%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU294+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:52 AM UTC 2026
% Result : Theorem 30.36s 30.69s
% Output : Proof 30.48s
% 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_arytm_3,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( element(B,A)
=> ( ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B) ) ) ),
file('theBenchmark.p',cc1_arytm_3) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
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_arytm_3,axiom,
! [A] :
( ( ordinal(A)
& empty(A) )
=> ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc2_arytm_3) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_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_funct_1,axiom,
! [A] :
( function(A)
<=> ! [B,C,D] :
( ( in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) )
=> C = D ) ),
file('theBenchmark.p',d1_funct_1) ).
fof(d1_funct_2,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( B = empty_set
=> ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set ) )
& ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) ) ) ),
file('theBenchmark.p',d1_funct_2) ).
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_wellord2,axiom,
! [A,B] :
( equipotent(A,B)
<=> ? [C] :
( relation_rng(C) = B
& relation_dom(C) = A
& one_to_one(C)
& function(C)
& relation(C) ) ),
file('theBenchmark.p',d4_wellord2) ).
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(l30_wellord2,lemma,
! [A,B] :
( relation(B)
=> ~ ( ! [C] :
( relation(C)
=> ~ well_orders(C,A) )
& equipotent(A,relation_field(B))
& well_ordering(B) ) ),
file('theBenchmark.p',l30_wellord2) ).
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_arytm_3,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_arytm_3) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_funct_2,axiom,
! [A,B] :
? [C] :
( quasi_total(C,A,B)
& function(C)
& relation(C)
& relation_of2(C,A,B) ),
file('theBenchmark.p',rc1_funct_2) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_partfun1,axiom,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc1_partfun1) ).
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_finset_1,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_finset_1) ).
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_partfun1,axiom,
! [A,B] :
? [C] :
( function(C)
& relation(C)
& relation_of2(C,A,B) ),
file('theBenchmark.p',rc2_partfun1) ).
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_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
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(redefinition_r2_wellord2,axiom,
! [A,B] :
( equipotent(A,B)
<=> are_equipotent(A,B) ),
file('theBenchmark.p',redefinition_r2_wellord2) ).
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(reflexivity_r2_wellord2,axiom,
! [A,B] : equipotent(A,A),
file('theBenchmark.p',reflexivity_r2_wellord2) ).
fof(s1_funct_1__e10_24__wellord2__1,lemma,
! [A,B] :
( ( relation(B)
& ~ empty(A) )
=> ( ! [C,D,E] :
( ( ? [H] :
( ! [I] :
( in(I,H)
=> in(ordered_pair(E,I),B) )
& in(E,H)
& C = H )
& in(C,A)
& ? [F] :
( ! [G] :
( in(G,F)
=> in(ordered_pair(D,G),B) )
& in(D,F)
& C = F )
& in(C,A) )
=> D = E )
=> ? [C] :
( ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( ? [J] :
( ! [K] :
( in(K,J)
=> in(ordered_pair(E,K),B) )
& in(E,J)
& D = J )
& in(D,A)
& in(D,A) ) )
& function(C)
& relation(C) ) ) ),
file('theBenchmark.p',s1_funct_1__e10_24__wellord2__1) ).
fof(s1_funct_1__e16_22__wellord2__1,lemma,
! [A] :
( ! [B,C,D] :
( ( D = singleton(B)
& in(B,A)
& C = singleton(B)
& in(B,A) )
=> C = D )
=> ? [B] :
( ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( D = singleton(C)
& in(C,A)
& in(C,A) ) )
& function(B)
& relation(B) ) ),
file('theBenchmark.p',s1_funct_1__e16_22__wellord2__1) ).
fof(s1_ordinal1__e8_6__wellord2,lemma,
! [A] :
( ? [B] :
( in(B,A)
& ordinal(B) )
=> ? [B] :
( ! [C] :
( ordinal(C)
=> ( in(C,A)
=> ordinal_subset(B,C) ) )
& in(B,A)
& ordinal(B) ) ),
file('theBenchmark.p',s1_ordinal1__e8_6__wellord2) ).
fof(s1_relat_1__e6_21__wellord2,lemma,
! [A,B,C] :
( ( function(C)
& relation(C)
& relation(B) )
=> ? [D] :
( ! [E,F] :
( in(ordered_pair(E,F),D)
<=> ( in(ordered_pair(apply(C,E),apply(C,F)),B)
& in(F,A)
& in(E,A) ) )
& relation(D) ) ),
file('theBenchmark.p',s1_relat_1__e6_21__wellord2) ).
fof(s1_tarski__e10_24__wellord2__1,axiom,
! [A,B] :
( ( relation(B)
& ~ empty(A) )
=> ( ! [C,D,E] :
( ( ? [H] :
( ! [I] :
( in(I,H)
=> in(ordered_pair(E,I),B) )
& in(E,H)
& C = H )
& in(C,A)
& ? [F] :
( ! [G] :
( in(G,F)
=> in(ordered_pair(D,G),B) )
& in(D,F)
& C = F )
& in(C,A) )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ? [J] :
( ! [K] :
( in(K,J)
=> in(ordered_pair(D,K),B) )
& in(D,J)
& E = J )
& in(E,A)
& in(E,A) ) ) ) ),
file('theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
fof(s1_tarski__e10_24__wellord2__2,axiom,
! [A,B] :
( ( relation(B)
& ~ empty(A) )
=> ! [C] :
( ! [D,E,F] :
( ( ? [K,L] :
( ? [M] :
( ! [N] :
( in(N,M)
=> in(ordered_pair(L,N),B) )
& in(L,M)
& K = M )
& in(K,A)
& ordered_pair(K,L) = F )
& D = F
& ? [G,H] :
( ? [I] :
( ! [J] :
( in(J,I)
=> in(ordered_pair(H,J),B) )
& in(H,I)
& G = I )
& in(G,A)
& ordered_pair(G,H) = E )
& D = E )
=> E = F )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( ? [O,P] :
( ? [Q] :
( ! [R] :
( in(R,Q)
=> in(ordered_pair(P,R),B) )
& in(P,Q)
& O = Q )
& in(O,A)
& ordered_pair(O,P) = E )
& F = E
& in(F,cartesian_product2(A,C)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
fof(s1_tarski__e16_22__wellord2__1,axiom,
! [A] :
( ! [B,C,D] :
( ( D = singleton(B)
& in(B,A)
& C = singleton(B)
& in(B,A) )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( C = singleton(D)
& in(D,A)
& in(D,A) ) ) ),
file('theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
fof(s1_tarski__e16_22__wellord2__2,axiom,
! [A,B] :
( ! [C,D,E] :
( ( ? [H,I] :
( I = singleton(H)
& in(H,A)
& ordered_pair(H,I) = E )
& C = E
& ? [F,G] :
( G = singleton(F)
& in(F,A)
& ordered_pair(F,G) = D )
& C = D )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ? [J,K] :
( K = singleton(J)
& in(J,A)
& ordered_pair(J,K) = D )
& E = D
& in(E,cartesian_product2(A,B)) ) ) ),
file('theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(s1_tarski__e6_21__wellord2__1,axiom,
! [A,B,C] :
( ( function(C)
& relation(C)
& relation(B) )
=> ( ! [D,E,F] :
( ( ? [I,J] :
( in(ordered_pair(apply(C,I),apply(C,J)),B)
& F = ordered_pair(I,J) )
& D = F
& ? [G,H] :
( in(ordered_pair(apply(C,G),apply(C,H)),B)
& E = ordered_pair(G,H) )
& D = E )
=> E = F )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( ? [K,L] :
( in(ordered_pair(apply(C,K),apply(C,L)),B)
& E = ordered_pair(K,L) )
& F = E
& in(F,cartesian_product2(A,A)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
fof(s1_tarski__e6_22__wellord2__1,axiom,
! [A] :
( ! [B,C,D] :
( ( ordinal(D)
& B = D
& ordinal(C)
& B = C )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ordinal(C)
& D = C
& in(D,A) ) ) ),
file('theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(s1_tarski__e8_6__wellord2__1,axiom,
! [A,B] :
( ordinal(B)
=> ( ! [C,D,E] :
( ( ? [G] :
( in(G,A)
& E = G
& ordinal(G) )
& C = E
& ? [F] :
( in(F,A)
& D = F
& ordinal(F) )
& C = D )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ? [H] :
( in(H,A)
& D = H
& ordinal(H) )
& E = D
& in(E,succ(B)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(s1_xboole_0__e10_24__wellord2__1,lemma,
! [A,B] :
( ( relation(B)
& ~ empty(A) )
=> ! [C] :
? [D] :
! [E] :
( in(E,D)
<=> ( ? [F,G] :
( ? [H] :
( ! [I] :
( in(I,H)
=> in(ordered_pair(G,I),B) )
& in(G,H)
& F = H )
& in(F,A)
& ordered_pair(F,G) = E )
& in(E,cartesian_product2(A,C)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
fof(s1_xboole_0__e16_22__wellord2__1,lemma,
! [A,B] :
? [C] :
! [D] :
( in(D,C)
<=> ( ? [E,F] :
( F = singleton(E)
& in(E,A)
& ordered_pair(E,F) = D )
& in(D,cartesian_product2(A,B)) ) ),
file('theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(s1_xboole_0__e6_21__wellord2__1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C)
& relation(B) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ( ? [F,G] :
( in(ordered_pair(apply(C,F),apply(C,G)),B)
& E = ordered_pair(F,G) )
& in(E,cartesian_product2(A,A)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(s1_xboole_0__e6_22__wellord2,lemma,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
file('theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(s1_xboole_0__e8_6__wellord2__1,lemma,
! [A,B] :
( ordinal(B)
=> ? [C] :
! [D] :
( in(D,C)
<=> ( ? [E] :
( in(E,A)
& D = E
& ordinal(E) )
& in(D,succ(B)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(s2_funct_1__e10_24__wellord2,lemma,
! [A,B] :
( ( relation(B)
& ~ empty(A) )
=> ( ( ! [C] :
~ ( ! [D] :
~ ? [J] :
( ! [K] :
( in(K,J)
=> in(ordered_pair(D,K),B) )
& in(D,J)
& C = J )
& in(C,A) )
& ! [C,D,E] :
( ( ? [H] :
( ! [I] :
( in(I,H)
=> in(ordered_pair(E,I),B) )
& in(E,H)
& C = H )
& ? [F] :
( ! [G] :
( in(G,F)
=> in(ordered_pair(D,G),B) )
& in(D,F)
& C = F )
& in(C,A) )
=> D = E ) )
=> ? [C] :
( ! [D] :
( in(D,A)
=> ? [L] :
( ! [M] :
( in(M,L)
=> in(ordered_pair(apply(C,D),M),B) )
& in(apply(C,D),L)
& D = L ) )
& relation_dom(C) = A
& function(C)
& relation(C) ) ) ),
file('theBenchmark.p',s2_funct_1__e10_24__wellord2) ).
fof(s2_funct_1__e16_22__wellord2__1,lemma,
! [A] :
( ( ! [B] :
~ ( ! [C] : C != singleton(B)
& in(B,A) )
& ! [B,C,D] :
( ( D = singleton(B)
& C = singleton(B)
& in(B,A) )
=> C = D ) )
=> ? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ) ),
file('theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(s3_funct_1__e16_22__wellord2,lemma,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(symmetry_r2_wellord2,axiom,
! [A,B] :
( equipotent(A,B)
=> equipotent(B,A) ),
file('theBenchmark.p',symmetry_r2_wellord2) ).
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(t13_finset_1,conjecture,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_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_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
file('theBenchmark.p',t21_funct_2) ).
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(t25_wellord2,lemma,
! [A,B] :
( relation(B)
=> ( well_orders(B,A)
=> ( well_ordering(relation_restriction(B,A))
& relation_field(relation_restriction(B,A)) = A ) ) ),
file('theBenchmark.p',t25_wellord2) ).
fof(t26_wellord2,lemma,
! [A] :
? [B] :
( well_orders(B,A)
& relation(B) ),
file('theBenchmark.p',t26_wellord2) ).
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_wellord2,lemma,
! [A] :
( ~ empty(A)
=> ~ ( ! [B] :
( ( function(B)
& relation(B) )
=> ~ ( ! [C] :
( in(C,A)
=> in(apply(B,C),C) )
& relation_dom(B) = A ) )
& ! [B] :
~ ( B = empty_set
& in(B,A) ) ) ),
file('theBenchmark.p',t28_wellord2) ).
fof(t28_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t2_wellord2,lemma,
! [A] : reflexive(inclusion_relation(A)),
file('theBenchmark.p',t2_wellord2) ).
fof(t2_xboole_1,lemma,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t30_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t31_ordinal1,lemma,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('theBenchmark.p',t31_ordinal1) ).
fof(t31_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( well_founded_relation(B)
=> well_founded_relation(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t31_wellord1) ).
fof(t32_ordinal1,lemma,
! [A,B] :
( ordinal(B)
=> ~ ( ! [C] :
( ordinal(C)
=> ~ ( ! [D] :
( ordinal(D)
=> ( in(D,A)
=> ordinal_subset(C,D) ) )
& in(C,A) ) )
& A != empty_set
& subset(A,B) ) ),
file('theBenchmark.p',t32_ordinal1) ).
fof(t32_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t32_wellord1) ).
fof(t33_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
fof(t33_xboole_1,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_zfmisc_1,lemma,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('theBenchmark.p',t33_zfmisc_1) ).
fof(t34_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t35_funct_1,lemma,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t36_xboole_1,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t37_xboole_1,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t37_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',t37_zfmisc_1) ).
fof(t38_zfmisc_1,lemma,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t39_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( ( subset(A,relation_field(B))
& well_ordering(B) )
=> relation_field(relation_restriction(B,A)) = A ) ),
file('theBenchmark.p',t39_wellord1) ).
fof(t39_xboole_1,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('theBenchmark.p',t39_xboole_1) ).
fof(t39_zfmisc_1,lemma,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_ordinal1,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('theBenchmark.p',t3_ordinal1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t3_wellord2,lemma,
! [A] : transitive(inclusion_relation(A)),
file('theBenchmark.p',t3_wellord2) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t3_xboole_1,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t40_xboole_1,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t41_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('theBenchmark.p',t41_ordinal1) ).
fof(t42_ordinal1,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('theBenchmark.p',t42_ordinal1) ).
fof(t43_subset_1,lemma,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,powerset(A))
=> ( disjoint(B,C)
<=> subset(B,subset_complement(A,C)) ) ) ),
file('theBenchmark.p',t43_subset_1) ).
fof(t44_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_dom(relation_composition(A,B)),relation_dom(A)) ) ),
file('theBenchmark.p',t44_relat_1) ).
fof(t45_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> subset(relation_rng(relation_composition(A,B)),relation_rng(B)) ) ),
file('theBenchmark.p',t45_relat_1) ).
fof(t45_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t46_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( B != empty_set
=> ! [E] :
( in(E,relation_inverse_image(D,C))
<=> ( in(apply(D,E),C)
& in(E,A) ) ) ) ),
file('theBenchmark.p',t46_funct_2) ).
fof(t46_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t46_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
fof(t46_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('theBenchmark.p',t46_zfmisc_1) ).
fof(t47_relat_1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('theBenchmark.p',t47_relat_1) ).
fof(t47_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
fof(t48_setfam_1,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t48_setfam_1) ).
fof(t48_xboole_1,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t49_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> relation_isomorphism(B,A,function_inverse(C)) ) ) ) ),
file('theBenchmark.p',t49_wellord1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_wellord2,lemma,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('theBenchmark.p',t4_wellord2) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t50_subset_1,lemma,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t53_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( well_founded_relation(A)
=> well_founded_relation(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( connected(A)
=> connected(B) )
& ( transitive(A)
=> transitive(B) )
& ( reflexive(A)
=> reflexive(B) ) ) ) ) ) ),
file('theBenchmark.p',t53_wellord1) ).
fof(t54_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('theBenchmark.p',t54_funct_1) ).
fof(t54_subset_1,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t54_wellord1,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('theBenchmark.p',t54_wellord1) ).
fof(t55_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t56_relat_1,lemma,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t57_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('theBenchmark.p',t57_funct_1) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('theBenchmark.p',t5_wellord1) ).
fof(t5_wellord2,lemma,
! [A] : antisymmetric(inclusion_relation(A)),
file('theBenchmark.p',t5_wellord2) ).
fof(t60_relat_1,lemma,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(t60_xboole_1,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('theBenchmark.p',t60_xboole_1) ).
fof(t62_funct_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t63_xboole_1,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('theBenchmark.p',t63_xboole_1) ).
fof(t64_relat_1,lemma,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t65_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('theBenchmark.p',t65_relat_1) ).
fof(t65_zfmisc_1,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t68_funct_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t69_enumset1,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t6_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( in(C,A)
=> ( in(apply(D,C),relation_rng(D))
| B = empty_set ) ) ),
file('theBenchmark.p',t6_funct_2) ).
fof(t6_wellord2,lemma,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('theBenchmark.p',t6_wellord2) ).
fof(t6_zfmisc_1,lemma,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t70_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t71_relat_1,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t72_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_1) ).
fof(t74_relat_1,lemma,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('theBenchmark.p',t74_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t7_mcart_1,lemma,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('theBenchmark.p',t7_mcart_1) ).
fof(t7_tarski,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('theBenchmark.p',t7_tarski) ).
fof(t7_wellord2,lemma,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('theBenchmark.p',t7_wellord2) ).
fof(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t83_xboole_1,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t86_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t86_relat_1) ).
fof(t88_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(t8_wellord1,lemma,
! [A] :
( relation(A)
=> ( well_orders(A,relation_field(A))
<=> well_ordering(A) ) ),
file('theBenchmark.p',t8_wellord1) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t90_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('theBenchmark.p',t90_relat_1) ).
fof(t92_zfmisc_1,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(t94_relat_1,lemma,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('theBenchmark.p',t94_relat_1) ).
fof(t99_relat_1,lemma,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_zfmisc_1,lemma,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t9_funct_2,lemma,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( subset(B,C)
=> ( ( relation_of2_as_subset(D,A,C)
& quasi_total(D,A,C)
& function(D) )
| ( A != empty_set
& B = empty_set ) ) ) ),
file('theBenchmark.p',t9_funct_2) ).
fof(t9_tarski,axiom,
! [A] :
? [B] :
( ! [C] :
~ ( ~ in(C,B)
& ~ are_equipotent(C,B)
& subset(C,B) )
& ! [C] :
~ ( ! [D] :
~ ( ! [E] :
( subset(E,C)
=> in(E,D) )
& in(D,B) )
& in(C,B) )
& ! [C,D] :
( ( subset(D,C)
& in(C,B) )
=> in(D,B) )
& in(A,B) ),
file('theBenchmark.p',t9_tarski) ).
fof(t9_zfmisc_1,lemma,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_0,U_1] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2,U_3] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ! [B] :
( ( ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B) )
| ~ element(B,A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_arytm_3]) ).
fof(f_3_2,plain,
! [U_5] :
( ! [U_4] :
( ( ordinal(U_4)
& epsilon_connected(U_4)
& epsilon_transitive(U_4) )
| ~ element(U_4,U_5) )
| ~ ordinal(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_4] :
( ordinal(U_4)
| ~ sP0(U_4) )
& ! [U_4] :
( epsilon_connected(U_4)
| ~ sP0(U_4) )
& ! [U_4] :
( epsilon_transitive(U_4)
| ~ sP0(U_4) )
& ! [U_4,U_5] :
( sP0(U_4)
| ~ element(U_4,U_5)
| ~ ordinal(U_5) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_4)
| ~ element(U_4,U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( epsilon_transitive(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( epsilon_connected(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_7,plain,
( ordinal(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_4_2,plain,
! [U_6] :
( finite(U_6)
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_6] :
( finite(U_6)
| ~ empty(U_6) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( finite(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_5_2,plain,
! [U_7] :
( function(U_7)
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_7] :
( function(U_7)
| ~ empty(U_7) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( function(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_6_2,plain,
! [U_8] :
( ( epsilon_connected(U_8)
& epsilon_transitive(U_8) )
| ~ ordinal(U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_8] :
( epsilon_connected(U_8)
| ~ sP1(U_8) )
& ! [U_8] :
( epsilon_transitive(U_8)
| ~ sP1(U_8) )
& ! [U_8] :
( sP1(U_8)
| ~ ordinal(U_8) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP1(U_8)
| ~ ordinal(U_8) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( epsilon_transitive(U_8)
| ~ sP1(U_8) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( epsilon_connected(U_8)
| ~ sP1(U_8) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_7_2,plain,
! [U_9] :
( relation(U_9)
| ~ empty(U_9) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_9] :
( relation(U_9)
| ~ empty(U_9) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( relation(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_8_2,plain,
! [U_12,U_11,U_10] :
( relation(U_10)
| ~ element(U_10,powerset(cartesian_product2(U_12,U_11))) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_10,U_12,U_11] :
( relation(U_10)
| ~ element(U_10,powerset(cartesian_product2(U_12,U_11))) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( relation(U_10)
| ~ element(U_10,powerset(cartesian_product2(U_12,U_11))) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc2_arytm_3]) ).
fof(f_9_2,plain,
! [U_13] :
( ( natural(U_13)
& ordinal(U_13)
& epsilon_connected(U_13)
& epsilon_transitive(U_13) )
| ~ ordinal(U_13)
| ~ empty(U_13) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_13] :
( natural(U_13)
| ~ sP2(U_13) )
& ! [U_13] :
( ordinal(U_13)
| ~ sP2(U_13) )
& ! [U_13] :
( epsilon_connected(U_13)
| ~ sP2(U_13) )
& ! [U_13] :
( epsilon_transitive(U_13)
| ~ sP2(U_13) )
& ! [U_13] :
( sP2(U_13)
| ~ ordinal(U_13)
| ~ empty(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP2(U_13)
| ~ ordinal(U_13)
| ~ empty(U_13) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( epsilon_transitive(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( epsilon_connected(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( ordinal(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_8,plain,
( natural(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_10_2,plain,
! [U_15] :
( ! [U_14] :
( finite(U_14)
| ~ element(U_14,powerset(U_15)) )
| ~ finite(U_15) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_15,U_14] :
( finite(U_14)
| ~ element(U_14,powerset(U_15))
| ~ finite(U_15) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( finite(U_14)
| ~ element(U_14,powerset(U_15))
| ~ finite(U_15) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_16] :
( ( one_to_one(U_16)
& function(U_16)
& relation(U_16) )
| ~ function(U_16)
| ~ empty(U_16)
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_16] :
( one_to_one(U_16)
| ~ sP3(U_16) )
& ! [U_16] :
( function(U_16)
| ~ sP3(U_16) )
& ! [U_16] :
( relation(U_16)
| ~ sP3(U_16) )
& ! [U_16] :
( sP3(U_16)
| ~ function(U_16)
| ~ empty(U_16)
| ~ relation(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP3(U_16)
| ~ function(U_16)
| ~ empty(U_16)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( relation(U_16)
| ~ sP3(U_16) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( function(U_16)
| ~ sP3(U_16) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( one_to_one(U_16)
| ~ sP3(U_16) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_12_2,plain,
! [U_17] :
( ordinal(U_17)
| ~ epsilon_connected(U_17)
| ~ epsilon_transitive(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_17] :
( ordinal(U_17)
| ~ epsilon_connected(U_17)
| ~ epsilon_transitive(U_17) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( ordinal(U_17)
| ~ epsilon_connected(U_17)
| ~ epsilon_transitive(U_17) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_13_2,plain,
! [U_18] :
( ( ordinal(U_18)
& epsilon_connected(U_18)
& epsilon_transitive(U_18) )
| ~ empty(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_18] :
( ordinal(U_18)
| ~ sP4(U_18) )
& ! [U_18] :
( epsilon_connected(U_18)
| ~ sP4(U_18) )
& ! [U_18] :
( epsilon_transitive(U_18)
| ~ sP4(U_18) )
& ! [U_18] :
( sP4(U_18)
| ~ empty(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP4(U_18)
| ~ empty(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( epsilon_transitive(U_18)
| ~ sP4(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( epsilon_connected(U_18)
| ~ sP4(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
( ordinal(U_18)
| ~ sP4(U_18) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_14_2,plain,
! [U_20,U_19] : unordered_pair(U_20,U_19) = unordered_pair(U_19,U_20),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_20,U_19] : unordered_pair(U_20,U_19) = unordered_pair(U_19,U_20),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
unordered_pair(U_20,U_19) = unordered_pair(U_19,U_20),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_15_2,plain,
! [U_22,U_21] : set_union2(U_22,U_21) = set_union2(U_21,U_22),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_21,U_22] : set_union2(U_22,U_21) = set_union2(U_21,U_22),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
set_union2(U_22,U_21) = set_union2(U_21,U_22),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_16_2,plain,
! [U_24,U_23] : set_intersection2(U_24,U_23) = set_intersection2(U_23,U_24),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_23,U_24] : set_intersection2(U_24,U_23) = set_intersection2(U_23,U_24),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
set_intersection2(U_24,U_23) = set_intersection2(U_23,U_24),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_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_17_2,plain,
! [U_26,U_25] :
( ordinal_subset(U_25,U_26)
| ordinal_subset(U_26,U_25)
| ~ ordinal(U_25)
| ~ ordinal(U_26) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_25,U_26] :
( ordinal_subset(U_25,U_26)
| ordinal_subset(U_26,U_25)
| ~ ordinal(U_25)
| ~ ordinal(U_26) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( ordinal_subset(U_25,U_26)
| ordinal_subset(U_26,U_25)
| ~ ordinal(U_25)
| ~ ordinal(U_26) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_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_18_2,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ? [U_30,U_29] :
( ( ~ in(ordered_pair(U_30,U_29),U_31)
& U_30 = U_29
& in(U_30,U_32) )
| ( ( U_30 != U_29
| ~ in(U_30,U_32) )
& in(ordered_pair(U_30,U_29),U_31) ) ) )
& ( ! [U_28,U_27] :
( ( in(ordered_pair(U_28,U_27),U_31)
| U_28 != U_27
| ~ in(U_28,U_32) )
& ( ( U_28 = U_27
& in(U_28,U_32) )
| ~ in(ordered_pair(U_28,U_27),U_31) ) )
| U_31 != identity_relation(U_32) ) )
| ~ relation(U_31) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ? [U_40,U_38] :
( ~ in(ordered_pair(U_40,U_38),U_31)
& U_40 = U_38
& in(U_40,U_32) )
| ? [U_39,U_37] :
( ( U_39 != U_37
| ~ in(U_39,U_32) )
& in(ordered_pair(U_39,U_37),U_31) ) )
& ( ( ! [U_36,U_34] :
( in(ordered_pair(U_36,U_34),U_31)
| U_36 != U_34
| ~ in(U_36,U_32) )
& ! [U_35,U_33] :
( ( U_35 = U_33
& in(U_35,U_32) )
| ~ in(ordered_pair(U_35,U_33),U_31) ) )
| U_31 != identity_relation(U_32) ) )
| ~ relation(U_31) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ? [U_40,U_38] :
( ~ in(ordered_pair(U_40,U_38),U_31)
& U_40 = U_38
& in(U_40,U_32) )
| ? [U_37] :
( ( sK1(U_32,U_31) != U_37
| ~ in(sK1(U_32,U_31),U_32) )
& in(ordered_pair(sK1(U_32,U_31),U_37),U_31) ) )
& ( ( ! [U_36,U_34] :
( in(ordered_pair(U_36,U_34),U_31)
| U_36 != U_34
| ~ in(U_36,U_32) )
& ! [U_35,U_33] :
( ( U_35 = U_33
& in(U_35,U_32) )
| ~ in(ordered_pair(U_35,U_33),U_31) ) )
| U_31 != identity_relation(U_32) ) )
| ~ relation(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_39,sK1(U_32,U_31))],[f_18_3]) ).
fof(f_18_5,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ? [U_40,U_38] :
( ~ in(ordered_pair(U_40,U_38),U_31)
& U_40 = U_38
& in(U_40,U_32) )
| ( ( sK1(U_32,U_31) != sK2(U_32,U_31)
| ~ in(sK1(U_32,U_31),U_32) )
& in(ordered_pair(sK1(U_32,U_31),sK2(U_32,U_31)),U_31) ) )
& ( ( ! [U_36,U_34] :
( in(ordered_pair(U_36,U_34),U_31)
| U_36 != U_34
| ~ in(U_36,U_32) )
& ! [U_35,U_33] :
( ( U_35 = U_33
& in(U_35,U_32) )
| ~ in(ordered_pair(U_35,U_33),U_31) ) )
| U_31 != identity_relation(U_32) ) )
| ~ relation(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_37,sK2(U_32,U_31))],[f_18_4]) ).
fof(f_18_6,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ? [U_38] :
( ~ in(ordered_pair(sK3(U_32,U_31),U_38),U_31)
& sK3(U_32,U_31) = U_38
& in(sK3(U_32,U_31),U_32) )
| ( ( sK1(U_32,U_31) != sK2(U_32,U_31)
| ~ in(sK1(U_32,U_31),U_32) )
& in(ordered_pair(sK1(U_32,U_31),sK2(U_32,U_31)),U_31) ) )
& ( ( ! [U_36,U_34] :
( in(ordered_pair(U_36,U_34),U_31)
| U_36 != U_34
| ~ in(U_36,U_32) )
& ! [U_35,U_33] :
( ( U_35 = U_33
& in(U_35,U_32) )
| ~ in(ordered_pair(U_35,U_33),U_31) ) )
| U_31 != identity_relation(U_32) ) )
| ~ relation(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_40,sK3(U_32,U_31))],[f_18_5]) ).
fof(f_18_7,plain,
! [U_32,U_31] :
( ( ( U_31 = identity_relation(U_32)
| ( ~ in(ordered_pair(sK3(U_32,U_31),sK4(U_32,U_31)),U_31)
& sK3(U_32,U_31) = sK4(U_32,U_31)
& in(sK3(U_32,U_31),U_32) )
| ( ( sK1(U_32,U_31) != sK2(U_32,U_31)
| ~ in(sK1(U_32,U_31),U_32) )
& in(ordered_pair(sK1(U_32,U_31),sK2(U_32,U_31)),U_31) ) )
& ( ( ! [U_36,U_34] :
( in(ordered_pair(U_36,U_34),U_31)
| U_36 != U_34
| ~ in(U_36,U_32) )
& ! [U_35,U_33] :
( ( U_35 = U_33
& in(U_35,U_32) )
| ~ in(ordered_pair(U_35,U_33),U_31) ) )
| U_31 != identity_relation(U_32) ) )
| ~ relation(U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_38,sK4(U_32,U_31))],[f_18_6]) ).
fof(f_18_8,plain,
( ! [U_31,U_32] :
( ~ in(ordered_pair(sK3(U_32,U_31),sK4(U_32,U_31)),U_31)
| ~ sP8(U_31,U_32) )
& ! [U_31,U_32] :
( sK3(U_32,U_31) = sK4(U_32,U_31)
| ~ sP8(U_31,U_32) )
& ! [U_31,U_32] :
( in(sK3(U_32,U_31),U_32)
| ~ sP8(U_31,U_32) )
& ! [U_31,U_32] :
( sK1(U_32,U_31) != sK2(U_32,U_31)
| ~ in(sK1(U_32,U_31),U_32)
| ~ sP7(U_31,U_32) )
& ! [U_31,U_32] :
( in(ordered_pair(sK1(U_32,U_31),sK2(U_32,U_31)),U_31)
| ~ sP7(U_31,U_32) )
& ! [U_35,U_32,U_33] :
( U_35 = U_33
| ~ sP5(U_35,U_32,U_33) )
& ! [U_35,U_32,U_33] :
( in(U_35,U_32)
| ~ sP5(U_35,U_32,U_33) )
& ! [U_35,U_31,U_32,U_33,U_34,U_36] :
( in(ordered_pair(U_36,U_34),U_31)
| U_36 != U_34
| ~ in(U_36,U_32)
| ~ sP6(U_35,U_31,U_32,U_33,U_34,U_36) )
& ! [U_35,U_31,U_32,U_33,U_34,U_36] :
( sP5(U_35,U_32,U_33)
| ~ in(ordered_pair(U_35,U_33),U_31)
| ~ sP6(U_35,U_31,U_32,U_33,U_34,U_36) )
& ! [U_35,U_31,U_32,U_33,U_34,U_36] :
( U_31 = identity_relation(U_32)
| sP8(U_31,U_32)
| sP7(U_31,U_32)
| ~ sP9(U_35,U_31,U_32,U_33,U_34,U_36) )
& ! [U_35,U_31,U_32,U_33,U_34,U_36] :
( sP6(U_35,U_31,U_32,U_33,U_34,U_36)
| U_31 != identity_relation(U_32)
| ~ sP9(U_35,U_31,U_32,U_33,U_34,U_36) )
& ! [U_35,U_31,U_32,U_33,U_34,U_36] :
( sP9(U_35,U_31,U_32,U_33,U_34,U_36)
| ~ relation(U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6,sP7,sP8,sP9])],[f_18_7]) ).
cnf(f_18_9,plain,
( sP9(U_35,U_31,U_32,U_33,U_34,U_36)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_10,plain,
( sP6(U_35,U_31,U_32,U_33,U_34,U_36)
| U_31 != identity_relation(U_32)
| ~ sP9(U_35,U_31,U_32,U_33,U_34,U_36) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_11,plain,
( U_31 = identity_relation(U_32)
| sP8(U_31,U_32)
| sP7(U_31,U_32)
| ~ sP9(U_35,U_31,U_32,U_33,U_34,U_36) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_12,plain,
( sP5(U_35,U_32,U_33)
| ~ in(ordered_pair(U_35,U_33),U_31)
| ~ sP6(U_35,U_31,U_32,U_33,U_34,U_36) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_13,plain,
( in(ordered_pair(U_36,U_34),U_31)
| U_36 != U_34
| ~ in(U_36,U_32)
| ~ sP6(U_35,U_31,U_32,U_33,U_34,U_36) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_14,plain,
( in(U_35,U_32)
| ~ sP5(U_35,U_32,U_33) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_15,plain,
( U_35 = U_33
| ~ sP5(U_35,U_32,U_33) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_16,plain,
( in(ordered_pair(sK1(U_32,U_31),sK2(U_32,U_31)),U_31)
| ~ sP7(U_31,U_32) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_17,plain,
( sK1(U_32,U_31) != sK2(U_32,U_31)
| ~ in(sK1(U_32,U_31),U_32)
| ~ sP7(U_31,U_32) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_18,plain,
( in(sK3(U_32,U_31),U_32)
| ~ sP8(U_31,U_32) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_19,plain,
( sK3(U_32,U_31) = sK4(U_32,U_31)
| ~ sP8(U_31,U_32) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_20,plain,
( ~ in(ordered_pair(sK3(U_32,U_31),sK4(U_32,U_31)),U_31)
| ~ sP8(U_31,U_32) ),
inference(clausify,[status(thm)],[f_18_8]) ).
fof(f_19_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_19_2,plain,
! [U_42,U_41] :
( ( U_42 = U_41
| ~ subset(U_41,U_42)
| ~ subset(U_42,U_41) )
& ( ( subset(U_41,U_42)
& subset(U_42,U_41) )
| U_42 != U_41 ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_46,U_44] :
( U_46 = U_44
| ~ subset(U_44,U_46)
| ~ subset(U_46,U_44) )
& ! [U_45,U_43] :
( ( subset(U_43,U_45)
& subset(U_45,U_43) )
| U_45 != U_43 ) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
( ! [U_45,U_43] :
( subset(U_43,U_45)
| ~ sP10(U_45,U_43) )
& ! [U_45,U_43] :
( subset(U_45,U_43)
| ~ sP10(U_45,U_43) )
& ! [U_46,U_44] :
( U_46 = U_44
| ~ subset(U_44,U_46)
| ~ subset(U_46,U_44) )
& ! [U_45,U_43] :
( sP10(U_45,U_43)
| U_45 != U_43 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_19_3]) ).
cnf(f_19_5,plain,
( sP10(U_45,U_43)
| U_45 != U_43 ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
( U_46 = U_44
| ~ subset(U_44,U_46)
| ~ subset(U_46,U_44) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_7,plain,
( subset(U_45,U_43)
| ~ sP10(U_45,U_43) ),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_8,plain,
( subset(U_43,U_45)
| ~ sP10(U_45,U_43) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_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_20_2,plain,
! [U_53] :
( ! [U_52,U_51] :
( ( ( U_51 = relation_dom_restriction(U_53,U_52)
| ? [U_50,U_49] :
( ( ~ in(ordered_pair(U_50,U_49),U_51)
& in(ordered_pair(U_50,U_49),U_53)
& in(U_50,U_52) )
| ( ( ~ in(ordered_pair(U_50,U_49),U_53)
| ~ in(U_50,U_52) )
& in(ordered_pair(U_50,U_49),U_51) ) ) )
& ( ! [U_48,U_47] :
( ( in(ordered_pair(U_48,U_47),U_51)
| ~ in(ordered_pair(U_48,U_47),U_53)
| ~ in(U_48,U_52) )
& ( ( in(ordered_pair(U_48,U_47),U_53)
& in(U_48,U_52) )
| ~ in(ordered_pair(U_48,U_47),U_51) ) )
| U_51 != relation_dom_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_53) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_53] :
( ! [U_52,U_51] :
( ( ( U_51 = relation_dom_restriction(U_53,U_52)
| ? [U_61,U_59] :
( ~ in(ordered_pair(U_61,U_59),U_51)
& in(ordered_pair(U_61,U_59),U_53)
& in(U_61,U_52) )
| ? [U_60,U_58] :
( ( ~ in(ordered_pair(U_60,U_58),U_53)
| ~ in(U_60,U_52) )
& in(ordered_pair(U_60,U_58),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_53)
| ~ in(U_57,U_52) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_53)
& in(U_56,U_52) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_dom_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_53) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_53] :
( ! [U_52,U_51] :
( ( ( U_51 = relation_dom_restriction(U_53,U_52)
| ? [U_61,U_59] :
( ~ in(ordered_pair(U_61,U_59),U_51)
& in(ordered_pair(U_61,U_59),U_53)
& in(U_61,U_52) )
| ? [U_58] :
( ( ~ in(ordered_pair(sK5(U_53,U_52,U_51),U_58),U_53)
| ~ in(sK5(U_53,U_52,U_51),U_52) )
& in(ordered_pair(sK5(U_53,U_52,U_51),U_58),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_53)
| ~ in(U_57,U_52) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_53)
& in(U_56,U_52) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_dom_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_60,sK5(U_53,U_52,U_51))],[f_20_3]) ).
fof(f_20_5,plain,
! [U_53] :
( ! [U_52,U_51] :
( ( ( U_51 = relation_dom_restriction(U_53,U_52)
| ? [U_61,U_59] :
( ~ in(ordered_pair(U_61,U_59),U_51)
& in(ordered_pair(U_61,U_59),U_53)
& in(U_61,U_52) )
| ( ( ~ in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_53)
| ~ in(sK5(U_53,U_52,U_51),U_52) )
& in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_53)
| ~ in(U_57,U_52) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_53)
& in(U_56,U_52) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_dom_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_58,sK6(U_53,U_52,U_51))],[f_20_4]) ).
fof(f_20_6,plain,
! [U_53] :
( ! [U_52,U_51] :
( ( ( U_51 = relation_dom_restriction(U_53,U_52)
| ? [U_59] :
( ~ in(ordered_pair(sK7(U_53,U_52,U_51),U_59),U_51)
& in(ordered_pair(sK7(U_53,U_52,U_51),U_59),U_53)
& in(sK7(U_53,U_52,U_51),U_52) )
| ( ( ~ in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_53)
| ~ in(sK5(U_53,U_52,U_51),U_52) )
& in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_53)
| ~ in(U_57,U_52) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_53)
& in(U_56,U_52) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_dom_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_61,sK7(U_53,U_52,U_51))],[f_20_5]) ).
fof(f_20_7,plain,
! [U_53] :
( ! [U_52,U_51] :
( ( ( U_51 = relation_dom_restriction(U_53,U_52)
| ( ~ in(ordered_pair(sK7(U_53,U_52,U_51),sK8(U_53,U_52,U_51)),U_51)
& in(ordered_pair(sK7(U_53,U_52,U_51),sK8(U_53,U_52,U_51)),U_53)
& in(sK7(U_53,U_52,U_51),U_52) )
| ( ( ~ in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_53)
| ~ in(sK5(U_53,U_52,U_51),U_52) )
& in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_51) ) )
& ( ( ! [U_57,U_55] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_53)
| ~ in(U_57,U_52) )
& ! [U_56,U_54] :
( ( in(ordered_pair(U_56,U_54),U_53)
& in(U_56,U_52) )
| ~ in(ordered_pair(U_56,U_54),U_51) ) )
| U_51 != relation_dom_restriction(U_53,U_52) ) )
| ~ relation(U_51) )
| ~ relation(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_59,sK8(U_53,U_52,U_51))],[f_20_6]) ).
fof(f_20_8,plain,
( ! [U_53,U_51,U_52] :
( ~ in(ordered_pair(sK7(U_53,U_52,U_51),sK8(U_53,U_52,U_51)),U_51)
| ~ sP14(U_53,U_51,U_52) )
& ! [U_53,U_51,U_52] :
( in(ordered_pair(sK7(U_53,U_52,U_51),sK8(U_53,U_52,U_51)),U_53)
| ~ sP14(U_53,U_51,U_52) )
& ! [U_53,U_51,U_52] :
( in(sK7(U_53,U_52,U_51),U_52)
| ~ sP14(U_53,U_51,U_52) )
& ! [U_53,U_51,U_52] :
( ~ in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_53)
| ~ in(sK5(U_53,U_52,U_51),U_52)
| ~ sP13(U_53,U_51,U_52) )
& ! [U_53,U_51,U_52] :
( in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_51)
| ~ sP13(U_53,U_51,U_52) )
& ! [U_53,U_52,U_56,U_54] :
( in(ordered_pair(U_56,U_54),U_53)
| ~ sP11(U_53,U_52,U_56,U_54) )
& ! [U_53,U_52,U_56,U_54] :
( in(U_56,U_52)
| ~ sP11(U_53,U_52,U_56,U_54) )
& ! [U_53,U_51,U_52,U_56,U_54,U_55,U_57] :
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_53)
| ~ in(U_57,U_52)
| ~ sP12(U_53,U_51,U_52,U_56,U_54,U_55,U_57) )
& ! [U_53,U_51,U_52,U_56,U_54,U_55,U_57] :
( sP11(U_53,U_52,U_56,U_54)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ sP12(U_53,U_51,U_52,U_56,U_54,U_55,U_57) )
& ! [U_53,U_51,U_52,U_56,U_54,U_55,U_57] :
( U_51 = relation_dom_restriction(U_53,U_52)
| sP14(U_53,U_51,U_52)
| sP13(U_53,U_51,U_52)
| ~ sP15(U_53,U_51,U_52,U_56,U_54,U_55,U_57) )
& ! [U_53,U_51,U_52,U_56,U_54,U_55,U_57] :
( sP12(U_53,U_51,U_52,U_56,U_54,U_55,U_57)
| U_51 != relation_dom_restriction(U_53,U_52)
| ~ sP15(U_53,U_51,U_52,U_56,U_54,U_55,U_57) )
& ! [U_53,U_51,U_52,U_56,U_54,U_55,U_57] :
( sP15(U_53,U_51,U_52,U_56,U_54,U_55,U_57)
| ~ relation(U_51)
| ~ relation(U_53) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12,sP13,sP14,sP15])],[f_20_7]) ).
cnf(f_20_9,plain,
( sP15(U_53,U_51,U_52,U_56,U_54,U_55,U_57)
| ~ relation(U_51)
| ~ relation(U_53) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_10,plain,
( sP12(U_53,U_51,U_52,U_56,U_54,U_55,U_57)
| U_51 != relation_dom_restriction(U_53,U_52)
| ~ sP15(U_53,U_51,U_52,U_56,U_54,U_55,U_57) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_11,plain,
( U_51 = relation_dom_restriction(U_53,U_52)
| sP14(U_53,U_51,U_52)
| sP13(U_53,U_51,U_52)
| ~ sP15(U_53,U_51,U_52,U_56,U_54,U_55,U_57) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_12,plain,
( sP11(U_53,U_52,U_56,U_54)
| ~ in(ordered_pair(U_56,U_54),U_51)
| ~ sP12(U_53,U_51,U_52,U_56,U_54,U_55,U_57) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_13,plain,
( in(ordered_pair(U_57,U_55),U_51)
| ~ in(ordered_pair(U_57,U_55),U_53)
| ~ in(U_57,U_52)
| ~ sP12(U_53,U_51,U_52,U_56,U_54,U_55,U_57) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_14,plain,
( in(U_56,U_52)
| ~ sP11(U_53,U_52,U_56,U_54) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_15,plain,
( in(ordered_pair(U_56,U_54),U_53)
| ~ sP11(U_53,U_52,U_56,U_54) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_16,plain,
( in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_51)
| ~ sP13(U_53,U_51,U_52) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_17,plain,
( ~ in(ordered_pair(sK5(U_53,U_52,U_51),sK6(U_53,U_52,U_51)),U_53)
| ~ in(sK5(U_53,U_52,U_51),U_52)
| ~ sP13(U_53,U_51,U_52) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_18,plain,
( in(sK7(U_53,U_52,U_51),U_52)
| ~ sP14(U_53,U_51,U_52) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_19,plain,
( in(ordered_pair(sK7(U_53,U_52,U_51),sK8(U_53,U_52,U_51)),U_53)
| ~ sP14(U_53,U_51,U_52) ),
inference(clausify,[status(thm)],[f_20_8]) ).
cnf(f_20_20,plain,
( ~ in(ordered_pair(sK7(U_53,U_52,U_51),sK8(U_53,U_52,U_51)),U_51)
| ~ sP14(U_53,U_51,U_52) ),
inference(clausify,[status(thm)],[f_20_8]) ).
fof(f_21_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_21_2,plain,
! [U_70] :
( ! [U_69,U_68] :
( ( U_68 = relation_image(U_70,U_69)
| ? [U_67] :
( ( ~ in(U_67,U_68)
& ? [U_66] :
( U_67 = apply(U_70,U_66)
& in(U_66,U_69)
& in(U_66,relation_dom(U_70)) ) )
| ( ! [U_65] :
( U_67 != apply(U_70,U_65)
| ~ in(U_65,U_69)
| ~ in(U_65,relation_dom(U_70)) )
& in(U_67,U_68) ) ) )
& ( ! [U_64] :
( ( in(U_64,U_68)
| ! [U_63] :
( U_64 != apply(U_70,U_63)
| ~ in(U_63,U_69)
| ~ in(U_63,relation_dom(U_70)) ) )
& ( ? [U_62] :
( U_64 = apply(U_70,U_62)
& in(U_62,U_69)
& in(U_62,relation_dom(U_70)) )
| ~ in(U_64,U_68) ) )
| U_68 != relation_image(U_70,U_69) ) )
| ~ function(U_70)
| ~ relation(U_70) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ? [U_74] :
( ~ in(U_74,U_76)
& ? [U_66] :
( U_74 = apply(U_70,U_66)
& in(U_66,U_78)
& in(U_66,relation_dom(U_70)) ) )
| ? [U_73] :
( ! [U_65] :
( U_73 != apply(U_70,U_65)
| ~ in(U_65,U_78)
| ~ in(U_65,relation_dom(U_70)) )
& in(U_73,U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( U_72 != apply(U_70,U_63)
| ~ in(U_63,U_77)
| ~ in(U_63,relation_dom(U_70)) ) )
& ! [U_71] :
( ? [U_62] :
( U_71 = apply(U_70,U_62)
& in(U_62,U_77)
& in(U_62,relation_dom(U_70)) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ function(U_70)
| ~ relation(U_70) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ? [U_74] :
( ~ in(U_74,U_76)
& ? [U_66] :
( U_74 = apply(U_70,U_66)
& in(U_66,U_78)
& in(U_66,relation_dom(U_70)) ) )
| ? [U_73] :
( ! [U_65] :
( U_73 != apply(U_70,U_65)
| ~ in(U_65,U_78)
| ~ in(U_65,relation_dom(U_70)) )
& in(U_73,U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( U_72 != apply(U_70,U_63)
| ~ in(U_63,U_77)
| ~ in(U_63,relation_dom(U_70)) ) )
& ! [U_71] :
( ( U_71 = apply(U_70,sK9(U_70,U_77,U_75,U_71))
& in(sK9(U_70,U_77,U_75,U_71),U_77)
& in(sK9(U_70,U_77,U_75,U_71),relation_dom(U_70)) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ function(U_70)
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_62,sK9(U_70,U_77,U_75,U_71))],[f_21_3]) ).
fof(f_21_5,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ? [U_74] :
( ~ in(U_74,U_76)
& ? [U_66] :
( U_74 = apply(U_70,U_66)
& in(U_66,U_78)
& in(U_66,relation_dom(U_70)) ) )
| ( ! [U_65] :
( sK10(U_70,U_78,U_76) != apply(U_70,U_65)
| ~ in(U_65,U_78)
| ~ in(U_65,relation_dom(U_70)) )
& in(sK10(U_70,U_78,U_76),U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( U_72 != apply(U_70,U_63)
| ~ in(U_63,U_77)
| ~ in(U_63,relation_dom(U_70)) ) )
& ! [U_71] :
( ( U_71 = apply(U_70,sK9(U_70,U_77,U_75,U_71))
& in(sK9(U_70,U_77,U_75,U_71),U_77)
& in(sK9(U_70,U_77,U_75,U_71),relation_dom(U_70)) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ function(U_70)
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_73,sK10(U_70,U_78,U_76))],[f_21_4]) ).
fof(f_21_6,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ( ~ in(sK11(U_70,U_78,U_76),U_76)
& ? [U_66] :
( sK11(U_70,U_78,U_76) = apply(U_70,U_66)
& in(U_66,U_78)
& in(U_66,relation_dom(U_70)) ) )
| ( ! [U_65] :
( sK10(U_70,U_78,U_76) != apply(U_70,U_65)
| ~ in(U_65,U_78)
| ~ in(U_65,relation_dom(U_70)) )
& in(sK10(U_70,U_78,U_76),U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( U_72 != apply(U_70,U_63)
| ~ in(U_63,U_77)
| ~ in(U_63,relation_dom(U_70)) ) )
& ! [U_71] :
( ( U_71 = apply(U_70,sK9(U_70,U_77,U_75,U_71))
& in(sK9(U_70,U_77,U_75,U_71),U_77)
& in(sK9(U_70,U_77,U_75,U_71),relation_dom(U_70)) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ function(U_70)
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_74,sK11(U_70,U_78,U_76))],[f_21_5]) ).
fof(f_21_7,plain,
! [U_70] :
( ( ! [U_78,U_76] :
( U_76 = relation_image(U_70,U_78)
| ( ~ in(sK11(U_70,U_78,U_76),U_76)
& sK11(U_70,U_78,U_76) = apply(U_70,sK12(U_70,U_78,U_76))
& in(sK12(U_70,U_78,U_76),U_78)
& in(sK12(U_70,U_78,U_76),relation_dom(U_70)) )
| ( ! [U_65] :
( sK10(U_70,U_78,U_76) != apply(U_70,U_65)
| ~ in(U_65,U_78)
| ~ in(U_65,relation_dom(U_70)) )
& in(sK10(U_70,U_78,U_76),U_76) ) )
& ! [U_77,U_75] :
( ( ! [U_72] :
( in(U_72,U_75)
| ! [U_63] :
( U_72 != apply(U_70,U_63)
| ~ in(U_63,U_77)
| ~ in(U_63,relation_dom(U_70)) ) )
& ! [U_71] :
( ( U_71 = apply(U_70,sK9(U_70,U_77,U_75,U_71))
& in(sK9(U_70,U_77,U_75,U_71),U_77)
& in(sK9(U_70,U_77,U_75,U_71),relation_dom(U_70)) )
| ~ in(U_71,U_75) ) )
| U_75 != relation_image(U_70,U_77) ) )
| ~ function(U_70)
| ~ relation(U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_66,sK12(U_70,U_78,U_76))],[f_21_6]) ).
fof(f_21_8,plain,
( ! [U_78,U_76,U_70] :
( ~ in(sK11(U_70,U_78,U_76),U_76)
| ~ sP19(U_78,U_76,U_70) )
& ! [U_78,U_76,U_70] :
( sK11(U_70,U_78,U_76) = apply(U_70,sK12(U_70,U_78,U_76))
| ~ sP19(U_78,U_76,U_70) )
& ! [U_78,U_76,U_70] :
( in(sK12(U_70,U_78,U_76),U_78)
| ~ sP19(U_78,U_76,U_70) )
& ! [U_78,U_76,U_70] :
( in(sK12(U_70,U_78,U_76),relation_dom(U_70))
| ~ sP19(U_78,U_76,U_70) )
& ! [U_78,U_76,U_70,U_65] :
( sK10(U_70,U_78,U_76) != apply(U_70,U_65)
| ~ in(U_65,U_78)
| ~ in(U_65,relation_dom(U_70))
| ~ sP18(U_78,U_76,U_70,U_65) )
& ! [U_78,U_76,U_70,U_65] :
( in(sK10(U_70,U_78,U_76),U_76)
| ~ sP18(U_78,U_76,U_70,U_65) )
& ! [U_75,U_70,U_77,U_71] :
( U_71 = apply(U_70,sK9(U_70,U_77,U_75,U_71))
| ~ sP16(U_75,U_70,U_77,U_71) )
& ! [U_75,U_70,U_77,U_71] :
( in(sK9(U_70,U_77,U_75,U_71),U_77)
| ~ sP16(U_75,U_70,U_77,U_71) )
& ! [U_75,U_70,U_77,U_71] :
( in(sK9(U_70,U_77,U_75,U_71),relation_dom(U_70))
| ~ sP16(U_75,U_70,U_77,U_71) )
& ! [U_75,U_63,U_70,U_77,U_72,U_71] :
( in(U_72,U_75)
| U_72 != apply(U_70,U_63)
| ~ in(U_63,U_77)
| ~ in(U_63,relation_dom(U_70))
| ~ sP17(U_75,U_63,U_70,U_77,U_72,U_71) )
& ! [U_75,U_63,U_70,U_77,U_72,U_71] :
( sP16(U_75,U_70,U_77,U_71)
| ~ in(U_71,U_75)
| ~ sP17(U_75,U_63,U_70,U_77,U_72,U_71) )
& ! [U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65] :
( U_76 = relation_image(U_70,U_78)
| sP19(U_78,U_76,U_70)
| sP18(U_78,U_76,U_70,U_65)
| ~ sP20(U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65) )
& ! [U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65] :
( sP17(U_75,U_63,U_70,U_77,U_72,U_71)
| U_75 != relation_image(U_70,U_77)
| ~ sP20(U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65) )
& ! [U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65] :
( sP20(U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65)
| ~ function(U_70)
| ~ relation(U_70) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17,sP18,sP19,sP20])],[f_21_7]) ).
cnf(f_21_9,plain,
( sP20(U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65)
| ~ function(U_70)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_10,plain,
( sP17(U_75,U_63,U_70,U_77,U_72,U_71)
| U_75 != relation_image(U_70,U_77)
| ~ sP20(U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_11,plain,
( U_76 = relation_image(U_70,U_78)
| sP19(U_78,U_76,U_70)
| sP18(U_78,U_76,U_70,U_65)
| ~ sP20(U_75,U_78,U_76,U_63,U_70,U_77,U_72,U_71,U_65) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_12,plain,
( sP16(U_75,U_70,U_77,U_71)
| ~ in(U_71,U_75)
| ~ sP17(U_75,U_63,U_70,U_77,U_72,U_71) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_13,plain,
( in(U_72,U_75)
| U_72 != apply(U_70,U_63)
| ~ in(U_63,U_77)
| ~ in(U_63,relation_dom(U_70))
| ~ sP17(U_75,U_63,U_70,U_77,U_72,U_71) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_14,plain,
( in(sK9(U_70,U_77,U_75,U_71),relation_dom(U_70))
| ~ sP16(U_75,U_70,U_77,U_71) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_15,plain,
( in(sK9(U_70,U_77,U_75,U_71),U_77)
| ~ sP16(U_75,U_70,U_77,U_71) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_16,plain,
( U_71 = apply(U_70,sK9(U_70,U_77,U_75,U_71))
| ~ sP16(U_75,U_70,U_77,U_71) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_17,plain,
( in(sK10(U_70,U_78,U_76),U_76)
| ~ sP18(U_78,U_76,U_70,U_65) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_18,plain,
( sK10(U_70,U_78,U_76) != apply(U_70,U_65)
| ~ in(U_65,U_78)
| ~ in(U_65,relation_dom(U_70))
| ~ sP18(U_78,U_76,U_70,U_65) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_19,plain,
( in(sK12(U_70,U_78,U_76),relation_dom(U_70))
| ~ sP19(U_78,U_76,U_70) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_20,plain,
( in(sK12(U_70,U_78,U_76),U_78)
| ~ sP19(U_78,U_76,U_70) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_21,plain,
( sK11(U_70,U_78,U_76) = apply(U_70,sK12(U_70,U_78,U_76))
| ~ sP19(U_78,U_76,U_70) ),
inference(clausify,[status(thm)],[f_21_8]) ).
cnf(f_21_22,plain,
( ~ in(sK11(U_70,U_78,U_76),U_76)
| ~ sP19(U_78,U_76,U_70) ),
inference(clausify,[status(thm)],[f_21_8]) ).
fof(f_22_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_22_2,plain,
! [U_85,U_84] :
( ! [U_83] :
( ( ( U_83 = relation_rng_restriction(U_85,U_84)
| ? [U_82,U_81] :
( ( ~ in(ordered_pair(U_82,U_81),U_83)
& in(ordered_pair(U_82,U_81),U_84)
& in(U_81,U_85) )
| ( ( ~ in(ordered_pair(U_82,U_81),U_84)
| ~ in(U_81,U_85) )
& in(ordered_pair(U_82,U_81),U_83) ) ) )
& ( ! [U_80,U_79] :
( ( in(ordered_pair(U_80,U_79),U_83)
| ~ in(ordered_pair(U_80,U_79),U_84)
| ~ in(U_79,U_85) )
& ( ( in(ordered_pair(U_80,U_79),U_84)
& in(U_79,U_85) )
| ~ in(ordered_pair(U_80,U_79),U_83) ) )
| U_83 != relation_rng_restriction(U_85,U_84) ) )
| ~ relation(U_83) )
| ~ relation(U_84) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_85,U_84] :
( ! [U_83] :
( ( ( U_83 = relation_rng_restriction(U_85,U_84)
| ? [U_93,U_91] :
( ~ in(ordered_pair(U_93,U_91),U_83)
& in(ordered_pair(U_93,U_91),U_84)
& in(U_91,U_85) )
| ? [U_92,U_90] :
( ( ~ in(ordered_pair(U_92,U_90),U_84)
| ~ in(U_90,U_85) )
& in(ordered_pair(U_92,U_90),U_83) ) )
& ( ( ! [U_89,U_87] :
( in(ordered_pair(U_89,U_87),U_83)
| ~ in(ordered_pair(U_89,U_87),U_84)
| ~ in(U_87,U_85) )
& ! [U_88,U_86] :
( ( in(ordered_pair(U_88,U_86),U_84)
& in(U_86,U_85) )
| ~ in(ordered_pair(U_88,U_86),U_83) ) )
| U_83 != relation_rng_restriction(U_85,U_84) ) )
| ~ relation(U_83) )
| ~ relation(U_84) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_85,U_84] :
( ! [U_83] :
( ( ( U_83 = relation_rng_restriction(U_85,U_84)
| ? [U_93,U_91] :
( ~ in(ordered_pair(U_93,U_91),U_83)
& in(ordered_pair(U_93,U_91),U_84)
& in(U_91,U_85) )
| ? [U_90] :
( ( ~ in(ordered_pair(sK13(U_85,U_84,U_83),U_90),U_84)
| ~ in(U_90,U_85) )
& in(ordered_pair(sK13(U_85,U_84,U_83),U_90),U_83) ) )
& ( ( ! [U_89,U_87] :
( in(ordered_pair(U_89,U_87),U_83)
| ~ in(ordered_pair(U_89,U_87),U_84)
| ~ in(U_87,U_85) )
& ! [U_88,U_86] :
( ( in(ordered_pair(U_88,U_86),U_84)
& in(U_86,U_85) )
| ~ in(ordered_pair(U_88,U_86),U_83) ) )
| U_83 != relation_rng_restriction(U_85,U_84) ) )
| ~ relation(U_83) )
| ~ relation(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_92,sK13(U_85,U_84,U_83))],[f_22_3]) ).
fof(f_22_5,plain,
! [U_85,U_84] :
( ! [U_83] :
( ( ( U_83 = relation_rng_restriction(U_85,U_84)
| ? [U_93,U_91] :
( ~ in(ordered_pair(U_93,U_91),U_83)
& in(ordered_pair(U_93,U_91),U_84)
& in(U_91,U_85) )
| ( ( ~ in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_84)
| ~ in(sK14(U_85,U_84,U_83),U_85) )
& in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_83) ) )
& ( ( ! [U_89,U_87] :
( in(ordered_pair(U_89,U_87),U_83)
| ~ in(ordered_pair(U_89,U_87),U_84)
| ~ in(U_87,U_85) )
& ! [U_88,U_86] :
( ( in(ordered_pair(U_88,U_86),U_84)
& in(U_86,U_85) )
| ~ in(ordered_pair(U_88,U_86),U_83) ) )
| U_83 != relation_rng_restriction(U_85,U_84) ) )
| ~ relation(U_83) )
| ~ relation(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_90,sK14(U_85,U_84,U_83))],[f_22_4]) ).
fof(f_22_6,plain,
! [U_85,U_84] :
( ! [U_83] :
( ( ( U_83 = relation_rng_restriction(U_85,U_84)
| ? [U_91] :
( ~ in(ordered_pair(sK15(U_85,U_84,U_83),U_91),U_83)
& in(ordered_pair(sK15(U_85,U_84,U_83),U_91),U_84)
& in(U_91,U_85) )
| ( ( ~ in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_84)
| ~ in(sK14(U_85,U_84,U_83),U_85) )
& in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_83) ) )
& ( ( ! [U_89,U_87] :
( in(ordered_pair(U_89,U_87),U_83)
| ~ in(ordered_pair(U_89,U_87),U_84)
| ~ in(U_87,U_85) )
& ! [U_88,U_86] :
( ( in(ordered_pair(U_88,U_86),U_84)
& in(U_86,U_85) )
| ~ in(ordered_pair(U_88,U_86),U_83) ) )
| U_83 != relation_rng_restriction(U_85,U_84) ) )
| ~ relation(U_83) )
| ~ relation(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_93,sK15(U_85,U_84,U_83))],[f_22_5]) ).
fof(f_22_7,plain,
! [U_85,U_84] :
( ! [U_83] :
( ( ( U_83 = relation_rng_restriction(U_85,U_84)
| ( ~ in(ordered_pair(sK15(U_85,U_84,U_83),sK16(U_85,U_84,U_83)),U_83)
& in(ordered_pair(sK15(U_85,U_84,U_83),sK16(U_85,U_84,U_83)),U_84)
& in(sK16(U_85,U_84,U_83),U_85) )
| ( ( ~ in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_84)
| ~ in(sK14(U_85,U_84,U_83),U_85) )
& in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_83) ) )
& ( ( ! [U_89,U_87] :
( in(ordered_pair(U_89,U_87),U_83)
| ~ in(ordered_pair(U_89,U_87),U_84)
| ~ in(U_87,U_85) )
& ! [U_88,U_86] :
( ( in(ordered_pair(U_88,U_86),U_84)
& in(U_86,U_85) )
| ~ in(ordered_pair(U_88,U_86),U_83) ) )
| U_83 != relation_rng_restriction(U_85,U_84) ) )
| ~ relation(U_83) )
| ~ relation(U_84) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_91,sK16(U_85,U_84,U_83))],[f_22_6]) ).
fof(f_22_8,plain,
( ! [U_83,U_85,U_84] :
( ~ in(ordered_pair(sK15(U_85,U_84,U_83),sK16(U_85,U_84,U_83)),U_83)
| ~ sP24(U_83,U_85,U_84) )
& ! [U_83,U_85,U_84] :
( in(ordered_pair(sK15(U_85,U_84,U_83),sK16(U_85,U_84,U_83)),U_84)
| ~ sP24(U_83,U_85,U_84) )
& ! [U_83,U_85,U_84] :
( in(sK16(U_85,U_84,U_83),U_85)
| ~ sP24(U_83,U_85,U_84) )
& ! [U_83,U_85,U_84] :
( ~ in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_84)
| ~ in(sK14(U_85,U_84,U_83),U_85)
| ~ sP23(U_83,U_85,U_84) )
& ! [U_83,U_85,U_84] :
( in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_83)
| ~ sP23(U_83,U_85,U_84) )
& ! [U_85,U_84,U_86,U_88] :
( in(ordered_pair(U_88,U_86),U_84)
| ~ sP21(U_85,U_84,U_86,U_88) )
& ! [U_85,U_84,U_86,U_88] :
( in(U_86,U_85)
| ~ sP21(U_85,U_84,U_86,U_88) )
& ! [U_89,U_83,U_85,U_84,U_86,U_87,U_88] :
( in(ordered_pair(U_89,U_87),U_83)
| ~ in(ordered_pair(U_89,U_87),U_84)
| ~ in(U_87,U_85)
| ~ sP22(U_89,U_83,U_85,U_84,U_86,U_87,U_88) )
& ! [U_89,U_83,U_85,U_84,U_86,U_87,U_88] :
( sP21(U_85,U_84,U_86,U_88)
| ~ in(ordered_pair(U_88,U_86),U_83)
| ~ sP22(U_89,U_83,U_85,U_84,U_86,U_87,U_88) )
& ! [U_89,U_83,U_85,U_84,U_86,U_87,U_88] :
( U_83 = relation_rng_restriction(U_85,U_84)
| sP24(U_83,U_85,U_84)
| sP23(U_83,U_85,U_84)
| ~ sP25(U_89,U_83,U_85,U_84,U_86,U_87,U_88) )
& ! [U_89,U_83,U_85,U_84,U_86,U_87,U_88] :
( sP22(U_89,U_83,U_85,U_84,U_86,U_87,U_88)
| U_83 != relation_rng_restriction(U_85,U_84)
| ~ sP25(U_89,U_83,U_85,U_84,U_86,U_87,U_88) )
& ! [U_89,U_83,U_85,U_84,U_86,U_87,U_88] :
( sP25(U_89,U_83,U_85,U_84,U_86,U_87,U_88)
| ~ relation(U_83)
| ~ relation(U_84) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22,sP23,sP24,sP25])],[f_22_7]) ).
cnf(f_22_9,plain,
( sP25(U_89,U_83,U_85,U_84,U_86,U_87,U_88)
| ~ relation(U_83)
| ~ relation(U_84) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_10,plain,
( sP22(U_89,U_83,U_85,U_84,U_86,U_87,U_88)
| U_83 != relation_rng_restriction(U_85,U_84)
| ~ sP25(U_89,U_83,U_85,U_84,U_86,U_87,U_88) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_11,plain,
( U_83 = relation_rng_restriction(U_85,U_84)
| sP24(U_83,U_85,U_84)
| sP23(U_83,U_85,U_84)
| ~ sP25(U_89,U_83,U_85,U_84,U_86,U_87,U_88) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_12,plain,
( sP21(U_85,U_84,U_86,U_88)
| ~ in(ordered_pair(U_88,U_86),U_83)
| ~ sP22(U_89,U_83,U_85,U_84,U_86,U_87,U_88) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_13,plain,
( in(ordered_pair(U_89,U_87),U_83)
| ~ in(ordered_pair(U_89,U_87),U_84)
| ~ in(U_87,U_85)
| ~ sP22(U_89,U_83,U_85,U_84,U_86,U_87,U_88) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_14,plain,
( in(U_86,U_85)
| ~ sP21(U_85,U_84,U_86,U_88) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_15,plain,
( in(ordered_pair(U_88,U_86),U_84)
| ~ sP21(U_85,U_84,U_86,U_88) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_16,plain,
( in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_83)
| ~ sP23(U_83,U_85,U_84) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_17,plain,
( ~ in(ordered_pair(sK13(U_85,U_84,U_83),sK14(U_85,U_84,U_83)),U_84)
| ~ in(sK14(U_85,U_84,U_83),U_85)
| ~ sP23(U_83,U_85,U_84) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_18,plain,
( in(sK16(U_85,U_84,U_83),U_85)
| ~ sP24(U_83,U_85,U_84) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_19,plain,
( in(ordered_pair(sK15(U_85,U_84,U_83),sK16(U_85,U_84,U_83)),U_84)
| ~ sP24(U_83,U_85,U_84) ),
inference(clausify,[status(thm)],[f_22_8]) ).
cnf(f_22_20,plain,
( ~ in(ordered_pair(sK15(U_85,U_84,U_83),sK16(U_85,U_84,U_83)),U_83)
| ~ sP24(U_83,U_85,U_84) ),
inference(clausify,[status(thm)],[f_22_8]) ).
fof(f_23_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_23_2,plain,
! [U_94] :
( ( ( antisymmetric(U_94)
| ~ is_antisymmetric_in(U_94,relation_field(U_94)) )
& ( is_antisymmetric_in(U_94,relation_field(U_94))
| ~ antisymmetric(U_94) ) )
| ~ relation(U_94) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_94] :
( antisymmetric(U_94)
| ~ is_antisymmetric_in(U_94,relation_field(U_94))
| ~ sP26(U_94) )
& ! [U_94] :
( is_antisymmetric_in(U_94,relation_field(U_94))
| ~ antisymmetric(U_94)
| ~ sP26(U_94) )
& ! [U_94] :
( sP26(U_94)
| ~ relation(U_94) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_23_2]) ).
cnf(f_23_4,plain,
( sP26(U_94)
| ~ relation(U_94) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( is_antisymmetric_in(U_94,relation_field(U_94))
| ~ antisymmetric(U_94)
| ~ sP26(U_94) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( antisymmetric(U_94)
| ~ is_antisymmetric_in(U_94,relation_field(U_94))
| ~ sP26(U_94) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_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_24_2,plain,
! [U_99] :
( ! [U_98,U_97] :
( ( U_97 = relation_inverse_image(U_99,U_98)
| ? [U_96] :
( ( ~ in(U_96,U_97)
& in(apply(U_99,U_96),U_98)
& in(U_96,relation_dom(U_99)) )
| ( ( ~ in(apply(U_99,U_96),U_98)
| ~ in(U_96,relation_dom(U_99)) )
& in(U_96,U_97) ) ) )
& ( ! [U_95] :
( ( in(U_95,U_97)
| ~ in(apply(U_99,U_95),U_98)
| ~ in(U_95,relation_dom(U_99)) )
& ( ( in(apply(U_99,U_95),U_98)
& in(U_95,relation_dom(U_99)) )
| ~ in(U_95,U_97) ) )
| U_97 != relation_inverse_image(U_99,U_98) ) )
| ~ function(U_99)
| ~ relation(U_99) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_99] :
( ( ! [U_107,U_105] :
( U_105 = relation_inverse_image(U_99,U_107)
| ? [U_103] :
( ~ in(U_103,U_105)
& in(apply(U_99,U_103),U_107)
& in(U_103,relation_dom(U_99)) )
| ? [U_102] :
( ( ~ in(apply(U_99,U_102),U_107)
| ~ in(U_102,relation_dom(U_99)) )
& in(U_102,U_105) ) )
& ! [U_106,U_104] :
( ( ! [U_101] :
( in(U_101,U_104)
| ~ in(apply(U_99,U_101),U_106)
| ~ in(U_101,relation_dom(U_99)) )
& ! [U_100] :
( ( in(apply(U_99,U_100),U_106)
& in(U_100,relation_dom(U_99)) )
| ~ in(U_100,U_104) ) )
| U_104 != relation_inverse_image(U_99,U_106) ) )
| ~ function(U_99)
| ~ relation(U_99) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
! [U_99] :
( ( ! [U_107,U_105] :
( U_105 = relation_inverse_image(U_99,U_107)
| ? [U_103] :
( ~ in(U_103,U_105)
& in(apply(U_99,U_103),U_107)
& in(U_103,relation_dom(U_99)) )
| ( ( ~ in(apply(U_99,sK17(U_99,U_107,U_105)),U_107)
| ~ in(sK17(U_99,U_107,U_105),relation_dom(U_99)) )
& in(sK17(U_99,U_107,U_105),U_105) ) )
& ! [U_106,U_104] :
( ( ! [U_101] :
( in(U_101,U_104)
| ~ in(apply(U_99,U_101),U_106)
| ~ in(U_101,relation_dom(U_99)) )
& ! [U_100] :
( ( in(apply(U_99,U_100),U_106)
& in(U_100,relation_dom(U_99)) )
| ~ in(U_100,U_104) ) )
| U_104 != relation_inverse_image(U_99,U_106) ) )
| ~ function(U_99)
| ~ relation(U_99) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_102,sK17(U_99,U_107,U_105))],[f_24_3]) ).
fof(f_24_5,plain,
! [U_99] :
( ( ! [U_107,U_105] :
( U_105 = relation_inverse_image(U_99,U_107)
| ( ~ in(sK18(U_99,U_107,U_105),U_105)
& in(apply(U_99,sK18(U_99,U_107,U_105)),U_107)
& in(sK18(U_99,U_107,U_105),relation_dom(U_99)) )
| ( ( ~ in(apply(U_99,sK17(U_99,U_107,U_105)),U_107)
| ~ in(sK17(U_99,U_107,U_105),relation_dom(U_99)) )
& in(sK17(U_99,U_107,U_105),U_105) ) )
& ! [U_106,U_104] :
( ( ! [U_101] :
( in(U_101,U_104)
| ~ in(apply(U_99,U_101),U_106)
| ~ in(U_101,relation_dom(U_99)) )
& ! [U_100] :
( ( in(apply(U_99,U_100),U_106)
& in(U_100,relation_dom(U_99)) )
| ~ in(U_100,U_104) ) )
| U_104 != relation_inverse_image(U_99,U_106) ) )
| ~ function(U_99)
| ~ relation(U_99) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_103,sK18(U_99,U_107,U_105))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_105,U_107,U_99] :
( ~ in(sK18(U_99,U_107,U_105),U_105)
| ~ sP30(U_105,U_107,U_99) )
& ! [U_105,U_107,U_99] :
( in(apply(U_99,sK18(U_99,U_107,U_105)),U_107)
| ~ sP30(U_105,U_107,U_99) )
& ! [U_105,U_107,U_99] :
( in(sK18(U_99,U_107,U_105),relation_dom(U_99))
| ~ sP30(U_105,U_107,U_99) )
& ! [U_105,U_107,U_99] :
( ~ in(apply(U_99,sK17(U_99,U_107,U_105)),U_107)
| ~ in(sK17(U_99,U_107,U_105),relation_dom(U_99))
| ~ sP29(U_105,U_107,U_99) )
& ! [U_105,U_107,U_99] :
( in(sK17(U_99,U_107,U_105),U_105)
| ~ sP29(U_105,U_107,U_99) )
& ! [U_106,U_100,U_99] :
( in(apply(U_99,U_100),U_106)
| ~ sP27(U_106,U_100,U_99) )
& ! [U_106,U_100,U_99] :
( in(U_100,relation_dom(U_99))
| ~ sP27(U_106,U_100,U_99) )
& ! [U_104,U_106,U_101,U_100,U_99] :
( in(U_101,U_104)
| ~ in(apply(U_99,U_101),U_106)
| ~ in(U_101,relation_dom(U_99))
| ~ sP28(U_104,U_106,U_101,U_100,U_99) )
& ! [U_104,U_106,U_101,U_100,U_99] :
( sP27(U_106,U_100,U_99)
| ~ in(U_100,U_104)
| ~ sP28(U_104,U_106,U_101,U_100,U_99) )
& ! [U_104,U_106,U_105,U_107,U_101,U_100,U_99] :
( U_105 = relation_inverse_image(U_99,U_107)
| sP30(U_105,U_107,U_99)
| sP29(U_105,U_107,U_99)
| ~ sP31(U_104,U_106,U_105,U_107,U_101,U_100,U_99) )
& ! [U_104,U_106,U_105,U_107,U_101,U_100,U_99] :
( sP28(U_104,U_106,U_101,U_100,U_99)
| U_104 != relation_inverse_image(U_99,U_106)
| ~ sP31(U_104,U_106,U_105,U_107,U_101,U_100,U_99) )
& ! [U_104,U_106,U_105,U_107,U_101,U_100,U_99] :
( sP31(U_104,U_106,U_105,U_107,U_101,U_100,U_99)
| ~ function(U_99)
| ~ relation(U_99) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27,sP28,sP29,sP30,sP31])],[f_24_5]) ).
cnf(f_24_7,plain,
( sP31(U_104,U_106,U_105,U_107,U_101,U_100,U_99)
| ~ function(U_99)
| ~ relation(U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_8,plain,
( sP28(U_104,U_106,U_101,U_100,U_99)
| U_104 != relation_inverse_image(U_99,U_106)
| ~ sP31(U_104,U_106,U_105,U_107,U_101,U_100,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_9,plain,
( U_105 = relation_inverse_image(U_99,U_107)
| sP30(U_105,U_107,U_99)
| sP29(U_105,U_107,U_99)
| ~ sP31(U_104,U_106,U_105,U_107,U_101,U_100,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_10,plain,
( sP27(U_106,U_100,U_99)
| ~ in(U_100,U_104)
| ~ sP28(U_104,U_106,U_101,U_100,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_11,plain,
( in(U_101,U_104)
| ~ in(apply(U_99,U_101),U_106)
| ~ in(U_101,relation_dom(U_99))
| ~ sP28(U_104,U_106,U_101,U_100,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_12,plain,
( in(U_100,relation_dom(U_99))
| ~ sP27(U_106,U_100,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_13,plain,
( in(apply(U_99,U_100),U_106)
| ~ sP27(U_106,U_100,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_14,plain,
( in(sK17(U_99,U_107,U_105),U_105)
| ~ sP29(U_105,U_107,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_15,plain,
( ~ in(apply(U_99,sK17(U_99,U_107,U_105)),U_107)
| ~ in(sK17(U_99,U_107,U_105),relation_dom(U_99))
| ~ sP29(U_105,U_107,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_16,plain,
( in(sK18(U_99,U_107,U_105),relation_dom(U_99))
| ~ sP30(U_105,U_107,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_17,plain,
( in(apply(U_99,sK18(U_99,U_107,U_105)),U_107)
| ~ sP30(U_105,U_107,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
cnf(f_24_18,plain,
( ~ in(sK18(U_99,U_107,U_105),U_105)
| ~ sP30(U_105,U_107,U_99) ),
inference(clausify,[status(thm)],[f_24_6]) ).
fof(f_25_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_25_2,plain,
! [U_116] :
( ! [U_115,U_114] :
( ( U_114 = relation_image(U_116,U_115)
| ? [U_113] :
( ( ~ in(U_113,U_114)
& ? [U_112] :
( in(U_112,U_115)
& in(ordered_pair(U_112,U_113),U_116) ) )
| ( ! [U_111] :
( ~ in(U_111,U_115)
| ~ in(ordered_pair(U_111,U_113),U_116) )
& in(U_113,U_114) ) ) )
& ( ! [U_110] :
( ( in(U_110,U_114)
| ! [U_109] :
( ~ in(U_109,U_115)
| ~ in(ordered_pair(U_109,U_110),U_116) ) )
& ( ? [U_108] :
( in(U_108,U_115)
& in(ordered_pair(U_108,U_110),U_116) )
| ~ in(U_110,U_114) ) )
| U_114 != relation_image(U_116,U_115) ) )
| ~ relation(U_116) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_116] :
( ( ! [U_124,U_122] :
( U_122 = relation_image(U_116,U_124)
| ? [U_120] :
( ~ in(U_120,U_122)
& ? [U_112] :
( in(U_112,U_124)
& in(ordered_pair(U_112,U_120),U_116) ) )
| ? [U_119] :
( ! [U_111] :
( ~ in(U_111,U_124)
| ~ in(ordered_pair(U_111,U_119),U_116) )
& in(U_119,U_122) ) )
& ! [U_123,U_121] :
( ( ! [U_118] :
( in(U_118,U_121)
| ! [U_109] :
( ~ in(U_109,U_123)
| ~ in(ordered_pair(U_109,U_118),U_116) ) )
& ! [U_117] :
( ? [U_108] :
( in(U_108,U_123)
& in(ordered_pair(U_108,U_117),U_116) )
| ~ in(U_117,U_121) ) )
| U_121 != relation_image(U_116,U_123) ) )
| ~ relation(U_116) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
! [U_116] :
( ( ! [U_124,U_122] :
( U_122 = relation_image(U_116,U_124)
| ? [U_120] :
( ~ in(U_120,U_122)
& ? [U_112] :
( in(U_112,U_124)
& in(ordered_pair(U_112,U_120),U_116) ) )
| ? [U_119] :
( ! [U_111] :
( ~ in(U_111,U_124)
| ~ in(ordered_pair(U_111,U_119),U_116) )
& in(U_119,U_122) ) )
& ! [U_123,U_121] :
( ( ! [U_118] :
( in(U_118,U_121)
| ! [U_109] :
( ~ in(U_109,U_123)
| ~ in(ordered_pair(U_109,U_118),U_116) ) )
& ! [U_117] :
( ( in(sK19(U_116,U_123,U_121,U_117),U_123)
& in(ordered_pair(sK19(U_116,U_123,U_121,U_117),U_117),U_116) )
| ~ in(U_117,U_121) ) )
| U_121 != relation_image(U_116,U_123) ) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_108,sK19(U_116,U_123,U_121,U_117))],[f_25_3]) ).
fof(f_25_5,plain,
! [U_116] :
( ( ! [U_124,U_122] :
( U_122 = relation_image(U_116,U_124)
| ? [U_120] :
( ~ in(U_120,U_122)
& ? [U_112] :
( in(U_112,U_124)
& in(ordered_pair(U_112,U_120),U_116) ) )
| ( ! [U_111] :
( ~ in(U_111,U_124)
| ~ in(ordered_pair(U_111,sK20(U_116,U_124,U_122)),U_116) )
& in(sK20(U_116,U_124,U_122),U_122) ) )
& ! [U_123,U_121] :
( ( ! [U_118] :
( in(U_118,U_121)
| ! [U_109] :
( ~ in(U_109,U_123)
| ~ in(ordered_pair(U_109,U_118),U_116) ) )
& ! [U_117] :
( ( in(sK19(U_116,U_123,U_121,U_117),U_123)
& in(ordered_pair(sK19(U_116,U_123,U_121,U_117),U_117),U_116) )
| ~ in(U_117,U_121) ) )
| U_121 != relation_image(U_116,U_123) ) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_119,sK20(U_116,U_124,U_122))],[f_25_4]) ).
fof(f_25_6,plain,
! [U_116] :
( ( ! [U_124,U_122] :
( U_122 = relation_image(U_116,U_124)
| ( ~ in(sK21(U_116,U_124,U_122),U_122)
& ? [U_112] :
( in(U_112,U_124)
& in(ordered_pair(U_112,sK21(U_116,U_124,U_122)),U_116) ) )
| ( ! [U_111] :
( ~ in(U_111,U_124)
| ~ in(ordered_pair(U_111,sK20(U_116,U_124,U_122)),U_116) )
& in(sK20(U_116,U_124,U_122),U_122) ) )
& ! [U_123,U_121] :
( ( ! [U_118] :
( in(U_118,U_121)
| ! [U_109] :
( ~ in(U_109,U_123)
| ~ in(ordered_pair(U_109,U_118),U_116) ) )
& ! [U_117] :
( ( in(sK19(U_116,U_123,U_121,U_117),U_123)
& in(ordered_pair(sK19(U_116,U_123,U_121,U_117),U_117),U_116) )
| ~ in(U_117,U_121) ) )
| U_121 != relation_image(U_116,U_123) ) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_120,sK21(U_116,U_124,U_122))],[f_25_5]) ).
fof(f_25_7,plain,
! [U_116] :
( ( ! [U_124,U_122] :
( U_122 = relation_image(U_116,U_124)
| ( ~ in(sK21(U_116,U_124,U_122),U_122)
& in(sK22(U_116,U_124,U_122),U_124)
& in(ordered_pair(sK22(U_116,U_124,U_122),sK21(U_116,U_124,U_122)),U_116) )
| ( ! [U_111] :
( ~ in(U_111,U_124)
| ~ in(ordered_pair(U_111,sK20(U_116,U_124,U_122)),U_116) )
& in(sK20(U_116,U_124,U_122),U_122) ) )
& ! [U_123,U_121] :
( ( ! [U_118] :
( in(U_118,U_121)
| ! [U_109] :
( ~ in(U_109,U_123)
| ~ in(ordered_pair(U_109,U_118),U_116) ) )
& ! [U_117] :
( ( in(sK19(U_116,U_123,U_121,U_117),U_123)
& in(ordered_pair(sK19(U_116,U_123,U_121,U_117),U_117),U_116) )
| ~ in(U_117,U_121) ) )
| U_121 != relation_image(U_116,U_123) ) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_112,sK22(U_116,U_124,U_122))],[f_25_6]) ).
fof(f_25_8,plain,
( ! [U_116,U_124,U_122] :
( ~ in(sK21(U_116,U_124,U_122),U_122)
| ~ sP35(U_116,U_124,U_122) )
& ! [U_116,U_124,U_122] :
( in(sK22(U_116,U_124,U_122),U_124)
| ~ sP35(U_116,U_124,U_122) )
& ! [U_116,U_124,U_122] :
( in(ordered_pair(sK22(U_116,U_124,U_122),sK21(U_116,U_124,U_122)),U_116)
| ~ sP35(U_116,U_124,U_122) )
& ! [U_116,U_124,U_111,U_122] :
( ~ in(U_111,U_124)
| ~ in(ordered_pair(U_111,sK20(U_116,U_124,U_122)),U_116)
| ~ sP34(U_116,U_124,U_111,U_122) )
& ! [U_116,U_124,U_111,U_122] :
( in(sK20(U_116,U_124,U_122),U_122)
| ~ sP34(U_116,U_124,U_111,U_122) )
& ! [U_116,U_123,U_117,U_121] :
( in(sK19(U_116,U_123,U_121,U_117),U_123)
| ~ sP32(U_116,U_123,U_117,U_121) )
& ! [U_116,U_123,U_117,U_121] :
( in(ordered_pair(sK19(U_116,U_123,U_121,U_117),U_117),U_116)
| ~ sP32(U_116,U_123,U_117,U_121) )
& ! [U_116,U_118,U_123,U_117,U_121,U_109] :
( in(U_118,U_121)
| ~ in(U_109,U_123)
| ~ in(ordered_pair(U_109,U_118),U_116)
| ~ sP33(U_116,U_118,U_123,U_117,U_121,U_109) )
& ! [U_116,U_118,U_123,U_117,U_121,U_109] :
( sP32(U_116,U_123,U_117,U_121)
| ~ in(U_117,U_121)
| ~ sP33(U_116,U_118,U_123,U_117,U_121,U_109) )
& ! [U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122] :
( U_122 = relation_image(U_116,U_124)
| sP35(U_116,U_124,U_122)
| sP34(U_116,U_124,U_111,U_122)
| ~ sP36(U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122) )
& ! [U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122] :
( sP33(U_116,U_118,U_123,U_117,U_121,U_109)
| U_121 != relation_image(U_116,U_123)
| ~ sP36(U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122) )
& ! [U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122] :
( sP36(U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122)
| ~ relation(U_116) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32,sP33,sP34,sP35,sP36])],[f_25_7]) ).
cnf(f_25_9,plain,
( sP36(U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122)
| ~ relation(U_116) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_10,plain,
( sP33(U_116,U_118,U_123,U_117,U_121,U_109)
| U_121 != relation_image(U_116,U_123)
| ~ sP36(U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_11,plain,
( U_122 = relation_image(U_116,U_124)
| sP35(U_116,U_124,U_122)
| sP34(U_116,U_124,U_111,U_122)
| ~ sP36(U_116,U_118,U_124,U_123,U_117,U_111,U_121,U_109,U_122) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_12,plain,
( sP32(U_116,U_123,U_117,U_121)
| ~ in(U_117,U_121)
| ~ sP33(U_116,U_118,U_123,U_117,U_121,U_109) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_13,plain,
( in(U_118,U_121)
| ~ in(U_109,U_123)
| ~ in(ordered_pair(U_109,U_118),U_116)
| ~ sP33(U_116,U_118,U_123,U_117,U_121,U_109) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_14,plain,
( in(ordered_pair(sK19(U_116,U_123,U_121,U_117),U_117),U_116)
| ~ sP32(U_116,U_123,U_117,U_121) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_15,plain,
( in(sK19(U_116,U_123,U_121,U_117),U_123)
| ~ sP32(U_116,U_123,U_117,U_121) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_16,plain,
( in(sK20(U_116,U_124,U_122),U_122)
| ~ sP34(U_116,U_124,U_111,U_122) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_17,plain,
( ~ in(U_111,U_124)
| ~ in(ordered_pair(U_111,sK20(U_116,U_124,U_122)),U_116)
| ~ sP34(U_116,U_124,U_111,U_122) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_18,plain,
( in(ordered_pair(sK22(U_116,U_124,U_122),sK21(U_116,U_124,U_122)),U_116)
| ~ sP35(U_116,U_124,U_122) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_19,plain,
( in(sK22(U_116,U_124,U_122),U_124)
| ~ sP35(U_116,U_124,U_122) ),
inference(clausify,[status(thm)],[f_25_8]) ).
cnf(f_25_20,plain,
( ~ in(sK21(U_116,U_124,U_122),U_122)
| ~ sP35(U_116,U_124,U_122) ),
inference(clausify,[status(thm)],[f_25_8]) ).
fof(f_26_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_26_2,plain,
! [U_133] :
( ! [U_132,U_131] :
( ( U_131 = relation_inverse_image(U_133,U_132)
| ? [U_130] :
( ( ~ in(U_130,U_131)
& ? [U_129] :
( in(U_129,U_132)
& in(ordered_pair(U_130,U_129),U_133) ) )
| ( ! [U_128] :
( ~ in(U_128,U_132)
| ~ in(ordered_pair(U_130,U_128),U_133) )
& in(U_130,U_131) ) ) )
& ( ! [U_127] :
( ( in(U_127,U_131)
| ! [U_126] :
( ~ in(U_126,U_132)
| ~ in(ordered_pair(U_127,U_126),U_133) ) )
& ( ? [U_125] :
( in(U_125,U_132)
& in(ordered_pair(U_127,U_125),U_133) )
| ~ in(U_127,U_131) ) )
| U_131 != relation_inverse_image(U_133,U_132) ) )
| ~ relation(U_133) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ? [U_129] :
( in(U_129,U_141)
& in(ordered_pair(U_137,U_129),U_133) ) )
| ? [U_136] :
( ! [U_128] :
( ~ in(U_128,U_141)
| ~ in(ordered_pair(U_136,U_128),U_133) )
& in(U_136,U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( ~ in(U_126,U_140)
| ~ in(ordered_pair(U_135,U_126),U_133) ) )
& ! [U_134] :
( ? [U_125] :
( in(U_125,U_140)
& in(ordered_pair(U_134,U_125),U_133) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ relation(U_133) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ? [U_129] :
( in(U_129,U_141)
& in(ordered_pair(U_137,U_129),U_133) ) )
| ? [U_136] :
( ! [U_128] :
( ~ in(U_128,U_141)
| ~ in(ordered_pair(U_136,U_128),U_133) )
& in(U_136,U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( ~ in(U_126,U_140)
| ~ in(ordered_pair(U_135,U_126),U_133) ) )
& ! [U_134] :
( ( in(sK23(U_133,U_140,U_138,U_134),U_140)
& in(ordered_pair(U_134,sK23(U_133,U_140,U_138,U_134)),U_133) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_125,sK23(U_133,U_140,U_138,U_134))],[f_26_3]) ).
fof(f_26_5,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ? [U_129] :
( in(U_129,U_141)
& in(ordered_pair(U_137,U_129),U_133) ) )
| ( ! [U_128] :
( ~ in(U_128,U_141)
| ~ in(ordered_pair(sK24(U_133,U_141,U_139),U_128),U_133) )
& in(sK24(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( ~ in(U_126,U_140)
| ~ in(ordered_pair(U_135,U_126),U_133) ) )
& ! [U_134] :
( ( in(sK23(U_133,U_140,U_138,U_134),U_140)
& in(ordered_pair(U_134,sK23(U_133,U_140,U_138,U_134)),U_133) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_136,sK24(U_133,U_141,U_139))],[f_26_4]) ).
fof(f_26_6,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ( ~ in(sK25(U_133,U_141,U_139),U_139)
& ? [U_129] :
( in(U_129,U_141)
& in(ordered_pair(sK25(U_133,U_141,U_139),U_129),U_133) ) )
| ( ! [U_128] :
( ~ in(U_128,U_141)
| ~ in(ordered_pair(sK24(U_133,U_141,U_139),U_128),U_133) )
& in(sK24(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( ~ in(U_126,U_140)
| ~ in(ordered_pair(U_135,U_126),U_133) ) )
& ! [U_134] :
( ( in(sK23(U_133,U_140,U_138,U_134),U_140)
& in(ordered_pair(U_134,sK23(U_133,U_140,U_138,U_134)),U_133) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_137,sK25(U_133,U_141,U_139))],[f_26_5]) ).
fof(f_26_7,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_inverse_image(U_133,U_141)
| ( ~ in(sK25(U_133,U_141,U_139),U_139)
& in(sK26(U_133,U_141,U_139),U_141)
& in(ordered_pair(sK25(U_133,U_141,U_139),sK26(U_133,U_141,U_139)),U_133) )
| ( ! [U_128] :
( ~ in(U_128,U_141)
| ~ in(ordered_pair(sK24(U_133,U_141,U_139),U_128),U_133) )
& in(sK24(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( ~ in(U_126,U_140)
| ~ in(ordered_pair(U_135,U_126),U_133) ) )
& ! [U_134] :
( ( in(sK23(U_133,U_140,U_138,U_134),U_140)
& in(ordered_pair(U_134,sK23(U_133,U_140,U_138,U_134)),U_133) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_inverse_image(U_133,U_140) ) )
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_129,sK26(U_133,U_141,U_139))],[f_26_6]) ).
fof(f_26_8,plain,
( ! [U_133,U_141,U_139] :
( ~ in(sK25(U_133,U_141,U_139),U_139)
| ~ sP40(U_133,U_141,U_139) )
& ! [U_133,U_141,U_139] :
( in(sK26(U_133,U_141,U_139),U_141)
| ~ sP40(U_133,U_141,U_139) )
& ! [U_133,U_141,U_139] :
( in(ordered_pair(sK25(U_133,U_141,U_139),sK26(U_133,U_141,U_139)),U_133)
| ~ sP40(U_133,U_141,U_139) )
& ! [U_133,U_128,U_141,U_139] :
( ~ in(U_128,U_141)
| ~ in(ordered_pair(sK24(U_133,U_141,U_139),U_128),U_133)
| ~ sP39(U_133,U_128,U_141,U_139) )
& ! [U_133,U_128,U_141,U_139] :
( in(sK24(U_133,U_141,U_139),U_139)
| ~ sP39(U_133,U_128,U_141,U_139) )
& ! [U_133,U_140,U_138,U_134] :
( in(sK23(U_133,U_140,U_138,U_134),U_140)
| ~ sP37(U_133,U_140,U_138,U_134) )
& ! [U_133,U_140,U_138,U_134] :
( in(ordered_pair(U_134,sK23(U_133,U_140,U_138,U_134)),U_133)
| ~ sP37(U_133,U_140,U_138,U_134) )
& ! [U_133,U_140,U_135,U_138,U_126,U_134] :
( in(U_135,U_138)
| ~ in(U_126,U_140)
| ~ in(ordered_pair(U_135,U_126),U_133)
| ~ sP38(U_133,U_140,U_135,U_138,U_126,U_134) )
& ! [U_133,U_140,U_135,U_138,U_126,U_134] :
( sP37(U_133,U_140,U_138,U_134)
| ~ in(U_134,U_138)
| ~ sP38(U_133,U_140,U_135,U_138,U_126,U_134) )
& ! [U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134] :
( U_139 = relation_inverse_image(U_133,U_141)
| sP40(U_133,U_141,U_139)
| sP39(U_133,U_128,U_141,U_139)
| ~ sP41(U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134) )
& ! [U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134] :
( sP38(U_133,U_140,U_135,U_138,U_126,U_134)
| U_138 != relation_inverse_image(U_133,U_140)
| ~ sP41(U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134) )
& ! [U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134] :
( sP41(U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134)
| ~ relation(U_133) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37,sP38,sP39,sP40,sP41])],[f_26_7]) ).
cnf(f_26_9,plain,
( sP41(U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_10,plain,
( sP38(U_133,U_140,U_135,U_138,U_126,U_134)
| U_138 != relation_inverse_image(U_133,U_140)
| ~ sP41(U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_11,plain,
( U_139 = relation_inverse_image(U_133,U_141)
| sP40(U_133,U_141,U_139)
| sP39(U_133,U_128,U_141,U_139)
| ~ sP41(U_133,U_140,U_128,U_141,U_135,U_139,U_138,U_126,U_134) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_12,plain,
( sP37(U_133,U_140,U_138,U_134)
| ~ in(U_134,U_138)
| ~ sP38(U_133,U_140,U_135,U_138,U_126,U_134) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_13,plain,
( in(U_135,U_138)
| ~ in(U_126,U_140)
| ~ in(ordered_pair(U_135,U_126),U_133)
| ~ sP38(U_133,U_140,U_135,U_138,U_126,U_134) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_14,plain,
( in(ordered_pair(U_134,sK23(U_133,U_140,U_138,U_134)),U_133)
| ~ sP37(U_133,U_140,U_138,U_134) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_15,plain,
( in(sK23(U_133,U_140,U_138,U_134),U_140)
| ~ sP37(U_133,U_140,U_138,U_134) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_16,plain,
( in(sK24(U_133,U_141,U_139),U_139)
| ~ sP39(U_133,U_128,U_141,U_139) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_17,plain,
( ~ in(U_128,U_141)
| ~ in(ordered_pair(sK24(U_133,U_141,U_139),U_128),U_133)
| ~ sP39(U_133,U_128,U_141,U_139) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_18,plain,
( in(ordered_pair(sK25(U_133,U_141,U_139),sK26(U_133,U_141,U_139)),U_133)
| ~ sP40(U_133,U_141,U_139) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_19,plain,
( in(sK26(U_133,U_141,U_139),U_141)
| ~ sP40(U_133,U_141,U_139) ),
inference(clausify,[status(thm)],[f_26_8]) ).
cnf(f_26_20,plain,
( ~ in(sK25(U_133,U_141,U_139),U_139)
| ~ sP40(U_133,U_141,U_139) ),
inference(clausify,[status(thm)],[f_26_8]) ).
fof(f_27_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_27_2,plain,
! [U_142] :
( ( ( connected(U_142)
| ~ is_connected_in(U_142,relation_field(U_142)) )
& ( is_connected_in(U_142,relation_field(U_142))
| ~ connected(U_142) ) )
| ~ relation(U_142) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_142] :
( connected(U_142)
| ~ is_connected_in(U_142,relation_field(U_142))
| ~ sP42(U_142) )
& ! [U_142] :
( is_connected_in(U_142,relation_field(U_142))
| ~ connected(U_142)
| ~ sP42(U_142) )
& ! [U_142] :
( sP42(U_142)
| ~ relation(U_142) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP42(U_142)
| ~ relation(U_142) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( is_connected_in(U_142,relation_field(U_142))
| ~ connected(U_142)
| ~ sP42(U_142) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( connected(U_142)
| ~ is_connected_in(U_142,relation_field(U_142))
| ~ sP42(U_142) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_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_28_2,plain,
! [U_143] :
( ( ( transitive(U_143)
| ~ is_transitive_in(U_143,relation_field(U_143)) )
& ( is_transitive_in(U_143,relation_field(U_143))
| ~ transitive(U_143) ) )
| ~ relation(U_143) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ! [U_143] :
( transitive(U_143)
| ~ is_transitive_in(U_143,relation_field(U_143))
| ~ sP43(U_143) )
& ! [U_143] :
( is_transitive_in(U_143,relation_field(U_143))
| ~ transitive(U_143)
| ~ sP43(U_143) )
& ! [U_143] :
( sP43(U_143)
| ~ relation(U_143) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_28_2]) ).
cnf(f_28_4,plain,
( sP43(U_143)
| ~ relation(U_143) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
( is_transitive_in(U_143,relation_field(U_143))
| ~ transitive(U_143)
| ~ sP43(U_143) ),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
( transitive(U_143)
| ~ is_transitive_in(U_143,relation_field(U_143))
| ~ sP43(U_143) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_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_29_2,plain,
! [U_149,U_148,U_147,U_146] :
( ( U_146 = unordered_triple(U_149,U_148,U_147)
| ? [U_145] :
( ( ~ in(U_145,U_146)
& ( U_145 = U_147
| U_145 = U_148
| U_145 = U_149 ) )
| ( U_145 != U_147
& U_145 != U_148
& U_145 != U_149
& in(U_145,U_146) ) ) )
& ( ! [U_144] :
( ( in(U_144,U_146)
| ( U_144 != U_147
& U_144 != U_148
& U_144 != U_149 ) )
& ( U_144 = U_147
| U_144 = U_148
| U_144 = U_149
| ~ in(U_144,U_146) ) )
| U_146 != unordered_triple(U_149,U_148,U_147) ) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ! [U_161,U_159,U_157,U_155] :
( U_155 = unordered_triple(U_161,U_159,U_157)
| ? [U_153] :
( ~ in(U_153,U_155)
& ( U_153 = U_157
| U_153 = U_159
| U_153 = U_161 ) )
| ? [U_152] :
( U_152 != U_157
& U_152 != U_159
& U_152 != U_161
& in(U_152,U_155) ) )
& ! [U_160,U_158,U_156,U_154] :
( ( ! [U_151] :
( in(U_151,U_154)
| ( U_151 != U_156
& U_151 != U_158
& U_151 != U_160 ) )
& ! [U_150] :
( U_150 = U_156
| U_150 = U_158
| U_150 = U_160
| ~ in(U_150,U_154) ) )
| U_154 != unordered_triple(U_160,U_158,U_156) ) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_161,U_159,U_157,U_155] :
( U_155 = unordered_triple(U_161,U_159,U_157)
| ? [U_153] :
( ~ in(U_153,U_155)
& ( U_153 = U_157
| U_153 = U_159
| U_153 = U_161 ) )
| ( sK27(U_161,U_159,U_157,U_155) != U_157
& sK27(U_161,U_159,U_157,U_155) != U_159
& sK27(U_161,U_159,U_157,U_155) != U_161
& in(sK27(U_161,U_159,U_157,U_155),U_155) ) )
& ! [U_160,U_158,U_156,U_154] :
( ( ! [U_151] :
( in(U_151,U_154)
| ( U_151 != U_156
& U_151 != U_158
& U_151 != U_160 ) )
& ! [U_150] :
( U_150 = U_156
| U_150 = U_158
| U_150 = U_160
| ~ in(U_150,U_154) ) )
| U_154 != unordered_triple(U_160,U_158,U_156) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_152,sK27(U_161,U_159,U_157,U_155))],[f_29_3]) ).
fof(f_29_5,plain,
( ! [U_161,U_159,U_157,U_155] :
( U_155 = unordered_triple(U_161,U_159,U_157)
| ( ~ in(sK28(U_161,U_159,U_157,U_155),U_155)
& ( sK28(U_161,U_159,U_157,U_155) = U_157
| sK28(U_161,U_159,U_157,U_155) = U_159
| sK28(U_161,U_159,U_157,U_155) = U_161 ) )
| ( sK27(U_161,U_159,U_157,U_155) != U_157
& sK27(U_161,U_159,U_157,U_155) != U_159
& sK27(U_161,U_159,U_157,U_155) != U_161
& in(sK27(U_161,U_159,U_157,U_155),U_155) ) )
& ! [U_160,U_158,U_156,U_154] :
( ( ! [U_151] :
( in(U_151,U_154)
| ( U_151 != U_156
& U_151 != U_158
& U_151 != U_160 ) )
& ! [U_150] :
( U_150 = U_156
| U_150 = U_158
| U_150 = U_160
| ~ in(U_150,U_154) ) )
| U_154 != unordered_triple(U_160,U_158,U_156) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_153,sK28(U_161,U_159,U_157,U_155))],[f_29_4]) ).
fof(f_29_6,plain,
( ! [U_161,U_157,U_159,U_155] :
( ~ in(sK28(U_161,U_159,U_157,U_155),U_155)
| ~ sP47(U_161,U_157,U_159,U_155) )
& ! [U_161,U_157,U_159,U_155] :
( sK28(U_161,U_159,U_157,U_155) = U_157
| sK28(U_161,U_159,U_157,U_155) = U_159
| sK28(U_161,U_159,U_157,U_155) = U_161
| ~ sP47(U_161,U_157,U_159,U_155) )
& ! [U_161,U_157,U_159,U_155] :
( sK27(U_161,U_159,U_157,U_155) != U_157
| ~ sP46(U_161,U_157,U_159,U_155) )
& ! [U_161,U_157,U_159,U_155] :
( sK27(U_161,U_159,U_157,U_155) != U_159
| ~ sP46(U_161,U_157,U_159,U_155) )
& ! [U_161,U_157,U_159,U_155] :
( sK27(U_161,U_159,U_157,U_155) != U_161
| ~ sP46(U_161,U_157,U_159,U_155) )
& ! [U_161,U_157,U_159,U_155] :
( in(sK27(U_161,U_159,U_157,U_155),U_155)
| ~ sP46(U_161,U_157,U_159,U_155) )
& ! [U_160,U_158,U_151,U_156] :
( U_151 != U_156
| ~ sP44(U_160,U_158,U_151,U_156) )
& ! [U_160,U_158,U_151,U_156] :
( U_151 != U_158
| ~ sP44(U_160,U_158,U_151,U_156) )
& ! [U_160,U_158,U_151,U_156] :
( U_151 != U_160
| ~ sP44(U_160,U_158,U_151,U_156) )
& ! [U_150,U_160,U_158,U_154,U_151,U_156] :
( in(U_151,U_154)
| sP44(U_160,U_158,U_151,U_156)
| ~ sP45(U_150,U_160,U_158,U_154,U_151,U_156) )
& ! [U_150,U_160,U_158,U_154,U_151,U_156] :
( U_150 = U_156
| U_150 = U_158
| U_150 = U_160
| ~ in(U_150,U_154)
| ~ sP45(U_150,U_160,U_158,U_154,U_151,U_156) )
& ! [U_161,U_157,U_159,U_155] :
( U_155 = unordered_triple(U_161,U_159,U_157)
| sP47(U_161,U_157,U_159,U_155)
| sP46(U_161,U_157,U_159,U_155) )
& ! [U_150,U_160,U_158,U_154,U_151,U_156] :
( sP45(U_150,U_160,U_158,U_154,U_151,U_156)
| U_154 != unordered_triple(U_160,U_158,U_156) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44,sP45,sP46,sP47])],[f_29_5]) ).
cnf(f_29_7,plain,
( sP45(U_150,U_160,U_158,U_154,U_151,U_156)
| U_154 != unordered_triple(U_160,U_158,U_156) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_8,plain,
( U_155 = unordered_triple(U_161,U_159,U_157)
| sP47(U_161,U_157,U_159,U_155)
| sP46(U_161,U_157,U_159,U_155) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_9,plain,
( U_150 = U_156
| U_150 = U_158
| U_150 = U_160
| ~ in(U_150,U_154)
| ~ sP45(U_150,U_160,U_158,U_154,U_151,U_156) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_10,plain,
( in(U_151,U_154)
| sP44(U_160,U_158,U_151,U_156)
| ~ sP45(U_150,U_160,U_158,U_154,U_151,U_156) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_11,plain,
( U_151 != U_160
| ~ sP44(U_160,U_158,U_151,U_156) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_12,plain,
( U_151 != U_158
| ~ sP44(U_160,U_158,U_151,U_156) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_13,plain,
( U_151 != U_156
| ~ sP44(U_160,U_158,U_151,U_156) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_14,plain,
( in(sK27(U_161,U_159,U_157,U_155),U_155)
| ~ sP46(U_161,U_157,U_159,U_155) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_15,plain,
( sK27(U_161,U_159,U_157,U_155) != U_161
| ~ sP46(U_161,U_157,U_159,U_155) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_16,plain,
( sK27(U_161,U_159,U_157,U_155) != U_159
| ~ sP46(U_161,U_157,U_159,U_155) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_17,plain,
( sK27(U_161,U_159,U_157,U_155) != U_157
| ~ sP46(U_161,U_157,U_159,U_155) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_18,plain,
( sK28(U_161,U_159,U_157,U_155) = U_157
| sK28(U_161,U_159,U_157,U_155) = U_159
| sK28(U_161,U_159,U_157,U_155) = U_161
| ~ sP47(U_161,U_157,U_159,U_155) ),
inference(clausify,[status(thm)],[f_29_6]) ).
cnf(f_29_19,plain,
( ~ in(sK28(U_161,U_159,U_157,U_155),U_155)
| ~ sP47(U_161,U_157,U_159,U_155) ),
inference(clausify,[status(thm)],[f_29_6]) ).
fof(f_30_1,plain,
! [A] :
( ( function(A)
| ? [B,C,D] :
( C != D
& in(ordered_pair(B,D),A)
& in(ordered_pair(B,C),A) ) )
& ( ! [B,C,D] :
( C = D
| ~ in(ordered_pair(B,D),A)
| ~ in(ordered_pair(B,C),A) )
| ~ function(A) ) ),
inference(fof_nnf,[status(thm)],[d1_funct_1]) ).
fof(f_30_2,plain,
! [U_168] :
( ( function(U_168)
| ? [U_167,U_166,U_165] :
( U_166 != U_165
& in(ordered_pair(U_167,U_165),U_168)
& in(ordered_pair(U_167,U_166),U_168) ) )
& ( ! [U_164,U_163,U_162] :
( U_163 = U_162
| ~ in(ordered_pair(U_164,U_162),U_168)
| ~ in(ordered_pair(U_164,U_163),U_168) )
| ~ function(U_168) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_170] :
( function(U_170)
| ? [U_167,U_166,U_165] :
( U_166 != U_165
& in(ordered_pair(U_167,U_165),U_170)
& in(ordered_pair(U_167,U_166),U_170) ) )
& ! [U_169] :
( ! [U_164,U_163,U_162] :
( U_163 = U_162
| ~ in(ordered_pair(U_164,U_162),U_169)
| ~ in(ordered_pair(U_164,U_163),U_169) )
| ~ function(U_169) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_170] :
( function(U_170)
| ? [U_166,U_165] :
( U_166 != U_165
& in(ordered_pair(sK29(U_170),U_165),U_170)
& in(ordered_pair(sK29(U_170),U_166),U_170) ) )
& ! [U_169] :
( ! [U_164,U_163,U_162] :
( U_163 = U_162
| ~ in(ordered_pair(U_164,U_162),U_169)
| ~ in(ordered_pair(U_164,U_163),U_169) )
| ~ function(U_169) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_167,sK29(U_170))],[f_30_3]) ).
fof(f_30_5,plain,
( ! [U_170] :
( function(U_170)
| ? [U_165] :
( sK30(U_170) != U_165
& in(ordered_pair(sK29(U_170),U_165),U_170)
& in(ordered_pair(sK29(U_170),sK30(U_170)),U_170) ) )
& ! [U_169] :
( ! [U_164,U_163,U_162] :
( U_163 = U_162
| ~ in(ordered_pair(U_164,U_162),U_169)
| ~ in(ordered_pair(U_164,U_163),U_169) )
| ~ function(U_169) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_166,sK30(U_170))],[f_30_4]) ).
fof(f_30_6,plain,
( ! [U_170] :
( function(U_170)
| ( sK30(U_170) != sK31(U_170)
& in(ordered_pair(sK29(U_170),sK31(U_170)),U_170)
& in(ordered_pair(sK29(U_170),sK30(U_170)),U_170) ) )
& ! [U_169] :
( ! [U_164,U_163,U_162] :
( U_163 = U_162
| ~ in(ordered_pair(U_164,U_162),U_169)
| ~ in(ordered_pair(U_164,U_163),U_169) )
| ~ function(U_169) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_165,sK31(U_170))],[f_30_5]) ).
fof(f_30_7,plain,
( ! [U_170] :
( sK30(U_170) != sK31(U_170)
| ~ sP48(U_170) )
& ! [U_170] :
( in(ordered_pair(sK29(U_170),sK31(U_170)),U_170)
| ~ sP48(U_170) )
& ! [U_170] :
( in(ordered_pair(sK29(U_170),sK30(U_170)),U_170)
| ~ sP48(U_170) )
& ! [U_170] :
( function(U_170)
| sP48(U_170) )
& ! [U_163,U_169,U_164,U_162] :
( U_163 = U_162
| ~ in(ordered_pair(U_164,U_162),U_169)
| ~ in(ordered_pair(U_164,U_163),U_169)
| ~ function(U_169) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_30_6]) ).
