(U_832,U_831),U_832)
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( sK146(U_832,U_831) = sK148(U_832,U_831)
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( ordinal(sK148(U_832,U_831))
| ~ sP196(U_831,U_832) )
& ! [U_831,U_832] :
( sK145(U_832,U_831) = sK146(U_832,U_831)
| ~ sP196(U_831,U_832) )
& ! [U_833,U_827,U_828,U_831,U_832,U_834] :
( sP198(U_833,U_827,U_828,U_831,U_832,U_834)
| sP196(U_831,U_832)
| ~ ordinal(U_831) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196,sP197,sP198])],[f_199_11]) ).
cnf(f_199_13,plain,
( sP198(U_833,U_827,U_828,U_831,U_832,U_834)
| sP196(U_831,U_832)
| ~ ordinal(U_831) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_14,plain,
( sK145(U_832,U_831) = sK146(U_832,U_831)
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_15,plain,
( ordinal(sK148(U_832,U_831))
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_16,plain,
( sK146(U_832,U_831) = sK148(U_832,U_831)
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_17,plain,
( in(sK148(U_832,U_831),U_832)
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_18,plain,
( sK145(U_832,U_831) = sK147(U_832,U_831)
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_19,plain,
( ordinal(sK149(U_832,U_831))
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_20,plain,
( sK147(U_832,U_831) = sK149(U_832,U_831)
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_21,plain,
( in(sK149(U_832,U_831),U_832)
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_22,plain,
( sK146(U_832,U_831) != sK147(U_832,U_831)
| ~ sP196(U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_23,plain,
( sP197(U_833,U_831,U_832)
| ~ in(U_833,sK150(U_832,U_831))
| ~ sP198(U_833,U_827,U_828,U_831,U_832,U_834) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_24,plain,
( in(U_834,sK150(U_832,U_831))
| U_828 != U_834
| ~ in(U_828,succ(U_831))
| ~ in(U_827,U_832)
| U_834 != U_827
| ~ ordinal(U_827)
| ~ sP198(U_833,U_827,U_828,U_831,U_832,U_834) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_25,plain,
( ordinal(sK151(U_832,U_831,U_833))
| ~ sP197(U_833,U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_26,plain,
( U_833 = sK151(U_832,U_831,U_833)
| ~ sP197(U_833,U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_27,plain,
( in(sK151(U_832,U_831,U_833),U_832)
| ~ sP197(U_833,U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_28,plain,
( in(sK152(U_832,U_831,U_833),succ(U_831))
| ~ sP197(U_833,U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
cnf(f_199_29,plain,
( sK152(U_832,U_831,U_833) = U_833
| ~ sP197(U_833,U_831,U_832) ),
inference(clausify,[status(thm)],[f_199_12]) ).
fof(f_200_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,A)
| D != E
| ~ ordinal(E) )
| ~ in(D,succ(B)) )
& ( ( ? [E] :
( in(E,A)
& D = E
& ordinal(E) )
& in(D,succ(B)) )
| ~ in(D,C) ) )
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e8_6__wellord2__1]) ).
fof(f_200_2,plain,
! [U_840,U_839] :
( ? [U_838] :
! [U_837] :
( ( in(U_837,U_838)
| ! [U_836] :
( ~ in(U_836,U_840)
| U_837 != U_836
| ~ ordinal(U_836) )
| ~ in(U_837,succ(U_839)) )
& ( ( ? [U_835] :
( in(U_835,U_840)
& U_837 = U_835
& ordinal(U_835) )
& in(U_837,succ(U_839)) )
| ~ in(U_837,U_838) ) )
| ~ ordinal(U_839) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_840,U_839] :
( ? [U_838] :
( ! [U_842] :
( in(U_842,U_838)
| ! [U_836] :
( ~ in(U_836,U_840)
| U_842 != U_836
| ~ ordinal(U_836) )
| ~ in(U_842,succ(U_839)) )
& ! [U_841] :
( ( ? [U_835] :
( in(U_835,U_840)
& U_841 = U_835
& ordinal(U_835) )
& in(U_841,succ(U_839)) )
| ~ in(U_841,U_838) ) )
| ~ ordinal(U_839) ),
inference(miniscope,[status(thm)],[f_200_2]) ).
fof(f_200_4,plain,
! [U_840,U_839] :
( ( ! [U_842] :
( in(U_842,sK153(U_840,U_839))
| ! [U_836] :
( ~ in(U_836,U_840)
| U_842 != U_836
| ~ ordinal(U_836) )
| ~ in(U_842,succ(U_839)) )
& ! [U_841] :
( ( ? [U_835] :
( in(U_835,U_840)
& U_841 = U_835
& ordinal(U_835) )
& in(U_841,succ(U_839)) )
| ~ in(U_841,sK153(U_840,U_839)) ) )
| ~ ordinal(U_839) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_838,sK153(U_840,U_839))],[f_200_3]) ).
fof(f_200_5,plain,
! [U_840,U_839] :
( ( ! [U_842] :
( in(U_842,sK153(U_840,U_839))
| ! [U_836] :
( ~ in(U_836,U_840)
| U_842 != U_836
| ~ ordinal(U_836) )
| ~ in(U_842,succ(U_839)) )
& ! [U_841] :
( ( in(sK154(U_840,U_839,U_841),U_840)
& U_841 = sK154(U_840,U_839,U_841)
& ordinal(sK154(U_840,U_839,U_841))
& in(U_841,succ(U_839)) )
| ~ in(U_841,sK153(U_840,U_839)) ) )
| ~ ordinal(U_839) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_835,sK154(U_840,U_839,U_841))],[f_200_4]) ).
fof(f_200_6,plain,
( ! [U_840,U_839,U_841] :
( in(sK154(U_840,U_839,U_841),U_840)
| ~ sP199(U_840,U_839,U_841) )
& ! [U_840,U_839,U_841] :
( U_841 = sK154(U_840,U_839,U_841)
| ~ sP199(U_840,U_839,U_841) )
& ! [U_840,U_839,U_841] :
( ordinal(sK154(U_840,U_839,U_841))
| ~ sP199(U_840,U_839,U_841) )
& ! [U_840,U_839,U_841] :
( in(U_841,succ(U_839))
| ~ sP199(U_840,U_839,U_841) )
& ! [U_840,U_836,U_839,U_842,U_841] :
( in(U_842,sK153(U_840,U_839))
| ~ in(U_836,U_840)
| U_842 != U_836
| ~ ordinal(U_836)
| ~ in(U_842,succ(U_839))
| ~ sP200(U_840,U_836,U_839,U_842,U_841) )
& ! [U_840,U_836,U_839,U_842,U_841] :
( sP199(U_840,U_839,U_841)
| ~ in(U_841,sK153(U_840,U_839))
| ~ sP200(U_840,U_836,U_839,U_842,U_841) )
& ! [U_840,U_836,U_839,U_842,U_841] :
( sP200(U_840,U_836,U_839,U_842,U_841)
| ~ ordinal(U_839) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199,sP200])],[f_200_5]) ).
cnf(f_200_7,plain,
( sP200(U_840,U_836,U_839,U_842,U_841)
| ~ ordinal(U_839) ),
inference(clausify,[status(thm)],[f_200_6]) ).
cnf(f_200_8,plain,
( sP199(U_840,U_839,U_841)
| ~ in(U_841,sK153(U_840,U_839))
| ~ sP200(U_840,U_836,U_839,U_842,U_841) ),
inference(clausify,[status(thm)],[f_200_6]) ).
cnf(f_200_9,plain,
( in(U_842,sK153(U_840,U_839))
| ~ in(U_836,U_840)
| U_842 != U_836
| ~ ordinal(U_836)
| ~ in(U_842,succ(U_839))
| ~ sP200(U_840,U_836,U_839,U_842,U_841) ),
inference(clausify,[status(thm)],[f_200_6]) ).
cnf(f_200_10,plain,
( in(U_841,succ(U_839))
| ~ sP199(U_840,U_839,U_841) ),
inference(clausify,[status(thm)],[f_200_6]) ).
cnf(f_200_11,plain,
( ordinal(sK154(U_840,U_839,U_841))
| ~ sP199(U_840,U_839,U_841) ),
inference(clausify,[status(thm)],[f_200_6]) ).
cnf(f_200_12,plain,
( U_841 = sK154(U_840,U_839,U_841)
| ~ sP199(U_840,U_839,U_841) ),
inference(clausify,[status(thm)],[f_200_6]) ).
cnf(f_200_13,plain,
( in(sK154(U_840,U_839,U_841),U_840)
| ~ sP199(U_840,U_839,U_841) ),
inference(clausify,[status(thm)],[f_200_6]) ).
fof(f_201_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_201_2,plain,
! [U_844,U_843] :
( disjoint(U_843,U_844)
| ~ disjoint(U_844,U_843) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_843,U_844] :
( disjoint(U_843,U_844)
| ~ disjoint(U_844,U_843) ),
inference(definitional_conversion,[status(esa)],[f_201_2]) ).
cnf(f_201_4,plain,
( disjoint(U_843,U_844)
| ~ disjoint(U_844,U_843) ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_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_202_2,plain,
! [U_848,U_847,U_846,U_845] :
( ( in(ordered_pair(U_848,U_847),cartesian_product2(U_846,U_845))
| ~ in(U_847,U_845)
| ~ in(U_848,U_846) )
& ( ( in(U_847,U_845)
& in(U_848,U_846) )
| ~ in(ordered_pair(U_848,U_847),cartesian_product2(U_846,U_845)) ) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
( ! [U_856,U_854,U_852,U_850] :
( in(ordered_pair(U_856,U_854),cartesian_product2(U_852,U_850))
| ~ in(U_854,U_850)
| ~ in(U_856,U_852) )
& ! [U_855,U_853,U_851,U_849] :
( ( in(U_853,U_849)
& in(U_855,U_851) )
| ~ in(ordered_pair(U_855,U_853),cartesian_product2(U_851,U_849)) ) ),
inference(miniscope,[status(thm)],[f_202_2]) ).
fof(f_202_4,plain,
( ! [U_849,U_851,U_855,U_853] :
( in(U_853,U_849)
| ~ sP201(U_849,U_851,U_855,U_853) )
& ! [U_849,U_851,U_855,U_853] :
( in(U_855,U_851)
| ~ sP201(U_849,U_851,U_855,U_853) )
& ! [U_856,U_854,U_852,U_850] :
( in(ordered_pair(U_856,U_854),cartesian_product2(U_852,U_850))
| ~ in(U_854,U_850)
| ~ in(U_856,U_852) )
& ! [U_849,U_851,U_855,U_853] :
( sP201(U_849,U_851,U_855,U_853)
| ~ in(ordered_pair(U_855,U_853),cartesian_product2(U_851,U_849)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_202_3]) ).
cnf(f_202_5,plain,
( sP201(U_849,U_851,U_855,U_853)
| ~ in(ordered_pair(U_855,U_853),cartesian_product2(U_851,U_849)) ),
inference(clausify,[status(thm)],[f_202_4]) ).
cnf(f_202_6,plain,
( in(ordered_pair(U_856,U_854),cartesian_product2(U_852,U_850))
| ~ in(U_854,U_850)
| ~ in(U_856,U_852) ),
inference(clausify,[status(thm)],[f_202_4]) ).
cnf(f_202_7,plain,
( in(U_855,U_851)
| ~ sP201(U_849,U_851,U_855,U_853) ),
inference(clausify,[status(thm)],[f_202_4]) ).
cnf(f_202_8,plain,
( in(U_853,U_849)
| ~ sP201(U_849,U_851,U_855,U_853) ),
inference(clausify,[status(thm)],[f_202_4]) ).
fof(f_203_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_203_2,plain,
! [U_857] : in(U_857,succ(U_857)),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_857] : in(U_857,succ(U_857)),
inference(definitional_conversion,[status(esa)],[f_203_2]) ).
cnf(f_203_4,plain,
in(U_857,succ(U_857)),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_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_204_2,plain,
! [U_861,U_860,U_859,U_858] :
( U_861 = U_858
| U_861 = U_859
| unordered_pair(U_861,U_860) != unordered_pair(U_859,U_858) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_861,U_860,U_859] :
( ! [U_858] :
( U_861 = U_858
| unordered_pair(U_861,U_860) != unordered_pair(U_859,U_858) )
| U_861 = U_859 ),
inference(miniscope,[status(thm)],[f_204_2]) ).
fof(f_204_4,plain,
! [U_860,U_859,U_858,U_861] :
( U_861 = U_858
| unordered_pair(U_861,U_860) != unordered_pair(U_859,U_858)
| U_861 = U_859 ),
inference(definitional_conversion,[status(esa)],[f_204_3]) ).
cnf(f_204_5,plain,
( U_861 = U_858
| unordered_pair(U_861,U_860) != unordered_pair(U_859,U_858)
| U_861 = U_859 ),
inference(clausify,[status(thm)],[f_204_4]) ).
fof(f_205_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_205_2,plain,
! [U_864,U_863,U_862] :
( ( ( in(U_864,relation_rng(relation_rng_restriction(U_863,U_862)))
| ~ in(U_864,relation_rng(U_862))
| ~ in(U_864,U_863) )
& ( ( in(U_864,relation_rng(U_862))
& in(U_864,U_863) )
| ~ in(U_864,relation_rng(relation_rng_restriction(U_863,U_862))) ) )
| ~ relation(U_862) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
( ! [U_862,U_863,U_864] :
( in(U_864,relation_rng(U_862))
| ~ sP202(U_862,U_863,U_864) )
& ! [U_862,U_863,U_864] :
( in(U_864,U_863)
| ~ sP202(U_862,U_863,U_864) )
& ! [U_862,U_863,U_864] :
( in(U_864,relation_rng(relation_rng_restriction(U_863,U_862)))
| ~ in(U_864,relation_rng(U_862))
| ~ in(U_864,U_863)
| ~ sP203(U_862,U_863,U_864) )
& ! [U_862,U_863,U_864] :
( sP202(U_862,U_863,U_864)
| ~ in(U_864,relation_rng(relation_rng_restriction(U_863,U_862)))
| ~ sP203(U_862,U_863,U_864) )
& ! [U_862,U_863,U_864] :
( sP203(U_862,U_863,U_864)
| ~ relation(U_862) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202,sP203])],[f_205_2]) ).
cnf(f_205_4,plain,
( sP203(U_862,U_863,U_864)
| ~ relation(U_862) ),
inference(clausify,[status(thm)],[f_205_3]) ).
cnf(f_205_5,plain,
( sP202(U_862,U_863,U_864)
| ~ in(U_864,relation_rng(relation_rng_restriction(U_863,U_862)))
| ~ sP203(U_862,U_863,U_864) ),
inference(clausify,[status(thm)],[f_205_3]) ).
cnf(f_205_6,plain,
( in(U_864,relation_rng(relation_rng_restriction(U_863,U_862)))
| ~ in(U_864,relation_rng(U_862))
| ~ in(U_864,U_863)
| ~ sP203(U_862,U_863,U_864) ),
inference(clausify,[status(thm)],[f_205_3]) ).
cnf(f_205_7,plain,
( in(U_864,U_863)
| ~ sP202(U_862,U_863,U_864) ),
inference(clausify,[status(thm)],[f_205_3]) ).
cnf(f_205_8,plain,
( in(U_864,relation_rng(U_862))
| ~ sP202(U_862,U_863,U_864) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_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_206_2,plain,
! [U_866,U_865] :
( subset(relation_rng(relation_rng_restriction(U_866,U_865)),U_866)
| ~ relation(U_865) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_866,U_865] :
( subset(relation_rng(relation_rng_restriction(U_866,U_865)),U_866)
| ~ relation(U_865) ),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
( subset(relation_rng(relation_rng_restriction(U_866,U_865)),U_866)
| ~ relation(U_865) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_207_2,plain,
! [U_868,U_867] :
( subset(relation_rng_restriction(U_868,U_867),U_867)
| ~ relation(U_867) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_867,U_868] :
( subset(relation_rng_restriction(U_868,U_867),U_867)
| ~ relation(U_867) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( subset(relation_rng_restriction(U_868,U_867),U_867)
| ~ relation(U_867) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_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_208_2,plain,
! [U_870,U_869] :
( subset(relation_rng(relation_rng_restriction(U_870,U_869)),relation_rng(U_869))
| ~ relation(U_869) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_870,U_869] :
( subset(relation_rng(relation_rng_restriction(U_870,U_869)),relation_rng(U_869))
| ~ relation(U_869) ),
inference(definitional_conversion,[status(esa)],[f_208_2]) ).
cnf(f_208_4,plain,
( subset(relation_rng(relation_rng_restriction(U_870,U_869)),relation_rng(U_869))
| ~ relation(U_869) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_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_209_2,plain,
! [U_873,U_872,U_871] :
( ( subset(cartesian_product2(U_871,U_873),cartesian_product2(U_871,U_872))
& subset(cartesian_product2(U_873,U_871),cartesian_product2(U_872,U_871)) )
| ~ subset(U_873,U_872) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_873,U_872] :
( ( ! [U_875] : subset(cartesian_product2(U_875,U_873),cartesian_product2(U_875,U_872))
& ! [U_874] : subset(cartesian_product2(U_873,U_874),cartesian_product2(U_872,U_874)) )
| ~ subset(U_873,U_872) ),
inference(miniscope,[status(thm)],[f_209_2]) ).
fof(f_209_4,plain,
( ! [U_872,U_873,U_874,U_875] :
( subset(cartesian_product2(U_875,U_873),cartesian_product2(U_875,U_872))
| ~ sP204(U_872,U_873,U_874,U_875) )
& ! [U_872,U_873,U_874,U_875] :
( subset(cartesian_product2(U_873,U_874),cartesian_product2(U_872,U_874))
| ~ sP204(U_872,U_873,U_874,U_875) )
& ! [U_872,U_873,U_874,U_875] :
( sP204(U_872,U_873,U_874,U_875)
| ~ subset(U_873,U_872) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_209_3]) ).
cnf(f_209_5,plain,
( sP204(U_872,U_873,U_874,U_875)
| ~ subset(U_873,U_872) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_6,plain,
( subset(cartesian_product2(U_873,U_874),cartesian_product2(U_872,U_874))
| ~ sP204(U_872,U_873,U_874,U_875) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_7,plain,
( subset(cartesian_product2(U_875,U_873),cartesian_product2(U_875,U_872))
| ~ sP204(U_872,U_873,U_874,U_875) ),
inference(clausify,[status(thm)],[f_209_4]) ).
fof(f_210_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_210_2,plain,
! [U_877,U_876] :
( relation_rng(relation_rng_restriction(U_877,U_876)) = set_intersection2(relation_rng(U_876),U_877)
| ~ relation(U_876) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_876,U_877] :
( relation_rng(relation_rng_restriction(U_877,U_876)) = set_intersection2(relation_rng(U_876),U_877)
| ~ relation(U_876) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( relation_rng(relation_rng_restriction(U_877,U_876)) = set_intersection2(relation_rng(U_876),U_877)
| ~ relation(U_876) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_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_211_2,plain,
! [U_881,U_880,U_879,U_878] :
( subset(cartesian_product2(U_881,U_879),cartesian_product2(U_880,U_878))
| ~ subset(U_879,U_878)
| ~ subset(U_881,U_880) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_878,U_879,U_880,U_881] :
( subset(cartesian_product2(U_881,U_879),cartesian_product2(U_880,U_878))
| ~ subset(U_879,U_878)
| ~ subset(U_881,U_880) ),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
( subset(cartesian_product2(U_881,U_879),cartesian_product2(U_880,U_878))
| ~ subset(U_879,U_878)
| ~ subset(U_881,U_880) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_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_212_2,plain,
! [U_884,U_883,U_882] :
( ( subset(relation_rng(U_882),U_883)
& subset(relation_dom(U_882),U_884) )
| ~ relation_of2_as_subset(U_882,U_884,U_883) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
( ! [U_882,U_883,U_884] :
( subset(relation_rng(U_882),U_883)
| ~ sP205(U_882,U_883,U_884) )
& ! [U_882,U_883,U_884] :
( subset(relation_dom(U_882),U_884)
| ~ sP205(U_882,U_883,U_884) )
& ! [U_882,U_883,U_884] :
( sP205(U_882,U_883,U_884)
| ~ relation_of2_as_subset(U_882,U_884,U_883) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_212_2]) ).
cnf(f_212_4,plain,
( sP205(U_882,U_883,U_884)
| ~ relation_of2_as_subset(U_882,U_884,U_883) ),
inference(clausify,[status(thm)],[f_212_3]) ).
cnf(f_212_5,plain,
( subset(relation_dom(U_882),U_884)
| ~ sP205(U_882,U_883,U_884) ),
inference(clausify,[status(thm)],[f_212_3]) ).
cnf(f_212_6,plain,
( subset(relation_rng(U_882),U_883)
| ~ sP205(U_882,U_883,U_884) ),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_213_2,plain,
! [U_886,U_885] :
( set_union2(U_886,U_885) = U_885
| ~ subset(U_886,U_885) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_886,U_885] :
( set_union2(U_886,U_885) = U_885
| ~ subset(U_886,U_885) ),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
( set_union2(U_886,U_885) = U_885
| ~ subset(U_886,U_885) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_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_214_2,plain,
! [U_892] :
? [U_891] :
( ! [U_890] :
( in(U_890,U_891)
| are_equipotent(U_890,U_891)
| ~ subset(U_890,U_891) )
& ! [U_889] :
( in(powerset(U_889),U_891)
| ~ in(U_889,U_891) )
& ! [U_888,U_887] :
( in(U_887,U_891)
| ~ subset(U_887,U_888)
| ~ in(U_888,U_891) )
& in(U_892,U_891) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_892] :
( ! [U_890] :
( in(U_890,sK155(U_892))
| are_equipotent(U_890,sK155(U_892))
| ~ subset(U_890,sK155(U_892)) )
& ! [U_889] :
( in(powerset(U_889),sK155(U_892))
| ~ in(U_889,sK155(U_892)) )
& ! [U_888,U_887] :
( in(U_887,sK155(U_892))
| ~ subset(U_887,U_888)
| ~ in(U_888,sK155(U_892)) )
& in(U_892,sK155(U_892)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_891,sK155(U_892))],[f_214_2]) ).
fof(f_214_4,plain,
( ! [U_890,U_892] :
( in(U_890,sK155(U_892))
| are_equipotent(U_890,sK155(U_892))
| ~ subset(U_890,sK155(U_892)) )
& ! [U_889,U_892] :
( in(powerset(U_889),sK155(U_892))
| ~ in(U_889,sK155(U_892)) )
& ! [U_888,U_887,U_892] :
( in(U_887,sK155(U_892))
| ~ subset(U_887,U_888)
| ~ in(U_888,sK155(U_892)) )
& ! [U_892] : in(U_892,sK155(U_892)) ),
inference(definitional_conversion,[status(esa)],[f_214_3]) ).
cnf(f_214_5,plain,
in(U_892,sK155(U_892)),
inference(clausify,[status(thm)],[f_214_4]) ).
cnf(f_214_6,plain,
( in(U_887,sK155(U_892))
| ~ subset(U_887,U_888)
| ~ in(U_888,sK155(U_892)) ),
inference(clausify,[status(thm)],[f_214_4]) ).
cnf(f_214_7,plain,
( in(powerset(U_889),sK155(U_892))
| ~ in(U_889,sK155(U_892)) ),
inference(clausify,[status(thm)],[f_214_4]) ).
cnf(f_214_8,plain,
( in(U_890,sK155(U_892))
| are_equipotent(U_890,sK155(U_892))
| ~ subset(U_890,sK155(U_892)) ),
inference(clausify,[status(thm)],[f_214_4]) ).
fof(f_215_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_215_2,plain,
! [U_895,U_894,U_893] :
( relation_dom_restriction(relation_rng_restriction(U_895,U_893),U_894) = relation_rng_restriction(U_895,relation_dom_restriction(U_893,U_894))
| ~ relation(U_893) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_894,U_895,U_893] :
( relation_dom_restriction(relation_rng_restriction(U_895,U_893),U_894) = relation_rng_restriction(U_895,relation_dom_restriction(U_893,U_894))
| ~ relation(U_893) ),
inference(definitional_conversion,[status(esa)],[f_215_2]) ).
cnf(f_215_4,plain,
( relation_dom_restriction(relation_rng_restriction(U_895,U_893),U_894) = relation_rng_restriction(U_895,relation_dom_restriction(U_893,U_894))
| ~ relation(U_893) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_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_216_2,plain,
! [U_900,U_899,U_898] :
( ( ( in(U_900,relation_image(U_898,U_899))
| ! [U_897] :
( ~ in(U_897,U_899)
| ~ in(ordered_pair(U_897,U_900),U_898)
| ~ in(U_897,relation_dom(U_898)) ) )
& ( ? [U_896] :
( in(U_896,U_899)
& in(ordered_pair(U_896,U_900),U_898)
& in(U_896,relation_dom(U_898)) )
| ~ in(U_900,relation_image(U_898,U_899)) ) )
| ~ relation(U_898) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_900,U_899,U_898] :
( ( ( in(U_900,relation_image(U_898,U_899))
| ! [U_897] :
( ~ in(U_897,U_899)
| ~ in(ordered_pair(U_897,U_900),U_898)
| ~ in(U_897,relation_dom(U_898)) ) )
& ( ( in(sK156(U_900,U_899,U_898),U_899)
& in(ordered_pair(sK156(U_900,U_899,U_898),U_900),U_898)
& in(sK156(U_900,U_899,U_898),relation_dom(U_898)) )
| ~ in(U_900,relation_image(U_898,U_899)) ) )
| ~ relation(U_898) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_896,sK156(U_900,U_899,U_898))],[f_216_2]) ).
