%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU355+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 : n009.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 08:59:04 AM UTC 2026
% Result : Theorem 249.64s 250.02s
% Output : Proof 249.84s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(abstractness_v1_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('theBenchmark.p',abstractness_v1_orders_2) ).
fof(abstractness_v3_lattices,axiom,
! [A] :
( latt_str(A)
=> ( strict_latt_str(A)
=> A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A)) ) ),
file('theBenchmark.p',abstractness_v3_lattices) ).
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(cc10_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( element(B,A)
=> v1_xcmplx_0(B) ) ),
file('theBenchmark.p',cc10_membered) ).
fof(cc11_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc11_membered) ).
fof(cc12_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc12_membered) ).
fof(cc13_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc13_membered) ).
fof(cc14_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& natural(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc14_membered) ).
fof(cc15_membered,axiom,
! [A] :
( empty(A)
=> ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) ) ),
file('theBenchmark.p',cc15_membered) ).
fof(cc16_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> v1_membered(B) ) ),
file('theBenchmark.p',cc16_membered) ).
fof(cc17_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc17_membered) ).
fof(cc18_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc18_membered) ).
fof(cc19_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc19_membered) ).
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_finsub_1,axiom,
! [A] :
( preboolean(A)
=> ( diff_closed(A)
& cup_closed(A) ) ),
file('theBenchmark.p',cc1_finsub_1) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_funct_2,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> ( ( v1_partfun1(C,A,B)
& function(C) )
=> ( quasi_total(C,A,B)
& function(C) ) ) ),
file('theBenchmark.p',cc1_funct_2) ).
fof(cc1_lattices,axiom,
! [A] :
( latt_str(A)
=> ( ( lattice(A)
& ~ empty_carrier(A) )
=> ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc1_lattices) ).
fof(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ),
file('theBenchmark.p',cc1_membered) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_partfun1,axiom,
! [A] :
( ( transitive(A)
& symmetric(A)
& relation(A) )
=> ( reflexive(A)
& relation(A) ) ),
file('theBenchmark.p',cc1_partfun1) ).
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(cc20_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc20_membered) ).
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_finsub_1,axiom,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
=> preboolean(A) ),
file('theBenchmark.p',cc2_finsub_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_funct_2,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> ( ( bijective(C,A,B)
& quasi_total(C,A,B)
& function(C) )
=> ( onto(C,A,B)
& quasi_total(C,A,B)
& one_to_one(C)
& function(C) ) ) ),
file('theBenchmark.p',cc2_funct_2) ).
fof(cc2_lattices,axiom,
! [A] :
( latt_str(A)
=> ( ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ( lattice(A)
& ~ empty_carrier(A) ) ) ),
file('theBenchmark.p',cc2_lattices) ).
fof(cc2_membered,axiom,
! [A] :
( v4_membered(A)
=> v3_membered(A) ),
file('theBenchmark.p',cc2_membered) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_arytm_3,axiom,
! [A] :
( element(A,omega)
=> ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_arytm_3) ).
fof(cc3_funct_2,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> ( ( onto(C,A,B)
& quasi_total(C,A,B)
& one_to_one(C)
& function(C) )
=> ( bijective(C,A,B)
& quasi_total(C,A,B)
& function(C) ) ) ),
file('theBenchmark.p',cc3_funct_2) ).
fof(cc3_membered,axiom,
! [A] :
( v3_membered(A)
=> v2_membered(A) ),
file('theBenchmark.p',cc3_membered) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(cc4_funct_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ( ( quasi_total(B,A,A)
& reflexive(B)
& v1_partfun1(B,A,A)
& function(B) )
=> ( bijective(B,A,A)
& onto(B,A,A)
& quasi_total(B,A,A)
& one_to_one(B)
& function(B) ) ) ),
file('theBenchmark.p',cc4_funct_2) ).
fof(cc4_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ),
file('theBenchmark.p',cc4_membered) ).
fof(cc5_funct_2,axiom,
! [A,B] :
( ~ empty(B)
=> ! [C] :
( relation_of2(C,A,B)
=> ( ( quasi_total(C,A,B)
& function(C) )
=> ( quasi_total(C,A,B)
& v1_partfun1(C,A,B)
& function(C) ) ) ) ),
file('theBenchmark.p',cc5_funct_2) ).
fof(cc6_funct_2,axiom,
! [A,B] :
( ( ~ empty(B)
& ~ empty(A) )
=> ! [C] :
( relation_of2(C,A,B)
=> ( ( quasi_total(C,A,B)
& function(C) )
=> ( quasi_total(C,A,B)
& v1_partfun1(C,A,B)
& ~ empty(C)
& function(C) ) ) ) ),
file('theBenchmark.p',cc6_funct_2) ).
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_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join_commut(A,C,B) ),
file('theBenchmark.p',commutativity_k3_lattices) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(commutativity_k4_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> meet_commut(A,B,C) = meet_commut(A,C,B) ),
file('theBenchmark.p',commutativity_k4_lattices) ).
fof(commutativity_k4_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_union2(A,B,C) = subset_union2(A,C,B) ),
file('theBenchmark.p',commutativity_k4_subset_1) ).
fof(commutativity_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = subset_intersection2(A,C,B) ),
file('theBenchmark.p',commutativity_k5_subset_1) ).
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_grcat_1,axiom,
! [A] :
( one_sorted_str(A)
=> identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)) ),
file('theBenchmark.p',d11_grcat_1) ).
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_lattices,axiom,
! [A] :
( ( meet_semilatt_str(A)
& ~ empty_carrier(A) )
=> ( lower_bounded_semilattstr(A)
<=> ? [B] :
( ! [C] :
( element(C,the_carrier(A))
=> ( meet(A,C,B) = B
& meet(A,B,C) = B ) )
& element(B,the_carrier(A)) ) ) ),
file('theBenchmark.p',d13_lattices) ).
fof(d13_pre_topc,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( C = topstr_closure(A,B)
<=> ! [D] :
( in(D,the_carrier(A))
=> ( in(D,C)
<=> ! [E] :
( element(E,powerset(the_carrier(A)))
=> ~ ( disjoint(B,E)
& in(D,E)
& open_subset(E,A) ) ) ) ) ) ) ) ),
file('theBenchmark.p',d13_pre_topc) ).
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_lattice3,axiom,
! [A] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( latt_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,C)
=> below(A,B,D) ) ) ) ) ),
file('theBenchmark.p',d16_lattice3) ).
fof(d16_lattices,axiom,
! [A] :
( ( meet_semilatt_str(A)
& ~ empty_carrier(A) )
=> ( lower_bounded_semilattstr(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( B = bottom_of_semilattstr(A)
<=> ! [C] :
( element(C,the_carrier(A))
=> ( meet(A,C,B) = B
& meet(A,B,C) = B ) ) ) ) ) ),
file('theBenchmark.p',d16_lattices) ).
fof(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_relat_2) ).
fof(d17_lattice3,axiom,
! [A] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( latt_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,C)
=> below(A,D,B) ) ) ) ) ),
file('theBenchmark.p',d17_lattice3) ).
fof(d1_binop_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] : apply_binary(A,B,C) = apply(A,ordered_pair(B,C)) ),
file('theBenchmark.p',d1_binop_1) ).
fof(d1_connsp_2,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( point_neighbourhood(C,A,B)
<=> in(B,interior(A,C)) ) ) ) ),
file('theBenchmark.p',d1_connsp_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_finset_1,axiom,
! [A] :
( finite(A)
<=> ? [B] :
( in(relation_dom(B),omega)
& relation_rng(B) = A
& function(B)
& relation(B) ) ),
file('theBenchmark.p',d1_finset_1) ).
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_lattice3,axiom,
! [A,B] :
( ( latt_str(B)
& strict_latt_str(B) )
=> ( B = boole_lattice(A)
<=> ( ! [C] :
( element(C,powerset(A))
=> ! [D] :
( element(D,powerset(A))
=> ( apply_binary(the_L_meet(B),C,D) = subset_intersection2(A,C,D)
& apply_binary(the_L_join(B),C,D) = subset_union2(A,C,D) ) ) )
& the_carrier(B) = powerset(A) ) ) ),
file('theBenchmark.p',d1_lattice3) ).
fof(d1_lattices,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> join(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C) ) ) ),
file('theBenchmark.p',d1_lattices) ).
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_pre_topc,axiom,
! [A] :
( top_str(A)
=> ( topological_space(A)
<=> ( ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( ( in(C,the_topology(A))
& in(B,the_topology(A)) )
=> in(subset_intersection2(the_carrier(A),B,C),the_topology(A)) ) ) )
& ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( subset(B,the_topology(A))
=> in(union_of_subsets(the_carrier(A),B),the_topology(A)) ) )
& in(the_carrier(A),the_topology(A)) ) ) ),
file('theBenchmark.p',d1_pre_topc) ).
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_struct_0,axiom,
! [A] :
( one_sorted_str(A)
=> ( empty_carrier(A)
<=> empty(the_carrier(A)) ) ),
file('theBenchmark.p',d1_struct_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_tops_1,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ),
file('theBenchmark.p',d1_tops_1) ).
fof(d1_tops_2,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( open_subsets(B,A)
<=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( in(C,B)
=> open_subset(C,A) ) ) ) ) ),
file('theBenchmark.p',d1_tops_2) ).
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(d21_lattice3,axiom,
! [A] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> ( ( latt_str(A)
& complete_latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( C = join_of_latt_set(A,B)
<=> ( ! [D] :
( element(D,the_carrier(A))
=> ( latt_element_smaller(A,D,B)
=> below(A,C,D) ) )
& latt_element_smaller(A,C,B) ) ) ) ) ),
file('theBenchmark.p',d21_lattice3) ).
fof(d22_lattice3,axiom,
! [A] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> ! [B] : meet_of_latt_set(A,B) = join_of_latt_set(A,a_2_2_lattice3(A,B)) ),
file('theBenchmark.p',d22_lattice3) ).
fof(d2_compts_1,axiom,
! [A] :
( centered(A)
<=> ( ! [B] :
~ ( set_meet(B) = empty_set
& finite(B)
& subset(B,A)
& B != empty_set )
& A != empty_set ) ),
file('theBenchmark.p',d2_compts_1) ).
fof(d2_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A)) ),
file('theBenchmark.p',d2_lattice3) ).
fof(d2_lattices,axiom,
! [A] :
( ( meet_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> meet(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C) ) ) ),
file('theBenchmark.p',d2_lattices) ).
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_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> empty_carrier_subset(A) = empty_set ),
file('theBenchmark.p',d2_pre_topc) ).
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_tex_2,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> B != union(A) ) ),
file('theBenchmark.p',d2_tex_2) ).
fof(d2_tops_2,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( closed_subsets(B,A)
<=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( in(C,B)
=> closed_subset(C,A) ) ) ) ) ),
file('theBenchmark.p',d2_tops_2) ).
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_compts_1,axiom,
! [A] :
( top_str(A)
=> ( compact_top_space(A)
<=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( ! [C] :
( element(C,powerset(powerset(the_carrier(A))))
=> ~ ( finite(C)
& is_a_cover_of_carrier(A,C)
& subset(C,B) ) )
& open_subsets(B,A)
& is_a_cover_of_carrier(A,B) ) ) ) ),
file('theBenchmark.p',d3_compts_1) ).
fof(d3_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> cast_to_el_of_LattPOSet(A,B) = B ) ),
file('theBenchmark.p',d3_lattice3) ).
fof(d3_lattices,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below(A,B,C)
<=> join(A,B,C) = C ) ) ) ),
file('theBenchmark.p',d3_lattices) ).
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_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
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_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(poset_of_lattice(A)))
=> cast_to_el_of_lattice(A,B) = B ) ),
file('theBenchmark.p',d4_lattice3) ).
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_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( transitive_relstr(A)
<=> is_transitive_in(the_InternalRel(A),the_carrier(A)) ) ),
file('theBenchmark.p',d5_orders_2) ).
fof(d5_ordinal2,axiom,
! [A] :
( A = omega
<=> ( ! [B] :
( ordinal(B)
=> ( ( being_limit_ordinal(B)
& in(empty_set,B) )
=> subset(A,B) ) )
& ordinal(A)
& being_limit_ordinal(A)
& in(empty_set,A) ) ),
file('theBenchmark.p',d5_ordinal2) ).
fof(d5_pre_topc,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> in(B,the_topology(A)) ) ) ),
file('theBenchmark.p',d5_pre_topc) ).
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_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( antisymmetric_relstr(A)
<=> is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) ) ),
file('theBenchmark.p',d6_orders_2) ).
fof(d6_ordinal1,axiom,
! [A] :
( being_limit_ordinal(A)
<=> A = union(A) ),
file('theBenchmark.p',d6_ordinal1) ).
fof(d6_pre_topc,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) ) ) ),
file('theBenchmark.p',d6_pre_topc) ).
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_filter_1,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> relation_of_lattice(A) = a_1_0_filter_1(A) ),
file('theBenchmark.p',d8_filter_1) ).
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_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('theBenchmark.p',d8_lattice3) ).
fof(d8_lattices,axiom,
! [A] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> ( meet_absorbing(A)
<=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> join(A,meet(A,B,C),C) = C ) ) ) ),
file('theBenchmark.p',d8_lattices) ).
fof(d8_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ),
file('theBenchmark.p',d8_pre_topc) ).
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_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,D,C) ) ) ) ) ),
file('theBenchmark.p',d9_lattice3) ).
fof(d9_orders_2,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
file('theBenchmark.p',d9_orders_2) ).
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_g1_orders_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) ) ),
file('theBenchmark.p',dt_g1_orders_2) ).
fof(dt_g3_lattices,axiom,
! [A,B,C] :
( ( relation_of2(C,cartesian_product2(A,A),A)
& quasi_total(C,cartesian_product2(A,A),A)
& function(C)
& relation_of2(B,cartesian_product2(A,A),A)
& quasi_total(B,cartesian_product2(A,A),A)
& function(B) )
=> ( latt_str(latt_str_of(A,B,C))
& strict_latt_str(latt_str_of(A,B,C)) ) ),
file('theBenchmark.p',dt_g3_lattices) ).
fof(dt_k10_filter_1,axiom,
! [A,B,C,D] :
( ( element(D,the_carrier(B))
& element(C,the_carrier(A))
& latt_str(B)
& lattice(B)
& ~ empty_carrier(B)
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> element(k10_filter_1(A,B,C,D),the_carrier(k8_filter_1(A,B))) ),
file('theBenchmark.p',dt_k10_filter_1) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
fof(dt_k15_lattice3,axiom,
! [A,B] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> element(join_of_latt_set(A,B),the_carrier(A)) ),
file('theBenchmark.p',dt_k15_lattice3) ).
fof(dt_k16_lattice3,axiom,
! [A,B] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> element(meet_of_latt_set(A,B),the_carrier(A)) ),
file('theBenchmark.p',dt_k16_lattice3) ).
fof(dt_k1_binop_1,axiom,
$true,
file('theBenchmark.p',dt_k1_binop_1) ).
fof(dt_k1_domain_1,axiom,
! [A,B,C,D] :
( ( element(D,B)
& element(C,A)
& ~ empty(B)
& ~ empty(A) )
=> element(ordered_pair_as_product_element(A,B,C,D),cartesian_product2(A,B)) ),
file('theBenchmark.p',dt_k1_domain_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_lattice3,axiom,
! [A] :
( latt_str(boole_lattice(A))
& strict_latt_str(boole_lattice(A)) ),
file('theBenchmark.p',dt_k1_lattice3) ).
fof(dt_k1_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& ~ empty_carrier(A) )
=> element(join(A,B,C),the_carrier(A)) ),
file('theBenchmark.p',dt_k1_lattices) ).
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_pcomps_1,axiom,
! [A] : element(k1_pcomps_1(A),powerset(powerset(A))),
file('theBenchmark.p',dt_k1_pcomps_1) ).
fof(dt_k1_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> element(empty_carrier_subset(A),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k1_pre_topc) ).
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_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A) )
=> element(interior(A,B),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k1_tops_1) ).
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_binop_1,axiom,
! [A,B,C,D,E,F] :
( ( element(F,B)
& element(E,A)
& relation_of2(D,cartesian_product2(A,B),C)
& quasi_total(D,cartesian_product2(A,B),C)
& function(D)
& ~ empty(B)
& ~ empty(A) )
=> element(apply_binary_as_element(A,B,C,D,E,F),C) ),
file('theBenchmark.p',dt_k2_binop_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_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ( relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A))
& v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A))
& transitive(k2_lattice3(A))
& antisymmetric(k2_lattice3(A))
& reflexive(k2_lattice3(A)) ) ),
file('theBenchmark.p',dt_k2_lattice3) ).
fof(dt_k2_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& ~ empty_carrier(A) )
=> element(meet(A,B,C),the_carrier(A)) ),
file('theBenchmark.p',dt_k2_lattices) ).
fof(dt_k2_mcart_1,axiom,
$true,
file('theBenchmark.p',dt_k2_mcart_1) ).
fof(dt_k2_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k2_pre_topc) ).
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_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ( rel_str(poset_of_lattice(A))
& antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A)) ) ),
file('theBenchmark.p',dt_k3_lattice3) ).
fof(dt_k3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> element(join_commut(A,B,C),the_carrier(A)) ),
file('theBenchmark.p',dt_k3_lattices) ).
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_lattice3,axiom,
! [A,B] :
( ( element(B,the_carrier(A))
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A))) ),
file('theBenchmark.p',dt_k4_lattice3) ).
fof(dt_k4_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> element(meet_commut(A,B,C),the_carrier(A)) ),
file('theBenchmark.p',dt_k4_lattices) ).
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_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_union2(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k4_subset_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_lattice3,axiom,
! [A,B] :
( ( element(B,the_carrier(poset_of_lattice(A)))
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> element(cast_to_el_of_lattice(A,B),the_carrier(A)) ),
file('theBenchmark.p',dt_k5_lattice3) ).
fof(dt_k5_lattices,axiom,
! [A] :
( ( meet_semilatt_str(A)
& ~ empty_carrier(A) )
=> element(bottom_of_semilattstr(A),the_carrier(A)) ),
file('theBenchmark.p',dt_k5_lattices) ).
fof(dt_k5_ordinal2,axiom,
$true,
file('theBenchmark.p',dt_k5_ordinal2) ).
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_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_intersection2(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k5_subset_1) ).
fof(dt_k6_partfun1,axiom,
! [A] :
( relation_of2_as_subset(identity_as_relation_of(A),A,A)
& v1_partfun1(identity_as_relation_of(A),A,A) ),
file('theBenchmark.p',dt_k6_partfun1) ).
fof(dt_k6_pre_topc,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k6_pre_topc) ).
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_grcat_1,axiom,
! [A] :
( one_sorted_str(A)
=> ( relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A))
& quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A))
& function(identity_on_carrier(A)) ) ),
file('theBenchmark.p',dt_k7_grcat_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_filter_1,axiom,
! [A,B] :
( ( latt_str(B)
& ~ empty_carrier(B)
& latt_str(A)
& ~ empty_carrier(A) )
=> ( latt_str(k8_filter_1(A,B))
& strict_latt_str(k8_filter_1(A,B)) ) ),
file('theBenchmark.p',dt_k8_filter_1) ).
fof(dt_k8_funct_2,axiom,
! [A,B,C,D] :
( ( element(D,A)
& relation_of2(C,A,B)
& quasi_total(C,A,B)
& function(C)
& ~ empty(A) )
=> element(apply_as_element(A,B,C,D),B) ),
file('theBenchmark.p',dt_k8_funct_2) ).
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_filter_1,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> relation(relation_of_lattice(A)) ),
file('theBenchmark.p',dt_k9_filter_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_relat_1) ).
fof(dt_l1_lattices,axiom,
! [A] :
( meet_semilatt_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_lattices) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_lattices,axiom,
! [A] :
( join_semilatt_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
fof(dt_l3_lattices,axiom,
! [A] :
( latt_str(A)
=> ( join_semilatt_str(A)
& meet_semilatt_str(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(dt_m1_connsp_2,axiom,
! [A,B] :
( ( element(B,the_carrier(A))
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [C] :
( point_neighbourhood(C,A,B)
=> element(C,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',dt_m1_connsp_2) ).
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(dt_u1_lattices,axiom,
! [A] :
( meet_semilatt_str(A)
=> ( relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_meet(A)) ) ),
file('theBenchmark.p',dt_u1_lattices) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( rel_str(A)
=> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) ),
file('theBenchmark.p',dt_u1_orders_2) ).
fof(dt_u1_pre_topc,axiom,
! [A] :
( top_str(A)
=> element(the_topology(A),powerset(powerset(the_carrier(A)))) ),
file('theBenchmark.p',dt_u1_pre_topc) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(dt_u2_lattices,axiom,
! [A] :
( join_semilatt_str(A)
=> ( relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A)) ) ),
file('theBenchmark.p',dt_u2_lattices) ).
fof(existence_l1_lattices,axiom,
? [A] : meet_semilatt_str(A),
file('theBenchmark.p',existence_l1_lattices) ).
fof(existence_l1_orders_2,axiom,
? [A] : rel_str(A),
file('theBenchmark.p',existence_l1_orders_2) ).
fof(existence_l1_pre_topc,axiom,
? [A] : top_str(A),
file('theBenchmark.p',existence_l1_pre_topc) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_lattices,axiom,
? [A] : join_semilatt_str(A),
file('theBenchmark.p',existence_l2_lattices) ).
fof(existence_l3_lattices,axiom,
? [A] : latt_str(A),
file('theBenchmark.p',existence_l3_lattices) ).
fof(existence_m1_connsp_2,axiom,
! [A,B] :
( ( element(B,the_carrier(A))
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ? [C] : point_neighbourhood(C,A,B) ),
file('theBenchmark.p',existence_m1_connsp_2) ).
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_finset_1,axiom,
! [A,B] :
( finite(B)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',fc10_finset_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_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',fc11_finset_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_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',fc12_finset_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_finset_1,axiom,
! [A,B] :
( ( finite(B)
& function(A)
& relation(A) )
=> finite(relation_image(A,B)) ),
file('theBenchmark.p',fc13_finset_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_finset_1,axiom,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
file('theBenchmark.p',fc1_finset_1) ).
fof(fc1_finsub_1,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('theBenchmark.p',fc1_finsub_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_lattice3,axiom,
! [A] :
( strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
file('theBenchmark.p',fc1_lattice3) ).
fof(fc1_orders_2,axiom,
! [A,B] :
( ( relation_of2(B,A,A)
& ~ empty(A) )
=> ( strict_rel_str(rel_str_of(A,B))
& ~ empty_carrier(rel_str_of(A,B)) ) ),
file('theBenchmark.p',fc1_orders_2) ).
fof(fc1_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_ordinal2,axiom,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
file('theBenchmark.p',fc1_ordinal2) ).
fof(fc1_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> ( v5_membered(empty_carrier_subset(A))
& v4_membered(empty_carrier_subset(A))
& v3_membered(empty_carrier_subset(A))
& v2_membered(empty_carrier_subset(A))
& v1_membered(empty_carrier_subset(A))
& empty(empty_carrier_subset(A)) ) ),
file('theBenchmark.p',fc1_pre_topc) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_relat_1) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
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(fc27_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(set_intersection2(A,B)) ),
file('theBenchmark.p',fc27_membered) ).
fof(fc28_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(set_intersection2(B,A)) ),
file('theBenchmark.p',fc28_membered) ).
fof(fc29_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc29_membered) ).
fof(fc2_arytm_3,axiom,
! [A] :
( ( natural(A)
& ordinal(A) )
=> ( natural(succ(A))
& ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc2_arytm_3) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(fc2_lattice2,axiom,
! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ( v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v1_binop_1(the_L_join(A),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A))
& relation(the_L_join(A)) ) ),
file('theBenchmark.p',fc2_lattice2) ).
fof(fc2_lattice3,axiom,
! [A] :
( lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
file('theBenchmark.p',fc2_lattice3) ).
fof(fc2_orders_2,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A) )
=> ( v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A))
& transitive(the_InternalRel(A))
& antisymmetric(the_InternalRel(A))
& reflexive(the_InternalRel(A))
& relation(the_InternalRel(A)) ) ),
file('theBenchmark.p',fc2_orders_2) ).
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_partfun1,axiom,
! [A] :
( transitive(identity_relation(A))
& antisymmetric(identity_relation(A))
& symmetric(identity_relation(A))
& reflexive(identity_relation(A))
& function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_partfun1) ).
fof(fc2_pre_topc,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('theBenchmark.p',fc2_pre_topc) ).
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_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> closed_subset(topstr_closure(A,B),A) ),
file('theBenchmark.p',fc2_tops_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc30_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc30_membered) ).
fof(fc31_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc31_membered) ).
fof(fc32_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc32_membered) ).
fof(fc33_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc33_membered) ).
fof(fc34_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc34_membered) ).
fof(fc35_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v5_membered(set_intersection2(A,B))
& v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc35_membered) ).
fof(fc36_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v5_membered(set_intersection2(B,A))
& v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc36_membered) ).
fof(fc37_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(set_difference(A,B)) ),
file('theBenchmark.p',fc37_membered) ).
fof(fc38_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc38_membered) ).
fof(fc39_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc39_membered) ).
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_lattice2,axiom,
! [A] :
( ( join_semilatt_str(A)
& join_associative(A)
& ~ empty_carrier(A) )
=> ( v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v2_binop_1(the_L_join(A),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A))
& relation(the_L_join(A)) ) ),
file('theBenchmark.p',fc3_lattice2) ).
fof(fc3_lattices,axiom,
! [A,B,C] :
( ( relation_of2(C,cartesian_product2(A,A),A)
& quasi_total(C,cartesian_product2(A,A),A)
& function(C)
& relation_of2(B,cartesian_product2(A,A),A)
& quasi_total(B,cartesian_product2(A,A),A)
& function(B)
& ~ empty(A) )
=> ( strict_latt_str(latt_str_of(A,B,C))
& ~ empty_carrier(latt_str_of(A,B,C)) ) ),
file('theBenchmark.p',fc3_lattices) ).
fof(fc3_orders_2,axiom,
! [A,B] :
( ( relation_of2(B,A,A)
& v1_partfun1(B,A,A)
& transitive(B)
& antisymmetric(B)
& reflexive(B) )
=> ( antisymmetric_relstr(rel_str_of(A,B))
& transitive_relstr(rel_str_of(A,B))
& reflexive_relstr(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) ) ),
file('theBenchmark.p',fc3_orders_2) ).
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_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& closed_subset(B,A)
& top_str(A)
& topological_space(A) )
=> open_subset(subset_complement(the_carrier(A),B),A) ),
file('theBenchmark.p',fc3_tops_1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc40_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc40_membered) ).
fof(fc41_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v5_membered(set_difference(A,B))
& v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc41_membered) ).
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_lattice2,axiom,
! [A] :
( ( meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ( v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v1_binop_1(the_L_meet(A),the_carrier(A))
& quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_meet(A))
& relation(the_L_meet(A)) ) ),
file('theBenchmark.p',fc4_lattice2) ).
fof(fc4_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ( antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A))
& ~ empty_carrier(poset_of_lattice(A)) ) ),
file('theBenchmark.p',fc4_lattice3) ).
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(fc4_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& open_subset(B,A)
& top_str(A)
& topological_space(A) )
=> closed_subset(subset_complement(the_carrier(A),B),A) ),
file('theBenchmark.p',fc4_tops_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_lattice2,axiom,
! [A] :
( ( meet_semilatt_str(A)
& meet_associative(A)
& ~ empty_carrier(A) )
=> ( v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v2_binop_1(the_L_meet(A),the_carrier(A))
& quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_meet(A))
& relation(the_L_meet(A)) ) ),
file('theBenchmark.p',fc5_lattice2) ).
fof(fc5_pre_topc,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> closed_subset(cast_as_carrier_subset(A),A) ),
file('theBenchmark.p',fc5_pre_topc) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_membered,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc6_membered) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc6_tops_1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> open_subset(interior(A,B),A) ),
file('theBenchmark.p',fc6_tops_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_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('theBenchmark.p',fc9_finset_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(fraenkel_a_1_0_filter_1,axiom,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ( in(A,a_1_0_filter_1(B))
<=> ? [C,D] :
( below_refl(B,C,D)
& A = ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
& element(D,the_carrier(B))
& element(C,the_carrier(B)) ) ) ),
file('theBenchmark.p',fraenkel_a_1_0_filter_1) ).
fof(fraenkel_a_2_2_lattice3,axiom,
! [A,B,C] :
( ( latt_str(B)
& ~ empty_carrier(B) )
=> ( in(A,a_2_2_lattice3(B,C))
<=> ? [D] :
( latt_set_smaller(B,D,C)
& A = D
& element(D,the_carrier(B)) ) ) ),
file('theBenchmark.p',fraenkel_a_2_2_lattice3) ).
fof(fraenkel_a_2_3_lattice3,axiom,
! [A,B,C] :
( ( latt_str(B)
& complete_latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ( in(A,a_2_3_lattice3(B,C))
<=> ? [D] :
( latt_set_smaller(B,D,C)
& A = D
& element(D,the_carrier(B)) ) ) ),
file('theBenchmark.p',fraenkel_a_2_3_lattice3) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ! [C,D] :
( rel_str_of(A,B) = rel_str_of(C,D)
=> ( B = D
& A = C ) ) ),
file('theBenchmark.p',free_g1_orders_2) ).
fof(free_g3_lattices,axiom,
! [A,B,C] :
( ( relation_of2(C,cartesian_product2(A,A),A)
& quasi_total(C,cartesian_product2(A,A),A)
& function(C)
& relation_of2(B,cartesian_product2(A,A),A)
& quasi_total(B,cartesian_product2(A,A),A)
& function(B) )
=> ! [D,E,F] :
( latt_str_of(A,B,C) = latt_str_of(D,E,F)
=> ( C = F
& B = E
& A = D ) ) ),
file('theBenchmark.p',free_g3_lattices) ).
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(idempotence_k4_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_union2(A,B,B) = B ),
file('theBenchmark.p',idempotence_k4_subset_1) ).
fof(idempotence_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,B) = B ),
file('theBenchmark.p',idempotence_k5_subset_1) ).
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(l40_tops_1,lemma,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(C,subset_complement(the_carrier(A),B))
<=> ~ in(C,B) ) ) ) ),
file('theBenchmark.p',l40_tops_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_membered,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_membered) ).
fof(rc1_orders_2,axiom,
? [A] :
( strict_rel_str(A)
& rel_str(A) ),
file('theBenchmark.p',rc1_orders_2) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_ordinal2,axiom,
? [A] :
( being_limit_ordinal(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal2) ).
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_tops_1,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ? [B] :
( open_subset(B,A)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc1_tops_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_funct_2,axiom,
! [A] :
? [B] :
( bijective(B,A,A)
& onto(B,A,A)
& quasi_total(B,A,A)
& one_to_one(B)
& function(B)
& relation(B)
& relation_of2(B,A,A) ),
file('theBenchmark.p',rc2_funct_2) ).
fof(rc2_orders_2,axiom,
? [A] :
( antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('theBenchmark.p',rc2_orders_2) ).
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_tex_2,axiom,
! [A] :
? [B] :
( ~ proper_element(B,powerset(A))
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_tex_2) ).
fof(rc2_tops_1,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ? [B] :
( closed_subset(B,A)
& open_subset(B,A)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc2_tops_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_lattices,axiom,
? [A] :
( strict_latt_str(A)
& latt_str(A) ),
file('theBenchmark.p',rc3_lattices) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_partfun1,axiom,
! [A] :
? [B] :
( v1_partfun1(B,A,A)
& transitive(B)
& antisymmetric(B)
& symmetric(B)
& reflexive(B)
& relation(B)
& relation_of2(B,A,A) ),
file('theBenchmark.p',rc3_partfun1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc4_finset_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(rc6_lattices,axiom,
? [A] :
( strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('theBenchmark.p',rc6_lattices) ).
fof(rc6_pre_topc,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ? [B] :
( closed_subset(B,A)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc6_pre_topc) ).
fof(rc7_pre_topc,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ? [B] :
( closed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc7_pre_topc) ).
fof(rc9_lattices,axiom,
? [A] :
( lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('theBenchmark.p',rc9_lattices) ).
fof(redefinition_k10_filter_1,axiom,
! [A,B,C,D] :
( ( element(D,the_carrier(B))
& element(C,the_carrier(A))
& latt_str(B)
& lattice(B)
& ~ empty_carrier(B)
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> k10_filter_1(A,B,C,D) = ordered_pair(C,D) ),
file('theBenchmark.p',redefinition_k10_filter_1) ).
fof(redefinition_k1_domain_1,axiom,
! [A,B,C,D] :
( ( element(D,B)
& element(C,A)
& ~ empty(B)
& ~ empty(A) )
=> ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D) ),
file('theBenchmark.p',redefinition_k1_domain_1) ).
fof(redefinition_k1_pcomps_1,axiom,
! [A] : k1_pcomps_1(A) = powerset(A),
file('theBenchmark.p',redefinition_k1_pcomps_1) ).
fof(redefinition_k2_binop_1,axiom,
! [A,B,C,D,E,F] :
( ( element(F,B)
& element(E,A)
& relation_of2(D,cartesian_product2(A,B),C)
& quasi_total(D,cartesian_product2(A,B),C)
& function(D)
& ~ empty(B)
& ~ empty(A) )
=> apply_binary_as_element(A,B,C,D,E,F) = apply_binary(D,E,F) ),
file('theBenchmark.p',redefinition_k2_binop_1) ).
fof(redefinition_k2_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> k2_lattice3(A) = relation_of_lattice(A) ),
file('theBenchmark.p',redefinition_k2_lattice3) ).
fof(redefinition_k3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join(A,B,C) ),
file('theBenchmark.p',redefinition_k3_lattices) ).
fof(redefinition_k4_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> meet_commut(A,B,C) = meet(A,B,C) ),
file('theBenchmark.p',redefinition_k4_lattices) ).
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_k4_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_union2(A,B,C) = set_union2(B,C) ),
file('theBenchmark.p',redefinition_k4_subset_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_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = set_intersection2(B,C) ),
file('theBenchmark.p',redefinition_k5_subset_1) ).
fof(redefinition_k6_partfun1,axiom,
! [A] : identity_as_relation_of(A) = identity_relation(A),
file('theBenchmark.p',redefinition_k6_partfun1) ).
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_k8_funct_2,axiom,
! [A,B,C,D] :
( ( element(D,A)
& relation_of2(C,A,B)
& quasi_total(C,A,B)
& function(C)
& ~ empty(A) )
=> apply_as_element(A,B,C,D) = apply(C,D) ),
file('theBenchmark.p',redefinition_k8_funct_2) ).
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(redefinition_r3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& latt_str(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ( below_refl(A,B,C)
<=> below(A,B,C) ) ),
file('theBenchmark.p',redefinition_r3_lattices) ).
fof(redefinition_r3_orders_2,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& rel_str(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> ( related_reflexive(A,B,C)
<=> related(A,B,C) ) ),
file('theBenchmark.p',redefinition_r3_orders_2) ).
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(reflexivity_r3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& latt_str(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> below_refl(A,B,B) ),
file('theBenchmark.p',reflexivity_r3_lattices) ).
fof(reflexivity_r3_orders_2,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& rel_str(A)
& reflexive_relstr(A)
& ~ empty_carrier(A) )
=> related_reflexive(A,B,B) ),
file('theBenchmark.p',reflexivity_r3_orders_2) ).
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_funct_1__e4_7_1__tops_2__1,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ( ! [C,D,E] :
( ( ! [G] :
( element(G,powerset(the_carrier(A)))
=> ( G = C
=> E = subset_complement(the_carrier(A),G) ) )
& in(C,complements_of_subsets(the_carrier(A),B))
& ! [F] :
( element(F,powerset(the_carrier(A)))
=> ( F = C
=> D = subset_complement(the_carrier(A),F) ) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
=> D = E )
=> ? [C] :
( ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = D
=> E = subset_complement(the_carrier(A),H) ) )
& in(D,complements_of_subsets(the_carrier(A),B))
& in(D,complements_of_subsets(the_carrier(A),B)) ) )
& function(C)
& relation(C) ) ) ),
file('theBenchmark.p',s1_funct_1__e4_7_1__tops_2__1) ).
fof(s1_funct_1__e4_7_2__tops_2__1,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ( ! [C,D,E] :
( ( ! [G] :
( element(G,powerset(the_carrier(A)))
=> ( G = C
=> E = subset_complement(the_carrier(A),G) ) )
& in(C,B)
& ! [F] :
( element(F,powerset(the_carrier(A)))
=> ( F = C
=> D = subset_complement(the_carrier(A),F) ) )
& in(C,B) )
=> D = E )
=> ? [C] :
( ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = D
=> E = subset_complement(the_carrier(A),H) ) )
& in(D,B)
& in(D,B) ) )
& function(C)
& relation(C) ) ) ),
file('theBenchmark.p',s1_funct_1__e4_7_2__tops_2__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_ordinal2__e18_27__finset_1,lemma,
( ( ! [D] :
( ordinal(D)
=> ( ( ! [K] :
( ordinal(K)
=> ( in(K,D)
=> ( in(K,omega)
=> ! [L] :
( element(L,powerset(powerset(K)))
=> ~ ( ! [M] :
~ ( ! [N] :
( ( subset(M,N)
& in(N,L) )
=> N = M )
& in(M,L) )
& L != empty_set ) ) ) ) )
& being_limit_ordinal(D) )
=> ( ( in(D,omega)
=> ! [O] :
( element(O,powerset(powerset(D)))
=> ~ ( ! [P] :
~ ( ! [Q] :
( ( subset(P,Q)
& in(Q,O) )
=> Q = P )
& in(P,O) )
& O != empty_set ) ) )
| D = empty_set ) ) )
& ! [D] :
( ordinal(D)
=> ( ( in(D,omega)
=> ! [E] :
( element(E,powerset(powerset(D)))
=> ~ ( ! [F] :
~ ( ! [G] :
( ( subset(F,G)
& in(G,E) )
=> G = F )
& in(F,E) )
& E != empty_set ) ) )
=> ( in(succ(D),omega)
=> ! [H] :
( element(H,powerset(powerset(succ(D))))
=> ~ ( ! [I] :
~ ( ! [J] :
( ( subset(I,J)
& in(J,H) )
=> J = I )
& in(I,H) )
& H != empty_set ) ) ) ) )
& ( in(empty_set,omega)
=> ! [A] :
( element(A,powerset(powerset(empty_set)))
=> ~ ( ! [B] :
~ ( ! [C] :
( ( subset(B,C)
& in(C,A) )
=> C = B )
& in(B,A) )
& A != empty_set ) ) ) )
=> ! [D] :
( ordinal(D)
=> ( in(D,omega)
=> ! [R] :
( element(R,powerset(powerset(D)))
=> ~ ( ! [S] :
~ ( ! [T] :
( ( subset(S,T)
& in(T,R) )
=> T = S )
& in(S,R) )
& R != empty_set ) ) ) ) ),
file('theBenchmark.p',s1_ordinal2__e18_27__finset_1) ).
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__e18_27__finset_1__1,axiom,
! [A] :
( ordinal(A)
=> ( ! [B,C,D] :
( ( ? [I] :
( ( in(I,omega)
=> ! [J] :
( element(J,powerset(powerset(I)))
=> ~ ( ! [K] :
~ ( ! [L] :
( ( subset(K,L)
& in(L,J) )
=> L = K )
& in(K,J) )
& J != empty_set ) ) )
& D = I
& ordinal(I) )
& B = D
& ? [E] :
( ( in(E,omega)
=> ! [F] :
( element(F,powerset(powerset(E)))
=> ~ ( ! [G] :
~ ( ! [H] :
( ( subset(G,H)
& in(H,F) )
=> H = G )
& in(G,F) )
& F != empty_set ) ) )
& C = E
& ordinal(E) )
& B = C )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ? [M] :
( ( in(M,omega)
=> ! [N] :
( element(N,powerset(powerset(M)))
=> ~ ( ! [O] :
~ ( ! [P] :
( ( subset(O,P)
& in(P,N) )
=> P = O )
& in(O,N) )
& N != empty_set ) ) )
& C = M
& ordinal(M) )
& D = C
& in(D,succ(A)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e18_27__finset_1__1) ).
fof(s1_tarski__e1_40__pre_topc__1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> ( ! [C,D,E] :
( ( ? [G] :
( subset(B,E)
& closed_subset(G,A)
& G = E
& element(G,powerset(the_carrier(A))) )
& C = E
& ? [F] :
( subset(B,D)
& closed_subset(F,A)
& F = D
& element(F,powerset(the_carrier(A))) )
& C = D )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ? [H] :
( subset(B,D)
& closed_subset(H,A)
& H = D
& element(H,powerset(the_carrier(A))) )
& E = D
& in(E,powerset(the_carrier(A))) ) ) ) ),
file('theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
fof(s1_tarski__e2_37_1_1__pre_topc__1,axiom,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& top_str(A)
& topological_space(A) )
=> ( ! [C,D,E] :
( ( in(set_difference(cast_as_carrier_subset(A),E),B)
& C = E
& in(set_difference(cast_as_carrier_subset(A),D),B)
& C = D )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( in(set_difference(cast_as_carrier_subset(A),D),B)
& E = D
& in(E,powerset(the_carrier(A))) ) ) ) ),
file('theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).
fof(s1_tarski__e4_27_3_1__finset_1__1,axiom,
! [A,B] :
( ( element(B,powerset(powerset(succ(A))))
& ordinal(A) )
=> ( ! [C,D,E] :
( ( ? [G] :
( E = set_difference(G,singleton(A))
& in(G,B) )
& C = E
& ? [F] :
( D = set_difference(F,singleton(A))
& in(F,B) )
& C = D )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ? [H] :
( D = set_difference(H,singleton(A))
& in(H,B) )
& E = D
& in(E,powerset(A)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e4_27_3_1__finset_1__1) ).
fof(s1_tarski__e4_7_1__tops_2__1,axiom,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ( ! [C,D,E] :
( ( ! [G] :
( element(G,powerset(the_carrier(A)))
=> ( G = C
=> E = subset_complement(the_carrier(A),G) ) )
& in(C,complements_of_subsets(the_carrier(A),B))
& ! [F] :
( element(F,powerset(the_carrier(A)))
=> ( F = C
=> D = subset_complement(the_carrier(A),F) ) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = E
=> D = subset_complement(the_carrier(A),H) ) )
& in(E,complements_of_subsets(the_carrier(A),B))
& in(E,complements_of_subsets(the_carrier(A),B)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e4_7_1__tops_2__1) ).
fof(s1_tarski__e4_7_1__tops_2__2,axiom,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ! [C] :
( ! [D,E,F] :
( ( ? [J,K] :
( ! [L] :
( element(L,powerset(the_carrier(A)))
=> ( L = J
=> K = subset_complement(the_carrier(A),L) ) )
& in(J,complements_of_subsets(the_carrier(A),B))
& ordered_pair(J,K) = F )
& D = F
& ? [G,H] :
( ! [I] :
( element(I,powerset(the_carrier(A)))
=> ( I = G
=> H = subset_complement(the_carrier(A),I) ) )
& in(G,complements_of_subsets(the_carrier(A),B))
& ordered_pair(G,H) = E )
& D = E )
=> E = F )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( ? [M,N] :
( ! [O] :
( element(O,powerset(the_carrier(A)))
=> ( O = M
=> N = subset_complement(the_carrier(A),O) ) )
& in(M,complements_of_subsets(the_carrier(A),B))
& ordered_pair(M,N) = E )
& F = E
& in(F,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e4_7_1__tops_2__2) ).
fof(s1_tarski__e4_7_2__tops_2__1,axiom,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ( ! [C,D,E] :
( ( ! [G] :
( element(G,powerset(the_carrier(A)))
=> ( G = C
=> E = subset_complement(the_carrier(A),G) ) )
& in(C,B)
& ! [F] :
( element(F,powerset(the_carrier(A)))
=> ( F = C
=> D = subset_complement(the_carrier(A),F) ) )
& in(C,B) )
=> D = E )
=> ? [C] :
! [D] :
( in(D,C)
<=> ? [E] :
( ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = E
=> D = subset_complement(the_carrier(A),H) ) )
& in(E,B)
& in(E,B) ) ) ) ),
file('theBenchmark.p',s1_tarski__e4_7_2__tops_2__1) ).
fof(s1_tarski__e4_7_2__tops_2__2,axiom,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ! [C] :
( ! [D,E,F] :
( ( ? [J,K] :
( ! [L] :
( element(L,powerset(the_carrier(A)))
=> ( L = J
=> K = subset_complement(the_carrier(A),L) ) )
& in(J,B)
& ordered_pair(J,K) = F )
& D = F
& ? [G,H] :
( ! [I] :
( element(I,powerset(the_carrier(A)))
=> ( I = G
=> H = subset_complement(the_carrier(A),I) ) )
& in(G,B)
& ordered_pair(G,H) = E )
& D = E )
=> E = F )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( ? [M,N] :
( ! [O] :
( element(O,powerset(the_carrier(A)))
=> ( O = M
=> N = subset_complement(the_carrier(A),O) ) )
& in(M,B)
& ordered_pair(M,N) = E )
& F = E
& in(F,cartesian_product2(B,C)) ) ) ) ),
file('theBenchmark.p',s1_tarski__e4_7_2__tops_2__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__e6_27__finset_1__1,axiom,
! [A,B,C] :
( ( function(C)
& relation(C)
& element(B,powerset(powerset(A))) )
=> ( ! [D,E,F] :
( ( in(relation_image(C,F),B)
& D = F
& in(relation_image(C,E),B)
& D = E )
=> E = F )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( in(relation_image(C,E),B)
& F = E
& in(F,powerset(relation_dom(C))) ) ) ) ),
file('theBenchmark.p',s1_tarski__e6_27__finset_1__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__e18_27__finset_1__1,lemma,
! [A] :
( ordinal(A)
=> ? [B] :
! [C] :
( in(C,B)
<=> ( ? [D] :
( ( in(D,omega)
=> ! [E] :
( element(E,powerset(powerset(D)))
=> ~ ( ! [F] :
~ ( ! [G] :
( ( subset(F,G)
& in(G,E) )
=> G = F )
& in(F,E) )
& E != empty_set ) ) )
& C = D
& ordinal(D) )
& in(C,succ(A)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e18_27__finset_1__1) ).
fof(s1_xboole_0__e1_40__pre_topc__1,lemma,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) )
& in(D,powerset(the_carrier(A))) ) ) ),
file('theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(s1_xboole_0__e2_37_1_1__pre_topc__1,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& top_str(A)
& topological_space(A) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(set_difference(cast_as_carrier_subset(A),D),B)
& in(D,powerset(the_carrier(A))) ) ) ),
file('theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
fof(s1_xboole_0__e4_27_3_1__finset_1,lemma,
! [A,B] :
( ( element(B,powerset(powerset(succ(A))))
& ordinal(A) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( ? [E] :
( D = set_difference(E,singleton(A))
& in(E,B) )
& in(D,powerset(A)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e4_27_3_1__finset_1) ).
fof(s1_xboole_0__e4_7_1__tops_2__1,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ! [C] :
? [D] :
! [E] :
( in(E,D)
<=> ( ? [F,G] :
( ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = F
=> G = subset_complement(the_carrier(A),H) ) )
& in(F,complements_of_subsets(the_carrier(A),B))
& ordered_pair(F,G) = E )
& in(E,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e4_7_1__tops_2__1) ).
fof(s1_xboole_0__e4_7_2__tops_2__1,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ! [C] :
? [D] :
! [E] :
( in(E,D)
<=> ( ? [F,G] :
( ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = F
=> G = subset_complement(the_carrier(A),H) ) )
& in(F,B)
& ordered_pair(F,G) = E )
& in(E,cartesian_product2(B,C)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e4_7_2__tops_2__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__e6_27__finset_1,lemma,
! [A,B,C] :
( ( function(C)
& relation(C)
& element(B,powerset(powerset(A))) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ( in(relation_image(C,E),B)
& in(E,powerset(relation_dom(C))) ) ) ),
file('theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(s1_xboole_0__e8_6__wellord2__1,lemma,
! [A,B] :
( ordinal(B)
=> ? [C] :
! [D] :
( in(D,C)
<=> ( ? [E] :
( in(E,A)
& D = E
& ordinal(E) )
& in(D,succ(B)) ) ) ),
file('theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(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(s2_funct_1__e4_7_1__tops_2,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ( ( ! [C] :
~ ( ! [D] :
~ ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = C
=> D = subset_complement(the_carrier(A),H) ) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
& ! [C,D,E] :
( ( ! [G] :
( element(G,powerset(the_carrier(A)))
=> ( G = C
=> E = subset_complement(the_carrier(A),G) ) )
& ! [F] :
( element(F,powerset(the_carrier(A)))
=> ( F = C
=> D = subset_complement(the_carrier(A),F) ) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
=> D = E ) )
=> ? [C] :
( ! [D] :
( in(D,complements_of_subsets(the_carrier(A),B))
=> ! [I] :
( element(I,powerset(the_carrier(A)))
=> ( I = D
=> apply(C,D) = subset_complement(the_carrier(A),I) ) ) )
& relation_dom(C) = complements_of_subsets(the_carrier(A),B)
& function(C)
& relation(C) ) ) ),
file('theBenchmark.p',s2_funct_1__e4_7_1__tops_2) ).
fof(s2_funct_1__e4_7_2__tops_2,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& one_sorted_str(A) )
=> ( ( ! [C] :
~ ( ! [D] :
~ ! [H] :
( element(H,powerset(the_carrier(A)))
=> ( H = C
=> D = subset_complement(the_carrier(A),H) ) )
& in(C,B) )
& ! [C,D,E] :
( ( ! [G] :
( element(G,powerset(the_carrier(A)))
=> ( G = C
=> E = subset_complement(the_carrier(A),G) ) )
& ! [F] :
( element(F,powerset(the_carrier(A)))
=> ( F = C
=> D = subset_complement(the_carrier(A),F) ) )
& in(C,B) )
=> D = E ) )
=> ? [C] :
( ! [D] :
( in(D,B)
=> ! [I] :
( element(I,powerset(the_carrier(A)))
=> ( I = D
=> apply(C,D) = subset_complement(the_carrier(A),I) ) ) )
& relation_dom(C) = B
& function(C)
& relation(C) ) ) ),
file('theBenchmark.p',s2_funct_1__e4_7_2__tops_2) ).
fof(s2_ordinal1__e18_27__finset_1__1,lemma,
( ! [A] :
( ordinal(A)
=> ( ! [B] :
( ordinal(B)
=> ( in(B,A)
=> ( in(B,omega)
=> ! [C] :
( element(C,powerset(powerset(B)))
=> ~ ( ! [D] :
~ ( ! [E] :
( ( subset(D,E)
& in(E,C) )
=> E = D )
& in(D,C) )
& C != empty_set ) ) ) ) )
=> ( in(A,omega)
=> ! [F] :
( element(F,powerset(powerset(A)))
=> ~ ( ! [G] :
~ ( ! [H] :
( ( subset(G,H)
& in(H,F) )
=> H = G )
& in(G,F) )
& F != empty_set ) ) ) ) )
=> ! [A] :
( ordinal(A)
=> ( in(A,omega)
=> ! [I] :
( element(I,powerset(powerset(A)))
=> ~ ( ! [J] :
~ ( ! [K] :
( ( subset(J,K)
& in(K,I) )
=> K = J )
& in(J,I) )
& I != empty_set ) ) ) ) ),
file('theBenchmark.p',s2_ordinal1__e18_27__finset_1__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(s3_subset_1__e1_40__pre_topc,lemma,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> ? [C] :
( ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) ) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ),
file('theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(s3_subset_1__e2_37_1_1__pre_topc,lemma,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& top_str(A)
& topological_space(A) )
=> ? [C] :
( ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> in(set_difference(cast_as_carrier_subset(A),D),B) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ),
file('theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
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_tops_2,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
& ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ) ),
file('theBenchmark.p',t10_tops_2) ).
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(t11_tops_2,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ),
file('theBenchmark.p',t11_tops_2) ).
fof(t12_pre_topc,lemma,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',t12_pre_topc) ).
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_tops_2,lemma,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ),
file('theBenchmark.p',t12_tops_2) ).
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_compts_1,lemma,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ( compact_top_space(A)
<=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( meet_of_subsets(the_carrier(A),B) = empty_set
& closed_subsets(B,A)
& centered(B) ) ) ) ),
file('theBenchmark.p',t13_compts_1) ).
fof(t13_finset_1,lemma,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t13_tops_2,lemma,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( finite(complements_of_subsets(the_carrier(A),B))
<=> finite(B) ) ) ),
file('theBenchmark.p',t13_tops_2) ).
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(t15_finset_1,lemma,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',t15_finset_1) ).
fof(t15_pre_topc,lemma,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
file('theBenchmark.p',t15_pre_topc) ).
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_tops_2,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( closed_subsets(B,A)
<=> open_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t16_tops_2) ).
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_finset_1,lemma,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( finite(A)
=> finite(relation_image(B,A)) ) ),
file('theBenchmark.p',t17_finset_1) ).
fof(t17_pre_topc,lemma,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
file('theBenchmark.p',t17_pre_topc) ).
fof(t17_tops_2,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( open_subsets(B,A)
<=> closed_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t17_tops_2) ).
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_finset_1,lemma,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(powerset(A)))
=> ~ ( ! [C] :
~ ( ! [D] :
( ( subset(C,D)
& in(D,B) )
=> D = C )
& in(C,B) )
& B != empty_set ) ) ),
file('theBenchmark.p',t18_finset_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_lattice3,lemma,
! [A,B] :
( element(B,the_carrier(boole_lattice(A)))
=> ! [C] :
( element(C,the_carrier(boole_lattice(A)))
=> ( meet(boole_lattice(A),B,C) = set_intersection2(B,C)
& join(boole_lattice(A),B,C) = set_union2(B,C) ) ) ),
file('theBenchmark.p',t1_lattice3) ).
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_pre_topc,lemma,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) ),
file('theBenchmark.p',t22_pre_topc) ).
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_lattices,lemma,
! [A] :
( ( latt_str(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> below(A,meet_commut(A,B,C),B) ) ) ),
file('theBenchmark.p',t23_lattices) ).
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_orders_2,lemma,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( related(A,C,B)
& related(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t25_orders_2) ).
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_finset_1,lemma,
! [A] :
( ( function(A)
& relation(A) )
=> ( finite(relation_dom(A))
=> finite(relation_rng(A)) ) ),
file('theBenchmark.p',t26_finset_1) ).
fof(t26_lattices,lemma,
! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( below(A,C,B)
& below(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t26_lattices) ).
fof(t26_orders_2,lemma,
! [A] :
( ( rel_str(A)
& transitive_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ( ( related(A,C,D)
& related(A,B,C) )
=> related(A,B,D) ) ) ) ) ),
file('theBenchmark.p',t26_orders_2) ).
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_lattice3,lemma,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(B))
=> ( latt_set_smaller(B,C,A)
<=> relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) ) ) ),
file('theBenchmark.p',t28_lattice3) ).
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(t29_lattice3,lemma,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
file('theBenchmark.p',t29_lattice3) ).
fof(t29_tops_1,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t29_tops_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_lattice3,lemma,
! [A,B] :
( element(B,the_carrier(boole_lattice(A)))
=> ! [C] :
( element(C,the_carrier(boole_lattice(A)))
=> ( below(boole_lattice(A),B,C)
<=> subset(B,C) ) ) ),
file('theBenchmark.p',t2_lattice3) ).
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_lattice3,lemma,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(B))
=> ( latt_element_smaller(B,C,A)
<=> relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) ) ) ),
file('theBenchmark.p',t30_lattice3) ).
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(t30_tops_1,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t30_tops_1) ).
fof(t31_lattice3,lemma,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_set_smaller(poset_of_lattice(B),A,C)
<=> latt_element_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
file('theBenchmark.p',t31_lattice3) ).
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_filter_1,lemma,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A))
<=> below_refl(A,B,C) ) ) ) ),
file('theBenchmark.p',t32_filter_1) ).
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(t34_lattice3,lemma,
! [A] :
( ( latt_str(A)
& complete_latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( B = meet_of_latt_set(A,C)
<=> ( ! [D] :
( element(D,the_carrier(A))
=> ( latt_set_smaller(A,D,C)
=> below_refl(A,D,B) ) )
& latt_set_smaller(A,B,C) ) ) ) ),
file('theBenchmark.p',t34_lattice3) ).
