%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU268+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 : n012.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 08:58:47 AM UTC 2026
% Result : Theorem 282.03s 282.58s
% Output : Proof 282.28s
% 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(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,conjecture,
! [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_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t41_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('theBenchmark.p',t41_ordinal1) ).
fof(t42_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('theBenchmark.p',t42_ordinal1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t49_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> relation_isomorphism(B,A,function_inverse(C)) ) ) ) ),
file('theBenchmark.p',t49_wellord1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t53_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( well_founded_relation(A)
=> well_founded_relation(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( connected(A)
=> connected(B) )
& ( transitive(A)
=> transitive(B) )
& ( reflexive(A)
=> reflexive(B) ) ) ) ) ) ),
file('theBenchmark.p',t53_wellord1) ).
fof(t54_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t54_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('theBenchmark.p',t54_wellord1) ).
fof(t55_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t57_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t62_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t68_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t70_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t72_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_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_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]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
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]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
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]) ).
cnf(f_3_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
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]) ).
cnf(f_4_3,plain,
( epsilon_transitive(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( epsilon_connected(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
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]) ).
cnf(f_5_3,plain,
( relation(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
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]) ).
cnf(f_6_3,plain,
( relation(U_7)
| ~ element(U_7,powerset(cartesian_product2(U_9,U_8))) ),
inference(clausify,[status(thm)],[f_6_2]) ).
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]) ).
cnf(f_7_3,plain,
( relation(U_10)
| ~ function(U_10)
| ~ empty(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( function(U_10)
| ~ function(U_10)
| ~ empty(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( one_to_one(U_10)
| ~ function(U_10)
| ~ empty(U_10)
| ~ relation(U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
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]) ).
cnf(f_8_3,plain,
( ordinal(U_11)
| ~ epsilon_connected(U_11)
| ~ epsilon_transitive(U_11) ),
inference(clausify,[status(thm)],[f_8_2]) ).
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]) ).
cnf(f_9_3,plain,
( epsilon_transitive(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( epsilon_connected(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_5,plain,
( ordinal(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
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]) ).
cnf(f_10_3,plain,
unordered_pair(U_14,U_13) = unordered_pair(U_13,U_14),
inference(clausify,[status(thm)],[f_10_2]) ).
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]) ).
cnf(f_11_3,plain,
set_union2(U_16,U_15) = set_union2(U_15,U_16),
inference(clausify,[status(thm)],[f_11_2]) ).
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]) ).
cnf(f_12_3,plain,
set_intersection2(U_18,U_17) = set_intersection2(U_17,U_18),
inference(clausify,[status(thm)],[f_12_2]) ).
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]) ).
cnf(f_13_3,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_2]) ).
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]) ).
cnf(f_14_8,plain,
( in(U_29,U_26)
| ~ in(ordered_pair(U_29,U_27),U_25)
| U_25 != identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_9,plain,
( U_29 = U_27
| ~ in(ordered_pair(U_29,U_27),U_25)
| U_25 != identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_10,plain,
( in(ordered_pair(U_30,U_28),U_25)
| U_30 != U_28
| ~ in(U_30,U_26)
| U_25 != identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_11,plain,
( in(sK3(U_26,U_25),U_26)
| in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25)
| U_25 = identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_12,plain,
( sK3(U_26,U_25) = sK4(U_26,U_25)
| in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25)
| U_25 = identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_13,plain,
( ~ in(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_25)
| in(ordered_pair(sK1(U_26,U_25),sK2(U_26,U_25)),U_25)
| U_25 = identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_14,plain,
( 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)
| U_25 = identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_15,plain,
( sK3(U_26,U_25) = sK4(U_26,U_25)
| sK1(U_26,U_25) != sK2(U_26,U_25)
| ~ in(sK1(U_26,U_25),U_26)
| U_25 = identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
cnf(f_14_16,plain,
( ~ in(ordered_pair(sK3(U_26,U_25),sK4(U_26,U_25)),U_25)
| sK1(U_26,U_25) != sK2(U_26,U_25)
| ~ in(sK1(U_26,U_25),U_26)
| U_25 = identity_relation(U_26)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_14_7]) ).
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]) ).
cnf(f_15_4,plain,
( subset(U_39,U_37)
| U_39 != U_37 ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( subset(U_37,U_39)
| U_39 != U_37 ),
inference(clausify,[status(thm)],[f_15_3]) ).
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_3]) ).
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]) ).
cnf(f_16_8,plain,
( 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(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,plain,
( in(ordered_pair(U_50,U_48),U_47)
| ~ 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(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,plain,
( in(ordered_pair(U_51,U_49),U_45)
| ~ in(ordered_pair(U_51,U_49),U_47)
| ~ in(U_51,U_46)
| U_45 != relation_dom_restriction(U_47,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_11,plain,
( 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_45)
| U_45 = relation_dom_restriction(U_47,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_12,plain,
( in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_47)
| in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45)
| U_45 = relation_dom_restriction(U_47,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_13,plain,
( ~ in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_45)
| in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_45)
| U_45 = relation_dom_restriction(U_47,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_14,plain,
( 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)
| U_45 = relation_dom_restriction(U_47,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_15,plain,
( in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_47)
| ~ in(ordered_pair(sK5(U_47,U_46,U_45),sK6(U_47,U_46,U_45)),U_47)
| ~ in(sK5(U_47,U_46,U_45),U_46)
| U_45 = relation_dom_restriction(U_47,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_16,plain,
( ~ in(ordered_pair(sK7(U_47,U_46,U_45),sK8(U_47,U_46,U_45)),U_45)
| ~ 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)
| U_45 = relation_dom_restriction(U_47,U_46)
| ~ relation(U_45)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_16_7]) ).
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]) ).
cnf(f_17_8,plain,
( 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(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_9,plain,
( in(sK9(U_64,U_71,U_69,U_65),U_71)
| ~ in(U_65,U_69)
| U_69 != relation_image(U_64,U_71)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_10,plain,
( U_65 = apply(U_64,sK9(U_64,U_71,U_69,U_65))
| ~ in(U_65,U_69)
| U_69 != relation_image(U_64,U_71)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_11,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))
| U_69 != relation_image(U_64,U_71)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_12,plain,
( in(sK12(U_64,U_72,U_70),relation_dom(U_64))
| in(sK10(U_64,U_72,U_70),U_70)
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_13,plain,
( in(sK12(U_64,U_72,U_70),U_72)
| in(sK10(U_64,U_72,U_70),U_70)
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_14,plain,
( sK11(U_64,U_72,U_70) = apply(U_64,sK12(U_64,U_72,U_70))
| in(sK10(U_64,U_72,U_70),U_70)
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_15,plain,
( ~ in(sK11(U_64,U_72,U_70),U_70)
| in(sK10(U_64,U_72,U_70),U_70)
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_16,plain,
( in(sK12(U_64,U_72,U_70),relation_dom(U_64))
| sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64))
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_17,plain,
( in(sK12(U_64,U_72,U_70),U_72)
| sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64))
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_18,plain,
( sK11(U_64,U_72,U_70) = apply(U_64,sK12(U_64,U_72,U_70))
| sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64))
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
cnf(f_17_19,plain,
( ~ in(sK11(U_64,U_72,U_70),U_70)
| sK10(U_64,U_72,U_70) != apply(U_64,U_59)
| ~ in(U_59,U_72)
| ~ in(U_59,relation_dom(U_64))
| U_70 = relation_image(U_64,U_72)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_17_7]) ).
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]) ).
cnf(f_18_8,plain,
( 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(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_9,plain,
( in(ordered_pair(U_82,U_80),U_78)
| ~ 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(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_10,plain,
( in(ordered_pair(U_83,U_81),U_77)
| ~ in(ordered_pair(U_83,U_81),U_78)
| ~ in(U_81,U_79)
| U_77 != relation_rng_restriction(U_79,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_11,plain,
( 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_77)
| U_77 = relation_rng_restriction(U_79,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_12,plain,
( in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_78)
| in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77)
| U_77 = relation_rng_restriction(U_79,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_13,plain,
( ~ in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_77)
| in(ordered_pair(sK13(U_79,U_78,U_77),sK14(U_79,U_78,U_77)),U_77)
| U_77 = relation_rng_restriction(U_79,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_14,plain,
( 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)
| U_77 = relation_rng_restriction(U_79,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_15,plain,
( in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,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)
| U_77 = relation_rng_restriction(U_79,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_7]) ).
cnf(f_18_16,plain,
( ~ in(ordered_pair(sK15(U_79,U_78,U_77),sK16(U_79,U_78,U_77)),U_77)
| ~ 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)
| U_77 = relation_rng_restriction(U_79,U_78)
| ~ relation(U_77)
| ~ relation(U_78) ),
inference(clausify,[status(thm)],[f_18_7]) ).
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]) ).
cnf(f_19_3,plain,
( is_antisymmetric_in(U_88,relation_field(U_88))
| ~ antisymmetric(U_88)
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( antisymmetric(U_88)
| ~ is_antisymmetric_in(U_88,relation_field(U_88))
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_19_2]) ).
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]) ).
cnf(f_20_6,plain,
( 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(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_7,plain,
( in(apply(U_93,U_94),U_100)
| ~ in(U_94,U_98)
| U_98 != relation_inverse_image(U_93,U_100)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_8,plain,
( in(U_95,U_98)
| ~ in(apply(U_93,U_95),U_100)
| ~ in(U_95,relation_dom(U_93))
| U_98 != relation_inverse_image(U_93,U_100)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_9,plain,
( in(sK18(U_93,U_101,U_99),relation_dom(U_93))
| in(sK17(U_93,U_101,U_99),U_99)
| U_99 = relation_inverse_image(U_93,U_101)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_10,plain,
( in(apply(U_93,sK18(U_93,U_101,U_99)),U_101)
| in(sK17(U_93,U_101,U_99),U_99)
| U_99 = relation_inverse_image(U_93,U_101)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_11,plain,
( ~ in(sK18(U_93,U_101,U_99),U_99)
| in(sK17(U_93,U_101,U_99),U_99)
| U_99 = relation_inverse_image(U_93,U_101)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_12,plain,
( 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))
| U_99 = relation_inverse_image(U_93,U_101)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_13,plain,
( in(apply(U_93,sK18(U_93,U_101,U_99)),U_101)
| ~ 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))
| U_99 = relation_inverse_image(U_93,U_101)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
cnf(f_20_14,plain,
( ~ in(sK18(U_93,U_101,U_99),U_99)
| ~ 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))
| U_99 = relation_inverse_image(U_93,U_101)
| ~ function(U_93)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_20_5]) ).
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]) ).
cnf(f_21_8,plain,
( 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(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_9,plain,
( in(sK19(U_110,U_117,U_115,U_111),U_117)
| ~ in(U_111,U_115)
| U_115 != relation_image(U_110,U_117)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_10,plain,
( in(U_112,U_115)
| ~ in(U_103,U_117)
| ~ in(ordered_pair(U_103,U_112),U_110)
| U_115 != relation_image(U_110,U_117)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_11,plain,
( in(ordered_pair(sK22(U_110,U_118,U_116),sK21(U_110,U_118,U_116)),U_110)
| in(sK20(U_110,U_118,U_116),U_116)
| U_116 = relation_image(U_110,U_118)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_12,plain,
( in(sK22(U_110,U_118,U_116),U_118)
| in(sK20(U_110,U_118,U_116),U_116)
| U_116 = relation_image(U_110,U_118)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_13,plain,
( ~ in(sK21(U_110,U_118,U_116),U_116)
| in(sK20(U_110,U_118,U_116),U_116)
| U_116 = relation_image(U_110,U_118)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_14,plain,
( in(ordered_pair(sK22(U_110,U_118,U_116),sK21(U_110,U_118,U_116)),U_110)
| ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110)
| U_116 = relation_image(U_110,U_118)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_15,plain,
( in(sK22(U_110,U_118,U_116),U_118)
| ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110)
| U_116 = relation_image(U_110,U_118)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_16,plain,
( ~ in(sK21(U_110,U_118,U_116),U_116)
| ~ in(U_105,U_118)
| ~ in(ordered_pair(U_105,sK20(U_110,U_118,U_116)),U_110)
| U_116 = relation_image(U_110,U_118)
| ~ relation(U_110) ),
inference(clausify,[status(thm)],[f_21_7]) ).
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]) ).
cnf(f_22_8,plain,
( 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(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_9,plain,
( in(sK23(U_127,U_134,U_132,U_128),U_134)
| ~ in(U_128,U_132)
| U_132 != relation_inverse_image(U_127,U_134)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_10,plain,
( in(U_129,U_132)
| ~ in(U_120,U_134)
| ~ in(ordered_pair(U_129,U_120),U_127)
| U_132 != relation_inverse_image(U_127,U_134)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_11,plain,
( in(ordered_pair(sK25(U_127,U_135,U_133),sK26(U_127,U_135,U_133)),U_127)
| in(sK24(U_127,U_135,U_133),U_133)
| U_133 = relation_inverse_image(U_127,U_135)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_12,plain,
( in(sK26(U_127,U_135,U_133),U_135)
| in(sK24(U_127,U_135,U_133),U_133)
| U_133 = relation_inverse_image(U_127,U_135)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_13,plain,
( ~ in(sK25(U_127,U_135,U_133),U_133)
| in(sK24(U_127,U_135,U_133),U_133)
| U_133 = relation_inverse_image(U_127,U_135)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_14,plain,
( in(ordered_pair(sK25(U_127,U_135,U_133),sK26(U_127,U_135,U_133)),U_127)
| ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127)
| U_133 = relation_inverse_image(U_127,U_135)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_15,plain,
( in(sK26(U_127,U_135,U_133),U_135)
| ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127)
| U_133 = relation_inverse_image(U_127,U_135)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
cnf(f_22_16,plain,
( ~ in(sK25(U_127,U_135,U_133),U_133)
| ~ in(U_122,U_135)
| ~ in(ordered_pair(sK24(U_127,U_135,U_133),U_122),U_127)
| U_133 = relation_inverse_image(U_127,U_135)
| ~ relation(U_127) ),
inference(clausify,[status(thm)],[f_22_7]) ).
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]) ).
cnf(f_23_3,plain,
( is_connected_in(U_136,relation_field(U_136))
| ~ connected(U_136)
| ~ relation(U_136) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( connected(U_136)
| ~ is_connected_in(U_136,relation_field(U_136))
| ~ relation(U_136) ),
inference(clausify,[status(thm)],[f_23_2]) ).
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]) ).
cnf(f_24_3,plain,
( is_transitive_in(U_137,relation_field(U_137))
| ~ transitive(U_137)
| ~ relation(U_137) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( transitive(U_137)
| ~ is_transitive_in(U_137,relation_field(U_137))
| ~ relation(U_137) ),
inference(clausify,[status(thm)],[f_24_2]) ).
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]) ).
cnf(f_25_6,plain,
( 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(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_7,plain,
( U_145 != U_154
| in(U_145,U_148)
| U_148 != unordered_triple(U_154,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_8,plain,
( U_145 != U_152
| in(U_145,U_148)
| U_148 != unordered_triple(U_154,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_9,plain,
( U_145 != U_150
| in(U_145,U_148)
| U_148 != unordered_triple(U_154,U_152,U_150) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_10,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
| in(sK27(U_155,U_153,U_151,U_149),U_149)
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_11,plain,
( ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
| in(sK27(U_155,U_153,U_151,U_149),U_149)
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_12,plain,
( sK27(U_155,U_153,U_151,U_149) != U_155
| sK28(U_155,U_153,U_151,U_149) = U_151
| sK28(U_155,U_153,U_151,U_149) = U_153
| sK28(U_155,U_153,U_151,U_149) = U_155
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_13,plain,
( sK27(U_155,U_153,U_151,U_149) != U_153
| 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
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_14,plain,
( sK27(U_155,U_153,U_151,U_149) != 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
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_15,plain,
( sK27(U_155,U_153,U_151,U_149) != U_155
| ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_16,plain,
( sK27(U_155,U_153,U_151,U_149) != U_153
| ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_17,plain,
( sK27(U_155,U_153,U_151,U_149) != U_151
| ~ in(sK28(U_155,U_153,U_151,U_149),U_149)
| U_149 = unordered_triple(U_155,U_153,U_151) ),
inference(clausify,[status(thm)],[f_25_5]) ).
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]) ).
cnf(f_26_6,plain,
( U_163 != ordered_pair(U_159,U_158)
| U_164 = U_159
| U_164 != pair_first(U_163)
| U_163 != ordered_pair(U_157,U_156) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_7,plain,
( U_165 != sK29(U_163,U_165)
| U_165 = pair_first(U_163)
| U_163 != ordered_pair(U_157,U_156) ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_8,plain,
( U_163 = ordered_pair(sK29(U_163,U_165),sK30(U_163,U_165))
| U_165 = pair_first(U_163)
| U_163 != ordered_pair(U_157,U_156) ),
inference(clausify,[status(thm)],[f_26_5]) ).
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]) ).
cnf(f_27_3,plain,
succ(U_166) = set_union2(U_166,singleton(U_166)),
inference(clausify,[status(thm)],[f_27_2]) ).
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]) ).
cnf(f_28_7,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_6]) ).
cnf(f_28_8,plain,
( in(sK33(U_175),U_175)
| relation(U_175) ),
inference(clausify,[status(thm)],[f_28_6]) ).
cnf(f_28_9,plain,
( sK33(U_175) != ordered_pair(U_171,U_170)
| relation(U_175) ),
inference(clausify,[status(thm)],[f_28_6]) ).
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]) ).
cnf(f_29_5,plain,
( 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(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( in(sK34(U_179,U_181),U_181)
| is_reflexive_in(U_179,U_181)
| ~ relation(U_179) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_7,plain,
( ~ in(ordered_pair(sK34(U_179,U_181),sK34(U_179,U_181)),U_179)
| is_reflexive_in(U_179,U_181)
| ~ relation(U_179) ),
inference(clausify,[status(thm)],[f_29_4]) ).
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]) ).
cnf(f_30_4,plain,
( subset(U_185,cartesian_product2(U_189,U_187))
| ~ relation_of2(U_185,U_189,U_187) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( relation_of2(U_186,U_190,U_188)
| ~ subset(U_186,cartesian_product2(U_190,U_188)) ),
inference(clausify,[status(thm)],[f_30_3]) ).
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]) ).
cnf(f_31_8,plain,
( 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(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_9,plain,
( in(sK35(U_209,U_205,U_200),U_209)
| in(U_200,U_205)
| U_205 != set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_10,plain,
( ~ in(U_200,sK35(U_209,U_205,U_200))
| in(U_200,U_205)
| U_205 != set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_11,plain,
( in(sK38(U_209,U_206),U_195)
| ~ in(U_195,U_209)
| in(sK36(U_209,U_206),U_206)
| U_206 = set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_12,plain,
( ~ in(sK38(U_209,U_206),U_206)
| in(sK36(U_209,U_206),U_206)
| U_206 = set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_13,plain,
( in(sK37(U_209,U_206),U_209)
| in(sK38(U_209,U_206),U_195)
| ~ in(U_195,U_209)
| U_206 = set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_14,plain,
( ~ in(sK36(U_209,U_206),sK37(U_209,U_206))
| in(sK38(U_209,U_206),U_195)
| ~ in(U_195,U_209)
| U_206 = set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_15,plain,
( in(sK37(U_209,U_206),U_209)
| ~ in(sK38(U_209,U_206),U_206)
| U_206 = set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_16,plain,
( ~ in(sK36(U_209,U_206),sK37(U_209,U_206))
| ~ in(sK38(U_209,U_206),U_206)
| U_206 = set_meet(U_209)
| U_209 = empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_17,plain,
( U_207 = empty_set
| U_207 != set_meet(U_210)
| U_210 != empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
cnf(f_31_18,plain,
( U_208 = set_meet(U_210)
| U_208 != empty_set
| U_210 != empty_set ),
inference(clausify,[status(thm)],[f_31_7]) ).
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]) ).
cnf(f_32_6,plain,
( U_215 = U_221
| ~ in(U_215,U_219)
| U_219 != singleton(U_221) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( in(U_216,U_219)
| U_216 != U_221
| U_219 != singleton(U_221) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( sK40(U_222,U_220) = U_222
| in(sK39(U_222,U_220),U_220)
| U_220 = singleton(U_222) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( ~ in(sK40(U_222,U_220),U_220)
| in(sK39(U_222,U_220),U_220)
| U_220 = singleton(U_222) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_10,plain,
( sK40(U_222,U_220) = U_222
| sK39(U_222,U_220) != U_222
| U_220 = singleton(U_222) ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_11,plain,
( ~ in(sK40(U_222,U_220),U_220)
| sK39(U_222,U_220) != U_222
| U_220 = singleton(U_222) ),
inference(clausify,[status(thm)],[f_32_5]) ).
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]) ).
cnf(f_33_6,plain,
( U_228 != U_234
| ~ in(U_228,U_232)
| U_232 != fiber(U_227,U_234)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,plain,
( in(ordered_pair(U_228,U_234),U_227)
| ~ in(U_228,U_232)
| U_232 != fiber(U_227,U_234)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_8,plain,
( in(U_229,U_232)
| ~ in(ordered_pair(U_229,U_234),U_227)
| U_229 = U_234
| U_232 != fiber(U_227,U_234)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_9,plain,
( sK42(U_227,U_235,U_233) != U_235
| in(sK41(U_227,U_235,U_233),U_233)
| U_233 = fiber(U_227,U_235)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_10,plain,
( in(ordered_pair(sK42(U_227,U_235,U_233),U_235),U_227)
| in(sK41(U_227,U_235,U_233),U_233)
| U_233 = fiber(U_227,U_235)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_11,plain,
( ~ in(sK42(U_227,U_235,U_233),U_233)
| in(sK41(U_227,U_235,U_233),U_233)
| U_233 = fiber(U_227,U_235)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_12,plain,
( 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
| U_233 = fiber(U_227,U_235)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_13,plain,
( in(ordered_pair(sK42(U_227,U_235,U_233),U_235),U_227)
| ~ in(ordered_pair(sK41(U_227,U_235,U_233),U_235),U_227)
| sK41(U_227,U_235,U_233) = U_235
| U_233 = fiber(U_227,U_235)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_14,plain,
( ~ in(sK42(U_227,U_235,U_233),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
| U_233 = fiber(U_227,U_235)
| ~ relation(U_227) ),
inference(clausify,[status(thm)],[f_33_5]) ).
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]) ).
cnf(f_34_5,plain,
( relation_field(U_240) = U_241
| U_240 != inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
( subset(U_237,U_236)
| ~ in(ordered_pair(U_237,U_236),U_240)
| ~ in(U_236,U_241)
| ~ in(U_237,U_241)
| U_240 != inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,plain,
( in(ordered_pair(U_237,U_236),U_240)
| ~ subset(U_237,U_236)
| ~ in(U_236,U_241)
| ~ in(U_237,U_241)
| U_240 != inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_8,plain,
( in(sK43(U_241,U_240),U_241)
| relation_field(U_240) != U_241
| U_240 = inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_9,plain,
( in(sK44(U_241,U_240),U_241)
| relation_field(U_240) != U_241
| U_240 = inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_10,plain,
( 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)
| relation_field(U_240) != U_241
| U_240 = inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_11,plain,
( ~ in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240)
| in(ordered_pair(sK43(U_241,U_240),sK44(U_241,U_240)),U_240)
| relation_field(U_240) != U_241
| U_240 = inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_12,plain,
( subset(sK43(U_241,U_240),sK44(U_241,U_240))
| ~ subset(sK43(U_241,U_240),sK44(U_241,U_240))
| relation_field(U_240) != U_241
| U_240 = inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_13,plain,
( ~ 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))
| relation_field(U_240) != U_241
| U_240 = inclusion_relation(U_241)
| ~ relation(U_240) ),
inference(clausify,[status(thm)],[f_34_4]) ).
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]) ).
cnf(f_35_5,plain,
( ~ in(U_242,U_245)
| U_245 != empty_set ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( U_246 = empty_set
| in(sK45(U_246),U_246) ),
inference(clausify,[status(thm)],[f_35_4]) ).
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]) ).
cnf(f_36_6,plain,
( subset(U_251,U_257)
| ~ in(U_251,U_255)
| U_255 != powerset(U_257) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_7,plain,
( in(U_252,U_255)
| ~ subset(U_252,U_257)
| U_255 != powerset(U_257) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_8,plain,
( subset(sK47(U_258,U_256),U_258)
| in(sK46(U_258,U_256),U_256)
| U_256 = powerset(U_258) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_9,plain,
( ~ in(sK47(U_258,U_256),U_256)
| in(sK46(U_258,U_256),U_256)
| U_256 = powerset(U_258) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_10,plain,
( subset(sK47(U_258,U_256),U_258)
| ~ subset(sK46(U_258,U_256),U_258)
| U_256 = powerset(U_258) ),
inference(clausify,[status(thm)],[f_36_5]) ).
cnf(f_36_11,plain,
( ~ in(sK47(U_258,U_256),U_256)
| ~ subset(sK46(U_258,U_256),U_258)
| U_256 = powerset(U_258) ),
inference(clausify,[status(thm)],[f_36_5]) ).