cnf(f_30_8,plain,
( U_163 = U_162
| ~ in(ordered_pair(U_164,U_162),U_169)
| ~ in(ordered_pair(U_164,U_163),U_169)
| ~ function(U_169) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_9,plain,
( function(U_170)
| sP48(U_170) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_10,plain,
( in(ordered_pair(sK29(U_170),sK30(U_170)),U_170)
| ~ sP48(U_170) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_11,plain,
( in(ordered_pair(sK29(U_170),sK31(U_170)),U_170)
| ~ sP48(U_170) ),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_12,plain,
( sK30(U_170) != sK31(U_170)
| ~ sP48(U_170) ),
inference(clausify,[status(thm)],[f_30_7]) ).
fof(f_31_1,plain,
! [A,B,C] :
( ( ( ( ( quasi_total(C,A,B)
| C != empty_set )
& ( C = empty_set
| ~ quasi_total(C,A,B) ) )
| A = empty_set
| B != empty_set )
& ( ( ( quasi_total(C,A,B)
| A != relation_dom_as_subset(A,B,C) )
& ( A = relation_dom_as_subset(A,B,C)
| ~ quasi_total(C,A,B) ) )
| ( A != empty_set
& B = empty_set ) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[d1_funct_2]) ).
fof(f_31_2,plain,
! [U_173,U_172,U_171] :
( ( ( ( ( quasi_total(U_171,U_173,U_172)
| U_171 != empty_set )
& ( U_171 = empty_set
| ~ quasi_total(U_171,U_173,U_172) ) )
| U_173 = empty_set
| U_172 != empty_set )
& ( ( ( quasi_total(U_171,U_173,U_172)
| U_173 != relation_dom_as_subset(U_173,U_172,U_171) )
& ( U_173 = relation_dom_as_subset(U_173,U_172,U_171)
| ~ quasi_total(U_171,U_173,U_172) ) )
| ( U_173 != empty_set
& U_172 = empty_set ) ) )
| ~ relation_of2_as_subset(U_171,U_173,U_172) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_171,U_173,U_172] :
( quasi_total(U_171,U_173,U_172)
| U_171 != empty_set
| ~ sP51(U_171,U_173,U_172) )
& ! [U_171,U_173,U_172] :
( U_171 = empty_set
| ~ quasi_total(U_171,U_173,U_172)
| ~ sP51(U_171,U_173,U_172) )
& ! [U_171,U_173,U_172] :
( quasi_total(U_171,U_173,U_172)
| U_173 != relation_dom_as_subset(U_173,U_172,U_171)
| ~ sP50(U_171,U_173,U_172) )
& ! [U_171,U_173,U_172] :
( U_173 = relation_dom_as_subset(U_173,U_172,U_171)
| ~ quasi_total(U_171,U_173,U_172)
| ~ sP50(U_171,U_173,U_172) )
& ! [U_173,U_172] :
( U_173 != empty_set
| ~ sP49(U_173,U_172) )
& ! [U_173,U_172] :
( U_172 = empty_set
| ~ sP49(U_173,U_172) )
& ! [U_171,U_173,U_172] :
( sP51(U_171,U_173,U_172)
| U_173 = empty_set
| U_172 != empty_set
| ~ sP52(U_171,U_173,U_172) )
& ! [U_171,U_173,U_172] :
( sP50(U_171,U_173,U_172)
| sP49(U_173,U_172)
| ~ sP52(U_171,U_173,U_172) )
& ! [U_171,U_173,U_172] :
( sP52(U_171,U_173,U_172)
| ~ relation_of2_as_subset(U_171,U_173,U_172) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50,sP51,sP52])],[f_31_2]) ).
cnf(f_31_4,plain,
( sP52(U_171,U_173,U_172)
| ~ relation_of2_as_subset(U_171,U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( sP50(U_171,U_173,U_172)
| sP49(U_173,U_172)
| ~ sP52(U_171,U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_6,plain,
( sP51(U_171,U_173,U_172)
| U_173 = empty_set
| U_172 != empty_set
| ~ sP52(U_171,U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_7,plain,
( U_172 = empty_set
| ~ sP49(U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_8,plain,
( U_173 != empty_set
| ~ sP49(U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_9,plain,
( U_173 = relation_dom_as_subset(U_173,U_172,U_171)
| ~ quasi_total(U_171,U_173,U_172)
| ~ sP50(U_171,U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_10,plain,
( quasi_total(U_171,U_173,U_172)
| U_173 != relation_dom_as_subset(U_173,U_172,U_171)
| ~ sP50(U_171,U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_11,plain,
( U_171 = empty_set
| ~ quasi_total(U_171,U_173,U_172)
| ~ sP51(U_171,U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_12,plain,
( quasi_total(U_171,U_173,U_172)
| U_171 != empty_set
| ~ sP51(U_171,U_173,U_172) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_181] :
( ! [U_180] :
( ( U_180 = pair_first(U_181)
| ? [U_179,U_178] :
( U_180 != U_179
& U_181 = ordered_pair(U_179,U_178) ) )
& ( ! [U_177,U_176] :
( U_180 = U_177
| U_181 != ordered_pair(U_177,U_176) )
| U_180 != pair_first(U_181) ) )
| ! [U_175,U_174] : U_181 != ordered_pair(U_175,U_174) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_181] :
( ( ! [U_183] :
( U_183 = pair_first(U_181)
| ? [U_179] :
( ? [U_178] : U_181 = ordered_pair(U_179,U_178)
& U_183 != U_179 ) )
& ! [U_182] :
( ! [U_177] :
( ! [U_176] : U_181 != ordered_pair(U_177,U_176)
| U_182 = U_177 )
| U_182 != pair_first(U_181) ) )
| ! [U_175,U_174] : U_181 != ordered_pair(U_175,U_174) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_181] :
( ( ! [U_183] :
( U_183 = pair_first(U_181)
| ( ? [U_178] : U_181 = ordered_pair(sK32(U_181,U_183),U_178)
& U_183 != sK32(U_181,U_183) ) )
& ! [U_182] :
( ! [U_177] :
( ! [U_176] : U_181 != ordered_pair(U_177,U_176)
| U_182 = U_177 )
| U_182 != pair_first(U_181) ) )
| ! [U_175,U_174] : U_181 != ordered_pair(U_175,U_174) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_179,sK32(U_181,U_183))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_181] :
( ( ! [U_183] :
( U_183 = pair_first(U_181)
| ( U_181 = ordered_pair(sK32(U_181,U_183),sK33(U_181,U_183))
& U_183 != sK32(U_181,U_183) ) )
& ! [U_182] :
( ! [U_177] :
( ! [U_176] : U_181 != ordered_pair(U_177,U_176)
| U_182 = U_177 )
| U_182 != pair_first(U_181) ) )
| ! [U_175,U_174] : U_181 != ordered_pair(U_175,U_174) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_178,sK33(U_181,U_183))],[f_32_4]) ).
fof(f_32_6,plain,
( ! [U_183,U_181] :
( U_181 = ordered_pair(sK32(U_181,U_183),sK33(U_181,U_183))
| ~ sP53(U_183,U_181) )
& ! [U_183,U_181] :
( U_183 != sK32(U_181,U_183)
| ~ sP53(U_183,U_181) )
& ! [U_177,U_176,U_182,U_183,U_181] :
( U_183 = pair_first(U_181)
| sP53(U_183,U_181)
| ~ sP54(U_177,U_176,U_182,U_183,U_181) )
& ! [U_177,U_176,U_182,U_183,U_181] :
( U_181 != ordered_pair(U_177,U_176)
| U_182 = U_177
| U_182 != pair_first(U_181)
| ~ sP54(U_177,U_176,U_182,U_183,U_181) )
& ! [U_177,U_176,U_182,U_174,U_175,U_183,U_181] :
( sP54(U_177,U_176,U_182,U_183,U_181)
| U_181 != ordered_pair(U_175,U_174) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53,sP54])],[f_32_5]) ).
cnf(f_32_7,plain,
( sP54(U_177,U_176,U_182,U_183,U_181)
| U_181 != ordered_pair(U_175,U_174) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_8,plain,
( U_181 != ordered_pair(U_177,U_176)
| U_182 = U_177
| U_182 != pair_first(U_181)
| ~ sP54(U_177,U_176,U_182,U_183,U_181) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_9,plain,
( U_183 = pair_first(U_181)
| sP53(U_183,U_181)
| ~ sP54(U_177,U_176,U_182,U_183,U_181) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_10,plain,
( U_183 != sK32(U_181,U_183)
| ~ sP53(U_183,U_181) ),
inference(clausify,[status(thm)],[f_32_6]) ).
cnf(f_32_11,plain,
( U_181 = ordered_pair(sK32(U_181,U_183),sK33(U_181,U_183))
| ~ sP53(U_183,U_181) ),
inference(clausify,[status(thm)],[f_32_6]) ).
fof(f_33_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_33_2,plain,
! [U_184] : succ(U_184) = set_union2(U_184,singleton(U_184)),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_184] : succ(U_184) = set_union2(U_184,singleton(U_184)),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
succ(U_184) = set_union2(U_184,singleton(U_184)),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_191] :
( ( relation(U_191)
| ? [U_190] :
( ! [U_189,U_188] : U_190 != ordered_pair(U_189,U_188)
& in(U_190,U_191) ) )
& ( ! [U_187] :
( ? [U_186,U_185] : U_187 = ordered_pair(U_186,U_185)
| ~ in(U_187,U_191) )
| ~ relation(U_191) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_193] :
( relation(U_193)
| ? [U_190] :
( ! [U_189,U_188] : U_190 != ordered_pair(U_189,U_188)
& in(U_190,U_193) ) )
& ! [U_192] :
( ! [U_187] :
( ? [U_186,U_185] : U_187 = ordered_pair(U_186,U_185)
| ~ in(U_187,U_192) )
| ~ relation(U_192) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_193] :
( relation(U_193)
| ? [U_190] :
( ! [U_189,U_188] : U_190 != ordered_pair(U_189,U_188)
& in(U_190,U_193) ) )
& ! [U_192] :
( ! [U_187] :
( ? [U_185] : U_187 = ordered_pair(sK34(U_192,U_187),U_185)
| ~ in(U_187,U_192) )
| ~ relation(U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_186,sK34(U_192,U_187))],[f_34_3]) ).
fof(f_34_5,plain,
( ! [U_193] :
( relation(U_193)
| ? [U_190] :
( ! [U_189,U_188] : U_190 != ordered_pair(U_189,U_188)
& in(U_190,U_193) ) )
& ! [U_192] :
( ! [U_187] :
( U_187 = ordered_pair(sK34(U_192,U_187),sK35(U_192,U_187))
| ~ in(U_187,U_192) )
| ~ relation(U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_185,sK35(U_192,U_187))],[f_34_4]) ).
fof(f_34_6,plain,
( ! [U_193] :
( relation(U_193)
| ( ! [U_189,U_188] : sK36(U_193) != ordered_pair(U_189,U_188)
& in(sK36(U_193),U_193) ) )
& ! [U_192] :
( ! [U_187] :
( U_187 = ordered_pair(sK34(U_192,U_187),sK35(U_192,U_187))
| ~ in(U_187,U_192) )
| ~ relation(U_192) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_190,sK36(U_193))],[f_34_5]) ).
fof(f_34_7,plain,
( ! [U_188,U_189,U_193] :
( sK36(U_193) != ordered_pair(U_189,U_188)
| ~ sP55(U_188,U_189,U_193) )
& ! [U_188,U_189,U_193] :
( in(sK36(U_193),U_193)
| ~ sP55(U_188,U_189,U_193) )
& ! [U_188,U_189,U_193] :
( relation(U_193)
| sP55(U_188,U_189,U_193) )
& ! [U_187,U_192] :
( U_187 = ordered_pair(sK34(U_192,U_187),sK35(U_192,U_187))
| ~ in(U_187,U_192)
| ~ relation(U_192) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_34_6]) ).
cnf(f_34_8,plain,
( U_187 = ordered_pair(sK34(U_192,U_187),sK35(U_192,U_187))
| ~ in(U_187,U_192)
| ~ relation(U_192) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_9,plain,
( relation(U_193)
| sP55(U_188,U_189,U_193) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_10,plain,
( in(sK36(U_193),U_193)
| ~ sP55(U_188,U_189,U_193) ),
inference(clausify,[status(thm)],[f_34_7]) ).
cnf(f_34_11,plain,
( sK36(U_193) != ordered_pair(U_189,U_188)
| ~ sP55(U_188,U_189,U_193) ),
inference(clausify,[status(thm)],[f_34_7]) ).
fof(f_35_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_35_2,plain,
! [U_197] :
( ! [U_196] :
( ( is_reflexive_in(U_197,U_196)
| ? [U_195] :
( ~ in(ordered_pair(U_195,U_195),U_197)
& in(U_195,U_196) ) )
& ( ! [U_194] :
( in(ordered_pair(U_194,U_194),U_197)
| ~ in(U_194,U_196) )
| ~ is_reflexive_in(U_197,U_196) ) )
| ~ relation(U_197) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_197] :
( ( ! [U_199] :
( is_reflexive_in(U_197,U_199)
| ? [U_195] :
( ~ in(ordered_pair(U_195,U_195),U_197)
& in(U_195,U_199) ) )
& ! [U_198] :
( ! [U_194] :
( in(ordered_pair(U_194,U_194),U_197)
| ~ in(U_194,U_198) )
| ~ is_reflexive_in(U_197,U_198) ) )
| ~ relation(U_197) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
fof(f_35_4,plain,
! [U_197] :
( ( ! [U_199] :
( is_reflexive_in(U_197,U_199)
| ( ~ in(ordered_pair(sK37(U_197,U_199),sK37(U_197,U_199)),U_197)
& in(sK37(U_197,U_199),U_199) ) )
& ! [U_198] :
( ! [U_194] :
( in(ordered_pair(U_194,U_194),U_197)
| ~ in(U_194,U_198) )
| ~ is_reflexive_in(U_197,U_198) ) )
| ~ relation(U_197) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_195,sK37(U_197,U_199))],[f_35_3]) ).
fof(f_35_5,plain,
( ! [U_197,U_199] :
( ~ in(ordered_pair(sK37(U_197,U_199),sK37(U_197,U_199)),U_197)
| ~ sP56(U_197,U_199) )
& ! [U_197,U_199] :
( in(sK37(U_197,U_199),U_199)
| ~ sP56(U_197,U_199) )
& ! [U_194,U_197,U_199,U_198] :
( is_reflexive_in(U_197,U_199)
| sP56(U_197,U_199)
| ~ sP57(U_194,U_197,U_199,U_198) )
& ! [U_194,U_197,U_199,U_198] :
( in(ordered_pair(U_194,U_194),U_197)
| ~ in(U_194,U_198)
| ~ is_reflexive_in(U_197,U_198)
| ~ sP57(U_194,U_197,U_199,U_198) )
& ! [U_194,U_197,U_199,U_198] :
( sP57(U_194,U_197,U_199,U_198)
| ~ relation(U_197) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56,sP57])],[f_35_4]) ).
cnf(f_35_6,plain,
( sP57(U_194,U_197,U_199,U_198)
| ~ relation(U_197) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_7,plain,
( in(ordered_pair(U_194,U_194),U_197)
| ~ in(U_194,U_198)
| ~ is_reflexive_in(U_197,U_198)
| ~ sP57(U_194,U_197,U_199,U_198) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_8,plain,
( is_reflexive_in(U_197,U_199)
| sP56(U_197,U_199)
| ~ sP57(U_194,U_197,U_199,U_198) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_9,plain,
( in(sK37(U_197,U_199),U_199)
| ~ sP56(U_197,U_199) ),
inference(clausify,[status(thm)],[f_35_5]) ).
cnf(f_35_10,plain,
( ~ in(ordered_pair(sK37(U_197,U_199),sK37(U_197,U_199)),U_197)
| ~ sP56(U_197,U_199) ),
inference(clausify,[status(thm)],[f_35_5]) ).
fof(f_36_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_36_2,plain,
! [U_202,U_201,U_200] :
( ( relation_of2(U_200,U_202,U_201)
| ~ subset(U_200,cartesian_product2(U_202,U_201)) )
& ( subset(U_200,cartesian_product2(U_202,U_201))
| ~ relation_of2(U_200,U_202,U_201) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_208,U_206,U_204] :
( relation_of2(U_204,U_208,U_206)
| ~ subset(U_204,cartesian_product2(U_208,U_206)) )
& ! [U_207,U_205,U_203] :
( subset(U_203,cartesian_product2(U_207,U_205))
| ~ relation_of2(U_203,U_207,U_205) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_206,U_204,U_208] :
( relation_of2(U_204,U_208,U_206)
| ~ subset(U_204,cartesian_product2(U_208,U_206)) )
& ! [U_205,U_203,U_207] :
( subset(U_203,cartesian_product2(U_207,U_205))
| ~ relation_of2(U_203,U_207,U_205) ) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
( subset(U_203,cartesian_product2(U_207,U_205))
| ~ relation_of2(U_203,U_207,U_205) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
( relation_of2(U_204,U_208,U_206)
| ~ subset(U_204,cartesian_product2(U_208,U_206)) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_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_37_2,plain,
! [U_216,U_215] :
( ( ( ( U_215 = set_meet(U_216)
| U_215 != empty_set )
& ( U_215 = empty_set
| U_215 != set_meet(U_216) ) )
| U_216 != empty_set )
& ( ( ( U_215 = set_meet(U_216)
| ? [U_214] :
( ( ~ in(U_214,U_215)
& ! [U_213] :
( in(U_214,U_213)
| ~ in(U_213,U_216) ) )
| ( ? [U_212] :
( ~ in(U_214,U_212)
& in(U_212,U_216) )
& in(U_214,U_215) ) ) )
& ( ! [U_211] :
( ( in(U_211,U_215)
| ? [U_210] :
( ~ in(U_211,U_210)
& in(U_210,U_216) ) )
& ( ! [U_209] :
( in(U_211,U_209)
| ~ in(U_209,U_216) )
| ~ in(U_211,U_215) ) )
| U_215 != set_meet(U_216) ) )
| U_216 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_228] :
( ( ! [U_226] :
( U_226 = set_meet(U_228)
| U_226 != empty_set )
& ! [U_225] :
( U_225 = empty_set
| U_225 != set_meet(U_228) ) )
| U_228 != empty_set )
& ! [U_227] :
( ( ! [U_224] :
( U_224 = set_meet(U_227)
| ? [U_220] :
( ~ in(U_220,U_224)
& ! [U_213] :
( in(U_220,U_213)
| ~ in(U_213,U_227) ) )
| ? [U_219] :
( ? [U_212] :
( ~ in(U_219,U_212)
& in(U_212,U_227) )
& in(U_219,U_224) ) )
& ! [U_223] :
( ( ! [U_218] :
( in(U_218,U_223)
| ? [U_210] :
( ~ in(U_218,U_210)
& in(U_210,U_227) ) )
& ! [U_217] :
( ! [U_209] :
( in(U_217,U_209)
| ~ in(U_209,U_227) )
| ~ in(U_217,U_223) ) )
| U_223 != set_meet(U_227) ) )
| U_227 = empty_set ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_228] :
( ( ! [U_226] :
( U_226 = set_meet(U_228)
| U_226 != empty_set )
& ! [U_225] :
( U_225 = empty_set
| U_225 != set_meet(U_228) ) )
| U_228 != empty_set )
& ! [U_227] :
( ( ! [U_224] :
( U_224 = set_meet(U_227)
| ? [U_220] :
( ~ in(U_220,U_224)
& ! [U_213] :
( in(U_220,U_213)
| ~ in(U_213,U_227) ) )
| ? [U_219] :
( ? [U_212] :
( ~ in(U_219,U_212)
& in(U_212,U_227) )
& in(U_219,U_224) ) )
& ! [U_223] :
( ( ! [U_218] :
( in(U_218,U_223)
| ( ~ in(U_218,sK38(U_227,U_223,U_218))
& in(sK38(U_227,U_223,U_218),U_227) ) )
& ! [U_217] :
( ! [U_209] :
( in(U_217,U_209)
| ~ in(U_209,U_227) )
| ~ in(U_217,U_223) ) )
| U_223 != set_meet(U_227) ) )
| U_227 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_210,sK38(U_227,U_223,U_218))],[f_37_3]) ).
fof(f_37_5,plain,
( ! [U_228] :
( ( ! [U_226] :
( U_226 = set_meet(U_228)
| U_226 != empty_set )
& ! [U_225] :
( U_225 = empty_set
| U_225 != set_meet(U_228) ) )
| U_228 != empty_set )
& ! [U_227] :
( ( ! [U_224] :
( U_224 = set_meet(U_227)
| ? [U_220] :
( ~ in(U_220,U_224)
& ! [U_213] :
( in(U_220,U_213)
| ~ in(U_213,U_227) ) )
| ( ? [U_212] :
( ~ in(sK39(U_227,U_224),U_212)
& in(U_212,U_227) )
& in(sK39(U_227,U_224),U_224) ) )
& ! [U_223] :
( ( ! [U_218] :
( in(U_218,U_223)
| ( ~ in(U_218,sK38(U_227,U_223,U_218))
& in(sK38(U_227,U_223,U_218),U_227) ) )
& ! [U_217] :
( ! [U_209] :
( in(U_217,U_209)
| ~ in(U_209,U_227) )
| ~ in(U_217,U_223) ) )
| U_223 != set_meet(U_227) ) )
| U_227 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_219,sK39(U_227,U_224))],[f_37_4]) ).
fof(f_37_6,plain,
( ! [U_228] :
( ( ! [U_226] :
( U_226 = set_meet(U_228)
| U_226 != empty_set )
& ! [U_225] :
( U_225 = empty_set
| U_225 != set_meet(U_228) ) )
| U_228 != empty_set )
& ! [U_227] :
( ( ! [U_224] :
( U_224 = set_meet(U_227)
| ? [U_220] :
( ~ in(U_220,U_224)
& ! [U_213] :
( in(U_220,U_213)
| ~ in(U_213,U_227) ) )
| ( ~ in(sK39(U_227,U_224),sK40(U_227,U_224))
& in(sK40(U_227,U_224),U_227)
& in(sK39(U_227,U_224),U_224) ) )
& ! [U_223] :
( ( ! [U_218] :
( in(U_218,U_223)
| ( ~ in(U_218,sK38(U_227,U_223,U_218))
& in(sK38(U_227,U_223,U_218),U_227) ) )
& ! [U_217] :
( ! [U_209] :
( in(U_217,U_209)
| ~ in(U_209,U_227) )
| ~ in(U_217,U_223) ) )
| U_223 != set_meet(U_227) ) )
| U_227 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_212,sK40(U_227,U_224))],[f_37_5]) ).
fof(f_37_7,plain,
( ! [U_228] :
( ( ! [U_226] :
( U_226 = set_meet(U_228)
| U_226 != empty_set )
& ! [U_225] :
( U_225 = empty_set
| U_225 != set_meet(U_228) ) )
| U_228 != empty_set )
& ! [U_227] :
( ( ! [U_224] :
( U_224 = set_meet(U_227)
| ( ~ in(sK41(U_227,U_224),U_224)
& ! [U_213] :
( in(sK41(U_227,U_224),U_213)
| ~ in(U_213,U_227) ) )
| ( ~ in(sK39(U_227,U_224),sK40(U_227,U_224))
& in(sK40(U_227,U_224),U_227)
& in(sK39(U_227,U_224),U_224) ) )
& ! [U_223] :
( ( ! [U_218] :
( in(U_218,U_223)
| ( ~ in(U_218,sK38(U_227,U_223,U_218))
& in(sK38(U_227,U_223,U_218),U_227) ) )
& ! [U_217] :
( ! [U_209] :
( in(U_217,U_209)
| ~ in(U_209,U_227) )
| ~ in(U_217,U_223) ) )
| U_223 != set_meet(U_227) ) )
| U_227 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_220,sK41(U_227,U_224))],[f_37_6]) ).
fof(f_37_8,plain,
( ! [U_228,U_225,U_226] :
( U_226 = set_meet(U_228)
| U_226 != empty_set
| ~ sP63(U_228,U_225,U_226) )
& ! [U_228,U_225,U_226] :
( U_225 = empty_set
| U_225 != set_meet(U_228)
| ~ sP63(U_228,U_225,U_226) )
& ! [U_224,U_213,U_227] :
( ~ in(sK41(U_227,U_224),U_224)
| ~ sP61(U_224,U_213,U_227) )
& ! [U_224,U_213,U_227] :
( in(sK41(U_227,U_224),U_213)
| ~ in(U_213,U_227)
| ~ sP61(U_224,U_213,U_227) )
& ! [U_224,U_227] :
( ~ in(sK39(U_227,U_224),sK40(U_227,U_224))
| ~ sP60(U_224,U_227) )
& ! [U_224,U_227] :
( in(sK40(U_227,U_224),U_227)
| ~ sP60(U_224,U_227) )
& ! [U_224,U_227] :
( in(sK39(U_227,U_224),U_224)
| ~ sP60(U_224,U_227) )
& ! [U_223,U_218,U_227] :
( ~ in(U_218,sK38(U_227,U_223,U_218))
| ~ sP58(U_223,U_218,U_227) )
& ! [U_223,U_218,U_227] :
( in(sK38(U_227,U_223,U_218),U_227)
| ~ sP58(U_223,U_218,U_227) )
& ! [U_209,U_223,U_217,U_218,U_227] :
( in(U_218,U_223)
| sP58(U_223,U_218,U_227)
| ~ sP59(U_209,U_223,U_217,U_218,U_227) )
& ! [U_209,U_223,U_217,U_218,U_227] :
( in(U_217,U_209)
| ~ in(U_209,U_227)
| ~ in(U_217,U_223)
| ~ sP59(U_209,U_223,U_217,U_218,U_227) )
& ! [U_224,U_209,U_223,U_213,U_217,U_218,U_227] :
( U_224 = set_meet(U_227)
| sP61(U_224,U_213,U_227)
| sP60(U_224,U_227)
| ~ sP62(U_224,U_209,U_223,U_213,U_217,U_218,U_227) )
& ! [U_224,U_209,U_223,U_213,U_217,U_218,U_227] :
( sP59(U_209,U_223,U_217,U_218,U_227)
| U_223 != set_meet(U_227)
| ~ sP62(U_224,U_209,U_223,U_213,U_217,U_218,U_227) )
& ! [U_228,U_225,U_226] :
( sP63(U_228,U_225,U_226)
| U_228 != empty_set )
& ! [U_224,U_209,U_223,U_213,U_217,U_218,U_227] :
( sP62(U_224,U_209,U_223,U_213,U_217,U_218,U_227)
| U_227 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58,sP59,sP60,sP61,sP62,sP63])],[f_37_7]) ).
cnf(f_37_9,plain,
( sP62(U_224,U_209,U_223,U_213,U_217,U_218,U_227)
| U_227 = empty_set ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_10,plain,
( sP63(U_228,U_225,U_226)
| U_228 != empty_set ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_11,plain,
( sP59(U_209,U_223,U_217,U_218,U_227)
| U_223 != set_meet(U_227)
| ~ sP62(U_224,U_209,U_223,U_213,U_217,U_218,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_12,plain,
( U_224 = set_meet(U_227)
| sP61(U_224,U_213,U_227)
| sP60(U_224,U_227)
| ~ sP62(U_224,U_209,U_223,U_213,U_217,U_218,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_13,plain,
( in(U_217,U_209)
| ~ in(U_209,U_227)
| ~ in(U_217,U_223)
| ~ sP59(U_209,U_223,U_217,U_218,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_14,plain,
( in(U_218,U_223)
| sP58(U_223,U_218,U_227)
| ~ sP59(U_209,U_223,U_217,U_218,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_15,plain,
( in(sK38(U_227,U_223,U_218),U_227)
| ~ sP58(U_223,U_218,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_16,plain,
( ~ in(U_218,sK38(U_227,U_223,U_218))
| ~ sP58(U_223,U_218,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_17,plain,
( in(sK39(U_227,U_224),U_224)
| ~ sP60(U_224,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_18,plain,
( in(sK40(U_227,U_224),U_227)
| ~ sP60(U_224,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_19,plain,
( ~ in(sK39(U_227,U_224),sK40(U_227,U_224))
| ~ sP60(U_224,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_20,plain,
( in(sK41(U_227,U_224),U_213)
| ~ in(U_213,U_227)
| ~ sP61(U_224,U_213,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_21,plain,
( ~ in(sK41(U_227,U_224),U_224)
| ~ sP61(U_224,U_213,U_227) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_22,plain,
( U_225 = empty_set
| U_225 != set_meet(U_228)
| ~ sP63(U_228,U_225,U_226) ),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(f_37_23,plain,
( U_226 = set_meet(U_228)
| U_226 != empty_set
| ~ sP63(U_228,U_225,U_226) ),
inference(clausify,[status(thm)],[f_37_8]) ).
fof(f_38_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_38_2,plain,
! [U_232,U_231] :
( ( U_231 = singleton(U_232)
| ? [U_230] :
( ( ~ in(U_230,U_231)
& U_230 = U_232 )
| ( U_230 != U_232
& in(U_230,U_231) ) ) )
& ( ! [U_229] :
( ( in(U_229,U_231)
| U_229 != U_232 )
& ( U_229 = U_232
| ~ in(U_229,U_231) ) )
| U_231 != singleton(U_232) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_240,U_238] :
( U_238 = singleton(U_240)
| ? [U_236] :
( ~ in(U_236,U_238)
& U_236 = U_240 )
| ? [U_235] :
( U_235 != U_240
& in(U_235,U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| U_234 != U_239 )
& ! [U_233] :
( U_233 = U_239
| ~ in(U_233,U_237) ) )
| U_237 != singleton(U_239) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_240,U_238] :
( U_238 = singleton(U_240)
| ? [U_236] :
( ~ in(U_236,U_238)
& U_236 = U_240 )
| ( sK42(U_240,U_238) != U_240
& in(sK42(U_240,U_238),U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| U_234 != U_239 )
& ! [U_233] :
( U_233 = U_239
| ~ in(U_233,U_237) ) )
| U_237 != singleton(U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_235,sK42(U_240,U_238))],[f_38_3]) ).
fof(f_38_5,plain,
( ! [U_240,U_238] :
( U_238 = singleton(U_240)
| ( ~ in(sK43(U_240,U_238),U_238)
& sK43(U_240,U_238) = U_240 )
| ( sK42(U_240,U_238) != U_240
& in(sK42(U_240,U_238),U_238) ) )
& ! [U_239,U_237] :
( ( ! [U_234] :
( in(U_234,U_237)
| U_234 != U_239 )
& ! [U_233] :
( U_233 = U_239
| ~ in(U_233,U_237) ) )
| U_237 != singleton(U_239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_236,sK43(U_240,U_238))],[f_38_4]) ).
fof(f_38_6,plain,
( ! [U_240,U_238] :
( ~ in(sK43(U_240,U_238),U_238)
| ~ sP66(U_240,U_238) )
& ! [U_240,U_238] :
( sK43(U_240,U_238) = U_240
| ~ sP66(U_240,U_238) )
& ! [U_240,U_238] :
( sK42(U_240,U_238) != U_240
| ~ sP65(U_240,U_238) )
& ! [U_240,U_238] :
( in(sK42(U_240,U_238),U_238)
| ~ sP65(U_240,U_238) )
& ! [U_234,U_233,U_237,U_239] :
( in(U_234,U_237)
| U_234 != U_239
| ~ sP64(U_234,U_233,U_237,U_239) )
& ! [U_234,U_233,U_237,U_239] :
( U_233 = U_239
| ~ in(U_233,U_237)
| ~ sP64(U_234,U_233,U_237,U_239) )
& ! [U_240,U_238] :
( U_238 = singleton(U_240)
| sP66(U_240,U_238)
| sP65(U_240,U_238) )
& ! [U_234,U_233,U_237,U_239] :
( sP64(U_234,U_233,U_237,U_239)
| U_237 != singleton(U_239) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64,sP65,sP66])],[f_38_5]) ).
cnf(f_38_7,plain,
( sP64(U_234,U_233,U_237,U_239)
| U_237 != singleton(U_239) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_8,plain,
( U_238 = singleton(U_240)
| sP66(U_240,U_238)
| sP65(U_240,U_238) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_9,plain,
( U_233 = U_239
| ~ in(U_233,U_237)
| ~ sP64(U_234,U_233,U_237,U_239) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_10,plain,
( in(U_234,U_237)
| U_234 != U_239
| ~ sP64(U_234,U_233,U_237,U_239) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_11,plain,
( in(sK42(U_240,U_238),U_238)
| ~ sP65(U_240,U_238) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_12,plain,
( sK42(U_240,U_238) != U_240
| ~ sP65(U_240,U_238) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_13,plain,
( sK43(U_240,U_238) = U_240
| ~ sP66(U_240,U_238) ),
inference(clausify,[status(thm)],[f_38_6]) ).
cnf(f_38_14,plain,
( ~ in(sK43(U_240,U_238),U_238)
| ~ sP66(U_240,U_238) ),
inference(clausify,[status(thm)],[f_38_6]) ).
fof(f_39_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_39_2,plain,
! [U_245] :
( ! [U_244,U_243] :
( ( U_243 = fiber(U_245,U_244)
| ? [U_242] :
( ( ~ in(U_242,U_243)
& in(ordered_pair(U_242,U_244),U_245)
& U_242 != U_244 )
| ( ( ~ in(ordered_pair(U_242,U_244),U_245)
| U_242 = U_244 )
& in(U_242,U_243) ) ) )
& ( ! [U_241] :
( ( in(U_241,U_243)
| ~ in(ordered_pair(U_241,U_244),U_245)
| U_241 = U_244 )
& ( ( in(ordered_pair(U_241,U_244),U_245)
& U_241 != U_244 )
| ~ in(U_241,U_243) ) )
| U_243 != fiber(U_245,U_244) ) )
| ~ relation(U_245) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_245] :
( ( ! [U_253,U_251] :
( U_251 = fiber(U_245,U_253)
| ? [U_249] :
( ~ in(U_249,U_251)
& in(ordered_pair(U_249,U_253),U_245)
& U_249 != U_253 )
| ? [U_248] :
( ( ~ in(ordered_pair(U_248,U_253),U_245)
| U_248 = U_253 )
& in(U_248,U_251) ) )
& ! [U_252,U_250] :
( ( ! [U_247] :
( in(U_247,U_250)
| ~ in(ordered_pair(U_247,U_252),U_245)
| U_247 = U_252 )
& ! [U_246] :
( ( in(ordered_pair(U_246,U_252),U_245)
& U_246 != U_252 )
| ~ in(U_246,U_250) ) )
| U_250 != fiber(U_245,U_252) ) )
| ~ relation(U_245) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_245] :
( ( ! [U_253,U_251] :
( U_251 = fiber(U_245,U_253)
| ? [U_249] :
( ~ in(U_249,U_251)
& in(ordered_pair(U_249,U_253),U_245)
& U_249 != U_253 )
| ( ( ~ in(ordered_pair(sK44(U_245,U_253,U_251),U_253),U_245)
| sK44(U_245,U_253,U_251) = U_253 )
& in(sK44(U_245,U_253,U_251),U_251) ) )
& ! [U_252,U_250] :
( ( ! [U_247] :
( in(U_247,U_250)
| ~ in(ordered_pair(U_247,U_252),U_245)
| U_247 = U_252 )
& ! [U_246] :
( ( in(ordered_pair(U_246,U_252),U_245)
& U_246 != U_252 )
| ~ in(U_246,U_250) ) )
| U_250 != fiber(U_245,U_252) ) )
| ~ relation(U_245) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_248,sK44(U_245,U_253,U_251))],[f_39_3]) ).
fof(f_39_5,plain,
! [U_245] :
( ( ! [U_253,U_251] :
( U_251 = fiber(U_245,U_253)
| ( ~ in(sK45(U_245,U_253,U_251),U_251)
& in(ordered_pair(sK45(U_245,U_253,U_251),U_253),U_245)
& sK45(U_245,U_253,U_251) != U_253 )
| ( ( ~ in(ordered_pair(sK44(U_245,U_253,U_251),U_253),U_245)
| sK44(U_245,U_253,U_251) = U_253 )
& in(sK44(U_245,U_253,U_251),U_251) ) )
& ! [U_252,U_250] :
( ( ! [U_247] :
( in(U_247,U_250)
| ~ in(ordered_pair(U_247,U_252),U_245)
| U_247 = U_252 )
& ! [U_246] :
( ( in(ordered_pair(U_246,U_252),U_245)
& U_246 != U_252 )
| ~ in(U_246,U_250) ) )
| U_250 != fiber(U_245,U_252) ) )
| ~ relation(U_245) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_249,sK45(U_245,U_253,U_251))],[f_39_4]) ).
fof(f_39_6,plain,
( ! [U_245,U_253,U_251] :
( ~ in(sK45(U_245,U_253,U_251),U_251)
| ~ sP70(U_245,U_253,U_251) )
& ! [U_245,U_253,U_251] :
( in(ordered_pair(sK45(U_245,U_253,U_251),U_253),U_245)
| ~ sP70(U_245,U_253,U_251) )
& ! [U_245,U_253,U_251] :
( sK45(U_245,U_253,U_251) != U_253
| ~ sP70(U_245,U_253,U_251) )
& ! [U_245,U_253,U_251] :
( ~ in(ordered_pair(sK44(U_245,U_253,U_251),U_253),U_245)
| sK44(U_245,U_253,U_251) = U_253
| ~ sP69(U_245,U_253,U_251) )
& ! [U_245,U_253,U_251] :
( in(sK44(U_245,U_253,U_251),U_251)
| ~ sP69(U_245,U_253,U_251) )
& ! [U_246,U_245,U_252] :
( in(ordered_pair(U_246,U_252),U_245)
| ~ sP67(U_246,U_245,U_252) )
& ! [U_246,U_245,U_252] :
( U_246 != U_252
| ~ sP67(U_246,U_245,U_252) )
& ! [U_247,U_246,U_245,U_252,U_250] :
( in(U_247,U_250)
| ~ in(ordered_pair(U_247,U_252),U_245)
| U_247 = U_252
| ~ sP68(U_247,U_246,U_245,U_252,U_250) )
& ! [U_247,U_246,U_245,U_252,U_250] :
( sP67(U_246,U_245,U_252)
| ~ in(U_246,U_250)
| ~ sP68(U_247,U_246,U_245,U_252,U_250) )
& ! [U_247,U_246,U_245,U_253,U_252,U_251,U_250] :
( U_251 = fiber(U_245,U_253)
| sP70(U_245,U_253,U_251)
| sP69(U_245,U_253,U_251)
| ~ sP71(U_247,U_246,U_245,U_253,U_252,U_251,U_250) )
& ! [U_247,U_246,U_245,U_253,U_252,U_251,U_250] :
( sP68(U_247,U_246,U_245,U_252,U_250)
| U_250 != fiber(U_245,U_252)
| ~ sP71(U_247,U_246,U_245,U_253,U_252,U_251,U_250) )
& ! [U_247,U_246,U_245,U_253,U_252,U_251,U_250] :
( sP71(U_247,U_246,U_245,U_253,U_252,U_251,U_250)
| ~ relation(U_245) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67,sP68,sP69,sP70,sP71])],[f_39_5]) ).
cnf(f_39_7,plain,
( sP71(U_247,U_246,U_245,U_253,U_252,U_251,U_250)
| ~ relation(U_245) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_8,plain,
( sP68(U_247,U_246,U_245,U_252,U_250)
| U_250 != fiber(U_245,U_252)
| ~ sP71(U_247,U_246,U_245,U_253,U_252,U_251,U_250) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_9,plain,
( U_251 = fiber(U_245,U_253)
| sP70(U_245,U_253,U_251)
| sP69(U_245,U_253,U_251)
| ~ sP71(U_247,U_246,U_245,U_253,U_252,U_251,U_250) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_10,plain,
( sP67(U_246,U_245,U_252)
| ~ in(U_246,U_250)
| ~ sP68(U_247,U_246,U_245,U_252,U_250) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_11,plain,
( in(U_247,U_250)
| ~ in(ordered_pair(U_247,U_252),U_245)
| U_247 = U_252
| ~ sP68(U_247,U_246,U_245,U_252,U_250) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_12,plain,
( U_246 != U_252
| ~ sP67(U_246,U_245,U_252) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_13,plain,
( in(ordered_pair(U_246,U_252),U_245)
| ~ sP67(U_246,U_245,U_252) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_14,plain,
( in(sK44(U_245,U_253,U_251),U_251)
| ~ sP69(U_245,U_253,U_251) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_15,plain,
( ~ in(ordered_pair(sK44(U_245,U_253,U_251),U_253),U_245)
| sK44(U_245,U_253,U_251) = U_253
| ~ sP69(U_245,U_253,U_251) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_16,plain,
( sK45(U_245,U_253,U_251) != U_253
| ~ sP70(U_245,U_253,U_251) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_17,plain,
( in(ordered_pair(sK45(U_245,U_253,U_251),U_253),U_245)
| ~ sP70(U_245,U_253,U_251) ),
inference(clausify,[status(thm)],[f_39_6]) ).
cnf(f_39_18,plain,
( ~ in(sK45(U_245,U_253,U_251),U_251)
| ~ sP70(U_245,U_253,U_251) ),
inference(clausify,[status(thm)],[f_39_6]) ).
fof(f_40_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_40_2,plain,
! [U_259,U_258] :
( ( ( U_258 = inclusion_relation(U_259)
| ? [U_257,U_256] :
( ( ( ~ in(ordered_pair(U_257,U_256),U_258)
& subset(U_257,U_256) )
| ( ~ subset(U_257,U_256)
& in(ordered_pair(U_257,U_256),U_258) ) )
& in(U_256,U_259)
& in(U_257,U_259) )
| relation_field(U_258) != U_259 )
& ( ( ! [U_255,U_254] :
( ( ( in(ordered_pair(U_255,U_254),U_258)
| ~ subset(U_255,U_254) )
& ( subset(U_255,U_254)
| ~ in(ordered_pair(U_255,U_254),U_258) ) )
| ~ in(U_254,U_259)
| ~ in(U_255,U_259) )
& relation_field(U_258) = U_259 )
| U_258 != inclusion_relation(U_259) ) )
| ~ relation(U_258) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_259,U_258] :
( ( ( U_258 = inclusion_relation(U_259)
| ? [U_256] :
( ( ( ~ in(ordered_pair(sK46(U_259,U_258),U_256),U_258)
& subset(sK46(U_259,U_258),U_256) )
| ( ~ subset(sK46(U_259,U_258),U_256)
& in(ordered_pair(sK46(U_259,U_258),U_256),U_258) ) )
& in(U_256,U_259)
& in(sK46(U_259,U_258),U_259) )
| relation_field(U_258) != U_259 )
& ( ( ! [U_255,U_254] :
( ( ( in(ordered_pair(U_255,U_254),U_258)
| ~ subset(U_255,U_254) )
& ( subset(U_255,U_254)
| ~ in(ordered_pair(U_255,U_254),U_258) ) )
| ~ in(U_254,U_259)
| ~ in(U_255,U_259) )
& relation_field(U_258) = U_259 )
| U_258 != inclusion_relation(U_259) ) )
| ~ relation(U_258) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_257,sK46(U_259,U_258))],[f_40_2]) ).
fof(f_40_4,plain,
! [U_259,U_258] :
( ( ( U_258 = inclusion_relation(U_259)
| ( ( ( ~ in(ordered_pair(sK46(U_259,U_258),sK47(U_259,U_258)),U_258)
& subset(sK46(U_259,U_258),sK47(U_259,U_258)) )
| ( ~ subset(sK46(U_259,U_258),sK47(U_259,U_258))
& in(ordered_pair(sK46(U_259,U_258),sK47(U_259,U_258)),U_258) ) )
& in(sK47(U_259,U_258),U_259)
& in(sK46(U_259,U_258),U_259) )
| relation_field(U_258) != U_259 )
& ( ( ! [U_255,U_254] :
( ( ( in(ordered_pair(U_255,U_254),U_258)
| ~ subset(U_255,U_254) )
& ( subset(U_255,U_254)
| ~ in(ordered_pair(U_255,U_254),U_258) ) )
| ~ in(U_254,U_259)
| ~ in(U_255,U_259) )
& relation_field(U_258) = U_259 )
| U_258 != inclusion_relation(U_259) ) )
| ~ relation(U_258) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_256,sK47(U_259,U_258))],[f_40_3]) ).
fof(f_40_5,plain,
( ! [U_259,U_258] :
( ~ in(ordered_pair(sK46(U_259,U_258),sK47(U_259,U_258)),U_258)
| ~ sP75(U_259,U_258) )
& ! [U_259,U_258] :
( subset(sK46(U_259,U_258),sK47(U_259,U_258))
| ~ sP75(U_259,U_258) )
& ! [U_259,U_258] :
( ~ subset(sK46(U_259,U_258),sK47(U_259,U_258))
| ~ sP74(U_259,U_258) )
& ! [U_259,U_258] :
( in(ordered_pair(sK46(U_259,U_258),sK47(U_259,U_258)),U_258)
| ~ sP74(U_259,U_258) )
& ! [U_259,U_258] :
( sP75(U_259,U_258)
| sP74(U_259,U_258)
| ~ sP76(U_259,U_258) )
& ! [U_259,U_258] :
( in(sK47(U_259,U_258),U_259)
| ~ sP76(U_259,U_258) )
& ! [U_259,U_258] :
( in(sK46(U_259,U_258),U_259)
| ~ sP76(U_259,U_258) )
& ! [U_254,U_255,U_258] :
( in(ordered_pair(U_255,U_254),U_258)
| ~ subset(U_255,U_254)
| ~ sP72(U_254,U_255,U_258) )
& ! [U_254,U_255,U_258] :
( subset(U_255,U_254)
| ~ in(ordered_pair(U_255,U_254),U_258)
| ~ sP72(U_254,U_255,U_258) )
& ! [U_259,U_254,U_255,U_258] :
( sP72(U_254,U_255,U_258)
| ~ in(U_254,U_259)
| ~ in(U_255,U_259)
| ~ sP73(U_259,U_254,U_255,U_258) )
& ! [U_259,U_254,U_255,U_258] :
( relation_field(U_258) = U_259
| ~ sP73(U_259,U_254,U_255,U_258) )
& ! [U_259,U_254,U_255,U_258] :
( U_258 = inclusion_relation(U_259)
| sP76(U_259,U_258)
| relation_field(U_258) != U_259
| ~ sP77(U_259,U_254,U_255,U_258) )
& ! [U_259,U_254,U_255,U_258] :
( sP73(U_259,U_254,U_255,U_258)
| U_258 != inclusion_relation(U_259)
| ~ sP77(U_259,U_254,U_255,U_258) )
& ! [U_259,U_254,U_255,U_258] :
( sP77(U_259,U_254,U_255,U_258)
| ~ relation(U_258) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72,sP73,sP74,sP75,sP76,sP77])],[f_40_4]) ).
cnf(f_40_6,plain,
( sP77(U_259,U_254,U_255,U_258)
| ~ relation(U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_7,plain,
( sP73(U_259,U_254,U_255,U_258)
| U_258 != inclusion_relation(U_259)
| ~ sP77(U_259,U_254,U_255,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_8,plain,
( U_258 = inclusion_relation(U_259)
| sP76(U_259,U_258)
| relation_field(U_258) != U_259
| ~ sP77(U_259,U_254,U_255,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_9,plain,
( relation_field(U_258) = U_259
| ~ sP73(U_259,U_254,U_255,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_10,plain,
( sP72(U_254,U_255,U_258)
| ~ in(U_254,U_259)
| ~ in(U_255,U_259)
| ~ sP73(U_259,U_254,U_255,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_11,plain,
( subset(U_255,U_254)
| ~ in(ordered_pair(U_255,U_254),U_258)
| ~ sP72(U_254,U_255,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_12,plain,
( in(ordered_pair(U_255,U_254),U_258)
| ~ subset(U_255,U_254)
| ~ sP72(U_254,U_255,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_13,plain,
( in(sK46(U_259,U_258),U_259)
| ~ sP76(U_259,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_14,plain,
( in(sK47(U_259,U_258),U_259)
| ~ sP76(U_259,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_15,plain,
( sP75(U_259,U_258)
| sP74(U_259,U_258)
| ~ sP76(U_259,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_16,plain,
( in(ordered_pair(sK46(U_259,U_258),sK47(U_259,U_258)),U_258)
| ~ sP74(U_259,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_17,plain,
( ~ subset(sK46(U_259,U_258),sK47(U_259,U_258))
| ~ sP74(U_259,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_18,plain,
( subset(sK46(U_259,U_258),sK47(U_259,U_258))
| ~ sP75(U_259,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_19,plain,
( ~ in(ordered_pair(sK46(U_259,U_258),sK47(U_259,U_258)),U_258)
| ~ sP75(U_259,U_258) ),
inference(clausify,[status(thm)],[f_40_5]) ).
fof(f_41_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_41_2,plain,
! [U_262] :
( ( U_262 = empty_set
| ? [U_261] : in(U_261,U_262) )
& ( ! [U_260] : ~ in(U_260,U_262)
| U_262 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_264] :
( U_264 = empty_set
| ? [U_261] : in(U_261,U_264) )
& ! [U_263] :
( ! [U_260] : ~ in(U_260,U_263)
| U_263 != empty_set ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
( ! [U_264] :
( U_264 = empty_set
| in(sK48(U_264),U_264) )
& ! [U_263] :
( ! [U_260] : ~ in(U_260,U_263)
| U_263 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_261,sK48(U_264))],[f_41_3]) ).
fof(f_41_5,plain,
( ! [U_264] :
( U_264 = empty_set
| in(sK48(U_264),U_264) )
& ! [U_260,U_263] :
( ~ in(U_260,U_263)
| U_263 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_41_4]) ).
cnf(f_41_6,plain,
( ~ in(U_260,U_263)
| U_263 != empty_set ),
inference(clausify,[status(thm)],[f_41_5]) ).
cnf(f_41_7,plain,
( U_264 = empty_set
| in(sK48(U_264),U_264) ),
inference(clausify,[status(thm)],[f_41_5]) ).
fof(f_42_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_42_2,plain,
! [U_268,U_267] :
( ( U_267 = powerset(U_268)
| ? [U_266] :
( ( ~ in(U_266,U_267)
& subset(U_266,U_268) )
| ( ~ subset(U_266,U_268)
& in(U_266,U_267) ) ) )
& ( ! [U_265] :
( ( in(U_265,U_267)
| ~ subset(U_265,U_268) )
& ( subset(U_265,U_268)
| ~ in(U_265,U_267) ) )
| U_267 != powerset(U_268) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_276,U_274] :
( U_274 = powerset(U_276)
| ? [U_272] :
( ~ in(U_272,U_274)
& subset(U_272,U_276) )
| ? [U_271] :
( ~ subset(U_271,U_276)
& in(U_271,U_274) ) )
& ! [U_275,U_273] :
( ( ! [U_270] :
( in(U_270,U_273)
| ~ subset(U_270,U_275) )
& ! [U_269] :
( subset(U_269,U_275)
| ~ in(U_269,U_273) ) )
| U_273 != powerset(U_275) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_276,U_274] :
( U_274 = powerset(U_276)
| ? [U_272] :
( ~ in(U_272,U_274)
& subset(U_272,U_276) )
| ( ~ subset(sK49(U_276,U_274),U_276)
& in(sK49(U_276,U_274),U_274) ) )
& ! [U_275,U_273] :
( ( ! [U_270] :
( in(U_270,U_273)
| ~ subset(U_270,U_275) )
& ! [U_269] :
( subset(U_269,U_275)
| ~ in(U_269,U_273) ) )
| U_273 != powerset(U_275) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_271,sK49(U_276,U_274))],[f_42_3]) ).
fof(f_42_5,plain,
( ! [U_276,U_274] :
( U_274 = powerset(U_276)
| ( ~ in(sK50(U_276,U_274),U_274)
& subset(sK50(U_276,U_274),U_276) )
| ( ~ subset(sK49(U_276,U_274),U_276)
& in(sK49(U_276,U_274),U_274) ) )
& ! [U_275,U_273] :
( ( ! [U_270] :
( in(U_270,U_273)
| ~ subset(U_270,U_275) )
& ! [U_269] :
( subset(U_269,U_275)
| ~ in(U_269,U_273) ) )
| U_273 != powerset(U_275) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_272,sK50(U_276,U_274))],[f_42_4]) ).
fof(f_42_6,plain,
( ! [U_274,U_276] :
( ~ in(sK50(U_276,U_274),U_274)
| ~ sP80(U_274,U_276) )
& ! [U_274,U_276] :
( subset(sK50(U_276,U_274),U_276)
| ~ sP80(U_274,U_276) )
& ! [U_274,U_276] :
( ~ subset(sK49(U_276,U_274),U_276)
| ~ sP79(U_274,U_276) )
& ! [U_274,U_276] :
( in(sK49(U_276,U_274),U_274)
| ~ sP79(U_274,U_276) )
& ! [U_270,U_275,U_269,U_273] :
( in(U_270,U_273)
| ~ subset(U_270,U_275)
| ~ sP78(U_270,U_275,U_269,U_273) )
& ! [U_270,U_275,U_269,U_273] :
( subset(U_269,U_275)
| ~ in(U_269,U_273)
| ~ sP78(U_270,U_275,U_269,U_273) )
& ! [U_274,U_276] :
( U_274 = powerset(U_276)
| sP80(U_274,U_276)
| sP79(U_274,U_276) )
& ! [U_270,U_275,U_269,U_273] :
( sP78(U_270,U_275,U_269,U_273)
| U_273 != powerset(U_275) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78,sP79,sP80])],[f_42_5]) ).
cnf(f_42_7,plain,
( sP78(U_270,U_275,U_269,U_273)
| U_273 != powerset(U_275) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_8,plain,
( U_274 = powerset(U_276)
| sP80(U_274,U_276)
| sP79(U_274,U_276) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_9,plain,
( subset(U_269,U_275)
| ~ in(U_269,U_273)
| ~ sP78(U_270,U_275,U_269,U_273) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_10,plain,
( in(U_270,U_273)
| ~ subset(U_270,U_275)
| ~ sP78(U_270,U_275,U_269,U_273) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_11,plain,
( in(sK49(U_276,U_274),U_274)
| ~ sP79(U_274,U_276) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_12,plain,
( ~ subset(sK49(U_276,U_274),U_276)
| ~ sP79(U_274,U_276) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_13,plain,
( subset(sK50(U_276,U_274),U_276)
| ~ sP80(U_274,U_276) ),
inference(clausify,[status(thm)],[f_42_6]) ).
cnf(f_42_14,plain,
( ~ in(sK50(U_276,U_274),U_274)
| ~ sP80(U_274,U_276) ),
inference(clausify,[status(thm)],[f_42_6]) ).
fof(f_43_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_43_2,plain,
! [U_284] :
( ! [U_283] :
( ( U_283 = pair_second(U_284)
| ? [U_282,U_281] :
( U_283 != U_281
& U_284 = ordered_pair(U_282,U_281) ) )
& ( ! [U_280,U_279] :
( U_283 = U_279
| U_284 != ordered_pair(U_280,U_279) )
| U_283 != pair_second(U_284) ) )
| ! [U_278,U_277] : U_284 != ordered_pair(U_278,U_277) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_284] :
( ( ! [U_286] :
( U_286 = pair_second(U_284)
| ? [U_282,U_281] :
( U_286 != U_281
& U_284 = ordered_pair(U_282,U_281) ) )
& ! [U_285] :
( ! [U_280,U_279] :
( U_285 = U_279
| U_284 != ordered_pair(U_280,U_279) )
| U_285 != pair_second(U_284) ) )
| ! [U_278,U_277] : U_284 != ordered_pair(U_278,U_277) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_284] :
( ( ! [U_286] :
( U_286 = pair_second(U_284)
| ? [U_281] :
( U_286 != U_281
& U_284 = ordered_pair(sK51(U_284,U_286),U_281) ) )
& ! [U_285] :
( ! [U_280,U_279] :
( U_285 = U_279
| U_284 != ordered_pair(U_280,U_279) )
| U_285 != pair_second(U_284) ) )
| ! [U_278,U_277] : U_284 != ordered_pair(U_278,U_277) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_282,sK51(U_284,U_286))],[f_43_3]) ).
fof(f_43_5,plain,
! [U_284] :
( ( ! [U_286] :
( U_286 = pair_second(U_284)
| ( U_286 != sK52(U_284,U_286)
& U_284 = ordered_pair(sK51(U_284,U_286),sK52(U_284,U_286)) ) )
& ! [U_285] :
( ! [U_280,U_279] :
( U_285 = U_279
| U_284 != ordered_pair(U_280,U_279) )
| U_285 != pair_second(U_284) ) )
| ! [U_278,U_277] : U_284 != ordered_pair(U_278,U_277) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_281,sK52(U_284,U_286))],[f_43_4]) ).
fof(f_43_6,plain,
( ! [U_284,U_286] :
( U_286 != sK52(U_284,U_286)
| ~ sP81(U_284,U_286) )
& ! [U_284,U_286] :
( U_284 = ordered_pair(sK51(U_284,U_286),sK52(U_284,U_286))
| ~ sP81(U_284,U_286) )
& ! [U_279,U_285,U_284,U_280,U_286] :
( U_286 = pair_second(U_284)
| sP81(U_284,U_286)
| ~ sP82(U_279,U_285,U_284,U_280,U_286) )
& ! [U_279,U_285,U_284,U_280,U_286] :
( U_285 = U_279
| U_284 != ordered_pair(U_280,U_279)
| U_285 != pair_second(U_284)
| ~ sP82(U_279,U_285,U_284,U_280,U_286) )
& ! [U_279,U_285,U_278,U_284,U_277,U_280,U_286] :
( sP82(U_279,U_285,U_284,U_280,U_286)
| U_284 != ordered_pair(U_278,U_277) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81,sP82])],[f_43_5]) ).
cnf(f_43_7,plain,
( sP82(U_279,U_285,U_284,U_280,U_286)
| U_284 != ordered_pair(U_278,U_277) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_8,plain,
( U_285 = U_279
| U_284 != ordered_pair(U_280,U_279)
| U_285 != pair_second(U_284)
| ~ sP82(U_279,U_285,U_284,U_280,U_286) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_9,plain,
( U_286 = pair_second(U_284)
| sP81(U_284,U_286)
| ~ sP82(U_279,U_285,U_284,U_280,U_286) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_10,plain,
( U_284 = ordered_pair(sK51(U_284,U_286),sK52(U_284,U_286))
| ~ sP81(U_284,U_286) ),
inference(clausify,[status(thm)],[f_43_6]) ).
cnf(f_43_11,plain,
( U_286 != sK52(U_284,U_286)
| ~ sP81(U_284,U_286) ),
inference(clausify,[status(thm)],[f_43_6]) ).
fof(f_44_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_44_2,plain,
! [U_289] :
( ( epsilon_transitive(U_289)
| ? [U_288] :
( ~ subset(U_288,U_289)
& in(U_288,U_289) ) )
& ( ! [U_287] :
( subset(U_287,U_289)
| ~ in(U_287,U_289) )
| ~ epsilon_transitive(U_289) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_291] :
( epsilon_transitive(U_291)
| ? [U_288] :
( ~ subset(U_288,U_291)
& in(U_288,U_291) ) )
& ! [U_290] :
( ! [U_287] :
( subset(U_287,U_290)
| ~ in(U_287,U_290) )
| ~ epsilon_transitive(U_290) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
( ! [U_291] :
( epsilon_transitive(U_291)
| ( ~ subset(sK53(U_291),U_291)
& in(sK53(U_291),U_291) ) )
& ! [U_290] :
( ! [U_287] :
( subset(U_287,U_290)
| ~ in(U_287,U_290) )
| ~ epsilon_transitive(U_290) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_288,sK53(U_291))],[f_44_3]) ).
fof(f_44_5,plain,
( ! [U_291] :
( ~ subset(sK53(U_291),U_291)
| ~ sP83(U_291) )
& ! [U_291] :
( in(sK53(U_291),U_291)
| ~ sP83(U_291) )
& ! [U_291] :
( epsilon_transitive(U_291)
| sP83(U_291) )
& ! [U_287,U_290] :
( subset(U_287,U_290)
| ~ in(U_287,U_290)
| ~ epsilon_transitive(U_290) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_44_4]) ).
cnf(f_44_6,plain,
( subset(U_287,U_290)
| ~ in(U_287,U_290)
| ~ epsilon_transitive(U_290) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_7,plain,
( epsilon_transitive(U_291)
| sP83(U_291) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_8,plain,
( in(sK53(U_291),U_291)
| ~ sP83(U_291) ),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_9,plain,
( ~ subset(sK53(U_291),U_291)
| ~ sP83(U_291) ),
inference(clausify,[status(thm)],[f_44_5]) ).
fof(f_45_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_45_2,plain,
! [U_297] :
( ! [U_296] :
( ( ( U_297 = U_296
| ? [U_295,U_294] :
( ( ~ in(ordered_pair(U_295,U_294),U_297)
& in(ordered_pair(U_295,U_294),U_296) )
| ( ~ in(ordered_pair(U_295,U_294),U_296)
& in(ordered_pair(U_295,U_294),U_297) ) ) )
& ( ! [U_293,U_292] :
( ( in(ordered_pair(U_293,U_292),U_297)
| ~ in(ordered_pair(U_293,U_292),U_296) )
& ( in(ordered_pair(U_293,U_292),U_296)
| ~ in(ordered_pair(U_293,U_292),U_297) ) )
| U_297 != U_296 ) )
| ~ relation(U_296) )
| ~ relation(U_297) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_297] :
( ! [U_296] :
( ( ( U_297 = U_296
| ? [U_305,U_303] :
( ~ in(ordered_pair(U_305,U_303),U_297)
& in(ordered_pair(U_305,U_303),U_296) )
| ? [U_304,U_302] :
( ~ in(ordered_pair(U_304,U_302),U_296)
& in(ordered_pair(U_304,U_302),U_297) ) )
& ( ( ! [U_301,U_299] :
( in(ordered_pair(U_301,U_299),U_297)
| ~ in(ordered_pair(U_301,U_299),U_296) )
& ! [U_300,U_298] :
( in(ordered_pair(U_300,U_298),U_296)
| ~ in(ordered_pair(U_300,U_298),U_297) ) )
| U_297 != U_296 ) )
| ~ relation(U_296) )
| ~ relation(U_297) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
! [U_297] :
( ! [U_296] :
( ( ( U_297 = U_296
| ? [U_305,U_303] :
( ~ in(ordered_pair(U_305,U_303),U_297)
& in(ordered_pair(U_305,U_303),U_296) )
| ? [U_302] :
( ~ in(ordered_pair(sK54(U_297,U_296),U_302),U_296)
& in(ordered_pair(sK54(U_297,U_296),U_302),U_297) ) )
& ( ( ! [U_301,U_299] :
( in(ordered_pair(U_301,U_299),U_297)
| ~ in(ordered_pair(U_301,U_299),U_296) )
& ! [U_300,U_298] :
( in(ordered_pair(U_300,U_298),U_296)
| ~ in(ordered_pair(U_300,U_298),U_297) ) )
| U_297 != U_296 ) )
| ~ relation(U_296) )
| ~ relation(U_297) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_304,sK54(U_297,U_296))],[f_45_3]) ).
fof(f_45_5,plain,
! [U_297] :
( ! [U_296] :
( ( ( U_297 = U_296
| ? [U_305,U_303] :
( ~ in(ordered_pair(U_305,U_303),U_297)
& in(ordered_pair(U_305,U_303),U_296) )
| ( ~ in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_296)
& in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_297) ) )
& ( ( ! [U_301,U_299] :
( in(ordered_pair(U_301,U_299),U_297)
| ~ in(ordered_pair(U_301,U_299),U_296) )
& ! [U_300,U_298] :
( in(ordered_pair(U_300,U_298),U_296)
| ~ in(ordered_pair(U_300,U_298),U_297) ) )
| U_297 != U_296 ) )
| ~ relation(U_296) )
| ~ relation(U_297) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_302,sK55(U_297,U_296))],[f_45_4]) ).
fof(f_45_6,plain,
! [U_297] :
( ! [U_296] :
( ( ( U_297 = U_296
| ? [U_303] :
( ~ in(ordered_pair(sK56(U_297,U_296),U_303),U_297)
& in(ordered_pair(sK56(U_297,U_296),U_303),U_296) )
| ( ~ in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_296)
& in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_297) ) )
& ( ( ! [U_301,U_299] :
( in(ordered_pair(U_301,U_299),U_297)
| ~ in(ordered_pair(U_301,U_299),U_296) )
& ! [U_300,U_298] :
( in(ordered_pair(U_300,U_298),U_296)
| ~ in(ordered_pair(U_300,U_298),U_297) ) )
| U_297 != U_296 ) )
| ~ relation(U_296) )
| ~ relation(U_297) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_305,sK56(U_297,U_296))],[f_45_5]) ).
fof(f_45_7,plain,
! [U_297] :
( ! [U_296] :
( ( ( U_297 = U_296
| ( ~ in(ordered_pair(sK56(U_297,U_296),sK57(U_297,U_296)),U_297)
& in(ordered_pair(sK56(U_297,U_296),sK57(U_297,U_296)),U_296) )
| ( ~ in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_296)
& in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_297) ) )
& ( ( ! [U_301,U_299] :
( in(ordered_pair(U_301,U_299),U_297)
| ~ in(ordered_pair(U_301,U_299),U_296) )
& ! [U_300,U_298] :
( in(ordered_pair(U_300,U_298),U_296)
| ~ in(ordered_pair(U_300,U_298),U_297) ) )
| U_297 != U_296 ) )
| ~ relation(U_296) )
| ~ relation(U_297) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_303,sK57(U_297,U_296))],[f_45_6]) ).
fof(f_45_8,plain,
( ! [U_296,U_297] :
( ~ in(ordered_pair(sK56(U_297,U_296),sK57(U_297,U_296)),U_297)
| ~ sP86(U_296,U_297) )
& ! [U_296,U_297] :
( in(ordered_pair(sK56(U_297,U_296),sK57(U_297,U_296)),U_296)
| ~ sP86(U_296,U_297) )
& ! [U_296,U_297] :
( ~ in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_296)
| ~ sP85(U_296,U_297) )
& ! [U_296,U_297] :
( in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_297)
| ~ sP85(U_296,U_297) )
& ! [U_296,U_300,U_301,U_297,U_298,U_299] :
( in(ordered_pair(U_301,U_299),U_297)
| ~ in(ordered_pair(U_301,U_299),U_296)
| ~ sP84(U_296,U_300,U_301,U_297,U_298,U_299) )
& ! [U_296,U_300,U_301,U_297,U_298,U_299] :
( in(ordered_pair(U_300,U_298),U_296)
| ~ in(ordered_pair(U_300,U_298),U_297)
| ~ sP84(U_296,U_300,U_301,U_297,U_298,U_299) )
& ! [U_296,U_300,U_301,U_297,U_298,U_299] :
( U_297 = U_296
| sP86(U_296,U_297)
| sP85(U_296,U_297)
| ~ sP87(U_296,U_300,U_301,U_297,U_298,U_299) )
& ! [U_296,U_300,U_301,U_297,U_298,U_299] :
( sP84(U_296,U_300,U_301,U_297,U_298,U_299)
| U_297 != U_296
| ~ sP87(U_296,U_300,U_301,U_297,U_298,U_299) )
& ! [U_296,U_300,U_301,U_297,U_298,U_299] :
( sP87(U_296,U_300,U_301,U_297,U_298,U_299)
| ~ relation(U_296)
| ~ relation(U_297) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84,sP85,sP86,sP87])],[f_45_7]) ).
cnf(f_45_9,plain,
( sP87(U_296,U_300,U_301,U_297,U_298,U_299)
| ~ relation(U_296)
| ~ relation(U_297) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_10,plain,
( sP84(U_296,U_300,U_301,U_297,U_298,U_299)
| U_297 != U_296
| ~ sP87(U_296,U_300,U_301,U_297,U_298,U_299) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_11,plain,
( U_297 = U_296
| sP86(U_296,U_297)
| sP85(U_296,U_297)
| ~ sP87(U_296,U_300,U_301,U_297,U_298,U_299) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_12,plain,
( in(ordered_pair(U_300,U_298),U_296)
| ~ in(ordered_pair(U_300,U_298),U_297)
| ~ sP84(U_296,U_300,U_301,U_297,U_298,U_299) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_13,plain,
( in(ordered_pair(U_301,U_299),U_297)
| ~ in(ordered_pair(U_301,U_299),U_296)
| ~ sP84(U_296,U_300,U_301,U_297,U_298,U_299) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_14,plain,
( in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_297)
| ~ sP85(U_296,U_297) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_15,plain,
( ~ in(ordered_pair(sK54(U_297,U_296),sK55(U_297,U_296)),U_296)
| ~ sP85(U_296,U_297) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_16,plain,
( in(ordered_pair(sK56(U_297,U_296),sK57(U_297,U_296)),U_296)
| ~ sP86(U_296,U_297) ),
inference(clausify,[status(thm)],[f_45_8]) ).
cnf(f_45_17,plain,
( ~ in(ordered_pair(sK56(U_297,U_296),sK57(U_297,U_296)),U_297)
| ~ sP86(U_296,U_297) ),
inference(clausify,[status(thm)],[f_45_8]) ).
fof(f_46_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_46_2,plain,
! [U_307,U_306] :
( ( ( ( element(U_306,U_307)
| ~ empty(U_306) )
& ( empty(U_306)
| ~ element(U_306,U_307) ) )
| ~ empty(U_307) )
& ( ( ( element(U_306,U_307)
| ~ in(U_306,U_307) )
& ( in(U_306,U_307)
| ~ element(U_306,U_307) ) )
| empty(U_307) ) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_315] :
( ( ! [U_313] :
( element(U_313,U_315)
| ~ empty(U_313) )
& ! [U_312] :
( empty(U_312)
| ~ element(U_312,U_315) ) )
| ~ empty(U_315) )
& ! [U_314] :
( ( ! [U_311] :
( element(U_311,U_314)
| ~ in(U_311,U_314) )
& ! [U_310] :
( in(U_310,U_314)
| ~ element(U_310,U_314) ) )
| empty(U_314) ) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
( ! [U_312,U_315,U_313] :
( element(U_313,U_315)
| ~ empty(U_313)
| ~ sP89(U_312,U_315,U_313) )
& ! [U_312,U_315,U_313] :
( empty(U_312)
| ~ element(U_312,U_315)
| ~ sP89(U_312,U_315,U_313) )
& ! [U_314,U_310,U_311] :
( element(U_311,U_314)
| ~ in(U_311,U_314)
| ~ sP88(U_314,U_310,U_311) )
& ! [U_314,U_310,U_311] :
( in(U_310,U_314)
| ~ element(U_310,U_314)
| ~ sP88(U_314,U_310,U_311) )
& ! [U_312,U_315,U_313] :
( sP89(U_312,U_315,U_313)
| ~ empty(U_315) )
& ! [U_314,U_310,U_311] :
( sP88(U_314,U_310,U_311)
| empty(U_314) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88,sP89])],[f_46_3]) ).
cnf(f_46_5,plain,
( sP88(U_314,U_310,U_311)
| empty(U_314) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_6,plain,
( sP89(U_312,U_315,U_313)
| ~ empty(U_315) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_7,plain,
( in(U_310,U_314)
| ~ element(U_310,U_314)
| ~ sP88(U_314,U_310,U_311) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_8,plain,
( element(U_311,U_314)
| ~ in(U_311,U_314)
| ~ sP88(U_314,U_310,U_311) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_9,plain,
( empty(U_312)
| ~ element(U_312,U_315)
| ~ sP89(U_312,U_315,U_313) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_10,plain,
( element(U_313,U_315)
| ~ empty(U_313)
| ~ sP89(U_312,U_315,U_313) ),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_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_47_2,plain,
! [U_320,U_319,U_318] :
( ( U_318 = unordered_pair(U_320,U_319)
| ? [U_317] :
( ( ~ in(U_317,U_318)
& ( U_317 = U_319
| U_317 = U_320 ) )
| ( U_317 != U_319
& U_317 != U_320
& in(U_317,U_318) ) ) )
& ( ! [U_316] :
( ( in(U_316,U_318)
| ( U_316 != U_319
& U_316 != U_320 ) )
& ( U_316 = U_319
| U_316 = U_320
| ~ in(U_316,U_318) ) )
| U_318 != unordered_pair(U_320,U_319) ) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( ! [U_330,U_328,U_326] :
( U_326 = unordered_pair(U_330,U_328)
| ? [U_324] :
( ~ in(U_324,U_326)
& ( U_324 = U_328
| U_324 = U_330 ) )
| ? [U_323] :
( U_323 != U_328
& U_323 != U_330
& in(U_323,U_326) ) )
& ! [U_329,U_327,U_325] :
( ( ! [U_322] :
( in(U_322,U_325)
| ( U_322 != U_327
& U_322 != U_329 ) )
& ! [U_321] :
( U_321 = U_327
| U_321 = U_329
| ~ in(U_321,U_325) ) )
| U_325 != unordered_pair(U_329,U_327) ) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
( ! [U_330,U_328,U_326] :
( U_326 = unordered_pair(U_330,U_328)
| ? [U_324] :
( ~ in(U_324,U_326)
& ( U_324 = U_328
| U_324 = U_330 ) )
| ( sK58(U_330,U_328,U_326) != U_328
& sK58(U_330,U_328,U_326) != U_330
& in(sK58(U_330,U_328,U_326),U_326) ) )
& ! [U_329,U_327,U_325] :
( ( ! [U_322] :
( in(U_322,U_325)
| ( U_322 != U_327
& U_322 != U_329 ) )
& ! [U_321] :
( U_321 = U_327
| U_321 = U_329
| ~ in(U_321,U_325) ) )
| U_325 != unordered_pair(U_329,U_327) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_323,sK58(U_330,U_328,U_326))],[f_47_3]) ).
fof(f_47_5,plain,
( ! [U_330,U_328,U_326] :
( U_326 = unordered_pair(U_330,U_328)
| ( ~ in(sK59(U_330,U_328,U_326),U_326)
& ( sK59(U_330,U_328,U_326) = U_328
| sK59(U_330,U_328,U_326) = U_330 ) )
| ( sK58(U_330,U_328,U_326) != U_328
& sK58(U_330,U_328,U_326) != U_330
& in(sK58(U_330,U_328,U_326),U_326) ) )
& ! [U_329,U_327,U_325] :
( ( ! [U_322] :
( in(U_322,U_325)
| ( U_322 != U_327
& U_322 != U_329 ) )
& ! [U_321] :
( U_321 = U_327
| U_321 = U_329
| ~ in(U_321,U_325) ) )
| U_325 != unordered_pair(U_329,U_327) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_324,sK59(U_330,U_328,U_326))],[f_47_4]) ).
fof(f_47_6,plain,
( ! [U_330,U_328,U_326] :
( ~ in(sK59(U_330,U_328,U_326),U_326)
| ~ sP93(U_330,U_328,U_326) )
& ! [U_330,U_328,U_326] :
( sK59(U_330,U_328,U_326) = U_328
| sK59(U_330,U_328,U_326) = U_330
| ~ sP93(U_330,U_328,U_326) )
& ! [U_330,U_328,U_326] :
( sK58(U_330,U_328,U_326) != U_328
| ~ sP92(U_330,U_328,U_326) )
& ! [U_330,U_328,U_326] :
( sK58(U_330,U_328,U_326) != U_330
| ~ sP92(U_330,U_328,U_326) )
& ! [U_330,U_328,U_326] :
( in(sK58(U_330,U_328,U_326),U_326)
| ~ sP92(U_330,U_328,U_326) )
& ! [U_322,U_329,U_327] :
( U_322 != U_327
| ~ sP90(U_322,U_329,U_327) )
& ! [U_322,U_329,U_327] :
( U_322 != U_329
| ~ sP90(U_322,U_329,U_327) )
& ! [U_322,U_325,U_329,U_327,U_321] :
( in(U_322,U_325)
| sP90(U_322,U_329,U_327)
| ~ sP91(U_322,U_325,U_329,U_327,U_321) )
& ! [U_322,U_325,U_329,U_327,U_321] :
( U_321 = U_327
| U_321 = U_329
| ~ in(U_321,U_325)
| ~ sP91(U_322,U_325,U_329,U_327,U_321) )
& ! [U_330,U_328,U_326] :
( U_326 = unordered_pair(U_330,U_328)
| sP93(U_330,U_328,U_326)
| sP92(U_330,U_328,U_326) )
& ! [U_322,U_325,U_329,U_327,U_321] :
( sP91(U_322,U_325,U_329,U_327,U_321)
| U_325 != unordered_pair(U_329,U_327) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90,sP91,sP92,sP93])],[f_47_5]) ).
cnf(f_47_7,plain,
( sP91(U_322,U_325,U_329,U_327,U_321)
| U_325 != unordered_pair(U_329,U_327) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_8,plain,
( U_326 = unordered_pair(U_330,U_328)
| sP93(U_330,U_328,U_326)
| sP92(U_330,U_328,U_326) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_9,plain,
( U_321 = U_327
| U_321 = U_329
| ~ in(U_321,U_325)
| ~ sP91(U_322,U_325,U_329,U_327,U_321) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_10,plain,
( in(U_322,U_325)
| sP90(U_322,U_329,U_327)
| ~ sP91(U_322,U_325,U_329,U_327,U_321) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_11,plain,
( U_322 != U_329
| ~ sP90(U_322,U_329,U_327) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_12,plain,
( U_322 != U_327
| ~ sP90(U_322,U_329,U_327) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_13,plain,
( in(sK58(U_330,U_328,U_326),U_326)
| ~ sP92(U_330,U_328,U_326) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_14,plain,
( sK58(U_330,U_328,U_326) != U_330
| ~ sP92(U_330,U_328,U_326) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_15,plain,
( sK58(U_330,U_328,U_326) != U_328
| ~ sP92(U_330,U_328,U_326) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_16,plain,
( sK59(U_330,U_328,U_326) = U_328
| sK59(U_330,U_328,U_326) = U_330
| ~ sP93(U_330,U_328,U_326) ),
inference(clausify,[status(thm)],[f_47_6]) ).
cnf(f_47_17,plain,
( ~ in(sK59(U_330,U_328,U_326),U_326)
| ~ sP93(U_330,U_328,U_326) ),
inference(clausify,[status(thm)],[f_47_6]) ).
fof(f_48_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_48_2,plain,
! [U_335] :
( ( ( well_founded_relation(U_335)
| ? [U_334] :
( ! [U_333] :
( ~ disjoint(fiber(U_335,U_333),U_334)
| ~ in(U_333,U_334) )
& U_334 != empty_set
& subset(U_334,relation_field(U_335)) ) )
& ( ! [U_332] :
( ? [U_331] :
( disjoint(fiber(U_335,U_331),U_332)
& in(U_331,U_332) )
| U_332 = empty_set
| ~ subset(U_332,relation_field(U_335)) )
| ~ well_founded_relation(U_335) ) )
| ~ relation(U_335) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_335] :
( ( ( well_founded_relation(U_335)
| ? [U_334] :
( ! [U_333] :
( ~ disjoint(fiber(U_335,U_333),U_334)
| ~ in(U_333,U_334) )
& U_334 != empty_set
& subset(U_334,relation_field(U_335)) ) )
& ( ! [U_332] :
( ( disjoint(fiber(U_335,sK60(U_335,U_332)),U_332)
& in(sK60(U_335,U_332),U_332) )
| U_332 = empty_set
| ~ subset(U_332,relation_field(U_335)) )
| ~ well_founded_relation(U_335) ) )
| ~ relation(U_335) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_331,sK60(U_335,U_332))],[f_48_2]) ).
fof(f_48_4,plain,
! [U_335] :
( ( ( well_founded_relation(U_335)
| ( ! [U_333] :
( ~ disjoint(fiber(U_335,U_333),sK61(U_335))
| ~ in(U_333,sK61(U_335)) )
& sK61(U_335) != empty_set
& subset(sK61(U_335),relation_field(U_335)) ) )
& ( ! [U_332] :
( ( disjoint(fiber(U_335,sK60(U_335,U_332)),U_332)
& in(sK60(U_335,U_332),U_332) )
| U_332 = empty_set
| ~ subset(U_332,relation_field(U_335)) )
| ~ well_founded_relation(U_335) ) )
| ~ relation(U_335) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_334,sK61(U_335))],[f_48_3]) ).
fof(f_48_5,plain,
( ! [U_333,U_335] :
( ~ disjoint(fiber(U_335,U_333),sK61(U_335))
| ~ in(U_333,sK61(U_335))
| ~ sP95(U_333,U_335) )
& ! [U_333,U_335] :
( sK61(U_335) != empty_set
| ~ sP95(U_333,U_335) )
& ! [U_333,U_335] :
( subset(sK61(U_335),relation_field(U_335))
| ~ sP95(U_333,U_335) )
& ! [U_332,U_335] :
( disjoint(fiber(U_335,sK60(U_335,U_332)),U_332)
| ~ sP94(U_332,U_335) )
& ! [U_332,U_335] :
( in(sK60(U_335,U_332),U_332)
| ~ sP94(U_332,U_335) )
& ! [U_333,U_332,U_335] :
( well_founded_relation(U_335)
| sP95(U_333,U_335)
| ~ sP96(U_333,U_332,U_335) )
& ! [U_333,U_332,U_335] :
( sP94(U_332,U_335)
| U_332 = empty_set
| ~ subset(U_332,relation_field(U_335))
| ~ well_founded_relation(U_335)
| ~ sP96(U_333,U_332,U_335) )
& ! [U_333,U_332,U_335] :
( sP96(U_333,U_332,U_335)
| ~ relation(U_335) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94,sP95,sP96])],[f_48_4]) ).
cnf(f_48_6,plain,
( sP96(U_333,U_332,U_335)
| ~ relation(U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_7,plain,
( sP94(U_332,U_335)
| U_332 = empty_set
| ~ subset(U_332,relation_field(U_335))
| ~ well_founded_relation(U_335)
| ~ sP96(U_333,U_332,U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_8,plain,
( well_founded_relation(U_335)
| sP95(U_333,U_335)
| ~ sP96(U_333,U_332,U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_9,plain,
( in(sK60(U_335,U_332),U_332)
| ~ sP94(U_332,U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_10,plain,
( disjoint(fiber(U_335,sK60(U_335,U_332)),U_332)
| ~ sP94(U_332,U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_11,plain,
( subset(sK61(U_335),relation_field(U_335))
| ~ sP95(U_333,U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_12,plain,
( sK61(U_335) != empty_set
| ~ sP95(U_333,U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_13,plain,
( ~ disjoint(fiber(U_335,U_333),sK61(U_335))
| ~ in(U_333,sK61(U_335))
| ~ sP95(U_333,U_335) ),
inference(clausify,[status(thm)],[f_48_5]) ).
fof(f_49_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_49_2,plain,
! [U_340,U_339,U_338] :
( ( U_338 = set_union2(U_340,U_339)
| ? [U_337] :
( ( ~ in(U_337,U_338)
& ( in(U_337,U_339)
| in(U_337,U_340) ) )
| ( ~ in(U_337,U_339)
& ~ in(U_337,U_340)
& in(U_337,U_338) ) ) )
& ( ! [U_336] :
( ( in(U_336,U_338)
| ( ~ in(U_336,U_339)
& ~ in(U_336,U_340) ) )
& ( in(U_336,U_339)
| in(U_336,U_340)
| ~ in(U_336,U_338) ) )
| U_338 != set_union2(U_340,U_339) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_350,U_348,U_346] :
( U_346 = set_union2(U_350,U_348)
| ? [U_344] :
( ~ in(U_344,U_346)
& ( in(U_344,U_348)
| in(U_344,U_350) ) )
| ? [U_343] :
( ~ in(U_343,U_348)
& ~ in(U_343,U_350)
& in(U_343,U_346) ) )
& ! [U_349,U_347,U_345] :
( ( ! [U_342] :
( in(U_342,U_345)
| ( ~ in(U_342,U_347)
& ~ in(U_342,U_349) ) )
& ! [U_341] :
( in(U_341,U_347)
| in(U_341,U_349)
| ~ in(U_341,U_345) ) )
| U_345 != set_union2(U_349,U_347) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_350,U_348,U_346] :
( U_346 = set_union2(U_350,U_348)
| ? [U_344] :
( ~ in(U_344,U_346)
& ( in(U_344,U_348)
| in(U_344,U_350) ) )
| ( ~ in(sK62(U_350,U_348,U_346),U_348)
& ~ in(sK62(U_350,U_348,U_346),U_350)
& in(sK62(U_350,U_348,U_346),U_346) ) )
& ! [U_349,U_347,U_345] :
( ( ! [U_342] :
( in(U_342,U_345)
| ( ~ in(U_342,U_347)
& ~ in(U_342,U_349) ) )
& ! [U_341] :
( in(U_341,U_347)
| in(U_341,U_349)
| ~ in(U_341,U_345) ) )
| U_345 != set_union2(U_349,U_347) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_343,sK62(U_350,U_348,U_346))],[f_49_3]) ).
fof(f_49_5,plain,
( ! [U_350,U_348,U_346] :
( U_346 = set_union2(U_350,U_348)
| ( ~ in(sK63(U_350,U_348,U_346),U_346)
& ( in(sK63(U_350,U_348,U_346),U_348)
| in(sK63(U_350,U_348,U_346),U_350) ) )
| ( ~ in(sK62(U_350,U_348,U_346),U_348)
& ~ in(sK62(U_350,U_348,U_346),U_350)
& in(sK62(U_350,U_348,U_346),U_346) ) )
& ! [U_349,U_347,U_345] :
( ( ! [U_342] :
( in(U_342,U_345)
| ( ~ in(U_342,U_347)
& ~ in(U_342,U_349) ) )
& ! [U_341] :
( in(U_341,U_347)
| in(U_341,U_349)
| ~ in(U_341,U_345) ) )
| U_345 != set_union2(U_349,U_347) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_344,sK63(U_350,U_348,U_346))],[f_49_4]) ).
fof(f_49_6,plain,
( ! [U_348,U_350,U_346] :
( ~ in(sK63(U_350,U_348,U_346),U_346)
| ~ sP100(U_348,U_350,U_346) )
& ! [U_348,U_350,U_346] :
( in(sK63(U_350,U_348,U_346),U_348)
| in(sK63(U_350,U_348,U_346),U_350)
| ~ sP100(U_348,U_350,U_346) )
& ! [U_348,U_350,U_346] :
( ~ in(sK62(U_350,U_348,U_346),U_348)
| ~ sP99(U_348,U_350,U_346) )
& ! [U_348,U_350,U_346] :
( ~ in(sK62(U_350,U_348,U_346),U_350)
| ~ sP99(U_348,U_350,U_346) )
& ! [U_348,U_350,U_346] :
( in(sK62(U_350,U_348,U_346),U_346)
| ~ sP99(U_348,U_350,U_346) )
& ! [U_347,U_342,U_349] :
( ~ in(U_342,U_347)
| ~ sP97(U_347,U_342,U_349) )
& ! [U_347,U_342,U_349] :
( ~ in(U_342,U_349)
| ~ sP97(U_347,U_342,U_349) )
& ! [U_341,U_347,U_342,U_349,U_345] :
( in(U_342,U_345)
| sP97(U_347,U_342,U_349)
| ~ sP98(U_341,U_347,U_342,U_349,U_345) )
& ! [U_341,U_347,U_342,U_349,U_345] :
( in(U_341,U_347)
| in(U_341,U_349)
| ~ in(U_341,U_345)
| ~ sP98(U_341,U_347,U_342,U_349,U_345) )
& ! [U_348,U_350,U_346] :
( U_346 = set_union2(U_350,U_348)
| sP100(U_348,U_350,U_346)
| sP99(U_348,U_350,U_346) )
& ! [U_341,U_347,U_342,U_349,U_345] :
( sP98(U_341,U_347,U_342,U_349,U_345)
| U_345 != set_union2(U_349,U_347) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97,sP98,sP99,sP100])],[f_49_5]) ).
cnf(f_49_7,plain,
( sP98(U_341,U_347,U_342,U_349,U_345)
| U_345 != set_union2(U_349,U_347) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_8,plain,
( U_346 = set_union2(U_350,U_348)
| sP100(U_348,U_350,U_346)
| sP99(U_348,U_350,U_346) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_9,plain,
( in(U_341,U_347)
| in(U_341,U_349)
| ~ in(U_341,U_345)
| ~ sP98(U_341,U_347,U_342,U_349,U_345) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_10,plain,
( in(U_342,U_345)
| sP97(U_347,U_342,U_349)
| ~ sP98(U_341,U_347,U_342,U_349,U_345) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_11,plain,
( ~ in(U_342,U_349)
| ~ sP97(U_347,U_342,U_349) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_12,plain,
( ~ in(U_342,U_347)
| ~ sP97(U_347,U_342,U_349) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_13,plain,
( in(sK62(U_350,U_348,U_346),U_346)
| ~ sP99(U_348,U_350,U_346) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_14,plain,
( ~ in(sK62(U_350,U_348,U_346),U_350)
| ~ sP99(U_348,U_350,U_346) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_15,plain,
( ~ in(sK62(U_350,U_348,U_346),U_348)
| ~ sP99(U_348,U_350,U_346) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_16,plain,
( in(sK63(U_350,U_348,U_346),U_348)
| in(sK63(U_350,U_348,U_346),U_350)
| ~ sP100(U_348,U_350,U_346) ),
inference(clausify,[status(thm)],[f_49_6]) ).
cnf(f_49_17,plain,
( ~ in(sK63(U_350,U_348,U_346),U_346)
| ~ sP100(U_348,U_350,U_346) ),
inference(clausify,[status(thm)],[f_49_6]) ).
fof(f_50_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_50_2,plain,
! [U_363,U_362,U_361] :
( ( U_361 = cartesian_product2(U_363,U_362)
| ? [U_360] :
( ( ~ in(U_360,U_361)
& ? [U_359,U_358] :
( U_360 = ordered_pair(U_359,U_358)
& in(U_358,U_362)
& in(U_359,U_363) ) )
| ( ! [U_357,U_356] :
( U_360 != ordered_pair(U_357,U_356)
| ~ in(U_356,U_362)
| ~ in(U_357,U_363) )
& in(U_360,U_361) ) ) )
& ( ! [U_355] :
( ( in(U_355,U_361)
| ! [U_354,U_353] :
( U_355 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_362)
| ~ in(U_354,U_363) ) )
& ( ? [U_352,U_351] :
( U_355 = ordered_pair(U_352,U_351)
& in(U_351,U_362)
& in(U_352,U_363) )
| ~ in(U_355,U_361) ) )
| U_361 != cartesian_product2(U_363,U_362) ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ! [U_373,U_371,U_369] :
( U_369 = cartesian_product2(U_373,U_371)
| ? [U_367] :
( ~ in(U_367,U_369)
& ? [U_359] :
( ? [U_358] :
( U_367 = ordered_pair(U_359,U_358)
& in(U_358,U_371) )
& in(U_359,U_373) ) )
| ? [U_366] :
( ! [U_357] :
( ! [U_356] :
( U_366 != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371) )
| ~ in(U_357,U_373) )
& in(U_366,U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ! [U_354] :
( ! [U_353] :
( U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370) )
| ~ in(U_354,U_372) ) )
& ! [U_364] :
( ? [U_352] :
( ? [U_351] :
( U_364 = ordered_pair(U_352,U_351)
& in(U_351,U_370) )
& in(U_352,U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
fof(f_50_4,plain,
( ! [U_373,U_371,U_369] :
( U_369 = cartesian_product2(U_373,U_371)
| ? [U_367] :
( ~ in(U_367,U_369)
& ? [U_359] :
( ? [U_358] :
( U_367 = ordered_pair(U_359,U_358)
& in(U_358,U_371) )
& in(U_359,U_373) ) )
| ? [U_366] :
( ! [U_357] :
( ! [U_356] :
( U_366 != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371) )
| ~ in(U_357,U_373) )
& in(U_366,U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ! [U_354] :
( ! [U_353] :
( U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370) )
| ~ in(U_354,U_372) ) )
& ! [U_364] :
( ( ? [U_351] :
( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),U_351)
& in(U_351,U_370) )
& in(sK64(U_372,U_370,U_368,U_364),U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_352,sK64(U_372,U_370,U_368,U_364))],[f_50_3]) ).
fof(f_50_5,plain,
( ! [U_373,U_371,U_369] :
( U_369 = cartesian_product2(U_373,U_371)
| ? [U_367] :
( ~ in(U_367,U_369)
& ? [U_359] :
( ? [U_358] :
( U_367 = ordered_pair(U_359,U_358)
& in(U_358,U_371) )
& in(U_359,U_373) ) )
| ? [U_366] :
( ! [U_357] :
( ! [U_356] :
( U_366 != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371) )
| ~ in(U_357,U_373) )
& in(U_366,U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ! [U_354] :
( ! [U_353] :
( U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370) )
| ~ in(U_354,U_372) ) )
& ! [U_364] :
( ( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),sK65(U_372,U_370,U_368,U_364))
& in(sK65(U_372,U_370,U_368,U_364),U_370)
& in(sK64(U_372,U_370,U_368,U_364),U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_351,sK65(U_372,U_370,U_368,U_364))],[f_50_4]) ).
fof(f_50_6,plain,
( ! [U_373,U_371,U_369] :
( U_369 = cartesian_product2(U_373,U_371)
| ? [U_367] :
( ~ in(U_367,U_369)
& ? [U_359] :
( ? [U_358] :
( U_367 = ordered_pair(U_359,U_358)
& in(U_358,U_371) )
& in(U_359,U_373) ) )
| ( ! [U_357] :
( ! [U_356] :
( sK66(U_373,U_371,U_369) != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371) )
| ~ in(U_357,U_373) )
& in(sK66(U_373,U_371,U_369),U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ! [U_354] :
( ! [U_353] :
( U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370) )
| ~ in(U_354,U_372) ) )
& ! [U_364] :
( ( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),sK65(U_372,U_370,U_368,U_364))
& in(sK65(U_372,U_370,U_368,U_364),U_370)
& in(sK64(U_372,U_370,U_368,U_364),U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_366,sK66(U_373,U_371,U_369))],[f_50_5]) ).
fof(f_50_7,plain,
( ! [U_373,U_371,U_369] :
( U_369 = cartesian_product2(U_373,U_371)
| ( ~ in(sK67(U_373,U_371,U_369),U_369)
& ? [U_359] :
( ? [U_358] :
( sK67(U_373,U_371,U_369) = ordered_pair(U_359,U_358)
& in(U_358,U_371) )
& in(U_359,U_373) ) )
| ( ! [U_357] :
( ! [U_356] :
( sK66(U_373,U_371,U_369) != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371) )
| ~ in(U_357,U_373) )
& in(sK66(U_373,U_371,U_369),U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ! [U_354] :
( ! [U_353] :
( U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370) )
| ~ in(U_354,U_372) ) )
& ! [U_364] :
( ( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),sK65(U_372,U_370,U_368,U_364))
& in(sK65(U_372,U_370,U_368,U_364),U_370)
& in(sK64(U_372,U_370,U_368,U_364),U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_367,sK67(U_373,U_371,U_369))],[f_50_6]) ).
fof(f_50_8,plain,
( ! [U_373,U_371,U_369] :
( U_369 = cartesian_product2(U_373,U_371)
| ( ~ in(sK67(U_373,U_371,U_369),U_369)
& ? [U_358] :
( sK67(U_373,U_371,U_369) = ordered_pair(sK68(U_373,U_371,U_369),U_358)
& in(U_358,U_371) )
& in(sK68(U_373,U_371,U_369),U_373) )
| ( ! [U_357] :
( ! [U_356] :
( sK66(U_373,U_371,U_369) != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371) )
| ~ in(U_357,U_373) )
& in(sK66(U_373,U_371,U_369),U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ! [U_354] :
( ! [U_353] :
( U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370) )
| ~ in(U_354,U_372) ) )
& ! [U_364] :
( ( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),sK65(U_372,U_370,U_368,U_364))
& in(sK65(U_372,U_370,U_368,U_364),U_370)
& in(sK64(U_372,U_370,U_368,U_364),U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_359,sK68(U_373,U_371,U_369))],[f_50_7]) ).
fof(f_50_9,plain,
( ! [U_373,U_371,U_369] :
( U_369 = cartesian_product2(U_373,U_371)
| ( ~ in(sK67(U_373,U_371,U_369),U_369)
& sK67(U_373,U_371,U_369) = ordered_pair(sK68(U_373,U_371,U_369),sK69(U_373,U_371,U_369))
& in(sK69(U_373,U_371,U_369),U_371)
& in(sK68(U_373,U_371,U_369),U_373) )
| ( ! [U_357] :
( ! [U_356] :
( sK66(U_373,U_371,U_369) != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371) )
| ~ in(U_357,U_373) )
& in(sK66(U_373,U_371,U_369),U_369) ) )
& ! [U_372,U_370,U_368] :
( ( ! [U_365] :
( in(U_365,U_368)
| ! [U_354] :
( ! [U_353] :
( U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370) )
| ~ in(U_354,U_372) ) )
& ! [U_364] :
( ( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),sK65(U_372,U_370,U_368,U_364))
& in(sK65(U_372,U_370,U_368,U_364),U_370)
& in(sK64(U_372,U_370,U_368,U_364),U_372) )
| ~ in(U_364,U_368) ) )
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_358,sK69(U_373,U_371,U_369))],[f_50_8]) ).
fof(f_50_10,plain,
( ! [U_369,U_371,U_373] :
( ~ in(sK67(U_373,U_371,U_369),U_369)
| ~ sP104(U_369,U_371,U_373) )
& ! [U_369,U_371,U_373] :
( sK67(U_373,U_371,U_369) = ordered_pair(sK68(U_373,U_371,U_369),sK69(U_373,U_371,U_369))
| ~ sP104(U_369,U_371,U_373) )
& ! [U_369,U_371,U_373] :
( in(sK69(U_373,U_371,U_369),U_371)
| ~ sP104(U_369,U_371,U_373) )
& ! [U_369,U_371,U_373] :
( in(sK68(U_373,U_371,U_369),U_373)
| ~ sP104(U_369,U_371,U_373) )
& ! [U_357,U_369,U_356,U_371,U_373] :
( sK66(U_373,U_371,U_369) != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371)
| ~ in(U_357,U_373)
| ~ sP103(U_357,U_369,U_356,U_371,U_373) )
& ! [U_357,U_369,U_356,U_371,U_373] :
( in(sK66(U_373,U_371,U_369),U_369)
| ~ sP103(U_357,U_369,U_356,U_371,U_373) )
& ! [U_364,U_370,U_368,U_372] :
( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),sK65(U_372,U_370,U_368,U_364))
| ~ sP101(U_364,U_370,U_368,U_372) )
& ! [U_364,U_370,U_368,U_372] :
( in(sK65(U_372,U_370,U_368,U_364),U_370)
| ~ sP101(U_364,U_370,U_368,U_372) )
& ! [U_364,U_370,U_368,U_372] :
( in(sK64(U_372,U_370,U_368,U_364),U_372)
| ~ sP101(U_364,U_370,U_368,U_372) )
& ! [U_353,U_364,U_365,U_354,U_370,U_368,U_372] :
( in(U_365,U_368)
| U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370)
| ~ in(U_354,U_372)
| ~ sP102(U_353,U_364,U_365,U_354,U_370,U_368,U_372) )
& ! [U_353,U_364,U_365,U_354,U_370,U_368,U_372] :
( sP101(U_364,U_370,U_368,U_372)
| ~ in(U_364,U_368)
| ~ sP102(U_353,U_364,U_365,U_354,U_370,U_368,U_372) )
& ! [U_357,U_369,U_356,U_371,U_373] :
( U_369 = cartesian_product2(U_373,U_371)
| sP104(U_369,U_371,U_373)
| sP103(U_357,U_369,U_356,U_371,U_373) )
& ! [U_353,U_364,U_365,U_354,U_370,U_368,U_372] :
( sP102(U_353,U_364,U_365,U_354,U_370,U_368,U_372)
| U_368 != cartesian_product2(U_372,U_370) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101,sP102,sP103,sP104])],[f_50_9]) ).
cnf(f_50_11,plain,
( sP102(U_353,U_364,U_365,U_354,U_370,U_368,U_372)
| U_368 != cartesian_product2(U_372,U_370) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_12,plain,
( U_369 = cartesian_product2(U_373,U_371)
| sP104(U_369,U_371,U_373)
| sP103(U_357,U_369,U_356,U_371,U_373) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_13,plain,
( sP101(U_364,U_370,U_368,U_372)
| ~ in(U_364,U_368)
| ~ sP102(U_353,U_364,U_365,U_354,U_370,U_368,U_372) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_14,plain,
( in(U_365,U_368)
| U_365 != ordered_pair(U_354,U_353)
| ~ in(U_353,U_370)
| ~ in(U_354,U_372)
| ~ sP102(U_353,U_364,U_365,U_354,U_370,U_368,U_372) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_15,plain,
( in(sK64(U_372,U_370,U_368,U_364),U_372)
| ~ sP101(U_364,U_370,U_368,U_372) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_16,plain,
( in(sK65(U_372,U_370,U_368,U_364),U_370)
| ~ sP101(U_364,U_370,U_368,U_372) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_17,plain,
( U_364 = ordered_pair(sK64(U_372,U_370,U_368,U_364),sK65(U_372,U_370,U_368,U_364))
| ~ sP101(U_364,U_370,U_368,U_372) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_18,plain,
( in(sK66(U_373,U_371,U_369),U_369)
| ~ sP103(U_357,U_369,U_356,U_371,U_373) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_19,plain,
( sK66(U_373,U_371,U_369) != ordered_pair(U_357,U_356)
| ~ in(U_356,U_371)
| ~ in(U_357,U_373)
| ~ sP103(U_357,U_369,U_356,U_371,U_373) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_20,plain,
( in(sK68(U_373,U_371,U_369),U_373)
| ~ sP104(U_369,U_371,U_373) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_21,plain,
( in(sK69(U_373,U_371,U_369),U_371)
| ~ sP104(U_369,U_371,U_373) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_22,plain,
( sK67(U_373,U_371,U_369) = ordered_pair(sK68(U_373,U_371,U_369),sK69(U_373,U_371,U_369))
| ~ sP104(U_369,U_371,U_373) ),
inference(clausify,[status(thm)],[f_50_10]) ).
cnf(f_50_23,plain,
( ~ in(sK67(U_373,U_371,U_369),U_369)
| ~ sP104(U_369,U_371,U_373) ),
inference(clausify,[status(thm)],[f_50_10]) ).
fof(f_51_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_51_2,plain,
! [U_378] :
( ( epsilon_connected(U_378)
| ? [U_377,U_376] :
( ~ in(U_376,U_377)
& U_377 != U_376
& ~ in(U_377,U_376)
& in(U_376,U_378)
& in(U_377,U_378) ) )
& ( ! [U_375,U_374] :
( in(U_374,U_375)
| U_375 = U_374
| in(U_375,U_374)
| ~ in(U_374,U_378)
| ~ in(U_375,U_378) )
| ~ epsilon_connected(U_378) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_380] :
( epsilon_connected(U_380)
| ? [U_377] :
( ? [U_376] :
( ~ in(U_376,U_377)
& U_377 != U_376
& ~ in(U_377,U_376)
& in(U_376,U_380) )
& in(U_377,U_380) ) )
& ! [U_379] :
( ! [U_375] :
( ! [U_374] :
( in(U_374,U_375)
| U_375 = U_374
| in(U_375,U_374)
| ~ in(U_374,U_379) )
| ~ in(U_375,U_379) )
| ~ epsilon_connected(U_379) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_380] :
( epsilon_connected(U_380)
| ( ? [U_376] :
( ~ in(U_376,sK70(U_380))
& sK70(U_380) != U_376
& ~ in(sK70(U_380),U_376)
& in(U_376,U_380) )
& in(sK70(U_380),U_380) ) )
& ! [U_379] :
( ! [U_375] :
( ! [U_374] :
( in(U_374,U_375)
| U_375 = U_374
| in(U_375,U_374)
| ~ in(U_374,U_379) )
| ~ in(U_375,U_379) )
| ~ epsilon_connected(U_379) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_377,sK70(U_380))],[f_51_3]) ).
fof(f_51_5,plain,
( ! [U_380] :
( epsilon_connected(U_380)
| ( ~ in(sK71(U_380),sK70(U_380))
& sK70(U_380) != sK71(U_380)
& ~ in(sK70(U_380),sK71(U_380))
& in(sK71(U_380),U_380)
& in(sK70(U_380),U_380) ) )
& ! [U_379] :
( ! [U_375] :
( ! [U_374] :
( in(U_374,U_375)
| U_375 = U_374
| in(U_375,U_374)
| ~ in(U_374,U_379) )
| ~ in(U_375,U_379) )
| ~ epsilon_connected(U_379) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_376,sK71(U_380))],[f_51_4]) ).
fof(f_51_6,plain,
( ! [U_380] :
( ~ in(sK71(U_380),sK70(U_380))
| ~ sP105(U_380) )
& ! [U_380] :
( sK70(U_380) != sK71(U_380)
| ~ sP105(U_380) )
& ! [U_380] :
( ~ in(sK70(U_380),sK71(U_380))
| ~ sP105(U_380) )
& ! [U_380] :
( in(sK71(U_380),U_380)
| ~ sP105(U_380) )
& ! [U_380] :
( in(sK70(U_380),U_380)
| ~ sP105(U_380) )
& ! [U_380] :
( epsilon_connected(U_380)
| sP105(U_380) )
& ! [U_374,U_375,U_379] :
( in(U_374,U_375)
| U_375 = U_374
| in(U_375,U_374)
| ~ in(U_374,U_379)
| ~ in(U_375,U_379)
| ~ epsilon_connected(U_379) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_51_5]) ).
cnf(f_51_7,plain,
( in(U_374,U_375)
| U_375 = U_374
| in(U_375,U_374)
| ~ in(U_374,U_379)
| ~ in(U_375,U_379)
| ~ epsilon_connected(U_379) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_8,plain,
( epsilon_connected(U_380)
| sP105(U_380) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_9,plain,
( in(sK70(U_380),U_380)
| ~ sP105(U_380) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_10,plain,
( in(sK71(U_380),U_380)
| ~ sP105(U_380) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_11,plain,
( ~ in(sK70(U_380),sK71(U_380))
| ~ sP105(U_380) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_12,plain,
( sK70(U_380) != sK71(U_380)
| ~ sP105(U_380) ),
inference(clausify,[status(thm)],[f_51_6]) ).
cnf(f_51_13,plain,
( ~ in(sK71(U_380),sK70(U_380))
| ~ sP105(U_380) ),
inference(clausify,[status(thm)],[f_51_6]) ).
fof(f_52_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_52_2,plain,
! [U_386] :
( ! [U_385] :
( ( ( subset(U_386,U_385)
| ? [U_384,U_383] :
( ~ in(ordered_pair(U_384,U_383),U_385)
& in(ordered_pair(U_384,U_383),U_386) ) )
& ( ! [U_382,U_381] :
( in(ordered_pair(U_382,U_381),U_385)
| ~ in(ordered_pair(U_382,U_381),U_386) )
| ~ subset(U_386,U_385) ) )
| ~ relation(U_385) )
| ~ relation(U_386) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_386] :
( ! [U_385] :
( ( ( subset(U_386,U_385)
| ? [U_383] :
( ~ in(ordered_pair(sK72(U_386,U_385),U_383),U_385)
& in(ordered_pair(sK72(U_386,U_385),U_383),U_386) ) )
& ( ! [U_382,U_381] :
( in(ordered_pair(U_382,U_381),U_385)
| ~ in(ordered_pair(U_382,U_381),U_386) )
| ~ subset(U_386,U_385) ) )
| ~ relation(U_385) )
| ~ relation(U_386) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_384,sK72(U_386,U_385))],[f_52_2]) ).
fof(f_52_4,plain,
! [U_386] :
( ! [U_385] :
( ( ( subset(U_386,U_385)
| ( ~ in(ordered_pair(sK72(U_386,U_385),sK73(U_386,U_385)),U_385)
& in(ordered_pair(sK72(U_386,U_385),sK73(U_386,U_385)),U_386) ) )
& ( ! [U_382,U_381] :
( in(ordered_pair(U_382,U_381),U_385)
| ~ in(ordered_pair(U_382,U_381),U_386) )
| ~ subset(U_386,U_385) ) )
| ~ relation(U_385) )
| ~ relation(U_386) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_383,sK73(U_386,U_385))],[f_52_3]) ).
fof(f_52_5,plain,
( ! [U_385,U_386] :
( ~ in(ordered_pair(sK72(U_386,U_385),sK73(U_386,U_385)),U_385)
| ~ sP106(U_385,U_386) )
& ! [U_385,U_386] :
( in(ordered_pair(sK72(U_386,U_385),sK73(U_386,U_385)),U_386)
| ~ sP106(U_385,U_386) )
& ! [U_385,U_386,U_381,U_382] :
( subset(U_386,U_385)
| sP106(U_385,U_386)
| ~ sP107(U_385,U_386,U_381,U_382) )
& ! [U_385,U_386,U_381,U_382] :
( in(ordered_pair(U_382,U_381),U_385)
| ~ in(ordered_pair(U_382,U_381),U_386)
| ~ subset(U_386,U_385)
| ~ sP107(U_385,U_386,U_381,U_382) )
& ! [U_385,U_386,U_381,U_382] :
( sP107(U_385,U_386,U_381,U_382)
| ~ relation(U_385)
| ~ relation(U_386) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106,sP107])],[f_52_4]) ).
cnf(f_52_6,plain,
( sP107(U_385,U_386,U_381,U_382)
| ~ relation(U_385)
| ~ relation(U_386) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_7,plain,
( in(ordered_pair(U_382,U_381),U_385)
| ~ in(ordered_pair(U_382,U_381),U_386)
| ~ subset(U_386,U_385)
| ~ sP107(U_385,U_386,U_381,U_382) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_8,plain,
( subset(U_386,U_385)
| sP106(U_385,U_386)
| ~ sP107(U_385,U_386,U_381,U_382) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_9,plain,
( in(ordered_pair(sK72(U_386,U_385),sK73(U_386,U_385)),U_386)
| ~ sP106(U_385,U_386) ),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_10,plain,
( ~ in(ordered_pair(sK72(U_386,U_385),sK73(U_386,U_385)),U_385)
| ~ sP106(U_385,U_386) ),
inference(clausify,[status(thm)],[f_52_5]) ).
fof(f_53_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_53_2,plain,
! [U_390,U_389] :
( ( subset(U_390,U_389)
| ? [U_388] :
( ~ in(U_388,U_389)
& in(U_388,U_390) ) )
& ( ! [U_387] :
( in(U_387,U_389)
| ~ in(U_387,U_390) )
| ~ subset(U_390,U_389) ) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ! [U_394,U_392] :
( subset(U_394,U_392)
| ? [U_388] :
( ~ in(U_388,U_392)
& in(U_388,U_394) ) )
& ! [U_393,U_391] :
( ! [U_387] :
( in(U_387,U_391)
| ~ in(U_387,U_393) )
| ~ subset(U_393,U_391) ) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
( ! [U_394,U_392] :
( subset(U_394,U_392)
| ( ~ in(sK74(U_394,U_392),U_392)
& in(sK74(U_394,U_392),U_394) ) )
& ! [U_393,U_391] :
( ! [U_387] :
( in(U_387,U_391)
| ~ in(U_387,U_393) )
| ~ subset(U_393,U_391) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_388,sK74(U_394,U_392))],[f_53_3]) ).
fof(f_53_5,plain,
( ! [U_394,U_392] :
( ~ in(sK74(U_394,U_392),U_392)
| ~ sP108(U_394,U_392) )
& ! [U_394,U_392] :
( in(sK74(U_394,U_392),U_394)
| ~ sP108(U_394,U_392) )
& ! [U_394,U_392] :
( subset(U_394,U_392)
| sP108(U_394,U_392) )
& ! [U_387,U_393,U_391] :
( in(U_387,U_391)
| ~ in(U_387,U_393)
| ~ subset(U_393,U_391) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_53_4]) ).
cnf(f_53_6,plain,
( in(U_387,U_391)
| ~ in(U_387,U_393)
| ~ subset(U_393,U_391) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_7,plain,
( subset(U_394,U_392)
| sP108(U_394,U_392) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_8,plain,
( in(sK74(U_394,U_392),U_394)
| ~ sP108(U_394,U_392) ),
inference(clausify,[status(thm)],[f_53_5]) ).
cnf(f_53_9,plain,
( ~ in(sK74(U_394,U_392),U_392)
| ~ sP108(U_394,U_392) ),
inference(clausify,[status(thm)],[f_53_5]) ).