fof(f_216_4,plain,
( ! [U_898,U_899,U_900] :
( in(sK156(U_900,U_899,U_898),U_899)
| ~ sP206(U_898,U_899,U_900) )
& ! [U_898,U_899,U_900] :
( in(ordered_pair(sK156(U_900,U_899,U_898),U_900),U_898)
| ~ sP206(U_898,U_899,U_900) )
& ! [U_898,U_899,U_900] :
( in(sK156(U_900,U_899,U_898),relation_dom(U_898))
| ~ sP206(U_898,U_899,U_900) )
& ! [U_898,U_897,U_899,U_900] :
( in(U_900,relation_image(U_898,U_899))
| ~ in(U_897,U_899)
| ~ in(ordered_pair(U_897,U_900),U_898)
| ~ in(U_897,relation_dom(U_898))
| ~ sP207(U_898,U_897,U_899,U_900) )
& ! [U_898,U_897,U_899,U_900] :
( sP206(U_898,U_899,U_900)
| ~ in(U_900,relation_image(U_898,U_899))
| ~ sP207(U_898,U_897,U_899,U_900) )
& ! [U_898,U_897,U_899,U_900] :
( sP207(U_898,U_897,U_899,U_900)
| ~ relation(U_898) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206,sP207])],[f_216_3]) ).
cnf(f_216_5,plain,
( sP207(U_898,U_897,U_899,U_900)
| ~ relation(U_898) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_6,plain,
( sP206(U_898,U_899,U_900)
| ~ in(U_900,relation_image(U_898,U_899))
| ~ sP207(U_898,U_897,U_899,U_900) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_7,plain,
( in(U_900,relation_image(U_898,U_899))
| ~ in(U_897,U_899)
| ~ in(ordered_pair(U_897,U_900),U_898)
| ~ in(U_897,relation_dom(U_898))
| ~ sP207(U_898,U_897,U_899,U_900) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_8,plain,
( in(sK156(U_900,U_899,U_898),relation_dom(U_898))
| ~ sP206(U_898,U_899,U_900) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_9,plain,
( in(ordered_pair(sK156(U_900,U_899,U_898),U_900),U_898)
| ~ sP206(U_898,U_899,U_900) ),
inference(clausify,[status(thm)],[f_216_4]) ).
cnf(f_216_10,plain,
( in(sK156(U_900,U_899,U_898),U_899)
| ~ sP206(U_898,U_899,U_900) ),
inference(clausify,[status(thm)],[f_216_4]) ).
fof(f_217_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_217_2,plain,
! [U_902,U_901] :
( subset(relation_image(U_901,U_902),relation_rng(U_901))
| ~ relation(U_901) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_902,U_901] :
( subset(relation_image(U_901,U_902),relation_rng(U_901))
| ~ relation(U_901) ),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
( subset(relation_image(U_901,U_902),relation_rng(U_901))
| ~ relation(U_901) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_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_218_2,plain,
! [U_904,U_903] :
( subset(relation_image(U_903,relation_inverse_image(U_903,U_904)),U_904)
| ~ function(U_903)
| ~ relation(U_903) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_904,U_903] :
( subset(relation_image(U_903,relation_inverse_image(U_903,U_904)),U_904)
| ~ function(U_903)
| ~ relation(U_903) ),
inference(definitional_conversion,[status(esa)],[f_218_2]) ).
cnf(f_218_4,plain,
( subset(relation_image(U_903,relation_inverse_image(U_903,U_904)),U_904)
| ~ function(U_903)
| ~ relation(U_903) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_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_219_2,plain,
! [U_906,U_905] :
( relation_image(U_905,U_906) = relation_image(U_905,set_intersection2(relation_dom(U_905),U_906))
| ~ relation(U_905) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_906,U_905] :
( relation_image(U_905,U_906) = relation_image(U_905,set_intersection2(relation_dom(U_905),U_906))
| ~ relation(U_905) ),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
( relation_image(U_905,U_906) = relation_image(U_905,set_intersection2(relation_dom(U_905),U_906))
| ~ relation(U_905) ),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_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_220_2,plain,
! [U_908,U_907] :
( subset(U_908,relation_inverse_image(U_907,relation_image(U_907,U_908)))
| ~ subset(U_908,relation_dom(U_907))
| ~ relation(U_907) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_908,U_907] :
( subset(U_908,relation_inverse_image(U_907,relation_image(U_907,U_908)))
| ~ subset(U_908,relation_dom(U_907))
| ~ relation(U_907) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( subset(U_908,relation_inverse_image(U_907,relation_image(U_907,U_908)))
| ~ subset(U_908,relation_dom(U_907))
| ~ relation(U_907) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_221_2,plain,
! [U_909] :
( relation_image(U_909,relation_dom(U_909)) = relation_rng(U_909)
| ~ relation(U_909) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_909] :
( relation_image(U_909,relation_dom(U_909)) = relation_rng(U_909)
| ~ relation(U_909) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( relation_image(U_909,relation_dom(U_909)) = relation_rng(U_909)
| ~ relation(U_909) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_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_222_2,plain,
! [U_911,U_910] :
( relation_image(U_910,relation_inverse_image(U_910,U_911)) = U_911
| ~ subset(U_911,relation_rng(U_910))
| ~ function(U_910)
| ~ relation(U_910) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_910,U_911] :
( relation_image(U_910,relation_inverse_image(U_910,U_911)) = U_911
| ~ subset(U_911,relation_rng(U_910))
| ~ function(U_910)
| ~ relation(U_910) ),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
( relation_image(U_910,relation_inverse_image(U_910,U_911)) = U_911
| ~ subset(U_911,relation_rng(U_910))
| ~ function(U_910)
| ~ relation(U_910) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_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_223_2,plain,
! [U_915,U_914,U_913,U_912] :
( relation_of2_as_subset(U_912,U_913,U_914)
| ~ subset(relation_rng(U_912),U_914)
| ~ relation_of2_as_subset(U_912,U_913,U_915) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_914,U_915,U_912,U_913] :
( relation_of2_as_subset(U_912,U_913,U_914)
| ~ subset(relation_rng(U_912),U_914)
| ~ relation_of2_as_subset(U_912,U_913,U_915) ),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
( relation_of2_as_subset(U_912,U_913,U_914)
| ~ subset(relation_rng(U_912),U_914)
| ~ relation_of2_as_subset(U_912,U_913,U_915) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_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_224_2,plain,
! [U_917] :
( ! [U_916] :
( relation_rng(relation_composition(U_917,U_916)) = relation_image(U_916,relation_rng(U_917))
| ~ relation(U_916) )
| ~ relation(U_917) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_916,U_917] :
( relation_rng(relation_composition(U_917,U_916)) = relation_image(U_916,relation_rng(U_917))
| ~ relation(U_916)
| ~ relation(U_917) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( relation_rng(relation_composition(U_917,U_916)) = relation_image(U_916,relation_rng(U_917))
| ~ relation(U_916)
| ~ relation(U_917) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_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_225_2,plain,
! [U_922,U_921,U_920] :
( ( ( in(U_922,relation_inverse_image(U_920,U_921))
| ! [U_919] :
( ~ in(U_919,U_921)
| ~ in(ordered_pair(U_922,U_919),U_920)
| ~ in(U_919,relation_rng(U_920)) ) )
& ( ? [U_918] :
( in(U_918,U_921)
& in(ordered_pair(U_922,U_918),U_920)
& in(U_918,relation_rng(U_920)) )
| ~ in(U_922,relation_inverse_image(U_920,U_921)) ) )
| ~ relation(U_920) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_922,U_921,U_920] :
( ( ( in(U_922,relation_inverse_image(U_920,U_921))
| ! [U_919] :
( ~ in(U_919,U_921)
| ~ in(ordered_pair(U_922,U_919),U_920)
| ~ in(U_919,relation_rng(U_920)) ) )
& ( ( in(sK157(U_922,U_921,U_920),U_921)
& in(ordered_pair(U_922,sK157(U_922,U_921,U_920)),U_920)
& in(sK157(U_922,U_921,U_920),relation_rng(U_920)) )
| ~ in(U_922,relation_inverse_image(U_920,U_921)) ) )
| ~ relation(U_920) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_918,sK157(U_922,U_921,U_920))],[f_225_2]) ).
fof(f_225_4,plain,
( ! [U_920,U_921,U_922] :
( in(sK157(U_922,U_921,U_920),U_921)
| ~ sP208(U_920,U_921,U_922) )
& ! [U_920,U_921,U_922] :
( in(ordered_pair(U_922,sK157(U_922,U_921,U_920)),U_920)
| ~ sP208(U_920,U_921,U_922) )
& ! [U_920,U_921,U_922] :
( in(sK157(U_922,U_921,U_920),relation_rng(U_920))
| ~ sP208(U_920,U_921,U_922) )
& ! [U_919,U_920,U_921,U_922] :
( in(U_922,relation_inverse_image(U_920,U_921))
| ~ in(U_919,U_921)
| ~ in(ordered_pair(U_922,U_919),U_920)
| ~ in(U_919,relation_rng(U_920))
| ~ sP209(U_919,U_920,U_921,U_922) )
& ! [U_919,U_920,U_921,U_922] :
( sP208(U_920,U_921,U_922)
| ~ in(U_922,relation_inverse_image(U_920,U_921))
| ~ sP209(U_919,U_920,U_921,U_922) )
& ! [U_919,U_920,U_921,U_922] :
( sP209(U_919,U_920,U_921,U_922)
| ~ relation(U_920) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208,sP209])],[f_225_3]) ).
cnf(f_225_5,plain,
( sP209(U_919,U_920,U_921,U_922)
| ~ relation(U_920) ),
inference(clausify,[status(thm)],[f_225_4]) ).
cnf(f_225_6,plain,
( sP208(U_920,U_921,U_922)
| ~ in(U_922,relation_inverse_image(U_920,U_921))
| ~ sP209(U_919,U_920,U_921,U_922) ),
inference(clausify,[status(thm)],[f_225_4]) ).
cnf(f_225_7,plain,
( in(U_922,relation_inverse_image(U_920,U_921))
| ~ in(U_919,U_921)
| ~ in(ordered_pair(U_922,U_919),U_920)
| ~ in(U_919,relation_rng(U_920))
| ~ sP209(U_919,U_920,U_921,U_922) ),
inference(clausify,[status(thm)],[f_225_4]) ).
cnf(f_225_8,plain,
( in(sK157(U_922,U_921,U_920),relation_rng(U_920))
| ~ sP208(U_920,U_921,U_922) ),
inference(clausify,[status(thm)],[f_225_4]) ).
cnf(f_225_9,plain,
( in(ordered_pair(U_922,sK157(U_922,U_921,U_920)),U_920)
| ~ sP208(U_920,U_921,U_922) ),
inference(clausify,[status(thm)],[f_225_4]) ).
cnf(f_225_10,plain,
( in(sK157(U_922,U_921,U_920),U_921)
| ~ sP208(U_920,U_921,U_922) ),
inference(clausify,[status(thm)],[f_225_4]) ).
fof(f_226_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_226_2,plain,
! [U_924,U_923] :
( subset(relation_inverse_image(U_923,U_924),relation_dom(U_923))
| ~ relation(U_923) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_923,U_924] :
( subset(relation_inverse_image(U_923,U_924),relation_dom(U_923))
| ~ relation(U_923) ),
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
( subset(relation_inverse_image(U_923,U_924),relation_dom(U_923))
| ~ relation(U_923) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [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)],[t16_relset_1]) ).
fof(f_227_2,plain,
! [U_928,U_927,U_926,U_925] :
( relation_of2_as_subset(U_925,U_926,U_927)
| ~ subset(U_928,U_927)
| ~ relation_of2_as_subset(U_925,U_926,U_928) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_927,U_928,U_926,U_925] :
( relation_of2_as_subset(U_925,U_926,U_927)
| ~ subset(U_928,U_927)
| ~ relation_of2_as_subset(U_925,U_926,U_928) ),
inference(definitional_conversion,[status(esa)],[f_227_2]) ).
cnf(f_227_4,plain,
( relation_of2_as_subset(U_925,U_926,U_927)
| ~ subset(U_928,U_927)
| ~ relation_of2_as_subset(U_925,U_926,U_928) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_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_228_2,plain,
! [U_931,U_930,U_929] :
( ( ( in(U_931,relation_restriction(U_929,U_930))
| ~ in(U_931,cartesian_product2(U_930,U_930))
| ~ in(U_931,U_929) )
& ( ( in(U_931,cartesian_product2(U_930,U_930))
& in(U_931,U_929) )
| ~ in(U_931,relation_restriction(U_929,U_930)) ) )
| ~ relation(U_929) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
( ! [U_930,U_929,U_931] :
( in(U_931,cartesian_product2(U_930,U_930))
| ~ sP210(U_930,U_929,U_931) )
& ! [U_930,U_929,U_931] :
( in(U_931,U_929)
| ~ sP210(U_930,U_929,U_931) )
& ! [U_930,U_929,U_931] :
( in(U_931,relation_restriction(U_929,U_930))
| ~ in(U_931,cartesian_product2(U_930,U_930))
| ~ in(U_931,U_929)
| ~ sP211(U_930,U_929,U_931) )
& ! [U_930,U_929,U_931] :
( sP210(U_930,U_929,U_931)
| ~ in(U_931,relation_restriction(U_929,U_930))
| ~ sP211(U_930,U_929,U_931) )
& ! [U_930,U_929,U_931] :
( sP211(U_930,U_929,U_931)
| ~ relation(U_929) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210,sP211])],[f_228_2]) ).
cnf(f_228_4,plain,
( sP211(U_930,U_929,U_931)
| ~ relation(U_929) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_5,plain,
( sP210(U_930,U_929,U_931)
| ~ in(U_931,relation_restriction(U_929,U_930))
| ~ sP211(U_930,U_929,U_931) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_6,plain,
( in(U_931,relation_restriction(U_929,U_930))
| ~ in(U_931,cartesian_product2(U_930,U_930))
| ~ in(U_931,U_929)
| ~ sP211(U_930,U_929,U_931) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_7,plain,
( in(U_931,U_929)
| ~ sP210(U_930,U_929,U_931) ),
inference(clausify,[status(thm)],[f_228_3]) ).
cnf(f_228_8,plain,
( in(U_931,cartesian_product2(U_930,U_930))
| ~ sP210(U_930,U_929,U_931) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_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_229_2,plain,
! [U_933,U_932] :
( relation_inverse_image(U_932,U_933) != empty_set
| ~ subset(U_933,relation_rng(U_932))
| U_933 = empty_set
| ~ relation(U_932) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_933,U_932] :
( relation_inverse_image(U_932,U_933) != empty_set
| ~ subset(U_933,relation_rng(U_932))
| U_933 = empty_set
| ~ relation(U_932) ),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
( relation_inverse_image(U_932,U_933) != empty_set
| ~ subset(U_933,relation_rng(U_932))
| U_933 = empty_set
| ~ relation(U_932) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_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_230_2,plain,
! [U_936,U_935,U_934] :
( subset(relation_inverse_image(U_934,U_936),relation_inverse_image(U_934,U_935))
| ~ subset(U_936,U_935)
| ~ relation(U_934) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_935,U_934,U_936] :
( subset(relation_inverse_image(U_934,U_936),relation_inverse_image(U_934,U_935))
| ~ subset(U_936,U_935)
| ~ relation(U_934) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( subset(relation_inverse_image(U_934,U_936),relation_inverse_image(U_934,U_935))
| ~ subset(U_936,U_935)
| ~ relation(U_934) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_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_231_2,plain,
! [U_938,U_937] :
( relation_restriction(U_937,U_938) = relation_dom_restriction(relation_rng_restriction(U_938,U_937),U_938)
| ~ relation(U_937) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_938,U_937] :
( relation_restriction(U_937,U_938) = relation_dom_restriction(relation_rng_restriction(U_938,U_937),U_938)
| ~ relation(U_937) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( relation_restriction(U_937,U_938) = relation_dom_restriction(relation_rng_restriction(U_938,U_937),U_938)
| ~ relation(U_937) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_232_2,plain,
! [U_940,U_939] : subset(set_intersection2(U_940,U_939),U_940),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_939,U_940] : subset(set_intersection2(U_940,U_939),U_940),
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
subset(set_intersection2(U_940,U_939),U_940),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_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_233_2,plain,
! [U_942,U_941] :
( relation_restriction(U_941,U_942) = relation_rng_restriction(U_942,relation_dom_restriction(U_941,U_942))
| ~ relation(U_941) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_941,U_942] :
( relation_restriction(U_941,U_942) = relation_rng_restriction(U_942,relation_dom_restriction(U_941,U_942))
| ~ relation(U_941) ),
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
( relation_restriction(U_941,U_942) = relation_rng_restriction(U_942,relation_dom_restriction(U_941,U_942))
| ~ relation(U_941) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_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_234_2,plain,
! [U_945,U_944,U_943] :
( ( in(U_945,U_944)
& in(U_945,relation_field(U_943)) )
| ~ in(U_945,relation_field(relation_restriction(U_943,U_944)))
| ~ relation(U_943) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
( ! [U_945,U_944,U_943] :
( in(U_945,U_944)
| ~ sP212(U_945,U_944,U_943) )
& ! [U_945,U_944,U_943] :
( in(U_945,relation_field(U_943))
| ~ sP212(U_945,U_944,U_943) )
& ! [U_945,U_944,U_943] :
( sP212(U_945,U_944,U_943)
| ~ in(U_945,relation_field(relation_restriction(U_943,U_944)))
| ~ relation(U_943) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_234_2]) ).
cnf(f_234_4,plain,
( sP212(U_945,U_944,U_943)
| ~ in(U_945,relation_field(relation_restriction(U_943,U_944)))
| ~ relation(U_943) ),
inference(clausify,[status(thm)],[f_234_3]) ).
cnf(f_234_5,plain,
( in(U_945,relation_field(U_943))
| ~ sP212(U_945,U_944,U_943) ),
inference(clausify,[status(thm)],[f_234_3]) ).
cnf(f_234_6,plain,
( in(U_945,U_944)
| ~ sP212(U_945,U_944,U_943) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_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_235_2,plain,
! [U_948,U_947,U_946] :
( subset(U_948,set_intersection2(U_947,U_946))
| ~ subset(U_948,U_946)
| ~ subset(U_948,U_947) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_946,U_948,U_947] :
( subset(U_948,set_intersection2(U_947,U_946))
| ~ subset(U_948,U_946)
| ~ subset(U_948,U_947) ),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
( subset(U_948,set_intersection2(U_947,U_946))
| ~ subset(U_948,U_946)
| ~ subset(U_948,U_947) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_236_2,plain,
! [U_949] : set_union2(U_949,empty_set) = U_949,
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_949] : set_union2(U_949,empty_set) = U_949,
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
set_union2(U_949,empty_set) = U_949,
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_237_2,plain,
! [U_951,U_950] :
( element(U_951,U_950)
| ~ in(U_951,U_950) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_950,U_951] :
( element(U_951,U_950)
| ~ in(U_951,U_950) ),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
( element(U_951,U_950)
| ~ in(U_951,U_950) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_238_2,plain,
! [U_954,U_953,U_952] :
( subset(U_954,U_952)
| ~ subset(U_953,U_952)
| ~ subset(U_954,U_953) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_953,U_952,U_954] :
( subset(U_954,U_952)
| ~ subset(U_953,U_952)
| ~ subset(U_954,U_953) ),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
( subset(U_954,U_952)
| ~ subset(U_953,U_952)
| ~ subset(U_954,U_953) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_239_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_239_1]) ).
cnf(f_239_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_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_240_2,plain,
! [U_957,U_956,U_955] :
( ( in(U_956,relation_rng(U_955))
& in(U_957,relation_dom(U_955)) )
| ~ in(ordered_pair(U_957,U_956),U_955)
| ~ relation(U_955) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
( ! [U_955,U_956,U_957] :
( in(U_956,relation_rng(U_955))
| ~ sP213(U_955,U_956,U_957) )
& ! [U_955,U_956,U_957] :
( in(U_957,relation_dom(U_955))
| ~ sP213(U_955,U_956,U_957) )
& ! [U_955,U_956,U_957] :
( sP213(U_955,U_956,U_957)
| ~ in(ordered_pair(U_957,U_956),U_955)
| ~ relation(U_955) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_240_2]) ).
cnf(f_240_4,plain,
( sP213(U_955,U_956,U_957)
| ~ in(ordered_pair(U_957,U_956),U_955)
| ~ relation(U_955) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_5,plain,
( in(U_957,relation_dom(U_955))
| ~ sP213(U_955,U_956,U_957) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_6,plain,
( in(U_956,relation_rng(U_955))
| ~ sP213(U_955,U_956,U_957) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_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_241_2,plain,
! [U_959,U_958] :
( ( subset(relation_field(relation_restriction(U_958,U_959)),U_959)
& subset(relation_field(relation_restriction(U_958,U_959)),relation_field(U_958)) )
| ~ relation(U_958) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
( ! [U_959,U_958] :
( subset(relation_field(relation_restriction(U_958,U_959)),U_959)
| ~ sP214(U_959,U_958) )
& ! [U_959,U_958] :
( subset(relation_field(relation_restriction(U_958,U_959)),relation_field(U_958))
| ~ sP214(U_959,U_958) )
& ! [U_959,U_958] :
( sP214(U_959,U_958)
| ~ relation(U_958) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_241_2]) ).
cnf(f_241_4,plain,
( sP214(U_959,U_958)
| ~ relation(U_958) ),
inference(clausify,[status(thm)],[f_241_3]) ).
cnf(f_241_5,plain,
( subset(relation_field(relation_restriction(U_958,U_959)),relation_field(U_958))
| ~ sP214(U_959,U_958) ),
inference(clausify,[status(thm)],[f_241_3]) ).
cnf(f_241_6,plain,
( subset(relation_field(relation_restriction(U_958,U_959)),U_959)
| ~ sP214(U_959,U_958) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_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_242_2,plain,
! [U_962,U_961] :
( ! [U_960] :
( ( ( in(U_962,relation_dom(relation_composition(U_960,U_961)))
| ~ in(apply(U_960,U_962),relation_dom(U_961))
| ~ in(U_962,relation_dom(U_960)) )
& ( ( in(apply(U_960,U_962),relation_dom(U_961))
& in(U_962,relation_dom(U_960)) )
| ~ in(U_962,relation_dom(relation_composition(U_960,U_961))) ) )
| ~ function(U_960)
| ~ relation(U_960) )
| ~ function(U_961)
| ~ relation(U_961) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
( ! [U_960,U_961,U_962] :
( in(apply(U_960,U_962),relation_dom(U_961))
| ~ sP215(U_960,U_961,U_962) )
& ! [U_960,U_961,U_962] :
( in(U_962,relation_dom(U_960))
| ~ sP215(U_960,U_961,U_962) )
& ! [U_960,U_961,U_962] :
( in(U_962,relation_dom(relation_composition(U_960,U_961)))
| ~ in(apply(U_960,U_962),relation_dom(U_961))
| ~ in(U_962,relation_dom(U_960))
| ~ sP216(U_960,U_961,U_962) )
& ! [U_960,U_961,U_962] :
( sP215(U_960,U_961,U_962)
| ~ in(U_962,relation_dom(relation_composition(U_960,U_961)))
| ~ sP216(U_960,U_961,U_962) )
& ! [U_960,U_961,U_962] :
( sP216(U_960,U_961,U_962)
| ~ function(U_960)
| ~ relation(U_960)
| ~ function(U_961)
| ~ relation(U_961) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215,sP216])],[f_242_2]) ).
cnf(f_242_4,plain,
( sP216(U_960,U_961,U_962)
| ~ function(U_960)
| ~ relation(U_960)
| ~ function(U_961)
| ~ relation(U_961) ),
inference(clausify,[status(thm)],[f_242_3]) ).
cnf(f_242_5,plain,
( sP215(U_960,U_961,U_962)
| ~ in(U_962,relation_dom(relation_composition(U_960,U_961)))
| ~ sP216(U_960,U_961,U_962) ),
inference(clausify,[status(thm)],[f_242_3]) ).
cnf(f_242_6,plain,
( in(U_962,relation_dom(relation_composition(U_960,U_961)))
| ~ in(apply(U_960,U_962),relation_dom(U_961))
| ~ in(U_962,relation_dom(U_960))
| ~ sP216(U_960,U_961,U_962) ),
inference(clausify,[status(thm)],[f_242_3]) ).
cnf(f_242_7,plain,
( in(U_962,relation_dom(U_960))
| ~ sP215(U_960,U_961,U_962) ),
inference(clausify,[status(thm)],[f_242_3]) ).
cnf(f_242_8,plain,
( in(apply(U_960,U_962),relation_dom(U_961))
| ~ sP215(U_960,U_961,U_962) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_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_243_2,plain,
! [U_964] :
( ! [U_963] :
( in(U_964,U_963)
| ~ proper_subset(U_964,U_963)
| ~ ordinal(U_963) )
| ~ epsilon_transitive(U_964) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_964,U_963] :
( in(U_964,U_963)
| ~ proper_subset(U_964,U_963)
| ~ ordinal(U_963)
| ~ epsilon_transitive(U_964) ),
inference(definitional_conversion,[status(esa)],[f_243_2]) ).
cnf(f_243_4,plain,
( in(U_964,U_963)
| ~ proper_subset(U_964,U_963)
| ~ ordinal(U_963)
| ~ epsilon_transitive(U_964) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_244_2,plain,
! [U_965] :
( subset(U_965,cartesian_product2(relation_dom(U_965),relation_rng(U_965)))
| ~ relation(U_965) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_965] :
( subset(U_965,cartesian_product2(relation_dom(U_965),relation_rng(U_965)))
| ~ relation(U_965) ),
inference(definitional_conversion,[status(esa)],[f_244_2]) ).
cnf(f_244_4,plain,
( subset(U_965,cartesian_product2(relation_dom(U_965),relation_rng(U_965)))
| ~ relation(U_965) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_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_245_2,plain,
! [U_968,U_967,U_966] :
( subset(fiber(relation_restriction(U_966,U_968),U_967),fiber(U_966,U_967))
| ~ relation(U_966) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_967,U_968,U_966] :
( subset(fiber(relation_restriction(U_966,U_968),U_967),fiber(U_966,U_967))
| ~ relation(U_966) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( subset(fiber(relation_restriction(U_966,U_968),U_967),fiber(U_966,U_967))
| ~ relation(U_966) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_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_246_2,plain,
! [U_971,U_970] :
( ! [U_969] :
( apply(relation_composition(U_969,U_970),U_971) = apply(U_970,apply(U_969,U_971))
| ~ in(U_971,relation_dom(relation_composition(U_969,U_970)))
| ~ function(U_969)
| ~ relation(U_969) )
| ~ function(U_970)
| ~ relation(U_970) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_971,U_970,U_969] :
( apply(relation_composition(U_969,U_970),U_971) = apply(U_970,apply(U_969,U_971))
| ~ in(U_971,relation_dom(relation_composition(U_969,U_970)))
| ~ function(U_969)
| ~ relation(U_969)
| ~ function(U_970)
| ~ relation(U_970) ),
inference(definitional_conversion,[status(esa)],[f_246_2]) ).