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]) ).
cnf(f_37_6,plain,
( U_267 = U_261
| U_266 != ordered_pair(U_262,U_261)
| U_267 != pair_second(U_266)
| U_266 != ordered_pair(U_260,U_259) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_7,plain,
( U_266 = ordered_pair(sK48(U_266,U_268),sK49(U_266,U_268))
| U_268 = pair_second(U_266)
| U_266 != ordered_pair(U_260,U_259) ),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(f_37_8,plain,
( U_268 != sK49(U_266,U_268)
| U_268 = pair_second(U_266)
| U_266 != ordered_pair(U_260,U_259) ),
inference(clausify,[status(thm)],[f_37_5]) ).
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]) ).
cnf(f_38_5,plain,
( subset(U_269,U_272)
| ~ in(U_269,U_272)
| ~ epsilon_transitive(U_272) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( in(sK50(U_273),U_273)
| epsilon_transitive(U_273) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
( ~ subset(sK50(U_273),U_273)
| epsilon_transitive(U_273) ),
inference(clausify,[status(thm)],[f_38_4]) ).
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]) ).
cnf(f_39_8,plain,
( 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(clausify,[status(thm)],[f_39_7]) ).
cnf(f_39_9,plain,
( in(ordered_pair(U_283,U_281),U_279)
| ~ in(ordered_pair(U_283,U_281),U_278)
| U_279 != U_278
| ~ relation(U_278)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_39_7]) ).
cnf(f_39_10,plain,
( 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_279)
| U_279 = U_278
| ~ relation(U_278)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_39_7]) ).
cnf(f_39_11,plain,
( ~ in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_279)
| in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_279)
| U_279 = U_278
| ~ relation(U_278)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_39_7]) ).
cnf(f_39_12,plain,
( 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)
| U_279 = U_278
| ~ relation(U_278)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_39_7]) ).
cnf(f_39_13,plain,
( ~ in(ordered_pair(sK53(U_279,U_278),sK54(U_279,U_278)),U_279)
| ~ in(ordered_pair(sK51(U_279,U_278),sK52(U_279,U_278)),U_278)
| U_279 = U_278
| ~ relation(U_278)
| ~ relation(U_279) ),
inference(clausify,[status(thm)],[f_39_7]) ).
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]) ).
cnf(f_40_4,plain,
( in(U_292,U_296)
| ~ element(U_292,U_296)
| empty(U_296) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( element(U_293,U_296)
| ~ in(U_293,U_296)
| empty(U_296) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_6,plain,
( empty(U_294)
| ~ element(U_294,U_297)
| ~ empty(U_297) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_7,plain,
( element(U_295,U_297)
| ~ empty(U_295)
| ~ empty(U_297) ),
inference(clausify,[status(thm)],[f_40_3]) ).
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]) ).
cnf(f_41_6,plain,
( U_303 = U_309
| U_303 = U_311
| ~ in(U_303,U_307)
| U_307 != unordered_pair(U_311,U_309) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_7,plain,
( U_304 != U_311
| in(U_304,U_307)
| U_307 != unordered_pair(U_311,U_309) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_8,plain,
( U_304 != U_309
| in(U_304,U_307)
| U_307 != unordered_pair(U_311,U_309) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_9,plain,
( sK56(U_312,U_310,U_308) = U_310
| sK56(U_312,U_310,U_308) = U_312
| in(sK55(U_312,U_310,U_308),U_308)
| U_308 = unordered_pair(U_312,U_310) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_10,plain,
( ~ in(sK56(U_312,U_310,U_308),U_308)
| in(sK55(U_312,U_310,U_308),U_308)
| U_308 = unordered_pair(U_312,U_310) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_11,plain,
( sK55(U_312,U_310,U_308) != U_312
| sK56(U_312,U_310,U_308) = U_310
| sK56(U_312,U_310,U_308) = U_312
| U_308 = unordered_pair(U_312,U_310) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_12,plain,
( sK55(U_312,U_310,U_308) != U_310
| sK56(U_312,U_310,U_308) = U_310
| sK56(U_312,U_310,U_308) = U_312
| U_308 = unordered_pair(U_312,U_310) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_13,plain,
( sK55(U_312,U_310,U_308) != U_312
| ~ in(sK56(U_312,U_310,U_308),U_308)
| U_308 = unordered_pair(U_312,U_310) ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_14,plain,
( sK55(U_312,U_310,U_308) != U_310
| ~ in(sK56(U_312,U_310,U_308),U_308)
| U_308 = unordered_pair(U_312,U_310) ),
inference(clausify,[status(thm)],[f_41_5]) ).
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]) ).
cnf(f_42_5,plain,
( 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(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
( disjoint(fiber(U_317,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(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_7,plain,
( subset(sK58(U_317),relation_field(U_317))
| well_founded_relation(U_317)
| ~ relation(U_317) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_8,plain,
( sK58(U_317) != empty_set
| well_founded_relation(U_317)
| ~ relation(U_317) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_9,plain,
( ~ disjoint(fiber(U_317,U_315),sK58(U_317))
| ~ in(U_315,sK58(U_317))
| well_founded_relation(U_317)
| ~ relation(U_317) ),
inference(clausify,[status(thm)],[f_42_4]) ).
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]) ).
cnf(f_43_6,plain,
( in(U_323,U_329)
| in(U_323,U_331)
| ~ in(U_323,U_327)
| U_327 != set_union2(U_331,U_329) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_7,plain,
( ~ in(U_324,U_331)
| in(U_324,U_327)
| U_327 != set_union2(U_331,U_329) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_8,plain,
( ~ in(U_324,U_329)
| in(U_324,U_327)
| U_327 != set_union2(U_331,U_329) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_9,plain,
( 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_328)
| U_328 = set_union2(U_332,U_330) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_10,plain,
( ~ in(sK60(U_332,U_330,U_328),U_328)
| in(sK59(U_332,U_330,U_328),U_328)
| U_328 = set_union2(U_332,U_330) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_11,plain,
( ~ in(sK59(U_332,U_330,U_328),U_332)
| in(sK60(U_332,U_330,U_328),U_330)
| in(sK60(U_332,U_330,U_328),U_332)
| U_328 = set_union2(U_332,U_330) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_12,plain,
( ~ in(sK59(U_332,U_330,U_328),U_330)
| in(sK60(U_332,U_330,U_328),U_330)
| in(sK60(U_332,U_330,U_328),U_332)
| U_328 = set_union2(U_332,U_330) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_13,plain,
( ~ in(sK59(U_332,U_330,U_328),U_332)
| ~ in(sK60(U_332,U_330,U_328),U_328)
| U_328 = set_union2(U_332,U_330) ),
inference(clausify,[status(thm)],[f_43_5]) ).
cnf(f_43_14,plain,
( ~ in(sK59(U_332,U_330,U_328),U_330)
| ~ in(sK60(U_332,U_330,U_328),U_328)
| U_328 = set_union2(U_332,U_330) ),
inference(clausify,[status(thm)],[f_43_5]) ).
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]) ).
cnf(f_44_10,plain,
( 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(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_11,plain,
( in(sK62(U_354,U_352,U_350,U_346),U_352)
| ~ in(U_346,U_350)
| U_350 != cartesian_product2(U_354,U_352) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_12,plain,
( U_346 = ordered_pair(sK61(U_354,U_352,U_350,U_346),sK62(U_354,U_352,U_350,U_346))
| ~ in(U_346,U_350)
| U_350 != cartesian_product2(U_354,U_352) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_13,plain,
( in(U_347,U_350)
| U_347 != ordered_pair(U_336,U_335)
| ~ in(U_335,U_352)
| ~ in(U_336,U_354)
| U_350 != cartesian_product2(U_354,U_352) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_14,plain,
( in(sK65(U_355,U_353,U_351),U_355)
| in(sK63(U_355,U_353,U_351),U_351)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_15,plain,
( in(sK66(U_355,U_353,U_351),U_353)
| in(sK63(U_355,U_353,U_351),U_351)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_16,plain,
( sK64(U_355,U_353,U_351) = ordered_pair(sK65(U_355,U_353,U_351),sK66(U_355,U_353,U_351))
| in(sK63(U_355,U_353,U_351),U_351)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_17,plain,
( ~ in(sK64(U_355,U_353,U_351),U_351)
| in(sK63(U_355,U_353,U_351),U_351)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_18,plain,
( in(sK65(U_355,U_353,U_351),U_355)
| sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353)
| ~ in(U_339,U_355)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_19,plain,
( in(sK66(U_355,U_353,U_351),U_353)
| sK63(U_355,U_353,U_351) != ordered_pair(U_339,U_338)
| ~ in(U_338,U_353)
| ~ in(U_339,U_355)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_20,plain,
( sK64(U_355,U_353,U_351) = ordered_pair(sK65(U_355,U_353,U_351),sK66(U_355,U_353,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)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
cnf(f_44_21,plain,
( ~ in(sK64(U_355,U_353,U_351),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)
| U_351 = cartesian_product2(U_355,U_353) ),
inference(clausify,[status(thm)],[f_44_9]) ).
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]) ).
cnf(f_45_6,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_5]) ).
cnf(f_45_7,plain,
( in(sK67(U_362),U_362)
| epsilon_connected(U_362) ),
inference(clausify,[status(thm)],[f_45_5]) ).
cnf(f_45_8,plain,
( in(sK68(U_362),U_362)
| epsilon_connected(U_362) ),
inference(clausify,[status(thm)],[f_45_5]) ).
cnf(f_45_9,plain,
( ~ in(sK67(U_362),sK68(U_362))
| epsilon_connected(U_362) ),
inference(clausify,[status(thm)],[f_45_5]) ).
cnf(f_45_10,plain,
( sK67(U_362) != sK68(U_362)
| epsilon_connected(U_362) ),
inference(clausify,[status(thm)],[f_45_5]) ).
cnf(f_45_11,plain,
( ~ in(sK68(U_362),sK67(U_362))
| epsilon_connected(U_362) ),
inference(clausify,[status(thm)],[f_45_5]) ).
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]) ).
cnf(f_46_5,plain,
( 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(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_6,plain,
( in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_368)
| subset(U_368,U_367)
| ~ relation(U_367)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_7,plain,
( ~ in(ordered_pair(sK69(U_368,U_367),sK70(U_368,U_367)),U_367)
| subset(U_368,U_367)
| ~ relation(U_367)
| ~ relation(U_368) ),
inference(clausify,[status(thm)],[f_46_4]) ).
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]) ).
cnf(f_47_5,plain,
( in(U_369,U_373)
| ~ in(U_369,U_375)
| ~ subset(U_375,U_373) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_6,plain,
( in(sK71(U_376,U_374),U_376)
| subset(U_376,U_374) ),
inference(clausify,[status(thm)],[f_47_4]) ).
cnf(f_47_7,plain,
( ~ in(sK71(U_376,U_374),U_374)
| subset(U_376,U_374) ),
inference(clausify,[status(thm)],[f_47_4]) ).
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]) ).
cnf(f_48_6,plain,
( 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(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_7,plain,
( disjoint(fiber(U_382,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(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_8,plain,
( subset(sK73(U_382,U_384),U_384)
| is_well_founded_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_9,plain,
( sK73(U_382,U_384) != empty_set
| is_well_founded_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_10,plain,
( ~ disjoint(fiber(U_382,U_379),sK73(U_382,U_384))
| ~ in(U_379,sK73(U_382,U_384))
| is_well_founded_in(U_382,U_384)
| ~ relation(U_382) ),
inference(clausify,[status(thm)],[f_48_5]) ).
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]) ).
cnf(f_49_6,plain,
( in(U_390,U_398)
| ~ in(U_390,U_394)
| U_394 != set_intersection2(U_398,U_396) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_7,plain,
( in(U_390,U_396)
| ~ in(U_390,U_394)
| U_394 != set_intersection2(U_398,U_396) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_8,plain,
( in(U_391,U_394)
| ~ in(U_391,U_396)
| ~ in(U_391,U_398)
| U_394 != set_intersection2(U_398,U_396) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_9,plain,
( in(sK75(U_399,U_397,U_395),U_399)
| in(sK74(U_399,U_397,U_395),U_395)
| U_395 = set_intersection2(U_399,U_397) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_10,plain,
( in(sK75(U_399,U_397,U_395),U_397)
| in(sK74(U_399,U_397,U_395),U_395)
| U_395 = set_intersection2(U_399,U_397) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_11,plain,
( ~ in(sK75(U_399,U_397,U_395),U_395)
| in(sK74(U_399,U_397,U_395),U_395)
| U_395 = set_intersection2(U_399,U_397) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_12,plain,
( 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)
| U_395 = set_intersection2(U_399,U_397) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_13,plain,
( in(sK75(U_399,U_397,U_395),U_397)
| ~ in(sK74(U_399,U_397,U_395),U_397)
| ~ in(sK74(U_399,U_397,U_395),U_399)
| U_395 = set_intersection2(U_399,U_397) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_14,plain,
( ~ in(sK75(U_399,U_397,U_395),U_395)
| ~ in(sK74(U_399,U_397,U_395),U_397)
| ~ in(sK74(U_399,U_397,U_395),U_399)
| U_395 = set_intersection2(U_399,U_397) ),
inference(clausify,[status(thm)],[f_49_5]) ).
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]) ).
cnf(f_50_4,plain,
( 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(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_5,plain,
( U_406 = apply(U_402,U_409)
| ~ in(ordered_pair(U_409,U_406),U_402)
| ~ in(U_409,relation_dom(U_402))
| ~ function(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_6,plain,
( U_407 = empty_set
| U_407 != apply(U_402,U_410)
| in(U_410,relation_dom(U_402))
| ~ function(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_7,plain,
( U_408 = apply(U_402,U_410)
| U_408 != empty_set
| in(U_410,relation_dom(U_402))
| ~ function(U_402)
| ~ relation(U_402) ),
inference(clausify,[status(thm)],[f_50_3]) ).
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]) ).
cnf(f_51_4,plain,
( epsilon_transitive(U_412)
| ~ ordinal(U_412) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( epsilon_connected(U_412)
| ~ ordinal(U_412) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_6,plain,
( ordinal(U_413)
| ~ epsilon_connected(U_413)
| ~ epsilon_transitive(U_413) ),
inference(clausify,[status(thm)],[f_51_3]) ).
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]) ).
cnf(f_52_8,plain,
( 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(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_9,plain,
( in(U_423,U_426)
| ~ in(ordered_pair(U_423,U_415),U_421)
| U_426 != relation_dom(U_421)
| ~ relation(U_421) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_10,plain,
( in(ordered_pair(sK78(U_421,U_427),sK79(U_421,U_427)),U_421)
| in(sK77(U_421,U_427),U_427)
| U_427 = relation_dom(U_421)
| ~ relation(U_421) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_11,plain,
( ~ in(sK78(U_421,U_427),U_427)
| in(sK77(U_421,U_427),U_427)
| U_427 = relation_dom(U_421)
| ~ relation(U_421) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_12,plain,
( in(ordered_pair(sK78(U_421,U_427),sK79(U_421,U_427)),U_421)
| ~ in(ordered_pair(sK77(U_421,U_427),U_417),U_421)
| U_427 = relation_dom(U_421)
| ~ relation(U_421) ),
inference(clausify,[status(thm)],[f_52_7]) ).
cnf(f_52_13,plain,
( ~ in(sK78(U_421,U_427),U_427)
| ~ in(ordered_pair(sK77(U_421,U_427),U_417),U_421)
| U_427 = relation_dom(U_421)
| ~ relation(U_421) ),
inference(clausify,[status(thm)],[f_52_7]) ).
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]) ).
cnf(f_53_6,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)
| ~ relation(U_433) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_7,plain,
( in(sK80(U_433,U_435),U_435)
| is_antisymmetric_in(U_433,U_435)
| ~ relation(U_433) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_8,plain,
( in(sK81(U_433,U_435),U_435)
| is_antisymmetric_in(U_433,U_435)
| ~ relation(U_433) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_9,plain,
( in(ordered_pair(sK80(U_433,U_435),sK81(U_433,U_435)),U_433)
| is_antisymmetric_in(U_433,U_435)
| ~ relation(U_433) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_10,plain,
( in(ordered_pair(sK81(U_433,U_435),sK80(U_433,U_435)),U_433)
| is_antisymmetric_in(U_433,U_435)
| ~ relation(U_433) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_11,plain,
( sK80(U_433,U_435) != sK81(U_433,U_435)
| is_antisymmetric_in(U_433,U_435)
| ~ relation(U_433) ),
inference(clausify,[status(thm)],[f_53_5]) ).
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]) ).
cnf(f_54_3,plain,
cast_to_subset(U_436) = U_436,
inference(clausify,[status(thm)],[f_54_2]) ).
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]) ).
cnf(f_55_8,plain,
( in(U_445,sK82(U_451,U_449,U_445))
| ~ in(U_445,U_449)
| U_449 != union(U_451) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_9,plain,
( in(sK82(U_451,U_449,U_445),U_451)
| ~ in(U_445,U_449)
| U_449 != union(U_451) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_10,plain,
( in(U_446,U_449)
| ~ in(U_438,U_451)
| ~ in(U_446,U_438)
| U_449 != union(U_451) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_11,plain,
( in(sK84(U_452,U_450),sK85(U_452,U_450))
| in(sK83(U_452,U_450),U_450)
| U_450 = union(U_452) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_12,plain,
( in(sK85(U_452,U_450),U_452)
| in(sK83(U_452,U_450),U_450)
| U_450 = union(U_452) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_13,plain,
( ~ in(sK84(U_452,U_450),U_450)
| in(sK83(U_452,U_450),U_450)
| U_450 = union(U_452) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_14,plain,
( in(sK84(U_452,U_450),sK85(U_452,U_450))
| ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440)
| U_450 = union(U_452) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_15,plain,
( in(sK85(U_452,U_450),U_452)
| ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440)
| U_450 = union(U_452) ),
inference(clausify,[status(thm)],[f_55_7]) ).
cnf(f_55_16,plain,
( ~ in(sK84(U_452,U_450),U_450)
| ~ in(U_440,U_452)
| ~ in(sK83(U_452,U_450),U_440)
| U_450 = union(U_452) ),
inference(clausify,[status(thm)],[f_55_7]) ).
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]) ).
cnf(f_56_3,plain,
( reflexive(U_453)
| ~ well_ordering(U_453)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_56_2]) ).
cnf(f_56_4,plain,
( transitive(U_453)
| ~ well_ordering(U_453)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_56_2]) ).
cnf(f_56_5,plain,
( antisymmetric(U_453)
| ~ well_ordering(U_453)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_56_2]) ).
cnf(f_56_6,plain,
( connected(U_453)
| ~ well_ordering(U_453)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_56_2]) ).
cnf(f_56_7,plain,
( well_founded_relation(U_453)
| ~ well_ordering(U_453)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_56_2]) ).
cnf(f_56_8,plain,
( well_ordering(U_453)
| ~ well_founded_relation(U_453)
| ~ connected(U_453)
| ~ antisymmetric(U_453)
| ~ transitive(U_453)
| ~ reflexive(U_453)
| ~ relation(U_453) ),
inference(clausify,[status(thm)],[f_56_2]) ).
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]) ).
cnf(f_57_6,plain,
( in(U_459,U_467)
| ~ in(U_459,U_463)
| U_463 != set_difference(U_467,U_465) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_7,plain,
( ~ in(U_459,U_465)
| ~ in(U_459,U_463)
| U_463 != set_difference(U_467,U_465) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_8,plain,
( in(U_460,U_463)
| in(U_460,U_465)
| ~ in(U_460,U_467)
| U_463 != set_difference(U_467,U_465) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_9,plain,
( in(sK87(U_468,U_466,U_464),U_468)
| in(sK86(U_468,U_466,U_464),U_464)
| U_464 = set_difference(U_468,U_466) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_10,plain,
( ~ in(sK87(U_468,U_466,U_464),U_466)
| in(sK86(U_468,U_466,U_464),U_464)
| U_464 = set_difference(U_468,U_466) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_11,plain,
( ~ in(sK87(U_468,U_466,U_464),U_464)
| in(sK86(U_468,U_466,U_464),U_464)
| U_464 = set_difference(U_468,U_466) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_12,plain,
( 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)
| U_464 = set_difference(U_468,U_466) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_13,plain,
( ~ in(sK87(U_468,U_466,U_464),U_466)
| in(sK86(U_468,U_466,U_464),U_466)
| ~ in(sK86(U_468,U_466,U_464),U_468)
| U_464 = set_difference(U_468,U_466) ),
inference(clausify,[status(thm)],[f_57_5]) ).
cnf(f_57_14,plain,
( ~ in(sK87(U_468,U_466,U_464),U_464)
| in(sK86(U_468,U_466,U_464),U_466)
| ~ in(sK86(U_468,U_466,U_464),U_468)
| U_464 = set_difference(U_468,U_466) ),
inference(clausify,[status(thm)],[f_57_5]) ).
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]) ).
cnf(f_58_8,plain,
( 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(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_9,plain,
( U_477 = apply(U_476,sK88(U_476,U_481,U_477))
| ~ in(U_477,U_481)
| U_481 != relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_10,plain,
( in(U_478,U_481)
| U_478 != apply(U_476,U_470)
| ~ in(U_470,relation_dom(U_476))
| U_481 != relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_11,plain,
( in(sK91(U_476,U_482),relation_dom(U_476))
| in(sK89(U_476,U_482),U_482)
| U_482 = relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_12,plain,
( sK90(U_476,U_482) = apply(U_476,sK91(U_476,U_482))
| in(sK89(U_476,U_482),U_482)
| U_482 = relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_13,plain,
( ~ in(sK90(U_476,U_482),U_482)
| in(sK89(U_476,U_482),U_482)
| U_482 = relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_14,plain,
( in(sK91(U_476,U_482),relation_dom(U_476))
| sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476))
| U_482 = relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_15,plain,
( sK90(U_476,U_482) = apply(U_476,sK91(U_476,U_482))
| sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476))
| U_482 = relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
cnf(f_58_16,plain,
( ~ in(sK90(U_476,U_482),U_482)
| sK89(U_476,U_482) != apply(U_476,U_472)
| ~ in(U_472,relation_dom(U_476))
| U_482 = relation_rng(U_476)
| ~ function(U_476)
| ~ relation(U_476) ),
inference(clausify,[status(thm)],[f_58_7]) ).
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]) ).
cnf(f_59_8,plain,
( 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(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_9,plain,
( in(U_492,U_495)
| ~ in(ordered_pair(U_484,U_492),U_490)
| U_495 != relation_rng(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_10,plain,
( in(ordered_pair(sK95(U_490,U_496),sK94(U_490,U_496)),U_490)
| in(sK93(U_490,U_496),U_496)
| U_496 = relation_rng(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_11,plain,
( ~ in(sK94(U_490,U_496),U_496)
| in(sK93(U_490,U_496),U_496)
| U_496 = relation_rng(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_12,plain,
( in(ordered_pair(sK95(U_490,U_496),sK94(U_490,U_496)),U_490)
| ~ in(ordered_pair(U_486,sK93(U_490,U_496)),U_490)
| U_496 = relation_rng(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_59_7]) ).
cnf(f_59_13,plain,
( ~ in(sK94(U_490,U_496),U_496)
| ~ in(ordered_pair(U_486,sK93(U_490,U_496)),U_490)
| U_496 = relation_rng(U_490)
| ~ relation(U_490) ),
inference(clausify,[status(thm)],[f_59_7]) ).
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]) ).
cnf(f_60_3,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_2]) ).
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]) ).
cnf(f_61_3,plain,
ordered_pair(U_500,U_499) = unordered_pair(unordered_pair(U_500,U_499),singleton(U_500)),
inference(clausify,[status(thm)],[f_61_2]) ).
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]) ).
cnf(f_62_4,plain,
( is_reflexive_in(U_502,U_503)
| ~ well_orders(U_502,U_503)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( is_transitive_in(U_502,U_503)
| ~ well_orders(U_502,U_503)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_6,plain,
( is_antisymmetric_in(U_502,U_503)
| ~ well_orders(U_502,U_503)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_7,plain,
( is_connected_in(U_502,U_503)
| ~ well_orders(U_502,U_503)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_8,plain,
( is_well_founded_in(U_502,U_503)
| ~ well_orders(U_502,U_503)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_9,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)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_62_3]) ).
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]) ).
cnf(f_63_4,plain,
( U_506 = union(U_506)
| ~ being_limit_ordinal(U_506) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
( being_limit_ordinal(U_507)
| U_507 != union(U_507) ),
inference(clausify,[status(thm)],[f_63_3]) ).
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]) ).
cnf(f_64_3,plain,
( relation_field(U_508) = set_union2(relation_dom(U_508),relation_rng(U_508))
| ~ relation(U_508) ),
inference(clausify,[status(thm)],[f_64_2]) ).