fof(f_54_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_54_2,plain,
! [U_400] :
( ! [U_399] :
( ( is_well_founded_in(U_400,U_399)
| ? [U_398] :
( ! [U_397] :
( ~ disjoint(fiber(U_400,U_397),U_398)
| ~ in(U_397,U_398) )
& U_398 != empty_set
& subset(U_398,U_399) ) )
& ( ! [U_396] :
( ? [U_395] :
( disjoint(fiber(U_400,U_395),U_396)
& in(U_395,U_396) )
| U_396 = empty_set
| ~ subset(U_396,U_399) )
| ~ is_well_founded_in(U_400,U_399) ) )
| ~ relation(U_400) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_400] :
( ( ! [U_402] :
( is_well_founded_in(U_400,U_402)
| ? [U_398] :
( ! [U_397] :
( ~ disjoint(fiber(U_400,U_397),U_398)
| ~ in(U_397,U_398) )
& U_398 != empty_set
& subset(U_398,U_402) ) )
& ! [U_401] :
( ! [U_396] :
( ? [U_395] :
( disjoint(fiber(U_400,U_395),U_396)
& in(U_395,U_396) )
| U_396 = empty_set
| ~ subset(U_396,U_401) )
| ~ is_well_founded_in(U_400,U_401) ) )
| ~ relation(U_400) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_400] :
( ( ! [U_402] :
( is_well_founded_in(U_400,U_402)
| ? [U_398] :
( ! [U_397] :
( ~ disjoint(fiber(U_400,U_397),U_398)
| ~ in(U_397,U_398) )
& U_398 != empty_set
& subset(U_398,U_402) ) )
& ! [U_401] :
( ! [U_396] :
( ( disjoint(fiber(U_400,sK75(U_400,U_401,U_396)),U_396)
& in(sK75(U_400,U_401,U_396),U_396) )
| U_396 = empty_set
| ~ subset(U_396,U_401) )
| ~ is_well_founded_in(U_400,U_401) ) )
| ~ relation(U_400) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_395,sK75(U_400,U_401,U_396))],[f_54_3]) ).
fof(f_54_5,plain,
! [U_400] :
( ( ! [U_402] :
( is_well_founded_in(U_400,U_402)
| ( ! [U_397] :
( ~ disjoint(fiber(U_400,U_397),sK76(U_400,U_402))
| ~ in(U_397,sK76(U_400,U_402)) )
& sK76(U_400,U_402) != empty_set
& subset(sK76(U_400,U_402),U_402) ) )
& ! [U_401] :
( ! [U_396] :
( ( disjoint(fiber(U_400,sK75(U_400,U_401,U_396)),U_396)
& in(sK75(U_400,U_401,U_396),U_396) )
| U_396 = empty_set
| ~ subset(U_396,U_401) )
| ~ is_well_founded_in(U_400,U_401) ) )
| ~ relation(U_400) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_398,sK76(U_400,U_402))],[f_54_4]) ).
fof(f_54_6,plain,
( ! [U_397,U_400,U_402] :
( ~ disjoint(fiber(U_400,U_397),sK76(U_400,U_402))
| ~ in(U_397,sK76(U_400,U_402))
| ~ sP110(U_397,U_400,U_402) )
& ! [U_397,U_400,U_402] :
( sK76(U_400,U_402) != empty_set
| ~ sP110(U_397,U_400,U_402) )
& ! [U_397,U_400,U_402] :
( subset(sK76(U_400,U_402),U_402)
| ~ sP110(U_397,U_400,U_402) )
& ! [U_400,U_401,U_396] :
( disjoint(fiber(U_400,sK75(U_400,U_401,U_396)),U_396)
| ~ sP109(U_400,U_401,U_396) )
& ! [U_400,U_401,U_396] :
( in(sK75(U_400,U_401,U_396),U_396)
| ~ sP109(U_400,U_401,U_396) )
& ! [U_397,U_400,U_402,U_401,U_396] :
( is_well_founded_in(U_400,U_402)
| sP110(U_397,U_400,U_402)
| ~ sP111(U_397,U_400,U_402,U_401,U_396) )
& ! [U_397,U_400,U_402,U_401,U_396] :
( sP109(U_400,U_401,U_396)
| U_396 = empty_set
| ~ subset(U_396,U_401)
| ~ is_well_founded_in(U_400,U_401)
| ~ sP111(U_397,U_400,U_402,U_401,U_396) )
& ! [U_397,U_400,U_402,U_401,U_396] :
( sP111(U_397,U_400,U_402,U_401,U_396)
| ~ relation(U_400) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109,sP110,sP111])],[f_54_5]) ).
cnf(f_54_7,plain,
( sP111(U_397,U_400,U_402,U_401,U_396)
| ~ relation(U_400) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_8,plain,
( sP109(U_400,U_401,U_396)
| U_396 = empty_set
| ~ subset(U_396,U_401)
| ~ is_well_founded_in(U_400,U_401)
| ~ sP111(U_397,U_400,U_402,U_401,U_396) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_9,plain,
( is_well_founded_in(U_400,U_402)
| sP110(U_397,U_400,U_402)
| ~ sP111(U_397,U_400,U_402,U_401,U_396) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_10,plain,
( in(sK75(U_400,U_401,U_396),U_396)
| ~ sP109(U_400,U_401,U_396) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_11,plain,
( disjoint(fiber(U_400,sK75(U_400,U_401,U_396)),U_396)
| ~ sP109(U_400,U_401,U_396) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_12,plain,
( subset(sK76(U_400,U_402),U_402)
| ~ sP110(U_397,U_400,U_402) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_13,plain,
( sK76(U_400,U_402) != empty_set
| ~ sP110(U_397,U_400,U_402) ),
inference(clausify,[status(thm)],[f_54_6]) ).
cnf(f_54_14,plain,
( ~ disjoint(fiber(U_400,U_397),sK76(U_400,U_402))
| ~ in(U_397,sK76(U_400,U_402))
| ~ sP110(U_397,U_400,U_402) ),
inference(clausify,[status(thm)],[f_54_6]) ).
fof(f_55_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_55_2,plain,
! [U_407,U_406,U_405] :
( ( U_405 = set_intersection2(U_407,U_406)
| ? [U_404] :
( ( ~ in(U_404,U_405)
& in(U_404,U_406)
& in(U_404,U_407) )
| ( ( ~ in(U_404,U_406)
| ~ in(U_404,U_407) )
& in(U_404,U_405) ) ) )
& ( ! [U_403] :
( ( in(U_403,U_405)
| ~ in(U_403,U_406)
| ~ in(U_403,U_407) )
& ( ( in(U_403,U_406)
& in(U_403,U_407) )
| ~ in(U_403,U_405) ) )
| U_405 != set_intersection2(U_407,U_406) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_417,U_415,U_413] :
( U_413 = set_intersection2(U_417,U_415)
| ? [U_411] :
( ~ in(U_411,U_413)
& in(U_411,U_415)
& in(U_411,U_417) )
| ? [U_410] :
( ( ~ in(U_410,U_415)
| ~ in(U_410,U_417) )
& in(U_410,U_413) ) )
& ! [U_416,U_414,U_412] :
( ( ! [U_409] :
( in(U_409,U_412)
| ~ in(U_409,U_414)
| ~ in(U_409,U_416) )
& ! [U_408] :
( ( in(U_408,U_414)
& in(U_408,U_416) )
| ~ in(U_408,U_412) ) )
| U_412 != set_intersection2(U_416,U_414) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
( ! [U_417,U_415,U_413] :
( U_413 = set_intersection2(U_417,U_415)
| ? [U_411] :
( ~ in(U_411,U_413)
& in(U_411,U_415)
& in(U_411,U_417) )
| ( ( ~ in(sK77(U_417,U_415,U_413),U_415)
| ~ in(sK77(U_417,U_415,U_413),U_417) )
& in(sK77(U_417,U_415,U_413),U_413) ) )
& ! [U_416,U_414,U_412] :
( ( ! [U_409] :
( in(U_409,U_412)
| ~ in(U_409,U_414)
| ~ in(U_409,U_416) )
& ! [U_408] :
( ( in(U_408,U_414)
& in(U_408,U_416) )
| ~ in(U_408,U_412) ) )
| U_412 != set_intersection2(U_416,U_414) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_410,sK77(U_417,U_415,U_413))],[f_55_3]) ).
fof(f_55_5,plain,
( ! [U_417,U_415,U_413] :
( U_413 = set_intersection2(U_417,U_415)
| ( ~ in(sK78(U_417,U_415,U_413),U_413)
& in(sK78(U_417,U_415,U_413),U_415)
& in(sK78(U_417,U_415,U_413),U_417) )
| ( ( ~ in(sK77(U_417,U_415,U_413),U_415)
| ~ in(sK77(U_417,U_415,U_413),U_417) )
& in(sK77(U_417,U_415,U_413),U_413) ) )
& ! [U_416,U_414,U_412] :
( ( ! [U_409] :
( in(U_409,U_412)
| ~ in(U_409,U_414)
| ~ in(U_409,U_416) )
& ! [U_408] :
( ( in(U_408,U_414)
& in(U_408,U_416) )
| ~ in(U_408,U_412) ) )
| U_412 != set_intersection2(U_416,U_414) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_411,sK78(U_417,U_415,U_413))],[f_55_4]) ).
fof(f_55_6,plain,
( ! [U_417,U_415,U_413] :
( ~ in(sK78(U_417,U_415,U_413),U_413)
| ~ sP115(U_417,U_415,U_413) )
& ! [U_417,U_415,U_413] :
( in(sK78(U_417,U_415,U_413),U_415)
| ~ sP115(U_417,U_415,U_413) )
& ! [U_417,U_415,U_413] :
( in(sK78(U_417,U_415,U_413),U_417)
| ~ sP115(U_417,U_415,U_413) )
& ! [U_417,U_415,U_413] :
( ~ in(sK77(U_417,U_415,U_413),U_415)
| ~ in(sK77(U_417,U_415,U_413),U_417)
| ~ sP114(U_417,U_415,U_413) )
& ! [U_417,U_415,U_413] :
( in(sK77(U_417,U_415,U_413),U_413)
| ~ sP114(U_417,U_415,U_413) )
& ! [U_408,U_416,U_414] :
( in(U_408,U_414)
| ~ sP112(U_408,U_416,U_414) )
& ! [U_408,U_416,U_414] :
( in(U_408,U_416)
| ~ sP112(U_408,U_416,U_414) )
& ! [U_412,U_409,U_408,U_416,U_414] :
( in(U_409,U_412)
| ~ in(U_409,U_414)
| ~ in(U_409,U_416)
| ~ sP113(U_412,U_409,U_408,U_416,U_414) )
& ! [U_412,U_409,U_408,U_416,U_414] :
( sP112(U_408,U_416,U_414)
| ~ in(U_408,U_412)
| ~ sP113(U_412,U_409,U_408,U_416,U_414) )
& ! [U_417,U_415,U_413] :
( U_413 = set_intersection2(U_417,U_415)
| sP115(U_417,U_415,U_413)
| sP114(U_417,U_415,U_413) )
& ! [U_412,U_409,U_408,U_416,U_414] :
( sP113(U_412,U_409,U_408,U_416,U_414)
| U_412 != set_intersection2(U_416,U_414) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112,sP113,sP114,sP115])],[f_55_5]) ).
cnf(f_55_7,plain,
( sP113(U_412,U_409,U_408,U_416,U_414)
| U_412 != set_intersection2(U_416,U_414) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_8,plain,
( U_413 = set_intersection2(U_417,U_415)
| sP115(U_417,U_415,U_413)
| sP114(U_417,U_415,U_413) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_9,plain,
( sP112(U_408,U_416,U_414)
| ~ in(U_408,U_412)
| ~ sP113(U_412,U_409,U_408,U_416,U_414) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_10,plain,
( in(U_409,U_412)
| ~ in(U_409,U_414)
| ~ in(U_409,U_416)
| ~ sP113(U_412,U_409,U_408,U_416,U_414) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_11,plain,
( in(U_408,U_416)
| ~ sP112(U_408,U_416,U_414) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_12,plain,
( in(U_408,U_414)
| ~ sP112(U_408,U_416,U_414) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_13,plain,
( in(sK77(U_417,U_415,U_413),U_413)
| ~ sP114(U_417,U_415,U_413) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_14,plain,
( ~ in(sK77(U_417,U_415,U_413),U_415)
| ~ in(sK77(U_417,U_415,U_413),U_417)
| ~ sP114(U_417,U_415,U_413) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_15,plain,
( in(sK78(U_417,U_415,U_413),U_417)
| ~ sP115(U_417,U_415,U_413) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_16,plain,
( in(sK78(U_417,U_415,U_413),U_415)
| ~ sP115(U_417,U_415,U_413) ),
inference(clausify,[status(thm)],[f_55_6]) ).
cnf(f_55_17,plain,
( ~ in(sK78(U_417,U_415,U_413),U_413)
| ~ sP115(U_417,U_415,U_413) ),
inference(clausify,[status(thm)],[f_55_6]) ).
fof(f_56_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_56_2,plain,
! [U_420] :
( ! [U_419,U_418] :
( ( ( ( U_418 = apply(U_420,U_419)
| U_418 != empty_set )
& ( U_418 = empty_set
| U_418 != apply(U_420,U_419) ) )
| in(U_419,relation_dom(U_420)) )
& ( ( ( U_418 = apply(U_420,U_419)
| ~ in(ordered_pair(U_419,U_418),U_420) )
& ( in(ordered_pair(U_419,U_418),U_420)
| U_418 != apply(U_420,U_419) ) )
| ~ in(U_419,relation_dom(U_420)) ) )
| ~ function(U_420)
| ~ relation(U_420) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_420] :
( ( ! [U_428] :
( ( ! [U_426] :
( U_426 = apply(U_420,U_428)
| U_426 != empty_set )
& ! [U_425] :
( U_425 = empty_set
| U_425 != apply(U_420,U_428) ) )
| in(U_428,relation_dom(U_420)) )
& ! [U_427] :
( ( ! [U_424] :
( U_424 = apply(U_420,U_427)
| ~ in(ordered_pair(U_427,U_424),U_420) )
& ! [U_423] :
( in(ordered_pair(U_427,U_423),U_420)
| U_423 != apply(U_420,U_427) ) )
| ~ in(U_427,relation_dom(U_420)) ) )
| ~ function(U_420)
| ~ relation(U_420) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
( ! [U_426,U_425,U_428,U_420] :
( U_426 = apply(U_420,U_428)
| U_426 != empty_set
| ~ sP117(U_426,U_425,U_428,U_420) )
& ! [U_426,U_425,U_428,U_420] :
( U_425 = empty_set
| U_425 != apply(U_420,U_428)
| ~ sP117(U_426,U_425,U_428,U_420) )
& ! [U_427,U_423,U_420,U_424] :
( U_424 = apply(U_420,U_427)
| ~ in(ordered_pair(U_427,U_424),U_420)
| ~ sP116(U_427,U_423,U_420,U_424) )
& ! [U_427,U_423,U_420,U_424] :
( in(ordered_pair(U_427,U_423),U_420)
| U_423 != apply(U_420,U_427)
| ~ sP116(U_427,U_423,U_420,U_424) )
& ! [U_427,U_426,U_425,U_423,U_428,U_420,U_424] :
( sP117(U_426,U_425,U_428,U_420)
| in(U_428,relation_dom(U_420))
| ~ sP118(U_427,U_426,U_425,U_423,U_428,U_420,U_424) )
& ! [U_427,U_426,U_425,U_423,U_428,U_420,U_424] :
( sP116(U_427,U_423,U_420,U_424)
| ~ in(U_427,relation_dom(U_420))
| ~ sP118(U_427,U_426,U_425,U_423,U_428,U_420,U_424) )
& ! [U_427,U_426,U_425,U_423,U_428,U_420,U_424] :
( sP118(U_427,U_426,U_425,U_423,U_428,U_420,U_424)
| ~ function(U_420)
| ~ relation(U_420) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116,sP117,sP118])],[f_56_3]) ).
cnf(f_56_5,plain,
( sP118(U_427,U_426,U_425,U_423,U_428,U_420,U_424)
| ~ function(U_420)
| ~ relation(U_420) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_6,plain,
( sP116(U_427,U_423,U_420,U_424)
| ~ in(U_427,relation_dom(U_420))
| ~ sP118(U_427,U_426,U_425,U_423,U_428,U_420,U_424) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_7,plain,
( sP117(U_426,U_425,U_428,U_420)
| in(U_428,relation_dom(U_420))
| ~ sP118(U_427,U_426,U_425,U_423,U_428,U_420,U_424) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_8,plain,
( in(ordered_pair(U_427,U_423),U_420)
| U_423 != apply(U_420,U_427)
| ~ sP116(U_427,U_423,U_420,U_424) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_9,plain,
( U_424 = apply(U_420,U_427)
| ~ in(ordered_pair(U_427,U_424),U_420)
| ~ sP116(U_427,U_423,U_420,U_424) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_10,plain,
( U_425 = empty_set
| U_425 != apply(U_420,U_428)
| ~ sP117(U_426,U_425,U_428,U_420) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_11,plain,
( U_426 = apply(U_420,U_428)
| U_426 != empty_set
| ~ sP117(U_426,U_425,U_428,U_420) ),
inference(clausify,[status(thm)],[f_56_4]) ).
fof(f_57_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_57_2,plain,
! [U_429] :
( ( ordinal(U_429)
| ~ epsilon_connected(U_429)
| ~ epsilon_transitive(U_429) )
& ( ( epsilon_connected(U_429)
& epsilon_transitive(U_429) )
| ~ ordinal(U_429) ) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_431] :
( ordinal(U_431)
| ~ epsilon_connected(U_431)
| ~ epsilon_transitive(U_431) )
& ! [U_430] :
( ( epsilon_connected(U_430)
& epsilon_transitive(U_430) )
| ~ ordinal(U_430) ) ),
inference(miniscope,[status(thm)],[f_57_2]) ).
fof(f_57_4,plain,
( ! [U_430] :
( epsilon_connected(U_430)
| ~ sP119(U_430) )
& ! [U_430] :
( epsilon_transitive(U_430)
| ~ sP119(U_430) )
& ! [U_431] :
( ordinal(U_431)
| ~ epsilon_connected(U_431)
| ~ epsilon_transitive(U_431) )
& ! [U_430] :
( sP119(U_430)
| ~ ordinal(U_430) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_57_3]) ).
cnf(f_57_5,plain,
( sP119(U_430)
| ~ ordinal(U_430) ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_6,plain,
( ordinal(U_431)
| ~ epsilon_connected(U_431)
| ~ epsilon_transitive(U_431) ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_7,plain,
( epsilon_transitive(U_430)
| ~ sP119(U_430) ),
inference(clausify,[status(thm)],[f_57_4]) ).
cnf(f_57_8,plain,
( epsilon_connected(U_430)
| ~ sP119(U_430) ),
inference(clausify,[status(thm)],[f_57_4]) ).
fof(f_58_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_58_2,plain,
! [U_439] :
( ! [U_438] :
( ( U_438 = relation_dom(U_439)
| ? [U_437] :
( ( ~ in(U_437,U_438)
& ? [U_436] : in(ordered_pair(U_437,U_436),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(U_437,U_435),U_439)
& in(U_437,U_438) ) ) )
& ( ! [U_434] :
( ( in(U_434,U_438)
| ! [U_433] : ~ in(ordered_pair(U_434,U_433),U_439) )
& ( ? [U_432] : in(ordered_pair(U_434,U_432),U_439)
| ~ in(U_434,U_438) ) )
| U_438 != relation_dom(U_439) ) )
| ~ relation(U_439) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_dom(U_439)
| ? [U_443] :
( ~ in(U_443,U_445)
& ? [U_436] : in(ordered_pair(U_443,U_436),U_439) )
| ? [U_442] :
( ! [U_435] : ~ in(ordered_pair(U_442,U_435),U_439)
& in(U_442,U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_441,U_433),U_439) )
& ! [U_440] :
( ? [U_432] : in(ordered_pair(U_440,U_432),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_dom(U_439) ) )
| ~ relation(U_439) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
fof(f_58_4,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_dom(U_439)
| ? [U_443] :
( ~ in(U_443,U_445)
& ? [U_436] : in(ordered_pair(U_443,U_436),U_439) )
| ? [U_442] :
( ! [U_435] : ~ in(ordered_pair(U_442,U_435),U_439)
& in(U_442,U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_441,U_433),U_439) )
& ! [U_440] :
( in(ordered_pair(U_440,sK79(U_439,U_444,U_440)),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_dom(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_432,sK79(U_439,U_444,U_440))],[f_58_3]) ).
fof(f_58_5,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_dom(U_439)
| ? [U_443] :
( ~ in(U_443,U_445)
& ? [U_436] : in(ordered_pair(U_443,U_436),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(sK80(U_439,U_445),U_435),U_439)
& in(sK80(U_439,U_445),U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_441,U_433),U_439) )
& ! [U_440] :
( in(ordered_pair(U_440,sK79(U_439,U_444,U_440)),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_dom(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_442,sK80(U_439,U_445))],[f_58_4]) ).
fof(f_58_6,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_dom(U_439)
| ( ~ in(sK81(U_439,U_445),U_445)
& ? [U_436] : in(ordered_pair(sK81(U_439,U_445),U_436),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(sK80(U_439,U_445),U_435),U_439)
& in(sK80(U_439,U_445),U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_441,U_433),U_439) )
& ! [U_440] :
( in(ordered_pair(U_440,sK79(U_439,U_444,U_440)),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_dom(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_443,sK81(U_439,U_445))],[f_58_5]) ).
fof(f_58_7,plain,
! [U_439] :
( ( ! [U_445] :
( U_445 = relation_dom(U_439)
| ( ~ in(sK81(U_439,U_445),U_445)
& in(ordered_pair(sK81(U_439,U_445),sK82(U_439,U_445)),U_439) )
| ( ! [U_435] : ~ in(ordered_pair(sK80(U_439,U_445),U_435),U_439)
& in(sK80(U_439,U_445),U_445) ) )
& ! [U_444] :
( ( ! [U_441] :
( in(U_441,U_444)
| ! [U_433] : ~ in(ordered_pair(U_441,U_433),U_439) )
& ! [U_440] :
( in(ordered_pair(U_440,sK79(U_439,U_444,U_440)),U_439)
| ~ in(U_440,U_444) ) )
| U_444 != relation_dom(U_439) ) )
| ~ relation(U_439) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_436,sK82(U_439,U_445))],[f_58_6]) ).
fof(f_58_8,plain,
( ! [U_445,U_439] :
( ~ in(sK81(U_439,U_445),U_445)
| ~ sP122(U_445,U_439) )
& ! [U_445,U_439] :
( in(ordered_pair(sK81(U_439,U_445),sK82(U_439,U_445)),U_439)
| ~ sP122(U_445,U_439) )
& ! [U_445,U_435,U_439] :
( ~ in(ordered_pair(sK80(U_439,U_445),U_435),U_439)
| ~ sP121(U_445,U_435,U_439) )
& ! [U_445,U_435,U_439] :
( in(sK80(U_439,U_445),U_445)
| ~ sP121(U_445,U_435,U_439) )
& ! [U_441,U_440,U_439,U_433,U_444] :
( in(U_441,U_444)
| ~ in(ordered_pair(U_441,U_433),U_439)
| ~ sP120(U_441,U_440,U_439,U_433,U_444) )
& ! [U_441,U_440,U_439,U_433,U_444] :
( in(ordered_pair(U_440,sK79(U_439,U_444,U_440)),U_439)
| ~ in(U_440,U_444)
| ~ sP120(U_441,U_440,U_439,U_433,U_444) )
& ! [U_445,U_441,U_440,U_435,U_439,U_433,U_444] :
( U_445 = relation_dom(U_439)
| sP122(U_445,U_439)
| sP121(U_445,U_435,U_439)
| ~ sP123(U_445,U_441,U_440,U_435,U_439,U_433,U_444) )
& ! [U_445,U_441,U_440,U_435,U_439,U_433,U_444] :
( sP120(U_441,U_440,U_439,U_433,U_444)
| U_444 != relation_dom(U_439)
| ~ sP123(U_445,U_441,U_440,U_435,U_439,U_433,U_444) )
& ! [U_445,U_441,U_440,U_435,U_439,U_433,U_444] :
( sP123(U_445,U_441,U_440,U_435,U_439,U_433,U_444)
| ~ relation(U_439) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120,sP121,sP122,sP123])],[f_58_7]) ).
cnf(f_58_9,plain,
( sP123(U_445,U_441,U_440,U_435,U_439,U_433,U_444)
| ~ relation(U_439) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_10,plain,
( sP120(U_441,U_440,U_439,U_433,U_444)
| U_444 != relation_dom(U_439)
| ~ sP123(U_445,U_441,U_440,U_435,U_439,U_433,U_444) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_11,plain,
( U_445 = relation_dom(U_439)
| sP122(U_445,U_439)
| sP121(U_445,U_435,U_439)
| ~ sP123(U_445,U_441,U_440,U_435,U_439,U_433,U_444) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_12,plain,
( in(ordered_pair(U_440,sK79(U_439,U_444,U_440)),U_439)
| ~ in(U_440,U_444)
| ~ sP120(U_441,U_440,U_439,U_433,U_444) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_13,plain,
( in(U_441,U_444)
| ~ in(ordered_pair(U_441,U_433),U_439)
| ~ sP120(U_441,U_440,U_439,U_433,U_444) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_14,plain,
( in(sK80(U_439,U_445),U_445)
| ~ sP121(U_445,U_435,U_439) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_15,plain,
( ~ in(ordered_pair(sK80(U_439,U_445),U_435),U_439)
| ~ sP121(U_445,U_435,U_439) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_16,plain,
( in(ordered_pair(sK81(U_439,U_445),sK82(U_439,U_445)),U_439)
| ~ sP122(U_445,U_439) ),
inference(clausify,[status(thm)],[f_58_8]) ).
cnf(f_58_17,plain,
( ~ in(sK81(U_439,U_445),U_445)
| ~ sP122(U_445,U_439) ),
inference(clausify,[status(thm)],[f_58_8]) ).
fof(f_59_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_59_2,plain,
! [U_451] :
( ! [U_450] :
( ( is_antisymmetric_in(U_451,U_450)
| ? [U_449,U_448] :
( U_449 != U_448
& in(ordered_pair(U_448,U_449),U_451)
& in(ordered_pair(U_449,U_448),U_451)
& in(U_448,U_450)
& in(U_449,U_450) ) )
& ( ! [U_447,U_446] :
( U_447 = U_446
| ~ in(ordered_pair(U_446,U_447),U_451)
| ~ in(ordered_pair(U_447,U_446),U_451)
| ~ in(U_446,U_450)
| ~ in(U_447,U_450) )
| ~ is_antisymmetric_in(U_451,U_450) ) )
| ~ relation(U_451) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_451] :
( ( ! [U_453] :
( is_antisymmetric_in(U_451,U_453)
| ? [U_449,U_448] :
( U_449 != U_448
& in(ordered_pair(U_448,U_449),U_451)
& in(ordered_pair(U_449,U_448),U_451)
& in(U_448,U_453)
& in(U_449,U_453) ) )
& ! [U_452] :
( ! [U_447,U_446] :
( U_447 = U_446
| ~ in(ordered_pair(U_446,U_447),U_451)
| ~ in(ordered_pair(U_447,U_446),U_451)
| ~ in(U_446,U_452)
| ~ in(U_447,U_452) )
| ~ is_antisymmetric_in(U_451,U_452) ) )
| ~ relation(U_451) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
! [U_451] :
( ( ! [U_453] :
( is_antisymmetric_in(U_451,U_453)
| ? [U_448] :
( sK83(U_451,U_453) != U_448
& in(ordered_pair(U_448,sK83(U_451,U_453)),U_451)
& in(ordered_pair(sK83(U_451,U_453),U_448),U_451)
& in(U_448,U_453)
& in(sK83(U_451,U_453),U_453) ) )
& ! [U_452] :
( ! [U_447,U_446] :
( U_447 = U_446
| ~ in(ordered_pair(U_446,U_447),U_451)
| ~ in(ordered_pair(U_447,U_446),U_451)
| ~ in(U_446,U_452)
| ~ in(U_447,U_452) )
| ~ is_antisymmetric_in(U_451,U_452) ) )
| ~ relation(U_451) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_449,sK83(U_451,U_453))],[f_59_3]) ).
fof(f_59_5,plain,
! [U_451] :
( ( ! [U_453] :
( is_antisymmetric_in(U_451,U_453)
| ( sK83(U_451,U_453) != sK84(U_451,U_453)
& in(ordered_pair(sK84(U_451,U_453),sK83(U_451,U_453)),U_451)
& in(ordered_pair(sK83(U_451,U_453),sK84(U_451,U_453)),U_451)
& in(sK84(U_451,U_453),U_453)
& in(sK83(U_451,U_453),U_453) ) )
& ! [U_452] :
( ! [U_447,U_446] :
( U_447 = U_446
| ~ in(ordered_pair(U_446,U_447),U_451)
| ~ in(ordered_pair(U_447,U_446),U_451)
| ~ in(U_446,U_452)
| ~ in(U_447,U_452) )
| ~ is_antisymmetric_in(U_451,U_452) ) )
| ~ relation(U_451) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_448,sK84(U_451,U_453))],[f_59_4]) ).
fof(f_59_6,plain,
( ! [U_451,U_453] :
( sK83(U_451,U_453) != sK84(U_451,U_453)
| ~ sP124(U_451,U_453) )
& ! [U_451,U_453] :
( in(ordered_pair(sK84(U_451,U_453),sK83(U_451,U_453)),U_451)
| ~ sP124(U_451,U_453) )
& ! [U_451,U_453] :
( in(ordered_pair(sK83(U_451,U_453),sK84(U_451,U_453)),U_451)
| ~ sP124(U_451,U_453) )
& ! [U_451,U_453] :
( in(sK84(U_451,U_453),U_453)
| ~ sP124(U_451,U_453) )
& ! [U_451,U_453] :
( in(sK83(U_451,U_453),U_453)
| ~ sP124(U_451,U_453) )
& ! [U_451,U_447,U_446,U_453,U_452] :
( is_antisymmetric_in(U_451,U_453)
| sP124(U_451,U_453)
| ~ sP125(U_451,U_447,U_446,U_453,U_452) )
& ! [U_451,U_447,U_446,U_453,U_452] :
( U_447 = U_446
| ~ in(ordered_pair(U_446,U_447),U_451)
| ~ in(ordered_pair(U_447,U_446),U_451)
| ~ in(U_446,U_452)
| ~ in(U_447,U_452)
| ~ is_antisymmetric_in(U_451,U_452)
| ~ sP125(U_451,U_447,U_446,U_453,U_452) )
& ! [U_451,U_447,U_446,U_453,U_452] :
( sP125(U_451,U_447,U_446,U_453,U_452)
| ~ relation(U_451) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124,sP125])],[f_59_5]) ).
cnf(f_59_7,plain,
( sP125(U_451,U_447,U_446,U_453,U_452)
| ~ relation(U_451) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_8,plain,
( U_447 = U_446
| ~ in(ordered_pair(U_446,U_447),U_451)
| ~ in(ordered_pair(U_447,U_446),U_451)
| ~ in(U_446,U_452)
| ~ in(U_447,U_452)
| ~ is_antisymmetric_in(U_451,U_452)
| ~ sP125(U_451,U_447,U_446,U_453,U_452) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_9,plain,
( is_antisymmetric_in(U_451,U_453)
| sP124(U_451,U_453)
| ~ sP125(U_451,U_447,U_446,U_453,U_452) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_10,plain,
( in(sK83(U_451,U_453),U_453)
| ~ sP124(U_451,U_453) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_11,plain,
( in(sK84(U_451,U_453),U_453)
| ~ sP124(U_451,U_453) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_12,plain,
( in(ordered_pair(sK83(U_451,U_453),sK84(U_451,U_453)),U_451)
| ~ sP124(U_451,U_453) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_13,plain,
( in(ordered_pair(sK84(U_451,U_453),sK83(U_451,U_453)),U_451)
| ~ sP124(U_451,U_453) ),
inference(clausify,[status(thm)],[f_59_6]) ).
cnf(f_59_14,plain,
( sK83(U_451,U_453) != sK84(U_451,U_453)
| ~ sP124(U_451,U_453) ),
inference(clausify,[status(thm)],[f_59_6]) ).
fof(f_60_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_60_2,plain,
! [U_454] : cast_to_subset(U_454) = U_454,
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_454] : cast_to_subset(U_454) = U_454,
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
cast_to_subset(U_454) = U_454,
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_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_61_2,plain,
! [U_462,U_461] :
( ( U_461 = union(U_462)
| ? [U_460] :
( ( ~ in(U_460,U_461)
& ? [U_459] :
( in(U_459,U_462)
& in(U_460,U_459) ) )
| ( ! [U_458] :
( ~ in(U_458,U_462)
| ~ in(U_460,U_458) )
& in(U_460,U_461) ) ) )
& ( ! [U_457] :
( ( in(U_457,U_461)
| ! [U_456] :
( ~ in(U_456,U_462)
| ~ in(U_457,U_456) ) )
& ( ? [U_455] :
( in(U_455,U_462)
& in(U_457,U_455) )
| ~ in(U_457,U_461) ) )
| U_461 != union(U_462) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ! [U_470,U_468] :
( U_468 = union(U_470)
| ? [U_466] :
( ~ in(U_466,U_468)
& ? [U_459] :
( in(U_459,U_470)
& in(U_466,U_459) ) )
| ? [U_465] :
( ! [U_458] :
( ~ in(U_458,U_470)
| ~ in(U_465,U_458) )
& in(U_465,U_468) ) )
& ! [U_469,U_467] :
( ( ! [U_464] :
( in(U_464,U_467)
| ! [U_456] :
( ~ in(U_456,U_469)
| ~ in(U_464,U_456) ) )
& ! [U_463] :
( ? [U_455] :
( in(U_455,U_469)
& in(U_463,U_455) )
| ~ in(U_463,U_467) ) )
| U_467 != union(U_469) ) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
fof(f_61_4,plain,
( ! [U_470,U_468] :
( U_468 = union(U_470)
| ? [U_466] :
( ~ in(U_466,U_468)
& ? [U_459] :
( in(U_459,U_470)
& in(U_466,U_459) ) )
| ? [U_465] :
( ! [U_458] :
( ~ in(U_458,U_470)
| ~ in(U_465,U_458) )
& in(U_465,U_468) ) )
& ! [U_469,U_467] :
( ( ! [U_464] :
( in(U_464,U_467)
| ! [U_456] :
( ~ in(U_456,U_469)
| ~ in(U_464,U_456) ) )
& ! [U_463] :
( ( in(sK85(U_469,U_467,U_463),U_469)
& in(U_463,sK85(U_469,U_467,U_463)) )
| ~ in(U_463,U_467) ) )
| U_467 != union(U_469) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_455,sK85(U_469,U_467,U_463))],[f_61_3]) ).
fof(f_61_5,plain,
( ! [U_470,U_468] :
( U_468 = union(U_470)
| ? [U_466] :
( ~ in(U_466,U_468)
& ? [U_459] :
( in(U_459,U_470)
& in(U_466,U_459) ) )
| ( ! [U_458] :
( ~ in(U_458,U_470)
| ~ in(sK86(U_470,U_468),U_458) )
& in(sK86(U_470,U_468),U_468) ) )
& ! [U_469,U_467] :
( ( ! [U_464] :
( in(U_464,U_467)
| ! [U_456] :
( ~ in(U_456,U_469)
| ~ in(U_464,U_456) ) )
& ! [U_463] :
( ( in(sK85(U_469,U_467,U_463),U_469)
& in(U_463,sK85(U_469,U_467,U_463)) )
| ~ in(U_463,U_467) ) )
| U_467 != union(U_469) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_465,sK86(U_470,U_468))],[f_61_4]) ).
fof(f_61_6,plain,
( ! [U_470,U_468] :
( U_468 = union(U_470)
| ( ~ in(sK87(U_470,U_468),U_468)
& ? [U_459] :
( in(U_459,U_470)
& in(sK87(U_470,U_468),U_459) ) )
| ( ! [U_458] :
( ~ in(U_458,U_470)
| ~ in(sK86(U_470,U_468),U_458) )
& in(sK86(U_470,U_468),U_468) ) )
& ! [U_469,U_467] :
( ( ! [U_464] :
( in(U_464,U_467)
| ! [U_456] :
( ~ in(U_456,U_469)
| ~ in(U_464,U_456) ) )
& ! [U_463] :
( ( in(sK85(U_469,U_467,U_463),U_469)
& in(U_463,sK85(U_469,U_467,U_463)) )
| ~ in(U_463,U_467) ) )
| U_467 != union(U_469) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_466,sK87(U_470,U_468))],[f_61_5]) ).
fof(f_61_7,plain,
( ! [U_470,U_468] :
( U_468 = union(U_470)
| ( ~ in(sK87(U_470,U_468),U_468)
& in(sK88(U_470,U_468),U_470)
& in(sK87(U_470,U_468),sK88(U_470,U_468)) )
| ( ! [U_458] :
( ~ in(U_458,U_470)
| ~ in(sK86(U_470,U_468),U_458) )
& in(sK86(U_470,U_468),U_468) ) )
& ! [U_469,U_467] :
( ( ! [U_464] :
( in(U_464,U_467)
| ! [U_456] :
( ~ in(U_456,U_469)
| ~ in(U_464,U_456) ) )
& ! [U_463] :
( ( in(sK85(U_469,U_467,U_463),U_469)
& in(U_463,sK85(U_469,U_467,U_463)) )
| ~ in(U_463,U_467) ) )
| U_467 != union(U_469) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_459,sK88(U_470,U_468))],[f_61_6]) ).
fof(f_61_8,plain,
( ! [U_470,U_468] :
( ~ in(sK87(U_470,U_468),U_468)
| ~ sP129(U_470,U_468) )
& ! [U_470,U_468] :
( in(sK88(U_470,U_468),U_470)
| ~ sP129(U_470,U_468) )
& ! [U_470,U_468] :
( in(sK87(U_470,U_468),sK88(U_470,U_468))
| ~ sP129(U_470,U_468) )
& ! [U_458,U_470,U_468] :
( ~ in(U_458,U_470)
| ~ in(sK86(U_470,U_468),U_458)
| ~ sP128(U_458,U_470,U_468) )
& ! [U_458,U_470,U_468] :
( in(sK86(U_470,U_468),U_468)
| ~ sP128(U_458,U_470,U_468) )
& ! [U_463,U_469,U_467] :
( in(sK85(U_469,U_467,U_463),U_469)
| ~ sP126(U_463,U_469,U_467) )
& ! [U_463,U_469,U_467] :
( in(U_463,sK85(U_469,U_467,U_463))
| ~ sP126(U_463,U_469,U_467) )
& ! [U_456,U_464,U_463,U_469,U_467] :
( in(U_464,U_467)
| ~ in(U_456,U_469)
| ~ in(U_464,U_456)
| ~ sP127(U_456,U_464,U_463,U_469,U_467) )
& ! [U_456,U_464,U_463,U_469,U_467] :
( sP126(U_463,U_469,U_467)
| ~ in(U_463,U_467)
| ~ sP127(U_456,U_464,U_463,U_469,U_467) )
& ! [U_458,U_470,U_468] :
( U_468 = union(U_470)
| sP129(U_470,U_468)
| sP128(U_458,U_470,U_468) )
& ! [U_456,U_464,U_463,U_469,U_467] :
( sP127(U_456,U_464,U_463,U_469,U_467)
| U_467 != union(U_469) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126,sP127,sP128,sP129])],[f_61_7]) ).
cnf(f_61_9,plain,
( sP127(U_456,U_464,U_463,U_469,U_467)
| U_467 != union(U_469) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_10,plain,
( U_468 = union(U_470)
| sP129(U_470,U_468)
| sP128(U_458,U_470,U_468) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_11,plain,
( sP126(U_463,U_469,U_467)
| ~ in(U_463,U_467)
| ~ sP127(U_456,U_464,U_463,U_469,U_467) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_12,plain,
( in(U_464,U_467)
| ~ in(U_456,U_469)
| ~ in(U_464,U_456)
| ~ sP127(U_456,U_464,U_463,U_469,U_467) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_13,plain,
( in(U_463,sK85(U_469,U_467,U_463))
| ~ sP126(U_463,U_469,U_467) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_14,plain,
( in(sK85(U_469,U_467,U_463),U_469)
| ~ sP126(U_463,U_469,U_467) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_15,plain,
( in(sK86(U_470,U_468),U_468)
| ~ sP128(U_458,U_470,U_468) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_16,plain,
( ~ in(U_458,U_470)
| ~ in(sK86(U_470,U_468),U_458)
| ~ sP128(U_458,U_470,U_468) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_17,plain,
( in(sK87(U_470,U_468),sK88(U_470,U_468))
| ~ sP129(U_470,U_468) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_18,plain,
( in(sK88(U_470,U_468),U_470)
| ~ sP129(U_470,U_468) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_19,plain,
( ~ in(sK87(U_470,U_468),U_468)
| ~ sP129(U_470,U_468) ),
inference(clausify,[status(thm)],[f_61_8]) ).
fof(f_62_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_62_2,plain,
! [U_471] :
( ( ( well_ordering(U_471)
| ~ well_founded_relation(U_471)
| ~ connected(U_471)
| ~ antisymmetric(U_471)
| ~ transitive(U_471)
| ~ reflexive(U_471) )
& ( ( well_founded_relation(U_471)
& connected(U_471)
& antisymmetric(U_471)
& transitive(U_471)
& reflexive(U_471) )
| ~ well_ordering(U_471) ) )
| ~ relation(U_471) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
( ! [U_471] :
( well_founded_relation(U_471)
| ~ sP130(U_471) )
& ! [U_471] :
( connected(U_471)
| ~ sP130(U_471) )
& ! [U_471] :
( antisymmetric(U_471)
| ~ sP130(U_471) )
& ! [U_471] :
( transitive(U_471)
| ~ sP130(U_471) )
& ! [U_471] :
( reflexive(U_471)
| ~ sP130(U_471) )
& ! [U_471] :
( well_ordering(U_471)
| ~ well_founded_relation(U_471)
| ~ connected(U_471)
| ~ antisymmetric(U_471)
| ~ transitive(U_471)
| ~ reflexive(U_471)
| ~ sP131(U_471) )
& ! [U_471] :
( sP130(U_471)
| ~ well_ordering(U_471)
| ~ sP131(U_471) )
& ! [U_471] :
( sP131(U_471)
| ~ relation(U_471) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130,sP131])],[f_62_2]) ).
cnf(f_62_4,plain,
( sP131(U_471)
| ~ relation(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( sP130(U_471)
| ~ well_ordering(U_471)
| ~ sP131(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_6,plain,
( well_ordering(U_471)
| ~ well_founded_relation(U_471)
| ~ connected(U_471)
| ~ antisymmetric(U_471)
| ~ transitive(U_471)
| ~ reflexive(U_471)
| ~ sP131(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_7,plain,
( reflexive(U_471)
| ~ sP130(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_8,plain,
( transitive(U_471)
| ~ sP130(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_9,plain,
( antisymmetric(U_471)
| ~ sP130(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_10,plain,
( connected(U_471)
| ~ sP130(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_11,plain,
( well_founded_relation(U_471)
| ~ sP130(U_471) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [A,B] :
( ( equipotent(A,B)
| ! [C] :
( relation_rng(C) != B
| relation_dom(C) != A
| ~ one_to_one(C)
| ~ function(C)
| ~ relation(C) ) )
& ( ? [C] :
( relation_rng(C) = B
& relation_dom(C) = A
& one_to_one(C)
& function(C)
& relation(C) )
| ~ equipotent(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_wellord2]) ).
fof(f_63_2,plain,
! [U_475,U_474] :
( ( equipotent(U_475,U_474)
| ! [U_473] :
( relation_rng(U_473) != U_474
| relation_dom(U_473) != U_475
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) ) )
& ( ? [U_472] :
( relation_rng(U_472) = U_474
& relation_dom(U_472) = U_475
& one_to_one(U_472)
& function(U_472)
& relation(U_472) )
| ~ equipotent(U_475,U_474) ) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ! [U_479,U_477] :
( equipotent(U_479,U_477)
| ! [U_473] :
( relation_rng(U_473) != U_477
| relation_dom(U_473) != U_479
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) ) )
& ! [U_478,U_476] :
( ? [U_472] :
( relation_rng(U_472) = U_476
& relation_dom(U_472) = U_478
& one_to_one(U_472)
& function(U_472)
& relation(U_472) )
| ~ equipotent(U_478,U_476) ) ),
inference(miniscope,[status(thm)],[f_63_2]) ).
fof(f_63_4,plain,
( ! [U_479,U_477] :
( equipotent(U_479,U_477)
| ! [U_473] :
( relation_rng(U_473) != U_477
| relation_dom(U_473) != U_479
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) ) )
& ! [U_478,U_476] :
( ( relation_rng(sK89(U_478,U_476)) = U_476
& relation_dom(sK89(U_478,U_476)) = U_478
& one_to_one(sK89(U_478,U_476))
& function(sK89(U_478,U_476))
& relation(sK89(U_478,U_476)) )
| ~ equipotent(U_478,U_476) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_472,sK89(U_478,U_476))],[f_63_3]) ).
fof(f_63_5,plain,
( ! [U_476,U_478] :
( relation_rng(sK89(U_478,U_476)) = U_476
| ~ sP132(U_476,U_478) )
& ! [U_476,U_478] :
( relation_dom(sK89(U_478,U_476)) = U_478
| ~ sP132(U_476,U_478) )
& ! [U_476,U_478] :
( one_to_one(sK89(U_478,U_476))
| ~ sP132(U_476,U_478) )
& ! [U_476,U_478] :
( function(sK89(U_478,U_476))
| ~ sP132(U_476,U_478) )
& ! [U_476,U_478] :
( relation(sK89(U_478,U_476))
| ~ sP132(U_476,U_478) )
& ! [U_473,U_479,U_477] :
( equipotent(U_479,U_477)
| relation_rng(U_473) != U_477
| relation_dom(U_473) != U_479
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) )
& ! [U_476,U_478] :
( sP132(U_476,U_478)
| ~ equipotent(U_478,U_476) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_63_4]) ).
cnf(f_63_6,plain,
( sP132(U_476,U_478)
| ~ equipotent(U_478,U_476) ),
inference(clausify,[status(thm)],[f_63_5]) ).
cnf(f_63_7,plain,
( equipotent(U_479,U_477)
| relation_rng(U_473) != U_477
| relation_dom(U_473) != U_479
| ~ one_to_one(U_473)
| ~ function(U_473)
| ~ relation(U_473) ),
inference(clausify,[status(thm)],[f_63_5]) ).
cnf(f_63_8,plain,
( relation(sK89(U_478,U_476))
| ~ sP132(U_476,U_478) ),
inference(clausify,[status(thm)],[f_63_5]) ).
cnf(f_63_9,plain,
( function(sK89(U_478,U_476))
| ~ sP132(U_476,U_478) ),
inference(clausify,[status(thm)],[f_63_5]) ).
cnf(f_63_10,plain,
( one_to_one(sK89(U_478,U_476))
| ~ sP132(U_476,U_478) ),
inference(clausify,[status(thm)],[f_63_5]) ).
cnf(f_63_11,plain,
( relation_dom(sK89(U_478,U_476)) = U_478
| ~ sP132(U_476,U_478) ),
inference(clausify,[status(thm)],[f_63_5]) ).
cnf(f_63_12,plain,
( relation_rng(sK89(U_478,U_476)) = U_476
| ~ sP132(U_476,U_478) ),
inference(clausify,[status(thm)],[f_63_5]) ).
fof(f_64_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_64_2,plain,
! [U_484,U_483,U_482] :
( ( U_482 = set_difference(U_484,U_483)
| ? [U_481] :
( ( ~ in(U_481,U_482)
& ~ in(U_481,U_483)
& in(U_481,U_484) )
| ( ( in(U_481,U_483)
| ~ in(U_481,U_484) )
& in(U_481,U_482) ) ) )
& ( ! [U_480] :
( ( in(U_480,U_482)
| in(U_480,U_483)
| ~ in(U_480,U_484) )
& ( ( ~ in(U_480,U_483)
& in(U_480,U_484) )
| ~ in(U_480,U_482) ) )
| U_482 != set_difference(U_484,U_483) ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_494,U_492,U_490] :
( U_490 = set_difference(U_494,U_492)
| ? [U_488] :
( ~ in(U_488,U_490)
& ~ in(U_488,U_492)
& in(U_488,U_494) )
| ? [U_487] :
( ( in(U_487,U_492)
| ~ in(U_487,U_494) )
& in(U_487,U_490) ) )
& ! [U_493,U_491,U_489] :
( ( ! [U_486] :
( in(U_486,U_489)
| in(U_486,U_491)
| ~ in(U_486,U_493) )
& ! [U_485] :
( ( ~ in(U_485,U_491)
& in(U_485,U_493) )
| ~ in(U_485,U_489) ) )
| U_489 != set_difference(U_493,U_491) ) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
fof(f_64_4,plain,
( ! [U_494,U_492,U_490] :
( U_490 = set_difference(U_494,U_492)
| ? [U_488] :
( ~ in(U_488,U_490)
& ~ in(U_488,U_492)
& in(U_488,U_494) )
| ( ( in(sK90(U_494,U_492,U_490),U_492)
| ~ in(sK90(U_494,U_492,U_490),U_494) )
& in(sK90(U_494,U_492,U_490),U_490) ) )
& ! [U_493,U_491,U_489] :
( ( ! [U_486] :
( in(U_486,U_489)
| in(U_486,U_491)
| ~ in(U_486,U_493) )
& ! [U_485] :
( ( ~ in(U_485,U_491)
& in(U_485,U_493) )
| ~ in(U_485,U_489) ) )
| U_489 != set_difference(U_493,U_491) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_487,sK90(U_494,U_492,U_490))],[f_64_3]) ).
fof(f_64_5,plain,
( ! [U_494,U_492,U_490] :
( U_490 = set_difference(U_494,U_492)
| ( ~ in(sK91(U_494,U_492,U_490),U_490)
& ~ in(sK91(U_494,U_492,U_490),U_492)
& in(sK91(U_494,U_492,U_490),U_494) )
| ( ( in(sK90(U_494,U_492,U_490),U_492)
| ~ in(sK90(U_494,U_492,U_490),U_494) )
& in(sK90(U_494,U_492,U_490),U_490) ) )
& ! [U_493,U_491,U_489] :
( ( ! [U_486] :
( in(U_486,U_489)
| in(U_486,U_491)
| ~ in(U_486,U_493) )
& ! [U_485] :
( ( ~ in(U_485,U_491)
& in(U_485,U_493) )
| ~ in(U_485,U_489) ) )
| U_489 != set_difference(U_493,U_491) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_488,sK91(U_494,U_492,U_490))],[f_64_4]) ).
fof(f_64_6,plain,
( ! [U_492,U_490,U_494] :
( ~ in(sK91(U_494,U_492,U_490),U_490)
| ~ sP136(U_492,U_490,U_494) )
& ! [U_492,U_490,U_494] :
( ~ in(sK91(U_494,U_492,U_490),U_492)
| ~ sP136(U_492,U_490,U_494) )
& ! [U_492,U_490,U_494] :
( in(sK91(U_494,U_492,U_490),U_494)
| ~ sP136(U_492,U_490,U_494) )
& ! [U_492,U_490,U_494] :
( in(sK90(U_494,U_492,U_490),U_492)
| ~ in(sK90(U_494,U_492,U_490),U_494)
| ~ sP135(U_492,U_490,U_494) )
& ! [U_492,U_490,U_494] :
( in(sK90(U_494,U_492,U_490),U_490)
| ~ sP135(U_492,U_490,U_494) )
& ! [U_485,U_491,U_493] :
( ~ in(U_485,U_491)
| ~ sP133(U_485,U_491,U_493) )
& ! [U_485,U_491,U_493] :
( in(U_485,U_493)
| ~ sP133(U_485,U_491,U_493) )
& ! [U_486,U_485,U_489,U_491,U_493] :
( in(U_486,U_489)
| in(U_486,U_491)
| ~ in(U_486,U_493)
| ~ sP134(U_486,U_485,U_489,U_491,U_493) )
& ! [U_486,U_485,U_489,U_491,U_493] :
( sP133(U_485,U_491,U_493)
| ~ in(U_485,U_489)
| ~ sP134(U_486,U_485,U_489,U_491,U_493) )
& ! [U_492,U_490,U_494] :
( U_490 = set_difference(U_494,U_492)
| sP136(U_492,U_490,U_494)
| sP135(U_492,U_490,U_494) )
& ! [U_486,U_485,U_489,U_491,U_493] :
( sP134(U_486,U_485,U_489,U_491,U_493)
| U_489 != set_difference(U_493,U_491) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133,sP134,sP135,sP136])],[f_64_5]) ).
cnf(f_64_7,plain,
( sP134(U_486,U_485,U_489,U_491,U_493)
| U_489 != set_difference(U_493,U_491) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_8,plain,
( U_490 = set_difference(U_494,U_492)
| sP136(U_492,U_490,U_494)
| sP135(U_492,U_490,U_494) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_9,plain,
( sP133(U_485,U_491,U_493)
| ~ in(U_485,U_489)
| ~ sP134(U_486,U_485,U_489,U_491,U_493) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_10,plain,
( in(U_486,U_489)
| in(U_486,U_491)
| ~ in(U_486,U_493)
| ~ sP134(U_486,U_485,U_489,U_491,U_493) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_11,plain,
( in(U_485,U_493)
| ~ sP133(U_485,U_491,U_493) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_12,plain,
( ~ in(U_485,U_491)
| ~ sP133(U_485,U_491,U_493) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_13,plain,
( in(sK90(U_494,U_492,U_490),U_490)
| ~ sP135(U_492,U_490,U_494) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_14,plain,
( in(sK90(U_494,U_492,U_490),U_492)
| ~ in(sK90(U_494,U_492,U_490),U_494)
| ~ sP135(U_492,U_490,U_494) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_15,plain,
( in(sK91(U_494,U_492,U_490),U_494)
| ~ sP136(U_492,U_490,U_494) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_16,plain,
( ~ in(sK91(U_494,U_492,U_490),U_492)
| ~ sP136(U_492,U_490,U_494) ),
inference(clausify,[status(thm)],[f_64_6]) ).
cnf(f_64_17,plain,
( ~ in(sK91(U_494,U_492,U_490),U_490)
| ~ sP136(U_492,U_490,U_494) ),
inference(clausify,[status(thm)],[f_64_6]) ).
fof(f_65_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_65_2,plain,
! [U_502] :
( ! [U_501] :
( ( U_501 = relation_rng(U_502)
| ? [U_500] :
( ( ~ in(U_500,U_501)
& ? [U_499] :
( U_500 = apply(U_502,U_499)
& in(U_499,relation_dom(U_502)) ) )
| ( ! [U_498] :
( U_500 != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502)) )
& in(U_500,U_501) ) ) )
& ( ! [U_497] :
( ( in(U_497,U_501)
| ! [U_496] :
( U_497 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502)) ) )
& ( ? [U_495] :
( U_497 = apply(U_502,U_495)
& in(U_495,relation_dom(U_502)) )
| ~ in(U_497,U_501) ) )
| U_501 != relation_rng(U_502) ) )
| ~ function(U_502)
| ~ relation(U_502) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_502] :
( ( ! [U_508] :
( U_508 = relation_rng(U_502)
| ? [U_506] :
( ~ in(U_506,U_508)
& ? [U_499] :
( U_506 = apply(U_502,U_499)
& in(U_499,relation_dom(U_502)) ) )
| ? [U_505] :
( ! [U_498] :
( U_505 != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502)) )
& in(U_505,U_508) ) )
& ! [U_507] :
( ( ! [U_504] :
( in(U_504,U_507)
| ! [U_496] :
( U_504 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502)) ) )
& ! [U_503] :
( ? [U_495] :
( U_503 = apply(U_502,U_495)
& in(U_495,relation_dom(U_502)) )
| ~ in(U_503,U_507) ) )
| U_507 != relation_rng(U_502) ) )
| ~ function(U_502)
| ~ relation(U_502) ),
inference(miniscope,[status(thm)],[f_65_2]) ).
fof(f_65_4,plain,
! [U_502] :
( ( ! [U_508] :
( U_508 = relation_rng(U_502)
| ? [U_506] :
( ~ in(U_506,U_508)
& ? [U_499] :
( U_506 = apply(U_502,U_499)
& in(U_499,relation_dom(U_502)) ) )
| ? [U_505] :
( ! [U_498] :
( U_505 != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502)) )
& in(U_505,U_508) ) )
& ! [U_507] :
( ( ! [U_504] :
( in(U_504,U_507)
| ! [U_496] :
( U_504 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502)) ) )
& ! [U_503] :
( ( U_503 = apply(U_502,sK92(U_502,U_507,U_503))
& in(sK92(U_502,U_507,U_503),relation_dom(U_502)) )
| ~ in(U_503,U_507) ) )
| U_507 != relation_rng(U_502) ) )
| ~ function(U_502)
| ~ relation(U_502) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_495,sK92(U_502,U_507,U_503))],[f_65_3]) ).
fof(f_65_5,plain,
! [U_502] :
( ( ! [U_508] :
( U_508 = relation_rng(U_502)
| ? [U_506] :
( ~ in(U_506,U_508)
& ? [U_499] :
( U_506 = apply(U_502,U_499)
& in(U_499,relation_dom(U_502)) ) )
| ( ! [U_498] :
( sK93(U_502,U_508) != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502)) )
& in(sK93(U_502,U_508),U_508) ) )
& ! [U_507] :
( ( ! [U_504] :
( in(U_504,U_507)
| ! [U_496] :
( U_504 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502)) ) )
& ! [U_503] :
( ( U_503 = apply(U_502,sK92(U_502,U_507,U_503))
& in(sK92(U_502,U_507,U_503),relation_dom(U_502)) )
| ~ in(U_503,U_507) ) )
| U_507 != relation_rng(U_502) ) )
| ~ function(U_502)
| ~ relation(U_502) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_505,sK93(U_502,U_508))],[f_65_4]) ).
fof(f_65_6,plain,
! [U_502] :
( ( ! [U_508] :
( U_508 = relation_rng(U_502)
| ( ~ in(sK94(U_502,U_508),U_508)
& ? [U_499] :
( sK94(U_502,U_508) = apply(U_502,U_499)
& in(U_499,relation_dom(U_502)) ) )
| ( ! [U_498] :
( sK93(U_502,U_508) != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502)) )
& in(sK93(U_502,U_508),U_508) ) )
& ! [U_507] :
( ( ! [U_504] :
( in(U_504,U_507)
| ! [U_496] :
( U_504 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502)) ) )
& ! [U_503] :
( ( U_503 = apply(U_502,sK92(U_502,U_507,U_503))
& in(sK92(U_502,U_507,U_503),relation_dom(U_502)) )
| ~ in(U_503,U_507) ) )
| U_507 != relation_rng(U_502) ) )
| ~ function(U_502)
| ~ relation(U_502) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_506,sK94(U_502,U_508))],[f_65_5]) ).
fof(f_65_7,plain,
! [U_502] :
( ( ! [U_508] :
( U_508 = relation_rng(U_502)
| ( ~ in(sK94(U_502,U_508),U_508)
& sK94(U_502,U_508) = apply(U_502,sK95(U_502,U_508))
& in(sK95(U_502,U_508),relation_dom(U_502)) )
| ( ! [U_498] :
( sK93(U_502,U_508) != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502)) )
& in(sK93(U_502,U_508),U_508) ) )
& ! [U_507] :
( ( ! [U_504] :
( in(U_504,U_507)
| ! [U_496] :
( U_504 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502)) ) )
& ! [U_503] :
( ( U_503 = apply(U_502,sK92(U_502,U_507,U_503))
& in(sK92(U_502,U_507,U_503),relation_dom(U_502)) )
| ~ in(U_503,U_507) ) )
| U_507 != relation_rng(U_502) ) )
| ~ function(U_502)
| ~ relation(U_502) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_499,sK95(U_502,U_508))],[f_65_6]) ).
fof(f_65_8,plain,
( ! [U_502,U_508] :
( ~ in(sK94(U_502,U_508),U_508)
| ~ sP140(U_502,U_508) )
& ! [U_502,U_508] :
( sK94(U_502,U_508) = apply(U_502,sK95(U_502,U_508))
| ~ sP140(U_502,U_508) )
& ! [U_502,U_508] :
( in(sK95(U_502,U_508),relation_dom(U_502))
| ~ sP140(U_502,U_508) )
& ! [U_502,U_498,U_508] :
( sK93(U_502,U_508) != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502))
| ~ sP139(U_502,U_498,U_508) )
& ! [U_502,U_498,U_508] :
( in(sK93(U_502,U_508),U_508)
| ~ sP139(U_502,U_498,U_508) )
& ! [U_502,U_507,U_503] :
( U_503 = apply(U_502,sK92(U_502,U_507,U_503))
| ~ sP137(U_502,U_507,U_503) )
& ! [U_502,U_507,U_503] :
( in(sK92(U_502,U_507,U_503),relation_dom(U_502))
| ~ sP137(U_502,U_507,U_503) )
& ! [U_502,U_496,U_507,U_504,U_503] :
( in(U_504,U_507)
| U_504 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502))
| ~ sP138(U_502,U_496,U_507,U_504,U_503) )
& ! [U_502,U_496,U_507,U_504,U_503] :
( sP137(U_502,U_507,U_503)
| ~ in(U_503,U_507)
| ~ sP138(U_502,U_496,U_507,U_504,U_503) )
& ! [U_502,U_498,U_508,U_496,U_507,U_504,U_503] :
( U_508 = relation_rng(U_502)
| sP140(U_502,U_508)
| sP139(U_502,U_498,U_508)
| ~ sP141(U_502,U_498,U_508,U_496,U_507,U_504,U_503) )
& ! [U_502,U_498,U_508,U_496,U_507,U_504,U_503] :
( sP138(U_502,U_496,U_507,U_504,U_503)
| U_507 != relation_rng(U_502)
| ~ sP141(U_502,U_498,U_508,U_496,U_507,U_504,U_503) )
& ! [U_502,U_498,U_508,U_496,U_507,U_504,U_503] :
( sP141(U_502,U_498,U_508,U_496,U_507,U_504,U_503)
| ~ function(U_502)
| ~ relation(U_502) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137,sP138,sP139,sP140,sP141])],[f_65_7]) ).
cnf(f_65_9,plain,
( sP141(U_502,U_498,U_508,U_496,U_507,U_504,U_503)
| ~ function(U_502)
| ~ relation(U_502) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_10,plain,
( sP138(U_502,U_496,U_507,U_504,U_503)
| U_507 != relation_rng(U_502)
| ~ sP141(U_502,U_498,U_508,U_496,U_507,U_504,U_503) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_11,plain,
( U_508 = relation_rng(U_502)
| sP140(U_502,U_508)
| sP139(U_502,U_498,U_508)
| ~ sP141(U_502,U_498,U_508,U_496,U_507,U_504,U_503) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_12,plain,
( sP137(U_502,U_507,U_503)
| ~ in(U_503,U_507)
| ~ sP138(U_502,U_496,U_507,U_504,U_503) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_13,plain,
( in(U_504,U_507)
| U_504 != apply(U_502,U_496)
| ~ in(U_496,relation_dom(U_502))
| ~ sP138(U_502,U_496,U_507,U_504,U_503) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_14,plain,
( in(sK92(U_502,U_507,U_503),relation_dom(U_502))
| ~ sP137(U_502,U_507,U_503) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_15,plain,
( U_503 = apply(U_502,sK92(U_502,U_507,U_503))
| ~ sP137(U_502,U_507,U_503) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_16,plain,
( in(sK93(U_502,U_508),U_508)
| ~ sP139(U_502,U_498,U_508) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_17,plain,
( sK93(U_502,U_508) != apply(U_502,U_498)
| ~ in(U_498,relation_dom(U_502))
| ~ sP139(U_502,U_498,U_508) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_18,plain,
( in(sK95(U_502,U_508),relation_dom(U_502))
| ~ sP140(U_502,U_508) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_19,plain,
( sK94(U_502,U_508) = apply(U_502,sK95(U_502,U_508))
| ~ sP140(U_502,U_508) ),
inference(clausify,[status(thm)],[f_65_8]) ).
cnf(f_65_20,plain,
( ~ in(sK94(U_502,U_508),U_508)
| ~ sP140(U_502,U_508) ),
inference(clausify,[status(thm)],[f_65_8]) ).
fof(f_66_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_66_2,plain,
! [U_516] :
( ! [U_515] :
( ( U_515 = relation_rng(U_516)
| ? [U_514] :
( ( ~ in(U_514,U_515)
& ? [U_513] : in(ordered_pair(U_513,U_514),U_516) )
| ( ! [U_512] : ~ in(ordered_pair(U_512,U_514),U_516)
& in(U_514,U_515) ) ) )
& ( ! [U_511] :
( ( in(U_511,U_515)
| ! [U_510] : ~ in(ordered_pair(U_510,U_511),U_516) )
& ( ? [U_509] : in(ordered_pair(U_509,U_511),U_516)
| ~ in(U_511,U_515) ) )
| U_515 != relation_rng(U_516) ) )
| ~ relation(U_516) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_516] :
( ( ! [U_522] :
( U_522 = relation_rng(U_516)
| ? [U_520] :
( ~ in(U_520,U_522)
& ? [U_513] : in(ordered_pair(U_513,U_520),U_516) )
| ? [U_519] :
( ! [U_512] : ~ in(ordered_pair(U_512,U_519),U_516)
& in(U_519,U_522) ) )
& ! [U_521] :
( ( ! [U_518] :
( in(U_518,U_521)
| ! [U_510] : ~ in(ordered_pair(U_510,U_518),U_516) )
& ! [U_517] :
( ? [U_509] : in(ordered_pair(U_509,U_517),U_516)
| ~ in(U_517,U_521) ) )
| U_521 != relation_rng(U_516) ) )
| ~ relation(U_516) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
! [U_516] :
( ( ! [U_522] :
( U_522 = relation_rng(U_516)
| ? [U_520] :
( ~ in(U_520,U_522)
& ? [U_513] : in(ordered_pair(U_513,U_520),U_516) )
| ? [U_519] :
( ! [U_512] : ~ in(ordered_pair(U_512,U_519),U_516)
& in(U_519,U_522) ) )
& ! [U_521] :
( ( ! [U_518] :
( in(U_518,U_521)
| ! [U_510] : ~ in(ordered_pair(U_510,U_518),U_516) )
& ! [U_517] :
( in(ordered_pair(sK96(U_516,U_521,U_517),U_517),U_516)
| ~ in(U_517,U_521) ) )
| U_521 != relation_rng(U_516) ) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_509,sK96(U_516,U_521,U_517))],[f_66_3]) ).
fof(f_66_5,plain,
! [U_516] :
( ( ! [U_522] :
( U_522 = relation_rng(U_516)
| ? [U_520] :
( ~ in(U_520,U_522)
& ? [U_513] : in(ordered_pair(U_513,U_520),U_516) )
| ( ! [U_512] : ~ in(ordered_pair(U_512,sK97(U_516,U_522)),U_516)
& in(sK97(U_516,U_522),U_522) ) )
& ! [U_521] :
( ( ! [U_518] :
( in(U_518,U_521)
| ! [U_510] : ~ in(ordered_pair(U_510,U_518),U_516) )
& ! [U_517] :
( in(ordered_pair(sK96(U_516,U_521,U_517),U_517),U_516)
| ~ in(U_517,U_521) ) )
| U_521 != relation_rng(U_516) ) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_519,sK97(U_516,U_522))],[f_66_4]) ).
fof(f_66_6,plain,
! [U_516] :
( ( ! [U_522] :
( U_522 = relation_rng(U_516)
| ( ~ in(sK98(U_516,U_522),U_522)
& ? [U_513] : in(ordered_pair(U_513,sK98(U_516,U_522)),U_516) )
| ( ! [U_512] : ~ in(ordered_pair(U_512,sK97(U_516,U_522)),U_516)
& in(sK97(U_516,U_522),U_522) ) )
& ! [U_521] :
( ( ! [U_518] :
( in(U_518,U_521)
| ! [U_510] : ~ in(ordered_pair(U_510,U_518),U_516) )
& ! [U_517] :
( in(ordered_pair(sK96(U_516,U_521,U_517),U_517),U_516)
| ~ in(U_517,U_521) ) )
| U_521 != relation_rng(U_516) ) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_520,sK98(U_516,U_522))],[f_66_5]) ).
fof(f_66_7,plain,
! [U_516] :
( ( ! [U_522] :
( U_522 = relation_rng(U_516)
| ( ~ in(sK98(U_516,U_522),U_522)
& in(ordered_pair(sK99(U_516,U_522),sK98(U_516,U_522)),U_516) )
| ( ! [U_512] : ~ in(ordered_pair(U_512,sK97(U_516,U_522)),U_516)
& in(sK97(U_516,U_522),U_522) ) )
& ! [U_521] :
( ( ! [U_518] :
( in(U_518,U_521)
| ! [U_510] : ~ in(ordered_pair(U_510,U_518),U_516) )
& ! [U_517] :
( in(ordered_pair(sK96(U_516,U_521,U_517),U_517),U_516)
| ~ in(U_517,U_521) ) )
| U_521 != relation_rng(U_516) ) )
| ~ relation(U_516) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_513,sK99(U_516,U_522))],[f_66_6]) ).
fof(f_66_8,plain,
( ! [U_516,U_522] :
( ~ in(sK98(U_516,U_522),U_522)
| ~ sP144(U_516,U_522) )
& ! [U_516,U_522] :
( in(ordered_pair(sK99(U_516,U_522),sK98(U_516,U_522)),U_516)
| ~ sP144(U_516,U_522) )
& ! [U_512,U_516,U_522] :
( ~ in(ordered_pair(U_512,sK97(U_516,U_522)),U_516)
| ~ sP143(U_512,U_516,U_522) )
& ! [U_512,U_516,U_522] :
( in(sK97(U_516,U_522),U_522)
| ~ sP143(U_512,U_516,U_522) )
& ! [U_518,U_517,U_521,U_516,U_510] :
( in(U_518,U_521)
| ~ in(ordered_pair(U_510,U_518),U_516)
| ~ sP142(U_518,U_517,U_521,U_516,U_510) )
& ! [U_518,U_517,U_521,U_516,U_510] :
( in(ordered_pair(sK96(U_516,U_521,U_517),U_517),U_516)
| ~ in(U_517,U_521)
| ~ sP142(U_518,U_517,U_521,U_516,U_510) )
& ! [U_518,U_512,U_517,U_521,U_516,U_510,U_522] :
( U_522 = relation_rng(U_516)
| sP144(U_516,U_522)
| sP143(U_512,U_516,U_522)
| ~ sP145(U_518,U_512,U_517,U_521,U_516,U_510,U_522) )
& ! [U_518,U_512,U_517,U_521,U_516,U_510,U_522] :
( sP142(U_518,U_517,U_521,U_516,U_510)
| U_521 != relation_rng(U_516)
| ~ sP145(U_518,U_512,U_517,U_521,U_516,U_510,U_522) )
& ! [U_518,U_512,U_517,U_521,U_516,U_510,U_522] :
( sP145(U_518,U_512,U_517,U_521,U_516,U_510,U_522)
| ~ relation(U_516) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142,sP143,sP144,sP145])],[f_66_7]) ).
cnf(f_66_9,plain,
( sP145(U_518,U_512,U_517,U_521,U_516,U_510,U_522)
| ~ relation(U_516) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_10,plain,
( sP142(U_518,U_517,U_521,U_516,U_510)
| U_521 != relation_rng(U_516)
| ~ sP145(U_518,U_512,U_517,U_521,U_516,U_510,U_522) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_11,plain,
( U_522 = relation_rng(U_516)
| sP144(U_516,U_522)
| sP143(U_512,U_516,U_522)
| ~ sP145(U_518,U_512,U_517,U_521,U_516,U_510,U_522) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_12,plain,
( in(ordered_pair(sK96(U_516,U_521,U_517),U_517),U_516)
| ~ in(U_517,U_521)
| ~ sP142(U_518,U_517,U_521,U_516,U_510) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_13,plain,
( in(U_518,U_521)
| ~ in(ordered_pair(U_510,U_518),U_516)
| ~ sP142(U_518,U_517,U_521,U_516,U_510) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_14,plain,
( in(sK97(U_516,U_522),U_522)
| ~ sP143(U_512,U_516,U_522) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_15,plain,
( ~ in(ordered_pair(U_512,sK97(U_516,U_522)),U_516)
| ~ sP143(U_512,U_516,U_522) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_16,plain,
( in(ordered_pair(sK99(U_516,U_522),sK98(U_516,U_522)),U_516)
| ~ sP144(U_516,U_522) ),
inference(clausify,[status(thm)],[f_66_8]) ).
cnf(f_66_17,plain,
( ~ in(sK98(U_516,U_522),U_522)
| ~ sP144(U_516,U_522) ),
inference(clausify,[status(thm)],[f_66_8]) ).
fof(f_67_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_67_2,plain,
! [U_524,U_523] :
( subset_complement(U_524,U_523) = set_difference(U_524,U_523)
| ~ element(U_523,powerset(U_524)) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_524,U_523] :
( subset_complement(U_524,U_523) = set_difference(U_524,U_523)
| ~ element(U_523,powerset(U_524)) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( subset_complement(U_524,U_523) = set_difference(U_524,U_523)
| ~ element(U_523,powerset(U_524)) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_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_68_2,plain,
! [U_526,U_525] : ordered_pair(U_526,U_525) = unordered_pair(unordered_pair(U_526,U_525),singleton(U_526)),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_526,U_525] : ordered_pair(U_526,U_525) = unordered_pair(unordered_pair(U_526,U_525),singleton(U_526)),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
ordered_pair(U_526,U_525) = unordered_pair(unordered_pair(U_526,U_525),singleton(U_526)),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_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_69_2,plain,
! [U_528] :
( ! [U_527] :
( ( well_orders(U_528,U_527)
| ~ is_well_founded_in(U_528,U_527)
| ~ is_connected_in(U_528,U_527)
| ~ is_antisymmetric_in(U_528,U_527)
| ~ is_transitive_in(U_528,U_527)
| ~ is_reflexive_in(U_528,U_527) )
& ( ( is_well_founded_in(U_528,U_527)
& is_connected_in(U_528,U_527)
& is_antisymmetric_in(U_528,U_527)
& is_transitive_in(U_528,U_527)
& is_reflexive_in(U_528,U_527) )
| ~ well_orders(U_528,U_527) ) )
| ~ relation(U_528) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_528] :
( ( ! [U_530] :
( well_orders(U_528,U_530)
| ~ is_well_founded_in(U_528,U_530)
| ~ is_connected_in(U_528,U_530)
| ~ is_antisymmetric_in(U_528,U_530)
| ~ is_transitive_in(U_528,U_530)
| ~ is_reflexive_in(U_528,U_530) )
& ! [U_529] :
( ( is_well_founded_in(U_528,U_529)
& is_connected_in(U_528,U_529)
& is_antisymmetric_in(U_528,U_529)
& is_transitive_in(U_528,U_529)
& is_reflexive_in(U_528,U_529) )
| ~ well_orders(U_528,U_529) ) )
| ~ relation(U_528) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
( ! [U_529,U_528] :
( is_well_founded_in(U_528,U_529)
| ~ sP146(U_529,U_528) )
& ! [U_529,U_528] :
( is_connected_in(U_528,U_529)
| ~ sP146(U_529,U_528) )
& ! [U_529,U_528] :
( is_antisymmetric_in(U_528,U_529)
| ~ sP146(U_529,U_528) )
& ! [U_529,U_528] :
( is_transitive_in(U_528,U_529)
| ~ sP146(U_529,U_528) )
& ! [U_529,U_528] :
( is_reflexive_in(U_528,U_529)
| ~ sP146(U_529,U_528) )
& ! [U_530,U_529,U_528] :
( well_orders(U_528,U_530)
| ~ is_well_founded_in(U_528,U_530)
| ~ is_connected_in(U_528,U_530)
| ~ is_antisymmetric_in(U_528,U_530)
| ~ is_transitive_in(U_528,U_530)
| ~ is_reflexive_in(U_528,U_530)
| ~ sP147(U_530,U_529,U_528) )
& ! [U_530,U_529,U_528] :
( sP146(U_529,U_528)
| ~ well_orders(U_528,U_529)
| ~ sP147(U_530,U_529,U_528) )
& ! [U_530,U_529,U_528] :
( sP147(U_530,U_529,U_528)
| ~ relation(U_528) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146,sP147])],[f_69_3]) ).
cnf(f_69_5,plain,
( sP147(U_530,U_529,U_528)
| ~ relation(U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_6,plain,
( sP146(U_529,U_528)
| ~ well_orders(U_528,U_529)
| ~ sP147(U_530,U_529,U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_7,plain,
( well_orders(U_528,U_530)
| ~ is_well_founded_in(U_528,U_530)
| ~ is_connected_in(U_528,U_530)
| ~ is_antisymmetric_in(U_528,U_530)
| ~ is_transitive_in(U_528,U_530)
| ~ is_reflexive_in(U_528,U_530)
| ~ sP147(U_530,U_529,U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_8,plain,
( is_reflexive_in(U_528,U_529)
| ~ sP146(U_529,U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_9,plain,
( is_transitive_in(U_528,U_529)
| ~ sP146(U_529,U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_10,plain,
( is_antisymmetric_in(U_528,U_529)
| ~ sP146(U_529,U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_11,plain,
( is_connected_in(U_528,U_529)
| ~ sP146(U_529,U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_12,plain,
( is_well_founded_in(U_528,U_529)
| ~ sP146(U_529,U_528) ),
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_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_70_2,plain,
! [U_531] :
( ( being_limit_ordinal(U_531)
| U_531 != union(U_531) )
& ( U_531 = union(U_531)
| ~ being_limit_ordinal(U_531) ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ! [U_533] :
( being_limit_ordinal(U_533)
| U_533 != union(U_533) )
& ! [U_532] :
( U_532 = union(U_532)
| ~ being_limit_ordinal(U_532) ) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
fof(f_70_4,plain,
( ! [U_533] :
( being_limit_ordinal(U_533)
| U_533 != union(U_533) )
& ! [U_532] :
( U_532 = union(U_532)
| ~ being_limit_ordinal(U_532) ) ),
inference(definitional_conversion,[status(esa)],[f_70_3]) ).
cnf(f_70_5,plain,
( U_532 = union(U_532)
| ~ being_limit_ordinal(U_532) ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_6,plain,
( being_limit_ordinal(U_533)
| U_533 != union(U_533) ),
inference(clausify,[status(thm)],[f_70_4]) ).
fof(f_71_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_71_2,plain,
! [U_534] :
( relation_field(U_534) = set_union2(relation_dom(U_534),relation_rng(U_534))
| ~ relation(U_534) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_534] :
( relation_field(U_534) = set_union2(relation_dom(U_534),relation_rng(U_534))
| ~ relation(U_534) ),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
( relation_field(U_534) = set_union2(relation_dom(U_534),relation_rng(U_534))
| ~ relation(U_534) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_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_72_2,plain,
! [U_540] :
( ! [U_539] :
( ( is_connected_in(U_540,U_539)
| ? [U_538,U_537] :
( ~ in(ordered_pair(U_537,U_538),U_540)
& ~ in(ordered_pair(U_538,U_537),U_540)
& U_538 != U_537
& in(U_537,U_539)
& in(U_538,U_539) ) )
& ( ! [U_536,U_535] :
( in(ordered_pair(U_535,U_536),U_540)
| in(ordered_pair(U_536,U_535),U_540)
| U_536 = U_535
| ~ in(U_535,U_539)
| ~ in(U_536,U_539) )
| ~ is_connected_in(U_540,U_539) ) )
| ~ relation(U_540) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_540] :
( ( ! [U_542] :
( is_connected_in(U_540,U_542)
| ? [U_538] :
( ? [U_537] :
( ~ in(ordered_pair(U_537,U_538),U_540)
& ~ in(ordered_pair(U_538,U_537),U_540)
& U_538 != U_537
& in(U_537,U_542) )
& in(U_538,U_542) ) )
& ! [U_541] :
( ! [U_536] :
( ! [U_535] :
( in(ordered_pair(U_535,U_536),U_540)
| in(ordered_pair(U_536,U_535),U_540)
| U_536 = U_535
| ~ in(U_535,U_541) )
| ~ in(U_536,U_541) )
| ~ is_connected_in(U_540,U_541) ) )
| ~ relation(U_540) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
! [U_540] :
( ( ! [U_542] :
( is_connected_in(U_540,U_542)
| ( ? [U_537] :
( ~ in(ordered_pair(U_537,sK100(U_540,U_542)),U_540)
& ~ in(ordered_pair(sK100(U_540,U_542),U_537),U_540)
& sK100(U_540,U_542) != U_537
& in(U_537,U_542) )
& in(sK100(U_540,U_542),U_542) ) )
& ! [U_541] :
( ! [U_536] :
( ! [U_535] :
( in(ordered_pair(U_535,U_536),U_540)
| in(ordered_pair(U_536,U_535),U_540)
| U_536 = U_535
| ~ in(U_535,U_541) )
| ~ in(U_536,U_541) )
| ~ is_connected_in(U_540,U_541) ) )
| ~ relation(U_540) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_538,sK100(U_540,U_542))],[f_72_3]) ).
fof(f_72_5,plain,
! [U_540] :
( ( ! [U_542] :
( is_connected_in(U_540,U_542)
| ( ~ in(ordered_pair(sK101(U_540,U_542),sK100(U_540,U_542)),U_540)
& ~ in(ordered_pair(sK100(U_540,U_542),sK101(U_540,U_542)),U_540)
& sK100(U_540,U_542) != sK101(U_540,U_542)
& in(sK101(U_540,U_542),U_542)
& in(sK100(U_540,U_542),U_542) ) )
& ! [U_541] :
( ! [U_536] :
( ! [U_535] :
( in(ordered_pair(U_535,U_536),U_540)
| in(ordered_pair(U_536,U_535),U_540)
| U_536 = U_535
| ~ in(U_535,U_541) )
| ~ in(U_536,U_541) )
| ~ is_connected_in(U_540,U_541) ) )
| ~ relation(U_540) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_537,sK101(U_540,U_542))],[f_72_4]) ).
fof(f_72_6,plain,
( ! [U_540,U_542] :
( ~ in(ordered_pair(sK101(U_540,U_542),sK100(U_540,U_542)),U_540)
| ~ sP148(U_540,U_542) )
& ! [U_540,U_542] :
( ~ in(ordered_pair(sK100(U_540,U_542),sK101(U_540,U_542)),U_540)
| ~ sP148(U_540,U_542) )
& ! [U_540,U_542] :
( sK100(U_540,U_542) != sK101(U_540,U_542)
| ~ sP148(U_540,U_542) )
& ! [U_540,U_542] :
( in(sK101(U_540,U_542),U_542)
| ~ sP148(U_540,U_542) )
& ! [U_540,U_542] :
( in(sK100(U_540,U_542),U_542)
| ~ sP148(U_540,U_542) )
& ! [U_535,U_536,U_540,U_541,U_542] :
( is_connected_in(U_540,U_542)
| sP148(U_540,U_542)
| ~ sP149(U_535,U_536,U_540,U_541,U_542) )
& ! [U_535,U_536,U_540,U_541,U_542] :
( in(ordered_pair(U_535,U_536),U_540)
| in(ordered_pair(U_536,U_535),U_540)
| U_536 = U_535
| ~ in(U_535,U_541)
| ~ in(U_536,U_541)
| ~ is_connected_in(U_540,U_541)
| ~ sP149(U_535,U_536,U_540,U_541,U_542) )
& ! [U_535,U_536,U_540,U_541,U_542] :
( sP149(U_535,U_536,U_540,U_541,U_542)
| ~ relation(U_540) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148,sP149])],[f_72_5]) ).
cnf(f_72_7,plain,
( sP149(U_535,U_536,U_540,U_541,U_542)
| ~ relation(U_540) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_8,plain,
( in(ordered_pair(U_535,U_536),U_540)
| in(ordered_pair(U_536,U_535),U_540)
| U_536 = U_535
| ~ in(U_535,U_541)
| ~ in(U_536,U_541)
| ~ is_connected_in(U_540,U_541)
| ~ sP149(U_535,U_536,U_540,U_541,U_542) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_9,plain,
( is_connected_in(U_540,U_542)
| sP148(U_540,U_542)
| ~ sP149(U_535,U_536,U_540,U_541,U_542) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_10,plain,
( in(sK100(U_540,U_542),U_542)
| ~ sP148(U_540,U_542) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_11,plain,
( in(sK101(U_540,U_542),U_542)
| ~ sP148(U_540,U_542) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_12,plain,
( sK100(U_540,U_542) != sK101(U_540,U_542)
| ~ sP148(U_540,U_542) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_13,plain,
( ~ in(ordered_pair(sK100(U_540,U_542),sK101(U_540,U_542)),U_540)
| ~ sP148(U_540,U_542) ),
inference(clausify,[status(thm)],[f_72_6]) ).
cnf(f_72_14,plain,
( ~ in(ordered_pair(sK101(U_540,U_542),sK100(U_540,U_542)),U_540)
| ~ sP148(U_540,U_542) ),
inference(clausify,[status(thm)],[f_72_6]) ).
fof(f_73_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_73_2,plain,
! [U_544] :
( ! [U_543] : relation_restriction(U_544,U_543) = set_intersection2(U_544,cartesian_product2(U_543,U_543))
| ~ relation(U_544) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_543,U_544] :
( relation_restriction(U_544,U_543) = set_intersection2(U_544,cartesian_product2(U_543,U_543))
| ~ relation(U_544) ),
inference(definitional_conversion,[status(esa)],[f_73_2]) ).
cnf(f_73_4,plain,
( relation_restriction(U_544,U_543) = set_intersection2(U_544,cartesian_product2(U_543,U_543))
| ~ relation(U_544) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_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_74_2,plain,
! [U_550] :
( ! [U_549] :
( ( ( U_549 = relation_inverse(U_550)
| ? [U_548,U_547] :
( ( ~ in(ordered_pair(U_548,U_547),U_549)
& in(ordered_pair(U_547,U_548),U_550) )
| ( ~ in(ordered_pair(U_547,U_548),U_550)
& in(ordered_pair(U_548,U_547),U_549) ) ) )
& ( ! [U_546,U_545] :
( ( in(ordered_pair(U_546,U_545),U_549)
| ~ in(ordered_pair(U_545,U_546),U_550) )
& ( in(ordered_pair(U_545,U_546),U_550)
| ~ in(ordered_pair(U_546,U_545),U_549) ) )
| U_549 != relation_inverse(U_550) ) )
| ~ relation(U_549) )
| ~ relation(U_550) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_550] :
( ! [U_549] :
( ( ( U_549 = relation_inverse(U_550)
| ? [U_558,U_556] :
( ~ in(ordered_pair(U_558,U_556),U_549)
& in(ordered_pair(U_556,U_558),U_550) )
| ? [U_557,U_555] :
( ~ in(ordered_pair(U_555,U_557),U_550)
& in(ordered_pair(U_557,U_555),U_549) ) )
& ( ( ! [U_554,U_552] :
( in(ordered_pair(U_554,U_552),U_549)
| ~ in(ordered_pair(U_552,U_554),U_550) )
& ! [U_553,U_551] :
( in(ordered_pair(U_551,U_553),U_550)
| ~ in(ordered_pair(U_553,U_551),U_549) ) )
| U_549 != relation_inverse(U_550) ) )
| ~ relation(U_549) )
| ~ relation(U_550) ),
inference(miniscope,[status(thm)],[f_74_2]) ).
fof(f_74_4,plain,
! [U_550] :
( ! [U_549] :
( ( ( U_549 = relation_inverse(U_550)
| ? [U_558,U_556] :
( ~ in(ordered_pair(U_558,U_556),U_549)
& in(ordered_pair(U_556,U_558),U_550) )
| ? [U_555] :
( ~ in(ordered_pair(U_555,sK102(U_550,U_549)),U_550)
& in(ordered_pair(sK102(U_550,U_549),U_555),U_549) ) )
& ( ( ! [U_554,U_552] :
( in(ordered_pair(U_554,U_552),U_549)
| ~ in(ordered_pair(U_552,U_554),U_550) )
& ! [U_553,U_551] :
( in(ordered_pair(U_551,U_553),U_550)
| ~ in(ordered_pair(U_553,U_551),U_549) ) )
| U_549 != relation_inverse(U_550) ) )
| ~ relation(U_549) )
| ~ relation(U_550) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_557,sK102(U_550,U_549))],[f_74_3]) ).
fof(f_74_5,plain,
! [U_550] :
( ! [U_549] :
( ( ( U_549 = relation_inverse(U_550)
| ? [U_558,U_556] :
( ~ in(ordered_pair(U_558,U_556),U_549)
& in(ordered_pair(U_556,U_558),U_550) )
| ( ~ in(ordered_pair(sK103(U_550,U_549),sK102(U_550,U_549)),U_550)
& in(ordered_pair(sK102(U_550,U_549),sK103(U_550,U_549)),U_549) ) )
& ( ( ! [U_554,U_552] :
( in(ordered_pair(U_554,U_552),U_549)
| ~ in(ordered_pair(U_552,U_554),U_550) )
& ! [U_553,U_551] :
( in(ordered_pair(U_551,U_553),U_550)
| ~ in(ordered_pair(U_553,U_551),U_549) ) )
| U_549 != relation_inverse(U_550) ) )
| ~ relation(U_549) )
| ~ relation(U_550) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_555,sK103(U_550,U_549))],[f_74_4]) ).
fof(f_74_6,plain,
! [U_550] :
( ! [U_549] :
( ( ( U_549 = relation_inverse(U_550)
| ? [U_556] :
( ~ in(ordered_pair(sK104(U_550,U_549),U_556),U_549)
& in(ordered_pair(U_556,sK104(U_550,U_549)),U_550) )
| ( ~ in(ordered_pair(sK103(U_550,U_549),sK102(U_550,U_549)),U_550)
& in(ordered_pair(sK102(U_550,U_549),sK103(U_550,U_549)),U_549) ) )
& ( ( ! [U_554,U_552] :
( in(ordered_pair(U_554,U_552),U_549)
| ~ in(ordered_pair(U_552,U_554),U_550) )
& ! [U_553,U_551] :
( in(ordered_pair(U_551,U_553),U_550)
| ~ in(ordered_pair(U_553,U_551),U_549) ) )
| U_549 != relation_inverse(U_550) ) )
| ~ relation(U_549) )
| ~ relation(U_550) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_558,sK104(U_550,U_549))],[f_74_5]) ).
fof(f_74_7,plain,
! [U_550] :
( ! [U_549] :
( ( ( U_549 = relation_inverse(U_550)
| ( ~ in(ordered_pair(sK104(U_550,U_549),sK105(U_550,U_549)),U_549)
& in(ordered_pair(sK105(U_550,U_549),sK104(U_550,U_549)),U_550) )
| ( ~ in(ordered_pair(sK103(U_550,U_549),sK102(U_550,U_549)),U_550)
& in(ordered_pair(sK102(U_550,U_549),sK103(U_550,U_549)),U_549) ) )
& ( ( ! [U_554,U_552] :
( in(ordered_pair(U_554,U_552),U_549)
| ~ in(ordered_pair(U_552,U_554),U_550) )
& ! [U_553,U_551] :
( in(ordered_pair(U_551,U_553),U_550)
| ~ in(ordered_pair(U_553,U_551),U_549) ) )
| U_549 != relation_inverse(U_550) ) )
| ~ relation(U_549) )
| ~ relation(U_550) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_556,sK105(U_550,U_549))],[f_74_6]) ).
fof(f_74_8,plain,
( ! [U_549,U_550] :
( ~ in(ordered_pair(sK104(U_550,U_549),sK105(U_550,U_549)),U_549)
| ~ sP152(U_549,U_550) )
& ! [U_549,U_550] :
( in(ordered_pair(sK105(U_550,U_549),sK104(U_550,U_549)),U_550)
| ~ sP152(U_549,U_550) )
& ! [U_549,U_550] :
( ~ in(ordered_pair(sK103(U_550,U_549),sK102(U_550,U_549)),U_550)
| ~ sP151(U_549,U_550) )
& ! [U_549,U_550] :
( in(ordered_pair(sK102(U_550,U_549),sK103(U_550,U_549)),U_549)
| ~ sP151(U_549,U_550) )
& ! [U_549,U_553,U_550,U_554,U_551,U_552] :
( in(ordered_pair(U_554,U_552),U_549)
| ~ in(ordered_pair(U_552,U_554),U_550)
| ~ sP150(U_549,U_553,U_550,U_554,U_551,U_552) )
& ! [U_549,U_553,U_550,U_554,U_551,U_552] :
( in(ordered_pair(U_551,U_553),U_550)
| ~ in(ordered_pair(U_553,U_551),U_549)
| ~ sP150(U_549,U_553,U_550,U_554,U_551,U_552) )
& ! [U_549,U_553,U_550,U_554,U_551,U_552] :
( U_549 = relation_inverse(U_550)
| sP152(U_549,U_550)
| sP151(U_549,U_550)
| ~ sP153(U_549,U_553,U_550,U_554,U_551,U_552) )
& ! [U_549,U_553,U_550,U_554,U_551,U_552] :
( sP150(U_549,U_553,U_550,U_554,U_551,U_552)
| U_549 != relation_inverse(U_550)
| ~ sP153(U_549,U_553,U_550,U_554,U_551,U_552) )
& ! [U_549,U_553,U_550,U_554,U_551,U_552] :
( sP153(U_549,U_553,U_550,U_554,U_551,U_552)
| ~ relation(U_549)
| ~ relation(U_550) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150,sP151,sP152,sP153])],[f_74_7]) ).
cnf(f_74_9,plain,
( sP153(U_549,U_553,U_550,U_554,U_551,U_552)
| ~ relation(U_549)
| ~ relation(U_550) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_10,plain,
( sP150(U_549,U_553,U_550,U_554,U_551,U_552)
| U_549 != relation_inverse(U_550)
| ~ sP153(U_549,U_553,U_550,U_554,U_551,U_552) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_11,plain,
( U_549 = relation_inverse(U_550)
| sP152(U_549,U_550)
| sP151(U_549,U_550)
| ~ sP153(U_549,U_553,U_550,U_554,U_551,U_552) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_12,plain,
( in(ordered_pair(U_551,U_553),U_550)
| ~ in(ordered_pair(U_553,U_551),U_549)
| ~ sP150(U_549,U_553,U_550,U_554,U_551,U_552) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_13,plain,
( in(ordered_pair(U_554,U_552),U_549)
| ~ in(ordered_pair(U_552,U_554),U_550)
| ~ sP150(U_549,U_553,U_550,U_554,U_551,U_552) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_14,plain,
( in(ordered_pair(sK102(U_550,U_549),sK103(U_550,U_549)),U_549)
| ~ sP151(U_549,U_550) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_15,plain,
( ~ in(ordered_pair(sK103(U_550,U_549),sK102(U_550,U_549)),U_550)
| ~ sP151(U_549,U_550) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_16,plain,
( in(ordered_pair(sK105(U_550,U_549),sK104(U_550,U_549)),U_550)
| ~ sP152(U_549,U_550) ),
inference(clausify,[status(thm)],[f_74_8]) ).
cnf(f_74_17,plain,
( ~ in(ordered_pair(sK104(U_550,U_549),sK105(U_550,U_549)),U_549)
| ~ sP152(U_549,U_550) ),
inference(clausify,[status(thm)],[f_74_8]) ).
fof(f_75_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_75_2,plain,
! [U_565] :
( ! [U_564] :
( ! [U_563] :
( ( ( relation_isomorphism(U_565,U_564,U_563)
| ? [U_562,U_561] :
( ( ~ in(ordered_pair(U_562,U_561),U_565)
& in(ordered_pair(apply(U_563,U_562),apply(U_563,U_561)),U_564)
& in(U_561,relation_field(U_565))
& in(U_562,relation_field(U_565)) )
| ( ( ~ in(ordered_pair(apply(U_563,U_562),apply(U_563,U_561)),U_564)
| ~ in(U_561,relation_field(U_565))
| ~ in(U_562,relation_field(U_565)) )
& in(ordered_pair(U_562,U_561),U_565) ) )
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565) )
& ( ( ! [U_560,U_559] :
( ( in(ordered_pair(U_560,U_559),U_565)
| ~ in(ordered_pair(apply(U_563,U_560),apply(U_563,U_559)),U_564)
| ~ in(U_559,relation_field(U_565))
| ~ in(U_560,relation_field(U_565)) )
& ( ( in(ordered_pair(apply(U_563,U_560),apply(U_563,U_559)),U_564)
& in(U_559,relation_field(U_565))
& in(U_560,relation_field(U_565)) )
| ~ in(ordered_pair(U_560,U_559),U_565) ) )
& one_to_one(U_563)
& relation_rng(U_563) = relation_field(U_564)
& relation_dom(U_563) = relation_field(U_565) )
| ~ relation_isomorphism(U_565,U_564,U_563) ) )
| ~ function(U_563)
| ~ relation(U_563) )
| ~ relation(U_564) )
| ~ relation(U_565) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_565] :
( ! [U_564] :
( ! [U_563] :
( ( ( relation_isomorphism(U_565,U_564,U_563)
| ? [U_573,U_571] :
( ~ in(ordered_pair(U_573,U_571),U_565)
& in(ordered_pair(apply(U_563,U_573),apply(U_563,U_571)),U_564)
& in(U_571,relation_field(U_565))
& in(U_573,relation_field(U_565)) )
| ? [U_572,U_570] :
( ( ~ in(ordered_pair(apply(U_563,U_572),apply(U_563,U_570)),U_564)
| ~ in(U_570,relation_field(U_565))
| ~ in(U_572,relation_field(U_565)) )
& in(ordered_pair(U_572,U_570),U_565) )
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565) )
& ( ( ! [U_569,U_567] :
( in(ordered_pair(U_569,U_567),U_565)
| ~ in(ordered_pair(apply(U_563,U_569),apply(U_563,U_567)),U_564)
| ~ in(U_567,relation_field(U_565))
| ~ in(U_569,relation_field(U_565)) )
& ! [U_568,U_566] :
( ( in(ordered_pair(apply(U_563,U_568),apply(U_563,U_566)),U_564)
& in(U_566,relation_field(U_565))
& in(U_568,relation_field(U_565)) )
| ~ in(ordered_pair(U_568,U_566),U_565) )
& one_to_one(U_563)
& relation_rng(U_563) = relation_field(U_564)
& relation_dom(U_563) = relation_field(U_565) )
| ~ relation_isomorphism(U_565,U_564,U_563) ) )
| ~ function(U_563)
| ~ relation(U_563) )
| ~ relation(U_564) )
| ~ relation(U_565) ),
inference(miniscope,[status(thm)],[f_75_2]) ).
fof(f_75_4,plain,
! [U_565] :
( ! [U_564] :
( ! [U_563] :
( ( ( relation_isomorphism(U_565,U_564,U_563)
| ? [U_573,U_571] :
( ~ in(ordered_pair(U_573,U_571),U_565)
& in(ordered_pair(apply(U_563,U_573),apply(U_563,U_571)),U_564)
& in(U_571,relation_field(U_565))
& in(U_573,relation_field(U_565)) )
| ? [U_570] :
( ( ~ in(ordered_pair(apply(U_563,sK106(U_565,U_564,U_563)),apply(U_563,U_570)),U_564)
| ~ in(U_570,relation_field(U_565))
| ~ in(sK106(U_565,U_564,U_563),relation_field(U_565)) )
& in(ordered_pair(sK106(U_565,U_564,U_563),U_570),U_565) )
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565) )
& ( ( ! [U_569,U_567] :
( in(ordered_pair(U_569,U_567),U_565)
| ~ in(ordered_pair(apply(U_563,U_569),apply(U_563,U_567)),U_564)
| ~ in(U_567,relation_field(U_565))
| ~ in(U_569,relation_field(U_565)) )
& ! [U_568,U_566] :
( ( in(ordered_pair(apply(U_563,U_568),apply(U_563,U_566)),U_564)
& in(U_566,relation_field(U_565))
& in(U_568,relation_field(U_565)) )
| ~ in(ordered_pair(U_568,U_566),U_565) )
& one_to_one(U_563)
& relation_rng(U_563) = relation_field(U_564)
& relation_dom(U_563) = relation_field(U_565) )
| ~ relation_isomorphism(U_565,U_564,U_563) ) )
| ~ function(U_563)
| ~ relation(U_563) )
| ~ relation(U_564) )
| ~ relation(U_565) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_572,sK106(U_565,U_564,U_563))],[f_75_3]) ).
fof(f_75_5,plain,
! [U_565] :
( ! [U_564] :
( ! [U_563] :
( ( ( relation_isomorphism(U_565,U_564,U_563)
| ? [U_573,U_571] :
( ~ in(ordered_pair(U_573,U_571),U_565)
& in(ordered_pair(apply(U_563,U_573),apply(U_563,U_571)),U_564)
& in(U_571,relation_field(U_565))
& in(U_573,relation_field(U_565)) )
| ( ( ~ in(ordered_pair(apply(U_563,sK106(U_565,U_564,U_563)),apply(U_563,sK107(U_565,U_564,U_563))),U_564)
| ~ in(sK107(U_565,U_564,U_563),relation_field(U_565))
| ~ in(sK106(U_565,U_564,U_563),relation_field(U_565)) )
& in(ordered_pair(sK106(U_565,U_564,U_563),sK107(U_565,U_564,U_563)),U_565) )
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565) )
& ( ( ! [U_569,U_567] :
( in(ordered_pair(U_569,U_567),U_565)
| ~ in(ordered_pair(apply(U_563,U_569),apply(U_563,U_567)),U_564)
| ~ in(U_567,relation_field(U_565))
| ~ in(U_569,relation_field(U_565)) )
& ! [U_568,U_566] :
( ( in(ordered_pair(apply(U_563,U_568),apply(U_563,U_566)),U_564)
& in(U_566,relation_field(U_565))
& in(U_568,relation_field(U_565)) )
| ~ in(ordered_pair(U_568,U_566),U_565) )
& one_to_one(U_563)
& relation_rng(U_563) = relation_field(U_564)
& relation_dom(U_563) = relation_field(U_565) )
| ~ relation_isomorphism(U_565,U_564,U_563) ) )
| ~ function(U_563)
| ~ relation(U_563) )
| ~ relation(U_564) )
| ~ relation(U_565) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_570,sK107(U_565,U_564,U_563))],[f_75_4]) ).
fof(f_75_6,plain,
! [U_565] :
( ! [U_564] :
( ! [U_563] :
( ( ( relation_isomorphism(U_565,U_564,U_563)
| ? [U_571] :
( ~ in(ordered_pair(sK108(U_565,U_564,U_563),U_571),U_565)
& in(ordered_pair(apply(U_563,sK108(U_565,U_564,U_563)),apply(U_563,U_571)),U_564)
& in(U_571,relation_field(U_565))
& in(sK108(U_565,U_564,U_563),relation_field(U_565)) )
| ( ( ~ in(ordered_pair(apply(U_563,sK106(U_565,U_564,U_563)),apply(U_563,sK107(U_565,U_564,U_563))),U_564)
| ~ in(sK107(U_565,U_564,U_563),relation_field(U_565))
| ~ in(sK106(U_565,U_564,U_563),relation_field(U_565)) )
& in(ordered_pair(sK106(U_565,U_564,U_563),sK107(U_565,U_564,U_563)),U_565) )
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565) )
& ( ( ! [U_569,U_567] :
( in(ordered_pair(U_569,U_567),U_565)
| ~ in(ordered_pair(apply(U_563,U_569),apply(U_563,U_567)),U_564)
| ~ in(U_567,relation_field(U_565))
| ~ in(U_569,relation_field(U_565)) )
& ! [U_568,U_566] :
( ( in(ordered_pair(apply(U_563,U_568),apply(U_563,U_566)),U_564)
& in(U_566,relation_field(U_565))
& in(U_568,relation_field(U_565)) )
| ~ in(ordered_pair(U_568,U_566),U_565) )
& one_to_one(U_563)
& relation_rng(U_563) = relation_field(U_564)
& relation_dom(U_563) = relation_field(U_565) )
| ~ relation_isomorphism(U_565,U_564,U_563) ) )
| ~ function(U_563)
| ~ relation(U_563) )
| ~ relation(U_564) )
| ~ relation(U_565) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_573,sK108(U_565,U_564,U_563))],[f_75_5]) ).
fof(f_75_7,plain,
! [U_565] :
( ! [U_564] :
( ! [U_563] :
( ( ( relation_isomorphism(U_565,U_564,U_563)
| ( ~ in(ordered_pair(sK108(U_565,U_564,U_563),sK109(U_565,U_564,U_563)),U_565)
& in(ordered_pair(apply(U_563,sK108(U_565,U_564,U_563)),apply(U_563,sK109(U_565,U_564,U_563))),U_564)
& in(sK109(U_565,U_564,U_563),relation_field(U_565))
& in(sK108(U_565,U_564,U_563),relation_field(U_565)) )
| ( ( ~ in(ordered_pair(apply(U_563,sK106(U_565,U_564,U_563)),apply(U_563,sK107(U_565,U_564,U_563))),U_564)
| ~ in(sK107(U_565,U_564,U_563),relation_field(U_565))
| ~ in(sK106(U_565,U_564,U_563),relation_field(U_565)) )
& in(ordered_pair(sK106(U_565,U_564,U_563),sK107(U_565,U_564,U_563)),U_565) )
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565) )
& ( ( ! [U_569,U_567] :
( in(ordered_pair(U_569,U_567),U_565)
| ~ in(ordered_pair(apply(U_563,U_569),apply(U_563,U_567)),U_564)
| ~ in(U_567,relation_field(U_565))
| ~ in(U_569,relation_field(U_565)) )
& ! [U_568,U_566] :
( ( in(ordered_pair(apply(U_563,U_568),apply(U_563,U_566)),U_564)
& in(U_566,relation_field(U_565))
& in(U_568,relation_field(U_565)) )
| ~ in(ordered_pair(U_568,U_566),U_565) )
& one_to_one(U_563)
& relation_rng(U_563) = relation_field(U_564)
& relation_dom(U_563) = relation_field(U_565) )
| ~ relation_isomorphism(U_565,U_564,U_563) ) )
| ~ function(U_563)
| ~ relation(U_563) )
| ~ relation(U_564) )
| ~ relation(U_565) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_571,sK109(U_565,U_564,U_563))],[f_75_6]) ).
fof(f_75_8,plain,
( ! [U_565,U_563,U_564] :
( ~ in(ordered_pair(sK108(U_565,U_564,U_563),sK109(U_565,U_564,U_563)),U_565)
| ~ sP157(U_565,U_563,U_564) )
& ! [U_565,U_563,U_564] :
( in(ordered_pair(apply(U_563,sK108(U_565,U_564,U_563)),apply(U_563,sK109(U_565,U_564,U_563))),U_564)
| ~ sP157(U_565,U_563,U_564) )
& ! [U_565,U_563,U_564] :
( in(sK109(U_565,U_564,U_563),relation_field(U_565))
| ~ sP157(U_565,U_563,U_564) )
& ! [U_565,U_563,U_564] :
( in(sK108(U_565,U_564,U_563),relation_field(U_565))
| ~ sP157(U_565,U_563,U_564) )
& ! [U_565,U_563,U_564] :
( ~ in(ordered_pair(apply(U_563,sK106(U_565,U_564,U_563)),apply(U_563,sK107(U_565,U_564,U_563))),U_564)
| ~ in(sK107(U_565,U_564,U_563),relation_field(U_565))
| ~ in(sK106(U_565,U_564,U_563),relation_field(U_565))
| ~ sP156(U_565,U_563,U_564) )
& ! [U_565,U_563,U_564] :
( in(ordered_pair(sK106(U_565,U_564,U_563),sK107(U_565,U_564,U_563)),U_565)
| ~ sP156(U_565,U_563,U_564) )
& ! [U_568,U_565,U_566,U_563,U_564] :
( in(ordered_pair(apply(U_563,U_568),apply(U_563,U_566)),U_564)
| ~ sP154(U_568,U_565,U_566,U_563,U_564) )
& ! [U_568,U_565,U_566,U_563,U_564] :
( in(U_566,relation_field(U_565))
| ~ sP154(U_568,U_565,U_566,U_563,U_564) )
& ! [U_568,U_565,U_566,U_563,U_564] :
( in(U_568,relation_field(U_565))
| ~ sP154(U_568,U_565,U_566,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( in(ordered_pair(U_569,U_567),U_565)
| ~ in(ordered_pair(apply(U_563,U_569),apply(U_563,U_567)),U_564)
| ~ in(U_567,relation_field(U_565))
| ~ in(U_569,relation_field(U_565))
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( sP154(U_568,U_565,U_566,U_563,U_564)
| ~ in(ordered_pair(U_568,U_566),U_565)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( one_to_one(U_563)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( relation_rng(U_563) = relation_field(U_564)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( relation_dom(U_563) = relation_field(U_565)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( relation_isomorphism(U_565,U_564,U_563)
| sP157(U_565,U_563,U_564)
| sP156(U_565,U_563,U_564)
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565)
| ~ sP158(U_568,U_565,U_567,U_566,U_569,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564)
| ~ relation_isomorphism(U_565,U_564,U_563)
| ~ sP158(U_568,U_565,U_567,U_566,U_569,U_563,U_564) )
& ! [U_568,U_565,U_567,U_566,U_569,U_563,U_564] :
( sP158(U_568,U_565,U_567,U_566,U_569,U_563,U_564)
| ~ function(U_563)
| ~ relation(U_563)
| ~ relation(U_564)
| ~ relation(U_565) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154,sP155,sP156,sP157,sP158])],[f_75_7]) ).
cnf(f_75_9,plain,
( sP158(U_568,U_565,U_567,U_566,U_569,U_563,U_564)
| ~ function(U_563)
| ~ relation(U_563)
| ~ relation(U_564)
| ~ relation(U_565) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_10,plain,
( sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564)
| ~ relation_isomorphism(U_565,U_564,U_563)
| ~ sP158(U_568,U_565,U_567,U_566,U_569,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_11,plain,
( relation_isomorphism(U_565,U_564,U_563)
| sP157(U_565,U_563,U_564)
| sP156(U_565,U_563,U_564)
| ~ one_to_one(U_563)
| relation_rng(U_563) != relation_field(U_564)
| relation_dom(U_563) != relation_field(U_565)
| ~ sP158(U_568,U_565,U_567,U_566,U_569,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_12,plain,
( relation_dom(U_563) = relation_field(U_565)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_13,plain,
( relation_rng(U_563) = relation_field(U_564)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_14,plain,
( one_to_one(U_563)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_15,plain,
( sP154(U_568,U_565,U_566,U_563,U_564)
| ~ in(ordered_pair(U_568,U_566),U_565)
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_16,plain,
( in(ordered_pair(U_569,U_567),U_565)
| ~ in(ordered_pair(apply(U_563,U_569),apply(U_563,U_567)),U_564)
| ~ in(U_567,relation_field(U_565))
| ~ in(U_569,relation_field(U_565))
| ~ sP155(U_568,U_565,U_567,U_566,U_569,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_17,plain,
( in(U_568,relation_field(U_565))
| ~ sP154(U_568,U_565,U_566,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_18,plain,
( in(U_566,relation_field(U_565))
| ~ sP154(U_568,U_565,U_566,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_19,plain,
( in(ordered_pair(apply(U_563,U_568),apply(U_563,U_566)),U_564)
| ~ sP154(U_568,U_565,U_566,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_20,plain,
( in(ordered_pair(sK106(U_565,U_564,U_563),sK107(U_565,U_564,U_563)),U_565)
| ~ sP156(U_565,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_21,plain,
( ~ in(ordered_pair(apply(U_563,sK106(U_565,U_564,U_563)),apply(U_563,sK107(U_565,U_564,U_563))),U_564)
| ~ in(sK107(U_565,U_564,U_563),relation_field(U_565))
| ~ in(sK106(U_565,U_564,U_563),relation_field(U_565))
| ~ sP156(U_565,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_22,plain,
( in(sK108(U_565,U_564,U_563),relation_field(U_565))
| ~ sP157(U_565,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_23,plain,
( in(sK109(U_565,U_564,U_563),relation_field(U_565))
| ~ sP157(U_565,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_24,plain,
( in(ordered_pair(apply(U_563,sK108(U_565,U_564,U_563)),apply(U_563,sK109(U_565,U_564,U_563))),U_564)
| ~ sP157(U_565,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
cnf(f_75_25,plain,
( ~ in(ordered_pair(sK108(U_565,U_564,U_563),sK109(U_565,U_564,U_563)),U_565)
| ~ sP157(U_565,U_563,U_564) ),
inference(clausify,[status(thm)],[f_75_8]) ).
fof(f_76_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_76_2,plain,
! [U_575,U_574] :
( ( disjoint(U_575,U_574)
| set_intersection2(U_575,U_574) != empty_set )
& ( set_intersection2(U_575,U_574) = empty_set
| ~ disjoint(U_575,U_574) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_579,U_577] :
( disjoint(U_579,U_577)
| set_intersection2(U_579,U_577) != empty_set )
& ! [U_578,U_576] :
( set_intersection2(U_578,U_576) = empty_set
| ~ disjoint(U_578,U_576) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
fof(f_76_4,plain,
( ! [U_579,U_577] :
( disjoint(U_579,U_577)
| set_intersection2(U_579,U_577) != empty_set )
& ! [U_576,U_578] :
( set_intersection2(U_578,U_576) = empty_set
| ~ disjoint(U_578,U_576) ) ),
inference(definitional_conversion,[status(esa)],[f_76_3]) ).