cnf(f_246_4,plain,
( apply(relation_composition(U_969,U_970),U_971) = apply(U_970,apply(U_969,U_971))
| ~ in(U_971,relation_dom(relation_composition(U_969,U_970)))
| ~ function(U_969)
| ~ relation(U_969)
| ~ function(U_970)
| ~ relation(U_970) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
! [A,B,C] :
( ( ( ! [D] :
( ? [E] : in(ordered_pair(D,E),C)
| ~ in(D,B) )
| relation_dom_as_subset(B,A,C) != B )
& ( relation_dom_as_subset(B,A,C) = B
| ? [D] :
( ! [E] : ~ in(ordered_pair(D,E),C)
& in(D,B) ) ) )
| ~ relation_of2_as_subset(C,B,A) ),
inference(fof_nnf,[status(thm)],[t22_relset_1]) ).
fof(f_247_2,plain,
! [U_978,U_977,U_976] :
( ( ( ! [U_975] :
( ? [U_974] : in(ordered_pair(U_975,U_974),U_976)
| ~ in(U_975,U_977) )
| relation_dom_as_subset(U_977,U_978,U_976) != U_977 )
& ( relation_dom_as_subset(U_977,U_978,U_976) = U_977
| ? [U_973] :
( ! [U_972] : ~ in(ordered_pair(U_973,U_972),U_976)
& in(U_973,U_977) ) ) )
| ~ relation_of2_as_subset(U_976,U_977,U_978) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_978,U_977,U_976] :
( ( ( ! [U_975] :
( ? [U_974] : in(ordered_pair(U_975,U_974),U_976)
| ~ in(U_975,U_977) )
| relation_dom_as_subset(U_977,U_978,U_976) != U_977 )
& ( relation_dom_as_subset(U_977,U_978,U_976) = U_977
| ( ! [U_972] : ~ in(ordered_pair(sK158(U_978,U_977,U_976),U_972),U_976)
& in(sK158(U_978,U_977,U_976),U_977) ) ) )
| ~ relation_of2_as_subset(U_976,U_977,U_978) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_973,sK158(U_978,U_977,U_976))],[f_247_2]) ).
fof(f_247_4,plain,
! [U_978,U_977,U_976] :
( ( ( ! [U_975] :
( in(ordered_pair(U_975,sK159(U_978,U_977,U_976,U_975)),U_976)
| ~ in(U_975,U_977) )
| relation_dom_as_subset(U_977,U_978,U_976) != U_977 )
& ( relation_dom_as_subset(U_977,U_978,U_976) = U_977
| ( ! [U_972] : ~ in(ordered_pair(sK158(U_978,U_977,U_976),U_972),U_976)
& in(sK158(U_978,U_977,U_976),U_977) ) ) )
| ~ relation_of2_as_subset(U_976,U_977,U_978) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_974,sK159(U_978,U_977,U_976,U_975))],[f_247_3]) ).
fof(f_247_5,plain,
( ! [U_978,U_976,U_977,U_972] :
( ~ in(ordered_pair(sK158(U_978,U_977,U_976),U_972),U_976)
| ~ sP217(U_978,U_976,U_977,U_972) )
& ! [U_978,U_976,U_977,U_972] :
( in(sK158(U_978,U_977,U_976),U_977)
| ~ sP217(U_978,U_976,U_977,U_972) )
& ! [U_975,U_978,U_976,U_977,U_972] :
( in(ordered_pair(U_975,sK159(U_978,U_977,U_976,U_975)),U_976)
| ~ in(U_975,U_977)
| relation_dom_as_subset(U_977,U_978,U_976) != U_977
| ~ sP218(U_975,U_978,U_976,U_977,U_972) )
& ! [U_975,U_978,U_976,U_977,U_972] :
( relation_dom_as_subset(U_977,U_978,U_976) = U_977
| sP217(U_978,U_976,U_977,U_972)
| ~ sP218(U_975,U_978,U_976,U_977,U_972) )
& ! [U_975,U_978,U_976,U_977,U_972] :
( sP218(U_975,U_978,U_976,U_977,U_972)
| ~ relation_of2_as_subset(U_976,U_977,U_978) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217,sP218])],[f_247_4]) ).
cnf(f_247_6,plain,
( sP218(U_975,U_978,U_976,U_977,U_972)
| ~ relation_of2_as_subset(U_976,U_977,U_978) ),
inference(clausify,[status(thm)],[f_247_5]) ).
cnf(f_247_7,plain,
( relation_dom_as_subset(U_977,U_978,U_976) = U_977
| sP217(U_978,U_976,U_977,U_972)
| ~ sP218(U_975,U_978,U_976,U_977,U_972) ),
inference(clausify,[status(thm)],[f_247_5]) ).
cnf(f_247_8,plain,
( in(ordered_pair(U_975,sK159(U_978,U_977,U_976,U_975)),U_976)
| ~ in(U_975,U_977)
| relation_dom_as_subset(U_977,U_978,U_976) != U_977
| ~ sP218(U_975,U_978,U_976,U_977,U_972) ),
inference(clausify,[status(thm)],[f_247_5]) ).
cnf(f_247_9,plain,
( in(sK158(U_978,U_977,U_976),U_977)
| ~ sP217(U_978,U_976,U_977,U_972) ),
inference(clausify,[status(thm)],[f_247_5]) ).
cnf(f_247_10,plain,
( ~ in(ordered_pair(sK158(U_978,U_977,U_976),U_972),U_976)
| ~ sP217(U_978,U_976,U_977,U_972) ),
inference(clausify,[status(thm)],[f_247_5]) ).
fof(f_248_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_248_2,plain,
! [U_980,U_979] :
( reflexive(relation_restriction(U_979,U_980))
| ~ reflexive(U_979)
| ~ relation(U_979) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_979,U_980] :
( reflexive(relation_restriction(U_979,U_980))
| ~ reflexive(U_979)
| ~ relation(U_979) ),
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
( reflexive(relation_restriction(U_979,U_980))
| ~ reflexive(U_979)
| ~ relation(U_979) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_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_249_2,plain,
! [U_983,U_982] :
( ! [U_981] :
( apply(relation_composition(U_982,U_981),U_983) = apply(U_981,apply(U_982,U_983))
| ~ in(U_983,relation_dom(U_982))
| ~ function(U_981)
| ~ relation(U_981) )
| ~ function(U_982)
| ~ relation(U_982) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_982,U_983,U_981] :
( apply(relation_composition(U_982,U_981),U_983) = apply(U_981,apply(U_982,U_983))
| ~ in(U_983,relation_dom(U_982))
| ~ function(U_981)
| ~ relation(U_981)
| ~ function(U_982)
| ~ relation(U_982) ),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
( apply(relation_composition(U_982,U_981),U_983) = apply(U_981,apply(U_982,U_983))
| ~ in(U_983,relation_dom(U_982))
| ~ function(U_981)
| ~ relation(U_981)
| ~ function(U_982)
| ~ relation(U_982) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_250_2,plain,
! [U_985,U_984] :
( ordinal(U_985)
| ~ in(U_985,U_984)
| ~ ordinal(U_984) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_984,U_985] :
( ordinal(U_985)
| ~ in(U_985,U_984)
| ~ ordinal(U_984) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( ordinal(U_985)
| ~ in(U_985,U_984)
| ~ ordinal(U_984) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_1,plain,
! [A,B,C] :
( ( ( ! [D] :
( ? [E] : in(ordered_pair(E,D),C)
| ~ in(D,B) )
| relation_rng_as_subset(A,B,C) != B )
& ( relation_rng_as_subset(A,B,C) = B
| ? [D] :
( ! [E] : ~ in(ordered_pair(E,D),C)
& in(D,B) ) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[t23_relset_1]) ).
fof(f_251_2,plain,
! [U_992,U_991,U_990] :
( ( ( ! [U_989] :
( ? [U_988] : in(ordered_pair(U_988,U_989),U_990)
| ~ in(U_989,U_991) )
| relation_rng_as_subset(U_992,U_991,U_990) != U_991 )
& ( relation_rng_as_subset(U_992,U_991,U_990) = U_991
| ? [U_987] :
( ! [U_986] : ~ in(ordered_pair(U_986,U_987),U_990)
& in(U_987,U_991) ) ) )
| ~ relation_of2_as_subset(U_990,U_992,U_991) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_992,U_991,U_990] :
( ( ( ! [U_989] :
( ? [U_988] : in(ordered_pair(U_988,U_989),U_990)
| ~ in(U_989,U_991) )
| relation_rng_as_subset(U_992,U_991,U_990) != U_991 )
& ( relation_rng_as_subset(U_992,U_991,U_990) = U_991
| ( ! [U_986] : ~ in(ordered_pair(U_986,sK160(U_992,U_991,U_990)),U_990)
& in(sK160(U_992,U_991,U_990),U_991) ) ) )
| ~ relation_of2_as_subset(U_990,U_992,U_991) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_987,sK160(U_992,U_991,U_990))],[f_251_2]) ).
fof(f_251_4,plain,
! [U_992,U_991,U_990] :
( ( ( ! [U_989] :
( in(ordered_pair(sK161(U_992,U_991,U_990,U_989),U_989),U_990)
| ~ in(U_989,U_991) )
| relation_rng_as_subset(U_992,U_991,U_990) != U_991 )
& ( relation_rng_as_subset(U_992,U_991,U_990) = U_991
| ( ! [U_986] : ~ in(ordered_pair(U_986,sK160(U_992,U_991,U_990)),U_990)
& in(sK160(U_992,U_991,U_990),U_991) ) ) )
| ~ relation_of2_as_subset(U_990,U_992,U_991) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_988,sK161(U_992,U_991,U_990,U_989))],[f_251_3]) ).
fof(f_251_5,plain,
( ! [U_986,U_990,U_991,U_992] :
( ~ in(ordered_pair(U_986,sK160(U_992,U_991,U_990)),U_990)
| ~ sP219(U_986,U_990,U_991,U_992) )
& ! [U_986,U_990,U_991,U_992] :
( in(sK160(U_992,U_991,U_990),U_991)
| ~ sP219(U_986,U_990,U_991,U_992) )
& ! [U_986,U_989,U_990,U_991,U_992] :
( in(ordered_pair(sK161(U_992,U_991,U_990,U_989),U_989),U_990)
| ~ in(U_989,U_991)
| relation_rng_as_subset(U_992,U_991,U_990) != U_991
| ~ sP220(U_986,U_989,U_990,U_991,U_992) )
& ! [U_986,U_989,U_990,U_991,U_992] :
( relation_rng_as_subset(U_992,U_991,U_990) = U_991
| sP219(U_986,U_990,U_991,U_992)
| ~ sP220(U_986,U_989,U_990,U_991,U_992) )
& ! [U_986,U_989,U_990,U_991,U_992] :
( sP220(U_986,U_989,U_990,U_991,U_992)
| ~ relation_of2_as_subset(U_990,U_992,U_991) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219,sP220])],[f_251_4]) ).
cnf(f_251_6,plain,
( sP220(U_986,U_989,U_990,U_991,U_992)
| ~ relation_of2_as_subset(U_990,U_992,U_991) ),
inference(clausify,[status(thm)],[f_251_5]) ).
cnf(f_251_7,plain,
( relation_rng_as_subset(U_992,U_991,U_990) = U_991
| sP219(U_986,U_990,U_991,U_992)
| ~ sP220(U_986,U_989,U_990,U_991,U_992) ),
inference(clausify,[status(thm)],[f_251_5]) ).
cnf(f_251_8,plain,
( in(ordered_pair(sK161(U_992,U_991,U_990,U_989),U_989),U_990)
| ~ in(U_989,U_991)
| relation_rng_as_subset(U_992,U_991,U_990) != U_991
| ~ sP220(U_986,U_989,U_990,U_991,U_992) ),
inference(clausify,[status(thm)],[f_251_5]) ).
cnf(f_251_9,plain,
( in(sK160(U_992,U_991,U_990),U_991)
| ~ sP219(U_986,U_990,U_991,U_992) ),
inference(clausify,[status(thm)],[f_251_5]) ).
cnf(f_251_10,plain,
( ~ in(ordered_pair(U_986,sK160(U_992,U_991,U_990)),U_990)
| ~ sP219(U_986,U_990,U_991,U_992) ),
inference(clausify,[status(thm)],[f_251_5]) ).
fof(f_252_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_252_2,plain,
! [U_994,U_993] :
( connected(relation_restriction(U_993,U_994))
| ~ connected(U_993)
| ~ relation(U_993) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_994,U_993] :
( connected(relation_restriction(U_993,U_994))
| ~ connected(U_993)
| ~ relation(U_993) ),
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
( connected(relation_restriction(U_993,U_994))
| ~ connected(U_993)
| ~ relation(U_993) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_996] :
( ! [U_995] :
( in(U_995,U_996)
| U_996 = U_995
| in(U_996,U_995)
| ~ ordinal(U_995) )
| ~ ordinal(U_996) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
! [U_996,U_995] :
( in(U_995,U_996)
| U_996 = U_995
| in(U_996,U_995)
| ~ ordinal(U_995)
| ~ ordinal(U_996) ),
inference(definitional_conversion,[status(esa)],[f_253_2]) ).
cnf(f_253_4,plain,
( in(U_995,U_996)
| U_996 = U_995
| in(U_996,U_995)
| ~ ordinal(U_995)
| ~ ordinal(U_996) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_254_2,plain,
! [U_998,U_997] :
( transitive(relation_restriction(U_997,U_998))
| ~ transitive(U_997)
| ~ relation(U_997) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_998,U_997] :
( transitive(relation_restriction(U_997,U_998))
| ~ transitive(U_997)
| ~ relation(U_997) ),
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
( transitive(relation_restriction(U_997,U_998))
| ~ transitive(U_997)
| ~ relation(U_997) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_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_255_2,plain,
! [U_1000] :
( ! [U_999] :
( ( subset(relation_rng(U_1000),relation_rng(U_999))
& subset(relation_dom(U_1000),relation_dom(U_999)) )
| ~ subset(U_1000,U_999)
| ~ relation(U_999) )
| ~ relation(U_1000) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
( ! [U_1000,U_999] :
( subset(relation_rng(U_1000),relation_rng(U_999))
| ~ sP221(U_1000,U_999) )
& ! [U_1000,U_999] :
( subset(relation_dom(U_1000),relation_dom(U_999))
| ~ sP221(U_1000,U_999) )
& ! [U_1000,U_999] :
( sP221(U_1000,U_999)
| ~ subset(U_1000,U_999)
| ~ relation(U_999)
| ~ relation(U_1000) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_255_2]) ).
cnf(f_255_4,plain,
( sP221(U_1000,U_999)
| ~ subset(U_1000,U_999)
| ~ relation(U_999)
| ~ relation(U_1000) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_5,plain,
( subset(relation_dom(U_1000),relation_dom(U_999))
| ~ sP221(U_1000,U_999) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_6,plain,
( subset(relation_rng(U_1000),relation_rng(U_999))
| ~ sP221(U_1000,U_999) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_256_2,plain,
! [U_1002,U_1001] :
( antisymmetric(relation_restriction(U_1001,U_1002))
| ~ antisymmetric(U_1001)
| ~ relation(U_1001) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_1002,U_1001] :
( antisymmetric(relation_restriction(U_1001,U_1002))
| ~ antisymmetric(U_1001)
| ~ relation(U_1001) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( antisymmetric(relation_restriction(U_1001,U_1002))
| ~ antisymmetric(U_1001)
| ~ relation(U_1001) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_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_257_2,plain,
! [U_1005,U_1004,U_1003] :
( subset(set_intersection2(U_1005,U_1003),set_intersection2(U_1004,U_1003))
| ~ subset(U_1005,U_1004) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_1005,U_1004] :
( ! [U_1003] : subset(set_intersection2(U_1005,U_1003),set_intersection2(U_1004,U_1003))
| ~ subset(U_1005,U_1004) ),
inference(miniscope,[status(thm)],[f_257_2]) ).
fof(f_257_4,plain,
! [U_1003,U_1004,U_1005] :
( subset(set_intersection2(U_1005,U_1003),set_intersection2(U_1004,U_1003))
| ~ subset(U_1005,U_1004) ),
inference(definitional_conversion,[status(esa)],[f_257_3]) ).
cnf(f_257_5,plain,
( subset(set_intersection2(U_1005,U_1003),set_intersection2(U_1004,U_1003))
| ~ subset(U_1005,U_1004) ),
inference(clausify,[status(thm)],[f_257_4]) ).
fof(f_258_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_258_2,plain,
! [U_1007,U_1006] :
( set_intersection2(U_1007,U_1006) = U_1007
| ~ subset(U_1007,U_1006) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_1007,U_1006] :
( set_intersection2(U_1007,U_1006) = U_1007
| ~ subset(U_1007,U_1006) ),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
( set_intersection2(U_1007,U_1006) = U_1007
| ~ subset(U_1007,U_1006) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_259_2,plain,
! [U_1008] : set_intersection2(U_1008,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_1008] : set_intersection2(U_1008,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
set_intersection2(U_1008,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_260_2,plain,
! [U_1010,U_1009] :
( in(U_1010,U_1009)
| empty(U_1009)
| ~ element(U_1010,U_1009) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_1010,U_1009] :
( in(U_1010,U_1009)
| empty(U_1009)
| ~ element(U_1010,U_1009) ),
inference(definitional_conversion,[status(esa)],[f_260_2]) ).
cnf(f_260_4,plain,
( in(U_1010,U_1009)
| empty(U_1009)
| ~ element(U_1010,U_1009) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_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_261_2,plain,
! [U_1013,U_1012] :
( U_1013 = U_1012
| ? [U_1011] :
( ( ~ in(U_1011,U_1013)
& in(U_1011,U_1012) )
| ( ~ in(U_1011,U_1012)
& in(U_1011,U_1013) ) ) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
! [U_1013,U_1012] :
( U_1013 = U_1012
| ? [U_1015] :
( ~ in(U_1015,U_1013)
& in(U_1015,U_1012) )
| ? [U_1014] :
( ~ in(U_1014,U_1012)
& in(U_1014,U_1013) ) ),
inference(miniscope,[status(thm)],[f_261_2]) ).
fof(f_261_4,plain,
! [U_1013,U_1012] :
( U_1013 = U_1012
| ? [U_1015] :
( ~ in(U_1015,U_1013)
& in(U_1015,U_1012) )
| ( ~ in(sK162(U_1013,U_1012),U_1012)
& in(sK162(U_1013,U_1012),U_1013) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_1014,sK162(U_1013,U_1012))],[f_261_3]) ).
fof(f_261_5,plain,
! [U_1013,U_1012] :
( U_1013 = U_1012
| ( ~ in(sK163(U_1013,U_1012),U_1013)
& in(sK163(U_1013,U_1012),U_1012) )
| ( ~ in(sK162(U_1013,U_1012),U_1012)
& in(sK162(U_1013,U_1012),U_1013) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_1015,sK163(U_1013,U_1012))],[f_261_4]) ).
fof(f_261_6,plain,
( ! [U_1012,U_1013] :
( ~ in(sK163(U_1013,U_1012),U_1013)
| ~ sP223(U_1012,U_1013) )
& ! [U_1012,U_1013] :
( in(sK163(U_1013,U_1012),U_1012)
| ~ sP223(U_1012,U_1013) )
& ! [U_1012,U_1013] :
( ~ in(sK162(U_1013,U_1012),U_1012)
| ~ sP222(U_1012,U_1013) )
& ! [U_1012,U_1013] :
( in(sK162(U_1013,U_1012),U_1013)
| ~ sP222(U_1012,U_1013) )
& ! [U_1012,U_1013] :
( U_1013 = U_1012
| sP223(U_1012,U_1013)
| sP222(U_1012,U_1013) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222,sP223])],[f_261_5]) ).
cnf(f_261_7,plain,
( U_1013 = U_1012
| sP223(U_1012,U_1013)
| sP222(U_1012,U_1013) ),
inference(clausify,[status(thm)],[f_261_6]) ).
cnf(f_261_8,plain,
( in(sK162(U_1013,U_1012),U_1013)
| ~ sP222(U_1012,U_1013) ),
inference(clausify,[status(thm)],[f_261_6]) ).
cnf(f_261_9,plain,
( ~ in(sK162(U_1013,U_1012),U_1012)
| ~ sP222(U_1012,U_1013) ),
inference(clausify,[status(thm)],[f_261_6]) ).
cnf(f_261_10,plain,
( in(sK163(U_1013,U_1012),U_1012)
| ~ sP223(U_1012,U_1013) ),
inference(clausify,[status(thm)],[f_261_6]) ).
cnf(f_261_11,plain,
( ~ in(sK163(U_1013,U_1012),U_1013)
| ~ sP223(U_1012,U_1013) ),
inference(clausify,[status(thm)],[f_261_6]) ).
fof(f_262_1,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t2_wellord2]) ).
fof(f_262_2,plain,
! [U_1016] : reflexive(inclusion_relation(U_1016)),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_1016] : reflexive(inclusion_relation(U_1016)),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
reflexive(inclusion_relation(U_1016)),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_263_2,plain,
! [U_1017] : subset(empty_set,U_1017),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_1017] : subset(empty_set,U_1017),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
subset(empty_set,U_1017),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_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_264_2,plain,
! [U_1020,U_1019,U_1018] :
( ( in(U_1019,relation_field(U_1018))
& in(U_1020,relation_field(U_1018)) )
| ~ in(ordered_pair(U_1020,U_1019),U_1018)
| ~ relation(U_1018) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
( ! [U_1020,U_1018,U_1019] :
( in(U_1019,relation_field(U_1018))
| ~ sP224(U_1020,U_1018,U_1019) )
& ! [U_1020,U_1018,U_1019] :
( in(U_1020,relation_field(U_1018))
| ~ sP224(U_1020,U_1018,U_1019) )
& ! [U_1020,U_1018,U_1019] :
( sP224(U_1020,U_1018,U_1019)
| ~ in(ordered_pair(U_1020,U_1019),U_1018)
| ~ relation(U_1018) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_264_2]) ).
cnf(f_264_4,plain,
( sP224(U_1020,U_1018,U_1019)
| ~ in(ordered_pair(U_1020,U_1019),U_1018)
| ~ relation(U_1018) ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_5,plain,
( in(U_1020,relation_field(U_1018))
| ~ sP224(U_1020,U_1018,U_1019) ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_6,plain,
( in(U_1019,relation_field(U_1018))
| ~ sP224(U_1020,U_1018,U_1019) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_265_2,plain,
! [U_1022] :
( ordinal(U_1022)
| ? [U_1021] :
( ( ~ subset(U_1021,U_1022)
| ~ ordinal(U_1021) )
& in(U_1021,U_1022) ) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_1022] :
( ordinal(U_1022)
| ( ( ~ subset(sK164(U_1022),U_1022)
| ~ ordinal(sK164(U_1022)) )
& in(sK164(U_1022),U_1022) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_1021,sK164(U_1022))],[f_265_2]) ).
fof(f_265_4,plain,
( ! [U_1022] :
( ~ subset(sK164(U_1022),U_1022)
| ~ ordinal(sK164(U_1022))
| ~ sP225(U_1022) )
& ! [U_1022] :
( in(sK164(U_1022),U_1022)
| ~ sP225(U_1022) )
& ! [U_1022] :
( ordinal(U_1022)
| sP225(U_1022) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_265_3]) ).
cnf(f_265_5,plain,
( ordinal(U_1022)
| sP225(U_1022) ),
inference(clausify,[status(thm)],[f_265_4]) ).
cnf(f_265_6,plain,
( in(sK164(U_1022),U_1022)
| ~ sP225(U_1022) ),
inference(clausify,[status(thm)],[f_265_4]) ).
cnf(f_265_7,plain,
( ~ subset(sK164(U_1022),U_1022)
| ~ ordinal(sK164(U_1022))
| ~ sP225(U_1022) ),
inference(clausify,[status(thm)],[f_265_4]) ).
fof(f_266_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_266_2,plain,
! [U_1024,U_1023] :
( well_founded_relation(relation_restriction(U_1023,U_1024))
| ~ well_founded_relation(U_1023)
| ~ relation(U_1023) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_1023,U_1024] :
( well_founded_relation(relation_restriction(U_1023,U_1024))
| ~ well_founded_relation(U_1023)
| ~ relation(U_1023) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( well_founded_relation(relation_restriction(U_1023,U_1024))
| ~ well_founded_relation(U_1023)
| ~ relation(U_1023) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_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_267_2,plain,
! [U_1028,U_1027] :
( ? [U_1026] :
( ! [U_1025] :
( ordinal_subset(U_1026,U_1025)
| ~ in(U_1025,U_1028)
| ~ ordinal(U_1025) )
& in(U_1026,U_1028)
& ordinal(U_1026) )
| U_1028 = empty_set
| ~ subset(U_1028,U_1027)
| ~ ordinal(U_1027) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_1028,U_1027] :
( ( ! [U_1025] :
( ordinal_subset(sK165(U_1028,U_1027),U_1025)
| ~ in(U_1025,U_1028)
| ~ ordinal(U_1025) )
& in(sK165(U_1028,U_1027),U_1028)
& ordinal(sK165(U_1028,U_1027)) )
| U_1028 = empty_set
| ~ subset(U_1028,U_1027)
| ~ ordinal(U_1027) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_1026,sK165(U_1028,U_1027))],[f_267_2]) ).