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_lattice3,lemma,
! [A] :
( bottom_of_semilattstr(boole_lattice(A)) = empty_set
& lower_bounded_semilattstr(boole_lattice(A)) ),
file('theBenchmark.p',t3_lattice3) ).
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_pre_topc,lemma,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( in(C,B)
=> closed_subset(C,A) ) )
=> closed_subset(meet_of_subsets(the_carrier(A),B),A) ) ) ),
file('theBenchmark.p',t44_pre_topc) ).
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(t44_tops_1,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(interior(A,B),B) ) ),
file('theBenchmark.p',t44_tops_1) ).
fof(t45_pre_topc,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( in(C,the_carrier(A))
=> ( in(C,topstr_closure(A,B))
<=> ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( ( subset(B,D)
& closed_subset(D,A) )
=> in(C,D) ) ) ) ) ) ),
file('theBenchmark.p',t45_pre_topc) ).
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_pre_topc,lemma,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ? [C] :
( topstr_closure(A,B) = meet_of_subsets(the_carrier(A),C)
& ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> ( subset(B,D)
& closed_subset(D,A) ) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ) ),
file('theBenchmark.p',t46_pre_topc) ).
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_pre_topc,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset(B,topstr_closure(A,B)) ) ),
file('theBenchmark.p',t48_pre_topc) ).
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_lattice3,lemma,
! [A] :
( ( latt_str(A)
& complete_latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ( bottom_of_semilattstr(A) = join_of_latt_set(A,empty_set)
& latt_str(A)
& lower_bounded_semilattstr(A)
& lattice(A)
& ~ empty_carrier(A) ) ),
file('theBenchmark.p',t50_lattice3) ).
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(t51_tops_1,lemma,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
file('theBenchmark.p',t51_tops_1) ).
fof(t52_pre_topc,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( ( ( topstr_closure(A,B) = B
& topological_space(A) )
=> closed_subset(B,A) )
& ( closed_subset(B,A)
=> topstr_closure(A,B) = B ) ) ) ),
file('theBenchmark.p',t52_pre_topc) ).
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(t55_tops_1,lemma,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( top_str(B)
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ! [D] :
( element(D,powerset(the_carrier(B)))
=> ( ( interior(A,C) = C
=> open_subset(C,A) )
& ( open_subset(D,B)
=> interior(B,D) = D ) ) ) ) ) ),
file('theBenchmark.p',t55_tops_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_connsp_2,lemma,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( in(C,B)
& open_subset(B,A) )
=> point_neighbourhood(B,A,C) ) ) ) ),
file('theBenchmark.p',t5_connsp_2) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_tex_2,lemma,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
file('theBenchmark.p',t5_tex_2) ).
fof(t5_tops_2,lemma,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( B = empty_set
& is_a_cover_of_carrier(A,B) ) ) ),
file('theBenchmark.p',t5_tops_2) ).
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_yellow_0,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('theBenchmark.p',t6_yellow_0) ).
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_lattice3,lemma,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below_refl(A,B,C)
<=> related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C)) ) ) ) ),
file('theBenchmark.p',t7_lattice3) ).
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(t91_tmap_1,lemma,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B ) ),
file('theBenchmark.p',t91_tmap_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] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2]) ).
fof(f_1_2,plain,
! [U_0] :
( U_0 = rel_str_of(the_carrier(U_0),the_InternalRel(U_0))
| ~ strict_rel_str(U_0)
| ~ rel_str(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_0] :
( U_0 = rel_str_of(the_carrier(U_0),the_InternalRel(U_0))
| ~ strict_rel_str(U_0)
| ~ rel_str(U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( U_0 = rel_str_of(the_carrier(U_0),the_InternalRel(U_0))
| ~ strict_rel_str(U_0)
| ~ rel_str(U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A] :
( A = latt_str_of(the_carrier(A),the_L_join(A),the_L_meet(A))
| ~ strict_latt_str(A)
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[abstractness_v3_lattices]) ).
fof(f_2_2,plain,
! [U_1] :
( U_1 = latt_str_of(the_carrier(U_1),the_L_join(U_1),the_L_meet(U_1))
| ~ strict_latt_str(U_1)
| ~ latt_str(U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_1] :
( U_1 = latt_str_of(the_carrier(U_1),the_L_join(U_1),the_L_meet(U_1))
| ~ strict_latt_str(U_1)
| ~ latt_str(U_1) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( U_1 = latt_str_of(the_carrier(U_1),the_L_join(U_1),the_L_meet(U_1))
| ~ strict_latt_str(U_1)
| ~ latt_str(U_1) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_3_2,plain,
! [U_3,U_2] :
( ~ in(U_2,U_3)
| ~ in(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_2,U_3] :
( ~ in(U_2,U_3)
| ~ in(U_3,U_2) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( ~ in(U_2,U_3)
| ~ in(U_3,U_2) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_4_2,plain,
! [U_5,U_4] :
( ~ proper_subset(U_4,U_5)
| ~ proper_subset(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_4] :
( ~ proper_subset(U_4,U_5)
| ~ proper_subset(U_5,U_4) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ proper_subset(U_4,U_5)
| ~ proper_subset(U_5,U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ! [B] :
( v1_xcmplx_0(B)
| ~ element(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_5_2,plain,
! [U_7] :
( ! [U_6] :
( v1_xcmplx_0(U_6)
| ~ element(U_6,U_7) )
| ~ v1_membered(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_7,U_6] :
( v1_xcmplx_0(U_6)
| ~ element(U_6,U_7)
| ~ v1_membered(U_7) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( v1_xcmplx_0(U_6)
| ~ element(U_6,U_7)
| ~ v1_membered(U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( ! [B] :
( ( v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc11_membered]) ).
fof(f_6_2,plain,
! [U_9] :
( ! [U_8] :
( ( v1_xreal_0(U_8)
& v1_xcmplx_0(U_8) )
| ~ element(U_8,U_9) )
| ~ v2_membered(U_9) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_8] :
( v1_xreal_0(U_8)
| ~ sP0(U_8) )
& ! [U_8] :
( v1_xcmplx_0(U_8)
| ~ sP0(U_8) )
& ! [U_9,U_8] :
( sP0(U_8)
| ~ element(U_8,U_9)
| ~ v2_membered(U_9) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP0(U_8)
| ~ element(U_8,U_9)
| ~ v2_membered(U_9) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( v1_xcmplx_0(U_8)
| ~ sP0(U_8) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( v1_xreal_0(U_8)
| ~ sP0(U_8) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc12_membered]) ).
fof(f_7_2,plain,
! [U_11] :
( ! [U_10] :
( ( v1_rat_1(U_10)
& v1_xreal_0(U_10)
& v1_xcmplx_0(U_10) )
| ~ element(U_10,U_11) )
| ~ v3_membered(U_11) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_10] :
( v1_rat_1(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( v1_xreal_0(U_10)
| ~ sP1(U_10) )
& ! [U_10] :
( v1_xcmplx_0(U_10)
| ~ sP1(U_10) )
& ! [U_10,U_11] :
( sP1(U_10)
| ~ element(U_10,U_11)
| ~ v3_membered(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP1(U_10)
| ~ element(U_10,U_11)
| ~ v3_membered(U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( v1_xcmplx_0(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( v1_xreal_0(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( v1_rat_1(U_10)
| ~ sP1(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc13_membered]) ).
fof(f_8_2,plain,
! [U_13] :
( ! [U_12] :
( ( v1_rat_1(U_12)
& v1_int_1(U_12)
& v1_xreal_0(U_12)
& v1_xcmplx_0(U_12) )
| ~ element(U_12,U_13) )
| ~ v4_membered(U_13) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_12] :
( v1_rat_1(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( v1_int_1(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( v1_xreal_0(U_12)
| ~ sP2(U_12) )
& ! [U_12] :
( v1_xcmplx_0(U_12)
| ~ sP2(U_12) )
& ! [U_12,U_13] :
( sP2(U_12)
| ~ element(U_12,U_13)
| ~ v4_membered(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP2(U_12)
| ~ element(U_12,U_13)
| ~ v4_membered(U_13) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( v1_xcmplx_0(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( v1_xreal_0(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( v1_int_1(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_8,plain,
( v1_rat_1(U_12)
| ~ sP2(U_12) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& natural(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc14_membered]) ).
fof(f_9_2,plain,
! [U_15] :
( ! [U_14] :
( ( v1_rat_1(U_14)
& v1_int_1(U_14)
& v1_xreal_0(U_14)
& natural(U_14)
& v1_xcmplx_0(U_14) )
| ~ element(U_14,U_15) )
| ~ v5_membered(U_15) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_14] :
( v1_rat_1(U_14)
| ~ sP3(U_14) )
& ! [U_14] :
( v1_int_1(U_14)
| ~ sP3(U_14) )
& ! [U_14] :
( v1_xreal_0(U_14)
| ~ sP3(U_14) )
& ! [U_14] :
( natural(U_14)
| ~ sP3(U_14) )
& ! [U_14] :
( v1_xcmplx_0(U_14)
| ~ sP3(U_14) )
& ! [U_14,U_15] :
( sP3(U_14)
| ~ element(U_14,U_15)
| ~ v5_membered(U_15) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP3(U_14)
| ~ element(U_14,U_15)
| ~ v5_membered(U_15) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( v1_xcmplx_0(U_14)
| ~ sP3(U_14) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( natural(U_14)
| ~ sP3(U_14) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( v1_xreal_0(U_14)
| ~ sP3(U_14) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_8,plain,
( v1_int_1(U_14)
| ~ sP3(U_14) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_9,plain,
( v1_rat_1(U_14)
| ~ sP3(U_14) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] :
( ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc15_membered]) ).
fof(f_10_2,plain,
! [U_16] :
( ( v5_membered(U_16)
& v4_membered(U_16)
& v3_membered(U_16)
& v2_membered(U_16)
& v1_membered(U_16) )
| ~ empty(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_16] :
( v5_membered(U_16)
| ~ sP4(U_16) )
& ! [U_16] :
( v4_membered(U_16)
| ~ sP4(U_16) )
& ! [U_16] :
( v3_membered(U_16)
| ~ sP4(U_16) )
& ! [U_16] :
( v2_membered(U_16)
| ~ sP4(U_16) )
& ! [U_16] :
( v1_membered(U_16)
| ~ sP4(U_16) )
& ! [U_16] :
( sP4(U_16)
| ~ empty(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_10_2]) ).
cnf(f_10_4,plain,
( sP4(U_16)
| ~ empty(U_16) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( v1_membered(U_16)
| ~ sP4(U_16) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( v2_membered(U_16)
| ~ sP4(U_16) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( v3_membered(U_16)
| ~ sP4(U_16) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_8,plain,
( v4_membered(U_16)
| ~ sP4(U_16) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_9,plain,
( v5_membered(U_16)
| ~ sP4(U_16) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ element(B,powerset(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_11_2,plain,
! [U_18] :
( ! [U_17] :
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18)) )
| ~ v1_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_17,U_18] :
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v1_membered(U_18) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v1_membered(U_18) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( ! [B] :
( ( v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc17_membered]) ).
fof(f_12_2,plain,
! [U_20] :
( ! [U_19] :
( ( v2_membered(U_19)
& v1_membered(U_19) )
| ~ element(U_19,powerset(U_20)) )
| ~ v2_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_19] :
( v2_membered(U_19)
| ~ sP5(U_19) )
& ! [U_19] :
( v1_membered(U_19)
| ~ sP5(U_19) )
& ! [U_20,U_19] :
( sP5(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v2_membered(U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP5(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v2_membered(U_20) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( v1_membered(U_19)
| ~ sP5(U_19) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( v2_membered(U_19)
| ~ sP5(U_19) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
( ! [B] :
( ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc18_membered]) ).
fof(f_13_2,plain,
! [U_22] :
( ! [U_21] :
( ( v3_membered(U_21)
& v2_membered(U_21)
& v1_membered(U_21) )
| ~ element(U_21,powerset(U_22)) )
| ~ v3_membered(U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_21] :
( v3_membered(U_21)
| ~ sP6(U_21) )
& ! [U_21] :
( v2_membered(U_21)
| ~ sP6(U_21) )
& ! [U_21] :
( v1_membered(U_21)
| ~ sP6(U_21) )
& ! [U_21,U_22] :
( sP6(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v3_membered(U_22) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP6(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v3_membered(U_22) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( v1_membered(U_21)
| ~ sP6(U_21) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( v2_membered(U_21)
| ~ sP6(U_21) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
( v3_membered(U_21)
| ~ sP6(U_21) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
( ! [B] :
( ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc19_membered]) ).
fof(f_14_2,plain,
! [U_24] :
( ! [U_23] :
( ( v4_membered(U_23)
& v3_membered(U_23)
& v2_membered(U_23)
& v1_membered(U_23) )
| ~ element(U_23,powerset(U_24)) )
| ~ v4_membered(U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_23] :
( v4_membered(U_23)
| ~ sP7(U_23) )
& ! [U_23] :
( v3_membered(U_23)
| ~ sP7(U_23) )
& ! [U_23] :
( v2_membered(U_23)
| ~ sP7(U_23) )
& ! [U_23] :
( v1_membered(U_23)
| ~ sP7(U_23) )
& ! [U_24,U_23] :
( sP7(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_14_2]) ).
cnf(f_14_4,plain,
( sP7(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( v1_membered(U_23)
| ~ sP7(U_23) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( v2_membered(U_23)
| ~ sP7(U_23) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_7,plain,
( v3_membered(U_23)
| ~ sP7(U_23) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_8,plain,
( v4_membered(U_23)
| ~ sP7(U_23) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_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_15_2,plain,
! [U_26] :
( ! [U_25] :
( ( ordinal(U_25)
& epsilon_connected(U_25)
& epsilon_transitive(U_25) )
| ~ element(U_25,U_26) )
| ~ ordinal(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_25] :
( ordinal(U_25)
| ~ sP8(U_25) )
& ! [U_25] :
( epsilon_connected(U_25)
| ~ sP8(U_25) )
& ! [U_25] :
( epsilon_transitive(U_25)
| ~ sP8(U_25) )
& ! [U_26,U_25] :
( sP8(U_25)
| ~ element(U_25,U_26)
| ~ ordinal(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_15_2]) ).
cnf(f_15_4,plain,
( sP8(U_25)
| ~ element(U_25,U_26)
| ~ ordinal(U_26) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( epsilon_transitive(U_25)
| ~ sP8(U_25) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( epsilon_connected(U_25)
| ~ sP8(U_25) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_7,plain,
( ordinal(U_25)
| ~ sP8(U_25) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_16_2,plain,
! [U_27] :
( finite(U_27)
| ~ empty(U_27) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_27] :
( finite(U_27)
| ~ empty(U_27) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( finite(U_27)
| ~ empty(U_27) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(fof_nnf,[status(thm)],[cc1_finsub_1]) ).
fof(f_17_2,plain,
! [U_28] :
( ( diff_closed(U_28)
& cup_closed(U_28) )
| ~ preboolean(U_28) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_28] :
( diff_closed(U_28)
| ~ sP9(U_28) )
& ! [U_28] :
( cup_closed(U_28)
| ~ sP9(U_28) )
& ! [U_28] :
( sP9(U_28)
| ~ preboolean(U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_17_2]) ).
cnf(f_17_4,plain,
( sP9(U_28)
| ~ preboolean(U_28) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
( cup_closed(U_28)
| ~ sP9(U_28) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
( diff_closed(U_28)
| ~ sP9(U_28) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_18_2,plain,
! [U_29] :
( function(U_29)
| ~ empty(U_29) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_29] :
( function(U_29)
| ~ empty(U_29) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( function(U_29)
| ~ empty(U_29) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B,C] :
( ( quasi_total(C,A,B)
& function(C) )
| ~ v1_partfun1(C,A,B)
| ~ function(C)
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[cc1_funct_2]) ).
fof(f_19_2,plain,
! [U_32,U_31,U_30] :
( ( quasi_total(U_30,U_32,U_31)
& function(U_30) )
| ~ v1_partfun1(U_30,U_32,U_31)
| ~ function(U_30)
| ~ relation_of2(U_30,U_32,U_31) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_30,U_31,U_32] :
( quasi_total(U_30,U_32,U_31)
| ~ sP10(U_30,U_31,U_32) )
& ! [U_30,U_31,U_32] :
( function(U_30)
| ~ sP10(U_30,U_31,U_32) )
& ! [U_30,U_31,U_32] :
( sP10(U_30,U_31,U_32)
| ~ v1_partfun1(U_30,U_32,U_31)
| ~ function(U_30)
| ~ relation_of2(U_30,U_32,U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_19_2]) ).
cnf(f_19_4,plain,
( sP10(U_30,U_31,U_32)
| ~ v1_partfun1(U_30,U_32,U_31)
| ~ function(U_30)
| ~ relation_of2(U_30,U_32,U_31) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( function(U_30)
| ~ sP10(U_30,U_31,U_32) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( quasi_total(U_30,U_32,U_31)
| ~ sP10(U_30,U_31,U_32) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) )
| ~ lattice(A)
| empty_carrier(A)
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[cc1_lattices]) ).
fof(f_20_2,plain,
! [U_33] :
( ( join_absorbing(U_33)
& meet_absorbing(U_33)
& meet_associative(U_33)
& meet_commutative(U_33)
& join_associative(U_33)
& join_commutative(U_33)
& ~ empty_carrier(U_33) )
| ~ lattice(U_33)
| empty_carrier(U_33)
| ~ latt_str(U_33) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_33] :
( join_absorbing(U_33)
| ~ sP11(U_33) )
& ! [U_33] :
( meet_absorbing(U_33)
| ~ sP11(U_33) )
& ! [U_33] :
( meet_associative(U_33)
| ~ sP11(U_33) )
& ! [U_33] :
( meet_commutative(U_33)
| ~ sP11(U_33) )
& ! [U_33] :
( join_associative(U_33)
| ~ sP11(U_33) )
& ! [U_33] :
( join_commutative(U_33)
| ~ sP11(U_33) )
& ! [U_33] :
( ~ empty_carrier(U_33)
| ~ sP11(U_33) )
& ! [U_33] :
( sP11(U_33)
| ~ lattice(U_33)
| empty_carrier(U_33)
| ~ latt_str(U_33) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_20_2]) ).
cnf(f_20_4,plain,
( sP11(U_33)
| ~ lattice(U_33)
| empty_carrier(U_33)
| ~ latt_str(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( ~ empty_carrier(U_33)
| ~ sP11(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( join_commutative(U_33)
| ~ sP11(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( join_associative(U_33)
| ~ sP11(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_8,plain,
( meet_commutative(U_33)
| ~ sP11(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_9,plain,
( meet_associative(U_33)
| ~ sP11(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_10,plain,
( meet_absorbing(U_33)
| ~ sP11(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_11,plain,
( join_absorbing(U_33)
| ~ sP11(U_33) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_21_2,plain,
! [U_34] :
( v4_membered(U_34)
| ~ v5_membered(U_34) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_34] :
( v4_membered(U_34)
| ~ v5_membered(U_34) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( v4_membered(U_34)
| ~ v5_membered(U_34) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_22_2,plain,
! [U_35] :
( ( epsilon_connected(U_35)
& epsilon_transitive(U_35) )
| ~ ordinal(U_35) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_35] :
( epsilon_connected(U_35)
| ~ sP12(U_35) )
& ! [U_35] :
( epsilon_transitive(U_35)
| ~ sP12(U_35) )
& ! [U_35] :
( sP12(U_35)
| ~ ordinal(U_35) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_22_2]) ).
cnf(f_22_4,plain,
( sP12(U_35)
| ~ ordinal(U_35) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( epsilon_transitive(U_35)
| ~ sP12(U_35) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( epsilon_connected(U_35)
| ~ sP12(U_35) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] :
( ( reflexive(A)
& relation(A) )
| ~ transitive(A)
| ~ symmetric(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc1_partfun1]) ).
fof(f_23_2,plain,
! [U_36] :
( ( reflexive(U_36)
& relation(U_36) )
| ~ transitive(U_36)
| ~ symmetric(U_36)
| ~ relation(U_36) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_36] :
( reflexive(U_36)
| ~ sP13(U_36) )
& ! [U_36] :
( relation(U_36)
| ~ sP13(U_36) )
& ! [U_36] :
( sP13(U_36)
| ~ transitive(U_36)
| ~ symmetric(U_36)
| ~ relation(U_36) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_23_2]) ).
cnf(f_23_4,plain,
( sP13(U_36)
| ~ transitive(U_36)
| ~ symmetric(U_36)
| ~ relation(U_36) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( relation(U_36)
| ~ sP13(U_36) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( reflexive(U_36)
| ~ sP13(U_36) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_24_2,plain,
! [U_37] :
( relation(U_37)
| ~ empty(U_37) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_37] :
( relation(U_37)
| ~ empty(U_37) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( relation(U_37)
| ~ empty(U_37) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_25_2,plain,
! [U_40,U_39,U_38] :
( relation(U_38)
| ~ element(U_38,powerset(cartesian_product2(U_40,U_39))) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_39,U_40,U_38] :
( relation(U_38)
| ~ element(U_38,powerset(cartesian_product2(U_40,U_39))) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( relation(U_38)
| ~ element(U_38,powerset(cartesian_product2(U_40,U_39))) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A] :
( ! [B] :
( ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc20_membered]) ).
fof(f_26_2,plain,
! [U_42] :
( ! [U_41] :
( ( v5_membered(U_41)
& v4_membered(U_41)
& v3_membered(U_41)
& v2_membered(U_41)
& v1_membered(U_41) )
| ~ element(U_41,powerset(U_42)) )
| ~ v5_membered(U_42) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_41] :
( v5_membered(U_41)
| ~ sP14(U_41) )
& ! [U_41] :
( v4_membered(U_41)
| ~ sP14(U_41) )
& ! [U_41] :
( v3_membered(U_41)
| ~ sP14(U_41) )
& ! [U_41] :
( v2_membered(U_41)
| ~ sP14(U_41) )
& ! [U_41] :
( v1_membered(U_41)
| ~ sP14(U_41) )
& ! [U_41,U_42] :
( sP14(U_41)
| ~ element(U_41,powerset(U_42))
| ~ v5_membered(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_26_2]) ).
cnf(f_26_4,plain,
( sP14(U_41)
| ~ element(U_41,powerset(U_42))
| ~ v5_membered(U_42) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( v1_membered(U_41)
| ~ sP14(U_41) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( v2_membered(U_41)
| ~ sP14(U_41) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_7,plain,
( v3_membered(U_41)
| ~ sP14(U_41) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_8,plain,
( v4_membered(U_41)
| ~ sP14(U_41) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_9,plain,
( v5_membered(U_41)
| ~ sP14(U_41) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_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_27_2,plain,
! [U_43] :
( ( natural(U_43)
& ordinal(U_43)
& epsilon_connected(U_43)
& epsilon_transitive(U_43) )
| ~ ordinal(U_43)
| ~ empty(U_43) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_43] :
( natural(U_43)
| ~ sP15(U_43) )
& ! [U_43] :
( ordinal(U_43)
| ~ sP15(U_43) )
& ! [U_43] :
( epsilon_connected(U_43)
| ~ sP15(U_43) )
& ! [U_43] :
( epsilon_transitive(U_43)
| ~ sP15(U_43) )
& ! [U_43] :
( sP15(U_43)
| ~ ordinal(U_43)
| ~ empty(U_43) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP15(U_43)
| ~ ordinal(U_43)
| ~ empty(U_43) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( epsilon_transitive(U_43)
| ~ sP15(U_43) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( epsilon_connected(U_43)
| ~ sP15(U_43) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_7,plain,
( ordinal(U_43)
| ~ sP15(U_43) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_8,plain,
( natural(U_43)
| ~ sP15(U_43) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_28_2,plain,
! [U_45] :
( ! [U_44] :
( finite(U_44)
| ~ element(U_44,powerset(U_45)) )
| ~ finite(U_45) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_45,U_44] :
( finite(U_44)
| ~ element(U_44,powerset(U_45))
| ~ finite(U_45) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( finite(U_44)
| ~ element(U_44,powerset(U_45))
| ~ finite(U_45) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(fof_nnf,[status(thm)],[cc2_finsub_1]) ).
fof(f_29_2,plain,
! [U_46] :
( preboolean(U_46)
| ~ diff_closed(U_46)
| ~ cup_closed(U_46) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_46] :
( preboolean(U_46)
| ~ diff_closed(U_46)
| ~ cup_closed(U_46) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( preboolean(U_46)
| ~ diff_closed(U_46)
| ~ cup_closed(U_46) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_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_30_2,plain,
! [U_47] :
( ( one_to_one(U_47)
& function(U_47)
& relation(U_47) )
| ~ function(U_47)
| ~ empty(U_47)
| ~ relation(U_47) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_47] :
( one_to_one(U_47)
| ~ sP16(U_47) )
& ! [U_47] :
( function(U_47)
| ~ sP16(U_47) )
& ! [U_47] :
( relation(U_47)
| ~ sP16(U_47) )
& ! [U_47] :
( sP16(U_47)
| ~ function(U_47)
| ~ empty(U_47)
| ~ relation(U_47) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_30_2]) ).
cnf(f_30_4,plain,
( sP16(U_47)
| ~ function(U_47)
| ~ empty(U_47)
| ~ relation(U_47) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( relation(U_47)
| ~ sP16(U_47) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
( function(U_47)
| ~ sP16(U_47) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_7,plain,
( one_to_one(U_47)
| ~ sP16(U_47) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B,C] :
( ( onto(C,A,B)
& quasi_total(C,A,B)
& one_to_one(C)
& function(C) )
| ~ bijective(C,A,B)
| ~ quasi_total(C,A,B)
| ~ function(C)
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[cc2_funct_2]) ).
fof(f_31_2,plain,
! [U_50,U_49,U_48] :
( ( onto(U_48,U_50,U_49)
& quasi_total(U_48,U_50,U_49)
& one_to_one(U_48)
& function(U_48) )
| ~ bijective(U_48,U_50,U_49)
| ~ quasi_total(U_48,U_50,U_49)
| ~ function(U_48)
| ~ relation_of2(U_48,U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_49,U_50,U_48] :
( onto(U_48,U_50,U_49)
| ~ sP17(U_49,U_50,U_48) )
& ! [U_49,U_50,U_48] :
( quasi_total(U_48,U_50,U_49)
| ~ sP17(U_49,U_50,U_48) )
& ! [U_49,U_50,U_48] :
( one_to_one(U_48)
| ~ sP17(U_49,U_50,U_48) )
& ! [U_49,U_50,U_48] :
( function(U_48)
| ~ sP17(U_49,U_50,U_48) )
& ! [U_49,U_50,U_48] :
( sP17(U_49,U_50,U_48)
| ~ bijective(U_48,U_50,U_49)
| ~ quasi_total(U_48,U_50,U_49)
| ~ function(U_48)
| ~ relation_of2(U_48,U_50,U_49) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_31_2]) ).
cnf(f_31_4,plain,
( sP17(U_49,U_50,U_48)
| ~ bijective(U_48,U_50,U_49)
| ~ quasi_total(U_48,U_50,U_49)
| ~ function(U_48)
| ~ relation_of2(U_48,U_50,U_49) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( function(U_48)
| ~ sP17(U_49,U_50,U_48) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_6,plain,
( one_to_one(U_48)
| ~ sP17(U_49,U_50,U_48) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_7,plain,
( quasi_total(U_48,U_50,U_49)
| ~ sP17(U_49,U_50,U_48) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_8,plain,
( onto(U_48,U_50,U_49)
| ~ sP17(U_49,U_50,U_48) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] :
( ( lattice(A)
& ~ empty_carrier(A) )
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_associative(A)
| ~ meet_commutative(A)
| ~ join_associative(A)
| ~ join_commutative(A)
| empty_carrier(A)
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[cc2_lattices]) ).
fof(f_32_2,plain,
! [U_51] :
( ( lattice(U_51)
& ~ empty_carrier(U_51) )
| ~ join_absorbing(U_51)
| ~ meet_absorbing(U_51)
| ~ meet_associative(U_51)
| ~ meet_commutative(U_51)
| ~ join_associative(U_51)
| ~ join_commutative(U_51)
| empty_carrier(U_51)
| ~ latt_str(U_51) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_51] :
( lattice(U_51)
| ~ sP18(U_51) )
& ! [U_51] :
( ~ empty_carrier(U_51)
| ~ sP18(U_51) )
& ! [U_51] :
( sP18(U_51)
| ~ join_absorbing(U_51)
| ~ meet_absorbing(U_51)
| ~ meet_associative(U_51)
| ~ meet_commutative(U_51)
| ~ join_associative(U_51)
| ~ join_commutative(U_51)
| empty_carrier(U_51)
| ~ latt_str(U_51) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_32_2]) ).
cnf(f_32_4,plain,
( sP18(U_51)
| ~ join_absorbing(U_51)
| ~ meet_absorbing(U_51)
| ~ meet_associative(U_51)
| ~ meet_commutative(U_51)
| ~ join_associative(U_51)
| ~ join_commutative(U_51)
| empty_carrier(U_51)
| ~ latt_str(U_51) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( ~ empty_carrier(U_51)
| ~ sP18(U_51) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_6,plain,
( lattice(U_51)
| ~ sP18(U_51) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_33_2,plain,
! [U_52] :
( v3_membered(U_52)
| ~ v4_membered(U_52) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_52] :
( v3_membered(U_52)
| ~ v4_membered(U_52) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( v3_membered(U_52)
| ~ v4_membered(U_52) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_34_2,plain,
! [U_53] :
( ordinal(U_53)
| ~ epsilon_connected(U_53)
| ~ epsilon_transitive(U_53) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_53] :
( ordinal(U_53)
| ~ epsilon_connected(U_53)
| ~ epsilon_transitive(U_53) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( ordinal(U_53)
| ~ epsilon_connected(U_53)
| ~ epsilon_transitive(U_53) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A] :
( ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ element(A,omega) ),
inference(fof_nnf,[status(thm)],[cc3_arytm_3]) ).
fof(f_35_2,plain,
! [U_54] :
( ( natural(U_54)
& ordinal(U_54)
& epsilon_connected(U_54)
& epsilon_transitive(U_54) )
| ~ element(U_54,omega) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_54] :
( natural(U_54)
| ~ sP19(U_54) )
& ! [U_54] :
( ordinal(U_54)
| ~ sP19(U_54) )
& ! [U_54] :
( epsilon_connected(U_54)
| ~ sP19(U_54) )
& ! [U_54] :
( epsilon_transitive(U_54)
| ~ sP19(U_54) )
& ! [U_54] :
( sP19(U_54)
| ~ element(U_54,omega) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_35_2]) ).
cnf(f_35_4,plain,
( sP19(U_54)
| ~ element(U_54,omega) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( epsilon_transitive(U_54)
| ~ sP19(U_54) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( epsilon_connected(U_54)
| ~ sP19(U_54) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_7,plain,
( ordinal(U_54)
| ~ sP19(U_54) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_8,plain,
( natural(U_54)
| ~ sP19(U_54) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B,C] :
( ( bijective(C,A,B)
& quasi_total(C,A,B)
& function(C) )
| ~ onto(C,A,B)
| ~ quasi_total(C,A,B)
| ~ one_to_one(C)
| ~ function(C)
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[cc3_funct_2]) ).
fof(f_36_2,plain,
! [U_57,U_56,U_55] :
( ( bijective(U_55,U_57,U_56)
& quasi_total(U_55,U_57,U_56)
& function(U_55) )
| ~ onto(U_55,U_57,U_56)
| ~ quasi_total(U_55,U_57,U_56)
| ~ one_to_one(U_55)
| ~ function(U_55)
| ~ relation_of2(U_55,U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_55,U_56,U_57] :
( bijective(U_55,U_57,U_56)
| ~ sP20(U_55,U_56,U_57) )
& ! [U_55,U_56,U_57] :
( quasi_total(U_55,U_57,U_56)
| ~ sP20(U_55,U_56,U_57) )
& ! [U_55,U_56,U_57] :
( function(U_55)
| ~ sP20(U_55,U_56,U_57) )
& ! [U_55,U_56,U_57] :
( sP20(U_55,U_56,U_57)
| ~ onto(U_55,U_57,U_56)
| ~ quasi_total(U_55,U_57,U_56)
| ~ one_to_one(U_55)
| ~ function(U_55)
| ~ relation_of2(U_55,U_57,U_56) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_36_2]) ).
cnf(f_36_4,plain,
( sP20(U_55,U_56,U_57)
| ~ onto(U_55,U_57,U_56)
| ~ quasi_total(U_55,U_57,U_56)
| ~ one_to_one(U_55)
| ~ function(U_55)
| ~ relation_of2(U_55,U_57,U_56) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( function(U_55)
| ~ sP20(U_55,U_56,U_57) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
( quasi_total(U_55,U_57,U_56)
| ~ sP20(U_55,U_56,U_57) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_7,plain,
( bijective(U_55,U_57,U_56)
| ~ sP20(U_55,U_56,U_57) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_37_2,plain,
! [U_58] :
( v2_membered(U_58)
| ~ v3_membered(U_58) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_58] :
( v2_membered(U_58)
| ~ v3_membered(U_58) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( v2_membered(U_58)
| ~ v3_membered(U_58) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_38_2,plain,
! [U_59] :
( ( ordinal(U_59)
& epsilon_connected(U_59)
& epsilon_transitive(U_59) )
| ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_59] :
( ordinal(U_59)
| ~ sP21(U_59) )
& ! [U_59] :
( epsilon_connected(U_59)
| ~ sP21(U_59) )
& ! [U_59] :
( epsilon_transitive(U_59)
| ~ sP21(U_59) )
& ! [U_59] :
( sP21(U_59)
| ~ empty(U_59) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_38_2]) ).
cnf(f_38_4,plain,
( sP21(U_59)
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( epsilon_transitive(U_59)
| ~ sP21(U_59) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
( epsilon_connected(U_59)
| ~ sP21(U_59) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_7,plain,
( ordinal(U_59)
| ~ sP21(U_59) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
( ( bijective(B,A,A)
& onto(B,A,A)
& quasi_total(B,A,A)
& one_to_one(B)
& function(B) )
| ~ quasi_total(B,A,A)
| ~ reflexive(B)
| ~ v1_partfun1(B,A,A)
| ~ function(B)
| ~ relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[cc4_funct_2]) ).
fof(f_39_2,plain,
! [U_61,U_60] :
( ( bijective(U_60,U_61,U_61)
& onto(U_60,U_61,U_61)
& quasi_total(U_60,U_61,U_61)
& one_to_one(U_60)
& function(U_60) )
| ~ quasi_total(U_60,U_61,U_61)
| ~ reflexive(U_60)
| ~ v1_partfun1(U_60,U_61,U_61)
| ~ function(U_60)
| ~ relation_of2(U_60,U_61,U_61) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_61,U_60] :
( bijective(U_60,U_61,U_61)
| ~ sP22(U_61,U_60) )
& ! [U_61,U_60] :
( onto(U_60,U_61,U_61)
| ~ sP22(U_61,U_60) )
& ! [U_61,U_60] :
( quasi_total(U_60,U_61,U_61)
| ~ sP22(U_61,U_60) )
& ! [U_61,U_60] :
( one_to_one(U_60)
| ~ sP22(U_61,U_60) )
& ! [U_61,U_60] :
( function(U_60)
| ~ sP22(U_61,U_60) )
& ! [U_61,U_60] :
( sP22(U_61,U_60)
| ~ quasi_total(U_60,U_61,U_61)
| ~ reflexive(U_60)
| ~ v1_partfun1(U_60,U_61,U_61)
| ~ function(U_60)
| ~ relation_of2(U_60,U_61,U_61) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_39_2]) ).
cnf(f_39_4,plain,
( sP22(U_61,U_60)
| ~ quasi_total(U_60,U_61,U_61)
| ~ reflexive(U_60)
| ~ v1_partfun1(U_60,U_61,U_61)
| ~ function(U_60)
| ~ relation_of2(U_60,U_61,U_61) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( function(U_60)
| ~ sP22(U_61,U_60) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
( one_to_one(U_60)
| ~ sP22(U_61,U_60) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_7,plain,
( quasi_total(U_60,U_61,U_61)
| ~ sP22(U_61,U_60) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_8,plain,
( onto(U_60,U_61,U_61)
| ~ sP22(U_61,U_60) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_9,plain,
( bijective(U_60,U_61,U_61)
| ~ sP22(U_61,U_60) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_40_2,plain,
! [U_62] :
( v1_membered(U_62)
| ~ v2_membered(U_62) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_62] :
( v1_membered(U_62)
| ~ v2_membered(U_62) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( v1_membered(U_62)
| ~ v2_membered(U_62) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] :
( ! [C] :
( ( quasi_total(C,A,B)
& v1_partfun1(C,A,B)
& function(C) )
| ~ quasi_total(C,A,B)
| ~ function(C)
| ~ relation_of2(C,A,B) )
| empty(B) ),
inference(fof_nnf,[status(thm)],[cc5_funct_2]) ).
fof(f_41_2,plain,
! [U_65,U_64] :
( ! [U_63] :
( ( quasi_total(U_63,U_65,U_64)
& v1_partfun1(U_63,U_65,U_64)
& function(U_63) )
| ~ quasi_total(U_63,U_65,U_64)
| ~ function(U_63)
| ~ relation_of2(U_63,U_65,U_64) )
| empty(U_64) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_64,U_63,U_65] :
( quasi_total(U_63,U_65,U_64)
| ~ sP23(U_64,U_63,U_65) )
& ! [U_64,U_63,U_65] :
( v1_partfun1(U_63,U_65,U_64)
| ~ sP23(U_64,U_63,U_65) )
& ! [U_64,U_63,U_65] :
( function(U_63)
| ~ sP23(U_64,U_63,U_65) )
& ! [U_64,U_63,U_65] :
( sP23(U_64,U_63,U_65)
| ~ quasi_total(U_63,U_65,U_64)
| ~ function(U_63)
| ~ relation_of2(U_63,U_65,U_64)
| empty(U_64) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_41_2]) ).
cnf(f_41_4,plain,
( sP23(U_64,U_63,U_65)
| ~ quasi_total(U_63,U_65,U_64)
| ~ function(U_63)
| ~ relation_of2(U_63,U_65,U_64)
| empty(U_64) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( function(U_63)
| ~ sP23(U_64,U_63,U_65) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
( v1_partfun1(U_63,U_65,U_64)
| ~ sP23(U_64,U_63,U_65) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_7,plain,
( quasi_total(U_63,U_65,U_64)
| ~ sP23(U_64,U_63,U_65) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
( ! [C] :
( ( quasi_total(C,A,B)
& v1_partfun1(C,A,B)
& ~ empty(C)
& function(C) )
| ~ quasi_total(C,A,B)
| ~ function(C)
| ~ relation_of2(C,A,B) )
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[cc6_funct_2]) ).
fof(f_42_2,plain,
! [U_68,U_67] :
( ! [U_66] :
( ( quasi_total(U_66,U_68,U_67)
& v1_partfun1(U_66,U_68,U_67)
& ~ empty(U_66)
& function(U_66) )
| ~ quasi_total(U_66,U_68,U_67)
| ~ function(U_66)
| ~ relation_of2(U_66,U_68,U_67) )
| empty(U_67)
| empty(U_68) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_66,U_68,U_67] :
( quasi_total(U_66,U_68,U_67)
| ~ sP24(U_66,U_68,U_67) )
& ! [U_66,U_68,U_67] :
( v1_partfun1(U_66,U_68,U_67)
| ~ sP24(U_66,U_68,U_67) )
& ! [U_66,U_68,U_67] :
( ~ empty(U_66)
| ~ sP24(U_66,U_68,U_67) )
& ! [U_66,U_68,U_67] :
( function(U_66)
| ~ sP24(U_66,U_68,U_67) )
& ! [U_66,U_68,U_67] :
( sP24(U_66,U_68,U_67)
| ~ quasi_total(U_66,U_68,U_67)
| ~ function(U_66)
| ~ relation_of2(U_66,U_68,U_67)
| empty(U_67)
| empty(U_68) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_42_2]) ).
cnf(f_42_4,plain,
( sP24(U_66,U_68,U_67)
| ~ quasi_total(U_66,U_68,U_67)
| ~ function(U_66)
| ~ relation_of2(U_66,U_68,U_67)
| empty(U_67)
| empty(U_68) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
( function(U_66)
| ~ sP24(U_66,U_68,U_67) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_6,plain,
( ~ empty(U_66)
| ~ sP24(U_66,U_68,U_67) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_7,plain,
( v1_partfun1(U_66,U_68,U_67)
| ~ sP24(U_66,U_68,U_67) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_8,plain,
( quasi_total(U_66,U_68,U_67)
| ~ sP24(U_66,U_68,U_67) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_43_2,plain,
! [U_70,U_69] : unordered_pair(U_70,U_69) = unordered_pair(U_69,U_70),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_70,U_69] : unordered_pair(U_70,U_69) = unordered_pair(U_69,U_70),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
unordered_pair(U_70,U_69) = unordered_pair(U_69,U_70),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_44_2,plain,
! [U_72,U_71] : set_union2(U_72,U_71) = set_union2(U_71,U_72),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_72,U_71] : set_union2(U_72,U_71) = set_union2(U_71,U_72),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
set_union2(U_72,U_71) = set_union2(U_71,U_72),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B,C] :
( join_commut(A,B,C) = join_commut(A,C,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[commutativity_k3_lattices]) ).
fof(f_45_2,plain,
! [U_75,U_74,U_73] :
( join_commut(U_75,U_74,U_73) = join_commut(U_75,U_73,U_74)
| ~ element(U_73,the_carrier(U_75))
| ~ element(U_74,the_carrier(U_75))
| ~ join_semilatt_str(U_75)
| ~ join_commutative(U_75)
| empty_carrier(U_75) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_75,U_73,U_74] :
( join_commut(U_75,U_74,U_73) = join_commut(U_75,U_73,U_74)
| ~ element(U_73,the_carrier(U_75))
| ~ element(U_74,the_carrier(U_75))
| ~ join_semilatt_str(U_75)
| ~ join_commutative(U_75)
| empty_carrier(U_75) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( join_commut(U_75,U_74,U_73) = join_commut(U_75,U_73,U_74)
| ~ element(U_73,the_carrier(U_75))
| ~ element(U_74,the_carrier(U_75))
| ~ join_semilatt_str(U_75)
| ~ join_commutative(U_75)
| empty_carrier(U_75) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_46_2,plain,
! [U_77,U_76] : set_intersection2(U_77,U_76) = set_intersection2(U_76,U_77),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_76,U_77] : set_intersection2(U_77,U_76) = set_intersection2(U_76,U_77),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
set_intersection2(U_77,U_76) = set_intersection2(U_76,U_77),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet_commut(A,C,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[commutativity_k4_lattices]) ).
fof(f_47_2,plain,
! [U_80,U_79,U_78] :
( meet_commut(U_80,U_79,U_78) = meet_commut(U_80,U_78,U_79)
| ~ element(U_78,the_carrier(U_80))
| ~ element(U_79,the_carrier(U_80))
| ~ meet_semilatt_str(U_80)
| ~ meet_commutative(U_80)
| empty_carrier(U_80) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_80,U_79,U_78] :
( meet_commut(U_80,U_79,U_78) = meet_commut(U_80,U_78,U_79)
| ~ element(U_78,the_carrier(U_80))
| ~ element(U_79,the_carrier(U_80))
| ~ meet_semilatt_str(U_80)
| ~ meet_commutative(U_80)
| empty_carrier(U_80) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( meet_commut(U_80,U_79,U_78) = meet_commut(U_80,U_78,U_79)
| ~ element(U_78,the_carrier(U_80))
| ~ element(U_79,the_carrier(U_80))
| ~ meet_semilatt_str(U_80)
| ~ meet_commutative(U_80)
| empty_carrier(U_80) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B,C] :
( subset_union2(A,B,C) = subset_union2(A,C,B)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[commutativity_k4_subset_1]) ).
fof(f_48_2,plain,
! [U_83,U_82,U_81] :
( subset_union2(U_83,U_82,U_81) = subset_union2(U_83,U_81,U_82)
| ~ element(U_81,powerset(U_83))
| ~ element(U_82,powerset(U_83)) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_83,U_82,U_81] :
( subset_union2(U_83,U_82,U_81) = subset_union2(U_83,U_81,U_82)
| ~ element(U_81,powerset(U_83))
| ~ element(U_82,powerset(U_83)) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( subset_union2(U_83,U_82,U_81) = subset_union2(U_83,U_81,U_82)
| ~ element(U_81,powerset(U_83))
| ~ element(U_82,powerset(U_83)) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B,C] :
( subset_intersection2(A,B,C) = subset_intersection2(A,C,B)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[commutativity_k5_subset_1]) ).
fof(f_49_2,plain,
! [U_86,U_85,U_84] :
( subset_intersection2(U_86,U_85,U_84) = subset_intersection2(U_86,U_84,U_85)
| ~ element(U_84,powerset(U_86))
| ~ element(U_85,powerset(U_86)) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_85,U_84,U_86] :
( subset_intersection2(U_86,U_85,U_84) = subset_intersection2(U_86,U_84,U_85)
| ~ element(U_84,powerset(U_86))
| ~ element(U_85,powerset(U_86)) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( subset_intersection2(U_86,U_85,U_84) = subset_intersection2(U_86,U_84,U_85)
| ~ element(U_84,powerset(U_86))
| ~ element(U_85,powerset(U_86)) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_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_50_2,plain,
! [U_88,U_87] :
( ordinal_subset(U_87,U_88)
| ordinal_subset(U_88,U_87)
| ~ ordinal(U_87)
| ~ ordinal(U_88) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_88,U_87] :
( ordinal_subset(U_87,U_88)
| ordinal_subset(U_88,U_87)
| ~ ordinal(U_87)
| ~ ordinal(U_88) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( ordinal_subset(U_87,U_88)
| ordinal_subset(U_88,U_87)
| ~ ordinal(U_87)
| ~ ordinal(U_88) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_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_51_2,plain,
! [U_94,U_93] :
( ( ( U_93 = identity_relation(U_94)
| ? [U_92,U_91] :
( ( ~ in(ordered_pair(U_92,U_91),U_93)
& U_92 = U_91
& in(U_92,U_94) )
| ( ( U_92 != U_91
| ~ in(U_92,U_94) )
& in(ordered_pair(U_92,U_91),U_93) ) ) )
& ( ! [U_90,U_89] :
( ( in(ordered_pair(U_90,U_89),U_93)
| U_90 != U_89
| ~ in(U_90,U_94) )
& ( ( U_90 = U_89
& in(U_90,U_94) )
| ~ in(ordered_pair(U_90,U_89),U_93) ) )
| U_93 != identity_relation(U_94) ) )
| ~ relation(U_93) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_94,U_93] :
( ( ( U_93 = identity_relation(U_94)
| ? [U_102,U_100] :
( ~ in(ordered_pair(U_102,U_100),U_93)
& U_102 = U_100
& in(U_102,U_94) )
| ? [U_101,U_99] :
( ( U_101 != U_99
| ~ in(U_101,U_94) )
& in(ordered_pair(U_101,U_99),U_93) ) )
& ( ( ! [U_98,U_96] :
( in(ordered_pair(U_98,U_96),U_93)
| U_98 != U_96
| ~ in(U_98,U_94) )
& ! [U_97,U_95] :
( ( U_97 = U_95
& in(U_97,U_94) )
| ~ in(ordered_pair(U_97,U_95),U_93) ) )
| U_93 != identity_relation(U_94) ) )
| ~ relation(U_93) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
! [U_94,U_93] :
( ( ( U_93 = identity_relation(U_94)
| ? [U_102,U_100] :
( ~ in(ordered_pair(U_102,U_100),U_93)
& U_102 = U_100
& in(U_102,U_94) )
| ? [U_99] :
( ( sK1(U_94,U_93) != U_99
| ~ in(sK1(U_94,U_93),U_94) )
& in(ordered_pair(sK1(U_94,U_93),U_99),U_93) ) )
& ( ( ! [U_98,U_96] :
( in(ordered_pair(U_98,U_96),U_93)
| U_98 != U_96
| ~ in(U_98,U_94) )
& ! [U_97,U_95] :
( ( U_97 = U_95
& in(U_97,U_94) )
| ~ in(ordered_pair(U_97,U_95),U_93) ) )
| U_93 != identity_relation(U_94) ) )
| ~ relation(U_93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_101,sK1(U_94,U_93))],[f_51_3]) ).
fof(f_51_5,plain,
! [U_94,U_93] :
( ( ( U_93 = identity_relation(U_94)
| ? [U_102,U_100] :
( ~ in(ordered_pair(U_102,U_100),U_93)
& U_102 = U_100
& in(U_102,U_94) )
| ( ( sK1(U_94,U_93) != sK2(U_94,U_93)
| ~ in(sK1(U_94,U_93),U_94) )
& in(ordered_pair(sK1(U_94,U_93),sK2(U_94,U_93)),U_93) ) )
& ( ( ! [U_98,U_96] :
( in(ordered_pair(U_98,U_96),U_93)
| U_98 != U_96
| ~ in(U_98,U_94) )
& ! [U_97,U_95] :
( ( U_97 = U_95
& in(U_97,U_94) )
| ~ in(ordered_pair(U_97,U_95),U_93) ) )
| U_93 != identity_relation(U_94) ) )
| ~ relation(U_93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_99,sK2(U_94,U_93))],[f_51_4]) ).
fof(f_51_6,plain,
! [U_94,U_93] :
( ( ( U_93 = identity_relation(U_94)
| ? [U_100] :
( ~ in(ordered_pair(sK3(U_94,U_93),U_100),U_93)
& sK3(U_94,U_93) = U_100
& in(sK3(U_94,U_93),U_94) )
| ( ( sK1(U_94,U_93) != sK2(U_94,U_93)
| ~ in(sK1(U_94,U_93),U_94) )
& in(ordered_pair(sK1(U_94,U_93),sK2(U_94,U_93)),U_93) ) )
& ( ( ! [U_98,U_96] :
( in(ordered_pair(U_98,U_96),U_93)
| U_98 != U_96
| ~ in(U_98,U_94) )
& ! [U_97,U_95] :
( ( U_97 = U_95
& in(U_97,U_94) )
| ~ in(ordered_pair(U_97,U_95),U_93) ) )
| U_93 != identity_relation(U_94) ) )
| ~ relation(U_93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_102,sK3(U_94,U_93))],[f_51_5]) ).
fof(f_51_7,plain,
! [U_94,U_93] :
( ( ( U_93 = identity_relation(U_94)
| ( ~ in(ordered_pair(sK3(U_94,U_93),sK4(U_94,U_93)),U_93)
& sK3(U_94,U_93) = sK4(U_94,U_93)
& in(sK3(U_94,U_93),U_94) )
| ( ( sK1(U_94,U_93) != sK2(U_94,U_93)
| ~ in(sK1(U_94,U_93),U_94) )
& in(ordered_pair(sK1(U_94,U_93),sK2(U_94,U_93)),U_93) ) )
& ( ( ! [U_98,U_96] :
( in(ordered_pair(U_98,U_96),U_93)
| U_98 != U_96
| ~ in(U_98,U_94) )
& ! [U_97,U_95] :
( ( U_97 = U_95
& in(U_97,U_94) )
| ~ in(ordered_pair(U_97,U_95),U_93) ) )
| U_93 != identity_relation(U_94) ) )
| ~ relation(U_93) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_100,sK4(U_94,U_93))],[f_51_6]) ).
fof(f_51_8,plain,
( ! [U_93,U_94] :
( ~ in(ordered_pair(sK3(U_94,U_93),sK4(U_94,U_93)),U_93)
| ~ sP28(U_93,U_94) )
& ! [U_93,U_94] :
( sK3(U_94,U_93) = sK4(U_94,U_93)
| ~ sP28(U_93,U_94) )
& ! [U_93,U_94] :
( in(sK3(U_94,U_93),U_94)
| ~ sP28(U_93,U_94) )
& ! [U_93,U_94] :
( sK1(U_94,U_93) != sK2(U_94,U_93)
| ~ in(sK1(U_94,U_93),U_94)
| ~ sP27(U_93,U_94) )
& ! [U_93,U_94] :
( in(ordered_pair(sK1(U_94,U_93),sK2(U_94,U_93)),U_93)
| ~ sP27(U_93,U_94) )
& ! [U_94,U_95,U_97] :
( U_97 = U_95
| ~ sP25(U_94,U_95,U_97) )
& ! [U_94,U_95,U_97] :
( in(U_97,U_94)
| ~ sP25(U_94,U_95,U_97) )
& ! [U_98,U_93,U_94,U_95,U_96,U_97] :
( in(ordered_pair(U_98,U_96),U_93)
| U_98 != U_96
| ~ in(U_98,U_94)
| ~ sP26(U_98,U_93,U_94,U_95,U_96,U_97) )
& ! [U_98,U_93,U_94,U_95,U_96,U_97] :
( sP25(U_94,U_95,U_97)
| ~ in(ordered_pair(U_97,U_95),U_93)
| ~ sP26(U_98,U_93,U_94,U_95,U_96,U_97) )
& ! [U_98,U_93,U_94,U_95,U_96,U_97] :
( U_93 = identity_relation(U_94)
| sP28(U_93,U_94)
| sP27(U_93,U_94)
| ~ sP29(U_98,U_93,U_94,U_95,U_96,U_97) )
& ! [U_98,U_93,U_94,U_95,U_96,U_97] :
( sP26(U_98,U_93,U_94,U_95,U_96,U_97)
| U_93 != identity_relation(U_94)
| ~ sP29(U_98,U_93,U_94,U_95,U_96,U_97) )
& ! [U_98,U_93,U_94,U_95,U_96,U_97] :
( sP29(U_98,U_93,U_94,U_95,U_96,U_97)
| ~ relation(U_93) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26,sP27,sP28,sP29])],[f_51_7]) ).
cnf(f_51_9,plain,
( sP29(U_98,U_93,U_94,U_95,U_96,U_97)
| ~ relation(U_93) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_10,plain,
( sP26(U_98,U_93,U_94,U_95,U_96,U_97)
| U_93 != identity_relation(U_94)
| ~ sP29(U_98,U_93,U_94,U_95,U_96,U_97) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_11,plain,
( U_93 = identity_relation(U_94)
| sP28(U_93,U_94)
| sP27(U_93,U_94)
| ~ sP29(U_98,U_93,U_94,U_95,U_96,U_97) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_12,plain,
( sP25(U_94,U_95,U_97)
| ~ in(ordered_pair(U_97,U_95),U_93)
| ~ sP26(U_98,U_93,U_94,U_95,U_96,U_97) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_13,plain,
( in(ordered_pair(U_98,U_96),U_93)
| U_98 != U_96
| ~ in(U_98,U_94)
| ~ sP26(U_98,U_93,U_94,U_95,U_96,U_97) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_14,plain,
( in(U_97,U_94)
| ~ sP25(U_94,U_95,U_97) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_15,plain,
( U_97 = U_95
| ~ sP25(U_94,U_95,U_97) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_16,plain,
( in(ordered_pair(sK1(U_94,U_93),sK2(U_94,U_93)),U_93)
| ~ sP27(U_93,U_94) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_17,plain,
( sK1(U_94,U_93) != sK2(U_94,U_93)
| ~ in(sK1(U_94,U_93),U_94)
| ~ sP27(U_93,U_94) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_18,plain,
( in(sK3(U_94,U_93),U_94)
| ~ sP28(U_93,U_94) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_19,plain,
( sK3(U_94,U_93) = sK4(U_94,U_93)
| ~ sP28(U_93,U_94) ),
inference(clausify,[status(thm)],[f_51_8]) ).
cnf(f_51_20,plain,
( ~ in(ordered_pair(sK3(U_94,U_93),sK4(U_94,U_93)),U_93)
| ~ sP28(U_93,U_94) ),
inference(clausify,[status(thm)],[f_51_8]) ).
fof(f_52_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_52_2,plain,
! [U_104,U_103] :
( ( U_104 = U_103
| ~ subset(U_103,U_104)
| ~ subset(U_104,U_103) )
& ( ( subset(U_103,U_104)
& subset(U_104,U_103) )
| U_104 != U_103 ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_108,U_106] :
( U_108 = U_106
| ~ subset(U_106,U_108)
| ~ subset(U_108,U_106) )
& ! [U_107,U_105] :
( ( subset(U_105,U_107)
& subset(U_107,U_105) )
| U_107 != U_105 ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
( ! [U_107,U_105] :
( subset(U_105,U_107)
| ~ sP30(U_107,U_105) )
& ! [U_107,U_105] :
( subset(U_107,U_105)
| ~ sP30(U_107,U_105) )
& ! [U_106,U_108] :
( U_108 = U_106
| ~ subset(U_106,U_108)
| ~ subset(U_108,U_106) )
& ! [U_107,U_105] :
( sP30(U_107,U_105)
| U_107 != U_105 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_52_3]) ).