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]) ).
cnf(f_65_6,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)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_65_5]) ).
cnf(f_65_7,plain,
( in(sK96(U_514,U_516),U_516)
| is_connected_in(U_514,U_516)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_65_5]) ).
cnf(f_65_8,plain,
( in(sK97(U_514,U_516),U_516)
| is_connected_in(U_514,U_516)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_65_5]) ).
cnf(f_65_9,plain,
( sK96(U_514,U_516) != sK97(U_514,U_516)
| is_connected_in(U_514,U_516)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_65_5]) ).
cnf(f_65_10,plain,
( ~ in(ordered_pair(sK96(U_514,U_516),sK97(U_514,U_516)),U_514)
| is_connected_in(U_514,U_516)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_65_5]) ).
cnf(f_65_11,plain,
( ~ in(ordered_pair(sK97(U_514,U_516),sK96(U_514,U_516)),U_514)
| is_connected_in(U_514,U_516)
| ~ relation(U_514) ),
inference(clausify,[status(thm)],[f_65_5]) ).
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]) ).
cnf(f_66_3,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_2]) ).
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]) ).
cnf(f_67_8,plain,
( 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(clausify,[status(thm)],[f_67_7]) ).
cnf(f_67_9,plain,
( in(ordered_pair(U_528,U_526),U_523)
| ~ in(ordered_pair(U_526,U_528),U_524)
| U_523 != relation_inverse(U_524)
| ~ relation(U_523)
| ~ relation(U_524) ),
inference(clausify,[status(thm)],[f_67_7]) ).
cnf(f_67_10,plain,
( in(ordered_pair(sK101(U_524,U_523),sK100(U_524,U_523)),U_524)
| in(ordered_pair(sK98(U_524,U_523),sK99(U_524,U_523)),U_523)
| U_523 = relation_inverse(U_524)
| ~ relation(U_523)
| ~ relation(U_524) ),
inference(clausify,[status(thm)],[f_67_7]) ).
cnf(f_67_11,plain,
( ~ in(ordered_pair(sK100(U_524,U_523),sK101(U_524,U_523)),U_523)
| in(ordered_pair(sK98(U_524,U_523),sK99(U_524,U_523)),U_523)
| U_523 = relation_inverse(U_524)
| ~ relation(U_523)
| ~ relation(U_524) ),
inference(clausify,[status(thm)],[f_67_7]) ).
cnf(f_67_12,plain,
( 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)
| U_523 = relation_inverse(U_524)
| ~ relation(U_523)
| ~ relation(U_524) ),
inference(clausify,[status(thm)],[f_67_7]) ).
cnf(f_67_13,plain,
( ~ in(ordered_pair(sK100(U_524,U_523),sK101(U_524,U_523)),U_523)
| ~ in(ordered_pair(sK99(U_524,U_523),sK98(U_524,U_523)),U_524)
| U_523 = relation_inverse(U_524)
| ~ relation(U_523)
| ~ relation(U_524) ),
inference(clausify,[status(thm)],[f_67_7]) ).
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]) ).
cnf(f_68_8,plain,
( 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(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_9,plain,
( relation_rng(U_537) = relation_field(U_538)
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_10,plain,
( one_to_one(U_537)
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_11,plain,
( in(U_542,relation_field(U_539))
| ~ in(ordered_pair(U_542,U_540),U_539)
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_12,plain,
( in(U_540,relation_field(U_539))
| ~ in(ordered_pair(U_542,U_540),U_539)
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_13,plain,
( in(ordered_pair(apply(U_537,U_542),apply(U_537,U_540)),U_538)
| ~ in(ordered_pair(U_542,U_540),U_539)
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_14,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))
| ~ relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_15,plain,
( in(sK104(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)
| relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_16,plain,
( in(sK105(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)
| relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_17,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)
| 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)
| relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_18,plain,
( ~ in(ordered_pair(sK104(U_539,U_538,U_537),sK105(U_539,U_538,U_537)),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)
| relation_isomorphism(U_539,U_538,U_537)
| ~ function(U_537)
| ~ relation(U_537)
| ~ relation(U_538)
| ~ relation(U_539) ),
inference(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_19,plain,
( 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))
| ~ 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(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_20,plain,
( in(sK105(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))
| ~ 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(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_21,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)
| ~ 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))
| ~ 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(clausify,[status(thm)],[f_68_7]) ).
cnf(f_68_22,plain,
( ~ 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,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))
| ~ 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(clausify,[status(thm)],[f_68_7]) ).
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]) ).
cnf(f_69_4,plain,
( set_intersection2(U_552,U_550) = empty_set
| ~ disjoint(U_552,U_550) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_5,plain,
( disjoint(U_553,U_551)
| set_intersection2(U_553,U_551) != empty_set ),
inference(clausify,[status(thm)],[f_69_3]) ).
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]) ).
cnf(f_70_5,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)
| ~ function(U_558)
| ~ relation(U_558) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_6,plain,
( in(sK106(U_558),relation_dom(U_558))
| one_to_one(U_558)
| ~ function(U_558)
| ~ relation(U_558) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_7,plain,
( in(sK107(U_558),relation_dom(U_558))
| one_to_one(U_558)
| ~ function(U_558)
| ~ relation(U_558) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_8,plain,
( apply(U_558,sK106(U_558)) = apply(U_558,sK107(U_558))
| one_to_one(U_558)
| ~ function(U_558)
| ~ relation(U_558) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_9,plain,
( sK106(U_558) != sK107(U_558)
| one_to_one(U_558)
| ~ function(U_558)
| ~ relation(U_558) ),
inference(clausify,[status(thm)],[f_70_4]) ).
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]) ).
cnf(f_71_10,plain,
( 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(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_11,plain,
( in(ordered_pair(sK108(U_569,U_568,U_567,U_572,U_570),U_570),U_568)
| ~ 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(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_12,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)
| U_567 != relation_composition(U_569,U_568)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_13,plain,
( in(ordered_pair(sK111(U_569,U_568,U_567),sK113(U_569,U_568,U_567)),U_569)
| in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567)
| U_567 = relation_composition(U_569,U_568)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_14,plain,
( in(ordered_pair(sK113(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_568)
| in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567)
| U_567 = relation_composition(U_569,U_568)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_15,plain,
( ~ in(ordered_pair(sK111(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_567)
| in(ordered_pair(sK109(U_569,U_568,U_567),sK110(U_569,U_568,U_567)),U_567)
| U_567 = relation_composition(U_569,U_568)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_16,plain,
( in(ordered_pair(sK111(U_569,U_568,U_567),sK113(U_569,U_568,U_567)),U_569)
| ~ 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)
| U_567 = relation_composition(U_569,U_568)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_17,plain,
( in(ordered_pair(sK113(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),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)
| U_567 = relation_composition(U_569,U_568)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_9]) ).
cnf(f_71_18,plain,
( ~ in(ordered_pair(sK111(U_569,U_568,U_567),sK112(U_569,U_568,U_567)),U_567)
| ~ 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)
| U_567 = relation_composition(U_569,U_568)
| ~ relation(U_567)
| ~ relation(U_568)
| ~ relation(U_569) ),
inference(clausify,[status(thm)],[f_71_9]) ).
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]) ).
cnf(f_72_7,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)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_8,plain,
( in(sK114(U_585,U_587),U_587)
| is_transitive_in(U_585,U_587)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_9,plain,
( in(sK115(U_585,U_587),U_587)
| is_transitive_in(U_585,U_587)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_10,plain,
( in(sK116(U_585,U_587),U_587)
| is_transitive_in(U_585,U_587)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_11,plain,
( in(ordered_pair(sK114(U_585,U_587),sK115(U_585,U_587)),U_585)
| is_transitive_in(U_585,U_587)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_12,plain,
( in(ordered_pair(sK115(U_585,U_587),sK116(U_585,U_587)),U_585)
| is_transitive_in(U_585,U_587)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_13,plain,
( ~ in(ordered_pair(sK114(U_585,U_587),sK116(U_585,U_587)),U_585)
| is_transitive_in(U_585,U_587)
| ~ relation(U_585) ),
inference(clausify,[status(thm)],[f_72_6]) ).
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]) ).
cnf(f_73_4,plain,
( 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(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_5,plain,
( in(U_588,U_590)
| ~ in(subset_complement(U_592,U_588),U_591)
| ~ 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(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_6,plain,
( element(sK117(U_592,U_591,U_590),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(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_7,plain,
( in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591)
| in(sK117(U_592,U_591,U_590),U_590)
| U_590 = complements_of_subsets(U_592,U_591)
| ~ element(U_590,powerset(powerset(U_592)))
| ~ element(U_591,powerset(powerset(U_592))) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_8,plain,
( ~ in(sK117(U_592,U_591,U_590),U_590)
| in(sK117(U_592,U_591,U_590),U_590)
| U_590 = complements_of_subsets(U_592,U_591)
| ~ element(U_590,powerset(powerset(U_592)))
| ~ element(U_591,powerset(powerset(U_592))) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_9,plain,
( 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)
| U_590 = complements_of_subsets(U_592,U_591)
| ~ element(U_590,powerset(powerset(U_592)))
| ~ element(U_591,powerset(powerset(U_592))) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_10,plain,
( ~ in(sK117(U_592,U_591,U_590),U_590)
| ~ in(subset_complement(U_592,sK117(U_592,U_591,U_590)),U_591)
| U_590 = complements_of_subsets(U_592,U_591)
| ~ element(U_590,powerset(powerset(U_592)))
| ~ element(U_591,powerset(powerset(U_592))) ),
inference(clausify,[status(thm)],[f_73_3]) ).
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]) ).
cnf(f_74_4,plain,
( subset(U_597,U_595)
| ~ proper_subset(U_597,U_595) ),
inference(clausify,[status(thm)],[f_74_3]) ).
cnf(f_74_5,plain,
( U_597 != U_595
| ~ proper_subset(U_597,U_595) ),
inference(clausify,[status(thm)],[f_74_3]) ).
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_3]) ).
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]) ).
cnf(f_75_3,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_2]) ).
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]) ).
cnf(f_76_3,plain,
( is_reflexive_in(U_600,relation_field(U_600))
| ~ reflexive(U_600)
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( reflexive(U_600)
| ~ is_reflexive_in(U_600,relation_field(U_600))
| ~ relation(U_600) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_77_2,plain,
$true,
inference(clausify,[status(thm)],[f_77_1]) ).
fof(f_78_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
cnf(f_78_2,plain,
$true,
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_79_2,plain,
$true,
inference(clausify,[status(thm)],[f_79_1]) ).
fof(f_80_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_mcart_1]) ).
cnf(f_80_2,plain,
$true,
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
cnf(f_81_2,plain,
$true,
inference(clausify,[status(thm)],[f_81_1]) ).
fof(f_82_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_82_2,plain,
$true,
inference(clausify,[status(thm)],[f_82_1]) ).
fof(f_83_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_83_2,plain,
$true,
inference(clausify,[status(thm)],[f_83_1]) ).
fof(f_84_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_84_2,plain,
$true,
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
cnf(f_85_2,plain,
$true,
inference(clausify,[status(thm)],[f_85_1]) ).
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]) ).
cnf(f_86_3,plain,
relation(inclusion_relation(U_601)),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_87_2,plain,
$true,
inference(clausify,[status(thm)],[f_87_1]) ).
fof(f_88_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_88_2,plain,
$true,
inference(clausify,[status(thm)],[f_88_1]) ).
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]) ).
cnf(f_89_3,plain,
( relation(function_inverse(U_602))
| ~ function(U_602)
| ~ relation(U_602) ),
inference(clausify,[status(thm)],[f_89_2]) ).
cnf(f_89_4,plain,
( function(function_inverse(U_602))
| ~ function(U_602)
| ~ relation(U_602) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_mcart_1]) ).
cnf(f_90_2,plain,
$true,
inference(clausify,[status(thm)],[f_90_1]) ).
fof(f_91_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_91_2,plain,
$true,
inference(clausify,[status(thm)],[f_91_1]) ).
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]) ).
cnf(f_92_3,plain,
element(cast_to_subset(U_603),powerset(U_603)),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_93_2,plain,
$true,
inference(clausify,[status(thm)],[f_93_1]) ).
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]) ).
cnf(f_94_4,plain,
( relation(relation_restriction(U_605,U_604))
| ~ relation(U_605) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_95_2,plain,
$true,
inference(clausify,[status(thm)],[f_95_1]) ).
fof(f_96_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_96_2,plain,
$true,
inference(clausify,[status(thm)],[f_96_1]) ).
fof(f_97_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_97_2,plain,
$true,
inference(clausify,[status(thm)],[f_97_1]) ).
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]) ).
cnf(f_98_3,plain,
( element(subset_complement(U_607,U_606),powerset(U_607))
| ~ element(U_606,powerset(U_607)) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_99_2,plain,
$true,
inference(clausify,[status(thm)],[f_99_1]) ).
fof(f_100_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_100_2,plain,
$true,
inference(clausify,[status(thm)],[f_100_1]) ).
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]) ).
cnf(f_101_3,plain,
( relation(relation_inverse(U_608))
| ~ relation(U_608) ),
inference(clausify,[status(thm)],[f_101_2]) ).
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]) ).
cnf(f_102_3,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_2]) ).
fof(f_103_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_103_2,plain,
$true,
inference(clausify,[status(thm)],[f_103_1]) ).
fof(f_104_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_104_2,plain,
$true,
inference(clausify,[status(thm)],[f_104_1]) ).
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]) ).
cnf(f_105_3,plain,
( relation(relation_composition(U_613,U_612))
| ~ relation(U_612)
| ~ relation(U_613) ),
inference(clausify,[status(thm)],[f_105_2]) ).
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]) ).
cnf(f_106_3,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_2]) ).
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]) ).
cnf(f_107_3,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_2]) ).
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]) ).
cnf(f_108_3,plain,
relation(identity_relation(U_619)),
inference(clausify,[status(thm)],[f_108_2]) ).
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]) ).
cnf(f_109_3,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_2]) ).
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]) ).
cnf(f_110_3,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_2]) ).
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]) ).
cnf(f_111_4,plain,
( relation(relation_dom_restriction(U_626,U_625))
| ~ relation(U_626) ),
inference(clausify,[status(thm)],[f_111_3]) ).
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]) ).
cnf(f_112_3,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_2]) ).
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]) ).
cnf(f_113_3,plain,
( relation(relation_rng_restriction(U_630,U_629))
| ~ relation(U_629) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_114_2,plain,
$true,
inference(clausify,[status(thm)],[f_114_1]) ).
fof(f_115_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
cnf(f_115_2,plain,
$true,
inference(clausify,[status(thm)],[f_115_1]) ).
fof(f_116_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_116_2,plain,
$true,
inference(clausify,[status(thm)],[f_116_1]) ).
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]) ).
cnf(f_117_3,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_2]) ).
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]) ).
cnf(f_118_4,plain,
relation_of2(sK118(U_636,U_635),U_636,U_635),
inference(clausify,[status(thm)],[f_118_3]) ).
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]) ).
cnf(f_119_4,plain,
element(sK119(U_638),U_638),
inference(clausify,[status(thm)],[f_119_3]) ).
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]) ).
cnf(f_120_4,plain,
relation_of2_as_subset(sK120(U_641,U_640),U_641,U_640),
inference(clausify,[status(thm)],[f_120_3]) ).
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]) ).
cnf(f_121_3,plain,
( empty(relation_composition(U_642,U_643))
| ~ relation(U_642)
| ~ empty(U_643) ),
inference(clausify,[status(thm)],[f_121_2]) ).
cnf(f_121_4,plain,
( relation(relation_composition(U_642,U_643))
| ~ relation(U_642)
| ~ empty(U_643) ),
inference(clausify,[status(thm)],[f_121_2]) ).
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]) ).
cnf(f_122_3,plain,
( empty(relation_inverse(U_644))
| ~ empty(U_644) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( relation(relation_inverse(U_644))
| ~ empty(U_644) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_123_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_123_1]) ).
cnf(f_123_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_123_1]) ).
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]) ).
cnf(f_124_4,plain,
( relation(relation_dom_restriction(U_646,U_647))
| ~ relation_empty_yielding(U_646)
| ~ relation(U_646) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_646,U_648))
| ~ relation_empty_yielding(U_646)
| ~ relation(U_646) ),
inference(clausify,[status(thm)],[f_124_3]) ).
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]) ).
cnf(f_125_3,plain,
( relation(relation_composition(U_650,U_649))
| ~ function(U_649)
| ~ relation(U_649)
| ~ function(U_650)
| ~ relation(U_650) ),
inference(clausify,[status(thm)],[f_125_2]) ).
cnf(f_125_4,plain,
( function(relation_composition(U_650,U_649))
| ~ function(U_649)
| ~ relation(U_649)
| ~ function(U_650)
| ~ relation(U_650) ),
inference(clausify,[status(thm)],[f_125_2]) ).
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]) ).
cnf(f_126_3,plain,
~ empty(succ(U_651)),
inference(clausify,[status(thm)],[f_126_2]) ).
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]) ).
cnf(f_127_3,plain,
( relation(set_intersection2(U_653,U_652))
| ~ relation(U_652)
| ~ relation(U_653) ),
inference(clausify,[status(thm)],[f_127_2]) ).
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]) ).
cnf(f_128_3,plain,
~ empty(powerset(U_654)),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_129_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_129_1]) ).
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]) ).
cnf(f_130_3,plain,
~ empty(ordered_pair(U_656,U_655)),
inference(clausify,[status(thm)],[f_130_2]) ).
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]) ).
cnf(f_131_4,plain,
relation(identity_relation(U_658)),
inference(clausify,[status(thm)],[f_131_3]) ).
cnf(f_131_5,plain,
function(identity_relation(U_659)),
inference(clausify,[status(thm)],[f_131_3]) ).
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]) ).
cnf(f_132_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
cnf(f_132_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
cnf(f_132_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
cnf(f_132_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
cnf(f_132_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
cnf(f_132_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
cnf(f_132_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_132_1]) ).
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]) ).
cnf(f_133_3,plain,
( relation(set_union2(U_661,U_660))
| ~ relation(U_660)
| ~ relation(U_661) ),
inference(clausify,[status(thm)],[f_133_2]) ).
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]) ).
cnf(f_134_3,plain,
~ empty(singleton(U_662)),
inference(clausify,[status(thm)],[f_134_2]) ).
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]) ).
cnf(f_135_4,plain,
( ~ empty(set_union2(U_664,U_663))
| empty(U_664) ),
inference(clausify,[status(thm)],[f_135_3]) ).
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]) ).
cnf(f_136_3,plain,
( relation(relation_inverse(U_665))
| ~ one_to_one(U_665)
| ~ function(U_665)
| ~ relation(U_665) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_4,plain,
( function(relation_inverse(U_665))
| ~ one_to_one(U_665)
| ~ function(U_665)
| ~ relation(U_665) ),
inference(clausify,[status(thm)],[f_136_2]) ).
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]) ).
cnf(f_137_3,plain,
( ~ empty(succ(U_666))
| ~ ordinal(U_666) ),
inference(clausify,[status(thm)],[f_137_2]) ).
cnf(f_137_4,plain,
( epsilon_transitive(succ(U_666))
| ~ ordinal(U_666) ),
inference(clausify,[status(thm)],[f_137_2]) ).
cnf(f_137_5,plain,
( epsilon_connected(succ(U_666))
| ~ ordinal(U_666) ),
inference(clausify,[status(thm)],[f_137_2]) ).
cnf(f_137_6,plain,
( ordinal(succ(U_666))
| ~ ordinal(U_666) ),
inference(clausify,[status(thm)],[f_137_2]) ).
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]) ).
cnf(f_138_3,plain,
( relation(set_difference(U_668,U_667))
| ~ relation(U_667)
| ~ relation(U_668) ),
inference(clausify,[status(thm)],[f_138_2]) ).
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]) ).
cnf(f_139_3,plain,
~ empty(unordered_pair(U_670,U_669)),
inference(clausify,[status(thm)],[f_139_2]) ).
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]) ).
cnf(f_140_4,plain,
( ~ empty(set_union2(U_671,U_672))
| empty(U_672) ),
inference(clausify,[status(thm)],[f_140_3]) ).
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]) ).
cnf(f_141_4,plain,
( relation(relation_dom_restriction(U_674,U_675))
| ~ function(U_674)
| ~ relation(U_674) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_5,plain,
( function(relation_dom_restriction(U_674,U_676))
| ~ function(U_674)
| ~ relation(U_674) ),
inference(clausify,[status(thm)],[f_141_3]) ).
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]) ).
cnf(f_142_3,plain,
( epsilon_transitive(union(U_677))
| ~ ordinal(U_677) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( epsilon_connected(union(U_677))
| ~ ordinal(U_677) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_5,plain,
( ordinal(union(U_677))
| ~ ordinal(U_677) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_143_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_143_1]) ).
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]) ).
cnf(f_144_3,plain,
( ~ empty(cartesian_product2(U_679,U_678))
| empty(U_678)
| empty(U_679) ),
inference(clausify,[status(thm)],[f_144_2]) ).
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]) ).
cnf(f_145_3,plain,
( relation(relation_rng_restriction(U_681,U_680))
| ~ function(U_680)
| ~ relation(U_680) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( function(relation_rng_restriction(U_681,U_680))
| ~ function(U_680)
| ~ relation(U_680) ),
inference(clausify,[status(thm)],[f_145_2]) ).
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]) ).
cnf(f_146_3,plain,
( ~ empty(relation_dom(U_682))
| ~ relation(U_682)
| empty(U_682) ),
inference(clausify,[status(thm)],[f_146_2]) ).
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]) ).
cnf(f_147_3,plain,
( ~ empty(relation_rng(U_683))
| ~ relation(U_683)
| empty(U_683) ),
inference(clausify,[status(thm)],[f_147_2]) ).
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]) ).
cnf(f_148_3,plain,
( empty(relation_dom(U_684))
| ~ empty(U_684) ),
inference(clausify,[status(thm)],[f_148_2]) ).
cnf(f_148_4,plain,
( relation(relation_dom(U_684))
| ~ empty(U_684) ),
inference(clausify,[status(thm)],[f_148_2]) ).
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]) ).
cnf(f_149_3,plain,
( empty(relation_rng(U_685))
| ~ empty(U_685) ),
inference(clausify,[status(thm)],[f_149_2]) ).
cnf(f_149_4,plain,
( relation(relation_rng(U_685))
| ~ empty(U_685) ),
inference(clausify,[status(thm)],[f_149_2]) ).
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]) ).
cnf(f_150_3,plain,
( empty(relation_composition(U_687,U_686))
| ~ relation(U_686)
| ~ empty(U_687) ),
inference(clausify,[status(thm)],[f_150_2]) ).
cnf(f_150_4,plain,
( relation(relation_composition(U_687,U_686))
| ~ relation(U_686)
| ~ empty(U_687) ),
inference(clausify,[status(thm)],[f_150_2]) ).
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]) ).
cnf(f_151_4,plain,
set_union2(U_689,U_689) = U_689,
inference(clausify,[status(thm)],[f_151_3]) ).
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]) ).
cnf(f_152_4,plain,
set_intersection2(U_691,U_691) = U_691,
inference(clausify,[status(thm)],[f_152_3]) ).
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]) ).
cnf(f_153_3,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_2]) ).
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]) ).
cnf(f_154_3,plain,
( relation_inverse(relation_inverse(U_694)) = U_694
| ~ relation(U_694) ),
inference(clausify,[status(thm)],[f_154_2]) ).
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]) ).
cnf(f_155_3,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_2]) ).
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]) ).
cnf(f_156_4,plain,
~ proper_subset(U_698,U_698),
inference(clausify,[status(thm)],[f_156_3]) ).
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]) ).
cnf(f_157_4,plain,
( in(ordered_pair(U_699,U_699),U_701)
| ~ in(U_699,relation_field(U_701))
| ~ reflexive(U_701)
| ~ relation(U_701) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( in(sK121(U_701),relation_field(U_701))
| reflexive(U_701)
| ~ relation(U_701) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( ~ in(ordered_pair(sK121(U_701),sK121(U_701)),U_701)
| reflexive(U_701)
| ~ relation(U_701) ),
inference(clausify,[status(thm)],[f_157_3]) ).
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]) ).
cnf(f_158_3,plain,
singleton(U_702) != empty_set,
inference(clausify,[status(thm)],[f_158_2]) ).
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]) ).
cnf(f_159_3,plain,
( set_union2(singleton(U_704),U_703) = U_703
| ~ in(U_704,U_703) ),
inference(clausify,[status(thm)],[f_159_2]) ).
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]) ).
cnf(f_160_3,plain,
( ~ in(U_706,U_705)
| ~ disjoint(singleton(U_706),U_705) ),
inference(clausify,[status(thm)],[f_160_2]) ).
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]) ).
cnf(f_161_3,plain,
( disjoint(singleton(U_708),U_707)
| in(U_708,U_707) ),
inference(clausify,[status(thm)],[f_161_2]) ).
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]) ).
cnf(f_162_3,plain,
( subset(relation_dom(relation_rng_restriction(U_710,U_709)),relation_dom(U_709))
| ~ relation(U_709) ),
inference(clausify,[status(thm)],[f_162_2]) ).
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]) ).
cnf(f_163_6,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)
| ~ relation(U_717) ),
inference(clausify,[status(thm)],[f_163_5]) ).
cnf(f_163_7,plain,
( in(ordered_pair(sK122(U_717),sK123(U_717)),U_717)
| transitive(U_717)
| ~ relation(U_717) ),
inference(clausify,[status(thm)],[f_163_5]) ).
cnf(f_163_8,plain,
( in(ordered_pair(sK123(U_717),sK124(U_717)),U_717)
| transitive(U_717)
| ~ relation(U_717) ),
inference(clausify,[status(thm)],[f_163_5]) ).
cnf(f_163_9,plain,
( ~ in(ordered_pair(sK122(U_717),sK124(U_717)),U_717)
| transitive(U_717)
| ~ relation(U_717) ),
inference(clausify,[status(thm)],[f_163_5]) ).