fof(f_267_4,plain,
( ! [U_1027,U_1025,U_1028] :
( ordinal_subset(sK165(U_1028,U_1027),U_1025)
| ~ in(U_1025,U_1028)
| ~ ordinal(U_1025)
| ~ sP226(U_1027,U_1025,U_1028) )
& ! [U_1027,U_1025,U_1028] :
( in(sK165(U_1028,U_1027),U_1028)
| ~ sP226(U_1027,U_1025,U_1028) )
& ! [U_1027,U_1025,U_1028] :
( ordinal(sK165(U_1028,U_1027))
| ~ sP226(U_1027,U_1025,U_1028) )
& ! [U_1027,U_1025,U_1028] :
( sP226(U_1027,U_1025,U_1028)
| U_1028 = empty_set
| ~ subset(U_1028,U_1027)
| ~ ordinal(U_1027) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_267_3]) ).
cnf(f_267_5,plain,
( sP226(U_1027,U_1025,U_1028)
| U_1028 = empty_set
| ~ subset(U_1028,U_1027)
| ~ ordinal(U_1027) ),
inference(clausify,[status(thm)],[f_267_4]) ).
cnf(f_267_6,plain,
( ordinal(sK165(U_1028,U_1027))
| ~ sP226(U_1027,U_1025,U_1028) ),
inference(clausify,[status(thm)],[f_267_4]) ).
cnf(f_267_7,plain,
( in(sK165(U_1028,U_1027),U_1028)
| ~ sP226(U_1027,U_1025,U_1028) ),
inference(clausify,[status(thm)],[f_267_4]) ).
cnf(f_267_8,plain,
( ordinal_subset(sK165(U_1028,U_1027),U_1025)
| ~ in(U_1025,U_1028)
| ~ ordinal(U_1025)
| ~ sP226(U_1027,U_1025,U_1028) ),
inference(clausify,[status(thm)],[f_267_4]) ).
fof(f_268_1,plain,
! [A,B] :
( well_ordering(relation_restriction(B,A))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t32_wellord1]) ).
fof(f_268_2,plain,
! [U_1030,U_1029] :
( well_ordering(relation_restriction(U_1029,U_1030))
| ~ well_ordering(U_1029)
| ~ relation(U_1029) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_1030,U_1029] :
( well_ordering(relation_restriction(U_1029,U_1030))
| ~ well_ordering(U_1029)
| ~ relation(U_1029) ),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
( well_ordering(relation_restriction(U_1029,U_1030))
| ~ well_ordering(U_1029)
| ~ relation(U_1029) ),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_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_269_2,plain,
! [U_1032] :
( ! [U_1031] :
( ( ( in(U_1032,U_1031)
| ~ ordinal_subset(succ(U_1032),U_1031) )
& ( ordinal_subset(succ(U_1032),U_1031)
| ~ in(U_1032,U_1031) ) )
| ~ ordinal(U_1031) )
| ~ ordinal(U_1032) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_1031,U_1032] :
( in(U_1032,U_1031)
| ~ ordinal_subset(succ(U_1032),U_1031)
| ~ sP227(U_1031,U_1032) )
& ! [U_1031,U_1032] :
( ordinal_subset(succ(U_1032),U_1031)
| ~ in(U_1032,U_1031)
| ~ sP227(U_1031,U_1032) )
& ! [U_1031,U_1032] :
( sP227(U_1031,U_1032)
| ~ ordinal(U_1031)
| ~ ordinal(U_1032) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_269_2]) ).
cnf(f_269_4,plain,
( sP227(U_1031,U_1032)
| ~ ordinal(U_1031)
| ~ ordinal(U_1032) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( ordinal_subset(succ(U_1032),U_1031)
| ~ in(U_1032,U_1031)
| ~ sP227(U_1031,U_1032) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_6,plain,
( in(U_1032,U_1031)
| ~ ordinal_subset(succ(U_1032),U_1031)
| ~ sP227(U_1031,U_1032) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_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_270_2,plain,
! [U_1035,U_1034,U_1033] :
( subset(set_difference(U_1035,U_1033),set_difference(U_1034,U_1033))
| ~ subset(U_1035,U_1034) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_1035,U_1034] :
( ! [U_1033] : subset(set_difference(U_1035,U_1033),set_difference(U_1034,U_1033))
| ~ subset(U_1035,U_1034) ),
inference(miniscope,[status(thm)],[f_270_2]) ).
fof(f_270_4,plain,
! [U_1034,U_1035,U_1033] :
( subset(set_difference(U_1035,U_1033),set_difference(U_1034,U_1033))
| ~ subset(U_1035,U_1034) ),
inference(definitional_conversion,[status(esa)],[f_270_3]) ).
cnf(f_270_5,plain,
( subset(set_difference(U_1035,U_1033),set_difference(U_1034,U_1033))
| ~ subset(U_1035,U_1034) ),
inference(clausify,[status(thm)],[f_270_4]) ).
fof(f_271_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_271_2,plain,
! [U_1039,U_1038,U_1037,U_1036] :
( ( U_1038 = U_1036
& U_1039 = U_1037 )
| ordered_pair(U_1039,U_1038) != ordered_pair(U_1037,U_1036) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
( ! [U_1037,U_1038,U_1036,U_1039] :
( U_1038 = U_1036
| ~ sP228(U_1037,U_1038,U_1036,U_1039) )
& ! [U_1037,U_1038,U_1036,U_1039] :
( U_1039 = U_1037
| ~ sP228(U_1037,U_1038,U_1036,U_1039) )
& ! [U_1037,U_1038,U_1036,U_1039] :
( sP228(U_1037,U_1038,U_1036,U_1039)
| ordered_pair(U_1039,U_1038) != ordered_pair(U_1037,U_1036) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_271_2]) ).
cnf(f_271_4,plain,
( sP228(U_1037,U_1038,U_1036,U_1039)
| ordered_pair(U_1039,U_1038) != ordered_pair(U_1037,U_1036) ),
inference(clausify,[status(thm)],[f_271_3]) ).
cnf(f_271_5,plain,
( U_1039 = U_1037
| ~ sP228(U_1037,U_1038,U_1036,U_1039) ),
inference(clausify,[status(thm)],[f_271_3]) ).
cnf(f_271_6,plain,
( U_1038 = U_1036
| ~ sP228(U_1037,U_1038,U_1036,U_1039) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_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_272_2,plain,
! [U_1043,U_1042] :
( ( ( U_1042 = identity_relation(U_1043)
| ? [U_1041] :
( apply(U_1042,U_1041) != U_1041
& in(U_1041,U_1043) )
| relation_dom(U_1042) != U_1043 )
& ( ( ! [U_1040] :
( apply(U_1042,U_1040) = U_1040
| ~ in(U_1040,U_1043) )
& relation_dom(U_1042) = U_1043 )
| U_1042 != identity_relation(U_1043) ) )
| ~ function(U_1042)
| ~ relation(U_1042) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_1043,U_1042] :
( ( ( U_1042 = identity_relation(U_1043)
| ( apply(U_1042,sK166(U_1043,U_1042)) != sK166(U_1043,U_1042)
& in(sK166(U_1043,U_1042),U_1043) )
| relation_dom(U_1042) != U_1043 )
& ( ( ! [U_1040] :
( apply(U_1042,U_1040) = U_1040
| ~ in(U_1040,U_1043) )
& relation_dom(U_1042) = U_1043 )
| U_1042 != identity_relation(U_1043) ) )
| ~ function(U_1042)
| ~ relation(U_1042) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_1041,sK166(U_1043,U_1042))],[f_272_2]) ).
fof(f_272_4,plain,
( ! [U_1042,U_1043] :
( apply(U_1042,sK166(U_1043,U_1042)) != sK166(U_1043,U_1042)
| ~ sP230(U_1042,U_1043) )
& ! [U_1042,U_1043] :
( in(sK166(U_1043,U_1042),U_1043)
| ~ sP230(U_1042,U_1043) )
& ! [U_1040,U_1042,U_1043] :
( apply(U_1042,U_1040) = U_1040
| ~ in(U_1040,U_1043)
| ~ sP229(U_1040,U_1042,U_1043) )
& ! [U_1040,U_1042,U_1043] :
( relation_dom(U_1042) = U_1043
| ~ sP229(U_1040,U_1042,U_1043) )
& ! [U_1040,U_1042,U_1043] :
( U_1042 = identity_relation(U_1043)
| sP230(U_1042,U_1043)
| relation_dom(U_1042) != U_1043
| ~ sP231(U_1040,U_1042,U_1043) )
& ! [U_1040,U_1042,U_1043] :
( sP229(U_1040,U_1042,U_1043)
| U_1042 != identity_relation(U_1043)
| ~ sP231(U_1040,U_1042,U_1043) )
& ! [U_1040,U_1042,U_1043] :
( sP231(U_1040,U_1042,U_1043)
| ~ function(U_1042)
| ~ relation(U_1042) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229,sP230,sP231])],[f_272_3]) ).
cnf(f_272_5,plain,
( sP231(U_1040,U_1042,U_1043)
| ~ function(U_1042)
| ~ relation(U_1042) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_6,plain,
( sP229(U_1040,U_1042,U_1043)
| U_1042 != identity_relation(U_1043)
| ~ sP231(U_1040,U_1042,U_1043) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_7,plain,
( U_1042 = identity_relation(U_1043)
| sP230(U_1042,U_1043)
| relation_dom(U_1042) != U_1043
| ~ sP231(U_1040,U_1042,U_1043) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_8,plain,
( relation_dom(U_1042) = U_1043
| ~ sP229(U_1040,U_1042,U_1043) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_9,plain,
( apply(U_1042,U_1040) = U_1040
| ~ in(U_1040,U_1043)
| ~ sP229(U_1040,U_1042,U_1043) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_10,plain,
( in(sK166(U_1043,U_1042),U_1043)
| ~ sP230(U_1042,U_1043) ),
inference(clausify,[status(thm)],[f_272_4]) ).
cnf(f_272_11,plain,
( apply(U_1042,sK166(U_1043,U_1042)) != sK166(U_1043,U_1042)
| ~ sP230(U_1042,U_1043) ),
inference(clausify,[status(thm)],[f_272_4]) ).
fof(f_273_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_273_2,plain,
! [U_1045,U_1044] :
( apply(identity_relation(U_1045),U_1044) = U_1044
| ~ in(U_1044,U_1045) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_1044,U_1045] :
( apply(identity_relation(U_1045),U_1044) = U_1044
| ~ in(U_1044,U_1045) ),
inference(definitional_conversion,[status(esa)],[f_273_2]) ).
cnf(f_273_4,plain,
( apply(identity_relation(U_1045),U_1044) = U_1044
| ~ in(U_1044,U_1045) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_274_2,plain,
! [U_1047,U_1046] : subset(set_difference(U_1047,U_1046),U_1047),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_1046,U_1047] : subset(set_difference(U_1047,U_1046),U_1047),
inference(definitional_conversion,[status(esa)],[f_274_2]) ).
cnf(f_274_4,plain,
subset(set_difference(U_1047,U_1046),U_1047),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_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_275_2,plain,
! [U_1048] :
( ( relation_dom(U_1048) = relation_rng(relation_inverse(U_1048))
& relation_rng(U_1048) = relation_dom(relation_inverse(U_1048)) )
| ~ relation(U_1048) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_1048] :
( relation_dom(U_1048) = relation_rng(relation_inverse(U_1048))
| ~ sP232(U_1048) )
& ! [U_1048] :
( relation_rng(U_1048) = relation_dom(relation_inverse(U_1048))
| ~ sP232(U_1048) )
& ! [U_1048] :
( sP232(U_1048)
| ~ relation(U_1048) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_275_2]) ).
cnf(f_275_4,plain,
( sP232(U_1048)
| ~ relation(U_1048) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_5,plain,
( relation_rng(U_1048) = relation_dom(relation_inverse(U_1048))
| ~ sP232(U_1048) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_6,plain,
( relation_dom(U_1048) = relation_rng(relation_inverse(U_1048))
| ~ sP232(U_1048) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_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_276_2,plain,
! [U_1050,U_1049] :
( ( set_difference(U_1050,U_1049) = empty_set
| ~ subset(U_1050,U_1049) )
& ( subset(U_1050,U_1049)
| set_difference(U_1050,U_1049) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
( ! [U_1054,U_1052] :
( set_difference(U_1054,U_1052) = empty_set
| ~ subset(U_1054,U_1052) )
& ! [U_1053,U_1051] :
( subset(U_1053,U_1051)
| set_difference(U_1053,U_1051) != empty_set ) ),
inference(miniscope,[status(thm)],[f_276_2]) ).
fof(f_276_4,plain,
( ! [U_1052,U_1054] :
( set_difference(U_1054,U_1052) = empty_set
| ~ subset(U_1054,U_1052) )
& ! [U_1051,U_1053] :
( subset(U_1053,U_1051)
| set_difference(U_1053,U_1051) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_276_3]) ).
cnf(f_276_5,plain,
( subset(U_1053,U_1051)
| set_difference(U_1053,U_1051) != empty_set ),
inference(clausify,[status(thm)],[f_276_4]) ).
cnf(f_276_6,plain,
( set_difference(U_1054,U_1052) = empty_set
| ~ subset(U_1054,U_1052) ),
inference(clausify,[status(thm)],[f_276_4]) ).
fof(f_277_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_277_2,plain,
! [U_1056,U_1055] :
( ( subset(singleton(U_1056),U_1055)
| ~ in(U_1056,U_1055) )
& ( in(U_1056,U_1055)
| ~ subset(singleton(U_1056),U_1055) ) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
( ! [U_1060,U_1058] :
( subset(singleton(U_1060),U_1058)
| ~ in(U_1060,U_1058) )
& ! [U_1059,U_1057] :
( in(U_1059,U_1057)
| ~ subset(singleton(U_1059),U_1057) ) ),
inference(miniscope,[status(thm)],[f_277_2]) ).
fof(f_277_4,plain,
( ! [U_1058,U_1060] :
( subset(singleton(U_1060),U_1058)
| ~ in(U_1060,U_1058) )
& ! [U_1057,U_1059] :
( in(U_1059,U_1057)
| ~ subset(singleton(U_1059),U_1057) ) ),
inference(definitional_conversion,[status(esa)],[f_277_3]) ).
cnf(f_277_5,plain,
( in(U_1059,U_1057)
| ~ subset(singleton(U_1059),U_1057) ),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_6,plain,
( subset(singleton(U_1060),U_1058)
| ~ in(U_1060,U_1058) ),
inference(clausify,[status(thm)],[f_277_4]) ).
fof(f_278_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_278_2,plain,
! [U_1063,U_1062,U_1061] :
( ( subset(unordered_pair(U_1063,U_1062),U_1061)
| ~ in(U_1062,U_1061)
| ~ in(U_1063,U_1061) )
& ( ( in(U_1062,U_1061)
& in(U_1063,U_1061) )
| ~ subset(unordered_pair(U_1063,U_1062),U_1061) ) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
( ! [U_1069,U_1067,U_1065] :
( subset(unordered_pair(U_1069,U_1067),U_1065)
| ~ in(U_1067,U_1065)
| ~ in(U_1069,U_1065) )
& ! [U_1068,U_1066,U_1064] :
( ( in(U_1066,U_1064)
& in(U_1068,U_1064) )
| ~ subset(unordered_pair(U_1068,U_1066),U_1064) ) ),
inference(miniscope,[status(thm)],[f_278_2]) ).
fof(f_278_4,plain,
( ! [U_1068,U_1064,U_1066] :
( in(U_1066,U_1064)
| ~ sP233(U_1068,U_1064,U_1066) )
& ! [U_1068,U_1064,U_1066] :
( in(U_1068,U_1064)
| ~ sP233(U_1068,U_1064,U_1066) )
& ! [U_1067,U_1065,U_1069] :
( subset(unordered_pair(U_1069,U_1067),U_1065)
| ~ in(U_1067,U_1065)
| ~ in(U_1069,U_1065) )
& ! [U_1068,U_1064,U_1066] :
( sP233(U_1068,U_1064,U_1066)
| ~ subset(unordered_pair(U_1068,U_1066),U_1064) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_278_3]) ).
cnf(f_278_5,plain,
( sP233(U_1068,U_1064,U_1066)
| ~ subset(unordered_pair(U_1068,U_1066),U_1064) ),
inference(clausify,[status(thm)],[f_278_4]) ).
cnf(f_278_6,plain,
( subset(unordered_pair(U_1069,U_1067),U_1065)
| ~ in(U_1067,U_1065)
| ~ in(U_1069,U_1065) ),
inference(clausify,[status(thm)],[f_278_4]) ).
cnf(f_278_7,plain,
( in(U_1068,U_1064)
| ~ sP233(U_1068,U_1064,U_1066) ),
inference(clausify,[status(thm)],[f_278_4]) ).
cnf(f_278_8,plain,
( in(U_1066,U_1064)
| ~ sP233(U_1068,U_1064,U_1066) ),
inference(clausify,[status(thm)],[f_278_4]) ).
fof(f_279_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_279_2,plain,
! [U_1071,U_1070] :
( relation_field(relation_restriction(U_1070,U_1071)) = U_1071
| ~ subset(U_1071,relation_field(U_1070))
| ~ well_ordering(U_1070)
| ~ relation(U_1070) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1070,U_1071] :
( relation_field(relation_restriction(U_1070,U_1071)) = U_1071
| ~ subset(U_1071,relation_field(U_1070))
| ~ well_ordering(U_1070)
| ~ relation(U_1070) ),
inference(definitional_conversion,[status(esa)],[f_279_2]) ).
cnf(f_279_4,plain,
( relation_field(relation_restriction(U_1070,U_1071)) = U_1071
| ~ subset(U_1071,relation_field(U_1070))
| ~ well_ordering(U_1070)
| ~ relation(U_1070) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_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_280_2,plain,
! [U_1073,U_1072] : set_union2(U_1073,set_difference(U_1072,U_1073)) = set_union2(U_1073,U_1072),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_1072,U_1073] : set_union2(U_1073,set_difference(U_1072,U_1073)) = set_union2(U_1073,U_1072),
inference(definitional_conversion,[status(esa)],[f_280_2]) ).
cnf(f_280_4,plain,
set_union2(U_1073,set_difference(U_1072,U_1073)) = set_union2(U_1073,U_1072),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_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_281_2,plain,
! [U_1075,U_1074] :
( ( subset(U_1075,singleton(U_1074))
| ( U_1075 != singleton(U_1074)
& U_1075 != empty_set ) )
& ( U_1075 = singleton(U_1074)
| U_1075 = empty_set
| ~ subset(U_1075,singleton(U_1074)) ) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
( ! [U_1079,U_1077] :
( subset(U_1079,singleton(U_1077))
| ( U_1079 != singleton(U_1077)
& U_1079 != empty_set ) )
& ! [U_1078,U_1076] :
( U_1078 = singleton(U_1076)
| U_1078 = empty_set
| ~ subset(U_1078,singleton(U_1076)) ) ),
inference(miniscope,[status(thm)],[f_281_2]) ).
fof(f_281_4,plain,
( ! [U_1077,U_1079] :
( U_1079 != singleton(U_1077)
| ~ sP234(U_1077,U_1079) )
& ! [U_1077,U_1079] :
( U_1079 != empty_set
| ~ sP234(U_1077,U_1079) )
& ! [U_1077,U_1079] :
( subset(U_1079,singleton(U_1077))
| sP234(U_1077,U_1079) )
& ! [U_1078,U_1076] :
( U_1078 = singleton(U_1076)
| U_1078 = empty_set
| ~ subset(U_1078,singleton(U_1076)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_281_3]) ).
cnf(f_281_5,plain,
( U_1078 = singleton(U_1076)
| U_1078 = empty_set
| ~ subset(U_1078,singleton(U_1076)) ),
inference(clausify,[status(thm)],[f_281_4]) ).
cnf(f_281_6,plain,
( subset(U_1079,singleton(U_1077))
| sP234(U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_281_4]) ).
cnf(f_281_7,plain,
( U_1079 != empty_set
| ~ sP234(U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_281_4]) ).
cnf(f_281_8,plain,
( U_1079 != singleton(U_1077)
| ~ sP234(U_1077,U_1079) ),
inference(clausify,[status(thm)],[f_281_4]) ).
fof(f_282_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_282_2,plain,
! [U_1080] : set_difference(U_1080,empty_set) = U_1080,
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_1080] : set_difference(U_1080,empty_set) = U_1080,
inference(definitional_conversion,[status(esa)],[f_282_2]) ).
cnf(f_282_4,plain,
set_difference(U_1080,empty_set) = U_1080,
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_283_2,plain,
! [U_1083,U_1082,U_1081] :
( ~ in(U_1081,U_1083)
| ~ in(U_1082,U_1081)
| ~ in(U_1083,U_1082) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1083,U_1082] :
( ! [U_1081] :
( ~ in(U_1081,U_1083)
| ~ in(U_1082,U_1081) )
| ~ in(U_1083,U_1082) ),
inference(miniscope,[status(thm)],[f_283_2]) ).
fof(f_283_4,plain,
! [U_1082,U_1081,U_1083] :
( ~ in(U_1081,U_1083)
| ~ in(U_1082,U_1081)
| ~ in(U_1083,U_1082) ),
inference(definitional_conversion,[status(esa)],[f_283_3]) ).
cnf(f_283_5,plain,
( ~ in(U_1081,U_1083)
| ~ in(U_1082,U_1081)
| ~ in(U_1083,U_1082) ),
inference(clausify,[status(thm)],[f_283_4]) ).
fof(f_284_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_284_2,plain,
! [U_1085,U_1084] :
( ( element(U_1085,powerset(U_1084))
| ~ subset(U_1085,U_1084) )
& ( subset(U_1085,U_1084)
| ~ element(U_1085,powerset(U_1084)) ) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
( ! [U_1089,U_1087] :
( element(U_1089,powerset(U_1087))
| ~ subset(U_1089,U_1087) )
& ! [U_1088,U_1086] :
( subset(U_1088,U_1086)
| ~ element(U_1088,powerset(U_1086)) ) ),
inference(miniscope,[status(thm)],[f_284_2]) ).
fof(f_284_4,plain,
( ! [U_1089,U_1087] :
( element(U_1089,powerset(U_1087))
| ~ subset(U_1089,U_1087) )
& ! [U_1088,U_1086] :
( subset(U_1088,U_1086)
| ~ element(U_1088,powerset(U_1086)) ) ),
inference(definitional_conversion,[status(esa)],[f_284_3]) ).
cnf(f_284_5,plain,
( subset(U_1088,U_1086)
| ~ element(U_1088,powerset(U_1086)) ),
inference(clausify,[status(thm)],[f_284_4]) ).
cnf(f_284_6,plain,
( element(U_1089,powerset(U_1087))
| ~ subset(U_1089,U_1087) ),
inference(clausify,[status(thm)],[f_284_4]) ).
fof(f_285_1,plain,
! [A] : transitive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t3_wellord2]) ).
fof(f_285_2,plain,
! [U_1090] : transitive(inclusion_relation(U_1090)),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1090] : transitive(inclusion_relation(U_1090)),
inference(definitional_conversion,[status(esa)],[f_285_2]) ).
cnf(f_285_4,plain,
transitive(inclusion_relation(U_1090)),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_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_286_2,plain,
! [U_1094,U_1093] :
( ( ~ disjoint(U_1094,U_1093)
| ! [U_1092] :
( ~ in(U_1092,U_1093)
| ~ in(U_1092,U_1094) ) )
& ( ? [U_1091] :
( in(U_1091,U_1093)
& in(U_1091,U_1094) )
| disjoint(U_1094,U_1093) ) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
( ! [U_1098,U_1096] :
( ~ disjoint(U_1098,U_1096)
| ! [U_1092] :
( ~ in(U_1092,U_1096)
| ~ in(U_1092,U_1098) ) )
& ! [U_1097,U_1095] :
( ? [U_1091] :
( in(U_1091,U_1095)
& in(U_1091,U_1097) )
| disjoint(U_1097,U_1095) ) ),
inference(miniscope,[status(thm)],[f_286_2]) ).
fof(f_286_4,plain,
( ! [U_1098,U_1096] :
( ~ disjoint(U_1098,U_1096)
| ! [U_1092] :
( ~ in(U_1092,U_1096)
| ~ in(U_1092,U_1098) ) )
& ! [U_1097,U_1095] :
( ( in(sK167(U_1097,U_1095),U_1095)
& in(sK167(U_1097,U_1095),U_1097) )
| disjoint(U_1097,U_1095) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_1091,sK167(U_1097,U_1095))],[f_286_3]) ).
fof(f_286_5,plain,
( ! [U_1095,U_1097] :
( in(sK167(U_1097,U_1095),U_1095)
| ~ sP235(U_1095,U_1097) )
& ! [U_1095,U_1097] :
( in(sK167(U_1097,U_1095),U_1097)
| ~ sP235(U_1095,U_1097) )
& ! [U_1092,U_1098,U_1096] :
( ~ disjoint(U_1098,U_1096)
| ~ in(U_1092,U_1096)
| ~ in(U_1092,U_1098) )
& ! [U_1095,U_1097] :
( sP235(U_1095,U_1097)
| disjoint(U_1097,U_1095) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_286_4]) ).
cnf(f_286_6,plain,
( sP235(U_1095,U_1097)
| disjoint(U_1097,U_1095) ),
inference(clausify,[status(thm)],[f_286_5]) ).
cnf(f_286_7,plain,
( ~ disjoint(U_1098,U_1096)
| ~ in(U_1092,U_1096)
| ~ in(U_1092,U_1098) ),
inference(clausify,[status(thm)],[f_286_5]) ).
cnf(f_286_8,plain,
( in(sK167(U_1097,U_1095),U_1097)
| ~ sP235(U_1095,U_1097) ),
inference(clausify,[status(thm)],[f_286_5]) ).
cnf(f_286_9,plain,
( in(sK167(U_1097,U_1095),U_1095)
| ~ sP235(U_1095,U_1097) ),
inference(clausify,[status(thm)],[f_286_5]) ).