cnf(f_76_5,plain,
( set_intersection2(U_578,U_576) = empty_set
| ~ disjoint(U_578,U_576) ),
inference(clausify,[status(thm)],[f_76_4]) ).
cnf(f_76_6,plain,
( disjoint(U_579,U_577)
| set_intersection2(U_579,U_577) != empty_set ),
inference(clausify,[status(thm)],[f_76_4]) ).
fof(f_77_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_77_2,plain,
! [U_584] :
( ( ( one_to_one(U_584)
| ? [U_583,U_582] :
( U_583 != U_582
& apply(U_584,U_583) = apply(U_584,U_582)
& in(U_582,relation_dom(U_584))
& in(U_583,relation_dom(U_584)) ) )
& ( ! [U_581,U_580] :
( U_581 = U_580
| apply(U_584,U_581) != apply(U_584,U_580)
| ~ in(U_580,relation_dom(U_584))
| ~ in(U_581,relation_dom(U_584)) )
| ~ one_to_one(U_584) ) )
| ~ function(U_584)
| ~ relation(U_584) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_584] :
( ( ( one_to_one(U_584)
| ? [U_582] :
( sK110(U_584) != U_582
& apply(U_584,sK110(U_584)) = apply(U_584,U_582)
& in(U_582,relation_dom(U_584))
& in(sK110(U_584),relation_dom(U_584)) ) )
& ( ! [U_581,U_580] :
( U_581 = U_580
| apply(U_584,U_581) != apply(U_584,U_580)
| ~ in(U_580,relation_dom(U_584))
| ~ in(U_581,relation_dom(U_584)) )
| ~ one_to_one(U_584) ) )
| ~ function(U_584)
| ~ relation(U_584) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_583,sK110(U_584))],[f_77_2]) ).
fof(f_77_4,plain,
! [U_584] :
( ( ( one_to_one(U_584)
| ( sK110(U_584) != sK111(U_584)
& apply(U_584,sK110(U_584)) = apply(U_584,sK111(U_584))
& in(sK111(U_584),relation_dom(U_584))
& in(sK110(U_584),relation_dom(U_584)) ) )
& ( ! [U_581,U_580] :
( U_581 = U_580
| apply(U_584,U_581) != apply(U_584,U_580)
| ~ in(U_580,relation_dom(U_584))
| ~ in(U_581,relation_dom(U_584)) )
| ~ one_to_one(U_584) ) )
| ~ function(U_584)
| ~ relation(U_584) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_582,sK111(U_584))],[f_77_3]) ).
fof(f_77_5,plain,
( ! [U_584] :
( sK110(U_584) != sK111(U_584)
| ~ sP159(U_584) )
& ! [U_584] :
( apply(U_584,sK110(U_584)) = apply(U_584,sK111(U_584))
| ~ sP159(U_584) )
& ! [U_584] :
( in(sK111(U_584),relation_dom(U_584))
| ~ sP159(U_584) )
& ! [U_584] :
( in(sK110(U_584),relation_dom(U_584))
| ~ sP159(U_584) )
& ! [U_580,U_581,U_584] :
( one_to_one(U_584)
| sP159(U_584)
| ~ sP160(U_580,U_581,U_584) )
& ! [U_580,U_581,U_584] :
( U_581 = U_580
| apply(U_584,U_581) != apply(U_584,U_580)
| ~ in(U_580,relation_dom(U_584))
| ~ in(U_581,relation_dom(U_584))
| ~ one_to_one(U_584)
| ~ sP160(U_580,U_581,U_584) )
& ! [U_580,U_581,U_584] :
( sP160(U_580,U_581,U_584)
| ~ function(U_584)
| ~ relation(U_584) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159,sP160])],[f_77_4]) ).
cnf(f_77_6,plain,
( sP160(U_580,U_581,U_584)
| ~ function(U_584)
| ~ relation(U_584) ),
inference(clausify,[status(thm)],[f_77_5]) ).
cnf(f_77_7,plain,
( U_581 = U_580
| apply(U_584,U_581) != apply(U_584,U_580)
| ~ in(U_580,relation_dom(U_584))
| ~ in(U_581,relation_dom(U_584))
| ~ one_to_one(U_584)
| ~ sP160(U_580,U_581,U_584) ),
inference(clausify,[status(thm)],[f_77_5]) ).
cnf(f_77_8,plain,
( one_to_one(U_584)
| sP159(U_584)
| ~ sP160(U_580,U_581,U_584) ),
inference(clausify,[status(thm)],[f_77_5]) ).
cnf(f_77_9,plain,
( in(sK110(U_584),relation_dom(U_584))
| ~ sP159(U_584) ),
inference(clausify,[status(thm)],[f_77_5]) ).
cnf(f_77_10,plain,
( in(sK111(U_584),relation_dom(U_584))
| ~ sP159(U_584) ),
inference(clausify,[status(thm)],[f_77_5]) ).
cnf(f_77_11,plain,
( apply(U_584,sK110(U_584)) = apply(U_584,sK111(U_584))
| ~ sP159(U_584) ),
inference(clausify,[status(thm)],[f_77_5]) ).
cnf(f_77_12,plain,
( sK110(U_584) != sK111(U_584)
| ~ sP159(U_584) ),
inference(clausify,[status(thm)],[f_77_5]) ).
fof(f_78_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_78_2,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ? [U_592,U_591] :
( ( ~ in(ordered_pair(U_592,U_591),U_593)
& ? [U_590] :
( in(ordered_pair(U_590,U_591),U_594)
& in(ordered_pair(U_592,U_590),U_595) ) )
| ( ! [U_589] :
( ~ in(ordered_pair(U_589,U_591),U_594)
| ~ in(ordered_pair(U_592,U_589),U_595) )
& in(ordered_pair(U_592,U_591),U_593) ) ) )
& ( ! [U_588,U_587] :
( ( in(ordered_pair(U_588,U_587),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_587),U_594)
| ~ in(ordered_pair(U_588,U_586),U_595) ) )
& ( ? [U_585] :
( in(ordered_pair(U_585,U_587),U_594)
& in(ordered_pair(U_588,U_585),U_595) )
| ~ in(ordered_pair(U_588,U_587),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ? [U_603,U_601] :
( ~ in(ordered_pair(U_603,U_601),U_593)
& ? [U_590] :
( in(ordered_pair(U_590,U_601),U_594)
& in(ordered_pair(U_603,U_590),U_595) ) )
| ? [U_602,U_600] :
( ! [U_589] :
( ~ in(ordered_pair(U_589,U_600),U_594)
| ~ in(ordered_pair(U_602,U_589),U_595) )
& in(ordered_pair(U_602,U_600),U_593) ) )
& ( ( ! [U_599,U_597] :
( in(ordered_pair(U_599,U_597),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595) ) )
& ! [U_598,U_596] :
( ? [U_585] :
( in(ordered_pair(U_585,U_596),U_594)
& in(ordered_pair(U_598,U_585),U_595) )
| ~ in(ordered_pair(U_598,U_596),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
fof(f_78_4,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ? [U_603,U_601] :
( ~ in(ordered_pair(U_603,U_601),U_593)
& ? [U_590] :
( in(ordered_pair(U_590,U_601),U_594)
& in(ordered_pair(U_603,U_590),U_595) ) )
| ? [U_602,U_600] :
( ! [U_589] :
( ~ in(ordered_pair(U_589,U_600),U_594)
| ~ in(ordered_pair(U_602,U_589),U_595) )
& in(ordered_pair(U_602,U_600),U_593) ) )
& ( ( ! [U_599,U_597] :
( in(ordered_pair(U_599,U_597),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595) ) )
& ! [U_598,U_596] :
( ( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
& in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595) )
| ~ in(ordered_pair(U_598,U_596),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_585,sK112(U_595,U_594,U_593,U_598,U_596))],[f_78_3]) ).
fof(f_78_5,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ? [U_603,U_601] :
( ~ in(ordered_pair(U_603,U_601),U_593)
& ? [U_590] :
( in(ordered_pair(U_590,U_601),U_594)
& in(ordered_pair(U_603,U_590),U_595) ) )
| ? [U_600] :
( ! [U_589] :
( ~ in(ordered_pair(U_589,U_600),U_594)
| ~ in(ordered_pair(sK113(U_595,U_594,U_593),U_589),U_595) )
& in(ordered_pair(sK113(U_595,U_594,U_593),U_600),U_593) ) )
& ( ( ! [U_599,U_597] :
( in(ordered_pair(U_599,U_597),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595) ) )
& ! [U_598,U_596] :
( ( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
& in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595) )
| ~ in(ordered_pair(U_598,U_596),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_602,sK113(U_595,U_594,U_593))],[f_78_4]) ).
fof(f_78_6,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ? [U_603,U_601] :
( ~ in(ordered_pair(U_603,U_601),U_593)
& ? [U_590] :
( in(ordered_pair(U_590,U_601),U_594)
& in(ordered_pair(U_603,U_590),U_595) ) )
| ( ! [U_589] :
( ~ in(ordered_pair(U_589,sK114(U_595,U_594,U_593)),U_594)
| ~ in(ordered_pair(sK113(U_595,U_594,U_593),U_589),U_595) )
& in(ordered_pair(sK113(U_595,U_594,U_593),sK114(U_595,U_594,U_593)),U_593) ) )
& ( ( ! [U_599,U_597] :
( in(ordered_pair(U_599,U_597),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595) ) )
& ! [U_598,U_596] :
( ( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
& in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595) )
| ~ in(ordered_pair(U_598,U_596),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_600,sK114(U_595,U_594,U_593))],[f_78_5]) ).
fof(f_78_7,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ? [U_601] :
( ~ in(ordered_pair(sK115(U_595,U_594,U_593),U_601),U_593)
& ? [U_590] :
( in(ordered_pair(U_590,U_601),U_594)
& in(ordered_pair(sK115(U_595,U_594,U_593),U_590),U_595) ) )
| ( ! [U_589] :
( ~ in(ordered_pair(U_589,sK114(U_595,U_594,U_593)),U_594)
| ~ in(ordered_pair(sK113(U_595,U_594,U_593),U_589),U_595) )
& in(ordered_pair(sK113(U_595,U_594,U_593),sK114(U_595,U_594,U_593)),U_593) ) )
& ( ( ! [U_599,U_597] :
( in(ordered_pair(U_599,U_597),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595) ) )
& ! [U_598,U_596] :
( ( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
& in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595) )
| ~ in(ordered_pair(U_598,U_596),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_603,sK115(U_595,U_594,U_593))],[f_78_6]) ).
fof(f_78_8,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ( ~ in(ordered_pair(sK115(U_595,U_594,U_593),sK116(U_595,U_594,U_593)),U_593)
& ? [U_590] :
( in(ordered_pair(U_590,sK116(U_595,U_594,U_593)),U_594)
& in(ordered_pair(sK115(U_595,U_594,U_593),U_590),U_595) ) )
| ( ! [U_589] :
( ~ in(ordered_pair(U_589,sK114(U_595,U_594,U_593)),U_594)
| ~ in(ordered_pair(sK113(U_595,U_594,U_593),U_589),U_595) )
& in(ordered_pair(sK113(U_595,U_594,U_593),sK114(U_595,U_594,U_593)),U_593) ) )
& ( ( ! [U_599,U_597] :
( in(ordered_pair(U_599,U_597),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595) ) )
& ! [U_598,U_596] :
( ( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
& in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595) )
| ~ in(ordered_pair(U_598,U_596),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_601,sK116(U_595,U_594,U_593))],[f_78_7]) ).
fof(f_78_9,plain,
! [U_595] :
( ! [U_594] :
( ! [U_593] :
( ( ( U_593 = relation_composition(U_595,U_594)
| ( ~ in(ordered_pair(sK115(U_595,U_594,U_593),sK116(U_595,U_594,U_593)),U_593)
& in(ordered_pair(sK117(U_595,U_594,U_593),sK116(U_595,U_594,U_593)),U_594)
& in(ordered_pair(sK115(U_595,U_594,U_593),sK117(U_595,U_594,U_593)),U_595) )
| ( ! [U_589] :
( ~ in(ordered_pair(U_589,sK114(U_595,U_594,U_593)),U_594)
| ~ in(ordered_pair(sK113(U_595,U_594,U_593),U_589),U_595) )
& in(ordered_pair(sK113(U_595,U_594,U_593),sK114(U_595,U_594,U_593)),U_593) ) )
& ( ( ! [U_599,U_597] :
( in(ordered_pair(U_599,U_597),U_593)
| ! [U_586] :
( ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595) ) )
& ! [U_598,U_596] :
( ( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
& in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595) )
| ~ in(ordered_pair(U_598,U_596),U_593) ) )
| U_593 != relation_composition(U_595,U_594) ) )
| ~ relation(U_593) )
| ~ relation(U_594) )
| ~ relation(U_595) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_590,sK117(U_595,U_594,U_593))],[f_78_8]) ).
fof(f_78_10,plain,
( ! [U_595,U_594,U_593] :
( ~ in(ordered_pair(sK115(U_595,U_594,U_593),sK116(U_595,U_594,U_593)),U_593)
| ~ sP164(U_595,U_594,U_593) )
& ! [U_595,U_594,U_593] :
( in(ordered_pair(sK117(U_595,U_594,U_593),sK116(U_595,U_594,U_593)),U_594)
| ~ sP164(U_595,U_594,U_593) )
& ! [U_595,U_594,U_593] :
( in(ordered_pair(sK115(U_595,U_594,U_593),sK117(U_595,U_594,U_593)),U_595)
| ~ sP164(U_595,U_594,U_593) )
& ! [U_595,U_594,U_589,U_593] :
( ~ in(ordered_pair(U_589,sK114(U_595,U_594,U_593)),U_594)
| ~ in(ordered_pair(sK113(U_595,U_594,U_593),U_589),U_595)
| ~ sP163(U_595,U_594,U_589,U_593) )
& ! [U_595,U_594,U_589,U_593] :
( in(ordered_pair(sK113(U_595,U_594,U_593),sK114(U_595,U_594,U_593)),U_593)
| ~ sP163(U_595,U_594,U_589,U_593) )
& ! [U_595,U_594,U_598,U_593,U_596] :
( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
| ~ sP161(U_595,U_594,U_598,U_593,U_596) )
& ! [U_595,U_594,U_598,U_593,U_596] :
( in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595)
| ~ sP161(U_595,U_594,U_598,U_593,U_596) )
& ! [U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586] :
( in(ordered_pair(U_599,U_597),U_593)
| ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595)
| ~ sP162(U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586) )
& ! [U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586] :
( sP161(U_595,U_594,U_598,U_593,U_596)
| ~ in(ordered_pair(U_598,U_596),U_593)
| ~ sP162(U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586) )
& ! [U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586] :
( U_593 = relation_composition(U_595,U_594)
| sP164(U_595,U_594,U_593)
| sP163(U_595,U_594,U_589,U_593)
| ~ sP165(U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586) )
& ! [U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586] :
( sP162(U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586)
| U_593 != relation_composition(U_595,U_594)
| ~ sP165(U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586) )
& ! [U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586] :
( sP165(U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586)
| ~ relation(U_593)
| ~ relation(U_594)
| ~ relation(U_595) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161,sP162,sP163,sP164,sP165])],[f_78_9]) ).
cnf(f_78_11,plain,
( sP165(U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586)
| ~ relation(U_593)
| ~ relation(U_594)
| ~ relation(U_595) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_12,plain,
( sP162(U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586)
| U_593 != relation_composition(U_595,U_594)
| ~ sP165(U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_13,plain,
( U_593 = relation_composition(U_595,U_594)
| sP164(U_595,U_594,U_593)
| sP163(U_595,U_594,U_589,U_593)
| ~ sP165(U_595,U_594,U_589,U_598,U_593,U_599,U_597,U_596,U_586) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_14,plain,
( sP161(U_595,U_594,U_598,U_593,U_596)
| ~ in(ordered_pair(U_598,U_596),U_593)
| ~ sP162(U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_15,plain,
( in(ordered_pair(U_599,U_597),U_593)
| ~ in(ordered_pair(U_586,U_597),U_594)
| ~ in(ordered_pair(U_599,U_586),U_595)
| ~ sP162(U_595,U_594,U_598,U_593,U_599,U_597,U_596,U_586) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_16,plain,
( in(ordered_pair(U_598,sK112(U_595,U_594,U_593,U_598,U_596)),U_595)
| ~ sP161(U_595,U_594,U_598,U_593,U_596) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_17,plain,
( in(ordered_pair(sK112(U_595,U_594,U_593,U_598,U_596),U_596),U_594)
| ~ sP161(U_595,U_594,U_598,U_593,U_596) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_18,plain,
( in(ordered_pair(sK113(U_595,U_594,U_593),sK114(U_595,U_594,U_593)),U_593)
| ~ sP163(U_595,U_594,U_589,U_593) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_19,plain,
( ~ in(ordered_pair(U_589,sK114(U_595,U_594,U_593)),U_594)
| ~ in(ordered_pair(sK113(U_595,U_594,U_593),U_589),U_595)
| ~ sP163(U_595,U_594,U_589,U_593) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_20,plain,
( in(ordered_pair(sK115(U_595,U_594,U_593),sK117(U_595,U_594,U_593)),U_595)
| ~ sP164(U_595,U_594,U_593) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_21,plain,
( in(ordered_pair(sK117(U_595,U_594,U_593),sK116(U_595,U_594,U_593)),U_594)
| ~ sP164(U_595,U_594,U_593) ),
inference(clausify,[status(thm)],[f_78_10]) ).
cnf(f_78_22,plain,
( ~ in(ordered_pair(sK115(U_595,U_594,U_593),sK116(U_595,U_594,U_593)),U_593)
| ~ sP164(U_595,U_594,U_593) ),
inference(clausify,[status(thm)],[f_78_10]) ).
fof(f_79_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_79_2,plain,
! [U_611] :
( ! [U_610] :
( ( is_transitive_in(U_611,U_610)
| ? [U_609,U_608,U_607] :
( ~ in(ordered_pair(U_609,U_607),U_611)
& in(ordered_pair(U_608,U_607),U_611)
& in(ordered_pair(U_609,U_608),U_611)
& in(U_607,U_610)
& in(U_608,U_610)
& in(U_609,U_610) ) )
& ( ! [U_606,U_605,U_604] :
( in(ordered_pair(U_606,U_604),U_611)
| ~ in(ordered_pair(U_605,U_604),U_611)
| ~ in(ordered_pair(U_606,U_605),U_611)
| ~ in(U_604,U_610)
| ~ in(U_605,U_610)
| ~ in(U_606,U_610) )
| ~ is_transitive_in(U_611,U_610) ) )
| ~ relation(U_611) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_611] :
( ( ! [U_613] :
( is_transitive_in(U_611,U_613)
| ? [U_609,U_608,U_607] :
( ~ in(ordered_pair(U_609,U_607),U_611)
& in(ordered_pair(U_608,U_607),U_611)
& in(ordered_pair(U_609,U_608),U_611)
& in(U_607,U_613)
& in(U_608,U_613)
& in(U_609,U_613) ) )
& ! [U_612] :
( ! [U_606,U_605,U_604] :
( in(ordered_pair(U_606,U_604),U_611)
| ~ in(ordered_pair(U_605,U_604),U_611)
| ~ in(ordered_pair(U_606,U_605),U_611)
| ~ in(U_604,U_612)
| ~ in(U_605,U_612)
| ~ in(U_606,U_612) )
| ~ is_transitive_in(U_611,U_612) ) )
| ~ relation(U_611) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
fof(f_79_4,plain,
! [U_611] :
( ( ! [U_613] :
( is_transitive_in(U_611,U_613)
| ? [U_608,U_607] :
( ~ in(ordered_pair(sK118(U_611,U_613),U_607),U_611)
& in(ordered_pair(U_608,U_607),U_611)
& in(ordered_pair(sK118(U_611,U_613),U_608),U_611)
& in(U_607,U_613)
& in(U_608,U_613)
& in(sK118(U_611,U_613),U_613) ) )
& ! [U_612] :
( ! [U_606,U_605,U_604] :
( in(ordered_pair(U_606,U_604),U_611)
| ~ in(ordered_pair(U_605,U_604),U_611)
| ~ in(ordered_pair(U_606,U_605),U_611)
| ~ in(U_604,U_612)
| ~ in(U_605,U_612)
| ~ in(U_606,U_612) )
| ~ is_transitive_in(U_611,U_612) ) )
| ~ relation(U_611) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_609,sK118(U_611,U_613))],[f_79_3]) ).
fof(f_79_5,plain,
! [U_611] :
( ( ! [U_613] :
( is_transitive_in(U_611,U_613)
| ? [U_607] :
( ~ in(ordered_pair(sK118(U_611,U_613),U_607),U_611)
& in(ordered_pair(sK119(U_611,U_613),U_607),U_611)
& in(ordered_pair(sK118(U_611,U_613),sK119(U_611,U_613)),U_611)
& in(U_607,U_613)
& in(sK119(U_611,U_613),U_613)
& in(sK118(U_611,U_613),U_613) ) )
& ! [U_612] :
( ! [U_606,U_605,U_604] :
( in(ordered_pair(U_606,U_604),U_611)
| ~ in(ordered_pair(U_605,U_604),U_611)
| ~ in(ordered_pair(U_606,U_605),U_611)
| ~ in(U_604,U_612)
| ~ in(U_605,U_612)
| ~ in(U_606,U_612) )
| ~ is_transitive_in(U_611,U_612) ) )
| ~ relation(U_611) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_608,sK119(U_611,U_613))],[f_79_4]) ).
fof(f_79_6,plain,
! [U_611] :
( ( ! [U_613] :
( is_transitive_in(U_611,U_613)
| ( ~ in(ordered_pair(sK118(U_611,U_613),sK120(U_611,U_613)),U_611)
& in(ordered_pair(sK119(U_611,U_613),sK120(U_611,U_613)),U_611)
& in(ordered_pair(sK118(U_611,U_613),sK119(U_611,U_613)),U_611)
& in(sK120(U_611,U_613),U_613)
& in(sK119(U_611,U_613),U_613)
& in(sK118(U_611,U_613),U_613) ) )
& ! [U_612] :
( ! [U_606,U_605,U_604] :
( in(ordered_pair(U_606,U_604),U_611)
| ~ in(ordered_pair(U_605,U_604),U_611)
| ~ in(ordered_pair(U_606,U_605),U_611)
| ~ in(U_604,U_612)
| ~ in(U_605,U_612)
| ~ in(U_606,U_612) )
| ~ is_transitive_in(U_611,U_612) ) )
| ~ relation(U_611) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_607,sK120(U_611,U_613))],[f_79_5]) ).
fof(f_79_7,plain,
( ! [U_613,U_611] :
( ~ in(ordered_pair(sK118(U_611,U_613),sK120(U_611,U_613)),U_611)
| ~ sP166(U_613,U_611) )
& ! [U_613,U_611] :
( in(ordered_pair(sK119(U_611,U_613),sK120(U_611,U_613)),U_611)
| ~ sP166(U_613,U_611) )
& ! [U_613,U_611] :
( in(ordered_pair(sK118(U_611,U_613),sK119(U_611,U_613)),U_611)
| ~ sP166(U_613,U_611) )
& ! [U_613,U_611] :
( in(sK120(U_611,U_613),U_613)
| ~ sP166(U_613,U_611) )
& ! [U_613,U_611] :
( in(sK119(U_611,U_613),U_613)
| ~ sP166(U_613,U_611) )
& ! [U_613,U_611] :
( in(sK118(U_611,U_613),U_613)
| ~ sP166(U_613,U_611) )
& ! [U_613,U_606,U_612,U_604,U_611,U_605] :
( is_transitive_in(U_611,U_613)
| sP166(U_613,U_611)
| ~ sP167(U_613,U_606,U_612,U_604,U_611,U_605) )
& ! [U_613,U_606,U_612,U_604,U_611,U_605] :
( in(ordered_pair(U_606,U_604),U_611)
| ~ in(ordered_pair(U_605,U_604),U_611)
| ~ in(ordered_pair(U_606,U_605),U_611)
| ~ in(U_604,U_612)
| ~ in(U_605,U_612)
| ~ in(U_606,U_612)
| ~ is_transitive_in(U_611,U_612)
| ~ sP167(U_613,U_606,U_612,U_604,U_611,U_605) )
& ! [U_613,U_606,U_612,U_604,U_611,U_605] :
( sP167(U_613,U_606,U_612,U_604,U_611,U_605)
| ~ relation(U_611) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166,sP167])],[f_79_6]) ).
cnf(f_79_8,plain,
( sP167(U_613,U_606,U_612,U_604,U_611,U_605)
| ~ relation(U_611) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_9,plain,
( in(ordered_pair(U_606,U_604),U_611)
| ~ in(ordered_pair(U_605,U_604),U_611)
| ~ in(ordered_pair(U_606,U_605),U_611)
| ~ in(U_604,U_612)
| ~ in(U_605,U_612)
| ~ in(U_606,U_612)
| ~ is_transitive_in(U_611,U_612)
| ~ sP167(U_613,U_606,U_612,U_604,U_611,U_605) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_10,plain,
( is_transitive_in(U_611,U_613)
| sP166(U_613,U_611)
| ~ sP167(U_613,U_606,U_612,U_604,U_611,U_605) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_11,plain,
( in(sK118(U_611,U_613),U_613)
| ~ sP166(U_613,U_611) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_12,plain,
( in(sK119(U_611,U_613),U_613)
| ~ sP166(U_613,U_611) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_13,plain,
( in(sK120(U_611,U_613),U_613)
| ~ sP166(U_613,U_611) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_14,plain,
( in(ordered_pair(sK118(U_611,U_613),sK119(U_611,U_613)),U_611)
| ~ sP166(U_613,U_611) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_15,plain,
( in(ordered_pair(sK119(U_611,U_613),sK120(U_611,U_613)),U_611)
| ~ sP166(U_613,U_611) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_16,plain,
( ~ in(ordered_pair(sK118(U_611,U_613),sK120(U_611,U_613)),U_611)
| ~ sP166(U_613,U_611) ),
inference(clausify,[status(thm)],[f_79_7]) ).
fof(f_80_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_80_2,plain,
! [U_618,U_617] :
( ! [U_616] :
( ( ( U_616 = complements_of_subsets(U_618,U_617)
| ? [U_615] :
( ( ( ~ in(U_615,U_616)
& in(subset_complement(U_618,U_615),U_617) )
| ( ~ in(subset_complement(U_618,U_615),U_617)
& in(U_615,U_616) ) )
& element(U_615,powerset(U_618)) ) )
& ( ! [U_614] :
( ( ( in(U_614,U_616)
| ~ in(subset_complement(U_618,U_614),U_617) )
& ( in(subset_complement(U_618,U_614),U_617)
| ~ in(U_614,U_616) ) )
| ~ element(U_614,powerset(U_618)) )
| U_616 != complements_of_subsets(U_618,U_617) ) )
| ~ element(U_616,powerset(powerset(U_618))) )
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_618,U_617] :
( ! [U_616] :
( ( ( U_616 = complements_of_subsets(U_618,U_617)
| ( ( ( ~ in(sK121(U_618,U_617,U_616),U_616)
& in(subset_complement(U_618,sK121(U_618,U_617,U_616)),U_617) )
| ( ~ in(subset_complement(U_618,sK121(U_618,U_617,U_616)),U_617)
& in(sK121(U_618,U_617,U_616),U_616) ) )
& element(sK121(U_618,U_617,U_616),powerset(U_618)) ) )
& ( ! [U_614] :
( ( ( in(U_614,U_616)
| ~ in(subset_complement(U_618,U_614),U_617) )
& ( in(subset_complement(U_618,U_614),U_617)
| ~ in(U_614,U_616) ) )
| ~ element(U_614,powerset(U_618)) )
| U_616 != complements_of_subsets(U_618,U_617) ) )
| ~ element(U_616,powerset(powerset(U_618))) )
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_615,sK121(U_618,U_617,U_616))],[f_80_2]) ).
fof(f_80_4,plain,
( ! [U_618,U_616,U_617] :
( ~ in(sK121(U_618,U_617,U_616),U_616)
| ~ sP170(U_618,U_616,U_617) )
& ! [U_618,U_616,U_617] :
( in(subset_complement(U_618,sK121(U_618,U_617,U_616)),U_617)
| ~ sP170(U_618,U_616,U_617) )
& ! [U_618,U_616,U_617] :
( ~ in(subset_complement(U_618,sK121(U_618,U_617,U_616)),U_617)
| ~ sP169(U_618,U_616,U_617) )
& ! [U_618,U_616,U_617] :
( in(sK121(U_618,U_617,U_616),U_616)
| ~ sP169(U_618,U_616,U_617) )
& ! [U_618,U_616,U_617] :
( sP170(U_618,U_616,U_617)
| sP169(U_618,U_616,U_617)
| ~ sP171(U_618,U_616,U_617) )
& ! [U_618,U_616,U_617] :
( element(sK121(U_618,U_617,U_616),powerset(U_618))
| ~ sP171(U_618,U_616,U_617) )
& ! [U_618,U_614,U_616,U_617] :
( in(U_614,U_616)
| ~ in(subset_complement(U_618,U_614),U_617)
| ~ sP168(U_618,U_614,U_616,U_617) )
& ! [U_618,U_614,U_616,U_617] :
( in(subset_complement(U_618,U_614),U_617)
| ~ in(U_614,U_616)
| ~ sP168(U_618,U_614,U_616,U_617) )
& ! [U_618,U_614,U_616,U_617] :
( U_616 = complements_of_subsets(U_618,U_617)
| sP171(U_618,U_616,U_617)
| ~ sP172(U_618,U_614,U_616,U_617) )
& ! [U_618,U_614,U_616,U_617] :
( sP168(U_618,U_614,U_616,U_617)
| ~ element(U_614,powerset(U_618))
| U_616 != complements_of_subsets(U_618,U_617)
| ~ sP172(U_618,U_614,U_616,U_617) )
& ! [U_618,U_614,U_616,U_617] :
( sP172(U_618,U_614,U_616,U_617)
| ~ element(U_616,powerset(powerset(U_618)))
| ~ element(U_617,powerset(powerset(U_618))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169,sP170,sP171,sP172])],[f_80_3]) ).
cnf(f_80_5,plain,
( sP172(U_618,U_614,U_616,U_617)
| ~ element(U_616,powerset(powerset(U_618)))
| ~ element(U_617,powerset(powerset(U_618))) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_6,plain,
( sP168(U_618,U_614,U_616,U_617)
| ~ element(U_614,powerset(U_618))
| U_616 != complements_of_subsets(U_618,U_617)
| ~ sP172(U_618,U_614,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_7,plain,
( U_616 = complements_of_subsets(U_618,U_617)
| sP171(U_618,U_616,U_617)
| ~ sP172(U_618,U_614,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_8,plain,
( in(subset_complement(U_618,U_614),U_617)
| ~ in(U_614,U_616)
| ~ sP168(U_618,U_614,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_9,plain,
( in(U_614,U_616)
| ~ in(subset_complement(U_618,U_614),U_617)
| ~ sP168(U_618,U_614,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_10,plain,
( element(sK121(U_618,U_617,U_616),powerset(U_618))
| ~ sP171(U_618,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_11,plain,
( sP170(U_618,U_616,U_617)
| sP169(U_618,U_616,U_617)
| ~ sP171(U_618,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_12,plain,
( in(sK121(U_618,U_617,U_616),U_616)
| ~ sP169(U_618,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_13,plain,
( ~ in(subset_complement(U_618,sK121(U_618,U_617,U_616)),U_617)
| ~ sP169(U_618,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_14,plain,
( in(subset_complement(U_618,sK121(U_618,U_617,U_616)),U_617)
| ~ sP170(U_618,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
cnf(f_80_15,plain,
( ~ in(sK121(U_618,U_617,U_616),U_616)
| ~ sP170(U_618,U_616,U_617) ),
inference(clausify,[status(thm)],[f_80_4]) ).
fof(f_81_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_81_2,plain,
! [U_620,U_619] :
( ( proper_subset(U_620,U_619)
| U_620 = U_619
| ~ subset(U_620,U_619) )
& ( ( U_620 != U_619
& subset(U_620,U_619) )
| ~ proper_subset(U_620,U_619) ) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
( ! [U_624,U_622] :
( proper_subset(U_624,U_622)
| U_624 = U_622
| ~ subset(U_624,U_622) )
& ! [U_623,U_621] :
( ( U_623 != U_621
& subset(U_623,U_621) )
| ~ proper_subset(U_623,U_621) ) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
fof(f_81_4,plain,
( ! [U_623,U_621] :
( U_623 != U_621
| ~ sP173(U_623,U_621) )
& ! [U_623,U_621] :
( subset(U_623,U_621)
| ~ sP173(U_623,U_621) )
& ! [U_622,U_624] :
( proper_subset(U_624,U_622)
| U_624 = U_622
| ~ subset(U_624,U_622) )
& ! [U_623,U_621] :
( sP173(U_623,U_621)
| ~ proper_subset(U_623,U_621) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_81_3]) ).
cnf(f_81_5,plain,
( sP173(U_623,U_621)
| ~ proper_subset(U_623,U_621) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_6,plain,
( proper_subset(U_624,U_622)
| U_624 = U_622
| ~ subset(U_624,U_622) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_7,plain,
( subset(U_623,U_621)
| ~ sP173(U_623,U_621) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_8,plain,
( U_623 != U_621
| ~ sP173(U_623,U_621) ),
inference(clausify,[status(thm)],[f_81_4]) ).
fof(f_82_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_82_2,plain,
! [U_625] :
( function_inverse(U_625) = relation_inverse(U_625)
| ~ one_to_one(U_625)
| ~ function(U_625)
| ~ relation(U_625) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_625] :
( function_inverse(U_625) = relation_inverse(U_625)
| ~ one_to_one(U_625)
| ~ function(U_625)
| ~ relation(U_625) ),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
( function_inverse(U_625) = relation_inverse(U_625)
| ~ one_to_one(U_625)
| ~ function(U_625)
| ~ relation(U_625) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_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_83_2,plain,
! [U_626] :
( ( ( reflexive(U_626)
| ~ is_reflexive_in(U_626,relation_field(U_626)) )
& ( is_reflexive_in(U_626,relation_field(U_626))
| ~ reflexive(U_626) ) )
| ~ relation(U_626) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_626] :
( reflexive(U_626)
| ~ is_reflexive_in(U_626,relation_field(U_626))
| ~ sP174(U_626) )
& ! [U_626] :
( is_reflexive_in(U_626,relation_field(U_626))
| ~ reflexive(U_626)
| ~ sP174(U_626) )
& ! [U_626] :
( sP174(U_626)
| ~ relation(U_626) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_83_2]) ).
cnf(f_83_4,plain,
( sP174(U_626)
| ~ relation(U_626) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
( is_reflexive_in(U_626,relation_field(U_626))
| ~ reflexive(U_626)
| ~ sP174(U_626) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_6,plain,
( reflexive(U_626)
| ~ is_reflexive_in(U_626,relation_field(U_626))
| ~ sP174(U_626) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
fof(f_84_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_84_1]) ).
cnf(f_84_3,plain,
$true,
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
fof(f_85_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_85_1]) ).
cnf(f_85_3,plain,
$true,
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
fof(f_86_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_86_1]) ).
cnf(f_86_3,plain,
$true,
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_mcart_1]) ).
fof(f_87_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_87_1]) ).
cnf(f_87_3,plain,
$true,
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
fof(f_88_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_88_1]) ).
cnf(f_88_3,plain,
$true,
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_89_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_89_1]) ).
cnf(f_89_3,plain,
$true,
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
fof(f_90_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_90_1]) ).
cnf(f_90_3,plain,
$true,
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_91_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_91_1]) ).
cnf(f_91_3,plain,
$true,
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
fof(f_92_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_92_1]) ).
cnf(f_92_3,plain,
$true,
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [A] : relation(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k1_wellord2]) ).
fof(f_93_2,plain,
! [U_627] : relation(inclusion_relation(U_627)),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_627] : relation(inclusion_relation(U_627)),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_4,plain,
relation(inclusion_relation(U_627)),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_94_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_94_1]) ).
cnf(f_94_3,plain,
$true,
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_95_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_95_1]) ).
cnf(f_95_3,plain,
$true,
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_funct_1]) ).
fof(f_96_2,plain,
! [U_628] :
( ( function(function_inverse(U_628))
& relation(function_inverse(U_628)) )
| ~ function(U_628)
| ~ relation(U_628) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
( ! [U_628] :
( function(function_inverse(U_628))
| ~ sP175(U_628) )
& ! [U_628] :
( relation(function_inverse(U_628))
| ~ sP175(U_628) )
& ! [U_628] :
( sP175(U_628)
| ~ function(U_628)
| ~ relation(U_628) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_96_2]) ).
cnf(f_96_4,plain,
( sP175(U_628)
| ~ function(U_628)
| ~ relation(U_628) ),
inference(clausify,[status(thm)],[f_96_3]) ).
cnf(f_96_5,plain,
( relation(function_inverse(U_628))
| ~ sP175(U_628) ),
inference(clausify,[status(thm)],[f_96_3]) ).
cnf(f_96_6,plain,
( function(function_inverse(U_628))
| ~ sP175(U_628) ),
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_mcart_1]) ).
fof(f_97_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_97_1]) ).
cnf(f_97_3,plain,
$true,
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
fof(f_98_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_98_1]) ).
cnf(f_98_3,plain,
$true,
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_99_2,plain,
! [U_629] : element(cast_to_subset(U_629),powerset(U_629)),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_629] : element(cast_to_subset(U_629),powerset(U_629)),
inference(definitional_conversion,[status(esa)],[f_99_2]) ).
cnf(f_99_4,plain,
element(cast_to_subset(U_629),powerset(U_629)),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_100_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_100_1]) ).
cnf(f_100_3,plain,
$true,
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_101_2,plain,
! [U_631,U_630] :
( relation(relation_restriction(U_631,U_630))
| ~ relation(U_631) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_631] :
( ! [U_630] : relation(relation_restriction(U_631,U_630))
| ~ relation(U_631) ),
inference(miniscope,[status(thm)],[f_101_2]) ).
fof(f_101_4,plain,
! [U_630,U_631] :
( relation(relation_restriction(U_631,U_630))
| ~ relation(U_631) ),
inference(definitional_conversion,[status(esa)],[f_101_3]) ).
cnf(f_101_5,plain,
( relation(relation_restriction(U_631,U_630))
| ~ relation(U_631) ),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_102_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_102_1]) ).
cnf(f_102_3,plain,
$true,
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_103_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_103_1]) ).
cnf(f_103_3,plain,
$true,
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_104_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_104_1]) ).
cnf(f_104_3,plain,
$true,
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_105_2,plain,
! [U_633,U_632] :
( element(subset_complement(U_633,U_632),powerset(U_633))
| ~ element(U_632,powerset(U_633)) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_632,U_633] :
( element(subset_complement(U_633,U_632),powerset(U_633))
| ~ element(U_632,powerset(U_633)) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( element(subset_complement(U_633,U_632),powerset(U_633))
| ~ element(U_632,powerset(U_633)) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_106_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_106_1]) ).
cnf(f_106_3,plain,
$true,
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_107_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_107_1]) ).
cnf(f_107_3,plain,
$true,
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_108_2,plain,
! [U_634] :
( relation(relation_inverse(U_634))
| ~ relation(U_634) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_634] :
( relation(relation_inverse(U_634))
| ~ relation(U_634) ),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
( relation(relation_inverse(U_634))
| ~ relation(U_634) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_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_109_2,plain,
! [U_637,U_636,U_635] :
( element(relation_dom_as_subset(U_637,U_636,U_635),powerset(U_637))
| ~ relation_of2(U_635,U_637,U_636) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_636,U_635,U_637] :
( element(relation_dom_as_subset(U_637,U_636,U_635),powerset(U_637))
| ~ relation_of2(U_635,U_637,U_636) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( element(relation_dom_as_subset(U_637,U_636,U_635),powerset(U_637))
| ~ relation_of2(U_635,U_637,U_636) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_110_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_110_1]) ).
cnf(f_110_3,plain,
$true,
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_111_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_111_1]) ).
cnf(f_111_3,plain,
$true,
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_112_2,plain,
! [U_639,U_638] :
( relation(relation_composition(U_639,U_638))
| ~ relation(U_638)
| ~ relation(U_639) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_638,U_639] :
( relation(relation_composition(U_639,U_638))
| ~ relation(U_638)
| ~ relation(U_639) ),
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
( relation(relation_composition(U_639,U_638))
| ~ relation(U_638)
| ~ relation(U_639) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_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_113_2,plain,
! [U_642,U_641,U_640] :
( element(relation_rng_as_subset(U_642,U_641,U_640),powerset(U_641))
| ~ relation_of2(U_640,U_642,U_641) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_642,U_640,U_641] :
( element(relation_rng_as_subset(U_642,U_641,U_640),powerset(U_641))
| ~ relation_of2(U_640,U_642,U_641) ),
inference(definitional_conversion,[status(esa)],[f_113_2]) ).
cnf(f_113_4,plain,
( element(relation_rng_as_subset(U_642,U_641,U_640),powerset(U_641))
| ~ relation_of2(U_640,U_642,U_641) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_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_114_2,plain,
! [U_644,U_643] :
( element(union_of_subsets(U_644,U_643),powerset(U_644))
| ~ element(U_643,powerset(powerset(U_644))) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_643,U_644] :
( element(union_of_subsets(U_644,U_643),powerset(U_644))
| ~ element(U_643,powerset(powerset(U_644))) ),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
( element(union_of_subsets(U_644,U_643),powerset(U_644))
| ~ element(U_643,powerset(powerset(U_644))) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_115_2,plain,
! [U_645] : relation(identity_relation(U_645)),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_645] : relation(identity_relation(U_645)),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
relation(identity_relation(U_645)),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_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_116_2,plain,
! [U_647,U_646] :
( element(meet_of_subsets(U_647,U_646),powerset(U_647))
| ~ element(U_646,powerset(powerset(U_647))) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_646,U_647] :
( element(meet_of_subsets(U_647,U_646),powerset(U_647))
| ~ element(U_646,powerset(powerset(U_647))) ),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
( element(meet_of_subsets(U_647,U_646),powerset(U_647))
| ~ element(U_646,powerset(powerset(U_647))) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_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_117_2,plain,
! [U_650,U_649,U_648] :
( element(subset_difference(U_650,U_649,U_648),powerset(U_650))
| ~ element(U_648,powerset(U_650))
| ~ element(U_649,powerset(U_650)) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_649,U_648,U_650] :
( element(subset_difference(U_650,U_649,U_648),powerset(U_650))
| ~ element(U_648,powerset(U_650))
| ~ element(U_649,powerset(U_650)) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( element(subset_difference(U_650,U_649,U_648),powerset(U_650))
| ~ element(U_648,powerset(U_650))
| ~ element(U_649,powerset(U_650)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_118_2,plain,
! [U_652,U_651] :
( relation(relation_dom_restriction(U_652,U_651))
| ~ relation(U_652) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_652] :
( ! [U_651] : relation(relation_dom_restriction(U_652,U_651))
| ~ relation(U_652) ),
inference(miniscope,[status(thm)],[f_118_2]) ).
fof(f_118_4,plain,
! [U_652,U_651] :
( relation(relation_dom_restriction(U_652,U_651))
| ~ relation(U_652) ),
inference(definitional_conversion,[status(esa)],[f_118_3]) ).
cnf(f_118_5,plain,
( relation(relation_dom_restriction(U_652,U_651))
| ~ relation(U_652) ),
inference(clausify,[status(thm)],[f_118_4]) ).
fof(f_119_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_119_2,plain,
! [U_654,U_653] :
( element(complements_of_subsets(U_654,U_653),powerset(powerset(U_654)))
| ~ element(U_653,powerset(powerset(U_654))) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_653,U_654] :
( element(complements_of_subsets(U_654,U_653),powerset(powerset(U_654)))
| ~ element(U_653,powerset(powerset(U_654))) ),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
( element(complements_of_subsets(U_654,U_653),powerset(powerset(U_654)))
| ~ element(U_653,powerset(powerset(U_654))) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_120_2,plain,
! [U_656,U_655] :
( relation(relation_rng_restriction(U_656,U_655))
| ~ relation(U_655) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_655,U_656] :
( relation(relation_rng_restriction(U_656,U_655))
| ~ relation(U_655) ),
inference(definitional_conversion,[status(esa)],[f_120_2]) ).
cnf(f_120_4,plain,
( relation(relation_rng_restriction(U_656,U_655))
| ~ relation(U_655) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
fof(f_121_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_121_1]) ).
cnf(f_121_3,plain,
$true,
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_122_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_122_1]) ).
cnf(f_122_3,plain,
$true,
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_123_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_123_1]) ).
cnf(f_123_3,plain,
$true,
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_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_124_2,plain,
! [U_659,U_658,U_657] :
( element(U_657,powerset(cartesian_product2(U_659,U_658)))
| ~ relation_of2_as_subset(U_657,U_659,U_658) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_657,U_658,U_659] :
( element(U_657,powerset(cartesian_product2(U_659,U_658)))
| ~ relation_of2_as_subset(U_657,U_659,U_658) ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( element(U_657,powerset(cartesian_product2(U_659,U_658)))
| ~ relation_of2_as_subset(U_657,U_659,U_658) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_125_2,plain,
! [U_662,U_661] :
? [U_660] : relation_of2(U_660,U_662,U_661),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_662,U_661] : relation_of2(sK122(U_662,U_661),U_662,U_661),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_660,sK122(U_662,U_661))],[f_125_2]) ).
fof(f_125_4,plain,
! [U_661,U_662] : relation_of2(sK122(U_662,U_661),U_662,U_661),
inference(definitional_conversion,[status(esa)],[f_125_3]) ).
cnf(f_125_5,plain,
relation_of2(sK122(U_662,U_661),U_662,U_661),
inference(clausify,[status(thm)],[f_125_4]) ).
fof(f_126_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_126_2,plain,
! [U_664] :
? [U_663] : element(U_663,U_664),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_664] : element(sK123(U_664),U_664),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_663,sK123(U_664))],[f_126_2]) ).
fof(f_126_4,plain,
! [U_664] : element(sK123(U_664),U_664),
inference(definitional_conversion,[status(esa)],[f_126_3]) ).
cnf(f_126_5,plain,
element(sK123(U_664),U_664),
inference(clausify,[status(thm)],[f_126_4]) ).
fof(f_127_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_127_2,plain,
! [U_667,U_666] :
? [U_665] : relation_of2_as_subset(U_665,U_667,U_666),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_667,U_666] : relation_of2_as_subset(sK124(U_667,U_666),U_667,U_666),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_665,sK124(U_667,U_666))],[f_127_2]) ).
fof(f_127_4,plain,
! [U_666,U_667] : relation_of2_as_subset(sK124(U_667,U_666),U_667,U_666),
inference(definitional_conversion,[status(esa)],[f_127_3]) ).
cnf(f_127_5,plain,
relation_of2_as_subset(sK124(U_667,U_666),U_667,U_666),
inference(clausify,[status(thm)],[f_127_4]) ).
fof(f_128_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_128_2,plain,
! [U_669,U_668] :
( ( relation(relation_composition(U_668,U_669))
& empty(relation_composition(U_668,U_669)) )
| ~ relation(U_668)
| ~ empty(U_669) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_668,U_669] :
( relation(relation_composition(U_668,U_669))
| ~ sP176(U_668,U_669) )
& ! [U_668,U_669] :
( empty(relation_composition(U_668,U_669))
| ~ sP176(U_668,U_669) )
& ! [U_668,U_669] :
( sP176(U_668,U_669)
| ~ relation(U_668)
| ~ empty(U_669) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_128_2]) ).
cnf(f_128_4,plain,
( sP176(U_668,U_669)
| ~ relation(U_668)
| ~ empty(U_669) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( empty(relation_composition(U_668,U_669))
| ~ sP176(U_668,U_669) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_6,plain,
( relation(relation_composition(U_668,U_669))
| ~ sP176(U_668,U_669) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_129_2,plain,
! [U_670] :
( ( relation(relation_inverse(U_670))
& empty(relation_inverse(U_670)) )
| ~ empty(U_670) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_670] :
( relation(relation_inverse(U_670))
| ~ sP177(U_670) )
& ! [U_670] :
( empty(relation_inverse(U_670))
| ~ sP177(U_670) )
& ! [U_670] :
( sP177(U_670)
| ~ empty(U_670) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_129_2]) ).
cnf(f_129_4,plain,
( sP177(U_670)
| ~ empty(U_670) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_5,plain,
( empty(relation_inverse(U_670))
| ~ sP177(U_670) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_6,plain,
( relation(relation_inverse(U_670))
| ~ sP177(U_670) ),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_130_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_130_1]) ).
cnf(f_130_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_130_2]) ).
cnf(f_130_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_130_2]) ).
cnf(f_130_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_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_131_2,plain,
! [U_672,U_671] :
( ( relation_empty_yielding(relation_dom_restriction(U_672,U_671))
& relation(relation_dom_restriction(U_672,U_671)) )
| ~ relation_empty_yielding(U_672)
| ~ relation(U_672) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_672] :
( ( ! [U_674] : relation_empty_yielding(relation_dom_restriction(U_672,U_674))
& ! [U_673] : relation(relation_dom_restriction(U_672,U_673)) )
| ~ relation_empty_yielding(U_672)
| ~ relation(U_672) ),
inference(miniscope,[status(thm)],[f_131_2]) ).
fof(f_131_4,plain,
( ! [U_673,U_672,U_674] :
( relation_empty_yielding(relation_dom_restriction(U_672,U_674))
| ~ sP178(U_673,U_672,U_674) )
& ! [U_673,U_672,U_674] :
( relation(relation_dom_restriction(U_672,U_673))
| ~ sP178(U_673,U_672,U_674) )
& ! [U_673,U_672,U_674] :
( sP178(U_673,U_672,U_674)
| ~ relation_empty_yielding(U_672)
| ~ relation(U_672) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_131_3]) ).
cnf(f_131_5,plain,
( sP178(U_673,U_672,U_674)
| ~ relation_empty_yielding(U_672)
| ~ relation(U_672) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_6,plain,
( relation(relation_dom_restriction(U_672,U_673))
| ~ sP178(U_673,U_672,U_674) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_7,plain,
( relation_empty_yielding(relation_dom_restriction(U_672,U_674))
| ~ sP178(U_673,U_672,U_674) ),
inference(clausify,[status(thm)],[f_131_4]) ).
fof(f_132_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_132_2,plain,
! [U_676,U_675] :
( ( function(relation_composition(U_676,U_675))
& relation(relation_composition(U_676,U_675)) )
| ~ function(U_675)
| ~ relation(U_675)
| ~ function(U_676)
| ~ relation(U_676) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
( ! [U_676,U_675] :
( function(relation_composition(U_676,U_675))
| ~ sP179(U_676,U_675) )
& ! [U_676,U_675] :
( relation(relation_composition(U_676,U_675))
| ~ sP179(U_676,U_675) )
& ! [U_676,U_675] :
( sP179(U_676,U_675)
| ~ function(U_675)
| ~ relation(U_675)
| ~ function(U_676)
| ~ relation(U_676) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_132_2]) ).
cnf(f_132_4,plain,
( sP179(U_676,U_675)
| ~ function(U_675)
| ~ relation(U_675)
| ~ function(U_676)
| ~ relation(U_676) ),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_5,plain,
( relation(relation_composition(U_676,U_675))
| ~ sP179(U_676,U_675) ),
inference(clausify,[status(thm)],[f_132_3]) ).
cnf(f_132_6,plain,
( function(relation_composition(U_676,U_675))
| ~ sP179(U_676,U_675) ),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_133_2,plain,
! [U_677] : ~ empty(succ(U_677)),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_677] : ~ empty(succ(U_677)),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
~ empty(succ(U_677)),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_134_2,plain,
! [U_679,U_678] :
( relation(set_intersection2(U_679,U_678))
| ~ relation(U_678)
| ~ relation(U_679) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_678,U_679] :
( relation(set_intersection2(U_679,U_678))
| ~ relation(U_678)
| ~ relation(U_679) ),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
( relation(set_intersection2(U_679,U_678))
| ~ relation(U_678)
| ~ relation(U_679) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_135_2,plain,
! [U_680] : ~ empty(powerset(U_680)),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_680] : ~ empty(powerset(U_680)),
inference(definitional_conversion,[status(esa)],[f_135_2]) ).
cnf(f_135_4,plain,
~ empty(powerset(U_680)),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_136_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_136_1]) ).
cnf(f_136_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_137_2,plain,
! [U_682,U_681] : ~ empty(ordered_pair(U_682,U_681)),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_681,U_682] : ~ empty(ordered_pair(U_682,U_681)),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
~ empty(ordered_pair(U_682,U_681)),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_138_2,plain,
! [U_683] :
( function(identity_relation(U_683))
& relation(identity_relation(U_683)) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
( ! [U_685] : function(identity_relation(U_685))
& ! [U_684] : relation(identity_relation(U_684)) ),
inference(miniscope,[status(thm)],[f_138_2]) ).
fof(f_138_4,plain,
( ! [U_685] : function(identity_relation(U_685))
& ! [U_684] : relation(identity_relation(U_684)) ),
inference(definitional_conversion,[status(esa)],[f_138_3]) ).
cnf(f_138_5,plain,
relation(identity_relation(U_684)),
inference(clausify,[status(thm)],[f_138_4]) ).
cnf(f_138_6,plain,
function(identity_relation(U_685)),
inference(clausify,[status(thm)],[f_138_4]) ).
fof(f_139_1,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
fof(f_139_2,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_139_1]) ).
cnf(f_139_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_140_2,plain,
! [U_687,U_686] :
( relation(set_union2(U_687,U_686))
| ~ relation(U_686)
| ~ relation(U_687) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_687,U_686] :
( relation(set_union2(U_687,U_686))
| ~ relation(U_686)
| ~ relation(U_687) ),
inference(definitional_conversion,[status(esa)],[f_140_2]) ).
cnf(f_140_4,plain,
( relation(set_union2(U_687,U_686))
| ~ relation(U_686)
| ~ relation(U_687) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_141_2,plain,
! [U_688] : ~ empty(singleton(U_688)),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_688] : ~ empty(singleton(U_688)),
inference(definitional_conversion,[status(esa)],[f_141_2]) ).
cnf(f_141_4,plain,
~ empty(singleton(U_688)),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_142_2,plain,
! [U_690,U_689] :
( ~ empty(set_union2(U_690,U_689))
| empty(U_690) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_690] :
( ! [U_689] : ~ empty(set_union2(U_690,U_689))
| empty(U_690) ),
inference(miniscope,[status(thm)],[f_142_2]) ).
fof(f_142_4,plain,
! [U_689,U_690] :
( ~ empty(set_union2(U_690,U_689))
| empty(U_690) ),
inference(definitional_conversion,[status(esa)],[f_142_3]) ).
cnf(f_142_5,plain,
( ~ empty(set_union2(U_690,U_689))
| empty(U_690) ),
inference(clausify,[status(thm)],[f_142_4]) ).
fof(f_143_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_143_2,plain,
! [U_691] :
( ( function(relation_inverse(U_691))
& relation(relation_inverse(U_691)) )
| ~ one_to_one(U_691)
| ~ function(U_691)
| ~ relation(U_691) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
( ! [U_691] :
( function(relation_inverse(U_691))
| ~ sP180(U_691) )
& ! [U_691] :
( relation(relation_inverse(U_691))
| ~ sP180(U_691) )
& ! [U_691] :
( sP180(U_691)
| ~ one_to_one(U_691)
| ~ function(U_691)
| ~ relation(U_691) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_143_2]) ).
cnf(f_143_4,plain,
( sP180(U_691)
| ~ one_to_one(U_691)
| ~ function(U_691)
| ~ relation(U_691) ),
inference(clausify,[status(thm)],[f_143_3]) ).
cnf(f_143_5,plain,
( relation(relation_inverse(U_691))
| ~ sP180(U_691) ),
inference(clausify,[status(thm)],[f_143_3]) ).
cnf(f_143_6,plain,
( function(relation_inverse(U_691))
| ~ sP180(U_691) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_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_144_2,plain,
! [U_692] :
( ( ordinal(succ(U_692))
& epsilon_connected(succ(U_692))
& epsilon_transitive(succ(U_692))
& ~ empty(succ(U_692)) )
| ~ ordinal(U_692) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_692] :
( ordinal(succ(U_692))
| ~ sP181(U_692) )
& ! [U_692] :
( epsilon_connected(succ(U_692))
| ~ sP181(U_692) )
& ! [U_692] :
( epsilon_transitive(succ(U_692))
| ~ sP181(U_692) )
& ! [U_692] :
( ~ empty(succ(U_692))
| ~ sP181(U_692) )
& ! [U_692] :
( sP181(U_692)
| ~ ordinal(U_692) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_144_2]) ).
cnf(f_144_4,plain,
( sP181(U_692)
| ~ ordinal(U_692) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_5,plain,
( ~ empty(succ(U_692))
| ~ sP181(U_692) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_6,plain,
( epsilon_transitive(succ(U_692))
| ~ sP181(U_692) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_7,plain,
( epsilon_connected(succ(U_692))
| ~ sP181(U_692) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_8,plain,
( ordinal(succ(U_692))
| ~ sP181(U_692) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_145_2,plain,
! [U_694,U_693] :
( relation(set_difference(U_694,U_693))
| ~ relation(U_693)
| ~ relation(U_694) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_693,U_694] :
( relation(set_difference(U_694,U_693))
| ~ relation(U_693)
| ~ relation(U_694) ),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
( relation(set_difference(U_694,U_693))
| ~ relation(U_693)
| ~ relation(U_694) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_146_2,plain,
! [U_696,U_695] : ~ empty(unordered_pair(U_696,U_695)),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_696,U_695] : ~ empty(unordered_pair(U_696,U_695)),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
~ empty(unordered_pair(U_696,U_695)),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_147_2,plain,
! [U_698,U_697] :
( ~ empty(set_union2(U_697,U_698))
| empty(U_698) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_698] :
( ! [U_697] : ~ empty(set_union2(U_697,U_698))
| empty(U_698) ),
inference(miniscope,[status(thm)],[f_147_2]) ).
fof(f_147_4,plain,
! [U_697,U_698] :
( ~ empty(set_union2(U_697,U_698))
| empty(U_698) ),
inference(definitional_conversion,[status(esa)],[f_147_3]) ).
cnf(f_147_5,plain,
( ~ empty(set_union2(U_697,U_698))
| empty(U_698) ),
inference(clausify,[status(thm)],[f_147_4]) ).
fof(f_148_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_148_2,plain,
! [U_700,U_699] :
( ( function(relation_dom_restriction(U_700,U_699))
& relation(relation_dom_restriction(U_700,U_699)) )
| ~ function(U_700)
| ~ relation(U_700) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_700] :
( ( ! [U_702] : function(relation_dom_restriction(U_700,U_702))
& ! [U_701] : relation(relation_dom_restriction(U_700,U_701)) )
| ~ function(U_700)
| ~ relation(U_700) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
fof(f_148_4,plain,
( ! [U_700,U_701,U_702] :
( function(relation_dom_restriction(U_700,U_702))
| ~ sP182(U_700,U_701,U_702) )
& ! [U_700,U_701,U_702] :
( relation(relation_dom_restriction(U_700,U_701))
| ~ sP182(U_700,U_701,U_702) )
& ! [U_700,U_701,U_702] :
( sP182(U_700,U_701,U_702)
| ~ function(U_700)
| ~ relation(U_700) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_148_3]) ).
cnf(f_148_5,plain,
( sP182(U_700,U_701,U_702)
| ~ function(U_700)
| ~ relation(U_700) ),
inference(clausify,[status(thm)],[f_148_4]) ).
cnf(f_148_6,plain,
( relation(relation_dom_restriction(U_700,U_701))
| ~ sP182(U_700,U_701,U_702) ),
inference(clausify,[status(thm)],[f_148_4]) ).
cnf(f_148_7,plain,
( function(relation_dom_restriction(U_700,U_702))
| ~ sP182(U_700,U_701,U_702) ),
inference(clausify,[status(thm)],[f_148_4]) ).
fof(f_149_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_149_2,plain,
! [U_703] :
( ( ordinal(union(U_703))
& epsilon_connected(union(U_703))
& epsilon_transitive(union(U_703)) )
| ~ ordinal(U_703) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
( ! [U_703] :
( ordinal(union(U_703))
| ~ sP183(U_703) )
& ! [U_703] :
( epsilon_connected(union(U_703))
| ~ sP183(U_703) )
& ! [U_703] :
( epsilon_transitive(union(U_703))
| ~ sP183(U_703) )
& ! [U_703] :
( sP183(U_703)
| ~ ordinal(U_703) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_149_2]) ).
cnf(f_149_4,plain,
( sP183(U_703)
| ~ ordinal(U_703) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_5,plain,
( epsilon_transitive(union(U_703))
| ~ sP183(U_703) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_6,plain,
( epsilon_connected(union(U_703))
| ~ sP183(U_703) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_7,plain,
( ordinal(union(U_703))
| ~ sP183(U_703) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_150_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_150_1]) ).
cnf(f_150_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_150_2]) ).
cnf(f_150_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_151_2,plain,
! [U_705,U_704] :
( ~ empty(cartesian_product2(U_705,U_704))
| empty(U_704)
| empty(U_705) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_704,U_705] :
( ~ empty(cartesian_product2(U_705,U_704))
| empty(U_704)
| empty(U_705) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( ~ empty(cartesian_product2(U_705,U_704))
| empty(U_704)
| empty(U_705) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_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_152_2,plain,
! [U_707,U_706] :
( ( function(relation_rng_restriction(U_707,U_706))
& relation(relation_rng_restriction(U_707,U_706)) )
| ~ function(U_706)
| ~ relation(U_706) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
( ! [U_707,U_706] :
( function(relation_rng_restriction(U_707,U_706))
| ~ sP184(U_707,U_706) )
& ! [U_707,U_706] :
( relation(relation_rng_restriction(U_707,U_706))
| ~ sP184(U_707,U_706) )
& ! [U_707,U_706] :
( sP184(U_707,U_706)
| ~ function(U_706)
| ~ relation(U_706) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_152_2]) ).
cnf(f_152_4,plain,
( sP184(U_707,U_706)
| ~ function(U_706)
| ~ relation(U_706) ),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_5,plain,
( relation(relation_rng_restriction(U_707,U_706))
| ~ sP184(U_707,U_706) ),
inference(clausify,[status(thm)],[f_152_3]) ).
cnf(f_152_6,plain,
( function(relation_rng_restriction(U_707,U_706))
| ~ sP184(U_707,U_706) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_153_2,plain,
! [U_708] :
( ~ empty(relation_dom(U_708))
| ~ relation(U_708)
| empty(U_708) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_708] :
( ~ empty(relation_dom(U_708))
| ~ relation(U_708)
| empty(U_708) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( ~ empty(relation_dom(U_708))
| ~ relation(U_708)
| empty(U_708) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_154_2,plain,
! [U_709] :
( ~ empty(relation_rng(U_709))
| ~ relation(U_709)
| empty(U_709) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_709] :
( ~ empty(relation_rng(U_709))
| ~ relation(U_709)
| empty(U_709) ),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
( ~ empty(relation_rng(U_709))
| ~ relation(U_709)
| empty(U_709) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_155_2,plain,
! [U_710] :
( ( relation(relation_dom(U_710))
& empty(relation_dom(U_710)) )
| ~ empty(U_710) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( ! [U_710] :
( relation(relation_dom(U_710))
| ~ sP185(U_710) )
& ! [U_710] :
( empty(relation_dom(U_710))
| ~ sP185(U_710) )
& ! [U_710] :
( sP185(U_710)
| ~ empty(U_710) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_155_2]) ).
cnf(f_155_4,plain,
( sP185(U_710)
| ~ empty(U_710) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( empty(relation_dom(U_710))
| ~ sP185(U_710) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_6,plain,
( relation(relation_dom(U_710))
| ~ sP185(U_710) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_156_2,plain,
! [U_711] :
( ( relation(relation_rng(U_711))
& empty(relation_rng(U_711)) )
| ~ empty(U_711) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ! [U_711] :
( relation(relation_rng(U_711))
| ~ sP186(U_711) )
& ! [U_711] :
( empty(relation_rng(U_711))
| ~ sP186(U_711) )
& ! [U_711] :
( sP186(U_711)
| ~ empty(U_711) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_156_2]) ).
cnf(f_156_4,plain,
( sP186(U_711)
| ~ empty(U_711) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_5,plain,
( empty(relation_rng(U_711))
| ~ sP186(U_711) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_6,plain,
( relation(relation_rng(U_711))
| ~ sP186(U_711) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_713,U_712] :
( ( relation(relation_composition(U_713,U_712))
& empty(relation_composition(U_713,U_712)) )
| ~ relation(U_712)
| ~ empty(U_713) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_713,U_712] :
( relation(relation_composition(U_713,U_712))
| ~ sP187(U_713,U_712) )
& ! [U_713,U_712] :
( empty(relation_composition(U_713,U_712))
| ~ sP187(U_713,U_712) )
& ! [U_713,U_712] :
( sP187(U_713,U_712)
| ~ relation(U_712)
| ~ empty(U_713) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_157_2]) ).
cnf(f_157_4,plain,
( sP187(U_713,U_712)
| ~ relation(U_712)
| ~ empty(U_713) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( empty(relation_composition(U_713,U_712))
| ~ sP187(U_713,U_712) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( relation(relation_composition(U_713,U_712))
| ~ sP187(U_713,U_712) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_158_2,plain,
! [U_715,U_714] : set_union2(U_715,U_715) = U_715,
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_715] : set_union2(U_715,U_715) = U_715,
inference(miniscope,[status(thm)],[f_158_2]) ).
fof(f_158_4,plain,
! [U_715] : set_union2(U_715,U_715) = U_715,
inference(definitional_conversion,[status(esa)],[f_158_3]) ).
cnf(f_158_5,plain,
set_union2(U_715,U_715) = U_715,
inference(clausify,[status(thm)],[f_158_4]) ).
fof(f_159_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_159_2,plain,
! [U_717,U_716] : set_intersection2(U_717,U_717) = U_717,
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_717] : set_intersection2(U_717,U_717) = U_717,
inference(miniscope,[status(thm)],[f_159_2]) ).
fof(f_159_4,plain,
! [U_717] : set_intersection2(U_717,U_717) = U_717,
inference(definitional_conversion,[status(esa)],[f_159_3]) ).
cnf(f_159_5,plain,
set_intersection2(U_717,U_717) = U_717,
inference(clausify,[status(thm)],[f_159_4]) ).
fof(f_160_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_160_2,plain,
! [U_719,U_718] :
( subset_complement(U_719,subset_complement(U_719,U_718)) = U_718
| ~ element(U_718,powerset(U_719)) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_718,U_719] :
( subset_complement(U_719,subset_complement(U_719,U_718)) = U_718
| ~ element(U_718,powerset(U_719)) ),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
( subset_complement(U_719,subset_complement(U_719,U_718)) = U_718
| ~ element(U_718,powerset(U_719)) ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_161_2,plain,
! [U_720] :
( relation_inverse(relation_inverse(U_720)) = U_720
| ~ relation(U_720) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_720] :
( relation_inverse(relation_inverse(U_720)) = U_720
| ~ relation(U_720) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( relation_inverse(relation_inverse(U_720)) = U_720
| ~ relation(U_720) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_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_162_2,plain,
! [U_722,U_721] :
( complements_of_subsets(U_722,complements_of_subsets(U_722,U_721)) = U_721
| ~ element(U_721,powerset(powerset(U_722))) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_721,U_722] :
( complements_of_subsets(U_722,complements_of_subsets(U_722,U_721)) = U_721
| ~ element(U_721,powerset(powerset(U_722))) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( complements_of_subsets(U_722,complements_of_subsets(U_722,U_721)) = U_721
| ~ element(U_721,powerset(powerset(U_722))) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_163_2,plain,
! [U_724,U_723] : ~ proper_subset(U_724,U_724),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_724] : ~ proper_subset(U_724,U_724),
inference(miniscope,[status(thm)],[f_163_2]) ).
fof(f_163_4,plain,
! [U_724] : ~ proper_subset(U_724,U_724),
inference(definitional_conversion,[status(esa)],[f_163_3]) ).
cnf(f_163_5,plain,
~ proper_subset(U_724,U_724),
inference(clausify,[status(thm)],[f_163_4]) ).
fof(f_164_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_164_2,plain,
! [U_727] :
( ( ( reflexive(U_727)
| ? [U_726] :
( ~ in(ordered_pair(U_726,U_726),U_727)
& in(U_726,relation_field(U_727)) ) )
& ( ! [U_725] :
( in(ordered_pair(U_725,U_725),U_727)
| ~ in(U_725,relation_field(U_727)) )
| ~ reflexive(U_727) ) )
| ~ relation(U_727) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_727] :
( ( ( reflexive(U_727)
| ( ~ in(ordered_pair(sK125(U_727),sK125(U_727)),U_727)
& in(sK125(U_727),relation_field(U_727)) ) )
& ( ! [U_725] :
( in(ordered_pair(U_725,U_725),U_727)
| ~ in(U_725,relation_field(U_727)) )
| ~ reflexive(U_727) ) )
| ~ relation(U_727) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_726,sK125(U_727))],[f_164_2]) ).
fof(f_164_4,plain,
( ! [U_727] :
( ~ in(ordered_pair(sK125(U_727),sK125(U_727)),U_727)
| ~ sP188(U_727) )
& ! [U_727] :
( in(sK125(U_727),relation_field(U_727))
| ~ sP188(U_727) )
& ! [U_725,U_727] :
( reflexive(U_727)
| sP188(U_727)
| ~ sP189(U_725,U_727) )
& ! [U_725,U_727] :
( in(ordered_pair(U_725,U_725),U_727)
| ~ in(U_725,relation_field(U_727))
| ~ reflexive(U_727)
| ~ sP189(U_725,U_727) )
& ! [U_725,U_727] :
( sP189(U_725,U_727)
| ~ relation(U_727) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188,sP189])],[f_164_3]) ).
cnf(f_164_5,plain,
( sP189(U_725,U_727)
| ~ relation(U_727) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_6,plain,
( in(ordered_pair(U_725,U_725),U_727)
| ~ in(U_725,relation_field(U_727))
| ~ reflexive(U_727)
| ~ sP189(U_725,U_727) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_7,plain,
( reflexive(U_727)
| sP188(U_727)
| ~ sP189(U_725,U_727) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_8,plain,
( in(sK125(U_727),relation_field(U_727))
| ~ sP188(U_727) ),
inference(clausify,[status(thm)],[f_164_4]) ).
cnf(f_164_9,plain,
( ~ in(ordered_pair(sK125(U_727),sK125(U_727)),U_727)
| ~ sP188(U_727) ),
inference(clausify,[status(thm)],[f_164_4]) ).
fof(f_165_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_165_2,plain,
! [U_728] : singleton(U_728) != empty_set,
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_728] : singleton(U_728) != empty_set,
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
singleton(U_728) != empty_set,
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_166_2,plain,
! [U_730,U_729] :
( set_union2(singleton(U_730),U_729) = U_729
| ~ in(U_730,U_729) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_729,U_730] :
( set_union2(singleton(U_730),U_729) = U_729
| ~ in(U_730,U_729) ),
inference(definitional_conversion,[status(esa)],[f_166_2]) ).
cnf(f_166_4,plain,
( set_union2(singleton(U_730),U_729) = U_729
| ~ in(U_730,U_729) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_167_2,plain,
! [U_732,U_731] :
( ~ in(U_732,U_731)
| ~ disjoint(singleton(U_732),U_731) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_732,U_731] :
( ~ in(U_732,U_731)
| ~ disjoint(singleton(U_732),U_731) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( ~ in(U_732,U_731)
| ~ disjoint(singleton(U_732),U_731) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_168_2,plain,
! [U_734,U_733] :
( disjoint(singleton(U_734),U_733)
| in(U_734,U_733) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_734,U_733] :
( disjoint(singleton(U_734),U_733)
| in(U_734,U_733) ),
inference(definitional_conversion,[status(esa)],[f_168_2]) ).
cnf(f_168_4,plain,
( disjoint(singleton(U_734),U_733)
| in(U_734,U_733) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_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_169_2,plain,
! [U_736,U_735] :
( subset(relation_dom(relation_rng_restriction(U_736,U_735)),relation_dom(U_735))
| ~ relation(U_735) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_735,U_736] :
( subset(relation_dom(relation_rng_restriction(U_736,U_735)),relation_dom(U_735))
| ~ relation(U_735) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( subset(relation_dom(relation_rng_restriction(U_736,U_735)),relation_dom(U_735))
| ~ relation(U_735) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_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_170_2,plain,
! [U_743] :
( ( ( transitive(U_743)
| ? [U_742,U_741,U_740] :
( ~ in(ordered_pair(U_742,U_740),U_743)
& in(ordered_pair(U_741,U_740),U_743)
& in(ordered_pair(U_742,U_741),U_743) ) )
& ( ! [U_739,U_738,U_737] :
( in(ordered_pair(U_739,U_737),U_743)
| ~ in(ordered_pair(U_738,U_737),U_743)
| ~ in(ordered_pair(U_739,U_738),U_743) )
| ~ transitive(U_743) ) )
| ~ relation(U_743) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_743] :
( ( ( transitive(U_743)
| ? [U_741,U_740] :
( ~ in(ordered_pair(sK126(U_743),U_740),U_743)
& in(ordered_pair(U_741,U_740),U_743)
& in(ordered_pair(sK126(U_743),U_741),U_743) ) )
& ( ! [U_739,U_738,U_737] :
( in(ordered_pair(U_739,U_737),U_743)
| ~ in(ordered_pair(U_738,U_737),U_743)
| ~ in(ordered_pair(U_739,U_738),U_743) )
| ~ transitive(U_743) ) )
| ~ relation(U_743) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_742,sK126(U_743))],[f_170_2]) ).
fof(f_170_4,plain,
! [U_743] :
( ( ( transitive(U_743)
| ? [U_740] :
( ~ in(ordered_pair(sK126(U_743),U_740),U_743)
& in(ordered_pair(sK127(U_743),U_740),U_743)
& in(ordered_pair(sK126(U_743),sK127(U_743)),U_743) ) )
& ( ! [U_739,U_738,U_737] :
( in(ordered_pair(U_739,U_737),U_743)
| ~ in(ordered_pair(U_738,U_737),U_743)
| ~ in(ordered_pair(U_739,U_738),U_743) )
| ~ transitive(U_743) ) )
| ~ relation(U_743) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_741,sK127(U_743))],[f_170_3]) ).
fof(f_170_5,plain,
! [U_743] :
( ( ( transitive(U_743)
| ( ~ in(ordered_pair(sK126(U_743),sK128(U_743)),U_743)
& in(ordered_pair(sK127(U_743),sK128(U_743)),U_743)
& in(ordered_pair(sK126(U_743),sK127(U_743)),U_743) ) )
& ( ! [U_739,U_738,U_737] :
( in(ordered_pair(U_739,U_737),U_743)
| ~ in(ordered_pair(U_738,U_737),U_743)
| ~ in(ordered_pair(U_739,U_738),U_743) )
| ~ transitive(U_743) ) )
| ~ relation(U_743) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_740,sK128(U_743))],[f_170_4]) ).
fof(f_170_6,plain,
( ! [U_743] :
( ~ in(ordered_pair(sK126(U_743),sK128(U_743)),U_743)
| ~ sP190(U_743) )
& ! [U_743] :
( in(ordered_pair(sK127(U_743),sK128(U_743)),U_743)
| ~ sP190(U_743) )
& ! [U_743] :
( in(ordered_pair(sK126(U_743),sK127(U_743)),U_743)
| ~ sP190(U_743) )
& ! [U_737,U_738,U_739,U_743] :
( transitive(U_743)
| sP190(U_743)
| ~ sP191(U_737,U_738,U_739,U_743) )
& ! [U_737,U_738,U_739,U_743] :
( in(ordered_pair(U_739,U_737),U_743)
| ~ in(ordered_pair(U_738,U_737),U_743)
| ~ in(ordered_pair(U_739,U_738),U_743)
| ~ transitive(U_743)
| ~ sP191(U_737,U_738,U_739,U_743) )
& ! [U_737,U_738,U_739,U_743] :
( sP191(U_737,U_738,U_739,U_743)
| ~ relation(U_743) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190,sP191])],[f_170_5]) ).
cnf(f_170_7,plain,
( sP191(U_737,U_738,U_739,U_743)
| ~ relation(U_743) ),
inference(clausify,[status(thm)],[f_170_6]) ).
cnf(f_170_8,plain,
( in(ordered_pair(U_739,U_737),U_743)
| ~ in(ordered_pair(U_738,U_737),U_743)
| ~ in(ordered_pair(U_739,U_738),U_743)
| ~ transitive(U_743)
| ~ sP191(U_737,U_738,U_739,U_743) ),
inference(clausify,[status(thm)],[f_170_6]) ).
cnf(f_170_9,plain,
( transitive(U_743)
| sP190(U_743)
| ~ sP191(U_737,U_738,U_739,U_743) ),
inference(clausify,[status(thm)],[f_170_6]) ).
cnf(f_170_10,plain,
( in(ordered_pair(sK126(U_743),sK127(U_743)),U_743)
| ~ sP190(U_743) ),
inference(clausify,[status(thm)],[f_170_6]) ).
cnf(f_170_11,plain,
( in(ordered_pair(sK127(U_743),sK128(U_743)),U_743)
| ~ sP190(U_743) ),
inference(clausify,[status(thm)],[f_170_6]) ).
cnf(f_170_12,plain,
( ~ in(ordered_pair(sK126(U_743),sK128(U_743)),U_743)
| ~ sP190(U_743) ),
inference(clausify,[status(thm)],[f_170_6]) ).
fof(f_171_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_171_2,plain,
! [U_745,U_744] :
( ( subset(singleton(U_745),U_744)
| ~ in(U_745,U_744) )
& ( in(U_745,U_744)
| ~ subset(singleton(U_745),U_744) ) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
( ! [U_749,U_747] :
( subset(singleton(U_749),U_747)
| ~ in(U_749,U_747) )
& ! [U_748,U_746] :
( in(U_748,U_746)
| ~ subset(singleton(U_748),U_746) ) ),
inference(miniscope,[status(thm)],[f_171_2]) ).
fof(f_171_4,plain,
( ! [U_749,U_747] :
( subset(singleton(U_749),U_747)
| ~ in(U_749,U_747) )
& ! [U_748,U_746] :
( in(U_748,U_746)
| ~ subset(singleton(U_748),U_746) ) ),
inference(definitional_conversion,[status(esa)],[f_171_3]) ).
cnf(f_171_5,plain,
( in(U_748,U_746)
| ~ subset(singleton(U_748),U_746) ),
inference(clausify,[status(thm)],[f_171_4]) ).
cnf(f_171_6,plain,
( subset(singleton(U_749),U_747)
| ~ in(U_749,U_747) ),
inference(clausify,[status(thm)],[f_171_4]) ).
fof(f_172_1,plain,
! [A,B] :
( ? [C] :
( well_orders(C,A)
& relation(C) )
| ~ equipotent(A,relation_field(B))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[l30_wellord2]) ).
fof(f_172_2,plain,
! [U_752,U_751] :
( ? [U_750] :
( well_orders(U_750,U_752)
& relation(U_750) )
| ~ equipotent(U_752,relation_field(U_751))
| ~ well_ordering(U_751)
| ~ relation(U_751) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_752,U_751] :
( ( well_orders(sK129(U_752,U_751),U_752)
& relation(sK129(U_752,U_751)) )
| ~ equipotent(U_752,relation_field(U_751))
| ~ well_ordering(U_751)
| ~ relation(U_751) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_750,sK129(U_752,U_751))],[f_172_2]) ).
fof(f_172_4,plain,
( ! [U_751,U_752] :
( well_orders(sK129(U_752,U_751),U_752)
| ~ sP192(U_751,U_752) )
& ! [U_751,U_752] :
( relation(sK129(U_752,U_751))
| ~ sP192(U_751,U_752) )
& ! [U_751,U_752] :
( sP192(U_751,U_752)
| ~ equipotent(U_752,relation_field(U_751))
| ~ well_ordering(U_751)
| ~ relation(U_751) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_172_3]) ).
cnf(f_172_5,plain,
( sP192(U_751,U_752)
| ~ equipotent(U_752,relation_field(U_751))
| ~ well_ordering(U_751)
| ~ relation(U_751) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_6,plain,
( relation(sK129(U_752,U_751))
| ~ sP192(U_751,U_752) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_7,plain,
( well_orders(sK129(U_752,U_751),U_752)
| ~ sP192(U_751,U_752) ),
inference(clausify,[status(thm)],[f_172_4]) ).
fof(f_173_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_173_2,plain,
! [U_754,U_753] :
( ( set_difference(U_754,U_753) = empty_set
| ~ subset(U_754,U_753) )
& ( subset(U_754,U_753)
| set_difference(U_754,U_753) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
( ! [U_758,U_756] :
( set_difference(U_758,U_756) = empty_set
| ~ subset(U_758,U_756) )
& ! [U_757,U_755] :
( subset(U_757,U_755)
| set_difference(U_757,U_755) != empty_set ) ),
inference(miniscope,[status(thm)],[f_173_2]) ).
fof(f_173_4,plain,
( ! [U_756,U_758] :
( set_difference(U_758,U_756) = empty_set
| ~ subset(U_758,U_756) )
& ! [U_755,U_757] :
( subset(U_757,U_755)
| set_difference(U_757,U_755) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_173_3]) ).
cnf(f_173_5,plain,
( subset(U_757,U_755)
| set_difference(U_757,U_755) != empty_set ),
inference(clausify,[status(thm)],[f_173_4]) ).
cnf(f_173_6,plain,
( set_difference(U_758,U_756) = empty_set
| ~ subset(U_758,U_756) ),
inference(clausify,[status(thm)],[f_173_4]) ).
fof(f_174_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_174_2,plain,
! [U_761,U_760] :
( ! [U_759] :
( in(U_759,U_761)
| ~ in(U_759,U_760) )
| ~ element(U_760,powerset(U_761)) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_761,U_760,U_759] :
( in(U_759,U_761)
| ~ in(U_759,U_760)
| ~ element(U_760,powerset(U_761)) ),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
( in(U_759,U_761)
| ~ in(U_759,U_760)
| ~ element(U_760,powerset(U_761)) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_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_175_2,plain,
! [U_766] :
( ( ( antisymmetric(U_766)
| ? [U_765,U_764] :
( U_765 != U_764
& in(ordered_pair(U_764,U_765),U_766)
& in(ordered_pair(U_765,U_764),U_766) ) )
& ( ! [U_763,U_762] :
( U_763 = U_762
| ~ in(ordered_pair(U_762,U_763),U_766)
| ~ in(ordered_pair(U_763,U_762),U_766) )
| ~ antisymmetric(U_766) ) )
| ~ relation(U_766) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_766] :
( ( ( antisymmetric(U_766)
| ? [U_764] :
( sK130(U_766) != U_764
& in(ordered_pair(U_764,sK130(U_766)),U_766)
& in(ordered_pair(sK130(U_766),U_764),U_766) ) )
& ( ! [U_763,U_762] :
( U_763 = U_762
| ~ in(ordered_pair(U_762,U_763),U_766)
| ~ in(ordered_pair(U_763,U_762),U_766) )
| ~ antisymmetric(U_766) ) )
| ~ relation(U_766) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_765,sK130(U_766))],[f_175_2]) ).
fof(f_175_4,plain,
! [U_766] :
( ( ( antisymmetric(U_766)
| ( sK130(U_766) != sK131(U_766)
& in(ordered_pair(sK131(U_766),sK130(U_766)),U_766)
& in(ordered_pair(sK130(U_766),sK131(U_766)),U_766) ) )
& ( ! [U_763,U_762] :
( U_763 = U_762
| ~ in(ordered_pair(U_762,U_763),U_766)
| ~ in(ordered_pair(U_763,U_762),U_766) )
| ~ antisymmetric(U_766) ) )
| ~ relation(U_766) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_764,sK131(U_766))],[f_175_3]) ).
fof(f_175_5,plain,
( ! [U_766] :
( sK130(U_766) != sK131(U_766)
| ~ sP193(U_766) )
& ! [U_766] :
( in(ordered_pair(sK131(U_766),sK130(U_766)),U_766)
| ~ sP193(U_766) )
& ! [U_766] :
( in(ordered_pair(sK130(U_766),sK131(U_766)),U_766)
| ~ sP193(U_766) )
& ! [U_762,U_763,U_766] :
( antisymmetric(U_766)
| sP193(U_766)
| ~ sP194(U_762,U_763,U_766) )
& ! [U_762,U_763,U_766] :
( U_763 = U_762
| ~ in(ordered_pair(U_762,U_763),U_766)
| ~ in(ordered_pair(U_763,U_762),U_766)
| ~ antisymmetric(U_766)
| ~ sP194(U_762,U_763,U_766) )
& ! [U_762,U_763,U_766] :
( sP194(U_762,U_763,U_766)
| ~ relation(U_766) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193,sP194])],[f_175_4]) ).
cnf(f_175_6,plain,
( sP194(U_762,U_763,U_766)
| ~ relation(U_766) ),
inference(clausify,[status(thm)],[f_175_5]) ).
cnf(f_175_7,plain,
( U_763 = U_762
| ~ in(ordered_pair(U_762,U_763),U_766)
| ~ in(ordered_pair(U_763,U_762),U_766)
| ~ antisymmetric(U_766)
| ~ sP194(U_762,U_763,U_766) ),
inference(clausify,[status(thm)],[f_175_5]) ).
cnf(f_175_8,plain,
( antisymmetric(U_766)
| sP193(U_766)
| ~ sP194(U_762,U_763,U_766) ),
inference(clausify,[status(thm)],[f_175_5]) ).
cnf(f_175_9,plain,
( in(ordered_pair(sK130(U_766),sK131(U_766)),U_766)
| ~ sP193(U_766) ),
inference(clausify,[status(thm)],[f_175_5]) ).
cnf(f_175_10,plain,
( in(ordered_pair(sK131(U_766),sK130(U_766)),U_766)
| ~ sP193(U_766) ),
inference(clausify,[status(thm)],[f_175_5]) ).
cnf(f_175_11,plain,
( sK130(U_766) != sK131(U_766)
| ~ sP193(U_766) ),
inference(clausify,[status(thm)],[f_175_5]) ).
fof(f_176_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_176_2,plain,
! [U_769,U_768,U_767] :
( subset(U_769,set_difference(U_768,singleton(U_767)))
| in(U_767,U_769)
| ~ subset(U_769,U_768) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_769,U_768] :
( ! [U_767] :
( subset(U_769,set_difference(U_768,singleton(U_767)))
| in(U_767,U_769) )
| ~ subset(U_769,U_768) ),
inference(miniscope,[status(thm)],[f_176_2]) ).
fof(f_176_4,plain,
! [U_769,U_768,U_767] :
( subset(U_769,set_difference(U_768,singleton(U_767)))
| in(U_767,U_769)
| ~ subset(U_769,U_768) ),
inference(definitional_conversion,[status(esa)],[f_176_3]) ).
cnf(f_176_5,plain,
( subset(U_769,set_difference(U_768,singleton(U_767)))
| in(U_767,U_769)
| ~ subset(U_769,U_768) ),
inference(clausify,[status(thm)],[f_176_4]) ).
fof(f_177_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_177_2,plain,
! [U_774] :
( ( ( connected(U_774)
| ? [U_773,U_772] :
( ~ in(ordered_pair(U_772,U_773),U_774)
& ~ in(ordered_pair(U_773,U_772),U_774)
& U_773 != U_772
& in(U_772,relation_field(U_774))
& in(U_773,relation_field(U_774)) ) )
& ( ! [U_771,U_770] :
( in(ordered_pair(U_770,U_771),U_774)
| in(ordered_pair(U_771,U_770),U_774)
| U_771 = U_770
| ~ in(U_770,relation_field(U_774))
| ~ in(U_771,relation_field(U_774)) )
| ~ connected(U_774) ) )
| ~ relation(U_774) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_774] :
( ( ( connected(U_774)
| ? [U_773] :
( ? [U_772] :
( ~ in(ordered_pair(U_772,U_773),U_774)
& ~ in(ordered_pair(U_773,U_772),U_774)
& U_773 != U_772
& in(U_772,relation_field(U_774)) )
& in(U_773,relation_field(U_774)) ) )
& ( ! [U_771] :
( ! [U_770] :
( in(ordered_pair(U_770,U_771),U_774)
| in(ordered_pair(U_771,U_770),U_774)
| U_771 = U_770
| ~ in(U_770,relation_field(U_774)) )
| ~ in(U_771,relation_field(U_774)) )
| ~ connected(U_774) ) )
| ~ relation(U_774) ),
inference(miniscope,[status(thm)],[f_177_2]) ).
fof(f_177_4,plain,
! [U_774] :
( ( ( connected(U_774)
| ( ? [U_772] :
( ~ in(ordered_pair(U_772,sK132(U_774)),U_774)
& ~ in(ordered_pair(sK132(U_774),U_772),U_774)
& sK132(U_774) != U_772
& in(U_772,relation_field(U_774)) )
& in(sK132(U_774),relation_field(U_774)) ) )
& ( ! [U_771] :
( ! [U_770] :
( in(ordered_pair(U_770,U_771),U_774)
| in(ordered_pair(U_771,U_770),U_774)
| U_771 = U_770
| ~ in(U_770,relation_field(U_774)) )
| ~ in(U_771,relation_field(U_774)) )
| ~ connected(U_774) ) )
| ~ relation(U_774) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_773,sK132(U_774))],[f_177_3]) ).
fof(f_177_5,plain,
! [U_774] :
( ( ( connected(U_774)
| ( ~ in(ordered_pair(sK133(U_774),sK132(U_774)),U_774)
& ~ in(ordered_pair(sK132(U_774),sK133(U_774)),U_774)
& sK132(U_774) != sK133(U_774)
& in(sK133(U_774),relation_field(U_774))
& in(sK132(U_774),relation_field(U_774)) ) )
& ( ! [U_771] :
( ! [U_770] :
( in(ordered_pair(U_770,U_771),U_774)
| in(ordered_pair(U_771,U_770),U_774)
| U_771 = U_770
| ~ in(U_770,relation_field(U_774)) )
| ~ in(U_771,relation_field(U_774)) )
| ~ connected(U_774) ) )
| ~ relation(U_774) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_772,sK133(U_774))],[f_177_4]) ).
fof(f_177_6,plain,
( ! [U_774] :
( ~ in(ordered_pair(sK133(U_774),sK132(U_774)),U_774)
| ~ sP195(U_774) )
& ! [U_774] :
( ~ in(ordered_pair(sK132(U_774),sK133(U_774)),U_774)
| ~ sP195(U_774) )
& ! [U_774] :
( sK132(U_774) != sK133(U_774)
| ~ sP195(U_774) )
& ! [U_774] :
( in(sK133(U_774),relation_field(U_774))
| ~ sP195(U_774) )
& ! [U_774] :
( in(sK132(U_774),relation_field(U_774))
| ~ sP195(U_774) )
& ! [U_771,U_774,U_770] :
( connected(U_774)
| sP195(U_774)
| ~ sP196(U_771,U_774,U_770) )
& ! [U_771,U_774,U_770] :
( in(ordered_pair(U_770,U_771),U_774)
| in(ordered_pair(U_771,U_770),U_774)
| U_771 = U_770
| ~ in(U_770,relation_field(U_774))
| ~ in(U_771,relation_field(U_774))
| ~ connected(U_774)
| ~ sP196(U_771,U_774,U_770) )
& ! [U_771,U_774,U_770] :
( sP196(U_771,U_774,U_770)
| ~ relation(U_774) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195,sP196])],[f_177_5]) ).
cnf(f_177_7,plain,
( sP196(U_771,U_774,U_770)
| ~ relation(U_774) ),
inference(clausify,[status(thm)],[f_177_6]) ).
cnf(f_177_8,plain,
( in(ordered_pair(U_770,U_771),U_774)
| in(ordered_pair(U_771,U_770),U_774)
| U_771 = U_770
| ~ in(U_770,relation_field(U_774))
| ~ in(U_771,relation_field(U_774))
| ~ connected(U_774)
| ~ sP196(U_771,U_774,U_770) ),
inference(clausify,[status(thm)],[f_177_6]) ).
cnf(f_177_9,plain,
( connected(U_774)
| sP195(U_774)
| ~ sP196(U_771,U_774,U_770) ),
inference(clausify,[status(thm)],[f_177_6]) ).
cnf(f_177_10,plain,
( in(sK132(U_774),relation_field(U_774))
| ~ sP195(U_774) ),
inference(clausify,[status(thm)],[f_177_6]) ).
cnf(f_177_11,plain,
( in(sK133(U_774),relation_field(U_774))
| ~ sP195(U_774) ),
inference(clausify,[status(thm)],[f_177_6]) ).
cnf(f_177_12,plain,
( sK132(U_774) != sK133(U_774)
| ~ sP195(U_774) ),
inference(clausify,[status(thm)],[f_177_6]) ).
cnf(f_177_13,plain,
( ~ in(ordered_pair(sK132(U_774),sK133(U_774)),U_774)
| ~ sP195(U_774) ),
inference(clausify,[status(thm)],[f_177_6]) ).
cnf(f_177_14,plain,
( ~ in(ordered_pair(sK133(U_774),sK132(U_774)),U_774)
| ~ sP195(U_774) ),
inference(clausify,[status(thm)],[f_177_6]) ).
fof(f_178_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_178_2,plain,
! [U_776,U_775] :
( ( subset(U_776,singleton(U_775))
| ( U_776 != singleton(U_775)
& U_776 != empty_set ) )
& ( U_776 = singleton(U_775)
| U_776 = empty_set
| ~ subset(U_776,singleton(U_775)) ) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
( ! [U_780,U_778] :
( subset(U_780,singleton(U_778))
| ( U_780 != singleton(U_778)
& U_780 != empty_set ) )
& ! [U_779,U_777] :
( U_779 = singleton(U_777)
| U_779 = empty_set
| ~ subset(U_779,singleton(U_777)) ) ),
inference(miniscope,[status(thm)],[f_178_2]) ).
fof(f_178_4,plain,
( ! [U_780,U_778] :
( U_780 != singleton(U_778)
| ~ sP197(U_780,U_778) )
& ! [U_780,U_778] :
( U_780 != empty_set
| ~ sP197(U_780,U_778) )
& ! [U_780,U_778] :
( subset(U_780,singleton(U_778))
| sP197(U_780,U_778) )
& ! [U_779,U_777] :
( U_779 = singleton(U_777)
| U_779 = empty_set
| ~ subset(U_779,singleton(U_777)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_178_3]) ).
cnf(f_178_5,plain,
( U_779 = singleton(U_777)
| U_779 = empty_set
| ~ subset(U_779,singleton(U_777)) ),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_6,plain,
( subset(U_780,singleton(U_778))
| sP197(U_780,U_778) ),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_7,plain,
( U_780 != empty_set
| ~ sP197(U_780,U_778) ),
inference(clausify,[status(thm)],[f_178_4]) ).
cnf(f_178_8,plain,
( U_780 != singleton(U_778)
| ~ sP197(U_780,U_778) ),
inference(clausify,[status(thm)],[f_178_4]) ).
fof(f_179_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_179_2,plain,
! [U_782,U_781] :
( subset(U_782,union(U_781))
| ~ in(U_782,U_781) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_782,U_781] :
( subset(U_782,union(U_781))
| ~ in(U_782,U_781) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( subset(U_782,union(U_781))
| ~ in(U_782,U_781) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_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_180_2,plain,
! [U_786,U_785,U_784,U_783] :
( ( in(ordered_pair(U_786,U_785),cartesian_product2(U_784,U_783))
| ~ in(U_785,U_783)
| ~ in(U_786,U_784) )
& ( ( in(U_785,U_783)
& in(U_786,U_784) )
| ~ in(ordered_pair(U_786,U_785),cartesian_product2(U_784,U_783)) ) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( ! [U_794,U_792,U_790,U_788] :
( in(ordered_pair(U_794,U_792),cartesian_product2(U_790,U_788))
| ~ in(U_792,U_788)
| ~ in(U_794,U_790) )
& ! [U_793,U_791,U_789,U_787] :
( ( in(U_791,U_787)
& in(U_793,U_789) )
| ~ in(ordered_pair(U_793,U_791),cartesian_product2(U_789,U_787)) ) ),
inference(miniscope,[status(thm)],[f_180_2]) ).
fof(f_180_4,plain,
( ! [U_787,U_793,U_791,U_789] :
( in(U_791,U_787)
| ~ sP198(U_787,U_793,U_791,U_789) )
& ! [U_787,U_793,U_791,U_789] :
( in(U_793,U_789)
| ~ sP198(U_787,U_793,U_791,U_789) )
& ! [U_794,U_790,U_788,U_792] :
( in(ordered_pair(U_794,U_792),cartesian_product2(U_790,U_788))
| ~ in(U_792,U_788)
| ~ in(U_794,U_790) )
& ! [U_787,U_793,U_791,U_789] :
( sP198(U_787,U_793,U_791,U_789)
| ~ in(ordered_pair(U_793,U_791),cartesian_product2(U_789,U_787)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_180_3]) ).
cnf(f_180_5,plain,
( sP198(U_787,U_793,U_791,U_789)
| ~ in(ordered_pair(U_793,U_791),cartesian_product2(U_789,U_787)) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_6,plain,
( in(ordered_pair(U_794,U_792),cartesian_product2(U_790,U_788))
| ~ in(U_792,U_788)
| ~ in(U_794,U_790) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_7,plain,
( in(U_793,U_789)
| ~ sP198(U_787,U_793,U_791,U_789) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_8,plain,
( in(U_791,U_787)
| ~ sP198(U_787,U_793,U_791,U_789) ),
inference(clausify,[status(thm)],[f_180_4]) ).
fof(f_181_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_181_2,plain,
! [U_797,U_796] :
( element(U_797,powerset(U_796))
| ? [U_795] :
( ~ in(U_795,U_796)
& in(U_795,U_797) ) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_797,U_796] :
( element(U_797,powerset(U_796))
| ( ~ in(sK134(U_797,U_796),U_796)
& in(sK134(U_797,U_796),U_797) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_795,sK134(U_797,U_796))],[f_181_2]) ).
fof(f_181_4,plain,
( ! [U_797,U_796] :
( ~ in(sK134(U_797,U_796),U_796)
| ~ sP199(U_797,U_796) )
& ! [U_797,U_796] :
( in(sK134(U_797,U_796),U_797)
| ~ sP199(U_797,U_796) )
& ! [U_797,U_796] :
( element(U_797,powerset(U_796))
| sP199(U_797,U_796) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_181_3]) ).
cnf(f_181_5,plain,
( element(U_797,powerset(U_796))
| sP199(U_797,U_796) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_6,plain,
( in(sK134(U_797,U_796),U_797)
| ~ sP199(U_797,U_796) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_7,plain,
( ~ in(sK134(U_797,U_796),U_796)
| ~ sP199(U_797,U_796) ),
inference(clausify,[status(thm)],[f_181_4]) ).
fof(f_182_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_182_2,plain,
! [U_800,U_799,U_798] :
( ( ( in(U_799,relation_dom(relation_dom_restriction(U_798,U_800)))
| ~ in(U_799,U_800)
| ~ in(U_799,relation_dom(U_798)) )
& ( ( in(U_799,U_800)
& in(U_799,relation_dom(U_798)) )
| ~ in(U_799,relation_dom(relation_dom_restriction(U_798,U_800))) ) )
| ~ function(U_798)
| ~ relation(U_798) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( ! [U_798,U_799,U_800] :
( in(U_799,U_800)
| ~ sP200(U_798,U_799,U_800) )
& ! [U_798,U_799,U_800] :
( in(U_799,relation_dom(U_798))
| ~ sP200(U_798,U_799,U_800) )
& ! [U_798,U_799,U_800] :
( in(U_799,relation_dom(relation_dom_restriction(U_798,U_800)))
| ~ in(U_799,U_800)
| ~ in(U_799,relation_dom(U_798))
| ~ sP201(U_798,U_799,U_800) )
& ! [U_798,U_799,U_800] :
( sP200(U_798,U_799,U_800)
| ~ in(U_799,relation_dom(relation_dom_restriction(U_798,U_800)))
| ~ sP201(U_798,U_799,U_800) )
& ! [U_798,U_799,U_800] :
( sP201(U_798,U_799,U_800)
| ~ function(U_798)
| ~ relation(U_798) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200,sP201])],[f_182_2]) ).
cnf(f_182_4,plain,
( sP201(U_798,U_799,U_800)
| ~ function(U_798)
| ~ relation(U_798) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_5,plain,
( sP200(U_798,U_799,U_800)
| ~ in(U_799,relation_dom(relation_dom_restriction(U_798,U_800)))
| ~ sP201(U_798,U_799,U_800) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_6,plain,
( in(U_799,relation_dom(relation_dom_restriction(U_798,U_800)))
| ~ in(U_799,U_800)
| ~ in(U_799,relation_dom(U_798))
| ~ sP201(U_798,U_799,U_800) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_7,plain,
( in(U_799,relation_dom(U_798))
| ~ sP200(U_798,U_799,U_800) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_8,plain,
( in(U_799,U_800)
| ~ sP200(U_798,U_799,U_800) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_arytm_3]) ).
fof(f_183_2,plain,
? [U_801] :
( natural(U_801)
& ordinal(U_801)
& epsilon_connected(U_801)
& epsilon_transitive(U_801)
& ~ empty(U_801) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( natural(sK135)
& ordinal(sK135)
& epsilon_connected(sK135)
& epsilon_transitive(sK135)
& ~ empty(sK135) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_801,sK135)],[f_183_2]) ).
fof(f_183_4,plain,
( natural(sK135)
& ordinal(sK135)
& epsilon_connected(sK135)
& epsilon_transitive(sK135)
& ~ empty(sK135) ),
inference(definitional_conversion,[status(esa)],[f_183_3]) ).
cnf(f_183_5,plain,
~ empty(sK135),
inference(clausify,[status(thm)],[f_183_4]) ).
cnf(f_183_6,plain,
epsilon_transitive(sK135),
inference(clausify,[status(thm)],[f_183_4]) ).
cnf(f_183_7,plain,
epsilon_connected(sK135),
inference(clausify,[status(thm)],[f_183_4]) ).
cnf(f_183_8,plain,
ordinal(sK135),
inference(clausify,[status(thm)],[f_183_4]) ).
cnf(f_183_9,plain,
natural(sK135),
inference(clausify,[status(thm)],[f_183_4]) ).
fof(f_184_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_184_2,plain,
? [U_802] :
( finite(U_802)
& ~ empty(U_802) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
( finite(sK136)
& ~ empty(sK136) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_802,sK136)],[f_184_2]) ).
fof(f_184_4,plain,
( finite(sK136)
& ~ empty(sK136) ),
inference(definitional_conversion,[status(esa)],[f_184_3]) ).
cnf(f_184_5,plain,
~ empty(sK136),
inference(clausify,[status(thm)],[f_184_4]) ).
cnf(f_184_6,plain,
finite(sK136),
inference(clausify,[status(thm)],[f_184_4]) ).
fof(f_185_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_185_2,plain,
? [U_803] :
( function(U_803)
& relation(U_803) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( function(sK137)
& relation(sK137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_803,sK137)],[f_185_2]) ).
fof(f_185_4,plain,
( function(sK137)
& relation(sK137) ),
inference(definitional_conversion,[status(esa)],[f_185_3]) ).
cnf(f_185_5,plain,
relation(sK137),
inference(clausify,[status(thm)],[f_185_4]) ).
cnf(f_185_6,plain,
function(sK137),
inference(clausify,[status(thm)],[f_185_4]) ).
fof(f_186_1,plain,
! [A,B] :
? [C] :
( quasi_total(C,A,B)
& function(C)
& relation(C)
& relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc1_funct_2]) ).
fof(f_186_2,plain,
! [U_806,U_805] :
? [U_804] :
( quasi_total(U_804,U_806,U_805)
& function(U_804)
& relation(U_804)
& relation_of2(U_804,U_806,U_805) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_806,U_805] :
( quasi_total(sK138(U_806,U_805),U_806,U_805)
& function(sK138(U_806,U_805))
& relation(sK138(U_806,U_805))
& relation_of2(sK138(U_806,U_805),U_806,U_805) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_804,sK138(U_806,U_805))],[f_186_2]) ).
fof(f_186_4,plain,
( ! [U_806,U_805] : quasi_total(sK138(U_806,U_805),U_806,U_805)
& ! [U_806,U_805] : function(sK138(U_806,U_805))
& ! [U_806,U_805] : relation(sK138(U_806,U_805))
& ! [U_806,U_805] : relation_of2(sK138(U_806,U_805),U_806,U_805) ),
inference(definitional_conversion,[status(esa)],[f_186_3]) ).
cnf(f_186_5,plain,
relation_of2(sK138(U_806,U_805),U_806,U_805),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_6,plain,
relation(sK138(U_806,U_805)),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_7,plain,
function(sK138(U_806,U_805)),
inference(clausify,[status(thm)],[f_186_4]) ).
cnf(f_186_8,plain,
quasi_total(sK138(U_806,U_805),U_806,U_805),
inference(clausify,[status(thm)],[f_186_4]) ).
fof(f_187_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_187_2,plain,
? [U_807] :
( ordinal(U_807)
& epsilon_connected(U_807)
& epsilon_transitive(U_807) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
( ordinal(sK139)
& epsilon_connected(sK139)
& epsilon_transitive(sK139) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_807,sK139)],[f_187_2]) ).
fof(f_187_4,plain,
( ordinal(sK139)
& epsilon_connected(sK139)
& epsilon_transitive(sK139) ),
inference(definitional_conversion,[status(esa)],[f_187_3]) ).
cnf(f_187_5,plain,
epsilon_transitive(sK139),
inference(clausify,[status(thm)],[f_187_4]) ).
cnf(f_187_6,plain,
epsilon_connected(sK139),
inference(clausify,[status(thm)],[f_187_4]) ).
cnf(f_187_7,plain,
ordinal(sK139),
inference(clausify,[status(thm)],[f_187_4]) ).
fof(f_188_1,plain,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_partfun1]) ).
fof(f_188_2,plain,
? [U_808] :
( empty(U_808)
& one_to_one(U_808)
& function(U_808)
& relation(U_808) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
( empty(sK140)
& one_to_one(sK140)
& function(sK140)
& relation(sK140) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_808,sK140)],[f_188_2]) ).
fof(f_188_4,plain,
( empty(sK140)
& one_to_one(sK140)
& function(sK140)
& relation(sK140) ),
inference(definitional_conversion,[status(esa)],[f_188_3]) ).
cnf(f_188_5,plain,
relation(sK140),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_6,plain,
function(sK140),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_7,plain,
one_to_one(sK140),
inference(clausify,[status(thm)],[f_188_4]) ).
cnf(f_188_8,plain,
empty(sK140),
inference(clausify,[status(thm)],[f_188_4]) ).
fof(f_189_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_189_2,plain,
? [U_809] :
( relation(U_809)
& empty(U_809) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( relation(sK141)
& empty(sK141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_809,sK141)],[f_189_2]) ).
fof(f_189_4,plain,
( relation(sK141)
& empty(sK141) ),
inference(definitional_conversion,[status(esa)],[f_189_3]) ).
cnf(f_189_5,plain,
empty(sK141),
inference(clausify,[status(thm)],[f_189_4]) ).
cnf(f_189_6,plain,
relation(sK141),
inference(clausify,[status(thm)],[f_189_4]) ).
fof(f_190_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_190_2,plain,
! [U_811] :
( ? [U_810] :
( ~ empty(U_810)
& element(U_810,powerset(U_811)) )
| empty(U_811) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_811] :
( ( ~ empty(sK142(U_811))
& element(sK142(U_811),powerset(U_811)) )
| empty(U_811) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_810,sK142(U_811))],[f_190_2]) ).
fof(f_190_4,plain,
( ! [U_811] :
( ~ empty(sK142(U_811))
| ~ sP202(U_811) )
& ! [U_811] :
( element(sK142(U_811),powerset(U_811))
| ~ sP202(U_811) )
& ! [U_811] :
( sP202(U_811)
| empty(U_811) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_190_3]) ).
cnf(f_190_5,plain,
( sP202(U_811)
| empty(U_811) ),
inference(clausify,[status(thm)],[f_190_4]) ).
cnf(f_190_6,plain,
( element(sK142(U_811),powerset(U_811))
| ~ sP202(U_811) ),
inference(clausify,[status(thm)],[f_190_4]) ).
cnf(f_190_7,plain,
( ~ empty(sK142(U_811))
| ~ sP202(U_811) ),
inference(clausify,[status(thm)],[f_190_4]) ).
fof(f_191_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_191_2,plain,
? [U_812] : empty(U_812),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
empty(sK143),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_812,sK143)],[f_191_2]) ).
fof(f_191_4,plain,
empty(sK143),
inference(definitional_conversion,[status(esa)],[f_191_3]) ).
cnf(f_191_5,plain,
empty(sK143),
inference(clausify,[status(thm)],[f_191_4]) ).
fof(f_192_1,plain,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_finset_1]) ).
fof(f_192_2,plain,
! [U_814] :
? [U_813] :
( finite(U_813)
& natural(U_813)
& ordinal(U_813)
& epsilon_connected(U_813)
& epsilon_transitive(U_813)
& one_to_one(U_813)
& function(U_813)
& relation(U_813)
& empty(U_813)
& element(U_813,powerset(U_814)) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_814] :
( finite(sK144(U_814))
& natural(sK144(U_814))
& ordinal(sK144(U_814))
& epsilon_connected(sK144(U_814))
& epsilon_transitive(sK144(U_814))
& one_to_one(sK144(U_814))
& function(sK144(U_814))
& relation(sK144(U_814))
& empty(sK144(U_814))
& element(sK144(U_814),powerset(U_814)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_813,sK144(U_814))],[f_192_2]) ).
fof(f_192_4,plain,
( ! [U_814] : finite(sK144(U_814))
& ! [U_814] : natural(sK144(U_814))
& ! [U_814] : ordinal(sK144(U_814))
& ! [U_814] : epsilon_connected(sK144(U_814))
& ! [U_814] : epsilon_transitive(sK144(U_814))
& ! [U_814] : one_to_one(sK144(U_814))
& ! [U_814] : function(sK144(U_814))
& ! [U_814] : relation(sK144(U_814))
& ! [U_814] : empty(sK144(U_814))
& ! [U_814] : element(sK144(U_814),powerset(U_814)) ),
inference(definitional_conversion,[status(esa)],[f_192_3]) ).
cnf(f_192_5,plain,
element(sK144(U_814),powerset(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_6,plain,
empty(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_7,plain,
relation(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_8,plain,
function(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_9,plain,
one_to_one(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_10,plain,
epsilon_transitive(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_11,plain,
epsilon_connected(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_12,plain,
ordinal(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_13,plain,
natural(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
cnf(f_192_14,plain,
finite(sK144(U_814)),
inference(clausify,[status(thm)],[f_192_4]) ).
fof(f_193_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_193_2,plain,
? [U_815] :
( function(U_815)
& empty(U_815)
& relation(U_815) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
( function(sK145)
& empty(sK145)
& relation(sK145) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_815,sK145)],[f_193_2]) ).
fof(f_193_4,plain,
( function(sK145)
& empty(sK145)
& relation(sK145) ),
inference(definitional_conversion,[status(esa)],[f_193_3]) ).
cnf(f_193_5,plain,
relation(sK145),
inference(clausify,[status(thm)],[f_193_4]) ).
cnf(f_193_6,plain,
empty(sK145),
inference(clausify,[status(thm)],[f_193_4]) ).
cnf(f_193_7,plain,
function(sK145),
inference(clausify,[status(thm)],[f_193_4]) ).
fof(f_194_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_194_2,plain,
? [U_816] :
( ordinal(U_816)
& epsilon_connected(U_816)
& epsilon_transitive(U_816)
& empty(U_816)
& one_to_one(U_816)
& function(U_816)
& relation(U_816) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ordinal(sK146)
& epsilon_connected(sK146)
& epsilon_transitive(sK146)
& empty(sK146)
& one_to_one(sK146)
& function(sK146)
& relation(sK146) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_816,sK146)],[f_194_2]) ).
fof(f_194_4,plain,
( ordinal(sK146)
& epsilon_connected(sK146)
& epsilon_transitive(sK146)
& empty(sK146)
& one_to_one(sK146)
& function(sK146)
& relation(sK146) ),
inference(definitional_conversion,[status(esa)],[f_194_3]) ).
cnf(f_194_5,plain,
relation(sK146),
inference(clausify,[status(thm)],[f_194_4]) ).
cnf(f_194_6,plain,
function(sK146),
inference(clausify,[status(thm)],[f_194_4]) ).
cnf(f_194_7,plain,
one_to_one(sK146),
inference(clausify,[status(thm)],[f_194_4]) ).
cnf(f_194_8,plain,
empty(sK146),
inference(clausify,[status(thm)],[f_194_4]) ).
cnf(f_194_9,plain,
epsilon_transitive(sK146),
inference(clausify,[status(thm)],[f_194_4]) ).