cnf(f_52_5,plain,
( sP30(U_107,U_105)
| U_107 != U_105 ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_6,plain,
( U_108 = U_106
| ~ subset(U_106,U_108)
| ~ subset(U_108,U_106) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_7,plain,
( subset(U_107,U_105)
| ~ sP30(U_107,U_105) ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_8,plain,
( subset(U_105,U_107)
| ~ sP30(U_107,U_105) ),
inference(clausify,[status(thm)],[f_52_4]) ).
fof(f_53_1,plain,
! [A] :
( identity_on_carrier(A) = identity_as_relation_of(the_carrier(A))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d11_grcat_1]) ).
fof(f_53_2,plain,
! [U_109] :
( identity_on_carrier(U_109) = identity_as_relation_of(the_carrier(U_109))
| ~ one_sorted_str(U_109) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_109] :
( identity_on_carrier(U_109) = identity_as_relation_of(the_carrier(U_109))
| ~ one_sorted_str(U_109) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( identity_on_carrier(U_109) = identity_as_relation_of(the_carrier(U_109))
| ~ one_sorted_str(U_109) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_2,plain,
! [U_116] :
( ! [U_115,U_114] :
( ( ( U_114 = relation_dom_restriction(U_116,U_115)
| ? [U_113,U_112] :
( ( ~ in(ordered_pair(U_113,U_112),U_114)
& in(ordered_pair(U_113,U_112),U_116)
& in(U_113,U_115) )
| ( ( ~ in(ordered_pair(U_113,U_112),U_116)
| ~ in(U_113,U_115) )
& in(ordered_pair(U_113,U_112),U_114) ) ) )
& ( ! [U_111,U_110] :
( ( in(ordered_pair(U_111,U_110),U_114)
| ~ in(ordered_pair(U_111,U_110),U_116)
| ~ in(U_111,U_115) )
& ( ( in(ordered_pair(U_111,U_110),U_116)
& in(U_111,U_115) )
| ~ in(ordered_pair(U_111,U_110),U_114) ) )
| U_114 != relation_dom_restriction(U_116,U_115) ) )
| ~ relation(U_114) )
| ~ relation(U_116) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_116] :
( ! [U_115,U_114] :
( ( ( U_114 = relation_dom_restriction(U_116,U_115)
| ? [U_124,U_122] :
( ~ in(ordered_pair(U_124,U_122),U_114)
& in(ordered_pair(U_124,U_122),U_116)
& in(U_124,U_115) )
| ? [U_123,U_121] :
( ( ~ in(ordered_pair(U_123,U_121),U_116)
| ~ in(U_123,U_115) )
& in(ordered_pair(U_123,U_121),U_114) ) )
& ( ( ! [U_120,U_118] :
( in(ordered_pair(U_120,U_118),U_114)
| ~ in(ordered_pair(U_120,U_118),U_116)
| ~ in(U_120,U_115) )
& ! [U_119,U_117] :
( ( in(ordered_pair(U_119,U_117),U_116)
& in(U_119,U_115) )
| ~ in(ordered_pair(U_119,U_117),U_114) ) )
| U_114 != relation_dom_restriction(U_116,U_115) ) )
| ~ relation(U_114) )
| ~ relation(U_116) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
! [U_116] :
( ! [U_115,U_114] :
( ( ( U_114 = relation_dom_restriction(U_116,U_115)
| ? [U_124,U_122] :
( ~ in(ordered_pair(U_124,U_122),U_114)
& in(ordered_pair(U_124,U_122),U_116)
& in(U_124,U_115) )
| ? [U_121] :
( ( ~ in(ordered_pair(sK5(U_116,U_115,U_114),U_121),U_116)
| ~ in(sK5(U_116,U_115,U_114),U_115) )
& in(ordered_pair(sK5(U_116,U_115,U_114),U_121),U_114) ) )
& ( ( ! [U_120,U_118] :
( in(ordered_pair(U_120,U_118),U_114)
| ~ in(ordered_pair(U_120,U_118),U_116)
| ~ in(U_120,U_115) )
& ! [U_119,U_117] :
( ( in(ordered_pair(U_119,U_117),U_116)
& in(U_119,U_115) )
| ~ in(ordered_pair(U_119,U_117),U_114) ) )
| U_114 != relation_dom_restriction(U_116,U_115) ) )
| ~ relation(U_114) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_123,sK5(U_116,U_115,U_114))],[f_54_3]) ).
fof(f_54_5,plain,
! [U_116] :
( ! [U_115,U_114] :
( ( ( U_114 = relation_dom_restriction(U_116,U_115)
| ? [U_124,U_122] :
( ~ in(ordered_pair(U_124,U_122),U_114)
& in(ordered_pair(U_124,U_122),U_116)
& in(U_124,U_115) )
| ( ( ~ in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_116)
| ~ in(sK5(U_116,U_115,U_114),U_115) )
& in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_114) ) )
& ( ( ! [U_120,U_118] :
( in(ordered_pair(U_120,U_118),U_114)
| ~ in(ordered_pair(U_120,U_118),U_116)
| ~ in(U_120,U_115) )
& ! [U_119,U_117] :
( ( in(ordered_pair(U_119,U_117),U_116)
& in(U_119,U_115) )
| ~ in(ordered_pair(U_119,U_117),U_114) ) )
| U_114 != relation_dom_restriction(U_116,U_115) ) )
| ~ relation(U_114) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_121,sK6(U_116,U_115,U_114))],[f_54_4]) ).
fof(f_54_6,plain,
! [U_116] :
( ! [U_115,U_114] :
( ( ( U_114 = relation_dom_restriction(U_116,U_115)
| ? [U_122] :
( ~ in(ordered_pair(sK7(U_116,U_115,U_114),U_122),U_114)
& in(ordered_pair(sK7(U_116,U_115,U_114),U_122),U_116)
& in(sK7(U_116,U_115,U_114),U_115) )
| ( ( ~ in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_116)
| ~ in(sK5(U_116,U_115,U_114),U_115) )
& in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_114) ) )
& ( ( ! [U_120,U_118] :
( in(ordered_pair(U_120,U_118),U_114)
| ~ in(ordered_pair(U_120,U_118),U_116)
| ~ in(U_120,U_115) )
& ! [U_119,U_117] :
( ( in(ordered_pair(U_119,U_117),U_116)
& in(U_119,U_115) )
| ~ in(ordered_pair(U_119,U_117),U_114) ) )
| U_114 != relation_dom_restriction(U_116,U_115) ) )
| ~ relation(U_114) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_124,sK7(U_116,U_115,U_114))],[f_54_5]) ).
fof(f_54_7,plain,
! [U_116] :
( ! [U_115,U_114] :
( ( ( U_114 = relation_dom_restriction(U_116,U_115)
| ( ~ in(ordered_pair(sK7(U_116,U_115,U_114),sK8(U_116,U_115,U_114)),U_114)
& in(ordered_pair(sK7(U_116,U_115,U_114),sK8(U_116,U_115,U_114)),U_116)
& in(sK7(U_116,U_115,U_114),U_115) )
| ( ( ~ in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_116)
| ~ in(sK5(U_116,U_115,U_114),U_115) )
& in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_114) ) )
& ( ( ! [U_120,U_118] :
( in(ordered_pair(U_120,U_118),U_114)
| ~ in(ordered_pair(U_120,U_118),U_116)
| ~ in(U_120,U_115) )
& ! [U_119,U_117] :
( ( in(ordered_pair(U_119,U_117),U_116)
& in(U_119,U_115) )
| ~ in(ordered_pair(U_119,U_117),U_114) ) )
| U_114 != relation_dom_restriction(U_116,U_115) ) )
| ~ relation(U_114) )
| ~ relation(U_116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_122,sK8(U_116,U_115,U_114))],[f_54_6]) ).
fof(f_54_8,plain,
( ! [U_115,U_116,U_114] :
( ~ in(ordered_pair(sK7(U_116,U_115,U_114),sK8(U_116,U_115,U_114)),U_114)
| ~ sP34(U_115,U_116,U_114) )
& ! [U_115,U_116,U_114] :
( in(ordered_pair(sK7(U_116,U_115,U_114),sK8(U_116,U_115,U_114)),U_116)
| ~ sP34(U_115,U_116,U_114) )
& ! [U_115,U_116,U_114] :
( in(sK7(U_116,U_115,U_114),U_115)
| ~ sP34(U_115,U_116,U_114) )
& ! [U_115,U_116,U_114] :
( ~ in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_116)
| ~ in(sK5(U_116,U_115,U_114),U_115)
| ~ sP33(U_115,U_116,U_114) )
& ! [U_115,U_116,U_114] :
( in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_114)
| ~ sP33(U_115,U_116,U_114) )
& ! [U_115,U_116,U_117,U_119] :
( in(ordered_pair(U_119,U_117),U_116)
| ~ sP31(U_115,U_116,U_117,U_119) )
& ! [U_115,U_116,U_117,U_119] :
( in(U_119,U_115)
| ~ sP31(U_115,U_116,U_117,U_119) )
& ! [U_115,U_120,U_116,U_117,U_118,U_119,U_114] :
( in(ordered_pair(U_120,U_118),U_114)
| ~ in(ordered_pair(U_120,U_118),U_116)
| ~ in(U_120,U_115)
| ~ sP32(U_115,U_120,U_116,U_117,U_118,U_119,U_114) )
& ! [U_115,U_120,U_116,U_117,U_118,U_119,U_114] :
( sP31(U_115,U_116,U_117,U_119)
| ~ in(ordered_pair(U_119,U_117),U_114)
| ~ sP32(U_115,U_120,U_116,U_117,U_118,U_119,U_114) )
& ! [U_115,U_120,U_116,U_117,U_118,U_119,U_114] :
( U_114 = relation_dom_restriction(U_116,U_115)
| sP34(U_115,U_116,U_114)
| sP33(U_115,U_116,U_114)
| ~ sP35(U_115,U_120,U_116,U_117,U_118,U_119,U_114) )
& ! [U_115,U_120,U_116,U_117,U_118,U_119,U_114] :
( sP32(U_115,U_120,U_116,U_117,U_118,U_119,U_114)
| U_114 != relation_dom_restriction(U_116,U_115)
| ~ sP35(U_115,U_120,U_116,U_117,U_118,U_119,U_114) )
& ! [U_115,U_120,U_116,U_117,U_118,U_119,U_114] :
( sP35(U_115,U_120,U_116,U_117,U_118,U_119,U_114)
| ~ relation(U_114)
| ~ relation(U_116) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31,sP32,sP33,sP34,sP35])],[f_54_7]) ).
cnf(f_54_9,plain,
( sP35(U_115,U_120,U_116,U_117,U_118,U_119,U_114)
| ~ relation(U_114)
| ~ relation(U_116) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_10,plain,
( sP32(U_115,U_120,U_116,U_117,U_118,U_119,U_114)
| U_114 != relation_dom_restriction(U_116,U_115)
| ~ sP35(U_115,U_120,U_116,U_117,U_118,U_119,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_11,plain,
( U_114 = relation_dom_restriction(U_116,U_115)
| sP34(U_115,U_116,U_114)
| sP33(U_115,U_116,U_114)
| ~ sP35(U_115,U_120,U_116,U_117,U_118,U_119,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_12,plain,
( sP31(U_115,U_116,U_117,U_119)
| ~ in(ordered_pair(U_119,U_117),U_114)
| ~ sP32(U_115,U_120,U_116,U_117,U_118,U_119,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_13,plain,
( in(ordered_pair(U_120,U_118),U_114)
| ~ in(ordered_pair(U_120,U_118),U_116)
| ~ in(U_120,U_115)
| ~ sP32(U_115,U_120,U_116,U_117,U_118,U_119,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_14,plain,
( in(U_119,U_115)
| ~ sP31(U_115,U_116,U_117,U_119) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_15,plain,
( in(ordered_pair(U_119,U_117),U_116)
| ~ sP31(U_115,U_116,U_117,U_119) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_16,plain,
( in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_114)
| ~ sP33(U_115,U_116,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_17,plain,
( ~ in(ordered_pair(sK5(U_116,U_115,U_114),sK6(U_116,U_115,U_114)),U_116)
| ~ in(sK5(U_116,U_115,U_114),U_115)
| ~ sP33(U_115,U_116,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_18,plain,
( in(sK7(U_116,U_115,U_114),U_115)
| ~ sP34(U_115,U_116,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_19,plain,
( in(ordered_pair(sK7(U_116,U_115,U_114),sK8(U_116,U_115,U_114)),U_116)
| ~ sP34(U_115,U_116,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
cnf(f_54_20,plain,
( ~ in(ordered_pair(sK7(U_116,U_115,U_114),sK8(U_116,U_115,U_114)),U_114)
| ~ sP34(U_115,U_116,U_114) ),
inference(clausify,[status(thm)],[f_54_8]) ).
fof(f_55_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_55_2,plain,
! [U_133] :
( ! [U_132,U_131] :
( ( U_131 = relation_image(U_133,U_132)
| ? [U_130] :
( ( ~ in(U_130,U_131)
& ? [U_129] :
( U_130 = apply(U_133,U_129)
& in(U_129,U_132)
& in(U_129,relation_dom(U_133)) ) )
| ( ! [U_128] :
( U_130 != apply(U_133,U_128)
| ~ in(U_128,U_132)
| ~ in(U_128,relation_dom(U_133)) )
& in(U_130,U_131) ) ) )
& ( ! [U_127] :
( ( in(U_127,U_131)
| ! [U_126] :
( U_127 != apply(U_133,U_126)
| ~ in(U_126,U_132)
| ~ in(U_126,relation_dom(U_133)) ) )
& ( ? [U_125] :
( U_127 = apply(U_133,U_125)
& in(U_125,U_132)
& in(U_125,relation_dom(U_133)) )
| ~ in(U_127,U_131) ) )
| U_131 != relation_image(U_133,U_132) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ? [U_129] :
( U_137 = apply(U_133,U_129)
& in(U_129,U_141)
& in(U_129,relation_dom(U_133)) ) )
| ? [U_136] :
( ! [U_128] :
( U_136 != apply(U_133,U_128)
| ~ in(U_128,U_141)
| ~ in(U_128,relation_dom(U_133)) )
& in(U_136,U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( U_135 != apply(U_133,U_126)
| ~ in(U_126,U_140)
| ~ in(U_126,relation_dom(U_133)) ) )
& ! [U_134] :
( ? [U_125] :
( U_134 = apply(U_133,U_125)
& in(U_125,U_140)
& in(U_125,relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ? [U_129] :
( U_137 = apply(U_133,U_129)
& in(U_129,U_141)
& in(U_129,relation_dom(U_133)) ) )
| ? [U_136] :
( ! [U_128] :
( U_136 != apply(U_133,U_128)
| ~ in(U_128,U_141)
| ~ in(U_128,relation_dom(U_133)) )
& in(U_136,U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( U_135 != apply(U_133,U_126)
| ~ in(U_126,U_140)
| ~ in(U_126,relation_dom(U_133)) ) )
& ! [U_134] :
( ( U_134 = apply(U_133,sK9(U_133,U_140,U_138,U_134))
& in(sK9(U_133,U_140,U_138,U_134),U_140)
& in(sK9(U_133,U_140,U_138,U_134),relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_125,sK9(U_133,U_140,U_138,U_134))],[f_55_3]) ).
fof(f_55_5,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_image(U_133,U_141)
| ? [U_137] :
( ~ in(U_137,U_139)
& ? [U_129] :
( U_137 = apply(U_133,U_129)
& in(U_129,U_141)
& in(U_129,relation_dom(U_133)) ) )
| ( ! [U_128] :
( sK10(U_133,U_141,U_139) != apply(U_133,U_128)
| ~ in(U_128,U_141)
| ~ in(U_128,relation_dom(U_133)) )
& in(sK10(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( U_135 != apply(U_133,U_126)
| ~ in(U_126,U_140)
| ~ in(U_126,relation_dom(U_133)) ) )
& ! [U_134] :
( ( U_134 = apply(U_133,sK9(U_133,U_140,U_138,U_134))
& in(sK9(U_133,U_140,U_138,U_134),U_140)
& in(sK9(U_133,U_140,U_138,U_134),relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_136,sK10(U_133,U_141,U_139))],[f_55_4]) ).
fof(f_55_6,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_image(U_133,U_141)
| ( ~ in(sK11(U_133,U_141,U_139),U_139)
& ? [U_129] :
( sK11(U_133,U_141,U_139) = apply(U_133,U_129)
& in(U_129,U_141)
& in(U_129,relation_dom(U_133)) ) )
| ( ! [U_128] :
( sK10(U_133,U_141,U_139) != apply(U_133,U_128)
| ~ in(U_128,U_141)
| ~ in(U_128,relation_dom(U_133)) )
& in(sK10(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( U_135 != apply(U_133,U_126)
| ~ in(U_126,U_140)
| ~ in(U_126,relation_dom(U_133)) ) )
& ! [U_134] :
( ( U_134 = apply(U_133,sK9(U_133,U_140,U_138,U_134))
& in(sK9(U_133,U_140,U_138,U_134),U_140)
& in(sK9(U_133,U_140,U_138,U_134),relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_137,sK11(U_133,U_141,U_139))],[f_55_5]) ).
fof(f_55_7,plain,
! [U_133] :
( ( ! [U_141,U_139] :
( U_139 = relation_image(U_133,U_141)
| ( ~ in(sK11(U_133,U_141,U_139),U_139)
& sK11(U_133,U_141,U_139) = apply(U_133,sK12(U_133,U_141,U_139))
& in(sK12(U_133,U_141,U_139),U_141)
& in(sK12(U_133,U_141,U_139),relation_dom(U_133)) )
| ( ! [U_128] :
( sK10(U_133,U_141,U_139) != apply(U_133,U_128)
| ~ in(U_128,U_141)
| ~ in(U_128,relation_dom(U_133)) )
& in(sK10(U_133,U_141,U_139),U_139) ) )
& ! [U_140,U_138] :
( ( ! [U_135] :
( in(U_135,U_138)
| ! [U_126] :
( U_135 != apply(U_133,U_126)
| ~ in(U_126,U_140)
| ~ in(U_126,relation_dom(U_133)) ) )
& ! [U_134] :
( ( U_134 = apply(U_133,sK9(U_133,U_140,U_138,U_134))
& in(sK9(U_133,U_140,U_138,U_134),U_140)
& in(sK9(U_133,U_140,U_138,U_134),relation_dom(U_133)) )
| ~ in(U_134,U_138) ) )
| U_138 != relation_image(U_133,U_140) ) )
| ~ function(U_133)
| ~ relation(U_133) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_129,sK12(U_133,U_141,U_139))],[f_55_6]) ).
fof(f_55_8,plain,
( ! [U_133,U_139,U_141] :
( ~ in(sK11(U_133,U_141,U_139),U_139)
| ~ sP39(U_133,U_139,U_141) )
& ! [U_133,U_139,U_141] :
( sK11(U_133,U_141,U_139) = apply(U_133,sK12(U_133,U_141,U_139))
| ~ sP39(U_133,U_139,U_141) )
& ! [U_133,U_139,U_141] :
( in(sK12(U_133,U_141,U_139),U_141)
| ~ sP39(U_133,U_139,U_141) )
& ! [U_133,U_139,U_141] :
( in(sK12(U_133,U_141,U_139),relation_dom(U_133))
| ~ sP39(U_133,U_139,U_141) )
& ! [U_128,U_133,U_139,U_141] :
( sK10(U_133,U_141,U_139) != apply(U_133,U_128)
| ~ in(U_128,U_141)
| ~ in(U_128,relation_dom(U_133))
| ~ sP38(U_128,U_133,U_139,U_141) )
& ! [U_128,U_133,U_139,U_141] :
( in(sK10(U_133,U_141,U_139),U_139)
| ~ sP38(U_128,U_133,U_139,U_141) )
& ! [U_134,U_133,U_138,U_140] :
( U_134 = apply(U_133,sK9(U_133,U_140,U_138,U_134))
| ~ sP36(U_134,U_133,U_138,U_140) )
& ! [U_134,U_133,U_138,U_140] :
( in(sK9(U_133,U_140,U_138,U_134),U_140)
| ~ sP36(U_134,U_133,U_138,U_140) )
& ! [U_134,U_133,U_138,U_140] :
( in(sK9(U_133,U_140,U_138,U_134),relation_dom(U_133))
| ~ sP36(U_134,U_133,U_138,U_140) )
& ! [U_134,U_126,U_135,U_133,U_138,U_140] :
( in(U_135,U_138)
| U_135 != apply(U_133,U_126)
| ~ in(U_126,U_140)
| ~ in(U_126,relation_dom(U_133))
| ~ sP37(U_134,U_126,U_135,U_133,U_138,U_140) )
& ! [U_134,U_126,U_135,U_133,U_138,U_140] :
( sP36(U_134,U_133,U_138,U_140)
| ~ in(U_134,U_138)
| ~ sP37(U_134,U_126,U_135,U_133,U_138,U_140) )
& ! [U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141] :
( U_139 = relation_image(U_133,U_141)
| sP39(U_133,U_139,U_141)
| sP38(U_128,U_133,U_139,U_141)
| ~ sP40(U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141) )
& ! [U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141] :
( sP37(U_134,U_126,U_135,U_133,U_138,U_140)
| U_138 != relation_image(U_133,U_140)
| ~ sP40(U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141) )
& ! [U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141] :
( sP40(U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141)
| ~ function(U_133)
| ~ relation(U_133) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36,sP37,sP38,sP39,sP40])],[f_55_7]) ).
cnf(f_55_9,plain,
( sP40(U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141)
| ~ function(U_133)
| ~ relation(U_133) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_10,plain,
( sP37(U_134,U_126,U_135,U_133,U_138,U_140)
| U_138 != relation_image(U_133,U_140)
| ~ sP40(U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_11,plain,
( U_139 = relation_image(U_133,U_141)
| sP39(U_133,U_139,U_141)
| sP38(U_128,U_133,U_139,U_141)
| ~ sP40(U_134,U_126,U_135,U_128,U_133,U_138,U_139,U_140,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_12,plain,
( sP36(U_134,U_133,U_138,U_140)
| ~ in(U_134,U_138)
| ~ sP37(U_134,U_126,U_135,U_133,U_138,U_140) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_13,plain,
( in(U_135,U_138)
| U_135 != apply(U_133,U_126)
| ~ in(U_126,U_140)
| ~ in(U_126,relation_dom(U_133))
| ~ sP37(U_134,U_126,U_135,U_133,U_138,U_140) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_14,plain,
( in(sK9(U_133,U_140,U_138,U_134),relation_dom(U_133))
| ~ sP36(U_134,U_133,U_138,U_140) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_15,plain,
( in(sK9(U_133,U_140,U_138,U_134),U_140)
| ~ sP36(U_134,U_133,U_138,U_140) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_16,plain,
( U_134 = apply(U_133,sK9(U_133,U_140,U_138,U_134))
| ~ sP36(U_134,U_133,U_138,U_140) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_17,plain,
( in(sK10(U_133,U_141,U_139),U_139)
| ~ sP38(U_128,U_133,U_139,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_18,plain,
( sK10(U_133,U_141,U_139) != apply(U_133,U_128)
| ~ in(U_128,U_141)
| ~ in(U_128,relation_dom(U_133))
| ~ sP38(U_128,U_133,U_139,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_19,plain,
( in(sK12(U_133,U_141,U_139),relation_dom(U_133))
| ~ sP39(U_133,U_139,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_20,plain,
( in(sK12(U_133,U_141,U_139),U_141)
| ~ sP39(U_133,U_139,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_21,plain,
( sK11(U_133,U_141,U_139) = apply(U_133,sK12(U_133,U_141,U_139))
| ~ sP39(U_133,U_139,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
cnf(f_55_22,plain,
( ~ in(sK11(U_133,U_141,U_139),U_139)
| ~ sP39(U_133,U_139,U_141) ),
inference(clausify,[status(thm)],[f_55_8]) ).
fof(f_56_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_56_2,plain,
! [U_148,U_147] :
( ! [U_146] :
( ( ( U_146 = relation_rng_restriction(U_148,U_147)
| ? [U_145,U_144] :
( ( ~ in(ordered_pair(U_145,U_144),U_146)
& in(ordered_pair(U_145,U_144),U_147)
& in(U_144,U_148) )
| ( ( ~ in(ordered_pair(U_145,U_144),U_147)
| ~ in(U_144,U_148) )
& in(ordered_pair(U_145,U_144),U_146) ) ) )
& ( ! [U_143,U_142] :
( ( in(ordered_pair(U_143,U_142),U_146)
| ~ in(ordered_pair(U_143,U_142),U_147)
| ~ in(U_142,U_148) )
& ( ( in(ordered_pair(U_143,U_142),U_147)
& in(U_142,U_148) )
| ~ in(ordered_pair(U_143,U_142),U_146) ) )
| U_146 != relation_rng_restriction(U_148,U_147) ) )
| ~ relation(U_146) )
| ~ relation(U_147) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_148,U_147] :
( ! [U_146] :
( ( ( U_146 = relation_rng_restriction(U_148,U_147)
| ? [U_156,U_154] :
( ~ in(ordered_pair(U_156,U_154),U_146)
& in(ordered_pair(U_156,U_154),U_147)
& in(U_154,U_148) )
| ? [U_155,U_153] :
( ( ~ in(ordered_pair(U_155,U_153),U_147)
| ~ in(U_153,U_148) )
& in(ordered_pair(U_155,U_153),U_146) ) )
& ( ( ! [U_152,U_150] :
( in(ordered_pair(U_152,U_150),U_146)
| ~ in(ordered_pair(U_152,U_150),U_147)
| ~ in(U_150,U_148) )
& ! [U_151,U_149] :
( ( in(ordered_pair(U_151,U_149),U_147)
& in(U_149,U_148) )
| ~ in(ordered_pair(U_151,U_149),U_146) ) )
| U_146 != relation_rng_restriction(U_148,U_147) ) )
| ~ relation(U_146) )
| ~ relation(U_147) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
! [U_148,U_147] :
( ! [U_146] :
( ( ( U_146 = relation_rng_restriction(U_148,U_147)
| ? [U_156,U_154] :
( ~ in(ordered_pair(U_156,U_154),U_146)
& in(ordered_pair(U_156,U_154),U_147)
& in(U_154,U_148) )
| ? [U_153] :
( ( ~ in(ordered_pair(sK13(U_148,U_147,U_146),U_153),U_147)
| ~ in(U_153,U_148) )
& in(ordered_pair(sK13(U_148,U_147,U_146),U_153),U_146) ) )
& ( ( ! [U_152,U_150] :
( in(ordered_pair(U_152,U_150),U_146)
| ~ in(ordered_pair(U_152,U_150),U_147)
| ~ in(U_150,U_148) )
& ! [U_151,U_149] :
( ( in(ordered_pair(U_151,U_149),U_147)
& in(U_149,U_148) )
| ~ in(ordered_pair(U_151,U_149),U_146) ) )
| U_146 != relation_rng_restriction(U_148,U_147) ) )
| ~ relation(U_146) )
| ~ relation(U_147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_155,sK13(U_148,U_147,U_146))],[f_56_3]) ).
fof(f_56_5,plain,
! [U_148,U_147] :
( ! [U_146] :
( ( ( U_146 = relation_rng_restriction(U_148,U_147)
| ? [U_156,U_154] :
( ~ in(ordered_pair(U_156,U_154),U_146)
& in(ordered_pair(U_156,U_154),U_147)
& in(U_154,U_148) )
| ( ( ~ in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_147)
| ~ in(sK14(U_148,U_147,U_146),U_148) )
& in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_146) ) )
& ( ( ! [U_152,U_150] :
( in(ordered_pair(U_152,U_150),U_146)
| ~ in(ordered_pair(U_152,U_150),U_147)
| ~ in(U_150,U_148) )
& ! [U_151,U_149] :
( ( in(ordered_pair(U_151,U_149),U_147)
& in(U_149,U_148) )
| ~ in(ordered_pair(U_151,U_149),U_146) ) )
| U_146 != relation_rng_restriction(U_148,U_147) ) )
| ~ relation(U_146) )
| ~ relation(U_147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_153,sK14(U_148,U_147,U_146))],[f_56_4]) ).
fof(f_56_6,plain,
! [U_148,U_147] :
( ! [U_146] :
( ( ( U_146 = relation_rng_restriction(U_148,U_147)
| ? [U_154] :
( ~ in(ordered_pair(sK15(U_148,U_147,U_146),U_154),U_146)
& in(ordered_pair(sK15(U_148,U_147,U_146),U_154),U_147)
& in(U_154,U_148) )
| ( ( ~ in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_147)
| ~ in(sK14(U_148,U_147,U_146),U_148) )
& in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_146) ) )
& ( ( ! [U_152,U_150] :
( in(ordered_pair(U_152,U_150),U_146)
| ~ in(ordered_pair(U_152,U_150),U_147)
| ~ in(U_150,U_148) )
& ! [U_151,U_149] :
( ( in(ordered_pair(U_151,U_149),U_147)
& in(U_149,U_148) )
| ~ in(ordered_pair(U_151,U_149),U_146) ) )
| U_146 != relation_rng_restriction(U_148,U_147) ) )
| ~ relation(U_146) )
| ~ relation(U_147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_156,sK15(U_148,U_147,U_146))],[f_56_5]) ).
fof(f_56_7,plain,
! [U_148,U_147] :
( ! [U_146] :
( ( ( U_146 = relation_rng_restriction(U_148,U_147)
| ( ~ in(ordered_pair(sK15(U_148,U_147,U_146),sK16(U_148,U_147,U_146)),U_146)
& in(ordered_pair(sK15(U_148,U_147,U_146),sK16(U_148,U_147,U_146)),U_147)
& in(sK16(U_148,U_147,U_146),U_148) )
| ( ( ~ in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_147)
| ~ in(sK14(U_148,U_147,U_146),U_148) )
& in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_146) ) )
& ( ( ! [U_152,U_150] :
( in(ordered_pair(U_152,U_150),U_146)
| ~ in(ordered_pair(U_152,U_150),U_147)
| ~ in(U_150,U_148) )
& ! [U_151,U_149] :
( ( in(ordered_pair(U_151,U_149),U_147)
& in(U_149,U_148) )
| ~ in(ordered_pair(U_151,U_149),U_146) ) )
| U_146 != relation_rng_restriction(U_148,U_147) ) )
| ~ relation(U_146) )
| ~ relation(U_147) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_154,sK16(U_148,U_147,U_146))],[f_56_6]) ).
fof(f_56_8,plain,
( ! [U_146,U_148,U_147] :
( ~ in(ordered_pair(sK15(U_148,U_147,U_146),sK16(U_148,U_147,U_146)),U_146)
| ~ sP44(U_146,U_148,U_147) )
& ! [U_146,U_148,U_147] :
( in(ordered_pair(sK15(U_148,U_147,U_146),sK16(U_148,U_147,U_146)),U_147)
| ~ sP44(U_146,U_148,U_147) )
& ! [U_146,U_148,U_147] :
( in(sK16(U_148,U_147,U_146),U_148)
| ~ sP44(U_146,U_148,U_147) )
& ! [U_146,U_148,U_147] :
( ~ in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_147)
| ~ in(sK14(U_148,U_147,U_146),U_148)
| ~ sP43(U_146,U_148,U_147) )
& ! [U_146,U_148,U_147] :
( in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_146)
| ~ sP43(U_146,U_148,U_147) )
& ! [U_149,U_151,U_148,U_147] :
( in(ordered_pair(U_151,U_149),U_147)
| ~ sP41(U_149,U_151,U_148,U_147) )
& ! [U_149,U_151,U_148,U_147] :
( in(U_149,U_148)
| ~ sP41(U_149,U_151,U_148,U_147) )
& ! [U_149,U_150,U_152,U_146,U_151,U_148,U_147] :
( in(ordered_pair(U_152,U_150),U_146)
| ~ in(ordered_pair(U_152,U_150),U_147)
| ~ in(U_150,U_148)
| ~ sP42(U_149,U_150,U_152,U_146,U_151,U_148,U_147) )
& ! [U_149,U_150,U_152,U_146,U_151,U_148,U_147] :
( sP41(U_149,U_151,U_148,U_147)
| ~ in(ordered_pair(U_151,U_149),U_146)
| ~ sP42(U_149,U_150,U_152,U_146,U_151,U_148,U_147) )
& ! [U_149,U_150,U_152,U_146,U_151,U_148,U_147] :
( U_146 = relation_rng_restriction(U_148,U_147)
| sP44(U_146,U_148,U_147)
| sP43(U_146,U_148,U_147)
| ~ sP45(U_149,U_150,U_152,U_146,U_151,U_148,U_147) )
& ! [U_149,U_150,U_152,U_146,U_151,U_148,U_147] :
( sP42(U_149,U_150,U_152,U_146,U_151,U_148,U_147)
| U_146 != relation_rng_restriction(U_148,U_147)
| ~ sP45(U_149,U_150,U_152,U_146,U_151,U_148,U_147) )
& ! [U_149,U_150,U_152,U_146,U_151,U_148,U_147] :
( sP45(U_149,U_150,U_152,U_146,U_151,U_148,U_147)
| ~ relation(U_146)
| ~ relation(U_147) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42,sP43,sP44,sP45])],[f_56_7]) ).
cnf(f_56_9,plain,
( sP45(U_149,U_150,U_152,U_146,U_151,U_148,U_147)
| ~ relation(U_146)
| ~ relation(U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_10,plain,
( sP42(U_149,U_150,U_152,U_146,U_151,U_148,U_147)
| U_146 != relation_rng_restriction(U_148,U_147)
| ~ sP45(U_149,U_150,U_152,U_146,U_151,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_11,plain,
( U_146 = relation_rng_restriction(U_148,U_147)
| sP44(U_146,U_148,U_147)
| sP43(U_146,U_148,U_147)
| ~ sP45(U_149,U_150,U_152,U_146,U_151,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_12,plain,
( sP41(U_149,U_151,U_148,U_147)
| ~ in(ordered_pair(U_151,U_149),U_146)
| ~ sP42(U_149,U_150,U_152,U_146,U_151,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_13,plain,
( in(ordered_pair(U_152,U_150),U_146)
| ~ in(ordered_pair(U_152,U_150),U_147)
| ~ in(U_150,U_148)
| ~ sP42(U_149,U_150,U_152,U_146,U_151,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_14,plain,
( in(U_149,U_148)
| ~ sP41(U_149,U_151,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_15,plain,
( in(ordered_pair(U_151,U_149),U_147)
| ~ sP41(U_149,U_151,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_16,plain,
( in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_146)
| ~ sP43(U_146,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_17,plain,
( ~ in(ordered_pair(sK13(U_148,U_147,U_146),sK14(U_148,U_147,U_146)),U_147)
| ~ in(sK14(U_148,U_147,U_146),U_148)
| ~ sP43(U_146,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_18,plain,
( in(sK16(U_148,U_147,U_146),U_148)
| ~ sP44(U_146,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_19,plain,
( in(ordered_pair(sK15(U_148,U_147,U_146),sK16(U_148,U_147,U_146)),U_147)
| ~ sP44(U_146,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
cnf(f_56_20,plain,
( ~ in(ordered_pair(sK15(U_148,U_147,U_146),sK16(U_148,U_147,U_146)),U_146)
| ~ sP44(U_146,U_148,U_147) ),
inference(clausify,[status(thm)],[f_56_8]) ).
fof(f_57_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_57_2,plain,
! [U_157] :
( ( ( antisymmetric(U_157)
| ~ is_antisymmetric_in(U_157,relation_field(U_157)) )
& ( is_antisymmetric_in(U_157,relation_field(U_157))
| ~ antisymmetric(U_157) ) )
| ~ relation(U_157) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_157] :
( antisymmetric(U_157)
| ~ is_antisymmetric_in(U_157,relation_field(U_157))
| ~ sP46(U_157) )
& ! [U_157] :
( is_antisymmetric_in(U_157,relation_field(U_157))
| ~ antisymmetric(U_157)
| ~ sP46(U_157) )
& ! [U_157] :
( sP46(U_157)
| ~ relation(U_157) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_57_2]) ).
cnf(f_57_4,plain,
( sP46(U_157)
| ~ relation(U_157) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( is_antisymmetric_in(U_157,relation_field(U_157))
| ~ antisymmetric(U_157)
| ~ sP46(U_157) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_6,plain,
( antisymmetric(U_157)
| ~ is_antisymmetric_in(U_157,relation_field(U_157))
| ~ sP46(U_157) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_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_58_2,plain,
! [U_162] :
( ! [U_161,U_160] :
( ( U_160 = relation_inverse_image(U_162,U_161)
| ? [U_159] :
( ( ~ in(U_159,U_160)
& in(apply(U_162,U_159),U_161)
& in(U_159,relation_dom(U_162)) )
| ( ( ~ in(apply(U_162,U_159),U_161)
| ~ in(U_159,relation_dom(U_162)) )
& in(U_159,U_160) ) ) )
& ( ! [U_158] :
( ( in(U_158,U_160)
| ~ in(apply(U_162,U_158),U_161)
| ~ in(U_158,relation_dom(U_162)) )
& ( ( in(apply(U_162,U_158),U_161)
& in(U_158,relation_dom(U_162)) )
| ~ in(U_158,U_160) ) )
| U_160 != relation_inverse_image(U_162,U_161) ) )
| ~ function(U_162)
| ~ relation(U_162) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_162] :
( ( ! [U_170,U_168] :
( U_168 = relation_inverse_image(U_162,U_170)
| ? [U_166] :
( ~ in(U_166,U_168)
& in(apply(U_162,U_166),U_170)
& in(U_166,relation_dom(U_162)) )
| ? [U_165] :
( ( ~ in(apply(U_162,U_165),U_170)
| ~ in(U_165,relation_dom(U_162)) )
& in(U_165,U_168) ) )
& ! [U_169,U_167] :
( ( ! [U_164] :
( in(U_164,U_167)
| ~ in(apply(U_162,U_164),U_169)
| ~ in(U_164,relation_dom(U_162)) )
& ! [U_163] :
( ( in(apply(U_162,U_163),U_169)
& in(U_163,relation_dom(U_162)) )
| ~ in(U_163,U_167) ) )
| U_167 != relation_inverse_image(U_162,U_169) ) )
| ~ function(U_162)
| ~ relation(U_162) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
fof(f_58_4,plain,
! [U_162] :
( ( ! [U_170,U_168] :
( U_168 = relation_inverse_image(U_162,U_170)
| ? [U_166] :
( ~ in(U_166,U_168)
& in(apply(U_162,U_166),U_170)
& in(U_166,relation_dom(U_162)) )
| ( ( ~ in(apply(U_162,sK17(U_162,U_170,U_168)),U_170)
| ~ in(sK17(U_162,U_170,U_168),relation_dom(U_162)) )
& in(sK17(U_162,U_170,U_168),U_168) ) )
& ! [U_169,U_167] :
( ( ! [U_164] :
( in(U_164,U_167)
| ~ in(apply(U_162,U_164),U_169)
| ~ in(U_164,relation_dom(U_162)) )
& ! [U_163] :
( ( in(apply(U_162,U_163),U_169)
& in(U_163,relation_dom(U_162)) )
| ~ in(U_163,U_167) ) )
| U_167 != relation_inverse_image(U_162,U_169) ) )
| ~ function(U_162)
| ~ relation(U_162) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_165,sK17(U_162,U_170,U_168))],[f_58_3]) ).
fof(f_58_5,plain,
! [U_162] :
( ( ! [U_170,U_168] :
( U_168 = relation_inverse_image(U_162,U_170)
| ( ~ in(sK18(U_162,U_170,U_168),U_168)
& in(apply(U_162,sK18(U_162,U_170,U_168)),U_170)
& in(sK18(U_162,U_170,U_168),relation_dom(U_162)) )
| ( ( ~ in(apply(U_162,sK17(U_162,U_170,U_168)),U_170)
| ~ in(sK17(U_162,U_170,U_168),relation_dom(U_162)) )
& in(sK17(U_162,U_170,U_168),U_168) ) )
& ! [U_169,U_167] :
( ( ! [U_164] :
( in(U_164,U_167)
| ~ in(apply(U_162,U_164),U_169)
| ~ in(U_164,relation_dom(U_162)) )
& ! [U_163] :
( ( in(apply(U_162,U_163),U_169)
& in(U_163,relation_dom(U_162)) )
| ~ in(U_163,U_167) ) )
| U_167 != relation_inverse_image(U_162,U_169) ) )
| ~ function(U_162)
| ~ relation(U_162) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_166,sK18(U_162,U_170,U_168))],[f_58_4]) ).
fof(f_58_6,plain,
( ! [U_162,U_170,U_168] :
( ~ in(sK18(U_162,U_170,U_168),U_168)
| ~ sP50(U_162,U_170,U_168) )
& ! [U_162,U_170,U_168] :
( in(apply(U_162,sK18(U_162,U_170,U_168)),U_170)
| ~ sP50(U_162,U_170,U_168) )
& ! [U_162,U_170,U_168] :
( in(sK18(U_162,U_170,U_168),relation_dom(U_162))
| ~ sP50(U_162,U_170,U_168) )
& ! [U_162,U_170,U_168] :
( ~ in(apply(U_162,sK17(U_162,U_170,U_168)),U_170)
| ~ in(sK17(U_162,U_170,U_168),relation_dom(U_162))
| ~ sP49(U_162,U_170,U_168) )
& ! [U_162,U_170,U_168] :
( in(sK17(U_162,U_170,U_168),U_168)
| ~ sP49(U_162,U_170,U_168) )
& ! [U_169,U_162,U_163] :
( in(apply(U_162,U_163),U_169)
| ~ sP47(U_169,U_162,U_163) )
& ! [U_169,U_162,U_163] :
( in(U_163,relation_dom(U_162))
| ~ sP47(U_169,U_162,U_163) )
& ! [U_167,U_164,U_169,U_162,U_163] :
( in(U_164,U_167)
| ~ in(apply(U_162,U_164),U_169)
| ~ in(U_164,relation_dom(U_162))
| ~ sP48(U_167,U_164,U_169,U_162,U_163) )
& ! [U_167,U_164,U_169,U_162,U_163] :
( sP47(U_169,U_162,U_163)
| ~ in(U_163,U_167)
| ~ sP48(U_167,U_164,U_169,U_162,U_163) )
& ! [U_167,U_164,U_169,U_162,U_163,U_170,U_168] :
( U_168 = relation_inverse_image(U_162,U_170)
| sP50(U_162,U_170,U_168)
| sP49(U_162,U_170,U_168)
| ~ sP51(U_167,U_164,U_169,U_162,U_163,U_170,U_168) )
& ! [U_167,U_164,U_169,U_162,U_163,U_170,U_168] :
( sP48(U_167,U_164,U_169,U_162,U_163)
| U_167 != relation_inverse_image(U_162,U_169)
| ~ sP51(U_167,U_164,U_169,U_162,U_163,U_170,U_168) )
& ! [U_167,U_164,U_169,U_162,U_163,U_170,U_168] :
( sP51(U_167,U_164,U_169,U_162,U_163,U_170,U_168)
| ~ function(U_162)
| ~ relation(U_162) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47,sP48,sP49,sP50,sP51])],[f_58_5]) ).
cnf(f_58_7,plain,
( sP51(U_167,U_164,U_169,U_162,U_163,U_170,U_168)
| ~ function(U_162)
| ~ relation(U_162) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_8,plain,
( sP48(U_167,U_164,U_169,U_162,U_163)
| U_167 != relation_inverse_image(U_162,U_169)
| ~ sP51(U_167,U_164,U_169,U_162,U_163,U_170,U_168) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_9,plain,
( U_168 = relation_inverse_image(U_162,U_170)
| sP50(U_162,U_170,U_168)
| sP49(U_162,U_170,U_168)
| ~ sP51(U_167,U_164,U_169,U_162,U_163,U_170,U_168) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_10,plain,
( sP47(U_169,U_162,U_163)
| ~ in(U_163,U_167)
| ~ sP48(U_167,U_164,U_169,U_162,U_163) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_11,plain,
( in(U_164,U_167)
| ~ in(apply(U_162,U_164),U_169)
| ~ in(U_164,relation_dom(U_162))
| ~ sP48(U_167,U_164,U_169,U_162,U_163) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_12,plain,
( in(U_163,relation_dom(U_162))
| ~ sP47(U_169,U_162,U_163) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_13,plain,
( in(apply(U_162,U_163),U_169)
| ~ sP47(U_169,U_162,U_163) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_14,plain,
( in(sK17(U_162,U_170,U_168),U_168)
| ~ sP49(U_162,U_170,U_168) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_15,plain,
( ~ in(apply(U_162,sK17(U_162,U_170,U_168)),U_170)
| ~ in(sK17(U_162,U_170,U_168),relation_dom(U_162))
| ~ sP49(U_162,U_170,U_168) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_16,plain,
( in(sK18(U_162,U_170,U_168),relation_dom(U_162))
| ~ sP50(U_162,U_170,U_168) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_17,plain,
( in(apply(U_162,sK18(U_162,U_170,U_168)),U_170)
| ~ sP50(U_162,U_170,U_168) ),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_18,plain,
( ~ in(sK18(U_162,U_170,U_168),U_168)
| ~ sP50(U_162,U_170,U_168) ),
inference(clausify,[status(thm)],[f_58_6]) ).
fof(f_59_1,plain,
! [A] :
( ( ( lower_bounded_semilattstr(A)
| ! [B] :
( ? [C] :
( ( meet(A,C,B) != B
| meet(A,B,C) != B )
& element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) ) )
& ( ? [B] :
( ! [C] :
( ( meet(A,C,B) = B
& meet(A,B,C) = B )
| ~ element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
| ~ lower_bounded_semilattstr(A) ) )
| ~ meet_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d13_lattices]) ).
fof(f_59_2,plain,
! [U_175] :
( ( ( lower_bounded_semilattstr(U_175)
| ! [U_174] :
( ? [U_173] :
( ( meet(U_175,U_173,U_174) != U_174
| meet(U_175,U_174,U_173) != U_174 )
& element(U_173,the_carrier(U_175)) )
| ~ element(U_174,the_carrier(U_175)) ) )
& ( ? [U_172] :
( ! [U_171] :
( ( meet(U_175,U_171,U_172) = U_172
& meet(U_175,U_172,U_171) = U_172 )
| ~ element(U_171,the_carrier(U_175)) )
& element(U_172,the_carrier(U_175)) )
| ~ lower_bounded_semilattstr(U_175) ) )
| ~ meet_semilatt_str(U_175)
| empty_carrier(U_175) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_175] :
( ( ( lower_bounded_semilattstr(U_175)
| ! [U_174] :
( ? [U_173] :
( ( meet(U_175,U_173,U_174) != U_174
| meet(U_175,U_174,U_173) != U_174 )
& element(U_173,the_carrier(U_175)) )
| ~ element(U_174,the_carrier(U_175)) ) )
& ( ( ! [U_171] :
( ( meet(U_175,U_171,sK19(U_175)) = sK19(U_175)
& meet(U_175,sK19(U_175),U_171) = sK19(U_175) )
| ~ element(U_171,the_carrier(U_175)) )
& element(sK19(U_175),the_carrier(U_175)) )
| ~ lower_bounded_semilattstr(U_175) ) )
| ~ meet_semilatt_str(U_175)
| empty_carrier(U_175) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_172,sK19(U_175))],[f_59_2]) ).
fof(f_59_4,plain,
! [U_175] :
( ( ( lower_bounded_semilattstr(U_175)
| ! [U_174] :
( ( ( meet(U_175,sK20(U_175,U_174),U_174) != U_174
| meet(U_175,U_174,sK20(U_175,U_174)) != U_174 )
& element(sK20(U_175,U_174),the_carrier(U_175)) )
| ~ element(U_174,the_carrier(U_175)) ) )
& ( ( ! [U_171] :
( ( meet(U_175,U_171,sK19(U_175)) = sK19(U_175)
& meet(U_175,sK19(U_175),U_171) = sK19(U_175) )
| ~ element(U_171,the_carrier(U_175)) )
& element(sK19(U_175),the_carrier(U_175)) )
| ~ lower_bounded_semilattstr(U_175) ) )
| ~ meet_semilatt_str(U_175)
| empty_carrier(U_175) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_173,sK20(U_175,U_174))],[f_59_3]) ).
fof(f_59_5,plain,
( ! [U_175,U_174] :
( meet(U_175,sK20(U_175,U_174),U_174) != U_174
| meet(U_175,U_174,sK20(U_175,U_174)) != U_174
| ~ sP54(U_175,U_174) )
& ! [U_175,U_174] :
( element(sK20(U_175,U_174),the_carrier(U_175))
| ~ sP54(U_175,U_174) )
& ! [U_175,U_171] :
( meet(U_175,U_171,sK19(U_175)) = sK19(U_175)
| ~ sP52(U_175,U_171) )
& ! [U_175,U_171] :
( meet(U_175,sK19(U_175),U_171) = sK19(U_175)
| ~ sP52(U_175,U_171) )
& ! [U_175,U_171] :
( sP52(U_175,U_171)
| ~ element(U_171,the_carrier(U_175))
| ~ sP53(U_175,U_171) )
& ! [U_175,U_171] :
( element(sK19(U_175),the_carrier(U_175))
| ~ sP53(U_175,U_171) )
& ! [U_175,U_171,U_174] :
( lower_bounded_semilattstr(U_175)
| sP54(U_175,U_174)
| ~ element(U_174,the_carrier(U_175))
| ~ sP55(U_175,U_171,U_174) )
& ! [U_175,U_171,U_174] :
( sP53(U_175,U_171)
| ~ lower_bounded_semilattstr(U_175)
| ~ sP55(U_175,U_171,U_174) )
& ! [U_175,U_171,U_174] :
( sP55(U_175,U_171,U_174)
| ~ meet_semilatt_str(U_175)
| empty_carrier(U_175) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52,sP53,sP54,sP55])],[f_59_4]) ).
cnf(f_59_6,plain,
( sP55(U_175,U_171,U_174)
| ~ meet_semilatt_str(U_175)
| empty_carrier(U_175) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_7,plain,
( sP53(U_175,U_171)
| ~ lower_bounded_semilattstr(U_175)
| ~ sP55(U_175,U_171,U_174) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_8,plain,
( lower_bounded_semilattstr(U_175)
| sP54(U_175,U_174)
| ~ element(U_174,the_carrier(U_175))
| ~ sP55(U_175,U_171,U_174) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_9,plain,
( element(sK19(U_175),the_carrier(U_175))
| ~ sP53(U_175,U_171) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_10,plain,
( sP52(U_175,U_171)
| ~ element(U_171,the_carrier(U_175))
| ~ sP53(U_175,U_171) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_11,plain,
( meet(U_175,sK19(U_175),U_171) = sK19(U_175)
| ~ sP52(U_175,U_171) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_12,plain,
( meet(U_175,U_171,sK19(U_175)) = sK19(U_175)
| ~ sP52(U_175,U_171) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_13,plain,
( element(sK20(U_175,U_174),the_carrier(U_175))
| ~ sP54(U_175,U_174) ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_14,plain,
( meet(U_175,sK20(U_175,U_174),U_174) != U_174
| meet(U_175,U_174,sK20(U_175,U_174)) != U_174
| ~ sP54(U_175,U_174) ),
inference(clausify,[status(thm)],[f_59_5]) ).
fof(f_60_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( C = topstr_closure(A,B)
| ? [D] :
( ( ( ~ in(D,C)
& ! [E] :
( ~ disjoint(B,E)
| ~ in(D,E)
| ~ open_subset(E,A)
| ~ element(E,powerset(the_carrier(A))) ) )
| ( ? [E] :
( disjoint(B,E)
& in(D,E)
& open_subset(E,A)
& element(E,powerset(the_carrier(A))) )
& in(D,C) ) )
& in(D,the_carrier(A)) ) )
& ( ! [D] :
( ( ( in(D,C)
| ? [E] :
( disjoint(B,E)
& in(D,E)
& open_subset(E,A)
& element(E,powerset(the_carrier(A))) ) )
& ( ! [E] :
( ~ disjoint(B,E)
| ~ in(D,E)
| ~ open_subset(E,A)
| ~ element(E,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ~ in(D,the_carrier(A)) )
| C != topstr_closure(A,B) ) )
| ~ element(C,powerset(the_carrier(A))) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d13_pre_topc]) ).
fof(f_60_2,plain,
! [U_184] :
( ! [U_183] :
( ! [U_182] :
( ( ( U_182 = topstr_closure(U_184,U_183)
| ? [U_181] :
( ( ( ~ in(U_181,U_182)
& ! [U_180] :
( ~ disjoint(U_183,U_180)
| ~ in(U_181,U_180)
| ~ open_subset(U_180,U_184)
| ~ element(U_180,powerset(the_carrier(U_184))) ) )
| ( ? [U_179] :
( disjoint(U_183,U_179)
& in(U_181,U_179)
& open_subset(U_179,U_184)
& element(U_179,powerset(the_carrier(U_184))) )
& in(U_181,U_182) ) )
& in(U_181,the_carrier(U_184)) ) )
& ( ! [U_178] :
( ( ( in(U_178,U_182)
| ? [U_177] :
( disjoint(U_183,U_177)
& in(U_178,U_177)
& open_subset(U_177,U_184)
& element(U_177,powerset(the_carrier(U_184))) ) )
& ( ! [U_176] :
( ~ disjoint(U_183,U_176)
| ~ in(U_178,U_176)
| ~ open_subset(U_176,U_184)
| ~ element(U_176,powerset(the_carrier(U_184))) )
| ~ in(U_178,U_182) ) )
| ~ in(U_178,the_carrier(U_184)) )
| U_182 != topstr_closure(U_184,U_183) ) )
| ~ element(U_182,powerset(the_carrier(U_184))) )
| ~ element(U_183,powerset(the_carrier(U_184))) )
| ~ top_str(U_184) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_184] :
( ! [U_183] :
( ! [U_182] :
( ( ( U_182 = topstr_closure(U_184,U_183)
| ? [U_181] :
( ( ( ~ in(U_181,U_182)
& ! [U_180] :
( ~ disjoint(U_183,U_180)
| ~ in(U_181,U_180)
| ~ open_subset(U_180,U_184)
| ~ element(U_180,powerset(the_carrier(U_184))) ) )
| ( ? [U_179] :
( disjoint(U_183,U_179)
& in(U_181,U_179)
& open_subset(U_179,U_184)
& element(U_179,powerset(the_carrier(U_184))) )
& in(U_181,U_182) ) )
& in(U_181,the_carrier(U_184)) ) )
& ( ! [U_178] :
( ( ( in(U_178,U_182)
| ( disjoint(U_183,sK21(U_184,U_183,U_182,U_178))
& in(U_178,sK21(U_184,U_183,U_182,U_178))
& open_subset(sK21(U_184,U_183,U_182,U_178),U_184)
& element(sK21(U_184,U_183,U_182,U_178),powerset(the_carrier(U_184))) ) )
& ( ! [U_176] :
( ~ disjoint(U_183,U_176)
| ~ in(U_178,U_176)
| ~ open_subset(U_176,U_184)
| ~ element(U_176,powerset(the_carrier(U_184))) )
| ~ in(U_178,U_182) ) )
| ~ in(U_178,the_carrier(U_184)) )
| U_182 != topstr_closure(U_184,U_183) ) )
| ~ element(U_182,powerset(the_carrier(U_184))) )
| ~ element(U_183,powerset(the_carrier(U_184))) )
| ~ top_str(U_184) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_177,sK21(U_184,U_183,U_182,U_178))],[f_60_2]) ).