fof(f_287_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_287_2,plain,
! [U_1099] :
( U_1099 = empty_set
| ~ subset(U_1099,empty_set) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_1099] :
( U_1099 = empty_set
| ~ subset(U_1099,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
( U_1099 = empty_set
| ~ subset(U_1099,empty_set) ),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_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_288_2,plain,
! [U_1101,U_1100] : set_difference(set_union2(U_1101,U_1100),U_1100) = set_difference(U_1101,U_1100),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1100,U_1101] : set_difference(set_union2(U_1101,U_1100),U_1100) = set_difference(U_1101,U_1100),
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
set_difference(set_union2(U_1101,U_1100),U_1100) = set_difference(U_1101,U_1100),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_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_289_2,plain,
! [U_1104] :
( ( ( being_limit_ordinal(U_1104)
| ? [U_1103] :
( ~ in(succ(U_1103),U_1104)
& in(U_1103,U_1104)
& ordinal(U_1103) ) )
& ( ! [U_1102] :
( in(succ(U_1102),U_1104)
| ~ in(U_1102,U_1104)
| ~ ordinal(U_1102) )
| ~ being_limit_ordinal(U_1104) ) )
| ~ ordinal(U_1104) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_1104] :
( ( ( being_limit_ordinal(U_1104)
| ( ~ in(succ(sK168(U_1104)),U_1104)
& in(sK168(U_1104),U_1104)
& ordinal(sK168(U_1104)) ) )
& ( ! [U_1102] :
( in(succ(U_1102),U_1104)
| ~ in(U_1102,U_1104)
| ~ ordinal(U_1102) )
| ~ being_limit_ordinal(U_1104) ) )
| ~ ordinal(U_1104) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_1103,sK168(U_1104))],[f_289_2]) ).
fof(f_289_4,plain,
( ! [U_1104] :
( ~ in(succ(sK168(U_1104)),U_1104)
| ~ sP236(U_1104) )
& ! [U_1104] :
( in(sK168(U_1104),U_1104)
| ~ sP236(U_1104) )
& ! [U_1104] :
( ordinal(sK168(U_1104))
| ~ sP236(U_1104) )
& ! [U_1104,U_1102] :
( being_limit_ordinal(U_1104)
| sP236(U_1104)
| ~ sP237(U_1104,U_1102) )
& ! [U_1104,U_1102] :
( in(succ(U_1102),U_1104)
| ~ in(U_1102,U_1104)
| ~ ordinal(U_1102)
| ~ being_limit_ordinal(U_1104)
| ~ sP237(U_1104,U_1102) )
& ! [U_1104,U_1102] :
( sP237(U_1104,U_1102)
| ~ ordinal(U_1104) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236,sP237])],[f_289_3]) ).
cnf(f_289_5,plain,
( sP237(U_1104,U_1102)
| ~ ordinal(U_1104) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_6,plain,
( in(succ(U_1102),U_1104)
| ~ in(U_1102,U_1104)
| ~ ordinal(U_1102)
| ~ being_limit_ordinal(U_1104)
| ~ sP237(U_1104,U_1102) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_7,plain,
( being_limit_ordinal(U_1104)
| sP236(U_1104)
| ~ sP237(U_1104,U_1102) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_8,plain,
( ordinal(sK168(U_1104))
| ~ sP236(U_1104) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_9,plain,
( in(sK168(U_1104),U_1104)
| ~ sP236(U_1104) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_10,plain,
( ~ in(succ(sK168(U_1104)),U_1104)
| ~ sP236(U_1104) ),
inference(clausify,[status(thm)],[f_289_4]) ).
fof(f_290_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_290_2,plain,
! [U_1107] :
( ( ( ~ being_limit_ordinal(U_1107)
| ! [U_1106] :
( U_1107 != succ(U_1106)
| ~ ordinal(U_1106) ) )
& ( ? [U_1105] :
( U_1107 = succ(U_1105)
& ordinal(U_1105) )
| being_limit_ordinal(U_1107) ) )
| ~ ordinal(U_1107) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_1107] :
( ( ( ~ being_limit_ordinal(U_1107)
| ! [U_1106] :
( U_1107 != succ(U_1106)
| ~ ordinal(U_1106) ) )
& ( ( U_1107 = succ(sK169(U_1107))
& ordinal(sK169(U_1107)) )
| being_limit_ordinal(U_1107) ) )
| ~ ordinal(U_1107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_1105,sK169(U_1107))],[f_290_2]) ).
fof(f_290_4,plain,
( ! [U_1107] :
( U_1107 = succ(sK169(U_1107))
| ~ sP238(U_1107) )
& ! [U_1107] :
( ordinal(sK169(U_1107))
| ~ sP238(U_1107) )
& ! [U_1106,U_1107] :
( ~ being_limit_ordinal(U_1107)
| U_1107 != succ(U_1106)
| ~ ordinal(U_1106)
| ~ sP239(U_1106,U_1107) )
& ! [U_1106,U_1107] :
( sP238(U_1107)
| being_limit_ordinal(U_1107)
| ~ sP239(U_1106,U_1107) )
& ! [U_1106,U_1107] :
( sP239(U_1106,U_1107)
| ~ ordinal(U_1107) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238,sP239])],[f_290_3]) ).
cnf(f_290_5,plain,
( sP239(U_1106,U_1107)
| ~ ordinal(U_1107) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_6,plain,
( sP238(U_1107)
| being_limit_ordinal(U_1107)
| ~ sP239(U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_7,plain,
( ~ being_limit_ordinal(U_1107)
| U_1107 != succ(U_1106)
| ~ ordinal(U_1106)
| ~ sP239(U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_8,plain,
( ordinal(sK169(U_1107))
| ~ sP238(U_1107) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_9,plain,
( U_1107 = succ(sK169(U_1107))
| ~ sP238(U_1107) ),
inference(clausify,[status(thm)],[f_290_4]) ).
fof(f_291_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_291_2,plain,
! [U_1110,U_1109] :
( ! [U_1108] :
( ( ( disjoint(U_1109,U_1108)
| ~ subset(U_1109,subset_complement(U_1110,U_1108)) )
& ( subset(U_1109,subset_complement(U_1110,U_1108))
| ~ disjoint(U_1109,U_1108) ) )
| ~ element(U_1108,powerset(U_1110)) )
| ~ element(U_1109,powerset(U_1110)) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
( ! [U_1109,U_1108,U_1110] :
( disjoint(U_1109,U_1108)
| ~ subset(U_1109,subset_complement(U_1110,U_1108))
| ~ sP240(U_1109,U_1108,U_1110) )
& ! [U_1109,U_1108,U_1110] :
( subset(U_1109,subset_complement(U_1110,U_1108))
| ~ disjoint(U_1109,U_1108)
| ~ sP240(U_1109,U_1108,U_1110) )
& ! [U_1109,U_1108,U_1110] :
( sP240(U_1109,U_1108,U_1110)
| ~ element(U_1108,powerset(U_1110))
| ~ element(U_1109,powerset(U_1110)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_291_2]) ).
cnf(f_291_4,plain,
( sP240(U_1109,U_1108,U_1110)
| ~ element(U_1108,powerset(U_1110))
| ~ element(U_1109,powerset(U_1110)) ),
inference(clausify,[status(thm)],[f_291_3]) ).
cnf(f_291_5,plain,
( subset(U_1109,subset_complement(U_1110,U_1108))
| ~ disjoint(U_1109,U_1108)
| ~ sP240(U_1109,U_1108,U_1110) ),
inference(clausify,[status(thm)],[f_291_3]) ).
cnf(f_291_6,plain,
( disjoint(U_1109,U_1108)
| ~ subset(U_1109,subset_complement(U_1110,U_1108))
| ~ sP240(U_1109,U_1108,U_1110) ),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_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_292_2,plain,
! [U_1112] :
( ! [U_1111] :
( subset(relation_dom(relation_composition(U_1112,U_1111)),relation_dom(U_1112))
| ~ relation(U_1111) )
| ~ relation(U_1112) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1111,U_1112] :
( subset(relation_dom(relation_composition(U_1112,U_1111)),relation_dom(U_1112))
| ~ relation(U_1111)
| ~ relation(U_1112) ),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
( subset(relation_dom(relation_composition(U_1112,U_1111)),relation_dom(U_1112))
| ~ relation(U_1111)
| ~ relation(U_1112) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_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_293_2,plain,
! [U_1114] :
( ! [U_1113] :
( subset(relation_rng(relation_composition(U_1114,U_1113)),relation_rng(U_1113))
| ~ relation(U_1113) )
| ~ relation(U_1114) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_1114,U_1113] :
( subset(relation_rng(relation_composition(U_1114,U_1113)),relation_rng(U_1113))
| ~ relation(U_1113)
| ~ relation(U_1114) ),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
( subset(relation_rng(relation_composition(U_1114,U_1113)),relation_rng(U_1113))
| ~ relation(U_1113)
| ~ relation(U_1114) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_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_294_2,plain,
! [U_1116,U_1115] :
( U_1115 = set_union2(U_1116,set_difference(U_1115,U_1116))
| ~ subset(U_1116,U_1115) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_1116,U_1115] :
( U_1115 = set_union2(U_1116,set_difference(U_1115,U_1116))
| ~ subset(U_1116,U_1115) ),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
( U_1115 = set_union2(U_1116,set_difference(U_1115,U_1116))
| ~ subset(U_1116,U_1115) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_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_295_2,plain,
! [U_1118] :
( ! [U_1117] :
( relation_dom(relation_composition(U_1118,U_1117)) = relation_dom(U_1118)
| ~ subset(relation_rng(U_1118),relation_dom(U_1117))
| ~ relation(U_1117) )
| ~ relation(U_1118) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1117,U_1118] :
( relation_dom(relation_composition(U_1118,U_1117)) = relation_dom(U_1118)
| ~ subset(relation_rng(U_1118),relation_dom(U_1117))
| ~ relation(U_1117)
| ~ relation(U_1118) ),
inference(definitional_conversion,[status(esa)],[f_295_2]) ).
cnf(f_295_4,plain,
( relation_dom(relation_composition(U_1118,U_1117)) = relation_dom(U_1118)
| ~ subset(relation_rng(U_1118),relation_dom(U_1117))
| ~ relation(U_1117)
| ~ relation(U_1118) ),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_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_296_2,plain,
! [U_1120,U_1119] :
( complements_of_subsets(U_1120,U_1119) != empty_set
| U_1119 = empty_set
| ~ element(U_1119,powerset(powerset(U_1120))) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_1119,U_1120] :
( complements_of_subsets(U_1120,U_1119) != empty_set
| U_1119 = empty_set
| ~ element(U_1119,powerset(powerset(U_1120))) ),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
( complements_of_subsets(U_1120,U_1119) != empty_set
| U_1119 = empty_set
| ~ element(U_1119,powerset(powerset(U_1120))) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_297_2,plain,
! [U_1122,U_1121] :
( set_union2(singleton(U_1122),U_1121) = U_1121
| ~ in(U_1122,U_1121) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_1122,U_1121] :
( set_union2(singleton(U_1122),U_1121) = U_1121
| ~ in(U_1122,U_1121) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( set_union2(singleton(U_1122),U_1121) = U_1121
| ~ in(U_1122,U_1121) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_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_298_2,plain,
! [U_1124] :
( ! [U_1123] :
( relation_rng(relation_composition(U_1123,U_1124)) = relation_rng(U_1124)
| ~ subset(relation_dom(U_1124),relation_rng(U_1123))
| ~ relation(U_1123) )
| ~ relation(U_1124) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_1123,U_1124] :
( relation_rng(relation_composition(U_1123,U_1124)) = relation_rng(U_1124)
| ~ subset(relation_dom(U_1124),relation_rng(U_1123))
| ~ relation(U_1123)
| ~ relation(U_1124) ),
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
( relation_rng(relation_composition(U_1123,U_1124)) = relation_rng(U_1124)
| ~ subset(relation_dom(U_1124),relation_rng(U_1123))
| ~ relation(U_1123)
| ~ relation(U_1124) ),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_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_299_2,plain,
! [U_1126,U_1125] :
( subset_difference(U_1126,cast_to_subset(U_1126),union_of_subsets(U_1126,U_1125)) = meet_of_subsets(U_1126,complements_of_subsets(U_1126,U_1125))
| U_1125 = empty_set
| ~ element(U_1125,powerset(powerset(U_1126))) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_1125,U_1126] :
( subset_difference(U_1126,cast_to_subset(U_1126),union_of_subsets(U_1126,U_1125)) = meet_of_subsets(U_1126,complements_of_subsets(U_1126,U_1125))
| U_1125 = empty_set
| ~ element(U_1125,powerset(powerset(U_1126))) ),
inference(definitional_conversion,[status(esa)],[f_299_2]) ).
cnf(f_299_4,plain,
( subset_difference(U_1126,cast_to_subset(U_1126),union_of_subsets(U_1126,U_1125)) = meet_of_subsets(U_1126,complements_of_subsets(U_1126,U_1125))
| U_1125 = empty_set
| ~ element(U_1125,powerset(powerset(U_1126))) ),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_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_300_2,plain,
! [U_1128,U_1127] :
( union_of_subsets(U_1128,complements_of_subsets(U_1128,U_1127)) = subset_difference(U_1128,cast_to_subset(U_1128),meet_of_subsets(U_1128,U_1127))
| U_1127 = empty_set
| ~ element(U_1127,powerset(powerset(U_1128))) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1127,U_1128] :
( union_of_subsets(U_1128,complements_of_subsets(U_1128,U_1127)) = subset_difference(U_1128,cast_to_subset(U_1128),meet_of_subsets(U_1128,U_1127))
| U_1127 = empty_set
| ~ element(U_1127,powerset(powerset(U_1128))) ),
inference(definitional_conversion,[status(esa)],[f_300_2]) ).
cnf(f_300_4,plain,
( union_of_subsets(U_1128,complements_of_subsets(U_1128,U_1127)) = subset_difference(U_1128,cast_to_subset(U_1128),meet_of_subsets(U_1128,U_1127))
| U_1127 = empty_set
| ~ element(U_1127,powerset(powerset(U_1128))) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_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_301_2,plain,
! [U_1130,U_1129] : set_difference(U_1130,set_difference(U_1130,U_1129)) = set_intersection2(U_1130,U_1129),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_1129,U_1130] : set_difference(U_1130,set_difference(U_1130,U_1129)) = set_intersection2(U_1130,U_1129),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
set_difference(U_1130,set_difference(U_1130,U_1129)) = set_intersection2(U_1130,U_1129),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_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_302_2,plain,
! [U_1133] :
( ! [U_1132] :
( ! [U_1131] :
( relation_isomorphism(U_1132,U_1133,function_inverse(U_1131))
| ~ relation_isomorphism(U_1133,U_1132,U_1131)
| ~ function(U_1131)
| ~ relation(U_1131) )
| ~ relation(U_1132) )
| ~ relation(U_1133) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_1131,U_1132,U_1133] :
( relation_isomorphism(U_1132,U_1133,function_inverse(U_1131))
| ~ relation_isomorphism(U_1133,U_1132,U_1131)
| ~ function(U_1131)
| ~ relation(U_1131)
| ~ relation(U_1132)
| ~ relation(U_1133) ),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
( relation_isomorphism(U_1132,U_1133,function_inverse(U_1131))
| ~ relation_isomorphism(U_1133,U_1132,U_1131)
| ~ function(U_1131)
| ~ relation(U_1131)
| ~ relation(U_1132)
| ~ relation(U_1133) ),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_303_2,plain,
! [U_1134] : set_difference(empty_set,U_1134) = empty_set,
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_1134] : set_difference(empty_set,U_1134) = empty_set,
inference(definitional_conversion,[status(esa)],[f_303_2]) ).
cnf(f_303_4,plain,
set_difference(empty_set,U_1134) = empty_set,
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_304_2,plain,
! [U_1137,U_1136,U_1135] :
( element(U_1137,U_1135)
| ~ element(U_1136,powerset(U_1135))
| ~ in(U_1137,U_1136) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1137,U_1136,U_1135] :
( element(U_1137,U_1135)
| ~ element(U_1136,powerset(U_1135))
| ~ in(U_1137,U_1136) ),
inference(definitional_conversion,[status(esa)],[f_304_2]) ).
cnf(f_304_4,plain,
( element(U_1137,U_1135)
| ~ element(U_1136,powerset(U_1135))
| ~ in(U_1137,U_1136) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_1,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t4_wellord2]) ).
fof(f_305_2,plain,
! [U_1138] :
( connected(inclusion_relation(U_1138))
| ~ ordinal(U_1138) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_1138] :
( connected(inclusion_relation(U_1138))
| ~ ordinal(U_1138) ),
inference(definitional_conversion,[status(esa)],[f_305_2]) ).
cnf(f_305_4,plain,
( connected(inclusion_relation(U_1138))
| ~ ordinal(U_1138) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_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_306_2,plain,
! [U_1142,U_1141] :
( ( ~ disjoint(U_1142,U_1141)
| ! [U_1140] : ~ in(U_1140,set_intersection2(U_1142,U_1141)) )
& ( ? [U_1139] : in(U_1139,set_intersection2(U_1142,U_1141))
| disjoint(U_1142,U_1141) ) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
( ! [U_1146,U_1144] :
( ~ disjoint(U_1146,U_1144)
| ! [U_1140] : ~ in(U_1140,set_intersection2(U_1146,U_1144)) )
& ! [U_1145,U_1143] :
( ? [U_1139] : in(U_1139,set_intersection2(U_1145,U_1143))
| disjoint(U_1145,U_1143) ) ),
inference(miniscope,[status(thm)],[f_306_2]) ).
fof(f_306_4,plain,
( ! [U_1146,U_1144] :
( ~ disjoint(U_1146,U_1144)
| ! [U_1140] : ~ in(U_1140,set_intersection2(U_1146,U_1144)) )
& ! [U_1145,U_1143] :
( in(sK170(U_1145,U_1143),set_intersection2(U_1145,U_1143))
| disjoint(U_1145,U_1143) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_1139,sK170(U_1145,U_1143))],[f_306_3]) ).
fof(f_306_5,plain,
( ! [U_1140,U_1146,U_1144] :
( ~ disjoint(U_1146,U_1144)
| ~ in(U_1140,set_intersection2(U_1146,U_1144)) )
& ! [U_1145,U_1143] :
( in(sK170(U_1145,U_1143),set_intersection2(U_1145,U_1143))
| disjoint(U_1145,U_1143) ) ),
inference(definitional_conversion,[status(esa)],[f_306_4]) ).
cnf(f_306_6,plain,
( in(sK170(U_1145,U_1143),set_intersection2(U_1145,U_1143))
| disjoint(U_1145,U_1143) ),
inference(clausify,[status(thm)],[f_306_5]) ).
cnf(f_306_7,plain,
( ~ disjoint(U_1146,U_1144)
| ~ in(U_1140,set_intersection2(U_1146,U_1144)) ),
inference(clausify,[status(thm)],[f_306_5]) ).
fof(f_307_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_307_2,plain,
! [U_1149] :
( ! [U_1148] :
( ! [U_1147] :
( in(U_1147,subset_complement(U_1149,U_1148))
| in(U_1147,U_1148)
| ~ element(U_1147,U_1149) )
| ~ element(U_1148,powerset(U_1149)) )
| U_1149 = empty_set ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_1148,U_1149,U_1147] :
( in(U_1147,subset_complement(U_1149,U_1148))
| in(U_1147,U_1148)
| ~ element(U_1147,U_1149)
| ~ element(U_1148,powerset(U_1149))
| U_1149 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( in(U_1147,subset_complement(U_1149,U_1148))
| in(U_1147,U_1148)
| ~ element(U_1147,U_1149)
| ~ element(U_1148,powerset(U_1149))
| U_1149 = empty_set ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_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_308_2,plain,
! [U_1152] :
( ! [U_1151] :
( ! [U_1150] :
( ( ( well_founded_relation(U_1151)
| ~ well_founded_relation(U_1152) )
& ( antisymmetric(U_1151)
| ~ antisymmetric(U_1152) )
& ( connected(U_1151)
| ~ connected(U_1152) )
& ( transitive(U_1151)
| ~ transitive(U_1152) )
& ( reflexive(U_1151)
| ~ reflexive(U_1152) ) )
| ~ relation_isomorphism(U_1152,U_1151,U_1150)
| ~ function(U_1150)
| ~ relation(U_1150) )
| ~ relation(U_1151) )
| ~ relation(U_1152) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
( ! [U_1152,U_1151] :
( well_founded_relation(U_1151)
| ~ well_founded_relation(U_1152)
| ~ sP241(U_1152,U_1151) )
& ! [U_1152,U_1151] :
( antisymmetric(U_1151)
| ~ antisymmetric(U_1152)
| ~ sP241(U_1152,U_1151) )
& ! [U_1152,U_1151] :
( connected(U_1151)
| ~ connected(U_1152)
| ~ sP241(U_1152,U_1151) )
& ! [U_1152,U_1151] :
( transitive(U_1151)
| ~ transitive(U_1152)
| ~ sP241(U_1152,U_1151) )
& ! [U_1152,U_1151] :
( reflexive(U_1151)
| ~ reflexive(U_1152)
| ~ sP241(U_1152,U_1151) )
& ! [U_1150,U_1152,U_1151] :
( sP241(U_1152,U_1151)
| ~ relation_isomorphism(U_1152,U_1151,U_1150)
| ~ function(U_1150)
| ~ relation(U_1150)
| ~ relation(U_1151)
| ~ relation(U_1152) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_308_2]) ).
cnf(f_308_4,plain,
( sP241(U_1152,U_1151)
| ~ relation_isomorphism(U_1152,U_1151,U_1150)
| ~ function(U_1150)
| ~ relation(U_1150)
| ~ relation(U_1151)
| ~ relation(U_1152) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_5,plain,
( reflexive(U_1151)
| ~ reflexive(U_1152)
| ~ sP241(U_1152,U_1151) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_6,plain,
( transitive(U_1151)
| ~ transitive(U_1152)
| ~ sP241(U_1152,U_1151) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_7,plain,
( connected(U_1151)
| ~ connected(U_1152)
| ~ sP241(U_1152,U_1151) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_8,plain,
( antisymmetric(U_1151)
| ~ antisymmetric(U_1152)
| ~ sP241(U_1152,U_1151) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_9,plain,
( well_founded_relation(U_1151)
| ~ well_founded_relation(U_1152)
| ~ sP241(U_1152,U_1151) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_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_309_2,plain,
! [U_1158] :
( ! [U_1157] :
( ( ( U_1157 = function_inverse(U_1158)
| ? [U_1156,U_1155] :
( ( ( U_1155 != apply(U_1157,U_1156)
| ~ in(U_1156,relation_rng(U_1158)) )
& U_1156 = apply(U_1158,U_1155)
& in(U_1155,relation_dom(U_1158)) )
| ( ( U_1156 != apply(U_1158,U_1155)
| ~ in(U_1155,relation_dom(U_1158)) )
& U_1155 = apply(U_1157,U_1156)
& in(U_1156,relation_rng(U_1158)) ) )
| relation_dom(U_1157) != relation_rng(U_1158) )
& ( ( ! [U_1154,U_1153] :
( ( ( U_1153 = apply(U_1157,U_1154)
& in(U_1154,relation_rng(U_1158)) )
| U_1154 != apply(U_1158,U_1153)
| ~ in(U_1153,relation_dom(U_1158)) )
& ( ( U_1154 = apply(U_1158,U_1153)
& in(U_1153,relation_dom(U_1158)) )
| U_1153 != apply(U_1157,U_1154)
| ~ in(U_1154,relation_rng(U_1158)) ) )
& relation_dom(U_1157) = relation_rng(U_1158) )
| U_1157 != function_inverse(U_1158) ) )
| ~ function(U_1157)
| ~ relation(U_1157) )
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_1158] :
( ! [U_1157] :
( ( ( U_1157 = function_inverse(U_1158)
| ? [U_1166,U_1164] :
( ( U_1164 != apply(U_1157,U_1166)
| ~ in(U_1166,relation_rng(U_1158)) )
& U_1166 = apply(U_1158,U_1164)
& in(U_1164,relation_dom(U_1158)) )
| ? [U_1165,U_1163] :
( ( U_1165 != apply(U_1158,U_1163)
| ~ in(U_1163,relation_dom(U_1158)) )
& U_1163 = apply(U_1157,U_1165)
& in(U_1165,relation_rng(U_1158)) )
| relation_dom(U_1157) != relation_rng(U_1158) )
& ( ( ! [U_1162,U_1160] :
( ( U_1160 = apply(U_1157,U_1162)
& in(U_1162,relation_rng(U_1158)) )
| U_1162 != apply(U_1158,U_1160)
| ~ in(U_1160,relation_dom(U_1158)) )
& ! [U_1161,U_1159] :
( ( U_1161 = apply(U_1158,U_1159)
& in(U_1159,relation_dom(U_1158)) )
| U_1159 != apply(U_1157,U_1161)
| ~ in(U_1161,relation_rng(U_1158)) )
& relation_dom(U_1157) = relation_rng(U_1158) )
| U_1157 != function_inverse(U_1158) ) )
| ~ function(U_1157)
| ~ relation(U_1157) )
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ),
inference(miniscope,[status(thm)],[f_309_2]) ).
fof(f_309_4,plain,
! [U_1158] :
( ! [U_1157] :
( ( ( U_1157 = function_inverse(U_1158)
| ? [U_1166,U_1164] :
( ( U_1164 != apply(U_1157,U_1166)
| ~ in(U_1166,relation_rng(U_1158)) )
& U_1166 = apply(U_1158,U_1164)
& in(U_1164,relation_dom(U_1158)) )
| ? [U_1163] :
( ( sK171(U_1158,U_1157) != apply(U_1158,U_1163)
| ~ in(U_1163,relation_dom(U_1158)) )
& U_1163 = apply(U_1157,sK171(U_1158,U_1157))
& in(sK171(U_1158,U_1157),relation_rng(U_1158)) )
| relation_dom(U_1157) != relation_rng(U_1158) )
& ( ( ! [U_1162,U_1160] :
( ( U_1160 = apply(U_1157,U_1162)
& in(U_1162,relation_rng(U_1158)) )
| U_1162 != apply(U_1158,U_1160)
| ~ in(U_1160,relation_dom(U_1158)) )
& ! [U_1161,U_1159] :
( ( U_1161 = apply(U_1158,U_1159)
& in(U_1159,relation_dom(U_1158)) )
| U_1159 != apply(U_1157,U_1161)
| ~ in(U_1161,relation_rng(U_1158)) )
& relation_dom(U_1157) = relation_rng(U_1158) )
| U_1157 != function_inverse(U_1158) ) )
| ~ function(U_1157)
| ~ relation(U_1157) )
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_1165,sK171(U_1158,U_1157))],[f_309_3]) ).