cnf(f_194_10,plain,
epsilon_connected(sK146),
inference(clausify,[status(thm)],[f_194_4]) ).
cnf(f_194_11,plain,
ordinal(sK146),
inference(clausify,[status(thm)],[f_194_4]) ).
fof(f_195_1,plain,
! [A,B] :
? [C] :
( function(C)
& relation(C)
& relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc2_partfun1]) ).
fof(f_195_2,plain,
! [U_819,U_818] :
? [U_817] :
( function(U_817)
& relation(U_817)
& relation_of2(U_817,U_819,U_818) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_819,U_818] :
( function(sK147(U_819,U_818))
& relation(sK147(U_819,U_818))
& relation_of2(sK147(U_819,U_818),U_819,U_818) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_817,sK147(U_819,U_818))],[f_195_2]) ).
fof(f_195_4,plain,
( ! [U_819,U_818] : function(sK147(U_819,U_818))
& ! [U_819,U_818] : relation(sK147(U_819,U_818))
& ! [U_819,U_818] : relation_of2(sK147(U_819,U_818),U_819,U_818) ),
inference(definitional_conversion,[status(esa)],[f_195_3]) ).
cnf(f_195_5,plain,
relation_of2(sK147(U_819,U_818),U_819,U_818),
inference(clausify,[status(thm)],[f_195_4]) ).
cnf(f_195_6,plain,
relation(sK147(U_819,U_818)),
inference(clausify,[status(thm)],[f_195_4]) ).
cnf(f_195_7,plain,
function(sK147(U_819,U_818)),
inference(clausify,[status(thm)],[f_195_4]) ).
fof(f_196_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_196_2,plain,
? [U_820] :
( relation(U_820)
& ~ empty(U_820) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( relation(sK148)
& ~ empty(sK148) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_820,sK148)],[f_196_2]) ).
fof(f_196_4,plain,
( relation(sK148)
& ~ empty(sK148) ),
inference(definitional_conversion,[status(esa)],[f_196_3]) ).
cnf(f_196_5,plain,
~ empty(sK148),
inference(clausify,[status(thm)],[f_196_4]) ).
cnf(f_196_6,plain,
relation(sK148),
inference(clausify,[status(thm)],[f_196_4]) ).
fof(f_197_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_197_2,plain,
! [U_822] :
? [U_821] :
( empty(U_821)
& element(U_821,powerset(U_822)) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_822] :
( empty(sK149(U_822))
& element(sK149(U_822),powerset(U_822)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_821,sK149(U_822))],[f_197_2]) ).
fof(f_197_4,plain,
( ! [U_822] : empty(sK149(U_822))
& ! [U_822] : element(sK149(U_822),powerset(U_822)) ),
inference(definitional_conversion,[status(esa)],[f_197_3]) ).
cnf(f_197_5,plain,
element(sK149(U_822),powerset(U_822)),
inference(clausify,[status(thm)],[f_197_4]) ).
cnf(f_197_6,plain,
empty(sK149(U_822)),
inference(clausify,[status(thm)],[f_197_4]) ).
fof(f_198_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_198_2,plain,
? [U_823] : ~ empty(U_823),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
~ empty(sK150),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_823,sK150)],[f_198_2]) ).
fof(f_198_4,plain,
~ empty(sK150),
inference(definitional_conversion,[status(esa)],[f_198_3]) ).
cnf(f_198_5,plain,
~ empty(sK150),
inference(clausify,[status(thm)],[f_198_4]) ).
fof(f_199_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_199_2,plain,
! [U_825] :
( ? [U_824] :
( finite(U_824)
& ~ empty(U_824)
& element(U_824,powerset(U_825)) )
| empty(U_825) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_825] :
( ( finite(sK151(U_825))
& ~ empty(sK151(U_825))
& element(sK151(U_825),powerset(U_825)) )
| empty(U_825) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_824,sK151(U_825))],[f_199_2]) ).
fof(f_199_4,plain,
( ! [U_825] :
( finite(sK151(U_825))
| ~ sP203(U_825) )
& ! [U_825] :
( ~ empty(sK151(U_825))
| ~ sP203(U_825) )
& ! [U_825] :
( element(sK151(U_825),powerset(U_825))
| ~ sP203(U_825) )
& ! [U_825] :
( sP203(U_825)
| empty(U_825) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_199_3]) ).
cnf(f_199_5,plain,
( sP203(U_825)
| empty(U_825) ),
inference(clausify,[status(thm)],[f_199_4]) ).
cnf(f_199_6,plain,
( element(sK151(U_825),powerset(U_825))
| ~ sP203(U_825) ),
inference(clausify,[status(thm)],[f_199_4]) ).
cnf(f_199_7,plain,
( ~ empty(sK151(U_825))
| ~ sP203(U_825) ),
inference(clausify,[status(thm)],[f_199_4]) ).
cnf(f_199_8,plain,
( finite(sK151(U_825))
| ~ sP203(U_825) ),
inference(clausify,[status(thm)],[f_199_4]) ).
fof(f_200_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_200_2,plain,
? [U_826] :
( one_to_one(U_826)
& function(U_826)
& relation(U_826) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
( one_to_one(sK152)
& function(sK152)
& relation(sK152) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_826,sK152)],[f_200_2]) ).
fof(f_200_4,plain,
( one_to_one(sK152)
& function(sK152)
& relation(sK152) ),
inference(definitional_conversion,[status(esa)],[f_200_3]) ).
cnf(f_200_5,plain,
relation(sK152),
inference(clausify,[status(thm)],[f_200_4]) ).
cnf(f_200_6,plain,
function(sK152),
inference(clausify,[status(thm)],[f_200_4]) ).
cnf(f_200_7,plain,
one_to_one(sK152),
inference(clausify,[status(thm)],[f_200_4]) ).
fof(f_201_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_201_2,plain,
? [U_827] :
( ordinal(U_827)
& epsilon_connected(U_827)
& epsilon_transitive(U_827)
& ~ empty(U_827) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
( ordinal(sK153)
& epsilon_connected(sK153)
& epsilon_transitive(sK153)
& ~ empty(sK153) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_827,sK153)],[f_201_2]) ).
fof(f_201_4,plain,
( ordinal(sK153)
& epsilon_connected(sK153)
& epsilon_transitive(sK153)
& ~ empty(sK153) ),
inference(definitional_conversion,[status(esa)],[f_201_3]) ).
cnf(f_201_5,plain,
~ empty(sK153),
inference(clausify,[status(thm)],[f_201_4]) ).
cnf(f_201_6,plain,
epsilon_transitive(sK153),
inference(clausify,[status(thm)],[f_201_4]) ).
cnf(f_201_7,plain,
epsilon_connected(sK153),
inference(clausify,[status(thm)],[f_201_4]) ).
cnf(f_201_8,plain,
ordinal(sK153),
inference(clausify,[status(thm)],[f_201_4]) ).
fof(f_202_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_202_2,plain,
? [U_828] :
( relation_empty_yielding(U_828)
& relation(U_828) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
( relation_empty_yielding(sK154)
& relation(sK154) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_828,sK154)],[f_202_2]) ).
fof(f_202_4,plain,
( relation_empty_yielding(sK154)
& relation(sK154) ),
inference(definitional_conversion,[status(esa)],[f_202_3]) ).
cnf(f_202_5,plain,
relation(sK154),
inference(clausify,[status(thm)],[f_202_4]) ).
cnf(f_202_6,plain,
relation_empty_yielding(sK154),
inference(clausify,[status(thm)],[f_202_4]) ).
fof(f_203_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_203_2,plain,
? [U_829] :
( function(U_829)
& relation_empty_yielding(U_829)
& relation(U_829) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
( function(sK155)
& relation_empty_yielding(sK155)
& relation(sK155) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_829,sK155)],[f_203_2]) ).
fof(f_203_4,plain,
( function(sK155)
& relation_empty_yielding(sK155)
& relation(sK155) ),
inference(definitional_conversion,[status(esa)],[f_203_3]) ).
cnf(f_203_5,plain,
relation(sK155),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_6,plain,
relation_empty_yielding(sK155),
inference(clausify,[status(thm)],[f_203_4]) ).
cnf(f_203_7,plain,
function(sK155),
inference(clausify,[status(thm)],[f_203_4]) ).
fof(f_204_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_204_2,plain,
! [U_832,U_831,U_830] :
( relation_dom_as_subset(U_832,U_831,U_830) = relation_dom(U_830)
| ~ relation_of2(U_830,U_832,U_831) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_830,U_831,U_832] :
( relation_dom_as_subset(U_832,U_831,U_830) = relation_dom(U_830)
| ~ relation_of2(U_830,U_832,U_831) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( relation_dom_as_subset(U_832,U_831,U_830) = relation_dom(U_830)
| ~ relation_of2(U_830,U_832,U_831) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_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_205_2,plain,
! [U_835,U_834,U_833] :
( relation_rng_as_subset(U_835,U_834,U_833) = relation_rng(U_833)
| ~ relation_of2(U_833,U_835,U_834) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_833,U_834,U_835] :
( relation_rng_as_subset(U_835,U_834,U_833) = relation_rng(U_833)
| ~ relation_of2(U_833,U_835,U_834) ),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
( relation_rng_as_subset(U_835,U_834,U_833) = relation_rng(U_833)
| ~ relation_of2(U_833,U_835,U_834) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_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_206_2,plain,
! [U_837,U_836] :
( union_of_subsets(U_837,U_836) = union(U_836)
| ~ element(U_836,powerset(powerset(U_837))) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_836,U_837] :
( union_of_subsets(U_837,U_836) = union(U_836)
| ~ element(U_836,powerset(powerset(U_837))) ),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
( union_of_subsets(U_837,U_836) = union(U_836)
| ~ element(U_836,powerset(powerset(U_837))) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_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_207_2,plain,
! [U_839,U_838] :
( meet_of_subsets(U_839,U_838) = set_meet(U_838)
| ~ element(U_838,powerset(powerset(U_839))) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_838,U_839] :
( meet_of_subsets(U_839,U_838) = set_meet(U_838)
| ~ element(U_838,powerset(powerset(U_839))) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( meet_of_subsets(U_839,U_838) = set_meet(U_838)
| ~ element(U_838,powerset(powerset(U_839))) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_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_208_2,plain,
! [U_842,U_841,U_840] :
( subset_difference(U_842,U_841,U_840) = set_difference(U_841,U_840)
| ~ element(U_840,powerset(U_842))
| ~ element(U_841,powerset(U_842)) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_840,U_841,U_842] :
( subset_difference(U_842,U_841,U_840) = set_difference(U_841,U_840)
| ~ element(U_840,powerset(U_842))
| ~ element(U_841,powerset(U_842)) ),
inference(definitional_conversion,[status(esa)],[f_208_2]) ).
cnf(f_208_4,plain,
( subset_difference(U_842,U_841,U_840) = set_difference(U_841,U_840)
| ~ element(U_840,powerset(U_842))
| ~ element(U_841,powerset(U_842)) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_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_209_2,plain,
! [U_845,U_844,U_843] :
( ( relation_of2_as_subset(U_843,U_845,U_844)
| ~ relation_of2(U_843,U_845,U_844) )
& ( relation_of2(U_843,U_845,U_844)
| ~ relation_of2_as_subset(U_843,U_845,U_844) ) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
( ! [U_851,U_849,U_847] :
( relation_of2_as_subset(U_847,U_851,U_849)
| ~ relation_of2(U_847,U_851,U_849) )
& ! [U_850,U_848,U_846] :
( relation_of2(U_846,U_850,U_848)
| ~ relation_of2_as_subset(U_846,U_850,U_848) ) ),
inference(miniscope,[status(thm)],[f_209_2]) ).
fof(f_209_4,plain,
( ! [U_851,U_849,U_847] :
( relation_of2_as_subset(U_847,U_851,U_849)
| ~ relation_of2(U_847,U_851,U_849) )
& ! [U_850,U_846,U_848] :
( relation_of2(U_846,U_850,U_848)
| ~ relation_of2_as_subset(U_846,U_850,U_848) ) ),
inference(definitional_conversion,[status(esa)],[f_209_3]) ).
cnf(f_209_5,plain,
( relation_of2(U_846,U_850,U_848)
| ~ relation_of2_as_subset(U_846,U_850,U_848) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_6,plain,
( relation_of2_as_subset(U_847,U_851,U_849)
| ~ relation_of2(U_847,U_851,U_849) ),
inference(clausify,[status(thm)],[f_209_4]) ).
fof(f_210_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_210_2,plain,
! [U_853,U_852] :
( ( ( ordinal_subset(U_853,U_852)
| ~ subset(U_853,U_852) )
& ( subset(U_853,U_852)
| ~ ordinal_subset(U_853,U_852) ) )
| ~ ordinal(U_852)
| ~ ordinal(U_853) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
( ! [U_852,U_853] :
( ordinal_subset(U_853,U_852)
| ~ subset(U_853,U_852)
| ~ sP204(U_852,U_853) )
& ! [U_852,U_853] :
( subset(U_853,U_852)
| ~ ordinal_subset(U_853,U_852)
| ~ sP204(U_852,U_853) )
& ! [U_852,U_853] :
( sP204(U_852,U_853)
| ~ ordinal(U_852)
| ~ ordinal(U_853) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_210_2]) ).
cnf(f_210_4,plain,
( sP204(U_852,U_853)
| ~ ordinal(U_852)
| ~ ordinal(U_853) ),
inference(clausify,[status(thm)],[f_210_3]) ).
cnf(f_210_5,plain,
( subset(U_853,U_852)
| ~ ordinal_subset(U_853,U_852)
| ~ sP204(U_852,U_853) ),
inference(clausify,[status(thm)],[f_210_3]) ).
cnf(f_210_6,plain,
( ordinal_subset(U_853,U_852)
| ~ subset(U_853,U_852)
| ~ sP204(U_852,U_853) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [A,B] :
( ( equipotent(A,B)
| ~ are_equipotent(A,B) )
& ( are_equipotent(A,B)
| ~ equipotent(A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_r2_wellord2]) ).
fof(f_211_2,plain,
! [U_855,U_854] :
( ( equipotent(U_855,U_854)
| ~ are_equipotent(U_855,U_854) )
& ( are_equipotent(U_855,U_854)
| ~ equipotent(U_855,U_854) ) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
( ! [U_859,U_857] :
( equipotent(U_859,U_857)
| ~ are_equipotent(U_859,U_857) )
& ! [U_858,U_856] :
( are_equipotent(U_858,U_856)
| ~ equipotent(U_858,U_856) ) ),
inference(miniscope,[status(thm)],[f_211_2]) ).
fof(f_211_4,plain,
( ! [U_859,U_857] :
( equipotent(U_859,U_857)
| ~ are_equipotent(U_859,U_857) )
& ! [U_856,U_858] :
( are_equipotent(U_858,U_856)
| ~ equipotent(U_858,U_856) ) ),
inference(definitional_conversion,[status(esa)],[f_211_3]) ).
cnf(f_211_5,plain,
( are_equipotent(U_858,U_856)
| ~ equipotent(U_858,U_856) ),
inference(clausify,[status(thm)],[f_211_4]) ).
cnf(f_211_6,plain,
( equipotent(U_859,U_857)
| ~ are_equipotent(U_859,U_857) ),
inference(clausify,[status(thm)],[f_211_4]) ).
fof(f_212_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_212_2,plain,
! [U_861,U_860] :
( ordinal_subset(U_861,U_861)
| ~ ordinal(U_860)
| ~ ordinal(U_861) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_861] :
( ! [U_860] : ~ ordinal(U_860)
| ~ ordinal(U_861)
| ordinal_subset(U_861,U_861) ),
inference(miniscope,[status(thm)],[f_212_2]) ).
fof(f_212_4,plain,
! [U_860,U_861] :
( ~ ordinal(U_860)
| ~ ordinal(U_861)
| ordinal_subset(U_861,U_861) ),
inference(definitional_conversion,[status(esa)],[f_212_3]) ).
cnf(f_212_5,plain,
( ~ ordinal(U_860)
| ~ ordinal(U_861)
| ordinal_subset(U_861,U_861) ),
inference(clausify,[status(thm)],[f_212_4]) ).
fof(f_213_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_213_2,plain,
! [U_863,U_862] : subset(U_863,U_863),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_863] : subset(U_863,U_863),
inference(miniscope,[status(thm)],[f_213_2]) ).
fof(f_213_4,plain,
! [U_863] : subset(U_863,U_863),
inference(definitional_conversion,[status(esa)],[f_213_3]) ).
cnf(f_213_5,plain,
subset(U_863,U_863),
inference(clausify,[status(thm)],[f_213_4]) ).
fof(f_214_1,plain,
! [A,B] : equipotent(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r2_wellord2]) ).
fof(f_214_2,plain,
! [U_865,U_864] : equipotent(U_865,U_865),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_865] : equipotent(U_865,U_865),
inference(miniscope,[status(thm)],[f_214_2]) ).
fof(f_214_4,plain,
! [U_865] : equipotent(U_865,U_865),
inference(definitional_conversion,[status(esa)],[f_214_3]) ).
cnf(f_214_5,plain,
equipotent(U_865,U_865),
inference(clausify,[status(thm)],[f_214_4]) ).
fof(f_215_1,plain,
! [A,B] :
( ? [C] :
( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ! [J] :
( ? [K] :
( ~ in(ordered_pair(E,K),B)
& in(K,J) )
| ~ in(E,J)
| D != J )
| ~ in(D,A)
| ~ in(D,A) )
& ( ( ? [J] :
( ! [K] :
( in(ordered_pair(E,K),B)
| ~ in(K,J) )
& in(E,J)
& D = J )
& in(D,A)
& in(D,A) )
| ~ in(ordered_pair(D,E),C) ) )
& function(C)
& relation(C) )
| ? [C,D,E] :
( D != E
& ? [H] :
( ! [I] :
( in(ordered_pair(E,I),B)
| ~ in(I,H) )
& in(E,H)
& C = H )
& in(C,A)
& ? [F] :
( ! [G] :
( in(ordered_pair(D,G),B)
| ~ in(G,F) )
& in(D,F)
& C = F )
& in(C,A) )
| ~ relation(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[s1_funct_1__e10_24__wellord2__1]) ).
fof(f_215_2,plain,
! [U_881,U_880] :
( ? [U_879] :
( ! [U_878,U_877] :
( ( in(ordered_pair(U_878,U_877),U_879)
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_877,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_877,U_876)
| U_878 != U_876 )
| ~ in(U_878,U_881)
| ~ in(U_878,U_881) )
& ( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_877,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_877,U_874)
& U_878 = U_874 )
& in(U_878,U_881)
& in(U_878,U_881) )
| ~ in(ordered_pair(U_878,U_877),U_879) ) )
& function(U_879)
& relation(U_879) )
| ? [U_872,U_871,U_870] :
( U_871 != U_870
& ? [U_869] :
( ! [U_868] :
( in(ordered_pair(U_870,U_868),U_880)
| ~ in(U_868,U_869) )
& in(U_870,U_869)
& U_872 = U_869 )
& in(U_872,U_881)
& ? [U_867] :
( ! [U_866] :
( in(ordered_pair(U_871,U_866),U_880)
| ~ in(U_866,U_867) )
& in(U_871,U_867)
& U_872 = U_867 )
& in(U_872,U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_881,U_880] :
( ? [U_879] :
( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),U_879)
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_882,U_874)
& U_884 = U_874 )
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),U_879) )
& function(U_879)
& relation(U_879) )
| ? [U_872,U_871,U_870] :
( U_871 != U_870
& ? [U_869] :
( ! [U_868] :
( in(ordered_pair(U_870,U_868),U_880)
| ~ in(U_868,U_869) )
& in(U_870,U_869)
& U_872 = U_869 )
& in(U_872,U_881)
& ? [U_867] :
( ! [U_866] :
( in(ordered_pair(U_871,U_866),U_880)
| ~ in(U_866,U_867) )
& in(U_871,U_867)
& U_872 = U_867 )
& in(U_872,U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(miniscope,[status(thm)],[f_215_2]) ).
fof(f_215_4,plain,
! [U_881,U_880] :
( ? [U_879] :
( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),U_879)
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_882,U_874)
& U_884 = U_874 )
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),U_879) )
& function(U_879)
& relation(U_879) )
| ? [U_871,U_870] :
( U_871 != U_870
& ? [U_869] :
( ! [U_868] :
( in(ordered_pair(U_870,U_868),U_880)
| ~ in(U_868,U_869) )
& in(U_870,U_869)
& sK156(U_881,U_880) = U_869 )
& in(sK156(U_881,U_880),U_881)
& ? [U_867] :
( ! [U_866] :
( in(ordered_pair(U_871,U_866),U_880)
| ~ in(U_866,U_867) )
& in(U_871,U_867)
& sK156(U_881,U_880) = U_867 )
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_872,sK156(U_881,U_880))],[f_215_3]) ).
fof(f_215_5,plain,
! [U_881,U_880] :
( ? [U_879] :
( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),U_879)
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_882,U_874)
& U_884 = U_874 )
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),U_879) )
& function(U_879)
& relation(U_879) )
| ? [U_870] :
( sK157(U_881,U_880) != U_870
& ? [U_869] :
( ! [U_868] :
( in(ordered_pair(U_870,U_868),U_880)
| ~ in(U_868,U_869) )
& in(U_870,U_869)
& sK156(U_881,U_880) = U_869 )
& in(sK156(U_881,U_880),U_881)
& ? [U_867] :
( ! [U_866] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,U_867) )
& in(sK157(U_881,U_880),U_867)
& sK156(U_881,U_880) = U_867 )
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_871,sK157(U_881,U_880))],[f_215_4]) ).
fof(f_215_6,plain,
! [U_881,U_880] :
( ? [U_879] :
( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),U_879)
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_882,U_874)
& U_884 = U_874 )
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),U_879) )
& function(U_879)
& relation(U_879) )
| ( sK157(U_881,U_880) != sK158(U_881,U_880)
& ? [U_869] :
( ! [U_868] :
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,U_869) )
& in(sK158(U_881,U_880),U_869)
& sK156(U_881,U_880) = U_869 )
& in(sK156(U_881,U_880),U_881)
& ? [U_867] :
( ! [U_866] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,U_867) )
& in(sK157(U_881,U_880),U_867)
& sK156(U_881,U_880) = U_867 )
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_870,sK158(U_881,U_880))],[f_215_5]) ).
fof(f_215_7,plain,
! [U_881,U_880] :
( ? [U_879] :
( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),U_879)
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_882,U_874)
& U_884 = U_874 )
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),U_879) )
& function(U_879)
& relation(U_879) )
| ( sK157(U_881,U_880) != sK158(U_881,U_880)
& ? [U_869] :
( ! [U_868] :
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,U_869) )
& in(sK158(U_881,U_880),U_869)
& sK156(U_881,U_880) = U_869 )
& in(sK156(U_881,U_880),U_881)
& ! [U_866] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,sK159(U_881,U_880)) )
& in(sK157(U_881,U_880),sK159(U_881,U_880))
& sK156(U_881,U_880) = sK159(U_881,U_880)
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_867,sK159(U_881,U_880))],[f_215_6]) ).
fof(f_215_8,plain,
! [U_881,U_880] :
( ? [U_879] :
( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),U_879)
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_882,U_874)
& U_884 = U_874 )
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),U_879) )
& function(U_879)
& relation(U_879) )
| ( sK157(U_881,U_880) != sK158(U_881,U_880)
& ! [U_868] :
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,sK160(U_881,U_880)) )
& in(sK158(U_881,U_880),sK160(U_881,U_880))
& sK156(U_881,U_880) = sK160(U_881,U_880)
& in(sK156(U_881,U_880),U_881)
& ! [U_866] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,sK159(U_881,U_880)) )
& in(sK157(U_881,U_880),sK159(U_881,U_880))
& sK156(U_881,U_880) = sK159(U_881,U_880)
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_869,sK160(U_881,U_880))],[f_215_7]) ).
fof(f_215_9,plain,
! [U_881,U_880] :
( ( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),sK161(U_881,U_880))
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ? [U_874] :
( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,U_874) )
& in(U_882,U_874)
& U_884 = U_874 )
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),sK161(U_881,U_880)) )
& function(sK161(U_881,U_880))
& relation(sK161(U_881,U_880)) )
| ( sK157(U_881,U_880) != sK158(U_881,U_880)
& ! [U_868] :
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,sK160(U_881,U_880)) )
& in(sK158(U_881,U_880),sK160(U_881,U_880))
& sK156(U_881,U_880) = sK160(U_881,U_880)
& in(sK156(U_881,U_880),U_881)
& ! [U_866] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,sK159(U_881,U_880)) )
& in(sK157(U_881,U_880),sK159(U_881,U_880))
& sK156(U_881,U_880) = sK159(U_881,U_880)
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_879,sK161(U_881,U_880))],[f_215_8]) ).
fof(f_215_10,plain,
! [U_881,U_880] :
( ( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),sK161(U_881,U_880))
| ! [U_876] :
( ? [U_875] :
( ~ in(ordered_pair(U_883,U_875),U_880)
& in(U_875,U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,sK162(U_881,U_880,U_884,U_882)) )
& in(U_882,sK162(U_881,U_880,U_884,U_882))
& U_884 = sK162(U_881,U_880,U_884,U_882)
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),sK161(U_881,U_880)) )
& function(sK161(U_881,U_880))
& relation(sK161(U_881,U_880)) )
| ( sK157(U_881,U_880) != sK158(U_881,U_880)
& ! [U_868] :
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,sK160(U_881,U_880)) )
& in(sK158(U_881,U_880),sK160(U_881,U_880))
& sK156(U_881,U_880) = sK160(U_881,U_880)
& in(sK156(U_881,U_880),U_881)
& ! [U_866] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,sK159(U_881,U_880)) )
& in(sK157(U_881,U_880),sK159(U_881,U_880))
& sK156(U_881,U_880) = sK159(U_881,U_880)
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_874,sK162(U_881,U_880,U_884,U_882))],[f_215_9]) ).
fof(f_215_11,plain,
! [U_881,U_880] :
( ( ! [U_885,U_883] :
( in(ordered_pair(U_885,U_883),sK161(U_881,U_880))
| ! [U_876] :
( ( ~ in(ordered_pair(U_883,sK163(U_881,U_880,U_885,U_883,U_876)),U_880)
& in(sK163(U_881,U_880,U_885,U_883,U_876),U_876) )
| ~ in(U_883,U_876)
| U_885 != U_876 )
| ~ in(U_885,U_881)
| ~ in(U_885,U_881) )
& ! [U_884,U_882] :
( ( ! [U_873] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,sK162(U_881,U_880,U_884,U_882)) )
& in(U_882,sK162(U_881,U_880,U_884,U_882))
& U_884 = sK162(U_881,U_880,U_884,U_882)
& in(U_884,U_881)
& in(U_884,U_881) )
| ~ in(ordered_pair(U_884,U_882),sK161(U_881,U_880)) )
& function(sK161(U_881,U_880))
& relation(sK161(U_881,U_880)) )
| ( sK157(U_881,U_880) != sK158(U_881,U_880)
& ! [U_868] :
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,sK160(U_881,U_880)) )
& in(sK158(U_881,U_880),sK160(U_881,U_880))
& sK156(U_881,U_880) = sK160(U_881,U_880)
& in(sK156(U_881,U_880),U_881)
& ! [U_866] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,sK159(U_881,U_880)) )
& in(sK157(U_881,U_880),sK159(U_881,U_880))
& sK156(U_881,U_880) = sK159(U_881,U_880)
& in(sK156(U_881,U_880),U_881) )
| ~ relation(U_880)
| empty(U_881) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_875,sK163(U_881,U_880,U_885,U_883,U_876))],[f_215_10]) ).
fof(f_215_12,plain,
( ! [U_876,U_880,U_881,U_885,U_883] :
( ~ in(ordered_pair(U_883,sK163(U_881,U_880,U_885,U_883,U_876)),U_880)
| ~ sP207(U_876,U_880,U_881,U_885,U_883) )
& ! [U_876,U_880,U_881,U_885,U_883] :
( in(sK163(U_881,U_880,U_885,U_883,U_876),U_876)
| ~ sP207(U_876,U_880,U_881,U_885,U_883) )
& ! [U_884,U_873,U_880,U_881,U_882] :
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,sK162(U_881,U_880,U_884,U_882))
| ~ sP206(U_884,U_873,U_880,U_881,U_882) )
& ! [U_884,U_873,U_880,U_881,U_882] :
( in(U_882,sK162(U_881,U_880,U_884,U_882))
| ~ sP206(U_884,U_873,U_880,U_881,U_882) )
& ! [U_884,U_873,U_880,U_881,U_882] :
( U_884 = sK162(U_881,U_880,U_884,U_882)
| ~ sP206(U_884,U_873,U_880,U_881,U_882) )
& ! [U_884,U_873,U_880,U_881,U_882] :
( in(U_884,U_881)
| ~ sP206(U_884,U_873,U_880,U_881,U_882) )
& ! [U_884,U_873,U_880,U_881,U_882] :
( in(U_884,U_881)
| ~ sP206(U_884,U_873,U_880,U_881,U_882) )
& ! [U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883] :
( in(ordered_pair(U_885,U_883),sK161(U_881,U_880))
| sP207(U_876,U_880,U_881,U_885,U_883)
| ~ in(U_883,U_876)
| U_885 != U_876
| ~ in(U_885,U_881)
| ~ in(U_885,U_881)
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) )
& ! [U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883] :
( sP206(U_884,U_873,U_880,U_881,U_882)
| ~ in(ordered_pair(U_884,U_882),sK161(U_881,U_880))
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) )
& ! [U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883] :
( function(sK161(U_881,U_880))
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) )
& ! [U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883] :
( relation(sK161(U_881,U_880))
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) )
& ! [U_866,U_868,U_880,U_881] :
( sK157(U_881,U_880) != sK158(U_881,U_880)
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,sK160(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( in(sK158(U_881,U_880),sK160(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( sK156(U_881,U_880) = sK160(U_881,U_880)
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( in(sK156(U_881,U_880),U_881)
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,sK159(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( in(sK157(U_881,U_880),sK159(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( sK156(U_881,U_880) = sK159(U_881,U_880)
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_868,U_880,U_881] :
( in(sK156(U_881,U_880),U_881)
| ~ sP205(U_866,U_868,U_880,U_881) )
& ! [U_866,U_884,U_868,U_873,U_876,U_880,U_881,U_882,U_885,U_883] :
( sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883)
| sP205(U_866,U_868,U_880,U_881)
| ~ relation(U_880)
| empty(U_881) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205,sP206,sP207,sP208])],[f_215_11]) ).
cnf(f_215_13,plain,
( sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883)
| sP205(U_866,U_868,U_880,U_881)
| ~ relation(U_880)
| empty(U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_14,plain,
( in(sK156(U_881,U_880),U_881)
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_15,plain,
( sK156(U_881,U_880) = sK159(U_881,U_880)
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_16,plain,
( in(sK157(U_881,U_880),sK159(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_17,plain,
( in(ordered_pair(sK157(U_881,U_880),U_866),U_880)
| ~ in(U_866,sK159(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_18,plain,
( in(sK156(U_881,U_880),U_881)
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_19,plain,
( sK156(U_881,U_880) = sK160(U_881,U_880)
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_20,plain,
( in(sK158(U_881,U_880),sK160(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_21,plain,
( in(ordered_pair(sK158(U_881,U_880),U_868),U_880)
| ~ in(U_868,sK160(U_881,U_880))
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_22,plain,
( sK157(U_881,U_880) != sK158(U_881,U_880)
| ~ sP205(U_866,U_868,U_880,U_881) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_23,plain,
( relation(sK161(U_881,U_880))
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_24,plain,
( function(sK161(U_881,U_880))
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_25,plain,
( sP206(U_884,U_873,U_880,U_881,U_882)
| ~ in(ordered_pair(U_884,U_882),sK161(U_881,U_880))
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_26,plain,
( in(ordered_pair(U_885,U_883),sK161(U_881,U_880))
| sP207(U_876,U_880,U_881,U_885,U_883)
| ~ in(U_883,U_876)
| U_885 != U_876
| ~ in(U_885,U_881)
| ~ in(U_885,U_881)
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_27,plain,
( in(U_884,U_881)
| ~ sP206(U_884,U_873,U_880,U_881,U_882) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_28,plain,
( in(U_884,U_881)
| ~ sP206(U_884,U_873,U_880,U_881,U_882) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_29,plain,
( U_884 = sK162(U_881,U_880,U_884,U_882)
| ~ sP206(U_884,U_873,U_880,U_881,U_882) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_30,plain,
( in(U_882,sK162(U_881,U_880,U_884,U_882))
| ~ sP206(U_884,U_873,U_880,U_881,U_882) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_31,plain,
( in(ordered_pair(U_882,U_873),U_880)
| ~ in(U_873,sK162(U_881,U_880,U_884,U_882))
| ~ sP206(U_884,U_873,U_880,U_881,U_882) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_32,plain,
( in(sK163(U_881,U_880,U_885,U_883,U_876),U_876)
| ~ sP207(U_876,U_880,U_881,U_885,U_883) ),
inference(clausify,[status(thm)],[f_215_12]) ).
cnf(f_215_33,plain,
( ~ in(ordered_pair(U_883,sK163(U_881,U_880,U_885,U_883,U_876)),U_880)
| ~ sP207(U_876,U_880,U_881,U_885,U_883) ),
inference(clausify,[status(thm)],[f_215_12]) ).
fof(f_216_1,plain,
! [A] :
( ? [B] :
( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| D != singleton(C)
| ~ in(C,A)
| ~ in(C,A) )
& ( ( D = singleton(C)
& in(C,A)
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
& function(B)
& relation(B) )
| ? [B,C,D] :
( C != D
& D = singleton(B)
& in(B,A)
& C = singleton(B)
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[s1_funct_1__e16_22__wellord2__1]) ).
fof(f_216_2,plain,
! [U_892] :
( ? [U_891] :
( ! [U_890,U_889] :
( ( in(ordered_pair(U_890,U_889),U_891)
| U_889 != singleton(U_890)
| ~ in(U_890,U_892)
| ~ in(U_890,U_892) )
& ( ( U_889 = singleton(U_890)
& in(U_890,U_892)
& in(U_890,U_892) )
| ~ in(ordered_pair(U_890,U_889),U_891) ) )
& function(U_891)
& relation(U_891) )
| ? [U_888,U_887,U_886] :
( U_887 != U_886
& U_886 = singleton(U_888)
& in(U_888,U_892)
& U_887 = singleton(U_888)
& in(U_888,U_892) ) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_892] :
( ? [U_891] :
( ! [U_896,U_894] :
( in(ordered_pair(U_896,U_894),U_891)
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ in(U_896,U_892) )
& ! [U_895,U_893] :
( ( U_893 = singleton(U_895)
& in(U_895,U_892)
& in(U_895,U_892) )
| ~ in(ordered_pair(U_895,U_893),U_891) )
& function(U_891)
& relation(U_891) )
| ? [U_888,U_887,U_886] :
( U_887 != U_886
& U_886 = singleton(U_888)
& in(U_888,U_892)
& U_887 = singleton(U_888)
& in(U_888,U_892) ) ),
inference(miniscope,[status(thm)],[f_216_2]) ).
fof(f_216_4,plain,
! [U_892] :
( ? [U_891] :
( ! [U_896,U_894] :
( in(ordered_pair(U_896,U_894),U_891)
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ in(U_896,U_892) )
& ! [U_895,U_893] :
( ( U_893 = singleton(U_895)
& in(U_895,U_892)
& in(U_895,U_892) )
| ~ in(ordered_pair(U_895,U_893),U_891) )
& function(U_891)
& relation(U_891) )
| ? [U_887,U_886] :
( U_887 != U_886
& U_886 = singleton(sK164(U_892))
& in(sK164(U_892),U_892)
& U_887 = singleton(sK164(U_892))
& in(sK164(U_892),U_892) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_888,sK164(U_892))],[f_216_3]) ).
fof(f_216_5,plain,
! [U_892] :
( ? [U_891] :
( ! [U_896,U_894] :
( in(ordered_pair(U_896,U_894),U_891)
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ in(U_896,U_892) )
& ! [U_895,U_893] :
( ( U_893 = singleton(U_895)
& in(U_895,U_892)
& in(U_895,U_892) )
| ~ in(ordered_pair(U_895,U_893),U_891) )
& function(U_891)
& relation(U_891) )
| ? [U_886] :
( sK165(U_892) != U_886
& U_886 = singleton(sK164(U_892))
& in(sK164(U_892),U_892)
& sK165(U_892) = singleton(sK164(U_892))
& in(sK164(U_892),U_892) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_887,sK165(U_892))],[f_216_4]) ).
fof(f_216_6,plain,
! [U_892] :
( ? [U_891] :
( ! [U_896,U_894] :
( in(ordered_pair(U_896,U_894),U_891)
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ in(U_896,U_892) )
& ! [U_895,U_893] :
( ( U_893 = singleton(U_895)
& in(U_895,U_892)
& in(U_895,U_892) )
| ~ in(ordered_pair(U_895,U_893),U_891) )
& function(U_891)
& relation(U_891) )
| ( sK165(U_892) != sK166(U_892)
& sK166(U_892) = singleton(sK164(U_892))
& in(sK164(U_892),U_892)
& sK165(U_892) = singleton(sK164(U_892))
& in(sK164(U_892),U_892) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_886,sK166(U_892))],[f_216_5]) ).
fof(f_216_7,plain,
! [U_892] :
( ( ! [U_896,U_894] :
( in(ordered_pair(U_896,U_894),sK167(U_892))
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ in(U_896,U_892) )
& ! [U_895,U_893] :
( ( U_893 = singleton(U_895)
& in(U_895,U_892)
& in(U_895,U_892) )
| ~ in(ordered_pair(U_895,U_893),sK167(U_892)) )
& function(sK167(U_892))
& relation(sK167(U_892)) )
| ( sK165(U_892) != sK166(U_892)
& sK166(U_892) = singleton(sK164(U_892))
& in(sK164(U_892),U_892)
& sK165(U_892) = singleton(sK164(U_892))
& in(sK164(U_892),U_892) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_891,sK167(U_892))],[f_216_6]) ).
fof(f_216_8,plain,
( ! [U_893,U_892,U_895] :
( U_893 = singleton(U_895)
| ~ sP210(U_893,U_892,U_895) )
& ! [U_893,U_892,U_895] :
( in(U_895,U_892)
| ~ sP210(U_893,U_892,U_895) )
& ! [U_893,U_892,U_895] :
( in(U_895,U_892)
| ~ sP210(U_893,U_892,U_895) )
& ! [U_894,U_893,U_892,U_895,U_896] :
( in(ordered_pair(U_896,U_894),sK167(U_892))
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ in(U_896,U_892)
| ~ sP211(U_894,U_893,U_892,U_895,U_896) )
& ! [U_894,U_893,U_892,U_895,U_896] :
( sP210(U_893,U_892,U_895)
| ~ in(ordered_pair(U_895,U_893),sK167(U_892))
| ~ sP211(U_894,U_893,U_892,U_895,U_896) )
& ! [U_894,U_893,U_892,U_895,U_896] :
( function(sK167(U_892))
| ~ sP211(U_894,U_893,U_892,U_895,U_896) )
& ! [U_894,U_893,U_892,U_895,U_896] :
( relation(sK167(U_892))
| ~ sP211(U_894,U_893,U_892,U_895,U_896) )
& ! [U_892] :
( sK165(U_892) != sK166(U_892)
| ~ sP209(U_892) )
& ! [U_892] :
( sK166(U_892) = singleton(sK164(U_892))
| ~ sP209(U_892) )
& ! [U_892] :
( in(sK164(U_892),U_892)
| ~ sP209(U_892) )
& ! [U_892] :
( sK165(U_892) = singleton(sK164(U_892))
| ~ sP209(U_892) )
& ! [U_892] :
( in(sK164(U_892),U_892)
| ~ sP209(U_892) )
& ! [U_894,U_893,U_892,U_895,U_896] :
( sP211(U_894,U_893,U_892,U_895,U_896)
| sP209(U_892) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209,sP210,sP211])],[f_216_7]) ).
cnf(f_216_9,plain,
( sP211(U_894,U_893,U_892,U_895,U_896)
| sP209(U_892) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_10,plain,
( in(sK164(U_892),U_892)
| ~ sP209(U_892) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_11,plain,
( sK165(U_892) = singleton(sK164(U_892))
| ~ sP209(U_892) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_12,plain,
( in(sK164(U_892),U_892)
| ~ sP209(U_892) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_13,plain,
( sK166(U_892) = singleton(sK164(U_892))
| ~ sP209(U_892) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_14,plain,
( sK165(U_892) != sK166(U_892)
| ~ sP209(U_892) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_15,plain,
( relation(sK167(U_892))
| ~ sP211(U_894,U_893,U_892,U_895,U_896) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_16,plain,
( function(sK167(U_892))
| ~ sP211(U_894,U_893,U_892,U_895,U_896) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_17,plain,
( sP210(U_893,U_892,U_895)
| ~ in(ordered_pair(U_895,U_893),sK167(U_892))
| ~ sP211(U_894,U_893,U_892,U_895,U_896) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_18,plain,
( in(ordered_pair(U_896,U_894),sK167(U_892))
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ in(U_896,U_892)
| ~ sP211(U_894,U_893,U_892,U_895,U_896) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_19,plain,
( in(U_895,U_892)
| ~ sP210(U_893,U_892,U_895) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_20,plain,
( in(U_895,U_892)
| ~ sP210(U_893,U_892,U_895) ),
inference(clausify,[status(thm)],[f_216_8]) ).
cnf(f_216_21,plain,
( U_893 = singleton(U_895)
| ~ sP210(U_893,U_892,U_895) ),
inference(clausify,[status(thm)],[f_216_8]) ).
fof(f_217_1,plain,
! [A] :
( ? [B] :
( ! [C] :
( ordinal_subset(B,C)
| ~ in(C,A)
| ~ ordinal(C) )
& in(B,A)
& ordinal(B) )
| ! [B] :
( ~ in(B,A)
| ~ ordinal(B) ) ),
inference(fof_nnf,[status(thm)],[s1_ordinal1__e8_6__wellord2]) ).
fof(f_217_2,plain,
! [U_900] :
( ? [U_899] :
( ! [U_898] :
( ordinal_subset(U_899,U_898)
| ~ in(U_898,U_900)
| ~ ordinal(U_898) )
& in(U_899,U_900)
& ordinal(U_899) )
| ! [U_897] :
( ~ in(U_897,U_900)
| ~ ordinal(U_897) ) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_900] :
( ( ! [U_898] :
( ordinal_subset(sK168(U_900),U_898)
| ~ in(U_898,U_900)
| ~ ordinal(U_898) )
& in(sK168(U_900),U_900)
& ordinal(sK168(U_900)) )
| ! [U_897] :
( ~ in(U_897,U_900)
| ~ ordinal(U_897) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_899,sK168(U_900))],[f_217_2]) ).
fof(f_217_4,plain,
( ! [U_900,U_898] :
( ordinal_subset(sK168(U_900),U_898)
| ~ in(U_898,U_900)
| ~ ordinal(U_898)
| ~ sP212(U_900,U_898) )
& ! [U_900,U_898] :
( in(sK168(U_900),U_900)
| ~ sP212(U_900,U_898) )
& ! [U_900,U_898] :
( ordinal(sK168(U_900))
| ~ sP212(U_900,U_898) )
& ! [U_897,U_900,U_898] :
( sP212(U_900,U_898)
| ~ in(U_897,U_900)
| ~ ordinal(U_897) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_217_3]) ).
cnf(f_217_5,plain,
( sP212(U_900,U_898)
| ~ in(U_897,U_900)
| ~ ordinal(U_897) ),
inference(clausify,[status(thm)],[f_217_4]) ).
cnf(f_217_6,plain,
( ordinal(sK168(U_900))
| ~ sP212(U_900,U_898) ),
inference(clausify,[status(thm)],[f_217_4]) ).
cnf(f_217_7,plain,
( in(sK168(U_900),U_900)
| ~ sP212(U_900,U_898) ),
inference(clausify,[status(thm)],[f_217_4]) ).
cnf(f_217_8,plain,
( ordinal_subset(sK168(U_900),U_898)
| ~ in(U_898,U_900)
| ~ ordinal(U_898)
| ~ sP212(U_900,U_898) ),
inference(clausify,[status(thm)],[f_217_4]) ).
fof(f_218_1,plain,
! [A,B,C] :
( ? [D] :
( ! [E,F] :
( ( in(ordered_pair(E,F),D)
| ~ in(ordered_pair(apply(C,E),apply(C,F)),B)
| ~ in(F,A)
| ~ in(E,A) )
& ( ( in(ordered_pair(apply(C,E),apply(C,F)),B)
& in(F,A)
& in(E,A) )
| ~ in(ordered_pair(E,F),D) ) )
& relation(D) )
| ~ function(C)
| ~ relation(C)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[s1_relat_1__e6_21__wellord2]) ).
fof(f_218_2,plain,
! [U_906,U_905,U_904] :
( ? [U_903] :
( ! [U_902,U_901] :
( ( in(ordered_pair(U_902,U_901),U_903)
| ~ in(ordered_pair(apply(U_904,U_902),apply(U_904,U_901)),U_905)
| ~ in(U_901,U_906)
| ~ in(U_902,U_906) )
& ( ( in(ordered_pair(apply(U_904,U_902),apply(U_904,U_901)),U_905)
& in(U_901,U_906)
& in(U_902,U_906) )
| ~ in(ordered_pair(U_902,U_901),U_903) ) )
& relation(U_903) )
| ~ function(U_904)
| ~ relation(U_904)
| ~ relation(U_905) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_906,U_905,U_904] :
( ? [U_903] :
( ! [U_910,U_908] :
( in(ordered_pair(U_910,U_908),U_903)
| ~ in(ordered_pair(apply(U_904,U_910),apply(U_904,U_908)),U_905)
| ~ in(U_908,U_906)
| ~ in(U_910,U_906) )
& ! [U_909,U_907] :
( ( in(ordered_pair(apply(U_904,U_909),apply(U_904,U_907)),U_905)
& in(U_907,U_906)
& in(U_909,U_906) )
| ~ in(ordered_pair(U_909,U_907),U_903) )
& relation(U_903) )
| ~ function(U_904)
| ~ relation(U_904)
| ~ relation(U_905) ),
inference(miniscope,[status(thm)],[f_218_2]) ).
fof(f_218_4,plain,
! [U_906,U_905,U_904] :
( ( ! [U_910,U_908] :
( in(ordered_pair(U_910,U_908),sK169(U_906,U_905,U_904))
| ~ in(ordered_pair(apply(U_904,U_910),apply(U_904,U_908)),U_905)
| ~ in(U_908,U_906)
| ~ in(U_910,U_906) )
& ! [U_909,U_907] :
( ( in(ordered_pair(apply(U_904,U_909),apply(U_904,U_907)),U_905)
& in(U_907,U_906)
& in(U_909,U_906) )
| ~ in(ordered_pair(U_909,U_907),sK169(U_906,U_905,U_904)) )
& relation(sK169(U_906,U_905,U_904)) )
| ~ function(U_904)
| ~ relation(U_904)
| ~ relation(U_905) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_903,sK169(U_906,U_905,U_904))],[f_218_3]) ).
fof(f_218_5,plain,
( ! [U_907,U_904,U_909,U_905,U_906] :
( in(ordered_pair(apply(U_904,U_909),apply(U_904,U_907)),U_905)
| ~ sP213(U_907,U_904,U_909,U_905,U_906) )
& ! [U_907,U_904,U_909,U_905,U_906] :
( in(U_907,U_906)
| ~ sP213(U_907,U_904,U_909,U_905,U_906) )
& ! [U_907,U_904,U_909,U_905,U_906] :
( in(U_909,U_906)
| ~ sP213(U_907,U_904,U_909,U_905,U_906) )
& ! [U_907,U_904,U_909,U_905,U_910,U_906,U_908] :
( in(ordered_pair(U_910,U_908),sK169(U_906,U_905,U_904))
| ~ in(ordered_pair(apply(U_904,U_910),apply(U_904,U_908)),U_905)
| ~ in(U_908,U_906)
| ~ in(U_910,U_906)
| ~ sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908) )
& ! [U_907,U_904,U_909,U_905,U_910,U_906,U_908] :
( sP213(U_907,U_904,U_909,U_905,U_906)
| ~ in(ordered_pair(U_909,U_907),sK169(U_906,U_905,U_904))
| ~ sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908) )
& ! [U_907,U_904,U_909,U_905,U_910,U_906,U_908] :
( relation(sK169(U_906,U_905,U_904))
| ~ sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908) )
& ! [U_907,U_904,U_909,U_905,U_910,U_906,U_908] :
( sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908)
| ~ function(U_904)
| ~ relation(U_904)
| ~ relation(U_905) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213,sP214])],[f_218_4]) ).
cnf(f_218_6,plain,
( sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908)
| ~ function(U_904)
| ~ relation(U_904)
| ~ relation(U_905) ),
inference(clausify,[status(thm)],[f_218_5]) ).
cnf(f_218_7,plain,
( relation(sK169(U_906,U_905,U_904))
| ~ sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908) ),
inference(clausify,[status(thm)],[f_218_5]) ).
cnf(f_218_8,plain,
( sP213(U_907,U_904,U_909,U_905,U_906)
| ~ in(ordered_pair(U_909,U_907),sK169(U_906,U_905,U_904))
| ~ sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908) ),
inference(clausify,[status(thm)],[f_218_5]) ).
cnf(f_218_9,plain,
( in(ordered_pair(U_910,U_908),sK169(U_906,U_905,U_904))
| ~ in(ordered_pair(apply(U_904,U_910),apply(U_904,U_908)),U_905)
| ~ in(U_908,U_906)
| ~ in(U_910,U_906)
| ~ sP214(U_907,U_904,U_909,U_905,U_910,U_906,U_908) ),
inference(clausify,[status(thm)],[f_218_5]) ).
cnf(f_218_10,plain,
( in(U_909,U_906)
| ~ sP213(U_907,U_904,U_909,U_905,U_906) ),
inference(clausify,[status(thm)],[f_218_5]) ).
cnf(f_218_11,plain,
( in(U_907,U_906)
| ~ sP213(U_907,U_904,U_909,U_905,U_906) ),
inference(clausify,[status(thm)],[f_218_5]) ).
cnf(f_218_12,plain,
( in(ordered_pair(apply(U_904,U_909),apply(U_904,U_907)),U_905)
| ~ sP213(U_907,U_904,U_909,U_905,U_906) ),
inference(clausify,[status(thm)],[f_218_5]) ).
fof(f_219_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ! [J] :
( ? [K] :
( ~ in(ordered_pair(D,K),B)
& in(K,J) )
| ~ in(D,J)
| E != J )
| ~ in(E,A)
| ~ in(E,A) ) )
& ( ? [E] :
( ? [J] :
( ! [K] :
( in(ordered_pair(D,K),B)
| ~ in(K,J) )
& in(D,J)
& E = J )
& in(E,A)
& in(E,A) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ? [H] :
( ! [I] :
( in(ordered_pair(E,I),B)
| ~ in(I,H) )
& in(E,H)
& C = H )
& in(C,A)
& ? [F] :
( ! [G] :
( in(ordered_pair(D,G),B)
| ~ in(G,F) )
& in(D,F)
& C = F )
& in(C,A) )
| ~ relation(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e10_24__wellord2__1]) ).
fof(f_219_2,plain,
! [U_927,U_926] :
( ? [U_925] :
! [U_924] :
( ( in(U_924,U_925)
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_924,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_924,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_924,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_924,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_924,U_925) ) )
| ? [U_917,U_916,U_915] :
( U_916 != U_915
& ? [U_914] :
( ! [U_913] :
( in(ordered_pair(U_915,U_913),U_926)
| ~ in(U_913,U_914) )
& in(U_915,U_914)
& U_917 = U_914 )
& in(U_917,U_927)
& ? [U_912] :
( ! [U_911] :
( in(ordered_pair(U_916,U_911),U_926)
| ~ in(U_911,U_912) )
& in(U_916,U_912)
& U_917 = U_912 )
& in(U_917,U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_927,U_926] :
( ? [U_925] :
( ! [U_929] :
( in(U_929,U_925)
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_928,U_925) ) )
| ? [U_917,U_916,U_915] :
( U_916 != U_915
& ? [U_914] :
( ! [U_913] :
( in(ordered_pair(U_915,U_913),U_926)
| ~ in(U_913,U_914) )
& in(U_915,U_914)
& U_917 = U_914 )
& in(U_917,U_927)
& ? [U_912] :
( ! [U_911] :
( in(ordered_pair(U_916,U_911),U_926)
| ~ in(U_911,U_912) )
& in(U_916,U_912)
& U_917 = U_912 )
& in(U_917,U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(miniscope,[status(thm)],[f_219_2]) ).
fof(f_219_4,plain,
! [U_927,U_926] :
( ? [U_925] :
( ! [U_929] :
( in(U_929,U_925)
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_928,U_925) ) )
| ? [U_916,U_915] :
( U_916 != U_915
& ? [U_914] :
( ! [U_913] :
( in(ordered_pair(U_915,U_913),U_926)
| ~ in(U_913,U_914) )
& in(U_915,U_914)
& sK170(U_927,U_926) = U_914 )
& in(sK170(U_927,U_926),U_927)
& ? [U_912] :
( ! [U_911] :
( in(ordered_pair(U_916,U_911),U_926)
| ~ in(U_911,U_912) )
& in(U_916,U_912)
& sK170(U_927,U_926) = U_912 )
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_917,sK170(U_927,U_926))],[f_219_3]) ).
fof(f_219_5,plain,
! [U_927,U_926] :
( ? [U_925] :
( ! [U_929] :
( in(U_929,U_925)
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_928,U_925) ) )
| ? [U_915] :
( sK171(U_927,U_926) != U_915
& ? [U_914] :
( ! [U_913] :
( in(ordered_pair(U_915,U_913),U_926)
| ~ in(U_913,U_914) )
& in(U_915,U_914)
& sK170(U_927,U_926) = U_914 )
& in(sK170(U_927,U_926),U_927)
& ? [U_912] :
( ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,U_912) )
& in(sK171(U_927,U_926),U_912)
& sK170(U_927,U_926) = U_912 )
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_916,sK171(U_927,U_926))],[f_219_4]) ).
fof(f_219_6,plain,
! [U_927,U_926] :
( ? [U_925] :
( ! [U_929] :
( in(U_929,U_925)
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_928,U_925) ) )
| ( sK171(U_927,U_926) != sK172(U_927,U_926)
& ? [U_914] :
( ! [U_913] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,U_914) )
& in(sK172(U_927,U_926),U_914)
& sK170(U_927,U_926) = U_914 )
& in(sK170(U_927,U_926),U_927)
& ? [U_912] :
( ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,U_912) )
& in(sK171(U_927,U_926),U_912)
& sK170(U_927,U_926) = U_912 )
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_915,sK172(U_927,U_926))],[f_219_5]) ).
fof(f_219_7,plain,
! [U_927,U_926] :
( ? [U_925] :
( ! [U_929] :
( in(U_929,U_925)
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_928,U_925) ) )
| ( sK171(U_927,U_926) != sK172(U_927,U_926)
& ? [U_914] :
( ! [U_913] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,U_914) )
& in(sK172(U_927,U_926),U_914)
& sK170(U_927,U_926) = U_914 )
& in(sK170(U_927,U_926),U_927)
& ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926)) )
& in(sK171(U_927,U_926),sK173(U_927,U_926))
& sK170(U_927,U_926) = sK173(U_927,U_926)
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_912,sK173(U_927,U_926))],[f_219_6]) ).
fof(f_219_8,plain,
! [U_927,U_926] :
( ? [U_925] :
( ! [U_929] :
( in(U_929,U_925)
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_928,U_925) ) )
| ( sK171(U_927,U_926) != sK172(U_927,U_926)
& ! [U_913] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,sK174(U_927,U_926)) )
& in(sK172(U_927,U_926),sK174(U_927,U_926))
& sK170(U_927,U_926) = sK174(U_927,U_926)
& in(sK170(U_927,U_926),U_927)
& ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926)) )
& in(sK171(U_927,U_926),sK173(U_927,U_926))
& sK170(U_927,U_926) = sK173(U_927,U_926)
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_914,sK174(U_927,U_926))],[f_219_7]) ).
fof(f_219_9,plain,
! [U_927,U_926] :
( ( ! [U_929] :
( in(U_929,sK175(U_927,U_926))
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ? [U_920] :
( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& U_920 = U_919 )
& in(U_920,U_927)
& in(U_920,U_927) )
| ~ in(U_928,sK175(U_927,U_926)) ) )
| ( sK171(U_927,U_926) != sK172(U_927,U_926)
& ! [U_913] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,sK174(U_927,U_926)) )
& in(sK172(U_927,U_926),sK174(U_927,U_926))
& sK170(U_927,U_926) = sK174(U_927,U_926)
& in(sK170(U_927,U_926),U_927)
& ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926)) )
& in(sK171(U_927,U_926),sK173(U_927,U_926))
& sK170(U_927,U_926) = sK173(U_927,U_926)
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_925,sK175(U_927,U_926))],[f_219_8]) ).
fof(f_219_10,plain,
! [U_927,U_926] :
( ( ! [U_929] :
( in(U_929,sK175(U_927,U_926))
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ( ? [U_919] :
( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,U_919) )
& in(U_928,U_919)
& sK176(U_927,U_926,U_928) = U_919 )
& in(sK176(U_927,U_926,U_928),U_927)
& in(sK176(U_927,U_926,U_928),U_927) )
| ~ in(U_928,sK175(U_927,U_926)) ) )
| ( sK171(U_927,U_926) != sK172(U_927,U_926)
& ! [U_913] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,sK174(U_927,U_926)) )
& in(sK172(U_927,U_926),sK174(U_927,U_926))
& sK170(U_927,U_926) = sK174(U_927,U_926)
& in(sK170(U_927,U_926),U_927)
& ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926)) )
& in(sK171(U_927,U_926),sK173(U_927,U_926))
& sK170(U_927,U_926) = sK173(U_927,U_926)
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_920,sK176(U_927,U_926,U_928))],[f_219_9]) ).
fof(f_219_11,plain,
! [U_927,U_926] :
( ( ! [U_929] :
( in(U_929,sK175(U_927,U_926))
| ! [U_923] :
( ! [U_922] :
( ? [U_921] :
( ~ in(ordered_pair(U_929,U_921),U_926)
& in(U_921,U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,sK177(U_927,U_926,U_928)) )
& in(U_928,sK177(U_927,U_926,U_928))
& sK176(U_927,U_926,U_928) = sK177(U_927,U_926,U_928)
& in(sK176(U_927,U_926,U_928),U_927)
& in(sK176(U_927,U_926,U_928),U_927) )
| ~ in(U_928,sK175(U_927,U_926)) ) )
| ( sK171(U_927,U_926) != sK172(U_927,U_926)
& ! [U_913] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,sK174(U_927,U_926)) )
& in(sK172(U_927,U_926),sK174(U_927,U_926))
& sK170(U_927,U_926) = sK174(U_927,U_926)
& in(sK170(U_927,U_926),U_927)
& ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926)) )
& in(sK171(U_927,U_926),sK173(U_927,U_926))
& sK170(U_927,U_926) = sK173(U_927,U_926)
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_919,sK177(U_927,U_926,U_928))],[f_219_10]) ).
fof(f_219_12,plain,
! [U_927,U_926] :
( ( ! [U_929] :
( in(U_929,sK175(U_927,U_926))
| ! [U_923] :
( ! [U_922] :
( ( ~ in(ordered_pair(U_929,sK178(U_927,U_926,U_929,U_923,U_922)),U_926)
& in(sK178(U_927,U_926,U_929,U_923,U_922),U_922) )
| ~ in(U_929,U_922)
| U_923 != U_922 )
| ~ in(U_923,U_927)
| ~ in(U_923,U_927) ) )
& ! [U_928] :
( ( ! [U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,sK177(U_927,U_926,U_928)) )
& in(U_928,sK177(U_927,U_926,U_928))
& sK176(U_927,U_926,U_928) = sK177(U_927,U_926,U_928)
& in(sK176(U_927,U_926,U_928),U_927)
& in(sK176(U_927,U_926,U_928),U_927) )
| ~ in(U_928,sK175(U_927,U_926)) ) )
| ( sK171(U_927,U_926) != sK172(U_927,U_926)
& ! [U_913] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,sK174(U_927,U_926)) )
& in(sK172(U_927,U_926),sK174(U_927,U_926))
& sK170(U_927,U_926) = sK174(U_927,U_926)
& in(sK170(U_927,U_926),U_927)
& ! [U_911] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926)) )
& in(sK171(U_927,U_926),sK173(U_927,U_926))
& sK170(U_927,U_926) = sK173(U_927,U_926)
& in(sK170(U_927,U_926),U_927) )
| ~ relation(U_926)
| empty(U_927) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_921,sK178(U_927,U_926,U_929,U_923,U_922))],[f_219_11]) ).
fof(f_219_13,plain,
( ! [U_926,U_923,U_929,U_922,U_927] :
( ~ in(ordered_pair(U_929,sK178(U_927,U_926,U_929,U_923,U_922)),U_926)
| ~ sP217(U_926,U_923,U_929,U_922,U_927) )
& ! [U_926,U_923,U_929,U_922,U_927] :
( in(sK178(U_927,U_926,U_929,U_923,U_922),U_922)
| ~ sP217(U_926,U_923,U_929,U_922,U_927) )
& ! [U_926,U_928,U_927,U_918] :
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,sK177(U_927,U_926,U_928))
| ~ sP216(U_926,U_928,U_927,U_918) )
& ! [U_926,U_928,U_927,U_918] :
( in(U_928,sK177(U_927,U_926,U_928))
| ~ sP216(U_926,U_928,U_927,U_918) )
& ! [U_926,U_928,U_927,U_918] :
( sK176(U_927,U_926,U_928) = sK177(U_927,U_926,U_928)
| ~ sP216(U_926,U_928,U_927,U_918) )
& ! [U_926,U_928,U_927,U_918] :
( in(sK176(U_927,U_926,U_928),U_927)
| ~ sP216(U_926,U_928,U_927,U_918) )
& ! [U_926,U_928,U_927,U_918] :
( in(sK176(U_927,U_926,U_928),U_927)
| ~ sP216(U_926,U_928,U_927,U_918) )
& ! [U_926,U_923,U_929,U_928,U_922,U_927,U_918] :
( in(U_929,sK175(U_927,U_926))
| sP217(U_926,U_923,U_929,U_922,U_927)
| ~ in(U_929,U_922)
| U_923 != U_922
| ~ in(U_923,U_927)
| ~ in(U_923,U_927)
| ~ sP218(U_926,U_923,U_929,U_928,U_922,U_927,U_918) )
& ! [U_926,U_923,U_929,U_928,U_922,U_927,U_918] :
( sP216(U_926,U_928,U_927,U_918)
| ~ in(U_928,sK175(U_927,U_926))
| ~ sP218(U_926,U_923,U_929,U_928,U_922,U_927,U_918) )
& ! [U_913,U_911,U_926,U_927] :
( sK171(U_927,U_926) != sK172(U_927,U_926)
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,sK174(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( in(sK172(U_927,U_926),sK174(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( sK170(U_927,U_926) = sK174(U_927,U_926)
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( in(sK170(U_927,U_926),U_927)
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( in(sK171(U_927,U_926),sK173(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( sK170(U_927,U_926) = sK173(U_927,U_926)
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_927] :
( in(sK170(U_927,U_926),U_927)
| ~ sP215(U_913,U_911,U_926,U_927) )
& ! [U_913,U_911,U_926,U_923,U_929,U_928,U_922,U_927,U_918] :
( sP218(U_926,U_923,U_929,U_928,U_922,U_927,U_918)
| sP215(U_913,U_911,U_926,U_927)
| ~ relation(U_926)
| empty(U_927) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215,sP216,sP217,sP218])],[f_219_12]) ).
cnf(f_219_14,plain,
( sP218(U_926,U_923,U_929,U_928,U_922,U_927,U_918)
| sP215(U_913,U_911,U_926,U_927)
| ~ relation(U_926)
| empty(U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_15,plain,
( in(sK170(U_927,U_926),U_927)
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_16,plain,
( sK170(U_927,U_926) = sK173(U_927,U_926)
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_17,plain,
( in(sK171(U_927,U_926),sK173(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_18,plain,
( in(ordered_pair(sK171(U_927,U_926),U_911),U_926)
| ~ in(U_911,sK173(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_19,plain,
( in(sK170(U_927,U_926),U_927)
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_20,plain,
( sK170(U_927,U_926) = sK174(U_927,U_926)
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_21,plain,
( in(sK172(U_927,U_926),sK174(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_22,plain,
( in(ordered_pair(sK172(U_927,U_926),U_913),U_926)
| ~ in(U_913,sK174(U_927,U_926))
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_23,plain,
( sK171(U_927,U_926) != sK172(U_927,U_926)
| ~ sP215(U_913,U_911,U_926,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_24,plain,
( sP216(U_926,U_928,U_927,U_918)
| ~ in(U_928,sK175(U_927,U_926))
| ~ sP218(U_926,U_923,U_929,U_928,U_922,U_927,U_918) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_25,plain,
( in(U_929,sK175(U_927,U_926))
| sP217(U_926,U_923,U_929,U_922,U_927)
| ~ in(U_929,U_922)
| U_923 != U_922
| ~ in(U_923,U_927)
| ~ in(U_923,U_927)
| ~ sP218(U_926,U_923,U_929,U_928,U_922,U_927,U_918) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_26,plain,
( in(sK176(U_927,U_926,U_928),U_927)
| ~ sP216(U_926,U_928,U_927,U_918) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_27,plain,
( in(sK176(U_927,U_926,U_928),U_927)
| ~ sP216(U_926,U_928,U_927,U_918) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_28,plain,
( sK176(U_927,U_926,U_928) = sK177(U_927,U_926,U_928)
| ~ sP216(U_926,U_928,U_927,U_918) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_29,plain,
( in(U_928,sK177(U_927,U_926,U_928))
| ~ sP216(U_926,U_928,U_927,U_918) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_30,plain,
( in(ordered_pair(U_928,U_918),U_926)
| ~ in(U_918,sK177(U_927,U_926,U_928))
| ~ sP216(U_926,U_928,U_927,U_918) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_31,plain,
( in(sK178(U_927,U_926,U_929,U_923,U_922),U_922)
| ~ sP217(U_926,U_923,U_929,U_922,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
cnf(f_219_32,plain,
( ~ in(ordered_pair(U_929,sK178(U_927,U_926,U_929,U_923,U_922)),U_926)
| ~ sP217(U_926,U_923,U_929,U_922,U_927) ),
inference(clausify,[status(thm)],[f_219_13]) ).
fof(f_220_1,plain,
! [A,B] :
( ! [C] :
( ? [D] :
! [E] :
( ( in(E,D)
| ! [F] :
( ! [O,P] :
( ! [Q] :
( ? [R] :
( ~ in(ordered_pair(P,R),B)
& in(R,Q) )
| ~ in(P,Q)
| O != Q )
| ~ in(O,A)
| ordered_pair(O,P) != E )
| F != E
| ~ in(F,cartesian_product2(A,C)) ) )
& ( ? [F] :
( ? [O,P] :
( ? [Q] :
( ! [R] :
( in(ordered_pair(P,R),B)
| ~ in(R,Q) )
& in(P,Q)
& O = Q )
& in(O,A)
& ordered_pair(O,P) = E )
& F = E
& in(F,cartesian_product2(A,C)) )
| ~ in(E,D) ) )
| ? [D,E,F] :
( E != F
& ? [K,L] :
( ? [M] :
( ! [N] :
( in(ordered_pair(L,N),B)
| ~ in(N,M) )
& in(L,M)
& K = M )
& in(K,A)
& ordered_pair(K,L) = F )
& D = F
& ? [G,H] :
( ? [I] :
( ! [J] :
( in(ordered_pair(H,J),B)
| ~ in(J,I) )
& in(H,I)
& G = I )
& in(G,A)
& ordered_pair(G,H) = E )
& D = E ) )
| ~ relation(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e10_24__wellord2__2]) ).
fof(f_220_2,plain,
! [U_955,U_954] :
( ! [U_953] :
( ? [U_952] :
! [U_951] :
( ( in(U_951,U_952)
| ! [U_950] :
( ! [U_949,U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ~ in(U_949,U_955)
| ordered_pair(U_949,U_948) != U_951 )
| U_950 != U_951
| ~ in(U_950,cartesian_product2(U_955,U_953)) ) )
& ( ? [U_945] :
( ? [U_944,U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& in(U_944,U_955)
& ordered_pair(U_944,U_943) = U_951 )
& U_945 = U_951
& in(U_945,cartesian_product2(U_955,U_953)) )
| ~ in(U_951,U_952) ) )
| ? [U_940,U_939,U_938] :
( U_939 != U_938
& ? [U_937,U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& in(U_937,U_955)
& ordered_pair(U_937,U_936) = U_938 )
& U_940 = U_938
& ? [U_933,U_932] :
( ? [U_931] :
( ! [U_930] :
( in(ordered_pair(U_932,U_930),U_954)
| ~ in(U_930,U_931) )
& in(U_932,U_931)
& U_933 = U_931 )
& in(U_933,U_955)
& ordered_pair(U_933,U_932) = U_939 )
& U_940 = U_939 ) )
| ~ relation(U_954)
| empty(U_955) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ? [U_940,U_939,U_938] :
( U_939 != U_938
& ? [U_937] :
( ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& ordered_pair(U_937,U_936) = U_938 )
& in(U_937,U_955) )
& U_940 = U_938
& ? [U_933] :
( ? [U_932] :
( ? [U_931] :
( ! [U_930] :
( in(ordered_pair(U_932,U_930),U_954)
| ~ in(U_930,U_931) )
& in(U_932,U_931)
& U_933 = U_931 )
& ordered_pair(U_933,U_932) = U_939 )
& in(U_933,U_955) )
& U_940 = U_939 )
| ~ relation(U_954)
| empty(U_955) ),
inference(miniscope,[status(thm)],[f_220_2]) ).
fof(f_220_4,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ? [U_939,U_938] :
( U_939 != U_938
& ? [U_937] :
( ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& ordered_pair(U_937,U_936) = U_938 )
& in(U_937,U_955) )
& sK179(U_955,U_954) = U_938
& ? [U_933] :
( ? [U_932] :
( ? [U_931] :
( ! [U_930] :
( in(ordered_pair(U_932,U_930),U_954)
| ~ in(U_930,U_931) )
& in(U_932,U_931)
& U_933 = U_931 )
& ordered_pair(U_933,U_932) = U_939 )
& in(U_933,U_955) )
& sK179(U_955,U_954) = U_939 )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_940,sK179(U_955,U_954))],[f_220_3]) ).
fof(f_220_5,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ? [U_938] :
( sK180(U_955,U_954) != U_938
& ? [U_937] :
( ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& ordered_pair(U_937,U_936) = U_938 )
& in(U_937,U_955) )
& sK179(U_955,U_954) = U_938
& ? [U_933] :
( ? [U_932] :
( ? [U_931] :
( ! [U_930] :
( in(ordered_pair(U_932,U_930),U_954)
| ~ in(U_930,U_931) )
& in(U_932,U_931)
& U_933 = U_931 )
& ordered_pair(U_933,U_932) = sK180(U_955,U_954) )
& in(U_933,U_955) )
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_939,sK180(U_955,U_954))],[f_220_4]) ).
fof(f_220_6,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ? [U_937] :
( ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& ordered_pair(U_937,U_936) = sK181(U_955,U_954) )
& in(U_937,U_955) )
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ? [U_933] :
( ? [U_932] :
( ? [U_931] :
( ! [U_930] :
( in(ordered_pair(U_932,U_930),U_954)
| ~ in(U_930,U_931) )
& in(U_932,U_931)
& U_933 = U_931 )
& ordered_pair(U_933,U_932) = sK180(U_955,U_954) )
& in(U_933,U_955) )
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_938,sK181(U_955,U_954))],[f_220_5]) ).
fof(f_220_7,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ? [U_937] :
( ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& ordered_pair(U_937,U_936) = sK181(U_955,U_954) )
& in(U_937,U_955) )
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ? [U_932] :
( ? [U_931] :
( ! [U_930] :
( in(ordered_pair(U_932,U_930),U_954)
| ~ in(U_930,U_931) )
& in(U_932,U_931)
& sK182(U_955,U_954) = U_931 )
& ordered_pair(sK182(U_955,U_954),U_932) = sK180(U_955,U_954) )
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_933,sK182(U_955,U_954))],[f_220_6]) ).
fof(f_220_8,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ? [U_937] :
( ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& ordered_pair(U_937,U_936) = sK181(U_955,U_954) )
& in(U_937,U_955) )
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ? [U_931] :
( ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,U_931) )
& in(sK183(U_955,U_954),U_931)
& sK182(U_955,U_954) = U_931 )
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_932,sK183(U_955,U_954))],[f_220_7]) ).
fof(f_220_9,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ? [U_937] :
( ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& U_937 = U_935 )
& ordered_pair(U_937,U_936) = sK181(U_955,U_954) )
& in(U_937,U_955) )
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_931,sK184(U_955,U_954))],[f_220_8]) ).
fof(f_220_10,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ? [U_936] :
( ? [U_935] :
( ! [U_934] :
( in(ordered_pair(U_936,U_934),U_954)
| ~ in(U_934,U_935) )
& in(U_936,U_935)
& sK185(U_955,U_954) = U_935 )
& ordered_pair(sK185(U_955,U_954),U_936) = sK181(U_955,U_954) )
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_937,sK185(U_955,U_954))],[f_220_9]) ).
fof(f_220_11,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ? [U_935] :
( ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,U_935) )
& in(sK186(U_955,U_954),U_935)
& sK185(U_955,U_954) = U_935 )
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_936,sK186(U_955,U_954))],[f_220_10]) ).
fof(f_220_12,plain,
! [U_955,U_954] :
( ! [U_953] :
? [U_952] :
( ! [U_957] :
( in(U_957,U_952)
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,U_952) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954)) )
& in(sK186(U_955,U_954),sK187(U_955,U_954))
& sK185(U_955,U_954) = sK187(U_955,U_954)
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_935,sK187(U_955,U_954))],[f_220_11]) ).
fof(f_220_13,plain,
! [U_955,U_954] :
( ! [U_953] :
( ! [U_957] :
( in(U_957,sK188(U_955,U_954,U_953))
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_944] :
( ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& U_944 = U_942 )
& ordered_pair(U_944,U_943) = U_956 )
& in(U_944,U_955) ) )
| ~ in(U_956,sK188(U_955,U_954,U_953)) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954)) )
& in(sK186(U_955,U_954),sK187(U_955,U_954))
& sK185(U_955,U_954) = sK187(U_955,U_954)
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_952,sK188(U_955,U_954,U_953))],[f_220_12]) ).
fof(f_220_14,plain,
! [U_955,U_954] :
( ! [U_953] :
( ! [U_957] :
( in(U_957,sK188(U_955,U_954,U_953))
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_943] :
( ? [U_942] :
( ! [U_941] :
( in(ordered_pair(U_943,U_941),U_954)
| ~ in(U_941,U_942) )
& in(U_943,U_942)
& sK189(U_955,U_954,U_953,U_956) = U_942 )
& ordered_pair(sK189(U_955,U_954,U_953,U_956),U_943) = U_956 )
& in(sK189(U_955,U_954,U_953,U_956),U_955) )
| ~ in(U_956,sK188(U_955,U_954,U_953)) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954)) )
& in(sK186(U_955,U_954),sK187(U_955,U_954))
& sK185(U_955,U_954) = sK187(U_955,U_954)
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_944,sK189(U_955,U_954,U_953,U_956))],[f_220_13]) ).
fof(f_220_15,plain,
! [U_955,U_954] :
( ! [U_953] :
( ! [U_957] :
( in(U_957,sK188(U_955,U_954,U_953))
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ? [U_942] :
( ! [U_941] :
( in(ordered_pair(sK190(U_955,U_954,U_953,U_956),U_941),U_954)
| ~ in(U_941,U_942) )
& in(sK190(U_955,U_954,U_953,U_956),U_942)
& sK189(U_955,U_954,U_953,U_956) = U_942 )
& ordered_pair(sK189(U_955,U_954,U_953,U_956),sK190(U_955,U_954,U_953,U_956)) = U_956
& in(sK189(U_955,U_954,U_953,U_956),U_955) )
| ~ in(U_956,sK188(U_955,U_954,U_953)) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954)) )
& in(sK186(U_955,U_954),sK187(U_955,U_954))
& sK185(U_955,U_954) = sK187(U_955,U_954)
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_943,sK190(U_955,U_954,U_953,U_956))],[f_220_14]) ).
fof(f_220_16,plain,
! [U_955,U_954] :
( ! [U_953] :
( ! [U_957] :
( in(U_957,sK188(U_955,U_954,U_953))
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( ? [U_945] :
( U_945 = U_956
& in(U_945,cartesian_product2(U_955,U_953)) )
& ! [U_941] :
( in(ordered_pair(sK190(U_955,U_954,U_953,U_956),U_941),U_954)
| ~ in(U_941,sK191(U_955,U_954,U_953,U_956)) )
& in(sK190(U_955,U_954,U_953,U_956),sK191(U_955,U_954,U_953,U_956))
& sK189(U_955,U_954,U_953,U_956) = sK191(U_955,U_954,U_953,U_956)
& ordered_pair(sK189(U_955,U_954,U_953,U_956),sK190(U_955,U_954,U_953,U_956)) = U_956
& in(sK189(U_955,U_954,U_953,U_956),U_955) )
| ~ in(U_956,sK188(U_955,U_954,U_953)) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954)) )
& in(sK186(U_955,U_954),sK187(U_955,U_954))
& sK185(U_955,U_954) = sK187(U_955,U_954)
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_942,sK191(U_955,U_954,U_953,U_956))],[f_220_15]) ).
fof(f_220_17,plain,
! [U_955,U_954] :
( ! [U_953] :
( ! [U_957] :
( in(U_957,sK188(U_955,U_954,U_953))
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ? [U_946] :
( ~ in(ordered_pair(U_948,U_946),U_954)
& in(U_946,U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( sK192(U_955,U_954,U_953,U_956) = U_956
& in(sK192(U_955,U_954,U_953,U_956),cartesian_product2(U_955,U_953))
& ! [U_941] :
( in(ordered_pair(sK190(U_955,U_954,U_953,U_956),U_941),U_954)
| ~ in(U_941,sK191(U_955,U_954,U_953,U_956)) )
& in(sK190(U_955,U_954,U_953,U_956),sK191(U_955,U_954,U_953,U_956))
& sK189(U_955,U_954,U_953,U_956) = sK191(U_955,U_954,U_953,U_956)
& ordered_pair(sK189(U_955,U_954,U_953,U_956),sK190(U_955,U_954,U_953,U_956)) = U_956
& in(sK189(U_955,U_954,U_953,U_956),U_955) )
| ~ in(U_956,sK188(U_955,U_954,U_953)) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954)) )
& in(sK186(U_955,U_954),sK187(U_955,U_954))
& sK185(U_955,U_954) = sK187(U_955,U_954)
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_945,sK192(U_955,U_954,U_953,U_956))],[f_220_16]) ).
fof(f_220_18,plain,
! [U_955,U_954] :
( ! [U_953] :
( ! [U_957] :
( in(U_957,sK188(U_955,U_954,U_953))
| ! [U_950] :
( U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953)) )
| ! [U_949] :
( ! [U_948] :
( ! [U_947] :
( ( ~ in(ordered_pair(U_948,sK193(U_955,U_954,U_953,U_957,U_949,U_948,U_947)),U_954)
& in(sK193(U_955,U_954,U_953,U_957,U_949,U_948,U_947),U_947) )
| ~ in(U_948,U_947)
| U_949 != U_947 )
| ordered_pair(U_949,U_948) != U_957 )
| ~ in(U_949,U_955) ) )
& ! [U_956] :
( ( sK192(U_955,U_954,U_953,U_956) = U_956
& in(sK192(U_955,U_954,U_953,U_956),cartesian_product2(U_955,U_953))
& ! [U_941] :
( in(ordered_pair(sK190(U_955,U_954,U_953,U_956),U_941),U_954)
| ~ in(U_941,sK191(U_955,U_954,U_953,U_956)) )
& in(sK190(U_955,U_954,U_953,U_956),sK191(U_955,U_954,U_953,U_956))
& sK189(U_955,U_954,U_953,U_956) = sK191(U_955,U_954,U_953,U_956)
& ordered_pair(sK189(U_955,U_954,U_953,U_956),sK190(U_955,U_954,U_953,U_956)) = U_956
& in(sK189(U_955,U_954,U_953,U_956),U_955) )
| ~ in(U_956,sK188(U_955,U_954,U_953)) ) )
| ( sK180(U_955,U_954) != sK181(U_955,U_954)
& ! [U_934] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954)) )
& in(sK186(U_955,U_954),sK187(U_955,U_954))
& sK185(U_955,U_954) = sK187(U_955,U_954)
& ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
& in(sK185(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK181(U_955,U_954)
& ! [U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954)) )
& in(sK183(U_955,U_954),sK184(U_955,U_954))
& sK182(U_955,U_954) = sK184(U_955,U_954)
& ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
& in(sK182(U_955,U_954),U_955)
& sK179(U_955,U_954) = sK180(U_955,U_954) )
| ~ relation(U_954)
| empty(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_946,sK193(U_955,U_954,U_953,U_957,U_949,U_948,U_947))],[f_220_17]) ).
fof(f_220_19,plain,
( ! [U_957,U_949,U_955,U_953,U_954,U_948,U_947] :
( ~ in(ordered_pair(U_948,sK193(U_955,U_954,U_953,U_957,U_949,U_948,U_947)),U_954)
| ~ sP221(U_957,U_949,U_955,U_953,U_954,U_948,U_947) )
& ! [U_957,U_949,U_955,U_953,U_954,U_948,U_947] :
( in(sK193(U_955,U_954,U_953,U_957,U_949,U_948,U_947),U_947)
| ~ sP221(U_957,U_949,U_955,U_953,U_954,U_948,U_947) )
& ! [U_955,U_953,U_954,U_956,U_941] :
( sK192(U_955,U_954,U_953,U_956) = U_956
| ~ sP220(U_955,U_953,U_954,U_956,U_941) )
& ! [U_955,U_953,U_954,U_956,U_941] :
( in(sK192(U_955,U_954,U_953,U_956),cartesian_product2(U_955,U_953))
| ~ sP220(U_955,U_953,U_954,U_956,U_941) )
& ! [U_955,U_953,U_954,U_956,U_941] :
( in(ordered_pair(sK190(U_955,U_954,U_953,U_956),U_941),U_954)
| ~ in(U_941,sK191(U_955,U_954,U_953,U_956))
| ~ sP220(U_955,U_953,U_954,U_956,U_941) )
& ! [U_955,U_953,U_954,U_956,U_941] :
( in(sK190(U_955,U_954,U_953,U_956),sK191(U_955,U_954,U_953,U_956))
| ~ sP220(U_955,U_953,U_954,U_956,U_941) )
& ! [U_955,U_953,U_954,U_956,U_941] :
( sK189(U_955,U_954,U_953,U_956) = sK191(U_955,U_954,U_953,U_956)
| ~ sP220(U_955,U_953,U_954,U_956,U_941) )
& ! [U_955,U_953,U_954,U_956,U_941] :
( ordered_pair(sK189(U_955,U_954,U_953,U_956),sK190(U_955,U_954,U_953,U_956)) = U_956
| ~ sP220(U_955,U_953,U_954,U_956,U_941) )
& ! [U_955,U_953,U_954,U_956,U_941] :
( in(sK189(U_955,U_954,U_953,U_956),U_955)
| ~ sP220(U_955,U_953,U_954,U_956,U_941) )
& ! [U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947] :
( in(U_957,sK188(U_955,U_954,U_953))
| U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953))
| sP221(U_957,U_949,U_955,U_953,U_954,U_948,U_947)
| ~ in(U_948,U_947)
| U_949 != U_947
| ordered_pair(U_949,U_948) != U_957
| ~ in(U_949,U_955)
| ~ sP222(U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947) )
& ! [U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947] :
( sP220(U_955,U_953,U_954,U_956,U_941)
| ~ in(U_956,sK188(U_955,U_954,U_953))
| ~ sP222(U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947) )
& ! [U_955,U_954,U_934,U_930] :
( sK180(U_955,U_954) != sK181(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( in(sK186(U_955,U_954),sK187(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( sK185(U_955,U_954) = sK187(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( in(sK185(U_955,U_954),U_955)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( sK179(U_955,U_954) = sK181(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( in(sK183(U_955,U_954),sK184(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( sK182(U_955,U_954) = sK184(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( in(sK182(U_955,U_954),U_955)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_955,U_954,U_934,U_930] :
( sK179(U_955,U_954) = sK180(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) )
& ! [U_957,U_949,U_955,U_953,U_954,U_950,U_934,U_956,U_930,U_941,U_948,U_947] :
( sP222(U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947)
| sP219(U_955,U_954,U_934,U_930)
| ~ relation(U_954)
| empty(U_955) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219,sP220,sP221,sP222])],[f_220_18]) ).
cnf(f_220_20,plain,
( sP222(U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947)
| sP219(U_955,U_954,U_934,U_930)
| ~ relation(U_954)
| empty(U_955) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_21,plain,
( sK179(U_955,U_954) = sK180(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_22,plain,
( in(sK182(U_955,U_954),U_955)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_23,plain,
( ordered_pair(sK182(U_955,U_954),sK183(U_955,U_954)) = sK180(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_24,plain,
( sK182(U_955,U_954) = sK184(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_25,plain,
( in(sK183(U_955,U_954),sK184(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_26,plain,
( in(ordered_pair(sK183(U_955,U_954),U_930),U_954)
| ~ in(U_930,sK184(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_27,plain,
( sK179(U_955,U_954) = sK181(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_28,plain,
( in(sK185(U_955,U_954),U_955)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_29,plain,
( ordered_pair(sK185(U_955,U_954),sK186(U_955,U_954)) = sK181(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_30,plain,
( sK185(U_955,U_954) = sK187(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_31,plain,
( in(sK186(U_955,U_954),sK187(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_32,plain,
( in(ordered_pair(sK186(U_955,U_954),U_934),U_954)
| ~ in(U_934,sK187(U_955,U_954))
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_33,plain,
( sK180(U_955,U_954) != sK181(U_955,U_954)
| ~ sP219(U_955,U_954,U_934,U_930) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_34,plain,
( sP220(U_955,U_953,U_954,U_956,U_941)
| ~ in(U_956,sK188(U_955,U_954,U_953))
| ~ sP222(U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_35,plain,
( in(U_957,sK188(U_955,U_954,U_953))
| U_950 != U_957
| ~ in(U_950,cartesian_product2(U_955,U_953))
| sP221(U_957,U_949,U_955,U_953,U_954,U_948,U_947)
| ~ in(U_948,U_947)
| U_949 != U_947
| ordered_pair(U_949,U_948) != U_957
| ~ in(U_949,U_955)
| ~ sP222(U_957,U_949,U_955,U_953,U_954,U_950,U_956,U_941,U_948,U_947) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_36,plain,
( in(sK189(U_955,U_954,U_953,U_956),U_955)
| ~ sP220(U_955,U_953,U_954,U_956,U_941) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_37,plain,
( ordered_pair(sK189(U_955,U_954,U_953,U_956),sK190(U_955,U_954,U_953,U_956)) = U_956
| ~ sP220(U_955,U_953,U_954,U_956,U_941) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_38,plain,
( sK189(U_955,U_954,U_953,U_956) = sK191(U_955,U_954,U_953,U_956)
| ~ sP220(U_955,U_953,U_954,U_956,U_941) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_39,plain,
( in(sK190(U_955,U_954,U_953,U_956),sK191(U_955,U_954,U_953,U_956))
| ~ sP220(U_955,U_953,U_954,U_956,U_941) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_40,plain,
( in(ordered_pair(sK190(U_955,U_954,U_953,U_956),U_941),U_954)
| ~ in(U_941,sK191(U_955,U_954,U_953,U_956))
| ~ sP220(U_955,U_953,U_954,U_956,U_941) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_41,plain,
( in(sK192(U_955,U_954,U_953,U_956),cartesian_product2(U_955,U_953))
| ~ sP220(U_955,U_953,U_954,U_956,U_941) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_42,plain,
( sK192(U_955,U_954,U_953,U_956) = U_956
| ~ sP220(U_955,U_953,U_954,U_956,U_941) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_43,plain,
( in(sK193(U_955,U_954,U_953,U_957,U_949,U_948,U_947),U_947)
| ~ sP221(U_957,U_949,U_955,U_953,U_954,U_948,U_947) ),
inference(clausify,[status(thm)],[f_220_19]) ).
cnf(f_220_44,plain,
( ~ in(ordered_pair(U_948,sK193(U_955,U_954,U_953,U_957,U_949,U_948,U_947)),U_954)
| ~ sP221(U_957,U_949,U_955,U_953,U_954,U_948,U_947) ),
inference(clausify,[status(thm)],[f_220_19]) ).
fof(f_221_1,plain,
! [A] :
( ? [B] :
! [C] :
( ( in(C,B)
| ! [D] :
( C != singleton(D)
| ~ in(D,A)
| ~ in(D,A) ) )
& ( ? [D] :
( C = singleton(D)
& in(D,A)
& in(D,A) )
| ~ in(C,B) ) )
| ? [B,C,D] :
( C != D
& D = singleton(B)
& in(B,A)
& C = singleton(B)
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e16_22__wellord2__1]) ).
fof(f_221_2,plain,
! [U_965] :
( ? [U_964] :
! [U_963] :
( ( in(U_963,U_964)
| ! [U_962] :
( U_963 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965) ) )
& ( ? [U_961] :
( U_963 = singleton(U_961)
& in(U_961,U_965)
& in(U_961,U_965) )
| ~ in(U_963,U_964) ) )
| ? [U_960,U_959,U_958] :
( U_959 != U_958
& U_958 = singleton(U_960)
& in(U_960,U_965)
& U_959 = singleton(U_960)
& in(U_960,U_965) ) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_965] :
( ? [U_964] :
( ! [U_967] :
( in(U_967,U_964)
| ! [U_962] :
( U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965) ) )
& ! [U_966] :
( ? [U_961] :
( U_966 = singleton(U_961)
& in(U_961,U_965)
& in(U_961,U_965) )
| ~ in(U_966,U_964) ) )
| ? [U_960,U_959,U_958] :
( U_959 != U_958
& U_958 = singleton(U_960)
& in(U_960,U_965)
& U_959 = singleton(U_960)
& in(U_960,U_965) ) ),
inference(miniscope,[status(thm)],[f_221_2]) ).
fof(f_221_4,plain,
! [U_965] :
( ? [U_964] :
( ! [U_967] :
( in(U_967,U_964)
| ! [U_962] :
( U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965) ) )
& ! [U_966] :
( ? [U_961] :
( U_966 = singleton(U_961)
& in(U_961,U_965)
& in(U_961,U_965) )
| ~ in(U_966,U_964) ) )
| ? [U_959,U_958] :
( U_959 != U_958
& U_958 = singleton(sK194(U_965))
& in(sK194(U_965),U_965)
& U_959 = singleton(sK194(U_965))
& in(sK194(U_965),U_965) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_960,sK194(U_965))],[f_221_3]) ).
fof(f_221_5,plain,
! [U_965] :
( ? [U_964] :
( ! [U_967] :
( in(U_967,U_964)
| ! [U_962] :
( U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965) ) )
& ! [U_966] :
( ? [U_961] :
( U_966 = singleton(U_961)
& in(U_961,U_965)
& in(U_961,U_965) )
| ~ in(U_966,U_964) ) )
| ? [U_958] :
( sK195(U_965) != U_958
& U_958 = singleton(sK194(U_965))
& in(sK194(U_965),U_965)
& sK195(U_965) = singleton(sK194(U_965))
& in(sK194(U_965),U_965) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_959,sK195(U_965))],[f_221_4]) ).
fof(f_221_6,plain,
! [U_965] :
( ? [U_964] :
( ! [U_967] :
( in(U_967,U_964)
| ! [U_962] :
( U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965) ) )
& ! [U_966] :
( ? [U_961] :
( U_966 = singleton(U_961)
& in(U_961,U_965)
& in(U_961,U_965) )
| ~ in(U_966,U_964) ) )
| ( sK195(U_965) != sK196(U_965)
& sK196(U_965) = singleton(sK194(U_965))
& in(sK194(U_965),U_965)
& sK195(U_965) = singleton(sK194(U_965))
& in(sK194(U_965),U_965) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_958,sK196(U_965))],[f_221_5]) ).
fof(f_221_7,plain,
! [U_965] :
( ( ! [U_967] :
( in(U_967,sK197(U_965))
| ! [U_962] :
( U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965) ) )
& ! [U_966] :
( ? [U_961] :
( U_966 = singleton(U_961)
& in(U_961,U_965)
& in(U_961,U_965) )
| ~ in(U_966,sK197(U_965)) ) )
| ( sK195(U_965) != sK196(U_965)
& sK196(U_965) = singleton(sK194(U_965))
& in(sK194(U_965),U_965)
& sK195(U_965) = singleton(sK194(U_965))
& in(sK194(U_965),U_965) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_964,sK197(U_965))],[f_221_6]) ).
fof(f_221_8,plain,
! [U_965] :
( ( ! [U_967] :
( in(U_967,sK197(U_965))
| ! [U_962] :
( U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965) ) )
& ! [U_966] :
( ( U_966 = singleton(sK198(U_965,U_966))
& in(sK198(U_965,U_966),U_965)
& in(sK198(U_965,U_966),U_965) )
| ~ in(U_966,sK197(U_965)) ) )
| ( sK195(U_965) != sK196(U_965)
& sK196(U_965) = singleton(sK194(U_965))
& in(sK194(U_965),U_965)
& sK195(U_965) = singleton(sK194(U_965))
& in(sK194(U_965),U_965) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_961,sK198(U_965,U_966))],[f_221_7]) ).
fof(f_221_9,plain,
( ! [U_965,U_966] :
( U_966 = singleton(sK198(U_965,U_966))
| ~ sP224(U_965,U_966) )
& ! [U_965,U_966] :
( in(sK198(U_965,U_966),U_965)
| ~ sP224(U_965,U_966) )
& ! [U_965,U_966] :
( in(sK198(U_965,U_966),U_965)
| ~ sP224(U_965,U_966) )
& ! [U_962,U_965,U_966,U_967] :
( in(U_967,sK197(U_965))
| U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965)
| ~ sP225(U_962,U_965,U_966,U_967) )
& ! [U_962,U_965,U_966,U_967] :
( sP224(U_965,U_966)
| ~ in(U_966,sK197(U_965))
| ~ sP225(U_962,U_965,U_966,U_967) )
& ! [U_965] :
( sK195(U_965) != sK196(U_965)
| ~ sP223(U_965) )
& ! [U_965] :
( sK196(U_965) = singleton(sK194(U_965))
| ~ sP223(U_965) )
& ! [U_965] :
( in(sK194(U_965),U_965)
| ~ sP223(U_965) )
& ! [U_965] :
( sK195(U_965) = singleton(sK194(U_965))
| ~ sP223(U_965) )
& ! [U_965] :
( in(sK194(U_965),U_965)
| ~ sP223(U_965) )
& ! [U_962,U_965,U_966,U_967] :
( sP225(U_962,U_965,U_966,U_967)
| sP223(U_965) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223,sP224,sP225])],[f_221_8]) ).
cnf(f_221_10,plain,
( sP225(U_962,U_965,U_966,U_967)
| sP223(U_965) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_11,plain,
( in(sK194(U_965),U_965)
| ~ sP223(U_965) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_12,plain,
( sK195(U_965) = singleton(sK194(U_965))
| ~ sP223(U_965) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_13,plain,
( in(sK194(U_965),U_965)
| ~ sP223(U_965) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_14,plain,
( sK196(U_965) = singleton(sK194(U_965))
| ~ sP223(U_965) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_15,plain,
( sK195(U_965) != sK196(U_965)
| ~ sP223(U_965) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_16,plain,
( sP224(U_965,U_966)
| ~ in(U_966,sK197(U_965))
| ~ sP225(U_962,U_965,U_966,U_967) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_17,plain,
( in(U_967,sK197(U_965))
| U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ in(U_962,U_965)
| ~ sP225(U_962,U_965,U_966,U_967) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_18,plain,
( in(sK198(U_965,U_966),U_965)
| ~ sP224(U_965,U_966) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_19,plain,
( in(sK198(U_965,U_966),U_965)
| ~ sP224(U_965,U_966) ),
inference(clausify,[status(thm)],[f_221_9]) ).
cnf(f_221_20,plain,
( U_966 = singleton(sK198(U_965,U_966))
| ~ sP224(U_965,U_966) ),
inference(clausify,[status(thm)],[f_221_9]) ).
fof(f_222_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ! [J,K] :
( K != singleton(J)
| ~ in(J,A)
| ordered_pair(J,K) != D )
| E != D
| ~ in(E,cartesian_product2(A,B)) ) )
& ( ? [E] :
( ? [J,K] :
( K = singleton(J)
& in(J,A)
& ordered_pair(J,K) = D )
& E = D
& in(E,cartesian_product2(A,B)) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ? [H,I] :
( I = singleton(H)
& in(H,A)
& ordered_pair(H,I) = E )
& C = E
& ? [F,G] :
( G = singleton(F)
& in(F,A)
& ordered_pair(F,G) = D )
& C = D ) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e16_22__wellord2__2]) ).
fof(f_222_2,plain,
! [U_984,U_983] :
( ? [U_982] :
! [U_981] :
( ( in(U_981,U_982)
| ! [U_980] :
( ! [U_979,U_978] :
( U_978 != singleton(U_979)
| ~ in(U_979,U_984)
| ordered_pair(U_979,U_978) != U_981 )
| U_980 != U_981
| ~ in(U_980,cartesian_product2(U_984,U_983)) ) )
& ( ? [U_977] :
( ? [U_976,U_975] :
( U_975 = singleton(U_976)
& in(U_976,U_984)
& ordered_pair(U_976,U_975) = U_981 )
& U_977 = U_981
& in(U_977,cartesian_product2(U_984,U_983)) )
| ~ in(U_981,U_982) ) )
| ? [U_974,U_973,U_972] :
( U_973 != U_972
& ? [U_971,U_970] :
( U_970 = singleton(U_971)
& in(U_971,U_984)
& ordered_pair(U_971,U_970) = U_972 )
& U_974 = U_972
& ? [U_969,U_968] :
( U_968 = singleton(U_969)
& in(U_969,U_984)
& ordered_pair(U_969,U_968) = U_973 )
& U_974 = U_973 ) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ? [U_974,U_973,U_972] :
( U_973 != U_972
& ? [U_971] :
( ? [U_970] :
( U_970 = singleton(U_971)
& ordered_pair(U_971,U_970) = U_972 )
& in(U_971,U_984) )
& U_974 = U_972
& ? [U_969] :
( ? [U_968] :
( U_968 = singleton(U_969)
& ordered_pair(U_969,U_968) = U_973 )
& in(U_969,U_984) )
& U_974 = U_973 ) ),
inference(miniscope,[status(thm)],[f_222_2]) ).
fof(f_222_4,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ? [U_973,U_972] :
( U_973 != U_972
& ? [U_971] :
( ? [U_970] :
( U_970 = singleton(U_971)
& ordered_pair(U_971,U_970) = U_972 )
& in(U_971,U_984) )
& sK199(U_984) = U_972
& ? [U_969] :
( ? [U_968] :
( U_968 = singleton(U_969)
& ordered_pair(U_969,U_968) = U_973 )
& in(U_969,U_984) )
& sK199(U_984) = U_973 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_974,sK199(U_984))],[f_222_3]) ).
fof(f_222_5,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ? [U_972] :
( sK200(U_984) != U_972
& ? [U_971] :
( ? [U_970] :
( U_970 = singleton(U_971)
& ordered_pair(U_971,U_970) = U_972 )
& in(U_971,U_984) )
& sK199(U_984) = U_972
& ? [U_969] :
( ? [U_968] :
( U_968 = singleton(U_969)
& ordered_pair(U_969,U_968) = sK200(U_984) )
& in(U_969,U_984) )
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_973,sK200(U_984))],[f_222_4]) ).
fof(f_222_6,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ( sK200(U_984) != sK201(U_984)
& ? [U_971] :
( ? [U_970] :
( U_970 = singleton(U_971)
& ordered_pair(U_971,U_970) = sK201(U_984) )
& in(U_971,U_984) )
& sK199(U_984) = sK201(U_984)
& ? [U_969] :
( ? [U_968] :
( U_968 = singleton(U_969)
& ordered_pair(U_969,U_968) = sK200(U_984) )
& in(U_969,U_984) )
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_972,sK201(U_984))],[f_222_5]) ).
fof(f_222_7,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ( sK200(U_984) != sK201(U_984)
& ? [U_971] :
( ? [U_970] :
( U_970 = singleton(U_971)
& ordered_pair(U_971,U_970) = sK201(U_984) )
& in(U_971,U_984) )
& sK199(U_984) = sK201(U_984)
& ? [U_968] :
( U_968 = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),U_968) = sK200(U_984) )
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_969,sK202(U_984))],[f_222_6]) ).
fof(f_222_8,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ( sK200(U_984) != sK201(U_984)
& ? [U_971] :
( ? [U_970] :
( U_970 = singleton(U_971)
& ordered_pair(U_971,U_970) = sK201(U_984) )
& in(U_971,U_984) )
& sK199(U_984) = sK201(U_984)
& sK203(U_984) = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_968,sK203(U_984))],[f_222_7]) ).
fof(f_222_9,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ( sK200(U_984) != sK201(U_984)
& ? [U_970] :
( U_970 = singleton(sK204(U_984))
& ordered_pair(sK204(U_984),U_970) = sK201(U_984) )
& in(sK204(U_984),U_984)
& sK199(U_984) = sK201(U_984)
& sK203(U_984) = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_971,sK204(U_984))],[f_222_8]) ).
fof(f_222_10,plain,
! [U_984] :
( ! [U_983] :
? [U_982] :
( ! [U_986] :
( in(U_986,U_982)
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,U_982) ) )
| ( sK200(U_984) != sK201(U_984)
& sK205(U_984) = singleton(sK204(U_984))
& ordered_pair(sK204(U_984),sK205(U_984)) = sK201(U_984)
& in(sK204(U_984),U_984)
& sK199(U_984) = sK201(U_984)
& sK203(U_984) = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_970,sK205(U_984))],[f_222_9]) ).
fof(f_222_11,plain,
! [U_984] :
( ! [U_983] :
( ! [U_986] :
( in(U_986,sK206(U_984,U_983))
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_976] :
( ? [U_975] :
( U_975 = singleton(U_976)
& ordered_pair(U_976,U_975) = U_985 )
& in(U_976,U_984) ) )
| ~ in(U_985,sK206(U_984,U_983)) ) )
| ( sK200(U_984) != sK201(U_984)
& sK205(U_984) = singleton(sK204(U_984))
& ordered_pair(sK204(U_984),sK205(U_984)) = sK201(U_984)
& in(sK204(U_984),U_984)
& sK199(U_984) = sK201(U_984)
& sK203(U_984) = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_982,sK206(U_984,U_983))],[f_222_10]) ).
fof(f_222_12,plain,
! [U_984] :
( ! [U_983] :
( ! [U_986] :
( in(U_986,sK206(U_984,U_983))
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& ? [U_975] :
( U_975 = singleton(sK207(U_984,U_983,U_985))
& ordered_pair(sK207(U_984,U_983,U_985),U_975) = U_985 )
& in(sK207(U_984,U_983,U_985),U_984) )
| ~ in(U_985,sK206(U_984,U_983)) ) )
| ( sK200(U_984) != sK201(U_984)
& sK205(U_984) = singleton(sK204(U_984))
& ordered_pair(sK204(U_984),sK205(U_984)) = sK201(U_984)
& in(sK204(U_984),U_984)
& sK199(U_984) = sK201(U_984)
& sK203(U_984) = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_976,sK207(U_984,U_983,U_985))],[f_222_11]) ).
fof(f_222_13,plain,
! [U_984] :
( ! [U_983] :
( ! [U_986] :
( in(U_986,sK206(U_984,U_983))
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( ? [U_977] :
( U_977 = U_985
& in(U_977,cartesian_product2(U_984,U_983)) )
& sK208(U_984,U_983,U_985) = singleton(sK207(U_984,U_983,U_985))
& ordered_pair(sK207(U_984,U_983,U_985),sK208(U_984,U_983,U_985)) = U_985
& in(sK207(U_984,U_983,U_985),U_984) )
| ~ in(U_985,sK206(U_984,U_983)) ) )
| ( sK200(U_984) != sK201(U_984)
& sK205(U_984) = singleton(sK204(U_984))
& ordered_pair(sK204(U_984),sK205(U_984)) = sK201(U_984)
& in(sK204(U_984),U_984)
& sK199(U_984) = sK201(U_984)
& sK203(U_984) = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_975,sK208(U_984,U_983,U_985))],[f_222_12]) ).
fof(f_222_14,plain,
! [U_984] :
( ! [U_983] :
( ! [U_986] :
( in(U_986,sK206(U_984,U_983))
| ! [U_980] :
( U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983)) )
| ! [U_979] :
( ! [U_978] :
( U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986 )
| ~ in(U_979,U_984) ) )
& ! [U_985] :
( ( sK209(U_984,U_983,U_985) = U_985
& in(sK209(U_984,U_983,U_985),cartesian_product2(U_984,U_983))
& sK208(U_984,U_983,U_985) = singleton(sK207(U_984,U_983,U_985))
& ordered_pair(sK207(U_984,U_983,U_985),sK208(U_984,U_983,U_985)) = U_985
& in(sK207(U_984,U_983,U_985),U_984) )
| ~ in(U_985,sK206(U_984,U_983)) ) )
| ( sK200(U_984) != sK201(U_984)
& sK205(U_984) = singleton(sK204(U_984))
& ordered_pair(sK204(U_984),sK205(U_984)) = sK201(U_984)
& in(sK204(U_984),U_984)
& sK199(U_984) = sK201(U_984)
& sK203(U_984) = singleton(sK202(U_984))
& ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
& in(sK202(U_984),U_984)
& sK199(U_984) = sK200(U_984) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_977,sK209(U_984,U_983,U_985))],[f_222_13]) ).
fof(f_222_15,plain,
( ! [U_983,U_984,U_985] :
( sK209(U_984,U_983,U_985) = U_985
| ~ sP227(U_983,U_984,U_985) )
& ! [U_983,U_984,U_985] :
( in(sK209(U_984,U_983,U_985),cartesian_product2(U_984,U_983))
| ~ sP227(U_983,U_984,U_985) )
& ! [U_983,U_984,U_985] :
( sK208(U_984,U_983,U_985) = singleton(sK207(U_984,U_983,U_985))
| ~ sP227(U_983,U_984,U_985) )
& ! [U_983,U_984,U_985] :
( ordered_pair(sK207(U_984,U_983,U_985),sK208(U_984,U_983,U_985)) = U_985
| ~ sP227(U_983,U_984,U_985) )
& ! [U_983,U_984,U_985] :
( in(sK207(U_984,U_983,U_985),U_984)
| ~ sP227(U_983,U_984,U_985) )
& ! [U_983,U_984,U_979,U_980,U_986,U_985,U_978] :
( in(U_986,sK206(U_984,U_983))
| U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983))
| U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986
| ~ in(U_979,U_984)
| ~ sP228(U_983,U_984,U_979,U_980,U_986,U_985,U_978) )
& ! [U_983,U_984,U_979,U_980,U_986,U_985,U_978] :
( sP227(U_983,U_984,U_985)
| ~ in(U_985,sK206(U_984,U_983))
| ~ sP228(U_983,U_984,U_979,U_980,U_986,U_985,U_978) )
& ! [U_984] :
( sK200(U_984) != sK201(U_984)
| ~ sP226(U_984) )
& ! [U_984] :
( sK205(U_984) = singleton(sK204(U_984))
| ~ sP226(U_984) )
& ! [U_984] :
( ordered_pair(sK204(U_984),sK205(U_984)) = sK201(U_984)
| ~ sP226(U_984) )
& ! [U_984] :
( in(sK204(U_984),U_984)
| ~ sP226(U_984) )
& ! [U_984] :
( sK199(U_984) = sK201(U_984)
| ~ sP226(U_984) )
& ! [U_984] :
( sK203(U_984) = singleton(sK202(U_984))
| ~ sP226(U_984) )
& ! [U_984] :
( ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
| ~ sP226(U_984) )
& ! [U_984] :
( in(sK202(U_984),U_984)
| ~ sP226(U_984) )
& ! [U_984] :
( sK199(U_984) = sK200(U_984)
| ~ sP226(U_984) )
& ! [U_983,U_984,U_979,U_980,U_986,U_985,U_978] :
( sP228(U_983,U_984,U_979,U_980,U_986,U_985,U_978)
| sP226(U_984) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226,sP227,sP228])],[f_222_14]) ).
cnf(f_222_16,plain,
( sP228(U_983,U_984,U_979,U_980,U_986,U_985,U_978)
| sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_17,plain,
( sK199(U_984) = sK200(U_984)
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_18,plain,
( in(sK202(U_984),U_984)
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_19,plain,
( ordered_pair(sK202(U_984),sK203(U_984)) = sK200(U_984)
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_20,plain,
( sK203(U_984) = singleton(sK202(U_984))
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_21,plain,
( sK199(U_984) = sK201(U_984)
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_22,plain,
( in(sK204(U_984),U_984)
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_23,plain,
( ordered_pair(sK204(U_984),sK205(U_984)) = sK201(U_984)
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_24,plain,
( sK205(U_984) = singleton(sK204(U_984))
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_25,plain,
( sK200(U_984) != sK201(U_984)
| ~ sP226(U_984) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_26,plain,
( sP227(U_983,U_984,U_985)
| ~ in(U_985,sK206(U_984,U_983))
| ~ sP228(U_983,U_984,U_979,U_980,U_986,U_985,U_978) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_27,plain,
( in(U_986,sK206(U_984,U_983))
| U_980 != U_986
| ~ in(U_980,cartesian_product2(U_984,U_983))
| U_978 != singleton(U_979)
| ordered_pair(U_979,U_978) != U_986
| ~ in(U_979,U_984)
| ~ sP228(U_983,U_984,U_979,U_980,U_986,U_985,U_978) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_28,plain,
( in(sK207(U_984,U_983,U_985),U_984)
| ~ sP227(U_983,U_984,U_985) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_29,plain,
( ordered_pair(sK207(U_984,U_983,U_985),sK208(U_984,U_983,U_985)) = U_985
| ~ sP227(U_983,U_984,U_985) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_30,plain,
( sK208(U_984,U_983,U_985) = singleton(sK207(U_984,U_983,U_985))
| ~ sP227(U_983,U_984,U_985) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_31,plain,
( in(sK209(U_984,U_983,U_985),cartesian_product2(U_984,U_983))
| ~ sP227(U_983,U_984,U_985) ),
inference(clausify,[status(thm)],[f_222_15]) ).
cnf(f_222_32,plain,
( sK209(U_984,U_983,U_985) = U_985
| ~ sP227(U_983,U_984,U_985) ),
inference(clausify,[status(thm)],[f_222_15]) ).
fof(f_223_1,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( ( in(E,D)
| ! [F] :
( ! [K,L] :
( ~ in(ordered_pair(apply(C,K),apply(C,L)),B)
| E != ordered_pair(K,L) )
| F != E
| ~ in(F,cartesian_product2(A,A)) ) )
& ( ? [F] :
( ? [K,L] :
( in(ordered_pair(apply(C,K),apply(C,L)),B)
& E = ordered_pair(K,L) )
& F = E
& in(F,cartesian_product2(A,A)) )
| ~ in(E,D) ) )
| ? [D,E,F] :
( E != F
& ? [I,J] :
( in(ordered_pair(apply(C,I),apply(C,J)),B)
& F = ordered_pair(I,J) )
& D = F
& ? [G,H] :
( in(ordered_pair(apply(C,G),apply(C,H)),B)
& E = ordered_pair(G,H) )
& D = E )
| ~ function(C)
| ~ relation(C)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e6_21__wellord2__1]) ).
fof(f_223_2,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
! [U_1000] :
( ( in(U_1000,U_1001)
| ! [U_999] :
( ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1000 != ordered_pair(U_998,U_997) )
| U_999 != U_1000
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) ) )
& ( ? [U_996] :
( ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1000 = ordered_pair(U_995,U_994) )
& U_996 = U_1000
& in(U_996,cartesian_product2(U_1004,U_1004)) )
| ~ in(U_1000,U_1001) ) )
| ? [U_993,U_992,U_991] :
( U_992 != U_991
& ? [U_990,U_989] :
( in(ordered_pair(apply(U_1002,U_990),apply(U_1002,U_989)),U_1003)
& U_991 = ordered_pair(U_990,U_989) )
& U_993 = U_991
& ? [U_988,U_987] :
( in(ordered_pair(apply(U_1002,U_988),apply(U_1002,U_987)),U_1003)
& U_992 = ordered_pair(U_988,U_987) )
& U_993 = U_992 )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ? [U_993,U_992,U_991] :
( U_992 != U_991
& ? [U_990,U_989] :
( in(ordered_pair(apply(U_1002,U_990),apply(U_1002,U_989)),U_1003)
& U_991 = ordered_pair(U_990,U_989) )
& U_993 = U_991
& ? [U_988,U_987] :
( in(ordered_pair(apply(U_1002,U_988),apply(U_1002,U_987)),U_1003)
& U_992 = ordered_pair(U_988,U_987) )
& U_993 = U_992 )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(miniscope,[status(thm)],[f_223_2]) ).