fof(f_60_4,plain,
! [U_184] :
( ! [U_183] :
( ! [U_182] :
( ( ( U_182 = topstr_closure(U_184,U_183)
| ( ( ( ~ in(sK22(U_184,U_183,U_182),U_182)
& ! [U_180] :
( ~ disjoint(U_183,U_180)
| ~ in(sK22(U_184,U_183,U_182),U_180)
| ~ open_subset(U_180,U_184)
| ~ element(U_180,powerset(the_carrier(U_184))) ) )
| ( ? [U_179] :
( disjoint(U_183,U_179)
& in(sK22(U_184,U_183,U_182),U_179)
& open_subset(U_179,U_184)
& element(U_179,powerset(the_carrier(U_184))) )
& in(sK22(U_184,U_183,U_182),U_182) ) )
& in(sK22(U_184,U_183,U_182),the_carrier(U_184)) ) )
& ( ! [U_178] :
( ( ( in(U_178,U_182)
| ( disjoint(U_183,sK21(U_184,U_183,U_182,U_178))
& in(U_178,sK21(U_184,U_183,U_182,U_178))
& open_subset(sK21(U_184,U_183,U_182,U_178),U_184)
& element(sK21(U_184,U_183,U_182,U_178),powerset(the_carrier(U_184))) ) )
& ( ! [U_176] :
( ~ disjoint(U_183,U_176)
| ~ in(U_178,U_176)
| ~ open_subset(U_176,U_184)
| ~ element(U_176,powerset(the_carrier(U_184))) )
| ~ in(U_178,U_182) ) )
| ~ in(U_178,the_carrier(U_184)) )
| U_182 != topstr_closure(U_184,U_183) ) )
| ~ element(U_182,powerset(the_carrier(U_184))) )
| ~ element(U_183,powerset(the_carrier(U_184))) )
| ~ top_str(U_184) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_181,sK22(U_184,U_183,U_182))],[f_60_3]) ).
fof(f_60_5,plain,
! [U_184] :
( ! [U_183] :
( ! [U_182] :
( ( ( U_182 = topstr_closure(U_184,U_183)
| ( ( ( ~ in(sK22(U_184,U_183,U_182),U_182)
& ! [U_180] :
( ~ disjoint(U_183,U_180)
| ~ in(sK22(U_184,U_183,U_182),U_180)
| ~ open_subset(U_180,U_184)
| ~ element(U_180,powerset(the_carrier(U_184))) ) )
| ( disjoint(U_183,sK23(U_184,U_183,U_182))
& in(sK22(U_184,U_183,U_182),sK23(U_184,U_183,U_182))
& open_subset(sK23(U_184,U_183,U_182),U_184)
& element(sK23(U_184,U_183,U_182),powerset(the_carrier(U_184)))
& in(sK22(U_184,U_183,U_182),U_182) ) )
& in(sK22(U_184,U_183,U_182),the_carrier(U_184)) ) )
& ( ! [U_178] :
( ( ( in(U_178,U_182)
| ( disjoint(U_183,sK21(U_184,U_183,U_182,U_178))
& in(U_178,sK21(U_184,U_183,U_182,U_178))
& open_subset(sK21(U_184,U_183,U_182,U_178),U_184)
& element(sK21(U_184,U_183,U_182,U_178),powerset(the_carrier(U_184))) ) )
& ( ! [U_176] :
( ~ disjoint(U_183,U_176)
| ~ in(U_178,U_176)
| ~ open_subset(U_176,U_184)
| ~ element(U_176,powerset(the_carrier(U_184))) )
| ~ in(U_178,U_182) ) )
| ~ in(U_178,the_carrier(U_184)) )
| U_182 != topstr_closure(U_184,U_183) ) )
| ~ element(U_182,powerset(the_carrier(U_184))) )
| ~ element(U_183,powerset(the_carrier(U_184))) )
| ~ top_str(U_184) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_179,sK23(U_184,U_183,U_182))],[f_60_4]) ).
fof(f_60_6,plain,
( ! [U_183,U_180,U_184,U_182] :
( ~ in(sK22(U_184,U_183,U_182),U_182)
| ~ sP59(U_183,U_180,U_184,U_182) )
& ! [U_183,U_180,U_184,U_182] :
( ~ disjoint(U_183,U_180)
| ~ in(sK22(U_184,U_183,U_182),U_180)
| ~ open_subset(U_180,U_184)
| ~ element(U_180,powerset(the_carrier(U_184)))
| ~ sP59(U_183,U_180,U_184,U_182) )
& ! [U_183,U_184,U_182] :
( disjoint(U_183,sK23(U_184,U_183,U_182))
| ~ sP58(U_183,U_184,U_182) )
& ! [U_183,U_184,U_182] :
( in(sK22(U_184,U_183,U_182),sK23(U_184,U_183,U_182))
| ~ sP58(U_183,U_184,U_182) )
& ! [U_183,U_184,U_182] :
( open_subset(sK23(U_184,U_183,U_182),U_184)
| ~ sP58(U_183,U_184,U_182) )
& ! [U_183,U_184,U_182] :
( element(sK23(U_184,U_183,U_182),powerset(the_carrier(U_184)))
| ~ sP58(U_183,U_184,U_182) )
& ! [U_183,U_184,U_182] :
( in(sK22(U_184,U_183,U_182),U_182)
| ~ sP58(U_183,U_184,U_182) )
& ! [U_183,U_180,U_184,U_182] :
( sP59(U_183,U_180,U_184,U_182)
| sP58(U_183,U_184,U_182)
| ~ sP60(U_183,U_180,U_184,U_182) )
& ! [U_183,U_180,U_184,U_182] :
( in(sK22(U_184,U_183,U_182),the_carrier(U_184))
| ~ sP60(U_183,U_180,U_184,U_182) )
& ! [U_183,U_184,U_182,U_178] :
( disjoint(U_183,sK21(U_184,U_183,U_182,U_178))
| ~ sP56(U_183,U_184,U_182,U_178) )
& ! [U_183,U_184,U_182,U_178] :
( in(U_178,sK21(U_184,U_183,U_182,U_178))
| ~ sP56(U_183,U_184,U_182,U_178) )
& ! [U_183,U_184,U_182,U_178] :
( open_subset(sK21(U_184,U_183,U_182,U_178),U_184)
| ~ sP56(U_183,U_184,U_182,U_178) )
& ! [U_183,U_184,U_182,U_178] :
( element(sK21(U_184,U_183,U_182,U_178),powerset(the_carrier(U_184)))
| ~ sP56(U_183,U_184,U_182,U_178) )
& ! [U_183,U_184,U_182,U_176,U_178] :
( in(U_178,U_182)
| sP56(U_183,U_184,U_182,U_178)
| ~ sP57(U_183,U_184,U_182,U_176,U_178) )
& ! [U_183,U_184,U_182,U_176,U_178] :
( ~ disjoint(U_183,U_176)
| ~ in(U_178,U_176)
| ~ open_subset(U_176,U_184)
| ~ element(U_176,powerset(the_carrier(U_184)))
| ~ in(U_178,U_182)
| ~ sP57(U_183,U_184,U_182,U_176,U_178) )
& ! [U_183,U_180,U_184,U_182,U_176,U_178] :
( U_182 = topstr_closure(U_184,U_183)
| sP60(U_183,U_180,U_184,U_182)
| ~ sP61(U_183,U_180,U_184,U_182,U_176,U_178) )
& ! [U_183,U_180,U_184,U_182,U_176,U_178] :
( sP57(U_183,U_184,U_182,U_176,U_178)
| ~ in(U_178,the_carrier(U_184))
| U_182 != topstr_closure(U_184,U_183)
| ~ sP61(U_183,U_180,U_184,U_182,U_176,U_178) )
& ! [U_183,U_180,U_184,U_182,U_176,U_178] :
( sP61(U_183,U_180,U_184,U_182,U_176,U_178)
| ~ element(U_182,powerset(the_carrier(U_184)))
| ~ element(U_183,powerset(the_carrier(U_184)))
| ~ top_str(U_184) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56,sP57,sP58,sP59,sP60,sP61])],[f_60_5]) ).
cnf(f_60_7,plain,
( sP61(U_183,U_180,U_184,U_182,U_176,U_178)
| ~ element(U_182,powerset(the_carrier(U_184)))
| ~ element(U_183,powerset(the_carrier(U_184)))
| ~ top_str(U_184) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_8,plain,
( sP57(U_183,U_184,U_182,U_176,U_178)
| ~ in(U_178,the_carrier(U_184))
| U_182 != topstr_closure(U_184,U_183)
| ~ sP61(U_183,U_180,U_184,U_182,U_176,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_9,plain,
( U_182 = topstr_closure(U_184,U_183)
| sP60(U_183,U_180,U_184,U_182)
| ~ sP61(U_183,U_180,U_184,U_182,U_176,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_10,plain,
( ~ disjoint(U_183,U_176)
| ~ in(U_178,U_176)
| ~ open_subset(U_176,U_184)
| ~ element(U_176,powerset(the_carrier(U_184)))
| ~ in(U_178,U_182)
| ~ sP57(U_183,U_184,U_182,U_176,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_11,plain,
( in(U_178,U_182)
| sP56(U_183,U_184,U_182,U_178)
| ~ sP57(U_183,U_184,U_182,U_176,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_12,plain,
( element(sK21(U_184,U_183,U_182,U_178),powerset(the_carrier(U_184)))
| ~ sP56(U_183,U_184,U_182,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_13,plain,
( open_subset(sK21(U_184,U_183,U_182,U_178),U_184)
| ~ sP56(U_183,U_184,U_182,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_14,plain,
( in(U_178,sK21(U_184,U_183,U_182,U_178))
| ~ sP56(U_183,U_184,U_182,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_15,plain,
( disjoint(U_183,sK21(U_184,U_183,U_182,U_178))
| ~ sP56(U_183,U_184,U_182,U_178) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_16,plain,
( in(sK22(U_184,U_183,U_182),the_carrier(U_184))
| ~ sP60(U_183,U_180,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_17,plain,
( sP59(U_183,U_180,U_184,U_182)
| sP58(U_183,U_184,U_182)
| ~ sP60(U_183,U_180,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_18,plain,
( in(sK22(U_184,U_183,U_182),U_182)
| ~ sP58(U_183,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_19,plain,
( element(sK23(U_184,U_183,U_182),powerset(the_carrier(U_184)))
| ~ sP58(U_183,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_20,plain,
( open_subset(sK23(U_184,U_183,U_182),U_184)
| ~ sP58(U_183,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_21,plain,
( in(sK22(U_184,U_183,U_182),sK23(U_184,U_183,U_182))
| ~ sP58(U_183,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_22,plain,
( disjoint(U_183,sK23(U_184,U_183,U_182))
| ~ sP58(U_183,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_23,plain,
( ~ disjoint(U_183,U_180)
| ~ in(sK22(U_184,U_183,U_182),U_180)
| ~ open_subset(U_180,U_184)
| ~ element(U_180,powerset(the_carrier(U_184)))
| ~ sP59(U_183,U_180,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_24,plain,
( ~ in(sK22(U_184,U_183,U_182),U_182)
| ~ sP59(U_183,U_180,U_184,U_182) ),
inference(clausify,[status(thm)],[f_60_6]) ).
fof(f_61_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_61_2,plain,
! [U_193] :
( ! [U_192,U_191] :
( ( U_191 = relation_image(U_193,U_192)
| ? [U_190] :
( ( ~ in(U_190,U_191)
& ? [U_189] :
( in(U_189,U_192)
& in(ordered_pair(U_189,U_190),U_193) ) )
| ( ! [U_188] :
( ~ in(U_188,U_192)
| ~ in(ordered_pair(U_188,U_190),U_193) )
& in(U_190,U_191) ) ) )
& ( ! [U_187] :
( ( in(U_187,U_191)
| ! [U_186] :
( ~ in(U_186,U_192)
| ~ in(ordered_pair(U_186,U_187),U_193) ) )
& ( ? [U_185] :
( in(U_185,U_192)
& in(ordered_pair(U_185,U_187),U_193) )
| ~ in(U_187,U_191) ) )
| U_191 != relation_image(U_193,U_192) ) )
| ~ relation(U_193) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_193] :
( ( ! [U_201,U_199] :
( U_199 = relation_image(U_193,U_201)
| ? [U_197] :
( ~ in(U_197,U_199)
& ? [U_189] :
( in(U_189,U_201)
& in(ordered_pair(U_189,U_197),U_193) ) )
| ? [U_196] :
( ! [U_188] :
( ~ in(U_188,U_201)
| ~ in(ordered_pair(U_188,U_196),U_193) )
& in(U_196,U_199) ) )
& ! [U_200,U_198] :
( ( ! [U_195] :
( in(U_195,U_198)
| ! [U_186] :
( ~ in(U_186,U_200)
| ~ in(ordered_pair(U_186,U_195),U_193) ) )
& ! [U_194] :
( ? [U_185] :
( in(U_185,U_200)
& in(ordered_pair(U_185,U_194),U_193) )
| ~ in(U_194,U_198) ) )
| U_198 != relation_image(U_193,U_200) ) )
| ~ relation(U_193) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
fof(f_61_4,plain,
! [U_193] :
( ( ! [U_201,U_199] :
( U_199 = relation_image(U_193,U_201)
| ? [U_197] :
( ~ in(U_197,U_199)
& ? [U_189] :
( in(U_189,U_201)
& in(ordered_pair(U_189,U_197),U_193) ) )
| ? [U_196] :
( ! [U_188] :
( ~ in(U_188,U_201)
| ~ in(ordered_pair(U_188,U_196),U_193) )
& in(U_196,U_199) ) )
& ! [U_200,U_198] :
( ( ! [U_195] :
( in(U_195,U_198)
| ! [U_186] :
( ~ in(U_186,U_200)
| ~ in(ordered_pair(U_186,U_195),U_193) ) )
& ! [U_194] :
( ( in(sK24(U_193,U_200,U_198,U_194),U_200)
& in(ordered_pair(sK24(U_193,U_200,U_198,U_194),U_194),U_193) )
| ~ in(U_194,U_198) ) )
| U_198 != relation_image(U_193,U_200) ) )
| ~ relation(U_193) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_185,sK24(U_193,U_200,U_198,U_194))],[f_61_3]) ).
fof(f_61_5,plain,
! [U_193] :
( ( ! [U_201,U_199] :
( U_199 = relation_image(U_193,U_201)
| ? [U_197] :
( ~ in(U_197,U_199)
& ? [U_189] :
( in(U_189,U_201)
& in(ordered_pair(U_189,U_197),U_193) ) )
| ( ! [U_188] :
( ~ in(U_188,U_201)
| ~ in(ordered_pair(U_188,sK25(U_193,U_201,U_199)),U_193) )
& in(sK25(U_193,U_201,U_199),U_199) ) )
& ! [U_200,U_198] :
( ( ! [U_195] :
( in(U_195,U_198)
| ! [U_186] :
( ~ in(U_186,U_200)
| ~ in(ordered_pair(U_186,U_195),U_193) ) )
& ! [U_194] :
( ( in(sK24(U_193,U_200,U_198,U_194),U_200)
& in(ordered_pair(sK24(U_193,U_200,U_198,U_194),U_194),U_193) )
| ~ in(U_194,U_198) ) )
| U_198 != relation_image(U_193,U_200) ) )
| ~ relation(U_193) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_196,sK25(U_193,U_201,U_199))],[f_61_4]) ).
fof(f_61_6,plain,
! [U_193] :
( ( ! [U_201,U_199] :
( U_199 = relation_image(U_193,U_201)
| ( ~ in(sK26(U_193,U_201,U_199),U_199)
& ? [U_189] :
( in(U_189,U_201)
& in(ordered_pair(U_189,sK26(U_193,U_201,U_199)),U_193) ) )
| ( ! [U_188] :
( ~ in(U_188,U_201)
| ~ in(ordered_pair(U_188,sK25(U_193,U_201,U_199)),U_193) )
& in(sK25(U_193,U_201,U_199),U_199) ) )
& ! [U_200,U_198] :
( ( ! [U_195] :
( in(U_195,U_198)
| ! [U_186] :
( ~ in(U_186,U_200)
| ~ in(ordered_pair(U_186,U_195),U_193) ) )
& ! [U_194] :
( ( in(sK24(U_193,U_200,U_198,U_194),U_200)
& in(ordered_pair(sK24(U_193,U_200,U_198,U_194),U_194),U_193) )
| ~ in(U_194,U_198) ) )
| U_198 != relation_image(U_193,U_200) ) )
| ~ relation(U_193) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_197,sK26(U_193,U_201,U_199))],[f_61_5]) ).
fof(f_61_7,plain,
! [U_193] :
( ( ! [U_201,U_199] :
( U_199 = relation_image(U_193,U_201)
| ( ~ in(sK26(U_193,U_201,U_199),U_199)
& in(sK27(U_193,U_201,U_199),U_201)
& in(ordered_pair(sK27(U_193,U_201,U_199),sK26(U_193,U_201,U_199)),U_193) )
| ( ! [U_188] :
( ~ in(U_188,U_201)
| ~ in(ordered_pair(U_188,sK25(U_193,U_201,U_199)),U_193) )
& in(sK25(U_193,U_201,U_199),U_199) ) )
& ! [U_200,U_198] :
( ( ! [U_195] :
( in(U_195,U_198)
| ! [U_186] :
( ~ in(U_186,U_200)
| ~ in(ordered_pair(U_186,U_195),U_193) ) )
& ! [U_194] :
( ( in(sK24(U_193,U_200,U_198,U_194),U_200)
& in(ordered_pair(sK24(U_193,U_200,U_198,U_194),U_194),U_193) )
| ~ in(U_194,U_198) ) )
| U_198 != relation_image(U_193,U_200) ) )
| ~ relation(U_193) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_189,sK27(U_193,U_201,U_199))],[f_61_6]) ).
fof(f_61_8,plain,
( ! [U_193,U_201,U_199] :
( ~ in(sK26(U_193,U_201,U_199),U_199)
| ~ sP65(U_193,U_201,U_199) )
& ! [U_193,U_201,U_199] :
( in(sK27(U_193,U_201,U_199),U_201)
| ~ sP65(U_193,U_201,U_199) )
& ! [U_193,U_201,U_199] :
( in(ordered_pair(sK27(U_193,U_201,U_199),sK26(U_193,U_201,U_199)),U_193)
| ~ sP65(U_193,U_201,U_199) )
& ! [U_188,U_193,U_201,U_199] :
( ~ in(U_188,U_201)
| ~ in(ordered_pair(U_188,sK25(U_193,U_201,U_199)),U_193)
| ~ sP64(U_188,U_193,U_201,U_199) )
& ! [U_188,U_193,U_201,U_199] :
( in(sK25(U_193,U_201,U_199),U_199)
| ~ sP64(U_188,U_193,U_201,U_199) )
& ! [U_198,U_194,U_193,U_200] :
( in(sK24(U_193,U_200,U_198,U_194),U_200)
| ~ sP62(U_198,U_194,U_193,U_200) )
& ! [U_198,U_194,U_193,U_200] :
( in(ordered_pair(sK24(U_193,U_200,U_198,U_194),U_194),U_193)
| ~ sP62(U_198,U_194,U_193,U_200) )
& ! [U_198,U_195,U_194,U_193,U_186,U_200] :
( in(U_195,U_198)
| ~ in(U_186,U_200)
| ~ in(ordered_pair(U_186,U_195),U_193)
| ~ sP63(U_198,U_195,U_194,U_193,U_186,U_200) )
& ! [U_198,U_195,U_194,U_193,U_186,U_200] :
( sP62(U_198,U_194,U_193,U_200)
| ~ in(U_194,U_198)
| ~ sP63(U_198,U_195,U_194,U_193,U_186,U_200) )
& ! [U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199] :
( U_199 = relation_image(U_193,U_201)
| sP65(U_193,U_201,U_199)
| sP64(U_188,U_193,U_201,U_199)
| ~ sP66(U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199) )
& ! [U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199] :
( sP63(U_198,U_195,U_194,U_193,U_186,U_200)
| U_198 != relation_image(U_193,U_200)
| ~ sP66(U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199) )
& ! [U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199] :
( sP66(U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199)
| ~ relation(U_193) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62,sP63,sP64,sP65,sP66])],[f_61_7]) ).
cnf(f_61_9,plain,
( sP66(U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199)
| ~ relation(U_193) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_10,plain,
( sP63(U_198,U_195,U_194,U_193,U_186,U_200)
| U_198 != relation_image(U_193,U_200)
| ~ sP66(U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_11,plain,
( U_199 = relation_image(U_193,U_201)
| sP65(U_193,U_201,U_199)
| sP64(U_188,U_193,U_201,U_199)
| ~ sP66(U_198,U_188,U_195,U_194,U_193,U_186,U_200,U_201,U_199) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_12,plain,
( sP62(U_198,U_194,U_193,U_200)
| ~ in(U_194,U_198)
| ~ sP63(U_198,U_195,U_194,U_193,U_186,U_200) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_13,plain,
( in(U_195,U_198)
| ~ in(U_186,U_200)
| ~ in(ordered_pair(U_186,U_195),U_193)
| ~ sP63(U_198,U_195,U_194,U_193,U_186,U_200) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_14,plain,
( in(ordered_pair(sK24(U_193,U_200,U_198,U_194),U_194),U_193)
| ~ sP62(U_198,U_194,U_193,U_200) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_15,plain,
( in(sK24(U_193,U_200,U_198,U_194),U_200)
| ~ sP62(U_198,U_194,U_193,U_200) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_16,plain,
( in(sK25(U_193,U_201,U_199),U_199)
| ~ sP64(U_188,U_193,U_201,U_199) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_17,plain,
( ~ in(U_188,U_201)
| ~ in(ordered_pair(U_188,sK25(U_193,U_201,U_199)),U_193)
| ~ sP64(U_188,U_193,U_201,U_199) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_18,plain,
( in(ordered_pair(sK27(U_193,U_201,U_199),sK26(U_193,U_201,U_199)),U_193)
| ~ sP65(U_193,U_201,U_199) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_19,plain,
( in(sK27(U_193,U_201,U_199),U_201)
| ~ sP65(U_193,U_201,U_199) ),
inference(clausify,[status(thm)],[f_61_8]) ).
cnf(f_61_20,plain,
( ~ in(sK26(U_193,U_201,U_199),U_199)
| ~ sP65(U_193,U_201,U_199) ),
inference(clausify,[status(thm)],[f_61_8]) ).
fof(f_62_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_62_2,plain,
! [U_210] :
( ! [U_209,U_208] :
( ( U_208 = relation_inverse_image(U_210,U_209)
| ? [U_207] :
( ( ~ in(U_207,U_208)
& ? [U_206] :
( in(U_206,U_209)
& in(ordered_pair(U_207,U_206),U_210) ) )
| ( ! [U_205] :
( ~ in(U_205,U_209)
| ~ in(ordered_pair(U_207,U_205),U_210) )
& in(U_207,U_208) ) ) )
& ( ! [U_204] :
( ( in(U_204,U_208)
| ! [U_203] :
( ~ in(U_203,U_209)
| ~ in(ordered_pair(U_204,U_203),U_210) ) )
& ( ? [U_202] :
( in(U_202,U_209)
& in(ordered_pair(U_204,U_202),U_210) )
| ~ in(U_204,U_208) ) )
| U_208 != relation_inverse_image(U_210,U_209) ) )
| ~ relation(U_210) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_210] :
( ( ! [U_218,U_216] :
( U_216 = relation_inverse_image(U_210,U_218)
| ? [U_214] :
( ~ in(U_214,U_216)
& ? [U_206] :
( in(U_206,U_218)
& in(ordered_pair(U_214,U_206),U_210) ) )
| ? [U_213] :
( ! [U_205] :
( ~ in(U_205,U_218)
| ~ in(ordered_pair(U_213,U_205),U_210) )
& in(U_213,U_216) ) )
& ! [U_217,U_215] :
( ( ! [U_212] :
( in(U_212,U_215)
| ! [U_203] :
( ~ in(U_203,U_217)
| ~ in(ordered_pair(U_212,U_203),U_210) ) )
& ! [U_211] :
( ? [U_202] :
( in(U_202,U_217)
& in(ordered_pair(U_211,U_202),U_210) )
| ~ in(U_211,U_215) ) )
| U_215 != relation_inverse_image(U_210,U_217) ) )
| ~ relation(U_210) ),
inference(miniscope,[status(thm)],[f_62_2]) ).
fof(f_62_4,plain,
! [U_210] :
( ( ! [U_218,U_216] :
( U_216 = relation_inverse_image(U_210,U_218)
| ? [U_214] :
( ~ in(U_214,U_216)
& ? [U_206] :
( in(U_206,U_218)
& in(ordered_pair(U_214,U_206),U_210) ) )
| ? [U_213] :
( ! [U_205] :
( ~ in(U_205,U_218)
| ~ in(ordered_pair(U_213,U_205),U_210) )
& in(U_213,U_216) ) )
& ! [U_217,U_215] :
( ( ! [U_212] :
( in(U_212,U_215)
| ! [U_203] :
( ~ in(U_203,U_217)
| ~ in(ordered_pair(U_212,U_203),U_210) ) )
& ! [U_211] :
( ( in(sK28(U_210,U_217,U_215,U_211),U_217)
& in(ordered_pair(U_211,sK28(U_210,U_217,U_215,U_211)),U_210) )
| ~ in(U_211,U_215) ) )
| U_215 != relation_inverse_image(U_210,U_217) ) )
| ~ relation(U_210) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_202,sK28(U_210,U_217,U_215,U_211))],[f_62_3]) ).
fof(f_62_5,plain,
! [U_210] :
( ( ! [U_218,U_216] :
( U_216 = relation_inverse_image(U_210,U_218)
| ? [U_214] :
( ~ in(U_214,U_216)
& ? [U_206] :
( in(U_206,U_218)
& in(ordered_pair(U_214,U_206),U_210) ) )
| ( ! [U_205] :
( ~ in(U_205,U_218)
| ~ in(ordered_pair(sK29(U_210,U_218,U_216),U_205),U_210) )
& in(sK29(U_210,U_218,U_216),U_216) ) )
& ! [U_217,U_215] :
( ( ! [U_212] :
( in(U_212,U_215)
| ! [U_203] :
( ~ in(U_203,U_217)
| ~ in(ordered_pair(U_212,U_203),U_210) ) )
& ! [U_211] :
( ( in(sK28(U_210,U_217,U_215,U_211),U_217)
& in(ordered_pair(U_211,sK28(U_210,U_217,U_215,U_211)),U_210) )
| ~ in(U_211,U_215) ) )
| U_215 != relation_inverse_image(U_210,U_217) ) )
| ~ relation(U_210) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_213,sK29(U_210,U_218,U_216))],[f_62_4]) ).
fof(f_62_6,plain,
! [U_210] :
( ( ! [U_218,U_216] :
( U_216 = relation_inverse_image(U_210,U_218)
| ( ~ in(sK30(U_210,U_218,U_216),U_216)
& ? [U_206] :
( in(U_206,U_218)
& in(ordered_pair(sK30(U_210,U_218,U_216),U_206),U_210) ) )
| ( ! [U_205] :
( ~ in(U_205,U_218)
| ~ in(ordered_pair(sK29(U_210,U_218,U_216),U_205),U_210) )
& in(sK29(U_210,U_218,U_216),U_216) ) )
& ! [U_217,U_215] :
( ( ! [U_212] :
( in(U_212,U_215)
| ! [U_203] :
( ~ in(U_203,U_217)
| ~ in(ordered_pair(U_212,U_203),U_210) ) )
& ! [U_211] :
( ( in(sK28(U_210,U_217,U_215,U_211),U_217)
& in(ordered_pair(U_211,sK28(U_210,U_217,U_215,U_211)),U_210) )
| ~ in(U_211,U_215) ) )
| U_215 != relation_inverse_image(U_210,U_217) ) )
| ~ relation(U_210) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_214,sK30(U_210,U_218,U_216))],[f_62_5]) ).
fof(f_62_7,plain,
! [U_210] :
( ( ! [U_218,U_216] :
( U_216 = relation_inverse_image(U_210,U_218)
| ( ~ in(sK30(U_210,U_218,U_216),U_216)
& in(sK31(U_210,U_218,U_216),U_218)
& in(ordered_pair(sK30(U_210,U_218,U_216),sK31(U_210,U_218,U_216)),U_210) )
| ( ! [U_205] :
( ~ in(U_205,U_218)
| ~ in(ordered_pair(sK29(U_210,U_218,U_216),U_205),U_210) )
& in(sK29(U_210,U_218,U_216),U_216) ) )
& ! [U_217,U_215] :
( ( ! [U_212] :
( in(U_212,U_215)
| ! [U_203] :
( ~ in(U_203,U_217)
| ~ in(ordered_pair(U_212,U_203),U_210) ) )
& ! [U_211] :
( ( in(sK28(U_210,U_217,U_215,U_211),U_217)
& in(ordered_pair(U_211,sK28(U_210,U_217,U_215,U_211)),U_210) )
| ~ in(U_211,U_215) ) )
| U_215 != relation_inverse_image(U_210,U_217) ) )
| ~ relation(U_210) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_206,sK31(U_210,U_218,U_216))],[f_62_6]) ).
fof(f_62_8,plain,
( ! [U_216,U_210,U_218] :
( ~ in(sK30(U_210,U_218,U_216),U_216)
| ~ sP70(U_216,U_210,U_218) )
& ! [U_216,U_210,U_218] :
( in(sK31(U_210,U_218,U_216),U_218)
| ~ sP70(U_216,U_210,U_218) )
& ! [U_216,U_210,U_218] :
( in(ordered_pair(sK30(U_210,U_218,U_216),sK31(U_210,U_218,U_216)),U_210)
| ~ sP70(U_216,U_210,U_218) )
& ! [U_205,U_216,U_210,U_218] :
( ~ in(U_205,U_218)
| ~ in(ordered_pair(sK29(U_210,U_218,U_216),U_205),U_210)
| ~ sP69(U_205,U_216,U_210,U_218) )
& ! [U_205,U_216,U_210,U_218] :
( in(sK29(U_210,U_218,U_216),U_216)
| ~ sP69(U_205,U_216,U_210,U_218) )
& ! [U_217,U_211,U_215,U_210] :
( in(sK28(U_210,U_217,U_215,U_211),U_217)
| ~ sP67(U_217,U_211,U_215,U_210) )
& ! [U_217,U_211,U_215,U_210] :
( in(ordered_pair(U_211,sK28(U_210,U_217,U_215,U_211)),U_210)
| ~ sP67(U_217,U_211,U_215,U_210) )
& ! [U_217,U_211,U_203,U_212,U_215,U_210] :
( in(U_212,U_215)
| ~ in(U_203,U_217)
| ~ in(ordered_pair(U_212,U_203),U_210)
| ~ sP68(U_217,U_211,U_203,U_212,U_215,U_210) )
& ! [U_217,U_211,U_203,U_212,U_215,U_210] :
( sP67(U_217,U_211,U_215,U_210)
| ~ in(U_211,U_215)
| ~ sP68(U_217,U_211,U_203,U_212,U_215,U_210) )
& ! [U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218] :
( U_216 = relation_inverse_image(U_210,U_218)
| sP70(U_216,U_210,U_218)
| sP69(U_205,U_216,U_210,U_218)
| ~ sP71(U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218) )
& ! [U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218] :
( sP68(U_217,U_211,U_203,U_212,U_215,U_210)
| U_215 != relation_inverse_image(U_210,U_217)
| ~ sP71(U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218) )
& ! [U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218] :
( sP71(U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218)
| ~ relation(U_210) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67,sP68,sP69,sP70,sP71])],[f_62_7]) ).
cnf(f_62_9,plain,
( sP71(U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218)
| ~ relation(U_210) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_10,plain,
( sP68(U_217,U_211,U_203,U_212,U_215,U_210)
| U_215 != relation_inverse_image(U_210,U_217)
| ~ sP71(U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_11,plain,
( U_216 = relation_inverse_image(U_210,U_218)
| sP70(U_216,U_210,U_218)
| sP69(U_205,U_216,U_210,U_218)
| ~ sP71(U_205,U_217,U_216,U_211,U_203,U_212,U_215,U_210,U_218) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_12,plain,
( sP67(U_217,U_211,U_215,U_210)
| ~ in(U_211,U_215)
| ~ sP68(U_217,U_211,U_203,U_212,U_215,U_210) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_13,plain,
( in(U_212,U_215)
| ~ in(U_203,U_217)
| ~ in(ordered_pair(U_212,U_203),U_210)
| ~ sP68(U_217,U_211,U_203,U_212,U_215,U_210) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_14,plain,
( in(ordered_pair(U_211,sK28(U_210,U_217,U_215,U_211)),U_210)
| ~ sP67(U_217,U_211,U_215,U_210) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_15,plain,
( in(sK28(U_210,U_217,U_215,U_211),U_217)
| ~ sP67(U_217,U_211,U_215,U_210) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_16,plain,
( in(sK29(U_210,U_218,U_216),U_216)
| ~ sP69(U_205,U_216,U_210,U_218) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_17,plain,
( ~ in(U_205,U_218)
| ~ in(ordered_pair(sK29(U_210,U_218,U_216),U_205),U_210)
| ~ sP69(U_205,U_216,U_210,U_218) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_18,plain,
( in(ordered_pair(sK30(U_210,U_218,U_216),sK31(U_210,U_218,U_216)),U_210)
| ~ sP70(U_216,U_210,U_218) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_19,plain,
( in(sK31(U_210,U_218,U_216),U_218)
| ~ sP70(U_216,U_210,U_218) ),
inference(clausify,[status(thm)],[f_62_8]) ).
cnf(f_62_20,plain,
( ~ in(sK30(U_210,U_218,U_216),U_216)
| ~ sP70(U_216,U_210,U_218) ),
inference(clausify,[status(thm)],[f_62_8]) ).
fof(f_63_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_63_2,plain,
! [U_219] :
( ( ( connected(U_219)
| ~ is_connected_in(U_219,relation_field(U_219)) )
& ( is_connected_in(U_219,relation_field(U_219))
| ~ connected(U_219) ) )
| ~ relation(U_219) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ! [U_219] :
( connected(U_219)
| ~ is_connected_in(U_219,relation_field(U_219))
| ~ sP72(U_219) )
& ! [U_219] :
( is_connected_in(U_219,relation_field(U_219))
| ~ connected(U_219)
| ~ sP72(U_219) )
& ! [U_219] :
( sP72(U_219)
| ~ relation(U_219) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_63_2]) ).
cnf(f_63_4,plain,
( sP72(U_219)
| ~ relation(U_219) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
( is_connected_in(U_219,relation_field(U_219))
| ~ connected(U_219)
| ~ sP72(U_219) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_6,plain,
( connected(U_219)
| ~ is_connected_in(U_219,relation_field(U_219))
| ~ sP72(U_219) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( latt_set_smaller(A,B,C)
| ? [D] :
( ~ below(A,B,D)
& in(D,C)
& element(D,the_carrier(A)) ) )
& ( ! [D] :
( below(A,B,D)
| ~ in(D,C)
| ~ element(D,the_carrier(A)) )
| ~ latt_set_smaller(A,B,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d16_lattice3]) ).
fof(f_64_2,plain,
! [U_224] :
( ! [U_223] :
( ! [U_222] :
( ( latt_set_smaller(U_224,U_223,U_222)
| ? [U_221] :
( ~ below(U_224,U_223,U_221)
& in(U_221,U_222)
& element(U_221,the_carrier(U_224)) ) )
& ( ! [U_220] :
( below(U_224,U_223,U_220)
| ~ in(U_220,U_222)
| ~ element(U_220,the_carrier(U_224)) )
| ~ latt_set_smaller(U_224,U_223,U_222) ) )
| ~ element(U_223,the_carrier(U_224)) )
| ~ latt_str(U_224)
| empty_carrier(U_224) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_224] :
( ! [U_223] :
( ( ! [U_226] :
( latt_set_smaller(U_224,U_223,U_226)
| ? [U_221] :
( ~ below(U_224,U_223,U_221)
& in(U_221,U_226)
& element(U_221,the_carrier(U_224)) ) )
& ! [U_225] :
( ! [U_220] :
( below(U_224,U_223,U_220)
| ~ in(U_220,U_225)
| ~ element(U_220,the_carrier(U_224)) )
| ~ latt_set_smaller(U_224,U_223,U_225) ) )
| ~ element(U_223,the_carrier(U_224)) )
| ~ latt_str(U_224)
| empty_carrier(U_224) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
fof(f_64_4,plain,
! [U_224] :
( ! [U_223] :
( ( ! [U_226] :
( latt_set_smaller(U_224,U_223,U_226)
| ( ~ below(U_224,U_223,sK32(U_224,U_223,U_226))
& in(sK32(U_224,U_223,U_226),U_226)
& element(sK32(U_224,U_223,U_226),the_carrier(U_224)) ) )
& ! [U_225] :
( ! [U_220] :
( below(U_224,U_223,U_220)
| ~ in(U_220,U_225)
| ~ element(U_220,the_carrier(U_224)) )
| ~ latt_set_smaller(U_224,U_223,U_225) ) )
| ~ element(U_223,the_carrier(U_224)) )
| ~ latt_str(U_224)
| empty_carrier(U_224) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_221,sK32(U_224,U_223,U_226))],[f_64_3]) ).
fof(f_64_5,plain,
( ! [U_224,U_223,U_226] :
( ~ below(U_224,U_223,sK32(U_224,U_223,U_226))
| ~ sP73(U_224,U_223,U_226) )
& ! [U_224,U_223,U_226] :
( in(sK32(U_224,U_223,U_226),U_226)
| ~ sP73(U_224,U_223,U_226) )
& ! [U_224,U_223,U_226] :
( element(sK32(U_224,U_223,U_226),the_carrier(U_224))
| ~ sP73(U_224,U_223,U_226) )
& ! [U_225,U_224,U_223,U_226,U_220] :
( latt_set_smaller(U_224,U_223,U_226)
| sP73(U_224,U_223,U_226)
| ~ sP74(U_225,U_224,U_223,U_226,U_220) )
& ! [U_225,U_224,U_223,U_226,U_220] :
( below(U_224,U_223,U_220)
| ~ in(U_220,U_225)
| ~ element(U_220,the_carrier(U_224))
| ~ latt_set_smaller(U_224,U_223,U_225)
| ~ sP74(U_225,U_224,U_223,U_226,U_220) )
& ! [U_225,U_224,U_223,U_226,U_220] :
( sP74(U_225,U_224,U_223,U_226,U_220)
| ~ element(U_223,the_carrier(U_224))
| ~ latt_str(U_224)
| empty_carrier(U_224) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73,sP74])],[f_64_4]) ).
cnf(f_64_6,plain,
( sP74(U_225,U_224,U_223,U_226,U_220)
| ~ element(U_223,the_carrier(U_224))
| ~ latt_str(U_224)
| empty_carrier(U_224) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_7,plain,
( below(U_224,U_223,U_220)
| ~ in(U_220,U_225)
| ~ element(U_220,the_carrier(U_224))
| ~ latt_set_smaller(U_224,U_223,U_225)
| ~ sP74(U_225,U_224,U_223,U_226,U_220) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_8,plain,
( latt_set_smaller(U_224,U_223,U_226)
| sP73(U_224,U_223,U_226)
| ~ sP74(U_225,U_224,U_223,U_226,U_220) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_9,plain,
( element(sK32(U_224,U_223,U_226),the_carrier(U_224))
| ~ sP73(U_224,U_223,U_226) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_10,plain,
( in(sK32(U_224,U_223,U_226),U_226)
| ~ sP73(U_224,U_223,U_226) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_11,plain,
( ~ below(U_224,U_223,sK32(U_224,U_223,U_226))
| ~ sP73(U_224,U_223,U_226) ),
inference(clausify,[status(thm)],[f_64_5]) ).
fof(f_65_1,plain,
! [A] :
( ! [B] :
( ( ( B = bottom_of_semilattstr(A)
| ? [C] :
( ( meet(A,C,B) != B
| meet(A,B,C) != B )
& element(C,the_carrier(A)) ) )
& ( ! [C] :
( ( meet(A,C,B) = B
& meet(A,B,C) = B )
| ~ element(C,the_carrier(A)) )
| B != bottom_of_semilattstr(A) ) )
| ~ element(B,the_carrier(A)) )
| ~ lower_bounded_semilattstr(A)
| ~ meet_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d16_lattices]) ).
fof(f_65_2,plain,
! [U_230] :
( ! [U_229] :
( ( ( U_229 = bottom_of_semilattstr(U_230)
| ? [U_228] :
( ( meet(U_230,U_228,U_229) != U_229
| meet(U_230,U_229,U_228) != U_229 )
& element(U_228,the_carrier(U_230)) ) )
& ( ! [U_227] :
( ( meet(U_230,U_227,U_229) = U_229
& meet(U_230,U_229,U_227) = U_229 )
| ~ element(U_227,the_carrier(U_230)) )
| U_229 != bottom_of_semilattstr(U_230) ) )
| ~ element(U_229,the_carrier(U_230)) )
| ~ lower_bounded_semilattstr(U_230)
| ~ meet_semilatt_str(U_230)
| empty_carrier(U_230) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_230] :
( ! [U_229] :
( ( ( U_229 = bottom_of_semilattstr(U_230)
| ( ( meet(U_230,sK33(U_230,U_229),U_229) != U_229
| meet(U_230,U_229,sK33(U_230,U_229)) != U_229 )
& element(sK33(U_230,U_229),the_carrier(U_230)) ) )
& ( ! [U_227] :
( ( meet(U_230,U_227,U_229) = U_229
& meet(U_230,U_229,U_227) = U_229 )
| ~ element(U_227,the_carrier(U_230)) )
| U_229 != bottom_of_semilattstr(U_230) ) )
| ~ element(U_229,the_carrier(U_230)) )
| ~ lower_bounded_semilattstr(U_230)
| ~ meet_semilatt_str(U_230)
| empty_carrier(U_230) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_228,sK33(U_230,U_229))],[f_65_2]) ).
fof(f_65_4,plain,
( ! [U_229,U_230] :
( meet(U_230,sK33(U_230,U_229),U_229) != U_229
| meet(U_230,U_229,sK33(U_230,U_229)) != U_229
| ~ sP76(U_229,U_230) )
& ! [U_229,U_230] :
( element(sK33(U_230,U_229),the_carrier(U_230))
| ~ sP76(U_229,U_230) )
& ! [U_227,U_229,U_230] :
( meet(U_230,U_227,U_229) = U_229
| ~ sP75(U_227,U_229,U_230) )
& ! [U_227,U_229,U_230] :
( meet(U_230,U_229,U_227) = U_229
| ~ sP75(U_227,U_229,U_230) )
& ! [U_227,U_229,U_230] :
( U_229 = bottom_of_semilattstr(U_230)
| sP76(U_229,U_230)
| ~ sP77(U_227,U_229,U_230) )
& ! [U_227,U_229,U_230] :
( sP75(U_227,U_229,U_230)
| ~ element(U_227,the_carrier(U_230))
| U_229 != bottom_of_semilattstr(U_230)
| ~ sP77(U_227,U_229,U_230) )
& ! [U_227,U_229,U_230] :
( sP77(U_227,U_229,U_230)
| ~ element(U_229,the_carrier(U_230))
| ~ lower_bounded_semilattstr(U_230)
| ~ meet_semilatt_str(U_230)
| empty_carrier(U_230) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75,sP76,sP77])],[f_65_3]) ).
cnf(f_65_5,plain,
( sP77(U_227,U_229,U_230)
| ~ element(U_229,the_carrier(U_230))
| ~ lower_bounded_semilattstr(U_230)
| ~ meet_semilatt_str(U_230)
| empty_carrier(U_230) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_6,plain,
( sP75(U_227,U_229,U_230)
| ~ element(U_227,the_carrier(U_230))
| U_229 != bottom_of_semilattstr(U_230)
| ~ sP77(U_227,U_229,U_230) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_7,plain,
( U_229 = bottom_of_semilattstr(U_230)
| sP76(U_229,U_230)
| ~ sP77(U_227,U_229,U_230) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_8,plain,
( meet(U_230,U_229,U_227) = U_229
| ~ sP75(U_227,U_229,U_230) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_9,plain,
( meet(U_230,U_227,U_229) = U_229
| ~ sP75(U_227,U_229,U_230) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_10,plain,
( element(sK33(U_230,U_229),the_carrier(U_230))
| ~ sP76(U_229,U_230) ),
inference(clausify,[status(thm)],[f_65_4]) ).
cnf(f_65_11,plain,
( meet(U_230,sK33(U_230,U_229),U_229) != U_229
| meet(U_230,U_229,sK33(U_230,U_229)) != U_229
| ~ sP76(U_229,U_230) ),
inference(clausify,[status(thm)],[f_65_4]) ).
fof(f_66_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_66_2,plain,
! [U_231] :
( ( ( transitive(U_231)
| ~ is_transitive_in(U_231,relation_field(U_231)) )
& ( is_transitive_in(U_231,relation_field(U_231))
| ~ transitive(U_231) ) )
| ~ relation(U_231) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_231] :
( transitive(U_231)
| ~ is_transitive_in(U_231,relation_field(U_231))
| ~ sP78(U_231) )
& ! [U_231] :
( is_transitive_in(U_231,relation_field(U_231))
| ~ transitive(U_231)
| ~ sP78(U_231) )
& ! [U_231] :
( sP78(U_231)
| ~ relation(U_231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_66_2]) ).
cnf(f_66_4,plain,
( sP78(U_231)
| ~ relation(U_231) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_5,plain,
( is_transitive_in(U_231,relation_field(U_231))
| ~ transitive(U_231)
| ~ sP78(U_231) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_6,plain,
( transitive(U_231)
| ~ is_transitive_in(U_231,relation_field(U_231))
| ~ sP78(U_231) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( latt_element_smaller(A,B,C)
| ? [D] :
( ~ below(A,D,B)
& in(D,C)
& element(D,the_carrier(A)) ) )
& ( ! [D] :
( below(A,D,B)
| ~ in(D,C)
| ~ element(D,the_carrier(A)) )
| ~ latt_element_smaller(A,B,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d17_lattice3]) ).
fof(f_67_2,plain,
! [U_236] :
( ! [U_235] :
( ! [U_234] :
( ( latt_element_smaller(U_236,U_235,U_234)
| ? [U_233] :
( ~ below(U_236,U_233,U_235)
& in(U_233,U_234)
& element(U_233,the_carrier(U_236)) ) )
& ( ! [U_232] :
( below(U_236,U_232,U_235)
| ~ in(U_232,U_234)
| ~ element(U_232,the_carrier(U_236)) )
| ~ latt_element_smaller(U_236,U_235,U_234) ) )
| ~ element(U_235,the_carrier(U_236)) )
| ~ latt_str(U_236)
| empty_carrier(U_236) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_236] :
( ! [U_235] :
( ( ! [U_238] :
( latt_element_smaller(U_236,U_235,U_238)
| ? [U_233] :
( ~ below(U_236,U_233,U_235)
& in(U_233,U_238)
& element(U_233,the_carrier(U_236)) ) )
& ! [U_237] :
( ! [U_232] :
( below(U_236,U_232,U_235)
| ~ in(U_232,U_237)
| ~ element(U_232,the_carrier(U_236)) )
| ~ latt_element_smaller(U_236,U_235,U_237) ) )
| ~ element(U_235,the_carrier(U_236)) )
| ~ latt_str(U_236)
| empty_carrier(U_236) ),
inference(miniscope,[status(thm)],[f_67_2]) ).
fof(f_67_4,plain,
! [U_236] :
( ! [U_235] :
( ( ! [U_238] :
( latt_element_smaller(U_236,U_235,U_238)
| ( ~ below(U_236,sK34(U_236,U_235,U_238),U_235)
& in(sK34(U_236,U_235,U_238),U_238)
& element(sK34(U_236,U_235,U_238),the_carrier(U_236)) ) )
& ! [U_237] :
( ! [U_232] :
( below(U_236,U_232,U_235)
| ~ in(U_232,U_237)
| ~ element(U_232,the_carrier(U_236)) )
| ~ latt_element_smaller(U_236,U_235,U_237) ) )
| ~ element(U_235,the_carrier(U_236)) )
| ~ latt_str(U_236)
| empty_carrier(U_236) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_233,sK34(U_236,U_235,U_238))],[f_67_3]) ).
fof(f_67_5,plain,
( ! [U_236,U_235,U_238] :
( ~ below(U_236,sK34(U_236,U_235,U_238),U_235)
| ~ sP79(U_236,U_235,U_238) )
& ! [U_236,U_235,U_238] :
( in(sK34(U_236,U_235,U_238),U_238)
| ~ sP79(U_236,U_235,U_238) )
& ! [U_236,U_235,U_238] :
( element(sK34(U_236,U_235,U_238),the_carrier(U_236))
| ~ sP79(U_236,U_235,U_238) )
& ! [U_236,U_235,U_232,U_238,U_237] :
( latt_element_smaller(U_236,U_235,U_238)
| sP79(U_236,U_235,U_238)
| ~ sP80(U_236,U_235,U_232,U_238,U_237) )
& ! [U_236,U_235,U_232,U_238,U_237] :
( below(U_236,U_232,U_235)
| ~ in(U_232,U_237)
| ~ element(U_232,the_carrier(U_236))
| ~ latt_element_smaller(U_236,U_235,U_237)
| ~ sP80(U_236,U_235,U_232,U_238,U_237) )
& ! [U_236,U_235,U_232,U_238,U_237] :
( sP80(U_236,U_235,U_232,U_238,U_237)
| ~ element(U_235,the_carrier(U_236))
| ~ latt_str(U_236)
| empty_carrier(U_236) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79,sP80])],[f_67_4]) ).
cnf(f_67_6,plain,
( sP80(U_236,U_235,U_232,U_238,U_237)
| ~ element(U_235,the_carrier(U_236))
| ~ latt_str(U_236)
| empty_carrier(U_236) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_7,plain,
( below(U_236,U_232,U_235)
| ~ in(U_232,U_237)
| ~ element(U_232,the_carrier(U_236))
| ~ latt_element_smaller(U_236,U_235,U_237)
| ~ sP80(U_236,U_235,U_232,U_238,U_237) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_8,plain,
( latt_element_smaller(U_236,U_235,U_238)
| sP79(U_236,U_235,U_238)
| ~ sP80(U_236,U_235,U_232,U_238,U_237) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_9,plain,
( element(sK34(U_236,U_235,U_238),the_carrier(U_236))
| ~ sP79(U_236,U_235,U_238) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_10,plain,
( in(sK34(U_236,U_235,U_238),U_238)
| ~ sP79(U_236,U_235,U_238) ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_11,plain,
( ~ below(U_236,sK34(U_236,U_235,U_238),U_235)
| ~ sP79(U_236,U_235,U_238) ),
inference(clausify,[status(thm)],[f_67_5]) ).
fof(f_68_1,plain,
! [A] :
( ! [B,C] : apply_binary(A,B,C) = apply(A,ordered_pair(B,C))
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d1_binop_1]) ).
fof(f_68_2,plain,
! [U_241] :
( ! [U_240,U_239] : apply_binary(U_241,U_240,U_239) = apply(U_241,ordered_pair(U_240,U_239))
| ~ function(U_241)
| ~ relation(U_241) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_241,U_239,U_240] :
( apply_binary(U_241,U_240,U_239) = apply(U_241,ordered_pair(U_240,U_239))
| ~ function(U_241)
| ~ relation(U_241) ),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
( apply_binary(U_241,U_240,U_239) = apply(U_241,ordered_pair(U_240,U_239))
| ~ function(U_241)
| ~ relation(U_241) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( point_neighbourhood(C,A,B)
| ~ in(B,interior(A,C)) )
& ( in(B,interior(A,C))
| ~ point_neighbourhood(C,A,B) ) )
| ~ element(C,powerset(the_carrier(A))) )
| ~ element(B,the_carrier(A)) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d1_connsp_2]) ).
fof(f_69_2,plain,
! [U_244] :
( ! [U_243] :
( ! [U_242] :
( ( ( point_neighbourhood(U_242,U_244,U_243)
| ~ in(U_243,interior(U_244,U_242)) )
& ( in(U_243,interior(U_244,U_242))
| ~ point_neighbourhood(U_242,U_244,U_243) ) )
| ~ element(U_242,powerset(the_carrier(U_244))) )
| ~ element(U_243,the_carrier(U_244)) )
| ~ top_str(U_244)
| ~ topological_space(U_244)
| empty_carrier(U_244) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ! [U_242,U_244,U_243] :
( point_neighbourhood(U_242,U_244,U_243)
| ~ in(U_243,interior(U_244,U_242))
| ~ sP81(U_242,U_244,U_243) )
& ! [U_242,U_244,U_243] :
( in(U_243,interior(U_244,U_242))
| ~ point_neighbourhood(U_242,U_244,U_243)
| ~ sP81(U_242,U_244,U_243) )
& ! [U_242,U_244,U_243] :
( sP81(U_242,U_244,U_243)
| ~ element(U_242,powerset(the_carrier(U_244)))
| ~ element(U_243,the_carrier(U_244))
| ~ top_str(U_244)
| ~ topological_space(U_244)
| empty_carrier(U_244) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_69_2]) ).
cnf(f_69_4,plain,
( sP81(U_242,U_244,U_243)
| ~ element(U_242,powerset(the_carrier(U_244)))
| ~ element(U_243,the_carrier(U_244))
| ~ top_str(U_244)
| ~ topological_space(U_244)
| empty_carrier(U_244) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_5,plain,
( in(U_243,interior(U_244,U_242))
| ~ point_neighbourhood(U_242,U_244,U_243)
| ~ sP81(U_242,U_244,U_243) ),
inference(clausify,[status(thm)],[f_69_3]) ).
cnf(f_69_6,plain,
( point_neighbourhood(U_242,U_244,U_243)
| ~ in(U_243,interior(U_244,U_242))
| ~ sP81(U_242,U_244,U_243) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_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_70_2,plain,
! [U_250,U_249,U_248,U_247] :
( ( U_247 = unordered_triple(U_250,U_249,U_248)
| ? [U_246] :
( ( ~ in(U_246,U_247)
& ( U_246 = U_248
| U_246 = U_249
| U_246 = U_250 ) )
| ( U_246 != U_248
& U_246 != U_249
& U_246 != U_250
& in(U_246,U_247) ) ) )
& ( ! [U_245] :
( ( in(U_245,U_247)
| ( U_245 != U_248
& U_245 != U_249
& U_245 != U_250 ) )
& ( U_245 = U_248
| U_245 = U_249
| U_245 = U_250
| ~ in(U_245,U_247) ) )
| U_247 != unordered_triple(U_250,U_249,U_248) ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ! [U_262,U_260,U_258,U_256] :
( U_256 = unordered_triple(U_262,U_260,U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& ( U_254 = U_258
| U_254 = U_260
| U_254 = U_262 ) )
| ? [U_253] :
( U_253 != U_258
& U_253 != U_260
& U_253 != U_262
& in(U_253,U_256) ) )
& ! [U_261,U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ( U_252 != U_257
& U_252 != U_259
& U_252 != U_261 ) )
& ! [U_251] :
( U_251 = U_257
| U_251 = U_259
| U_251 = U_261
| ~ in(U_251,U_255) ) )
| U_255 != unordered_triple(U_261,U_259,U_257) ) ),
inference(miniscope,[status(thm)],[f_70_2]) ).
fof(f_70_4,plain,
( ! [U_262,U_260,U_258,U_256] :
( U_256 = unordered_triple(U_262,U_260,U_258)
| ? [U_254] :
( ~ in(U_254,U_256)
& ( U_254 = U_258
| U_254 = U_260
| U_254 = U_262 ) )
| ( sK35(U_262,U_260,U_258,U_256) != U_258
& sK35(U_262,U_260,U_258,U_256) != U_260
& sK35(U_262,U_260,U_258,U_256) != U_262
& in(sK35(U_262,U_260,U_258,U_256),U_256) ) )
& ! [U_261,U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ( U_252 != U_257
& U_252 != U_259
& U_252 != U_261 ) )
& ! [U_251] :
( U_251 = U_257
| U_251 = U_259
| U_251 = U_261
| ~ in(U_251,U_255) ) )
| U_255 != unordered_triple(U_261,U_259,U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_253,sK35(U_262,U_260,U_258,U_256))],[f_70_3]) ).