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]) ).
cnf(f_164_4,plain,
( in(U_722,U_720)
| ~ subset(singleton(U_722),U_720) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_5,plain,
( subset(singleton(U_723),U_721)
| ~ in(U_723,U_721) ),
inference(clausify,[status(thm)],[f_164_3]) ).
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]) ).
cnf(f_165_4,plain,
( subset(U_728,U_726)
| set_difference(U_728,U_726) != empty_set ),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_5,plain,
( set_difference(U_729,U_727) = empty_set
| ~ subset(U_729,U_727) ),
inference(clausify,[status(thm)],[f_165_3]) ).
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]) ).
cnf(f_166_3,plain,
( in(U_730,U_732)
| ~ in(U_730,U_731)
| ~ element(U_731,powerset(U_732)) ),
inference(clausify,[status(thm)],[f_166_2]) ).
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]) ).
cnf(f_167_5,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)
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_167_4]) ).
cnf(f_167_6,plain,
( in(ordered_pair(sK125(U_737),sK126(U_737)),U_737)
| antisymmetric(U_737)
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_167_4]) ).
cnf(f_167_7,plain,
( in(ordered_pair(sK126(U_737),sK125(U_737)),U_737)
| antisymmetric(U_737)
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_167_4]) ).
cnf(f_167_8,plain,
( sK125(U_737) != sK126(U_737)
| antisymmetric(U_737)
| ~ relation(U_737) ),
inference(clausify,[status(thm)],[f_167_4]) ).
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]) ).
cnf(f_168_4,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_3]) ).
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]) ).
cnf(f_169_6,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)
| ~ relation(U_745) ),
inference(clausify,[status(thm)],[f_169_5]) ).
cnf(f_169_7,plain,
( in(sK127(U_745),relation_field(U_745))
| connected(U_745)
| ~ relation(U_745) ),
inference(clausify,[status(thm)],[f_169_5]) ).
cnf(f_169_8,plain,
( in(sK128(U_745),relation_field(U_745))
| connected(U_745)
| ~ relation(U_745) ),
inference(clausify,[status(thm)],[f_169_5]) ).
cnf(f_169_9,plain,
( sK127(U_745) != sK128(U_745)
| connected(U_745)
| ~ relation(U_745) ),
inference(clausify,[status(thm)],[f_169_5]) ).
cnf(f_169_10,plain,
( ~ in(ordered_pair(sK127(U_745),sK128(U_745)),U_745)
| connected(U_745)
| ~ relation(U_745) ),
inference(clausify,[status(thm)],[f_169_5]) ).
cnf(f_169_11,plain,
( ~ in(ordered_pair(sK128(U_745),sK127(U_745)),U_745)
| connected(U_745)
| ~ relation(U_745) ),
inference(clausify,[status(thm)],[f_169_5]) ).
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]) ).
cnf(f_170_4,plain,
( U_750 = singleton(U_748)
| U_750 = empty_set
| ~ subset(U_750,singleton(U_748)) ),
inference(clausify,[status(thm)],[f_170_3]) ).
cnf(f_170_5,plain,
( U_751 != empty_set
| subset(U_751,singleton(U_749)) ),
inference(clausify,[status(thm)],[f_170_3]) ).
cnf(f_170_6,plain,
( U_751 != singleton(U_749)
| subset(U_751,singleton(U_749)) ),
inference(clausify,[status(thm)],[f_170_3]) ).
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]) ).
cnf(f_171_3,plain,
( subset(U_753,union(U_752))
| ~ in(U_753,U_752) ),
inference(clausify,[status(thm)],[f_171_2]) ).
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]) ).
cnf(f_172_4,plain,
( in(U_764,U_760)
| ~ in(ordered_pair(U_764,U_762),cartesian_product2(U_760,U_758)) ),
inference(clausify,[status(thm)],[f_172_3]) ).
cnf(f_172_5,plain,
( in(U_762,U_758)
| ~ in(ordered_pair(U_764,U_762),cartesian_product2(U_760,U_758)) ),
inference(clausify,[status(thm)],[f_172_3]) ).
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_3]) ).
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]) ).
cnf(f_173_4,plain,
( in(sK129(U_768,U_767),U_768)
| element(U_768,powerset(U_767)) ),
inference(clausify,[status(thm)],[f_173_3]) ).
cnf(f_173_5,plain,
( ~ in(sK129(U_768,U_767),U_767)
| element(U_768,powerset(U_767)) ),
inference(clausify,[status(thm)],[f_173_3]) ).
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]) ).
cnf(f_174_3,plain,
( 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(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
( in(U_770,U_771)
| ~ in(U_770,relation_dom(relation_dom_restriction(U_769,U_771)))
| ~ function(U_769)
| ~ relation(U_769) ),
inference(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_5,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))
| ~ function(U_769)
| ~ relation(U_769) ),
inference(clausify,[status(thm)],[f_174_2]) ).
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]) ).
cnf(f_175_4,plain,
relation(sK130),
inference(clausify,[status(thm)],[f_175_3]) ).
cnf(f_175_5,plain,
function(sK130),
inference(clausify,[status(thm)],[f_175_3]) ).
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]) ).
cnf(f_176_4,plain,
epsilon_transitive(sK131),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_5,plain,
epsilon_connected(sK131),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_6,plain,
ordinal(sK131),
inference(clausify,[status(thm)],[f_176_3]) ).
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]) ).
cnf(f_177_4,plain,
empty(sK132),
inference(clausify,[status(thm)],[f_177_3]) ).
cnf(f_177_5,plain,
relation(sK132),
inference(clausify,[status(thm)],[f_177_3]) ).
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]) ).
cnf(f_178_4,plain,
( element(sK133(U_776),powerset(U_776))
| empty(U_776) ),
inference(clausify,[status(thm)],[f_178_3]) ).
cnf(f_178_5,plain,
( ~ empty(sK133(U_776))
| empty(U_776) ),
inference(clausify,[status(thm)],[f_178_3]) ).
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]) ).
cnf(f_179_4,plain,
empty(sK134),
inference(clausify,[status(thm)],[f_179_3]) ).
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]) ).
cnf(f_180_4,plain,
relation(sK135),
inference(clausify,[status(thm)],[f_180_3]) ).
cnf(f_180_5,plain,
empty(sK135),
inference(clausify,[status(thm)],[f_180_3]) ).
cnf(f_180_6,plain,
function(sK135),
inference(clausify,[status(thm)],[f_180_3]) ).
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]) ).
cnf(f_181_4,plain,
relation(sK136),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
function(sK136),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_6,plain,
one_to_one(sK136),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_7,plain,
empty(sK136),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_8,plain,
epsilon_transitive(sK136),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_9,plain,
epsilon_connected(sK136),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_10,plain,
ordinal(sK136),
inference(clausify,[status(thm)],[f_181_3]) ).
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]) ).
cnf(f_182_4,plain,
~ empty(sK137),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_5,plain,
relation(sK137),
inference(clausify,[status(thm)],[f_182_3]) ).
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]) ).
cnf(f_183_4,plain,
element(sK138(U_782),powerset(U_782)),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
empty(sK138(U_782)),
inference(clausify,[status(thm)],[f_183_3]) ).
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]) ).
cnf(f_184_4,plain,
~ empty(sK139),
inference(clausify,[status(thm)],[f_184_3]) ).
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]) ).
cnf(f_185_4,plain,
relation(sK140),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_5,plain,
function(sK140),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_6,plain,
one_to_one(sK140),
inference(clausify,[status(thm)],[f_185_3]) ).
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]) ).
cnf(f_186_4,plain,
~ empty(sK141),
inference(clausify,[status(thm)],[f_186_3]) ).
cnf(f_186_5,plain,
epsilon_transitive(sK141),
inference(clausify,[status(thm)],[f_186_3]) ).
cnf(f_186_6,plain,
epsilon_connected(sK141),
inference(clausify,[status(thm)],[f_186_3]) ).
cnf(f_186_7,plain,
ordinal(sK141),
inference(clausify,[status(thm)],[f_186_3]) ).
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]) ).
cnf(f_187_4,plain,
relation(sK142),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_5,plain,
relation_empty_yielding(sK142),
inference(clausify,[status(thm)],[f_187_3]) ).
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]) ).
cnf(f_188_4,plain,
relation(sK143),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_5,plain,
relation_empty_yielding(sK143),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_6,plain,
function(sK143),
inference(clausify,[status(thm)],[f_188_3]) ).
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]) ).
cnf(f_189_3,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_2]) ).
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]) ).
cnf(f_190_3,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_2]) ).
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]) ).
cnf(f_191_3,plain,
( union_of_subsets(U_795,U_794) = union(U_794)
| ~ element(U_794,powerset(powerset(U_795))) ),
inference(clausify,[status(thm)],[f_191_2]) ).
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]) ).
cnf(f_192_3,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_2]) ).
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]) ).
cnf(f_193_3,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_2]) ).
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]) ).
cnf(f_194_4,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_3]) ).
cnf(f_194_5,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_3]) ).
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]) ).
cnf(f_195_3,plain,
( subset(U_811,U_810)
| ~ ordinal_subset(U_811,U_810)
| ~ ordinal(U_810)
| ~ ordinal(U_811) ),
inference(clausify,[status(thm)],[f_195_2]) ).
cnf(f_195_4,plain,
( ordinal_subset(U_811,U_810)
| ~ subset(U_811,U_810)
| ~ ordinal(U_810)
| ~ ordinal(U_811) ),
inference(clausify,[status(thm)],[f_195_2]) ).
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]) ).
cnf(f_196_4,plain,
( ~ ordinal(U_812)
| ~ ordinal(U_813)
| ordinal_subset(U_813,U_813) ),
inference(clausify,[status(thm)],[f_196_3]) ).
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]) ).
cnf(f_197_4,plain,
subset(U_815,U_815),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_198_2,plain,
! [U_817,U_816] :
( disjoint(U_816,U_817)
| ~ disjoint(U_817,U_816) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( disjoint(U_816,U_817)
| ~ disjoint(U_817,U_816) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_821,U_820,U_819,U_818] :
( ( in(ordered_pair(U_821,U_820),cartesian_product2(U_819,U_818))
| ~ in(U_820,U_818)
| ~ in(U_821,U_819) )
& ( ( in(U_820,U_818)
& in(U_821,U_819) )
| ~ in(ordered_pair(U_821,U_820),cartesian_product2(U_819,U_818)) ) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
( ! [U_829,U_827,U_825,U_823] :
( in(ordered_pair(U_829,U_827),cartesian_product2(U_825,U_823))
| ~ in(U_827,U_823)
| ~ in(U_829,U_825) )
& ! [U_828,U_826,U_824,U_822] :
( ( in(U_826,U_822)
& in(U_828,U_824) )
| ~ in(ordered_pair(U_828,U_826),cartesian_product2(U_824,U_822)) ) ),
inference(miniscope,[status(thm)],[f_199_2]) ).
cnf(f_199_4,plain,
( in(U_828,U_824)
| ~ in(ordered_pair(U_828,U_826),cartesian_product2(U_824,U_822)) ),
inference(clausify,[status(thm)],[f_199_3]) ).
cnf(f_199_5,plain,
( in(U_826,U_822)
| ~ in(ordered_pair(U_828,U_826),cartesian_product2(U_824,U_822)) ),
inference(clausify,[status(thm)],[f_199_3]) ).
cnf(f_199_6,plain,
( in(ordered_pair(U_829,U_827),cartesian_product2(U_825,U_823))
| ~ in(U_827,U_823)
| ~ in(U_829,U_825) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_200_2,plain,
! [U_830] : in(U_830,succ(U_830)),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
in(U_830,succ(U_830)),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_834,U_833,U_832,U_831] :
( U_834 = U_831
| U_834 = U_832
| unordered_pair(U_834,U_833) != unordered_pair(U_832,U_831) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_834,U_833,U_832] :
( ! [U_831] :
( U_834 = U_831
| unordered_pair(U_834,U_833) != unordered_pair(U_832,U_831) )
| U_834 = U_832 ),
inference(miniscope,[status(thm)],[f_201_2]) ).
cnf(f_201_4,plain,
( U_834 = U_831
| unordered_pair(U_834,U_833) != unordered_pair(U_832,U_831)
| U_834 = U_832 ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_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_202_2,plain,
! [U_837,U_836,U_835] :
( ( ( in(U_837,relation_rng(relation_rng_restriction(U_836,U_835)))
| ~ in(U_837,relation_rng(U_835))
| ~ in(U_837,U_836) )
& ( ( in(U_837,relation_rng(U_835))
& in(U_837,U_836) )
| ~ in(U_837,relation_rng(relation_rng_restriction(U_836,U_835))) ) )
| ~ relation(U_835) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( in(U_837,U_836)
| ~ in(U_837,relation_rng(relation_rng_restriction(U_836,U_835)))
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_202_2]) ).
cnf(f_202_4,plain,
( in(U_837,relation_rng(U_835))
| ~ in(U_837,relation_rng(relation_rng_restriction(U_836,U_835)))
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_202_2]) ).
cnf(f_202_5,plain,
( in(U_837,relation_rng(relation_rng_restriction(U_836,U_835)))
| ~ in(U_837,relation_rng(U_835))
| ~ in(U_837,U_836)
| ~ relation(U_835) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_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_203_2,plain,
! [U_839,U_838] :
( subset(relation_rng(relation_rng_restriction(U_839,U_838)),U_839)
| ~ relation(U_838) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( subset(relation_rng(relation_rng_restriction(U_839,U_838)),U_839)
| ~ relation(U_838) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_204_2,plain,
! [U_841,U_840] :
( subset(relation_rng_restriction(U_841,U_840),U_840)
| ~ relation(U_840) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( subset(relation_rng_restriction(U_841,U_840),U_840)
| ~ relation(U_840) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_843,U_842] :
( subset(relation_rng(relation_rng_restriction(U_843,U_842)),relation_rng(U_842))
| ~ relation(U_842) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( subset(relation_rng(relation_rng_restriction(U_843,U_842)),relation_rng(U_842))
| ~ relation(U_842) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_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_206_2,plain,
! [U_846,U_845,U_844] :
( ( subset(cartesian_product2(U_844,U_846),cartesian_product2(U_844,U_845))
& subset(cartesian_product2(U_846,U_844),cartesian_product2(U_845,U_844)) )
| ~ subset(U_846,U_845) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_846,U_845] :
( ( ! [U_848] : subset(cartesian_product2(U_848,U_846),cartesian_product2(U_848,U_845))
& ! [U_847] : subset(cartesian_product2(U_846,U_847),cartesian_product2(U_845,U_847)) )
| ~ subset(U_846,U_845) ),
inference(miniscope,[status(thm)],[f_206_2]) ).
cnf(f_206_4,plain,
( subset(cartesian_product2(U_846,U_847),cartesian_product2(U_845,U_847))
| ~ subset(U_846,U_845) ),
inference(clausify,[status(thm)],[f_206_3]) ).
cnf(f_206_5,plain,
( subset(cartesian_product2(U_848,U_846),cartesian_product2(U_848,U_845))
| ~ subset(U_846,U_845) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_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_207_2,plain,
! [U_850,U_849] :
( relation_rng(relation_rng_restriction(U_850,U_849)) = set_intersection2(relation_rng(U_849),U_850)
| ~ relation(U_849) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( relation_rng(relation_rng_restriction(U_850,U_849)) = set_intersection2(relation_rng(U_849),U_850)
| ~ relation(U_849) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_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_208_2,plain,
! [U_854,U_853,U_852,U_851] :
( subset(cartesian_product2(U_854,U_852),cartesian_product2(U_853,U_851))
| ~ subset(U_852,U_851)
| ~ subset(U_854,U_853) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( subset(cartesian_product2(U_854,U_852),cartesian_product2(U_853,U_851))
| ~ subset(U_852,U_851)
| ~ subset(U_854,U_853) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_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_209_2,plain,
! [U_857,U_856,U_855] :
( ( subset(relation_rng(U_855),U_856)
& subset(relation_dom(U_855),U_857) )
| ~ relation_of2_as_subset(U_855,U_857,U_856) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( subset(relation_dom(U_855),U_857)
| ~ relation_of2_as_subset(U_855,U_857,U_856) ),
inference(clausify,[status(thm)],[f_209_2]) ).
cnf(f_209_4,plain,
( subset(relation_rng(U_855),U_856)
| ~ relation_of2_as_subset(U_855,U_857,U_856) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_210_2,plain,
! [U_859,U_858] :
( set_union2(U_859,U_858) = U_858
| ~ subset(U_859,U_858) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( set_union2(U_859,U_858) = U_858
| ~ subset(U_859,U_858) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_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_211_2,plain,
! [U_865] :
? [U_864] :
( ! [U_863] :
( in(U_863,U_864)
| are_equipotent(U_863,U_864)
| ~ subset(U_863,U_864) )
& ! [U_862] :
( in(powerset(U_862),U_864)
| ~ in(U_862,U_864) )
& ! [U_861,U_860] :
( in(U_860,U_864)
| ~ subset(U_860,U_861)
| ~ in(U_861,U_864) )
& in(U_865,U_864) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_865] :
( ! [U_863] :
( in(U_863,sK144(U_865))
| are_equipotent(U_863,sK144(U_865))
| ~ subset(U_863,sK144(U_865)) )
& ! [U_862] :
( in(powerset(U_862),sK144(U_865))
| ~ in(U_862,sK144(U_865)) )
& ! [U_861,U_860] :
( in(U_860,sK144(U_865))
| ~ subset(U_860,U_861)
| ~ in(U_861,sK144(U_865)) )
& in(U_865,sK144(U_865)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_864,sK144(U_865))],[f_211_2]) ).
cnf(f_211_4,plain,
in(U_865,sK144(U_865)),
inference(clausify,[status(thm)],[f_211_3]) ).
cnf(f_211_5,plain,
( in(U_860,sK144(U_865))
| ~ subset(U_860,U_861)
| ~ in(U_861,sK144(U_865)) ),
inference(clausify,[status(thm)],[f_211_3]) ).
cnf(f_211_6,plain,
( in(powerset(U_862),sK144(U_865))
| ~ in(U_862,sK144(U_865)) ),
inference(clausify,[status(thm)],[f_211_3]) ).
cnf(f_211_7,plain,
( in(U_863,sK144(U_865))
| are_equipotent(U_863,sK144(U_865))
| ~ subset(U_863,sK144(U_865)) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_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_212_2,plain,
! [U_868,U_867,U_866] :
( relation_dom_restriction(relation_rng_restriction(U_868,U_866),U_867) = relation_rng_restriction(U_868,relation_dom_restriction(U_866,U_867))
| ~ relation(U_866) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( relation_dom_restriction(relation_rng_restriction(U_868,U_866),U_867) = relation_rng_restriction(U_868,relation_dom_restriction(U_866,U_867))
| ~ relation(U_866) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_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_213_2,plain,
! [U_873,U_872,U_871] :
( ( ( in(U_873,relation_image(U_871,U_872))
| ! [U_870] :
( ~ in(U_870,U_872)
| ~ in(ordered_pair(U_870,U_873),U_871)
| ~ in(U_870,relation_dom(U_871)) ) )
& ( ? [U_869] :
( in(U_869,U_872)
& in(ordered_pair(U_869,U_873),U_871)
& in(U_869,relation_dom(U_871)) )
| ~ in(U_873,relation_image(U_871,U_872)) ) )
| ~ relation(U_871) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_873,U_872,U_871] :
( ( ( in(U_873,relation_image(U_871,U_872))
| ! [U_870] :
( ~ in(U_870,U_872)
| ~ in(ordered_pair(U_870,U_873),U_871)
| ~ in(U_870,relation_dom(U_871)) ) )
& ( ( in(sK145(U_873,U_872,U_871),U_872)
& in(ordered_pair(sK145(U_873,U_872,U_871),U_873),U_871)
& in(sK145(U_873,U_872,U_871),relation_dom(U_871)) )
| ~ in(U_873,relation_image(U_871,U_872)) ) )
| ~ relation(U_871) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_869,sK145(U_873,U_872,U_871))],[f_213_2]) ).
cnf(f_213_4,plain,
( in(sK145(U_873,U_872,U_871),relation_dom(U_871))
| ~ in(U_873,relation_image(U_871,U_872))
| ~ relation(U_871) ),
inference(clausify,[status(thm)],[f_213_3]) ).
cnf(f_213_5,plain,
( in(ordered_pair(sK145(U_873,U_872,U_871),U_873),U_871)
| ~ in(U_873,relation_image(U_871,U_872))
| ~ relation(U_871) ),
inference(clausify,[status(thm)],[f_213_3]) ).
cnf(f_213_6,plain,
( in(sK145(U_873,U_872,U_871),U_872)
| ~ in(U_873,relation_image(U_871,U_872))
| ~ relation(U_871) ),
inference(clausify,[status(thm)],[f_213_3]) ).
cnf(f_213_7,plain,
( in(U_873,relation_image(U_871,U_872))
| ~ in(U_870,U_872)
| ~ in(ordered_pair(U_870,U_873),U_871)
| ~ in(U_870,relation_dom(U_871))
| ~ relation(U_871) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_214_2,plain,
! [U_875,U_874] :
( subset(relation_image(U_874,U_875),relation_rng(U_874))
| ~ relation(U_874) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( subset(relation_image(U_874,U_875),relation_rng(U_874))
| ~ relation(U_874) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_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_215_2,plain,
! [U_877,U_876] :
( subset(relation_image(U_876,relation_inverse_image(U_876,U_877)),U_877)
| ~ function(U_876)
| ~ relation(U_876) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( subset(relation_image(U_876,relation_inverse_image(U_876,U_877)),U_877)
| ~ function(U_876)
| ~ relation(U_876) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_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_216_2,plain,
! [U_879,U_878] :
( relation_image(U_878,U_879) = relation_image(U_878,set_intersection2(relation_dom(U_878),U_879))
| ~ relation(U_878) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( relation_image(U_878,U_879) = relation_image(U_878,set_intersection2(relation_dom(U_878),U_879))
| ~ relation(U_878) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_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_217_2,plain,
! [U_881,U_880] :
( subset(U_881,relation_inverse_image(U_880,relation_image(U_880,U_881)))
| ~ subset(U_881,relation_dom(U_880))
| ~ relation(U_880) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( subset(U_881,relation_inverse_image(U_880,relation_image(U_880,U_881)))
| ~ subset(U_881,relation_dom(U_880))
| ~ relation(U_880) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_218_2,plain,
! [U_882] :
( relation_image(U_882,relation_dom(U_882)) = relation_rng(U_882)
| ~ relation(U_882) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( relation_image(U_882,relation_dom(U_882)) = relation_rng(U_882)
| ~ relation(U_882) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_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_219_2,plain,
! [U_884,U_883] :
( relation_image(U_883,relation_inverse_image(U_883,U_884)) = U_884
| ~ subset(U_884,relation_rng(U_883))
| ~ function(U_883)
| ~ relation(U_883) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( relation_image(U_883,relation_inverse_image(U_883,U_884)) = U_884
| ~ subset(U_884,relation_rng(U_883))
| ~ function(U_883)
| ~ relation(U_883) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_888,U_887,U_886,U_885] :
( relation_of2_as_subset(U_885,U_886,U_887)
| ~ subset(relation_rng(U_885),U_887)
| ~ relation_of2_as_subset(U_885,U_886,U_888) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( relation_of2_as_subset(U_885,U_886,U_887)
| ~ subset(relation_rng(U_885),U_887)
| ~ relation_of2_as_subset(U_885,U_886,U_888) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_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_221_2,plain,
! [U_890] :
( ! [U_889] :
( relation_rng(relation_composition(U_890,U_889)) = relation_image(U_889,relation_rng(U_890))
| ~ relation(U_889) )
| ~ relation(U_890) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( relation_rng(relation_composition(U_890,U_889)) = relation_image(U_889,relation_rng(U_890))
| ~ relation(U_889)
| ~ relation(U_890) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_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_222_2,plain,
! [U_895,U_894,U_893] :
( ( ( in(U_895,relation_inverse_image(U_893,U_894))
| ! [U_892] :
( ~ in(U_892,U_894)
| ~ in(ordered_pair(U_895,U_892),U_893)
| ~ in(U_892,relation_rng(U_893)) ) )
& ( ? [U_891] :
( in(U_891,U_894)
& in(ordered_pair(U_895,U_891),U_893)
& in(U_891,relation_rng(U_893)) )
| ~ in(U_895,relation_inverse_image(U_893,U_894)) ) )
| ~ relation(U_893) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_895,U_894,U_893] :
( ( ( in(U_895,relation_inverse_image(U_893,U_894))
| ! [U_892] :
( ~ in(U_892,U_894)
| ~ in(ordered_pair(U_895,U_892),U_893)
| ~ in(U_892,relation_rng(U_893)) ) )
& ( ( in(sK146(U_895,U_894,U_893),U_894)
& in(ordered_pair(U_895,sK146(U_895,U_894,U_893)),U_893)
& in(sK146(U_895,U_894,U_893),relation_rng(U_893)) )
| ~ in(U_895,relation_inverse_image(U_893,U_894)) ) )
| ~ relation(U_893) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_891,sK146(U_895,U_894,U_893))],[f_222_2]) ).