fof(f_309_5,plain,
! [U_1158] :
( ! [U_1157] :
( ( ( U_1157 = function_inverse(U_1158)
| ? [U_1166,U_1164] :
( ( U_1164 != apply(U_1157,U_1166)
| ~ in(U_1166,relation_rng(U_1158)) )
& U_1166 = apply(U_1158,U_1164)
& in(U_1164,relation_dom(U_1158)) )
| ( ( sK171(U_1158,U_1157) != apply(U_1158,sK172(U_1158,U_1157))
| ~ in(sK172(U_1158,U_1157),relation_dom(U_1158)) )
& sK172(U_1158,U_1157) = apply(U_1157,sK171(U_1158,U_1157))
& in(sK171(U_1158,U_1157),relation_rng(U_1158)) )
| relation_dom(U_1157) != relation_rng(U_1158) )
& ( ( ! [U_1162,U_1160] :
( ( U_1160 = apply(U_1157,U_1162)
& in(U_1162,relation_rng(U_1158)) )
| U_1162 != apply(U_1158,U_1160)
| ~ in(U_1160,relation_dom(U_1158)) )
& ! [U_1161,U_1159] :
( ( U_1161 = apply(U_1158,U_1159)
& in(U_1159,relation_dom(U_1158)) )
| U_1159 != apply(U_1157,U_1161)
| ~ in(U_1161,relation_rng(U_1158)) )
& relation_dom(U_1157) = relation_rng(U_1158) )
| U_1157 != function_inverse(U_1158) ) )
| ~ function(U_1157)
| ~ relation(U_1157) )
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_1163,sK172(U_1158,U_1157))],[f_309_4]) ).
fof(f_309_6,plain,
! [U_1158] :
( ! [U_1157] :
( ( ( U_1157 = function_inverse(U_1158)
| ? [U_1164] :
( ( U_1164 != apply(U_1157,sK173(U_1158,U_1157))
| ~ in(sK173(U_1158,U_1157),relation_rng(U_1158)) )
& sK173(U_1158,U_1157) = apply(U_1158,U_1164)
& in(U_1164,relation_dom(U_1158)) )
| ( ( sK171(U_1158,U_1157) != apply(U_1158,sK172(U_1158,U_1157))
| ~ in(sK172(U_1158,U_1157),relation_dom(U_1158)) )
& sK172(U_1158,U_1157) = apply(U_1157,sK171(U_1158,U_1157))
& in(sK171(U_1158,U_1157),relation_rng(U_1158)) )
| relation_dom(U_1157) != relation_rng(U_1158) )
& ( ( ! [U_1162,U_1160] :
( ( U_1160 = apply(U_1157,U_1162)
& in(U_1162,relation_rng(U_1158)) )
| U_1162 != apply(U_1158,U_1160)
| ~ in(U_1160,relation_dom(U_1158)) )
& ! [U_1161,U_1159] :
( ( U_1161 = apply(U_1158,U_1159)
& in(U_1159,relation_dom(U_1158)) )
| U_1159 != apply(U_1157,U_1161)
| ~ in(U_1161,relation_rng(U_1158)) )
& relation_dom(U_1157) = relation_rng(U_1158) )
| U_1157 != function_inverse(U_1158) ) )
| ~ function(U_1157)
| ~ relation(U_1157) )
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_1166,sK173(U_1158,U_1157))],[f_309_5]) ).
fof(f_309_7,plain,
! [U_1158] :
( ! [U_1157] :
( ( ( U_1157 = function_inverse(U_1158)
| ( ( sK174(U_1158,U_1157) != apply(U_1157,sK173(U_1158,U_1157))
| ~ in(sK173(U_1158,U_1157),relation_rng(U_1158)) )
& sK173(U_1158,U_1157) = apply(U_1158,sK174(U_1158,U_1157))
& in(sK174(U_1158,U_1157),relation_dom(U_1158)) )
| ( ( sK171(U_1158,U_1157) != apply(U_1158,sK172(U_1158,U_1157))
| ~ in(sK172(U_1158,U_1157),relation_dom(U_1158)) )
& sK172(U_1158,U_1157) = apply(U_1157,sK171(U_1158,U_1157))
& in(sK171(U_1158,U_1157),relation_rng(U_1158)) )
| relation_dom(U_1157) != relation_rng(U_1158) )
& ( ( ! [U_1162,U_1160] :
( ( U_1160 = apply(U_1157,U_1162)
& in(U_1162,relation_rng(U_1158)) )
| U_1162 != apply(U_1158,U_1160)
| ~ in(U_1160,relation_dom(U_1158)) )
& ! [U_1161,U_1159] :
( ( U_1161 = apply(U_1158,U_1159)
& in(U_1159,relation_dom(U_1158)) )
| U_1159 != apply(U_1157,U_1161)
| ~ in(U_1161,relation_rng(U_1158)) )
& relation_dom(U_1157) = relation_rng(U_1158) )
| U_1157 != function_inverse(U_1158) ) )
| ~ function(U_1157)
| ~ relation(U_1157) )
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_1164,sK174(U_1158,U_1157))],[f_309_6]) ).
fof(f_309_8,plain,
( ! [U_1157,U_1158] :
( sK174(U_1158,U_1157) != apply(U_1157,sK173(U_1158,U_1157))
| ~ in(sK173(U_1158,U_1157),relation_rng(U_1158))
| ~ sP246(U_1157,U_1158) )
& ! [U_1157,U_1158] :
( sK173(U_1158,U_1157) = apply(U_1158,sK174(U_1158,U_1157))
| ~ sP246(U_1157,U_1158) )
& ! [U_1157,U_1158] :
( in(sK174(U_1158,U_1157),relation_dom(U_1158))
| ~ sP246(U_1157,U_1158) )
& ! [U_1157,U_1158] :
( sK171(U_1158,U_1157) != apply(U_1158,sK172(U_1158,U_1157))
| ~ in(sK172(U_1158,U_1157),relation_dom(U_1158))
| ~ sP245(U_1157,U_1158) )
& ! [U_1157,U_1158] :
( sK172(U_1158,U_1157) = apply(U_1157,sK171(U_1158,U_1157))
| ~ sP245(U_1157,U_1158) )
& ! [U_1157,U_1158] :
( in(sK171(U_1158,U_1157),relation_rng(U_1158))
| ~ sP245(U_1157,U_1158) )
& ! [U_1157,U_1158,U_1160,U_1162] :
( U_1160 = apply(U_1157,U_1162)
| ~ sP243(U_1157,U_1158,U_1160,U_1162) )
& ! [U_1157,U_1158,U_1160,U_1162] :
( in(U_1162,relation_rng(U_1158))
| ~ sP243(U_1157,U_1158,U_1160,U_1162) )
& ! [U_1158,U_1159,U_1161] :
( U_1161 = apply(U_1158,U_1159)
| ~ sP242(U_1158,U_1159,U_1161) )
& ! [U_1158,U_1159,U_1161] :
( in(U_1159,relation_dom(U_1158))
| ~ sP242(U_1158,U_1159,U_1161) )
& ! [U_1157,U_1158,U_1160,U_1159,U_1162,U_1161] :
( sP243(U_1157,U_1158,U_1160,U_1162)
| U_1162 != apply(U_1158,U_1160)
| ~ in(U_1160,relation_dom(U_1158))
| ~ sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) )
& ! [U_1157,U_1158,U_1160,U_1159,U_1162,U_1161] :
( sP242(U_1158,U_1159,U_1161)
| U_1159 != apply(U_1157,U_1161)
| ~ in(U_1161,relation_rng(U_1158))
| ~ sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) )
& ! [U_1157,U_1158,U_1160,U_1159,U_1162,U_1161] :
( relation_dom(U_1157) = relation_rng(U_1158)
| ~ sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) )
& ! [U_1157,U_1158,U_1160,U_1159,U_1162,U_1161] :
( U_1157 = function_inverse(U_1158)
| sP246(U_1157,U_1158)
| sP245(U_1157,U_1158)
| relation_dom(U_1157) != relation_rng(U_1158)
| ~ sP247(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) )
& ! [U_1157,U_1158,U_1160,U_1159,U_1162,U_1161] :
( sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161)
| U_1157 != function_inverse(U_1158)
| ~ sP247(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) )
& ! [U_1157,U_1158,U_1160,U_1159,U_1162,U_1161] :
( sP247(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161)
| ~ function(U_1157)
| ~ relation(U_1157)
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242,sP243,sP244,sP245,sP246,sP247])],[f_309_7]) ).
cnf(f_309_9,plain,
( sP247(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161)
| ~ function(U_1157)
| ~ relation(U_1157)
| ~ one_to_one(U_1158)
| ~ function(U_1158)
| ~ relation(U_1158) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_10,plain,
( sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161)
| U_1157 != function_inverse(U_1158)
| ~ sP247(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_11,plain,
( U_1157 = function_inverse(U_1158)
| sP246(U_1157,U_1158)
| sP245(U_1157,U_1158)
| relation_dom(U_1157) != relation_rng(U_1158)
| ~ sP247(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_12,plain,
( relation_dom(U_1157) = relation_rng(U_1158)
| ~ sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_13,plain,
( sP242(U_1158,U_1159,U_1161)
| U_1159 != apply(U_1157,U_1161)
| ~ in(U_1161,relation_rng(U_1158))
| ~ sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_14,plain,
( sP243(U_1157,U_1158,U_1160,U_1162)
| U_1162 != apply(U_1158,U_1160)
| ~ in(U_1160,relation_dom(U_1158))
| ~ sP244(U_1157,U_1158,U_1160,U_1159,U_1162,U_1161) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_15,plain,
( in(U_1159,relation_dom(U_1158))
| ~ sP242(U_1158,U_1159,U_1161) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_16,plain,
( U_1161 = apply(U_1158,U_1159)
| ~ sP242(U_1158,U_1159,U_1161) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_17,plain,
( in(U_1162,relation_rng(U_1158))
| ~ sP243(U_1157,U_1158,U_1160,U_1162) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_18,plain,
( U_1160 = apply(U_1157,U_1162)
| ~ sP243(U_1157,U_1158,U_1160,U_1162) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_19,plain,
( in(sK171(U_1158,U_1157),relation_rng(U_1158))
| ~ sP245(U_1157,U_1158) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_20,plain,
( sK172(U_1158,U_1157) = apply(U_1157,sK171(U_1158,U_1157))
| ~ sP245(U_1157,U_1158) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_21,plain,
( sK171(U_1158,U_1157) != apply(U_1158,sK172(U_1158,U_1157))
| ~ in(sK172(U_1158,U_1157),relation_dom(U_1158))
| ~ sP245(U_1157,U_1158) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_22,plain,
( in(sK174(U_1158,U_1157),relation_dom(U_1158))
| ~ sP246(U_1157,U_1158) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_23,plain,
( sK173(U_1158,U_1157) = apply(U_1158,sK174(U_1158,U_1157))
| ~ sP246(U_1157,U_1158) ),
inference(clausify,[status(thm)],[f_309_8]) ).
cnf(f_309_24,plain,
( sK174(U_1158,U_1157) != apply(U_1157,sK173(U_1158,U_1157))
| ~ in(sK173(U_1158,U_1157),relation_rng(U_1158))
| ~ sP246(U_1157,U_1158) ),
inference(clausify,[status(thm)],[f_309_8]) ).
fof(f_310_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_310_2,plain,
! [U_1169,U_1168,U_1167] :
( ~ in(U_1168,U_1167)
| ~ in(U_1168,subset_complement(U_1169,U_1167))
| ~ element(U_1167,powerset(U_1169)) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_1168,U_1167,U_1169] :
( ~ in(U_1168,U_1167)
| ~ in(U_1168,subset_complement(U_1169,U_1167))
| ~ element(U_1167,powerset(U_1169)) ),
inference(definitional_conversion,[status(esa)],[f_310_2]) ).
cnf(f_310_4,plain,
( ~ in(U_1168,U_1167)
| ~ in(U_1168,subset_complement(U_1169,U_1167))
| ~ element(U_1167,powerset(U_1169)) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_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_311_2,plain,
! [U_1172] :
( ! [U_1171] :
( ! [U_1170] :
( well_ordering(U_1171)
| ~ relation_isomorphism(U_1172,U_1171,U_1170)
| ~ well_ordering(U_1172)
| ~ function(U_1170)
| ~ relation(U_1170) )
| ~ relation(U_1171) )
| ~ relation(U_1172) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
! [U_1172,U_1171,U_1170] :
( well_ordering(U_1171)
| ~ relation_isomorphism(U_1172,U_1171,U_1170)
| ~ well_ordering(U_1172)
| ~ function(U_1170)
| ~ relation(U_1170)
| ~ relation(U_1171)
| ~ relation(U_1172) ),
inference(definitional_conversion,[status(esa)],[f_311_2]) ).
cnf(f_311_4,plain,
( well_ordering(U_1171)
| ~ relation_isomorphism(U_1172,U_1171,U_1170)
| ~ well_ordering(U_1172)
| ~ function(U_1170)
| ~ relation(U_1170)
| ~ relation(U_1171)
| ~ relation(U_1172) ),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_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_312_2,plain,
! [U_1173] :
( ( relation_dom(U_1173) = relation_rng(function_inverse(U_1173))
& relation_rng(U_1173) = relation_dom(function_inverse(U_1173)) )
| ~ one_to_one(U_1173)
| ~ function(U_1173)
| ~ relation(U_1173) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
( ! [U_1173] :
( relation_dom(U_1173) = relation_rng(function_inverse(U_1173))
| ~ sP248(U_1173) )
& ! [U_1173] :
( relation_rng(U_1173) = relation_dom(function_inverse(U_1173))
| ~ sP248(U_1173) )
& ! [U_1173] :
( sP248(U_1173)
| ~ one_to_one(U_1173)
| ~ function(U_1173)
| ~ relation(U_1173) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248])],[f_312_2]) ).
cnf(f_312_4,plain,
( sP248(U_1173)
| ~ one_to_one(U_1173)
| ~ function(U_1173)
| ~ relation(U_1173) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_5,plain,
( relation_rng(U_1173) = relation_dom(function_inverse(U_1173))
| ~ sP248(U_1173) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_6,plain,
( relation_dom(U_1173) = relation_rng(function_inverse(U_1173))
| ~ sP248(U_1173) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_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_313_2,plain,
! [U_1176] :
( U_1176 = empty_set
| ? [U_1175,U_1174] : in(ordered_pair(U_1175,U_1174),U_1176)
| ~ relation(U_1176) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_1176] :
( U_1176 = empty_set
| ? [U_1174] : in(ordered_pair(sK175(U_1176),U_1174),U_1176)
| ~ relation(U_1176) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_1175,sK175(U_1176))],[f_313_2]) ).
fof(f_313_4,plain,
! [U_1176] :
( U_1176 = empty_set
| in(ordered_pair(sK175(U_1176),sK176(U_1176)),U_1176)
| ~ relation(U_1176) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_1174,sK176(U_1176))],[f_313_3]) ).
fof(f_313_5,plain,
! [U_1176] :
( U_1176 = empty_set
| in(ordered_pair(sK175(U_1176),sK176(U_1176)),U_1176)
| ~ relation(U_1176) ),
inference(definitional_conversion,[status(esa)],[f_313_4]) ).
cnf(f_313_6,plain,
( U_1176 = empty_set
| in(ordered_pair(sK175(U_1176),sK176(U_1176)),U_1176)
| ~ relation(U_1176) ),
inference(clausify,[status(thm)],[f_313_5]) ).
fof(f_314_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_314_2,plain,
! [U_1178,U_1177] :
( ( U_1178 = apply(relation_composition(function_inverse(U_1177),U_1177),U_1178)
& U_1178 = apply(U_1177,apply(function_inverse(U_1177),U_1178)) )
| ~ in(U_1178,relation_rng(U_1177))
| ~ one_to_one(U_1177)
| ~ function(U_1177)
| ~ relation(U_1177) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
( ! [U_1177,U_1178] :
( U_1178 = apply(relation_composition(function_inverse(U_1177),U_1177),U_1178)
| ~ sP249(U_1177,U_1178) )
& ! [U_1177,U_1178] :
( U_1178 = apply(U_1177,apply(function_inverse(U_1177),U_1178))
| ~ sP249(U_1177,U_1178) )
& ! [U_1177,U_1178] :
( sP249(U_1177,U_1178)
| ~ in(U_1178,relation_rng(U_1177))
| ~ one_to_one(U_1177)
| ~ function(U_1177)
| ~ relation(U_1177) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249])],[f_314_2]) ).
cnf(f_314_4,plain,
( sP249(U_1177,U_1178)
| ~ in(U_1178,relation_rng(U_1177))
| ~ one_to_one(U_1177)
| ~ function(U_1177)
| ~ relation(U_1177) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_5,plain,
( U_1178 = apply(U_1177,apply(function_inverse(U_1177),U_1178))
| ~ sP249(U_1177,U_1178) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_6,plain,
( U_1178 = apply(relation_composition(function_inverse(U_1177),U_1177),U_1178)
| ~ sP249(U_1177,U_1178) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_315_2,plain,
! [U_1181,U_1180,U_1179] :
( ~ empty(U_1179)
| ~ element(U_1180,powerset(U_1179))
| ~ in(U_1181,U_1180) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
! [U_1181,U_1180] :
( ! [U_1179] :
( ~ empty(U_1179)
| ~ element(U_1180,powerset(U_1179)) )
| ~ in(U_1181,U_1180) ),
inference(miniscope,[status(thm)],[f_315_2]) ).
fof(f_315_4,plain,
! [U_1179,U_1181,U_1180] :
( ~ empty(U_1179)
| ~ element(U_1180,powerset(U_1179))
| ~ in(U_1181,U_1180) ),
inference(definitional_conversion,[status(esa)],[f_315_3]) ).
cnf(f_315_5,plain,
( ~ empty(U_1179)
| ~ element(U_1180,powerset(U_1179))
| ~ in(U_1181,U_1180) ),
inference(clausify,[status(thm)],[f_315_4]) ).
fof(f_316_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_316_2,plain,
! [U_1182] :
( ( ( well_founded_relation(U_1182)
| ~ is_well_founded_in(U_1182,relation_field(U_1182)) )
& ( is_well_founded_in(U_1182,relation_field(U_1182))
| ~ well_founded_relation(U_1182) ) )
| ~ relation(U_1182) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
( ! [U_1182] :
( well_founded_relation(U_1182)
| ~ is_well_founded_in(U_1182,relation_field(U_1182))
| ~ sP250(U_1182) )
& ! [U_1182] :
( is_well_founded_in(U_1182,relation_field(U_1182))
| ~ well_founded_relation(U_1182)
| ~ sP250(U_1182) )
& ! [U_1182] :
( sP250(U_1182)
| ~ relation(U_1182) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP250])],[f_316_2]) ).
cnf(f_316_4,plain,
( sP250(U_1182)
| ~ relation(U_1182) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_5,plain,
( is_well_founded_in(U_1182,relation_field(U_1182))
| ~ well_founded_relation(U_1182)
| ~ sP250(U_1182) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_6,plain,
( well_founded_relation(U_1182)
| ~ is_well_founded_in(U_1182,relation_field(U_1182))
| ~ sP250(U_1182) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_1,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t5_wellord2]) ).
fof(f_317_2,plain,
! [U_1183] : antisymmetric(inclusion_relation(U_1183)),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_1183] : antisymmetric(inclusion_relation(U_1183)),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_4,plain,
antisymmetric(inclusion_relation(U_1183)),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
fof(f_318_2,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(definitional_conversion,[status(esa)],[f_318_1]) ).
cnf(f_318_3,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_318_2]) ).
cnf(f_318_4,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_319_2,plain,
! [U_1185,U_1184] :
( ~ proper_subset(U_1184,U_1185)
| ~ subset(U_1185,U_1184) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_1185,U_1184] :
( ~ proper_subset(U_1184,U_1185)
| ~ subset(U_1185,U_1184) ),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
( ~ proper_subset(U_1184,U_1185)
| ~ subset(U_1185,U_1184) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_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_320_2,plain,
! [U_1186] :
( one_to_one(function_inverse(U_1186))
| ~ one_to_one(U_1186)
| ~ function(U_1186)
| ~ relation(U_1186) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1186] :
( one_to_one(function_inverse(U_1186))
| ~ one_to_one(U_1186)
| ~ function(U_1186)
| ~ relation(U_1186) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( one_to_one(function_inverse(U_1186))
| ~ one_to_one(U_1186)
| ~ function(U_1186)
| ~ relation(U_1186) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_321_2,plain,
! [U_1189,U_1188,U_1187] :
( disjoint(U_1189,U_1187)
| ~ disjoint(U_1188,U_1187)
| ~ subset(U_1189,U_1188) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1188,U_1187,U_1189] :
( disjoint(U_1189,U_1187)
| ~ disjoint(U_1188,U_1187)
| ~ subset(U_1189,U_1188) ),
inference(definitional_conversion,[status(esa)],[f_321_2]) ).
cnf(f_321_4,plain,
( disjoint(U_1189,U_1187)
| ~ disjoint(U_1188,U_1187)
| ~ subset(U_1189,U_1188) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_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_322_2,plain,
! [U_1190] :
( U_1190 = empty_set
| ( relation_rng(U_1190) != empty_set
& relation_dom(U_1190) != empty_set )
| ~ relation(U_1190) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
( ! [U_1190] :
( relation_rng(U_1190) != empty_set
| ~ sP251(U_1190) )
& ! [U_1190] :
( relation_dom(U_1190) != empty_set
| ~ sP251(U_1190) )
& ! [U_1190] :
( U_1190 = empty_set
| sP251(U_1190)
| ~ relation(U_1190) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251])],[f_322_2]) ).
cnf(f_322_4,plain,
( U_1190 = empty_set
| sP251(U_1190)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_5,plain,
( relation_dom(U_1190) != empty_set
| ~ sP251(U_1190) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_6,plain,
( relation_rng(U_1190) != empty_set
| ~ sP251(U_1190) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_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_323_2,plain,
! [U_1191] :
( ( ( relation_dom(U_1191) = empty_set
| relation_rng(U_1191) != empty_set )
& ( relation_rng(U_1191) = empty_set
| relation_dom(U_1191) != empty_set ) )
| ~ relation(U_1191) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
( ! [U_1191] :
( relation_dom(U_1191) = empty_set
| relation_rng(U_1191) != empty_set
| ~ sP252(U_1191) )
& ! [U_1191] :
( relation_rng(U_1191) = empty_set
| relation_dom(U_1191) != empty_set
| ~ sP252(U_1191) )
& ! [U_1191] :
( sP252(U_1191)
| ~ relation(U_1191) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_323_2]) ).
cnf(f_323_4,plain,
( sP252(U_1191)
| ~ relation(U_1191) ),
inference(clausify,[status(thm)],[f_323_3]) ).
cnf(f_323_5,plain,
( relation_rng(U_1191) = empty_set
| relation_dom(U_1191) != empty_set
| ~ sP252(U_1191) ),
inference(clausify,[status(thm)],[f_323_3]) ).
cnf(f_323_6,plain,
( relation_dom(U_1191) = empty_set
| relation_rng(U_1191) != empty_set
| ~ sP252(U_1191) ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_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_324_2,plain,
! [U_1193,U_1192] :
( ( set_difference(U_1193,singleton(U_1192)) = U_1193
| in(U_1192,U_1193) )
& ( ~ in(U_1192,U_1193)
| set_difference(U_1193,singleton(U_1192)) != U_1193 ) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
( ! [U_1197,U_1195] :
( set_difference(U_1197,singleton(U_1195)) = U_1197
| in(U_1195,U_1197) )
& ! [U_1196,U_1194] :
( ~ in(U_1194,U_1196)
| set_difference(U_1196,singleton(U_1194)) != U_1196 ) ),
inference(miniscope,[status(thm)],[f_324_2]) ).
fof(f_324_4,plain,
( ! [U_1195,U_1197] :
( set_difference(U_1197,singleton(U_1195)) = U_1197
| in(U_1195,U_1197) )
& ! [U_1194,U_1196] :
( ~ in(U_1194,U_1196)
| set_difference(U_1196,singleton(U_1194)) != U_1196 ) ),
inference(definitional_conversion,[status(esa)],[f_324_3]) ).
cnf(f_324_5,plain,
( ~ in(U_1194,U_1196)
| set_difference(U_1196,singleton(U_1194)) != U_1196 ),
inference(clausify,[status(thm)],[f_324_4]) ).
cnf(f_324_6,plain,
( set_difference(U_1197,singleton(U_1195)) = U_1197
| in(U_1195,U_1197) ),
inference(clausify,[status(thm)],[f_324_4]) ).
fof(f_325_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_325_2,plain,
! [U_1202,U_1201] :
( ! [U_1200] :
( ( ( U_1201 = relation_dom_restriction(U_1200,U_1202)
| ? [U_1199] :
( apply(U_1201,U_1199) != apply(U_1200,U_1199)
& in(U_1199,relation_dom(U_1201)) )
| relation_dom(U_1201) != set_intersection2(relation_dom(U_1200),U_1202) )
& ( ( ! [U_1198] :
( apply(U_1201,U_1198) = apply(U_1200,U_1198)
| ~ in(U_1198,relation_dom(U_1201)) )
& relation_dom(U_1201) = set_intersection2(relation_dom(U_1200),U_1202) )
| U_1201 != relation_dom_restriction(U_1200,U_1202) ) )
| ~ function(U_1200)
| ~ relation(U_1200) )
| ~ function(U_1201)
| ~ relation(U_1201) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1202,U_1201] :
( ! [U_1200] :
( ( ( U_1201 = relation_dom_restriction(U_1200,U_1202)
| ( apply(U_1201,sK177(U_1202,U_1201,U_1200)) != apply(U_1200,sK177(U_1202,U_1201,U_1200))
& in(sK177(U_1202,U_1201,U_1200),relation_dom(U_1201)) )
| relation_dom(U_1201) != set_intersection2(relation_dom(U_1200),U_1202) )
& ( ( ! [U_1198] :
( apply(U_1201,U_1198) = apply(U_1200,U_1198)
| ~ in(U_1198,relation_dom(U_1201)) )
& relation_dom(U_1201) = set_intersection2(relation_dom(U_1200),U_1202) )
| U_1201 != relation_dom_restriction(U_1200,U_1202) ) )
| ~ function(U_1200)
| ~ relation(U_1200) )
| ~ function(U_1201)
| ~ relation(U_1201) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_1199,sK177(U_1202,U_1201,U_1200))],[f_325_2]) ).