fof(f_223_4,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ? [U_992,U_991] :
( U_992 != U_991
& ? [U_990,U_989] :
( in(ordered_pair(apply(U_1002,U_990),apply(U_1002,U_989)),U_1003)
& U_991 = ordered_pair(U_990,U_989) )
& sK210(U_1004,U_1003,U_1002) = U_991
& ? [U_988,U_987] :
( in(ordered_pair(apply(U_1002,U_988),apply(U_1002,U_987)),U_1003)
& U_992 = ordered_pair(U_988,U_987) )
& sK210(U_1004,U_1003,U_1002) = U_992 )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_993,sK210(U_1004,U_1003,U_1002))],[f_223_3]) ).
fof(f_223_5,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ? [U_991] :
( sK211(U_1004,U_1003,U_1002) != U_991
& ? [U_990,U_989] :
( in(ordered_pair(apply(U_1002,U_990),apply(U_1002,U_989)),U_1003)
& U_991 = ordered_pair(U_990,U_989) )
& sK210(U_1004,U_1003,U_1002) = U_991
& ? [U_988,U_987] :
( in(ordered_pair(apply(U_1002,U_988),apply(U_1002,U_987)),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(U_988,U_987) )
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_992,sK211(U_1004,U_1003,U_1002))],[f_223_4]) ).
fof(f_223_6,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& ? [U_990,U_989] :
( in(ordered_pair(apply(U_1002,U_990),apply(U_1002,U_989)),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(U_990,U_989) )
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& ? [U_988,U_987] :
( in(ordered_pair(apply(U_1002,U_988),apply(U_1002,U_987)),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(U_988,U_987) )
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_991,sK212(U_1004,U_1003,U_1002))],[f_223_5]) ).
fof(f_223_7,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& ? [U_990,U_989] :
( in(ordered_pair(apply(U_1002,U_990),apply(U_1002,U_989)),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(U_990,U_989) )
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& ? [U_987] :
( in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,U_987)),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),U_987) )
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_988,sK213(U_1004,U_1003,U_1002))],[f_223_6]) ).
fof(f_223_8,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& ? [U_990,U_989] :
( in(ordered_pair(apply(U_1002,U_990),apply(U_1002,U_989)),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(U_990,U_989) )
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_987,sK214(U_1004,U_1003,U_1002))],[f_223_7]) ).
fof(f_223_9,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& ? [U_989] :
( in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,U_989)),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),U_989) )
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_990,sK215(U_1004,U_1003,U_1002))],[f_223_8]) ).
fof(f_223_10,plain,
! [U_1004,U_1003,U_1002] :
( ? [U_1001] :
( ! [U_1006] :
( in(U_1006,U_1001)
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,U_1001) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,sK216(U_1004,U_1003,U_1002))),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),sK216(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_989,sK216(U_1004,U_1003,U_1002))],[f_223_9]) ).
fof(f_223_11,plain,
! [U_1004,U_1003,U_1002] :
( ( ! [U_1006] :
( in(U_1006,sK217(U_1004,U_1003,U_1002))
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_995,U_994] :
( in(ordered_pair(apply(U_1002,U_995),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(U_995,U_994) ) )
| ~ in(U_1005,sK217(U_1004,U_1003,U_1002)) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,sK216(U_1004,U_1003,U_1002))),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),sK216(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_1001,sK217(U_1004,U_1003,U_1002))],[f_223_10]) ).
fof(f_223_12,plain,
! [U_1004,U_1003,U_1002] :
( ( ! [U_1006] :
( in(U_1006,sK217(U_1004,U_1003,U_1002))
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& ? [U_994] :
( in(ordered_pair(apply(U_1002,sK218(U_1004,U_1003,U_1002,U_1005)),apply(U_1002,U_994)),U_1003)
& U_1005 = ordered_pair(sK218(U_1004,U_1003,U_1002,U_1005),U_994) ) )
| ~ in(U_1005,sK217(U_1004,U_1003,U_1002)) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,sK216(U_1004,U_1003,U_1002))),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),sK216(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_995,sK218(U_1004,U_1003,U_1002,U_1005))],[f_223_11]) ).
fof(f_223_13,plain,
! [U_1004,U_1003,U_1002] :
( ( ! [U_1006] :
( in(U_1006,sK217(U_1004,U_1003,U_1002))
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( ? [U_996] :
( U_996 = U_1005
& in(U_996,cartesian_product2(U_1004,U_1004)) )
& in(ordered_pair(apply(U_1002,sK218(U_1004,U_1003,U_1002,U_1005)),apply(U_1002,sK219(U_1004,U_1003,U_1002,U_1005))),U_1003)
& U_1005 = ordered_pair(sK218(U_1004,U_1003,U_1002,U_1005),sK219(U_1004,U_1003,U_1002,U_1005)) )
| ~ in(U_1005,sK217(U_1004,U_1003,U_1002)) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,sK216(U_1004,U_1003,U_1002))),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),sK216(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_994,sK219(U_1004,U_1003,U_1002,U_1005))],[f_223_12]) ).
fof(f_223_14,plain,
! [U_1004,U_1003,U_1002] :
( ( ! [U_1006] :
( in(U_1006,sK217(U_1004,U_1003,U_1002))
| ! [U_999] :
( U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004)) )
| ! [U_998,U_997] :
( ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997) ) )
& ! [U_1005] :
( ( sK220(U_1004,U_1003,U_1002,U_1005) = U_1005
& in(sK220(U_1004,U_1003,U_1002,U_1005),cartesian_product2(U_1004,U_1004))
& in(ordered_pair(apply(U_1002,sK218(U_1004,U_1003,U_1002,U_1005)),apply(U_1002,sK219(U_1004,U_1003,U_1002,U_1005))),U_1003)
& U_1005 = ordered_pair(sK218(U_1004,U_1003,U_1002,U_1005),sK219(U_1004,U_1003,U_1002,U_1005)) )
| ~ in(U_1005,sK217(U_1004,U_1003,U_1002)) ) )
| ( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,sK216(U_1004,U_1003,U_1002))),U_1003)
& sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),sK216(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
& in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
& sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
& sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002) )
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_996,sK220(U_1004,U_1003,U_1002,U_1005))],[f_223_13]) ).
fof(f_223_15,plain,
( ! [U_1005,U_1002,U_1003,U_1004] :
( sK220(U_1004,U_1003,U_1002,U_1005) = U_1005
| ~ sP230(U_1005,U_1002,U_1003,U_1004) )
& ! [U_1005,U_1002,U_1003,U_1004] :
( in(sK220(U_1004,U_1003,U_1002,U_1005),cartesian_product2(U_1004,U_1004))
| ~ sP230(U_1005,U_1002,U_1003,U_1004) )
& ! [U_1005,U_1002,U_1003,U_1004] :
( in(ordered_pair(apply(U_1002,sK218(U_1004,U_1003,U_1002,U_1005)),apply(U_1002,sK219(U_1004,U_1003,U_1002,U_1005))),U_1003)
| ~ sP230(U_1005,U_1002,U_1003,U_1004) )
& ! [U_1005,U_1002,U_1003,U_1004] :
( U_1005 = ordered_pair(sK218(U_1004,U_1003,U_1002,U_1005),sK219(U_1004,U_1003,U_1002,U_1005))
| ~ sP230(U_1005,U_1002,U_1003,U_1004) )
& ! [U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997] :
( in(U_1006,sK217(U_1004,U_1003,U_1002))
| U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004))
| ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997)
| ~ sP231(U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997) )
& ! [U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997] :
( sP230(U_1005,U_1002,U_1003,U_1004)
| ~ in(U_1005,sK217(U_1004,U_1003,U_1002))
| ~ sP231(U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997) )
& ! [U_1002,U_1003,U_1004] :
( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
| ~ sP229(U_1002,U_1003,U_1004) )
& ! [U_1002,U_1003,U_1004] :
( in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,sK216(U_1004,U_1003,U_1002))),U_1003)
| ~ sP229(U_1002,U_1003,U_1004) )
& ! [U_1002,U_1003,U_1004] :
( sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),sK216(U_1004,U_1003,U_1002))
| ~ sP229(U_1002,U_1003,U_1004) )
& ! [U_1002,U_1003,U_1004] :
( sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
| ~ sP229(U_1002,U_1003,U_1004) )
& ! [U_1002,U_1003,U_1004] :
( in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
| ~ sP229(U_1002,U_1003,U_1004) )
& ! [U_1002,U_1003,U_1004] :
( sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
| ~ sP229(U_1002,U_1003,U_1004) )
& ! [U_1002,U_1003,U_1004] :
( sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002)
| ~ sP229(U_1002,U_1003,U_1004) )
& ! [U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997] :
( sP231(U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997)
| sP229(U_1002,U_1003,U_1004)
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229,sP230,sP231])],[f_223_14]) ).
cnf(f_223_16,plain,
( sP231(U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997)
| sP229(U_1002,U_1003,U_1004)
| ~ function(U_1002)
| ~ relation(U_1002)
| ~ relation(U_1003) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_17,plain,
( sK210(U_1004,U_1003,U_1002) = sK211(U_1004,U_1003,U_1002)
| ~ sP229(U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_18,plain,
( sK211(U_1004,U_1003,U_1002) = ordered_pair(sK213(U_1004,U_1003,U_1002),sK214(U_1004,U_1003,U_1002))
| ~ sP229(U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_19,plain,
( in(ordered_pair(apply(U_1002,sK213(U_1004,U_1003,U_1002)),apply(U_1002,sK214(U_1004,U_1003,U_1002))),U_1003)
| ~ sP229(U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_20,plain,
( sK210(U_1004,U_1003,U_1002) = sK212(U_1004,U_1003,U_1002)
| ~ sP229(U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_21,plain,
( sK212(U_1004,U_1003,U_1002) = ordered_pair(sK215(U_1004,U_1003,U_1002),sK216(U_1004,U_1003,U_1002))
| ~ sP229(U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_22,plain,
( in(ordered_pair(apply(U_1002,sK215(U_1004,U_1003,U_1002)),apply(U_1002,sK216(U_1004,U_1003,U_1002))),U_1003)
| ~ sP229(U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_23,plain,
( sK211(U_1004,U_1003,U_1002) != sK212(U_1004,U_1003,U_1002)
| ~ sP229(U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_24,plain,
( sP230(U_1005,U_1002,U_1003,U_1004)
| ~ in(U_1005,sK217(U_1004,U_1003,U_1002))
| ~ sP231(U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_25,plain,
( in(U_1006,sK217(U_1004,U_1003,U_1002))
| U_999 != U_1006
| ~ in(U_999,cartesian_product2(U_1004,U_1004))
| ~ in(ordered_pair(apply(U_1002,U_998),apply(U_1002,U_997)),U_1003)
| U_1006 != ordered_pair(U_998,U_997)
| ~ sP231(U_1006,U_1005,U_999,U_1002,U_1003,U_998,U_1004,U_997) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_26,plain,
( U_1005 = ordered_pair(sK218(U_1004,U_1003,U_1002,U_1005),sK219(U_1004,U_1003,U_1002,U_1005))
| ~ sP230(U_1005,U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_27,plain,
( in(ordered_pair(apply(U_1002,sK218(U_1004,U_1003,U_1002,U_1005)),apply(U_1002,sK219(U_1004,U_1003,U_1002,U_1005))),U_1003)
| ~ sP230(U_1005,U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_28,plain,
( in(sK220(U_1004,U_1003,U_1002,U_1005),cartesian_product2(U_1004,U_1004))
| ~ sP230(U_1005,U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
cnf(f_223_29,plain,
( sK220(U_1004,U_1003,U_1002,U_1005) = U_1005
| ~ sP230(U_1005,U_1002,U_1003,U_1004) ),
inference(clausify,[status(thm)],[f_223_15]) ).
fof(f_224_1,plain,
! [A] :
( ? [B] :
! [C] :
( ( in(C,B)
| ! [D] :
( ~ ordinal(C)
| D != C
| ~ in(D,A) ) )
& ( ? [D] :
( ordinal(C)
& D = C
& in(D,A) )
| ~ in(C,B) ) )
| ? [B,C,D] :
( C != D
& ordinal(D)
& B = D
& ordinal(C)
& B = C ) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e6_22__wellord2__1]) ).
fof(f_224_2,plain,
! [U_1014] :
( ? [U_1013] :
! [U_1012] :
( ( in(U_1012,U_1013)
| ! [U_1011] :
( ~ ordinal(U_1012)
| U_1011 != U_1012
| ~ in(U_1011,U_1014) ) )
& ( ? [U_1010] :
( ordinal(U_1012)
& U_1010 = U_1012
& in(U_1010,U_1014) )
| ~ in(U_1012,U_1013) ) )
| ? [U_1009,U_1008,U_1007] :
( U_1008 != U_1007
& ordinal(U_1007)
& U_1009 = U_1007
& ordinal(U_1008)
& U_1009 = U_1008 ) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
( ! [U_1014] :
? [U_1013] :
( ! [U_1016] :
( in(U_1016,U_1013)
| ! [U_1011] :
( U_1011 != U_1016
| ~ in(U_1011,U_1014) )
| ~ ordinal(U_1016) )
& ! [U_1015] :
( ( ? [U_1010] :
( U_1010 = U_1015
& in(U_1010,U_1014) )
& ordinal(U_1015) )
| ~ in(U_1015,U_1013) ) )
| ? [U_1009,U_1008,U_1007] :
( U_1008 != U_1007
& ordinal(U_1007)
& U_1009 = U_1007
& ordinal(U_1008)
& U_1009 = U_1008 ) ),
inference(miniscope,[status(thm)],[f_224_2]) ).
fof(f_224_4,plain,
( ! [U_1014] :
? [U_1013] :
( ! [U_1016] :
( in(U_1016,U_1013)
| ! [U_1011] :
( U_1011 != U_1016
| ~ in(U_1011,U_1014) )
| ~ ordinal(U_1016) )
& ! [U_1015] :
( ( ? [U_1010] :
( U_1010 = U_1015
& in(U_1010,U_1014) )
& ordinal(U_1015) )
| ~ in(U_1015,U_1013) ) )
| ? [U_1008,U_1007] :
( U_1008 != U_1007
& ordinal(U_1007)
& sK221 = U_1007
& ordinal(U_1008)
& sK221 = U_1008 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_1009,sK221)],[f_224_3]) ).
fof(f_224_5,plain,
( ! [U_1014] :
? [U_1013] :
( ! [U_1016] :
( in(U_1016,U_1013)
| ! [U_1011] :
( U_1011 != U_1016
| ~ in(U_1011,U_1014) )
| ~ ordinal(U_1016) )
& ! [U_1015] :
( ( ? [U_1010] :
( U_1010 = U_1015
& in(U_1010,U_1014) )
& ordinal(U_1015) )
| ~ in(U_1015,U_1013) ) )
| ? [U_1007] :
( sK222 != U_1007
& ordinal(U_1007)
& sK221 = U_1007
& ordinal(sK222)
& sK221 = sK222 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_1008,sK222)],[f_224_4]) ).
fof(f_224_6,plain,
( ! [U_1014] :
? [U_1013] :
( ! [U_1016] :
( in(U_1016,U_1013)
| ! [U_1011] :
( U_1011 != U_1016
| ~ in(U_1011,U_1014) )
| ~ ordinal(U_1016) )
& ! [U_1015] :
( ( ? [U_1010] :
( U_1010 = U_1015
& in(U_1010,U_1014) )
& ordinal(U_1015) )
| ~ in(U_1015,U_1013) ) )
| ( sK222 != sK223
& ordinal(sK223)
& sK221 = sK223
& ordinal(sK222)
& sK221 = sK222 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_1007,sK223)],[f_224_5]) ).
fof(f_224_7,plain,
( ! [U_1014] :
( ! [U_1016] :
( in(U_1016,sK224(U_1014))
| ! [U_1011] :
( U_1011 != U_1016
| ~ in(U_1011,U_1014) )
| ~ ordinal(U_1016) )
& ! [U_1015] :
( ( ? [U_1010] :
( U_1010 = U_1015
& in(U_1010,U_1014) )
& ordinal(U_1015) )
| ~ in(U_1015,sK224(U_1014)) ) )
| ( sK222 != sK223
& ordinal(sK223)
& sK221 = sK223
& ordinal(sK222)
& sK221 = sK222 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_1013,sK224(U_1014))],[f_224_6]) ).
fof(f_224_8,plain,
( ! [U_1014] :
( ! [U_1016] :
( in(U_1016,sK224(U_1014))
| ! [U_1011] :
( U_1011 != U_1016
| ~ in(U_1011,U_1014) )
| ~ ordinal(U_1016) )
& ! [U_1015] :
( ( sK225(U_1014,U_1015) = U_1015
& in(sK225(U_1014,U_1015),U_1014)
& ordinal(U_1015) )
| ~ in(U_1015,sK224(U_1014)) ) )
| ( sK222 != sK223
& ordinal(sK223)
& sK221 = sK223
& ordinal(sK222)
& sK221 = sK222 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_1010,sK225(U_1014,U_1015))],[f_224_7]) ).
fof(f_224_9,plain,
( ! [U_1015,U_1014] :
( sK225(U_1014,U_1015) = U_1015
| ~ sP233(U_1015,U_1014) )
& ! [U_1015,U_1014] :
( in(sK225(U_1014,U_1015),U_1014)
| ~ sP233(U_1015,U_1014) )
& ! [U_1015,U_1014] :
( ordinal(U_1015)
| ~ sP233(U_1015,U_1014) )
& ! [U_1015,U_1016,U_1011,U_1014] :
( in(U_1016,sK224(U_1014))
| U_1011 != U_1016
| ~ in(U_1011,U_1014)
| ~ ordinal(U_1016)
| ~ sP234(U_1015,U_1016,U_1011,U_1014) )
& ! [U_1015,U_1016,U_1011,U_1014] :
( sP233(U_1015,U_1014)
| ~ in(U_1015,sK224(U_1014))
| ~ sP234(U_1015,U_1016,U_1011,U_1014) )
& ( sK222 != sK223
| ~ sP232 )
& ( ordinal(sK223)
| ~ sP232 )
& ( sK221 = sK223
| ~ sP232 )
& ( ordinal(sK222)
| ~ sP232 )
& ( sK221 = sK222
| ~ sP232 )
& ! [U_1015,U_1016,U_1011,U_1014] :
( sP234(U_1015,U_1016,U_1011,U_1014)
| sP232 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232,sP233,sP234])],[f_224_8]) ).
cnf(f_224_10,plain,
( sP234(U_1015,U_1016,U_1011,U_1014)
| sP232 ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_11,plain,
( sK221 = sK222
| ~ sP232 ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_12,plain,
( ordinal(sK222)
| ~ sP232 ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_13,plain,
( sK221 = sK223
| ~ sP232 ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_14,plain,
( ordinal(sK223)
| ~ sP232 ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_15,plain,
( sK222 != sK223
| ~ sP232 ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_16,plain,
( sP233(U_1015,U_1014)
| ~ in(U_1015,sK224(U_1014))
| ~ sP234(U_1015,U_1016,U_1011,U_1014) ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_17,plain,
( in(U_1016,sK224(U_1014))
| U_1011 != U_1016
| ~ in(U_1011,U_1014)
| ~ ordinal(U_1016)
| ~ sP234(U_1015,U_1016,U_1011,U_1014) ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_18,plain,
( ordinal(U_1015)
| ~ sP233(U_1015,U_1014) ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_19,plain,
( in(sK225(U_1014,U_1015),U_1014)
| ~ sP233(U_1015,U_1014) ),
inference(clausify,[status(thm)],[f_224_9]) ).
cnf(f_224_20,plain,
( sK225(U_1014,U_1015) = U_1015
| ~ sP233(U_1015,U_1014) ),
inference(clausify,[status(thm)],[f_224_9]) ).
fof(f_225_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ! [H] :
( ~ in(H,A)
| D != H
| ~ ordinal(H) )
| E != D
| ~ in(E,succ(B)) ) )
& ( ? [E] :
( ? [H] :
( in(H,A)
& D = H
& ordinal(H) )
& E = D
& in(E,succ(B)) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ? [G] :
( in(G,A)
& E = G
& ordinal(G) )
& C = E
& ? [F] :
( in(F,A)
& D = F
& ordinal(F) )
& C = D )
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e8_6__wellord2__1]) ).
fof(f_225_2,plain,
! [U_1029,U_1028] :
( ? [U_1027] :
! [U_1026] :
( ( in(U_1026,U_1027)
| ! [U_1025] :
( ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1026 != U_1024
| ~ ordinal(U_1024) )
| U_1025 != U_1026
| ~ in(U_1025,succ(U_1028)) ) )
& ( ? [U_1023] :
( ? [U_1022] :
( in(U_1022,U_1029)
& U_1026 = U_1022
& ordinal(U_1022) )
& U_1023 = U_1026
& in(U_1023,succ(U_1028)) )
| ~ in(U_1026,U_1027) ) )
| ? [U_1021,U_1020,U_1019] :
( U_1020 != U_1019
& ? [U_1018] :
( in(U_1018,U_1029)
& U_1019 = U_1018
& ordinal(U_1018) )
& U_1021 = U_1019
& ? [U_1017] :
( in(U_1017,U_1029)
& U_1020 = U_1017
& ordinal(U_1017) )
& U_1021 = U_1020 )
| ~ ordinal(U_1028) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_1029,U_1028] :
( ? [U_1027] :
( ! [U_1031] :
( in(U_1031,U_1027)
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& ? [U_1022] :
( in(U_1022,U_1029)
& U_1030 = U_1022
& ordinal(U_1022) ) )
| ~ in(U_1030,U_1027) ) )
| ? [U_1021,U_1020,U_1019] :
( U_1020 != U_1019
& ? [U_1018] :
( in(U_1018,U_1029)
& U_1019 = U_1018
& ordinal(U_1018) )
& U_1021 = U_1019
& ? [U_1017] :
( in(U_1017,U_1029)
& U_1020 = U_1017
& ordinal(U_1017) )
& U_1021 = U_1020 )
| ~ ordinal(U_1028) ),
inference(miniscope,[status(thm)],[f_225_2]) ).
fof(f_225_4,plain,
! [U_1029,U_1028] :
( ? [U_1027] :
( ! [U_1031] :
( in(U_1031,U_1027)
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& ? [U_1022] :
( in(U_1022,U_1029)
& U_1030 = U_1022
& ordinal(U_1022) ) )
| ~ in(U_1030,U_1027) ) )
| ? [U_1020,U_1019] :
( U_1020 != U_1019
& ? [U_1018] :
( in(U_1018,U_1029)
& U_1019 = U_1018
& ordinal(U_1018) )
& sK226(U_1029,U_1028) = U_1019
& ? [U_1017] :
( in(U_1017,U_1029)
& U_1020 = U_1017
& ordinal(U_1017) )
& sK226(U_1029,U_1028) = U_1020 )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_1021,sK226(U_1029,U_1028))],[f_225_3]) ).
fof(f_225_5,plain,
! [U_1029,U_1028] :
( ? [U_1027] :
( ! [U_1031] :
( in(U_1031,U_1027)
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& ? [U_1022] :
( in(U_1022,U_1029)
& U_1030 = U_1022
& ordinal(U_1022) ) )
| ~ in(U_1030,U_1027) ) )
| ? [U_1019] :
( sK227(U_1029,U_1028) != U_1019
& ? [U_1018] :
( in(U_1018,U_1029)
& U_1019 = U_1018
& ordinal(U_1018) )
& sK226(U_1029,U_1028) = U_1019
& ? [U_1017] :
( in(U_1017,U_1029)
& sK227(U_1029,U_1028) = U_1017
& ordinal(U_1017) )
& sK226(U_1029,U_1028) = sK227(U_1029,U_1028) )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_1020,sK227(U_1029,U_1028))],[f_225_4]) ).
fof(f_225_6,plain,
! [U_1029,U_1028] :
( ? [U_1027] :
( ! [U_1031] :
( in(U_1031,U_1027)
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& ? [U_1022] :
( in(U_1022,U_1029)
& U_1030 = U_1022
& ordinal(U_1022) ) )
| ~ in(U_1030,U_1027) ) )
| ( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
& ? [U_1018] :
( in(U_1018,U_1029)
& sK228(U_1029,U_1028) = U_1018
& ordinal(U_1018) )
& sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
& ? [U_1017] :
( in(U_1017,U_1029)
& sK227(U_1029,U_1028) = U_1017
& ordinal(U_1017) )
& sK226(U_1029,U_1028) = sK227(U_1029,U_1028) )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_1019,sK228(U_1029,U_1028))],[f_225_5]) ).
fof(f_225_7,plain,
! [U_1029,U_1028] :
( ? [U_1027] :
( ! [U_1031] :
( in(U_1031,U_1027)
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& ? [U_1022] :
( in(U_1022,U_1029)
& U_1030 = U_1022
& ordinal(U_1022) ) )
| ~ in(U_1030,U_1027) ) )
| ( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
& ? [U_1018] :
( in(U_1018,U_1029)
& sK228(U_1029,U_1028) = U_1018
& ordinal(U_1018) )
& sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
& in(sK229(U_1029,U_1028),U_1029)
& sK227(U_1029,U_1028) = sK229(U_1029,U_1028)
& ordinal(sK229(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK227(U_1029,U_1028) )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_1017,sK229(U_1029,U_1028))],[f_225_6]) ).
fof(f_225_8,plain,
! [U_1029,U_1028] :
( ? [U_1027] :
( ! [U_1031] :
( in(U_1031,U_1027)
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& ? [U_1022] :
( in(U_1022,U_1029)
& U_1030 = U_1022
& ordinal(U_1022) ) )
| ~ in(U_1030,U_1027) ) )
| ( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
& in(sK230(U_1029,U_1028),U_1029)
& sK228(U_1029,U_1028) = sK230(U_1029,U_1028)
& ordinal(sK230(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
& in(sK229(U_1029,U_1028),U_1029)
& sK227(U_1029,U_1028) = sK229(U_1029,U_1028)
& ordinal(sK229(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK227(U_1029,U_1028) )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_1018,sK230(U_1029,U_1028))],[f_225_7]) ).
fof(f_225_9,plain,
! [U_1029,U_1028] :
( ( ! [U_1031] :
( in(U_1031,sK231(U_1029,U_1028))
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& ? [U_1022] :
( in(U_1022,U_1029)
& U_1030 = U_1022
& ordinal(U_1022) ) )
| ~ in(U_1030,sK231(U_1029,U_1028)) ) )
| ( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
& in(sK230(U_1029,U_1028),U_1029)
& sK228(U_1029,U_1028) = sK230(U_1029,U_1028)
& ordinal(sK230(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
& in(sK229(U_1029,U_1028),U_1029)
& sK227(U_1029,U_1028) = sK229(U_1029,U_1028)
& ordinal(sK229(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK227(U_1029,U_1028) )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_1027,sK231(U_1029,U_1028))],[f_225_8]) ).
fof(f_225_10,plain,
! [U_1029,U_1028] :
( ( ! [U_1031] :
( in(U_1031,sK231(U_1029,U_1028))
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( ? [U_1023] :
( U_1023 = U_1030
& in(U_1023,succ(U_1028)) )
& in(sK232(U_1029,U_1028,U_1030),U_1029)
& U_1030 = sK232(U_1029,U_1028,U_1030)
& ordinal(sK232(U_1029,U_1028,U_1030)) )
| ~ in(U_1030,sK231(U_1029,U_1028)) ) )
| ( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
& in(sK230(U_1029,U_1028),U_1029)
& sK228(U_1029,U_1028) = sK230(U_1029,U_1028)
& ordinal(sK230(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
& in(sK229(U_1029,U_1028),U_1029)
& sK227(U_1029,U_1028) = sK229(U_1029,U_1028)
& ordinal(sK229(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK227(U_1029,U_1028) )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_1022,sK232(U_1029,U_1028,U_1030))],[f_225_9]) ).
fof(f_225_11,plain,
! [U_1029,U_1028] :
( ( ! [U_1031] :
( in(U_1031,sK231(U_1029,U_1028))
| ! [U_1025] :
( U_1025 != U_1031
| ~ in(U_1025,succ(U_1028)) )
| ! [U_1024] :
( ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024) ) )
& ! [U_1030] :
( ( sK233(U_1029,U_1028,U_1030) = U_1030
& in(sK233(U_1029,U_1028,U_1030),succ(U_1028))
& in(sK232(U_1029,U_1028,U_1030),U_1029)
& U_1030 = sK232(U_1029,U_1028,U_1030)
& ordinal(sK232(U_1029,U_1028,U_1030)) )
| ~ in(U_1030,sK231(U_1029,U_1028)) ) )
| ( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
& in(sK230(U_1029,U_1028),U_1029)
& sK228(U_1029,U_1028) = sK230(U_1029,U_1028)
& ordinal(sK230(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
& in(sK229(U_1029,U_1028),U_1029)
& sK227(U_1029,U_1028) = sK229(U_1029,U_1028)
& ordinal(sK229(U_1029,U_1028))
& sK226(U_1029,U_1028) = sK227(U_1029,U_1028) )
| ~ ordinal(U_1028) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_1023,sK233(U_1029,U_1028,U_1030))],[f_225_10]) ).
fof(f_225_12,plain,
( ! [U_1028,U_1029,U_1030] :
( sK233(U_1029,U_1028,U_1030) = U_1030
| ~ sP236(U_1028,U_1029,U_1030) )
& ! [U_1028,U_1029,U_1030] :
( in(sK233(U_1029,U_1028,U_1030),succ(U_1028))
| ~ sP236(U_1028,U_1029,U_1030) )
& ! [U_1028,U_1029,U_1030] :
( in(sK232(U_1029,U_1028,U_1030),U_1029)
| ~ sP236(U_1028,U_1029,U_1030) )
& ! [U_1028,U_1029,U_1030] :
( U_1030 = sK232(U_1029,U_1028,U_1030)
| ~ sP236(U_1028,U_1029,U_1030) )
& ! [U_1028,U_1029,U_1030] :
( ordinal(sK232(U_1029,U_1028,U_1030))
| ~ sP236(U_1028,U_1029,U_1030) )
& ! [U_1028,U_1024,U_1029,U_1031,U_1030,U_1025] :
( in(U_1031,sK231(U_1029,U_1028))
| U_1025 != U_1031
| ~ in(U_1025,succ(U_1028))
| ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024)
| ~ sP237(U_1028,U_1024,U_1029,U_1031,U_1030,U_1025) )
& ! [U_1028,U_1024,U_1029,U_1031,U_1030,U_1025] :
( sP236(U_1028,U_1029,U_1030)
| ~ in(U_1030,sK231(U_1029,U_1028))
| ~ sP237(U_1028,U_1024,U_1029,U_1031,U_1030,U_1025) )
& ! [U_1028,U_1029] :
( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( in(sK230(U_1029,U_1028),U_1029)
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( sK228(U_1029,U_1028) = sK230(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( ordinal(sK230(U_1029,U_1028))
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( in(sK229(U_1029,U_1028),U_1029)
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( sK227(U_1029,U_1028) = sK229(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( ordinal(sK229(U_1029,U_1028))
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1029] :
( sK226(U_1029,U_1028) = sK227(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) )
& ! [U_1028,U_1024,U_1029,U_1031,U_1030,U_1025] :
( sP237(U_1028,U_1024,U_1029,U_1031,U_1030,U_1025)
| sP235(U_1028,U_1029)
| ~ ordinal(U_1028) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235,sP236,sP237])],[f_225_11]) ).
cnf(f_225_13,plain,
( sP237(U_1028,U_1024,U_1029,U_1031,U_1030,U_1025)
| sP235(U_1028,U_1029)
| ~ ordinal(U_1028) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_14,plain,
( sK226(U_1029,U_1028) = sK227(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_15,plain,
( ordinal(sK229(U_1029,U_1028))
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_16,plain,
( sK227(U_1029,U_1028) = sK229(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_17,plain,
( in(sK229(U_1029,U_1028),U_1029)
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_18,plain,
( sK226(U_1029,U_1028) = sK228(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_19,plain,
( ordinal(sK230(U_1029,U_1028))
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_20,plain,
( sK228(U_1029,U_1028) = sK230(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_21,plain,
( in(sK230(U_1029,U_1028),U_1029)
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_22,plain,
( sK227(U_1029,U_1028) != sK228(U_1029,U_1028)
| ~ sP235(U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_23,plain,
( sP236(U_1028,U_1029,U_1030)
| ~ in(U_1030,sK231(U_1029,U_1028))
| ~ sP237(U_1028,U_1024,U_1029,U_1031,U_1030,U_1025) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_24,plain,
( in(U_1031,sK231(U_1029,U_1028))
| U_1025 != U_1031
| ~ in(U_1025,succ(U_1028))
| ~ in(U_1024,U_1029)
| U_1031 != U_1024
| ~ ordinal(U_1024)
| ~ sP237(U_1028,U_1024,U_1029,U_1031,U_1030,U_1025) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_25,plain,
( ordinal(sK232(U_1029,U_1028,U_1030))
| ~ sP236(U_1028,U_1029,U_1030) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_26,plain,
( U_1030 = sK232(U_1029,U_1028,U_1030)
| ~ sP236(U_1028,U_1029,U_1030) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_27,plain,
( in(sK232(U_1029,U_1028,U_1030),U_1029)
| ~ sP236(U_1028,U_1029,U_1030) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_28,plain,
( in(sK233(U_1029,U_1028,U_1030),succ(U_1028))
| ~ sP236(U_1028,U_1029,U_1030) ),
inference(clausify,[status(thm)],[f_225_12]) ).
cnf(f_225_29,plain,
( sK233(U_1029,U_1028,U_1030) = U_1030
| ~ sP236(U_1028,U_1029,U_1030) ),
inference(clausify,[status(thm)],[f_225_12]) ).
fof(f_226_1,plain,
! [A,B] :
( ! [C] :
? [D] :
! [E] :
( ( in(E,D)
| ! [F,G] :
( ! [H] :
( ? [I] :
( ~ in(ordered_pair(G,I),B)
& in(I,H) )
| ~ in(G,H)
| F != H )
| ~ in(F,A)
| ordered_pair(F,G) != E )
| ~ in(E,cartesian_product2(A,C)) )
& ( ( ? [F,G] :
( ? [H] :
( ! [I] :
( in(ordered_pair(G,I),B)
| ~ in(I,H) )
& in(G,H)
& F = H )
& in(F,A)
& ordered_pair(F,G) = E )
& in(E,cartesian_product2(A,C)) )
| ~ in(E,D) ) )
| ~ relation(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e10_24__wellord2__1]) ).
fof(f_226_2,plain,
! [U_1044,U_1043] :
( ! [U_1042] :
? [U_1041] :
! [U_1040] :
( ( in(U_1040,U_1041)
| ! [U_1039,U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ~ in(ordered_pair(U_1038,U_1036),U_1043)
& in(U_1036,U_1037) )
| ~ in(U_1038,U_1037)
| U_1039 != U_1037 )
| ~ in(U_1039,U_1044)
| ordered_pair(U_1039,U_1038) != U_1040 )
| ~ in(U_1040,cartesian_product2(U_1044,U_1042)) )
& ( ( ? [U_1035,U_1034] :
( ? [U_1033] :
( ! [U_1032] :
( in(ordered_pair(U_1034,U_1032),U_1043)
| ~ in(U_1032,U_1033) )
& in(U_1034,U_1033)
& U_1035 = U_1033 )
& in(U_1035,U_1044)
& ordered_pair(U_1035,U_1034) = U_1040 )
& in(U_1040,cartesian_product2(U_1044,U_1042)) )
| ~ in(U_1040,U_1041) ) )
| ~ relation(U_1043)
| empty(U_1044) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_1044,U_1043] :
( ! [U_1042] :
? [U_1041] :
( ! [U_1046] :
( in(U_1046,U_1041)
| ! [U_1039] :
( ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ~ in(ordered_pair(U_1038,U_1036),U_1043)
& in(U_1036,U_1037) )
| ~ in(U_1038,U_1037)
| U_1039 != U_1037 )
| ordered_pair(U_1039,U_1038) != U_1046 )
| ~ in(U_1039,U_1044) )
| ~ in(U_1046,cartesian_product2(U_1044,U_1042)) )
& ! [U_1045] :
( ( ? [U_1035] :
( ? [U_1034] :
( ? [U_1033] :
( ! [U_1032] :
( in(ordered_pair(U_1034,U_1032),U_1043)
| ~ in(U_1032,U_1033) )
& in(U_1034,U_1033)
& U_1035 = U_1033 )
& ordered_pair(U_1035,U_1034) = U_1045 )
& in(U_1035,U_1044) )
& in(U_1045,cartesian_product2(U_1044,U_1042)) )
| ~ in(U_1045,U_1041) ) )
| ~ relation(U_1043)
| empty(U_1044) ),
inference(miniscope,[status(thm)],[f_226_2]) ).
fof(f_226_4,plain,
! [U_1044,U_1043] :
( ! [U_1042] :
( ! [U_1046] :
( in(U_1046,sK234(U_1044,U_1043,U_1042))
| ! [U_1039] :
( ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ~ in(ordered_pair(U_1038,U_1036),U_1043)
& in(U_1036,U_1037) )
| ~ in(U_1038,U_1037)
| U_1039 != U_1037 )
| ordered_pair(U_1039,U_1038) != U_1046 )
| ~ in(U_1039,U_1044) )
| ~ in(U_1046,cartesian_product2(U_1044,U_1042)) )
& ! [U_1045] :
( ( ? [U_1035] :
( ? [U_1034] :
( ? [U_1033] :
( ! [U_1032] :
( in(ordered_pair(U_1034,U_1032),U_1043)
| ~ in(U_1032,U_1033) )
& in(U_1034,U_1033)
& U_1035 = U_1033 )
& ordered_pair(U_1035,U_1034) = U_1045 )
& in(U_1035,U_1044) )
& in(U_1045,cartesian_product2(U_1044,U_1042)) )
| ~ in(U_1045,sK234(U_1044,U_1043,U_1042)) ) )
| ~ relation(U_1043)
| empty(U_1044) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_1041,sK234(U_1044,U_1043,U_1042))],[f_226_3]) ).
fof(f_226_5,plain,
! [U_1044,U_1043] :
( ! [U_1042] :
( ! [U_1046] :
( in(U_1046,sK234(U_1044,U_1043,U_1042))
| ! [U_1039] :
( ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ~ in(ordered_pair(U_1038,U_1036),U_1043)
& in(U_1036,U_1037) )
| ~ in(U_1038,U_1037)
| U_1039 != U_1037 )
| ordered_pair(U_1039,U_1038) != U_1046 )
| ~ in(U_1039,U_1044) )
| ~ in(U_1046,cartesian_product2(U_1044,U_1042)) )
& ! [U_1045] :
( ( ? [U_1034] :
( ? [U_1033] :
( ! [U_1032] :
( in(ordered_pair(U_1034,U_1032),U_1043)
| ~ in(U_1032,U_1033) )
& in(U_1034,U_1033)
& sK235(U_1044,U_1043,U_1042,U_1045) = U_1033 )
& ordered_pair(sK235(U_1044,U_1043,U_1042,U_1045),U_1034) = U_1045 )
& in(sK235(U_1044,U_1043,U_1042,U_1045),U_1044)
& in(U_1045,cartesian_product2(U_1044,U_1042)) )
| ~ in(U_1045,sK234(U_1044,U_1043,U_1042)) ) )
| ~ relation(U_1043)
| empty(U_1044) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_1035,sK235(U_1044,U_1043,U_1042,U_1045))],[f_226_4]) ).
fof(f_226_6,plain,
! [U_1044,U_1043] :
( ! [U_1042] :
( ! [U_1046] :
( in(U_1046,sK234(U_1044,U_1043,U_1042))
| ! [U_1039] :
( ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ~ in(ordered_pair(U_1038,U_1036),U_1043)
& in(U_1036,U_1037) )
| ~ in(U_1038,U_1037)
| U_1039 != U_1037 )
| ordered_pair(U_1039,U_1038) != U_1046 )
| ~ in(U_1039,U_1044) )
| ~ in(U_1046,cartesian_product2(U_1044,U_1042)) )
& ! [U_1045] :
( ( ? [U_1033] :
( ! [U_1032] :
( in(ordered_pair(sK236(U_1044,U_1043,U_1042,U_1045),U_1032),U_1043)
| ~ in(U_1032,U_1033) )
& in(sK236(U_1044,U_1043,U_1042,U_1045),U_1033)
& sK235(U_1044,U_1043,U_1042,U_1045) = U_1033 )
& ordered_pair(sK235(U_1044,U_1043,U_1042,U_1045),sK236(U_1044,U_1043,U_1042,U_1045)) = U_1045
& in(sK235(U_1044,U_1043,U_1042,U_1045),U_1044)
& in(U_1045,cartesian_product2(U_1044,U_1042)) )
| ~ in(U_1045,sK234(U_1044,U_1043,U_1042)) ) )
| ~ relation(U_1043)
| empty(U_1044) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_1034,sK236(U_1044,U_1043,U_1042,U_1045))],[f_226_5]) ).
fof(f_226_7,plain,
! [U_1044,U_1043] :
( ! [U_1042] :
( ! [U_1046] :
( in(U_1046,sK234(U_1044,U_1043,U_1042))
| ! [U_1039] :
( ! [U_1038] :
( ! [U_1037] :
( ? [U_1036] :
( ~ in(ordered_pair(U_1038,U_1036),U_1043)
& in(U_1036,U_1037) )
| ~ in(U_1038,U_1037)
| U_1039 != U_1037 )
| ordered_pair(U_1039,U_1038) != U_1046 )
| ~ in(U_1039,U_1044) )
| ~ in(U_1046,cartesian_product2(U_1044,U_1042)) )
& ! [U_1045] :
( ( ! [U_1032] :
( in(ordered_pair(sK236(U_1044,U_1043,U_1042,U_1045),U_1032),U_1043)
| ~ in(U_1032,sK237(U_1044,U_1043,U_1042,U_1045)) )
& in(sK236(U_1044,U_1043,U_1042,U_1045),sK237(U_1044,U_1043,U_1042,U_1045))
& sK235(U_1044,U_1043,U_1042,U_1045) = sK237(U_1044,U_1043,U_1042,U_1045)
& ordered_pair(sK235(U_1044,U_1043,U_1042,U_1045),sK236(U_1044,U_1043,U_1042,U_1045)) = U_1045
& in(sK235(U_1044,U_1043,U_1042,U_1045),U_1044)
& in(U_1045,cartesian_product2(U_1044,U_1042)) )
| ~ in(U_1045,sK234(U_1044,U_1043,U_1042)) ) )
| ~ relation(U_1043)
| empty(U_1044) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_1033,sK237(U_1044,U_1043,U_1042,U_1045))],[f_226_6]) ).
fof(f_226_8,plain,
! [U_1044,U_1043] :
( ! [U_1042] :
( ! [U_1046] :
( in(U_1046,sK234(U_1044,U_1043,U_1042))
| ! [U_1039] :
( ! [U_1038] :
( ! [U_1037] :
( ( ~ in(ordered_pair(U_1038,sK238(U_1044,U_1043,U_1042,U_1046,U_1039,U_1038,U_1037)),U_1043)
& in(sK238(U_1044,U_1043,U_1042,U_1046,U_1039,U_1038,U_1037),U_1037) )
| ~ in(U_1038,U_1037)
| U_1039 != U_1037 )
| ordered_pair(U_1039,U_1038) != U_1046 )
| ~ in(U_1039,U_1044) )
| ~ in(U_1046,cartesian_product2(U_1044,U_1042)) )
& ! [U_1045] :
( ( ! [U_1032] :
( in(ordered_pair(sK236(U_1044,U_1043,U_1042,U_1045),U_1032),U_1043)
| ~ in(U_1032,sK237(U_1044,U_1043,U_1042,U_1045)) )
& in(sK236(U_1044,U_1043,U_1042,U_1045),sK237(U_1044,U_1043,U_1042,U_1045))
& sK235(U_1044,U_1043,U_1042,U_1045) = sK237(U_1044,U_1043,U_1042,U_1045)
& ordered_pair(sK235(U_1044,U_1043,U_1042,U_1045),sK236(U_1044,U_1043,U_1042,U_1045)) = U_1045
& in(sK235(U_1044,U_1043,U_1042,U_1045),U_1044)
& in(U_1045,cartesian_product2(U_1044,U_1042)) )
| ~ in(U_1045,sK234(U_1044,U_1043,U_1042)) ) )
| ~ relation(U_1043)
| empty(U_1044) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_1036,sK238(U_1044,U_1043,U_1042,U_1046,U_1039,U_1038,U_1037))],[f_226_7]) ).
fof(f_226_9,plain,
( ! [U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046] :
( ~ in(ordered_pair(U_1038,sK238(U_1044,U_1043,U_1042,U_1046,U_1039,U_1038,U_1037)),U_1043)
| ~ sP239(U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046) )
& ! [U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046] :
( in(sK238(U_1044,U_1043,U_1042,U_1046,U_1039,U_1038,U_1037),U_1037)
| ~ sP239(U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046) )
& ! [U_1045,U_1042,U_1032,U_1043,U_1044] :
( in(ordered_pair(sK236(U_1044,U_1043,U_1042,U_1045),U_1032),U_1043)
| ~ in(U_1032,sK237(U_1044,U_1043,U_1042,U_1045))
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) )
& ! [U_1045,U_1042,U_1032,U_1043,U_1044] :
( in(sK236(U_1044,U_1043,U_1042,U_1045),sK237(U_1044,U_1043,U_1042,U_1045))
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) )
& ! [U_1045,U_1042,U_1032,U_1043,U_1044] :
( sK235(U_1044,U_1043,U_1042,U_1045) = sK237(U_1044,U_1043,U_1042,U_1045)
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) )
& ! [U_1045,U_1042,U_1032,U_1043,U_1044] :
( ordered_pair(sK235(U_1044,U_1043,U_1042,U_1045),sK236(U_1044,U_1043,U_1042,U_1045)) = U_1045
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) )
& ! [U_1045,U_1042,U_1032,U_1043,U_1044] :
( in(sK235(U_1044,U_1043,U_1042,U_1045),U_1044)
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) )
& ! [U_1045,U_1042,U_1032,U_1043,U_1044] :
( in(U_1045,cartesian_product2(U_1044,U_1042))
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) )
& ! [U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046] :
( in(U_1046,sK234(U_1044,U_1043,U_1042))
| sP239(U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046)
| ~ in(U_1038,U_1037)
| U_1039 != U_1037
| ordered_pair(U_1039,U_1038) != U_1046
| ~ in(U_1039,U_1044)
| ~ in(U_1046,cartesian_product2(U_1044,U_1042))
| ~ sP240(U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046) )
& ! [U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046] :
( sP238(U_1045,U_1042,U_1032,U_1043,U_1044)
| ~ in(U_1045,sK234(U_1044,U_1043,U_1042))
| ~ sP240(U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046) )
& ! [U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046] :
( sP240(U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046)
| ~ relation(U_1043)
| empty(U_1044) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238,sP239,sP240])],[f_226_8]) ).
cnf(f_226_10,plain,
( sP240(U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046)
| ~ relation(U_1043)
| empty(U_1044) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_11,plain,
( sP238(U_1045,U_1042,U_1032,U_1043,U_1044)
| ~ in(U_1045,sK234(U_1044,U_1043,U_1042))
| ~ sP240(U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_12,plain,
( in(U_1046,sK234(U_1044,U_1043,U_1042))
| sP239(U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046)
| ~ in(U_1038,U_1037)
| U_1039 != U_1037
| ordered_pair(U_1039,U_1038) != U_1046
| ~ in(U_1039,U_1044)
| ~ in(U_1046,cartesian_product2(U_1044,U_1042))
| ~ sP240(U_1038,U_1037,U_1045,U_1039,U_1042,U_1032,U_1043,U_1044,U_1046) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_13,plain,
( in(U_1045,cartesian_product2(U_1044,U_1042))
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_14,plain,
( in(sK235(U_1044,U_1043,U_1042,U_1045),U_1044)
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_15,plain,
( ordered_pair(sK235(U_1044,U_1043,U_1042,U_1045),sK236(U_1044,U_1043,U_1042,U_1045)) = U_1045
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_16,plain,
( sK235(U_1044,U_1043,U_1042,U_1045) = sK237(U_1044,U_1043,U_1042,U_1045)
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_17,plain,
( in(sK236(U_1044,U_1043,U_1042,U_1045),sK237(U_1044,U_1043,U_1042,U_1045))
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_18,plain,
( in(ordered_pair(sK236(U_1044,U_1043,U_1042,U_1045),U_1032),U_1043)
| ~ in(U_1032,sK237(U_1044,U_1043,U_1042,U_1045))
| ~ sP238(U_1045,U_1042,U_1032,U_1043,U_1044) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_19,plain,
( in(sK238(U_1044,U_1043,U_1042,U_1046,U_1039,U_1038,U_1037),U_1037)
| ~ sP239(U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046) ),
inference(clausify,[status(thm)],[f_226_9]) ).
cnf(f_226_20,plain,
( ~ in(ordered_pair(U_1038,sK238(U_1044,U_1043,U_1042,U_1046,U_1039,U_1038,U_1037)),U_1043)
| ~ sP239(U_1038,U_1037,U_1039,U_1042,U_1043,U_1044,U_1046) ),
inference(clausify,[status(thm)],[f_226_9]) ).
fof(f_227_1,plain,
! [A,B] :
? [C] :
! [D] :
( ( in(D,C)
| ! [E,F] :
( F != singleton(E)
| ~ in(E,A)
| ordered_pair(E,F) != D )
| ~ in(D,cartesian_product2(A,B)) )
& ( ( ? [E,F] :
( F = singleton(E)
& in(E,A)
& ordered_pair(E,F) = D )
& in(D,cartesian_product2(A,B)) )
| ~ in(D,C) ) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e16_22__wellord2__1]) ).
fof(f_227_2,plain,
! [U_1054,U_1053] :
? [U_1052] :
! [U_1051] :
( ( in(U_1051,U_1052)
| ! [U_1050,U_1049] :
( U_1049 != singleton(U_1050)
| ~ in(U_1050,U_1054)
| ordered_pair(U_1050,U_1049) != U_1051 )
| ~ in(U_1051,cartesian_product2(U_1054,U_1053)) )
& ( ( ? [U_1048,U_1047] :
( U_1047 = singleton(U_1048)
& in(U_1048,U_1054)
& ordered_pair(U_1048,U_1047) = U_1051 )
& in(U_1051,cartesian_product2(U_1054,U_1053)) )
| ~ in(U_1051,U_1052) ) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_1054,U_1053] :
? [U_1052] :
( ! [U_1056] :
( in(U_1056,U_1052)
| ! [U_1050] :
( ! [U_1049] :
( U_1049 != singleton(U_1050)
| ordered_pair(U_1050,U_1049) != U_1056 )
| ~ in(U_1050,U_1054) )
| ~ in(U_1056,cartesian_product2(U_1054,U_1053)) )
& ! [U_1055] :
( ( ? [U_1048] :
( ? [U_1047] :
( U_1047 = singleton(U_1048)
& ordered_pair(U_1048,U_1047) = U_1055 )
& in(U_1048,U_1054) )
& in(U_1055,cartesian_product2(U_1054,U_1053)) )
| ~ in(U_1055,U_1052) ) ),
inference(miniscope,[status(thm)],[f_227_2]) ).
fof(f_227_4,plain,
! [U_1054,U_1053] :
( ! [U_1056] :
( in(U_1056,sK239(U_1054,U_1053))
| ! [U_1050] :
( ! [U_1049] :
( U_1049 != singleton(U_1050)
| ordered_pair(U_1050,U_1049) != U_1056 )
| ~ in(U_1050,U_1054) )
| ~ in(U_1056,cartesian_product2(U_1054,U_1053)) )
& ! [U_1055] :
( ( ? [U_1048] :
( ? [U_1047] :
( U_1047 = singleton(U_1048)
& ordered_pair(U_1048,U_1047) = U_1055 )
& in(U_1048,U_1054) )
& in(U_1055,cartesian_product2(U_1054,U_1053)) )
| ~ in(U_1055,sK239(U_1054,U_1053)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_1052,sK239(U_1054,U_1053))],[f_227_3]) ).
fof(f_227_5,plain,
! [U_1054,U_1053] :
( ! [U_1056] :
( in(U_1056,sK239(U_1054,U_1053))
| ! [U_1050] :
( ! [U_1049] :
( U_1049 != singleton(U_1050)
| ordered_pair(U_1050,U_1049) != U_1056 )
| ~ in(U_1050,U_1054) )
| ~ in(U_1056,cartesian_product2(U_1054,U_1053)) )
& ! [U_1055] :
( ( ? [U_1047] :
( U_1047 = singleton(sK240(U_1054,U_1053,U_1055))
& ordered_pair(sK240(U_1054,U_1053,U_1055),U_1047) = U_1055 )
& in(sK240(U_1054,U_1053,U_1055),U_1054)
& in(U_1055,cartesian_product2(U_1054,U_1053)) )
| ~ in(U_1055,sK239(U_1054,U_1053)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_1048,sK240(U_1054,U_1053,U_1055))],[f_227_4]) ).
fof(f_227_6,plain,
! [U_1054,U_1053] :
( ! [U_1056] :
( in(U_1056,sK239(U_1054,U_1053))
| ! [U_1050] :
( ! [U_1049] :
( U_1049 != singleton(U_1050)
| ordered_pair(U_1050,U_1049) != U_1056 )
| ~ in(U_1050,U_1054) )
| ~ in(U_1056,cartesian_product2(U_1054,U_1053)) )
& ! [U_1055] :
( ( sK241(U_1054,U_1053,U_1055) = singleton(sK240(U_1054,U_1053,U_1055))
& ordered_pair(sK240(U_1054,U_1053,U_1055),sK241(U_1054,U_1053,U_1055)) = U_1055
& in(sK240(U_1054,U_1053,U_1055),U_1054)
& in(U_1055,cartesian_product2(U_1054,U_1053)) )
| ~ in(U_1055,sK239(U_1054,U_1053)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_1047,sK241(U_1054,U_1053,U_1055))],[f_227_5]) ).
fof(f_227_7,plain,
( ! [U_1053,U_1054,U_1055] :
( sK241(U_1054,U_1053,U_1055) = singleton(sK240(U_1054,U_1053,U_1055))
| ~ sP241(U_1053,U_1054,U_1055) )
& ! [U_1053,U_1054,U_1055] :
( ordered_pair(sK240(U_1054,U_1053,U_1055),sK241(U_1054,U_1053,U_1055)) = U_1055
| ~ sP241(U_1053,U_1054,U_1055) )
& ! [U_1053,U_1054,U_1055] :
( in(sK240(U_1054,U_1053,U_1055),U_1054)
| ~ sP241(U_1053,U_1054,U_1055) )
& ! [U_1053,U_1054,U_1055] :
( in(U_1055,cartesian_product2(U_1054,U_1053))
| ~ sP241(U_1053,U_1054,U_1055) )
& ! [U_1053,U_1054,U_1050,U_1056,U_1049] :
( in(U_1056,sK239(U_1054,U_1053))
| U_1049 != singleton(U_1050)
| ordered_pair(U_1050,U_1049) != U_1056
| ~ in(U_1050,U_1054)
| ~ in(U_1056,cartesian_product2(U_1054,U_1053)) )
& ! [U_1053,U_1054,U_1055] :
( sP241(U_1053,U_1054,U_1055)
| ~ in(U_1055,sK239(U_1054,U_1053)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_227_6]) ).
cnf(f_227_8,plain,
( sP241(U_1053,U_1054,U_1055)
| ~ in(U_1055,sK239(U_1054,U_1053)) ),
inference(clausify,[status(thm)],[f_227_7]) ).
cnf(f_227_9,plain,
( in(U_1056,sK239(U_1054,U_1053))
| U_1049 != singleton(U_1050)
| ordered_pair(U_1050,U_1049) != U_1056
| ~ in(U_1050,U_1054)
| ~ in(U_1056,cartesian_product2(U_1054,U_1053)) ),
inference(clausify,[status(thm)],[f_227_7]) ).
cnf(f_227_10,plain,
( in(U_1055,cartesian_product2(U_1054,U_1053))
| ~ sP241(U_1053,U_1054,U_1055) ),
inference(clausify,[status(thm)],[f_227_7]) ).
cnf(f_227_11,plain,
( in(sK240(U_1054,U_1053,U_1055),U_1054)
| ~ sP241(U_1053,U_1054,U_1055) ),
inference(clausify,[status(thm)],[f_227_7]) ).
cnf(f_227_12,plain,
( ordered_pair(sK240(U_1054,U_1053,U_1055),sK241(U_1054,U_1053,U_1055)) = U_1055
| ~ sP241(U_1053,U_1054,U_1055) ),
inference(clausify,[status(thm)],[f_227_7]) ).
cnf(f_227_13,plain,
( sK241(U_1054,U_1053,U_1055) = singleton(sK240(U_1054,U_1053,U_1055))
| ~ sP241(U_1053,U_1054,U_1055) ),
inference(clausify,[status(thm)],[f_227_7]) ).
fof(f_228_1,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( ( in(E,D)
| ! [F,G] :
( ~ in(ordered_pair(apply(C,F),apply(C,G)),B)
| E != ordered_pair(F,G) )
| ~ in(E,cartesian_product2(A,A)) )
& ( ( ? [F,G] :
( in(ordered_pair(apply(C,F),apply(C,G)),B)
& E = ordered_pair(F,G) )
& in(E,cartesian_product2(A,A)) )
| ~ in(E,D) ) )
| ~ function(C)
| ~ relation(C)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e6_21__wellord2__1]) ).
fof(f_228_2,plain,
! [U_1065,U_1064,U_1063] :
( ? [U_1062] :
! [U_1061] :
( ( in(U_1061,U_1062)
| ! [U_1060,U_1059] :
( ~ in(ordered_pair(apply(U_1063,U_1060),apply(U_1063,U_1059)),U_1064)
| U_1061 != ordered_pair(U_1060,U_1059) )
| ~ in(U_1061,cartesian_product2(U_1065,U_1065)) )
& ( ( ? [U_1058,U_1057] :
( in(ordered_pair(apply(U_1063,U_1058),apply(U_1063,U_1057)),U_1064)
& U_1061 = ordered_pair(U_1058,U_1057) )
& in(U_1061,cartesian_product2(U_1065,U_1065)) )
| ~ in(U_1061,U_1062) ) )
| ~ function(U_1063)
| ~ relation(U_1063)
| ~ relation(U_1064) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_1065,U_1064,U_1063] :
( ? [U_1062] :
( ! [U_1067] :
( in(U_1067,U_1062)
| ! [U_1060,U_1059] :
( ~ in(ordered_pair(apply(U_1063,U_1060),apply(U_1063,U_1059)),U_1064)
| U_1067 != ordered_pair(U_1060,U_1059) )
| ~ in(U_1067,cartesian_product2(U_1065,U_1065)) )
& ! [U_1066] :
( ( ? [U_1058,U_1057] :
( in(ordered_pair(apply(U_1063,U_1058),apply(U_1063,U_1057)),U_1064)
& U_1066 = ordered_pair(U_1058,U_1057) )
& in(U_1066,cartesian_product2(U_1065,U_1065)) )
| ~ in(U_1066,U_1062) ) )
| ~ function(U_1063)
| ~ relation(U_1063)
| ~ relation(U_1064) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
fof(f_228_4,plain,
! [U_1065,U_1064,U_1063] :
( ( ! [U_1067] :
( in(U_1067,sK242(U_1065,U_1064,U_1063))
| ! [U_1060,U_1059] :
( ~ in(ordered_pair(apply(U_1063,U_1060),apply(U_1063,U_1059)),U_1064)
| U_1067 != ordered_pair(U_1060,U_1059) )
| ~ in(U_1067,cartesian_product2(U_1065,U_1065)) )
& ! [U_1066] :
( ( ? [U_1058,U_1057] :
( in(ordered_pair(apply(U_1063,U_1058),apply(U_1063,U_1057)),U_1064)
& U_1066 = ordered_pair(U_1058,U_1057) )
& in(U_1066,cartesian_product2(U_1065,U_1065)) )
| ~ in(U_1066,sK242(U_1065,U_1064,U_1063)) ) )
| ~ function(U_1063)
| ~ relation(U_1063)
| ~ relation(U_1064) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_1062,sK242(U_1065,U_1064,U_1063))],[f_228_3]) ).
fof(f_228_5,plain,
! [U_1065,U_1064,U_1063] :
( ( ! [U_1067] :
( in(U_1067,sK242(U_1065,U_1064,U_1063))
| ! [U_1060,U_1059] :
( ~ in(ordered_pair(apply(U_1063,U_1060),apply(U_1063,U_1059)),U_1064)
| U_1067 != ordered_pair(U_1060,U_1059) )
| ~ in(U_1067,cartesian_product2(U_1065,U_1065)) )
& ! [U_1066] :
( ( ? [U_1057] :
( in(ordered_pair(apply(U_1063,sK243(U_1065,U_1064,U_1063,U_1066)),apply(U_1063,U_1057)),U_1064)
& U_1066 = ordered_pair(sK243(U_1065,U_1064,U_1063,U_1066),U_1057) )
& in(U_1066,cartesian_product2(U_1065,U_1065)) )
| ~ in(U_1066,sK242(U_1065,U_1064,U_1063)) ) )
| ~ function(U_1063)
| ~ relation(U_1063)
| ~ relation(U_1064) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_1058,sK243(U_1065,U_1064,U_1063,U_1066))],[f_228_4]) ).
fof(f_228_6,plain,
! [U_1065,U_1064,U_1063] :
( ( ! [U_1067] :
( in(U_1067,sK242(U_1065,U_1064,U_1063))
| ! [U_1060,U_1059] :
( ~ in(ordered_pair(apply(U_1063,U_1060),apply(U_1063,U_1059)),U_1064)
| U_1067 != ordered_pair(U_1060,U_1059) )
| ~ in(U_1067,cartesian_product2(U_1065,U_1065)) )
& ! [U_1066] :
( ( in(ordered_pair(apply(U_1063,sK243(U_1065,U_1064,U_1063,U_1066)),apply(U_1063,sK244(U_1065,U_1064,U_1063,U_1066))),U_1064)
& U_1066 = ordered_pair(sK243(U_1065,U_1064,U_1063,U_1066),sK244(U_1065,U_1064,U_1063,U_1066))
& in(U_1066,cartesian_product2(U_1065,U_1065)) )
| ~ in(U_1066,sK242(U_1065,U_1064,U_1063)) ) )
| ~ function(U_1063)
| ~ relation(U_1063)
| ~ relation(U_1064) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_1057,sK244(U_1065,U_1064,U_1063,U_1066))],[f_228_5]) ).
fof(f_228_7,plain,
( ! [U_1065,U_1066,U_1063,U_1064] :
( in(ordered_pair(apply(U_1063,sK243(U_1065,U_1064,U_1063,U_1066)),apply(U_1063,sK244(U_1065,U_1064,U_1063,U_1066))),U_1064)
| ~ sP242(U_1065,U_1066,U_1063,U_1064) )
& ! [U_1065,U_1066,U_1063,U_1064] :
( U_1066 = ordered_pair(sK243(U_1065,U_1064,U_1063,U_1066),sK244(U_1065,U_1064,U_1063,U_1066))
| ~ sP242(U_1065,U_1066,U_1063,U_1064) )
& ! [U_1065,U_1066,U_1063,U_1064] :
( in(U_1066,cartesian_product2(U_1065,U_1065))
| ~ sP242(U_1065,U_1066,U_1063,U_1064) )
& ! [U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067] :
( in(U_1067,sK242(U_1065,U_1064,U_1063))
| ~ in(ordered_pair(apply(U_1063,U_1060),apply(U_1063,U_1059)),U_1064)
| U_1067 != ordered_pair(U_1060,U_1059)
| ~ in(U_1067,cartesian_product2(U_1065,U_1065))
| ~ sP243(U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067) )
& ! [U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067] :
( sP242(U_1065,U_1066,U_1063,U_1064)
| ~ in(U_1066,sK242(U_1065,U_1064,U_1063))
| ~ sP243(U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067) )
& ! [U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067] :
( sP243(U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067)
| ~ function(U_1063)
| ~ relation(U_1063)
| ~ relation(U_1064) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242,sP243])],[f_228_6]) ).
cnf(f_228_8,plain,
( sP243(U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067)
| ~ function(U_1063)
| ~ relation(U_1063)
| ~ relation(U_1064) ),
inference(clausify,[status(thm)],[f_228_7]) ).
cnf(f_228_9,plain,
( sP242(U_1065,U_1066,U_1063,U_1064)
| ~ in(U_1066,sK242(U_1065,U_1064,U_1063))
| ~ sP243(U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067) ),
inference(clausify,[status(thm)],[f_228_7]) ).
cnf(f_228_10,plain,
( in(U_1067,sK242(U_1065,U_1064,U_1063))
| ~ in(ordered_pair(apply(U_1063,U_1060),apply(U_1063,U_1059)),U_1064)
| U_1067 != ordered_pair(U_1060,U_1059)
| ~ in(U_1067,cartesian_product2(U_1065,U_1065))
| ~ sP243(U_1059,U_1065,U_1066,U_1060,U_1063,U_1064,U_1067) ),
inference(clausify,[status(thm)],[f_228_7]) ).
cnf(f_228_11,plain,
( in(U_1066,cartesian_product2(U_1065,U_1065))
| ~ sP242(U_1065,U_1066,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_228_7]) ).
cnf(f_228_12,plain,
( U_1066 = ordered_pair(sK243(U_1065,U_1064,U_1063,U_1066),sK244(U_1065,U_1064,U_1063,U_1066))
| ~ sP242(U_1065,U_1066,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_228_7]) ).
cnf(f_228_13,plain,
( in(ordered_pair(apply(U_1063,sK243(U_1065,U_1064,U_1063,U_1066)),apply(U_1063,sK244(U_1065,U_1064,U_1063,U_1066))),U_1064)
| ~ sP242(U_1065,U_1066,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_228_7]) ).
fof(f_229_1,plain,
! [A] :
? [B] :
! [C] :
( ( in(C,B)
| ~ ordinal(C)
| ~ in(C,A) )
& ( ( ordinal(C)
& in(C,A) )
| ~ in(C,B) ) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e6_22__wellord2]) ).
fof(f_229_2,plain,
! [U_1070] :
? [U_1069] :
! [U_1068] :
( ( in(U_1068,U_1069)
| ~ ordinal(U_1068)
| ~ in(U_1068,U_1070) )
& ( ( ordinal(U_1068)
& in(U_1068,U_1070) )
| ~ in(U_1068,U_1069) ) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_1070] :
? [U_1069] :
( ! [U_1072] :
( in(U_1072,U_1069)
| ~ ordinal(U_1072)
| ~ in(U_1072,U_1070) )
& ! [U_1071] :
( ( ordinal(U_1071)
& in(U_1071,U_1070) )
| ~ in(U_1071,U_1069) ) ),
inference(miniscope,[status(thm)],[f_229_2]) ).
fof(f_229_4,plain,
! [U_1070] :
( ! [U_1072] :
( in(U_1072,sK245(U_1070))
| ~ ordinal(U_1072)
| ~ in(U_1072,U_1070) )
& ! [U_1071] :
( ( ordinal(U_1071)
& in(U_1071,U_1070) )
| ~ in(U_1071,sK245(U_1070)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_1069,sK245(U_1070))],[f_229_3]) ).
fof(f_229_5,plain,
( ! [U_1070,U_1071] :
( ordinal(U_1071)
| ~ sP244(U_1070,U_1071) )
& ! [U_1070,U_1071] :
( in(U_1071,U_1070)
| ~ sP244(U_1070,U_1071) )
& ! [U_1072,U_1070] :
( in(U_1072,sK245(U_1070))
| ~ ordinal(U_1072)
| ~ in(U_1072,U_1070) )
& ! [U_1070,U_1071] :
( sP244(U_1070,U_1071)
| ~ in(U_1071,sK245(U_1070)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_229_4]) ).
cnf(f_229_6,plain,
( sP244(U_1070,U_1071)
| ~ in(U_1071,sK245(U_1070)) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_7,plain,
( in(U_1072,sK245(U_1070))
| ~ ordinal(U_1072)
| ~ in(U_1072,U_1070) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_8,plain,
( in(U_1071,U_1070)
| ~ sP244(U_1070,U_1071) ),
inference(clausify,[status(thm)],[f_229_5]) ).
cnf(f_229_9,plain,
( ordinal(U_1071)
| ~ sP244(U_1070,U_1071) ),
inference(clausify,[status(thm)],[f_229_5]) ).
fof(f_230_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,A)
| D != E
| ~ ordinal(E) )
| ~ in(D,succ(B)) )
& ( ( ? [E] :
( in(E,A)
& D = E
& ordinal(E) )
& in(D,succ(B)) )
| ~ in(D,C) ) )
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e8_6__wellord2__1]) ).
fof(f_230_2,plain,
! [U_1078,U_1077] :
( ? [U_1076] :
! [U_1075] :
( ( in(U_1075,U_1076)
| ! [U_1074] :
( ~ in(U_1074,U_1078)
| U_1075 != U_1074
| ~ ordinal(U_1074) )
| ~ in(U_1075,succ(U_1077)) )
& ( ( ? [U_1073] :
( in(U_1073,U_1078)
& U_1075 = U_1073
& ordinal(U_1073) )
& in(U_1075,succ(U_1077)) )
| ~ in(U_1075,U_1076) ) )
| ~ ordinal(U_1077) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_1078,U_1077] :
( ? [U_1076] :
( ! [U_1080] :
( in(U_1080,U_1076)
| ! [U_1074] :
( ~ in(U_1074,U_1078)
| U_1080 != U_1074
| ~ ordinal(U_1074) )
| ~ in(U_1080,succ(U_1077)) )
& ! [U_1079] :
( ( ? [U_1073] :
( in(U_1073,U_1078)
& U_1079 = U_1073
& ordinal(U_1073) )
& in(U_1079,succ(U_1077)) )
| ~ in(U_1079,U_1076) ) )
| ~ ordinal(U_1077) ),
inference(miniscope,[status(thm)],[f_230_2]) ).
fof(f_230_4,plain,
! [U_1078,U_1077] :
( ( ! [U_1080] :
( in(U_1080,sK246(U_1078,U_1077))
| ! [U_1074] :
( ~ in(U_1074,U_1078)
| U_1080 != U_1074
| ~ ordinal(U_1074) )
| ~ in(U_1080,succ(U_1077)) )
& ! [U_1079] :
( ( ? [U_1073] :
( in(U_1073,U_1078)
& U_1079 = U_1073
& ordinal(U_1073) )
& in(U_1079,succ(U_1077)) )
| ~ in(U_1079,sK246(U_1078,U_1077)) ) )
| ~ ordinal(U_1077) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_1076,sK246(U_1078,U_1077))],[f_230_3]) ).
fof(f_230_5,plain,
! [U_1078,U_1077] :
( ( ! [U_1080] :
( in(U_1080,sK246(U_1078,U_1077))
| ! [U_1074] :
( ~ in(U_1074,U_1078)
| U_1080 != U_1074
| ~ ordinal(U_1074) )
| ~ in(U_1080,succ(U_1077)) )
& ! [U_1079] :
( ( in(sK247(U_1078,U_1077,U_1079),U_1078)
& U_1079 = sK247(U_1078,U_1077,U_1079)
& ordinal(sK247(U_1078,U_1077,U_1079))
& in(U_1079,succ(U_1077)) )
| ~ in(U_1079,sK246(U_1078,U_1077)) ) )
| ~ ordinal(U_1077) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_1073,sK247(U_1078,U_1077,U_1079))],[f_230_4]) ).
fof(f_230_6,plain,
( ! [U_1077,U_1078,U_1079] :
( in(sK247(U_1078,U_1077,U_1079),U_1078)
| ~ sP245(U_1077,U_1078,U_1079) )
& ! [U_1077,U_1078,U_1079] :
( U_1079 = sK247(U_1078,U_1077,U_1079)
| ~ sP245(U_1077,U_1078,U_1079) )
& ! [U_1077,U_1078,U_1079] :
( ordinal(sK247(U_1078,U_1077,U_1079))
| ~ sP245(U_1077,U_1078,U_1079) )
& ! [U_1077,U_1078,U_1079] :
( in(U_1079,succ(U_1077))
| ~ sP245(U_1077,U_1078,U_1079) )
& ! [U_1077,U_1078,U_1080,U_1079,U_1074] :
( in(U_1080,sK246(U_1078,U_1077))
| ~ in(U_1074,U_1078)
| U_1080 != U_1074
| ~ ordinal(U_1074)
| ~ in(U_1080,succ(U_1077))
| ~ sP246(U_1077,U_1078,U_1080,U_1079,U_1074) )
& ! [U_1077,U_1078,U_1080,U_1079,U_1074] :
( sP245(U_1077,U_1078,U_1079)
| ~ in(U_1079,sK246(U_1078,U_1077))
| ~ sP246(U_1077,U_1078,U_1080,U_1079,U_1074) )
& ! [U_1077,U_1078,U_1080,U_1079,U_1074] :
( sP246(U_1077,U_1078,U_1080,U_1079,U_1074)
| ~ ordinal(U_1077) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245,sP246])],[f_230_5]) ).
cnf(f_230_7,plain,
( sP246(U_1077,U_1078,U_1080,U_1079,U_1074)
| ~ ordinal(U_1077) ),
inference(clausify,[status(thm)],[f_230_6]) ).
cnf(f_230_8,plain,
( sP245(U_1077,U_1078,U_1079)
| ~ in(U_1079,sK246(U_1078,U_1077))
| ~ sP246(U_1077,U_1078,U_1080,U_1079,U_1074) ),
inference(clausify,[status(thm)],[f_230_6]) ).
cnf(f_230_9,plain,
( in(U_1080,sK246(U_1078,U_1077))
| ~ in(U_1074,U_1078)
| U_1080 != U_1074
| ~ ordinal(U_1074)
| ~ in(U_1080,succ(U_1077))
| ~ sP246(U_1077,U_1078,U_1080,U_1079,U_1074) ),
inference(clausify,[status(thm)],[f_230_6]) ).
cnf(f_230_10,plain,
( in(U_1079,succ(U_1077))
| ~ sP245(U_1077,U_1078,U_1079) ),
inference(clausify,[status(thm)],[f_230_6]) ).
cnf(f_230_11,plain,
( ordinal(sK247(U_1078,U_1077,U_1079))
| ~ sP245(U_1077,U_1078,U_1079) ),
inference(clausify,[status(thm)],[f_230_6]) ).
cnf(f_230_12,plain,
( U_1079 = sK247(U_1078,U_1077,U_1079)
| ~ sP245(U_1077,U_1078,U_1079) ),
inference(clausify,[status(thm)],[f_230_6]) ).
cnf(f_230_13,plain,
( in(sK247(U_1078,U_1077,U_1079),U_1078)
| ~ sP245(U_1077,U_1078,U_1079) ),
inference(clausify,[status(thm)],[f_230_6]) ).
fof(f_231_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ? [L] :
( ! [M] :
( in(ordered_pair(apply(C,D),M),B)
| ~ in(M,L) )
& in(apply(C,D),L)
& D = L )
| ~ in(D,A) )
& relation_dom(C) = A
& function(C)
& relation(C) )
| ? [C] :
( ! [D,J] :
( ? [K] :
( ~ in(ordered_pair(D,K),B)
& in(K,J) )
| ~ in(D,J)
| C != J )
& in(C,A) )
| ? [C,D,E] :
( D != E
& ? [H] :
( ! [I] :
( in(ordered_pair(E,I),B)
| ~ in(I,H) )
& in(E,H)
& C = H )
& ? [F] :
( ! [G] :
( in(ordered_pair(D,G),B)
| ~ in(G,F) )
& in(D,F)
& C = F )
& in(C,A) )
| ~ relation(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[s2_funct_1__e10_24__wellord2]) ).
fof(f_231_2,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ? [U_1091] :
( ! [U_1090,U_1089] :
( ? [U_1088] :
( ~ in(ordered_pair(U_1090,U_1088),U_1096)
& in(U_1088,U_1089) )
| ~ in(U_1090,U_1089)
| U_1091 != U_1089 )
& in(U_1091,U_1097) )
| ? [U_1087,U_1086,U_1085] :
( U_1086 != U_1085
& ? [U_1084] :
( ! [U_1083] :
( in(ordered_pair(U_1085,U_1083),U_1096)
| ~ in(U_1083,U_1084) )
& in(U_1085,U_1084)
& U_1087 = U_1084 )
& ? [U_1082] :
( ! [U_1081] :
( in(ordered_pair(U_1086,U_1081),U_1096)
| ~ in(U_1081,U_1082) )
& in(U_1086,U_1082)
& U_1087 = U_1082 )
& in(U_1087,U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ? [U_1091] :
( ! [U_1090,U_1089] :
( ? [U_1088] :
( ~ in(ordered_pair(U_1090,U_1088),U_1096)
& in(U_1088,U_1089) )
| ~ in(U_1090,U_1089)
| U_1091 != U_1089 )
& in(U_1091,U_1097) )
| ? [U_1086,U_1085] :
( U_1086 != U_1085
& ? [U_1084] :
( ! [U_1083] :
( in(ordered_pair(U_1085,U_1083),U_1096)
| ~ in(U_1083,U_1084) )
& in(U_1085,U_1084)
& sK248(U_1097,U_1096) = U_1084 )
& ? [U_1082] :
( ! [U_1081] :
( in(ordered_pair(U_1086,U_1081),U_1096)
| ~ in(U_1081,U_1082) )
& in(U_1086,U_1082)
& sK248(U_1097,U_1096) = U_1082 )
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_1087,sK248(U_1097,U_1096))],[f_231_2]) ).
fof(f_231_4,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ? [U_1091] :
( ! [U_1090,U_1089] :
( ? [U_1088] :
( ~ in(ordered_pair(U_1090,U_1088),U_1096)
& in(U_1088,U_1089) )
| ~ in(U_1090,U_1089)
| U_1091 != U_1089 )
& in(U_1091,U_1097) )
| ? [U_1085] :
( sK249(U_1097,U_1096) != U_1085
& ? [U_1084] :
( ! [U_1083] :
( in(ordered_pair(U_1085,U_1083),U_1096)
| ~ in(U_1083,U_1084) )
& in(U_1085,U_1084)
& sK248(U_1097,U_1096) = U_1084 )
& ? [U_1082] :
( ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,U_1082) )
& in(sK249(U_1097,U_1096),U_1082)
& sK248(U_1097,U_1096) = U_1082 )
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_1086,sK249(U_1097,U_1096))],[f_231_3]) ).
fof(f_231_5,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ? [U_1091] :
( ! [U_1090,U_1089] :
( ? [U_1088] :
( ~ in(ordered_pair(U_1090,U_1088),U_1096)
& in(U_1088,U_1089) )
| ~ in(U_1090,U_1089)
| U_1091 != U_1089 )
& in(U_1091,U_1097) )
| ( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
& ? [U_1084] :
( ! [U_1083] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,U_1084) )
& in(sK250(U_1097,U_1096),U_1084)
& sK248(U_1097,U_1096) = U_1084 )
& ? [U_1082] :
( ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,U_1082) )
& in(sK249(U_1097,U_1096),U_1082)
& sK248(U_1097,U_1096) = U_1082 )
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_1085,sK250(U_1097,U_1096))],[f_231_4]) ).
fof(f_231_6,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ? [U_1091] :
( ! [U_1090,U_1089] :
( ? [U_1088] :
( ~ in(ordered_pair(U_1090,U_1088),U_1096)
& in(U_1088,U_1089) )
| ~ in(U_1090,U_1089)
| U_1091 != U_1089 )
& in(U_1091,U_1097) )
| ( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
& ? [U_1084] :
( ! [U_1083] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,U_1084) )
& in(sK250(U_1097,U_1096),U_1084)
& sK248(U_1097,U_1096) = U_1084 )
& ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096)) )
& in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_1082,sK251(U_1097,U_1096))],[f_231_5]) ).
fof(f_231_7,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ? [U_1091] :
( ! [U_1090,U_1089] :
( ? [U_1088] :
( ~ in(ordered_pair(U_1090,U_1088),U_1096)
& in(U_1088,U_1089) )
| ~ in(U_1090,U_1089)
| U_1091 != U_1089 )
& in(U_1091,U_1097) )
| ( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
& ! [U_1083] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,sK252(U_1097,U_1096)) )
& in(sK250(U_1097,U_1096),sK252(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK252(U_1097,U_1096)
& ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096)) )
& in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_1084,sK252(U_1097,U_1096))],[f_231_6]) ).
fof(f_231_8,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ( ! [U_1090,U_1089] :
( ? [U_1088] :
( ~ in(ordered_pair(U_1090,U_1088),U_1096)
& in(U_1088,U_1089) )
| ~ in(U_1090,U_1089)
| sK253(U_1097,U_1096) != U_1089 )
& in(sK253(U_1097,U_1096),U_1097) )
| ( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
& ! [U_1083] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,sK252(U_1097,U_1096)) )
& in(sK250(U_1097,U_1096),sK252(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK252(U_1097,U_1096)
& ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096)) )
& in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_1091,sK253(U_1097,U_1096))],[f_231_7]) ).
fof(f_231_9,plain,
! [U_1097,U_1096] :
( ? [U_1095] :
( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(U_1095,U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(U_1095,U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(U_1095) = U_1097
& function(U_1095)
& relation(U_1095) )
| ( ! [U_1090,U_1089] :
( ( ~ in(ordered_pair(U_1090,sK254(U_1097,U_1096,U_1090,U_1089)),U_1096)
& in(sK254(U_1097,U_1096,U_1090,U_1089),U_1089) )
| ~ in(U_1090,U_1089)
| sK253(U_1097,U_1096) != U_1089 )
& in(sK253(U_1097,U_1096),U_1097) )
| ( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
& ! [U_1083] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,sK252(U_1097,U_1096)) )
& in(sK250(U_1097,U_1096),sK252(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK252(U_1097,U_1096)
& ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096)) )
& in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_1088,sK254(U_1097,U_1096,U_1090,U_1089))],[f_231_8]) ).
fof(f_231_10,plain,
! [U_1097,U_1096] :
( ( ! [U_1094] :
( ? [U_1093] :
( ! [U_1092] :
( in(ordered_pair(apply(sK255(U_1097,U_1096),U_1094),U_1092),U_1096)
| ~ in(U_1092,U_1093) )
& in(apply(sK255(U_1097,U_1096),U_1094),U_1093)
& U_1094 = U_1093 )
| ~ in(U_1094,U_1097) )
& relation_dom(sK255(U_1097,U_1096)) = U_1097
& function(sK255(U_1097,U_1096))
& relation(sK255(U_1097,U_1096)) )
| ( ! [U_1090,U_1089] :
( ( ~ in(ordered_pair(U_1090,sK254(U_1097,U_1096,U_1090,U_1089)),U_1096)
& in(sK254(U_1097,U_1096,U_1090,U_1089),U_1089) )
| ~ in(U_1090,U_1089)
| sK253(U_1097,U_1096) != U_1089 )
& in(sK253(U_1097,U_1096),U_1097) )
| ( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
& ! [U_1083] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,sK252(U_1097,U_1096)) )
& in(sK250(U_1097,U_1096),sK252(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK252(U_1097,U_1096)
& ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096)) )
& in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_1095,sK255(U_1097,U_1096))],[f_231_9]) ).
fof(f_231_11,plain,
! [U_1097,U_1096] :
( ( ! [U_1094] :
( ( ! [U_1092] :
( in(ordered_pair(apply(sK255(U_1097,U_1096),U_1094),U_1092),U_1096)
| ~ in(U_1092,sK256(U_1097,U_1096,U_1094)) )
& in(apply(sK255(U_1097,U_1096),U_1094),sK256(U_1097,U_1096,U_1094))
& U_1094 = sK256(U_1097,U_1096,U_1094) )
| ~ in(U_1094,U_1097) )
& relation_dom(sK255(U_1097,U_1096)) = U_1097
& function(sK255(U_1097,U_1096))
& relation(sK255(U_1097,U_1096)) )
| ( ! [U_1090,U_1089] :
( ( ~ in(ordered_pair(U_1090,sK254(U_1097,U_1096,U_1090,U_1089)),U_1096)
& in(sK254(U_1097,U_1096,U_1090,U_1089),U_1089) )
| ~ in(U_1090,U_1089)
| sK253(U_1097,U_1096) != U_1089 )
& in(sK253(U_1097,U_1096),U_1097) )
| ( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
& ! [U_1083] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,sK252(U_1097,U_1096)) )
& in(sK250(U_1097,U_1096),sK252(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK252(U_1097,U_1096)
& ! [U_1081] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096)) )
& in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
& sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
& in(sK248(U_1097,U_1096),U_1097) )
| ~ relation(U_1096)
| empty(U_1097) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_1093,sK256(U_1097,U_1096,U_1094))],[f_231_10]) ).
fof(f_231_12,plain,
( ! [U_1094,U_1092,U_1096,U_1097] :
( in(ordered_pair(apply(sK255(U_1097,U_1096),U_1094),U_1092),U_1096)
| ~ in(U_1092,sK256(U_1097,U_1096,U_1094))
| ~ sP250(U_1094,U_1092,U_1096,U_1097) )
& ! [U_1094,U_1092,U_1096,U_1097] :
( in(apply(sK255(U_1097,U_1096),U_1094),sK256(U_1097,U_1096,U_1094))
| ~ sP250(U_1094,U_1092,U_1096,U_1097) )
& ! [U_1094,U_1092,U_1096,U_1097] :
( U_1094 = sK256(U_1097,U_1096,U_1094)
| ~ sP250(U_1094,U_1092,U_1096,U_1097) )
& ! [U_1094,U_1092,U_1096,U_1097] :
( sP250(U_1094,U_1092,U_1096,U_1097)
| ~ in(U_1094,U_1097)
| ~ sP251(U_1094,U_1092,U_1096,U_1097) )
& ! [U_1094,U_1092,U_1096,U_1097] :
( relation_dom(sK255(U_1097,U_1096)) = U_1097
| ~ sP251(U_1094,U_1092,U_1096,U_1097) )
& ! [U_1094,U_1092,U_1096,U_1097] :
( function(sK255(U_1097,U_1096))
| ~ sP251(U_1094,U_1092,U_1096,U_1097) )
& ! [U_1094,U_1092,U_1096,U_1097] :
( relation(sK255(U_1097,U_1096))
| ~ sP251(U_1094,U_1092,U_1096,U_1097) )
& ! [U_1089,U_1090,U_1096,U_1097] :
( ~ in(ordered_pair(U_1090,sK254(U_1097,U_1096,U_1090,U_1089)),U_1096)
| ~ sP248(U_1089,U_1090,U_1096,U_1097) )
& ! [U_1089,U_1090,U_1096,U_1097] :
( in(sK254(U_1097,U_1096,U_1090,U_1089),U_1089)
| ~ sP248(U_1089,U_1090,U_1096,U_1097) )
& ! [U_1089,U_1090,U_1096,U_1097] :
( sP248(U_1089,U_1090,U_1096,U_1097)
| ~ in(U_1090,U_1089)
| sK253(U_1097,U_1096) != U_1089
| ~ sP249(U_1089,U_1090,U_1096,U_1097) )
& ! [U_1089,U_1090,U_1096,U_1097] :
( in(sK253(U_1097,U_1096),U_1097)
| ~ sP249(U_1089,U_1090,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,sK252(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( in(sK250(U_1097,U_1096),sK252(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( sK248(U_1097,U_1096) = sK252(U_1097,U_1096)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1083,U_1096,U_1097] :
( in(sK248(U_1097,U_1096),U_1097)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) )
& ! [U_1081,U_1089,U_1090,U_1083,U_1094,U_1092,U_1096,U_1097] :
( sP251(U_1094,U_1092,U_1096,U_1097)
| sP249(U_1089,U_1090,U_1096,U_1097)
| sP247(U_1081,U_1083,U_1096,U_1097)
| ~ relation(U_1096)
| empty(U_1097) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247,sP248,sP249,sP250,sP251])],[f_231_11]) ).
cnf(f_231_13,plain,
( sP251(U_1094,U_1092,U_1096,U_1097)
| sP249(U_1089,U_1090,U_1096,U_1097)
| sP247(U_1081,U_1083,U_1096,U_1097)
| ~ relation(U_1096)
| empty(U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_14,plain,
( in(sK248(U_1097,U_1096),U_1097)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_15,plain,
( sK248(U_1097,U_1096) = sK251(U_1097,U_1096)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_16,plain,
( in(sK249(U_1097,U_1096),sK251(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_17,plain,
( in(ordered_pair(sK249(U_1097,U_1096),U_1081),U_1096)
| ~ in(U_1081,sK251(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_18,plain,
( sK248(U_1097,U_1096) = sK252(U_1097,U_1096)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_19,plain,
( in(sK250(U_1097,U_1096),sK252(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_20,plain,
( in(ordered_pair(sK250(U_1097,U_1096),U_1083),U_1096)
| ~ in(U_1083,sK252(U_1097,U_1096))
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_21,plain,
( sK249(U_1097,U_1096) != sK250(U_1097,U_1096)
| ~ sP247(U_1081,U_1083,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_22,plain,
( in(sK253(U_1097,U_1096),U_1097)
| ~ sP249(U_1089,U_1090,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_23,plain,
( sP248(U_1089,U_1090,U_1096,U_1097)
| ~ in(U_1090,U_1089)
| sK253(U_1097,U_1096) != U_1089
| ~ sP249(U_1089,U_1090,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_24,plain,
( in(sK254(U_1097,U_1096,U_1090,U_1089),U_1089)
| ~ sP248(U_1089,U_1090,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_25,plain,
( ~ in(ordered_pair(U_1090,sK254(U_1097,U_1096,U_1090,U_1089)),U_1096)
| ~ sP248(U_1089,U_1090,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_26,plain,
( relation(sK255(U_1097,U_1096))
| ~ sP251(U_1094,U_1092,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_27,plain,
( function(sK255(U_1097,U_1096))
| ~ sP251(U_1094,U_1092,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_28,plain,
( relation_dom(sK255(U_1097,U_1096)) = U_1097
| ~ sP251(U_1094,U_1092,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_29,plain,
( sP250(U_1094,U_1092,U_1096,U_1097)
| ~ in(U_1094,U_1097)
| ~ sP251(U_1094,U_1092,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_30,plain,
( U_1094 = sK256(U_1097,U_1096,U_1094)
| ~ sP250(U_1094,U_1092,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_31,plain,
( in(apply(sK255(U_1097,U_1096),U_1094),sK256(U_1097,U_1096,U_1094))
| ~ sP250(U_1094,U_1092,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
cnf(f_231_32,plain,
( in(ordered_pair(apply(sK255(U_1097,U_1096),U_1094),U_1092),U_1096)
| ~ in(U_1092,sK256(U_1097,U_1096,U_1094))
| ~ sP250(U_1094,U_1092,U_1096,U_1097) ),
inference(clausify,[status(thm)],[f_231_12]) ).
fof(f_232_1,plain,
! [A] :
( ? [B] :
( ! [C] :
( apply(B,C) = singleton(C)
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) )
| ? [B] :
( ! [C] : C != singleton(B)
& in(B,A) )
| ? [B,C,D] :
( C != D
& D = singleton(B)
& C = singleton(B)
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[s2_funct_1__e16_22__wellord2__1]) ).
fof(f_232_2,plain,
! [U_1105] :
( ? [U_1104] :
( ! [U_1103] :
( apply(U_1104,U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105) )
& relation_dom(U_1104) = U_1105
& function(U_1104)
& relation(U_1104) )
| ? [U_1102] :
( ! [U_1101] : U_1101 != singleton(U_1102)
& in(U_1102,U_1105) )
| ? [U_1100,U_1099,U_1098] :
( U_1099 != U_1098
& U_1098 = singleton(U_1100)
& U_1099 = singleton(U_1100)
& in(U_1100,U_1105) ) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_1105] :
( ? [U_1104] :
( ! [U_1103] :
( apply(U_1104,U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105) )
& relation_dom(U_1104) = U_1105
& function(U_1104)
& relation(U_1104) )
| ? [U_1102] :
( ! [U_1101] : U_1101 != singleton(U_1102)
& in(U_1102,U_1105) )
| ? [U_1099,U_1098] :
( U_1099 != U_1098
& U_1098 = singleton(sK257(U_1105))
& U_1099 = singleton(sK257(U_1105))
& in(sK257(U_1105),U_1105) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_1100,sK257(U_1105))],[f_232_2]) ).
fof(f_232_4,plain,
! [U_1105] :
( ? [U_1104] :
( ! [U_1103] :
( apply(U_1104,U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105) )
& relation_dom(U_1104) = U_1105
& function(U_1104)
& relation(U_1104) )
| ? [U_1102] :
( ! [U_1101] : U_1101 != singleton(U_1102)
& in(U_1102,U_1105) )
| ? [U_1098] :
( sK258(U_1105) != U_1098
& U_1098 = singleton(sK257(U_1105))
& sK258(U_1105) = singleton(sK257(U_1105))
& in(sK257(U_1105),U_1105) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_1099,sK258(U_1105))],[f_232_3]) ).
fof(f_232_5,plain,
! [U_1105] :
( ? [U_1104] :
( ! [U_1103] :
( apply(U_1104,U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105) )
& relation_dom(U_1104) = U_1105
& function(U_1104)
& relation(U_1104) )
| ? [U_1102] :
( ! [U_1101] : U_1101 != singleton(U_1102)
& in(U_1102,U_1105) )
| ( sK258(U_1105) != sK259(U_1105)
& sK259(U_1105) = singleton(sK257(U_1105))
& sK258(U_1105) = singleton(sK257(U_1105))
& in(sK257(U_1105),U_1105) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_1098,sK259(U_1105))],[f_232_4]) ).
fof(f_232_6,plain,
! [U_1105] :
( ? [U_1104] :
( ! [U_1103] :
( apply(U_1104,U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105) )
& relation_dom(U_1104) = U_1105
& function(U_1104)
& relation(U_1104) )
| ( ! [U_1101] : U_1101 != singleton(sK260(U_1105))
& in(sK260(U_1105),U_1105) )
| ( sK258(U_1105) != sK259(U_1105)
& sK259(U_1105) = singleton(sK257(U_1105))
& sK258(U_1105) = singleton(sK257(U_1105))
& in(sK257(U_1105),U_1105) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_1102,sK260(U_1105))],[f_232_5]) ).
fof(f_232_7,plain,
! [U_1105] :
( ( ! [U_1103] :
( apply(sK261(U_1105),U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105) )
& relation_dom(sK261(U_1105)) = U_1105
& function(sK261(U_1105))
& relation(sK261(U_1105)) )
| ( ! [U_1101] : U_1101 != singleton(sK260(U_1105))
& in(sK260(U_1105),U_1105) )
| ( sK258(U_1105) != sK259(U_1105)
& sK259(U_1105) = singleton(sK257(U_1105))
& sK258(U_1105) = singleton(sK257(U_1105))
& in(sK257(U_1105),U_1105) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_1104,sK261(U_1105))],[f_232_6]) ).
fof(f_232_8,plain,
( ! [U_1105,U_1103] :
( apply(sK261(U_1105),U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105)
| ~ sP254(U_1105,U_1103) )
& ! [U_1105,U_1103] :
( relation_dom(sK261(U_1105)) = U_1105
| ~ sP254(U_1105,U_1103) )
& ! [U_1105,U_1103] :
( function(sK261(U_1105))
| ~ sP254(U_1105,U_1103) )
& ! [U_1105,U_1103] :
( relation(sK261(U_1105))
| ~ sP254(U_1105,U_1103) )
& ! [U_1105,U_1101] :
( U_1101 != singleton(sK260(U_1105))
| ~ sP253(U_1105,U_1101) )
& ! [U_1105,U_1101] :
( in(sK260(U_1105),U_1105)
| ~ sP253(U_1105,U_1101) )
& ! [U_1105] :
( sK258(U_1105) != sK259(U_1105)
| ~ sP252(U_1105) )
& ! [U_1105] :
( sK259(U_1105) = singleton(sK257(U_1105))
| ~ sP252(U_1105) )
& ! [U_1105] :
( sK258(U_1105) = singleton(sK257(U_1105))
| ~ sP252(U_1105) )
& ! [U_1105] :
( in(sK257(U_1105),U_1105)
| ~ sP252(U_1105) )
& ! [U_1105,U_1103,U_1101] :
( sP254(U_1105,U_1103)
| sP253(U_1105,U_1101)
| sP252(U_1105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252,sP253,sP254])],[f_232_7]) ).
cnf(f_232_9,plain,
( sP254(U_1105,U_1103)
| sP253(U_1105,U_1101)
| sP252(U_1105) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_10,plain,
( in(sK257(U_1105),U_1105)
| ~ sP252(U_1105) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_11,plain,
( sK258(U_1105) = singleton(sK257(U_1105))
| ~ sP252(U_1105) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_12,plain,
( sK259(U_1105) = singleton(sK257(U_1105))
| ~ sP252(U_1105) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_13,plain,
( sK258(U_1105) != sK259(U_1105)
| ~ sP252(U_1105) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_14,plain,
( in(sK260(U_1105),U_1105)
| ~ sP253(U_1105,U_1101) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_15,plain,
( U_1101 != singleton(sK260(U_1105))
| ~ sP253(U_1105,U_1101) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_16,plain,
( relation(sK261(U_1105))
| ~ sP254(U_1105,U_1103) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_17,plain,
( function(sK261(U_1105))
| ~ sP254(U_1105,U_1103) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_18,plain,
( relation_dom(sK261(U_1105)) = U_1105
| ~ sP254(U_1105,U_1103) ),
inference(clausify,[status(thm)],[f_232_8]) ).
cnf(f_232_19,plain,
( apply(sK261(U_1105),U_1103) = singleton(U_1103)
| ~ in(U_1103,U_1105)
| ~ sP254(U_1105,U_1103) ),
inference(clausify,[status(thm)],[f_232_8]) ).
fof(f_233_1,plain,
! [A] :
? [B] :
( ! [C] :
( apply(B,C) = singleton(C)
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[s3_funct_1__e16_22__wellord2]) ).
fof(f_233_2,plain,
! [U_1108] :
? [U_1107] :
( ! [U_1106] :
( apply(U_1107,U_1106) = singleton(U_1106)
| ~ in(U_1106,U_1108) )
& relation_dom(U_1107) = U_1108
& function(U_1107)
& relation(U_1107) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_1108] :
( ! [U_1106] :
( apply(sK262(U_1108),U_1106) = singleton(U_1106)
| ~ in(U_1106,U_1108) )
& relation_dom(sK262(U_1108)) = U_1108
& function(sK262(U_1108))
& relation(sK262(U_1108)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_1107,sK262(U_1108))],[f_233_2]) ).
fof(f_233_4,plain,
( ! [U_1108,U_1106] :
( apply(sK262(U_1108),U_1106) = singleton(U_1106)
| ~ in(U_1106,U_1108) )
& ! [U_1108] : relation_dom(sK262(U_1108)) = U_1108
& ! [U_1108] : function(sK262(U_1108))
& ! [U_1108] : relation(sK262(U_1108)) ),
inference(definitional_conversion,[status(esa)],[f_233_3]) ).
cnf(f_233_5,plain,
relation(sK262(U_1108)),
inference(clausify,[status(thm)],[f_233_4]) ).
cnf(f_233_6,plain,
function(sK262(U_1108)),
inference(clausify,[status(thm)],[f_233_4]) ).
cnf(f_233_7,plain,
relation_dom(sK262(U_1108)) = U_1108,
inference(clausify,[status(thm)],[f_233_4]) ).
cnf(f_233_8,plain,
( apply(sK262(U_1108),U_1106) = singleton(U_1106)
| ~ in(U_1106,U_1108) ),
inference(clausify,[status(thm)],[f_233_4]) ).
fof(f_234_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_234_2,plain,
! [U_1110,U_1109] :
( disjoint(U_1109,U_1110)
| ~ disjoint(U_1110,U_1109) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_1110,U_1109] :
( disjoint(U_1109,U_1110)
| ~ disjoint(U_1110,U_1109) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( disjoint(U_1109,U_1110)
| ~ disjoint(U_1110,U_1109) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [A,B] :
( equipotent(B,A)
| ~ equipotent(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r2_wellord2]) ).
fof(f_235_2,plain,
! [U_1112,U_1111] :
( equipotent(U_1111,U_1112)
| ~ equipotent(U_1112,U_1111) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_1112,U_1111] :
( equipotent(U_1111,U_1112)
| ~ equipotent(U_1112,U_1111) ),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
( equipotent(U_1111,U_1112)
| ~ equipotent(U_1112,U_1111) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_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_236_2,plain,
! [U_1116,U_1115,U_1114,U_1113] :
( ( in(ordered_pair(U_1116,U_1115),cartesian_product2(U_1114,U_1113))
| ~ in(U_1115,U_1113)
| ~ in(U_1116,U_1114) )
& ( ( in(U_1115,U_1113)
& in(U_1116,U_1114) )
| ~ in(ordered_pair(U_1116,U_1115),cartesian_product2(U_1114,U_1113)) ) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
( ! [U_1124,U_1122,U_1120,U_1118] :
( in(ordered_pair(U_1124,U_1122),cartesian_product2(U_1120,U_1118))
| ~ in(U_1122,U_1118)
| ~ in(U_1124,U_1120) )
& ! [U_1123,U_1121,U_1119,U_1117] :
( ( in(U_1121,U_1117)
& in(U_1123,U_1119) )
| ~ in(ordered_pair(U_1123,U_1121),cartesian_product2(U_1119,U_1117)) ) ),
inference(miniscope,[status(thm)],[f_236_2]) ).
fof(f_236_4,plain,
( ! [U_1121,U_1119,U_1123,U_1117] :
( in(U_1121,U_1117)
| ~ sP255(U_1121,U_1119,U_1123,U_1117) )
& ! [U_1121,U_1119,U_1123,U_1117] :
( in(U_1123,U_1119)
| ~ sP255(U_1121,U_1119,U_1123,U_1117) )
& ! [U_1122,U_1124,U_1120,U_1118] :
( in(ordered_pair(U_1124,U_1122),cartesian_product2(U_1120,U_1118))
| ~ in(U_1122,U_1118)
| ~ in(U_1124,U_1120) )
& ! [U_1121,U_1119,U_1123,U_1117] :
( sP255(U_1121,U_1119,U_1123,U_1117)
| ~ in(ordered_pair(U_1123,U_1121),cartesian_product2(U_1119,U_1117)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255])],[f_236_3]) ).
cnf(f_236_5,plain,
( sP255(U_1121,U_1119,U_1123,U_1117)
| ~ in(ordered_pair(U_1123,U_1121),cartesian_product2(U_1119,U_1117)) ),
inference(clausify,[status(thm)],[f_236_4]) ).
cnf(f_236_6,plain,
( in(ordered_pair(U_1124,U_1122),cartesian_product2(U_1120,U_1118))
| ~ in(U_1122,U_1118)
| ~ in(U_1124,U_1120) ),
inference(clausify,[status(thm)],[f_236_4]) ).
cnf(f_236_7,plain,
( in(U_1123,U_1119)
| ~ sP255(U_1121,U_1119,U_1123,U_1117) ),
inference(clausify,[status(thm)],[f_236_4]) ).
cnf(f_236_8,plain,
( in(U_1121,U_1117)
| ~ sP255(U_1121,U_1119,U_1123,U_1117) ),
inference(clausify,[status(thm)],[f_236_4]) ).
fof(f_237_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_237_2,plain,
! [U_1125] : in(U_1125,succ(U_1125)),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_1125] : in(U_1125,succ(U_1125)),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
in(U_1125,succ(U_1125)),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_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_238_2,plain,
! [U_1129,U_1128,U_1127,U_1126] :
( U_1129 = U_1126
| U_1129 = U_1127
| unordered_pair(U_1129,U_1128) != unordered_pair(U_1127,U_1126) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_1129,U_1128,U_1127] :
( ! [U_1126] :
( U_1129 = U_1126
| unordered_pair(U_1129,U_1128) != unordered_pair(U_1127,U_1126) )
| U_1129 = U_1127 ),
inference(miniscope,[status(thm)],[f_238_2]) ).
fof(f_238_4,plain,
! [U_1126,U_1127,U_1128,U_1129] :
( U_1129 = U_1126
| unordered_pair(U_1129,U_1128) != unordered_pair(U_1127,U_1126)
| U_1129 = U_1127 ),
inference(definitional_conversion,[status(esa)],[f_238_3]) ).
cnf(f_238_5,plain,
( U_1129 = U_1126
| unordered_pair(U_1129,U_1128) != unordered_pair(U_1127,U_1126)
| U_1129 = U_1127 ),
inference(clausify,[status(thm)],[f_238_4]) ).
fof(f_239_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_239_2,plain,
! [U_1132,U_1131,U_1130] :
( ( ( in(U_1132,relation_rng(relation_rng_restriction(U_1131,U_1130)))
| ~ in(U_1132,relation_rng(U_1130))
| ~ in(U_1132,U_1131) )
& ( ( in(U_1132,relation_rng(U_1130))
& in(U_1132,U_1131) )
| ~ in(U_1132,relation_rng(relation_rng_restriction(U_1131,U_1130))) ) )
| ~ relation(U_1130) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
( ! [U_1130,U_1131,U_1132] :
( in(U_1132,relation_rng(U_1130))
| ~ sP256(U_1130,U_1131,U_1132) )
& ! [U_1130,U_1131,U_1132] :
( in(U_1132,U_1131)
| ~ sP256(U_1130,U_1131,U_1132) )
& ! [U_1130,U_1131,U_1132] :
( in(U_1132,relation_rng(relation_rng_restriction(U_1131,U_1130)))
| ~ in(U_1132,relation_rng(U_1130))
| ~ in(U_1132,U_1131)
| ~ sP257(U_1130,U_1131,U_1132) )
& ! [U_1130,U_1131,U_1132] :
( sP256(U_1130,U_1131,U_1132)
| ~ in(U_1132,relation_rng(relation_rng_restriction(U_1131,U_1130)))
| ~ sP257(U_1130,U_1131,U_1132) )
& ! [U_1130,U_1131,U_1132] :
( sP257(U_1130,U_1131,U_1132)
| ~ relation(U_1130) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256,sP257])],[f_239_2]) ).
cnf(f_239_4,plain,
( sP257(U_1130,U_1131,U_1132)
| ~ relation(U_1130) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_5,plain,
( sP256(U_1130,U_1131,U_1132)
| ~ in(U_1132,relation_rng(relation_rng_restriction(U_1131,U_1130)))
| ~ sP257(U_1130,U_1131,U_1132) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_6,plain,
( in(U_1132,relation_rng(relation_rng_restriction(U_1131,U_1130)))
| ~ in(U_1132,relation_rng(U_1130))
| ~ in(U_1132,U_1131)
| ~ sP257(U_1130,U_1131,U_1132) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_7,plain,
( in(U_1132,U_1131)
| ~ sP256(U_1130,U_1131,U_1132) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_8,plain,
( in(U_1132,relation_rng(U_1130))
| ~ sP256(U_1130,U_1131,U_1132) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_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_240_2,plain,
! [U_1134,U_1133] :
( subset(relation_rng(relation_rng_restriction(U_1134,U_1133)),U_1134)
| ~ relation(U_1133) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_1134,U_1133] :
( subset(relation_rng(relation_rng_restriction(U_1134,U_1133)),U_1134)
| ~ relation(U_1133) ),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
( subset(relation_rng(relation_rng_restriction(U_1134,U_1133)),U_1134)
| ~ relation(U_1133) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_241_2,plain,
! [U_1136,U_1135] :
( subset(relation_rng_restriction(U_1136,U_1135),U_1135)
| ~ relation(U_1135) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
! [U_1136,U_1135] :
( subset(relation_rng_restriction(U_1136,U_1135),U_1135)
| ~ relation(U_1135) ),
inference(definitional_conversion,[status(esa)],[f_241_2]) ).
cnf(f_241_4,plain,
( subset(relation_rng_restriction(U_1136,U_1135),U_1135)
| ~ relation(U_1135) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_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_242_2,plain,
! [U_1138,U_1137] :
( subset(relation_rng(relation_rng_restriction(U_1138,U_1137)),relation_rng(U_1137))
| ~ relation(U_1137) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_1138,U_1137] :
( subset(relation_rng(relation_rng_restriction(U_1138,U_1137)),relation_rng(U_1137))
| ~ relation(U_1137) ),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
( subset(relation_rng(relation_rng_restriction(U_1138,U_1137)),relation_rng(U_1137))
| ~ relation(U_1137) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_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_243_2,plain,
! [U_1141,U_1140,U_1139] :
( ( subset(cartesian_product2(U_1139,U_1141),cartesian_product2(U_1139,U_1140))
& subset(cartesian_product2(U_1141,U_1139),cartesian_product2(U_1140,U_1139)) )
| ~ subset(U_1141,U_1140) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_1141,U_1140] :
( ( ! [U_1143] : subset(cartesian_product2(U_1143,U_1141),cartesian_product2(U_1143,U_1140))
& ! [U_1142] : subset(cartesian_product2(U_1141,U_1142),cartesian_product2(U_1140,U_1142)) )
| ~ subset(U_1141,U_1140) ),
inference(miniscope,[status(thm)],[f_243_2]) ).
fof(f_243_4,plain,
( ! [U_1140,U_1141,U_1142,U_1143] :
( subset(cartesian_product2(U_1143,U_1141),cartesian_product2(U_1143,U_1140))
| ~ sP258(U_1140,U_1141,U_1142,U_1143) )
& ! [U_1140,U_1141,U_1142,U_1143] :
( subset(cartesian_product2(U_1141,U_1142),cartesian_product2(U_1140,U_1142))
| ~ sP258(U_1140,U_1141,U_1142,U_1143) )
& ! [U_1140,U_1141,U_1142,U_1143] :
( sP258(U_1140,U_1141,U_1142,U_1143)
| ~ subset(U_1141,U_1140) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_243_3]) ).
cnf(f_243_5,plain,
( sP258(U_1140,U_1141,U_1142,U_1143)
| ~ subset(U_1141,U_1140) ),
inference(clausify,[status(thm)],[f_243_4]) ).
cnf(f_243_6,plain,
( subset(cartesian_product2(U_1141,U_1142),cartesian_product2(U_1140,U_1142))
| ~ sP258(U_1140,U_1141,U_1142,U_1143) ),
inference(clausify,[status(thm)],[f_243_4]) ).
cnf(f_243_7,plain,
( subset(cartesian_product2(U_1143,U_1141),cartesian_product2(U_1143,U_1140))
| ~ sP258(U_1140,U_1141,U_1142,U_1143) ),
inference(clausify,[status(thm)],[f_243_4]) ).
fof(f_244_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_244_2,plain,
! [U_1145,U_1144] :
( relation_rng(relation_rng_restriction(U_1145,U_1144)) = set_intersection2(relation_rng(U_1144),U_1145)
| ~ relation(U_1144) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_1144,U_1145] :
( relation_rng(relation_rng_restriction(U_1145,U_1144)) = set_intersection2(relation_rng(U_1144),U_1145)
| ~ relation(U_1144) ),
inference(definitional_conversion,[status(esa)],[f_244_2]) ).
cnf(f_244_4,plain,
( relation_rng(relation_rng_restriction(U_1145,U_1144)) = set_intersection2(relation_rng(U_1144),U_1145)
| ~ relation(U_1144) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_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_245_2,plain,
! [U_1149,U_1148,U_1147,U_1146] :
( subset(cartesian_product2(U_1149,U_1147),cartesian_product2(U_1148,U_1146))
| ~ subset(U_1147,U_1146)
| ~ subset(U_1149,U_1148) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_1146,U_1147,U_1148,U_1149] :
( subset(cartesian_product2(U_1149,U_1147),cartesian_product2(U_1148,U_1146))
| ~ subset(U_1147,U_1146)
| ~ subset(U_1149,U_1148) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( subset(cartesian_product2(U_1149,U_1147),cartesian_product2(U_1148,U_1146))
| ~ subset(U_1147,U_1146)
| ~ subset(U_1149,U_1148) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_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_246_2,plain,
! [U_1152,U_1151,U_1150] :
( ( subset(relation_rng(U_1150),U_1151)
& subset(relation_dom(U_1150),U_1152) )
| ~ relation_of2_as_subset(U_1150,U_1152,U_1151) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
( ! [U_1152,U_1151,U_1150] :
( subset(relation_rng(U_1150),U_1151)
| ~ sP259(U_1152,U_1151,U_1150) )
& ! [U_1152,U_1151,U_1150] :
( subset(relation_dom(U_1150),U_1152)
| ~ sP259(U_1152,U_1151,U_1150) )
& ! [U_1152,U_1151,U_1150] :
( sP259(U_1152,U_1151,U_1150)
| ~ relation_of2_as_subset(U_1150,U_1152,U_1151) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_246_2]) ).