cnf(f_222_4,plain,
( in(sK146(U_895,U_894,U_893),relation_rng(U_893))
| ~ in(U_895,relation_inverse_image(U_893,U_894))
| ~ relation(U_893) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_5,plain,
( in(ordered_pair(U_895,sK146(U_895,U_894,U_893)),U_893)
| ~ in(U_895,relation_inverse_image(U_893,U_894))
| ~ relation(U_893) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_6,plain,
( in(sK146(U_895,U_894,U_893),U_894)
| ~ in(U_895,relation_inverse_image(U_893,U_894))
| ~ relation(U_893) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_7,plain,
( in(U_895,relation_inverse_image(U_893,U_894))
| ~ in(U_892,U_894)
| ~ in(ordered_pair(U_895,U_892),U_893)
| ~ in(U_892,relation_rng(U_893))
| ~ relation(U_893) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_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_223_2,plain,
! [U_897,U_896] :
( subset(relation_inverse_image(U_896,U_897),relation_dom(U_896))
| ~ relation(U_896) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( subset(relation_inverse_image(U_896,U_897),relation_dom(U_896))
| ~ relation(U_896) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_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_224_2,plain,
! [U_901,U_900,U_899,U_898] :
( relation_of2_as_subset(U_898,U_899,U_900)
| ~ subset(U_901,U_900)
| ~ relation_of2_as_subset(U_898,U_899,U_901) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( relation_of2_as_subset(U_898,U_899,U_900)
| ~ subset(U_901,U_900)
| ~ relation_of2_as_subset(U_898,U_899,U_901) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_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_225_2,plain,
! [U_904,U_903,U_902] :
( ( ( in(U_904,relation_restriction(U_902,U_903))
| ~ in(U_904,cartesian_product2(U_903,U_903))
| ~ in(U_904,U_902) )
& ( ( in(U_904,cartesian_product2(U_903,U_903))
& in(U_904,U_902) )
| ~ in(U_904,relation_restriction(U_902,U_903)) ) )
| ~ relation(U_902) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( in(U_904,U_902)
| ~ in(U_904,relation_restriction(U_902,U_903))
| ~ relation(U_902) ),
inference(clausify,[status(thm)],[f_225_2]) ).
cnf(f_225_4,plain,
( in(U_904,cartesian_product2(U_903,U_903))
| ~ in(U_904,relation_restriction(U_902,U_903))
| ~ relation(U_902) ),
inference(clausify,[status(thm)],[f_225_2]) ).
cnf(f_225_5,plain,
( in(U_904,relation_restriction(U_902,U_903))
| ~ in(U_904,cartesian_product2(U_903,U_903))
| ~ in(U_904,U_902)
| ~ relation(U_902) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_906,U_905] :
( relation_inverse_image(U_905,U_906) != empty_set
| ~ subset(U_906,relation_rng(U_905))
| U_906 = empty_set
| ~ relation(U_905) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( relation_inverse_image(U_905,U_906) != empty_set
| ~ subset(U_906,relation_rng(U_905))
| U_906 = empty_set
| ~ relation(U_905) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_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_227_2,plain,
! [U_909,U_908,U_907] :
( subset(relation_inverse_image(U_907,U_909),relation_inverse_image(U_907,U_908))
| ~ subset(U_909,U_908)
| ~ relation(U_907) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( subset(relation_inverse_image(U_907,U_909),relation_inverse_image(U_907,U_908))
| ~ subset(U_909,U_908)
| ~ relation(U_907) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_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_228_2,plain,
! [U_911,U_910] :
( relation_restriction(U_910,U_911) = relation_dom_restriction(relation_rng_restriction(U_911,U_910),U_911)
| ~ relation(U_910) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
( relation_restriction(U_910,U_911) = relation_dom_restriction(relation_rng_restriction(U_911,U_910),U_911)
| ~ relation(U_910) ),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_229_2,plain,
! [U_913,U_912] : subset(set_intersection2(U_913,U_912),U_913),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
subset(set_intersection2(U_913,U_912),U_913),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_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_230_2,plain,
! [U_915,U_914] :
( relation_restriction(U_914,U_915) = relation_rng_restriction(U_915,relation_dom_restriction(U_914,U_915))
| ~ relation(U_914) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( relation_restriction(U_914,U_915) = relation_rng_restriction(U_915,relation_dom_restriction(U_914,U_915))
| ~ relation(U_914) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_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_231_2,plain,
! [U_918,U_917,U_916] :
( ( in(U_918,U_917)
& in(U_918,relation_field(U_916)) )
| ~ in(U_918,relation_field(relation_restriction(U_916,U_917)))
| ~ relation(U_916) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( in(U_918,relation_field(U_916))
| ~ in(U_918,relation_field(relation_restriction(U_916,U_917)))
| ~ relation(U_916) ),
inference(clausify,[status(thm)],[f_231_2]) ).
cnf(f_231_4,plain,
( in(U_918,U_917)
| ~ in(U_918,relation_field(relation_restriction(U_916,U_917)))
| ~ relation(U_916) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_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_232_2,plain,
! [U_921,U_920,U_919] :
( subset(U_921,set_intersection2(U_920,U_919))
| ~ subset(U_921,U_919)
| ~ subset(U_921,U_920) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
( subset(U_921,set_intersection2(U_920,U_919))
| ~ subset(U_921,U_919)
| ~ subset(U_921,U_920) ),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_233_2,plain,
! [U_922] : set_union2(U_922,empty_set) = U_922,
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
set_union2(U_922,empty_set) = U_922,
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_234_2,plain,
! [U_924,U_923] :
( element(U_924,U_923)
| ~ in(U_924,U_923) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( element(U_924,U_923)
| ~ in(U_924,U_923) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_235_2,plain,
! [U_927,U_926,U_925] :
( subset(U_927,U_925)
| ~ subset(U_926,U_925)
| ~ subset(U_927,U_926) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( subset(U_927,U_925)
| ~ subset(U_926,U_925)
| ~ subset(U_927,U_926) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
cnf(f_236_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_236_1]) ).
fof(f_237_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_237_2,plain,
! [U_930,U_929,U_928] :
( ( in(U_929,relation_rng(U_928))
& in(U_930,relation_dom(U_928)) )
| ~ in(ordered_pair(U_930,U_929),U_928)
| ~ relation(U_928) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( in(U_930,relation_dom(U_928))
| ~ in(ordered_pair(U_930,U_929),U_928)
| ~ relation(U_928) ),
inference(clausify,[status(thm)],[f_237_2]) ).
cnf(f_237_4,plain,
( in(U_929,relation_rng(U_928))
| ~ in(ordered_pair(U_930,U_929),U_928)
| ~ relation(U_928) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_932,U_931] :
( ( subset(relation_field(relation_restriction(U_931,U_932)),U_932)
& subset(relation_field(relation_restriction(U_931,U_932)),relation_field(U_931)) )
| ~ relation(U_931) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( subset(relation_field(relation_restriction(U_931,U_932)),relation_field(U_931))
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_238_2]) ).
cnf(f_238_4,plain,
( subset(relation_field(relation_restriction(U_931,U_932)),U_932)
| ~ relation(U_931) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_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_239_2,plain,
! [U_935,U_934] :
( ! [U_933] :
( ( ( in(U_935,relation_dom(relation_composition(U_933,U_934)))
| ~ in(apply(U_933,U_935),relation_dom(U_934))
| ~ in(U_935,relation_dom(U_933)) )
& ( ( in(apply(U_933,U_935),relation_dom(U_934))
& in(U_935,relation_dom(U_933)) )
| ~ in(U_935,relation_dom(relation_composition(U_933,U_934))) ) )
| ~ function(U_933)
| ~ relation(U_933) )
| ~ function(U_934)
| ~ relation(U_934) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( in(U_935,relation_dom(U_933))
| ~ in(U_935,relation_dom(relation_composition(U_933,U_934)))
| ~ function(U_933)
| ~ relation(U_933)
| ~ function(U_934)
| ~ relation(U_934) ),
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_239_4,plain,
( in(apply(U_933,U_935),relation_dom(U_934))
| ~ in(U_935,relation_dom(relation_composition(U_933,U_934)))
| ~ function(U_933)
| ~ relation(U_933)
| ~ function(U_934)
| ~ relation(U_934) ),
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_239_5,plain,
( in(U_935,relation_dom(relation_composition(U_933,U_934)))
| ~ in(apply(U_933,U_935),relation_dom(U_934))
| ~ in(U_935,relation_dom(U_933))
| ~ function(U_933)
| ~ relation(U_933)
| ~ function(U_934)
| ~ relation(U_934) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_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_240_2,plain,
! [U_937] :
( ! [U_936] :
( in(U_937,U_936)
| ~ proper_subset(U_937,U_936)
| ~ ordinal(U_936) )
| ~ epsilon_transitive(U_937) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( in(U_937,U_936)
| ~ proper_subset(U_937,U_936)
| ~ ordinal(U_936)
| ~ epsilon_transitive(U_937) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_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_241_2,plain,
! [U_938] :
( subset(U_938,cartesian_product2(relation_dom(U_938),relation_rng(U_938)))
| ~ relation(U_938) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( subset(U_938,cartesian_product2(relation_dom(U_938),relation_rng(U_938)))
| ~ relation(U_938) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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_242_2,plain,
! [U_941,U_940,U_939] :
( subset(fiber(relation_restriction(U_939,U_941),U_940),fiber(U_939,U_940))
| ~ relation(U_939) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( subset(fiber(relation_restriction(U_939,U_941),U_940),fiber(U_939,U_940))
| ~ relation(U_939) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_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_243_2,plain,
! [U_944,U_943] :
( ! [U_942] :
( apply(relation_composition(U_942,U_943),U_944) = apply(U_943,apply(U_942,U_944))
| ~ in(U_944,relation_dom(relation_composition(U_942,U_943)))
| ~ function(U_942)
| ~ relation(U_942) )
| ~ function(U_943)
| ~ relation(U_943) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( apply(relation_composition(U_942,U_943),U_944) = apply(U_943,apply(U_942,U_944))
| ~ in(U_944,relation_dom(relation_composition(U_942,U_943)))
| ~ function(U_942)
| ~ relation(U_942)
| ~ function(U_943)
| ~ relation(U_943) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_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_244_2,plain,
! [U_951,U_950,U_949] :
( ( ( ! [U_948] :
( ? [U_947] : in(ordered_pair(U_948,U_947),U_949)
| ~ in(U_948,U_950) )
| relation_dom_as_subset(U_950,U_951,U_949) != U_950 )
& ( relation_dom_as_subset(U_950,U_951,U_949) = U_950
| ? [U_946] :
( ! [U_945] : ~ in(ordered_pair(U_946,U_945),U_949)
& in(U_946,U_950) ) ) )
| ~ relation_of2_as_subset(U_949,U_950,U_951) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_951,U_950,U_949] :
( ( ( ! [U_948] :
( ? [U_947] : in(ordered_pair(U_948,U_947),U_949)
| ~ in(U_948,U_950) )
| relation_dom_as_subset(U_950,U_951,U_949) != U_950 )
& ( relation_dom_as_subset(U_950,U_951,U_949) = U_950
| ( ! [U_945] : ~ in(ordered_pair(sK147(U_951,U_950,U_949),U_945),U_949)
& in(sK147(U_951,U_950,U_949),U_950) ) ) )
| ~ relation_of2_as_subset(U_949,U_950,U_951) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_946,sK147(U_951,U_950,U_949))],[f_244_2]) ).
fof(f_244_4,plain,
! [U_951,U_950,U_949] :
( ( ( ! [U_948] :
( in(ordered_pair(U_948,sK148(U_951,U_950,U_949,U_948)),U_949)
| ~ in(U_948,U_950) )
| relation_dom_as_subset(U_950,U_951,U_949) != U_950 )
& ( relation_dom_as_subset(U_950,U_951,U_949) = U_950
| ( ! [U_945] : ~ in(ordered_pair(sK147(U_951,U_950,U_949),U_945),U_949)
& in(sK147(U_951,U_950,U_949),U_950) ) ) )
| ~ relation_of2_as_subset(U_949,U_950,U_951) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_947,sK148(U_951,U_950,U_949,U_948))],[f_244_3]) ).
cnf(f_244_5,plain,
( in(sK147(U_951,U_950,U_949),U_950)
| relation_dom_as_subset(U_950,U_951,U_949) = U_950
| ~ relation_of2_as_subset(U_949,U_950,U_951) ),
inference(clausify,[status(thm)],[f_244_4]) ).
cnf(f_244_6,plain,
( ~ in(ordered_pair(sK147(U_951,U_950,U_949),U_945),U_949)
| relation_dom_as_subset(U_950,U_951,U_949) = U_950
| ~ relation_of2_as_subset(U_949,U_950,U_951) ),
inference(clausify,[status(thm)],[f_244_4]) ).
cnf(f_244_7,plain,
( in(ordered_pair(U_948,sK148(U_951,U_950,U_949,U_948)),U_949)
| ~ in(U_948,U_950)
| relation_dom_as_subset(U_950,U_951,U_949) != U_950
| ~ relation_of2_as_subset(U_949,U_950,U_951) ),
inference(clausify,[status(thm)],[f_244_4]) ).
fof(f_245_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_245_2,plain,
! [U_953,U_952] :
( reflexive(relation_restriction(U_952,U_953))
| ~ reflexive(U_952)
| ~ relation(U_952) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( reflexive(relation_restriction(U_952,U_953))
| ~ reflexive(U_952)
| ~ relation(U_952) ),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_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_246_2,plain,
! [U_956,U_955] :
( ! [U_954] :
( apply(relation_composition(U_955,U_954),U_956) = apply(U_954,apply(U_955,U_956))
| ~ in(U_956,relation_dom(U_955))
| ~ function(U_954)
| ~ relation(U_954) )
| ~ function(U_955)
| ~ relation(U_955) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( apply(relation_composition(U_955,U_954),U_956) = apply(U_954,apply(U_955,U_956))
| ~ in(U_956,relation_dom(U_955))
| ~ function(U_954)
| ~ relation(U_954)
| ~ function(U_955)
| ~ relation(U_955) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_247_2,plain,
! [U_958,U_957] :
( ordinal(U_958)
| ~ in(U_958,U_957)
| ~ ordinal(U_957) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( ordinal(U_958)
| ~ in(U_958,U_957)
| ~ ordinal(U_957) ),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_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_248_2,plain,
! [U_965,U_964,U_963] :
( ( ( ! [U_962] :
( ? [U_961] : in(ordered_pair(U_961,U_962),U_963)
| ~ in(U_962,U_964) )
| relation_rng_as_subset(U_965,U_964,U_963) != U_964 )
& ( relation_rng_as_subset(U_965,U_964,U_963) = U_964
| ? [U_960] :
( ! [U_959] : ~ in(ordered_pair(U_959,U_960),U_963)
& in(U_960,U_964) ) ) )
| ~ relation_of2_as_subset(U_963,U_965,U_964) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_965,U_964,U_963] :
( ( ( ! [U_962] :
( ? [U_961] : in(ordered_pair(U_961,U_962),U_963)
| ~ in(U_962,U_964) )
| relation_rng_as_subset(U_965,U_964,U_963) != U_964 )
& ( relation_rng_as_subset(U_965,U_964,U_963) = U_964
| ( ! [U_959] : ~ in(ordered_pair(U_959,sK149(U_965,U_964,U_963)),U_963)
& in(sK149(U_965,U_964,U_963),U_964) ) ) )
| ~ relation_of2_as_subset(U_963,U_965,U_964) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_960,sK149(U_965,U_964,U_963))],[f_248_2]) ).
fof(f_248_4,plain,
! [U_965,U_964,U_963] :
( ( ( ! [U_962] :
( in(ordered_pair(sK150(U_965,U_964,U_963,U_962),U_962),U_963)
| ~ in(U_962,U_964) )
| relation_rng_as_subset(U_965,U_964,U_963) != U_964 )
& ( relation_rng_as_subset(U_965,U_964,U_963) = U_964
| ( ! [U_959] : ~ in(ordered_pair(U_959,sK149(U_965,U_964,U_963)),U_963)
& in(sK149(U_965,U_964,U_963),U_964) ) ) )
| ~ relation_of2_as_subset(U_963,U_965,U_964) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_961,sK150(U_965,U_964,U_963,U_962))],[f_248_3]) ).
cnf(f_248_5,plain,
( in(sK149(U_965,U_964,U_963),U_964)
| relation_rng_as_subset(U_965,U_964,U_963) = U_964
| ~ relation_of2_as_subset(U_963,U_965,U_964) ),
inference(clausify,[status(thm)],[f_248_4]) ).
cnf(f_248_6,plain,
( ~ in(ordered_pair(U_959,sK149(U_965,U_964,U_963)),U_963)
| relation_rng_as_subset(U_965,U_964,U_963) = U_964
| ~ relation_of2_as_subset(U_963,U_965,U_964) ),
inference(clausify,[status(thm)],[f_248_4]) ).
cnf(f_248_7,plain,
( in(ordered_pair(sK150(U_965,U_964,U_963,U_962),U_962),U_963)
| ~ in(U_962,U_964)
| relation_rng_as_subset(U_965,U_964,U_963) != U_964
| ~ relation_of2_as_subset(U_963,U_965,U_964) ),
inference(clausify,[status(thm)],[f_248_4]) ).
fof(f_249_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_249_2,plain,
! [U_967,U_966] :
( connected(relation_restriction(U_966,U_967))
| ~ connected(U_966)
| ~ relation(U_966) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
( connected(relation_restriction(U_966,U_967))
| ~ connected(U_966)
| ~ relation(U_966) ),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_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_250_2,plain,
! [U_969] :
( ! [U_968] :
( in(U_968,U_969)
| U_969 = U_968
| in(U_969,U_968)
| ~ ordinal(U_968) )
| ~ ordinal(U_969) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
( in(U_968,U_969)
| U_969 = U_968
| in(U_969,U_968)
| ~ ordinal(U_968)
| ~ ordinal(U_969) ),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_251_2,plain,
! [U_971,U_970] :
( transitive(relation_restriction(U_970,U_971))
| ~ transitive(U_970)
| ~ relation(U_970) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
( transitive(relation_restriction(U_970,U_971))
| ~ transitive(U_970)
| ~ relation(U_970) ),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_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_252_2,plain,
! [U_973] :
( ! [U_972] :
( ( subset(relation_rng(U_973),relation_rng(U_972))
& subset(relation_dom(U_973),relation_dom(U_972)) )
| ~ subset(U_973,U_972)
| ~ relation(U_972) )
| ~ relation(U_973) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
( subset(relation_dom(U_973),relation_dom(U_972))
| ~ subset(U_973,U_972)
| ~ relation(U_972)
| ~ relation(U_973) ),
inference(clausify,[status(thm)],[f_252_2]) ).
cnf(f_252_4,plain,
( subset(relation_rng(U_973),relation_rng(U_972))
| ~ subset(U_973,U_972)
| ~ relation(U_972)
| ~ relation(U_973) ),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_253_2,plain,
! [U_975,U_974] :
( antisymmetric(relation_restriction(U_974,U_975))
| ~ antisymmetric(U_974)
| ~ relation(U_974) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( antisymmetric(relation_restriction(U_974,U_975))
| ~ antisymmetric(U_974)
| ~ relation(U_974) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_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_254_2,plain,
! [U_978,U_977,U_976] :
( subset(set_intersection2(U_978,U_976),set_intersection2(U_977,U_976))
| ~ subset(U_978,U_977) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_978,U_977] :
( ! [U_976] : subset(set_intersection2(U_978,U_976),set_intersection2(U_977,U_976))
| ~ subset(U_978,U_977) ),
inference(miniscope,[status(thm)],[f_254_2]) ).
cnf(f_254_4,plain,
( subset(set_intersection2(U_978,U_976),set_intersection2(U_977,U_976))
| ~ subset(U_978,U_977) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_255_2,plain,
! [U_980,U_979] :
( set_intersection2(U_980,U_979) = U_980
| ~ subset(U_980,U_979) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( set_intersection2(U_980,U_979) = U_980
| ~ subset(U_980,U_979) ),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_256_2,plain,
! [U_981] : set_intersection2(U_981,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
set_intersection2(U_981,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_257_2,plain,
! [U_983,U_982] :
( in(U_983,U_982)
| empty(U_982)
| ~ element(U_983,U_982) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( in(U_983,U_982)
| empty(U_982)
| ~ element(U_983,U_982) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_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_258_2,plain,
! [U_986,U_985] :
( U_986 = U_985
| ? [U_984] :
( ( ~ in(U_984,U_986)
& in(U_984,U_985) )
| ( ~ in(U_984,U_985)
& in(U_984,U_986) ) ) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_986,U_985] :
( U_986 = U_985
| ? [U_988] :
( ~ in(U_988,U_986)
& in(U_988,U_985) )
| ? [U_987] :
( ~ in(U_987,U_985)
& in(U_987,U_986) ) ),
inference(miniscope,[status(thm)],[f_258_2]) ).
fof(f_258_4,plain,
! [U_986,U_985] :
( U_986 = U_985
| ? [U_988] :
( ~ in(U_988,U_986)
& in(U_988,U_985) )
| ( ~ in(sK151(U_986,U_985),U_985)
& in(sK151(U_986,U_985),U_986) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_987,sK151(U_986,U_985))],[f_258_3]) ).
fof(f_258_5,plain,
! [U_986,U_985] :
( U_986 = U_985
| ( ~ in(sK152(U_986,U_985),U_986)
& in(sK152(U_986,U_985),U_985) )
| ( ~ in(sK151(U_986,U_985),U_985)
& in(sK151(U_986,U_985),U_986) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_988,sK152(U_986,U_985))],[f_258_4]) ).
cnf(f_258_6,plain,
( in(sK152(U_986,U_985),U_985)
| in(sK151(U_986,U_985),U_986)
| U_986 = U_985 ),
inference(clausify,[status(thm)],[f_258_5]) ).
cnf(f_258_7,plain,
( ~ in(sK152(U_986,U_985),U_986)
| in(sK151(U_986,U_985),U_986)
| U_986 = U_985 ),
inference(clausify,[status(thm)],[f_258_5]) ).
cnf(f_258_8,plain,
( in(sK152(U_986,U_985),U_985)
| ~ in(sK151(U_986,U_985),U_985)
| U_986 = U_985 ),
inference(clausify,[status(thm)],[f_258_5]) ).
cnf(f_258_9,plain,
( ~ in(sK152(U_986,U_985),U_986)
| ~ in(sK151(U_986,U_985),U_985)
| U_986 = U_985 ),
inference(clausify,[status(thm)],[f_258_5]) ).
fof(f_259_1,negated_conjecture,
~ ! [A] : reflexive(inclusion_relation(A)),
inference(negate,[status(cth)],[t2_wellord2]) ).
fof(f_259_2,negated_conjecture,
? [A] : ~ reflexive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[f_259_1]) ).
fof(f_259_3,negated_conjecture,
? [U_989] : ~ reflexive(inclusion_relation(U_989)),
inference(variable_rename,[status(thm)],[f_259_2]) ).
fof(f_259_4,negated_conjecture,
~ reflexive(inclusion_relation(sK153)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_989,sK153)],[f_259_3]) ).
cnf(f_259_5,negated_conjecture,
~ reflexive(inclusion_relation(sK153)),
inference(clausify,[status(thm)],[f_259_4]) ).
fof(f_260_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_260_2,plain,
! [U_990] : subset(empty_set,U_990),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
subset(empty_set,U_990),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_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_261_2,plain,
! [U_993,U_992,U_991] :
( ( in(U_992,relation_field(U_991))
& in(U_993,relation_field(U_991)) )
| ~ in(ordered_pair(U_993,U_992),U_991)
| ~ relation(U_991) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( in(U_993,relation_field(U_991))
| ~ in(ordered_pair(U_993,U_992),U_991)
| ~ relation(U_991) ),
inference(clausify,[status(thm)],[f_261_2]) ).
cnf(f_261_4,plain,
( in(U_992,relation_field(U_991))
| ~ in(ordered_pair(U_993,U_992),U_991)
| ~ relation(U_991) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_262_2,plain,
! [U_995] :
( ordinal(U_995)
| ? [U_994] :
( ( ~ subset(U_994,U_995)
| ~ ordinal(U_994) )
& in(U_994,U_995) ) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_995] :
( ordinal(U_995)
| ( ( ~ subset(sK154(U_995),U_995)
| ~ ordinal(sK154(U_995)) )
& in(sK154(U_995),U_995) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_994,sK154(U_995))],[f_262_2]) ).
cnf(f_262_4,plain,
( in(sK154(U_995),U_995)
| ordinal(U_995) ),
inference(clausify,[status(thm)],[f_262_3]) ).