fof(f_325_4,plain,
( ! [U_1202,U_1200,U_1201] :
( apply(U_1201,sK177(U_1202,U_1201,U_1200)) != apply(U_1200,sK177(U_1202,U_1201,U_1200))
| ~ sP254(U_1202,U_1200,U_1201) )
& ! [U_1202,U_1200,U_1201] :
( in(sK177(U_1202,U_1201,U_1200),relation_dom(U_1201))
| ~ sP254(U_1202,U_1200,U_1201) )
& ! [U_1202,U_1198,U_1200,U_1201] :
( apply(U_1201,U_1198) = apply(U_1200,U_1198)
| ~ in(U_1198,relation_dom(U_1201))
| ~ sP253(U_1202,U_1198,U_1200,U_1201) )
& ! [U_1202,U_1198,U_1200,U_1201] :
( relation_dom(U_1201) = set_intersection2(relation_dom(U_1200),U_1202)
| ~ sP253(U_1202,U_1198,U_1200,U_1201) )
& ! [U_1202,U_1198,U_1200,U_1201] :
( U_1201 = relation_dom_restriction(U_1200,U_1202)
| sP254(U_1202,U_1200,U_1201)
| relation_dom(U_1201) != set_intersection2(relation_dom(U_1200),U_1202)
| ~ sP255(U_1202,U_1198,U_1200,U_1201) )
& ! [U_1202,U_1198,U_1200,U_1201] :
( sP253(U_1202,U_1198,U_1200,U_1201)
| U_1201 != relation_dom_restriction(U_1200,U_1202)
| ~ sP255(U_1202,U_1198,U_1200,U_1201) )
& ! [U_1202,U_1198,U_1200,U_1201] :
( sP255(U_1202,U_1198,U_1200,U_1201)
| ~ function(U_1200)
| ~ relation(U_1200)
| ~ function(U_1201)
| ~ relation(U_1201) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253,sP254,sP255])],[f_325_3]) ).
cnf(f_325_5,plain,
( sP255(U_1202,U_1198,U_1200,U_1201)
| ~ function(U_1200)
| ~ relation(U_1200)
| ~ function(U_1201)
| ~ relation(U_1201) ),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_6,plain,
( sP253(U_1202,U_1198,U_1200,U_1201)
| U_1201 != relation_dom_restriction(U_1200,U_1202)
| ~ sP255(U_1202,U_1198,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_7,plain,
( U_1201 = relation_dom_restriction(U_1200,U_1202)
| sP254(U_1202,U_1200,U_1201)
| relation_dom(U_1201) != set_intersection2(relation_dom(U_1200),U_1202)
| ~ sP255(U_1202,U_1198,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_8,plain,
( relation_dom(U_1201) = set_intersection2(relation_dom(U_1200),U_1202)
| ~ sP253(U_1202,U_1198,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_9,plain,
( apply(U_1201,U_1198) = apply(U_1200,U_1198)
| ~ in(U_1198,relation_dom(U_1201))
| ~ sP253(U_1202,U_1198,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_10,plain,
( in(sK177(U_1202,U_1201,U_1200),relation_dom(U_1201))
| ~ sP254(U_1202,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_325_4]) ).
cnf(f_325_11,plain,
( apply(U_1201,sK177(U_1202,U_1201,U_1200)) != apply(U_1200,sK177(U_1202,U_1201,U_1200))
| ~ sP254(U_1202,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_325_4]) ).
fof(f_326_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_326_2,plain,
! [U_1203] : unordered_pair(U_1203,U_1203) = singleton(U_1203),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1203] : unordered_pair(U_1203,U_1203) = singleton(U_1203),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
unordered_pair(U_1203,U_1203) = singleton(U_1203),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_327_2,plain,
! [U_1204] :
( U_1204 = empty_set
| ~ empty(U_1204) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1204] :
( U_1204 = empty_set
| ~ empty(U_1204) ),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
( U_1204 = empty_set
| ~ empty(U_1204) ),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_1,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t6_wellord2]) ).
fof(f_328_2,plain,
! [U_1205] :
( well_founded_relation(inclusion_relation(U_1205))
| ~ ordinal(U_1205) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
! [U_1205] :
( well_founded_relation(inclusion_relation(U_1205))
| ~ ordinal(U_1205) ),
inference(definitional_conversion,[status(esa)],[f_328_2]) ).
cnf(f_328_4,plain,
( well_founded_relation(inclusion_relation(U_1205))
| ~ ordinal(U_1205) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_329_2,plain,
! [U_1207,U_1206] :
( U_1207 = U_1206
| ~ subset(singleton(U_1207),singleton(U_1206)) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
! [U_1206,U_1207] :
( U_1207 = U_1206
| ~ subset(singleton(U_1207),singleton(U_1206)) ),
inference(definitional_conversion,[status(esa)],[f_329_2]) ).
cnf(f_329_4,plain,
( U_1207 = U_1206
| ~ subset(singleton(U_1207),singleton(U_1206)) ),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_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_330_2,plain,
! [U_1210,U_1209,U_1208] :
( apply(relation_dom_restriction(U_1208,U_1210),U_1209) = apply(U_1208,U_1209)
| ~ in(U_1209,relation_dom(relation_dom_restriction(U_1208,U_1210)))
| ~ function(U_1208)
| ~ relation(U_1208) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_1209,U_1208,U_1210] :
( apply(relation_dom_restriction(U_1208,U_1210),U_1209) = apply(U_1208,U_1209)
| ~ in(U_1209,relation_dom(relation_dom_restriction(U_1208,U_1210)))
| ~ function(U_1208)
| ~ relation(U_1208) ),
inference(definitional_conversion,[status(esa)],[f_330_2]) ).
cnf(f_330_4,plain,
( apply(relation_dom_restriction(U_1208,U_1210),U_1209) = apply(U_1208,U_1209)
| ~ in(U_1209,relation_dom(relation_dom_restriction(U_1208,U_1210)))
| ~ function(U_1208)
| ~ relation(U_1208) ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_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_331_2,plain,
! [U_1211] :
( relation_rng(identity_relation(U_1211)) = U_1211
& relation_dom(identity_relation(U_1211)) = U_1211 ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
( ! [U_1213] : relation_rng(identity_relation(U_1213)) = U_1213
& ! [U_1212] : relation_dom(identity_relation(U_1212)) = U_1212 ),
inference(miniscope,[status(thm)],[f_331_2]) ).
fof(f_331_4,plain,
( ! [U_1213] : relation_rng(identity_relation(U_1213)) = U_1213
& ! [U_1212] : relation_dom(identity_relation(U_1212)) = U_1212 ),
inference(definitional_conversion,[status(esa)],[f_331_3]) ).
cnf(f_331_5,plain,
relation_dom(identity_relation(U_1212)) = U_1212,
inference(clausify,[status(thm)],[f_331_4]) ).
cnf(f_331_6,plain,
relation_rng(identity_relation(U_1213)) = U_1213,
inference(clausify,[status(thm)],[f_331_4]) ).
fof(f_332_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_332_2,plain,
! [U_1216,U_1215,U_1214] :
( apply(relation_dom_restriction(U_1214,U_1216),U_1215) = apply(U_1214,U_1215)
| ~ in(U_1215,U_1216)
| ~ function(U_1214)
| ~ relation(U_1214) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_1215,U_1216,U_1214] :
( apply(relation_dom_restriction(U_1214,U_1216),U_1215) = apply(U_1214,U_1215)
| ~ in(U_1215,U_1216)
| ~ function(U_1214)
| ~ relation(U_1214) ),
inference(definitional_conversion,[status(esa)],[f_332_2]) ).
cnf(f_332_4,plain,
( apply(relation_dom_restriction(U_1214,U_1216),U_1215) = apply(U_1214,U_1215)
| ~ in(U_1215,U_1216)
| ~ function(U_1214)
| ~ relation(U_1214) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_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_333_2,plain,
! [U_1220,U_1219,U_1218,U_1217] :
( ( ( in(ordered_pair(U_1220,U_1219),relation_composition(identity_relation(U_1218),U_1217))
| ~ in(ordered_pair(U_1220,U_1219),U_1217)
| ~ in(U_1220,U_1218) )
& ( ( in(ordered_pair(U_1220,U_1219),U_1217)
& in(U_1220,U_1218) )
| ~ in(ordered_pair(U_1220,U_1219),relation_composition(identity_relation(U_1218),U_1217)) ) )
| ~ relation(U_1217) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
( ! [U_1217,U_1218,U_1219,U_1220] :
( in(ordered_pair(U_1220,U_1219),U_1217)
| ~ sP256(U_1217,U_1218,U_1219,U_1220) )
& ! [U_1217,U_1218,U_1219,U_1220] :
( in(U_1220,U_1218)
| ~ sP256(U_1217,U_1218,U_1219,U_1220) )
& ! [U_1217,U_1218,U_1219,U_1220] :
( in(ordered_pair(U_1220,U_1219),relation_composition(identity_relation(U_1218),U_1217))
| ~ in(ordered_pair(U_1220,U_1219),U_1217)
| ~ in(U_1220,U_1218)
| ~ sP257(U_1217,U_1218,U_1219,U_1220) )
& ! [U_1217,U_1218,U_1219,U_1220] :
( sP256(U_1217,U_1218,U_1219,U_1220)
| ~ in(ordered_pair(U_1220,U_1219),relation_composition(identity_relation(U_1218),U_1217))
| ~ sP257(U_1217,U_1218,U_1219,U_1220) )
& ! [U_1217,U_1218,U_1219,U_1220] :
( sP257(U_1217,U_1218,U_1219,U_1220)
| ~ relation(U_1217) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256,sP257])],[f_333_2]) ).
cnf(f_333_4,plain,
( sP257(U_1217,U_1218,U_1219,U_1220)
| ~ relation(U_1217) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_5,plain,
( sP256(U_1217,U_1218,U_1219,U_1220)
| ~ in(ordered_pair(U_1220,U_1219),relation_composition(identity_relation(U_1218),U_1217))
| ~ sP257(U_1217,U_1218,U_1219,U_1220) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_6,plain,
( in(ordered_pair(U_1220,U_1219),relation_composition(identity_relation(U_1218),U_1217))
| ~ in(ordered_pair(U_1220,U_1219),U_1217)
| ~ in(U_1220,U_1218)
| ~ sP257(U_1217,U_1218,U_1219,U_1220) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_7,plain,
( in(U_1220,U_1218)
| ~ sP256(U_1217,U_1218,U_1219,U_1220) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_8,plain,
( in(ordered_pair(U_1220,U_1219),U_1217)
| ~ sP256(U_1217,U_1218,U_1219,U_1220) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_334_2,plain,
! [U_1222,U_1221] :
( ~ empty(U_1221)
| ~ in(U_1222,U_1221) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1221,U_1222] :
( ~ empty(U_1221)
| ~ in(U_1222,U_1221) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( ~ empty(U_1221)
| ~ in(U_1222,U_1221) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_1,plain,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
inference(fof_nnf,[status(thm)],[t7_mcart_1]) ).
fof(f_335_2,plain,
! [U_1224,U_1223] :
( pair_second(ordered_pair(U_1224,U_1223)) = U_1223
& pair_first(ordered_pair(U_1224,U_1223)) = U_1224 ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
( ! [U_1228,U_1226] : pair_second(ordered_pair(U_1228,U_1226)) = U_1226
& ! [U_1227,U_1225] : pair_first(ordered_pair(U_1227,U_1225)) = U_1227 ),
inference(miniscope,[status(thm)],[f_335_2]) ).
fof(f_335_4,plain,
( ! [U_1228,U_1226] : pair_second(ordered_pair(U_1228,U_1226)) = U_1226
& ! [U_1227,U_1225] : pair_first(ordered_pair(U_1227,U_1225)) = U_1227 ),
inference(definitional_conversion,[status(esa)],[f_335_3]) ).
cnf(f_335_5,plain,
pair_first(ordered_pair(U_1227,U_1225)) = U_1227,
inference(clausify,[status(thm)],[f_335_4]) ).
cnf(f_335_6,plain,
pair_second(ordered_pair(U_1228,U_1226)) = U_1226,
inference(clausify,[status(thm)],[f_335_4]) ).
fof(f_336_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_336_2,plain,
! [U_1232,U_1231] :
( ? [U_1230] :
( ! [U_1229] :
( ~ in(U_1229,U_1230)
| ~ in(U_1229,U_1231) )
& in(U_1230,U_1231) )
| ~ in(U_1232,U_1231) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_1232,U_1231] :
( ( ! [U_1229] :
( ~ in(U_1229,sK178(U_1232,U_1231))
| ~ in(U_1229,U_1231) )
& in(sK178(U_1232,U_1231),U_1231) )
| ~ in(U_1232,U_1231) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_1230,sK178(U_1232,U_1231))],[f_336_2]) ).
fof(f_336_4,plain,
( ! [U_1229,U_1231,U_1232] :
( ~ in(U_1229,sK178(U_1232,U_1231))
| ~ in(U_1229,U_1231)
| ~ sP258(U_1229,U_1231,U_1232) )
& ! [U_1229,U_1231,U_1232] :
( in(sK178(U_1232,U_1231),U_1231)
| ~ sP258(U_1229,U_1231,U_1232) )
& ! [U_1229,U_1231,U_1232] :
( sP258(U_1229,U_1231,U_1232)
| ~ in(U_1232,U_1231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_336_3]) ).
cnf(f_336_5,plain,
( sP258(U_1229,U_1231,U_1232)
| ~ in(U_1232,U_1231) ),
inference(clausify,[status(thm)],[f_336_4]) ).
cnf(f_336_6,plain,
( in(sK178(U_1232,U_1231),U_1231)
| ~ sP258(U_1229,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_336_4]) ).
cnf(f_336_7,plain,
( ~ in(U_1229,sK178(U_1232,U_1231))
| ~ in(U_1229,U_1231)
| ~ sP258(U_1229,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_336_4]) ).
fof(f_337_1,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(negate,[status(cth)],[t7_wellord2]) ).
fof(f_337_2,negated_conjecture,
? [A] :
( ~ well_ordering(inclusion_relation(A))
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[f_337_1]) ).
fof(f_337_3,negated_conjecture,
? [U_1233] :
( ~ well_ordering(inclusion_relation(U_1233))
& ordinal(U_1233) ),
inference(variable_rename,[status(thm)],[f_337_2]) ).
fof(f_337_4,negated_conjecture,
( ~ well_ordering(inclusion_relation(sK179))
& ordinal(sK179) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_1233,sK179)],[f_337_3]) ).
fof(f_337_5,negated_conjecture,
( ~ well_ordering(inclusion_relation(sK179))
& ordinal(sK179) ),
inference(definitional_conversion,[status(esa)],[f_337_4]) ).
cnf(f_337_6,negated_conjecture,
ordinal(sK179),
inference(clausify,[status(thm)],[f_337_5]) ).
cnf(f_337_7,negated_conjecture,
~ well_ordering(inclusion_relation(sK179)),
inference(clausify,[status(thm)],[f_337_5]) ).
fof(f_338_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_338_2,plain,
! [U_1235,U_1234] : subset(U_1235,set_union2(U_1235,U_1234)),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1234,U_1235] : subset(U_1235,set_union2(U_1235,U_1234)),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
subset(U_1235,set_union2(U_1235,U_1234)),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_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_339_2,plain,
! [U_1237,U_1236] :
( ( disjoint(U_1237,U_1236)
| set_difference(U_1237,U_1236) != U_1237 )
& ( set_difference(U_1237,U_1236) = U_1237
| ~ disjoint(U_1237,U_1236) ) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
( ! [U_1241,U_1239] :
( disjoint(U_1241,U_1239)
| set_difference(U_1241,U_1239) != U_1241 )
& ! [U_1240,U_1238] :
( set_difference(U_1240,U_1238) = U_1240
| ~ disjoint(U_1240,U_1238) ) ),
inference(miniscope,[status(thm)],[f_339_2]) ).
fof(f_339_4,plain,
( ! [U_1241,U_1239] :
( disjoint(U_1241,U_1239)
| set_difference(U_1241,U_1239) != U_1241 )
& ! [U_1240,U_1238] :
( set_difference(U_1240,U_1238) = U_1240
| ~ disjoint(U_1240,U_1238) ) ),
inference(definitional_conversion,[status(esa)],[f_339_3]) ).
cnf(f_339_5,plain,
( set_difference(U_1240,U_1238) = U_1240
| ~ disjoint(U_1240,U_1238) ),
inference(clausify,[status(thm)],[f_339_4]) ).
cnf(f_339_6,plain,
( disjoint(U_1241,U_1239)
| set_difference(U_1241,U_1239) != U_1241 ),
inference(clausify,[status(thm)],[f_339_4]) ).
fof(f_340_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_340_2,plain,
! [U_1244,U_1243,U_1242] :
( ( ( in(U_1244,relation_dom(relation_dom_restriction(U_1242,U_1243)))
| ~ in(U_1244,relation_dom(U_1242))
| ~ in(U_1244,U_1243) )
& ( ( in(U_1244,relation_dom(U_1242))
& in(U_1244,U_1243) )
| ~ in(U_1244,relation_dom(relation_dom_restriction(U_1242,U_1243))) ) )
| ~ relation(U_1242) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
( ! [U_1242,U_1243,U_1244] :
( in(U_1244,relation_dom(U_1242))
| ~ sP259(U_1242,U_1243,U_1244) )
& ! [U_1242,U_1243,U_1244] :
( in(U_1244,U_1243)
| ~ sP259(U_1242,U_1243,U_1244) )
& ! [U_1242,U_1243,U_1244] :
( in(U_1244,relation_dom(relation_dom_restriction(U_1242,U_1243)))
| ~ in(U_1244,relation_dom(U_1242))
| ~ in(U_1244,U_1243)
| ~ sP260(U_1242,U_1243,U_1244) )
& ! [U_1242,U_1243,U_1244] :
( sP259(U_1242,U_1243,U_1244)
| ~ in(U_1244,relation_dom(relation_dom_restriction(U_1242,U_1243)))
| ~ sP260(U_1242,U_1243,U_1244) )
& ! [U_1242,U_1243,U_1244] :
( sP260(U_1242,U_1243,U_1244)
| ~ relation(U_1242) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259,sP260])],[f_340_2]) ).
cnf(f_340_4,plain,
( sP260(U_1242,U_1243,U_1244)
| ~ relation(U_1242) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_5,plain,
( sP259(U_1242,U_1243,U_1244)
| ~ in(U_1244,relation_dom(relation_dom_restriction(U_1242,U_1243)))
| ~ sP260(U_1242,U_1243,U_1244) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_6,plain,
( in(U_1244,relation_dom(relation_dom_restriction(U_1242,U_1243)))
| ~ in(U_1244,relation_dom(U_1242))
| ~ in(U_1244,U_1243)
| ~ sP260(U_1242,U_1243,U_1244) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_7,plain,
( in(U_1244,U_1243)
| ~ sP259(U_1242,U_1243,U_1244) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_8,plain,
( in(U_1244,relation_dom(U_1242))
| ~ sP259(U_1242,U_1243,U_1244) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_341_2,plain,
! [U_1246,U_1245] :
( subset(relation_dom_restriction(U_1245,U_1246),U_1245)
| ~ relation(U_1245) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1245,U_1246] :
( subset(relation_dom_restriction(U_1245,U_1246),U_1245)
| ~ relation(U_1245) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
( subset(relation_dom_restriction(U_1245,U_1246),U_1245)
| ~ relation(U_1245) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_342_2,plain,
! [U_1248,U_1247] :
( ~ empty(U_1247)
| U_1248 = U_1247
| ~ empty(U_1248) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_1248] :
( ! [U_1247] :
( ~ empty(U_1247)
| U_1248 = U_1247 )
| ~ empty(U_1248) ),
inference(miniscope,[status(thm)],[f_342_2]) ).
fof(f_342_4,plain,
! [U_1247,U_1248] :
( ~ empty(U_1247)
| U_1248 = U_1247
| ~ empty(U_1248) ),
inference(definitional_conversion,[status(esa)],[f_342_3]) ).
cnf(f_342_5,plain,
( ~ empty(U_1247)
| U_1248 = U_1247
| ~ empty(U_1248) ),
inference(clausify,[status(thm)],[f_342_4]) ).
fof(f_343_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_343_2,plain,
! [U_1251,U_1250,U_1249] :
( ( ( in(ordered_pair(U_1251,U_1250),U_1249)
| U_1250 != apply(U_1249,U_1251)
| ~ in(U_1251,relation_dom(U_1249)) )
& ( ( U_1250 = apply(U_1249,U_1251)
& in(U_1251,relation_dom(U_1249)) )
| ~ in(ordered_pair(U_1251,U_1250),U_1249) ) )
| ~ function(U_1249)
| ~ relation(U_1249) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
( ! [U_1250,U_1251,U_1249] :
( U_1250 = apply(U_1249,U_1251)
| ~ sP261(U_1250,U_1251,U_1249) )
& ! [U_1250,U_1251,U_1249] :
( in(U_1251,relation_dom(U_1249))
| ~ sP261(U_1250,U_1251,U_1249) )
& ! [U_1250,U_1251,U_1249] :
( in(ordered_pair(U_1251,U_1250),U_1249)
| U_1250 != apply(U_1249,U_1251)
| ~ in(U_1251,relation_dom(U_1249))
| ~ sP262(U_1250,U_1251,U_1249) )
& ! [U_1250,U_1251,U_1249] :
( sP261(U_1250,U_1251,U_1249)
| ~ in(ordered_pair(U_1251,U_1250),U_1249)
| ~ sP262(U_1250,U_1251,U_1249) )
& ! [U_1250,U_1251,U_1249] :
( sP262(U_1250,U_1251,U_1249)
| ~ function(U_1249)
| ~ relation(U_1249) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261,sP262])],[f_343_2]) ).
cnf(f_343_4,plain,
( sP262(U_1250,U_1251,U_1249)
| ~ function(U_1249)
| ~ relation(U_1249) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_5,plain,
( sP261(U_1250,U_1251,U_1249)
| ~ in(ordered_pair(U_1251,U_1250),U_1249)
| ~ sP262(U_1250,U_1251,U_1249) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_6,plain,
( in(ordered_pair(U_1251,U_1250),U_1249)
| U_1250 != apply(U_1249,U_1251)
| ~ in(U_1251,relation_dom(U_1249))
| ~ sP262(U_1250,U_1251,U_1249) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_7,plain,
( in(U_1251,relation_dom(U_1249))
| ~ sP261(U_1250,U_1251,U_1249) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_8,plain,
( U_1250 = apply(U_1249,U_1251)
| ~ sP261(U_1250,U_1251,U_1249) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_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_344_2,plain,
! [U_1252] :
( ( ( well_orders(U_1252,relation_field(U_1252))
| ~ well_ordering(U_1252) )
& ( well_ordering(U_1252)
| ~ well_orders(U_1252,relation_field(U_1252)) ) )
| ~ relation(U_1252) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
( ! [U_1252] :
( well_orders(U_1252,relation_field(U_1252))
| ~ well_ordering(U_1252)
| ~ sP263(U_1252) )
& ! [U_1252] :
( well_ordering(U_1252)
| ~ well_orders(U_1252,relation_field(U_1252))
| ~ sP263(U_1252) )
& ! [U_1252] :
( sP263(U_1252)
| ~ relation(U_1252) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263])],[f_344_2]) ).
cnf(f_344_4,plain,
( sP263(U_1252)
| ~ relation(U_1252) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_5,plain,
( well_ordering(U_1252)
| ~ well_orders(U_1252,relation_field(U_1252))
| ~ sP263(U_1252) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_6,plain,
( well_orders(U_1252,relation_field(U_1252))
| ~ well_ordering(U_1252)
| ~ sP263(U_1252) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_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_345_2,plain,
! [U_1255,U_1254,U_1253] :
( subset(set_union2(U_1255,U_1253),U_1254)
| ~ subset(U_1253,U_1254)
| ~ subset(U_1255,U_1254) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_1253,U_1255,U_1254] :
( subset(set_union2(U_1255,U_1253),U_1254)
| ~ subset(U_1253,U_1254)
| ~ subset(U_1255,U_1254) ),
inference(definitional_conversion,[status(esa)],[f_345_2]) ).
cnf(f_345_4,plain,
( subset(set_union2(U_1255,U_1253),U_1254)
| ~ subset(U_1253,U_1254)
| ~ subset(U_1255,U_1254) ),
inference(clausify,[status(thm)],[f_345_3]) ).
fof(f_346_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_346_2,plain,
! [U_1258,U_1257,U_1256] :
( U_1258 = U_1257
| singleton(U_1258) != unordered_pair(U_1257,U_1256) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_1258,U_1257] :
( ! [U_1256] : singleton(U_1258) != unordered_pair(U_1257,U_1256)
| U_1258 = U_1257 ),
inference(miniscope,[status(thm)],[f_346_2]) ).
fof(f_346_4,plain,
! [U_1257,U_1258,U_1256] :
( singleton(U_1258) != unordered_pair(U_1257,U_1256)
| U_1258 = U_1257 ),
inference(definitional_conversion,[status(esa)],[f_346_3]) ).
cnf(f_346_5,plain,
( singleton(U_1258) != unordered_pair(U_1257,U_1256)
| U_1258 = U_1257 ),
inference(clausify,[status(thm)],[f_346_4]) ).