fof(f_70_5,plain,
( ! [U_262,U_260,U_258,U_256] :
( U_256 = unordered_triple(U_262,U_260,U_258)
| ( ~ in(sK36(U_262,U_260,U_258,U_256),U_256)
& ( sK36(U_262,U_260,U_258,U_256) = U_258
| sK36(U_262,U_260,U_258,U_256) = U_260
| sK36(U_262,U_260,U_258,U_256) = U_262 ) )
| ( sK35(U_262,U_260,U_258,U_256) != U_258
& sK35(U_262,U_260,U_258,U_256) != U_260
& sK35(U_262,U_260,U_258,U_256) != U_262
& in(sK35(U_262,U_260,U_258,U_256),U_256) ) )
& ! [U_261,U_259,U_257,U_255] :
( ( ! [U_252] :
( in(U_252,U_255)
| ( U_252 != U_257
& U_252 != U_259
& U_252 != U_261 ) )
& ! [U_251] :
( U_251 = U_257
| U_251 = U_259
| U_251 = U_261
| ~ in(U_251,U_255) ) )
| U_255 != unordered_triple(U_261,U_259,U_257) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_254,sK36(U_262,U_260,U_258,U_256))],[f_70_4]) ).
fof(f_70_6,plain,
( ! [U_258,U_256,U_262,U_260] :
( ~ in(sK36(U_262,U_260,U_258,U_256),U_256)
| ~ sP85(U_258,U_256,U_262,U_260) )
& ! [U_258,U_256,U_262,U_260] :
( sK36(U_262,U_260,U_258,U_256) = U_258
| sK36(U_262,U_260,U_258,U_256) = U_260
| sK36(U_262,U_260,U_258,U_256) = U_262
| ~ sP85(U_258,U_256,U_262,U_260) )
& ! [U_258,U_256,U_262,U_260] :
( sK35(U_262,U_260,U_258,U_256) != U_258
| ~ sP84(U_258,U_256,U_262,U_260) )
& ! [U_258,U_256,U_262,U_260] :
( sK35(U_262,U_260,U_258,U_256) != U_260
| ~ sP84(U_258,U_256,U_262,U_260) )
& ! [U_258,U_256,U_262,U_260] :
( sK35(U_262,U_260,U_258,U_256) != U_262
| ~ sP84(U_258,U_256,U_262,U_260) )
& ! [U_258,U_256,U_262,U_260] :
( in(sK35(U_262,U_260,U_258,U_256),U_256)
| ~ sP84(U_258,U_256,U_262,U_260) )
& ! [U_259,U_261,U_252,U_257] :
( U_252 != U_257
| ~ sP82(U_259,U_261,U_252,U_257) )
& ! [U_259,U_261,U_252,U_257] :
( U_252 != U_259
| ~ sP82(U_259,U_261,U_252,U_257) )
& ! [U_259,U_261,U_252,U_257] :
( U_252 != U_261
| ~ sP82(U_259,U_261,U_252,U_257) )
& ! [U_259,U_255,U_261,U_251,U_252,U_257] :
( in(U_252,U_255)
| sP82(U_259,U_261,U_252,U_257)
| ~ sP83(U_259,U_255,U_261,U_251,U_252,U_257) )
& ! [U_259,U_255,U_261,U_251,U_252,U_257] :
( U_251 = U_257
| U_251 = U_259
| U_251 = U_261
| ~ in(U_251,U_255)
| ~ sP83(U_259,U_255,U_261,U_251,U_252,U_257) )
& ! [U_258,U_256,U_262,U_260] :
( U_256 = unordered_triple(U_262,U_260,U_258)
| sP85(U_258,U_256,U_262,U_260)
| sP84(U_258,U_256,U_262,U_260) )
& ! [U_259,U_255,U_261,U_251,U_252,U_257] :
( sP83(U_259,U_255,U_261,U_251,U_252,U_257)
| U_255 != unordered_triple(U_261,U_259,U_257) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82,sP83,sP84,sP85])],[f_70_5]) ).
cnf(f_70_7,plain,
( sP83(U_259,U_255,U_261,U_251,U_252,U_257)
| U_255 != unordered_triple(U_261,U_259,U_257) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_8,plain,
( U_256 = unordered_triple(U_262,U_260,U_258)
| sP85(U_258,U_256,U_262,U_260)
| sP84(U_258,U_256,U_262,U_260) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_9,plain,
( U_251 = U_257
| U_251 = U_259
| U_251 = U_261
| ~ in(U_251,U_255)
| ~ sP83(U_259,U_255,U_261,U_251,U_252,U_257) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_10,plain,
( in(U_252,U_255)
| sP82(U_259,U_261,U_252,U_257)
| ~ sP83(U_259,U_255,U_261,U_251,U_252,U_257) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_11,plain,
( U_252 != U_261
| ~ sP82(U_259,U_261,U_252,U_257) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_12,plain,
( U_252 != U_259
| ~ sP82(U_259,U_261,U_252,U_257) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_13,plain,
( U_252 != U_257
| ~ sP82(U_259,U_261,U_252,U_257) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_14,plain,
( in(sK35(U_262,U_260,U_258,U_256),U_256)
| ~ sP84(U_258,U_256,U_262,U_260) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_15,plain,
( sK35(U_262,U_260,U_258,U_256) != U_262
| ~ sP84(U_258,U_256,U_262,U_260) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_16,plain,
( sK35(U_262,U_260,U_258,U_256) != U_260
| ~ sP84(U_258,U_256,U_262,U_260) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_17,plain,
( sK35(U_262,U_260,U_258,U_256) != U_258
| ~ sP84(U_258,U_256,U_262,U_260) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_18,plain,
( sK36(U_262,U_260,U_258,U_256) = U_258
| sK36(U_262,U_260,U_258,U_256) = U_260
| sK36(U_262,U_260,U_258,U_256) = U_262
| ~ sP85(U_258,U_256,U_262,U_260) ),
inference(clausify,[status(thm)],[f_70_6]) ).
cnf(f_70_19,plain,
( ~ in(sK36(U_262,U_260,U_258,U_256),U_256)
| ~ sP85(U_258,U_256,U_262,U_260) ),
inference(clausify,[status(thm)],[f_70_6]) ).
fof(f_71_1,plain,
! [A] :
( ( finite(A)
| ! [B] :
( ~ in(relation_dom(B),omega)
| relation_rng(B) != A
| ~ function(B)
| ~ relation(B) ) )
& ( ? [B] :
( in(relation_dom(B),omega)
& relation_rng(B) = A
& function(B)
& relation(B) )
| ~ finite(A) ) ),
inference(fof_nnf,[status(thm)],[d1_finset_1]) ).
fof(f_71_2,plain,
! [U_265] :
( ( finite(U_265)
| ! [U_264] :
( ~ in(relation_dom(U_264),omega)
| relation_rng(U_264) != U_265
| ~ function(U_264)
| ~ relation(U_264) ) )
& ( ? [U_263] :
( in(relation_dom(U_263),omega)
& relation_rng(U_263) = U_265
& function(U_263)
& relation(U_263) )
| ~ finite(U_265) ) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
( ! [U_267] :
( finite(U_267)
| ! [U_264] :
( ~ in(relation_dom(U_264),omega)
| relation_rng(U_264) != U_267
| ~ function(U_264)
| ~ relation(U_264) ) )
& ! [U_266] :
( ? [U_263] :
( in(relation_dom(U_263),omega)
& relation_rng(U_263) = U_266
& function(U_263)
& relation(U_263) )
| ~ finite(U_266) ) ),
inference(miniscope,[status(thm)],[f_71_2]) ).
fof(f_71_4,plain,
( ! [U_267] :
( finite(U_267)
| ! [U_264] :
( ~ in(relation_dom(U_264),omega)
| relation_rng(U_264) != U_267
| ~ function(U_264)
| ~ relation(U_264) ) )
& ! [U_266] :
( ( in(relation_dom(sK37(U_266)),omega)
& relation_rng(sK37(U_266)) = U_266
& function(sK37(U_266))
& relation(sK37(U_266)) )
| ~ finite(U_266) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_263,sK37(U_266))],[f_71_3]) ).
fof(f_71_5,plain,
( ! [U_266] :
( in(relation_dom(sK37(U_266)),omega)
| ~ sP86(U_266) )
& ! [U_266] :
( relation_rng(sK37(U_266)) = U_266
| ~ sP86(U_266) )
& ! [U_266] :
( function(sK37(U_266))
| ~ sP86(U_266) )
& ! [U_266] :
( relation(sK37(U_266))
| ~ sP86(U_266) )
& ! [U_264,U_267] :
( finite(U_267)
| ~ in(relation_dom(U_264),omega)
| relation_rng(U_264) != U_267
| ~ function(U_264)
| ~ relation(U_264) )
& ! [U_266] :
( sP86(U_266)
| ~ finite(U_266) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_71_4]) ).
cnf(f_71_6,plain,
( sP86(U_266)
| ~ finite(U_266) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_7,plain,
( finite(U_267)
| ~ in(relation_dom(U_264),omega)
| relation_rng(U_264) != U_267
| ~ function(U_264)
| ~ relation(U_264) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_8,plain,
( relation(sK37(U_266))
| ~ sP86(U_266) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_9,plain,
( function(sK37(U_266))
| ~ sP86(U_266) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_10,plain,
( relation_rng(sK37(U_266)) = U_266
| ~ sP86(U_266) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_11,plain,
( in(relation_dom(sK37(U_266)),omega)
| ~ sP86(U_266) ),
inference(clausify,[status(thm)],[f_71_5]) ).
fof(f_72_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_72_2,plain,
! [U_274] :
( ( function(U_274)
| ? [U_273,U_272,U_271] :
( U_272 != U_271
& in(ordered_pair(U_273,U_271),U_274)
& in(ordered_pair(U_273,U_272),U_274) ) )
& ( ! [U_270,U_269,U_268] :
( U_269 = U_268
| ~ in(ordered_pair(U_270,U_268),U_274)
| ~ in(ordered_pair(U_270,U_269),U_274) )
| ~ function(U_274) ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ! [U_276] :
( function(U_276)
| ? [U_273,U_272,U_271] :
( U_272 != U_271
& in(ordered_pair(U_273,U_271),U_276)
& in(ordered_pair(U_273,U_272),U_276) ) )
& ! [U_275] :
( ! [U_270,U_269,U_268] :
( U_269 = U_268
| ~ in(ordered_pair(U_270,U_268),U_275)
| ~ in(ordered_pair(U_270,U_269),U_275) )
| ~ function(U_275) ) ),
inference(miniscope,[status(thm)],[f_72_2]) ).
fof(f_72_4,plain,
( ! [U_276] :
( function(U_276)
| ? [U_272,U_271] :
( U_272 != U_271
& in(ordered_pair(sK38(U_276),U_271),U_276)
& in(ordered_pair(sK38(U_276),U_272),U_276) ) )
& ! [U_275] :
( ! [U_270,U_269,U_268] :
( U_269 = U_268
| ~ in(ordered_pair(U_270,U_268),U_275)
| ~ in(ordered_pair(U_270,U_269),U_275) )
| ~ function(U_275) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_273,sK38(U_276))],[f_72_3]) ).
fof(f_72_5,plain,
( ! [U_276] :
( function(U_276)
| ? [U_271] :
( sK39(U_276) != U_271
& in(ordered_pair(sK38(U_276),U_271),U_276)
& in(ordered_pair(sK38(U_276),sK39(U_276)),U_276) ) )
& ! [U_275] :
( ! [U_270,U_269,U_268] :
( U_269 = U_268
| ~ in(ordered_pair(U_270,U_268),U_275)
| ~ in(ordered_pair(U_270,U_269),U_275) )
| ~ function(U_275) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_272,sK39(U_276))],[f_72_4]) ).
fof(f_72_6,plain,
( ! [U_276] :
( function(U_276)
| ( sK39(U_276) != sK40(U_276)
& in(ordered_pair(sK38(U_276),sK40(U_276)),U_276)
& in(ordered_pair(sK38(U_276),sK39(U_276)),U_276) ) )
& ! [U_275] :
( ! [U_270,U_269,U_268] :
( U_269 = U_268
| ~ in(ordered_pair(U_270,U_268),U_275)
| ~ in(ordered_pair(U_270,U_269),U_275) )
| ~ function(U_275) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_271,sK40(U_276))],[f_72_5]) ).
fof(f_72_7,plain,
( ! [U_276] :
( sK39(U_276) != sK40(U_276)
| ~ sP87(U_276) )
& ! [U_276] :
( in(ordered_pair(sK38(U_276),sK40(U_276)),U_276)
| ~ sP87(U_276) )
& ! [U_276] :
( in(ordered_pair(sK38(U_276),sK39(U_276)),U_276)
| ~ sP87(U_276) )
& ! [U_276] :
( function(U_276)
| sP87(U_276) )
& ! [U_268,U_275,U_270,U_269] :
( U_269 = U_268
| ~ in(ordered_pair(U_270,U_268),U_275)
| ~ in(ordered_pair(U_270,U_269),U_275)
| ~ function(U_275) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_72_6]) ).
cnf(f_72_8,plain,
( U_269 = U_268
| ~ in(ordered_pair(U_270,U_268),U_275)
| ~ in(ordered_pair(U_270,U_269),U_275)
| ~ function(U_275) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_9,plain,
( function(U_276)
| sP87(U_276) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_10,plain,
( in(ordered_pair(sK38(U_276),sK39(U_276)),U_276)
| ~ sP87(U_276) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_11,plain,
( in(ordered_pair(sK38(U_276),sK40(U_276)),U_276)
| ~ sP87(U_276) ),
inference(clausify,[status(thm)],[f_72_7]) ).
cnf(f_72_12,plain,
( sK39(U_276) != sK40(U_276)
| ~ sP87(U_276) ),
inference(clausify,[status(thm)],[f_72_7]) ).
fof(f_73_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_73_2,plain,
! [U_279,U_278,U_277] :
( ( ( ( ( quasi_total(U_277,U_279,U_278)
| U_277 != empty_set )
& ( U_277 = empty_set
| ~ quasi_total(U_277,U_279,U_278) ) )
| U_279 = empty_set
| U_278 != empty_set )
& ( ( ( quasi_total(U_277,U_279,U_278)
| U_279 != relation_dom_as_subset(U_279,U_278,U_277) )
& ( U_279 = relation_dom_as_subset(U_279,U_278,U_277)
| ~ quasi_total(U_277,U_279,U_278) ) )
| ( U_279 != empty_set
& U_278 = empty_set ) ) )
| ~ relation_of2_as_subset(U_277,U_279,U_278) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_279,U_278,U_277] :
( quasi_total(U_277,U_279,U_278)
| U_277 != empty_set
| ~ sP90(U_279,U_278,U_277) )
& ! [U_279,U_278,U_277] :
( U_277 = empty_set
| ~ quasi_total(U_277,U_279,U_278)
| ~ sP90(U_279,U_278,U_277) )
& ! [U_279,U_278,U_277] :
( quasi_total(U_277,U_279,U_278)
| U_279 != relation_dom_as_subset(U_279,U_278,U_277)
| ~ sP89(U_279,U_278,U_277) )
& ! [U_279,U_278,U_277] :
( U_279 = relation_dom_as_subset(U_279,U_278,U_277)
| ~ quasi_total(U_277,U_279,U_278)
| ~ sP89(U_279,U_278,U_277) )
& ! [U_279,U_278] :
( U_279 != empty_set
| ~ sP88(U_279,U_278) )
& ! [U_279,U_278] :
( U_278 = empty_set
| ~ sP88(U_279,U_278) )
& ! [U_279,U_278,U_277] :
( sP90(U_279,U_278,U_277)
| U_279 = empty_set
| U_278 != empty_set
| ~ sP91(U_279,U_278,U_277) )
& ! [U_279,U_278,U_277] :
( sP89(U_279,U_278,U_277)
| sP88(U_279,U_278)
| ~ sP91(U_279,U_278,U_277) )
& ! [U_279,U_278,U_277] :
( sP91(U_279,U_278,U_277)
| ~ relation_of2_as_subset(U_277,U_279,U_278) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88,sP89,sP90,sP91])],[f_73_2]) ).
cnf(f_73_4,plain,
( sP91(U_279,U_278,U_277)
| ~ relation_of2_as_subset(U_277,U_279,U_278) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_5,plain,
( sP89(U_279,U_278,U_277)
| sP88(U_279,U_278)
| ~ sP91(U_279,U_278,U_277) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_6,plain,
( sP90(U_279,U_278,U_277)
| U_279 = empty_set
| U_278 != empty_set
| ~ sP91(U_279,U_278,U_277) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_7,plain,
( U_278 = empty_set
| ~ sP88(U_279,U_278) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_8,plain,
( U_279 != empty_set
| ~ sP88(U_279,U_278) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_9,plain,
( U_279 = relation_dom_as_subset(U_279,U_278,U_277)
| ~ quasi_total(U_277,U_279,U_278)
| ~ sP89(U_279,U_278,U_277) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_10,plain,
( quasi_total(U_277,U_279,U_278)
| U_279 != relation_dom_as_subset(U_279,U_278,U_277)
| ~ sP89(U_279,U_278,U_277) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_11,plain,
( U_277 = empty_set
| ~ quasi_total(U_277,U_279,U_278)
| ~ sP90(U_279,U_278,U_277) ),
inference(clausify,[status(thm)],[f_73_3]) ).
cnf(f_73_12,plain,
( quasi_total(U_277,U_279,U_278)
| U_277 != empty_set
| ~ sP90(U_279,U_278,U_277) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [A,B] :
( ( ( B = boole_lattice(A)
| ? [C] :
( ? [D] :
( ( apply_binary(the_L_meet(B),C,D) != subset_intersection2(A,C,D)
| apply_binary(the_L_join(B),C,D) != subset_union2(A,C,D) )
& element(D,powerset(A)) )
& element(C,powerset(A)) )
| the_carrier(B) != powerset(A) )
& ( ( ! [C] :
( ! [D] :
( ( apply_binary(the_L_meet(B),C,D) = subset_intersection2(A,C,D)
& apply_binary(the_L_join(B),C,D) = subset_union2(A,C,D) )
| ~ element(D,powerset(A)) )
| ~ element(C,powerset(A)) )
& the_carrier(B) = powerset(A) )
| B != boole_lattice(A) ) )
| ~ latt_str(B)
| ~ strict_latt_str(B) ),
inference(fof_nnf,[status(thm)],[d1_lattice3]) ).
fof(f_74_2,plain,
! [U_285,U_284] :
( ( ( U_284 = boole_lattice(U_285)
| ? [U_283] :
( ? [U_282] :
( ( apply_binary(the_L_meet(U_284),U_283,U_282) != subset_intersection2(U_285,U_283,U_282)
| apply_binary(the_L_join(U_284),U_283,U_282) != subset_union2(U_285,U_283,U_282) )
& element(U_282,powerset(U_285)) )
& element(U_283,powerset(U_285)) )
| the_carrier(U_284) != powerset(U_285) )
& ( ( ! [U_281] :
( ! [U_280] :
( ( apply_binary(the_L_meet(U_284),U_281,U_280) = subset_intersection2(U_285,U_281,U_280)
& apply_binary(the_L_join(U_284),U_281,U_280) = subset_union2(U_285,U_281,U_280) )
| ~ element(U_280,powerset(U_285)) )
| ~ element(U_281,powerset(U_285)) )
& the_carrier(U_284) = powerset(U_285) )
| U_284 != boole_lattice(U_285) ) )
| ~ latt_str(U_284)
| ~ strict_latt_str(U_284) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_285,U_284] :
( ( ( U_284 = boole_lattice(U_285)
| ( ? [U_282] :
( ( apply_binary(the_L_meet(U_284),sK41(U_285,U_284),U_282) != subset_intersection2(U_285,sK41(U_285,U_284),U_282)
| apply_binary(the_L_join(U_284),sK41(U_285,U_284),U_282) != subset_union2(U_285,sK41(U_285,U_284),U_282) )
& element(U_282,powerset(U_285)) )
& element(sK41(U_285,U_284),powerset(U_285)) )
| the_carrier(U_284) != powerset(U_285) )
& ( ( ! [U_281] :
( ! [U_280] :
( ( apply_binary(the_L_meet(U_284),U_281,U_280) = subset_intersection2(U_285,U_281,U_280)
& apply_binary(the_L_join(U_284),U_281,U_280) = subset_union2(U_285,U_281,U_280) )
| ~ element(U_280,powerset(U_285)) )
| ~ element(U_281,powerset(U_285)) )
& the_carrier(U_284) = powerset(U_285) )
| U_284 != boole_lattice(U_285) ) )
| ~ latt_str(U_284)
| ~ strict_latt_str(U_284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_283,sK41(U_285,U_284))],[f_74_2]) ).
fof(f_74_4,plain,
! [U_285,U_284] :
( ( ( U_284 = boole_lattice(U_285)
| ( ( apply_binary(the_L_meet(U_284),sK41(U_285,U_284),sK42(U_285,U_284)) != subset_intersection2(U_285,sK41(U_285,U_284),sK42(U_285,U_284))
| apply_binary(the_L_join(U_284),sK41(U_285,U_284),sK42(U_285,U_284)) != subset_union2(U_285,sK41(U_285,U_284),sK42(U_285,U_284)) )
& element(sK42(U_285,U_284),powerset(U_285))
& element(sK41(U_285,U_284),powerset(U_285)) )
| the_carrier(U_284) != powerset(U_285) )
& ( ( ! [U_281] :
( ! [U_280] :
( ( apply_binary(the_L_meet(U_284),U_281,U_280) = subset_intersection2(U_285,U_281,U_280)
& apply_binary(the_L_join(U_284),U_281,U_280) = subset_union2(U_285,U_281,U_280) )
| ~ element(U_280,powerset(U_285)) )
| ~ element(U_281,powerset(U_285)) )
& the_carrier(U_284) = powerset(U_285) )
| U_284 != boole_lattice(U_285) ) )
| ~ latt_str(U_284)
| ~ strict_latt_str(U_284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_282,sK42(U_285,U_284))],[f_74_3]) ).
fof(f_74_5,plain,
( ! [U_284,U_285] :
( apply_binary(the_L_meet(U_284),sK41(U_285,U_284),sK42(U_285,U_284)) != subset_intersection2(U_285,sK41(U_285,U_284),sK42(U_285,U_284))
| apply_binary(the_L_join(U_284),sK41(U_285,U_284),sK42(U_285,U_284)) != subset_union2(U_285,sK41(U_285,U_284),sK42(U_285,U_284))
| ~ sP94(U_284,U_285) )
& ! [U_284,U_285] :
( element(sK42(U_285,U_284),powerset(U_285))
| ~ sP94(U_284,U_285) )
& ! [U_284,U_285] :
( element(sK41(U_285,U_284),powerset(U_285))
| ~ sP94(U_284,U_285) )
& ! [U_284,U_285,U_280,U_281] :
( apply_binary(the_L_meet(U_284),U_281,U_280) = subset_intersection2(U_285,U_281,U_280)
| ~ sP92(U_284,U_285,U_280,U_281) )
& ! [U_284,U_285,U_280,U_281] :
( apply_binary(the_L_join(U_284),U_281,U_280) = subset_union2(U_285,U_281,U_280)
| ~ sP92(U_284,U_285,U_280,U_281) )
& ! [U_284,U_285,U_280,U_281] :
( sP92(U_284,U_285,U_280,U_281)
| ~ element(U_280,powerset(U_285))
| ~ element(U_281,powerset(U_285))
| ~ sP93(U_284,U_285,U_280,U_281) )
& ! [U_284,U_285,U_280,U_281] :
( the_carrier(U_284) = powerset(U_285)
| ~ sP93(U_284,U_285,U_280,U_281) )
& ! [U_284,U_285,U_280,U_281] :
( U_284 = boole_lattice(U_285)
| sP94(U_284,U_285)
| the_carrier(U_284) != powerset(U_285)
| ~ sP95(U_284,U_285,U_280,U_281) )
& ! [U_284,U_285,U_280,U_281] :
( sP93(U_284,U_285,U_280,U_281)
| U_284 != boole_lattice(U_285)
| ~ sP95(U_284,U_285,U_280,U_281) )
& ! [U_284,U_285,U_280,U_281] :
( sP95(U_284,U_285,U_280,U_281)
| ~ latt_str(U_284)
| ~ strict_latt_str(U_284) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92,sP93,sP94,sP95])],[f_74_4]) ).
cnf(f_74_6,plain,
( sP95(U_284,U_285,U_280,U_281)
| ~ latt_str(U_284)
| ~ strict_latt_str(U_284) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_7,plain,
( sP93(U_284,U_285,U_280,U_281)
| U_284 != boole_lattice(U_285)
| ~ sP95(U_284,U_285,U_280,U_281) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_8,plain,
( U_284 = boole_lattice(U_285)
| sP94(U_284,U_285)
| the_carrier(U_284) != powerset(U_285)
| ~ sP95(U_284,U_285,U_280,U_281) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_9,plain,
( the_carrier(U_284) = powerset(U_285)
| ~ sP93(U_284,U_285,U_280,U_281) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_10,plain,
( sP92(U_284,U_285,U_280,U_281)
| ~ element(U_280,powerset(U_285))
| ~ element(U_281,powerset(U_285))
| ~ sP93(U_284,U_285,U_280,U_281) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_11,plain,
( apply_binary(the_L_join(U_284),U_281,U_280) = subset_union2(U_285,U_281,U_280)
| ~ sP92(U_284,U_285,U_280,U_281) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_12,plain,
( apply_binary(the_L_meet(U_284),U_281,U_280) = subset_intersection2(U_285,U_281,U_280)
| ~ sP92(U_284,U_285,U_280,U_281) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_13,plain,
( element(sK41(U_285,U_284),powerset(U_285))
| ~ sP94(U_284,U_285) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_14,plain,
( element(sK42(U_285,U_284),powerset(U_285))
| ~ sP94(U_284,U_285) ),
inference(clausify,[status(thm)],[f_74_5]) ).
cnf(f_74_15,plain,
( apply_binary(the_L_meet(U_284),sK41(U_285,U_284),sK42(U_285,U_284)) != subset_intersection2(U_285,sK41(U_285,U_284),sK42(U_285,U_284))
| apply_binary(the_L_join(U_284),sK41(U_285,U_284),sK42(U_285,U_284)) != subset_union2(U_285,sK41(U_285,U_284),sK42(U_285,U_284))
| ~ sP94(U_284,U_285) ),
inference(clausify,[status(thm)],[f_74_5]) ).
fof(f_75_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( join(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C)
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d1_lattices]) ).
fof(f_75_2,plain,
! [U_288] :
( ! [U_287] :
( ! [U_286] :
( join(U_288,U_287,U_286) = apply_binary_as_element(the_carrier(U_288),the_carrier(U_288),the_carrier(U_288),the_L_join(U_288),U_287,U_286)
| ~ element(U_286,the_carrier(U_288)) )
| ~ element(U_287,the_carrier(U_288)) )
| ~ join_semilatt_str(U_288)
| empty_carrier(U_288) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_288,U_287,U_286] :
( join(U_288,U_287,U_286) = apply_binary_as_element(the_carrier(U_288),the_carrier(U_288),the_carrier(U_288),the_L_join(U_288),U_287,U_286)
| ~ element(U_286,the_carrier(U_288))
| ~ element(U_287,the_carrier(U_288))
| ~ join_semilatt_str(U_288)
| empty_carrier(U_288) ),
inference(definitional_conversion,[status(esa)],[f_75_2]) ).
cnf(f_75_4,plain,
( join(U_288,U_287,U_286) = apply_binary_as_element(the_carrier(U_288),the_carrier(U_288),the_carrier(U_288),the_L_join(U_288),U_287,U_286)
| ~ element(U_286,the_carrier(U_288))
| ~ element(U_287,the_carrier(U_288))
| ~ join_semilatt_str(U_288)
| empty_carrier(U_288) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_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_76_2,plain,
! [U_296] :
( ! [U_295] :
( ( U_295 = pair_first(U_296)
| ? [U_294,U_293] :
( U_295 != U_294
& U_296 = ordered_pair(U_294,U_293) ) )
& ( ! [U_292,U_291] :
( U_295 = U_292
| U_296 != ordered_pair(U_292,U_291) )
| U_295 != pair_first(U_296) ) )
| ! [U_290,U_289] : U_296 != ordered_pair(U_290,U_289) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_296] :
( ( ! [U_298] :
( U_298 = pair_first(U_296)
| ? [U_294] :
( ? [U_293] : U_296 = ordered_pair(U_294,U_293)
& U_298 != U_294 ) )
& ! [U_297] :
( ! [U_292] :
( ! [U_291] : U_296 != ordered_pair(U_292,U_291)
| U_297 = U_292 )
| U_297 != pair_first(U_296) ) )
| ! [U_290,U_289] : U_296 != ordered_pair(U_290,U_289) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
fof(f_76_4,plain,
! [U_296] :
( ( ! [U_298] :
( U_298 = pair_first(U_296)
| ( ? [U_293] : U_296 = ordered_pair(sK43(U_296,U_298),U_293)
& U_298 != sK43(U_296,U_298) ) )
& ! [U_297] :
( ! [U_292] :
( ! [U_291] : U_296 != ordered_pair(U_292,U_291)
| U_297 = U_292 )
| U_297 != pair_first(U_296) ) )
| ! [U_290,U_289] : U_296 != ordered_pair(U_290,U_289) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_294,sK43(U_296,U_298))],[f_76_3]) ).
fof(f_76_5,plain,
! [U_296] :
( ( ! [U_298] :
( U_298 = pair_first(U_296)
| ( U_296 = ordered_pair(sK43(U_296,U_298),sK44(U_296,U_298))
& U_298 != sK43(U_296,U_298) ) )
& ! [U_297] :
( ! [U_292] :
( ! [U_291] : U_296 != ordered_pair(U_292,U_291)
| U_297 = U_292 )
| U_297 != pair_first(U_296) ) )
| ! [U_290,U_289] : U_296 != ordered_pair(U_290,U_289) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_293,sK44(U_296,U_298))],[f_76_4]) ).
fof(f_76_6,plain,
( ! [U_298,U_296] :
( U_296 = ordered_pair(sK43(U_296,U_298),sK44(U_296,U_298))
| ~ sP96(U_298,U_296) )
& ! [U_298,U_296] :
( U_298 != sK43(U_296,U_298)
| ~ sP96(U_298,U_296) )
& ! [U_291,U_292,U_298,U_297,U_296] :
( U_298 = pair_first(U_296)
| sP96(U_298,U_296)
| ~ sP97(U_291,U_292,U_298,U_297,U_296) )
& ! [U_291,U_292,U_298,U_297,U_296] :
( U_296 != ordered_pair(U_292,U_291)
| U_297 = U_292
| U_297 != pair_first(U_296)
| ~ sP97(U_291,U_292,U_298,U_297,U_296) )
& ! [U_291,U_292,U_298,U_297,U_289,U_290,U_296] :
( sP97(U_291,U_292,U_298,U_297,U_296)
| U_296 != ordered_pair(U_290,U_289) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96,sP97])],[f_76_5]) ).
cnf(f_76_7,plain,
( sP97(U_291,U_292,U_298,U_297,U_296)
| U_296 != ordered_pair(U_290,U_289) ),
inference(clausify,[status(thm)],[f_76_6]) ).
cnf(f_76_8,plain,
( U_296 != ordered_pair(U_292,U_291)
| U_297 = U_292
| U_297 != pair_first(U_296)
| ~ sP97(U_291,U_292,U_298,U_297,U_296) ),
inference(clausify,[status(thm)],[f_76_6]) ).
cnf(f_76_9,plain,
( U_298 = pair_first(U_296)
| sP96(U_298,U_296)
| ~ sP97(U_291,U_292,U_298,U_297,U_296) ),
inference(clausify,[status(thm)],[f_76_6]) ).
cnf(f_76_10,plain,
( U_298 != sK43(U_296,U_298)
| ~ sP96(U_298,U_296) ),
inference(clausify,[status(thm)],[f_76_6]) ).
cnf(f_76_11,plain,
( U_296 = ordered_pair(sK43(U_296,U_298),sK44(U_296,U_298))
| ~ sP96(U_298,U_296) ),
inference(clausify,[status(thm)],[f_76_6]) ).
fof(f_77_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_77_2,plain,
! [U_299] : succ(U_299) = set_union2(U_299,singleton(U_299)),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_299] : succ(U_299) = set_union2(U_299,singleton(U_299)),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
succ(U_299) = set_union2(U_299,singleton(U_299)),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [A] :
( ( ( topological_space(A)
| ? [B] :
( ? [C] :
( ~ in(subset_intersection2(the_carrier(A),B,C),the_topology(A))
& in(C,the_topology(A))
& in(B,the_topology(A))
& element(C,powerset(the_carrier(A))) )
& element(B,powerset(the_carrier(A))) )
| ? [B] :
( ~ in(union_of_subsets(the_carrier(A),B),the_topology(A))
& subset(B,the_topology(A))
& element(B,powerset(powerset(the_carrier(A)))) )
| ~ in(the_carrier(A),the_topology(A)) )
& ( ( ! [B] :
( ! [C] :
( in(subset_intersection2(the_carrier(A),B,C),the_topology(A))
| ~ in(C,the_topology(A))
| ~ in(B,the_topology(A))
| ~ element(C,powerset(the_carrier(A))) )
| ~ element(B,powerset(the_carrier(A))) )
& ! [B] :
( in(union_of_subsets(the_carrier(A),B),the_topology(A))
| ~ subset(B,the_topology(A))
| ~ element(B,powerset(powerset(the_carrier(A)))) )
& in(the_carrier(A),the_topology(A)) )
| ~ topological_space(A) ) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d1_pre_topc]) ).
fof(f_78_2,plain,
! [U_306] :
( ( ( topological_space(U_306)
| ? [U_305] :
( ? [U_304] :
( ~ in(subset_intersection2(the_carrier(U_306),U_305,U_304),the_topology(U_306))
& in(U_304,the_topology(U_306))
& in(U_305,the_topology(U_306))
& element(U_304,powerset(the_carrier(U_306))) )
& element(U_305,powerset(the_carrier(U_306))) )
| ? [U_303] :
( ~ in(union_of_subsets(the_carrier(U_306),U_303),the_topology(U_306))
& subset(U_303,the_topology(U_306))
& element(U_303,powerset(powerset(the_carrier(U_306)))) )
| ~ in(the_carrier(U_306),the_topology(U_306)) )
& ( ( ! [U_302] :
( ! [U_301] :
( in(subset_intersection2(the_carrier(U_306),U_302,U_301),the_topology(U_306))
| ~ in(U_301,the_topology(U_306))
| ~ in(U_302,the_topology(U_306))
| ~ element(U_301,powerset(the_carrier(U_306))) )
| ~ element(U_302,powerset(the_carrier(U_306))) )
& ! [U_300] :
( in(union_of_subsets(the_carrier(U_306),U_300),the_topology(U_306))
| ~ subset(U_300,the_topology(U_306))
| ~ element(U_300,powerset(powerset(the_carrier(U_306)))) )
& in(the_carrier(U_306),the_topology(U_306)) )
| ~ topological_space(U_306) ) )
| ~ top_str(U_306) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_306] :
( ( ( topological_space(U_306)
| ? [U_305] :
( ? [U_304] :
( ~ in(subset_intersection2(the_carrier(U_306),U_305,U_304),the_topology(U_306))
& in(U_304,the_topology(U_306))
& in(U_305,the_topology(U_306))
& element(U_304,powerset(the_carrier(U_306))) )
& element(U_305,powerset(the_carrier(U_306))) )
| ( ~ in(union_of_subsets(the_carrier(U_306),sK45(U_306)),the_topology(U_306))
& subset(sK45(U_306),the_topology(U_306))
& element(sK45(U_306),powerset(powerset(the_carrier(U_306)))) )
| ~ in(the_carrier(U_306),the_topology(U_306)) )
& ( ( ! [U_302] :
( ! [U_301] :
( in(subset_intersection2(the_carrier(U_306),U_302,U_301),the_topology(U_306))
| ~ in(U_301,the_topology(U_306))
| ~ in(U_302,the_topology(U_306))
| ~ element(U_301,powerset(the_carrier(U_306))) )
| ~ element(U_302,powerset(the_carrier(U_306))) )
& ! [U_300] :
( in(union_of_subsets(the_carrier(U_306),U_300),the_topology(U_306))
| ~ subset(U_300,the_topology(U_306))
| ~ element(U_300,powerset(powerset(the_carrier(U_306)))) )
& in(the_carrier(U_306),the_topology(U_306)) )
| ~ topological_space(U_306) ) )
| ~ top_str(U_306) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_303,sK45(U_306))],[f_78_2]) ).
fof(f_78_4,plain,
! [U_306] :
( ( ( topological_space(U_306)
| ( ? [U_304] :
( ~ in(subset_intersection2(the_carrier(U_306),sK46(U_306),U_304),the_topology(U_306))
& in(U_304,the_topology(U_306))
& in(sK46(U_306),the_topology(U_306))
& element(U_304,powerset(the_carrier(U_306))) )
& element(sK46(U_306),powerset(the_carrier(U_306))) )
| ( ~ in(union_of_subsets(the_carrier(U_306),sK45(U_306)),the_topology(U_306))
& subset(sK45(U_306),the_topology(U_306))
& element(sK45(U_306),powerset(powerset(the_carrier(U_306)))) )
| ~ in(the_carrier(U_306),the_topology(U_306)) )
& ( ( ! [U_302] :
( ! [U_301] :
( in(subset_intersection2(the_carrier(U_306),U_302,U_301),the_topology(U_306))
| ~ in(U_301,the_topology(U_306))
| ~ in(U_302,the_topology(U_306))
| ~ element(U_301,powerset(the_carrier(U_306))) )
| ~ element(U_302,powerset(the_carrier(U_306))) )
& ! [U_300] :
( in(union_of_subsets(the_carrier(U_306),U_300),the_topology(U_306))
| ~ subset(U_300,the_topology(U_306))
| ~ element(U_300,powerset(powerset(the_carrier(U_306)))) )
& in(the_carrier(U_306),the_topology(U_306)) )
| ~ topological_space(U_306) ) )
| ~ top_str(U_306) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_305,sK46(U_306))],[f_78_3]) ).
fof(f_78_5,plain,
! [U_306] :
( ( ( topological_space(U_306)
| ( ~ in(subset_intersection2(the_carrier(U_306),sK46(U_306),sK47(U_306)),the_topology(U_306))
& in(sK47(U_306),the_topology(U_306))
& in(sK46(U_306),the_topology(U_306))
& element(sK47(U_306),powerset(the_carrier(U_306)))
& element(sK46(U_306),powerset(the_carrier(U_306))) )
| ( ~ in(union_of_subsets(the_carrier(U_306),sK45(U_306)),the_topology(U_306))
& subset(sK45(U_306),the_topology(U_306))
& element(sK45(U_306),powerset(powerset(the_carrier(U_306)))) )
| ~ in(the_carrier(U_306),the_topology(U_306)) )
& ( ( ! [U_302] :
( ! [U_301] :
( in(subset_intersection2(the_carrier(U_306),U_302,U_301),the_topology(U_306))
| ~ in(U_301,the_topology(U_306))
| ~ in(U_302,the_topology(U_306))
| ~ element(U_301,powerset(the_carrier(U_306))) )
| ~ element(U_302,powerset(the_carrier(U_306))) )
& ! [U_300] :
( in(union_of_subsets(the_carrier(U_306),U_300),the_topology(U_306))
| ~ subset(U_300,the_topology(U_306))
| ~ element(U_300,powerset(powerset(the_carrier(U_306)))) )
& in(the_carrier(U_306),the_topology(U_306)) )
| ~ topological_space(U_306) ) )
| ~ top_str(U_306) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_304,sK47(U_306))],[f_78_4]) ).
fof(f_78_6,plain,
( ! [U_306] :
( ~ in(subset_intersection2(the_carrier(U_306),sK46(U_306),sK47(U_306)),the_topology(U_306))
| ~ sP100(U_306) )
& ! [U_306] :
( in(sK47(U_306),the_topology(U_306))
| ~ sP100(U_306) )
& ! [U_306] :
( in(sK46(U_306),the_topology(U_306))
| ~ sP100(U_306) )
& ! [U_306] :
( element(sK47(U_306),powerset(the_carrier(U_306)))
| ~ sP100(U_306) )
& ! [U_306] :
( element(sK46(U_306),powerset(the_carrier(U_306)))
| ~ sP100(U_306) )
& ! [U_306] :
( ~ in(union_of_subsets(the_carrier(U_306),sK45(U_306)),the_topology(U_306))
| ~ sP99(U_306) )
& ! [U_306] :
( subset(sK45(U_306),the_topology(U_306))
| ~ sP99(U_306) )
& ! [U_306] :
( element(sK45(U_306),powerset(powerset(the_carrier(U_306))))
| ~ sP99(U_306) )
& ! [U_306,U_301,U_300,U_302] :
( in(subset_intersection2(the_carrier(U_306),U_302,U_301),the_topology(U_306))
| ~ in(U_301,the_topology(U_306))
| ~ in(U_302,the_topology(U_306))
| ~ element(U_301,powerset(the_carrier(U_306)))
| ~ element(U_302,powerset(the_carrier(U_306)))
| ~ sP98(U_306,U_301,U_300,U_302) )
& ! [U_306,U_301,U_300,U_302] :
( in(union_of_subsets(the_carrier(U_306),U_300),the_topology(U_306))
| ~ subset(U_300,the_topology(U_306))
| ~ element(U_300,powerset(powerset(the_carrier(U_306))))
| ~ sP98(U_306,U_301,U_300,U_302) )
& ! [U_306,U_301,U_300,U_302] :
( in(the_carrier(U_306),the_topology(U_306))
| ~ sP98(U_306,U_301,U_300,U_302) )
& ! [U_306,U_301,U_300,U_302] :
( topological_space(U_306)
| sP100(U_306)
| sP99(U_306)
| ~ in(the_carrier(U_306),the_topology(U_306))
| ~ sP101(U_306,U_301,U_300,U_302) )
& ! [U_306,U_301,U_300,U_302] :
( sP98(U_306,U_301,U_300,U_302)
| ~ topological_space(U_306)
| ~ sP101(U_306,U_301,U_300,U_302) )
& ! [U_306,U_301,U_300,U_302] :
( sP101(U_306,U_301,U_300,U_302)
| ~ top_str(U_306) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98,sP99,sP100,sP101])],[f_78_5]) ).
cnf(f_78_7,plain,
( sP101(U_306,U_301,U_300,U_302)
| ~ top_str(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_8,plain,
( sP98(U_306,U_301,U_300,U_302)
| ~ topological_space(U_306)
| ~ sP101(U_306,U_301,U_300,U_302) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_9,plain,
( topological_space(U_306)
| sP100(U_306)
| sP99(U_306)
| ~ in(the_carrier(U_306),the_topology(U_306))
| ~ sP101(U_306,U_301,U_300,U_302) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_10,plain,
( in(the_carrier(U_306),the_topology(U_306))
| ~ sP98(U_306,U_301,U_300,U_302) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_11,plain,
( in(union_of_subsets(the_carrier(U_306),U_300),the_topology(U_306))
| ~ subset(U_300,the_topology(U_306))
| ~ element(U_300,powerset(powerset(the_carrier(U_306))))
| ~ sP98(U_306,U_301,U_300,U_302) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_12,plain,
( in(subset_intersection2(the_carrier(U_306),U_302,U_301),the_topology(U_306))
| ~ in(U_301,the_topology(U_306))
| ~ in(U_302,the_topology(U_306))
| ~ element(U_301,powerset(the_carrier(U_306)))
| ~ element(U_302,powerset(the_carrier(U_306)))
| ~ sP98(U_306,U_301,U_300,U_302) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_13,plain,
( element(sK45(U_306),powerset(powerset(the_carrier(U_306))))
| ~ sP99(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_14,plain,
( subset(sK45(U_306),the_topology(U_306))
| ~ sP99(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_15,plain,
( ~ in(union_of_subsets(the_carrier(U_306),sK45(U_306)),the_topology(U_306))
| ~ sP99(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_16,plain,
( element(sK46(U_306),powerset(the_carrier(U_306)))
| ~ sP100(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_17,plain,
( element(sK47(U_306),powerset(the_carrier(U_306)))
| ~ sP100(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_18,plain,
( in(sK46(U_306),the_topology(U_306))
| ~ sP100(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_19,plain,
( in(sK47(U_306),the_topology(U_306))
| ~ sP100(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
cnf(f_78_20,plain,
( ~ in(subset_intersection2(the_carrier(U_306),sK46(U_306),sK47(U_306)),the_topology(U_306))
| ~ sP100(U_306) ),
inference(clausify,[status(thm)],[f_78_6]) ).
fof(f_79_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_79_2,plain,
! [U_313] :
( ( relation(U_313)
| ? [U_312] :
( ! [U_311,U_310] : U_312 != ordered_pair(U_311,U_310)
& in(U_312,U_313) ) )
& ( ! [U_309] :
( ? [U_308,U_307] : U_309 = ordered_pair(U_308,U_307)
| ~ in(U_309,U_313) )
| ~ relation(U_313) ) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_315] :
( relation(U_315)
| ? [U_312] :
( ! [U_311,U_310] : U_312 != ordered_pair(U_311,U_310)
& in(U_312,U_315) ) )
& ! [U_314] :
( ! [U_309] :
( ? [U_308,U_307] : U_309 = ordered_pair(U_308,U_307)
| ~ in(U_309,U_314) )
| ~ relation(U_314) ) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
fof(f_79_4,plain,
( ! [U_315] :
( relation(U_315)
| ? [U_312] :
( ! [U_311,U_310] : U_312 != ordered_pair(U_311,U_310)
& in(U_312,U_315) ) )
& ! [U_314] :
( ! [U_309] :
( ? [U_307] : U_309 = ordered_pair(sK48(U_314,U_309),U_307)
| ~ in(U_309,U_314) )
| ~ relation(U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_308,sK48(U_314,U_309))],[f_79_3]) ).
fof(f_79_5,plain,
( ! [U_315] :
( relation(U_315)
| ? [U_312] :
( ! [U_311,U_310] : U_312 != ordered_pair(U_311,U_310)
& in(U_312,U_315) ) )
& ! [U_314] :
( ! [U_309] :
( U_309 = ordered_pair(sK48(U_314,U_309),sK49(U_314,U_309))
| ~ in(U_309,U_314) )
| ~ relation(U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_307,sK49(U_314,U_309))],[f_79_4]) ).
fof(f_79_6,plain,
( ! [U_315] :
( relation(U_315)
| ( ! [U_311,U_310] : sK50(U_315) != ordered_pair(U_311,U_310)
& in(sK50(U_315),U_315) ) )
& ! [U_314] :
( ! [U_309] :
( U_309 = ordered_pair(sK48(U_314,U_309),sK49(U_314,U_309))
| ~ in(U_309,U_314) )
| ~ relation(U_314) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_312,sK50(U_315))],[f_79_5]) ).
fof(f_79_7,plain,
( ! [U_315,U_310,U_311] :
( sK50(U_315) != ordered_pair(U_311,U_310)
| ~ sP102(U_315,U_310,U_311) )
& ! [U_315,U_310,U_311] :
( in(sK50(U_315),U_315)
| ~ sP102(U_315,U_310,U_311) )
& ! [U_315,U_310,U_311] :
( relation(U_315)
| sP102(U_315,U_310,U_311) )
& ! [U_314,U_309] :
( U_309 = ordered_pair(sK48(U_314,U_309),sK49(U_314,U_309))
| ~ in(U_309,U_314)
| ~ relation(U_314) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_79_6]) ).
cnf(f_79_8,plain,
( U_309 = ordered_pair(sK48(U_314,U_309),sK49(U_314,U_309))
| ~ in(U_309,U_314)
| ~ relation(U_314) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_9,plain,
( relation(U_315)
| sP102(U_315,U_310,U_311) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_10,plain,
( in(sK50(U_315),U_315)
| ~ sP102(U_315,U_310,U_311) ),
inference(clausify,[status(thm)],[f_79_7]) ).
cnf(f_79_11,plain,
( sK50(U_315) != ordered_pair(U_311,U_310)
| ~ sP102(U_315,U_310,U_311) ),
inference(clausify,[status(thm)],[f_79_7]) ).
fof(f_80_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_80_2,plain,
! [U_319] :
( ! [U_318] :
( ( is_reflexive_in(U_319,U_318)
| ? [U_317] :
( ~ in(ordered_pair(U_317,U_317),U_319)
& in(U_317,U_318) ) )
& ( ! [U_316] :
( in(ordered_pair(U_316,U_316),U_319)
| ~ in(U_316,U_318) )
| ~ is_reflexive_in(U_319,U_318) ) )
| ~ relation(U_319) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_319] :
( ( ! [U_321] :
( is_reflexive_in(U_319,U_321)
| ? [U_317] :
( ~ in(ordered_pair(U_317,U_317),U_319)
& in(U_317,U_321) ) )
& ! [U_320] :
( ! [U_316] :
( in(ordered_pair(U_316,U_316),U_319)
| ~ in(U_316,U_320) )
| ~ is_reflexive_in(U_319,U_320) ) )
| ~ relation(U_319) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
fof(f_80_4,plain,
! [U_319] :
( ( ! [U_321] :
( is_reflexive_in(U_319,U_321)
| ( ~ in(ordered_pair(sK51(U_319,U_321),sK51(U_319,U_321)),U_319)
& in(sK51(U_319,U_321),U_321) ) )
& ! [U_320] :
( ! [U_316] :
( in(ordered_pair(U_316,U_316),U_319)
| ~ in(U_316,U_320) )
| ~ is_reflexive_in(U_319,U_320) ) )
| ~ relation(U_319) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_317,sK51(U_319,U_321))],[f_80_3]) ).
fof(f_80_5,plain,
( ! [U_319,U_321] :
( ~ in(ordered_pair(sK51(U_319,U_321),sK51(U_319,U_321)),U_319)
| ~ sP103(U_319,U_321) )
& ! [U_319,U_321] :
( in(sK51(U_319,U_321),U_321)
| ~ sP103(U_319,U_321) )
& ! [U_319,U_316,U_320,U_321] :
( is_reflexive_in(U_319,U_321)
| sP103(U_319,U_321)
| ~ sP104(U_319,U_316,U_320,U_321) )
& ! [U_319,U_316,U_320,U_321] :
( in(ordered_pair(U_316,U_316),U_319)
| ~ in(U_316,U_320)
| ~ is_reflexive_in(U_319,U_320)
| ~ sP104(U_319,U_316,U_320,U_321) )
& ! [U_319,U_316,U_320,U_321] :
( sP104(U_319,U_316,U_320,U_321)
| ~ relation(U_319) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103,sP104])],[f_80_4]) ).
cnf(f_80_6,plain,
( sP104(U_319,U_316,U_320,U_321)
| ~ relation(U_319) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_7,plain,
( in(ordered_pair(U_316,U_316),U_319)
| ~ in(U_316,U_320)
| ~ is_reflexive_in(U_319,U_320)
| ~ sP104(U_319,U_316,U_320,U_321) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_8,plain,
( is_reflexive_in(U_319,U_321)
| sP103(U_319,U_321)
| ~ sP104(U_319,U_316,U_320,U_321) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_9,plain,
( in(sK51(U_319,U_321),U_321)
| ~ sP103(U_319,U_321) ),
inference(clausify,[status(thm)],[f_80_5]) ).
cnf(f_80_10,plain,
( ~ in(ordered_pair(sK51(U_319,U_321),sK51(U_319,U_321)),U_319)
| ~ sP103(U_319,U_321) ),
inference(clausify,[status(thm)],[f_80_5]) ).
fof(f_81_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_81_2,plain,
! [U_324,U_323,U_322] :
( ( relation_of2(U_322,U_324,U_323)
| ~ subset(U_322,cartesian_product2(U_324,U_323)) )
& ( subset(U_322,cartesian_product2(U_324,U_323))
| ~ relation_of2(U_322,U_324,U_323) ) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
( ! [U_330,U_328,U_326] :
( relation_of2(U_326,U_330,U_328)
| ~ subset(U_326,cartesian_product2(U_330,U_328)) )
& ! [U_329,U_327,U_325] :
( subset(U_325,cartesian_product2(U_329,U_327))
| ~ relation_of2(U_325,U_329,U_327) ) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
fof(f_81_4,plain,
( ! [U_326,U_328,U_330] :
( relation_of2(U_326,U_330,U_328)
| ~ subset(U_326,cartesian_product2(U_330,U_328)) )
& ! [U_325,U_329,U_327] :
( subset(U_325,cartesian_product2(U_329,U_327))
| ~ relation_of2(U_325,U_329,U_327) ) ),
inference(definitional_conversion,[status(esa)],[f_81_3]) ).
cnf(f_81_5,plain,
( subset(U_325,cartesian_product2(U_329,U_327))
| ~ relation_of2(U_325,U_329,U_327) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_6,plain,
( relation_of2(U_326,U_330,U_328)
| ~ subset(U_326,cartesian_product2(U_330,U_328)) ),
inference(clausify,[status(thm)],[f_81_4]) ).
fof(f_82_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_82_2,plain,
! [U_338,U_337] :
( ( ( ( U_337 = set_meet(U_338)
| U_337 != empty_set )
& ( U_337 = empty_set
| U_337 != set_meet(U_338) ) )
| U_338 != empty_set )
& ( ( ( U_337 = set_meet(U_338)
| ? [U_336] :
( ( ~ in(U_336,U_337)
& ! [U_335] :
( in(U_336,U_335)
| ~ in(U_335,U_338) ) )
| ( ? [U_334] :
( ~ in(U_336,U_334)
& in(U_334,U_338) )
& in(U_336,U_337) ) ) )
& ( ! [U_333] :
( ( in(U_333,U_337)
| ? [U_332] :
( ~ in(U_333,U_332)
& in(U_332,U_338) ) )
& ( ! [U_331] :
( in(U_333,U_331)
| ~ in(U_331,U_338) )
| ~ in(U_333,U_337) ) )
| U_337 != set_meet(U_338) ) )
| U_338 = empty_set ) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_350] :
( ( ! [U_348] :
( U_348 = set_meet(U_350)
| U_348 != empty_set )
& ! [U_347] :
( U_347 = empty_set
| U_347 != set_meet(U_350) ) )
| U_350 != empty_set )
& ! [U_349] :
( ( ! [U_346] :
( U_346 = set_meet(U_349)
| ? [U_342] :
( ~ in(U_342,U_346)
& ! [U_335] :
( in(U_342,U_335)
| ~ in(U_335,U_349) ) )
| ? [U_341] :
( ? [U_334] :
( ~ in(U_341,U_334)
& in(U_334,U_349) )
& in(U_341,U_346) ) )
& ! [U_345] :
( ( ! [U_340] :
( in(U_340,U_345)
| ? [U_332] :
( ~ in(U_340,U_332)
& in(U_332,U_349) ) )
& ! [U_339] :
( ! [U_331] :
( in(U_339,U_331)
| ~ in(U_331,U_349) )
| ~ in(U_339,U_345) ) )
| U_345 != set_meet(U_349) ) )
| U_349 = empty_set ) ),
inference(miniscope,[status(thm)],[f_82_2]) ).
fof(f_82_4,plain,
( ! [U_350] :
( ( ! [U_348] :
( U_348 = set_meet(U_350)
| U_348 != empty_set )
& ! [U_347] :
( U_347 = empty_set
| U_347 != set_meet(U_350) ) )
| U_350 != empty_set )
& ! [U_349] :
( ( ! [U_346] :
( U_346 = set_meet(U_349)
| ? [U_342] :
( ~ in(U_342,U_346)
& ! [U_335] :
( in(U_342,U_335)
| ~ in(U_335,U_349) ) )
| ? [U_341] :
( ? [U_334] :
( ~ in(U_341,U_334)
& in(U_334,U_349) )
& in(U_341,U_346) ) )
& ! [U_345] :
( ( ! [U_340] :
( in(U_340,U_345)
| ( ~ in(U_340,sK52(U_349,U_345,U_340))
& in(sK52(U_349,U_345,U_340),U_349) ) )
& ! [U_339] :
( ! [U_331] :
( in(U_339,U_331)
| ~ in(U_331,U_349) )
| ~ in(U_339,U_345) ) )
| U_345 != set_meet(U_349) ) )
| U_349 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_332,sK52(U_349,U_345,U_340))],[f_82_3]) ).