cnf(f_246_4,plain,
( sP259(U_1152,U_1151,U_1150)
| ~ relation_of2_as_subset(U_1150,U_1152,U_1151) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_5,plain,
( subset(relation_dom(U_1150),U_1152)
| ~ sP259(U_1152,U_1151,U_1150) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_6,plain,
( subset(relation_rng(U_1150),U_1151)
| ~ sP259(U_1152,U_1151,U_1150) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_247_2,plain,
! [U_1154,U_1153] :
( set_union2(U_1154,U_1153) = U_1153
| ~ subset(U_1154,U_1153) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_1154,U_1153] :
( set_union2(U_1154,U_1153) = U_1153
| ~ subset(U_1154,U_1153) ),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
( set_union2(U_1154,U_1153) = U_1153
| ~ subset(U_1154,U_1153) ),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_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_248_2,plain,
! [U_1160] :
? [U_1159] :
( ! [U_1158] :
( in(U_1158,U_1159)
| are_equipotent(U_1158,U_1159)
| ~ subset(U_1158,U_1159) )
& ! [U_1157] :
( in(powerset(U_1157),U_1159)
| ~ in(U_1157,U_1159) )
& ! [U_1156,U_1155] :
( in(U_1155,U_1159)
| ~ subset(U_1155,U_1156)
| ~ in(U_1156,U_1159) )
& in(U_1160,U_1159) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_1160] :
( ! [U_1158] :
( in(U_1158,sK263(U_1160))
| are_equipotent(U_1158,sK263(U_1160))
| ~ subset(U_1158,sK263(U_1160)) )
& ! [U_1157] :
( in(powerset(U_1157),sK263(U_1160))
| ~ in(U_1157,sK263(U_1160)) )
& ! [U_1156,U_1155] :
( in(U_1155,sK263(U_1160))
| ~ subset(U_1155,U_1156)
| ~ in(U_1156,sK263(U_1160)) )
& in(U_1160,sK263(U_1160)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_1159,sK263(U_1160))],[f_248_2]) ).
fof(f_248_4,plain,
( ! [U_1158,U_1160] :
( in(U_1158,sK263(U_1160))
| are_equipotent(U_1158,sK263(U_1160))
| ~ subset(U_1158,sK263(U_1160)) )
& ! [U_1157,U_1160] :
( in(powerset(U_1157),sK263(U_1160))
| ~ in(U_1157,sK263(U_1160)) )
& ! [U_1156,U_1155,U_1160] :
( in(U_1155,sK263(U_1160))
| ~ subset(U_1155,U_1156)
| ~ in(U_1156,sK263(U_1160)) )
& ! [U_1160] : in(U_1160,sK263(U_1160)) ),
inference(definitional_conversion,[status(esa)],[f_248_3]) ).
cnf(f_248_5,plain,
in(U_1160,sK263(U_1160)),
inference(clausify,[status(thm)],[f_248_4]) ).
cnf(f_248_6,plain,
( in(U_1155,sK263(U_1160))
| ~ subset(U_1155,U_1156)
| ~ in(U_1156,sK263(U_1160)) ),
inference(clausify,[status(thm)],[f_248_4]) ).
cnf(f_248_7,plain,
( in(powerset(U_1157),sK263(U_1160))
| ~ in(U_1157,sK263(U_1160)) ),
inference(clausify,[status(thm)],[f_248_4]) ).
cnf(f_248_8,plain,
( in(U_1158,sK263(U_1160))
| are_equipotent(U_1158,sK263(U_1160))
| ~ subset(U_1158,sK263(U_1160)) ),
inference(clausify,[status(thm)],[f_248_4]) ).
fof(f_249_1,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
inference(negate,[status(cth)],[t13_finset_1]) ).
fof(f_249_2,negated_conjecture,
? [A,B] :
( ~ finite(A)
& finite(B)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_249_1]) ).
fof(f_249_3,negated_conjecture,
? [U_1162,U_1161] :
( ~ finite(U_1162)
& finite(U_1161)
& subset(U_1162,U_1161) ),
inference(variable_rename,[status(thm)],[f_249_2]) ).
fof(f_249_4,negated_conjecture,
? [U_1162] :
( ? [U_1161] :
( finite(U_1161)
& subset(U_1162,U_1161) )
& ~ finite(U_1162) ),
inference(miniscope,[status(thm)],[f_249_3]) ).
fof(f_249_5,negated_conjecture,
( ? [U_1161] :
( finite(U_1161)
& subset(sK264,U_1161) )
& ~ finite(sK264) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_1162,sK264)],[f_249_4]) ).
fof(f_249_6,negated_conjecture,
( finite(sK265)
& subset(sK264,sK265)
& ~ finite(sK264) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_1161,sK265)],[f_249_5]) ).
fof(f_249_7,negated_conjecture,
( finite(sK265)
& subset(sK264,sK265)
& ~ finite(sK264) ),
inference(definitional_conversion,[status(esa)],[f_249_6]) ).
cnf(f_249_8,negated_conjecture,
~ finite(sK264),
inference(clausify,[status(thm)],[f_249_7]) ).
cnf(f_249_9,negated_conjecture,
subset(sK264,sK265),
inference(clausify,[status(thm)],[f_249_7]) ).
cnf(f_249_10,negated_conjecture,
finite(sK265),
inference(clausify,[status(thm)],[f_249_7]) ).
fof(f_250_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_250_2,plain,
! [U_1165,U_1164,U_1163] :
( relation_dom_restriction(relation_rng_restriction(U_1165,U_1163),U_1164) = relation_rng_restriction(U_1165,relation_dom_restriction(U_1163,U_1164))
| ~ relation(U_1163) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_1164,U_1163,U_1165] :
( relation_dom_restriction(relation_rng_restriction(U_1165,U_1163),U_1164) = relation_rng_restriction(U_1165,relation_dom_restriction(U_1163,U_1164))
| ~ relation(U_1163) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( relation_dom_restriction(relation_rng_restriction(U_1165,U_1163),U_1164) = relation_rng_restriction(U_1165,relation_dom_restriction(U_1163,U_1164))
| ~ relation(U_1163) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_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_251_2,plain,
! [U_1170,U_1169,U_1168] :
( ( ( in(U_1170,relation_image(U_1168,U_1169))
| ! [U_1167] :
( ~ in(U_1167,U_1169)
| ~ in(ordered_pair(U_1167,U_1170),U_1168)
| ~ in(U_1167,relation_dom(U_1168)) ) )
& ( ? [U_1166] :
( in(U_1166,U_1169)
& in(ordered_pair(U_1166,U_1170),U_1168)
& in(U_1166,relation_dom(U_1168)) )
| ~ in(U_1170,relation_image(U_1168,U_1169)) ) )
| ~ relation(U_1168) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_1170,U_1169,U_1168] :
( ( ( in(U_1170,relation_image(U_1168,U_1169))
| ! [U_1167] :
( ~ in(U_1167,U_1169)
| ~ in(ordered_pair(U_1167,U_1170),U_1168)
| ~ in(U_1167,relation_dom(U_1168)) ) )
& ( ( in(sK266(U_1170,U_1169,U_1168),U_1169)
& in(ordered_pair(sK266(U_1170,U_1169,U_1168),U_1170),U_1168)
& in(sK266(U_1170,U_1169,U_1168),relation_dom(U_1168)) )
| ~ in(U_1170,relation_image(U_1168,U_1169)) ) )
| ~ relation(U_1168) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_1166,sK266(U_1170,U_1169,U_1168))],[f_251_2]) ).
fof(f_251_4,plain,
( ! [U_1168,U_1169,U_1170] :
( in(sK266(U_1170,U_1169,U_1168),U_1169)
| ~ sP260(U_1168,U_1169,U_1170) )
& ! [U_1168,U_1169,U_1170] :
( in(ordered_pair(sK266(U_1170,U_1169,U_1168),U_1170),U_1168)
| ~ sP260(U_1168,U_1169,U_1170) )
& ! [U_1168,U_1169,U_1170] :
( in(sK266(U_1170,U_1169,U_1168),relation_dom(U_1168))
| ~ sP260(U_1168,U_1169,U_1170) )
& ! [U_1167,U_1168,U_1169,U_1170] :
( in(U_1170,relation_image(U_1168,U_1169))
| ~ in(U_1167,U_1169)
| ~ in(ordered_pair(U_1167,U_1170),U_1168)
| ~ in(U_1167,relation_dom(U_1168))
| ~ sP261(U_1167,U_1168,U_1169,U_1170) )
& ! [U_1167,U_1168,U_1169,U_1170] :
( sP260(U_1168,U_1169,U_1170)
| ~ in(U_1170,relation_image(U_1168,U_1169))
| ~ sP261(U_1167,U_1168,U_1169,U_1170) )
& ! [U_1167,U_1168,U_1169,U_1170] :
( sP261(U_1167,U_1168,U_1169,U_1170)
| ~ relation(U_1168) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260,sP261])],[f_251_3]) ).
cnf(f_251_5,plain,
( sP261(U_1167,U_1168,U_1169,U_1170)
| ~ relation(U_1168) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_6,plain,
( sP260(U_1168,U_1169,U_1170)
| ~ in(U_1170,relation_image(U_1168,U_1169))
| ~ sP261(U_1167,U_1168,U_1169,U_1170) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_7,plain,
( in(U_1170,relation_image(U_1168,U_1169))
| ~ in(U_1167,U_1169)
| ~ in(ordered_pair(U_1167,U_1170),U_1168)
| ~ in(U_1167,relation_dom(U_1168))
| ~ sP261(U_1167,U_1168,U_1169,U_1170) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_8,plain,
( in(sK266(U_1170,U_1169,U_1168),relation_dom(U_1168))
| ~ sP260(U_1168,U_1169,U_1170) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_9,plain,
( in(ordered_pair(sK266(U_1170,U_1169,U_1168),U_1170),U_1168)
| ~ sP260(U_1168,U_1169,U_1170) ),
inference(clausify,[status(thm)],[f_251_4]) ).
cnf(f_251_10,plain,
( in(sK266(U_1170,U_1169,U_1168),U_1169)
| ~ sP260(U_1168,U_1169,U_1170) ),
inference(clausify,[status(thm)],[f_251_4]) ).
fof(f_252_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_252_2,plain,
! [U_1172,U_1171] :
( subset(relation_image(U_1171,U_1172),relation_rng(U_1171))
| ~ relation(U_1171) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_1172,U_1171] :
( subset(relation_image(U_1171,U_1172),relation_rng(U_1171))
| ~ relation(U_1171) ),
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
( subset(relation_image(U_1171,U_1172),relation_rng(U_1171))
| ~ relation(U_1171) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_1174,U_1173] :
( subset(relation_image(U_1173,relation_inverse_image(U_1173,U_1174)),U_1174)
| ~ function(U_1173)
| ~ relation(U_1173) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
! [U_1173,U_1174] :
( subset(relation_image(U_1173,relation_inverse_image(U_1173,U_1174)),U_1174)
| ~ function(U_1173)
| ~ relation(U_1173) ),
inference(definitional_conversion,[status(esa)],[f_253_2]) ).
cnf(f_253_4,plain,
( subset(relation_image(U_1173,relation_inverse_image(U_1173,U_1174)),U_1174)
| ~ function(U_1173)
| ~ relation(U_1173) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_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_254_2,plain,
! [U_1176,U_1175] :
( relation_image(U_1175,U_1176) = relation_image(U_1175,set_intersection2(relation_dom(U_1175),U_1176))
| ~ relation(U_1175) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_1175,U_1176] :
( relation_image(U_1175,U_1176) = relation_image(U_1175,set_intersection2(relation_dom(U_1175),U_1176))
| ~ relation(U_1175) ),
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
( relation_image(U_1175,U_1176) = relation_image(U_1175,set_intersection2(relation_dom(U_1175),U_1176))
| ~ relation(U_1175) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_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_255_2,plain,
! [U_1178,U_1177] :
( subset(U_1178,relation_inverse_image(U_1177,relation_image(U_1177,U_1178)))
| ~ subset(U_1178,relation_dom(U_1177))
| ~ relation(U_1177) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_1177,U_1178] :
( subset(U_1178,relation_inverse_image(U_1177,relation_image(U_1177,U_1178)))
| ~ subset(U_1178,relation_dom(U_1177))
| ~ relation(U_1177) ),
inference(definitional_conversion,[status(esa)],[f_255_2]) ).
cnf(f_255_4,plain,
( subset(U_1178,relation_inverse_image(U_1177,relation_image(U_1177,U_1178)))
| ~ subset(U_1178,relation_dom(U_1177))
| ~ relation(U_1177) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_256_2,plain,
! [U_1179] :
( relation_image(U_1179,relation_dom(U_1179)) = relation_rng(U_1179)
| ~ relation(U_1179) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_1179] :
( relation_image(U_1179,relation_dom(U_1179)) = relation_rng(U_1179)
| ~ relation(U_1179) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( relation_image(U_1179,relation_dom(U_1179)) = relation_rng(U_1179)
| ~ relation(U_1179) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_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_257_2,plain,
! [U_1181,U_1180] :
( relation_image(U_1180,relation_inverse_image(U_1180,U_1181)) = U_1181
| ~ subset(U_1181,relation_rng(U_1180))
| ~ function(U_1180)
| ~ relation(U_1180) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_1180,U_1181] :
( relation_image(U_1180,relation_inverse_image(U_1180,U_1181)) = U_1181
| ~ subset(U_1181,relation_rng(U_1180))
| ~ function(U_1180)
| ~ relation(U_1180) ),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
( relation_image(U_1180,relation_inverse_image(U_1180,U_1181)) = U_1181
| ~ subset(U_1181,relation_rng(U_1180))
| ~ function(U_1180)
| ~ relation(U_1180) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_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_258_2,plain,
! [U_1185,U_1184,U_1183,U_1182] :
( relation_of2_as_subset(U_1182,U_1183,U_1184)
| ~ subset(relation_rng(U_1182),U_1184)
| ~ relation_of2_as_subset(U_1182,U_1183,U_1185) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_1185,U_1183,U_1184,U_1182] :
( relation_of2_as_subset(U_1182,U_1183,U_1184)
| ~ subset(relation_rng(U_1182),U_1184)
| ~ relation_of2_as_subset(U_1182,U_1183,U_1185) ),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
( relation_of2_as_subset(U_1182,U_1183,U_1184)
| ~ subset(relation_rng(U_1182),U_1184)
| ~ relation_of2_as_subset(U_1182,U_1183,U_1185) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_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_259_2,plain,
! [U_1187] :
( ! [U_1186] :
( relation_rng(relation_composition(U_1187,U_1186)) = relation_image(U_1186,relation_rng(U_1187))
| ~ relation(U_1186) )
| ~ relation(U_1187) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_1186,U_1187] :
( relation_rng(relation_composition(U_1187,U_1186)) = relation_image(U_1186,relation_rng(U_1187))
| ~ relation(U_1186)
| ~ relation(U_1187) ),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
( relation_rng(relation_composition(U_1187,U_1186)) = relation_image(U_1186,relation_rng(U_1187))
| ~ relation(U_1186)
| ~ relation(U_1187) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_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_260_2,plain,
! [U_1192,U_1191,U_1190] :
( ( ( in(U_1192,relation_inverse_image(U_1190,U_1191))
| ! [U_1189] :
( ~ in(U_1189,U_1191)
| ~ in(ordered_pair(U_1192,U_1189),U_1190)
| ~ in(U_1189,relation_rng(U_1190)) ) )
& ( ? [U_1188] :
( in(U_1188,U_1191)
& in(ordered_pair(U_1192,U_1188),U_1190)
& in(U_1188,relation_rng(U_1190)) )
| ~ in(U_1192,relation_inverse_image(U_1190,U_1191)) ) )
| ~ relation(U_1190) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_1192,U_1191,U_1190] :
( ( ( in(U_1192,relation_inverse_image(U_1190,U_1191))
| ! [U_1189] :
( ~ in(U_1189,U_1191)
| ~ in(ordered_pair(U_1192,U_1189),U_1190)
| ~ in(U_1189,relation_rng(U_1190)) ) )
& ( ( in(sK267(U_1192,U_1191,U_1190),U_1191)
& in(ordered_pair(U_1192,sK267(U_1192,U_1191,U_1190)),U_1190)
& in(sK267(U_1192,U_1191,U_1190),relation_rng(U_1190)) )
| ~ in(U_1192,relation_inverse_image(U_1190,U_1191)) ) )
| ~ relation(U_1190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_1188,sK267(U_1192,U_1191,U_1190))],[f_260_2]) ).
fof(f_260_4,plain,
( ! [U_1190,U_1191,U_1192] :
( in(sK267(U_1192,U_1191,U_1190),U_1191)
| ~ sP262(U_1190,U_1191,U_1192) )
& ! [U_1190,U_1191,U_1192] :
( in(ordered_pair(U_1192,sK267(U_1192,U_1191,U_1190)),U_1190)
| ~ sP262(U_1190,U_1191,U_1192) )
& ! [U_1190,U_1191,U_1192] :
( in(sK267(U_1192,U_1191,U_1190),relation_rng(U_1190))
| ~ sP262(U_1190,U_1191,U_1192) )
& ! [U_1189,U_1190,U_1191,U_1192] :
( in(U_1192,relation_inverse_image(U_1190,U_1191))
| ~ in(U_1189,U_1191)
| ~ in(ordered_pair(U_1192,U_1189),U_1190)
| ~ in(U_1189,relation_rng(U_1190))
| ~ sP263(U_1189,U_1190,U_1191,U_1192) )
& ! [U_1189,U_1190,U_1191,U_1192] :
( sP262(U_1190,U_1191,U_1192)
| ~ in(U_1192,relation_inverse_image(U_1190,U_1191))
| ~ sP263(U_1189,U_1190,U_1191,U_1192) )
& ! [U_1189,U_1190,U_1191,U_1192] :
( sP263(U_1189,U_1190,U_1191,U_1192)
| ~ relation(U_1190) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262,sP263])],[f_260_3]) ).
cnf(f_260_5,plain,
( sP263(U_1189,U_1190,U_1191,U_1192)
| ~ relation(U_1190) ),
inference(clausify,[status(thm)],[f_260_4]) ).
cnf(f_260_6,plain,
( sP262(U_1190,U_1191,U_1192)
| ~ in(U_1192,relation_inverse_image(U_1190,U_1191))
| ~ sP263(U_1189,U_1190,U_1191,U_1192) ),
inference(clausify,[status(thm)],[f_260_4]) ).
cnf(f_260_7,plain,
( in(U_1192,relation_inverse_image(U_1190,U_1191))
| ~ in(U_1189,U_1191)
| ~ in(ordered_pair(U_1192,U_1189),U_1190)
| ~ in(U_1189,relation_rng(U_1190))
| ~ sP263(U_1189,U_1190,U_1191,U_1192) ),
inference(clausify,[status(thm)],[f_260_4]) ).
cnf(f_260_8,plain,
( in(sK267(U_1192,U_1191,U_1190),relation_rng(U_1190))
| ~ sP262(U_1190,U_1191,U_1192) ),
inference(clausify,[status(thm)],[f_260_4]) ).
cnf(f_260_9,plain,
( in(ordered_pair(U_1192,sK267(U_1192,U_1191,U_1190)),U_1190)
| ~ sP262(U_1190,U_1191,U_1192) ),
inference(clausify,[status(thm)],[f_260_4]) ).
cnf(f_260_10,plain,
( in(sK267(U_1192,U_1191,U_1190),U_1191)
| ~ sP262(U_1190,U_1191,U_1192) ),
inference(clausify,[status(thm)],[f_260_4]) ).
fof(f_261_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_261_2,plain,
! [U_1194,U_1193] :
( subset(relation_inverse_image(U_1193,U_1194),relation_dom(U_1193))
| ~ relation(U_1193) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
! [U_1194,U_1193] :
( subset(relation_inverse_image(U_1193,U_1194),relation_dom(U_1193))
| ~ relation(U_1193) ),
inference(definitional_conversion,[status(esa)],[f_261_2]) ).
cnf(f_261_4,plain,
( subset(relation_inverse_image(U_1193,U_1194),relation_dom(U_1193))
| ~ relation(U_1193) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_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_262_2,plain,
! [U_1198,U_1197,U_1196,U_1195] :
( relation_of2_as_subset(U_1195,U_1196,U_1197)
| ~ subset(U_1198,U_1197)
| ~ relation_of2_as_subset(U_1195,U_1196,U_1198) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_1197,U_1196,U_1198,U_1195] :
( relation_of2_as_subset(U_1195,U_1196,U_1197)
| ~ subset(U_1198,U_1197)
| ~ relation_of2_as_subset(U_1195,U_1196,U_1198) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( relation_of2_as_subset(U_1195,U_1196,U_1197)
| ~ subset(U_1198,U_1197)
| ~ relation_of2_as_subset(U_1195,U_1196,U_1198) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_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_263_2,plain,
! [U_1201,U_1200,U_1199] :
( ( ( in(U_1201,relation_restriction(U_1199,U_1200))
| ~ in(U_1201,cartesian_product2(U_1200,U_1200))
| ~ in(U_1201,U_1199) )
& ( ( in(U_1201,cartesian_product2(U_1200,U_1200))
& in(U_1201,U_1199) )
| ~ in(U_1201,relation_restriction(U_1199,U_1200)) ) )
| ~ relation(U_1199) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
( ! [U_1201,U_1200,U_1199] :
( in(U_1201,cartesian_product2(U_1200,U_1200))
| ~ sP264(U_1201,U_1200,U_1199) )
& ! [U_1201,U_1200,U_1199] :
( in(U_1201,U_1199)
| ~ sP264(U_1201,U_1200,U_1199) )
& ! [U_1201,U_1200,U_1199] :
( in(U_1201,relation_restriction(U_1199,U_1200))
| ~ in(U_1201,cartesian_product2(U_1200,U_1200))
| ~ in(U_1201,U_1199)
| ~ sP265(U_1201,U_1200,U_1199) )
& ! [U_1201,U_1200,U_1199] :
( sP264(U_1201,U_1200,U_1199)
| ~ in(U_1201,relation_restriction(U_1199,U_1200))
| ~ sP265(U_1201,U_1200,U_1199) )
& ! [U_1201,U_1200,U_1199] :
( sP265(U_1201,U_1200,U_1199)
| ~ relation(U_1199) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264,sP265])],[f_263_2]) ).
cnf(f_263_4,plain,
( sP265(U_1201,U_1200,U_1199)
| ~ relation(U_1199) ),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_5,plain,
( sP264(U_1201,U_1200,U_1199)
| ~ in(U_1201,relation_restriction(U_1199,U_1200))
| ~ sP265(U_1201,U_1200,U_1199) ),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_6,plain,
( in(U_1201,relation_restriction(U_1199,U_1200))
| ~ in(U_1201,cartesian_product2(U_1200,U_1200))
| ~ in(U_1201,U_1199)
| ~ sP265(U_1201,U_1200,U_1199) ),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_7,plain,
( in(U_1201,U_1199)
| ~ sP264(U_1201,U_1200,U_1199) ),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_8,plain,
( in(U_1201,cartesian_product2(U_1200,U_1200))
| ~ sP264(U_1201,U_1200,U_1199) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_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_264_2,plain,
! [U_1203,U_1202] :
( relation_inverse_image(U_1202,U_1203) != empty_set
| ~ subset(U_1203,relation_rng(U_1202))
| U_1203 = empty_set
| ~ relation(U_1202) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_1203,U_1202] :
( relation_inverse_image(U_1202,U_1203) != empty_set
| ~ subset(U_1203,relation_rng(U_1202))
| U_1203 = empty_set
| ~ relation(U_1202) ),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
( relation_inverse_image(U_1202,U_1203) != empty_set
| ~ subset(U_1203,relation_rng(U_1202))
| U_1203 = empty_set
| ~ relation(U_1202) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_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_265_2,plain,
! [U_1206,U_1205,U_1204] :
( subset(relation_inverse_image(U_1204,U_1206),relation_inverse_image(U_1204,U_1205))
| ~ subset(U_1206,U_1205)
| ~ relation(U_1204) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_1206,U_1205,U_1204] :
( subset(relation_inverse_image(U_1204,U_1206),relation_inverse_image(U_1204,U_1205))
| ~ subset(U_1206,U_1205)
| ~ relation(U_1204) ),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_4,plain,
( subset(relation_inverse_image(U_1204,U_1206),relation_inverse_image(U_1204,U_1205))
| ~ subset(U_1206,U_1205)
| ~ relation(U_1204) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_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_266_2,plain,
! [U_1208,U_1207] :
( relation_restriction(U_1207,U_1208) = relation_dom_restriction(relation_rng_restriction(U_1208,U_1207),U_1208)
| ~ relation(U_1207) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_1208,U_1207] :
( relation_restriction(U_1207,U_1208) = relation_dom_restriction(relation_rng_restriction(U_1208,U_1207),U_1208)
| ~ relation(U_1207) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( relation_restriction(U_1207,U_1208) = relation_dom_restriction(relation_rng_restriction(U_1208,U_1207),U_1208)
| ~ relation(U_1207) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_267_2,plain,
! [U_1210,U_1209] : subset(set_intersection2(U_1210,U_1209),U_1210),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_1209,U_1210] : subset(set_intersection2(U_1210,U_1209),U_1210),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
subset(set_intersection2(U_1210,U_1209),U_1210),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_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_268_2,plain,
! [U_1212,U_1211] :
( relation_restriction(U_1211,U_1212) = relation_rng_restriction(U_1212,relation_dom_restriction(U_1211,U_1212))
| ~ relation(U_1211) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_1211,U_1212] :
( relation_restriction(U_1211,U_1212) = relation_rng_restriction(U_1212,relation_dom_restriction(U_1211,U_1212))
| ~ relation(U_1211) ),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
( relation_restriction(U_1211,U_1212) = relation_rng_restriction(U_1212,relation_dom_restriction(U_1211,U_1212))
| ~ relation(U_1211) ),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_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_269_2,plain,
! [U_1215,U_1214,U_1213] :
( ( in(U_1215,U_1214)
& in(U_1215,relation_field(U_1213)) )
| ~ in(U_1215,relation_field(relation_restriction(U_1213,U_1214)))
| ~ relation(U_1213) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_1213,U_1214,U_1215] :
( in(U_1215,U_1214)
| ~ sP266(U_1213,U_1214,U_1215) )
& ! [U_1213,U_1214,U_1215] :
( in(U_1215,relation_field(U_1213))
| ~ sP266(U_1213,U_1214,U_1215) )
& ! [U_1213,U_1214,U_1215] :
( sP266(U_1213,U_1214,U_1215)
| ~ in(U_1215,relation_field(relation_restriction(U_1213,U_1214)))
| ~ relation(U_1213) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266])],[f_269_2]) ).
cnf(f_269_4,plain,
( sP266(U_1213,U_1214,U_1215)
| ~ in(U_1215,relation_field(relation_restriction(U_1213,U_1214)))
| ~ relation(U_1213) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( in(U_1215,relation_field(U_1213))
| ~ sP266(U_1213,U_1214,U_1215) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_6,plain,
( in(U_1215,U_1214)
| ~ sP266(U_1213,U_1214,U_1215) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_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_270_2,plain,
! [U_1218,U_1217,U_1216] :
( subset(U_1218,set_intersection2(U_1217,U_1216))
| ~ subset(U_1218,U_1216)
| ~ subset(U_1218,U_1217) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_1216,U_1217,U_1218] :
( subset(U_1218,set_intersection2(U_1217,U_1216))
| ~ subset(U_1218,U_1216)
| ~ subset(U_1218,U_1217) ),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
( subset(U_1218,set_intersection2(U_1217,U_1216))
| ~ subset(U_1218,U_1216)
| ~ subset(U_1218,U_1217) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_271_2,plain,
! [U_1219] : set_union2(U_1219,empty_set) = U_1219,
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_1219] : set_union2(U_1219,empty_set) = U_1219,
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
set_union2(U_1219,empty_set) = U_1219,
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_272_2,plain,
! [U_1221,U_1220] :
( element(U_1221,U_1220)
| ~ in(U_1221,U_1220) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_1221,U_1220] :
( element(U_1221,U_1220)
| ~ in(U_1221,U_1220) ),
inference(definitional_conversion,[status(esa)],[f_272_2]) ).
cnf(f_272_4,plain,
( element(U_1221,U_1220)
| ~ in(U_1221,U_1220) ),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_273_2,plain,
! [U_1224,U_1223,U_1222] :
( subset(U_1224,U_1222)
| ~ subset(U_1223,U_1222)
| ~ subset(U_1224,U_1223) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_1224,U_1222,U_1223] :
( subset(U_1224,U_1222)
| ~ subset(U_1223,U_1222)
| ~ subset(U_1224,U_1223) ),
inference(definitional_conversion,[status(esa)],[f_273_2]) ).
cnf(f_273_4,plain,
( subset(U_1224,U_1222)
| ~ subset(U_1223,U_1222)
| ~ subset(U_1224,U_1223) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_274_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_274_1]) ).
cnf(f_274_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_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_275_2,plain,
! [U_1227,U_1226,U_1225] :
( ( in(U_1226,relation_rng(U_1225))
& in(U_1227,relation_dom(U_1225)) )
| ~ in(ordered_pair(U_1227,U_1226),U_1225)
| ~ relation(U_1225) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_1225,U_1226,U_1227] :
( in(U_1226,relation_rng(U_1225))
| ~ sP267(U_1225,U_1226,U_1227) )
& ! [U_1225,U_1226,U_1227] :
( in(U_1227,relation_dom(U_1225))
| ~ sP267(U_1225,U_1226,U_1227) )
& ! [U_1225,U_1226,U_1227] :
( sP267(U_1225,U_1226,U_1227)
| ~ in(ordered_pair(U_1227,U_1226),U_1225)
| ~ relation(U_1225) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_275_2]) ).
cnf(f_275_4,plain,
( sP267(U_1225,U_1226,U_1227)
| ~ in(ordered_pair(U_1227,U_1226),U_1225)
| ~ relation(U_1225) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_5,plain,
( in(U_1227,relation_dom(U_1225))
| ~ sP267(U_1225,U_1226,U_1227) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_6,plain,
( in(U_1226,relation_rng(U_1225))
| ~ sP267(U_1225,U_1226,U_1227) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_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_276_2,plain,
! [U_1229,U_1228] :
( ( subset(relation_field(relation_restriction(U_1228,U_1229)),U_1229)
& subset(relation_field(relation_restriction(U_1228,U_1229)),relation_field(U_1228)) )
| ~ relation(U_1228) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
( ! [U_1229,U_1228] :
( subset(relation_field(relation_restriction(U_1228,U_1229)),U_1229)
| ~ sP268(U_1229,U_1228) )
& ! [U_1229,U_1228] :
( subset(relation_field(relation_restriction(U_1228,U_1229)),relation_field(U_1228))
| ~ sP268(U_1229,U_1228) )
& ! [U_1229,U_1228] :
( sP268(U_1229,U_1228)
| ~ relation(U_1228) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268])],[f_276_2]) ).
cnf(f_276_4,plain,
( sP268(U_1229,U_1228)
| ~ relation(U_1228) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_5,plain,
( subset(relation_field(relation_restriction(U_1228,U_1229)),relation_field(U_1228))
| ~ sP268(U_1229,U_1228) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_6,plain,
( subset(relation_field(relation_restriction(U_1228,U_1229)),U_1229)
| ~ sP268(U_1229,U_1228) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_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_277_2,plain,
! [U_1232,U_1231] :
( ! [U_1230] :
( ( ( in(U_1232,relation_dom(relation_composition(U_1230,U_1231)))
| ~ in(apply(U_1230,U_1232),relation_dom(U_1231))
| ~ in(U_1232,relation_dom(U_1230)) )
& ( ( in(apply(U_1230,U_1232),relation_dom(U_1231))
& in(U_1232,relation_dom(U_1230)) )
| ~ in(U_1232,relation_dom(relation_composition(U_1230,U_1231))) ) )
| ~ function(U_1230)
| ~ relation(U_1230) )
| ~ function(U_1231)
| ~ relation(U_1231) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
( ! [U_1230,U_1231,U_1232] :
( in(apply(U_1230,U_1232),relation_dom(U_1231))
| ~ sP269(U_1230,U_1231,U_1232) )
& ! [U_1230,U_1231,U_1232] :
( in(U_1232,relation_dom(U_1230))
| ~ sP269(U_1230,U_1231,U_1232) )
& ! [U_1230,U_1231,U_1232] :
( in(U_1232,relation_dom(relation_composition(U_1230,U_1231)))
| ~ in(apply(U_1230,U_1232),relation_dom(U_1231))
| ~ in(U_1232,relation_dom(U_1230))
| ~ sP270(U_1230,U_1231,U_1232) )
& ! [U_1230,U_1231,U_1232] :
( sP269(U_1230,U_1231,U_1232)
| ~ in(U_1232,relation_dom(relation_composition(U_1230,U_1231)))
| ~ sP270(U_1230,U_1231,U_1232) )
& ! [U_1230,U_1231,U_1232] :
( sP270(U_1230,U_1231,U_1232)
| ~ function(U_1230)
| ~ relation(U_1230)
| ~ function(U_1231)
| ~ relation(U_1231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269,sP270])],[f_277_2]) ).
cnf(f_277_4,plain,
( sP270(U_1230,U_1231,U_1232)
| ~ function(U_1230)
| ~ relation(U_1230)
| ~ function(U_1231)
| ~ relation(U_1231) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_5,plain,
( sP269(U_1230,U_1231,U_1232)
| ~ in(U_1232,relation_dom(relation_composition(U_1230,U_1231)))
| ~ sP270(U_1230,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_6,plain,
( in(U_1232,relation_dom(relation_composition(U_1230,U_1231)))
| ~ in(apply(U_1230,U_1232),relation_dom(U_1231))
| ~ in(U_1232,relation_dom(U_1230))
| ~ sP270(U_1230,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_7,plain,
( in(U_1232,relation_dom(U_1230))
| ~ sP269(U_1230,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_8,plain,
( in(apply(U_1230,U_1232),relation_dom(U_1231))
| ~ sP269(U_1230,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [A,B,C,D] :
( ! [E] :
( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set
| ~ in(C,A)
| ~ function(E)
| ~ relation(E) )
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(fof_nnf,[status(thm)],[t21_funct_2]) ).
fof(f_278_2,plain,
! [U_1237,U_1236,U_1235,U_1234] :
( ! [U_1233] :
( apply(relation_composition(U_1234,U_1233),U_1235) = apply(U_1233,apply(U_1234,U_1235))
| U_1236 = empty_set
| ~ in(U_1235,U_1237)
| ~ function(U_1233)
| ~ relation(U_1233) )
| ~ relation_of2_as_subset(U_1234,U_1237,U_1236)
| ~ quasi_total(U_1234,U_1237,U_1236)
| ~ function(U_1234) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_1234,U_1236,U_1235,U_1237,U_1233] :
( apply(relation_composition(U_1234,U_1233),U_1235) = apply(U_1233,apply(U_1234,U_1235))
| U_1236 = empty_set
| ~ in(U_1235,U_1237)
| ~ function(U_1233)
| ~ relation(U_1233)
| ~ relation_of2_as_subset(U_1234,U_1237,U_1236)
| ~ quasi_total(U_1234,U_1237,U_1236)
| ~ function(U_1234) ),
inference(definitional_conversion,[status(esa)],[f_278_2]) ).
cnf(f_278_4,plain,
( apply(relation_composition(U_1234,U_1233),U_1235) = apply(U_1233,apply(U_1234,U_1235))
| U_1236 = empty_set
| ~ in(U_1235,U_1237)
| ~ function(U_1233)
| ~ relation(U_1233)
| ~ relation_of2_as_subset(U_1234,U_1237,U_1236)
| ~ quasi_total(U_1234,U_1237,U_1236)
| ~ function(U_1234) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_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_279_2,plain,
! [U_1239] :
( ! [U_1238] :
( in(U_1239,U_1238)
| ~ proper_subset(U_1239,U_1238)
| ~ ordinal(U_1238) )
| ~ epsilon_transitive(U_1239) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1239,U_1238] :
( in(U_1239,U_1238)
| ~ proper_subset(U_1239,U_1238)
| ~ ordinal(U_1238)
| ~ epsilon_transitive(U_1239) ),
inference(definitional_conversion,[status(esa)],[f_279_2]) ).
cnf(f_279_4,plain,
( in(U_1239,U_1238)
| ~ proper_subset(U_1239,U_1238)
| ~ ordinal(U_1238)
| ~ epsilon_transitive(U_1239) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_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_280_2,plain,
! [U_1240] :
( subset(U_1240,cartesian_product2(relation_dom(U_1240),relation_rng(U_1240)))
| ~ relation(U_1240) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_1240] :
( subset(U_1240,cartesian_product2(relation_dom(U_1240),relation_rng(U_1240)))
| ~ relation(U_1240) ),
inference(definitional_conversion,[status(esa)],[f_280_2]) ).
cnf(f_280_4,plain,
( subset(U_1240,cartesian_product2(relation_dom(U_1240),relation_rng(U_1240)))
| ~ relation(U_1240) ),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_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_281_2,plain,
! [U_1243,U_1242,U_1241] :
( subset(fiber(relation_restriction(U_1241,U_1243),U_1242),fiber(U_1241,U_1242))
| ~ relation(U_1241) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_1241,U_1242,U_1243] :
( subset(fiber(relation_restriction(U_1241,U_1243),U_1242),fiber(U_1241,U_1242))
| ~ relation(U_1241) ),
inference(definitional_conversion,[status(esa)],[f_281_2]) ).
cnf(f_281_4,plain,
( subset(fiber(relation_restriction(U_1241,U_1243),U_1242),fiber(U_1241,U_1242))
| ~ relation(U_1241) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_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_282_2,plain,
! [U_1246,U_1245] :
( ! [U_1244] :
( apply(relation_composition(U_1244,U_1245),U_1246) = apply(U_1245,apply(U_1244,U_1246))
| ~ in(U_1246,relation_dom(relation_composition(U_1244,U_1245)))
| ~ function(U_1244)
| ~ relation(U_1244) )
| ~ function(U_1245)
| ~ relation(U_1245) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_1244,U_1245,U_1246] :
( apply(relation_composition(U_1244,U_1245),U_1246) = apply(U_1245,apply(U_1244,U_1246))
| ~ in(U_1246,relation_dom(relation_composition(U_1244,U_1245)))
| ~ function(U_1244)
| ~ relation(U_1244)
| ~ function(U_1245)
| ~ relation(U_1245) ),
inference(definitional_conversion,[status(esa)],[f_282_2]) ).
cnf(f_282_4,plain,
( apply(relation_composition(U_1244,U_1245),U_1246) = apply(U_1245,apply(U_1244,U_1246))
| ~ in(U_1246,relation_dom(relation_composition(U_1244,U_1245)))
| ~ function(U_1244)
| ~ relation(U_1244)
| ~ function(U_1245)
| ~ relation(U_1245) ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_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_283_2,plain,
! [U_1253,U_1252,U_1251] :
( ( ( ! [U_1250] :
( ? [U_1249] : in(ordered_pair(U_1250,U_1249),U_1251)
| ~ in(U_1250,U_1252) )
| relation_dom_as_subset(U_1252,U_1253,U_1251) != U_1252 )
& ( relation_dom_as_subset(U_1252,U_1253,U_1251) = U_1252
| ? [U_1248] :
( ! [U_1247] : ~ in(ordered_pair(U_1248,U_1247),U_1251)
& in(U_1248,U_1252) ) ) )
| ~ relation_of2_as_subset(U_1251,U_1252,U_1253) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1253,U_1252,U_1251] :
( ( ( ! [U_1250] :
( ? [U_1249] : in(ordered_pair(U_1250,U_1249),U_1251)
| ~ in(U_1250,U_1252) )
| relation_dom_as_subset(U_1252,U_1253,U_1251) != U_1252 )
& ( relation_dom_as_subset(U_1252,U_1253,U_1251) = U_1252
| ( ! [U_1247] : ~ in(ordered_pair(sK268(U_1253,U_1252,U_1251),U_1247),U_1251)
& in(sK268(U_1253,U_1252,U_1251),U_1252) ) ) )
| ~ relation_of2_as_subset(U_1251,U_1252,U_1253) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_1248,sK268(U_1253,U_1252,U_1251))],[f_283_2]) ).
fof(f_283_4,plain,
! [U_1253,U_1252,U_1251] :
( ( ( ! [U_1250] :
( in(ordered_pair(U_1250,sK269(U_1253,U_1252,U_1251,U_1250)),U_1251)
| ~ in(U_1250,U_1252) )
| relation_dom_as_subset(U_1252,U_1253,U_1251) != U_1252 )
& ( relation_dom_as_subset(U_1252,U_1253,U_1251) = U_1252
| ( ! [U_1247] : ~ in(ordered_pair(sK268(U_1253,U_1252,U_1251),U_1247),U_1251)
& in(sK268(U_1253,U_1252,U_1251),U_1252) ) ) )
| ~ relation_of2_as_subset(U_1251,U_1252,U_1253) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_1249,sK269(U_1253,U_1252,U_1251,U_1250))],[f_283_3]) ).
fof(f_283_5,plain,
( ! [U_1251,U_1253,U_1252,U_1247] :
( ~ in(ordered_pair(sK268(U_1253,U_1252,U_1251),U_1247),U_1251)
| ~ sP271(U_1251,U_1253,U_1252,U_1247) )
& ! [U_1251,U_1253,U_1252,U_1247] :
( in(sK268(U_1253,U_1252,U_1251),U_1252)
| ~ sP271(U_1251,U_1253,U_1252,U_1247) )
& ! [U_1250,U_1251,U_1253,U_1252,U_1247] :
( in(ordered_pair(U_1250,sK269(U_1253,U_1252,U_1251,U_1250)),U_1251)
| ~ in(U_1250,U_1252)
| relation_dom_as_subset(U_1252,U_1253,U_1251) != U_1252
| ~ sP272(U_1250,U_1251,U_1253,U_1252,U_1247) )
& ! [U_1250,U_1251,U_1253,U_1252,U_1247] :
( relation_dom_as_subset(U_1252,U_1253,U_1251) = U_1252
| sP271(U_1251,U_1253,U_1252,U_1247)
| ~ sP272(U_1250,U_1251,U_1253,U_1252,U_1247) )
& ! [U_1250,U_1251,U_1253,U_1252,U_1247] :
( sP272(U_1250,U_1251,U_1253,U_1252,U_1247)
| ~ relation_of2_as_subset(U_1251,U_1252,U_1253) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271,sP272])],[f_283_4]) ).
cnf(f_283_6,plain,
( sP272(U_1250,U_1251,U_1253,U_1252,U_1247)
| ~ relation_of2_as_subset(U_1251,U_1252,U_1253) ),
inference(clausify,[status(thm)],[f_283_5]) ).
cnf(f_283_7,plain,
( relation_dom_as_subset(U_1252,U_1253,U_1251) = U_1252
| sP271(U_1251,U_1253,U_1252,U_1247)
| ~ sP272(U_1250,U_1251,U_1253,U_1252,U_1247) ),
inference(clausify,[status(thm)],[f_283_5]) ).
cnf(f_283_8,plain,
( in(ordered_pair(U_1250,sK269(U_1253,U_1252,U_1251,U_1250)),U_1251)
| ~ in(U_1250,U_1252)
| relation_dom_as_subset(U_1252,U_1253,U_1251) != U_1252
| ~ sP272(U_1250,U_1251,U_1253,U_1252,U_1247) ),
inference(clausify,[status(thm)],[f_283_5]) ).
cnf(f_283_9,plain,
( in(sK268(U_1253,U_1252,U_1251),U_1252)
| ~ sP271(U_1251,U_1253,U_1252,U_1247) ),
inference(clausify,[status(thm)],[f_283_5]) ).
cnf(f_283_10,plain,
( ~ in(ordered_pair(sK268(U_1253,U_1252,U_1251),U_1247),U_1251)
| ~ sP271(U_1251,U_1253,U_1252,U_1247) ),
inference(clausify,[status(thm)],[f_283_5]) ).
fof(f_284_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_284_2,plain,
! [U_1255,U_1254] :
( reflexive(relation_restriction(U_1254,U_1255))
| ~ reflexive(U_1254)
| ~ relation(U_1254) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_1255,U_1254] :
( reflexive(relation_restriction(U_1254,U_1255))
| ~ reflexive(U_1254)
| ~ relation(U_1254) ),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
( reflexive(relation_restriction(U_1254,U_1255))
| ~ reflexive(U_1254)
| ~ relation(U_1254) ),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_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_285_2,plain,
! [U_1258,U_1257] :
( ! [U_1256] :
( apply(relation_composition(U_1257,U_1256),U_1258) = apply(U_1256,apply(U_1257,U_1258))
| ~ in(U_1258,relation_dom(U_1257))
| ~ function(U_1256)
| ~ relation(U_1256) )
| ~ function(U_1257)
| ~ relation(U_1257) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1256,U_1257,U_1258] :
( apply(relation_composition(U_1257,U_1256),U_1258) = apply(U_1256,apply(U_1257,U_1258))
| ~ in(U_1258,relation_dom(U_1257))
| ~ function(U_1256)
| ~ relation(U_1256)
| ~ function(U_1257)
| ~ relation(U_1257) ),
inference(definitional_conversion,[status(esa)],[f_285_2]) ).
cnf(f_285_4,plain,
( apply(relation_composition(U_1257,U_1256),U_1258) = apply(U_1256,apply(U_1257,U_1258))
| ~ in(U_1258,relation_dom(U_1257))
| ~ function(U_1256)
| ~ relation(U_1256)
| ~ function(U_1257)
| ~ relation(U_1257) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_286_2,plain,
! [U_1260,U_1259] :
( ordinal(U_1260)
| ~ in(U_1260,U_1259)
| ~ ordinal(U_1259) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1259,U_1260] :
( ordinal(U_1260)
| ~ in(U_1260,U_1259)
| ~ ordinal(U_1259) ),
inference(definitional_conversion,[status(esa)],[f_286_2]) ).
cnf(f_286_4,plain,
( ordinal(U_1260)
| ~ in(U_1260,U_1259)
| ~ ordinal(U_1259) ),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_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_287_2,plain,
! [U_1267,U_1266,U_1265] :
( ( ( ! [U_1264] :
( ? [U_1263] : in(ordered_pair(U_1263,U_1264),U_1265)
| ~ in(U_1264,U_1266) )
| relation_rng_as_subset(U_1267,U_1266,U_1265) != U_1266 )
& ( relation_rng_as_subset(U_1267,U_1266,U_1265) = U_1266
| ? [U_1262] :
( ! [U_1261] : ~ in(ordered_pair(U_1261,U_1262),U_1265)
& in(U_1262,U_1266) ) ) )
| ~ relation_of2_as_subset(U_1265,U_1267,U_1266) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_1267,U_1266,U_1265] :
( ( ( ! [U_1264] :
( ? [U_1263] : in(ordered_pair(U_1263,U_1264),U_1265)
| ~ in(U_1264,U_1266) )
| relation_rng_as_subset(U_1267,U_1266,U_1265) != U_1266 )
& ( relation_rng_as_subset(U_1267,U_1266,U_1265) = U_1266
| ( ! [U_1261] : ~ in(ordered_pair(U_1261,sK270(U_1267,U_1266,U_1265)),U_1265)
& in(sK270(U_1267,U_1266,U_1265),U_1266) ) ) )
| ~ relation_of2_as_subset(U_1265,U_1267,U_1266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_1262,sK270(U_1267,U_1266,U_1265))],[f_287_2]) ).
fof(f_287_4,plain,
! [U_1267,U_1266,U_1265] :
( ( ( ! [U_1264] :
( in(ordered_pair(sK271(U_1267,U_1266,U_1265,U_1264),U_1264),U_1265)
| ~ in(U_1264,U_1266) )
| relation_rng_as_subset(U_1267,U_1266,U_1265) != U_1266 )
& ( relation_rng_as_subset(U_1267,U_1266,U_1265) = U_1266
| ( ! [U_1261] : ~ in(ordered_pair(U_1261,sK270(U_1267,U_1266,U_1265)),U_1265)
& in(sK270(U_1267,U_1266,U_1265),U_1266) ) ) )
| ~ relation_of2_as_subset(U_1265,U_1267,U_1266) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_1263,sK271(U_1267,U_1266,U_1265,U_1264))],[f_287_3]) ).
fof(f_287_5,plain,
( ! [U_1261,U_1267,U_1265,U_1266] :
( ~ in(ordered_pair(U_1261,sK270(U_1267,U_1266,U_1265)),U_1265)
| ~ sP273(U_1261,U_1267,U_1265,U_1266) )
& ! [U_1261,U_1267,U_1265,U_1266] :
( in(sK270(U_1267,U_1266,U_1265),U_1266)
| ~ sP273(U_1261,U_1267,U_1265,U_1266) )
& ! [U_1261,U_1264,U_1267,U_1265,U_1266] :
( in(ordered_pair(sK271(U_1267,U_1266,U_1265,U_1264),U_1264),U_1265)
| ~ in(U_1264,U_1266)
| relation_rng_as_subset(U_1267,U_1266,U_1265) != U_1266
| ~ sP274(U_1261,U_1264,U_1267,U_1265,U_1266) )
& ! [U_1261,U_1264,U_1267,U_1265,U_1266] :
( relation_rng_as_subset(U_1267,U_1266,U_1265) = U_1266
| sP273(U_1261,U_1267,U_1265,U_1266)
| ~ sP274(U_1261,U_1264,U_1267,U_1265,U_1266) )
& ! [U_1261,U_1264,U_1267,U_1265,U_1266] :
( sP274(U_1261,U_1264,U_1267,U_1265,U_1266)
| ~ relation_of2_as_subset(U_1265,U_1267,U_1266) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273,sP274])],[f_287_4]) ).
cnf(f_287_6,plain,
( sP274(U_1261,U_1264,U_1267,U_1265,U_1266)
| ~ relation_of2_as_subset(U_1265,U_1267,U_1266) ),
inference(clausify,[status(thm)],[f_287_5]) ).
cnf(f_287_7,plain,
( relation_rng_as_subset(U_1267,U_1266,U_1265) = U_1266
| sP273(U_1261,U_1267,U_1265,U_1266)
| ~ sP274(U_1261,U_1264,U_1267,U_1265,U_1266) ),
inference(clausify,[status(thm)],[f_287_5]) ).
cnf(f_287_8,plain,
( in(ordered_pair(sK271(U_1267,U_1266,U_1265,U_1264),U_1264),U_1265)
| ~ in(U_1264,U_1266)
| relation_rng_as_subset(U_1267,U_1266,U_1265) != U_1266
| ~ sP274(U_1261,U_1264,U_1267,U_1265,U_1266) ),
inference(clausify,[status(thm)],[f_287_5]) ).
cnf(f_287_9,plain,
( in(sK270(U_1267,U_1266,U_1265),U_1266)
| ~ sP273(U_1261,U_1267,U_1265,U_1266) ),
inference(clausify,[status(thm)],[f_287_5]) ).
cnf(f_287_10,plain,
( ~ in(ordered_pair(U_1261,sK270(U_1267,U_1266,U_1265)),U_1265)
| ~ sP273(U_1261,U_1267,U_1265,U_1266) ),
inference(clausify,[status(thm)],[f_287_5]) ).
fof(f_288_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_288_2,plain,
! [U_1269,U_1268] :
( connected(relation_restriction(U_1268,U_1269))
| ~ connected(U_1268)
| ~ relation(U_1268) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1269,U_1268] :
( connected(relation_restriction(U_1268,U_1269))
| ~ connected(U_1268)
| ~ relation(U_1268) ),
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
( connected(relation_restriction(U_1268,U_1269))
| ~ connected(U_1268)
| ~ relation(U_1268) ),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_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_289_2,plain,
! [U_1271] :
( ! [U_1270] :
( in(U_1270,U_1271)
| U_1271 = U_1270
| in(U_1271,U_1270)
| ~ ordinal(U_1270) )
| ~ ordinal(U_1271) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_1270,U_1271] :
( in(U_1270,U_1271)
| U_1271 = U_1270
| in(U_1271,U_1270)
| ~ ordinal(U_1270)
| ~ ordinal(U_1271) ),
inference(definitional_conversion,[status(esa)],[f_289_2]) ).
cnf(f_289_4,plain,
( in(U_1270,U_1271)
| U_1271 = U_1270
| in(U_1271,U_1270)
| ~ ordinal(U_1270)
| ~ ordinal(U_1271) ),
inference(clausify,[status(thm)],[f_289_3]) ).
fof(f_290_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_290_2,plain,
! [U_1273,U_1272] :
( transitive(relation_restriction(U_1272,U_1273))
| ~ transitive(U_1272)
| ~ relation(U_1272) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_1273,U_1272] :
( transitive(relation_restriction(U_1272,U_1273))
| ~ transitive(U_1272)
| ~ relation(U_1272) ),
inference(definitional_conversion,[status(esa)],[f_290_2]) ).
cnf(f_290_4,plain,
( transitive(relation_restriction(U_1272,U_1273))
| ~ transitive(U_1272)
| ~ relation(U_1272) ),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_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_291_2,plain,
! [U_1275] :
( ! [U_1274] :
( ( subset(relation_rng(U_1275),relation_rng(U_1274))
& subset(relation_dom(U_1275),relation_dom(U_1274)) )
| ~ subset(U_1275,U_1274)
| ~ relation(U_1274) )
| ~ relation(U_1275) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
( ! [U_1275,U_1274] :
( subset(relation_rng(U_1275),relation_rng(U_1274))
| ~ sP275(U_1275,U_1274) )
& ! [U_1275,U_1274] :
( subset(relation_dom(U_1275),relation_dom(U_1274))
| ~ sP275(U_1275,U_1274) )
& ! [U_1275,U_1274] :
( sP275(U_1275,U_1274)
| ~ subset(U_1275,U_1274)
| ~ relation(U_1274)
| ~ relation(U_1275) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275])],[f_291_2]) ).
cnf(f_291_4,plain,
( sP275(U_1275,U_1274)
| ~ subset(U_1275,U_1274)
| ~ relation(U_1274)
| ~ relation(U_1275) ),
inference(clausify,[status(thm)],[f_291_3]) ).
cnf(f_291_5,plain,
( subset(relation_dom(U_1275),relation_dom(U_1274))
| ~ sP275(U_1275,U_1274) ),
inference(clausify,[status(thm)],[f_291_3]) ).
cnf(f_291_6,plain,
( subset(relation_rng(U_1275),relation_rng(U_1274))
| ~ sP275(U_1275,U_1274) ),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_292_2,plain,
! [U_1277,U_1276] :
( antisymmetric(relation_restriction(U_1276,U_1277))
| ~ antisymmetric(U_1276)
| ~ relation(U_1276) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1277,U_1276] :
( antisymmetric(relation_restriction(U_1276,U_1277))
| ~ antisymmetric(U_1276)
| ~ relation(U_1276) ),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
( antisymmetric(relation_restriction(U_1276,U_1277))
| ~ antisymmetric(U_1276)
| ~ relation(U_1276) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [A,B] :
( ( well_ordering(relation_restriction(B,A))
& relation_field(relation_restriction(B,A)) = A )
| ~ well_orders(B,A)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord2]) ).
fof(f_293_2,plain,
! [U_1279,U_1278] :
( ( well_ordering(relation_restriction(U_1278,U_1279))
& relation_field(relation_restriction(U_1278,U_1279)) = U_1279 )
| ~ well_orders(U_1278,U_1279)
| ~ relation(U_1278) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
( ! [U_1278,U_1279] :
( well_ordering(relation_restriction(U_1278,U_1279))
| ~ sP276(U_1278,U_1279) )
& ! [U_1278,U_1279] :
( relation_field(relation_restriction(U_1278,U_1279)) = U_1279
| ~ sP276(U_1278,U_1279) )
& ! [U_1278,U_1279] :
( sP276(U_1278,U_1279)
| ~ well_orders(U_1278,U_1279)
| ~ relation(U_1278) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_293_2]) ).
cnf(f_293_4,plain,
( sP276(U_1278,U_1279)
| ~ well_orders(U_1278,U_1279)
| ~ relation(U_1278) ),
inference(clausify,[status(thm)],[f_293_3]) ).
cnf(f_293_5,plain,
( relation_field(relation_restriction(U_1278,U_1279)) = U_1279
| ~ sP276(U_1278,U_1279) ),
inference(clausify,[status(thm)],[f_293_3]) ).
cnf(f_293_6,plain,
( well_ordering(relation_restriction(U_1278,U_1279))
| ~ sP276(U_1278,U_1279) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_1,plain,
! [A] :
? [B] :
( well_orders(B,A)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t26_wellord2]) ).
fof(f_294_2,plain,
! [U_1281] :
? [U_1280] :
( well_orders(U_1280,U_1281)
& relation(U_1280) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_1281] :
( well_orders(sK272(U_1281),U_1281)
& relation(sK272(U_1281)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_1280,sK272(U_1281))],[f_294_2]) ).
fof(f_294_4,plain,
( ! [U_1281] : well_orders(sK272(U_1281),U_1281)
& ! [U_1281] : relation(sK272(U_1281)) ),
inference(definitional_conversion,[status(esa)],[f_294_3]) ).
cnf(f_294_5,plain,
relation(sK272(U_1281)),
inference(clausify,[status(thm)],[f_294_4]) ).
cnf(f_294_6,plain,
well_orders(sK272(U_1281),U_1281),
inference(clausify,[status(thm)],[f_294_4]) ).
fof(f_295_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_295_2,plain,
! [U_1284,U_1283,U_1282] :
( subset(set_intersection2(U_1284,U_1282),set_intersection2(U_1283,U_1282))
| ~ subset(U_1284,U_1283) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1284,U_1283] :
( ! [U_1282] : subset(set_intersection2(U_1284,U_1282),set_intersection2(U_1283,U_1282))
| ~ subset(U_1284,U_1283) ),
inference(miniscope,[status(thm)],[f_295_2]) ).
fof(f_295_4,plain,
! [U_1282,U_1283,U_1284] :
( subset(set_intersection2(U_1284,U_1282),set_intersection2(U_1283,U_1282))
| ~ subset(U_1284,U_1283) ),
inference(definitional_conversion,[status(esa)],[f_295_3]) ).
cnf(f_295_5,plain,
( subset(set_intersection2(U_1284,U_1282),set_intersection2(U_1283,U_1282))
| ~ subset(U_1284,U_1283) ),
inference(clausify,[status(thm)],[f_295_4]) ).
fof(f_296_1,plain,
! [A] :
( ? [B] :
( ! [C] :
( in(apply(B,C),C)
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) )
| ? [B] :
( B = empty_set
& in(B,A) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[t28_wellord2]) ).
fof(f_296_2,plain,
! [U_1288] :
( ? [U_1287] :
( ! [U_1286] :
( in(apply(U_1287,U_1286),U_1286)
| ~ in(U_1286,U_1288) )
& relation_dom(U_1287) = U_1288
& function(U_1287)
& relation(U_1287) )
| ? [U_1285] :
( U_1285 = empty_set
& in(U_1285,U_1288) )
| empty(U_1288) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_1288] :
( ? [U_1287] :
( ! [U_1286] :
( in(apply(U_1287,U_1286),U_1286)
| ~ in(U_1286,U_1288) )
& relation_dom(U_1287) = U_1288
& function(U_1287)
& relation(U_1287) )
| ( sK273(U_1288) = empty_set
& in(sK273(U_1288),U_1288) )
| empty(U_1288) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_1285,sK273(U_1288))],[f_296_2]) ).
fof(f_296_4,plain,
! [U_1288] :
( ( ! [U_1286] :
( in(apply(sK274(U_1288),U_1286),U_1286)
| ~ in(U_1286,U_1288) )
& relation_dom(sK274(U_1288)) = U_1288
& function(sK274(U_1288))
& relation(sK274(U_1288)) )
| ( sK273(U_1288) = empty_set
& in(sK273(U_1288),U_1288) )
| empty(U_1288) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_1287,sK274(U_1288))],[f_296_3]) ).
fof(f_296_5,plain,
( ! [U_1286,U_1288] :
( in(apply(sK274(U_1288),U_1286),U_1286)
| ~ in(U_1286,U_1288)
| ~ sP278(U_1286,U_1288) )
& ! [U_1286,U_1288] :
( relation_dom(sK274(U_1288)) = U_1288
| ~ sP278(U_1286,U_1288) )
& ! [U_1286,U_1288] :
( function(sK274(U_1288))
| ~ sP278(U_1286,U_1288) )
& ! [U_1286,U_1288] :
( relation(sK274(U_1288))
| ~ sP278(U_1286,U_1288) )
& ! [U_1288] :
( sK273(U_1288) = empty_set
| ~ sP277(U_1288) )
& ! [U_1288] :
( in(sK273(U_1288),U_1288)
| ~ sP277(U_1288) )
& ! [U_1286,U_1288] :
( sP278(U_1286,U_1288)
| sP277(U_1288)
| empty(U_1288) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277,sP278])],[f_296_4]) ).
cnf(f_296_6,plain,
( sP278(U_1286,U_1288)
| sP277(U_1288)
| empty(U_1288) ),
inference(clausify,[status(thm)],[f_296_5]) ).
cnf(f_296_7,plain,
( in(sK273(U_1288),U_1288)
| ~ sP277(U_1288) ),
inference(clausify,[status(thm)],[f_296_5]) ).
cnf(f_296_8,plain,
( sK273(U_1288) = empty_set
| ~ sP277(U_1288) ),
inference(clausify,[status(thm)],[f_296_5]) ).
cnf(f_296_9,plain,
( relation(sK274(U_1288))
| ~ sP278(U_1286,U_1288) ),
inference(clausify,[status(thm)],[f_296_5]) ).
cnf(f_296_10,plain,
( function(sK274(U_1288))
| ~ sP278(U_1286,U_1288) ),
inference(clausify,[status(thm)],[f_296_5]) ).
cnf(f_296_11,plain,
( relation_dom(sK274(U_1288)) = U_1288
| ~ sP278(U_1286,U_1288) ),
inference(clausify,[status(thm)],[f_296_5]) ).
cnf(f_296_12,plain,
( in(apply(sK274(U_1288),U_1286),U_1286)
| ~ in(U_1286,U_1288)
| ~ sP278(U_1286,U_1288) ),
inference(clausify,[status(thm)],[f_296_5]) ).
fof(f_297_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_297_2,plain,
! [U_1290,U_1289] :
( set_intersection2(U_1290,U_1289) = U_1290
| ~ subset(U_1290,U_1289) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_1290,U_1289] :
( set_intersection2(U_1290,U_1289) = U_1290
| ~ subset(U_1290,U_1289) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( set_intersection2(U_1290,U_1289) = U_1290
| ~ subset(U_1290,U_1289) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_298_2,plain,
! [U_1291] : set_intersection2(U_1291,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_1291] : set_intersection2(U_1291,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
set_intersection2(U_1291,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_299_2,plain,
! [U_1293,U_1292] :
( in(U_1293,U_1292)
| empty(U_1292)
| ~ element(U_1293,U_1292) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_1292,U_1293] :
( in(U_1293,U_1292)
| empty(U_1292)
| ~ element(U_1293,U_1292) ),
inference(definitional_conversion,[status(esa)],[f_299_2]) ).
cnf(f_299_4,plain,
( in(U_1293,U_1292)
| empty(U_1292)
| ~ element(U_1293,U_1292) ),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_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_300_2,plain,
! [U_1296,U_1295] :
( U_1296 = U_1295
| ? [U_1294] :
( ( ~ in(U_1294,U_1296)
& in(U_1294,U_1295) )
| ( ~ in(U_1294,U_1295)
& in(U_1294,U_1296) ) ) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1296,U_1295] :
( U_1296 = U_1295
| ? [U_1298] :
( ~ in(U_1298,U_1296)
& in(U_1298,U_1295) )
| ? [U_1297] :
( ~ in(U_1297,U_1295)
& in(U_1297,U_1296) ) ),
inference(miniscope,[status(thm)],[f_300_2]) ).
fof(f_300_4,plain,
! [U_1296,U_1295] :
( U_1296 = U_1295
| ? [U_1298] :
( ~ in(U_1298,U_1296)
& in(U_1298,U_1295) )
| ( ~ in(sK275(U_1296,U_1295),U_1295)
& in(sK275(U_1296,U_1295),U_1296) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_1297,sK275(U_1296,U_1295))],[f_300_3]) ).
fof(f_300_5,plain,
! [U_1296,U_1295] :
( U_1296 = U_1295
| ( ~ in(sK276(U_1296,U_1295),U_1296)
& in(sK276(U_1296,U_1295),U_1295) )
| ( ~ in(sK275(U_1296,U_1295),U_1295)
& in(sK275(U_1296,U_1295),U_1296) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_1298,sK276(U_1296,U_1295))],[f_300_4]) ).
fof(f_300_6,plain,
( ! [U_1295,U_1296] :
( ~ in(sK276(U_1296,U_1295),U_1296)
| ~ sP280(U_1295,U_1296) )
& ! [U_1295,U_1296] :
( in(sK276(U_1296,U_1295),U_1295)
| ~ sP280(U_1295,U_1296) )
& ! [U_1295,U_1296] :
( ~ in(sK275(U_1296,U_1295),U_1295)
| ~ sP279(U_1295,U_1296) )
& ! [U_1295,U_1296] :
( in(sK275(U_1296,U_1295),U_1296)
| ~ sP279(U_1295,U_1296) )
& ! [U_1295,U_1296] :
( U_1296 = U_1295
| sP280(U_1295,U_1296)
| sP279(U_1295,U_1296) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279,sP280])],[f_300_5]) ).
cnf(f_300_7,plain,
( U_1296 = U_1295
| sP280(U_1295,U_1296)
| sP279(U_1295,U_1296) ),
inference(clausify,[status(thm)],[f_300_6]) ).
cnf(f_300_8,plain,
( in(sK275(U_1296,U_1295),U_1296)
| ~ sP279(U_1295,U_1296) ),
inference(clausify,[status(thm)],[f_300_6]) ).
cnf(f_300_9,plain,
( ~ in(sK275(U_1296,U_1295),U_1295)
| ~ sP279(U_1295,U_1296) ),
inference(clausify,[status(thm)],[f_300_6]) ).
cnf(f_300_10,plain,
( in(sK276(U_1296,U_1295),U_1295)
| ~ sP280(U_1295,U_1296) ),
inference(clausify,[status(thm)],[f_300_6]) ).
cnf(f_300_11,plain,
( ~ in(sK276(U_1296,U_1295),U_1296)
| ~ sP280(U_1295,U_1296) ),
inference(clausify,[status(thm)],[f_300_6]) ).
fof(f_301_1,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t2_wellord2]) ).
fof(f_301_2,plain,
! [U_1299] : reflexive(inclusion_relation(U_1299)),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_1299] : reflexive(inclusion_relation(U_1299)),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
reflexive(inclusion_relation(U_1299)),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_302_2,plain,
! [U_1300] : subset(empty_set,U_1300),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_1300] : subset(empty_set,U_1300),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
subset(empty_set,U_1300),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_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_303_2,plain,
! [U_1303,U_1302,U_1301] :
( ( in(U_1302,relation_field(U_1301))
& in(U_1303,relation_field(U_1301)) )
| ~ in(ordered_pair(U_1303,U_1302),U_1301)
| ~ relation(U_1301) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
( ! [U_1302,U_1301,U_1303] :
( in(U_1302,relation_field(U_1301))
| ~ sP281(U_1302,U_1301,U_1303) )
& ! [U_1302,U_1301,U_1303] :
( in(U_1303,relation_field(U_1301))
| ~ sP281(U_1302,U_1301,U_1303) )
& ! [U_1302,U_1301,U_1303] :
( sP281(U_1302,U_1301,U_1303)
| ~ in(ordered_pair(U_1303,U_1302),U_1301)
| ~ relation(U_1301) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_303_2]) ).
cnf(f_303_4,plain,
( sP281(U_1302,U_1301,U_1303)
| ~ in(ordered_pair(U_1303,U_1302),U_1301)
| ~ relation(U_1301) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_5,plain,
( in(U_1303,relation_field(U_1301))
| ~ sP281(U_1302,U_1301,U_1303) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_6,plain,
( in(U_1302,relation_field(U_1301))
| ~ sP281(U_1302,U_1301,U_1303) ),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_304_2,plain,
! [U_1305] :
( ordinal(U_1305)
| ? [U_1304] :
( ( ~ subset(U_1304,U_1305)
| ~ ordinal(U_1304) )
& in(U_1304,U_1305) ) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1305] :
( ordinal(U_1305)
| ( ( ~ subset(sK277(U_1305),U_1305)
| ~ ordinal(sK277(U_1305)) )
& in(sK277(U_1305),U_1305) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_1304,sK277(U_1305))],[f_304_2]) ).
fof(f_304_4,plain,
( ! [U_1305] :
( ~ subset(sK277(U_1305),U_1305)
| ~ ordinal(sK277(U_1305))
| ~ sP282(U_1305) )
& ! [U_1305] :
( in(sK277(U_1305),U_1305)
| ~ sP282(U_1305) )
& ! [U_1305] :
( ordinal(U_1305)
| sP282(U_1305) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282])],[f_304_3]) ).
cnf(f_304_5,plain,
( ordinal(U_1305)
| sP282(U_1305) ),
inference(clausify,[status(thm)],[f_304_4]) ).
cnf(f_304_6,plain,
( in(sK277(U_1305),U_1305)
| ~ sP282(U_1305) ),
inference(clausify,[status(thm)],[f_304_4]) ).
cnf(f_304_7,plain,
( ~ subset(sK277(U_1305),U_1305)
| ~ ordinal(sK277(U_1305))
| ~ sP282(U_1305) ),
inference(clausify,[status(thm)],[f_304_4]) ).
fof(f_305_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_305_2,plain,
! [U_1307,U_1306] :
( well_founded_relation(relation_restriction(U_1306,U_1307))
| ~ well_founded_relation(U_1306)
| ~ relation(U_1306) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_1306,U_1307] :
( well_founded_relation(relation_restriction(U_1306,U_1307))
| ~ well_founded_relation(U_1306)
| ~ relation(U_1306) ),
inference(definitional_conversion,[status(esa)],[f_305_2]) ).
cnf(f_305_4,plain,
( well_founded_relation(relation_restriction(U_1306,U_1307))
| ~ well_founded_relation(U_1306)
| ~ relation(U_1306) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_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_306_2,plain,
! [U_1311,U_1310] :
( ? [U_1309] :
( ! [U_1308] :
( ordinal_subset(U_1309,U_1308)
| ~ in(U_1308,U_1311)
| ~ ordinal(U_1308) )
& in(U_1309,U_1311)
& ordinal(U_1309) )
| U_1311 = empty_set
| ~ subset(U_1311,U_1310)
| ~ ordinal(U_1310) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_1311,U_1310] :
( ( ! [U_1308] :
( ordinal_subset(sK278(U_1311,U_1310),U_1308)
| ~ in(U_1308,U_1311)
| ~ ordinal(U_1308) )
& in(sK278(U_1311,U_1310),U_1311)
& ordinal(sK278(U_1311,U_1310)) )
| U_1311 = empty_set
| ~ subset(U_1311,U_1310)
| ~ ordinal(U_1310) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_1309,sK278(U_1311,U_1310))],[f_306_2]) ).
fof(f_306_4,plain,
( ! [U_1310,U_1308,U_1311] :
( ordinal_subset(sK278(U_1311,U_1310),U_1308)
| ~ in(U_1308,U_1311)
| ~ ordinal(U_1308)
| ~ sP283(U_1310,U_1308,U_1311) )
& ! [U_1310,U_1308,U_1311] :
( in(sK278(U_1311,U_1310),U_1311)
| ~ sP283(U_1310,U_1308,U_1311) )
& ! [U_1310,U_1308,U_1311] :
( ordinal(sK278(U_1311,U_1310))
| ~ sP283(U_1310,U_1308,U_1311) )
& ! [U_1310,U_1308,U_1311] :
( sP283(U_1310,U_1308,U_1311)
| U_1311 = empty_set
| ~ subset(U_1311,U_1310)
| ~ ordinal(U_1310) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_306_3]) ).
cnf(f_306_5,plain,
( sP283(U_1310,U_1308,U_1311)
| U_1311 = empty_set
| ~ subset(U_1311,U_1310)
| ~ ordinal(U_1310) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_6,plain,
( ordinal(sK278(U_1311,U_1310))
| ~ sP283(U_1310,U_1308,U_1311) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_7,plain,
( in(sK278(U_1311,U_1310),U_1311)
| ~ sP283(U_1310,U_1308,U_1311) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_8,plain,
( ordinal_subset(sK278(U_1311,U_1310),U_1308)
| ~ in(U_1308,U_1311)
| ~ ordinal(U_1308)
| ~ sP283(U_1310,U_1308,U_1311) ),
inference(clausify,[status(thm)],[f_306_4]) ).
fof(f_307_1,plain,
! [A,B] :
( well_ordering(relation_restriction(B,A))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t32_wellord1]) ).
fof(f_307_2,plain,
! [U_1313,U_1312] :
( well_ordering(relation_restriction(U_1312,U_1313))
| ~ well_ordering(U_1312)
| ~ relation(U_1312) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_1312,U_1313] :
( well_ordering(relation_restriction(U_1312,U_1313))
| ~ well_ordering(U_1312)
| ~ relation(U_1312) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( well_ordering(relation_restriction(U_1312,U_1313))
| ~ well_ordering(U_1312)
| ~ relation(U_1312) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_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_308_2,plain,
! [U_1315] :
( ! [U_1314] :
( ( ( in(U_1315,U_1314)
| ~ ordinal_subset(succ(U_1315),U_1314) )
& ( ordinal_subset(succ(U_1315),U_1314)
| ~ in(U_1315,U_1314) ) )
| ~ ordinal(U_1314) )
| ~ ordinal(U_1315) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
( ! [U_1314,U_1315] :
( in(U_1315,U_1314)
| ~ ordinal_subset(succ(U_1315),U_1314)
| ~ sP284(U_1314,U_1315) )
& ! [U_1314,U_1315] :
( ordinal_subset(succ(U_1315),U_1314)
| ~ in(U_1315,U_1314)
| ~ sP284(U_1314,U_1315) )
& ! [U_1314,U_1315] :
( sP284(U_1314,U_1315)
| ~ ordinal(U_1314)
| ~ ordinal(U_1315) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_308_2]) ).
cnf(f_308_4,plain,
( sP284(U_1314,U_1315)
| ~ ordinal(U_1314)
| ~ ordinal(U_1315) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_5,plain,
( ordinal_subset(succ(U_1315),U_1314)
| ~ in(U_1315,U_1314)
| ~ sP284(U_1314,U_1315) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_6,plain,
( in(U_1315,U_1314)
| ~ ordinal_subset(succ(U_1315),U_1314)
| ~ sP284(U_1314,U_1315) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_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_309_2,plain,
! [U_1318,U_1317,U_1316] :
( subset(set_difference(U_1318,U_1316),set_difference(U_1317,U_1316))
| ~ subset(U_1318,U_1317) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_1318,U_1317] :
( ! [U_1316] : subset(set_difference(U_1318,U_1316),set_difference(U_1317,U_1316))
| ~ subset(U_1318,U_1317) ),
inference(miniscope,[status(thm)],[f_309_2]) ).
fof(f_309_4,plain,
! [U_1317,U_1318,U_1316] :
( subset(set_difference(U_1318,U_1316),set_difference(U_1317,U_1316))
| ~ subset(U_1318,U_1317) ),
inference(definitional_conversion,[status(esa)],[f_309_3]) ).
cnf(f_309_5,plain,
( subset(set_difference(U_1318,U_1316),set_difference(U_1317,U_1316))
| ~ subset(U_1318,U_1317) ),
inference(clausify,[status(thm)],[f_309_4]) ).
fof(f_310_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_310_2,plain,
! [U_1322,U_1321,U_1320,U_1319] :
( ( U_1321 = U_1319
& U_1322 = U_1320 )
| ordered_pair(U_1322,U_1321) != ordered_pair(U_1320,U_1319) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
( ! [U_1321,U_1320,U_1322,U_1319] :
( U_1321 = U_1319
| ~ sP285(U_1321,U_1320,U_1322,U_1319) )
& ! [U_1321,U_1320,U_1322,U_1319] :
( U_1322 = U_1320
| ~ sP285(U_1321,U_1320,U_1322,U_1319) )
& ! [U_1321,U_1320,U_1322,U_1319] :
( sP285(U_1321,U_1320,U_1322,U_1319)
| ordered_pair(U_1322,U_1321) != ordered_pair(U_1320,U_1319) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285])],[f_310_2]) ).
cnf(f_310_4,plain,
( sP285(U_1321,U_1320,U_1322,U_1319)
| ordered_pair(U_1322,U_1321) != ordered_pair(U_1320,U_1319) ),
inference(clausify,[status(thm)],[f_310_3]) ).
cnf(f_310_5,plain,
( U_1322 = U_1320
| ~ sP285(U_1321,U_1320,U_1322,U_1319) ),
inference(clausify,[status(thm)],[f_310_3]) ).
cnf(f_310_6,plain,
( U_1321 = U_1319
| ~ sP285(U_1321,U_1320,U_1322,U_1319) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_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_311_2,plain,
! [U_1326,U_1325] :
( ( ( U_1325 = identity_relation(U_1326)
| ? [U_1324] :
( apply(U_1325,U_1324) != U_1324
& in(U_1324,U_1326) )
| relation_dom(U_1325) != U_1326 )
& ( ( ! [U_1323] :
( apply(U_1325,U_1323) = U_1323
| ~ in(U_1323,U_1326) )
& relation_dom(U_1325) = U_1326 )
| U_1325 != identity_relation(U_1326) ) )
| ~ function(U_1325)
| ~ relation(U_1325) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
! [U_1326,U_1325] :
( ( ( U_1325 = identity_relation(U_1326)
| ( apply(U_1325,sK279(U_1326,U_1325)) != sK279(U_1326,U_1325)
& in(sK279(U_1326,U_1325),U_1326) )
| relation_dom(U_1325) != U_1326 )
& ( ( ! [U_1323] :
( apply(U_1325,U_1323) = U_1323
| ~ in(U_1323,U_1326) )
& relation_dom(U_1325) = U_1326 )
| U_1325 != identity_relation(U_1326) ) )
| ~ function(U_1325)
| ~ relation(U_1325) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_1324,sK279(U_1326,U_1325))],[f_311_2]) ).
fof(f_311_4,plain,
( ! [U_1326,U_1325] :
( apply(U_1325,sK279(U_1326,U_1325)) != sK279(U_1326,U_1325)
| ~ sP287(U_1326,U_1325) )
& ! [U_1326,U_1325] :
( in(sK279(U_1326,U_1325),U_1326)
| ~ sP287(U_1326,U_1325) )
& ! [U_1326,U_1325,U_1323] :
( apply(U_1325,U_1323) = U_1323
| ~ in(U_1323,U_1326)
| ~ sP286(U_1326,U_1325,U_1323) )
& ! [U_1326,U_1325,U_1323] :
( relation_dom(U_1325) = U_1326
| ~ sP286(U_1326,U_1325,U_1323) )
& ! [U_1326,U_1325,U_1323] :
( U_1325 = identity_relation(U_1326)
| sP287(U_1326,U_1325)
| relation_dom(U_1325) != U_1326
| ~ sP288(U_1326,U_1325,U_1323) )
& ! [U_1326,U_1325,U_1323] :
( sP286(U_1326,U_1325,U_1323)
| U_1325 != identity_relation(U_1326)
| ~ sP288(U_1326,U_1325,U_1323) )
& ! [U_1326,U_1325,U_1323] :
( sP288(U_1326,U_1325,U_1323)
| ~ function(U_1325)
| ~ relation(U_1325) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286,sP287,sP288])],[f_311_3]) ).
cnf(f_311_5,plain,
( sP288(U_1326,U_1325,U_1323)
| ~ function(U_1325)
| ~ relation(U_1325) ),
inference(clausify,[status(thm)],[f_311_4]) ).
cnf(f_311_6,plain,
( sP286(U_1326,U_1325,U_1323)
| U_1325 != identity_relation(U_1326)
| ~ sP288(U_1326,U_1325,U_1323) ),
inference(clausify,[status(thm)],[f_311_4]) ).
cnf(f_311_7,plain,
( U_1325 = identity_relation(U_1326)
| sP287(U_1326,U_1325)
| relation_dom(U_1325) != U_1326
| ~ sP288(U_1326,U_1325,U_1323) ),
inference(clausify,[status(thm)],[f_311_4]) ).
cnf(f_311_8,plain,
( relation_dom(U_1325) = U_1326
| ~ sP286(U_1326,U_1325,U_1323) ),
inference(clausify,[status(thm)],[f_311_4]) ).
cnf(f_311_9,plain,
( apply(U_1325,U_1323) = U_1323
| ~ in(U_1323,U_1326)
| ~ sP286(U_1326,U_1325,U_1323) ),
inference(clausify,[status(thm)],[f_311_4]) ).
cnf(f_311_10,plain,
( in(sK279(U_1326,U_1325),U_1326)
| ~ sP287(U_1326,U_1325) ),
inference(clausify,[status(thm)],[f_311_4]) ).
cnf(f_311_11,plain,
( apply(U_1325,sK279(U_1326,U_1325)) != sK279(U_1326,U_1325)
| ~ sP287(U_1326,U_1325) ),
inference(clausify,[status(thm)],[f_311_4]) ).
fof(f_312_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_312_2,plain,
! [U_1328,U_1327] :
( apply(identity_relation(U_1328),U_1327) = U_1327
| ~ in(U_1327,U_1328) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_1327,U_1328] :
( apply(identity_relation(U_1328),U_1327) = U_1327
| ~ in(U_1327,U_1328) ),
inference(definitional_conversion,[status(esa)],[f_312_2]) ).
cnf(f_312_4,plain,
( apply(identity_relation(U_1328),U_1327) = U_1327
| ~ in(U_1327,U_1328) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_313_2,plain,
! [U_1330,U_1329] : subset(set_difference(U_1330,U_1329),U_1330),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_1330,U_1329] : subset(set_difference(U_1330,U_1329),U_1330),
inference(definitional_conversion,[status(esa)],[f_313_2]) ).
cnf(f_313_4,plain,
subset(set_difference(U_1330,U_1329),U_1330),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_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_314_2,plain,
! [U_1331] :
( ( relation_dom(U_1331) = relation_rng(relation_inverse(U_1331))
& relation_rng(U_1331) = relation_dom(relation_inverse(U_1331)) )
| ~ relation(U_1331) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
( ! [U_1331] :
( relation_dom(U_1331) = relation_rng(relation_inverse(U_1331))
| ~ sP289(U_1331) )
& ! [U_1331] :
( relation_rng(U_1331) = relation_dom(relation_inverse(U_1331))
| ~ sP289(U_1331) )
& ! [U_1331] :
( sP289(U_1331)
| ~ relation(U_1331) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289])],[f_314_2]) ).
cnf(f_314_4,plain,
( sP289(U_1331)
| ~ relation(U_1331) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_5,plain,
( relation_rng(U_1331) = relation_dom(relation_inverse(U_1331))
| ~ sP289(U_1331) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_6,plain,
( relation_dom(U_1331) = relation_rng(relation_inverse(U_1331))
| ~ sP289(U_1331) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_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_315_2,plain,
! [U_1333,U_1332] :
( ( set_difference(U_1333,U_1332) = empty_set
| ~ subset(U_1333,U_1332) )
& ( subset(U_1333,U_1332)
| set_difference(U_1333,U_1332) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
( ! [U_1337,U_1335] :
( set_difference(U_1337,U_1335) = empty_set
| ~ subset(U_1337,U_1335) )
& ! [U_1336,U_1334] :
( subset(U_1336,U_1334)
| set_difference(U_1336,U_1334) != empty_set ) ),
inference(miniscope,[status(thm)],[f_315_2]) ).
fof(f_315_4,plain,
( ! [U_1337,U_1335] :
( set_difference(U_1337,U_1335) = empty_set
| ~ subset(U_1337,U_1335) )
& ! [U_1336,U_1334] :
( subset(U_1336,U_1334)
| set_difference(U_1336,U_1334) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_315_3]) ).
cnf(f_315_5,plain,
( subset(U_1336,U_1334)
| set_difference(U_1336,U_1334) != empty_set ),
inference(clausify,[status(thm)],[f_315_4]) ).
cnf(f_315_6,plain,
( set_difference(U_1337,U_1335) = empty_set
| ~ subset(U_1337,U_1335) ),
inference(clausify,[status(thm)],[f_315_4]) ).
fof(f_316_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_316_2,plain,
! [U_1339,U_1338] :
( ( subset(singleton(U_1339),U_1338)
| ~ in(U_1339,U_1338) )
& ( in(U_1339,U_1338)
| ~ subset(singleton(U_1339),U_1338) ) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
( ! [U_1343,U_1341] :
( subset(singleton(U_1343),U_1341)
| ~ in(U_1343,U_1341) )
& ! [U_1342,U_1340] :
( in(U_1342,U_1340)
| ~ subset(singleton(U_1342),U_1340) ) ),
inference(miniscope,[status(thm)],[f_316_2]) ).
fof(f_316_4,plain,
( ! [U_1341,U_1343] :
( subset(singleton(U_1343),U_1341)
| ~ in(U_1343,U_1341) )
& ! [U_1340,U_1342] :
( in(U_1342,U_1340)
| ~ subset(singleton(U_1342),U_1340) ) ),
inference(definitional_conversion,[status(esa)],[f_316_3]) ).
cnf(f_316_5,plain,
( in(U_1342,U_1340)
| ~ subset(singleton(U_1342),U_1340) ),
inference(clausify,[status(thm)],[f_316_4]) ).
cnf(f_316_6,plain,
( subset(singleton(U_1343),U_1341)
| ~ in(U_1343,U_1341) ),
inference(clausify,[status(thm)],[f_316_4]) ).
fof(f_317_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_317_2,plain,
! [U_1346,U_1345,U_1344] :
( ( subset(unordered_pair(U_1346,U_1345),U_1344)
| ~ in(U_1345,U_1344)
| ~ in(U_1346,U_1344) )
& ( ( in(U_1345,U_1344)
& in(U_1346,U_1344) )
| ~ subset(unordered_pair(U_1346,U_1345),U_1344) ) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
( ! [U_1352,U_1350,U_1348] :
( subset(unordered_pair(U_1352,U_1350),U_1348)
| ~ in(U_1350,U_1348)
| ~ in(U_1352,U_1348) )
& ! [U_1351,U_1349,U_1347] :
( ( in(U_1349,U_1347)
& in(U_1351,U_1347) )
| ~ subset(unordered_pair(U_1351,U_1349),U_1347) ) ),
inference(miniscope,[status(thm)],[f_317_2]) ).
fof(f_317_4,plain,
( ! [U_1347,U_1349,U_1351] :
( in(U_1349,U_1347)
| ~ sP290(U_1347,U_1349,U_1351) )
& ! [U_1347,U_1349,U_1351] :
( in(U_1351,U_1347)
| ~ sP290(U_1347,U_1349,U_1351) )
& ! [U_1352,U_1350,U_1348] :
( subset(unordered_pair(U_1352,U_1350),U_1348)
| ~ in(U_1350,U_1348)
| ~ in(U_1352,U_1348) )
& ! [U_1347,U_1349,U_1351] :
( sP290(U_1347,U_1349,U_1351)
| ~ subset(unordered_pair(U_1351,U_1349),U_1347) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290])],[f_317_3]) ).
cnf(f_317_5,plain,
( sP290(U_1347,U_1349,U_1351)
| ~ subset(unordered_pair(U_1351,U_1349),U_1347) ),
inference(clausify,[status(thm)],[f_317_4]) ).
cnf(f_317_6,plain,
( subset(unordered_pair(U_1352,U_1350),U_1348)
| ~ in(U_1350,U_1348)
| ~ in(U_1352,U_1348) ),
inference(clausify,[status(thm)],[f_317_4]) ).
cnf(f_317_7,plain,
( in(U_1351,U_1347)
| ~ sP290(U_1347,U_1349,U_1351) ),
inference(clausify,[status(thm)],[f_317_4]) ).
cnf(f_317_8,plain,
( in(U_1349,U_1347)
| ~ sP290(U_1347,U_1349,U_1351) ),
inference(clausify,[status(thm)],[f_317_4]) ).
fof(f_318_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_318_2,plain,
! [U_1354,U_1353] :
( relation_field(relation_restriction(U_1353,U_1354)) = U_1354
| ~ subset(U_1354,relation_field(U_1353))
| ~ well_ordering(U_1353)
| ~ relation(U_1353) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_1353,U_1354] :
( relation_field(relation_restriction(U_1353,U_1354)) = U_1354
| ~ subset(U_1354,relation_field(U_1353))
| ~ well_ordering(U_1353)
| ~ relation(U_1353) ),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_4,plain,
( relation_field(relation_restriction(U_1353,U_1354)) = U_1354
| ~ subset(U_1354,relation_field(U_1353))
| ~ well_ordering(U_1353)
| ~ relation(U_1353) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_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_319_2,plain,
! [U_1356,U_1355] : set_union2(U_1356,set_difference(U_1355,U_1356)) = set_union2(U_1356,U_1355),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_1355,U_1356] : set_union2(U_1356,set_difference(U_1355,U_1356)) = set_union2(U_1356,U_1355),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
set_union2(U_1356,set_difference(U_1355,U_1356)) = set_union2(U_1356,U_1355),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_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_320_2,plain,
! [U_1358,U_1357] :
( ( subset(U_1358,singleton(U_1357))
| ( U_1358 != singleton(U_1357)
& U_1358 != empty_set ) )
& ( U_1358 = singleton(U_1357)
| U_1358 = empty_set
| ~ subset(U_1358,singleton(U_1357)) ) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
( ! [U_1362,U_1360] :
( subset(U_1362,singleton(U_1360))
| ( U_1362 != singleton(U_1360)
& U_1362 != empty_set ) )
& ! [U_1361,U_1359] :
( U_1361 = singleton(U_1359)
| U_1361 = empty_set
| ~ subset(U_1361,singleton(U_1359)) ) ),
inference(miniscope,[status(thm)],[f_320_2]) ).
fof(f_320_4,plain,
( ! [U_1360,U_1362] :
( U_1362 != singleton(U_1360)
| ~ sP291(U_1360,U_1362) )
& ! [U_1360,U_1362] :
( U_1362 != empty_set
| ~ sP291(U_1360,U_1362) )
& ! [U_1360,U_1362] :
( subset(U_1362,singleton(U_1360))
| sP291(U_1360,U_1362) )
& ! [U_1361,U_1359] :
( U_1361 = singleton(U_1359)
| U_1361 = empty_set
| ~ subset(U_1361,singleton(U_1359)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291])],[f_320_3]) ).
cnf(f_320_5,plain,
( U_1361 = singleton(U_1359)
| U_1361 = empty_set
| ~ subset(U_1361,singleton(U_1359)) ),
inference(clausify,[status(thm)],[f_320_4]) ).
cnf(f_320_6,plain,
( subset(U_1362,singleton(U_1360))
| sP291(U_1360,U_1362) ),
inference(clausify,[status(thm)],[f_320_4]) ).
cnf(f_320_7,plain,
( U_1362 != empty_set
| ~ sP291(U_1360,U_1362) ),
inference(clausify,[status(thm)],[f_320_4]) ).
cnf(f_320_8,plain,
( U_1362 != singleton(U_1360)
| ~ sP291(U_1360,U_1362) ),
inference(clausify,[status(thm)],[f_320_4]) ).
fof(f_321_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_321_2,plain,
! [U_1363] : set_difference(U_1363,empty_set) = U_1363,
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1363] : set_difference(U_1363,empty_set) = U_1363,
inference(definitional_conversion,[status(esa)],[f_321_2]) ).
cnf(f_321_4,plain,
set_difference(U_1363,empty_set) = U_1363,
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_322_2,plain,
! [U_1366,U_1365,U_1364] :
( ~ in(U_1364,U_1366)
| ~ in(U_1365,U_1364)
| ~ in(U_1366,U_1365) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
! [U_1366,U_1365] :
( ! [U_1364] :
( ~ in(U_1364,U_1366)
| ~ in(U_1365,U_1364) )
| ~ in(U_1366,U_1365) ),
inference(miniscope,[status(thm)],[f_322_2]) ).
fof(f_322_4,plain,
! [U_1365,U_1364,U_1366] :
( ~ in(U_1364,U_1366)
| ~ in(U_1365,U_1364)
| ~ in(U_1366,U_1365) ),
inference(definitional_conversion,[status(esa)],[f_322_3]) ).
cnf(f_322_5,plain,
( ~ in(U_1364,U_1366)
| ~ in(U_1365,U_1364)
| ~ in(U_1366,U_1365) ),
inference(clausify,[status(thm)],[f_322_4]) ).
fof(f_323_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_323_2,plain,
! [U_1368,U_1367] :
( ( element(U_1368,powerset(U_1367))
| ~ subset(U_1368,U_1367) )
& ( subset(U_1368,U_1367)
| ~ element(U_1368,powerset(U_1367)) ) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
( ! [U_1372,U_1370] :
( element(U_1372,powerset(U_1370))
| ~ subset(U_1372,U_1370) )
& ! [U_1371,U_1369] :
( subset(U_1371,U_1369)
| ~ element(U_1371,powerset(U_1369)) ) ),
inference(miniscope,[status(thm)],[f_323_2]) ).
fof(f_323_4,plain,
( ! [U_1372,U_1370] :
( element(U_1372,powerset(U_1370))
| ~ subset(U_1372,U_1370) )
& ! [U_1369,U_1371] :
( subset(U_1371,U_1369)
| ~ element(U_1371,powerset(U_1369)) ) ),
inference(definitional_conversion,[status(esa)],[f_323_3]) ).
cnf(f_323_5,plain,
( subset(U_1371,U_1369)
| ~ element(U_1371,powerset(U_1369)) ),
inference(clausify,[status(thm)],[f_323_4]) ).
cnf(f_323_6,plain,
( element(U_1372,powerset(U_1370))
| ~ subset(U_1372,U_1370) ),
inference(clausify,[status(thm)],[f_323_4]) ).
fof(f_324_1,plain,
! [A] : transitive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t3_wellord2]) ).
fof(f_324_2,plain,
! [U_1373] : transitive(inclusion_relation(U_1373)),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
! [U_1373] : transitive(inclusion_relation(U_1373)),
inference(definitional_conversion,[status(esa)],[f_324_2]) ).
cnf(f_324_4,plain,
transitive(inclusion_relation(U_1373)),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_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_325_2,plain,
! [U_1377,U_1376] :
( ( ~ disjoint(U_1377,U_1376)
| ! [U_1375] :
( ~ in(U_1375,U_1376)
| ~ in(U_1375,U_1377) ) )
& ( ? [U_1374] :
( in(U_1374,U_1376)
& in(U_1374,U_1377) )
| disjoint(U_1377,U_1376) ) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
( ! [U_1381,U_1379] :
( ~ disjoint(U_1381,U_1379)
| ! [U_1375] :
( ~ in(U_1375,U_1379)
| ~ in(U_1375,U_1381) ) )
& ! [U_1380,U_1378] :
( ? [U_1374] :
( in(U_1374,U_1378)
& in(U_1374,U_1380) )
| disjoint(U_1380,U_1378) ) ),
inference(miniscope,[status(thm)],[f_325_2]) ).
fof(f_325_4,plain,
( ! [U_1381,U_1379] :
( ~ disjoint(U_1381,U_1379)
| ! [U_1375] :
( ~ in(U_1375,U_1379)
| ~ in(U_1375,U_1381) ) )
& ! [U_1380,U_1378] :
( ( in(sK280(U_1380,U_1378),U_1378)
& in(sK280(U_1380,U_1378),U_1380) )
| disjoint(U_1380,U_1378) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_1374,sK280(U_1380,U_1378))],[f_325_3]) ).
fof(f_325_5,plain,
( ! [U_1378,U_1380] :
( in(sK280(U_1380,U_1378),U_1378)
| ~ sP292(U_1378,U_1380) )
& ! [U_1378,U_1380] :
( in(sK280(U_1380,U_1378),U_1380)
| ~ sP292(U_1378,U_1380) )
& ! [U_1375,U_1381,U_1379] :
( ~ disjoint(U_1381,U_1379)
| ~ in(U_1375,U_1379)
| ~ in(U_1375,U_1381) )
& ! [U_1378,U_1380] :
( sP292(U_1378,U_1380)
| disjoint(U_1380,U_1378) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP292])],[f_325_4]) ).
cnf(f_325_6,plain,
( sP292(U_1378,U_1380)
| disjoint(U_1380,U_1378) ),
inference(clausify,[status(thm)],[f_325_5]) ).
cnf(f_325_7,plain,
( ~ disjoint(U_1381,U_1379)
| ~ in(U_1375,U_1379)
| ~ in(U_1375,U_1381) ),
inference(clausify,[status(thm)],[f_325_5]) ).
cnf(f_325_8,plain,
( in(sK280(U_1380,U_1378),U_1380)
| ~ sP292(U_1378,U_1380) ),
inference(clausify,[status(thm)],[f_325_5]) ).
cnf(f_325_9,plain,
( in(sK280(U_1380,U_1378),U_1378)
| ~ sP292(U_1378,U_1380) ),
inference(clausify,[status(thm)],[f_325_5]) ).
fof(f_326_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_326_2,plain,
! [U_1382] :
( U_1382 = empty_set
| ~ subset(U_1382,empty_set) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1382] :
( U_1382 = empty_set
| ~ subset(U_1382,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
( U_1382 = empty_set
| ~ subset(U_1382,empty_set) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_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_327_2,plain,
! [U_1384,U_1383] : set_difference(set_union2(U_1384,U_1383),U_1383) = set_difference(U_1384,U_1383),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1383,U_1384] : set_difference(set_union2(U_1384,U_1383),U_1383) = set_difference(U_1384,U_1383),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
set_difference(set_union2(U_1384,U_1383),U_1383) = set_difference(U_1384,U_1383),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_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_328_2,plain,
! [U_1387] :
( ( ( being_limit_ordinal(U_1387)
| ? [U_1386] :
( ~ in(succ(U_1386),U_1387)
& in(U_1386,U_1387)
& ordinal(U_1386) ) )
& ( ! [U_1385] :
( in(succ(U_1385),U_1387)
| ~ in(U_1385,U_1387)
| ~ ordinal(U_1385) )
| ~ being_limit_ordinal(U_1387) ) )
| ~ ordinal(U_1387) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
! [U_1387] :
( ( ( being_limit_ordinal(U_1387)
| ( ~ in(succ(sK281(U_1387)),U_1387)
& in(sK281(U_1387),U_1387)
& ordinal(sK281(U_1387)) ) )
& ( ! [U_1385] :
( in(succ(U_1385),U_1387)
| ~ in(U_1385,U_1387)
| ~ ordinal(U_1385) )
| ~ being_limit_ordinal(U_1387) ) )
| ~ ordinal(U_1387) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_1386,sK281(U_1387))],[f_328_2]) ).
fof(f_328_4,plain,
( ! [U_1387] :
( ~ in(succ(sK281(U_1387)),U_1387)
| ~ sP293(U_1387) )
& ! [U_1387] :
( in(sK281(U_1387),U_1387)
| ~ sP293(U_1387) )
& ! [U_1387] :
( ordinal(sK281(U_1387))
| ~ sP293(U_1387) )
& ! [U_1385,U_1387] :
( being_limit_ordinal(U_1387)
| sP293(U_1387)
| ~ sP294(U_1385,U_1387) )
& ! [U_1385,U_1387] :
( in(succ(U_1385),U_1387)
| ~ in(U_1385,U_1387)
| ~ ordinal(U_1385)
| ~ being_limit_ordinal(U_1387)
| ~ sP294(U_1385,U_1387) )
& ! [U_1385,U_1387] :
( sP294(U_1385,U_1387)
| ~ ordinal(U_1387) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293,sP294])],[f_328_3]) ).
cnf(f_328_5,plain,
( sP294(U_1385,U_1387)
| ~ ordinal(U_1387) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_6,plain,
( in(succ(U_1385),U_1387)
| ~ in(U_1385,U_1387)
| ~ ordinal(U_1385)
| ~ being_limit_ordinal(U_1387)
| ~ sP294(U_1385,U_1387) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_7,plain,
( being_limit_ordinal(U_1387)
| sP293(U_1387)
| ~ sP294(U_1385,U_1387) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_8,plain,
( ordinal(sK281(U_1387))
| ~ sP293(U_1387) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_9,plain,
( in(sK281(U_1387),U_1387)
| ~ sP293(U_1387) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_10,plain,
( ~ in(succ(sK281(U_1387)),U_1387)
| ~ sP293(U_1387) ),
inference(clausify,[status(thm)],[f_328_4]) ).
fof(f_329_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_329_2,plain,
! [U_1390] :
( ( ( ~ being_limit_ordinal(U_1390)
| ! [U_1389] :
( U_1390 != succ(U_1389)
| ~ ordinal(U_1389) ) )
& ( ? [U_1388] :
( U_1390 = succ(U_1388)
& ordinal(U_1388) )
| being_limit_ordinal(U_1390) ) )
| ~ ordinal(U_1390) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
! [U_1390] :
( ( ( ~ being_limit_ordinal(U_1390)
| ! [U_1389] :
( U_1390 != succ(U_1389)
| ~ ordinal(U_1389) ) )
& ( ( U_1390 = succ(sK282(U_1390))
& ordinal(sK282(U_1390)) )
| being_limit_ordinal(U_1390) ) )
| ~ ordinal(U_1390) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_1388,sK282(U_1390))],[f_329_2]) ).
fof(f_329_4,plain,
( ! [U_1390] :
( U_1390 = succ(sK282(U_1390))
| ~ sP295(U_1390) )
& ! [U_1390] :
( ordinal(sK282(U_1390))
| ~ sP295(U_1390) )
& ! [U_1390,U_1389] :
( ~ being_limit_ordinal(U_1390)
| U_1390 != succ(U_1389)
| ~ ordinal(U_1389)
| ~ sP296(U_1390,U_1389) )
& ! [U_1390,U_1389] :
( sP295(U_1390)
| being_limit_ordinal(U_1390)
| ~ sP296(U_1390,U_1389) )
& ! [U_1390,U_1389] :
( sP296(U_1390,U_1389)
| ~ ordinal(U_1390) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295,sP296])],[f_329_3]) ).
cnf(f_329_5,plain,
( sP296(U_1390,U_1389)
| ~ ordinal(U_1390) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_6,plain,
( sP295(U_1390)
| being_limit_ordinal(U_1390)
| ~ sP296(U_1390,U_1389) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_7,plain,
( ~ being_limit_ordinal(U_1390)
| U_1390 != succ(U_1389)
| ~ ordinal(U_1389)
| ~ sP296(U_1390,U_1389) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_8,plain,
( ordinal(sK282(U_1390))
| ~ sP295(U_1390) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_9,plain,
( U_1390 = succ(sK282(U_1390))
| ~ sP295(U_1390) ),
inference(clausify,[status(thm)],[f_329_4]) ).
fof(f_330_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_330_2,plain,
! [U_1393,U_1392] :
( ! [U_1391] :
( ( ( disjoint(U_1392,U_1391)
| ~ subset(U_1392,subset_complement(U_1393,U_1391)) )
& ( subset(U_1392,subset_complement(U_1393,U_1391))
| ~ disjoint(U_1392,U_1391) ) )
| ~ element(U_1391,powerset(U_1393)) )
| ~ element(U_1392,powerset(U_1393)) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
( ! [U_1392,U_1391,U_1393] :
( disjoint(U_1392,U_1391)
| ~ subset(U_1392,subset_complement(U_1393,U_1391))
| ~ sP297(U_1392,U_1391,U_1393) )
& ! [U_1392,U_1391,U_1393] :
( subset(U_1392,subset_complement(U_1393,U_1391))
| ~ disjoint(U_1392,U_1391)
| ~ sP297(U_1392,U_1391,U_1393) )
& ! [U_1392,U_1391,U_1393] :
( sP297(U_1392,U_1391,U_1393)
| ~ element(U_1391,powerset(U_1393))
| ~ element(U_1392,powerset(U_1393)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP297])],[f_330_2]) ).
cnf(f_330_4,plain,
( sP297(U_1392,U_1391,U_1393)
| ~ element(U_1391,powerset(U_1393))
| ~ element(U_1392,powerset(U_1393)) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_5,plain,
( subset(U_1392,subset_complement(U_1393,U_1391))
| ~ disjoint(U_1392,U_1391)
| ~ sP297(U_1392,U_1391,U_1393) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_6,plain,
( disjoint(U_1392,U_1391)
| ~ subset(U_1392,subset_complement(U_1393,U_1391))
| ~ sP297(U_1392,U_1391,U_1393) ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_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_331_2,plain,
! [U_1395] :
( ! [U_1394] :
( subset(relation_dom(relation_composition(U_1395,U_1394)),relation_dom(U_1395))
| ~ relation(U_1394) )
| ~ relation(U_1395) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1394,U_1395] :
( subset(relation_dom(relation_composition(U_1395,U_1394)),relation_dom(U_1395))
| ~ relation(U_1394)
| ~ relation(U_1395) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( subset(relation_dom(relation_composition(U_1395,U_1394)),relation_dom(U_1395))
| ~ relation(U_1394)
| ~ relation(U_1395) ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_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_332_2,plain,
! [U_1397] :
( ! [U_1396] :
( subset(relation_rng(relation_composition(U_1397,U_1396)),relation_rng(U_1396))
| ~ relation(U_1396) )
| ~ relation(U_1397) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_1396,U_1397] :
( subset(relation_rng(relation_composition(U_1397,U_1396)),relation_rng(U_1396))
| ~ relation(U_1396)
| ~ relation(U_1397) ),
inference(definitional_conversion,[status(esa)],[f_332_2]) ).
cnf(f_332_4,plain,
( subset(relation_rng(relation_composition(U_1397,U_1396)),relation_rng(U_1396))
| ~ relation(U_1396)
| ~ relation(U_1397) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_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_333_2,plain,
! [U_1399,U_1398] :
( U_1398 = set_union2(U_1399,set_difference(U_1398,U_1399))
| ~ subset(U_1399,U_1398) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_1398,U_1399] :
( U_1398 = set_union2(U_1399,set_difference(U_1398,U_1399))
| ~ subset(U_1399,U_1398) ),
inference(definitional_conversion,[status(esa)],[f_333_2]) ).
cnf(f_333_4,plain,
( U_1398 = set_union2(U_1399,set_difference(U_1398,U_1399))
| ~ subset(U_1399,U_1398) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
! [A,B,C,D] :
( ! [E] :
( ( in(E,relation_inverse_image(D,C))
| ~ in(apply(D,E),C)
| ~ in(E,A) )
& ( ( in(apply(D,E),C)
& in(E,A) )
| ~ in(E,relation_inverse_image(D,C)) ) )
| B = empty_set
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(fof_nnf,[status(thm)],[t46_funct_2]) ).
fof(f_334_2,plain,
! [U_1404,U_1403,U_1402,U_1401] :
( ! [U_1400] :
( ( in(U_1400,relation_inverse_image(U_1401,U_1402))
| ~ in(apply(U_1401,U_1400),U_1402)
| ~ in(U_1400,U_1404) )
& ( ( in(apply(U_1401,U_1400),U_1402)
& in(U_1400,U_1404) )
| ~ in(U_1400,relation_inverse_image(U_1401,U_1402)) ) )
| U_1403 = empty_set
| ~ relation_of2_as_subset(U_1401,U_1404,U_1403)
| ~ quasi_total(U_1401,U_1404,U_1403)
| ~ function(U_1401) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1404,U_1403,U_1402,U_1401] :
( ( ! [U_1406] :
( in(U_1406,relation_inverse_image(U_1401,U_1402))
| ~ in(apply(U_1401,U_1406),U_1402)
| ~ in(U_1406,U_1404) )
& ! [U_1405] :
( ( in(apply(U_1401,U_1405),U_1402)
& in(U_1405,U_1404) )
| ~ in(U_1405,relation_inverse_image(U_1401,U_1402)) ) )
| U_1403 = empty_set
| ~ relation_of2_as_subset(U_1401,U_1404,U_1403)
| ~ quasi_total(U_1401,U_1404,U_1403)
| ~ function(U_1401) ),
inference(miniscope,[status(thm)],[f_334_2]) ).
fof(f_334_4,plain,
( ! [U_1401,U_1402,U_1404,U_1405] :
( in(apply(U_1401,U_1405),U_1402)
| ~ sP298(U_1401,U_1402,U_1404,U_1405) )
& ! [U_1401,U_1402,U_1404,U_1405] :
( in(U_1405,U_1404)
| ~ sP298(U_1401,U_1402,U_1404,U_1405) )
& ! [U_1401,U_1402,U_1404,U_1405,U_1406] :
( in(U_1406,relation_inverse_image(U_1401,U_1402))
| ~ in(apply(U_1401,U_1406),U_1402)
| ~ in(U_1406,U_1404)
| ~ sP299(U_1401,U_1402,U_1404,U_1405,U_1406) )
& ! [U_1401,U_1402,U_1404,U_1405,U_1406] :
( sP298(U_1401,U_1402,U_1404,U_1405)
| ~ in(U_1405,relation_inverse_image(U_1401,U_1402))
| ~ sP299(U_1401,U_1402,U_1404,U_1405,U_1406) )
& ! [U_1401,U_1402,U_1403,U_1404,U_1405,U_1406] :
( sP299(U_1401,U_1402,U_1404,U_1405,U_1406)
| U_1403 = empty_set
| ~ relation_of2_as_subset(U_1401,U_1404,U_1403)
| ~ quasi_total(U_1401,U_1404,U_1403)
| ~ function(U_1401) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298,sP299])],[f_334_3]) ).
cnf(f_334_5,plain,
( sP299(U_1401,U_1402,U_1404,U_1405,U_1406)
| U_1403 = empty_set
| ~ relation_of2_as_subset(U_1401,U_1404,U_1403)
| ~ quasi_total(U_1401,U_1404,U_1403)
| ~ function(U_1401) ),
inference(clausify,[status(thm)],[f_334_4]) ).
cnf(f_334_6,plain,
( sP298(U_1401,U_1402,U_1404,U_1405)
| ~ in(U_1405,relation_inverse_image(U_1401,U_1402))
| ~ sP299(U_1401,U_1402,U_1404,U_1405,U_1406) ),
inference(clausify,[status(thm)],[f_334_4]) ).
cnf(f_334_7,plain,
( in(U_1406,relation_inverse_image(U_1401,U_1402))
| ~ in(apply(U_1401,U_1406),U_1402)
| ~ in(U_1406,U_1404)
| ~ sP299(U_1401,U_1402,U_1404,U_1405,U_1406) ),
inference(clausify,[status(thm)],[f_334_4]) ).
cnf(f_334_8,plain,
( in(U_1405,U_1404)
| ~ sP298(U_1401,U_1402,U_1404,U_1405) ),
inference(clausify,[status(thm)],[f_334_4]) ).
cnf(f_334_9,plain,
( in(apply(U_1401,U_1405),U_1402)
| ~ sP298(U_1401,U_1402,U_1404,U_1405) ),
inference(clausify,[status(thm)],[f_334_4]) ).
fof(f_335_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_335_2,plain,
! [U_1408] :
( ! [U_1407] :
( relation_dom(relation_composition(U_1408,U_1407)) = relation_dom(U_1408)
| ~ subset(relation_rng(U_1408),relation_dom(U_1407))
| ~ relation(U_1407) )
| ~ relation(U_1408) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_1408,U_1407] :
( relation_dom(relation_composition(U_1408,U_1407)) = relation_dom(U_1408)
| ~ subset(relation_rng(U_1408),relation_dom(U_1407))
| ~ relation(U_1407)
| ~ relation(U_1408) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( relation_dom(relation_composition(U_1408,U_1407)) = relation_dom(U_1408)
| ~ subset(relation_rng(U_1408),relation_dom(U_1407))
| ~ relation(U_1407)
| ~ relation(U_1408) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_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_336_2,plain,
! [U_1410,U_1409] :
( complements_of_subsets(U_1410,U_1409) != empty_set
| U_1409 = empty_set
| ~ element(U_1409,powerset(powerset(U_1410))) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_1409,U_1410] :
( complements_of_subsets(U_1410,U_1409) != empty_set
| U_1409 = empty_set
| ~ element(U_1409,powerset(powerset(U_1410))) ),
inference(definitional_conversion,[status(esa)],[f_336_2]) ).
cnf(f_336_4,plain,
( complements_of_subsets(U_1410,U_1409) != empty_set
| U_1409 = empty_set
| ~ element(U_1409,powerset(powerset(U_1410))) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_337_2,plain,
! [U_1412,U_1411] :
( set_union2(singleton(U_1412),U_1411) = U_1411
| ~ in(U_1412,U_1411) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_1411,U_1412] :
( set_union2(singleton(U_1412),U_1411) = U_1411
| ~ in(U_1412,U_1411) ),
inference(definitional_conversion,[status(esa)],[f_337_2]) ).