fof(f_347_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_347_2,plain,
! [U_1260,U_1259] :
( relation_dom(relation_dom_restriction(U_1259,U_1260)) = set_intersection2(relation_dom(U_1259),U_1260)
| ~ relation(U_1259) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_1259,U_1260] :
( relation_dom(relation_dom_restriction(U_1259,U_1260)) = set_intersection2(relation_dom(U_1259),U_1260)
| ~ relation(U_1259) ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( relation_dom(relation_dom_restriction(U_1259,U_1260)) = set_intersection2(relation_dom(U_1259),U_1260)
| ~ relation(U_1259) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_348_2,plain,
! [U_1262,U_1261] :
( subset(U_1262,union(U_1261))
| ~ in(U_1262,U_1261) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
! [U_1261,U_1262] :
( subset(U_1262,union(U_1261))
| ~ in(U_1262,U_1261) ),
inference(definitional_conversion,[status(esa)],[f_348_2]) ).
cnf(f_348_4,plain,
( subset(U_1262,union(U_1261))
| ~ in(U_1262,U_1261) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_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_349_2,plain,
! [U_1264,U_1263] :
( relation_dom_restriction(U_1263,U_1264) = relation_composition(identity_relation(U_1264),U_1263)
| ~ relation(U_1263) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_1263,U_1264] :
( relation_dom_restriction(U_1263,U_1264) = relation_composition(identity_relation(U_1264),U_1263)
| ~ relation(U_1263) ),
inference(definitional_conversion,[status(esa)],[f_349_2]) ).
cnf(f_349_4,plain,
( relation_dom_restriction(U_1263,U_1264) = relation_composition(identity_relation(U_1264),U_1263)
| ~ relation(U_1263) ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_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_350_2,plain,
! [U_1266,U_1265] :
( subset(relation_rng(relation_dom_restriction(U_1265,U_1266)),relation_rng(U_1265))
| ~ relation(U_1265) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1265,U_1266] :
( subset(relation_rng(relation_dom_restriction(U_1265,U_1266)),relation_rng(U_1265))
| ~ relation(U_1265) ),
inference(definitional_conversion,[status(esa)],[f_350_2]) ).
cnf(f_350_4,plain,
( subset(relation_rng(relation_dom_restriction(U_1265,U_1266)),relation_rng(U_1265))
| ~ relation(U_1265) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_351_2,plain,
! [U_1267] : union(powerset(U_1267)) = U_1267,
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
! [U_1267] : union(powerset(U_1267)) = U_1267,
inference(definitional_conversion,[status(esa)],[f_351_2]) ).
cnf(f_351_4,plain,
union(powerset(U_1267)) = U_1267,
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_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_352_2,plain,
! [U_1275] :
? [U_1274] :
( ! [U_1273] :
( in(U_1273,U_1274)
| are_equipotent(U_1273,U_1274)
| ~ subset(U_1273,U_1274) )
& ! [U_1272] :
( ? [U_1271] :
( ! [U_1270] :
( in(U_1270,U_1271)
| ~ subset(U_1270,U_1272) )
& in(U_1271,U_1274) )
| ~ in(U_1272,U_1274) )
& ! [U_1269,U_1268] :
( in(U_1268,U_1274)
| ~ subset(U_1268,U_1269)
| ~ in(U_1269,U_1274) )
& in(U_1275,U_1274) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
! [U_1275] :
( ! [U_1273] :
( in(U_1273,sK180(U_1275))
| are_equipotent(U_1273,sK180(U_1275))
| ~ subset(U_1273,sK180(U_1275)) )
& ! [U_1272] :
( ? [U_1271] :
( ! [U_1270] :
( in(U_1270,U_1271)
| ~ subset(U_1270,U_1272) )
& in(U_1271,sK180(U_1275)) )
| ~ in(U_1272,sK180(U_1275)) )
& ! [U_1269,U_1268] :
( in(U_1268,sK180(U_1275))
| ~ subset(U_1268,U_1269)
| ~ in(U_1269,sK180(U_1275)) )
& in(U_1275,sK180(U_1275)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_1274,sK180(U_1275))],[f_352_2]) ).
fof(f_352_4,plain,
! [U_1275] :
( ! [U_1273] :
( in(U_1273,sK180(U_1275))
| are_equipotent(U_1273,sK180(U_1275))
| ~ subset(U_1273,sK180(U_1275)) )
& ! [U_1272] :
( ( ! [U_1270] :
( in(U_1270,sK181(U_1275,U_1272))
| ~ subset(U_1270,U_1272) )
& in(sK181(U_1275,U_1272),sK180(U_1275)) )
| ~ in(U_1272,sK180(U_1275)) )
& ! [U_1269,U_1268] :
( in(U_1268,sK180(U_1275))
| ~ subset(U_1268,U_1269)
| ~ in(U_1269,sK180(U_1275)) )
& in(U_1275,sK180(U_1275)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_1271,sK181(U_1275,U_1272))],[f_352_3]) ).
fof(f_352_5,plain,
( ! [U_1270,U_1272,U_1275] :
( in(U_1270,sK181(U_1275,U_1272))
| ~ subset(U_1270,U_1272)
| ~ sP264(U_1270,U_1272,U_1275) )
& ! [U_1270,U_1272,U_1275] :
( in(sK181(U_1275,U_1272),sK180(U_1275))
| ~ sP264(U_1270,U_1272,U_1275) )
& ! [U_1273,U_1275] :
( in(U_1273,sK180(U_1275))
| are_equipotent(U_1273,sK180(U_1275))
| ~ subset(U_1273,sK180(U_1275)) )
& ! [U_1270,U_1272,U_1275] :
( sP264(U_1270,U_1272,U_1275)
| ~ in(U_1272,sK180(U_1275)) )
& ! [U_1269,U_1268,U_1275] :
( in(U_1268,sK180(U_1275))
| ~ subset(U_1268,U_1269)
| ~ in(U_1269,sK180(U_1275)) )
& ! [U_1275] : in(U_1275,sK180(U_1275)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264])],[f_352_4]) ).
cnf(f_352_6,plain,
in(U_1275,sK180(U_1275)),
inference(clausify,[status(thm)],[f_352_5]) ).
cnf(f_352_7,plain,
( in(U_1268,sK180(U_1275))
| ~ subset(U_1268,U_1269)
| ~ in(U_1269,sK180(U_1275)) ),
inference(clausify,[status(thm)],[f_352_5]) ).
cnf(f_352_8,plain,
( sP264(U_1270,U_1272,U_1275)
| ~ in(U_1272,sK180(U_1275)) ),
inference(clausify,[status(thm)],[f_352_5]) ).
cnf(f_352_9,plain,
( in(U_1273,sK180(U_1275))
| are_equipotent(U_1273,sK180(U_1275))
| ~ subset(U_1273,sK180(U_1275)) ),
inference(clausify,[status(thm)],[f_352_5]) ).
cnf(f_352_10,plain,
( in(sK181(U_1275,U_1272),sK180(U_1275))
| ~ sP264(U_1270,U_1272,U_1275) ),
inference(clausify,[status(thm)],[f_352_5]) ).
cnf(f_352_11,plain,
( in(U_1270,sK181(U_1275,U_1272))
| ~ subset(U_1270,U_1272)
| ~ sP264(U_1270,U_1272,U_1275) ),
inference(clausify,[status(thm)],[f_352_5]) ).
fof(f_353_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_353_2,plain,
! [U_1278,U_1277,U_1276] :
( U_1277 = U_1276
| singleton(U_1278) != unordered_pair(U_1277,U_1276) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
! [U_1276,U_1277,U_1278] :
( U_1277 = U_1276
| singleton(U_1278) != unordered_pair(U_1277,U_1276) ),
inference(definitional_conversion,[status(esa)],[f_353_2]) ).
cnf(f_353_4,plain,
( U_1277 = U_1276
| singleton(U_1278) != unordered_pair(U_1277,U_1276) ),
inference(clausify,[status(thm)],[f_353_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_84_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_84_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_88_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_88_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_95_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_95_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_99_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_99_3]) ).
cnf(f_100_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_100_3]) ).
cnf(f_103_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_103_3]) ).
cnf(f_104_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_104_3]) ).
cnf(f_114_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_114_3]) ).
cnf(f_115_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_115_3]) ).
cnf(f_116_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_116_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,
( pair_first(Eq_x_0) = pair_first(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( inclusion_relation(Eq_x_0) = inclusion_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( pair_second(Eq_x_0) = pair_second(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,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_29,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,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_31,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_32,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,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_34,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_35,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( relation_dom_as_subset(Eq_x_0,Eq_x_1,Eq_x_2) = relation_dom_as_subset(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_37,axiom,
( relation_rng_as_subset(Eq_x_0,Eq_x_1,Eq_x_2) = relation_rng_as_subset(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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,axiom,
( sK31(Eq_x_0,Eq_x_1) = sK31(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,
( 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_73,axiom,
( sK33(Eq_x_0) = sK33(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,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_75,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(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,
( 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_77,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_78,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_79,axiom,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK40(Eq_x_0,Eq_x_1) = sK40(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,
( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(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_82,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(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_83,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_84,axiom,
( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK45(Eq_x_0) = sK45(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,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_87,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_88,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_89,axiom,
( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK50(Eq_x_0) = sK50(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,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_92,axiom,
( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK54(Eq_x_0,Eq_x_1) = sK54(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(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,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(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_97,axiom,
( sK57(Eq_x_0,Eq_x_1) = sK57(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK58(Eq_x_0) = sK58(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,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_100,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_101,axiom,
( sK61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK61(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_102,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK62(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_103,axiom,
( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(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,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(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,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(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,
( 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_107,axiom,
( sK67(Eq_x_0) = sK67(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_108,axiom,
( sK68(Eq_x_0) = sK68(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK69(Eq_x_0,Eq_x_1) = sK69(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,
( sK70(Eq_x_0,Eq_x_1) = sK70(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,
( 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_112,axiom,
( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(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_113,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_114,axiom,
( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(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_115,axiom,
( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(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,
( 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_117,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_118,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_119,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_120,axiom,
( sK80(Eq_x_0,Eq_x_1) = sK80(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,
( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_122,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_123,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_124,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_125,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_126,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_127,axiom,
( sK87(Eq_x_0,Eq_x_1,Eq_x_2) = sK87(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_128,axiom,
( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(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_129,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_130,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_131,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_132,axiom,
( sK92(Eq_x_0,Eq_x_1,Eq_x_2) = sK92(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,
( 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_134,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_135,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_136,axiom,
( sK96(Eq_x_0,Eq_x_1) = sK96(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( sK97(Eq_x_0,Eq_x_1) = sK97(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_138,axiom,
( sK98(Eq_x_0,Eq_x_1) = sK98(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK99(Eq_x_0,Eq_x_1) = sK99(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_140,axiom,
( sK100(Eq_x_0,Eq_x_1) = sK100(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_141,axiom,
( sK101(Eq_x_0,Eq_x_1) = sK101(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK102(Eq_x_0,Eq_x_1,Eq_x_2) = sK102(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,
( 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_144,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_145,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_146,axiom,
( sK106(Eq_x_0) = sK106(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK107(Eq_x_0) = sK107(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK108(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_149,axiom,
( sK109(Eq_x_0,Eq_x_1,Eq_x_2) = sK109(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_150,axiom,
( sK110(Eq_x_0,Eq_x_1,Eq_x_2) = sK110(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_151,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_152,axiom,
( sK112(Eq_x_0,Eq_x_1,Eq_x_2) = sK112(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_153,axiom,
( sK113(Eq_x_0,Eq_x_1,Eq_x_2) = sK113(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_154,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_155,axiom,
( sK115(Eq_x_0,Eq_x_1) = sK115(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,axiom,
( sK116(Eq_x_0,Eq_x_1) = sK116(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_157,axiom,
( sK117(Eq_x_0,Eq_x_1,Eq_x_2) = sK117(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_158,axiom,
( sK118(Eq_x_0,Eq_x_1) = sK118(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,
( sK119(Eq_x_0) = sK119(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_160,axiom,
( sK120(Eq_x_0,Eq_x_1) = sK120(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_161,axiom,
( sK121(Eq_x_0) = sK121(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_162,axiom,
( sK122(Eq_x_0) = sK122(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_163,axiom,
( sK123(Eq_x_0) = sK123(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_164,axiom,
( sK124(Eq_x_0) = sK124(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( sK125(Eq_x_0) = sK125(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_166,axiom,
( sK126(Eq_x_0) = sK126(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_167,axiom,
( sK127(Eq_x_0) = sK127(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_168,axiom,
( sK128(Eq_x_0) = sK128(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_169,axiom,
( sK129(Eq_x_0,Eq_x_1) = sK129(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,
( sK133(Eq_x_0) = sK133(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,axiom,
( sK138(Eq_x_0) = sK138(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_172,axiom,
( sK144(Eq_x_0) = sK144(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_173,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_174,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_175,axiom,
( sK147(Eq_x_0,Eq_x_1) = sK147(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,
( 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_177,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_178,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_179,axiom,
( sK151(Eq_x_0,Eq_x_1,Eq_x_2) = sK151(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,
( sK152(Eq_x_0,Eq_x_1,Eq_x_2) = sK152(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_181,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_182,axiom,
( sK154(Eq_x_0,Eq_x_1,Eq_x_2) = sK154(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_183,axiom,
( sK155(Eq_x_0) = sK155(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_184,axiom,
( sK156(Eq_x_0,Eq_x_1,Eq_x_2) = sK156(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_185,axiom,
( sK157(Eq_x_0,Eq_x_1,Eq_x_2) = sK157(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_186,axiom,
( sK158(Eq_x_0,Eq_x_1,Eq_x_2) = sK158(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_187,axiom,
( sK159(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK159(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_188,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_189,axiom,
( sK161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK161(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_190,axiom,
( sK162(Eq_x_0,Eq_x_1) = sK162(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_191,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_192,axiom,
( sK164(Eq_x_0) = sK164(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_193,axiom,
( sK165(Eq_x_0,Eq_x_1) = sK165(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_194,axiom,
( sK166(Eq_x_0,Eq_x_1) = sK166(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_195,axiom,
( sK167(Eq_x_0,Eq_x_1) = sK167(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_196,axiom,
( sK168(Eq_x_0) = sK168(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_197,axiom,
( sK169(Eq_x_0) = sK169(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_198,axiom,
( sK170(Eq_x_0,Eq_x_1) = sK170(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_199,axiom,
( sK171(Eq_x_0,Eq_x_1) = sK171(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_200,axiom,
( sK172(Eq_x_0,Eq_x_1) = sK172(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_201,axiom,
( sK173(Eq_x_0,Eq_x_1) = sK173(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_202,axiom,
( sK174(Eq_x_0,Eq_x_1) = sK174(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_203,axiom,
( sK175(Eq_x_0) = sK175(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_204,axiom,
( sK176(Eq_x_0) = sK176(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_205,axiom,
( sK177(Eq_x_0,Eq_x_1,Eq_x_2) = sK177(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_206,axiom,
( sK178(Eq_x_0,Eq_x_1) = sK178(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_207,axiom,
( sK180(Eq_x_0) = sK180(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_208,axiom,
( sK181(Eq_x_0,Eq_x_1) = sK181(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_209,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_210,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_211,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_212,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_214,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_217,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_218,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_219,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_220,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_221,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,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_223,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_224,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_225,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_226,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_227,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_228,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_229,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_230,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_231,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_232,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_233,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_234,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_235,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_236,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_237,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_238,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_239,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_240,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_241,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_242,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,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_253,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_254,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_255,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_256,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_257,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_258,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_259,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_260,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_261,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_262,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_263,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_264,axiom,
( sP24(Eq_y_0)
| ~ sP24(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,axiom,
( sP40(Eq_y_0)
| ~ sP40(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_281,axiom,
( sP41(Eq_y_0)
| ~ sP41(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_282,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_283,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_284,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_285,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_286,axiom,
( sP46(Eq_y_0,Eq_y_1)
| ~ sP46(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_287,axiom,
( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP47(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_288,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP48(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_289,axiom,
( sP49(Eq_y_0,Eq_y_1)
| ~ sP49(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_290,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP50(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_291,axiom,
( sP51(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP51(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_292,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP52(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_293,axiom,
( sP53(Eq_y_0,Eq_y_1)
| ~ sP53(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_294,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_295,axiom,
( sP55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP55(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_296,axiom,
( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP56(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,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP57(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_298,axiom,
( sP58(Eq_y_0,Eq_y_1)
| ~ sP58(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_299,axiom,
( sP59(Eq_y_0,Eq_y_1)
| ~ sP59(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_300,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_301,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP61(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_302,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP62(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_303,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP63(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_304,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP64(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_305,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP65(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_306,axiom,
( sP66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP66(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_307,axiom,
( sP67(Eq_y_0,Eq_y_1)
| ~ sP67(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_308,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_309,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_310,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP70(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_311,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP71(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_312,axiom,
( sP72(Eq_y_0,Eq_y_1)
| ~ sP72(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_313,axiom,
( sP73(Eq_y_0,Eq_y_1)
| ~ sP73(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_314,axiom,
( sP74(Eq_y_0,Eq_y_1)
| ~ sP74(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_315,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP75(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_316,axiom,
( sP76(Eq_y_0)
| ~ sP76(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_317,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP77(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_318,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_319,axiom,
( sP79(Eq_y_0,Eq_y_1)
| ~ sP79(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,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP80(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_321,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP81(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_322,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_323,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_324,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP84(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,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP85(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,
( sP86(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP86(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_327,axiom,
( sP87(Eq_y_0,Eq_y_1)
| ~ sP87(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_328,axiom,
( sP88(Eq_y_0,Eq_y_1)
| ~ sP88(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_329,axiom,
( sP89(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP89(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,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP90(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_331,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP91(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_332,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_333,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_334,axiom,
( sP94(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP94(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_335,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP95(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_336,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_337,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_338,axiom,
( sP98(Eq_y_0)
| ~ sP98(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_339,axiom,
( sP99(Eq_y_0,Eq_y_1)
| ~ sP99(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_340,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_341,axiom,
( sP101(Eq_y_0,Eq_y_1)
| ~ sP101(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_342,axiom,
( sP102(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP102(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_343,axiom,
( sP103(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP103(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,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP104(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_345,axiom,
( sP105(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP105(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_346,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP106(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_347,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP107(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_348,axiom,
( sP108(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP108(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_349,axiom,
( sP109(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP109(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_350,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP110(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_351,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP111(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,
( sP112(Eq_y_0)
| ~ sP112(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_353,axiom,
( sP113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP113(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_354,axiom,
( sP114(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP114(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_355,axiom,
( sP115(Eq_y_0,Eq_y_1)
| ~ sP115(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_356,axiom,
( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP116(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_357,axiom,
( sP117(Eq_y_0,Eq_y_1)
| ~ sP117(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_358,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP118(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_359,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_360,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_361,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_362,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_363,axiom,
( sP123(Eq_y_0)
| ~ sP123(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_364,axiom,
( sP124(Eq_y_0)
| ~ sP124(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_365,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_366,axiom,
( sP126(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP126(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_367,axiom,
( sP127(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP127(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,
( sP128(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP128(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_369,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_370,axiom,
( sP130(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP130(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_371,axiom,
( sP131(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP131(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_372,axiom,
( sP132(Eq_y_0,Eq_y_1)
| ~ sP132(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,
( sP133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP133(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_374,axiom,
( sP134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP134(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_375,axiom,
( sP135(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP135(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_376,axiom,
( sP136(Eq_y_0,Eq_y_1)
| ~ sP136(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_377,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_378,axiom,
( sP138(Eq_y_0,Eq_y_1)
| ~ sP138(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_379,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_380,axiom,
( sP140(Eq_y_0,Eq_y_1)
| ~ sP140(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,
( sP141(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP141(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_382,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP142(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_383,axiom,
( sP143(Eq_y_0,Eq_y_1)
| ~ sP143(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,
( sP144(Eq_y_0,Eq_y_1)
| ~ sP144(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_385,axiom,
( sP145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP145(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_386,axiom,
( sP146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP146(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_387,axiom,
( sP147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP147(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_388,axiom,
( sP148(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP148(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_389,axiom,
( sP149(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP149(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,
( sP150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP150(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_391,axiom,
( sP151(Eq_y_0)
| ~ sP151(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_392,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_393,axiom,
( sP153(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP153(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_394,axiom,
( sP154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP154(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_395,axiom,
( sP155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP155(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_396,axiom,
( sP156(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP156(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,
( sP157(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)
| ~ sP157(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_398,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_399,axiom,
( sP159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP159(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_400,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP160(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_401,axiom,
( sP161(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP161(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,
( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP162(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_403,axiom,
( sP163(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP163(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,
( sP164(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP164(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_405,axiom,
( sP165(Eq_y_0,Eq_y_1)
| ~ sP165(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_406,axiom,
( sP166(Eq_y_0)
| ~ sP166(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_407,axiom,
( sP167(Eq_y_0)
| ~ sP167(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_408,axiom,
( sP168(Eq_y_0,Eq_y_1)
| ~ sP168(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_409,axiom,
( sP169(Eq_y_0)
| ~ sP169(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_410,axiom,
( sP170(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP170(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,
( 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_412,axiom,
( sP172(Eq_y_0)
| ~ sP172(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_413,axiom,
( sP173(Eq_y_0)
| ~ sP173(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_414,axiom,
( sP174(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP174(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,
( sP175(Eq_y_0)
| ~ sP175(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_416,axiom,
( sP176(Eq_y_0,Eq_y_1)
| ~ sP176(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,
( sP177(Eq_y_0)
| ~ sP177(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_418,axiom,
( sP178(Eq_y_0)
| ~ sP178(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_419,axiom,
( sP179(Eq_y_0,Eq_y_1)
| ~ sP179(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_420,axiom,
( sP180(Eq_y_0)
| ~ sP180(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_421,axiom,
( sP181(Eq_y_0,Eq_y_1)
| ~ sP181(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,
( sP182(Eq_y_0)
| ~ sP182(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_423,axiom,
( sP183(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP183(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_424,axiom,
( sP184(Eq_y_0)
| ~ sP184(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_425,axiom,
( sP185(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP185(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,
( sP186(Eq_y_0)
| ~ sP186(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_427,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_428,axiom,
( sP188(Eq_y_0,Eq_y_1)
| ~ sP188(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,
( sP189(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP189(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_430,axiom,
( sP190(Eq_y_0,Eq_y_1)
| ~ sP190(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_431,axiom,
( sP191(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP191(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_432,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_433,axiom,
( sP193(Eq_y_0)
| ~ sP193(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_434,axiom,
( sP194(Eq_y_0,Eq_y_1)
| ~ sP194(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_435,axiom,
( sP195(Eq_y_0,Eq_y_1)
| ~ sP195(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,
( sP196(Eq_y_0,Eq_y_1)
| ~ sP196(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_437,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_438,axiom,
( sP198(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP198(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,
( 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_440,axiom,
( sP200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP200(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_441,axiom,
( sP201(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP201(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_442,axiom,
( sP202(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP202(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_443,axiom,
( sP203(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP203(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_444,axiom,
( sP204(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP204(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_445,axiom,
( sP205(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP205(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_446,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_447,axiom,
( sP207(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP207(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,
( sP208(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP208(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,
( sP209(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP209(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,
( sP210(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP210(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_451,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_452,axiom,
( sP212(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP212(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,
( 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_454,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_455,axiom,
( sP215(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP215(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,
( sP216(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP216(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,
( sP217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP217(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_458,axiom,
( sP218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP218(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_459,axiom,
( sP219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP219(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_460,axiom,
( sP220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP220(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_461,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_462,axiom,
( sP222(Eq_y_0,Eq_y_1)
| ~ sP222(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_463,axiom,
( sP223(Eq_y_0,Eq_y_1)
| ~ sP223(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_464,axiom,
( sP224(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP224(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_465,axiom,
( sP225(Eq_y_0)
| ~ sP225(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_466,axiom,
( sP226(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP226(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_467,axiom,
( sP227(Eq_y_0,Eq_y_1)
| ~ sP227(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_468,axiom,
( sP228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP228(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_469,axiom,
( sP229(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP229(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_470,axiom,
( sP230(Eq_y_0,Eq_y_1)
| ~ sP230(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_471,axiom,
( sP231(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP231(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_472,axiom,
( sP232(Eq_y_0)
| ~ sP232(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_473,axiom,
( sP233(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP233(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_474,axiom,
( sP234(Eq_y_0,Eq_y_1)
| ~ sP234(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_475,axiom,
( sP235(Eq_y_0,Eq_y_1)
| ~ sP235(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_476,axiom,
( sP236(Eq_y_0)
| ~ sP236(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_477,axiom,
( sP237(Eq_y_0,Eq_y_1)
| ~ sP237(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_478,axiom,
( sP238(Eq_y_0)
| ~ sP238(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_479,axiom,
( sP239(Eq_y_0,Eq_y_1)
| ~ sP239(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_480,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_481,axiom,
( sP241(Eq_y_0,Eq_y_1)
| ~ sP241(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_482,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_483,axiom,
( sP243(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP243(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_484,axiom,
( sP244(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP244(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_485,axiom,
( sP245(Eq_y_0,Eq_y_1)
| ~ sP245(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_486,axiom,
( sP246(Eq_y_0,Eq_y_1)
| ~ sP246(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_487,axiom,
( sP247(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP247(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_488,axiom,
( sP248(Eq_y_0)
| ~ sP248(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_489,axiom,
( sP249(Eq_y_0,Eq_y_1)
| ~ sP249(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_490,axiom,
( sP250(Eq_y_0)
| ~ sP250(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_491,axiom,
( sP251(Eq_y_0)
| ~ sP251(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_492,axiom,
( sP252(Eq_y_0)
| ~ sP252(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_493,axiom,
( sP253(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP253(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_494,axiom,
( sP254(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP254(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_495,axiom,
( sP255(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP255(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_496,axiom,
( sP256(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP256(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_497,axiom,
( sP257(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP257(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_498,axiom,
( sP258(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP258(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_499,axiom,
( sP259(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP259(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_500,axiom,
( sP260(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP260(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_501,axiom,
( sP261(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP261(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_502,axiom,
( sP262(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP262(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_503,axiom,
( sP263(Eq_y_0)
| ~ sP263(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_504,axiom,
( sP264(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP264(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 : SEU275+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 19 23:49:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 39.56/39.80 % SZS status Theorem for theBenchmark
% 39.56/39.80 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------