fof(f_82_5,plain,
( ! [U_350] :
( ( ! [U_348] :
( U_348 = set_meet(U_350)
| U_348 != empty_set )
& ! [U_347] :
( U_347 = empty_set
| U_347 != set_meet(U_350) ) )
| U_350 != empty_set )
& ! [U_349] :
( ( ! [U_346] :
( U_346 = set_meet(U_349)
| ? [U_342] :
( ~ in(U_342,U_346)
& ! [U_335] :
( in(U_342,U_335)
| ~ in(U_335,U_349) ) )
| ( ? [U_334] :
( ~ in(sK53(U_349,U_346),U_334)
& in(U_334,U_349) )
& in(sK53(U_349,U_346),U_346) ) )
& ! [U_345] :
( ( ! [U_340] :
( in(U_340,U_345)
| ( ~ in(U_340,sK52(U_349,U_345,U_340))
& in(sK52(U_349,U_345,U_340),U_349) ) )
& ! [U_339] :
( ! [U_331] :
( in(U_339,U_331)
| ~ in(U_331,U_349) )
| ~ in(U_339,U_345) ) )
| U_345 != set_meet(U_349) ) )
| U_349 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_341,sK53(U_349,U_346))],[f_82_4]) ).
fof(f_82_6,plain,
( ! [U_350] :
( ( ! [U_348] :
( U_348 = set_meet(U_350)
| U_348 != empty_set )
& ! [U_347] :
( U_347 = empty_set
| U_347 != set_meet(U_350) ) )
| U_350 != empty_set )
& ! [U_349] :
( ( ! [U_346] :
( U_346 = set_meet(U_349)
| ? [U_342] :
( ~ in(U_342,U_346)
& ! [U_335] :
( in(U_342,U_335)
| ~ in(U_335,U_349) ) )
| ( ~ in(sK53(U_349,U_346),sK54(U_349,U_346))
& in(sK54(U_349,U_346),U_349)
& in(sK53(U_349,U_346),U_346) ) )
& ! [U_345] :
( ( ! [U_340] :
( in(U_340,U_345)
| ( ~ in(U_340,sK52(U_349,U_345,U_340))
& in(sK52(U_349,U_345,U_340),U_349) ) )
& ! [U_339] :
( ! [U_331] :
( in(U_339,U_331)
| ~ in(U_331,U_349) )
| ~ in(U_339,U_345) ) )
| U_345 != set_meet(U_349) ) )
| U_349 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_334,sK54(U_349,U_346))],[f_82_5]) ).
fof(f_82_7,plain,
( ! [U_350] :
( ( ! [U_348] :
( U_348 = set_meet(U_350)
| U_348 != empty_set )
& ! [U_347] :
( U_347 = empty_set
| U_347 != set_meet(U_350) ) )
| U_350 != empty_set )
& ! [U_349] :
( ( ! [U_346] :
( U_346 = set_meet(U_349)
| ( ~ in(sK55(U_349,U_346),U_346)
& ! [U_335] :
( in(sK55(U_349,U_346),U_335)
| ~ in(U_335,U_349) ) )
| ( ~ in(sK53(U_349,U_346),sK54(U_349,U_346))
& in(sK54(U_349,U_346),U_349)
& in(sK53(U_349,U_346),U_346) ) )
& ! [U_345] :
( ( ! [U_340] :
( in(U_340,U_345)
| ( ~ in(U_340,sK52(U_349,U_345,U_340))
& in(sK52(U_349,U_345,U_340),U_349) ) )
& ! [U_339] :
( ! [U_331] :
( in(U_339,U_331)
| ~ in(U_331,U_349) )
| ~ in(U_339,U_345) ) )
| U_345 != set_meet(U_349) ) )
| U_349 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_342,sK55(U_349,U_346))],[f_82_6]) ).
fof(f_82_8,plain,
( ! [U_347,U_350,U_348] :
( U_348 = set_meet(U_350)
| U_348 != empty_set
| ~ sP110(U_347,U_350,U_348) )
& ! [U_347,U_350,U_348] :
( U_347 = empty_set
| U_347 != set_meet(U_350)
| ~ sP110(U_347,U_350,U_348) )
& ! [U_335,U_346,U_349] :
( ~ in(sK55(U_349,U_346),U_346)
| ~ sP108(U_335,U_346,U_349) )
& ! [U_335,U_346,U_349] :
( in(sK55(U_349,U_346),U_335)
| ~ in(U_335,U_349)
| ~ sP108(U_335,U_346,U_349) )
& ! [U_346,U_349] :
( ~ in(sK53(U_349,U_346),sK54(U_349,U_346))
| ~ sP107(U_346,U_349) )
& ! [U_346,U_349] :
( in(sK54(U_349,U_346),U_349)
| ~ sP107(U_346,U_349) )
& ! [U_346,U_349] :
( in(sK53(U_349,U_346),U_346)
| ~ sP107(U_346,U_349) )
& ! [U_340,U_349,U_345] :
( ~ in(U_340,sK52(U_349,U_345,U_340))
| ~ sP105(U_340,U_349,U_345) )
& ! [U_340,U_349,U_345] :
( in(sK52(U_349,U_345,U_340),U_349)
| ~ sP105(U_340,U_349,U_345) )
& ! [U_339,U_340,U_331,U_349,U_345] :
( in(U_340,U_345)
| sP105(U_340,U_349,U_345)
| ~ sP106(U_339,U_340,U_331,U_349,U_345) )
& ! [U_339,U_340,U_331,U_349,U_345] :
( in(U_339,U_331)
| ~ in(U_331,U_349)
| ~ in(U_339,U_345)
| ~ sP106(U_339,U_340,U_331,U_349,U_345) )
& ! [U_335,U_339,U_340,U_346,U_331,U_349,U_345] :
( U_346 = set_meet(U_349)
| sP108(U_335,U_346,U_349)
| sP107(U_346,U_349)
| ~ sP109(U_335,U_339,U_340,U_346,U_331,U_349,U_345) )
& ! [U_335,U_339,U_340,U_346,U_331,U_349,U_345] :
( sP106(U_339,U_340,U_331,U_349,U_345)
| U_345 != set_meet(U_349)
| ~ sP109(U_335,U_339,U_340,U_346,U_331,U_349,U_345) )
& ! [U_347,U_350,U_348] :
( sP110(U_347,U_350,U_348)
| U_350 != empty_set )
& ! [U_335,U_339,U_340,U_346,U_331,U_349,U_345] :
( sP109(U_335,U_339,U_340,U_346,U_331,U_349,U_345)
| U_349 = empty_set ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105,sP106,sP107,sP108,sP109,sP110])],[f_82_7]) ).
cnf(f_82_9,plain,
( sP109(U_335,U_339,U_340,U_346,U_331,U_349,U_345)
| U_349 = empty_set ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_10,plain,
( sP110(U_347,U_350,U_348)
| U_350 != empty_set ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_11,plain,
( sP106(U_339,U_340,U_331,U_349,U_345)
| U_345 != set_meet(U_349)
| ~ sP109(U_335,U_339,U_340,U_346,U_331,U_349,U_345) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_12,plain,
( U_346 = set_meet(U_349)
| sP108(U_335,U_346,U_349)
| sP107(U_346,U_349)
| ~ sP109(U_335,U_339,U_340,U_346,U_331,U_349,U_345) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_13,plain,
( in(U_339,U_331)
| ~ in(U_331,U_349)
| ~ in(U_339,U_345)
| ~ sP106(U_339,U_340,U_331,U_349,U_345) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_14,plain,
( in(U_340,U_345)
| sP105(U_340,U_349,U_345)
| ~ sP106(U_339,U_340,U_331,U_349,U_345) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_15,plain,
( in(sK52(U_349,U_345,U_340),U_349)
| ~ sP105(U_340,U_349,U_345) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_16,plain,
( ~ in(U_340,sK52(U_349,U_345,U_340))
| ~ sP105(U_340,U_349,U_345) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_17,plain,
( in(sK53(U_349,U_346),U_346)
| ~ sP107(U_346,U_349) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_18,plain,
( in(sK54(U_349,U_346),U_349)
| ~ sP107(U_346,U_349) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_19,plain,
( ~ in(sK53(U_349,U_346),sK54(U_349,U_346))
| ~ sP107(U_346,U_349) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_20,plain,
( in(sK55(U_349,U_346),U_335)
| ~ in(U_335,U_349)
| ~ sP108(U_335,U_346,U_349) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_21,plain,
( ~ in(sK55(U_349,U_346),U_346)
| ~ sP108(U_335,U_346,U_349) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_22,plain,
( U_347 = empty_set
| U_347 != set_meet(U_350)
| ~ sP110(U_347,U_350,U_348) ),
inference(clausify,[status(thm)],[f_82_8]) ).
cnf(f_82_23,plain,
( U_348 = set_meet(U_350)
| U_348 != empty_set
| ~ sP110(U_347,U_350,U_348) ),
inference(clausify,[status(thm)],[f_82_8]) ).
fof(f_83_1,plain,
! [A] :
( ( ( empty_carrier(A)
| ~ empty(the_carrier(A)) )
& ( empty(the_carrier(A))
| ~ empty_carrier(A) ) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d1_struct_0]) ).
fof(f_83_2,plain,
! [U_351] :
( ( ( empty_carrier(U_351)
| ~ empty(the_carrier(U_351)) )
& ( empty(the_carrier(U_351))
| ~ empty_carrier(U_351) ) )
| ~ one_sorted_str(U_351) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_351] :
( empty_carrier(U_351)
| ~ empty(the_carrier(U_351))
| ~ sP111(U_351) )
& ! [U_351] :
( empty(the_carrier(U_351))
| ~ empty_carrier(U_351)
| ~ sP111(U_351) )
& ! [U_351] :
( sP111(U_351)
| ~ one_sorted_str(U_351) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_83_2]) ).
cnf(f_83_4,plain,
( sP111(U_351)
| ~ one_sorted_str(U_351) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
( empty(the_carrier(U_351))
| ~ empty_carrier(U_351)
| ~ sP111(U_351) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_6,plain,
( empty_carrier(U_351)
| ~ empty(the_carrier(U_351))
| ~ sP111(U_351) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_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_84_2,plain,
! [U_355,U_354] :
( ( U_354 = singleton(U_355)
| ? [U_353] :
( ( ~ in(U_353,U_354)
& U_353 = U_355 )
| ( U_353 != U_355
& in(U_353,U_354) ) ) )
& ( ! [U_352] :
( ( in(U_352,U_354)
| U_352 != U_355 )
& ( U_352 = U_355
| ~ in(U_352,U_354) ) )
| U_354 != singleton(U_355) ) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_363,U_361] :
( U_361 = singleton(U_363)
| ? [U_359] :
( ~ in(U_359,U_361)
& U_359 = U_363 )
| ? [U_358] :
( U_358 != U_363
& in(U_358,U_361) ) )
& ! [U_362,U_360] :
( ( ! [U_357] :
( in(U_357,U_360)
| U_357 != U_362 )
& ! [U_356] :
( U_356 = U_362
| ~ in(U_356,U_360) ) )
| U_360 != singleton(U_362) ) ),
inference(miniscope,[status(thm)],[f_84_2]) ).
fof(f_84_4,plain,
( ! [U_363,U_361] :
( U_361 = singleton(U_363)
| ? [U_359] :
( ~ in(U_359,U_361)
& U_359 = U_363 )
| ( sK56(U_363,U_361) != U_363
& in(sK56(U_363,U_361),U_361) ) )
& ! [U_362,U_360] :
( ( ! [U_357] :
( in(U_357,U_360)
| U_357 != U_362 )
& ! [U_356] :
( U_356 = U_362
| ~ in(U_356,U_360) ) )
| U_360 != singleton(U_362) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_358,sK56(U_363,U_361))],[f_84_3]) ).
fof(f_84_5,plain,
( ! [U_363,U_361] :
( U_361 = singleton(U_363)
| ( ~ in(sK57(U_363,U_361),U_361)
& sK57(U_363,U_361) = U_363 )
| ( sK56(U_363,U_361) != U_363
& in(sK56(U_363,U_361),U_361) ) )
& ! [U_362,U_360] :
( ( ! [U_357] :
( in(U_357,U_360)
| U_357 != U_362 )
& ! [U_356] :
( U_356 = U_362
| ~ in(U_356,U_360) ) )
| U_360 != singleton(U_362) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_359,sK57(U_363,U_361))],[f_84_4]) ).
fof(f_84_6,plain,
( ! [U_363,U_361] :
( ~ in(sK57(U_363,U_361),U_361)
| ~ sP114(U_363,U_361) )
& ! [U_363,U_361] :
( sK57(U_363,U_361) = U_363
| ~ sP114(U_363,U_361) )
& ! [U_363,U_361] :
( sK56(U_363,U_361) != U_363
| ~ sP113(U_363,U_361) )
& ! [U_363,U_361] :
( in(sK56(U_363,U_361),U_361)
| ~ sP113(U_363,U_361) )
& ! [U_357,U_356,U_362,U_360] :
( in(U_357,U_360)
| U_357 != U_362
| ~ sP112(U_357,U_356,U_362,U_360) )
& ! [U_357,U_356,U_362,U_360] :
( U_356 = U_362
| ~ in(U_356,U_360)
| ~ sP112(U_357,U_356,U_362,U_360) )
& ! [U_363,U_361] :
( U_361 = singleton(U_363)
| sP114(U_363,U_361)
| sP113(U_363,U_361) )
& ! [U_357,U_356,U_362,U_360] :
( sP112(U_357,U_356,U_362,U_360)
| U_360 != singleton(U_362) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112,sP113,sP114])],[f_84_5]) ).
cnf(f_84_7,plain,
( sP112(U_357,U_356,U_362,U_360)
| U_360 != singleton(U_362) ),
inference(clausify,[status(thm)],[f_84_6]) ).
cnf(f_84_8,plain,
( U_361 = singleton(U_363)
| sP114(U_363,U_361)
| sP113(U_363,U_361) ),
inference(clausify,[status(thm)],[f_84_6]) ).
cnf(f_84_9,plain,
( U_356 = U_362
| ~ in(U_356,U_360)
| ~ sP112(U_357,U_356,U_362,U_360) ),
inference(clausify,[status(thm)],[f_84_6]) ).
cnf(f_84_10,plain,
( in(U_357,U_360)
| U_357 != U_362
| ~ sP112(U_357,U_356,U_362,U_360) ),
inference(clausify,[status(thm)],[f_84_6]) ).
cnf(f_84_11,plain,
( in(sK56(U_363,U_361),U_361)
| ~ sP113(U_363,U_361) ),
inference(clausify,[status(thm)],[f_84_6]) ).
cnf(f_84_12,plain,
( sK56(U_363,U_361) != U_363
| ~ sP113(U_363,U_361) ),
inference(clausify,[status(thm)],[f_84_6]) ).
cnf(f_84_13,plain,
( sK57(U_363,U_361) = U_363
| ~ sP114(U_363,U_361) ),
inference(clausify,[status(thm)],[f_84_6]) ).
cnf(f_84_14,plain,
( ~ in(sK57(U_363,U_361),U_361)
| ~ sP114(U_363,U_361) ),
inference(clausify,[status(thm)],[f_84_6]) ).
fof(f_85_1,plain,
! [A] :
( ! [B] :
( interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d1_tops_1]) ).
fof(f_85_2,plain,
! [U_365] :
( ! [U_364] :
( interior(U_365,U_364) = subset_complement(the_carrier(U_365),topstr_closure(U_365,subset_complement(the_carrier(U_365),U_364)))
| ~ element(U_364,powerset(the_carrier(U_365))) )
| ~ top_str(U_365) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_364,U_365] :
( interior(U_365,U_364) = subset_complement(the_carrier(U_365),topstr_closure(U_365,subset_complement(the_carrier(U_365),U_364)))
| ~ element(U_364,powerset(the_carrier(U_365)))
| ~ top_str(U_365) ),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
( interior(U_365,U_364) = subset_complement(the_carrier(U_365),topstr_closure(U_365,subset_complement(the_carrier(U_365),U_364)))
| ~ element(U_364,powerset(the_carrier(U_365)))
| ~ top_str(U_365) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [A] :
( ! [B] :
( ( ( open_subsets(B,A)
| ? [C] :
( ~ open_subset(C,A)
& in(C,B)
& element(C,powerset(the_carrier(A))) ) )
& ( ! [C] :
( open_subset(C,A)
| ~ in(C,B)
| ~ element(C,powerset(the_carrier(A))) )
| ~ open_subsets(B,A) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d1_tops_2]) ).
fof(f_86_2,plain,
! [U_369] :
( ! [U_368] :
( ( ( open_subsets(U_368,U_369)
| ? [U_367] :
( ~ open_subset(U_367,U_369)
& in(U_367,U_368)
& element(U_367,powerset(the_carrier(U_369))) ) )
& ( ! [U_366] :
( open_subset(U_366,U_369)
| ~ in(U_366,U_368)
| ~ element(U_366,powerset(the_carrier(U_369))) )
| ~ open_subsets(U_368,U_369) ) )
| ~ element(U_368,powerset(powerset(the_carrier(U_369)))) )
| ~ top_str(U_369) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_369] :
( ! [U_368] :
( ( ( open_subsets(U_368,U_369)
| ( ~ open_subset(sK58(U_369,U_368),U_369)
& in(sK58(U_369,U_368),U_368)
& element(sK58(U_369,U_368),powerset(the_carrier(U_369))) ) )
& ( ! [U_366] :
( open_subset(U_366,U_369)
| ~ in(U_366,U_368)
| ~ element(U_366,powerset(the_carrier(U_369))) )
| ~ open_subsets(U_368,U_369) ) )
| ~ element(U_368,powerset(powerset(the_carrier(U_369)))) )
| ~ top_str(U_369) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_367,sK58(U_369,U_368))],[f_86_2]) ).
fof(f_86_4,plain,
( ! [U_369,U_368] :
( ~ open_subset(sK58(U_369,U_368),U_369)
| ~ sP115(U_369,U_368) )
& ! [U_369,U_368] :
( in(sK58(U_369,U_368),U_368)
| ~ sP115(U_369,U_368) )
& ! [U_369,U_368] :
( element(sK58(U_369,U_368),powerset(the_carrier(U_369)))
| ~ sP115(U_369,U_368) )
& ! [U_369,U_366,U_368] :
( open_subsets(U_368,U_369)
| sP115(U_369,U_368)
| ~ sP116(U_369,U_366,U_368) )
& ! [U_369,U_366,U_368] :
( open_subset(U_366,U_369)
| ~ in(U_366,U_368)
| ~ element(U_366,powerset(the_carrier(U_369)))
| ~ open_subsets(U_368,U_369)
| ~ sP116(U_369,U_366,U_368) )
& ! [U_369,U_366,U_368] :
( sP116(U_369,U_366,U_368)
| ~ element(U_368,powerset(powerset(the_carrier(U_369))))
| ~ top_str(U_369) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115,sP116])],[f_86_3]) ).
cnf(f_86_5,plain,
( sP116(U_369,U_366,U_368)
| ~ element(U_368,powerset(powerset(the_carrier(U_369))))
| ~ top_str(U_369) ),
inference(clausify,[status(thm)],[f_86_4]) ).
cnf(f_86_6,plain,
( open_subset(U_366,U_369)
| ~ in(U_366,U_368)
| ~ element(U_366,powerset(the_carrier(U_369)))
| ~ open_subsets(U_368,U_369)
| ~ sP116(U_369,U_366,U_368) ),
inference(clausify,[status(thm)],[f_86_4]) ).
cnf(f_86_7,plain,
( open_subsets(U_368,U_369)
| sP115(U_369,U_368)
| ~ sP116(U_369,U_366,U_368) ),
inference(clausify,[status(thm)],[f_86_4]) ).
cnf(f_86_8,plain,
( element(sK58(U_369,U_368),powerset(the_carrier(U_369)))
| ~ sP115(U_369,U_368) ),
inference(clausify,[status(thm)],[f_86_4]) ).
cnf(f_86_9,plain,
( in(sK58(U_369,U_368),U_368)
| ~ sP115(U_369,U_368) ),
inference(clausify,[status(thm)],[f_86_4]) ).
cnf(f_86_10,plain,
( ~ open_subset(sK58(U_369,U_368),U_369)
| ~ sP115(U_369,U_368) ),
inference(clausify,[status(thm)],[f_86_4]) ).
fof(f_87_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_87_2,plain,
! [U_374] :
( ! [U_373,U_372] :
( ( U_372 = fiber(U_374,U_373)
| ? [U_371] :
( ( ~ in(U_371,U_372)
& in(ordered_pair(U_371,U_373),U_374)
& U_371 != U_373 )
| ( ( ~ in(ordered_pair(U_371,U_373),U_374)
| U_371 = U_373 )
& in(U_371,U_372) ) ) )
& ( ! [U_370] :
( ( in(U_370,U_372)
| ~ in(ordered_pair(U_370,U_373),U_374)
| U_370 = U_373 )
& ( ( in(ordered_pair(U_370,U_373),U_374)
& U_370 != U_373 )
| ~ in(U_370,U_372) ) )
| U_372 != fiber(U_374,U_373) ) )
| ~ relation(U_374) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_374] :
( ( ! [U_382,U_380] :
( U_380 = fiber(U_374,U_382)
| ? [U_378] :
( ~ in(U_378,U_380)
& in(ordered_pair(U_378,U_382),U_374)
& U_378 != U_382 )
| ? [U_377] :
( ( ~ in(ordered_pair(U_377,U_382),U_374)
| U_377 = U_382 )
& in(U_377,U_380) ) )
& ! [U_381,U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ~ in(ordered_pair(U_376,U_381),U_374)
| U_376 = U_381 )
& ! [U_375] :
( ( in(ordered_pair(U_375,U_381),U_374)
& U_375 != U_381 )
| ~ in(U_375,U_379) ) )
| U_379 != fiber(U_374,U_381) ) )
| ~ relation(U_374) ),
inference(miniscope,[status(thm)],[f_87_2]) ).
fof(f_87_4,plain,
! [U_374] :
( ( ! [U_382,U_380] :
( U_380 = fiber(U_374,U_382)
| ? [U_378] :
( ~ in(U_378,U_380)
& in(ordered_pair(U_378,U_382),U_374)
& U_378 != U_382 )
| ( ( ~ in(ordered_pair(sK59(U_374,U_382,U_380),U_382),U_374)
| sK59(U_374,U_382,U_380) = U_382 )
& in(sK59(U_374,U_382,U_380),U_380) ) )
& ! [U_381,U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ~ in(ordered_pair(U_376,U_381),U_374)
| U_376 = U_381 )
& ! [U_375] :
( ( in(ordered_pair(U_375,U_381),U_374)
& U_375 != U_381 )
| ~ in(U_375,U_379) ) )
| U_379 != fiber(U_374,U_381) ) )
| ~ relation(U_374) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_377,sK59(U_374,U_382,U_380))],[f_87_3]) ).
fof(f_87_5,plain,
! [U_374] :
( ( ! [U_382,U_380] :
( U_380 = fiber(U_374,U_382)
| ( ~ in(sK60(U_374,U_382,U_380),U_380)
& in(ordered_pair(sK60(U_374,U_382,U_380),U_382),U_374)
& sK60(U_374,U_382,U_380) != U_382 )
| ( ( ~ in(ordered_pair(sK59(U_374,U_382,U_380),U_382),U_374)
| sK59(U_374,U_382,U_380) = U_382 )
& in(sK59(U_374,U_382,U_380),U_380) ) )
& ! [U_381,U_379] :
( ( ! [U_376] :
( in(U_376,U_379)
| ~ in(ordered_pair(U_376,U_381),U_374)
| U_376 = U_381 )
& ! [U_375] :
( ( in(ordered_pair(U_375,U_381),U_374)
& U_375 != U_381 )
| ~ in(U_375,U_379) ) )
| U_379 != fiber(U_374,U_381) ) )
| ~ relation(U_374) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_378,sK60(U_374,U_382,U_380))],[f_87_4]) ).
fof(f_87_6,plain,
( ! [U_382,U_374,U_380] :
( ~ in(sK60(U_374,U_382,U_380),U_380)
| ~ sP120(U_382,U_374,U_380) )
& ! [U_382,U_374,U_380] :
( in(ordered_pair(sK60(U_374,U_382,U_380),U_382),U_374)
| ~ sP120(U_382,U_374,U_380) )
& ! [U_382,U_374,U_380] :
( sK60(U_374,U_382,U_380) != U_382
| ~ sP120(U_382,U_374,U_380) )
& ! [U_382,U_374,U_380] :
( ~ in(ordered_pair(sK59(U_374,U_382,U_380),U_382),U_374)
| sK59(U_374,U_382,U_380) = U_382
| ~ sP119(U_382,U_374,U_380) )
& ! [U_382,U_374,U_380] :
( in(sK59(U_374,U_382,U_380),U_380)
| ~ sP119(U_382,U_374,U_380) )
& ! [U_375,U_381,U_374] :
( in(ordered_pair(U_375,U_381),U_374)
| ~ sP117(U_375,U_381,U_374) )
& ! [U_375,U_381,U_374] :
( U_375 != U_381
| ~ sP117(U_375,U_381,U_374) )
& ! [U_376,U_375,U_381,U_374,U_379] :
( in(U_376,U_379)
| ~ in(ordered_pair(U_376,U_381),U_374)
| U_376 = U_381
| ~ sP118(U_376,U_375,U_381,U_374,U_379) )
& ! [U_376,U_375,U_381,U_374,U_379] :
( sP117(U_375,U_381,U_374)
| ~ in(U_375,U_379)
| ~ sP118(U_376,U_375,U_381,U_374,U_379) )
& ! [U_376,U_375,U_381,U_382,U_374,U_379,U_380] :
( U_380 = fiber(U_374,U_382)
| sP120(U_382,U_374,U_380)
| sP119(U_382,U_374,U_380)
| ~ sP121(U_376,U_375,U_381,U_382,U_374,U_379,U_380) )
& ! [U_376,U_375,U_381,U_382,U_374,U_379,U_380] :
( sP118(U_376,U_375,U_381,U_374,U_379)
| U_379 != fiber(U_374,U_381)
| ~ sP121(U_376,U_375,U_381,U_382,U_374,U_379,U_380) )
& ! [U_376,U_375,U_381,U_382,U_374,U_379,U_380] :
( sP121(U_376,U_375,U_381,U_382,U_374,U_379,U_380)
| ~ relation(U_374) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117,sP118,sP119,sP120,sP121])],[f_87_5]) ).
cnf(f_87_7,plain,
( sP121(U_376,U_375,U_381,U_382,U_374,U_379,U_380)
| ~ relation(U_374) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_8,plain,
( sP118(U_376,U_375,U_381,U_374,U_379)
| U_379 != fiber(U_374,U_381)
| ~ sP121(U_376,U_375,U_381,U_382,U_374,U_379,U_380) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_9,plain,
( U_380 = fiber(U_374,U_382)
| sP120(U_382,U_374,U_380)
| sP119(U_382,U_374,U_380)
| ~ sP121(U_376,U_375,U_381,U_382,U_374,U_379,U_380) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_10,plain,
( sP117(U_375,U_381,U_374)
| ~ in(U_375,U_379)
| ~ sP118(U_376,U_375,U_381,U_374,U_379) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_11,plain,
( in(U_376,U_379)
| ~ in(ordered_pair(U_376,U_381),U_374)
| U_376 = U_381
| ~ sP118(U_376,U_375,U_381,U_374,U_379) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_12,plain,
( U_375 != U_381
| ~ sP117(U_375,U_381,U_374) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_13,plain,
( in(ordered_pair(U_375,U_381),U_374)
| ~ sP117(U_375,U_381,U_374) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_14,plain,
( in(sK59(U_374,U_382,U_380),U_380)
| ~ sP119(U_382,U_374,U_380) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_15,plain,
( ~ in(ordered_pair(sK59(U_374,U_382,U_380),U_382),U_374)
| sK59(U_374,U_382,U_380) = U_382
| ~ sP119(U_382,U_374,U_380) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_16,plain,
( sK60(U_374,U_382,U_380) != U_382
| ~ sP120(U_382,U_374,U_380) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_17,plain,
( in(ordered_pair(sK60(U_374,U_382,U_380),U_382),U_374)
| ~ sP120(U_382,U_374,U_380) ),
inference(clausify,[status(thm)],[f_87_6]) ).
cnf(f_87_18,plain,
( ~ in(sK60(U_374,U_382,U_380),U_380)
| ~ sP120(U_382,U_374,U_380) ),
inference(clausify,[status(thm)],[f_87_6]) ).
fof(f_88_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_88_2,plain,
! [U_388,U_387] :
( ( ( U_387 = inclusion_relation(U_388)
| ? [U_386,U_385] :
( ( ( ~ in(ordered_pair(U_386,U_385),U_387)
& subset(U_386,U_385) )
| ( ~ subset(U_386,U_385)
& in(ordered_pair(U_386,U_385),U_387) ) )
& in(U_385,U_388)
& in(U_386,U_388) )
| relation_field(U_387) != U_388 )
& ( ( ! [U_384,U_383] :
( ( ( in(ordered_pair(U_384,U_383),U_387)
| ~ subset(U_384,U_383) )
& ( subset(U_384,U_383)
| ~ in(ordered_pair(U_384,U_383),U_387) ) )
| ~ in(U_383,U_388)
| ~ in(U_384,U_388) )
& relation_field(U_387) = U_388 )
| U_387 != inclusion_relation(U_388) ) )
| ~ relation(U_387) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_388,U_387] :
( ( ( U_387 = inclusion_relation(U_388)
| ? [U_385] :
( ( ( ~ in(ordered_pair(sK61(U_388,U_387),U_385),U_387)
& subset(sK61(U_388,U_387),U_385) )
| ( ~ subset(sK61(U_388,U_387),U_385)
& in(ordered_pair(sK61(U_388,U_387),U_385),U_387) ) )
& in(U_385,U_388)
& in(sK61(U_388,U_387),U_388) )
| relation_field(U_387) != U_388 )
& ( ( ! [U_384,U_383] :
( ( ( in(ordered_pair(U_384,U_383),U_387)
| ~ subset(U_384,U_383) )
& ( subset(U_384,U_383)
| ~ in(ordered_pair(U_384,U_383),U_387) ) )
| ~ in(U_383,U_388)
| ~ in(U_384,U_388) )
& relation_field(U_387) = U_388 )
| U_387 != inclusion_relation(U_388) ) )
| ~ relation(U_387) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_386,sK61(U_388,U_387))],[f_88_2]) ).
fof(f_88_4,plain,
! [U_388,U_387] :
( ( ( U_387 = inclusion_relation(U_388)
| ( ( ( ~ in(ordered_pair(sK61(U_388,U_387),sK62(U_388,U_387)),U_387)
& subset(sK61(U_388,U_387),sK62(U_388,U_387)) )
| ( ~ subset(sK61(U_388,U_387),sK62(U_388,U_387))
& in(ordered_pair(sK61(U_388,U_387),sK62(U_388,U_387)),U_387) ) )
& in(sK62(U_388,U_387),U_388)
& in(sK61(U_388,U_387),U_388) )
| relation_field(U_387) != U_388 )
& ( ( ! [U_384,U_383] :
( ( ( in(ordered_pair(U_384,U_383),U_387)
| ~ subset(U_384,U_383) )
& ( subset(U_384,U_383)
| ~ in(ordered_pair(U_384,U_383),U_387) ) )
| ~ in(U_383,U_388)
| ~ in(U_384,U_388) )
& relation_field(U_387) = U_388 )
| U_387 != inclusion_relation(U_388) ) )
| ~ relation(U_387) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_385,sK62(U_388,U_387))],[f_88_3]) ).
fof(f_88_5,plain,
( ! [U_388,U_387] :
( ~ in(ordered_pair(sK61(U_388,U_387),sK62(U_388,U_387)),U_387)
| ~ sP125(U_388,U_387) )
& ! [U_388,U_387] :
( subset(sK61(U_388,U_387),sK62(U_388,U_387))
| ~ sP125(U_388,U_387) )
& ! [U_388,U_387] :
( ~ subset(sK61(U_388,U_387),sK62(U_388,U_387))
| ~ sP124(U_388,U_387) )
& ! [U_388,U_387] :
( in(ordered_pair(sK61(U_388,U_387),sK62(U_388,U_387)),U_387)
| ~ sP124(U_388,U_387) )
& ! [U_388,U_387] :
( sP125(U_388,U_387)
| sP124(U_388,U_387)
| ~ sP126(U_388,U_387) )
& ! [U_388,U_387] :
( in(sK62(U_388,U_387),U_388)
| ~ sP126(U_388,U_387) )
& ! [U_388,U_387] :
( in(sK61(U_388,U_387),U_388)
| ~ sP126(U_388,U_387) )
& ! [U_387,U_383,U_384] :
( in(ordered_pair(U_384,U_383),U_387)
| ~ subset(U_384,U_383)
| ~ sP122(U_387,U_383,U_384) )
& ! [U_387,U_383,U_384] :
( subset(U_384,U_383)
| ~ in(ordered_pair(U_384,U_383),U_387)
| ~ sP122(U_387,U_383,U_384) )
& ! [U_388,U_387,U_383,U_384] :
( sP122(U_387,U_383,U_384)
| ~ in(U_383,U_388)
| ~ in(U_384,U_388)
| ~ sP123(U_388,U_387,U_383,U_384) )
& ! [U_388,U_387,U_383,U_384] :
( relation_field(U_387) = U_388
| ~ sP123(U_388,U_387,U_383,U_384) )
& ! [U_388,U_387,U_383,U_384] :
( U_387 = inclusion_relation(U_388)
| sP126(U_388,U_387)
| relation_field(U_387) != U_388
| ~ sP127(U_388,U_387,U_383,U_384) )
& ! [U_388,U_387,U_383,U_384] :
( sP123(U_388,U_387,U_383,U_384)
| U_387 != inclusion_relation(U_388)
| ~ sP127(U_388,U_387,U_383,U_384) )
& ! [U_388,U_387,U_383,U_384] :
( sP127(U_388,U_387,U_383,U_384)
| ~ relation(U_387) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122,sP123,sP124,sP125,sP126,sP127])],[f_88_4]) ).
cnf(f_88_6,plain,
( sP127(U_388,U_387,U_383,U_384)
| ~ relation(U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_7,plain,
( sP123(U_388,U_387,U_383,U_384)
| U_387 != inclusion_relation(U_388)
| ~ sP127(U_388,U_387,U_383,U_384) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_8,plain,
( U_387 = inclusion_relation(U_388)
| sP126(U_388,U_387)
| relation_field(U_387) != U_388
| ~ sP127(U_388,U_387,U_383,U_384) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_9,plain,
( relation_field(U_387) = U_388
| ~ sP123(U_388,U_387,U_383,U_384) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_10,plain,
( sP122(U_387,U_383,U_384)
| ~ in(U_383,U_388)
| ~ in(U_384,U_388)
| ~ sP123(U_388,U_387,U_383,U_384) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_11,plain,
( subset(U_384,U_383)
| ~ in(ordered_pair(U_384,U_383),U_387)
| ~ sP122(U_387,U_383,U_384) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_12,plain,
( in(ordered_pair(U_384,U_383),U_387)
| ~ subset(U_384,U_383)
| ~ sP122(U_387,U_383,U_384) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_13,plain,
( in(sK61(U_388,U_387),U_388)
| ~ sP126(U_388,U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_14,plain,
( in(sK62(U_388,U_387),U_388)
| ~ sP126(U_388,U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_15,plain,
( sP125(U_388,U_387)
| sP124(U_388,U_387)
| ~ sP126(U_388,U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_16,plain,
( in(ordered_pair(sK61(U_388,U_387),sK62(U_388,U_387)),U_387)
| ~ sP124(U_388,U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_17,plain,
( ~ subset(sK61(U_388,U_387),sK62(U_388,U_387))
| ~ sP124(U_388,U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_18,plain,
( subset(sK61(U_388,U_387),sK62(U_388,U_387))
| ~ sP125(U_388,U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
cnf(f_88_19,plain,
( ~ in(ordered_pair(sK61(U_388,U_387),sK62(U_388,U_387)),U_387)
| ~ sP125(U_388,U_387) ),
inference(clausify,[status(thm)],[f_88_5]) ).
fof(f_89_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_89_2,plain,
! [U_391] :
( ( U_391 = empty_set
| ? [U_390] : in(U_390,U_391) )
& ( ! [U_389] : ~ in(U_389,U_391)
| U_391 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_393] :
( U_393 = empty_set
| ? [U_390] : in(U_390,U_393) )
& ! [U_392] :
( ! [U_389] : ~ in(U_389,U_392)
| U_392 != empty_set ) ),
inference(miniscope,[status(thm)],[f_89_2]) ).
fof(f_89_4,plain,
( ! [U_393] :
( U_393 = empty_set
| in(sK63(U_393),U_393) )
& ! [U_392] :
( ! [U_389] : ~ in(U_389,U_392)
| U_392 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_390,sK63(U_393))],[f_89_3]) ).
fof(f_89_5,plain,
( ! [U_393] :
( U_393 = empty_set
| in(sK63(U_393),U_393) )
& ! [U_392,U_389] :
( ~ in(U_389,U_392)
| U_392 != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_89_4]) ).
cnf(f_89_6,plain,
( ~ in(U_389,U_392)
| U_392 != empty_set ),
inference(clausify,[status(thm)],[f_89_5]) ).
cnf(f_89_7,plain,
( U_393 = empty_set
| in(sK63(U_393),U_393) ),
inference(clausify,[status(thm)],[f_89_5]) ).
fof(f_90_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_90_2,plain,
! [U_397,U_396] :
( ( U_396 = powerset(U_397)
| ? [U_395] :
( ( ~ in(U_395,U_396)
& subset(U_395,U_397) )
| ( ~ subset(U_395,U_397)
& in(U_395,U_396) ) ) )
& ( ! [U_394] :
( ( in(U_394,U_396)
| ~ subset(U_394,U_397) )
& ( subset(U_394,U_397)
| ~ in(U_394,U_396) ) )
| U_396 != powerset(U_397) ) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
( ! [U_405,U_403] :
( U_403 = powerset(U_405)
| ? [U_401] :
( ~ in(U_401,U_403)
& subset(U_401,U_405) )
| ? [U_400] :
( ~ subset(U_400,U_405)
& in(U_400,U_403) ) )
& ! [U_404,U_402] :
( ( ! [U_399] :
( in(U_399,U_402)
| ~ subset(U_399,U_404) )
& ! [U_398] :
( subset(U_398,U_404)
| ~ in(U_398,U_402) ) )
| U_402 != powerset(U_404) ) ),
inference(miniscope,[status(thm)],[f_90_2]) ).
fof(f_90_4,plain,
( ! [U_405,U_403] :
( U_403 = powerset(U_405)
| ? [U_401] :
( ~ in(U_401,U_403)
& subset(U_401,U_405) )
| ( ~ subset(sK64(U_405,U_403),U_405)
& in(sK64(U_405,U_403),U_403) ) )
& ! [U_404,U_402] :
( ( ! [U_399] :
( in(U_399,U_402)
| ~ subset(U_399,U_404) )
& ! [U_398] :
( subset(U_398,U_404)
| ~ in(U_398,U_402) ) )
| U_402 != powerset(U_404) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_400,sK64(U_405,U_403))],[f_90_3]) ).
fof(f_90_5,plain,
( ! [U_405,U_403] :
( U_403 = powerset(U_405)
| ( ~ in(sK65(U_405,U_403),U_403)
& subset(sK65(U_405,U_403),U_405) )
| ( ~ subset(sK64(U_405,U_403),U_405)
& in(sK64(U_405,U_403),U_403) ) )
& ! [U_404,U_402] :
( ( ! [U_399] :
( in(U_399,U_402)
| ~ subset(U_399,U_404) )
& ! [U_398] :
( subset(U_398,U_404)
| ~ in(U_398,U_402) ) )
| U_402 != powerset(U_404) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_401,sK65(U_405,U_403))],[f_90_4]) ).
fof(f_90_6,plain,
( ! [U_405,U_403] :
( ~ in(sK65(U_405,U_403),U_403)
| ~ sP130(U_405,U_403) )
& ! [U_405,U_403] :
( subset(sK65(U_405,U_403),U_405)
| ~ sP130(U_405,U_403) )
& ! [U_405,U_403] :
( ~ subset(sK64(U_405,U_403),U_405)
| ~ sP129(U_405,U_403) )
& ! [U_405,U_403] :
( in(sK64(U_405,U_403),U_403)
| ~ sP129(U_405,U_403) )
& ! [U_399,U_402,U_398,U_404] :
( in(U_399,U_402)
| ~ subset(U_399,U_404)
| ~ sP128(U_399,U_402,U_398,U_404) )
& ! [U_399,U_402,U_398,U_404] :
( subset(U_398,U_404)
| ~ in(U_398,U_402)
| ~ sP128(U_399,U_402,U_398,U_404) )
& ! [U_405,U_403] :
( U_403 = powerset(U_405)
| sP130(U_405,U_403)
| sP129(U_405,U_403) )
& ! [U_399,U_402,U_398,U_404] :
( sP128(U_399,U_402,U_398,U_404)
| U_402 != powerset(U_404) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128,sP129,sP130])],[f_90_5]) ).
cnf(f_90_7,plain,
( sP128(U_399,U_402,U_398,U_404)
| U_402 != powerset(U_404) ),
inference(clausify,[status(thm)],[f_90_6]) ).
cnf(f_90_8,plain,
( U_403 = powerset(U_405)
| sP130(U_405,U_403)
| sP129(U_405,U_403) ),
inference(clausify,[status(thm)],[f_90_6]) ).
cnf(f_90_9,plain,
( subset(U_398,U_404)
| ~ in(U_398,U_402)
| ~ sP128(U_399,U_402,U_398,U_404) ),
inference(clausify,[status(thm)],[f_90_6]) ).
cnf(f_90_10,plain,
( in(U_399,U_402)
| ~ subset(U_399,U_404)
| ~ sP128(U_399,U_402,U_398,U_404) ),
inference(clausify,[status(thm)],[f_90_6]) ).
cnf(f_90_11,plain,
( in(sK64(U_405,U_403),U_403)
| ~ sP129(U_405,U_403) ),
inference(clausify,[status(thm)],[f_90_6]) ).
cnf(f_90_12,plain,
( ~ subset(sK64(U_405,U_403),U_405)
| ~ sP129(U_405,U_403) ),
inference(clausify,[status(thm)],[f_90_6]) ).
cnf(f_90_13,plain,
( subset(sK65(U_405,U_403),U_405)
| ~ sP130(U_405,U_403) ),
inference(clausify,[status(thm)],[f_90_6]) ).
cnf(f_90_14,plain,
( ~ in(sK65(U_405,U_403),U_403)
| ~ sP130(U_405,U_403) ),
inference(clausify,[status(thm)],[f_90_6]) ).
fof(f_91_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = join_of_latt_set(A,B)
| ? [D] :
( ~ below(A,C,D)
& latt_element_smaller(A,D,B)
& element(D,the_carrier(A)) )
| ~ latt_element_smaller(A,C,B) )
& ( ( ! [D] :
( below(A,C,D)
| ~ latt_element_smaller(A,D,B)
| ~ element(D,the_carrier(A)) )
& latt_element_smaller(A,C,B) )
| C != join_of_latt_set(A,B) ) )
| ~ element(C,the_carrier(A)) )
| ~ latt_str(A)
| ~ complete_latt_str(A)
| ~ lattice(A)
| empty_carrier(A)
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d21_lattice3]) ).
fof(f_91_2,plain,
! [U_410] :
( ! [U_409,U_408] :
( ( ( U_408 = join_of_latt_set(U_410,U_409)
| ? [U_407] :
( ~ below(U_410,U_408,U_407)
& latt_element_smaller(U_410,U_407,U_409)
& element(U_407,the_carrier(U_410)) )
| ~ latt_element_smaller(U_410,U_408,U_409) )
& ( ( ! [U_406] :
( below(U_410,U_408,U_406)
| ~ latt_element_smaller(U_410,U_406,U_409)
| ~ element(U_406,the_carrier(U_410)) )
& latt_element_smaller(U_410,U_408,U_409) )
| U_408 != join_of_latt_set(U_410,U_409) ) )
| ~ element(U_408,the_carrier(U_410)) )
| ~ latt_str(U_410)
| ~ complete_latt_str(U_410)
| ~ lattice(U_410)
| empty_carrier(U_410)
| ~ latt_str(U_410)
| empty_carrier(U_410) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_410] :
( ! [U_409,U_408] :
( ( ( U_408 = join_of_latt_set(U_410,U_409)
| ( ~ below(U_410,U_408,sK66(U_410,U_409,U_408))
& latt_element_smaller(U_410,sK66(U_410,U_409,U_408),U_409)
& element(sK66(U_410,U_409,U_408),the_carrier(U_410)) )
| ~ latt_element_smaller(U_410,U_408,U_409) )
& ( ( ! [U_406] :
( below(U_410,U_408,U_406)
| ~ latt_element_smaller(U_410,U_406,U_409)
| ~ element(U_406,the_carrier(U_410)) )
& latt_element_smaller(U_410,U_408,U_409) )
| U_408 != join_of_latt_set(U_410,U_409) ) )
| ~ element(U_408,the_carrier(U_410)) )
| ~ latt_str(U_410)
| ~ complete_latt_str(U_410)
| ~ lattice(U_410)
| empty_carrier(U_410)
| ~ latt_str(U_410)
| empty_carrier(U_410) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_407,sK66(U_410,U_409,U_408))],[f_91_2]) ).
fof(f_91_4,plain,
( ! [U_409,U_408,U_410] :
( ~ below(U_410,U_408,sK66(U_410,U_409,U_408))
| ~ sP132(U_409,U_408,U_410) )
& ! [U_409,U_408,U_410] :
( latt_element_smaller(U_410,sK66(U_410,U_409,U_408),U_409)
| ~ sP132(U_409,U_408,U_410) )
& ! [U_409,U_408,U_410] :
( element(sK66(U_410,U_409,U_408),the_carrier(U_410))
| ~ sP132(U_409,U_408,U_410) )
& ! [U_409,U_406,U_408,U_410] :
( below(U_410,U_408,U_406)
| ~ latt_element_smaller(U_410,U_406,U_409)
| ~ element(U_406,the_carrier(U_410))
| ~ sP131(U_409,U_406,U_408,U_410) )
& ! [U_409,U_406,U_408,U_410] :
( latt_element_smaller(U_410,U_408,U_409)
| ~ sP131(U_409,U_406,U_408,U_410) )
& ! [U_409,U_406,U_408,U_410] :
( U_408 = join_of_latt_set(U_410,U_409)
| sP132(U_409,U_408,U_410)
| ~ latt_element_smaller(U_410,U_408,U_409)
| ~ sP133(U_409,U_406,U_408,U_410) )
& ! [U_409,U_406,U_408,U_410] :
( sP131(U_409,U_406,U_408,U_410)
| U_408 != join_of_latt_set(U_410,U_409)
| ~ sP133(U_409,U_406,U_408,U_410) )
& ! [U_409,U_406,U_408,U_410] :
( sP133(U_409,U_406,U_408,U_410)
| ~ element(U_408,the_carrier(U_410))
| ~ latt_str(U_410)
| ~ complete_latt_str(U_410)
| ~ lattice(U_410)
| empty_carrier(U_410)
| ~ latt_str(U_410)
| empty_carrier(U_410) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131,sP132,sP133])],[f_91_3]) ).
cnf(f_91_5,plain,
( sP133(U_409,U_406,U_408,U_410)
| ~ element(U_408,the_carrier(U_410))
| ~ latt_str(U_410)
| ~ complete_latt_str(U_410)
| ~ lattice(U_410)
| empty_carrier(U_410)
| ~ latt_str(U_410)
| empty_carrier(U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_6,plain,
( sP131(U_409,U_406,U_408,U_410)
| U_408 != join_of_latt_set(U_410,U_409)
| ~ sP133(U_409,U_406,U_408,U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_7,plain,
( U_408 = join_of_latt_set(U_410,U_409)
| sP132(U_409,U_408,U_410)
| ~ latt_element_smaller(U_410,U_408,U_409)
| ~ sP133(U_409,U_406,U_408,U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_8,plain,
( latt_element_smaller(U_410,U_408,U_409)
| ~ sP131(U_409,U_406,U_408,U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_9,plain,
( below(U_410,U_408,U_406)
| ~ latt_element_smaller(U_410,U_406,U_409)
| ~ element(U_406,the_carrier(U_410))
| ~ sP131(U_409,U_406,U_408,U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_10,plain,
( element(sK66(U_410,U_409,U_408),the_carrier(U_410))
| ~ sP132(U_409,U_408,U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_11,plain,
( latt_element_smaller(U_410,sK66(U_410,U_409,U_408),U_409)
| ~ sP132(U_409,U_408,U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_12,plain,
( ~ below(U_410,U_408,sK66(U_410,U_409,U_408))
| ~ sP132(U_409,U_408,U_410) ),
inference(clausify,[status(thm)],[f_91_4]) ).
fof(f_92_1,plain,
! [A] :
( ! [B] : meet_of_latt_set(A,B) = join_of_latt_set(A,a_2_2_lattice3(A,B))
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d22_lattice3]) ).
fof(f_92_2,plain,
! [U_412] :
( ! [U_411] : meet_of_latt_set(U_412,U_411) = join_of_latt_set(U_412,a_2_2_lattice3(U_412,U_411))
| ~ latt_str(U_412)
| empty_carrier(U_412) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_412,U_411] :
( meet_of_latt_set(U_412,U_411) = join_of_latt_set(U_412,a_2_2_lattice3(U_412,U_411))
| ~ latt_str(U_412)
| empty_carrier(U_412) ),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
( meet_of_latt_set(U_412,U_411) = join_of_latt_set(U_412,a_2_2_lattice3(U_412,U_411))
| ~ latt_str(U_412)
| empty_carrier(U_412) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [A] :
( ( centered(A)
| ? [B] :
( set_meet(B) = empty_set
& finite(B)
& subset(B,A)
& B != empty_set )
| A = empty_set )
& ( ( ! [B] :
( set_meet(B) != empty_set
| ~ finite(B)
| ~ subset(B,A)
| B = empty_set )
& A != empty_set )
| ~ centered(A) ) ),
inference(fof_nnf,[status(thm)],[d2_compts_1]) ).
fof(f_93_2,plain,
! [U_415] :
( ( centered(U_415)
| ? [U_414] :
( set_meet(U_414) = empty_set
& finite(U_414)
& subset(U_414,U_415)
& U_414 != empty_set )
| U_415 = empty_set )
& ( ( ! [U_413] :
( set_meet(U_413) != empty_set
| ~ finite(U_413)
| ~ subset(U_413,U_415)
| U_413 = empty_set )
& U_415 != empty_set )
| ~ centered(U_415) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_417] :
( centered(U_417)
| ? [U_414] :
( set_meet(U_414) = empty_set
& finite(U_414)
& subset(U_414,U_417)
& U_414 != empty_set )
| U_417 = empty_set )
& ! [U_416] :
( ( ! [U_413] :
( set_meet(U_413) != empty_set
| ~ finite(U_413)
| ~ subset(U_413,U_416)
| U_413 = empty_set )
& U_416 != empty_set )
| ~ centered(U_416) ) ),
inference(miniscope,[status(thm)],[f_93_2]) ).
fof(f_93_4,plain,
( ! [U_417] :
( centered(U_417)
| ( set_meet(sK67(U_417)) = empty_set
& finite(sK67(U_417))
& subset(sK67(U_417),U_417)
& sK67(U_417) != empty_set )
| U_417 = empty_set )
& ! [U_416] :
( ( ! [U_413] :
( set_meet(U_413) != empty_set
| ~ finite(U_413)
| ~ subset(U_413,U_416)
| U_413 = empty_set )
& U_416 != empty_set )
| ~ centered(U_416) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_414,sK67(U_417))],[f_93_3]) ).
fof(f_93_5,plain,
( ! [U_417] :
( set_meet(sK67(U_417)) = empty_set
| ~ sP135(U_417) )
& ! [U_417] :
( finite(sK67(U_417))
| ~ sP135(U_417) )
& ! [U_417] :
( subset(sK67(U_417),U_417)
| ~ sP135(U_417) )
& ! [U_417] :
( sK67(U_417) != empty_set
| ~ sP135(U_417) )
& ! [U_416,U_413] :
( set_meet(U_413) != empty_set
| ~ finite(U_413)
| ~ subset(U_413,U_416)
| U_413 = empty_set
| ~ sP134(U_416,U_413) )
& ! [U_416,U_413] :
( U_416 != empty_set
| ~ sP134(U_416,U_413) )
& ! [U_417] :
( centered(U_417)
| sP135(U_417)
| U_417 = empty_set )
& ! [U_416,U_413] :
( sP134(U_416,U_413)
| ~ centered(U_416) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134,sP135])],[f_93_4]) ).
cnf(f_93_6,plain,
( sP134(U_416,U_413)
| ~ centered(U_416) ),
inference(clausify,[status(thm)],[f_93_5]) ).
cnf(f_93_7,plain,
( centered(U_417)
| sP135(U_417)
| U_417 = empty_set ),
inference(clausify,[status(thm)],[f_93_5]) ).
cnf(f_93_8,plain,
( U_416 != empty_set
| ~ sP134(U_416,U_413) ),
inference(clausify,[status(thm)],[f_93_5]) ).
cnf(f_93_9,plain,
( set_meet(U_413) != empty_set
| ~ finite(U_413)
| ~ subset(U_413,U_416)
| U_413 = empty_set
| ~ sP134(U_416,U_413) ),
inference(clausify,[status(thm)],[f_93_5]) ).
cnf(f_93_10,plain,
( sK67(U_417) != empty_set
| ~ sP135(U_417) ),
inference(clausify,[status(thm)],[f_93_5]) ).
cnf(f_93_11,plain,
( subset(sK67(U_417),U_417)
| ~ sP135(U_417) ),
inference(clausify,[status(thm)],[f_93_5]) ).
cnf(f_93_12,plain,
( finite(sK67(U_417))
| ~ sP135(U_417) ),
inference(clausify,[status(thm)],[f_93_5]) ).
cnf(f_93_13,plain,
( set_meet(sK67(U_417)) = empty_set
| ~ sP135(U_417) ),
inference(clausify,[status(thm)],[f_93_5]) ).
fof(f_94_1,plain,
! [A] :
( poset_of_lattice(A) = rel_str_of(the_carrier(A),k2_lattice3(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d2_lattice3]) ).
fof(f_94_2,plain,
! [U_418] :
( poset_of_lattice(U_418) = rel_str_of(the_carrier(U_418),k2_lattice3(U_418))
| ~ latt_str(U_418)
| ~ lattice(U_418)
| empty_carrier(U_418) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_418] :
( poset_of_lattice(U_418) = rel_str_of(the_carrier(U_418),k2_lattice3(U_418))
| ~ latt_str(U_418)
| ~ lattice(U_418)
| empty_carrier(U_418) ),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
( poset_of_lattice(U_418) = rel_str_of(the_carrier(U_418),k2_lattice3(U_418))
| ~ latt_str(U_418)
| ~ lattice(U_418)
| empty_carrier(U_418) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( meet(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_meet(A),B,C)
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ meet_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d2_lattices]) ).
fof(f_95_2,plain,
! [U_421] :
( ! [U_420] :
( ! [U_419] :
( meet(U_421,U_420,U_419) = apply_binary_as_element(the_carrier(U_421),the_carrier(U_421),the_carrier(U_421),the_L_meet(U_421),U_420,U_419)
| ~ element(U_419,the_carrier(U_421)) )
| ~ element(U_420,the_carrier(U_421)) )
| ~ meet_semilatt_str(U_421)
| empty_carrier(U_421) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_421,U_419,U_420] :
( meet(U_421,U_420,U_419) = apply_binary_as_element(the_carrier(U_421),the_carrier(U_421),the_carrier(U_421),the_L_meet(U_421),U_420,U_419)
| ~ element(U_419,the_carrier(U_421))
| ~ element(U_420,the_carrier(U_421))
| ~ meet_semilatt_str(U_421)
| empty_carrier(U_421) ),
inference(definitional_conversion,[status(esa)],[f_95_2]) ).
cnf(f_95_4,plain,
( meet(U_421,U_420,U_419) = apply_binary_as_element(the_carrier(U_421),the_carrier(U_421),the_carrier(U_421),the_L_meet(U_421),U_420,U_419)
| ~ element(U_419,the_carrier(U_421))
| ~ element(U_420,the_carrier(U_421))
| ~ meet_semilatt_str(U_421)
| empty_carrier(U_421) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_429] :
( ! [U_428] :
( ( U_428 = pair_second(U_429)
| ? [U_427,U_426] :
( U_428 != U_426
& U_429 = ordered_pair(U_427,U_426) ) )
& ( ! [U_425,U_424] :
( U_428 = U_424
| U_429 != ordered_pair(U_425,U_424) )
| U_428 != pair_second(U_429) ) )
| ! [U_423,U_422] : U_429 != ordered_pair(U_423,U_422) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_429] :
( ( ! [U_431] :
( U_431 = pair_second(U_429)
| ? [U_427,U_426] :
( U_431 != U_426
& U_429 = ordered_pair(U_427,U_426) ) )
& ! [U_430] :
( ! [U_425,U_424] :
( U_430 = U_424
| U_429 != ordered_pair(U_425,U_424) )
| U_430 != pair_second(U_429) ) )
| ! [U_423,U_422] : U_429 != ordered_pair(U_423,U_422) ),
inference(miniscope,[status(thm)],[f_96_2]) ).