cnf(f_262_5,plain,
( ~ subset(sK154(U_995),U_995)
| ~ ordinal(sK154(U_995))
| ordinal(U_995) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_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_263_2,plain,
! [U_997,U_996] :
( well_founded_relation(relation_restriction(U_996,U_997))
| ~ well_founded_relation(U_996)
| ~ relation(U_996) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( well_founded_relation(relation_restriction(U_996,U_997))
| ~ well_founded_relation(U_996)
| ~ relation(U_996) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_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_264_2,plain,
! [U_1001,U_1000] :
( ? [U_999] :
( ! [U_998] :
( ordinal_subset(U_999,U_998)
| ~ in(U_998,U_1001)
| ~ ordinal(U_998) )
& in(U_999,U_1001)
& ordinal(U_999) )
| U_1001 = empty_set
| ~ subset(U_1001,U_1000)
| ~ ordinal(U_1000) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_1001,U_1000] :
( ( ! [U_998] :
( ordinal_subset(sK155(U_1001,U_1000),U_998)
| ~ in(U_998,U_1001)
| ~ ordinal(U_998) )
& in(sK155(U_1001,U_1000),U_1001)
& ordinal(sK155(U_1001,U_1000)) )
| U_1001 = empty_set
| ~ subset(U_1001,U_1000)
| ~ ordinal(U_1000) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_999,sK155(U_1001,U_1000))],[f_264_2]) ).
cnf(f_264_4,plain,
( ordinal(sK155(U_1001,U_1000))
| U_1001 = empty_set
| ~ subset(U_1001,U_1000)
| ~ ordinal(U_1000) ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_5,plain,
( in(sK155(U_1001,U_1000),U_1001)
| U_1001 = empty_set
| ~ subset(U_1001,U_1000)
| ~ ordinal(U_1000) ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_6,plain,
( ordinal_subset(sK155(U_1001,U_1000),U_998)
| ~ in(U_998,U_1001)
| ~ ordinal(U_998)
| U_1001 = empty_set
| ~ subset(U_1001,U_1000)
| ~ ordinal(U_1000) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [A,B] :
( well_ordering(relation_restriction(B,A))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t32_wellord1]) ).
fof(f_265_2,plain,
! [U_1003,U_1002] :
( well_ordering(relation_restriction(U_1002,U_1003))
| ~ well_ordering(U_1002)
| ~ relation(U_1002) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( well_ordering(relation_restriction(U_1002,U_1003))
| ~ well_ordering(U_1002)
| ~ relation(U_1002) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_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_266_2,plain,
! [U_1005] :
( ! [U_1004] :
( ( ( in(U_1005,U_1004)
| ~ ordinal_subset(succ(U_1005),U_1004) )
& ( ordinal_subset(succ(U_1005),U_1004)
| ~ in(U_1005,U_1004) ) )
| ~ ordinal(U_1004) )
| ~ ordinal(U_1005) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( ordinal_subset(succ(U_1005),U_1004)
| ~ in(U_1005,U_1004)
| ~ ordinal(U_1004)
| ~ ordinal(U_1005) ),
inference(clausify,[status(thm)],[f_266_2]) ).
cnf(f_266_4,plain,
( in(U_1005,U_1004)
| ~ ordinal_subset(succ(U_1005),U_1004)
| ~ ordinal(U_1004)
| ~ ordinal(U_1005) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_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_267_2,plain,
! [U_1008,U_1007,U_1006] :
( subset(set_difference(U_1008,U_1006),set_difference(U_1007,U_1006))
| ~ subset(U_1008,U_1007) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_1008,U_1007] :
( ! [U_1006] : subset(set_difference(U_1008,U_1006),set_difference(U_1007,U_1006))
| ~ subset(U_1008,U_1007) ),
inference(miniscope,[status(thm)],[f_267_2]) ).
cnf(f_267_4,plain,
( subset(set_difference(U_1008,U_1006),set_difference(U_1007,U_1006))
| ~ subset(U_1008,U_1007) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_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_268_2,plain,
! [U_1012,U_1011,U_1010,U_1009] :
( ( U_1011 = U_1009
& U_1012 = U_1010 )
| ordered_pair(U_1012,U_1011) != ordered_pair(U_1010,U_1009) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( U_1012 = U_1010
| ordered_pair(U_1012,U_1011) != ordered_pair(U_1010,U_1009) ),
inference(clausify,[status(thm)],[f_268_2]) ).
cnf(f_268_4,plain,
( U_1011 = U_1009
| ordered_pair(U_1012,U_1011) != ordered_pair(U_1010,U_1009) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_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_269_2,plain,
! [U_1016,U_1015] :
( ( ( U_1015 = identity_relation(U_1016)
| ? [U_1014] :
( apply(U_1015,U_1014) != U_1014
& in(U_1014,U_1016) )
| relation_dom(U_1015) != U_1016 )
& ( ( ! [U_1013] :
( apply(U_1015,U_1013) = U_1013
| ~ in(U_1013,U_1016) )
& relation_dom(U_1015) = U_1016 )
| U_1015 != identity_relation(U_1016) ) )
| ~ function(U_1015)
| ~ relation(U_1015) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
! [U_1016,U_1015] :
( ( ( U_1015 = identity_relation(U_1016)
| ( apply(U_1015,sK156(U_1016,U_1015)) != sK156(U_1016,U_1015)
& in(sK156(U_1016,U_1015),U_1016) )
| relation_dom(U_1015) != U_1016 )
& ( ( ! [U_1013] :
( apply(U_1015,U_1013) = U_1013
| ~ in(U_1013,U_1016) )
& relation_dom(U_1015) = U_1016 )
| U_1015 != identity_relation(U_1016) ) )
| ~ function(U_1015)
| ~ relation(U_1015) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_1014,sK156(U_1016,U_1015))],[f_269_2]) ).
cnf(f_269_4,plain,
( relation_dom(U_1015) = U_1016
| U_1015 != identity_relation(U_1016)
| ~ function(U_1015)
| ~ relation(U_1015) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( apply(U_1015,U_1013) = U_1013
| ~ in(U_1013,U_1016)
| U_1015 != identity_relation(U_1016)
| ~ function(U_1015)
| ~ relation(U_1015) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_6,plain,
( in(sK156(U_1016,U_1015),U_1016)
| relation_dom(U_1015) != U_1016
| U_1015 = identity_relation(U_1016)
| ~ function(U_1015)
| ~ relation(U_1015) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_7,plain,
( apply(U_1015,sK156(U_1016,U_1015)) != sK156(U_1016,U_1015)
| relation_dom(U_1015) != U_1016
| U_1015 = identity_relation(U_1016)
| ~ function(U_1015)
| ~ relation(U_1015) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_270_2,plain,
! [U_1018,U_1017] :
( apply(identity_relation(U_1018),U_1017) = U_1017
| ~ in(U_1017,U_1018) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
( apply(identity_relation(U_1018),U_1017) = U_1017
| ~ in(U_1017,U_1018) ),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_271_2,plain,
! [U_1020,U_1019] : subset(set_difference(U_1020,U_1019),U_1020),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
subset(set_difference(U_1020,U_1019),U_1020),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_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_272_2,plain,
! [U_1021] :
( ( relation_dom(U_1021) = relation_rng(relation_inverse(U_1021))
& relation_rng(U_1021) = relation_dom(relation_inverse(U_1021)) )
| ~ relation(U_1021) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( relation_rng(U_1021) = relation_dom(relation_inverse(U_1021))
| ~ relation(U_1021) ),
inference(clausify,[status(thm)],[f_272_2]) ).
cnf(f_272_4,plain,
( relation_dom(U_1021) = relation_rng(relation_inverse(U_1021))
| ~ relation(U_1021) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_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_273_2,plain,
! [U_1023,U_1022] :
( ( set_difference(U_1023,U_1022) = empty_set
| ~ subset(U_1023,U_1022) )
& ( subset(U_1023,U_1022)
| set_difference(U_1023,U_1022) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
( ! [U_1027,U_1025] :
( set_difference(U_1027,U_1025) = empty_set
| ~ subset(U_1027,U_1025) )
& ! [U_1026,U_1024] :
( subset(U_1026,U_1024)
| set_difference(U_1026,U_1024) != empty_set ) ),
inference(miniscope,[status(thm)],[f_273_2]) ).
cnf(f_273_4,plain,
( subset(U_1026,U_1024)
| set_difference(U_1026,U_1024) != empty_set ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_5,plain,
( set_difference(U_1027,U_1025) = empty_set
| ~ subset(U_1027,U_1025) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_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_274_2,plain,
! [U_1029,U_1028] :
( ( subset(singleton(U_1029),U_1028)
| ~ in(U_1029,U_1028) )
& ( in(U_1029,U_1028)
| ~ subset(singleton(U_1029),U_1028) ) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
( ! [U_1033,U_1031] :
( subset(singleton(U_1033),U_1031)
| ~ in(U_1033,U_1031) )
& ! [U_1032,U_1030] :
( in(U_1032,U_1030)
| ~ subset(singleton(U_1032),U_1030) ) ),
inference(miniscope,[status(thm)],[f_274_2]) ).
cnf(f_274_4,plain,
( in(U_1032,U_1030)
| ~ subset(singleton(U_1032),U_1030) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( subset(singleton(U_1033),U_1031)
| ~ in(U_1033,U_1031) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_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_275_2,plain,
! [U_1036,U_1035,U_1034] :
( ( subset(unordered_pair(U_1036,U_1035),U_1034)
| ~ in(U_1035,U_1034)
| ~ in(U_1036,U_1034) )
& ( ( in(U_1035,U_1034)
& in(U_1036,U_1034) )
| ~ subset(unordered_pair(U_1036,U_1035),U_1034) ) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_1042,U_1040,U_1038] :
( subset(unordered_pair(U_1042,U_1040),U_1038)
| ~ in(U_1040,U_1038)
| ~ in(U_1042,U_1038) )
& ! [U_1041,U_1039,U_1037] :
( ( in(U_1039,U_1037)
& in(U_1041,U_1037) )
| ~ subset(unordered_pair(U_1041,U_1039),U_1037) ) ),
inference(miniscope,[status(thm)],[f_275_2]) ).
cnf(f_275_4,plain,
( in(U_1041,U_1037)
| ~ subset(unordered_pair(U_1041,U_1039),U_1037) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_5,plain,
( in(U_1039,U_1037)
| ~ subset(unordered_pair(U_1041,U_1039),U_1037) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_6,plain,
( subset(unordered_pair(U_1042,U_1040),U_1038)
| ~ in(U_1040,U_1038)
| ~ in(U_1042,U_1038) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_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_276_2,plain,
! [U_1044,U_1043] :
( relation_field(relation_restriction(U_1043,U_1044)) = U_1044
| ~ subset(U_1044,relation_field(U_1043))
| ~ well_ordering(U_1043)
| ~ relation(U_1043) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( relation_field(relation_restriction(U_1043,U_1044)) = U_1044
| ~ subset(U_1044,relation_field(U_1043))
| ~ well_ordering(U_1043)
| ~ relation(U_1043) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_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_277_2,plain,
! [U_1046,U_1045] : set_union2(U_1046,set_difference(U_1045,U_1046)) = set_union2(U_1046,U_1045),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
set_union2(U_1046,set_difference(U_1045,U_1046)) = set_union2(U_1046,U_1045),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_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_278_2,plain,
! [U_1048,U_1047] :
( ( subset(U_1048,singleton(U_1047))
| ( U_1048 != singleton(U_1047)
& U_1048 != empty_set ) )
& ( U_1048 = singleton(U_1047)
| U_1048 = empty_set
| ~ subset(U_1048,singleton(U_1047)) ) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
( ! [U_1052,U_1050] :
( subset(U_1052,singleton(U_1050))
| ( U_1052 != singleton(U_1050)
& U_1052 != empty_set ) )
& ! [U_1051,U_1049] :
( U_1051 = singleton(U_1049)
| U_1051 = empty_set
| ~ subset(U_1051,singleton(U_1049)) ) ),
inference(miniscope,[status(thm)],[f_278_2]) ).
cnf(f_278_4,plain,
( U_1051 = singleton(U_1049)
| U_1051 = empty_set
| ~ subset(U_1051,singleton(U_1049)) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_5,plain,
( U_1052 != empty_set
| subset(U_1052,singleton(U_1050)) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_6,plain,
( U_1052 != singleton(U_1050)
| subset(U_1052,singleton(U_1050)) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_279_2,plain,
! [U_1053] : set_difference(U_1053,empty_set) = U_1053,
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
set_difference(U_1053,empty_set) = U_1053,
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_280_2,plain,
! [U_1056,U_1055,U_1054] :
( ~ in(U_1054,U_1056)
| ~ in(U_1055,U_1054)
| ~ in(U_1056,U_1055) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_1056,U_1055] :
( ! [U_1054] :
( ~ in(U_1054,U_1056)
| ~ in(U_1055,U_1054) )
| ~ in(U_1056,U_1055) ),
inference(miniscope,[status(thm)],[f_280_2]) ).
cnf(f_280_4,plain,
( ~ in(U_1054,U_1056)
| ~ in(U_1055,U_1054)
| ~ in(U_1056,U_1055) ),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_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_281_2,plain,
! [U_1058,U_1057] :
( ( element(U_1058,powerset(U_1057))
| ~ subset(U_1058,U_1057) )
& ( subset(U_1058,U_1057)
| ~ element(U_1058,powerset(U_1057)) ) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
( ! [U_1062,U_1060] :
( element(U_1062,powerset(U_1060))
| ~ subset(U_1062,U_1060) )
& ! [U_1061,U_1059] :
( subset(U_1061,U_1059)
| ~ element(U_1061,powerset(U_1059)) ) ),
inference(miniscope,[status(thm)],[f_281_2]) ).
cnf(f_281_4,plain,
( subset(U_1061,U_1059)
| ~ element(U_1061,powerset(U_1059)) ),
inference(clausify,[status(thm)],[f_281_3]) ).
cnf(f_281_5,plain,
( element(U_1062,powerset(U_1060))
| ~ subset(U_1062,U_1060) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_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_282_2,plain,
! [U_1066,U_1065] :
( ( ~ disjoint(U_1066,U_1065)
| ! [U_1064] :
( ~ in(U_1064,U_1065)
| ~ in(U_1064,U_1066) ) )
& ( ? [U_1063] :
( in(U_1063,U_1065)
& in(U_1063,U_1066) )
| disjoint(U_1066,U_1065) ) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
( ! [U_1070,U_1068] :
( ~ disjoint(U_1070,U_1068)
| ! [U_1064] :
( ~ in(U_1064,U_1068)
| ~ in(U_1064,U_1070) ) )
& ! [U_1069,U_1067] :
( ? [U_1063] :
( in(U_1063,U_1067)
& in(U_1063,U_1069) )
| disjoint(U_1069,U_1067) ) ),
inference(miniscope,[status(thm)],[f_282_2]) ).
fof(f_282_4,plain,
( ! [U_1070,U_1068] :
( ~ disjoint(U_1070,U_1068)
| ! [U_1064] :
( ~ in(U_1064,U_1068)
| ~ in(U_1064,U_1070) ) )
& ! [U_1069,U_1067] :
( ( in(sK157(U_1069,U_1067),U_1067)
& in(sK157(U_1069,U_1067),U_1069) )
| disjoint(U_1069,U_1067) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_1063,sK157(U_1069,U_1067))],[f_282_3]) ).
cnf(f_282_5,plain,
( in(sK157(U_1069,U_1067),U_1069)
| disjoint(U_1069,U_1067) ),
inference(clausify,[status(thm)],[f_282_4]) ).
cnf(f_282_6,plain,
( in(sK157(U_1069,U_1067),U_1067)
| disjoint(U_1069,U_1067) ),
inference(clausify,[status(thm)],[f_282_4]) ).
cnf(f_282_7,plain,
( ~ disjoint(U_1070,U_1068)
| ~ in(U_1064,U_1068)
| ~ in(U_1064,U_1070) ),
inference(clausify,[status(thm)],[f_282_4]) ).
fof(f_283_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_283_2,plain,
! [U_1071] :
( U_1071 = empty_set
| ~ subset(U_1071,empty_set) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( U_1071 = empty_set
| ~ subset(U_1071,empty_set) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_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_284_2,plain,
! [U_1073,U_1072] : set_difference(set_union2(U_1073,U_1072),U_1072) = set_difference(U_1073,U_1072),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
set_difference(set_union2(U_1073,U_1072),U_1072) = set_difference(U_1073,U_1072),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_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_285_2,plain,
! [U_1076] :
( ( ( being_limit_ordinal(U_1076)
| ? [U_1075] :
( ~ in(succ(U_1075),U_1076)
& in(U_1075,U_1076)
& ordinal(U_1075) ) )
& ( ! [U_1074] :
( in(succ(U_1074),U_1076)
| ~ in(U_1074,U_1076)
| ~ ordinal(U_1074) )
| ~ being_limit_ordinal(U_1076) ) )
| ~ ordinal(U_1076) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1076] :
( ( ( being_limit_ordinal(U_1076)
| ( ~ in(succ(sK158(U_1076)),U_1076)
& in(sK158(U_1076),U_1076)
& ordinal(sK158(U_1076)) ) )
& ( ! [U_1074] :
( in(succ(U_1074),U_1076)
| ~ in(U_1074,U_1076)
| ~ ordinal(U_1074) )
| ~ being_limit_ordinal(U_1076) ) )
| ~ ordinal(U_1076) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_1075,sK158(U_1076))],[f_285_2]) ).
cnf(f_285_4,plain,
( in(succ(U_1074),U_1076)
| ~ in(U_1074,U_1076)
| ~ ordinal(U_1074)
| ~ being_limit_ordinal(U_1076)
| ~ ordinal(U_1076) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_5,plain,
( ordinal(sK158(U_1076))
| being_limit_ordinal(U_1076)
| ~ ordinal(U_1076) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_6,plain,
( in(sK158(U_1076),U_1076)
| being_limit_ordinal(U_1076)
| ~ ordinal(U_1076) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_7,plain,
( ~ in(succ(sK158(U_1076)),U_1076)
| being_limit_ordinal(U_1076)
| ~ ordinal(U_1076) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_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_286_2,plain,
! [U_1079] :
( ( ( ~ being_limit_ordinal(U_1079)
| ! [U_1078] :
( U_1079 != succ(U_1078)
| ~ ordinal(U_1078) ) )
& ( ? [U_1077] :
( U_1079 = succ(U_1077)
& ordinal(U_1077) )
| being_limit_ordinal(U_1079) ) )
| ~ ordinal(U_1079) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1079] :
( ( ( ~ being_limit_ordinal(U_1079)
| ! [U_1078] :
( U_1079 != succ(U_1078)
| ~ ordinal(U_1078) ) )
& ( ( U_1079 = succ(sK159(U_1079))
& ordinal(sK159(U_1079)) )
| being_limit_ordinal(U_1079) ) )
| ~ ordinal(U_1079) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_1077,sK159(U_1079))],[f_286_2]) ).
cnf(f_286_4,plain,
( ordinal(sK159(U_1079))
| being_limit_ordinal(U_1079)
| ~ ordinal(U_1079) ),
inference(clausify,[status(thm)],[f_286_3]) ).
cnf(f_286_5,plain,
( U_1079 = succ(sK159(U_1079))
| being_limit_ordinal(U_1079)
| ~ ordinal(U_1079) ),
inference(clausify,[status(thm)],[f_286_3]) ).
cnf(f_286_6,plain,
( ~ being_limit_ordinal(U_1079)
| U_1079 != succ(U_1078)
| ~ ordinal(U_1078)
| ~ ordinal(U_1079) ),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_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_287_2,plain,
! [U_1082,U_1081] :
( ! [U_1080] :
( ( ( disjoint(U_1081,U_1080)
| ~ subset(U_1081,subset_complement(U_1082,U_1080)) )
& ( subset(U_1081,subset_complement(U_1082,U_1080))
| ~ disjoint(U_1081,U_1080) ) )
| ~ element(U_1080,powerset(U_1082)) )
| ~ element(U_1081,powerset(U_1082)) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( subset(U_1081,subset_complement(U_1082,U_1080))
| ~ disjoint(U_1081,U_1080)
| ~ element(U_1080,powerset(U_1082))
| ~ element(U_1081,powerset(U_1082)) ),
inference(clausify,[status(thm)],[f_287_2]) ).
cnf(f_287_4,plain,
( disjoint(U_1081,U_1080)
| ~ subset(U_1081,subset_complement(U_1082,U_1080))
| ~ element(U_1080,powerset(U_1082))
| ~ element(U_1081,powerset(U_1082)) ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_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_288_2,plain,
! [U_1084] :
( ! [U_1083] :
( subset(relation_dom(relation_composition(U_1084,U_1083)),relation_dom(U_1084))
| ~ relation(U_1083) )
| ~ relation(U_1084) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( subset(relation_dom(relation_composition(U_1084,U_1083)),relation_dom(U_1084))
| ~ relation(U_1083)
| ~ relation(U_1084) ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_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_289_2,plain,
! [U_1086] :
( ! [U_1085] :
( subset(relation_rng(relation_composition(U_1086,U_1085)),relation_rng(U_1085))
| ~ relation(U_1085) )
| ~ relation(U_1086) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( subset(relation_rng(relation_composition(U_1086,U_1085)),relation_rng(U_1085))
| ~ relation(U_1085)
| ~ relation(U_1086) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_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_290_2,plain,
! [U_1088,U_1087] :
( U_1087 = set_union2(U_1088,set_difference(U_1087,U_1088))
| ~ subset(U_1088,U_1087) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( U_1087 = set_union2(U_1088,set_difference(U_1087,U_1088))
| ~ subset(U_1088,U_1087) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_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_291_2,plain,
! [U_1090] :
( ! [U_1089] :
( relation_dom(relation_composition(U_1090,U_1089)) = relation_dom(U_1090)
| ~ subset(relation_rng(U_1090),relation_dom(U_1089))
| ~ relation(U_1089) )
| ~ relation(U_1090) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( relation_dom(relation_composition(U_1090,U_1089)) = relation_dom(U_1090)
| ~ subset(relation_rng(U_1090),relation_dom(U_1089))
| ~ relation(U_1089)
| ~ relation(U_1090) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_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_292_2,plain,
! [U_1092,U_1091] :
( complements_of_subsets(U_1092,U_1091) != empty_set
| U_1091 = empty_set
| ~ element(U_1091,powerset(powerset(U_1092))) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
( complements_of_subsets(U_1092,U_1091) != empty_set
| U_1091 = empty_set
| ~ element(U_1091,powerset(powerset(U_1092))) ),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_293_2,plain,
! [U_1094,U_1093] :
( set_union2(singleton(U_1094),U_1093) = U_1093
| ~ in(U_1094,U_1093) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
( set_union2(singleton(U_1094),U_1093) = U_1093
| ~ in(U_1094,U_1093) ),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_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_294_2,plain,
! [U_1096] :
( ! [U_1095] :
( relation_rng(relation_composition(U_1095,U_1096)) = relation_rng(U_1096)
| ~ subset(relation_dom(U_1096),relation_rng(U_1095))
| ~ relation(U_1095) )
| ~ relation(U_1096) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( relation_rng(relation_composition(U_1095,U_1096)) = relation_rng(U_1096)
| ~ subset(relation_dom(U_1096),relation_rng(U_1095))
| ~ relation(U_1095)
| ~ relation(U_1096) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_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_295_2,plain,
! [U_1098,U_1097] :
( subset_difference(U_1098,cast_to_subset(U_1098),union_of_subsets(U_1098,U_1097)) = meet_of_subsets(U_1098,complements_of_subsets(U_1098,U_1097))
| U_1097 = empty_set
| ~ element(U_1097,powerset(powerset(U_1098))) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
( subset_difference(U_1098,cast_to_subset(U_1098),union_of_subsets(U_1098,U_1097)) = meet_of_subsets(U_1098,complements_of_subsets(U_1098,U_1097))
| U_1097 = empty_set
| ~ element(U_1097,powerset(powerset(U_1098))) ),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_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_296_2,plain,
! [U_1100,U_1099] :
( union_of_subsets(U_1100,complements_of_subsets(U_1100,U_1099)) = subset_difference(U_1100,cast_to_subset(U_1100),meet_of_subsets(U_1100,U_1099))
| U_1099 = empty_set
| ~ element(U_1099,powerset(powerset(U_1100))) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
( union_of_subsets(U_1100,complements_of_subsets(U_1100,U_1099)) = subset_difference(U_1100,cast_to_subset(U_1100),meet_of_subsets(U_1100,U_1099))
| U_1099 = empty_set
| ~ element(U_1099,powerset(powerset(U_1100))) ),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_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_297_2,plain,
! [U_1102,U_1101] : set_difference(U_1102,set_difference(U_1102,U_1101)) = set_intersection2(U_1102,U_1101),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
set_difference(U_1102,set_difference(U_1102,U_1101)) = set_intersection2(U_1102,U_1101),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_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_298_2,plain,
! [U_1105] :
( ! [U_1104] :
( ! [U_1103] :
( relation_isomorphism(U_1104,U_1105,function_inverse(U_1103))
| ~ relation_isomorphism(U_1105,U_1104,U_1103)
| ~ function(U_1103)
| ~ relation(U_1103) )
| ~ relation(U_1104) )
| ~ relation(U_1105) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( relation_isomorphism(U_1104,U_1105,function_inverse(U_1103))
| ~ relation_isomorphism(U_1105,U_1104,U_1103)
| ~ function(U_1103)
| ~ relation(U_1103)
| ~ relation(U_1104)
| ~ relation(U_1105) ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_299_2,plain,
! [U_1106] : set_difference(empty_set,U_1106) = empty_set,
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
set_difference(empty_set,U_1106) = empty_set,
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_300_2,plain,
! [U_1109,U_1108,U_1107] :
( element(U_1109,U_1107)
| ~ element(U_1108,powerset(U_1107))
| ~ in(U_1109,U_1108) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
( element(U_1109,U_1107)
| ~ element(U_1108,powerset(U_1107))
| ~ in(U_1109,U_1108) ),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_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_301_2,plain,
! [U_1113,U_1112] :
( ( ~ disjoint(U_1113,U_1112)
| ! [U_1111] : ~ in(U_1111,set_intersection2(U_1113,U_1112)) )
& ( ? [U_1110] : in(U_1110,set_intersection2(U_1113,U_1112))
| disjoint(U_1113,U_1112) ) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
( ! [U_1117,U_1115] :
( ~ disjoint(U_1117,U_1115)
| ! [U_1111] : ~ in(U_1111,set_intersection2(U_1117,U_1115)) )
& ! [U_1116,U_1114] :
( ? [U_1110] : in(U_1110,set_intersection2(U_1116,U_1114))
| disjoint(U_1116,U_1114) ) ),
inference(miniscope,[status(thm)],[f_301_2]) ).