cnf(f_337_4,plain,
( set_union2(singleton(U_1412),U_1411) = U_1411
| ~ in(U_1412,U_1411) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_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_338_2,plain,
! [U_1414] :
( ! [U_1413] :
( relation_rng(relation_composition(U_1413,U_1414)) = relation_rng(U_1414)
| ~ subset(relation_dom(U_1414),relation_rng(U_1413))
| ~ relation(U_1413) )
| ~ relation(U_1414) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1413,U_1414] :
( relation_rng(relation_composition(U_1413,U_1414)) = relation_rng(U_1414)
| ~ subset(relation_dom(U_1414),relation_rng(U_1413))
| ~ relation(U_1413)
| ~ relation(U_1414) ),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
( relation_rng(relation_composition(U_1413,U_1414)) = relation_rng(U_1414)
| ~ subset(relation_dom(U_1414),relation_rng(U_1413))
| ~ relation(U_1413)
| ~ relation(U_1414) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_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_339_2,plain,
! [U_1416,U_1415] :
( subset_difference(U_1416,cast_to_subset(U_1416),union_of_subsets(U_1416,U_1415)) = meet_of_subsets(U_1416,complements_of_subsets(U_1416,U_1415))
| U_1415 = empty_set
| ~ element(U_1415,powerset(powerset(U_1416))) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_1415,U_1416] :
( subset_difference(U_1416,cast_to_subset(U_1416),union_of_subsets(U_1416,U_1415)) = meet_of_subsets(U_1416,complements_of_subsets(U_1416,U_1415))
| U_1415 = empty_set
| ~ element(U_1415,powerset(powerset(U_1416))) ),
inference(definitional_conversion,[status(esa)],[f_339_2]) ).
cnf(f_339_4,plain,
( subset_difference(U_1416,cast_to_subset(U_1416),union_of_subsets(U_1416,U_1415)) = meet_of_subsets(U_1416,complements_of_subsets(U_1416,U_1415))
| U_1415 = empty_set
| ~ element(U_1415,powerset(powerset(U_1416))) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_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_340_2,plain,
! [U_1418,U_1417] :
( union_of_subsets(U_1418,complements_of_subsets(U_1418,U_1417)) = subset_difference(U_1418,cast_to_subset(U_1418),meet_of_subsets(U_1418,U_1417))
| U_1417 = empty_set
| ~ element(U_1417,powerset(powerset(U_1418))) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
! [U_1418,U_1417] :
( union_of_subsets(U_1418,complements_of_subsets(U_1418,U_1417)) = subset_difference(U_1418,cast_to_subset(U_1418),meet_of_subsets(U_1418,U_1417))
| U_1417 = empty_set
| ~ element(U_1417,powerset(powerset(U_1418))) ),
inference(definitional_conversion,[status(esa)],[f_340_2]) ).
cnf(f_340_4,plain,
( union_of_subsets(U_1418,complements_of_subsets(U_1418,U_1417)) = subset_difference(U_1418,cast_to_subset(U_1418),meet_of_subsets(U_1418,U_1417))
| U_1417 = empty_set
| ~ element(U_1417,powerset(powerset(U_1418))) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_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_341_2,plain,
! [U_1420,U_1419] : set_difference(U_1420,set_difference(U_1420,U_1419)) = set_intersection2(U_1420,U_1419),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1420,U_1419] : set_difference(U_1420,set_difference(U_1420,U_1419)) = set_intersection2(U_1420,U_1419),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
set_difference(U_1420,set_difference(U_1420,U_1419)) = set_intersection2(U_1420,U_1419),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_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_342_2,plain,
! [U_1423] :
( ! [U_1422] :
( ! [U_1421] :
( relation_isomorphism(U_1422,U_1423,function_inverse(U_1421))
| ~ relation_isomorphism(U_1423,U_1422,U_1421)
| ~ function(U_1421)
| ~ relation(U_1421) )
| ~ relation(U_1422) )
| ~ relation(U_1423) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_1421,U_1422,U_1423] :
( relation_isomorphism(U_1422,U_1423,function_inverse(U_1421))
| ~ relation_isomorphism(U_1423,U_1422,U_1421)
| ~ function(U_1421)
| ~ relation(U_1421)
| ~ relation(U_1422)
| ~ relation(U_1423) ),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,plain,
( relation_isomorphism(U_1422,U_1423,function_inverse(U_1421))
| ~ relation_isomorphism(U_1423,U_1422,U_1421)
| ~ function(U_1421)
| ~ relation(U_1421)
| ~ relation(U_1422)
| ~ relation(U_1423) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_343_2,plain,
! [U_1424] : set_difference(empty_set,U_1424) = empty_set,
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_1424] : set_difference(empty_set,U_1424) = empty_set,
inference(definitional_conversion,[status(esa)],[f_343_2]) ).
cnf(f_343_4,plain,
set_difference(empty_set,U_1424) = empty_set,
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_344_2,plain,
! [U_1427,U_1426,U_1425] :
( element(U_1427,U_1425)
| ~ element(U_1426,powerset(U_1425))
| ~ in(U_1427,U_1426) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_1427,U_1426,U_1425] :
( element(U_1427,U_1425)
| ~ element(U_1426,powerset(U_1425))
| ~ in(U_1427,U_1426) ),
inference(definitional_conversion,[status(esa)],[f_344_2]) ).
cnf(f_344_4,plain,
( element(U_1427,U_1425)
| ~ element(U_1426,powerset(U_1425))
| ~ in(U_1427,U_1426) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_1,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t4_wellord2]) ).
fof(f_345_2,plain,
! [U_1428] :
( connected(inclusion_relation(U_1428))
| ~ ordinal(U_1428) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_1428] :
( connected(inclusion_relation(U_1428))
| ~ ordinal(U_1428) ),
inference(definitional_conversion,[status(esa)],[f_345_2]) ).
cnf(f_345_4,plain,
( connected(inclusion_relation(U_1428))
| ~ ordinal(U_1428) ),
inference(clausify,[status(thm)],[f_345_3]) ).
fof(f_346_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_346_2,plain,
! [U_1432,U_1431] :
( ( ~ disjoint(U_1432,U_1431)
| ! [U_1430] : ~ in(U_1430,set_intersection2(U_1432,U_1431)) )
& ( ? [U_1429] : in(U_1429,set_intersection2(U_1432,U_1431))
| disjoint(U_1432,U_1431) ) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
( ! [U_1436,U_1434] :
( ~ disjoint(U_1436,U_1434)
| ! [U_1430] : ~ in(U_1430,set_intersection2(U_1436,U_1434)) )
& ! [U_1435,U_1433] :
( ? [U_1429] : in(U_1429,set_intersection2(U_1435,U_1433))
| disjoint(U_1435,U_1433) ) ),
inference(miniscope,[status(thm)],[f_346_2]) ).
fof(f_346_4,plain,
( ! [U_1436,U_1434] :
( ~ disjoint(U_1436,U_1434)
| ! [U_1430] : ~ in(U_1430,set_intersection2(U_1436,U_1434)) )
& ! [U_1435,U_1433] :
( in(sK283(U_1435,U_1433),set_intersection2(U_1435,U_1433))
| disjoint(U_1435,U_1433) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_1429,sK283(U_1435,U_1433))],[f_346_3]) ).
fof(f_346_5,plain,
( ! [U_1436,U_1430,U_1434] :
( ~ disjoint(U_1436,U_1434)
| ~ in(U_1430,set_intersection2(U_1436,U_1434)) )
& ! [U_1435,U_1433] :
( in(sK283(U_1435,U_1433),set_intersection2(U_1435,U_1433))
| disjoint(U_1435,U_1433) ) ),
inference(definitional_conversion,[status(esa)],[f_346_4]) ).
cnf(f_346_6,plain,
( in(sK283(U_1435,U_1433),set_intersection2(U_1435,U_1433))
| disjoint(U_1435,U_1433) ),
inference(clausify,[status(thm)],[f_346_5]) ).
cnf(f_346_7,plain,
( ~ disjoint(U_1436,U_1434)
| ~ in(U_1430,set_intersection2(U_1436,U_1434)) ),
inference(clausify,[status(thm)],[f_346_5]) ).
fof(f_347_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_347_2,plain,
! [U_1439] :
( ! [U_1438] :
( ! [U_1437] :
( in(U_1437,subset_complement(U_1439,U_1438))
| in(U_1437,U_1438)
| ~ element(U_1437,U_1439) )
| ~ element(U_1438,powerset(U_1439)) )
| U_1439 = empty_set ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_1438,U_1439,U_1437] :
( in(U_1437,subset_complement(U_1439,U_1438))
| in(U_1437,U_1438)
| ~ element(U_1437,U_1439)
| ~ element(U_1438,powerset(U_1439))
| U_1439 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( in(U_1437,subset_complement(U_1439,U_1438))
| in(U_1437,U_1438)
| ~ element(U_1437,U_1439)
| ~ element(U_1438,powerset(U_1439))
| U_1439 = empty_set ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_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_348_2,plain,
! [U_1442] :
( ! [U_1441] :
( ! [U_1440] :
( ( ( well_founded_relation(U_1441)
| ~ well_founded_relation(U_1442) )
& ( antisymmetric(U_1441)
| ~ antisymmetric(U_1442) )
& ( connected(U_1441)
| ~ connected(U_1442) )
& ( transitive(U_1441)
| ~ transitive(U_1442) )
& ( reflexive(U_1441)
| ~ reflexive(U_1442) ) )
| ~ relation_isomorphism(U_1442,U_1441,U_1440)
| ~ function(U_1440)
| ~ relation(U_1440) )
| ~ relation(U_1441) )
| ~ relation(U_1442) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
( ! [U_1442,U_1441] :
( well_founded_relation(U_1441)
| ~ well_founded_relation(U_1442)
| ~ sP300(U_1442,U_1441) )
& ! [U_1442,U_1441] :
( antisymmetric(U_1441)
| ~ antisymmetric(U_1442)
| ~ sP300(U_1442,U_1441) )
& ! [U_1442,U_1441] :
( connected(U_1441)
| ~ connected(U_1442)
| ~ sP300(U_1442,U_1441) )
& ! [U_1442,U_1441] :
( transitive(U_1441)
| ~ transitive(U_1442)
| ~ sP300(U_1442,U_1441) )
& ! [U_1442,U_1441] :
( reflexive(U_1441)
| ~ reflexive(U_1442)
| ~ sP300(U_1442,U_1441) )
& ! [U_1442,U_1440,U_1441] :
( sP300(U_1442,U_1441)
| ~ relation_isomorphism(U_1442,U_1441,U_1440)
| ~ function(U_1440)
| ~ relation(U_1440)
| ~ relation(U_1441)
| ~ relation(U_1442) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP300])],[f_348_2]) ).
cnf(f_348_4,plain,
( sP300(U_1442,U_1441)
| ~ relation_isomorphism(U_1442,U_1441,U_1440)
| ~ function(U_1440)
| ~ relation(U_1440)
| ~ relation(U_1441)
| ~ relation(U_1442) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_5,plain,
( reflexive(U_1441)
| ~ reflexive(U_1442)
| ~ sP300(U_1442,U_1441) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_6,plain,
( transitive(U_1441)
| ~ transitive(U_1442)
| ~ sP300(U_1442,U_1441) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_7,plain,
( connected(U_1441)
| ~ connected(U_1442)
| ~ sP300(U_1442,U_1441) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_8,plain,
( antisymmetric(U_1441)
| ~ antisymmetric(U_1442)
| ~ sP300(U_1442,U_1441) ),
inference(clausify,[status(thm)],[f_348_3]) ).
cnf(f_348_9,plain,
( well_founded_relation(U_1441)
| ~ well_founded_relation(U_1442)
| ~ sP300(U_1442,U_1441) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_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_349_2,plain,
! [U_1448] :
( ! [U_1447] :
( ( ( U_1447 = function_inverse(U_1448)
| ? [U_1446,U_1445] :
( ( ( U_1445 != apply(U_1447,U_1446)
| ~ in(U_1446,relation_rng(U_1448)) )
& U_1446 = apply(U_1448,U_1445)
& in(U_1445,relation_dom(U_1448)) )
| ( ( U_1446 != apply(U_1448,U_1445)
| ~ in(U_1445,relation_dom(U_1448)) )
& U_1445 = apply(U_1447,U_1446)
& in(U_1446,relation_rng(U_1448)) ) )
| relation_dom(U_1447) != relation_rng(U_1448) )
& ( ( ! [U_1444,U_1443] :
( ( ( U_1443 = apply(U_1447,U_1444)
& in(U_1444,relation_rng(U_1448)) )
| U_1444 != apply(U_1448,U_1443)
| ~ in(U_1443,relation_dom(U_1448)) )
& ( ( U_1444 = apply(U_1448,U_1443)
& in(U_1443,relation_dom(U_1448)) )
| U_1443 != apply(U_1447,U_1444)
| ~ in(U_1444,relation_rng(U_1448)) ) )
& relation_dom(U_1447) = relation_rng(U_1448) )
| U_1447 != function_inverse(U_1448) ) )
| ~ function(U_1447)
| ~ relation(U_1447) )
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_1448] :
( ! [U_1447] :
( ( ( U_1447 = function_inverse(U_1448)
| ? [U_1456,U_1454] :
( ( U_1454 != apply(U_1447,U_1456)
| ~ in(U_1456,relation_rng(U_1448)) )
& U_1456 = apply(U_1448,U_1454)
& in(U_1454,relation_dom(U_1448)) )
| ? [U_1455,U_1453] :
( ( U_1455 != apply(U_1448,U_1453)
| ~ in(U_1453,relation_dom(U_1448)) )
& U_1453 = apply(U_1447,U_1455)
& in(U_1455,relation_rng(U_1448)) )
| relation_dom(U_1447) != relation_rng(U_1448) )
& ( ( ! [U_1452,U_1450] :
( ( U_1450 = apply(U_1447,U_1452)
& in(U_1452,relation_rng(U_1448)) )
| U_1452 != apply(U_1448,U_1450)
| ~ in(U_1450,relation_dom(U_1448)) )
& ! [U_1451,U_1449] :
( ( U_1451 = apply(U_1448,U_1449)
& in(U_1449,relation_dom(U_1448)) )
| U_1449 != apply(U_1447,U_1451)
| ~ in(U_1451,relation_rng(U_1448)) )
& relation_dom(U_1447) = relation_rng(U_1448) )
| U_1447 != function_inverse(U_1448) ) )
| ~ function(U_1447)
| ~ relation(U_1447) )
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ),
inference(miniscope,[status(thm)],[f_349_2]) ).
fof(f_349_4,plain,
! [U_1448] :
( ! [U_1447] :
( ( ( U_1447 = function_inverse(U_1448)
| ? [U_1456,U_1454] :
( ( U_1454 != apply(U_1447,U_1456)
| ~ in(U_1456,relation_rng(U_1448)) )
& U_1456 = apply(U_1448,U_1454)
& in(U_1454,relation_dom(U_1448)) )
| ? [U_1453] :
( ( sK284(U_1448,U_1447) != apply(U_1448,U_1453)
| ~ in(U_1453,relation_dom(U_1448)) )
& U_1453 = apply(U_1447,sK284(U_1448,U_1447))
& in(sK284(U_1448,U_1447),relation_rng(U_1448)) )
| relation_dom(U_1447) != relation_rng(U_1448) )
& ( ( ! [U_1452,U_1450] :
( ( U_1450 = apply(U_1447,U_1452)
& in(U_1452,relation_rng(U_1448)) )
| U_1452 != apply(U_1448,U_1450)
| ~ in(U_1450,relation_dom(U_1448)) )
& ! [U_1451,U_1449] :
( ( U_1451 = apply(U_1448,U_1449)
& in(U_1449,relation_dom(U_1448)) )
| U_1449 != apply(U_1447,U_1451)
| ~ in(U_1451,relation_rng(U_1448)) )
& relation_dom(U_1447) = relation_rng(U_1448) )
| U_1447 != function_inverse(U_1448) ) )
| ~ function(U_1447)
| ~ relation(U_1447) )
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_1455,sK284(U_1448,U_1447))],[f_349_3]) ).
fof(f_349_5,plain,
! [U_1448] :
( ! [U_1447] :
( ( ( U_1447 = function_inverse(U_1448)
| ? [U_1456,U_1454] :
( ( U_1454 != apply(U_1447,U_1456)
| ~ in(U_1456,relation_rng(U_1448)) )
& U_1456 = apply(U_1448,U_1454)
& in(U_1454,relation_dom(U_1448)) )
| ( ( sK284(U_1448,U_1447) != apply(U_1448,sK285(U_1448,U_1447))
| ~ in(sK285(U_1448,U_1447),relation_dom(U_1448)) )
& sK285(U_1448,U_1447) = apply(U_1447,sK284(U_1448,U_1447))
& in(sK284(U_1448,U_1447),relation_rng(U_1448)) )
| relation_dom(U_1447) != relation_rng(U_1448) )
& ( ( ! [U_1452,U_1450] :
( ( U_1450 = apply(U_1447,U_1452)
& in(U_1452,relation_rng(U_1448)) )
| U_1452 != apply(U_1448,U_1450)
| ~ in(U_1450,relation_dom(U_1448)) )
& ! [U_1451,U_1449] :
( ( U_1451 = apply(U_1448,U_1449)
& in(U_1449,relation_dom(U_1448)) )
| U_1449 != apply(U_1447,U_1451)
| ~ in(U_1451,relation_rng(U_1448)) )
& relation_dom(U_1447) = relation_rng(U_1448) )
| U_1447 != function_inverse(U_1448) ) )
| ~ function(U_1447)
| ~ relation(U_1447) )
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_1453,sK285(U_1448,U_1447))],[f_349_4]) ).
fof(f_349_6,plain,
! [U_1448] :
( ! [U_1447] :
( ( ( U_1447 = function_inverse(U_1448)
| ? [U_1454] :
( ( U_1454 != apply(U_1447,sK286(U_1448,U_1447))
| ~ in(sK286(U_1448,U_1447),relation_rng(U_1448)) )
& sK286(U_1448,U_1447) = apply(U_1448,U_1454)
& in(U_1454,relation_dom(U_1448)) )
| ( ( sK284(U_1448,U_1447) != apply(U_1448,sK285(U_1448,U_1447))
| ~ in(sK285(U_1448,U_1447),relation_dom(U_1448)) )
& sK285(U_1448,U_1447) = apply(U_1447,sK284(U_1448,U_1447))
& in(sK284(U_1448,U_1447),relation_rng(U_1448)) )
| relation_dom(U_1447) != relation_rng(U_1448) )
& ( ( ! [U_1452,U_1450] :
( ( U_1450 = apply(U_1447,U_1452)
& in(U_1452,relation_rng(U_1448)) )
| U_1452 != apply(U_1448,U_1450)
| ~ in(U_1450,relation_dom(U_1448)) )
& ! [U_1451,U_1449] :
( ( U_1451 = apply(U_1448,U_1449)
& in(U_1449,relation_dom(U_1448)) )
| U_1449 != apply(U_1447,U_1451)
| ~ in(U_1451,relation_rng(U_1448)) )
& relation_dom(U_1447) = relation_rng(U_1448) )
| U_1447 != function_inverse(U_1448) ) )
| ~ function(U_1447)
| ~ relation(U_1447) )
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_1456,sK286(U_1448,U_1447))],[f_349_5]) ).
fof(f_349_7,plain,
! [U_1448] :
( ! [U_1447] :
( ( ( U_1447 = function_inverse(U_1448)
| ( ( sK287(U_1448,U_1447) != apply(U_1447,sK286(U_1448,U_1447))
| ~ in(sK286(U_1448,U_1447),relation_rng(U_1448)) )
& sK286(U_1448,U_1447) = apply(U_1448,sK287(U_1448,U_1447))
& in(sK287(U_1448,U_1447),relation_dom(U_1448)) )
| ( ( sK284(U_1448,U_1447) != apply(U_1448,sK285(U_1448,U_1447))
| ~ in(sK285(U_1448,U_1447),relation_dom(U_1448)) )
& sK285(U_1448,U_1447) = apply(U_1447,sK284(U_1448,U_1447))
& in(sK284(U_1448,U_1447),relation_rng(U_1448)) )
| relation_dom(U_1447) != relation_rng(U_1448) )
& ( ( ! [U_1452,U_1450] :
( ( U_1450 = apply(U_1447,U_1452)
& in(U_1452,relation_rng(U_1448)) )
| U_1452 != apply(U_1448,U_1450)
| ~ in(U_1450,relation_dom(U_1448)) )
& ! [U_1451,U_1449] :
( ( U_1451 = apply(U_1448,U_1449)
& in(U_1449,relation_dom(U_1448)) )
| U_1449 != apply(U_1447,U_1451)
| ~ in(U_1451,relation_rng(U_1448)) )
& relation_dom(U_1447) = relation_rng(U_1448) )
| U_1447 != function_inverse(U_1448) ) )
| ~ function(U_1447)
| ~ relation(U_1447) )
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_1454,sK287(U_1448,U_1447))],[f_349_6]) ).
fof(f_349_8,plain,
( ! [U_1447,U_1448] :
( sK287(U_1448,U_1447) != apply(U_1447,sK286(U_1448,U_1447))
| ~ in(sK286(U_1448,U_1447),relation_rng(U_1448))
| ~ sP305(U_1447,U_1448) )
& ! [U_1447,U_1448] :
( sK286(U_1448,U_1447) = apply(U_1448,sK287(U_1448,U_1447))
| ~ sP305(U_1447,U_1448) )
& ! [U_1447,U_1448] :
( in(sK287(U_1448,U_1447),relation_dom(U_1448))
| ~ sP305(U_1447,U_1448) )
& ! [U_1447,U_1448] :
( sK284(U_1448,U_1447) != apply(U_1448,sK285(U_1448,U_1447))
| ~ in(sK285(U_1448,U_1447),relation_dom(U_1448))
| ~ sP304(U_1447,U_1448) )
& ! [U_1447,U_1448] :
( sK285(U_1448,U_1447) = apply(U_1447,sK284(U_1448,U_1447))
| ~ sP304(U_1447,U_1448) )
& ! [U_1447,U_1448] :
( in(sK284(U_1448,U_1447),relation_rng(U_1448))
| ~ sP304(U_1447,U_1448) )
& ! [U_1447,U_1448,U_1450,U_1452] :
( U_1450 = apply(U_1447,U_1452)
| ~ sP302(U_1447,U_1448,U_1450,U_1452) )
& ! [U_1447,U_1448,U_1450,U_1452] :
( in(U_1452,relation_rng(U_1448))
| ~ sP302(U_1447,U_1448,U_1450,U_1452) )
& ! [U_1451,U_1448,U_1449] :
( U_1451 = apply(U_1448,U_1449)
| ~ sP301(U_1451,U_1448,U_1449) )
& ! [U_1451,U_1448,U_1449] :
( in(U_1449,relation_dom(U_1448))
| ~ sP301(U_1451,U_1448,U_1449) )
& ! [U_1451,U_1447,U_1448,U_1450,U_1452,U_1449] :
( sP302(U_1447,U_1448,U_1450,U_1452)
| U_1452 != apply(U_1448,U_1450)
| ~ in(U_1450,relation_dom(U_1448))
| ~ sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) )
& ! [U_1451,U_1447,U_1448,U_1450,U_1452,U_1449] :
( sP301(U_1451,U_1448,U_1449)
| U_1449 != apply(U_1447,U_1451)
| ~ in(U_1451,relation_rng(U_1448))
| ~ sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) )
& ! [U_1451,U_1447,U_1448,U_1450,U_1452,U_1449] :
( relation_dom(U_1447) = relation_rng(U_1448)
| ~ sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) )
& ! [U_1451,U_1447,U_1448,U_1450,U_1452,U_1449] :
( U_1447 = function_inverse(U_1448)
| sP305(U_1447,U_1448)
| sP304(U_1447,U_1448)
| relation_dom(U_1447) != relation_rng(U_1448)
| ~ sP306(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) )
& ! [U_1451,U_1447,U_1448,U_1450,U_1452,U_1449] :
( sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449)
| U_1447 != function_inverse(U_1448)
| ~ sP306(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) )
& ! [U_1451,U_1447,U_1448,U_1450,U_1452,U_1449] :
( sP306(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449)
| ~ function(U_1447)
| ~ relation(U_1447)
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP301,sP302,sP303,sP304,sP305,sP306])],[f_349_7]) ).
cnf(f_349_9,plain,
( sP306(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449)
| ~ function(U_1447)
| ~ relation(U_1447)
| ~ one_to_one(U_1448)
| ~ function(U_1448)
| ~ relation(U_1448) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_10,plain,
( sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449)
| U_1447 != function_inverse(U_1448)
| ~ sP306(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_11,plain,
( U_1447 = function_inverse(U_1448)
| sP305(U_1447,U_1448)
| sP304(U_1447,U_1448)
| relation_dom(U_1447) != relation_rng(U_1448)
| ~ sP306(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_12,plain,
( relation_dom(U_1447) = relation_rng(U_1448)
| ~ sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_13,plain,
( sP301(U_1451,U_1448,U_1449)
| U_1449 != apply(U_1447,U_1451)
| ~ in(U_1451,relation_rng(U_1448))
| ~ sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_14,plain,
( sP302(U_1447,U_1448,U_1450,U_1452)
| U_1452 != apply(U_1448,U_1450)
| ~ in(U_1450,relation_dom(U_1448))
| ~ sP303(U_1451,U_1447,U_1448,U_1450,U_1452,U_1449) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_15,plain,
( in(U_1449,relation_dom(U_1448))
| ~ sP301(U_1451,U_1448,U_1449) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_16,plain,
( U_1451 = apply(U_1448,U_1449)
| ~ sP301(U_1451,U_1448,U_1449) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_17,plain,
( in(U_1452,relation_rng(U_1448))
| ~ sP302(U_1447,U_1448,U_1450,U_1452) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_18,plain,
( U_1450 = apply(U_1447,U_1452)
| ~ sP302(U_1447,U_1448,U_1450,U_1452) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_19,plain,
( in(sK284(U_1448,U_1447),relation_rng(U_1448))
| ~ sP304(U_1447,U_1448) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_20,plain,
( sK285(U_1448,U_1447) = apply(U_1447,sK284(U_1448,U_1447))
| ~ sP304(U_1447,U_1448) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_21,plain,
( sK284(U_1448,U_1447) != apply(U_1448,sK285(U_1448,U_1447))
| ~ in(sK285(U_1448,U_1447),relation_dom(U_1448))
| ~ sP304(U_1447,U_1448) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_22,plain,
( in(sK287(U_1448,U_1447),relation_dom(U_1448))
| ~ sP305(U_1447,U_1448) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_23,plain,
( sK286(U_1448,U_1447) = apply(U_1448,sK287(U_1448,U_1447))
| ~ sP305(U_1447,U_1448) ),
inference(clausify,[status(thm)],[f_349_8]) ).
cnf(f_349_24,plain,
( sK287(U_1448,U_1447) != apply(U_1447,sK286(U_1448,U_1447))
| ~ in(sK286(U_1448,U_1447),relation_rng(U_1448))
| ~ sP305(U_1447,U_1448) ),
inference(clausify,[status(thm)],[f_349_8]) ).
fof(f_350_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_350_2,plain,
! [U_1459,U_1458,U_1457] :
( ~ in(U_1458,U_1457)
| ~ in(U_1458,subset_complement(U_1459,U_1457))
| ~ element(U_1457,powerset(U_1459)) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1459,U_1457,U_1458] :
( ~ in(U_1458,U_1457)
| ~ in(U_1458,subset_complement(U_1459,U_1457))
| ~ element(U_1457,powerset(U_1459)) ),
inference(definitional_conversion,[status(esa)],[f_350_2]) ).
cnf(f_350_4,plain,
( ~ in(U_1458,U_1457)
| ~ in(U_1458,subset_complement(U_1459,U_1457))
| ~ element(U_1457,powerset(U_1459)) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_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_351_2,plain,
! [U_1462] :
( ! [U_1461] :
( ! [U_1460] :
( well_ordering(U_1461)
| ~ relation_isomorphism(U_1462,U_1461,U_1460)
| ~ well_ordering(U_1462)
| ~ function(U_1460)
| ~ relation(U_1460) )
| ~ relation(U_1461) )
| ~ relation(U_1462) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
! [U_1460,U_1462,U_1461] :
( well_ordering(U_1461)
| ~ relation_isomorphism(U_1462,U_1461,U_1460)
| ~ well_ordering(U_1462)
| ~ function(U_1460)
| ~ relation(U_1460)
| ~ relation(U_1461)
| ~ relation(U_1462) ),
inference(definitional_conversion,[status(esa)],[f_351_2]) ).
cnf(f_351_4,plain,
( well_ordering(U_1461)
| ~ relation_isomorphism(U_1462,U_1461,U_1460)
| ~ well_ordering(U_1462)
| ~ function(U_1460)
| ~ relation(U_1460)
| ~ relation(U_1461)
| ~ relation(U_1462) ),
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_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_352_2,plain,
! [U_1463] :
( ( relation_dom(U_1463) = relation_rng(function_inverse(U_1463))
& relation_rng(U_1463) = relation_dom(function_inverse(U_1463)) )
| ~ one_to_one(U_1463)
| ~ function(U_1463)
| ~ relation(U_1463) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
( ! [U_1463] :
( relation_dom(U_1463) = relation_rng(function_inverse(U_1463))
| ~ sP307(U_1463) )
& ! [U_1463] :
( relation_rng(U_1463) = relation_dom(function_inverse(U_1463))
| ~ sP307(U_1463) )
& ! [U_1463] :
( sP307(U_1463)
| ~ one_to_one(U_1463)
| ~ function(U_1463)
| ~ relation(U_1463) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP307])],[f_352_2]) ).
cnf(f_352_4,plain,
( sP307(U_1463)
| ~ one_to_one(U_1463)
| ~ function(U_1463)
| ~ relation(U_1463) ),
inference(clausify,[status(thm)],[f_352_3]) ).
cnf(f_352_5,plain,
( relation_rng(U_1463) = relation_dom(function_inverse(U_1463))
| ~ sP307(U_1463) ),
inference(clausify,[status(thm)],[f_352_3]) ).
cnf(f_352_6,plain,
( relation_dom(U_1463) = relation_rng(function_inverse(U_1463))
| ~ sP307(U_1463) ),
inference(clausify,[status(thm)],[f_352_3]) ).
fof(f_353_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_353_2,plain,
! [U_1466] :
( U_1466 = empty_set
| ? [U_1465,U_1464] : in(ordered_pair(U_1465,U_1464),U_1466)
| ~ relation(U_1466) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
! [U_1466] :
( U_1466 = empty_set
| ? [U_1464] : in(ordered_pair(sK288(U_1466),U_1464),U_1466)
| ~ relation(U_1466) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_1465,sK288(U_1466))],[f_353_2]) ).
fof(f_353_4,plain,
! [U_1466] :
( U_1466 = empty_set
| in(ordered_pair(sK288(U_1466),sK289(U_1466)),U_1466)
| ~ relation(U_1466) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_1464,sK289(U_1466))],[f_353_3]) ).
fof(f_353_5,plain,
! [U_1466] :
( U_1466 = empty_set
| in(ordered_pair(sK288(U_1466),sK289(U_1466)),U_1466)
| ~ relation(U_1466) ),
inference(definitional_conversion,[status(esa)],[f_353_4]) ).
cnf(f_353_6,plain,
( U_1466 = empty_set
| in(ordered_pair(sK288(U_1466),sK289(U_1466)),U_1466)
| ~ relation(U_1466) ),
inference(clausify,[status(thm)],[f_353_5]) ).
fof(f_354_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_354_2,plain,
! [U_1468,U_1467] :
( ( U_1468 = apply(relation_composition(function_inverse(U_1467),U_1467),U_1468)
& U_1468 = apply(U_1467,apply(function_inverse(U_1467),U_1468)) )
| ~ in(U_1468,relation_rng(U_1467))
| ~ one_to_one(U_1467)
| ~ function(U_1467)
| ~ relation(U_1467) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
( ! [U_1467,U_1468] :
( U_1468 = apply(relation_composition(function_inverse(U_1467),U_1467),U_1468)
| ~ sP308(U_1467,U_1468) )
& ! [U_1467,U_1468] :
( U_1468 = apply(U_1467,apply(function_inverse(U_1467),U_1468))
| ~ sP308(U_1467,U_1468) )
& ! [U_1467,U_1468] :
( sP308(U_1467,U_1468)
| ~ in(U_1468,relation_rng(U_1467))
| ~ one_to_one(U_1467)
| ~ function(U_1467)
| ~ relation(U_1467) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308])],[f_354_2]) ).
cnf(f_354_4,plain,
( sP308(U_1467,U_1468)
| ~ in(U_1468,relation_rng(U_1467))
| ~ one_to_one(U_1467)
| ~ function(U_1467)
| ~ relation(U_1467) ),
inference(clausify,[status(thm)],[f_354_3]) ).
cnf(f_354_5,plain,
( U_1468 = apply(U_1467,apply(function_inverse(U_1467),U_1468))
| ~ sP308(U_1467,U_1468) ),
inference(clausify,[status(thm)],[f_354_3]) ).
cnf(f_354_6,plain,
( U_1468 = apply(relation_composition(function_inverse(U_1467),U_1467),U_1468)
| ~ sP308(U_1467,U_1468) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_355_2,plain,
! [U_1471,U_1470,U_1469] :
( ~ empty(U_1469)
| ~ element(U_1470,powerset(U_1469))
| ~ in(U_1471,U_1470) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
! [U_1471,U_1470] :
( ! [U_1469] :
( ~ empty(U_1469)
| ~ element(U_1470,powerset(U_1469)) )
| ~ in(U_1471,U_1470) ),
inference(miniscope,[status(thm)],[f_355_2]) ).
fof(f_355_4,plain,
! [U_1469,U_1471,U_1470] :
( ~ empty(U_1469)
| ~ element(U_1470,powerset(U_1469))
| ~ in(U_1471,U_1470) ),
inference(definitional_conversion,[status(esa)],[f_355_3]) ).
cnf(f_355_5,plain,
( ~ empty(U_1469)
| ~ element(U_1470,powerset(U_1469))
| ~ in(U_1471,U_1470) ),
inference(clausify,[status(thm)],[f_355_4]) ).
fof(f_356_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_356_2,plain,
! [U_1472] :
( ( ( well_founded_relation(U_1472)
| ~ is_well_founded_in(U_1472,relation_field(U_1472)) )
& ( is_well_founded_in(U_1472,relation_field(U_1472))
| ~ well_founded_relation(U_1472) ) )
| ~ relation(U_1472) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
( ! [U_1472] :
( well_founded_relation(U_1472)
| ~ is_well_founded_in(U_1472,relation_field(U_1472))
| ~ sP309(U_1472) )
& ! [U_1472] :
( is_well_founded_in(U_1472,relation_field(U_1472))
| ~ well_founded_relation(U_1472)
| ~ sP309(U_1472) )
& ! [U_1472] :
( sP309(U_1472)
| ~ relation(U_1472) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309])],[f_356_2]) ).
cnf(f_356_4,plain,
( sP309(U_1472)
| ~ relation(U_1472) ),
inference(clausify,[status(thm)],[f_356_3]) ).
cnf(f_356_5,plain,
( is_well_founded_in(U_1472,relation_field(U_1472))
| ~ well_founded_relation(U_1472)
| ~ sP309(U_1472) ),
inference(clausify,[status(thm)],[f_356_3]) ).
cnf(f_356_6,plain,
( well_founded_relation(U_1472)
| ~ is_well_founded_in(U_1472,relation_field(U_1472))
| ~ sP309(U_1472) ),
inference(clausify,[status(thm)],[f_356_3]) ).
fof(f_357_1,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t5_wellord2]) ).
fof(f_357_2,plain,
! [U_1473] : antisymmetric(inclusion_relation(U_1473)),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
! [U_1473] : antisymmetric(inclusion_relation(U_1473)),
inference(definitional_conversion,[status(esa)],[f_357_2]) ).
cnf(f_357_4,plain,
antisymmetric(inclusion_relation(U_1473)),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
fof(f_358_2,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(definitional_conversion,[status(esa)],[f_358_1]) ).
cnf(f_358_3,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_358_2]) ).
cnf(f_358_4,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_359_2,plain,
! [U_1475,U_1474] :
( ~ proper_subset(U_1474,U_1475)
| ~ subset(U_1475,U_1474) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_1474,U_1475] :
( ~ proper_subset(U_1474,U_1475)
| ~ subset(U_1475,U_1474) ),
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
( ~ proper_subset(U_1474,U_1475)
| ~ subset(U_1475,U_1474) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_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_360_2,plain,
! [U_1476] :
( one_to_one(function_inverse(U_1476))
| ~ one_to_one(U_1476)
| ~ function(U_1476)
| ~ relation(U_1476) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_1476] :
( one_to_one(function_inverse(U_1476))
| ~ one_to_one(U_1476)
| ~ function(U_1476)
| ~ relation(U_1476) ),
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
( one_to_one(function_inverse(U_1476))
| ~ one_to_one(U_1476)
| ~ function(U_1476)
| ~ relation(U_1476) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_361_2,plain,
! [U_1479,U_1478,U_1477] :
( disjoint(U_1479,U_1477)
| ~ disjoint(U_1478,U_1477)
| ~ subset(U_1479,U_1478) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_1479,U_1477,U_1478] :
( disjoint(U_1479,U_1477)
| ~ disjoint(U_1478,U_1477)
| ~ subset(U_1479,U_1478) ),
inference(definitional_conversion,[status(esa)],[f_361_2]) ).
cnf(f_361_4,plain,
( disjoint(U_1479,U_1477)
| ~ disjoint(U_1478,U_1477)
| ~ subset(U_1479,U_1478) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_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_362_2,plain,
! [U_1480] :
( U_1480 = empty_set
| ( relation_rng(U_1480) != empty_set
& relation_dom(U_1480) != empty_set )
| ~ relation(U_1480) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
( ! [U_1480] :
( relation_rng(U_1480) != empty_set
| ~ sP310(U_1480) )
& ! [U_1480] :
( relation_dom(U_1480) != empty_set
| ~ sP310(U_1480) )
& ! [U_1480] :
( U_1480 = empty_set
| sP310(U_1480)
| ~ relation(U_1480) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP310])],[f_362_2]) ).
cnf(f_362_4,plain,
( U_1480 = empty_set
| sP310(U_1480)
| ~ relation(U_1480) ),
inference(clausify,[status(thm)],[f_362_3]) ).
cnf(f_362_5,plain,
( relation_dom(U_1480) != empty_set
| ~ sP310(U_1480) ),
inference(clausify,[status(thm)],[f_362_3]) ).
cnf(f_362_6,plain,
( relation_rng(U_1480) != empty_set
| ~ sP310(U_1480) ),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_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_363_2,plain,
! [U_1481] :
( ( ( relation_dom(U_1481) = empty_set
| relation_rng(U_1481) != empty_set )
& ( relation_rng(U_1481) = empty_set
| relation_dom(U_1481) != empty_set ) )
| ~ relation(U_1481) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
( ! [U_1481] :
( relation_dom(U_1481) = empty_set
| relation_rng(U_1481) != empty_set
| ~ sP311(U_1481) )
& ! [U_1481] :
( relation_rng(U_1481) = empty_set
| relation_dom(U_1481) != empty_set
| ~ sP311(U_1481) )
& ! [U_1481] :
( sP311(U_1481)
| ~ relation(U_1481) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP311])],[f_363_2]) ).
cnf(f_363_4,plain,
( sP311(U_1481)
| ~ relation(U_1481) ),
inference(clausify,[status(thm)],[f_363_3]) ).
cnf(f_363_5,plain,
( relation_rng(U_1481) = empty_set
| relation_dom(U_1481) != empty_set
| ~ sP311(U_1481) ),
inference(clausify,[status(thm)],[f_363_3]) ).
cnf(f_363_6,plain,
( relation_dom(U_1481) = empty_set
| relation_rng(U_1481) != empty_set
| ~ sP311(U_1481) ),
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_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_364_2,plain,
! [U_1483,U_1482] :
( ( set_difference(U_1483,singleton(U_1482)) = U_1483
| in(U_1482,U_1483) )
& ( ~ in(U_1482,U_1483)
| set_difference(U_1483,singleton(U_1482)) != U_1483 ) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
( ! [U_1487,U_1485] :
( set_difference(U_1487,singleton(U_1485)) = U_1487
| in(U_1485,U_1487) )
& ! [U_1486,U_1484] :
( ~ in(U_1484,U_1486)
| set_difference(U_1486,singleton(U_1484)) != U_1486 ) ),
inference(miniscope,[status(thm)],[f_364_2]) ).
fof(f_364_4,plain,
( ! [U_1485,U_1487] :
( set_difference(U_1487,singleton(U_1485)) = U_1487
| in(U_1485,U_1487) )
& ! [U_1486,U_1484] :
( ~ in(U_1484,U_1486)
| set_difference(U_1486,singleton(U_1484)) != U_1486 ) ),
inference(definitional_conversion,[status(esa)],[f_364_3]) ).
cnf(f_364_5,plain,
( ~ in(U_1484,U_1486)
| set_difference(U_1486,singleton(U_1484)) != U_1486 ),
inference(clausify,[status(thm)],[f_364_4]) ).
cnf(f_364_6,plain,
( set_difference(U_1487,singleton(U_1485)) = U_1487
| in(U_1485,U_1487) ),
inference(clausify,[status(thm)],[f_364_4]) ).
fof(f_365_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_365_2,plain,
! [U_1492,U_1491] :
( ! [U_1490] :
( ( ( U_1491 = relation_dom_restriction(U_1490,U_1492)
| ? [U_1489] :
( apply(U_1491,U_1489) != apply(U_1490,U_1489)
& in(U_1489,relation_dom(U_1491)) )
| relation_dom(U_1491) != set_intersection2(relation_dom(U_1490),U_1492) )
& ( ( ! [U_1488] :
( apply(U_1491,U_1488) = apply(U_1490,U_1488)
| ~ in(U_1488,relation_dom(U_1491)) )
& relation_dom(U_1491) = set_intersection2(relation_dom(U_1490),U_1492) )
| U_1491 != relation_dom_restriction(U_1490,U_1492) ) )
| ~ function(U_1490)
| ~ relation(U_1490) )
| ~ function(U_1491)
| ~ relation(U_1491) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
! [U_1492,U_1491] :
( ! [U_1490] :
( ( ( U_1491 = relation_dom_restriction(U_1490,U_1492)
| ( apply(U_1491,sK290(U_1492,U_1491,U_1490)) != apply(U_1490,sK290(U_1492,U_1491,U_1490))
& in(sK290(U_1492,U_1491,U_1490),relation_dom(U_1491)) )
| relation_dom(U_1491) != set_intersection2(relation_dom(U_1490),U_1492) )
& ( ( ! [U_1488] :
( apply(U_1491,U_1488) = apply(U_1490,U_1488)
| ~ in(U_1488,relation_dom(U_1491)) )
& relation_dom(U_1491) = set_intersection2(relation_dom(U_1490),U_1492) )
| U_1491 != relation_dom_restriction(U_1490,U_1492) ) )
| ~ function(U_1490)
| ~ relation(U_1490) )
| ~ function(U_1491)
| ~ relation(U_1491) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_1489,sK290(U_1492,U_1491,U_1490))],[f_365_2]) ).
fof(f_365_4,plain,
( ! [U_1490,U_1491,U_1492] :
( apply(U_1491,sK290(U_1492,U_1491,U_1490)) != apply(U_1490,sK290(U_1492,U_1491,U_1490))
| ~ sP313(U_1490,U_1491,U_1492) )
& ! [U_1490,U_1491,U_1492] :
( in(sK290(U_1492,U_1491,U_1490),relation_dom(U_1491))
| ~ sP313(U_1490,U_1491,U_1492) )
& ! [U_1490,U_1491,U_1492,U_1488] :
( apply(U_1491,U_1488) = apply(U_1490,U_1488)
| ~ in(U_1488,relation_dom(U_1491))
| ~ sP312(U_1490,U_1491,U_1492,U_1488) )
& ! [U_1490,U_1491,U_1492,U_1488] :
( relation_dom(U_1491) = set_intersection2(relation_dom(U_1490),U_1492)
| ~ sP312(U_1490,U_1491,U_1492,U_1488) )
& ! [U_1490,U_1491,U_1492,U_1488] :
( U_1491 = relation_dom_restriction(U_1490,U_1492)
| sP313(U_1490,U_1491,U_1492)
| relation_dom(U_1491) != set_intersection2(relation_dom(U_1490),U_1492)
| ~ sP314(U_1490,U_1491,U_1492,U_1488) )
& ! [U_1490,U_1491,U_1492,U_1488] :
( sP312(U_1490,U_1491,U_1492,U_1488)
| U_1491 != relation_dom_restriction(U_1490,U_1492)
| ~ sP314(U_1490,U_1491,U_1492,U_1488) )
& ! [U_1490,U_1491,U_1492,U_1488] :
( sP314(U_1490,U_1491,U_1492,U_1488)
| ~ function(U_1490)
| ~ relation(U_1490)
| ~ function(U_1491)
| ~ relation(U_1491) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312,sP313,sP314])],[f_365_3]) ).
cnf(f_365_5,plain,
( sP314(U_1490,U_1491,U_1492,U_1488)
| ~ function(U_1490)
| ~ relation(U_1490)
| ~ function(U_1491)
| ~ relation(U_1491) ),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_6,plain,
( sP312(U_1490,U_1491,U_1492,U_1488)
| U_1491 != relation_dom_restriction(U_1490,U_1492)
| ~ sP314(U_1490,U_1491,U_1492,U_1488) ),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_7,plain,
( U_1491 = relation_dom_restriction(U_1490,U_1492)
| sP313(U_1490,U_1491,U_1492)
| relation_dom(U_1491) != set_intersection2(relation_dom(U_1490),U_1492)
| ~ sP314(U_1490,U_1491,U_1492,U_1488) ),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_8,plain,
( relation_dom(U_1491) = set_intersection2(relation_dom(U_1490),U_1492)
| ~ sP312(U_1490,U_1491,U_1492,U_1488) ),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_9,plain,
( apply(U_1491,U_1488) = apply(U_1490,U_1488)
| ~ in(U_1488,relation_dom(U_1491))
| ~ sP312(U_1490,U_1491,U_1492,U_1488) ),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_10,plain,
( in(sK290(U_1492,U_1491,U_1490),relation_dom(U_1491))
| ~ sP313(U_1490,U_1491,U_1492) ),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_11,plain,
( apply(U_1491,sK290(U_1492,U_1491,U_1490)) != apply(U_1490,sK290(U_1492,U_1491,U_1490))
| ~ sP313(U_1490,U_1491,U_1492) ),
inference(clausify,[status(thm)],[f_365_4]) ).
fof(f_366_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_366_2,plain,
! [U_1493] : unordered_pair(U_1493,U_1493) = singleton(U_1493),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
! [U_1493] : unordered_pair(U_1493,U_1493) = singleton(U_1493),
inference(definitional_conversion,[status(esa)],[f_366_2]) ).
cnf(f_366_4,plain,
unordered_pair(U_1493,U_1493) = singleton(U_1493),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_367_2,plain,
! [U_1494] :
( U_1494 = empty_set
| ~ empty(U_1494) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_1494] :
( U_1494 = empty_set
| ~ empty(U_1494) ),
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
( U_1494 = empty_set
| ~ empty(U_1494) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [A,B,C,D] :
( in(apply(D,C),relation_rng(D))
| B = empty_set
| ~ in(C,A)
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(fof_nnf,[status(thm)],[t6_funct_2]) ).
fof(f_368_2,plain,
! [U_1498,U_1497,U_1496,U_1495] :
( in(apply(U_1495,U_1496),relation_rng(U_1495))
| U_1497 = empty_set
| ~ in(U_1496,U_1498)
| ~ relation_of2_as_subset(U_1495,U_1498,U_1497)
| ~ quasi_total(U_1495,U_1498,U_1497)
| ~ function(U_1495) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_1495,U_1498,U_1497,U_1496] :
( in(apply(U_1495,U_1496),relation_rng(U_1495))
| U_1497 = empty_set
| ~ in(U_1496,U_1498)
| ~ relation_of2_as_subset(U_1495,U_1498,U_1497)
| ~ quasi_total(U_1495,U_1498,U_1497)
| ~ function(U_1495) ),
inference(definitional_conversion,[status(esa)],[f_368_2]) ).
cnf(f_368_4,plain,
( in(apply(U_1495,U_1496),relation_rng(U_1495))
| U_1497 = empty_set
| ~ in(U_1496,U_1498)
| ~ relation_of2_as_subset(U_1495,U_1498,U_1497)
| ~ quasi_total(U_1495,U_1498,U_1497)
| ~ function(U_1495) ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_1,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t6_wellord2]) ).
fof(f_369_2,plain,
! [U_1499] :
( well_founded_relation(inclusion_relation(U_1499))
| ~ ordinal(U_1499) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
! [U_1499] :
( well_founded_relation(inclusion_relation(U_1499))
| ~ ordinal(U_1499) ),
inference(definitional_conversion,[status(esa)],[f_369_2]) ).
cnf(f_369_4,plain,
( well_founded_relation(inclusion_relation(U_1499))
| ~ ordinal(U_1499) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_370_2,plain,
! [U_1501,U_1500] :
( U_1501 = U_1500
| ~ subset(singleton(U_1501),singleton(U_1500)) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
! [U_1501,U_1500] :
( U_1501 = U_1500
| ~ subset(singleton(U_1501),singleton(U_1500)) ),
inference(definitional_conversion,[status(esa)],[f_370_2]) ).
cnf(f_370_4,plain,
( U_1501 = U_1500
| ~ subset(singleton(U_1501),singleton(U_1500)) ),
inference(clausify,[status(thm)],[f_370_3]) ).
fof(f_371_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_371_2,plain,
! [U_1504,U_1503,U_1502] :
( apply(relation_dom_restriction(U_1502,U_1504),U_1503) = apply(U_1502,U_1503)
| ~ in(U_1503,relation_dom(relation_dom_restriction(U_1502,U_1504)))
| ~ function(U_1502)
| ~ relation(U_1502) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
! [U_1504,U_1502,U_1503] :
( apply(relation_dom_restriction(U_1502,U_1504),U_1503) = apply(U_1502,U_1503)
| ~ in(U_1503,relation_dom(relation_dom_restriction(U_1502,U_1504)))
| ~ function(U_1502)
| ~ relation(U_1502) ),
inference(definitional_conversion,[status(esa)],[f_371_2]) ).
cnf(f_371_4,plain,
( apply(relation_dom_restriction(U_1502,U_1504),U_1503) = apply(U_1502,U_1503)
| ~ in(U_1503,relation_dom(relation_dom_restriction(U_1502,U_1504)))
| ~ function(U_1502)
| ~ relation(U_1502) ),
inference(clausify,[status(thm)],[f_371_3]) ).
fof(f_372_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_372_2,plain,
! [U_1505] :
( relation_rng(identity_relation(U_1505)) = U_1505
& relation_dom(identity_relation(U_1505)) = U_1505 ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
( ! [U_1507] : relation_rng(identity_relation(U_1507)) = U_1507
& ! [U_1506] : relation_dom(identity_relation(U_1506)) = U_1506 ),
inference(miniscope,[status(thm)],[f_372_2]) ).
fof(f_372_4,plain,
( ! [U_1507] : relation_rng(identity_relation(U_1507)) = U_1507
& ! [U_1506] : relation_dom(identity_relation(U_1506)) = U_1506 ),
inference(definitional_conversion,[status(esa)],[f_372_3]) ).
cnf(f_372_5,plain,
relation_dom(identity_relation(U_1506)) = U_1506,
inference(clausify,[status(thm)],[f_372_4]) ).
cnf(f_372_6,plain,
relation_rng(identity_relation(U_1507)) = U_1507,
inference(clausify,[status(thm)],[f_372_4]) ).
fof(f_373_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_373_2,plain,
! [U_1510,U_1509,U_1508] :
( apply(relation_dom_restriction(U_1508,U_1510),U_1509) = apply(U_1508,U_1509)
| ~ in(U_1509,U_1510)
| ~ function(U_1508)
| ~ relation(U_1508) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
! [U_1508,U_1509,U_1510] :
( apply(relation_dom_restriction(U_1508,U_1510),U_1509) = apply(U_1508,U_1509)
| ~ in(U_1509,U_1510)
| ~ function(U_1508)
| ~ relation(U_1508) ),
inference(definitional_conversion,[status(esa)],[f_373_2]) ).
cnf(f_373_4,plain,
( apply(relation_dom_restriction(U_1508,U_1510),U_1509) = apply(U_1508,U_1509)
| ~ in(U_1509,U_1510)
| ~ function(U_1508)
| ~ relation(U_1508) ),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_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_374_2,plain,
! [U_1514,U_1513,U_1512,U_1511] :
( ( ( in(ordered_pair(U_1514,U_1513),relation_composition(identity_relation(U_1512),U_1511))
| ~ in(ordered_pair(U_1514,U_1513),U_1511)
| ~ in(U_1514,U_1512) )
& ( ( in(ordered_pair(U_1514,U_1513),U_1511)
& in(U_1514,U_1512) )
| ~ in(ordered_pair(U_1514,U_1513),relation_composition(identity_relation(U_1512),U_1511)) ) )
| ~ relation(U_1511) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
( ! [U_1511,U_1512,U_1513,U_1514] :
( in(ordered_pair(U_1514,U_1513),U_1511)
| ~ sP315(U_1511,U_1512,U_1513,U_1514) )
& ! [U_1511,U_1512,U_1513,U_1514] :
( in(U_1514,U_1512)
| ~ sP315(U_1511,U_1512,U_1513,U_1514) )
& ! [U_1511,U_1512,U_1513,U_1514] :
( in(ordered_pair(U_1514,U_1513),relation_composition(identity_relation(U_1512),U_1511))
| ~ in(ordered_pair(U_1514,U_1513),U_1511)
| ~ in(U_1514,U_1512)
| ~ sP316(U_1511,U_1512,U_1513,U_1514) )
& ! [U_1511,U_1512,U_1513,U_1514] :
( sP315(U_1511,U_1512,U_1513,U_1514)
| ~ in(ordered_pair(U_1514,U_1513),relation_composition(identity_relation(U_1512),U_1511))
| ~ sP316(U_1511,U_1512,U_1513,U_1514) )
& ! [U_1511,U_1512,U_1513,U_1514] :
( sP316(U_1511,U_1512,U_1513,U_1514)
| ~ relation(U_1511) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP315,sP316])],[f_374_2]) ).
cnf(f_374_4,plain,
( sP316(U_1511,U_1512,U_1513,U_1514)
| ~ relation(U_1511) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_5,plain,
( sP315(U_1511,U_1512,U_1513,U_1514)
| ~ in(ordered_pair(U_1514,U_1513),relation_composition(identity_relation(U_1512),U_1511))
| ~ sP316(U_1511,U_1512,U_1513,U_1514) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_6,plain,
( in(ordered_pair(U_1514,U_1513),relation_composition(identity_relation(U_1512),U_1511))
| ~ in(ordered_pair(U_1514,U_1513),U_1511)
| ~ in(U_1514,U_1512)
| ~ sP316(U_1511,U_1512,U_1513,U_1514) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_7,plain,
( in(U_1514,U_1512)
| ~ sP315(U_1511,U_1512,U_1513,U_1514) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_8,plain,
( in(ordered_pair(U_1514,U_1513),U_1511)
| ~ sP315(U_1511,U_1512,U_1513,U_1514) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_375_2,plain,
! [U_1516,U_1515] :
( ~ empty(U_1515)
| ~ in(U_1516,U_1515) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
! [U_1515,U_1516] :
( ~ empty(U_1515)
| ~ in(U_1516,U_1515) ),
inference(definitional_conversion,[status(esa)],[f_375_2]) ).
cnf(f_375_4,plain,
( ~ empty(U_1515)
| ~ in(U_1516,U_1515) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_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_376_2,plain,
! [U_1518,U_1517] :
( pair_second(ordered_pair(U_1518,U_1517)) = U_1517
& pair_first(ordered_pair(U_1518,U_1517)) = U_1518 ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
( ! [U_1522,U_1520] : pair_second(ordered_pair(U_1522,U_1520)) = U_1520
& ! [U_1521,U_1519] : pair_first(ordered_pair(U_1521,U_1519)) = U_1521 ),
inference(miniscope,[status(thm)],[f_376_2]) ).
fof(f_376_4,plain,
( ! [U_1520,U_1522] : pair_second(ordered_pair(U_1522,U_1520)) = U_1520
& ! [U_1521,U_1519] : pair_first(ordered_pair(U_1521,U_1519)) = U_1521 ),
inference(definitional_conversion,[status(esa)],[f_376_3]) ).
cnf(f_376_5,plain,
pair_first(ordered_pair(U_1521,U_1519)) = U_1521,
inference(clausify,[status(thm)],[f_376_4]) ).
cnf(f_376_6,plain,
pair_second(ordered_pair(U_1522,U_1520)) = U_1520,
inference(clausify,[status(thm)],[f_376_4]) ).
fof(f_377_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_377_2,plain,
! [U_1526,U_1525] :
( ? [U_1524] :
( ! [U_1523] :
( ~ in(U_1523,U_1524)
| ~ in(U_1523,U_1525) )
& in(U_1524,U_1525) )
| ~ in(U_1526,U_1525) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
! [U_1526,U_1525] :
( ( ! [U_1523] :
( ~ in(U_1523,sK291(U_1526,U_1525))
| ~ in(U_1523,U_1525) )
& in(sK291(U_1526,U_1525),U_1525) )
| ~ in(U_1526,U_1525) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_1524,sK291(U_1526,U_1525))],[f_377_2]) ).
fof(f_377_4,plain,
( ! [U_1523,U_1525,U_1526] :
( ~ in(U_1523,sK291(U_1526,U_1525))
| ~ in(U_1523,U_1525)
| ~ sP317(U_1523,U_1525,U_1526) )
& ! [U_1523,U_1525,U_1526] :
( in(sK291(U_1526,U_1525),U_1525)
| ~ sP317(U_1523,U_1525,U_1526) )
& ! [U_1523,U_1525,U_1526] :
( sP317(U_1523,U_1525,U_1526)
| ~ in(U_1526,U_1525) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP317])],[f_377_3]) ).
cnf(f_377_5,plain,
( sP317(U_1523,U_1525,U_1526)
| ~ in(U_1526,U_1525) ),
inference(clausify,[status(thm)],[f_377_4]) ).
cnf(f_377_6,plain,
( in(sK291(U_1526,U_1525),U_1525)
| ~ sP317(U_1523,U_1525,U_1526) ),
inference(clausify,[status(thm)],[f_377_4]) ).
cnf(f_377_7,plain,
( ~ in(U_1523,sK291(U_1526,U_1525))
| ~ in(U_1523,U_1525)
| ~ sP317(U_1523,U_1525,U_1526) ),
inference(clausify,[status(thm)],[f_377_4]) ).
fof(f_378_1,plain,
! [A] :
( well_ordering(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t7_wellord2]) ).
fof(f_378_2,plain,
! [U_1527] :
( well_ordering(inclusion_relation(U_1527))
| ~ ordinal(U_1527) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_1527] :
( well_ordering(inclusion_relation(U_1527))
| ~ ordinal(U_1527) ),
inference(definitional_conversion,[status(esa)],[f_378_2]) ).
cnf(f_378_4,plain,
( well_ordering(inclusion_relation(U_1527))
| ~ ordinal(U_1527) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_379_2,plain,
! [U_1529,U_1528] : subset(U_1529,set_union2(U_1529,U_1528)),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1528,U_1529] : subset(U_1529,set_union2(U_1529,U_1528)),
inference(definitional_conversion,[status(esa)],[f_379_2]) ).
cnf(f_379_4,plain,
subset(U_1529,set_union2(U_1529,U_1528)),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_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_380_2,plain,
! [U_1531,U_1530] :
( ( disjoint(U_1531,U_1530)
| set_difference(U_1531,U_1530) != U_1531 )
& ( set_difference(U_1531,U_1530) = U_1531
| ~ disjoint(U_1531,U_1530) ) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
( ! [U_1535,U_1533] :
( disjoint(U_1535,U_1533)
| set_difference(U_1535,U_1533) != U_1535 )
& ! [U_1534,U_1532] :
( set_difference(U_1534,U_1532) = U_1534
| ~ disjoint(U_1534,U_1532) ) ),
inference(miniscope,[status(thm)],[f_380_2]) ).
fof(f_380_4,plain,
( ! [U_1535,U_1533] :
( disjoint(U_1535,U_1533)
| set_difference(U_1535,U_1533) != U_1535 )
& ! [U_1534,U_1532] :
( set_difference(U_1534,U_1532) = U_1534
| ~ disjoint(U_1534,U_1532) ) ),
inference(definitional_conversion,[status(esa)],[f_380_3]) ).
cnf(f_380_5,plain,
( set_difference(U_1534,U_1532) = U_1534
| ~ disjoint(U_1534,U_1532) ),
inference(clausify,[status(thm)],[f_380_4]) ).
cnf(f_380_6,plain,
( disjoint(U_1535,U_1533)
| set_difference(U_1535,U_1533) != U_1535 ),
inference(clausify,[status(thm)],[f_380_4]) ).
fof(f_381_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_381_2,plain,
! [U_1538,U_1537,U_1536] :
( ( ( in(U_1538,relation_dom(relation_dom_restriction(U_1536,U_1537)))
| ~ in(U_1538,relation_dom(U_1536))
| ~ in(U_1538,U_1537) )
& ( ( in(U_1538,relation_dom(U_1536))
& in(U_1538,U_1537) )
| ~ in(U_1538,relation_dom(relation_dom_restriction(U_1536,U_1537))) ) )
| ~ relation(U_1536) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
( ! [U_1536,U_1537,U_1538] :
( in(U_1538,relation_dom(U_1536))
| ~ sP318(U_1536,U_1537,U_1538) )
& ! [U_1536,U_1537,U_1538] :
( in(U_1538,U_1537)
| ~ sP318(U_1536,U_1537,U_1538) )
& ! [U_1536,U_1537,U_1538] :
( in(U_1538,relation_dom(relation_dom_restriction(U_1536,U_1537)))
| ~ in(U_1538,relation_dom(U_1536))
| ~ in(U_1538,U_1537)
| ~ sP319(U_1536,U_1537,U_1538) )
& ! [U_1536,U_1537,U_1538] :
( sP318(U_1536,U_1537,U_1538)
| ~ in(U_1538,relation_dom(relation_dom_restriction(U_1536,U_1537)))
| ~ sP319(U_1536,U_1537,U_1538) )
& ! [U_1536,U_1537,U_1538] :
( sP319(U_1536,U_1537,U_1538)
| ~ relation(U_1536) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP318,sP319])],[f_381_2]) ).
cnf(f_381_4,plain,
( sP319(U_1536,U_1537,U_1538)
| ~ relation(U_1536) ),
inference(clausify,[status(thm)],[f_381_3]) ).
cnf(f_381_5,plain,
( sP318(U_1536,U_1537,U_1538)
| ~ in(U_1538,relation_dom(relation_dom_restriction(U_1536,U_1537)))
| ~ sP319(U_1536,U_1537,U_1538) ),
inference(clausify,[status(thm)],[f_381_3]) ).
cnf(f_381_6,plain,
( in(U_1538,relation_dom(relation_dom_restriction(U_1536,U_1537)))
| ~ in(U_1538,relation_dom(U_1536))
| ~ in(U_1538,U_1537)
| ~ sP319(U_1536,U_1537,U_1538) ),
inference(clausify,[status(thm)],[f_381_3]) ).
cnf(f_381_7,plain,
( in(U_1538,U_1537)
| ~ sP318(U_1536,U_1537,U_1538) ),
inference(clausify,[status(thm)],[f_381_3]) ).
cnf(f_381_8,plain,
( in(U_1538,relation_dom(U_1536))
| ~ sP318(U_1536,U_1537,U_1538) ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_382_2,plain,
! [U_1540,U_1539] :
( subset(relation_dom_restriction(U_1539,U_1540),U_1539)
| ~ relation(U_1539) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_1539,U_1540] :
( subset(relation_dom_restriction(U_1539,U_1540),U_1539)
| ~ relation(U_1539) ),
inference(definitional_conversion,[status(esa)],[f_382_2]) ).
cnf(f_382_4,plain,
( subset(relation_dom_restriction(U_1539,U_1540),U_1539)
| ~ relation(U_1539) ),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_383_2,plain,
! [U_1542,U_1541] :
( ~ empty(U_1541)
| U_1542 = U_1541
| ~ empty(U_1542) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_1542] :
( ! [U_1541] :
( ~ empty(U_1541)
| U_1542 = U_1541 )
| ~ empty(U_1542) ),
inference(miniscope,[status(thm)],[f_383_2]) ).
fof(f_383_4,plain,
! [U_1541,U_1542] :
( ~ empty(U_1541)
| U_1542 = U_1541
| ~ empty(U_1542) ),
inference(definitional_conversion,[status(esa)],[f_383_3]) ).
cnf(f_383_5,plain,
( ~ empty(U_1541)
| U_1542 = U_1541
| ~ empty(U_1542) ),
inference(clausify,[status(thm)],[f_383_4]) ).
fof(f_384_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_384_2,plain,
! [U_1545,U_1544,U_1543] :
( ( ( in(ordered_pair(U_1545,U_1544),U_1543)
| U_1544 != apply(U_1543,U_1545)
| ~ in(U_1545,relation_dom(U_1543)) )
& ( ( U_1544 = apply(U_1543,U_1545)
& in(U_1545,relation_dom(U_1543)) )
| ~ in(ordered_pair(U_1545,U_1544),U_1543) ) )
| ~ function(U_1543)
| ~ relation(U_1543) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
( ! [U_1544,U_1543,U_1545] :
( U_1544 = apply(U_1543,U_1545)
| ~ sP320(U_1544,U_1543,U_1545) )
& ! [U_1544,U_1543,U_1545] :
( in(U_1545,relation_dom(U_1543))
| ~ sP320(U_1544,U_1543,U_1545) )
& ! [U_1544,U_1543,U_1545] :
( in(ordered_pair(U_1545,U_1544),U_1543)
| U_1544 != apply(U_1543,U_1545)
| ~ in(U_1545,relation_dom(U_1543))
| ~ sP321(U_1544,U_1543,U_1545) )
& ! [U_1544,U_1543,U_1545] :
( sP320(U_1544,U_1543,U_1545)
| ~ in(ordered_pair(U_1545,U_1544),U_1543)
| ~ sP321(U_1544,U_1543,U_1545) )
& ! [U_1544,U_1543,U_1545] :
( sP321(U_1544,U_1543,U_1545)
| ~ function(U_1543)
| ~ relation(U_1543) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP320,sP321])],[f_384_2]) ).
cnf(f_384_4,plain,
( sP321(U_1544,U_1543,U_1545)
| ~ function(U_1543)
| ~ relation(U_1543) ),
inference(clausify,[status(thm)],[f_384_3]) ).
cnf(f_384_5,plain,
( sP320(U_1544,U_1543,U_1545)
| ~ in(ordered_pair(U_1545,U_1544),U_1543)
| ~ sP321(U_1544,U_1543,U_1545) ),
inference(clausify,[status(thm)],[f_384_3]) ).
cnf(f_384_6,plain,
( in(ordered_pair(U_1545,U_1544),U_1543)
| U_1544 != apply(U_1543,U_1545)
| ~ in(U_1545,relation_dom(U_1543))
| ~ sP321(U_1544,U_1543,U_1545) ),
inference(clausify,[status(thm)],[f_384_3]) ).
cnf(f_384_7,plain,
( in(U_1545,relation_dom(U_1543))
| ~ sP320(U_1544,U_1543,U_1545) ),
inference(clausify,[status(thm)],[f_384_3]) ).
cnf(f_384_8,plain,
( U_1544 = apply(U_1543,U_1545)
| ~ sP320(U_1544,U_1543,U_1545) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_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_385_2,plain,
! [U_1546] :
( ( ( well_orders(U_1546,relation_field(U_1546))
| ~ well_ordering(U_1546) )
& ( well_ordering(U_1546)
| ~ well_orders(U_1546,relation_field(U_1546)) ) )
| ~ relation(U_1546) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
( ! [U_1546] :
( well_orders(U_1546,relation_field(U_1546))
| ~ well_ordering(U_1546)
| ~ sP322(U_1546) )
& ! [U_1546] :
( well_ordering(U_1546)
| ~ well_orders(U_1546,relation_field(U_1546))
| ~ sP322(U_1546) )
& ! [U_1546] :
( sP322(U_1546)
| ~ relation(U_1546) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP322])],[f_385_2]) ).
cnf(f_385_4,plain,
( sP322(U_1546)
| ~ relation(U_1546) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_5,plain,
( well_ordering(U_1546)
| ~ well_orders(U_1546,relation_field(U_1546))
| ~ sP322(U_1546) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_6,plain,
( well_orders(U_1546,relation_field(U_1546))
| ~ well_ordering(U_1546)
| ~ sP322(U_1546) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_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_386_2,plain,
! [U_1549,U_1548,U_1547] :
( subset(set_union2(U_1549,U_1547),U_1548)
| ~ subset(U_1547,U_1548)
| ~ subset(U_1549,U_1548) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
! [U_1547,U_1548,U_1549] :
( subset(set_union2(U_1549,U_1547),U_1548)
| ~ subset(U_1547,U_1548)
| ~ subset(U_1549,U_1548) ),
inference(definitional_conversion,[status(esa)],[f_386_2]) ).
cnf(f_386_4,plain,
( subset(set_union2(U_1549,U_1547),U_1548)
| ~ subset(U_1547,U_1548)
| ~ subset(U_1549,U_1548) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_387_2,plain,
! [U_1552,U_1551,U_1550] :
( U_1552 = U_1551
| singleton(U_1552) != unordered_pair(U_1551,U_1550) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
! [U_1552,U_1551] :
( ! [U_1550] : singleton(U_1552) != unordered_pair(U_1551,U_1550)
| U_1552 = U_1551 ),
inference(miniscope,[status(thm)],[f_387_2]) ).
fof(f_387_4,plain,
! [U_1551,U_1550,U_1552] :
( singleton(U_1552) != unordered_pair(U_1551,U_1550)
| U_1552 = U_1551 ),
inference(definitional_conversion,[status(esa)],[f_387_3]) ).
cnf(f_387_5,plain,
( singleton(U_1552) != unordered_pair(U_1551,U_1550)
| U_1552 = U_1551 ),
inference(clausify,[status(thm)],[f_387_4]) ).
fof(f_388_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_388_2,plain,
! [U_1554,U_1553] :
( relation_dom(relation_dom_restriction(U_1553,U_1554)) = set_intersection2(relation_dom(U_1553),U_1554)
| ~ relation(U_1553) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
! [U_1553,U_1554] :
( relation_dom(relation_dom_restriction(U_1553,U_1554)) = set_intersection2(relation_dom(U_1553),U_1554)
| ~ relation(U_1553) ),
inference(definitional_conversion,[status(esa)],[f_388_2]) ).
cnf(f_388_4,plain,
( relation_dom(relation_dom_restriction(U_1553,U_1554)) = set_intersection2(relation_dom(U_1553),U_1554)
| ~ relation(U_1553) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_389_2,plain,
! [U_1556,U_1555] :
( subset(U_1556,union(U_1555))
| ~ in(U_1556,U_1555) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
! [U_1555,U_1556] :
( subset(U_1556,union(U_1555))
| ~ in(U_1556,U_1555) ),
inference(definitional_conversion,[status(esa)],[f_389_2]) ).
cnf(f_389_4,plain,
( subset(U_1556,union(U_1555))
| ~ in(U_1556,U_1555) ),
inference(clausify,[status(thm)],[f_389_3]) ).
fof(f_390_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_390_2,plain,
! [U_1558,U_1557] :
( relation_dom_restriction(U_1557,U_1558) = relation_composition(identity_relation(U_1558),U_1557)
| ~ relation(U_1557) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
! [U_1557,U_1558] :
( relation_dom_restriction(U_1557,U_1558) = relation_composition(identity_relation(U_1558),U_1557)
| ~ relation(U_1557) ),
inference(definitional_conversion,[status(esa)],[f_390_2]) ).
cnf(f_390_4,plain,
( relation_dom_restriction(U_1557,U_1558) = relation_composition(identity_relation(U_1558),U_1557)
| ~ relation(U_1557) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_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_391_2,plain,
! [U_1560,U_1559] :
( subset(relation_rng(relation_dom_restriction(U_1559,U_1560)),relation_rng(U_1559))
| ~ relation(U_1559) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_1559,U_1560] :
( subset(relation_rng(relation_dom_restriction(U_1559,U_1560)),relation_rng(U_1559))
| ~ relation(U_1559) ),
inference(definitional_conversion,[status(esa)],[f_391_2]) ).
cnf(f_391_4,plain,
( subset(relation_rng(relation_dom_restriction(U_1559,U_1560)),relation_rng(U_1559))
| ~ relation(U_1559) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_392_2,plain,
! [U_1561] : union(powerset(U_1561)) = U_1561,
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
! [U_1561] : union(powerset(U_1561)) = U_1561,
inference(definitional_conversion,[status(esa)],[f_392_2]) ).
cnf(f_392_4,plain,
union(powerset(U_1561)) = U_1561,
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_1,plain,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,C)
& quasi_total(D,A,C)
& function(D) )
| ( A != empty_set
& B = empty_set )
| ~ subset(B,C)
| ~ relation_of2_as_subset(D,A,B)
| ~ quasi_total(D,A,B)
| ~ function(D) ),
inference(fof_nnf,[status(thm)],[t9_funct_2]) ).
fof(f_393_2,plain,
! [U_1565,U_1564,U_1563,U_1562] :
( ( relation_of2_as_subset(U_1562,U_1565,U_1563)
& quasi_total(U_1562,U_1565,U_1563)
& function(U_1562) )
| ( U_1565 != empty_set
& U_1564 = empty_set )
| ~ subset(U_1564,U_1563)
| ~ relation_of2_as_subset(U_1562,U_1565,U_1564)
| ~ quasi_total(U_1562,U_1565,U_1564)
| ~ function(U_1562) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
( ! [U_1563,U_1562,U_1565] :
( relation_of2_as_subset(U_1562,U_1565,U_1563)
| ~ sP324(U_1563,U_1562,U_1565) )
& ! [U_1563,U_1562,U_1565] :
( quasi_total(U_1562,U_1565,U_1563)
| ~ sP324(U_1563,U_1562,U_1565) )
& ! [U_1563,U_1562,U_1565] :
( function(U_1562)
| ~ sP324(U_1563,U_1562,U_1565) )
& ! [U_1564,U_1565] :
( U_1565 != empty_set
| ~ sP323(U_1564,U_1565) )
& ! [U_1564,U_1565] :
( U_1564 = empty_set
| ~ sP323(U_1564,U_1565) )
& ! [U_1563,U_1562,U_1564,U_1565] :
( sP324(U_1563,U_1562,U_1565)
| sP323(U_1564,U_1565)
| ~ subset(U_1564,U_1563)
| ~ relation_of2_as_subset(U_1562,U_1565,U_1564)
| ~ quasi_total(U_1562,U_1565,U_1564)
| ~ function(U_1562) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323,sP324])],[f_393_2]) ).
cnf(f_393_4,plain,
( sP324(U_1563,U_1562,U_1565)
| sP323(U_1564,U_1565)
| ~ subset(U_1564,U_1563)
| ~ relation_of2_as_subset(U_1562,U_1565,U_1564)
| ~ quasi_total(U_1562,U_1565,U_1564)
| ~ function(U_1562) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_5,plain,
( U_1564 = empty_set
| ~ sP323(U_1564,U_1565) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_6,plain,
( U_1565 != empty_set
| ~ sP323(U_1564,U_1565) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_7,plain,
( function(U_1562)
| ~ sP324(U_1563,U_1562,U_1565) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_8,plain,
( quasi_total(U_1562,U_1565,U_1563)
| ~ sP324(U_1563,U_1562,U_1565) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_9,plain,
( relation_of2_as_subset(U_1562,U_1565,U_1563)
| ~ sP324(U_1563,U_1562,U_1565) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_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_394_2,plain,
! [U_1573] :
? [U_1572] :
( ! [U_1571] :
( in(U_1571,U_1572)
| are_equipotent(U_1571,U_1572)
| ~ subset(U_1571,U_1572) )
& ! [U_1570] :
( ? [U_1569] :
( ! [U_1568] :
( in(U_1568,U_1569)
| ~ subset(U_1568,U_1570) )
& in(U_1569,U_1572) )
| ~ in(U_1570,U_1572) )
& ! [U_1567,U_1566] :
( in(U_1566,U_1572)
| ~ subset(U_1566,U_1567)
| ~ in(U_1567,U_1572) )
& in(U_1573,U_1572) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1573] :
( ! [U_1571] :
( in(U_1571,sK292(U_1573))
| are_equipotent(U_1571,sK292(U_1573))
| ~ subset(U_1571,sK292(U_1573)) )
& ! [U_1570] :
( ? [U_1569] :
( ! [U_1568] :
( in(U_1568,U_1569)
| ~ subset(U_1568,U_1570) )
& in(U_1569,sK292(U_1573)) )
| ~ in(U_1570,sK292(U_1573)) )
& ! [U_1567,U_1566] :
( in(U_1566,sK292(U_1573))
| ~ subset(U_1566,U_1567)
| ~ in(U_1567,sK292(U_1573)) )
& in(U_1573,sK292(U_1573)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_1572,sK292(U_1573))],[f_394_2]) ).
fof(f_394_4,plain,
! [U_1573] :
( ! [U_1571] :
( in(U_1571,sK292(U_1573))
| are_equipotent(U_1571,sK292(U_1573))
| ~ subset(U_1571,sK292(U_1573)) )
& ! [U_1570] :
( ( ! [U_1568] :
( in(U_1568,sK293(U_1573,U_1570))
| ~ subset(U_1568,U_1570) )
& in(sK293(U_1573,U_1570),sK292(U_1573)) )
| ~ in(U_1570,sK292(U_1573)) )
& ! [U_1567,U_1566] :
( in(U_1566,sK292(U_1573))
| ~ subset(U_1566,U_1567)
| ~ in(U_1567,sK292(U_1573)) )
& in(U_1573,sK292(U_1573)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_1569,sK293(U_1573,U_1570))],[f_394_3]) ).
fof(f_394_5,plain,
( ! [U_1570,U_1568,U_1573] :
( in(U_1568,sK293(U_1573,U_1570))
| ~ subset(U_1568,U_1570)
| ~ sP325(U_1570,U_1568,U_1573) )
& ! [U_1570,U_1568,U_1573] :
( in(sK293(U_1573,U_1570),sK292(U_1573))
| ~ sP325(U_1570,U_1568,U_1573) )
& ! [U_1571,U_1573] :
( in(U_1571,sK292(U_1573))
| are_equipotent(U_1571,sK292(U_1573))
| ~ subset(U_1571,sK292(U_1573)) )
& ! [U_1570,U_1568,U_1573] :
( sP325(U_1570,U_1568,U_1573)
| ~ in(U_1570,sK292(U_1573)) )
& ! [U_1566,U_1573,U_1567] :
( in(U_1566,sK292(U_1573))
| ~ subset(U_1566,U_1567)
| ~ in(U_1567,sK292(U_1573)) )
& ! [U_1573] : in(U_1573,sK292(U_1573)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP325])],[f_394_4]) ).
cnf(f_394_6,plain,
in(U_1573,sK292(U_1573)),
inference(clausify,[status(thm)],[f_394_5]) ).
cnf(f_394_7,plain,
( in(U_1566,sK292(U_1573))
| ~ subset(U_1566,U_1567)
| ~ in(U_1567,sK292(U_1573)) ),
inference(clausify,[status(thm)],[f_394_5]) ).
cnf(f_394_8,plain,
( sP325(U_1570,U_1568,U_1573)
| ~ in(U_1570,sK292(U_1573)) ),
inference(clausify,[status(thm)],[f_394_5]) ).
cnf(f_394_9,plain,
( in(U_1571,sK292(U_1573))
| are_equipotent(U_1571,sK292(U_1573))
| ~ subset(U_1571,sK292(U_1573)) ),
inference(clausify,[status(thm)],[f_394_5]) ).
cnf(f_394_10,plain,
( in(sK293(U_1573,U_1570),sK292(U_1573))
| ~ sP325(U_1570,U_1568,U_1573) ),
inference(clausify,[status(thm)],[f_394_5]) ).
cnf(f_394_11,plain,
( in(U_1568,sK293(U_1573,U_1570))
| ~ subset(U_1568,U_1570)
| ~ sP325(U_1570,U_1568,U_1573) ),
inference(clausify,[status(thm)],[f_394_5]) ).
fof(f_395_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_395_2,plain,
! [U_1576,U_1575,U_1574] :
( U_1575 = U_1574
| singleton(U_1576) != unordered_pair(U_1575,U_1574) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_1576,U_1575,U_1574] :
( U_1575 = U_1574
| singleton(U_1576) != unordered_pair(U_1575,U_1574) ),
inference(definitional_conversion,[status(esa)],[f_395_2]) ).
cnf(f_395_4,plain,
( U_1575 = U_1574
| singleton(U_1576) != unordered_pair(U_1575,U_1574) ),
inference(clausify,[status(thm)],[f_395_3]) ).
cnf(f_84_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_84_3]) ).
cnf(f_85_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_85_3]) ).
cnf(f_86_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_86_3]) ).
cnf(f_87_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_87_3]) ).
cnf(f_88_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_88_3]) ).
cnf(f_89_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_89_3]) ).
cnf(f_90_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_90_3]) ).
cnf(f_91_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_91_3]) ).
cnf(f_92_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_92_3]) ).
cnf(f_94_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_94_3]) ).
cnf(f_95_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_95_3]) ).
cnf(f_97_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_97_3]) ).
cnf(f_98_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_98_3]) ).
cnf(f_100_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_100_3]) ).
cnf(f_102_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_102_3]) ).
cnf(f_103_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_103_3]) ).
cnf(f_104_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_104_3]) ).
cnf(f_106_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_106_3]) ).
cnf(f_107_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_107_3]) ).
cnf(f_110_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_110_3]) ).
cnf(f_111_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_111_3]) ).
cnf(f_121_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_121_3]) ).
cnf(f_122_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_122_3]) ).
cnf(f_123_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_123_3]) ).
cnf(f_215_26_simplified,plain,
( in(ordered_pair(U_885,U_883),sK161(U_881,U_880))
| sP207(U_876,U_880,U_881,U_885,U_883)
| ~ in(U_883,U_876)
| U_885 != U_876
| ~ in(U_885,U_881)
| ~ sP208(U_884,U_873,U_876,U_880,U_881,U_882,U_885,U_883) ),
inference(simplify_clause,[status(thm)],[f_215_26]) ).
cnf(f_216_18_simplified,plain,
( in(ordered_pair(U_896,U_894),sK167(U_892))
| U_894 != singleton(U_896)
| ~ in(U_896,U_892)
| ~ sP211(U_894,U_893,U_892,U_895,U_896) ),
inference(simplify_clause,[status(thm)],[f_216_18]) ).
cnf(f_219_25_simplified,plain,
( in(U_929,sK175(U_927,U_926))
| sP217(U_926,U_923,U_929,U_922,U_927)
| ~ in(U_929,U_922)
| U_923 != U_922
| ~ in(U_923,U_927)
| ~ sP218(U_926,U_923,U_929,U_928,U_922,U_927,U_918) ),
inference(simplify_clause,[status(thm)],[f_219_25]) ).
cnf(f_221_17_simplified,plain,
( in(U_967,sK197(U_965))
| U_967 != singleton(U_962)
| ~ in(U_962,U_965)
| ~ sP225(U_962,U_965,U_966,U_967) ),
inference(simplify_clause,[status(thm)],[f_221_17]) ).
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,
( 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_20,axiom,
( pair_first(Eq_x_0) = pair_first(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,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_25,axiom,
( inclusion_relation(Eq_x_0) = inclusion_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( pair_second(Eq_x_0) = pair_second(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,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_28,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| 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,
( 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_31,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_32,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_33,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,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_35,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_36,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| 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) = sK29(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK30(Eq_x_0) = sK30(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| 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,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( 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) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK36(Eq_x_0) = sK36(Eq_y_0)
| 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,Eq_x_2) = sK38(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_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) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_2) = sK44(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( 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) = sK48(Eq_y_0)
| 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,Eq_x_1) = sK50(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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) = sK53(Eq_y_0)
| 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) = sK55(Eq_y_0,Eq_y_1)
| 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) = sK56(Eq_y_0,Eq_y_1)
| 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,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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) = sK60(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_101,axiom,
( sK61(Eq_x_0) = sK61(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(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_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,Eq_x_3) = sK64(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_105,axiom,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK65(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_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,Eq_x_1,Eq_x_2) = sK67(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_108,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_109,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_110,axiom,
( sK70(Eq_x_0) = sK70(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_111,axiom,
( sK71(Eq_x_0) = sK71(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_112,axiom,
( sK72(Eq_x_0,Eq_x_1) = sK72(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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) = sK74(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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) = sK76(Eq_y_0,Eq_y_1)
| 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,Eq_x_2) = sK77(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(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_119,axiom,
( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(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_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) = sK82(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( 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,Eq_x_2) = sK85(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_126,axiom,
( sK86(Eq_x_0,Eq_x_1) = sK86(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,axiom,
( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_128,axiom,
( sK88(Eq_x_0,Eq_x_1) = sK88(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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,Eq_x_2) = sK90(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_131,axiom,
( sK91(Eq_x_0,Eq_x_1,Eq_x_2) = sK91(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,axiom,
( 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,Eq_x_2) = sK96(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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) = sK102(Eq_y_0,Eq_y_1)
| 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) = sK103(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,axiom,
( sK104(Eq_x_0,Eq_x_1) = sK104(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_145,axiom,
( sK105(Eq_x_0,Eq_x_1) = sK105(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK106(Eq_x_0,Eq_x_1,Eq_x_2) = sK106(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK108(Eq_x_0,Eq_x_1,Eq_x_2) = sK108(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_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) = sK110(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_151,axiom,
( sK111(Eq_x_0) = sK111(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_152,axiom,
( sK112(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK112(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_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,Eq_x_2) = sK114(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_155,axiom,
( sK115(Eq_x_0,Eq_x_1,Eq_x_2) = sK115(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_156,axiom,
( sK116(Eq_x_0,Eq_x_1,Eq_x_2) = sK116(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_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,Eq_x_1) = sK119(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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,Eq_x_1,Eq_x_2) = sK121(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_162,axiom,
( sK122(Eq_x_0,Eq_x_1) = sK122(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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,Eq_x_1) = sK124(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( 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,
( sK130(Eq_x_0) = sK130(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,axiom,
( sK131(Eq_x_0) = sK131(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_172,axiom,
( sK132(Eq_x_0) = sK132(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_173,axiom,
( sK133(Eq_x_0) = sK133(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_174,axiom,
( sK134(Eq_x_0,Eq_x_1) = sK134(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_175,axiom,
( sK138(Eq_x_0,Eq_x_1) = sK138(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_176,axiom,
( sK142(Eq_x_0) = sK142(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_177,axiom,
( sK144(Eq_x_0) = sK144(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_178,axiom,
( sK147(Eq_x_0,Eq_x_1) = sK147(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_179,axiom,
( sK149(Eq_x_0) = sK149(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_180,axiom,
( sK151(Eq_x_0) = sK151(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_181,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_182,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_183,axiom,
( sK158(Eq_x_0,Eq_x_1) = sK158(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,
( sK159(Eq_x_0,Eq_x_1) = sK159(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,
( 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_186,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_187,axiom,
( sK162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_188,axiom,
( sK163(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK163(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_189,axiom,
( sK164(Eq_x_0) = sK164(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_190,axiom,
( sK165(Eq_x_0) = sK165(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_191,axiom,
( sK166(Eq_x_0) = sK166(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_192,axiom,
( sK167(Eq_x_0) = sK167(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_193,axiom,
( sK168(Eq_x_0) = sK168(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_194,axiom,
( sK169(Eq_x_0,Eq_x_1,Eq_x_2) = sK169(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,
( 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_196,axiom,
( sK171(Eq_x_0,Eq_x_1) = sK171(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_197,axiom,
( sK172(Eq_x_0,Eq_x_1) = sK172(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_198,axiom,
( sK173(Eq_x_0,Eq_x_1) = sK173(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_199,axiom,
( sK174(Eq_x_0,Eq_x_1) = sK174(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_200,axiom,
( sK175(Eq_x_0,Eq_x_1) = sK175(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_201,axiom,
( sK176(Eq_x_0,Eq_x_1,Eq_x_2) = sK176(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_202,axiom,
( sK177(Eq_x_0,Eq_x_1,Eq_x_2) = sK177(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_203,axiom,
( sK178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK178(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_204,axiom,
( sK179(Eq_x_0,Eq_x_1) = sK179(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_205,axiom,
( sK180(Eq_x_0,Eq_x_1) = sK180(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_206,axiom,
( sK181(Eq_x_0,Eq_x_1) = sK181(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_207,axiom,
( sK182(Eq_x_0,Eq_x_1) = sK182(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_208,axiom,
( sK183(Eq_x_0,Eq_x_1) = sK183(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_209,axiom,
( sK184(Eq_x_0,Eq_x_1) = sK184(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_210,axiom,
( sK185(Eq_x_0,Eq_x_1) = sK185(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_211,axiom,
( sK186(Eq_x_0,Eq_x_1) = sK186(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_212,axiom,
( sK187(Eq_x_0,Eq_x_1) = sK187(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_213,axiom,
( sK188(Eq_x_0,Eq_x_1,Eq_x_2) = sK188(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_214,axiom,
( sK189(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK189(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_215,axiom,
( sK190(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK190(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_216,axiom,
( sK191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK191(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_217,axiom,
( sK192(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK192(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_218,axiom,
( sK193(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK193(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_219,axiom,
( sK194(Eq_x_0) = sK194(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_220,axiom,
( sK195(Eq_x_0) = sK195(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_221,axiom,
( sK196(Eq_x_0) = sK196(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_222,axiom,
( sK197(Eq_x_0) = sK197(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_223,axiom,
( sK198(Eq_x_0,Eq_x_1) = sK198(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_224,axiom,
( sK199(Eq_x_0) = sK199(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_225,axiom,
( sK200(Eq_x_0) = sK200(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_226,axiom,
( sK201(Eq_x_0) = sK201(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_227,axiom,
( sK202(Eq_x_0) = sK202(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_228,axiom,
( sK203(Eq_x_0) = sK203(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_229,axiom,
( sK204(Eq_x_0) = sK204(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_230,axiom,
( sK205(Eq_x_0) = sK205(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_231,axiom,
( sK206(Eq_x_0,Eq_x_1) = sK206(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_232,axiom,
( sK207(Eq_x_0,Eq_x_1,Eq_x_2) = sK207(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_233,axiom,
( sK208(Eq_x_0,Eq_x_1,Eq_x_2) = sK208(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_234,axiom,
( sK209(Eq_x_0,Eq_x_1,Eq_x_2) = sK209(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_235,axiom,
( sK210(Eq_x_0,Eq_x_1,Eq_x_2) = sK210(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_236,axiom,
( sK211(Eq_x_0,Eq_x_1,Eq_x_2) = sK211(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_237,axiom,
( sK212(Eq_x_0,Eq_x_1,Eq_x_2) = sK212(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_238,axiom,
( sK213(Eq_x_0,Eq_x_1,Eq_x_2) = sK213(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_239,axiom,
( sK214(Eq_x_0,Eq_x_1,Eq_x_2) = sK214(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_240,axiom,
( sK215(Eq_x_0,Eq_x_1,Eq_x_2) = sK215(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_241,axiom,
( sK216(Eq_x_0,Eq_x_1,Eq_x_2) = sK216(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_242,axiom,
( sK217(Eq_x_0,Eq_x_1,Eq_x_2) = sK217(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_243,axiom,
( sK218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK218(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_244,axiom,
( sK219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK219(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_245,axiom,
( sK220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK220(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_246,axiom,
( sK224(Eq_x_0) = sK224(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_247,axiom,
( sK225(Eq_x_0,Eq_x_1) = sK225(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_248,axiom,
( sK226(Eq_x_0,Eq_x_1) = sK226(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_249,axiom,
( sK227(Eq_x_0,Eq_x_1) = sK227(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_250,axiom,
( sK228(Eq_x_0,Eq_x_1) = sK228(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_251,axiom,
( sK229(Eq_x_0,Eq_x_1) = sK229(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_252,axiom,
( sK230(Eq_x_0,Eq_x_1) = sK230(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_253,axiom,
( sK231(Eq_x_0,Eq_x_1) = sK231(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_254,axiom,
( sK232(Eq_x_0,Eq_x_1,Eq_x_2) = sK232(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_255,axiom,
( sK233(Eq_x_0,Eq_x_1,Eq_x_2) = sK233(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_256,axiom,
( sK234(Eq_x_0,Eq_x_1,Eq_x_2) = sK234(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_257,axiom,
( sK235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK235(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_258,axiom,
( sK236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK236(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_259,axiom,
( sK237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK237(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_260,axiom,
( sK238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_261,axiom,
( sK239(Eq_x_0,Eq_x_1) = sK239(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_262,axiom,
( sK240(Eq_x_0,Eq_x_1,Eq_x_2) = sK240(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_263,axiom,
( sK241(Eq_x_0,Eq_x_1,Eq_x_2) = sK241(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_264,axiom,
( sK242(Eq_x_0,Eq_x_1,Eq_x_2) = sK242(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_265,axiom,
( sK243(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK243(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_266,axiom,
( sK244(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK244(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_267,axiom,
( sK245(Eq_x_0) = sK245(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_268,axiom,
( sK246(Eq_x_0,Eq_x_1) = sK246(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_269,axiom,
( sK247(Eq_x_0,Eq_x_1,Eq_x_2) = sK247(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_270,axiom,
( sK248(Eq_x_0,Eq_x_1) = sK248(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_271,axiom,
( sK249(Eq_x_0,Eq_x_1) = sK249(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_272,axiom,
( sK250(Eq_x_0,Eq_x_1) = sK250(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_273,axiom,
( sK251(Eq_x_0,Eq_x_1) = sK251(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_274,axiom,
( sK252(Eq_x_0,Eq_x_1) = sK252(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_275,axiom,
( sK253(Eq_x_0,Eq_x_1) = sK253(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_276,axiom,
( sK254(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK254(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_277,axiom,
( sK255(Eq_x_0,Eq_x_1) = sK255(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_278,axiom,
( sK256(Eq_x_0,Eq_x_1,Eq_x_2) = sK256(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_279,axiom,
( sK257(Eq_x_0) = sK257(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_280,axiom,
( sK258(Eq_x_0) = sK258(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_281,axiom,
( sK259(Eq_x_0) = sK259(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_282,axiom,
( sK260(Eq_x_0) = sK260(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_283,axiom,
( sK261(Eq_x_0) = sK261(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_284,axiom,
( sK262(Eq_x_0) = sK262(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_285,axiom,
( sK263(Eq_x_0) = sK263(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_286,axiom,
( sK266(Eq_x_0,Eq_x_1,Eq_x_2) = sK266(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_287,axiom,
( sK267(Eq_x_0,Eq_x_1,Eq_x_2) = sK267(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_288,axiom,
( sK268(Eq_x_0,Eq_x_1,Eq_x_2) = sK268(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_289,axiom,
( sK269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK269(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_290,axiom,
( sK270(Eq_x_0,Eq_x_1,Eq_x_2) = sK270(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_291,axiom,
( sK271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK271(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_292,axiom,
( sK272(Eq_x_0) = sK272(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_293,axiom,
( sK273(Eq_x_0) = sK273(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_294,axiom,
( sK274(Eq_x_0) = sK274(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_295,axiom,
( sK275(Eq_x_0,Eq_x_1) = sK275(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_296,axiom,
( sK276(Eq_x_0,Eq_x_1) = sK276(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_297,axiom,
( sK277(Eq_x_0) = sK277(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_298,axiom,
( sK278(Eq_x_0,Eq_x_1) = sK278(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_299,axiom,
( sK279(Eq_x_0,Eq_x_1) = sK279(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_300,axiom,
( sK280(Eq_x_0,Eq_x_1) = sK280(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_301,axiom,
( sK281(Eq_x_0) = sK281(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_302,axiom,
( sK282(Eq_x_0) = sK282(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_303,axiom,
( sK283(Eq_x_0,Eq_x_1) = sK283(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_304,axiom,
( sK284(Eq_x_0,Eq_x_1) = sK284(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_305,axiom,
( sK285(Eq_x_0,Eq_x_1) = sK285(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_306,axiom,
( sK286(Eq_x_0,Eq_x_1) = sK286(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_307,axiom,
( sK287(Eq_x_0,Eq_x_1) = sK287(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_308,axiom,
( sK288(Eq_x_0) = sK288(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_309,axiom,
( sK289(Eq_x_0) = sK289(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_310,axiom,
( sK290(Eq_x_0,Eq_x_1,Eq_x_2) = sK290(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_311,axiom,
( sK291(Eq_x_0,Eq_x_1) = sK291(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_312,axiom,
( sK292(Eq_x_0) = sK292(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_313,axiom,
( sK293(Eq_x_0,Eq_x_1) = sK293(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_314,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_315,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_316,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_317,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_318,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_319,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_320,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_321,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_322,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_323,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_324,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_325,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_326,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_327,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_328,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_329,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_330,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_331,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_332,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_333,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_334,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_335,axiom,
( quasi_total(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ quasi_total(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_336,axiom,
( 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_337,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_338,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_339,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_340,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_341,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_342,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_343,axiom,
( equipotent(Eq_y_0,Eq_y_1)
| ~ equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_344,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_345,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_346,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_347,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_348,axiom,
( are_equipotent(Eq_y_0,Eq_y_1)
| ~ are_equipotent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_349,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_350,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_351,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_352,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_353,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_354,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_355,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_356,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_357,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_358,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_359,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_360,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_361,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_362,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(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_363,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP14(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_364,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_365,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_366,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_367,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_368,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_369,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_370,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_371,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_372,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(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_373,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP24(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_374,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_375,axiom,
( sP26(Eq_y_0)
| ~ sP26(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_376,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_377,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_378,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_379,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_380,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_381,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_382,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_383,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_384,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP35(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_385,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_386,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_387,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_388,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_389,axiom,
( sP40(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_390,axiom,
( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_391,axiom,
( sP42(Eq_y_0)
| ~ sP42(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_392,axiom,
( sP43(Eq_y_0)
| ~ sP43(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_393,axiom,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_394,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_395,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_396,axiom,
( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_397,axiom,
( sP48(Eq_y_0)
| ~ sP48(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_398,axiom,
( sP49(Eq_y_0,Eq_y_1)
| ~ sP49(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_399,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP50(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_400,axiom,
( sP51(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_401,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_402,axiom,
( sP53(Eq_y_0,Eq_y_1)
| ~ sP53(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_403,axiom,
( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_404,axiom,
( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_405,axiom,
( sP56(Eq_y_0,Eq_y_1)
| ~ sP56(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_406,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_407,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_408,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_409,axiom,
( sP60(Eq_y_0,Eq_y_1)
| ~ sP60(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_410,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_411,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_412,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_413,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_414,axiom,
( sP65(Eq_y_0,Eq_y_1)
| ~ sP65(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_415,axiom,
( sP66(Eq_y_0,Eq_y_1)
| ~ sP66(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_416,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP67(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_417,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_418,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_419,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP70(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_420,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_421,axiom,
( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_422,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_423,axiom,
( sP74(Eq_y_0,Eq_y_1)
| ~ sP74(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_424,axiom,
( sP75(Eq_y_0,Eq_y_1)
| ~ sP75(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_425,axiom,
( sP76(Eq_y_0,Eq_y_1)
| ~ sP76(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_426,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_427,axiom,
( sP78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_428,axiom,
( sP79(Eq_y_0,Eq_y_1)
| ~ sP79(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_429,axiom,
( sP80(Eq_y_0,Eq_y_1)
| ~ sP80(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_430,axiom,
( sP81(Eq_y_0,Eq_y_1)
| ~ sP81(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_431,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_432,axiom,
( sP83(Eq_y_0)
| ~ sP83(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_433,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_434,axiom,
( sP85(Eq_y_0,Eq_y_1)
| ~ sP85(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_435,axiom,
( sP86(Eq_y_0,Eq_y_1)
| ~ sP86(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_436,axiom,
( sP87(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_437,axiom,
( sP88(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_438,axiom,
( sP89(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_439,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_440,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_441,axiom,
( sP92(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP92(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_442,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_443,axiom,
( sP94(Eq_y_0,Eq_y_1)
| ~ sP94(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_444,axiom,
( sP95(Eq_y_0,Eq_y_1)
| ~ sP95(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_445,axiom,
( sP96(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_446,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_447,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_448,axiom,
( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_449,axiom,
( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP100(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_450,axiom,
( sP101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_451,axiom,
( sP102(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP102(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_452,axiom,
( sP103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_453,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_454,axiom,
( sP105(Eq_y_0)
| ~ sP105(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_455,axiom,
( sP106(Eq_y_0,Eq_y_1)
| ~ sP106(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_456,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_457,axiom,
( sP108(Eq_y_0,Eq_y_1)
| ~ sP108(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_458,axiom,
( sP109(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP109(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_459,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP110(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_460,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_461,axiom,
( sP112(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP112(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_462,axiom,
( sP113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP113(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_463,axiom,
( sP114(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_464,axiom,
( sP115(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_465,axiom,
( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_466,axiom,
( sP117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_467,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_468,axiom,
( sP119(Eq_y_0)
| ~ sP119(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_469,axiom,
( sP120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_470,axiom,
( sP121(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP121(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_471,axiom,
( sP122(Eq_y_0,Eq_y_1)
| ~ sP122(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_472,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_473,axiom,
( sP124(Eq_y_0,Eq_y_1)
| ~ sP124(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_474,axiom,
( sP125(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_475,axiom,
( sP126(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP126(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_476,axiom,
( sP127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_477,axiom,
( sP128(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_478,axiom,
( sP129(Eq_y_0,Eq_y_1)
| ~ sP129(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_479,axiom,
( sP130(Eq_y_0)
| ~ sP130(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_480,axiom,
( sP131(Eq_y_0)
| ~ sP131(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_481,axiom,
( sP132(Eq_y_0,Eq_y_1)
| ~ sP132(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_482,axiom,
( sP133(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_483,axiom,
( sP134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_484,axiom,
( sP135(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_485,axiom,
( sP136(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP136(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_486,axiom,
( sP137(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP137(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_487,axiom,
( sP138(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_488,axiom,
( sP139(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP139(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_489,axiom,
( sP140(Eq_y_0,Eq_y_1)
| ~ sP140(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_490,axiom,
( sP141(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_491,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_492,axiom,
( sP143(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP143(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_493,axiom,
( sP144(Eq_y_0,Eq_y_1)
| ~ sP144(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_494,axiom,
( sP145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_495,axiom,
( sP146(Eq_y_0,Eq_y_1)
| ~ sP146(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_496,axiom,
( sP147(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP147(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_497,axiom,
( sP148(Eq_y_0,Eq_y_1)
| ~ sP148(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_498,axiom,
( sP149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_499,axiom,
( sP150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_500,axiom,
( sP151(Eq_y_0,Eq_y_1)
| ~ sP151(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_501,axiom,
( sP152(Eq_y_0,Eq_y_1)
| ~ sP152(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_502,axiom,
( sP153(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP153(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_503,axiom,
( sP154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_504,axiom,
( sP155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_505,axiom,
( sP156(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP156(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_506,axiom,
( sP157(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP157(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_507,axiom,
( sP158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_508,axiom,
( sP159(Eq_y_0)
| ~ sP159(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_509,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_510,axiom,
( sP161(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_511,axiom,
( sP162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_512,axiom,
( sP163(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP163(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_513,axiom,
( sP164(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP164(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_514,axiom,
( sP165(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_515,axiom,
( sP166(Eq_y_0,Eq_y_1)
| ~ sP166(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_516,axiom,
( sP167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP167(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_517,axiom,
( sP168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_518,axiom,
( sP169(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP169(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_519,axiom,
( sP170(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP170(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_520,axiom,
( sP171(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP171(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_521,axiom,
( sP172(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_522,axiom,
( sP173(Eq_y_0,Eq_y_1)
| ~ sP173(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_523,axiom,
( sP174(Eq_y_0)
| ~ sP174(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_524,axiom,
( sP175(Eq_y_0)
| ~ sP175(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_525,axiom,
( sP176(Eq_y_0,Eq_y_1)
| ~ sP176(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_526,axiom,
( sP177(Eq_y_0)
| ~ sP177(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_527,axiom,
( sP178(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP178(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_528,axiom,
( sP179(Eq_y_0,Eq_y_1)
| ~ sP179(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_529,axiom,
( sP180(Eq_y_0)
| ~ sP180(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_530,axiom,
( sP181(Eq_y_0)
| ~ sP181(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_531,axiom,
( sP182(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP182(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_532,axiom,
( sP183(Eq_y_0)
| ~ sP183(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_533,axiom,
( sP184(Eq_y_0,Eq_y_1)
| ~ sP184(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_534,axiom,
( sP185(Eq_y_0)
| ~ sP185(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_535,axiom,
( sP186(Eq_y_0)
| ~ sP186(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_536,axiom,
( sP187(Eq_y_0,Eq_y_1)
| ~ sP187(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_537,axiom,
( sP188(Eq_y_0)
| ~ sP188(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_538,axiom,
( sP189(Eq_y_0,Eq_y_1)
| ~ sP189(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_539,axiom,
( sP190(Eq_y_0)
| ~ sP190(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_540,axiom,
( sP191(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_541,axiom,
( sP192(Eq_y_0,Eq_y_1)
| ~ sP192(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_542,axiom,
( sP193(Eq_y_0)
| ~ sP193(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_543,axiom,
( sP194(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP194(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_544,axiom,
( sP195(Eq_y_0)
| ~ sP195(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_545,axiom,
( sP196(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP196(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_546,axiom,
( sP197(Eq_y_0,Eq_y_1)
| ~ sP197(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_547,axiom,
( sP198(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP198(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_548,axiom,
( sP199(Eq_y_0,Eq_y_1)
| ~ sP199(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_549,axiom,
( sP200(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP200(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_550,axiom,
( sP201(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP201(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_551,axiom,
( sP202(Eq_y_0)
| ~ sP202(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_552,axiom,
( sP203(Eq_y_0)
| ~ sP203(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_553,axiom,
( sP204(Eq_y_0,Eq_y_1)
| ~ sP204(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_554,axiom,
( sP205(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP205(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_555,axiom,
( sP206(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP206(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_556,axiom,
( sP207(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP207(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_557,axiom,
( sP208(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_558,axiom,
( sP209(Eq_y_0)
| ~ sP209(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_559,axiom,
( sP210(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP210(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_560,axiom,
( sP211(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_561,axiom,
( sP212(Eq_y_0,Eq_y_1)
| ~ sP212(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_562,axiom,
( sP213(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_563,axiom,
( sP214(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_564,axiom,
( sP215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_565,axiom,
( sP216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_566,axiom,
( sP217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_567,axiom,
( sP218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_568,axiom,
( sP219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_569,axiom,
( sP220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_570,axiom,
( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_571,axiom,
( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9)
| ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9)
| Eq_x_9 != Eq_y_9
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_572,axiom,
( sP223(Eq_y_0)
| ~ sP223(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_573,axiom,
( sP224(Eq_y_0,Eq_y_1)
| ~ sP224(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_574,axiom,
( sP225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_575,axiom,
( sP226(Eq_y_0)
| ~ sP226(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_576,axiom,
( sP227(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP227(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_577,axiom,
( sP228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_578,axiom,
( sP229(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP229(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_579,axiom,
( sP230(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_580,axiom,
( sP231(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP231(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_581,axiom,
( sP233(Eq_y_0,Eq_y_1)
| ~ sP233(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_582,axiom,
( sP234(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP234(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_583,axiom,
( sP235(Eq_y_0,Eq_y_1)
| ~ sP235(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_584,axiom,
( sP236(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP236(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_585,axiom,
( sP237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_586,axiom,
( sP238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_587,axiom,
( sP239(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_588,axiom,
( sP240(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8)
| ~ sP240(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8)
| Eq_x_8 != Eq_y_8
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_589,axiom,
( sP241(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP241(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_590,axiom,
( sP242(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP242(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_591,axiom,
( sP243(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP243(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_592,axiom,
( sP244(Eq_y_0,Eq_y_1)
| ~ sP244(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_593,axiom,
( sP245(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP245(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_594,axiom,
( sP246(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP246(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_595,axiom,
( sP247(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP247(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_596,axiom,
( sP248(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP248(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_597,axiom,
( sP249(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP249(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_598,axiom,
( sP250(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP250(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_599,axiom,
( sP251(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP251(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_600,axiom,
( sP252(Eq_y_0)
| ~ sP252(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_601,axiom,
( sP253(Eq_y_0,Eq_y_1)
| ~ sP253(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_602,axiom,
( sP254(Eq_y_0,Eq_y_1)
| ~ sP254(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_603,axiom,
( sP255(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP255(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_604,axiom,
( sP256(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP256(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_605,axiom,
( sP257(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP257(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_606,axiom,
( sP258(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_607,axiom,
( sP259(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP259(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_608,axiom,
( sP260(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP260(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_609,axiom,
( sP261(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP261(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_610,axiom,
( sP262(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP262(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_611,axiom,
( sP263(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_612,axiom,
( sP264(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP264(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_613,axiom,
( sP265(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP265(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_614,axiom,
( sP266(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP266(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_615,axiom,
( sP267(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP267(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_616,axiom,
( sP268(Eq_y_0,Eq_y_1)
| ~ sP268(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_617,axiom,
( sP269(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP269(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_618,axiom,
( sP270(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP270(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_619,axiom,
( sP271(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_620,axiom,
( sP272(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP272(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_621,axiom,
( sP273(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_622,axiom,
( sP274(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_623,axiom,
( sP275(Eq_y_0,Eq_y_1)
| ~ sP275(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_624,axiom,
( sP276(Eq_y_0,Eq_y_1)
| ~ sP276(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_625,axiom,
( sP277(Eq_y_0)
| ~ sP277(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_626,axiom,
( sP278(Eq_y_0,Eq_y_1)
| ~ sP278(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_627,axiom,
( sP279(Eq_y_0,Eq_y_1)
| ~ sP279(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_628,axiom,
( sP280(Eq_y_0,Eq_y_1)
| ~ sP280(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_629,axiom,
( sP281(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP281(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_630,axiom,
( sP282(Eq_y_0)
| ~ sP282(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_631,axiom,
( sP283(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP283(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_632,axiom,
( sP284(Eq_y_0,Eq_y_1)
| ~ sP284(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_633,axiom,
( sP285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_634,axiom,
( sP286(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP286(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_635,axiom,
( sP287(Eq_y_0,Eq_y_1)
| ~ sP287(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_636,axiom,
( sP288(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP288(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_637,axiom,
( sP289(Eq_y_0)
| ~ sP289(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_638,axiom,
( sP290(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP290(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_639,axiom,
( sP291(Eq_y_0,Eq_y_1)
| ~ sP291(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_640,axiom,
( sP292(Eq_y_0,Eq_y_1)
| ~ sP292(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_641,axiom,
( sP293(Eq_y_0)
| ~ sP293(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_642,axiom,
( sP294(Eq_y_0,Eq_y_1)
| ~ sP294(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_643,axiom,
( sP295(Eq_y_0)
| ~ sP295(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_644,axiom,
( sP296(Eq_y_0,Eq_y_1)
| ~ sP296(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_645,axiom,
( sP297(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP297(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_646,axiom,
( sP298(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_647,axiom,
( sP299(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_648,axiom,
( sP300(Eq_y_0,Eq_y_1)
| ~ sP300(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_649,axiom,
( sP301(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP301(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_650,axiom,
( sP302(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP302(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_651,axiom,
( sP303(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP303(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_652,axiom,
( sP304(Eq_y_0,Eq_y_1)
| ~ sP304(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_653,axiom,
( sP305(Eq_y_0,Eq_y_1)
| ~ sP305(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_654,axiom,
( sP306(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_655,axiom,
( sP307(Eq_y_0)
| ~ sP307(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_656,axiom,
( sP308(Eq_y_0,Eq_y_1)
| ~ sP308(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_657,axiom,
( sP309(Eq_y_0)
| ~ sP309(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_658,axiom,
( sP310(Eq_y_0)
| ~ sP310(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_659,axiom,
( sP311(Eq_y_0)
| ~ sP311(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_660,axiom,
( sP312(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP312(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_661,axiom,
( sP313(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP313(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_662,axiom,
( sP314(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP314(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_663,axiom,
( sP315(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP315(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_664,axiom,
( sP316(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP316(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_665,axiom,
( sP317(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP317(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_666,axiom,
( sP318(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP318(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_667,axiom,
( sP319(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP319(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_668,axiom,
( sP320(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP320(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_669,axiom,
( sP321(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP321(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_670,axiom,
( sP322(Eq_y_0)
| ~ sP322(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_671,axiom,
( sP323(Eq_y_0,Eq_y_1)
| ~ sP323(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_672,axiom,
( sP324(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP324(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_673,axiom,
( sP325(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP325(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU294+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:49:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 30.36/30.69 % SZS status Theorem for theBenchmark
% 30.36/30.69 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------