fof(f_96_4,plain,
! [U_429] :
( ( ! [U_431] :
( U_431 = pair_second(U_429)
| ? [U_426] :
( U_431 != U_426
& U_429 = ordered_pair(sK68(U_429,U_431),U_426) ) )
& ! [U_430] :
( ! [U_425,U_424] :
( U_430 = U_424
| U_429 != ordered_pair(U_425,U_424) )
| U_430 != pair_second(U_429) ) )
| ! [U_423,U_422] : U_429 != ordered_pair(U_423,U_422) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_427,sK68(U_429,U_431))],[f_96_3]) ).
fof(f_96_5,plain,
! [U_429] :
( ( ! [U_431] :
( U_431 = pair_second(U_429)
| ( U_431 != sK69(U_429,U_431)
& U_429 = ordered_pair(sK68(U_429,U_431),sK69(U_429,U_431)) ) )
& ! [U_430] :
( ! [U_425,U_424] :
( U_430 = U_424
| U_429 != ordered_pair(U_425,U_424) )
| U_430 != pair_second(U_429) ) )
| ! [U_423,U_422] : U_429 != ordered_pair(U_423,U_422) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_426,sK69(U_429,U_431))],[f_96_4]) ).
fof(f_96_6,plain,
( ! [U_429,U_431] :
( U_431 != sK69(U_429,U_431)
| ~ sP136(U_429,U_431) )
& ! [U_429,U_431] :
( U_429 = ordered_pair(sK68(U_429,U_431),sK69(U_429,U_431))
| ~ sP136(U_429,U_431) )
& ! [U_424,U_429,U_430,U_431,U_425] :
( U_431 = pair_second(U_429)
| sP136(U_429,U_431)
| ~ sP137(U_424,U_429,U_430,U_431,U_425) )
& ! [U_424,U_429,U_430,U_431,U_425] :
( U_430 = U_424
| U_429 != ordered_pair(U_425,U_424)
| U_430 != pair_second(U_429)
| ~ sP137(U_424,U_429,U_430,U_431,U_425) )
& ! [U_424,U_423,U_429,U_430,U_431,U_425,U_422] :
( sP137(U_424,U_429,U_430,U_431,U_425)
| U_429 != ordered_pair(U_423,U_422) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136,sP137])],[f_96_5]) ).
cnf(f_96_7,plain,
( sP137(U_424,U_429,U_430,U_431,U_425)
| U_429 != ordered_pair(U_423,U_422) ),
inference(clausify,[status(thm)],[f_96_6]) ).
cnf(f_96_8,plain,
( U_430 = U_424
| U_429 != ordered_pair(U_425,U_424)
| U_430 != pair_second(U_429)
| ~ sP137(U_424,U_429,U_430,U_431,U_425) ),
inference(clausify,[status(thm)],[f_96_6]) ).
cnf(f_96_9,plain,
( U_431 = pair_second(U_429)
| sP136(U_429,U_431)
| ~ sP137(U_424,U_429,U_430,U_431,U_425) ),
inference(clausify,[status(thm)],[f_96_6]) ).
cnf(f_96_10,plain,
( U_429 = ordered_pair(sK68(U_429,U_431),sK69(U_429,U_431))
| ~ sP136(U_429,U_431) ),
inference(clausify,[status(thm)],[f_96_6]) ).
cnf(f_96_11,plain,
( U_431 != sK69(U_429,U_431)
| ~ sP136(U_429,U_431) ),
inference(clausify,[status(thm)],[f_96_6]) ).
fof(f_97_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_97_2,plain,
! [U_434] :
( ( epsilon_transitive(U_434)
| ? [U_433] :
( ~ subset(U_433,U_434)
& in(U_433,U_434) ) )
& ( ! [U_432] :
( subset(U_432,U_434)
| ~ in(U_432,U_434) )
| ~ epsilon_transitive(U_434) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( ! [U_436] :
( epsilon_transitive(U_436)
| ? [U_433] :
( ~ subset(U_433,U_436)
& in(U_433,U_436) ) )
& ! [U_435] :
( ! [U_432] :
( subset(U_432,U_435)
| ~ in(U_432,U_435) )
| ~ epsilon_transitive(U_435) ) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
fof(f_97_4,plain,
( ! [U_436] :
( epsilon_transitive(U_436)
| ( ~ subset(sK70(U_436),U_436)
& in(sK70(U_436),U_436) ) )
& ! [U_435] :
( ! [U_432] :
( subset(U_432,U_435)
| ~ in(U_432,U_435) )
| ~ epsilon_transitive(U_435) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_433,sK70(U_436))],[f_97_3]) ).
fof(f_97_5,plain,
( ! [U_436] :
( ~ subset(sK70(U_436),U_436)
| ~ sP138(U_436) )
& ! [U_436] :
( in(sK70(U_436),U_436)
| ~ sP138(U_436) )
& ! [U_436] :
( epsilon_transitive(U_436)
| sP138(U_436) )
& ! [U_432,U_435] :
( subset(U_432,U_435)
| ~ in(U_432,U_435)
| ~ epsilon_transitive(U_435) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_97_4]) ).
cnf(f_97_6,plain,
( subset(U_432,U_435)
| ~ in(U_432,U_435)
| ~ epsilon_transitive(U_435) ),
inference(clausify,[status(thm)],[f_97_5]) ).
cnf(f_97_7,plain,
( epsilon_transitive(U_436)
| sP138(U_436) ),
inference(clausify,[status(thm)],[f_97_5]) ).
cnf(f_97_8,plain,
( in(sK70(U_436),U_436)
| ~ sP138(U_436) ),
inference(clausify,[status(thm)],[f_97_5]) ).
cnf(f_97_9,plain,
( ~ subset(sK70(U_436),U_436)
| ~ sP138(U_436) ),
inference(clausify,[status(thm)],[f_97_5]) ).
fof(f_98_1,plain,
! [A] :
( empty_carrier_subset(A) = empty_set
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d2_pre_topc]) ).
fof(f_98_2,plain,
! [U_437] :
( empty_carrier_subset(U_437) = empty_set
| ~ one_sorted_str(U_437) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_437] :
( empty_carrier_subset(U_437) = empty_set
| ~ one_sorted_str(U_437) ),
inference(definitional_conversion,[status(esa)],[f_98_2]) ).
cnf(f_98_4,plain,
( empty_carrier_subset(U_437) = empty_set
| ~ one_sorted_str(U_437) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_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_99_2,plain,
! [U_443] :
( ! [U_442] :
( ( ( U_443 = U_442
| ? [U_441,U_440] :
( ( ~ in(ordered_pair(U_441,U_440),U_443)
& in(ordered_pair(U_441,U_440),U_442) )
| ( ~ in(ordered_pair(U_441,U_440),U_442)
& in(ordered_pair(U_441,U_440),U_443) ) ) )
& ( ! [U_439,U_438] :
( ( in(ordered_pair(U_439,U_438),U_443)
| ~ in(ordered_pair(U_439,U_438),U_442) )
& ( in(ordered_pair(U_439,U_438),U_442)
| ~ in(ordered_pair(U_439,U_438),U_443) ) )
| U_443 != U_442 ) )
| ~ relation(U_442) )
| ~ relation(U_443) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_443] :
( ! [U_442] :
( ( ( U_443 = U_442
| ? [U_451,U_449] :
( ~ in(ordered_pair(U_451,U_449),U_443)
& in(ordered_pair(U_451,U_449),U_442) )
| ? [U_450,U_448] :
( ~ in(ordered_pair(U_450,U_448),U_442)
& in(ordered_pair(U_450,U_448),U_443) ) )
& ( ( ! [U_447,U_445] :
( in(ordered_pair(U_447,U_445),U_443)
| ~ in(ordered_pair(U_447,U_445),U_442) )
& ! [U_446,U_444] :
( in(ordered_pair(U_446,U_444),U_442)
| ~ in(ordered_pair(U_446,U_444),U_443) ) )
| U_443 != U_442 ) )
| ~ relation(U_442) )
| ~ relation(U_443) ),
inference(miniscope,[status(thm)],[f_99_2]) ).
fof(f_99_4,plain,
! [U_443] :
( ! [U_442] :
( ( ( U_443 = U_442
| ? [U_451,U_449] :
( ~ in(ordered_pair(U_451,U_449),U_443)
& in(ordered_pair(U_451,U_449),U_442) )
| ? [U_448] :
( ~ in(ordered_pair(sK71(U_443,U_442),U_448),U_442)
& in(ordered_pair(sK71(U_443,U_442),U_448),U_443) ) )
& ( ( ! [U_447,U_445] :
( in(ordered_pair(U_447,U_445),U_443)
| ~ in(ordered_pair(U_447,U_445),U_442) )
& ! [U_446,U_444] :
( in(ordered_pair(U_446,U_444),U_442)
| ~ in(ordered_pair(U_446,U_444),U_443) ) )
| U_443 != U_442 ) )
| ~ relation(U_442) )
| ~ relation(U_443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_450,sK71(U_443,U_442))],[f_99_3]) ).
fof(f_99_5,plain,
! [U_443] :
( ! [U_442] :
( ( ( U_443 = U_442
| ? [U_451,U_449] :
( ~ in(ordered_pair(U_451,U_449),U_443)
& in(ordered_pair(U_451,U_449),U_442) )
| ( ~ in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_442)
& in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_443) ) )
& ( ( ! [U_447,U_445] :
( in(ordered_pair(U_447,U_445),U_443)
| ~ in(ordered_pair(U_447,U_445),U_442) )
& ! [U_446,U_444] :
( in(ordered_pair(U_446,U_444),U_442)
| ~ in(ordered_pair(U_446,U_444),U_443) ) )
| U_443 != U_442 ) )
| ~ relation(U_442) )
| ~ relation(U_443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_448,sK72(U_443,U_442))],[f_99_4]) ).
fof(f_99_6,plain,
! [U_443] :
( ! [U_442] :
( ( ( U_443 = U_442
| ? [U_449] :
( ~ in(ordered_pair(sK73(U_443,U_442),U_449),U_443)
& in(ordered_pair(sK73(U_443,U_442),U_449),U_442) )
| ( ~ in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_442)
& in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_443) ) )
& ( ( ! [U_447,U_445] :
( in(ordered_pair(U_447,U_445),U_443)
| ~ in(ordered_pair(U_447,U_445),U_442) )
& ! [U_446,U_444] :
( in(ordered_pair(U_446,U_444),U_442)
| ~ in(ordered_pair(U_446,U_444),U_443) ) )
| U_443 != U_442 ) )
| ~ relation(U_442) )
| ~ relation(U_443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_451,sK73(U_443,U_442))],[f_99_5]) ).
fof(f_99_7,plain,
! [U_443] :
( ! [U_442] :
( ( ( U_443 = U_442
| ( ~ in(ordered_pair(sK73(U_443,U_442),sK74(U_443,U_442)),U_443)
& in(ordered_pair(sK73(U_443,U_442),sK74(U_443,U_442)),U_442) )
| ( ~ in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_442)
& in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_443) ) )
& ( ( ! [U_447,U_445] :
( in(ordered_pair(U_447,U_445),U_443)
| ~ in(ordered_pair(U_447,U_445),U_442) )
& ! [U_446,U_444] :
( in(ordered_pair(U_446,U_444),U_442)
| ~ in(ordered_pair(U_446,U_444),U_443) ) )
| U_443 != U_442 ) )
| ~ relation(U_442) )
| ~ relation(U_443) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_449,sK74(U_443,U_442))],[f_99_6]) ).
fof(f_99_8,plain,
( ! [U_442,U_443] :
( ~ in(ordered_pair(sK73(U_443,U_442),sK74(U_443,U_442)),U_443)
| ~ sP141(U_442,U_443) )
& ! [U_442,U_443] :
( in(ordered_pair(sK73(U_443,U_442),sK74(U_443,U_442)),U_442)
| ~ sP141(U_442,U_443) )
& ! [U_442,U_443] :
( ~ in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_442)
| ~ sP140(U_442,U_443) )
& ! [U_442,U_443] :
( in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_443)
| ~ sP140(U_442,U_443) )
& ! [U_447,U_442,U_443,U_444,U_445,U_446] :
( in(ordered_pair(U_447,U_445),U_443)
| ~ in(ordered_pair(U_447,U_445),U_442)
| ~ sP139(U_447,U_442,U_443,U_444,U_445,U_446) )
& ! [U_447,U_442,U_443,U_444,U_445,U_446] :
( in(ordered_pair(U_446,U_444),U_442)
| ~ in(ordered_pair(U_446,U_444),U_443)
| ~ sP139(U_447,U_442,U_443,U_444,U_445,U_446) )
& ! [U_447,U_442,U_443,U_444,U_445,U_446] :
( U_443 = U_442
| sP141(U_442,U_443)
| sP140(U_442,U_443)
| ~ sP142(U_447,U_442,U_443,U_444,U_445,U_446) )
& ! [U_447,U_442,U_443,U_444,U_445,U_446] :
( sP139(U_447,U_442,U_443,U_444,U_445,U_446)
| U_443 != U_442
| ~ sP142(U_447,U_442,U_443,U_444,U_445,U_446) )
& ! [U_447,U_442,U_443,U_444,U_445,U_446] :
( sP142(U_447,U_442,U_443,U_444,U_445,U_446)
| ~ relation(U_442)
| ~ relation(U_443) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139,sP140,sP141,sP142])],[f_99_7]) ).
cnf(f_99_9,plain,
( sP142(U_447,U_442,U_443,U_444,U_445,U_446)
| ~ relation(U_442)
| ~ relation(U_443) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_10,plain,
( sP139(U_447,U_442,U_443,U_444,U_445,U_446)
| U_443 != U_442
| ~ sP142(U_447,U_442,U_443,U_444,U_445,U_446) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_11,plain,
( U_443 = U_442
| sP141(U_442,U_443)
| sP140(U_442,U_443)
| ~ sP142(U_447,U_442,U_443,U_444,U_445,U_446) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_12,plain,
( in(ordered_pair(U_446,U_444),U_442)
| ~ in(ordered_pair(U_446,U_444),U_443)
| ~ sP139(U_447,U_442,U_443,U_444,U_445,U_446) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_13,plain,
( in(ordered_pair(U_447,U_445),U_443)
| ~ in(ordered_pair(U_447,U_445),U_442)
| ~ sP139(U_447,U_442,U_443,U_444,U_445,U_446) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_14,plain,
( in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_443)
| ~ sP140(U_442,U_443) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_15,plain,
( ~ in(ordered_pair(sK71(U_443,U_442),sK72(U_443,U_442)),U_442)
| ~ sP140(U_442,U_443) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_16,plain,
( in(ordered_pair(sK73(U_443,U_442),sK74(U_443,U_442)),U_442)
| ~ sP141(U_442,U_443) ),
inference(clausify,[status(thm)],[f_99_8]) ).
cnf(f_99_17,plain,
( ~ in(ordered_pair(sK73(U_443,U_442),sK74(U_443,U_442)),U_443)
| ~ sP141(U_442,U_443) ),
inference(clausify,[status(thm)],[f_99_8]) ).
fof(f_100_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_100_2,plain,
! [U_453,U_452] :
( ( ( ( element(U_452,U_453)
| ~ empty(U_452) )
& ( empty(U_452)
| ~ element(U_452,U_453) ) )
| ~ empty(U_453) )
& ( ( ( element(U_452,U_453)
| ~ in(U_452,U_453) )
& ( in(U_452,U_453)
| ~ element(U_452,U_453) ) )
| empty(U_453) ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ! [U_461] :
( ( ! [U_459] :
( element(U_459,U_461)
| ~ empty(U_459) )
& ! [U_458] :
( empty(U_458)
| ~ element(U_458,U_461) ) )
| ~ empty(U_461) )
& ! [U_460] :
( ( ! [U_457] :
( element(U_457,U_460)
| ~ in(U_457,U_460) )
& ! [U_456] :
( in(U_456,U_460)
| ~ element(U_456,U_460) ) )
| empty(U_460) ) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
fof(f_100_4,plain,
( ! [U_459,U_458,U_461] :
( element(U_459,U_461)
| ~ empty(U_459)
| ~ sP144(U_459,U_458,U_461) )
& ! [U_459,U_458,U_461] :
( empty(U_458)
| ~ element(U_458,U_461)
| ~ sP144(U_459,U_458,U_461) )
& ! [U_460,U_457,U_456] :
( element(U_457,U_460)
| ~ in(U_457,U_460)
| ~ sP143(U_460,U_457,U_456) )
& ! [U_460,U_457,U_456] :
( in(U_456,U_460)
| ~ element(U_456,U_460)
| ~ sP143(U_460,U_457,U_456) )
& ! [U_459,U_458,U_461] :
( sP144(U_459,U_458,U_461)
| ~ empty(U_461) )
& ! [U_460,U_457,U_456] :
( sP143(U_460,U_457,U_456)
| empty(U_460) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143,sP144])],[f_100_3]) ).
cnf(f_100_5,plain,
( sP143(U_460,U_457,U_456)
| empty(U_460) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_6,plain,
( sP144(U_459,U_458,U_461)
| ~ empty(U_461) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_7,plain,
( in(U_456,U_460)
| ~ element(U_456,U_460)
| ~ sP143(U_460,U_457,U_456) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_8,plain,
( element(U_457,U_460)
| ~ in(U_457,U_460)
| ~ sP143(U_460,U_457,U_456) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_9,plain,
( empty(U_458)
| ~ element(U_458,U_461)
| ~ sP144(U_459,U_458,U_461) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_10,plain,
( element(U_459,U_461)
| ~ empty(U_459)
| ~ sP144(U_459,U_458,U_461) ),
inference(clausify,[status(thm)],[f_100_4]) ).
fof(f_101_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_101_2,plain,
! [U_466,U_465,U_464] :
( ( U_464 = unordered_pair(U_466,U_465)
| ? [U_463] :
( ( ~ in(U_463,U_464)
& ( U_463 = U_465
| U_463 = U_466 ) )
| ( U_463 != U_465
& U_463 != U_466
& in(U_463,U_464) ) ) )
& ( ! [U_462] :
( ( in(U_462,U_464)
| ( U_462 != U_465
& U_462 != U_466 ) )
& ( U_462 = U_465
| U_462 = U_466
| ~ in(U_462,U_464) ) )
| U_464 != unordered_pair(U_466,U_465) ) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
( ! [U_476,U_474,U_472] :
( U_472 = unordered_pair(U_476,U_474)
| ? [U_470] :
( ~ in(U_470,U_472)
& ( U_470 = U_474
| U_470 = U_476 ) )
| ? [U_469] :
( U_469 != U_474
& U_469 != U_476
& in(U_469,U_472) ) )
& ! [U_475,U_473,U_471] :
( ( ! [U_468] :
( in(U_468,U_471)
| ( U_468 != U_473
& U_468 != U_475 ) )
& ! [U_467] :
( U_467 = U_473
| U_467 = U_475
| ~ in(U_467,U_471) ) )
| U_471 != unordered_pair(U_475,U_473) ) ),
inference(miniscope,[status(thm)],[f_101_2]) ).
fof(f_101_4,plain,
( ! [U_476,U_474,U_472] :
( U_472 = unordered_pair(U_476,U_474)
| ? [U_470] :
( ~ in(U_470,U_472)
& ( U_470 = U_474
| U_470 = U_476 ) )
| ( sK75(U_476,U_474,U_472) != U_474
& sK75(U_476,U_474,U_472) != U_476
& in(sK75(U_476,U_474,U_472),U_472) ) )
& ! [U_475,U_473,U_471] :
( ( ! [U_468] :
( in(U_468,U_471)
| ( U_468 != U_473
& U_468 != U_475 ) )
& ! [U_467] :
( U_467 = U_473
| U_467 = U_475
| ~ in(U_467,U_471) ) )
| U_471 != unordered_pair(U_475,U_473) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_469,sK75(U_476,U_474,U_472))],[f_101_3]) ).
fof(f_101_5,plain,
( ! [U_476,U_474,U_472] :
( U_472 = unordered_pair(U_476,U_474)
| ( ~ in(sK76(U_476,U_474,U_472),U_472)
& ( sK76(U_476,U_474,U_472) = U_474
| sK76(U_476,U_474,U_472) = U_476 ) )
| ( sK75(U_476,U_474,U_472) != U_474
& sK75(U_476,U_474,U_472) != U_476
& in(sK75(U_476,U_474,U_472),U_472) ) )
& ! [U_475,U_473,U_471] :
( ( ! [U_468] :
( in(U_468,U_471)
| ( U_468 != U_473
& U_468 != U_475 ) )
& ! [U_467] :
( U_467 = U_473
| U_467 = U_475
| ~ in(U_467,U_471) ) )
| U_471 != unordered_pair(U_475,U_473) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_470,sK76(U_476,U_474,U_472))],[f_101_4]) ).
fof(f_101_6,plain,
( ! [U_472,U_476,U_474] :
( ~ in(sK76(U_476,U_474,U_472),U_472)
| ~ sP148(U_472,U_476,U_474) )
& ! [U_472,U_476,U_474] :
( sK76(U_476,U_474,U_472) = U_474
| sK76(U_476,U_474,U_472) = U_476
| ~ sP148(U_472,U_476,U_474) )
& ! [U_472,U_476,U_474] :
( sK75(U_476,U_474,U_472) != U_474
| ~ sP147(U_472,U_476,U_474) )
& ! [U_472,U_476,U_474] :
( sK75(U_476,U_474,U_472) != U_476
| ~ sP147(U_472,U_476,U_474) )
& ! [U_472,U_476,U_474] :
( in(sK75(U_476,U_474,U_472),U_472)
| ~ sP147(U_472,U_476,U_474) )
& ! [U_468,U_473,U_475] :
( U_468 != U_473
| ~ sP145(U_468,U_473,U_475) )
& ! [U_468,U_473,U_475] :
( U_468 != U_475
| ~ sP145(U_468,U_473,U_475) )
& ! [U_467,U_471,U_468,U_473,U_475] :
( in(U_468,U_471)
| sP145(U_468,U_473,U_475)
| ~ sP146(U_467,U_471,U_468,U_473,U_475) )
& ! [U_467,U_471,U_468,U_473,U_475] :
( U_467 = U_473
| U_467 = U_475
| ~ in(U_467,U_471)
| ~ sP146(U_467,U_471,U_468,U_473,U_475) )
& ! [U_472,U_476,U_474] :
( U_472 = unordered_pair(U_476,U_474)
| sP148(U_472,U_476,U_474)
| sP147(U_472,U_476,U_474) )
& ! [U_467,U_471,U_468,U_473,U_475] :
( sP146(U_467,U_471,U_468,U_473,U_475)
| U_471 != unordered_pair(U_475,U_473) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145,sP146,sP147,sP148])],[f_101_5]) ).
cnf(f_101_7,plain,
( sP146(U_467,U_471,U_468,U_473,U_475)
| U_471 != unordered_pair(U_475,U_473) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_8,plain,
( U_472 = unordered_pair(U_476,U_474)
| sP148(U_472,U_476,U_474)
| sP147(U_472,U_476,U_474) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_9,plain,
( U_467 = U_473
| U_467 = U_475
| ~ in(U_467,U_471)
| ~ sP146(U_467,U_471,U_468,U_473,U_475) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_10,plain,
( in(U_468,U_471)
| sP145(U_468,U_473,U_475)
| ~ sP146(U_467,U_471,U_468,U_473,U_475) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_11,plain,
( U_468 != U_475
| ~ sP145(U_468,U_473,U_475) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_12,plain,
( U_468 != U_473
| ~ sP145(U_468,U_473,U_475) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_13,plain,
( in(sK75(U_476,U_474,U_472),U_472)
| ~ sP147(U_472,U_476,U_474) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_14,plain,
( sK75(U_476,U_474,U_472) != U_476
| ~ sP147(U_472,U_476,U_474) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_15,plain,
( sK75(U_476,U_474,U_472) != U_474
| ~ sP147(U_472,U_476,U_474) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_16,plain,
( sK76(U_476,U_474,U_472) = U_474
| sK76(U_476,U_474,U_472) = U_476
| ~ sP148(U_472,U_476,U_474) ),
inference(clausify,[status(thm)],[f_101_6]) ).
cnf(f_101_17,plain,
( ~ in(sK76(U_476,U_474,U_472),U_472)
| ~ sP148(U_472,U_476,U_474) ),
inference(clausify,[status(thm)],[f_101_6]) ).
fof(f_102_1,plain,
! [A,B] :
( ( ( proper_element(B,A)
| B = union(A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(fof_nnf,[status(thm)],[d2_tex_2]) ).
fof(f_102_2,plain,
! [U_478,U_477] :
( ( ( proper_element(U_477,U_478)
| U_477 = union(U_478) )
& ( U_477 != union(U_478)
| ~ proper_element(U_477,U_478) ) )
| ~ element(U_477,U_478) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
( ! [U_477,U_478] :
( proper_element(U_477,U_478)
| U_477 = union(U_478)
| ~ sP149(U_477,U_478) )
& ! [U_477,U_478] :
( U_477 != union(U_478)
| ~ proper_element(U_477,U_478)
| ~ sP149(U_477,U_478) )
& ! [U_477,U_478] :
( sP149(U_477,U_478)
| ~ element(U_477,U_478) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_102_2]) ).
cnf(f_102_4,plain,
( sP149(U_477,U_478)
| ~ element(U_477,U_478) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( U_477 != union(U_478)
| ~ proper_element(U_477,U_478)
| ~ sP149(U_477,U_478) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_6,plain,
( proper_element(U_477,U_478)
| U_477 = union(U_478)
| ~ sP149(U_477,U_478) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [A] :
( ! [B] :
( ( ( closed_subsets(B,A)
| ? [C] :
( ~ closed_subset(C,A)
& in(C,B)
& element(C,powerset(the_carrier(A))) ) )
& ( ! [C] :
( closed_subset(C,A)
| ~ in(C,B)
| ~ element(C,powerset(the_carrier(A))) )
| ~ closed_subsets(B,A) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d2_tops_2]) ).
fof(f_103_2,plain,
! [U_482] :
( ! [U_481] :
( ( ( closed_subsets(U_481,U_482)
| ? [U_480] :
( ~ closed_subset(U_480,U_482)
& in(U_480,U_481)
& element(U_480,powerset(the_carrier(U_482))) ) )
& ( ! [U_479] :
( closed_subset(U_479,U_482)
| ~ in(U_479,U_481)
| ~ element(U_479,powerset(the_carrier(U_482))) )
| ~ closed_subsets(U_481,U_482) ) )
| ~ element(U_481,powerset(powerset(the_carrier(U_482)))) )
| ~ top_str(U_482) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_482] :
( ! [U_481] :
( ( ( closed_subsets(U_481,U_482)
| ( ~ closed_subset(sK77(U_482,U_481),U_482)
& in(sK77(U_482,U_481),U_481)
& element(sK77(U_482,U_481),powerset(the_carrier(U_482))) ) )
& ( ! [U_479] :
( closed_subset(U_479,U_482)
| ~ in(U_479,U_481)
| ~ element(U_479,powerset(the_carrier(U_482))) )
| ~ closed_subsets(U_481,U_482) ) )
| ~ element(U_481,powerset(powerset(the_carrier(U_482)))) )
| ~ top_str(U_482) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_480,sK77(U_482,U_481))],[f_103_2]) ).
fof(f_103_4,plain,
( ! [U_482,U_481] :
( ~ closed_subset(sK77(U_482,U_481),U_482)
| ~ sP150(U_482,U_481) )
& ! [U_482,U_481] :
( in(sK77(U_482,U_481),U_481)
| ~ sP150(U_482,U_481) )
& ! [U_482,U_481] :
( element(sK77(U_482,U_481),powerset(the_carrier(U_482)))
| ~ sP150(U_482,U_481) )
& ! [U_479,U_482,U_481] :
( closed_subsets(U_481,U_482)
| sP150(U_482,U_481)
| ~ sP151(U_479,U_482,U_481) )
& ! [U_479,U_482,U_481] :
( closed_subset(U_479,U_482)
| ~ in(U_479,U_481)
| ~ element(U_479,powerset(the_carrier(U_482)))
| ~ closed_subsets(U_481,U_482)
| ~ sP151(U_479,U_482,U_481) )
& ! [U_479,U_482,U_481] :
( sP151(U_479,U_482,U_481)
| ~ element(U_481,powerset(powerset(the_carrier(U_482))))
| ~ top_str(U_482) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150,sP151])],[f_103_3]) ).
cnf(f_103_5,plain,
( sP151(U_479,U_482,U_481)
| ~ element(U_481,powerset(powerset(the_carrier(U_482))))
| ~ top_str(U_482) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_6,plain,
( closed_subset(U_479,U_482)
| ~ in(U_479,U_481)
| ~ element(U_479,powerset(the_carrier(U_482)))
| ~ closed_subsets(U_481,U_482)
| ~ sP151(U_479,U_482,U_481) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_7,plain,
( closed_subsets(U_481,U_482)
| sP150(U_482,U_481)
| ~ sP151(U_479,U_482,U_481) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_8,plain,
( element(sK77(U_482,U_481),powerset(the_carrier(U_482)))
| ~ sP150(U_482,U_481) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_9,plain,
( in(sK77(U_482,U_481),U_481)
| ~ sP150(U_482,U_481) ),
inference(clausify,[status(thm)],[f_103_4]) ).
cnf(f_103_10,plain,
( ~ closed_subset(sK77(U_482,U_481),U_482)
| ~ sP150(U_482,U_481) ),
inference(clausify,[status(thm)],[f_103_4]) ).
fof(f_104_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_104_2,plain,
! [U_487] :
( ( ( well_founded_relation(U_487)
| ? [U_486] :
( ! [U_485] :
( ~ disjoint(fiber(U_487,U_485),U_486)
| ~ in(U_485,U_486) )
& U_486 != empty_set
& subset(U_486,relation_field(U_487)) ) )
& ( ! [U_484] :
( ? [U_483] :
( disjoint(fiber(U_487,U_483),U_484)
& in(U_483,U_484) )
| U_484 = empty_set
| ~ subset(U_484,relation_field(U_487)) )
| ~ well_founded_relation(U_487) ) )
| ~ relation(U_487) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_487] :
( ( ( well_founded_relation(U_487)
| ? [U_486] :
( ! [U_485] :
( ~ disjoint(fiber(U_487,U_485),U_486)
| ~ in(U_485,U_486) )
& U_486 != empty_set
& subset(U_486,relation_field(U_487)) ) )
& ( ! [U_484] :
( ( disjoint(fiber(U_487,sK78(U_487,U_484)),U_484)
& in(sK78(U_487,U_484),U_484) )
| U_484 = empty_set
| ~ subset(U_484,relation_field(U_487)) )
| ~ well_founded_relation(U_487) ) )
| ~ relation(U_487) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_483,sK78(U_487,U_484))],[f_104_2]) ).
fof(f_104_4,plain,
! [U_487] :
( ( ( well_founded_relation(U_487)
| ( ! [U_485] :
( ~ disjoint(fiber(U_487,U_485),sK79(U_487))
| ~ in(U_485,sK79(U_487)) )
& sK79(U_487) != empty_set
& subset(sK79(U_487),relation_field(U_487)) ) )
& ( ! [U_484] :
( ( disjoint(fiber(U_487,sK78(U_487,U_484)),U_484)
& in(sK78(U_487,U_484),U_484) )
| U_484 = empty_set
| ~ subset(U_484,relation_field(U_487)) )
| ~ well_founded_relation(U_487) ) )
| ~ relation(U_487) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_486,sK79(U_487))],[f_104_3]) ).
fof(f_104_5,plain,
( ! [U_487,U_485] :
( ~ disjoint(fiber(U_487,U_485),sK79(U_487))
| ~ in(U_485,sK79(U_487))
| ~ sP153(U_487,U_485) )
& ! [U_487,U_485] :
( sK79(U_487) != empty_set
| ~ sP153(U_487,U_485) )
& ! [U_487,U_485] :
( subset(sK79(U_487),relation_field(U_487))
| ~ sP153(U_487,U_485) )
& ! [U_487,U_484] :
( disjoint(fiber(U_487,sK78(U_487,U_484)),U_484)
| ~ sP152(U_487,U_484) )
& ! [U_487,U_484] :
( in(sK78(U_487,U_484),U_484)
| ~ sP152(U_487,U_484) )
& ! [U_487,U_485,U_484] :
( well_founded_relation(U_487)
| sP153(U_487,U_485)
| ~ sP154(U_487,U_485,U_484) )
& ! [U_487,U_485,U_484] :
( sP152(U_487,U_484)
| U_484 = empty_set
| ~ subset(U_484,relation_field(U_487))
| ~ well_founded_relation(U_487)
| ~ sP154(U_487,U_485,U_484) )
& ! [U_487,U_485,U_484] :
( sP154(U_487,U_485,U_484)
| ~ relation(U_487) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152,sP153,sP154])],[f_104_4]) ).
cnf(f_104_6,plain,
( sP154(U_487,U_485,U_484)
| ~ relation(U_487) ),
inference(clausify,[status(thm)],[f_104_5]) ).
cnf(f_104_7,plain,
( sP152(U_487,U_484)
| U_484 = empty_set
| ~ subset(U_484,relation_field(U_487))
| ~ well_founded_relation(U_487)
| ~ sP154(U_487,U_485,U_484) ),
inference(clausify,[status(thm)],[f_104_5]) ).
cnf(f_104_8,plain,
( well_founded_relation(U_487)
| sP153(U_487,U_485)
| ~ sP154(U_487,U_485,U_484) ),
inference(clausify,[status(thm)],[f_104_5]) ).
cnf(f_104_9,plain,
( in(sK78(U_487,U_484),U_484)
| ~ sP152(U_487,U_484) ),
inference(clausify,[status(thm)],[f_104_5]) ).
cnf(f_104_10,plain,
( disjoint(fiber(U_487,sK78(U_487,U_484)),U_484)
| ~ sP152(U_487,U_484) ),
inference(clausify,[status(thm)],[f_104_5]) ).
cnf(f_104_11,plain,
( subset(sK79(U_487),relation_field(U_487))
| ~ sP153(U_487,U_485) ),
inference(clausify,[status(thm)],[f_104_5]) ).
cnf(f_104_12,plain,
( sK79(U_487) != empty_set
| ~ sP153(U_487,U_485) ),
inference(clausify,[status(thm)],[f_104_5]) ).
cnf(f_104_13,plain,
( ~ disjoint(fiber(U_487,U_485),sK79(U_487))
| ~ in(U_485,sK79(U_487))
| ~ sP153(U_487,U_485) ),
inference(clausify,[status(thm)],[f_104_5]) ).
fof(f_105_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_105_2,plain,
! [U_492,U_491,U_490] :
( ( U_490 = set_union2(U_492,U_491)
| ? [U_489] :
( ( ~ in(U_489,U_490)
& ( in(U_489,U_491)
| in(U_489,U_492) ) )
| ( ~ in(U_489,U_491)
& ~ in(U_489,U_492)
& in(U_489,U_490) ) ) )
& ( ! [U_488] :
( ( in(U_488,U_490)
| ( ~ in(U_488,U_491)
& ~ in(U_488,U_492) ) )
& ( in(U_488,U_491)
| in(U_488,U_492)
| ~ in(U_488,U_490) ) )
| U_490 != set_union2(U_492,U_491) ) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( ! [U_502,U_500,U_498] :
( U_498 = set_union2(U_502,U_500)
| ? [U_496] :
( ~ in(U_496,U_498)
& ( in(U_496,U_500)
| in(U_496,U_502) ) )
| ? [U_495] :
( ~ in(U_495,U_500)
& ~ in(U_495,U_502)
& in(U_495,U_498) ) )
& ! [U_501,U_499,U_497] :
( ( ! [U_494] :
( in(U_494,U_497)
| ( ~ in(U_494,U_499)
& ~ in(U_494,U_501) ) )
& ! [U_493] :
( in(U_493,U_499)
| in(U_493,U_501)
| ~ in(U_493,U_497) ) )
| U_497 != set_union2(U_501,U_499) ) ),
inference(miniscope,[status(thm)],[f_105_2]) ).
fof(f_105_4,plain,
( ! [U_502,U_500,U_498] :
( U_498 = set_union2(U_502,U_500)
| ? [U_496] :
( ~ in(U_496,U_498)
& ( in(U_496,U_500)
| in(U_496,U_502) ) )
| ( ~ in(sK80(U_502,U_500,U_498),U_500)
& ~ in(sK80(U_502,U_500,U_498),U_502)
& in(sK80(U_502,U_500,U_498),U_498) ) )
& ! [U_501,U_499,U_497] :
( ( ! [U_494] :
( in(U_494,U_497)
| ( ~ in(U_494,U_499)
& ~ in(U_494,U_501) ) )
& ! [U_493] :
( in(U_493,U_499)
| in(U_493,U_501)
| ~ in(U_493,U_497) ) )
| U_497 != set_union2(U_501,U_499) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_495,sK80(U_502,U_500,U_498))],[f_105_3]) ).
fof(f_105_5,plain,
( ! [U_502,U_500,U_498] :
( U_498 = set_union2(U_502,U_500)
| ( ~ in(sK81(U_502,U_500,U_498),U_498)
& ( in(sK81(U_502,U_500,U_498),U_500)
| in(sK81(U_502,U_500,U_498),U_502) ) )
| ( ~ in(sK80(U_502,U_500,U_498),U_500)
& ~ in(sK80(U_502,U_500,U_498),U_502)
& in(sK80(U_502,U_500,U_498),U_498) ) )
& ! [U_501,U_499,U_497] :
( ( ! [U_494] :
( in(U_494,U_497)
| ( ~ in(U_494,U_499)
& ~ in(U_494,U_501) ) )
& ! [U_493] :
( in(U_493,U_499)
| in(U_493,U_501)
| ~ in(U_493,U_497) ) )
| U_497 != set_union2(U_501,U_499) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_496,sK81(U_502,U_500,U_498))],[f_105_4]) ).
fof(f_105_6,plain,
( ! [U_500,U_502,U_498] :
( ~ in(sK81(U_502,U_500,U_498),U_498)
| ~ sP158(U_500,U_502,U_498) )
& ! [U_500,U_502,U_498] :
( in(sK81(U_502,U_500,U_498),U_500)
| in(sK81(U_502,U_500,U_498),U_502)
| ~ sP158(U_500,U_502,U_498) )
& ! [U_500,U_502,U_498] :
( ~ in(sK80(U_502,U_500,U_498),U_500)
| ~ sP157(U_500,U_502,U_498) )
& ! [U_500,U_502,U_498] :
( ~ in(sK80(U_502,U_500,U_498),U_502)
| ~ sP157(U_500,U_502,U_498) )
& ! [U_500,U_502,U_498] :
( in(sK80(U_502,U_500,U_498),U_498)
| ~ sP157(U_500,U_502,U_498) )
& ! [U_499,U_494,U_501] :
( ~ in(U_494,U_499)
| ~ sP155(U_499,U_494,U_501) )
& ! [U_499,U_494,U_501] :
( ~ in(U_494,U_501)
| ~ sP155(U_499,U_494,U_501) )
& ! [U_497,U_499,U_494,U_493,U_501] :
( in(U_494,U_497)
| sP155(U_499,U_494,U_501)
| ~ sP156(U_497,U_499,U_494,U_493,U_501) )
& ! [U_497,U_499,U_494,U_493,U_501] :
( in(U_493,U_499)
| in(U_493,U_501)
| ~ in(U_493,U_497)
| ~ sP156(U_497,U_499,U_494,U_493,U_501) )
& ! [U_500,U_502,U_498] :
( U_498 = set_union2(U_502,U_500)
| sP158(U_500,U_502,U_498)
| sP157(U_500,U_502,U_498) )
& ! [U_497,U_499,U_494,U_493,U_501] :
( sP156(U_497,U_499,U_494,U_493,U_501)
| U_497 != set_union2(U_501,U_499) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155,sP156,sP157,sP158])],[f_105_5]) ).
cnf(f_105_7,plain,
( sP156(U_497,U_499,U_494,U_493,U_501)
| U_497 != set_union2(U_501,U_499) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_8,plain,
( U_498 = set_union2(U_502,U_500)
| sP158(U_500,U_502,U_498)
| sP157(U_500,U_502,U_498) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_9,plain,
( in(U_493,U_499)
| in(U_493,U_501)
| ~ in(U_493,U_497)
| ~ sP156(U_497,U_499,U_494,U_493,U_501) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_10,plain,
( in(U_494,U_497)
| sP155(U_499,U_494,U_501)
| ~ sP156(U_497,U_499,U_494,U_493,U_501) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_11,plain,
( ~ in(U_494,U_501)
| ~ sP155(U_499,U_494,U_501) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_12,plain,
( ~ in(U_494,U_499)
| ~ sP155(U_499,U_494,U_501) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_13,plain,
( in(sK80(U_502,U_500,U_498),U_498)
| ~ sP157(U_500,U_502,U_498) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_14,plain,
( ~ in(sK80(U_502,U_500,U_498),U_502)
| ~ sP157(U_500,U_502,U_498) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_15,plain,
( ~ in(sK80(U_502,U_500,U_498),U_500)
| ~ sP157(U_500,U_502,U_498) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_16,plain,
( in(sK81(U_502,U_500,U_498),U_500)
| in(sK81(U_502,U_500,U_498),U_502)
| ~ sP158(U_500,U_502,U_498) ),
inference(clausify,[status(thm)],[f_105_6]) ).
cnf(f_105_17,plain,
( ~ in(sK81(U_502,U_500,U_498),U_498)
| ~ sP158(U_500,U_502,U_498) ),
inference(clausify,[status(thm)],[f_105_6]) ).
fof(f_106_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_106_2,plain,
! [U_515,U_514,U_513] :
( ( U_513 = cartesian_product2(U_515,U_514)
| ? [U_512] :
( ( ~ in(U_512,U_513)
& ? [U_511,U_510] :
( U_512 = ordered_pair(U_511,U_510)
& in(U_510,U_514)
& in(U_511,U_515) ) )
| ( ! [U_509,U_508] :
( U_512 != ordered_pair(U_509,U_508)
| ~ in(U_508,U_514)
| ~ in(U_509,U_515) )
& in(U_512,U_513) ) ) )
& ( ! [U_507] :
( ( in(U_507,U_513)
| ! [U_506,U_505] :
( U_507 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_514)
| ~ in(U_506,U_515) ) )
& ( ? [U_504,U_503] :
( U_507 = ordered_pair(U_504,U_503)
& in(U_503,U_514)
& in(U_504,U_515) )
| ~ in(U_507,U_513) ) )
| U_513 != cartesian_product2(U_515,U_514) ) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_525,U_523,U_521] :
( U_521 = cartesian_product2(U_525,U_523)
| ? [U_519] :
( ~ in(U_519,U_521)
& ? [U_511] :
( ? [U_510] :
( U_519 = ordered_pair(U_511,U_510)
& in(U_510,U_523) )
& in(U_511,U_525) ) )
| ? [U_518] :
( ! [U_509] :
( ! [U_508] :
( U_518 != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523) )
| ~ in(U_509,U_525) )
& in(U_518,U_521) ) )
& ! [U_524,U_522,U_520] :
( ( ! [U_517] :
( in(U_517,U_520)
| ! [U_506] :
( ! [U_505] :
( U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522) )
| ~ in(U_506,U_524) ) )
& ! [U_516] :
( ? [U_504] :
( ? [U_503] :
( U_516 = ordered_pair(U_504,U_503)
& in(U_503,U_522) )
& in(U_504,U_524) )
| ~ in(U_516,U_520) ) )
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(miniscope,[status(thm)],[f_106_2]) ).
fof(f_106_4,plain,
( ! [U_525,U_523,U_521] :
( U_521 = cartesian_product2(U_525,U_523)
| ? [U_519] :
( ~ in(U_519,U_521)
& ? [U_511] :
( ? [U_510] :
( U_519 = ordered_pair(U_511,U_510)
& in(U_510,U_523) )
& in(U_511,U_525) ) )
| ? [U_518] :
( ! [U_509] :
( ! [U_508] :
( U_518 != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523) )
| ~ in(U_509,U_525) )
& in(U_518,U_521) ) )
& ! [U_524,U_522,U_520] :
( ( ! [U_517] :
( in(U_517,U_520)
| ! [U_506] :
( ! [U_505] :
( U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522) )
| ~ in(U_506,U_524) ) )
& ! [U_516] :
( ( ? [U_503] :
( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),U_503)
& in(U_503,U_522) )
& in(sK82(U_524,U_522,U_520,U_516),U_524) )
| ~ in(U_516,U_520) ) )
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_504,sK82(U_524,U_522,U_520,U_516))],[f_106_3]) ).
fof(f_106_5,plain,
( ! [U_525,U_523,U_521] :
( U_521 = cartesian_product2(U_525,U_523)
| ? [U_519] :
( ~ in(U_519,U_521)
& ? [U_511] :
( ? [U_510] :
( U_519 = ordered_pair(U_511,U_510)
& in(U_510,U_523) )
& in(U_511,U_525) ) )
| ? [U_518] :
( ! [U_509] :
( ! [U_508] :
( U_518 != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523) )
| ~ in(U_509,U_525) )
& in(U_518,U_521) ) )
& ! [U_524,U_522,U_520] :
( ( ! [U_517] :
( in(U_517,U_520)
| ! [U_506] :
( ! [U_505] :
( U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522) )
| ~ in(U_506,U_524) ) )
& ! [U_516] :
( ( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),sK83(U_524,U_522,U_520,U_516))
& in(sK83(U_524,U_522,U_520,U_516),U_522)
& in(sK82(U_524,U_522,U_520,U_516),U_524) )
| ~ in(U_516,U_520) ) )
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_503,sK83(U_524,U_522,U_520,U_516))],[f_106_4]) ).
fof(f_106_6,plain,
( ! [U_525,U_523,U_521] :
( U_521 = cartesian_product2(U_525,U_523)
| ? [U_519] :
( ~ in(U_519,U_521)
& ? [U_511] :
( ? [U_510] :
( U_519 = ordered_pair(U_511,U_510)
& in(U_510,U_523) )
& in(U_511,U_525) ) )
| ( ! [U_509] :
( ! [U_508] :
( sK84(U_525,U_523,U_521) != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523) )
| ~ in(U_509,U_525) )
& in(sK84(U_525,U_523,U_521),U_521) ) )
& ! [U_524,U_522,U_520] :
( ( ! [U_517] :
( in(U_517,U_520)
| ! [U_506] :
( ! [U_505] :
( U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522) )
| ~ in(U_506,U_524) ) )
& ! [U_516] :
( ( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),sK83(U_524,U_522,U_520,U_516))
& in(sK83(U_524,U_522,U_520,U_516),U_522)
& in(sK82(U_524,U_522,U_520,U_516),U_524) )
| ~ in(U_516,U_520) ) )
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_518,sK84(U_525,U_523,U_521))],[f_106_5]) ).
fof(f_106_7,plain,
( ! [U_525,U_523,U_521] :
( U_521 = cartesian_product2(U_525,U_523)
| ( ~ in(sK85(U_525,U_523,U_521),U_521)
& ? [U_511] :
( ? [U_510] :
( sK85(U_525,U_523,U_521) = ordered_pair(U_511,U_510)
& in(U_510,U_523) )
& in(U_511,U_525) ) )
| ( ! [U_509] :
( ! [U_508] :
( sK84(U_525,U_523,U_521) != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523) )
| ~ in(U_509,U_525) )
& in(sK84(U_525,U_523,U_521),U_521) ) )
& ! [U_524,U_522,U_520] :
( ( ! [U_517] :
( in(U_517,U_520)
| ! [U_506] :
( ! [U_505] :
( U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522) )
| ~ in(U_506,U_524) ) )
& ! [U_516] :
( ( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),sK83(U_524,U_522,U_520,U_516))
& in(sK83(U_524,U_522,U_520,U_516),U_522)
& in(sK82(U_524,U_522,U_520,U_516),U_524) )
| ~ in(U_516,U_520) ) )
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_519,sK85(U_525,U_523,U_521))],[f_106_6]) ).
fof(f_106_8,plain,
( ! [U_525,U_523,U_521] :
( U_521 = cartesian_product2(U_525,U_523)
| ( ~ in(sK85(U_525,U_523,U_521),U_521)
& ? [U_510] :
( sK85(U_525,U_523,U_521) = ordered_pair(sK86(U_525,U_523,U_521),U_510)
& in(U_510,U_523) )
& in(sK86(U_525,U_523,U_521),U_525) )
| ( ! [U_509] :
( ! [U_508] :
( sK84(U_525,U_523,U_521) != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523) )
| ~ in(U_509,U_525) )
& in(sK84(U_525,U_523,U_521),U_521) ) )
& ! [U_524,U_522,U_520] :
( ( ! [U_517] :
( in(U_517,U_520)
| ! [U_506] :
( ! [U_505] :
( U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522) )
| ~ in(U_506,U_524) ) )
& ! [U_516] :
( ( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),sK83(U_524,U_522,U_520,U_516))
& in(sK83(U_524,U_522,U_520,U_516),U_522)
& in(sK82(U_524,U_522,U_520,U_516),U_524) )
| ~ in(U_516,U_520) ) )
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_511,sK86(U_525,U_523,U_521))],[f_106_7]) ).
fof(f_106_9,plain,
( ! [U_525,U_523,U_521] :
( U_521 = cartesian_product2(U_525,U_523)
| ( ~ in(sK85(U_525,U_523,U_521),U_521)
& sK85(U_525,U_523,U_521) = ordered_pair(sK86(U_525,U_523,U_521),sK87(U_525,U_523,U_521))
& in(sK87(U_525,U_523,U_521),U_523)
& in(sK86(U_525,U_523,U_521),U_525) )
| ( ! [U_509] :
( ! [U_508] :
( sK84(U_525,U_523,U_521) != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523) )
| ~ in(U_509,U_525) )
& in(sK84(U_525,U_523,U_521),U_521) ) )
& ! [U_524,U_522,U_520] :
( ( ! [U_517] :
( in(U_517,U_520)
| ! [U_506] :
( ! [U_505] :
( U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522) )
| ~ in(U_506,U_524) ) )
& ! [U_516] :
( ( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),sK83(U_524,U_522,U_520,U_516))
& in(sK83(U_524,U_522,U_520,U_516),U_522)
& in(sK82(U_524,U_522,U_520,U_516),U_524) )
| ~ in(U_516,U_520) ) )
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_510,sK87(U_525,U_523,U_521))],[f_106_8]) ).
fof(f_106_10,plain,
( ! [U_521,U_523,U_525] :
( ~ in(sK85(U_525,U_523,U_521),U_521)
| ~ sP162(U_521,U_523,U_525) )
& ! [U_521,U_523,U_525] :
( sK85(U_525,U_523,U_521) = ordered_pair(sK86(U_525,U_523,U_521),sK87(U_525,U_523,U_521))
| ~ sP162(U_521,U_523,U_525) )
& ! [U_521,U_523,U_525] :
( in(sK87(U_525,U_523,U_521),U_523)
| ~ sP162(U_521,U_523,U_525) )
& ! [U_521,U_523,U_525] :
( in(sK86(U_525,U_523,U_521),U_525)
| ~ sP162(U_521,U_523,U_525) )
& ! [U_509,U_508,U_521,U_523,U_525] :
( sK84(U_525,U_523,U_521) != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523)
| ~ in(U_509,U_525)
| ~ sP161(U_509,U_508,U_521,U_523,U_525) )
& ! [U_509,U_508,U_521,U_523,U_525] :
( in(sK84(U_525,U_523,U_521),U_521)
| ~ sP161(U_509,U_508,U_521,U_523,U_525) )
& ! [U_520,U_522,U_516,U_524] :
( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),sK83(U_524,U_522,U_520,U_516))
| ~ sP159(U_520,U_522,U_516,U_524) )
& ! [U_520,U_522,U_516,U_524] :
( in(sK83(U_524,U_522,U_520,U_516),U_522)
| ~ sP159(U_520,U_522,U_516,U_524) )
& ! [U_520,U_522,U_516,U_524] :
( in(sK82(U_524,U_522,U_520,U_516),U_524)
| ~ sP159(U_520,U_522,U_516,U_524) )
& ! [U_505,U_520,U_506,U_522,U_517,U_516,U_524] :
( in(U_517,U_520)
| U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522)
| ~ in(U_506,U_524)
| ~ sP160(U_505,U_520,U_506,U_522,U_517,U_516,U_524) )
& ! [U_505,U_520,U_506,U_522,U_517,U_516,U_524] :
( sP159(U_520,U_522,U_516,U_524)
| ~ in(U_516,U_520)
| ~ sP160(U_505,U_520,U_506,U_522,U_517,U_516,U_524) )
& ! [U_509,U_508,U_521,U_523,U_525] :
( U_521 = cartesian_product2(U_525,U_523)
| sP162(U_521,U_523,U_525)
| sP161(U_509,U_508,U_521,U_523,U_525) )
& ! [U_505,U_520,U_506,U_522,U_517,U_516,U_524] :
( sP160(U_505,U_520,U_506,U_522,U_517,U_516,U_524)
| U_520 != cartesian_product2(U_524,U_522) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159,sP160,sP161,sP162])],[f_106_9]) ).
cnf(f_106_11,plain,
( sP160(U_505,U_520,U_506,U_522,U_517,U_516,U_524)
| U_520 != cartesian_product2(U_524,U_522) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_12,plain,
( U_521 = cartesian_product2(U_525,U_523)
| sP162(U_521,U_523,U_525)
| sP161(U_509,U_508,U_521,U_523,U_525) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_13,plain,
( sP159(U_520,U_522,U_516,U_524)
| ~ in(U_516,U_520)
| ~ sP160(U_505,U_520,U_506,U_522,U_517,U_516,U_524) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_14,plain,
( in(U_517,U_520)
| U_517 != ordered_pair(U_506,U_505)
| ~ in(U_505,U_522)
| ~ in(U_506,U_524)
| ~ sP160(U_505,U_520,U_506,U_522,U_517,U_516,U_524) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_15,plain,
( in(sK82(U_524,U_522,U_520,U_516),U_524)
| ~ sP159(U_520,U_522,U_516,U_524) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_16,plain,
( in(sK83(U_524,U_522,U_520,U_516),U_522)
| ~ sP159(U_520,U_522,U_516,U_524) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_17,plain,
( U_516 = ordered_pair(sK82(U_524,U_522,U_520,U_516),sK83(U_524,U_522,U_520,U_516))
| ~ sP159(U_520,U_522,U_516,U_524) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_18,plain,
( in(sK84(U_525,U_523,U_521),U_521)
| ~ sP161(U_509,U_508,U_521,U_523,U_525) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_19,plain,
( sK84(U_525,U_523,U_521) != ordered_pair(U_509,U_508)
| ~ in(U_508,U_523)
| ~ in(U_509,U_525)
| ~ sP161(U_509,U_508,U_521,U_523,U_525) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_20,plain,
( in(sK86(U_525,U_523,U_521),U_525)
| ~ sP162(U_521,U_523,U_525) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_21,plain,
( in(sK87(U_525,U_523,U_521),U_523)
| ~ sP162(U_521,U_523,U_525) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_22,plain,
( sK85(U_525,U_523,U_521) = ordered_pair(sK86(U_525,U_523,U_521),sK87(U_525,U_523,U_521))
| ~ sP162(U_521,U_523,U_525) ),
inference(clausify,[status(thm)],[f_106_10]) ).
cnf(f_106_23,plain,
( ~ in(sK85(U_525,U_523,U_521),U_521)
| ~ sP162(U_521,U_523,U_525) ),
inference(clausify,[status(thm)],[f_106_10]) ).