fof(f_301_4,plain,
( ! [U_1117,U_1115] :
( ~ disjoint(U_1117,U_1115)
| ! [U_1111] : ~ in(U_1111,set_intersection2(U_1117,U_1115)) )
& ! [U_1116,U_1114] :
( in(sK160(U_1116,U_1114),set_intersection2(U_1116,U_1114))
| disjoint(U_1116,U_1114) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_1110,sK160(U_1116,U_1114))],[f_301_3]) ).
cnf(f_301_5,plain,
( in(sK160(U_1116,U_1114),set_intersection2(U_1116,U_1114))
| disjoint(U_1116,U_1114) ),
inference(clausify,[status(thm)],[f_301_4]) ).
cnf(f_301_6,plain,
( ~ disjoint(U_1117,U_1115)
| ~ in(U_1111,set_intersection2(U_1117,U_1115)) ),
inference(clausify,[status(thm)],[f_301_4]) ).
fof(f_302_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_302_2,plain,
! [U_1120] :
( ! [U_1119] :
( ! [U_1118] :
( in(U_1118,subset_complement(U_1120,U_1119))
| in(U_1118,U_1119)
| ~ element(U_1118,U_1120) )
| ~ element(U_1119,powerset(U_1120)) )
| U_1120 = empty_set ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( in(U_1118,subset_complement(U_1120,U_1119))
| in(U_1118,U_1119)
| ~ element(U_1118,U_1120)
| ~ element(U_1119,powerset(U_1120))
| U_1120 = empty_set ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_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_303_2,plain,
! [U_1123] :
( ! [U_1122] :
( ! [U_1121] :
( ( ( well_founded_relation(U_1122)
| ~ well_founded_relation(U_1123) )
& ( antisymmetric(U_1122)
| ~ antisymmetric(U_1123) )
& ( connected(U_1122)
| ~ connected(U_1123) )
& ( transitive(U_1122)
| ~ transitive(U_1123) )
& ( reflexive(U_1122)
| ~ reflexive(U_1123) ) )
| ~ relation_isomorphism(U_1123,U_1122,U_1121)
| ~ function(U_1121)
| ~ relation(U_1121) )
| ~ relation(U_1122) )
| ~ relation(U_1123) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
( reflexive(U_1122)
| ~ reflexive(U_1123)
| ~ relation_isomorphism(U_1123,U_1122,U_1121)
| ~ function(U_1121)
| ~ relation(U_1121)
| ~ relation(U_1122)
| ~ relation(U_1123) ),
inference(clausify,[status(thm)],[f_303_2]) ).
cnf(f_303_4,plain,
( transitive(U_1122)
| ~ transitive(U_1123)
| ~ relation_isomorphism(U_1123,U_1122,U_1121)
| ~ function(U_1121)
| ~ relation(U_1121)
| ~ relation(U_1122)
| ~ relation(U_1123) ),
inference(clausify,[status(thm)],[f_303_2]) ).
cnf(f_303_5,plain,
( connected(U_1122)
| ~ connected(U_1123)
| ~ relation_isomorphism(U_1123,U_1122,U_1121)
| ~ function(U_1121)
| ~ relation(U_1121)
| ~ relation(U_1122)
| ~ relation(U_1123) ),
inference(clausify,[status(thm)],[f_303_2]) ).
cnf(f_303_6,plain,
( antisymmetric(U_1122)
| ~ antisymmetric(U_1123)
| ~ relation_isomorphism(U_1123,U_1122,U_1121)
| ~ function(U_1121)
| ~ relation(U_1121)
| ~ relation(U_1122)
| ~ relation(U_1123) ),
inference(clausify,[status(thm)],[f_303_2]) ).
cnf(f_303_7,plain,
( well_founded_relation(U_1122)
| ~ well_founded_relation(U_1123)
| ~ relation_isomorphism(U_1123,U_1122,U_1121)
| ~ function(U_1121)
| ~ relation(U_1121)
| ~ relation(U_1122)
| ~ relation(U_1123) ),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_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_304_2,plain,
! [U_1129] :
( ! [U_1128] :
( ( ( U_1128 = function_inverse(U_1129)
| ? [U_1127,U_1126] :
( ( ( U_1126 != apply(U_1128,U_1127)
| ~ in(U_1127,relation_rng(U_1129)) )
& U_1127 = apply(U_1129,U_1126)
& in(U_1126,relation_dom(U_1129)) )
| ( ( U_1127 != apply(U_1129,U_1126)
| ~ in(U_1126,relation_dom(U_1129)) )
& U_1126 = apply(U_1128,U_1127)
& in(U_1127,relation_rng(U_1129)) ) )
| relation_dom(U_1128) != relation_rng(U_1129) )
& ( ( ! [U_1125,U_1124] :
( ( ( U_1124 = apply(U_1128,U_1125)
& in(U_1125,relation_rng(U_1129)) )
| U_1125 != apply(U_1129,U_1124)
| ~ in(U_1124,relation_dom(U_1129)) )
& ( ( U_1125 = apply(U_1129,U_1124)
& in(U_1124,relation_dom(U_1129)) )
| U_1124 != apply(U_1128,U_1125)
| ~ in(U_1125,relation_rng(U_1129)) ) )
& relation_dom(U_1128) = relation_rng(U_1129) )
| U_1128 != function_inverse(U_1129) ) )
| ~ function(U_1128)
| ~ relation(U_1128) )
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1129] :
( ! [U_1128] :
( ( ( U_1128 = function_inverse(U_1129)
| ? [U_1137,U_1135] :
( ( U_1135 != apply(U_1128,U_1137)
| ~ in(U_1137,relation_rng(U_1129)) )
& U_1137 = apply(U_1129,U_1135)
& in(U_1135,relation_dom(U_1129)) )
| ? [U_1136,U_1134] :
( ( U_1136 != apply(U_1129,U_1134)
| ~ in(U_1134,relation_dom(U_1129)) )
& U_1134 = apply(U_1128,U_1136)
& in(U_1136,relation_rng(U_1129)) )
| relation_dom(U_1128) != relation_rng(U_1129) )
& ( ( ! [U_1133,U_1131] :
( ( U_1131 = apply(U_1128,U_1133)
& in(U_1133,relation_rng(U_1129)) )
| U_1133 != apply(U_1129,U_1131)
| ~ in(U_1131,relation_dom(U_1129)) )
& ! [U_1132,U_1130] :
( ( U_1132 = apply(U_1129,U_1130)
& in(U_1130,relation_dom(U_1129)) )
| U_1130 != apply(U_1128,U_1132)
| ~ in(U_1132,relation_rng(U_1129)) )
& relation_dom(U_1128) = relation_rng(U_1129) )
| U_1128 != function_inverse(U_1129) ) )
| ~ function(U_1128)
| ~ relation(U_1128) )
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(miniscope,[status(thm)],[f_304_2]) ).
fof(f_304_4,plain,
! [U_1129] :
( ! [U_1128] :
( ( ( U_1128 = function_inverse(U_1129)
| ? [U_1137,U_1135] :
( ( U_1135 != apply(U_1128,U_1137)
| ~ in(U_1137,relation_rng(U_1129)) )
& U_1137 = apply(U_1129,U_1135)
& in(U_1135,relation_dom(U_1129)) )
| ? [U_1134] :
( ( sK161(U_1129,U_1128) != apply(U_1129,U_1134)
| ~ in(U_1134,relation_dom(U_1129)) )
& U_1134 = apply(U_1128,sK161(U_1129,U_1128))
& in(sK161(U_1129,U_1128),relation_rng(U_1129)) )
| relation_dom(U_1128) != relation_rng(U_1129) )
& ( ( ! [U_1133,U_1131] :
( ( U_1131 = apply(U_1128,U_1133)
& in(U_1133,relation_rng(U_1129)) )
| U_1133 != apply(U_1129,U_1131)
| ~ in(U_1131,relation_dom(U_1129)) )
& ! [U_1132,U_1130] :
( ( U_1132 = apply(U_1129,U_1130)
& in(U_1130,relation_dom(U_1129)) )
| U_1130 != apply(U_1128,U_1132)
| ~ in(U_1132,relation_rng(U_1129)) )
& relation_dom(U_1128) = relation_rng(U_1129) )
| U_1128 != function_inverse(U_1129) ) )
| ~ function(U_1128)
| ~ relation(U_1128) )
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_1136,sK161(U_1129,U_1128))],[f_304_3]) ).
fof(f_304_5,plain,
! [U_1129] :
( ! [U_1128] :
( ( ( U_1128 = function_inverse(U_1129)
| ? [U_1137,U_1135] :
( ( U_1135 != apply(U_1128,U_1137)
| ~ in(U_1137,relation_rng(U_1129)) )
& U_1137 = apply(U_1129,U_1135)
& in(U_1135,relation_dom(U_1129)) )
| ( ( sK161(U_1129,U_1128) != apply(U_1129,sK162(U_1129,U_1128))
| ~ in(sK162(U_1129,U_1128),relation_dom(U_1129)) )
& sK162(U_1129,U_1128) = apply(U_1128,sK161(U_1129,U_1128))
& in(sK161(U_1129,U_1128),relation_rng(U_1129)) )
| relation_dom(U_1128) != relation_rng(U_1129) )
& ( ( ! [U_1133,U_1131] :
( ( U_1131 = apply(U_1128,U_1133)
& in(U_1133,relation_rng(U_1129)) )
| U_1133 != apply(U_1129,U_1131)
| ~ in(U_1131,relation_dom(U_1129)) )
& ! [U_1132,U_1130] :
( ( U_1132 = apply(U_1129,U_1130)
& in(U_1130,relation_dom(U_1129)) )
| U_1130 != apply(U_1128,U_1132)
| ~ in(U_1132,relation_rng(U_1129)) )
& relation_dom(U_1128) = relation_rng(U_1129) )
| U_1128 != function_inverse(U_1129) ) )
| ~ function(U_1128)
| ~ relation(U_1128) )
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_1134,sK162(U_1129,U_1128))],[f_304_4]) ).
fof(f_304_6,plain,
! [U_1129] :
( ! [U_1128] :
( ( ( U_1128 = function_inverse(U_1129)
| ? [U_1135] :
( ( U_1135 != apply(U_1128,sK163(U_1129,U_1128))
| ~ in(sK163(U_1129,U_1128),relation_rng(U_1129)) )
& sK163(U_1129,U_1128) = apply(U_1129,U_1135)
& in(U_1135,relation_dom(U_1129)) )
| ( ( sK161(U_1129,U_1128) != apply(U_1129,sK162(U_1129,U_1128))
| ~ in(sK162(U_1129,U_1128),relation_dom(U_1129)) )
& sK162(U_1129,U_1128) = apply(U_1128,sK161(U_1129,U_1128))
& in(sK161(U_1129,U_1128),relation_rng(U_1129)) )
| relation_dom(U_1128) != relation_rng(U_1129) )
& ( ( ! [U_1133,U_1131] :
( ( U_1131 = apply(U_1128,U_1133)
& in(U_1133,relation_rng(U_1129)) )
| U_1133 != apply(U_1129,U_1131)
| ~ in(U_1131,relation_dom(U_1129)) )
& ! [U_1132,U_1130] :
( ( U_1132 = apply(U_1129,U_1130)
& in(U_1130,relation_dom(U_1129)) )
| U_1130 != apply(U_1128,U_1132)
| ~ in(U_1132,relation_rng(U_1129)) )
& relation_dom(U_1128) = relation_rng(U_1129) )
| U_1128 != function_inverse(U_1129) ) )
| ~ function(U_1128)
| ~ relation(U_1128) )
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_1137,sK163(U_1129,U_1128))],[f_304_5]) ).
fof(f_304_7,plain,
! [U_1129] :
( ! [U_1128] :
( ( ( U_1128 = function_inverse(U_1129)
| ( ( sK164(U_1129,U_1128) != apply(U_1128,sK163(U_1129,U_1128))
| ~ in(sK163(U_1129,U_1128),relation_rng(U_1129)) )
& sK163(U_1129,U_1128) = apply(U_1129,sK164(U_1129,U_1128))
& in(sK164(U_1129,U_1128),relation_dom(U_1129)) )
| ( ( sK161(U_1129,U_1128) != apply(U_1129,sK162(U_1129,U_1128))
| ~ in(sK162(U_1129,U_1128),relation_dom(U_1129)) )
& sK162(U_1129,U_1128) = apply(U_1128,sK161(U_1129,U_1128))
& in(sK161(U_1129,U_1128),relation_rng(U_1129)) )
| relation_dom(U_1128) != relation_rng(U_1129) )
& ( ( ! [U_1133,U_1131] :
( ( U_1131 = apply(U_1128,U_1133)
& in(U_1133,relation_rng(U_1129)) )
| U_1133 != apply(U_1129,U_1131)
| ~ in(U_1131,relation_dom(U_1129)) )
& ! [U_1132,U_1130] :
( ( U_1132 = apply(U_1129,U_1130)
& in(U_1130,relation_dom(U_1129)) )
| U_1130 != apply(U_1128,U_1132)
| ~ in(U_1132,relation_rng(U_1129)) )
& relation_dom(U_1128) = relation_rng(U_1129) )
| U_1128 != function_inverse(U_1129) ) )
| ~ function(U_1128)
| ~ relation(U_1128) )
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_1135,sK164(U_1129,U_1128))],[f_304_6]) ).
cnf(f_304_8,plain,
( relation_dom(U_1128) = relation_rng(U_1129)
| U_1128 != function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_9,plain,
( in(U_1130,relation_dom(U_1129))
| U_1130 != apply(U_1128,U_1132)
| ~ in(U_1132,relation_rng(U_1129))
| U_1128 != function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_10,plain,
( U_1132 = apply(U_1129,U_1130)
| U_1130 != apply(U_1128,U_1132)
| ~ in(U_1132,relation_rng(U_1129))
| U_1128 != function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_11,plain,
( in(U_1133,relation_rng(U_1129))
| U_1133 != apply(U_1129,U_1131)
| ~ in(U_1131,relation_dom(U_1129))
| U_1128 != function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_12,plain,
( U_1131 = apply(U_1128,U_1133)
| U_1133 != apply(U_1129,U_1131)
| ~ in(U_1131,relation_dom(U_1129))
| U_1128 != function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_13,plain,
( in(sK164(U_1129,U_1128),relation_dom(U_1129))
| in(sK161(U_1129,U_1128),relation_rng(U_1129))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_14,plain,
( sK163(U_1129,U_1128) = apply(U_1129,sK164(U_1129,U_1128))
| in(sK161(U_1129,U_1128),relation_rng(U_1129))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_15,plain,
( in(sK164(U_1129,U_1128),relation_dom(U_1129))
| sK162(U_1129,U_1128) = apply(U_1128,sK161(U_1129,U_1128))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_16,plain,
( sK163(U_1129,U_1128) = apply(U_1129,sK164(U_1129,U_1128))
| sK162(U_1129,U_1128) = apply(U_1128,sK161(U_1129,U_1128))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_17,plain,
( in(sK161(U_1129,U_1128),relation_rng(U_1129))
| sK164(U_1129,U_1128) != apply(U_1128,sK163(U_1129,U_1128))
| ~ in(sK163(U_1129,U_1128),relation_rng(U_1129))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_18,plain,
( sK162(U_1129,U_1128) = apply(U_1128,sK161(U_1129,U_1128))
| sK164(U_1129,U_1128) != apply(U_1128,sK163(U_1129,U_1128))
| ~ in(sK163(U_1129,U_1128),relation_rng(U_1129))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_19,plain,
( in(sK164(U_1129,U_1128),relation_dom(U_1129))
| sK161(U_1129,U_1128) != apply(U_1129,sK162(U_1129,U_1128))
| ~ in(sK162(U_1129,U_1128),relation_dom(U_1129))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_20,plain,
( sK163(U_1129,U_1128) = apply(U_1129,sK164(U_1129,U_1128))
| sK161(U_1129,U_1128) != apply(U_1129,sK162(U_1129,U_1128))
| ~ in(sK162(U_1129,U_1128),relation_dom(U_1129))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
cnf(f_304_21,plain,
( sK164(U_1129,U_1128) != apply(U_1128,sK163(U_1129,U_1128))
| ~ in(sK163(U_1129,U_1128),relation_rng(U_1129))
| sK161(U_1129,U_1128) != apply(U_1129,sK162(U_1129,U_1128))
| ~ in(sK162(U_1129,U_1128),relation_dom(U_1129))
| relation_dom(U_1128) != relation_rng(U_1129)
| U_1128 = function_inverse(U_1129)
| ~ function(U_1128)
| ~ relation(U_1128)
| ~ one_to_one(U_1129)
| ~ function(U_1129)
| ~ relation(U_1129) ),
inference(clausify,[status(thm)],[f_304_7]) ).
fof(f_305_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_305_2,plain,
! [U_1140,U_1139,U_1138] :
( ~ in(U_1139,U_1138)
| ~ in(U_1139,subset_complement(U_1140,U_1138))
| ~ element(U_1138,powerset(U_1140)) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
( ~ in(U_1139,U_1138)
| ~ in(U_1139,subset_complement(U_1140,U_1138))
| ~ element(U_1138,powerset(U_1140)) ),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_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_306_2,plain,
! [U_1143] :
( ! [U_1142] :
( ! [U_1141] :
( well_ordering(U_1142)
| ~ relation_isomorphism(U_1143,U_1142,U_1141)
| ~ well_ordering(U_1143)
| ~ function(U_1141)
| ~ relation(U_1141) )
| ~ relation(U_1142) )
| ~ relation(U_1143) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( well_ordering(U_1142)
| ~ relation_isomorphism(U_1143,U_1142,U_1141)
| ~ well_ordering(U_1143)
| ~ function(U_1141)
| ~ relation(U_1141)
| ~ relation(U_1142)
| ~ relation(U_1143) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_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_307_2,plain,
! [U_1144] :
( ( relation_dom(U_1144) = relation_rng(function_inverse(U_1144))
& relation_rng(U_1144) = relation_dom(function_inverse(U_1144)) )
| ~ one_to_one(U_1144)
| ~ function(U_1144)
| ~ relation(U_1144) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( relation_rng(U_1144) = relation_dom(function_inverse(U_1144))
| ~ one_to_one(U_1144)
| ~ function(U_1144)
| ~ relation(U_1144) ),
inference(clausify,[status(thm)],[f_307_2]) ).
cnf(f_307_4,plain,
( relation_dom(U_1144) = relation_rng(function_inverse(U_1144))
| ~ one_to_one(U_1144)
| ~ function(U_1144)
| ~ relation(U_1144) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_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_308_2,plain,
! [U_1147] :
( U_1147 = empty_set
| ? [U_1146,U_1145] : in(ordered_pair(U_1146,U_1145),U_1147)
| ~ relation(U_1147) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
! [U_1147] :
( U_1147 = empty_set
| ? [U_1145] : in(ordered_pair(sK165(U_1147),U_1145),U_1147)
| ~ relation(U_1147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_1146,sK165(U_1147))],[f_308_2]) ).
fof(f_308_4,plain,
! [U_1147] :
( U_1147 = empty_set
| in(ordered_pair(sK165(U_1147),sK166(U_1147)),U_1147)
| ~ relation(U_1147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_1145,sK166(U_1147))],[f_308_3]) ).
cnf(f_308_5,plain,
( U_1147 = empty_set
| in(ordered_pair(sK165(U_1147),sK166(U_1147)),U_1147)
| ~ relation(U_1147) ),
inference(clausify,[status(thm)],[f_308_4]) ).
fof(f_309_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_309_2,plain,
! [U_1149,U_1148] :
( ( U_1149 = apply(relation_composition(function_inverse(U_1148),U_1148),U_1149)
& U_1149 = apply(U_1148,apply(function_inverse(U_1148),U_1149)) )
| ~ in(U_1149,relation_rng(U_1148))
| ~ one_to_one(U_1148)
| ~ function(U_1148)
| ~ relation(U_1148) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
( U_1149 = apply(U_1148,apply(function_inverse(U_1148),U_1149))
| ~ in(U_1149,relation_rng(U_1148))
| ~ one_to_one(U_1148)
| ~ function(U_1148)
| ~ relation(U_1148) ),
inference(clausify,[status(thm)],[f_309_2]) ).
cnf(f_309_4,plain,
( U_1149 = apply(relation_composition(function_inverse(U_1148),U_1148),U_1149)
| ~ in(U_1149,relation_rng(U_1148))
| ~ one_to_one(U_1148)
| ~ function(U_1148)
| ~ relation(U_1148) ),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_310_2,plain,
! [U_1152,U_1151,U_1150] :
( ~ empty(U_1150)
| ~ element(U_1151,powerset(U_1150))
| ~ in(U_1152,U_1151) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_1152,U_1151] :
( ! [U_1150] :
( ~ empty(U_1150)
| ~ element(U_1151,powerset(U_1150)) )
| ~ in(U_1152,U_1151) ),
inference(miniscope,[status(thm)],[f_310_2]) ).
cnf(f_310_4,plain,
( ~ empty(U_1150)
| ~ element(U_1151,powerset(U_1150))
| ~ in(U_1152,U_1151) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_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_311_2,plain,
! [U_1153] :
( ( ( well_founded_relation(U_1153)
| ~ is_well_founded_in(U_1153,relation_field(U_1153)) )
& ( is_well_founded_in(U_1153,relation_field(U_1153))
| ~ well_founded_relation(U_1153) ) )
| ~ relation(U_1153) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( is_well_founded_in(U_1153,relation_field(U_1153))
| ~ well_founded_relation(U_1153)
| ~ relation(U_1153) ),
inference(clausify,[status(thm)],[f_311_2]) ).
cnf(f_311_4,plain,
( well_founded_relation(U_1153)
| ~ is_well_founded_in(U_1153,relation_field(U_1153))
| ~ relation(U_1153) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
cnf(f_312_2,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_312_1]) ).
cnf(f_312_3,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_312_1]) ).
fof(f_313_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_313_2,plain,
! [U_1155,U_1154] :
( ~ proper_subset(U_1154,U_1155)
| ~ subset(U_1155,U_1154) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
( ~ proper_subset(U_1154,U_1155)
| ~ subset(U_1155,U_1154) ),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_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_314_2,plain,
! [U_1156] :
( one_to_one(function_inverse(U_1156))
| ~ one_to_one(U_1156)
| ~ function(U_1156)
| ~ relation(U_1156) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
( one_to_one(function_inverse(U_1156))
| ~ one_to_one(U_1156)
| ~ function(U_1156)
| ~ relation(U_1156) ),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_315_2,plain,
! [U_1159,U_1158,U_1157] :
( disjoint(U_1159,U_1157)
| ~ disjoint(U_1158,U_1157)
| ~ subset(U_1159,U_1158) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
( disjoint(U_1159,U_1157)
| ~ disjoint(U_1158,U_1157)
| ~ subset(U_1159,U_1158) ),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_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_316_2,plain,
! [U_1160] :
( U_1160 = empty_set
| ( relation_rng(U_1160) != empty_set
& relation_dom(U_1160) != empty_set )
| ~ relation(U_1160) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( relation_dom(U_1160) != empty_set
| U_1160 = empty_set
| ~ relation(U_1160) ),
inference(clausify,[status(thm)],[f_316_2]) ).
cnf(f_316_4,plain,
( relation_rng(U_1160) != empty_set
| U_1160 = empty_set
| ~ relation(U_1160) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_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_317_2,plain,
! [U_1161] :
( ( ( relation_dom(U_1161) = empty_set
| relation_rng(U_1161) != empty_set )
& ( relation_rng(U_1161) = empty_set
| relation_dom(U_1161) != empty_set ) )
| ~ relation(U_1161) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( relation_rng(U_1161) = empty_set
| relation_dom(U_1161) != empty_set
| ~ relation(U_1161) ),
inference(clausify,[status(thm)],[f_317_2]) ).
cnf(f_317_4,plain,
( relation_dom(U_1161) = empty_set
| relation_rng(U_1161) != empty_set
| ~ relation(U_1161) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_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_318_2,plain,
! [U_1163,U_1162] :
( ( set_difference(U_1163,singleton(U_1162)) = U_1163
| in(U_1162,U_1163) )
& ( ~ in(U_1162,U_1163)
| set_difference(U_1163,singleton(U_1162)) != U_1163 ) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
( ! [U_1167,U_1165] :
( set_difference(U_1167,singleton(U_1165)) = U_1167
| in(U_1165,U_1167) )
& ! [U_1166,U_1164] :
( ~ in(U_1164,U_1166)
| set_difference(U_1166,singleton(U_1164)) != U_1166 ) ),
inference(miniscope,[status(thm)],[f_318_2]) ).
cnf(f_318_4,plain,
( ~ in(U_1164,U_1166)
| set_difference(U_1166,singleton(U_1164)) != U_1166 ),
inference(clausify,[status(thm)],[f_318_3]) ).
cnf(f_318_5,plain,
( set_difference(U_1167,singleton(U_1165)) = U_1167
| in(U_1165,U_1167) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_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_319_2,plain,
! [U_1172,U_1171] :
( ! [U_1170] :
( ( ( U_1171 = relation_dom_restriction(U_1170,U_1172)
| ? [U_1169] :
( apply(U_1171,U_1169) != apply(U_1170,U_1169)
& in(U_1169,relation_dom(U_1171)) )
| relation_dom(U_1171) != set_intersection2(relation_dom(U_1170),U_1172) )
& ( ( ! [U_1168] :
( apply(U_1171,U_1168) = apply(U_1170,U_1168)
| ~ in(U_1168,relation_dom(U_1171)) )
& relation_dom(U_1171) = set_intersection2(relation_dom(U_1170),U_1172) )
| U_1171 != relation_dom_restriction(U_1170,U_1172) ) )
| ~ function(U_1170)
| ~ relation(U_1170) )
| ~ function(U_1171)
| ~ relation(U_1171) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_1172,U_1171] :
( ! [U_1170] :
( ( ( U_1171 = relation_dom_restriction(U_1170,U_1172)
| ( apply(U_1171,sK167(U_1172,U_1171,U_1170)) != apply(U_1170,sK167(U_1172,U_1171,U_1170))
& in(sK167(U_1172,U_1171,U_1170),relation_dom(U_1171)) )
| relation_dom(U_1171) != set_intersection2(relation_dom(U_1170),U_1172) )
& ( ( ! [U_1168] :
( apply(U_1171,U_1168) = apply(U_1170,U_1168)
| ~ in(U_1168,relation_dom(U_1171)) )
& relation_dom(U_1171) = set_intersection2(relation_dom(U_1170),U_1172) )
| U_1171 != relation_dom_restriction(U_1170,U_1172) ) )
| ~ function(U_1170)
| ~ relation(U_1170) )
| ~ function(U_1171)
| ~ relation(U_1171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_1169,sK167(U_1172,U_1171,U_1170))],[f_319_2]) ).
cnf(f_319_4,plain,
( relation_dom(U_1171) = set_intersection2(relation_dom(U_1170),U_1172)
| U_1171 != relation_dom_restriction(U_1170,U_1172)
| ~ function(U_1170)
| ~ relation(U_1170)
| ~ function(U_1171)
| ~ relation(U_1171) ),
inference(clausify,[status(thm)],[f_319_3]) ).
cnf(f_319_5,plain,
( apply(U_1171,U_1168) = apply(U_1170,U_1168)
| ~ in(U_1168,relation_dom(U_1171))
| U_1171 != relation_dom_restriction(U_1170,U_1172)
| ~ function(U_1170)
| ~ relation(U_1170)
| ~ function(U_1171)
| ~ relation(U_1171) ),
inference(clausify,[status(thm)],[f_319_3]) ).
cnf(f_319_6,plain,
( in(sK167(U_1172,U_1171,U_1170),relation_dom(U_1171))
| relation_dom(U_1171) != set_intersection2(relation_dom(U_1170),U_1172)
| U_1171 = relation_dom_restriction(U_1170,U_1172)
| ~ function(U_1170)
| ~ relation(U_1170)
| ~ function(U_1171)
| ~ relation(U_1171) ),
inference(clausify,[status(thm)],[f_319_3]) ).
cnf(f_319_7,plain,
( apply(U_1171,sK167(U_1172,U_1171,U_1170)) != apply(U_1170,sK167(U_1172,U_1171,U_1170))
| relation_dom(U_1171) != set_intersection2(relation_dom(U_1170),U_1172)
| U_1171 = relation_dom_restriction(U_1170,U_1172)
| ~ function(U_1170)
| ~ relation(U_1170)
| ~ function(U_1171)
| ~ relation(U_1171) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_320_2,plain,
! [U_1173] : unordered_pair(U_1173,U_1173) = singleton(U_1173),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
unordered_pair(U_1173,U_1173) = singleton(U_1173),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_321_2,plain,
! [U_1174] :
( U_1174 = empty_set
| ~ empty(U_1174) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( U_1174 = empty_set
| ~ empty(U_1174) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_322_2,plain,
! [U_1176,U_1175] :
( U_1176 = U_1175
| ~ subset(singleton(U_1176),singleton(U_1175)) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( U_1176 = U_1175
| ~ subset(singleton(U_1176),singleton(U_1175)) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_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_323_2,plain,
! [U_1179,U_1178,U_1177] :
( apply(relation_dom_restriction(U_1177,U_1179),U_1178) = apply(U_1177,U_1178)
| ~ in(U_1178,relation_dom(relation_dom_restriction(U_1177,U_1179)))
| ~ function(U_1177)
| ~ relation(U_1177) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( apply(relation_dom_restriction(U_1177,U_1179),U_1178) = apply(U_1177,U_1178)
| ~ in(U_1178,relation_dom(relation_dom_restriction(U_1177,U_1179)))
| ~ function(U_1177)
| ~ relation(U_1177) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_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_324_2,plain,
! [U_1180] :
( relation_rng(identity_relation(U_1180)) = U_1180
& relation_dom(identity_relation(U_1180)) = U_1180 ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
( ! [U_1182] : relation_rng(identity_relation(U_1182)) = U_1182
& ! [U_1181] : relation_dom(identity_relation(U_1181)) = U_1181 ),
inference(miniscope,[status(thm)],[f_324_2]) ).
cnf(f_324_4,plain,
relation_dom(identity_relation(U_1181)) = U_1181,
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_5,plain,
relation_rng(identity_relation(U_1182)) = U_1182,
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_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_325_2,plain,
! [U_1185,U_1184,U_1183] :
( apply(relation_dom_restriction(U_1183,U_1185),U_1184) = apply(U_1183,U_1184)
| ~ in(U_1184,U_1185)
| ~ function(U_1183)
| ~ relation(U_1183) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( apply(relation_dom_restriction(U_1183,U_1185),U_1184) = apply(U_1183,U_1184)
| ~ in(U_1184,U_1185)
| ~ function(U_1183)
| ~ relation(U_1183) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_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_326_2,plain,
! [U_1189,U_1188,U_1187,U_1186] :
( ( ( in(ordered_pair(U_1189,U_1188),relation_composition(identity_relation(U_1187),U_1186))
| ~ in(ordered_pair(U_1189,U_1188),U_1186)
| ~ in(U_1189,U_1187) )
& ( ( in(ordered_pair(U_1189,U_1188),U_1186)
& in(U_1189,U_1187) )
| ~ in(ordered_pair(U_1189,U_1188),relation_composition(identity_relation(U_1187),U_1186)) ) )
| ~ relation(U_1186) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( in(U_1189,U_1187)
| ~ in(ordered_pair(U_1189,U_1188),relation_composition(identity_relation(U_1187),U_1186))
| ~ relation(U_1186) ),
inference(clausify,[status(thm)],[f_326_2]) ).
cnf(f_326_4,plain,
( in(ordered_pair(U_1189,U_1188),U_1186)
| ~ in(ordered_pair(U_1189,U_1188),relation_composition(identity_relation(U_1187),U_1186))
| ~ relation(U_1186) ),
inference(clausify,[status(thm)],[f_326_2]) ).
cnf(f_326_5,plain,
( in(ordered_pair(U_1189,U_1188),relation_composition(identity_relation(U_1187),U_1186))
| ~ in(ordered_pair(U_1189,U_1188),U_1186)
| ~ in(U_1189,U_1187)
| ~ relation(U_1186) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_327_2,plain,
! [U_1191,U_1190] :
( ~ empty(U_1190)
| ~ in(U_1191,U_1190) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( ~ empty(U_1190)
| ~ in(U_1191,U_1190) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_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_328_2,plain,
! [U_1193,U_1192] :
( pair_second(ordered_pair(U_1193,U_1192)) = U_1192
& pair_first(ordered_pair(U_1193,U_1192)) = U_1193 ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
( ! [U_1197,U_1195] : pair_second(ordered_pair(U_1197,U_1195)) = U_1195
& ! [U_1196,U_1194] : pair_first(ordered_pair(U_1196,U_1194)) = U_1196 ),
inference(miniscope,[status(thm)],[f_328_2]) ).
cnf(f_328_4,plain,
pair_first(ordered_pair(U_1196,U_1194)) = U_1196,
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_5,plain,
pair_second(ordered_pair(U_1197,U_1195)) = U_1195,
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_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_329_2,plain,
! [U_1201,U_1200] :
( ? [U_1199] :
( ! [U_1198] :
( ~ in(U_1198,U_1199)
| ~ in(U_1198,U_1200) )
& in(U_1199,U_1200) )
| ~ in(U_1201,U_1200) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
! [U_1201,U_1200] :
( ( ! [U_1198] :
( ~ in(U_1198,sK168(U_1201,U_1200))
| ~ in(U_1198,U_1200) )
& in(sK168(U_1201,U_1200),U_1200) )
| ~ in(U_1201,U_1200) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_1199,sK168(U_1201,U_1200))],[f_329_2]) ).
cnf(f_329_4,plain,
( in(sK168(U_1201,U_1200),U_1200)
| ~ in(U_1201,U_1200) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_5,plain,
( ~ in(U_1198,sK168(U_1201,U_1200))
| ~ in(U_1198,U_1200)
| ~ in(U_1201,U_1200) ),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_330_2,plain,
! [U_1203,U_1202] : subset(U_1203,set_union2(U_1203,U_1202)),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
subset(U_1203,set_union2(U_1203,U_1202)),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_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_331_2,plain,
! [U_1205,U_1204] :
( ( disjoint(U_1205,U_1204)
| set_difference(U_1205,U_1204) != U_1205 )
& ( set_difference(U_1205,U_1204) = U_1205
| ~ disjoint(U_1205,U_1204) ) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
( ! [U_1209,U_1207] :
( disjoint(U_1209,U_1207)
| set_difference(U_1209,U_1207) != U_1209 )
& ! [U_1208,U_1206] :
( set_difference(U_1208,U_1206) = U_1208
| ~ disjoint(U_1208,U_1206) ) ),
inference(miniscope,[status(thm)],[f_331_2]) ).
cnf(f_331_4,plain,
( set_difference(U_1208,U_1206) = U_1208
| ~ disjoint(U_1208,U_1206) ),
inference(clausify,[status(thm)],[f_331_3]) ).
cnf(f_331_5,plain,
( disjoint(U_1209,U_1207)
| set_difference(U_1209,U_1207) != U_1209 ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_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_332_2,plain,
! [U_1212,U_1211,U_1210] :
( ( ( in(U_1212,relation_dom(relation_dom_restriction(U_1210,U_1211)))
| ~ in(U_1212,relation_dom(U_1210))
| ~ in(U_1212,U_1211) )
& ( ( in(U_1212,relation_dom(U_1210))
& in(U_1212,U_1211) )
| ~ in(U_1212,relation_dom(relation_dom_restriction(U_1210,U_1211))) ) )
| ~ relation(U_1210) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
( in(U_1212,U_1211)
| ~ in(U_1212,relation_dom(relation_dom_restriction(U_1210,U_1211)))
| ~ relation(U_1210) ),
inference(clausify,[status(thm)],[f_332_2]) ).
cnf(f_332_4,plain,
( in(U_1212,relation_dom(U_1210))
| ~ in(U_1212,relation_dom(relation_dom_restriction(U_1210,U_1211)))
| ~ relation(U_1210) ),
inference(clausify,[status(thm)],[f_332_2]) ).
cnf(f_332_5,plain,
( in(U_1212,relation_dom(relation_dom_restriction(U_1210,U_1211)))
| ~ in(U_1212,relation_dom(U_1210))
| ~ in(U_1212,U_1211)
| ~ relation(U_1210) ),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_333_2,plain,
! [U_1214,U_1213] :
( subset(relation_dom_restriction(U_1213,U_1214),U_1213)
| ~ relation(U_1213) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
( subset(relation_dom_restriction(U_1213,U_1214),U_1213)
| ~ relation(U_1213) ),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_334_2,plain,
! [U_1216,U_1215] :
( ~ empty(U_1215)
| U_1216 = U_1215
| ~ empty(U_1216) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1216] :
( ! [U_1215] :
( ~ empty(U_1215)
| U_1216 = U_1215 )
| ~ empty(U_1216) ),
inference(miniscope,[status(thm)],[f_334_2]) ).
cnf(f_334_4,plain,
( ~ empty(U_1215)
| U_1216 = U_1215
| ~ empty(U_1216) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_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_335_2,plain,
! [U_1219,U_1218,U_1217] :
( ( ( in(ordered_pair(U_1219,U_1218),U_1217)
| U_1218 != apply(U_1217,U_1219)
| ~ in(U_1219,relation_dom(U_1217)) )
& ( ( U_1218 = apply(U_1217,U_1219)
& in(U_1219,relation_dom(U_1217)) )
| ~ in(ordered_pair(U_1219,U_1218),U_1217) ) )
| ~ function(U_1217)
| ~ relation(U_1217) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
( in(U_1219,relation_dom(U_1217))
| ~ in(ordered_pair(U_1219,U_1218),U_1217)
| ~ function(U_1217)
| ~ relation(U_1217) ),
inference(clausify,[status(thm)],[f_335_2]) ).
cnf(f_335_4,plain,
( U_1218 = apply(U_1217,U_1219)
| ~ in(ordered_pair(U_1219,U_1218),U_1217)
| ~ function(U_1217)
| ~ relation(U_1217) ),
inference(clausify,[status(thm)],[f_335_2]) ).
cnf(f_335_5,plain,
( in(ordered_pair(U_1219,U_1218),U_1217)
| U_1218 != apply(U_1217,U_1219)
| ~ in(U_1219,relation_dom(U_1217))
| ~ function(U_1217)
| ~ relation(U_1217) ),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_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_336_2,plain,
! [U_1220] :
( ( ( well_orders(U_1220,relation_field(U_1220))
| ~ well_ordering(U_1220) )
& ( well_ordering(U_1220)
| ~ well_orders(U_1220,relation_field(U_1220)) ) )
| ~ relation(U_1220) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( well_ordering(U_1220)
| ~ well_orders(U_1220,relation_field(U_1220))
| ~ relation(U_1220) ),
inference(clausify,[status(thm)],[f_336_2]) ).
cnf(f_336_4,plain,
( well_orders(U_1220,relation_field(U_1220))
| ~ well_ordering(U_1220)
| ~ relation(U_1220) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_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_337_2,plain,
! [U_1223,U_1222,U_1221] :
( subset(set_union2(U_1223,U_1221),U_1222)
| ~ subset(U_1221,U_1222)
| ~ subset(U_1223,U_1222) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
( subset(set_union2(U_1223,U_1221),U_1222)
| ~ subset(U_1221,U_1222)
| ~ subset(U_1223,U_1222) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_338_2,plain,
! [U_1226,U_1225,U_1224] :
( U_1226 = U_1225
| singleton(U_1226) != unordered_pair(U_1225,U_1224) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1226,U_1225] :
( ! [U_1224] : singleton(U_1226) != unordered_pair(U_1225,U_1224)
| U_1226 = U_1225 ),
inference(miniscope,[status(thm)],[f_338_2]) ).
cnf(f_338_4,plain,
( singleton(U_1226) != unordered_pair(U_1225,U_1224)
| U_1226 = U_1225 ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_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_339_2,plain,
! [U_1228,U_1227] :
( relation_dom(relation_dom_restriction(U_1227,U_1228)) = set_intersection2(relation_dom(U_1227),U_1228)
| ~ relation(U_1227) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
( relation_dom(relation_dom_restriction(U_1227,U_1228)) = set_intersection2(relation_dom(U_1227),U_1228)
| ~ relation(U_1227) ),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_340_2,plain,
! [U_1230,U_1229] :
( subset(U_1230,union(U_1229))
| ~ in(U_1230,U_1229) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
( subset(U_1230,union(U_1229))
| ~ in(U_1230,U_1229) ),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_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_341_2,plain,
! [U_1232,U_1231] :
( relation_dom_restriction(U_1231,U_1232) = relation_composition(identity_relation(U_1232),U_1231)
| ~ relation(U_1231) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( relation_dom_restriction(U_1231,U_1232) = relation_composition(identity_relation(U_1232),U_1231)
| ~ relation(U_1231) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_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_342_2,plain,
! [U_1234,U_1233] :
( subset(relation_rng(relation_dom_restriction(U_1233,U_1234)),relation_rng(U_1233))
| ~ relation(U_1233) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( subset(relation_rng(relation_dom_restriction(U_1233,U_1234)),relation_rng(U_1233))
| ~ relation(U_1233) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_343_2,plain,
! [U_1235] : union(powerset(U_1235)) = U_1235,
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
union(powerset(U_1235)) = U_1235,
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_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_344_2,plain,
! [U_1243] :
? [U_1242] :
( ! [U_1241] :
( in(U_1241,U_1242)
| are_equipotent(U_1241,U_1242)
| ~ subset(U_1241,U_1242) )
& ! [U_1240] :
( ? [U_1239] :
( ! [U_1238] :
( in(U_1238,U_1239)
| ~ subset(U_1238,U_1240) )
& in(U_1239,U_1242) )
| ~ in(U_1240,U_1242) )
& ! [U_1237,U_1236] :
( in(U_1236,U_1242)
| ~ subset(U_1236,U_1237)
| ~ in(U_1237,U_1242) )
& in(U_1243,U_1242) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_1243] :
( ! [U_1241] :
( in(U_1241,sK169(U_1243))
| are_equipotent(U_1241,sK169(U_1243))
| ~ subset(U_1241,sK169(U_1243)) )
& ! [U_1240] :
( ? [U_1239] :
( ! [U_1238] :
( in(U_1238,U_1239)
| ~ subset(U_1238,U_1240) )
& in(U_1239,sK169(U_1243)) )
| ~ in(U_1240,sK169(U_1243)) )
& ! [U_1237,U_1236] :
( in(U_1236,sK169(U_1243))
| ~ subset(U_1236,U_1237)
| ~ in(U_1237,sK169(U_1243)) )
& in(U_1243,sK169(U_1243)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_1242,sK169(U_1243))],[f_344_2]) ).
fof(f_344_4,plain,
! [U_1243] :
( ! [U_1241] :
( in(U_1241,sK169(U_1243))
| are_equipotent(U_1241,sK169(U_1243))
| ~ subset(U_1241,sK169(U_1243)) )
& ! [U_1240] :
( ( ! [U_1238] :
( in(U_1238,sK170(U_1243,U_1240))
| ~ subset(U_1238,U_1240) )
& in(sK170(U_1243,U_1240),sK169(U_1243)) )
| ~ in(U_1240,sK169(U_1243)) )
& ! [U_1237,U_1236] :
( in(U_1236,sK169(U_1243))
| ~ subset(U_1236,U_1237)
| ~ in(U_1237,sK169(U_1243)) )
& in(U_1243,sK169(U_1243)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_1239,sK170(U_1243,U_1240))],[f_344_3]) ).
cnf(f_344_5,plain,
in(U_1243,sK169(U_1243)),
inference(clausify,[status(thm)],[f_344_4]) ).
cnf(f_344_6,plain,
( in(U_1236,sK169(U_1243))
| ~ subset(U_1236,U_1237)
| ~ in(U_1237,sK169(U_1243)) ),
inference(clausify,[status(thm)],[f_344_4]) ).
cnf(f_344_7,plain,
( in(sK170(U_1243,U_1240),sK169(U_1243))
| ~ in(U_1240,sK169(U_1243)) ),
inference(clausify,[status(thm)],[f_344_4]) ).
cnf(f_344_8,plain,
( in(U_1238,sK170(U_1243,U_1240))
| ~ subset(U_1238,U_1240)
| ~ in(U_1240,sK169(U_1243)) ),
inference(clausify,[status(thm)],[f_344_4]) ).
cnf(f_344_9,plain,
( in(U_1241,sK169(U_1243))
| are_equipotent(U_1241,sK169(U_1243))
| ~ subset(U_1241,sK169(U_1243)) ),
inference(clausify,[status(thm)],[f_344_4]) ).
fof(f_345_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_345_2,plain,
! [U_1246,U_1245,U_1244] :
( U_1245 = U_1244
| singleton(U_1246) != unordered_pair(U_1245,U_1244) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( U_1245 = U_1244
| singleton(U_1246) != unordered_pair(U_1245,U_1244) ),
inference(clausify,[status(thm)],[f_345_2]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_7_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_4]) ).
cnf(f_34_11_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_34_11]) ).
cnf(f_34_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_34_12]) ).
cnf(f_73_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_73_8]) ).
cnf(f_73_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_73_9]) ).
cnf(f_77_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_77_2]) ).
cnf(f_78_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_78_2]) ).
cnf(f_79_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_79_2]) ).
cnf(f_80_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_80_2]) ).
cnf(f_81_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_81_2]) ).
cnf(f_82_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_82_2]) ).
cnf(f_83_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_83_2]) ).
cnf(f_84_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_84_2]) ).
cnf(f_85_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_85_2]) ).
cnf(f_87_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_87_2]) ).
cnf(f_88_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_88_2]) ).
cnf(f_90_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_90_2]) ).
cnf(f_91_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_91_2]) ).
cnf(f_93_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_93_2]) ).
cnf(f_95_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_95_2]) ).
cnf(f_96_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_96_2]) ).
cnf(f_97_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_97_2]) ).
cnf(f_99_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_99_2]) ).
cnf(f_100_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_100_2]) ).
cnf(f_103_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_103_2]) ).
cnf(f_104_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_104_2]) ).
cnf(f_114_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_114_2]) ).
cnf(f_115_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_115_2]) ).
cnf(f_116_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_116_2]) ).
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,Eq_x_2) = sK145(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_174,axiom,
( sK146(Eq_x_0,Eq_x_1,Eq_x_2) = sK146(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_175,axiom,
( sK147(Eq_x_0,Eq_x_1,Eq_x_2) = sK147(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_176,axiom,
( sK148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK148(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_177,axiom,
( sK149(Eq_x_0,Eq_x_1,Eq_x_2) = sK149(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_178,axiom,
( sK150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK150(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_179,axiom,
( sK151(Eq_x_0,Eq_x_1) = sK151(Eq_y_0,Eq_y_1)
| 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) = sK152(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_181,axiom,
( sK154(Eq_x_0) = sK154(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_182,axiom,
( sK155(Eq_x_0,Eq_x_1) = sK155(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_183,axiom,
( sK156(Eq_x_0,Eq_x_1) = sK156(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_184,axiom,
( sK157(Eq_x_0,Eq_x_1) = sK157(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_185,axiom,
( sK158(Eq_x_0) = sK158(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_186,axiom,
( sK159(Eq_x_0) = sK159(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_187,axiom,
( sK160(Eq_x_0,Eq_x_1) = sK160(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_188,axiom,
( sK161(Eq_x_0,Eq_x_1) = sK161(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_189,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_190,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_191,axiom,
( sK164(Eq_x_0,Eq_x_1) = sK164(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,
( sK165(Eq_x_0) = sK165(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_193,axiom,
( sK166(Eq_x_0) = sK166(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_194,axiom,
( sK167(Eq_x_0,Eq_x_1,Eq_x_2) = sK167(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_195,axiom,
( sK168(Eq_x_0,Eq_x_1) = sK168(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,
( sK169(Eq_x_0) = sK169(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_197,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_198,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_199,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_200,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_205,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_206,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_207,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_208,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_209,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_210,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,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_212,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,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_214,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,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_216,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_217,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_218,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_219,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_220,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_221,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,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_224,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_225,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_226,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_227,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_228,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU268+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.50 % Computer : n012.cluster.edu
% 0.02/0.50 % Model : x86_64 x86_64
% 0.02/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.50 % Memory : 8046.5625MB
% 0.02/0.50 % OS : Linux 6.8.0-71-generic
% 0.02/0.50 % CPULimit : 300
% 0.02/0.50 % WCLimit : 300
% 0.02/0.50 % DateTime : Sat Sep 19 23:43:37 UTC 2026
% 0.02/0.50 % CPUTime :
% 282.03/282.58 % SZS status Theorem for theBenchmark
% 282.03/282.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------