fof(f_107_1,plain,
! [A] :
( ( ( compact_top_space(A)
| ? [B] :
( ! [C] :
( ~ finite(C)
| ~ is_a_cover_of_carrier(A,C)
| ~ subset(C,B)
| ~ element(C,powerset(powerset(the_carrier(A)))) )
& open_subsets(B,A)
& is_a_cover_of_carrier(A,B)
& element(B,powerset(powerset(the_carrier(A)))) ) )
& ( ! [B] :
( ? [C] :
( finite(C)
& is_a_cover_of_carrier(A,C)
& subset(C,B)
& element(C,powerset(powerset(the_carrier(A)))) )
| ~ open_subsets(B,A)
| ~ is_a_cover_of_carrier(A,B)
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ compact_top_space(A) ) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d3_compts_1]) ).
fof(f_107_2,plain,
! [U_530] :
( ( ( compact_top_space(U_530)
| ? [U_529] :
( ! [U_528] :
( ~ finite(U_528)
| ~ is_a_cover_of_carrier(U_530,U_528)
| ~ subset(U_528,U_529)
| ~ element(U_528,powerset(powerset(the_carrier(U_530)))) )
& open_subsets(U_529,U_530)
& is_a_cover_of_carrier(U_530,U_529)
& element(U_529,powerset(powerset(the_carrier(U_530)))) ) )
& ( ! [U_527] :
( ? [U_526] :
( finite(U_526)
& is_a_cover_of_carrier(U_530,U_526)
& subset(U_526,U_527)
& element(U_526,powerset(powerset(the_carrier(U_530)))) )
| ~ open_subsets(U_527,U_530)
| ~ is_a_cover_of_carrier(U_530,U_527)
| ~ element(U_527,powerset(powerset(the_carrier(U_530)))) )
| ~ compact_top_space(U_530) ) )
| ~ top_str(U_530) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_530] :
( ( ( compact_top_space(U_530)
| ? [U_529] :
( ! [U_528] :
( ~ finite(U_528)
| ~ is_a_cover_of_carrier(U_530,U_528)
| ~ subset(U_528,U_529)
| ~ element(U_528,powerset(powerset(the_carrier(U_530)))) )
& open_subsets(U_529,U_530)
& is_a_cover_of_carrier(U_530,U_529)
& element(U_529,powerset(powerset(the_carrier(U_530)))) ) )
& ( ! [U_527] :
( ( finite(sK88(U_530,U_527))
& is_a_cover_of_carrier(U_530,sK88(U_530,U_527))
& subset(sK88(U_530,U_527),U_527)
& element(sK88(U_530,U_527),powerset(powerset(the_carrier(U_530)))) )
| ~ open_subsets(U_527,U_530)
| ~ is_a_cover_of_carrier(U_530,U_527)
| ~ element(U_527,powerset(powerset(the_carrier(U_530)))) )
| ~ compact_top_space(U_530) ) )
| ~ top_str(U_530) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_526,sK88(U_530,U_527))],[f_107_2]) ).
fof(f_107_4,plain,
! [U_530] :
( ( ( compact_top_space(U_530)
| ( ! [U_528] :
( ~ finite(U_528)
| ~ is_a_cover_of_carrier(U_530,U_528)
| ~ subset(U_528,sK89(U_530))
| ~ element(U_528,powerset(powerset(the_carrier(U_530)))) )
& open_subsets(sK89(U_530),U_530)
& is_a_cover_of_carrier(U_530,sK89(U_530))
& element(sK89(U_530),powerset(powerset(the_carrier(U_530)))) ) )
& ( ! [U_527] :
( ( finite(sK88(U_530,U_527))
& is_a_cover_of_carrier(U_530,sK88(U_530,U_527))
& subset(sK88(U_530,U_527),U_527)
& element(sK88(U_530,U_527),powerset(powerset(the_carrier(U_530)))) )
| ~ open_subsets(U_527,U_530)
| ~ is_a_cover_of_carrier(U_530,U_527)
| ~ element(U_527,powerset(powerset(the_carrier(U_530)))) )
| ~ compact_top_space(U_530) ) )
| ~ top_str(U_530) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_529,sK89(U_530))],[f_107_3]) ).
fof(f_107_5,plain,
( ! [U_530,U_528] :
( ~ finite(U_528)
| ~ is_a_cover_of_carrier(U_530,U_528)
| ~ subset(U_528,sK89(U_530))
| ~ element(U_528,powerset(powerset(the_carrier(U_530))))
| ~ sP164(U_530,U_528) )
& ! [U_530,U_528] :
( open_subsets(sK89(U_530),U_530)
| ~ sP164(U_530,U_528) )
& ! [U_530,U_528] :
( is_a_cover_of_carrier(U_530,sK89(U_530))
| ~ sP164(U_530,U_528) )
& ! [U_530,U_528] :
( element(sK89(U_530),powerset(powerset(the_carrier(U_530))))
| ~ sP164(U_530,U_528) )
& ! [U_530,U_527] :
( finite(sK88(U_530,U_527))
| ~ sP163(U_530,U_527) )
& ! [U_530,U_527] :
( is_a_cover_of_carrier(U_530,sK88(U_530,U_527))
| ~ sP163(U_530,U_527) )
& ! [U_530,U_527] :
( subset(sK88(U_530,U_527),U_527)
| ~ sP163(U_530,U_527) )
& ! [U_530,U_527] :
( element(sK88(U_530,U_527),powerset(powerset(the_carrier(U_530))))
| ~ sP163(U_530,U_527) )
& ! [U_530,U_527,U_528] :
( compact_top_space(U_530)
| sP164(U_530,U_528)
| ~ sP165(U_530,U_527,U_528) )
& ! [U_530,U_527,U_528] :
( sP163(U_530,U_527)
| ~ open_subsets(U_527,U_530)
| ~ is_a_cover_of_carrier(U_530,U_527)
| ~ element(U_527,powerset(powerset(the_carrier(U_530))))
| ~ compact_top_space(U_530)
| ~ sP165(U_530,U_527,U_528) )
& ! [U_530,U_527,U_528] :
( sP165(U_530,U_527,U_528)
| ~ top_str(U_530) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163,sP164,sP165])],[f_107_4]) ).
cnf(f_107_6,plain,
( sP165(U_530,U_527,U_528)
| ~ top_str(U_530) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_7,plain,
( sP163(U_530,U_527)
| ~ open_subsets(U_527,U_530)
| ~ is_a_cover_of_carrier(U_530,U_527)
| ~ element(U_527,powerset(powerset(the_carrier(U_530))))
| ~ compact_top_space(U_530)
| ~ sP165(U_530,U_527,U_528) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_8,plain,
( compact_top_space(U_530)
| sP164(U_530,U_528)
| ~ sP165(U_530,U_527,U_528) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_9,plain,
( element(sK88(U_530,U_527),powerset(powerset(the_carrier(U_530))))
| ~ sP163(U_530,U_527) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_10,plain,
( subset(sK88(U_530,U_527),U_527)
| ~ sP163(U_530,U_527) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_11,plain,
( is_a_cover_of_carrier(U_530,sK88(U_530,U_527))
| ~ sP163(U_530,U_527) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_12,plain,
( finite(sK88(U_530,U_527))
| ~ sP163(U_530,U_527) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_13,plain,
( element(sK89(U_530),powerset(powerset(the_carrier(U_530))))
| ~ sP164(U_530,U_528) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_14,plain,
( is_a_cover_of_carrier(U_530,sK89(U_530))
| ~ sP164(U_530,U_528) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_15,plain,
( open_subsets(sK89(U_530),U_530)
| ~ sP164(U_530,U_528) ),
inference(clausify,[status(thm)],[f_107_5]) ).
cnf(f_107_16,plain,
( ~ finite(U_528)
| ~ is_a_cover_of_carrier(U_530,U_528)
| ~ subset(U_528,sK89(U_530))
| ~ element(U_528,powerset(powerset(the_carrier(U_530))))
| ~ sP164(U_530,U_528) ),
inference(clausify,[status(thm)],[f_107_5]) ).
fof(f_108_1,plain,
! [A] :
( ! [B] :
( cast_to_el_of_LattPOSet(A,B) = B
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d3_lattice3]) ).
fof(f_108_2,plain,
! [U_532] :
( ! [U_531] :
( cast_to_el_of_LattPOSet(U_532,U_531) = U_531
| ~ element(U_531,the_carrier(U_532)) )
| ~ latt_str(U_532)
| ~ lattice(U_532)
| empty_carrier(U_532) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_532,U_531] :
( cast_to_el_of_LattPOSet(U_532,U_531) = U_531
| ~ element(U_531,the_carrier(U_532))
| ~ latt_str(U_532)
| ~ lattice(U_532)
| empty_carrier(U_532) ),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
( cast_to_el_of_LattPOSet(U_532,U_531) = U_531
| ~ element(U_531,the_carrier(U_532))
| ~ latt_str(U_532)
| ~ lattice(U_532)
| empty_carrier(U_532) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( below(A,B,C)
| join(A,B,C) != C )
& ( join(A,B,C) = C
| ~ below(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d3_lattices]) ).
fof(f_109_2,plain,
! [U_535] :
( ! [U_534] :
( ! [U_533] :
( ( ( below(U_535,U_534,U_533)
| join(U_535,U_534,U_533) != U_533 )
& ( join(U_535,U_534,U_533) = U_533
| ~ below(U_535,U_534,U_533) ) )
| ~ element(U_533,the_carrier(U_535)) )
| ~ element(U_534,the_carrier(U_535)) )
| ~ join_semilatt_str(U_535)
| empty_carrier(U_535) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_533,U_534,U_535] :
( below(U_535,U_534,U_533)
| join(U_535,U_534,U_533) != U_533
| ~ sP166(U_533,U_534,U_535) )
& ! [U_533,U_534,U_535] :
( join(U_535,U_534,U_533) = U_533
| ~ below(U_535,U_534,U_533)
| ~ sP166(U_533,U_534,U_535) )
& ! [U_533,U_534,U_535] :
( sP166(U_533,U_534,U_535)
| ~ element(U_533,the_carrier(U_535))
| ~ element(U_534,the_carrier(U_535))
| ~ join_semilatt_str(U_535)
| empty_carrier(U_535) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_109_2]) ).
cnf(f_109_4,plain,
( sP166(U_533,U_534,U_535)
| ~ element(U_533,the_carrier(U_535))
| ~ element(U_534,the_carrier(U_535))
| ~ join_semilatt_str(U_535)
| empty_carrier(U_535) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( join(U_535,U_534,U_533) = U_533
| ~ below(U_535,U_534,U_533)
| ~ sP166(U_533,U_534,U_535) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_6,plain,
( below(U_535,U_534,U_533)
| join(U_535,U_534,U_533) != U_533
| ~ sP166(U_533,U_534,U_535) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_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_110_2,plain,
! [U_540] :
( ( epsilon_connected(U_540)
| ? [U_539,U_538] :
( ~ in(U_538,U_539)
& U_539 != U_538
& ~ in(U_539,U_538)
& in(U_538,U_540)
& in(U_539,U_540) ) )
& ( ! [U_537,U_536] :
( in(U_536,U_537)
| U_537 = U_536
| in(U_537,U_536)
| ~ in(U_536,U_540)
| ~ in(U_537,U_540) )
| ~ epsilon_connected(U_540) ) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
( ! [U_542] :
( epsilon_connected(U_542)
| ? [U_539] :
( ? [U_538] :
( ~ in(U_538,U_539)
& U_539 != U_538
& ~ in(U_539,U_538)
& in(U_538,U_542) )
& in(U_539,U_542) ) )
& ! [U_541] :
( ! [U_537] :
( ! [U_536] :
( in(U_536,U_537)
| U_537 = U_536
| in(U_537,U_536)
| ~ in(U_536,U_541) )
| ~ in(U_537,U_541) )
| ~ epsilon_connected(U_541) ) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
fof(f_110_4,plain,
( ! [U_542] :
( epsilon_connected(U_542)
| ( ? [U_538] :
( ~ in(U_538,sK90(U_542))
& sK90(U_542) != U_538
& ~ in(sK90(U_542),U_538)
& in(U_538,U_542) )
& in(sK90(U_542),U_542) ) )
& ! [U_541] :
( ! [U_537] :
( ! [U_536] :
( in(U_536,U_537)
| U_537 = U_536
| in(U_537,U_536)
| ~ in(U_536,U_541) )
| ~ in(U_537,U_541) )
| ~ epsilon_connected(U_541) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_539,sK90(U_542))],[f_110_3]) ).
fof(f_110_5,plain,
( ! [U_542] :
( epsilon_connected(U_542)
| ( ~ in(sK91(U_542),sK90(U_542))
& sK90(U_542) != sK91(U_542)
& ~ in(sK90(U_542),sK91(U_542))
& in(sK91(U_542),U_542)
& in(sK90(U_542),U_542) ) )
& ! [U_541] :
( ! [U_537] :
( ! [U_536] :
( in(U_536,U_537)
| U_537 = U_536
| in(U_537,U_536)
| ~ in(U_536,U_541) )
| ~ in(U_537,U_541) )
| ~ epsilon_connected(U_541) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_538,sK91(U_542))],[f_110_4]) ).
fof(f_110_6,plain,
( ! [U_542] :
( ~ in(sK91(U_542),sK90(U_542))
| ~ sP167(U_542) )
& ! [U_542] :
( sK90(U_542) != sK91(U_542)
| ~ sP167(U_542) )
& ! [U_542] :
( ~ in(sK90(U_542),sK91(U_542))
| ~ sP167(U_542) )
& ! [U_542] :
( in(sK91(U_542),U_542)
| ~ sP167(U_542) )
& ! [U_542] :
( in(sK90(U_542),U_542)
| ~ sP167(U_542) )
& ! [U_542] :
( epsilon_connected(U_542)
| sP167(U_542) )
& ! [U_537,U_541,U_536] :
( in(U_536,U_537)
| U_537 = U_536
| in(U_537,U_536)
| ~ in(U_536,U_541)
| ~ in(U_537,U_541)
| ~ epsilon_connected(U_541) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_110_5]) ).
cnf(f_110_7,plain,
( in(U_536,U_537)
| U_537 = U_536
| in(U_537,U_536)
| ~ in(U_536,U_541)
| ~ in(U_537,U_541)
| ~ epsilon_connected(U_541) ),
inference(clausify,[status(thm)],[f_110_6]) ).
cnf(f_110_8,plain,
( epsilon_connected(U_542)
| sP167(U_542) ),
inference(clausify,[status(thm)],[f_110_6]) ).
cnf(f_110_9,plain,
( in(sK90(U_542),U_542)
| ~ sP167(U_542) ),
inference(clausify,[status(thm)],[f_110_6]) ).
cnf(f_110_10,plain,
( in(sK91(U_542),U_542)
| ~ sP167(U_542) ),
inference(clausify,[status(thm)],[f_110_6]) ).
cnf(f_110_11,plain,
( ~ in(sK90(U_542),sK91(U_542))
| ~ sP167(U_542) ),
inference(clausify,[status(thm)],[f_110_6]) ).
cnf(f_110_12,plain,
( sK90(U_542) != sK91(U_542)
| ~ sP167(U_542) ),
inference(clausify,[status(thm)],[f_110_6]) ).
cnf(f_110_13,plain,
( ~ in(sK91(U_542),sK90(U_542))
| ~ sP167(U_542) ),
inference(clausify,[status(thm)],[f_110_6]) ).
fof(f_111_1,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d3_pre_topc]) ).
fof(f_111_2,plain,
! [U_543] :
( cast_as_carrier_subset(U_543) = the_carrier(U_543)
| ~ one_sorted_str(U_543) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_543] :
( cast_as_carrier_subset(U_543) = the_carrier(U_543)
| ~ one_sorted_str(U_543) ),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
( cast_as_carrier_subset(U_543) = the_carrier(U_543)
| ~ one_sorted_str(U_543) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_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_112_2,plain,
! [U_549] :
( ! [U_548] :
( ( ( subset(U_549,U_548)
| ? [U_547,U_546] :
( ~ in(ordered_pair(U_547,U_546),U_548)
& in(ordered_pair(U_547,U_546),U_549) ) )
& ( ! [U_545,U_544] :
( in(ordered_pair(U_545,U_544),U_548)
| ~ in(ordered_pair(U_545,U_544),U_549) )
| ~ subset(U_549,U_548) ) )
| ~ relation(U_548) )
| ~ relation(U_549) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_549] :
( ! [U_548] :
( ( ( subset(U_549,U_548)
| ? [U_546] :
( ~ in(ordered_pair(sK92(U_549,U_548),U_546),U_548)
& in(ordered_pair(sK92(U_549,U_548),U_546),U_549) ) )
& ( ! [U_545,U_544] :
( in(ordered_pair(U_545,U_544),U_548)
| ~ in(ordered_pair(U_545,U_544),U_549) )
| ~ subset(U_549,U_548) ) )
| ~ relation(U_548) )
| ~ relation(U_549) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_547,sK92(U_549,U_548))],[f_112_2]) ).
fof(f_112_4,plain,
! [U_549] :
( ! [U_548] :
( ( ( subset(U_549,U_548)
| ( ~ in(ordered_pair(sK92(U_549,U_548),sK93(U_549,U_548)),U_548)
& in(ordered_pair(sK92(U_549,U_548),sK93(U_549,U_548)),U_549) ) )
& ( ! [U_545,U_544] :
( in(ordered_pair(U_545,U_544),U_548)
| ~ in(ordered_pair(U_545,U_544),U_549) )
| ~ subset(U_549,U_548) ) )
| ~ relation(U_548) )
| ~ relation(U_549) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_546,sK93(U_549,U_548))],[f_112_3]) ).
fof(f_112_5,plain,
( ! [U_548,U_549] :
( ~ in(ordered_pair(sK92(U_549,U_548),sK93(U_549,U_548)),U_548)
| ~ sP168(U_548,U_549) )
& ! [U_548,U_549] :
( in(ordered_pair(sK92(U_549,U_548),sK93(U_549,U_548)),U_549)
| ~ sP168(U_548,U_549) )
& ! [U_548,U_549,U_544,U_545] :
( subset(U_549,U_548)
| sP168(U_548,U_549)
| ~ sP169(U_548,U_549,U_544,U_545) )
& ! [U_548,U_549,U_544,U_545] :
( in(ordered_pair(U_545,U_544),U_548)
| ~ in(ordered_pair(U_545,U_544),U_549)
| ~ subset(U_549,U_548)
| ~ sP169(U_548,U_549,U_544,U_545) )
& ! [U_548,U_549,U_544,U_545] :
( sP169(U_548,U_549,U_544,U_545)
| ~ relation(U_548)
| ~ relation(U_549) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169])],[f_112_4]) ).
cnf(f_112_6,plain,
( sP169(U_548,U_549,U_544,U_545)
| ~ relation(U_548)
| ~ relation(U_549) ),
inference(clausify,[status(thm)],[f_112_5]) ).
cnf(f_112_7,plain,
( in(ordered_pair(U_545,U_544),U_548)
| ~ in(ordered_pair(U_545,U_544),U_549)
| ~ subset(U_549,U_548)
| ~ sP169(U_548,U_549,U_544,U_545) ),
inference(clausify,[status(thm)],[f_112_5]) ).
cnf(f_112_8,plain,
( subset(U_549,U_548)
| sP168(U_548,U_549)
| ~ sP169(U_548,U_549,U_544,U_545) ),
inference(clausify,[status(thm)],[f_112_5]) ).
cnf(f_112_9,plain,
( in(ordered_pair(sK92(U_549,U_548),sK93(U_549,U_548)),U_549)
| ~ sP168(U_548,U_549) ),
inference(clausify,[status(thm)],[f_112_5]) ).
cnf(f_112_10,plain,
( ~ in(ordered_pair(sK92(U_549,U_548),sK93(U_549,U_548)),U_548)
| ~ sP168(U_548,U_549) ),
inference(clausify,[status(thm)],[f_112_5]) ).
fof(f_113_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_113_2,plain,
! [U_553,U_552] :
( ( subset(U_553,U_552)
| ? [U_551] :
( ~ in(U_551,U_552)
& in(U_551,U_553) ) )
& ( ! [U_550] :
( in(U_550,U_552)
| ~ in(U_550,U_553) )
| ~ subset(U_553,U_552) ) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_557,U_555] :
( subset(U_557,U_555)
| ? [U_551] :
( ~ in(U_551,U_555)
& in(U_551,U_557) ) )
& ! [U_556,U_554] :
( ! [U_550] :
( in(U_550,U_554)
| ~ in(U_550,U_556) )
| ~ subset(U_556,U_554) ) ),
inference(miniscope,[status(thm)],[f_113_2]) ).
fof(f_113_4,plain,
( ! [U_557,U_555] :
( subset(U_557,U_555)
| ( ~ in(sK94(U_557,U_555),U_555)
& in(sK94(U_557,U_555),U_557) ) )
& ! [U_556,U_554] :
( ! [U_550] :
( in(U_550,U_554)
| ~ in(U_550,U_556) )
| ~ subset(U_556,U_554) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_551,sK94(U_557,U_555))],[f_113_3]) ).
fof(f_113_5,plain,
( ! [U_557,U_555] :
( ~ in(sK94(U_557,U_555),U_555)
| ~ sP170(U_557,U_555) )
& ! [U_557,U_555] :
( in(sK94(U_557,U_555),U_557)
| ~ sP170(U_557,U_555) )
& ! [U_557,U_555] :
( subset(U_557,U_555)
| sP170(U_557,U_555) )
& ! [U_556,U_554,U_550] :
( in(U_550,U_554)
| ~ in(U_550,U_556)
| ~ subset(U_556,U_554) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_113_4]) ).
cnf(f_113_6,plain,
( in(U_550,U_554)
| ~ in(U_550,U_556)
| ~ subset(U_556,U_554) ),
inference(clausify,[status(thm)],[f_113_5]) ).
cnf(f_113_7,plain,
( subset(U_557,U_555)
| sP170(U_557,U_555) ),
inference(clausify,[status(thm)],[f_113_5]) ).
cnf(f_113_8,plain,
( in(sK94(U_557,U_555),U_557)
| ~ sP170(U_557,U_555) ),
inference(clausify,[status(thm)],[f_113_5]) ).
cnf(f_113_9,plain,
( ~ in(sK94(U_557,U_555),U_555)
| ~ sP170(U_557,U_555) ),
inference(clausify,[status(thm)],[f_113_5]) ).
fof(f_114_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_114_2,plain,
! [U_563] :
( ! [U_562] :
( ( is_well_founded_in(U_563,U_562)
| ? [U_561] :
( ! [U_560] :
( ~ disjoint(fiber(U_563,U_560),U_561)
| ~ in(U_560,U_561) )
& U_561 != empty_set
& subset(U_561,U_562) ) )
& ( ! [U_559] :
( ? [U_558] :
( disjoint(fiber(U_563,U_558),U_559)
& in(U_558,U_559) )
| U_559 = empty_set
| ~ subset(U_559,U_562) )
| ~ is_well_founded_in(U_563,U_562) ) )
| ~ relation(U_563) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_563] :
( ( ! [U_565] :
( is_well_founded_in(U_563,U_565)
| ? [U_561] :
( ! [U_560] :
( ~ disjoint(fiber(U_563,U_560),U_561)
| ~ in(U_560,U_561) )
& U_561 != empty_set
& subset(U_561,U_565) ) )
& ! [U_564] :
( ! [U_559] :
( ? [U_558] :
( disjoint(fiber(U_563,U_558),U_559)
& in(U_558,U_559) )
| U_559 = empty_set
| ~ subset(U_559,U_564) )
| ~ is_well_founded_in(U_563,U_564) ) )
| ~ relation(U_563) ),
inference(miniscope,[status(thm)],[f_114_2]) ).
fof(f_114_4,plain,
! [U_563] :
( ( ! [U_565] :
( is_well_founded_in(U_563,U_565)
| ? [U_561] :
( ! [U_560] :
( ~ disjoint(fiber(U_563,U_560),U_561)
| ~ in(U_560,U_561) )
& U_561 != empty_set
& subset(U_561,U_565) ) )
& ! [U_564] :
( ! [U_559] :
( ( disjoint(fiber(U_563,sK95(U_563,U_564,U_559)),U_559)
& in(sK95(U_563,U_564,U_559),U_559) )
| U_559 = empty_set
| ~ subset(U_559,U_564) )
| ~ is_well_founded_in(U_563,U_564) ) )
| ~ relation(U_563) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_558,sK95(U_563,U_564,U_559))],[f_114_3]) ).
fof(f_114_5,plain,
! [U_563] :
( ( ! [U_565] :
( is_well_founded_in(U_563,U_565)
| ( ! [U_560] :
( ~ disjoint(fiber(U_563,U_560),sK96(U_563,U_565))
| ~ in(U_560,sK96(U_563,U_565)) )
& sK96(U_563,U_565) != empty_set
& subset(sK96(U_563,U_565),U_565) ) )
& ! [U_564] :
( ! [U_559] :
( ( disjoint(fiber(U_563,sK95(U_563,U_564,U_559)),U_559)
& in(sK95(U_563,U_564,U_559),U_559) )
| U_559 = empty_set
| ~ subset(U_559,U_564) )
| ~ is_well_founded_in(U_563,U_564) ) )
| ~ relation(U_563) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_561,sK96(U_563,U_565))],[f_114_4]) ).
fof(f_114_6,plain,
( ! [U_563,U_565,U_560] :
( ~ disjoint(fiber(U_563,U_560),sK96(U_563,U_565))
| ~ in(U_560,sK96(U_563,U_565))
| ~ sP172(U_563,U_565,U_560) )
& ! [U_563,U_565,U_560] :
( sK96(U_563,U_565) != empty_set
| ~ sP172(U_563,U_565,U_560) )
& ! [U_563,U_565,U_560] :
( subset(sK96(U_563,U_565),U_565)
| ~ sP172(U_563,U_565,U_560) )
& ! [U_564,U_563,U_559] :
( disjoint(fiber(U_563,sK95(U_563,U_564,U_559)),U_559)
| ~ sP171(U_564,U_563,U_559) )
& ! [U_564,U_563,U_559] :
( in(sK95(U_563,U_564,U_559),U_559)
| ~ sP171(U_564,U_563,U_559) )
& ! [U_564,U_563,U_565,U_559,U_560] :
( is_well_founded_in(U_563,U_565)
| sP172(U_563,U_565,U_560)
| ~ sP173(U_564,U_563,U_565,U_559,U_560) )
& ! [U_564,U_563,U_565,U_559,U_560] :
( sP171(U_564,U_563,U_559)
| U_559 = empty_set
| ~ subset(U_559,U_564)
| ~ is_well_founded_in(U_563,U_564)
| ~ sP173(U_564,U_563,U_565,U_559,U_560) )
& ! [U_564,U_563,U_565,U_559,U_560] :
( sP173(U_564,U_563,U_565,U_559,U_560)
| ~ relation(U_563) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171,sP172,sP173])],[f_114_5]) ).
cnf(f_114_7,plain,
( sP173(U_564,U_563,U_565,U_559,U_560)
| ~ relation(U_563) ),
inference(clausify,[status(thm)],[f_114_6]) ).
cnf(f_114_8,plain,
( sP171(U_564,U_563,U_559)
| U_559 = empty_set
| ~ subset(U_559,U_564)
| ~ is_well_founded_in(U_563,U_564)
| ~ sP173(U_564,U_563,U_565,U_559,U_560) ),
inference(clausify,[status(thm)],[f_114_6]) ).
cnf(f_114_9,plain,
( is_well_founded_in(U_563,U_565)
| sP172(U_563,U_565,U_560)
| ~ sP173(U_564,U_563,U_565,U_559,U_560) ),
inference(clausify,[status(thm)],[f_114_6]) ).
cnf(f_114_10,plain,
( in(sK95(U_563,U_564,U_559),U_559)
| ~ sP171(U_564,U_563,U_559) ),
inference(clausify,[status(thm)],[f_114_6]) ).
cnf(f_114_11,plain,
( disjoint(fiber(U_563,sK95(U_563,U_564,U_559)),U_559)
| ~ sP171(U_564,U_563,U_559) ),
inference(clausify,[status(thm)],[f_114_6]) ).
cnf(f_114_12,plain,
( subset(sK96(U_563,U_565),U_565)
| ~ sP172(U_563,U_565,U_560) ),
inference(clausify,[status(thm)],[f_114_6]) ).
cnf(f_114_13,plain,
( sK96(U_563,U_565) != empty_set
| ~ sP172(U_563,U_565,U_560) ),
inference(clausify,[status(thm)],[f_114_6]) ).
cnf(f_114_14,plain,
( ~ disjoint(fiber(U_563,U_560),sK96(U_563,U_565))
| ~ in(U_560,sK96(U_563,U_565))
| ~ sP172(U_563,U_565,U_560) ),
inference(clausify,[status(thm)],[f_114_6]) ).
fof(f_115_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_115_2,plain,
! [U_570,U_569,U_568] :
( ( U_568 = set_intersection2(U_570,U_569)
| ? [U_567] :
( ( ~ in(U_567,U_568)
& in(U_567,U_569)
& in(U_567,U_570) )
| ( ( ~ in(U_567,U_569)
| ~ in(U_567,U_570) )
& in(U_567,U_568) ) ) )
& ( ! [U_566] :
( ( in(U_566,U_568)
| ~ in(U_566,U_569)
| ~ in(U_566,U_570) )
& ( ( in(U_566,U_569)
& in(U_566,U_570) )
| ~ in(U_566,U_568) ) )
| U_568 != set_intersection2(U_570,U_569) ) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
( ! [U_580,U_578,U_576] :
( U_576 = set_intersection2(U_580,U_578)
| ? [U_574] :
( ~ in(U_574,U_576)
& in(U_574,U_578)
& in(U_574,U_580) )
| ? [U_573] :
( ( ~ in(U_573,U_578)
| ~ in(U_573,U_580) )
& in(U_573,U_576) ) )
& ! [U_579,U_577,U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ~ in(U_572,U_577)
| ~ in(U_572,U_579) )
& ! [U_571] :
( ( in(U_571,U_577)
& in(U_571,U_579) )
| ~ in(U_571,U_575) ) )
| U_575 != set_intersection2(U_579,U_577) ) ),
inference(miniscope,[status(thm)],[f_115_2]) ).
fof(f_115_4,plain,
( ! [U_580,U_578,U_576] :
( U_576 = set_intersection2(U_580,U_578)
| ? [U_574] :
( ~ in(U_574,U_576)
& in(U_574,U_578)
& in(U_574,U_580) )
| ( ( ~ in(sK97(U_580,U_578,U_576),U_578)
| ~ in(sK97(U_580,U_578,U_576),U_580) )
& in(sK97(U_580,U_578,U_576),U_576) ) )
& ! [U_579,U_577,U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ~ in(U_572,U_577)
| ~ in(U_572,U_579) )
& ! [U_571] :
( ( in(U_571,U_577)
& in(U_571,U_579) )
| ~ in(U_571,U_575) ) )
| U_575 != set_intersection2(U_579,U_577) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_573,sK97(U_580,U_578,U_576))],[f_115_3]) ).
fof(f_115_5,plain,
( ! [U_580,U_578,U_576] :
( U_576 = set_intersection2(U_580,U_578)
| ( ~ in(sK98(U_580,U_578,U_576),U_576)
& in(sK98(U_580,U_578,U_576),U_578)
& in(sK98(U_580,U_578,U_576),U_580) )
| ( ( ~ in(sK97(U_580,U_578,U_576),U_578)
| ~ in(sK97(U_580,U_578,U_576),U_580) )
& in(sK97(U_580,U_578,U_576),U_576) ) )
& ! [U_579,U_577,U_575] :
( ( ! [U_572] :
( in(U_572,U_575)
| ~ in(U_572,U_577)
| ~ in(U_572,U_579) )
& ! [U_571] :
( ( in(U_571,U_577)
& in(U_571,U_579) )
| ~ in(U_571,U_575) ) )
| U_575 != set_intersection2(U_579,U_577) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_574,sK98(U_580,U_578,U_576))],[f_115_4]) ).
fof(f_115_6,plain,
( ! [U_576,U_580,U_578] :
( ~ in(sK98(U_580,U_578,U_576),U_576)
| ~ sP177(U_576,U_580,U_578) )
& ! [U_576,U_580,U_578] :
( in(sK98(U_580,U_578,U_576),U_578)
| ~ sP177(U_576,U_580,U_578) )
& ! [U_576,U_580,U_578] :
( in(sK98(U_580,U_578,U_576),U_580)
| ~ sP177(U_576,U_580,U_578) )
& ! [U_576,U_580,U_578] :
( ~ in(sK97(U_580,U_578,U_576),U_578)
| ~ in(sK97(U_580,U_578,U_576),U_580)
| ~ sP176(U_576,U_580,U_578) )
& ! [U_576,U_580,U_578] :
( in(sK97(U_580,U_578,U_576),U_576)
| ~ sP176(U_576,U_580,U_578) )
& ! [U_579,U_571,U_577] :
( in(U_571,U_577)
| ~ sP174(U_579,U_571,U_577) )
& ! [U_579,U_571,U_577] :
( in(U_571,U_579)
| ~ sP174(U_579,U_571,U_577) )
& ! [U_579,U_572,U_571,U_577,U_575] :
( in(U_572,U_575)
| ~ in(U_572,U_577)
| ~ in(U_572,U_579)
| ~ sP175(U_579,U_572,U_571,U_577,U_575) )
& ! [U_579,U_572,U_571,U_577,U_575] :
( sP174(U_579,U_571,U_577)
| ~ in(U_571,U_575)
| ~ sP175(U_579,U_572,U_571,U_577,U_575) )
& ! [U_576,U_580,U_578] :
( U_576 = set_intersection2(U_580,U_578)
| sP177(U_576,U_580,U_578)
| sP176(U_576,U_580,U_578) )
& ! [U_579,U_572,U_571,U_577,U_575] :
( sP175(U_579,U_572,U_571,U_577,U_575)
| U_575 != set_intersection2(U_579,U_577) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174,sP175,sP176,sP177])],[f_115_5]) ).
cnf(f_115_7,plain,
( sP175(U_579,U_572,U_571,U_577,U_575)
| U_575 != set_intersection2(U_579,U_577) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_8,plain,
( U_576 = set_intersection2(U_580,U_578)
| sP177(U_576,U_580,U_578)
| sP176(U_576,U_580,U_578) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_9,plain,
( sP174(U_579,U_571,U_577)
| ~ in(U_571,U_575)
| ~ sP175(U_579,U_572,U_571,U_577,U_575) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_10,plain,
( in(U_572,U_575)
| ~ in(U_572,U_577)
| ~ in(U_572,U_579)
| ~ sP175(U_579,U_572,U_571,U_577,U_575) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_11,plain,
( in(U_571,U_579)
| ~ sP174(U_579,U_571,U_577) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_12,plain,
( in(U_571,U_577)
| ~ sP174(U_579,U_571,U_577) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_13,plain,
( in(sK97(U_580,U_578,U_576),U_576)
| ~ sP176(U_576,U_580,U_578) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_14,plain,
( ~ in(sK97(U_580,U_578,U_576),U_578)
| ~ in(sK97(U_580,U_578,U_576),U_580)
| ~ sP176(U_576,U_580,U_578) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_15,plain,
( in(sK98(U_580,U_578,U_576),U_580)
| ~ sP177(U_576,U_580,U_578) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_16,plain,
( in(sK98(U_580,U_578,U_576),U_578)
| ~ sP177(U_576,U_580,U_578) ),
inference(clausify,[status(thm)],[f_115_6]) ).
cnf(f_115_17,plain,
( ~ in(sK98(U_580,U_578,U_576),U_576)
| ~ sP177(U_576,U_580,U_578) ),
inference(clausify,[status(thm)],[f_115_6]) ).
fof(f_116_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_116_2,plain,
! [U_583] :
( ! [U_582,U_581] :
( ( ( ( U_581 = apply(U_583,U_582)
| U_581 != empty_set )
& ( U_581 = empty_set
| U_581 != apply(U_583,U_582) ) )
| in(U_582,relation_dom(U_583)) )
& ( ( ( U_581 = apply(U_583,U_582)
| ~ in(ordered_pair(U_582,U_581),U_583) )
& ( in(ordered_pair(U_582,U_581),U_583)
| U_581 != apply(U_583,U_582) ) )
| ~ in(U_582,relation_dom(U_583)) ) )
| ~ function(U_583)
| ~ relation(U_583) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_583] :
( ( ! [U_591] :
( ( ! [U_589] :
( U_589 = apply(U_583,U_591)
| U_589 != empty_set )
& ! [U_588] :
( U_588 = empty_set
| U_588 != apply(U_583,U_591) ) )
| in(U_591,relation_dom(U_583)) )
& ! [U_590] :
( ( ! [U_587] :
( U_587 = apply(U_583,U_590)
| ~ in(ordered_pair(U_590,U_587),U_583) )
& ! [U_586] :
( in(ordered_pair(U_590,U_586),U_583)
| U_586 != apply(U_583,U_590) ) )
| ~ in(U_590,relation_dom(U_583)) ) )
| ~ function(U_583)
| ~ relation(U_583) ),
inference(miniscope,[status(thm)],[f_116_2]) ).
fof(f_116_4,plain,
( ! [U_591,U_588,U_589,U_583] :
( U_589 = apply(U_583,U_591)
| U_589 != empty_set
| ~ sP179(U_591,U_588,U_589,U_583) )
& ! [U_591,U_588,U_589,U_583] :
( U_588 = empty_set
| U_588 != apply(U_583,U_591)
| ~ sP179(U_591,U_588,U_589,U_583) )
& ! [U_590,U_586,U_587,U_583] :
( U_587 = apply(U_583,U_590)
| ~ in(ordered_pair(U_590,U_587),U_583)
| ~ sP178(U_590,U_586,U_587,U_583) )
& ! [U_590,U_586,U_587,U_583] :
( in(ordered_pair(U_590,U_586),U_583)
| U_586 != apply(U_583,U_590)
| ~ sP178(U_590,U_586,U_587,U_583) )
& ! [U_590,U_586,U_591,U_587,U_588,U_589,U_583] :
( sP179(U_591,U_588,U_589,U_583)
| in(U_591,relation_dom(U_583))
| ~ sP180(U_590,U_586,U_591,U_587,U_588,U_589,U_583) )
& ! [U_590,U_586,U_591,U_587,U_588,U_589,U_583] :
( sP178(U_590,U_586,U_587,U_583)
| ~ in(U_590,relation_dom(U_583))
| ~ sP180(U_590,U_586,U_591,U_587,U_588,U_589,U_583) )
& ! [U_590,U_586,U_591,U_587,U_588,U_589,U_583] :
( sP180(U_590,U_586,U_591,U_587,U_588,U_589,U_583)
| ~ function(U_583)
| ~ relation(U_583) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178,sP179,sP180])],[f_116_3]) ).
cnf(f_116_5,plain,
( sP180(U_590,U_586,U_591,U_587,U_588,U_589,U_583)
| ~ function(U_583)
| ~ relation(U_583) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_6,plain,
( sP178(U_590,U_586,U_587,U_583)
| ~ in(U_590,relation_dom(U_583))
| ~ sP180(U_590,U_586,U_591,U_587,U_588,U_589,U_583) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_7,plain,
( sP179(U_591,U_588,U_589,U_583)
| in(U_591,relation_dom(U_583))
| ~ sP180(U_590,U_586,U_591,U_587,U_588,U_589,U_583) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_8,plain,
( in(ordered_pair(U_590,U_586),U_583)
| U_586 != apply(U_583,U_590)
| ~ sP178(U_590,U_586,U_587,U_583) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_9,plain,
( U_587 = apply(U_583,U_590)
| ~ in(ordered_pair(U_590,U_587),U_583)
| ~ sP178(U_590,U_586,U_587,U_583) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_10,plain,
( U_588 = empty_set
| U_588 != apply(U_583,U_591)
| ~ sP179(U_591,U_588,U_589,U_583) ),
inference(clausify,[status(thm)],[f_116_4]) ).
cnf(f_116_11,plain,
( U_589 = apply(U_583,U_591)
| U_589 != empty_set
| ~ sP179(U_591,U_588,U_589,U_583) ),
inference(clausify,[status(thm)],[f_116_4]) ).
fof(f_117_1,plain,
! [A] :
( ! [B] :
( cast_to_el_of_lattice(A,B) = B
| ~ element(B,the_carrier(poset_of_lattice(A))) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d4_lattice3]) ).
fof(f_117_2,plain,
! [U_593] :
( ! [U_592] :
( cast_to_el_of_lattice(U_593,U_592) = U_592
| ~ element(U_592,the_carrier(poset_of_lattice(U_593))) )
| ~ latt_str(U_593)
| ~ lattice(U_593)
| empty_carrier(U_593) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_592,U_593] :
( cast_to_el_of_lattice(U_593,U_592) = U_592
| ~ element(U_592,the_carrier(poset_of_lattice(U_593)))
| ~ latt_str(U_593)
| ~ lattice(U_593)
| empty_carrier(U_593) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( cast_to_el_of_lattice(U_593,U_592) = U_592
| ~ element(U_592,the_carrier(poset_of_lattice(U_593)))
| ~ latt_str(U_593)
| ~ lattice(U_593)
| empty_carrier(U_593) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_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_118_2,plain,
! [U_594] :
( ( ordinal(U_594)
| ~ epsilon_connected(U_594)
| ~ epsilon_transitive(U_594) )
& ( ( epsilon_connected(U_594)
& epsilon_transitive(U_594) )
| ~ ordinal(U_594) ) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
( ! [U_596] :
( ordinal(U_596)
| ~ epsilon_connected(U_596)
| ~ epsilon_transitive(U_596) )
& ! [U_595] :
( ( epsilon_connected(U_595)
& epsilon_transitive(U_595) )
| ~ ordinal(U_595) ) ),
inference(miniscope,[status(thm)],[f_118_2]) ).
fof(f_118_4,plain,
( ! [U_595] :
( epsilon_connected(U_595)
| ~ sP181(U_595) )
& ! [U_595] :
( epsilon_transitive(U_595)
| ~ sP181(U_595) )
& ! [U_596] :
( ordinal(U_596)
| ~ epsilon_connected(U_596)
| ~ epsilon_transitive(U_596) )
& ! [U_595] :
( sP181(U_595)
| ~ ordinal(U_595) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_118_3]) ).
cnf(f_118_5,plain,
( sP181(U_595)
| ~ ordinal(U_595) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_6,plain,
( ordinal(U_596)
| ~ epsilon_connected(U_596)
| ~ epsilon_transitive(U_596) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_7,plain,
( epsilon_transitive(U_595)
| ~ sP181(U_595) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_8,plain,
( epsilon_connected(U_595)
| ~ sP181(U_595) ),
inference(clausify,[status(thm)],[f_118_4]) ).
fof(f_119_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_119_2,plain,
! [U_604] :
( ! [U_603] :
( ( U_603 = relation_dom(U_604)
| ? [U_602] :
( ( ~ in(U_602,U_603)
& ? [U_601] : in(ordered_pair(U_602,U_601),U_604) )
| ( ! [U_600] : ~ in(ordered_pair(U_602,U_600),U_604)
& in(U_602,U_603) ) ) )
& ( ! [U_599] :
( ( in(U_599,U_603)
| ! [U_598] : ~ in(ordered_pair(U_599,U_598),U_604) )
& ( ? [U_597] : in(ordered_pair(U_599,U_597),U_604)
| ~ in(U_599,U_603) ) )
| U_603 != relation_dom(U_604) ) )
| ~ relation(U_604) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_604] :
( ( ! [U_610] :
( U_610 = relation_dom(U_604)
| ? [U_608] :
( ~ in(U_608,U_610)
& ? [U_601] : in(ordered_pair(U_608,U_601),U_604) )
| ? [U_607] :
( ! [U_600] : ~ in(ordered_pair(U_607,U_600),U_604)
& in(U_607,U_610) ) )
& ! [U_609] :
( ( ! [U_606] :
( in(U_606,U_609)
| ! [U_598] : ~ in(ordered_pair(U_606,U_598),U_604) )
& ! [U_605] :
( ? [U_597] : in(ordered_pair(U_605,U_597),U_604)
| ~ in(U_605,U_609) ) )
| U_609 != relation_dom(U_604) ) )
| ~ relation(U_604) ),
inference(miniscope,[status(thm)],[f_119_2]) ).
fof(f_119_4,plain,
! [U_604] :
( ( ! [U_610] :
( U_610 = relation_dom(U_604)
| ? [U_608] :
( ~ in(U_608,U_610)
& ? [U_601] : in(ordered_pair(U_608,U_601),U_604) )
| ? [U_607] :
( ! [U_600] : ~ in(ordered_pair(U_607,U_600),U_604)
& in(U_607,U_610) ) )
& ! [U_609] :
( ( ! [U_606] :
( in(U_606,U_609)
| ! [U_598] : ~ in(ordered_pair(U_606,U_598),U_604) )
& ! [U_605] :
( in(ordered_pair(U_605,sK99(U_604,U_609,U_605)),U_604)
| ~ in(U_605,U_609) ) )
| U_609 != relation_dom(U_604) ) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_597,sK99(U_604,U_609,U_605))],[f_119_3]) ).
fof(f_119_5,plain,
! [U_604] :
( ( ! [U_610] :
( U_610 = relation_dom(U_604)
| ? [U_608] :
( ~ in(U_608,U_610)
& ? [U_601] : in(ordered_pair(U_608,U_601),U_604) )
| ( ! [U_600] : ~ in(ordered_pair(sK100(U_604,U_610),U_600),U_604)
& in(sK100(U_604,U_610),U_610) ) )
& ! [U_609] :
( ( ! [U_606] :
( in(U_606,U_609)
| ! [U_598] : ~ in(ordered_pair(U_606,U_598),U_604) )
& ! [U_605] :
( in(ordered_pair(U_605,sK99(U_604,U_609,U_605)),U_604)
| ~ in(U_605,U_609) ) )
| U_609 != relation_dom(U_604) ) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_607,sK100(U_604,U_610))],[f_119_4]) ).
fof(f_119_6,plain,
! [U_604] :
( ( ! [U_610] :
( U_610 = relation_dom(U_604)
| ( ~ in(sK101(U_604,U_610),U_610)
& ? [U_601] : in(ordered_pair(sK101(U_604,U_610),U_601),U_604) )
| ( ! [U_600] : ~ in(ordered_pair(sK100(U_604,U_610),U_600),U_604)
& in(sK100(U_604,U_610),U_610) ) )
& ! [U_609] :
( ( ! [U_606] :
( in(U_606,U_609)
| ! [U_598] : ~ in(ordered_pair(U_606,U_598),U_604) )
& ! [U_605] :
( in(ordered_pair(U_605,sK99(U_604,U_609,U_605)),U_604)
| ~ in(U_605,U_609) ) )
| U_609 != relation_dom(U_604) ) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_608,sK101(U_604,U_610))],[f_119_5]) ).
fof(f_119_7,plain,
! [U_604] :
( ( ! [U_610] :
( U_610 = relation_dom(U_604)
| ( ~ in(sK101(U_604,U_610),U_610)
& in(ordered_pair(sK101(U_604,U_610),sK102(U_604,U_610)),U_604) )
| ( ! [U_600] : ~ in(ordered_pair(sK100(U_604,U_610),U_600),U_604)
& in(sK100(U_604,U_610),U_610) ) )
& ! [U_609] :
( ( ! [U_606] :
( in(U_606,U_609)
| ! [U_598] : ~ in(ordered_pair(U_606,U_598),U_604) )
& ! [U_605] :
( in(ordered_pair(U_605,sK99(U_604,U_609,U_605)),U_604)
| ~ in(U_605,U_609) ) )
| U_609 != relation_dom(U_604) ) )
| ~ relation(U_604) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_601,sK102(U_604,U_610))],[f_119_6]) ).
fof(f_119_8,plain,
( ! [U_610,U_604] :
( ~ in(sK101(U_604,U_610),U_610)
| ~ sP184(U_610,U_604) )
& ! [U_610,U_604] :
( in(ordered_pair(sK101(U_604,U_610),sK102(U_604,U_610)),U_604)
| ~ sP184(U_610,U_604) )
& ! [U_610,U_600,U_604] :
( ~ in(ordered_pair(sK100(U_604,U_610),U_600),U_604)
| ~ sP183(U_610,U_600,U_604) )
& ! [U_610,U_600,U_604] :
( in(sK100(U_604,U_610),U_610)
| ~ sP183(U_610,U_600,U_604) )
& ! [U_609,U_604,U_605,U_606,U_598] :
( in(U_606,U_609)
| ~ in(ordered_pair(U_606,U_598),U_604)
| ~ sP182(U_609,U_604,U_605,U_606,U_598) )
& ! [U_609,U_604,U_605,U_606,U_598] :
( in(ordered_pair(U_605,sK99(U_604,U_609,U_605)),U_604)
| ~ in(U_605,U_609)
| ~ sP182(U_609,U_604,U_605,U_606,U_598) )
& ! [U_609,U_610,U_600,U_604,U_605,U_606,U_598] :
( U_610 = relation_dom(U_604)
| sP184(U_610,U_604)
| sP183(U_610,U_600,U_604)
| ~ sP185(U_609,U_610,U_600,U_604,U_605,U_606,U_598) )
& ! [U_609,U_610,U_600,U_604,U_605,U_606,U_598] :
( sP182(U_609,U_604,U_605,U_606,U_598)
| U_609 != relation_dom(U_604)
| ~ sP185(U_609,U_610,U_600,U_604,U_605,U_606,U_598) )
& ! [U_609,U_610,U_600,U_604,U_605,U_606,U_598] :
( sP185(U_609,U_610,U_600,U_604,U_605,U_606,U_598)
| ~ relation(U_604) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182,sP183,sP184,sP185])],[f_119_7]) ).
cnf(f_119_9,plain,
( sP185(U_609,U_610,U_600,U_604,U_605,U_606,U_598)
| ~ relation(U_604) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_10,plain,
( sP182(U_609,U_604,U_605,U_606,U_598)
| U_609 != relation_dom(U_604)
| ~ sP185(U_609,U_610,U_600,U_604,U_605,U_606,U_598) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_11,plain,
( U_610 = relation_dom(U_604)
| sP184(U_610,U_604)
| sP183(U_610,U_600,U_604)
| ~ sP185(U_609,U_610,U_600,U_604,U_605,U_606,U_598) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_12,plain,
( in(ordered_pair(U_605,sK99(U_604,U_609,U_605)),U_604)
| ~ in(U_605,U_609)
| ~ sP182(U_609,U_604,U_605,U_606,U_598) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_13,plain,
( in(U_606,U_609)
| ~ in(ordered_pair(U_606,U_598),U_604)
| ~ sP182(U_609,U_604,U_605,U_606,U_598) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_14,plain,
( in(sK100(U_604,U_610),U_610)
| ~ sP183(U_610,U_600,U_604) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_15,plain,
( ~ in(ordered_pair(sK100(U_604,U_610),U_600),U_604)
| ~ sP183(U_610,U_600,U_604) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_16,plain,
( in(ordered_pair(sK101(U_604,U_610),sK102(U_604,U_610)),U_604)
| ~ sP184(U_610,U_604) ),
inference(clausify,[status(thm)],[f_119_8]) ).
cnf(f_119_17,plain,
( ~ in(sK101(U_604,U_610),U_610)
| ~ sP184(U_610,U_604) ),
inference(clausify,[status(thm)],[f_119_8]) ).
fof(f_120_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_120_2,plain,
! [U_616] :
( ! [U_615] :
( ( is_antisymmetric_in(U_616,U_615)
| ? [U_614,U_613] :
( U_614 != U_613
& in(ordered_pair(U_613,U_614),U_616)
& in(ordered_pair(U_614,U_613),U_616)
& in(U_613,U_615)
& in(U_614,U_615) ) )
& ( ! [U_612,U_611] :
( U_612 = U_611
| ~ in(ordered_pair(U_611,U_612),U_616)
| ~ in(ordered_pair(U_612,U_611),U_616)
| ~ in(U_611,U_615)
| ~ in(U_612,U_615) )
| ~ is_antisymmetric_in(U_616,U_615) ) )
| ~ relation(U_616) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_616] :
( ( ! [U_618] :
( is_antisymmetric_in(U_616,U_618)
| ? [U_614,U_613] :
( U_614 != U_613
& in(ordered_pair(U_613,U_614),U_616)
& in(ordered_pair(U_614,U_613),U_616)
& in(U_613,U_618)
& in(U_614,U_618) ) )
& ! [U_617] :
( ! [U_612,U_611] :
( U_612 = U_611
| ~ in(ordered_pair(U_611,U_612),U_616)
| ~ in(ordered_pair(U_612,U_611),U_616)
| ~ in(U_611,U_617)
| ~ in(U_612,U_617) )
| ~ is_antisymmetric_in(U_616,U_617) ) )
| ~ relation(U_616) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
fof(f_120_4,plain,
! [U_616] :
( ( ! [U_618] :
( is_antisymmetric_in(U_616,U_618)
| ? [U_613] :
( sK103(U_616,U_618) != U_613
& in(ordered_pair(U_613,sK103(U_616,U_618)),U_616)
& in(ordered_pair(sK103(U_616,U_618),U_613),U_616)
& in(U_613,U_618)
& in(sK103(U_616,U_618),U_618) ) )
& ! [U_617] :
( ! [U_612,U_611] :
( U_612 = U_611
| ~ in(ordered_pair(U_611,U_612),U_616)
| ~ in(ordered_pair(U_612,U_611),U_616)
| ~ in(U_611,U_617)
| ~ in(U_612,U_617) )
| ~ is_antisymmetric_in(U_616,U_617) ) )
| ~ relation(U_616) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_614,sK103(U_616,U_618))],[f_120_3]) ).
fof(f_120_5,plain,
! [U_616] :
( ( ! [U_618] :
( is_antisymmetric_in(U_616,U_618)
| ( sK103(U_616,U_618) != sK104(U_616,U_618)
& in(ordered_pair(sK104(U_616,U_618),sK103(U_616,U_618)),U_616)
& in(ordered_pair(sK103(U_616,U_618),sK104(U_616,U_618)),U_616)
& in(sK104(U_616,U_618),U_618)
& in(sK103(U_616,U_618),U_618) ) )
& ! [U_617] :
( ! [U_612,U_611] :
( U_612 = U_611
| ~ in(ordered_pair(U_611,U_612),U_616)
| ~ in(ordered_pair(U_612,U_611),U_616)
| ~ in(U_611,U_617)
| ~ in(U_612,U_617) )
| ~ is_antisymmetric_in(U_616,U_617) ) )
| ~ relation(U_616) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_613,sK104(U_616,U_618))],[f_120_4]) ).
fof(f_120_6,plain,
( ! [U_618,U_616] :
( sK103(U_616,U_618) != sK104(U_616,U_618)
| ~ sP186(U_618,U_616) )
& ! [U_618,U_616] :
( in(ordered_pair(sK104(U_616,U_618),sK103(U_616,U_618)),U_616)
| ~ sP186(U_618,U_616) )
& ! [U_618,U_616] :
( in(ordered_pair(sK103(U_616,U_618),sK104(U_616,U_618)),U_616)
| ~ sP186(U_618,U_616) )
& ! [U_618,U_616] :
( in(sK104(U_616,U_618),U_618)
| ~ sP186(U_618,U_616) )
& ! [U_618,U_616] :
( in(sK103(U_616,U_618),U_618)
| ~ sP186(U_618,U_616) )
& ! [U_612,U_618,U_616,U_611,U_617] :
( is_antisymmetric_in(U_616,U_618)
| sP186(U_618,U_616)
| ~ sP187(U_612,U_618,U_616,U_611,U_617) )
& ! [U_612,U_618,U_616,U_611,U_617] :
( U_612 = U_611
| ~ in(ordered_pair(U_611,U_612),U_616)
| ~ in(ordered_pair(U_612,U_611),U_616)
| ~ in(U_611,U_617)
| ~ in(U_612,U_617)
| ~ is_antisymmetric_in(U_616,U_617)
| ~ sP187(U_612,U_618,U_616,U_611,U_617) )
& ! [U_612,U_618,U_616,U_611,U_617] :
( sP187(U_612,U_618,U_616,U_611,U_617)
| ~ relation(U_616) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186,sP187])],[f_120_5]) ).
cnf(f_120_7,plain,
( sP187(U_612,U_618,U_616,U_611,U_617)
| ~ relation(U_616) ),
inference(clausify,[status(thm)],[f_120_6]) ).
cnf(f_120_8,plain,
( U_612 = U_611
| ~ in(ordered_pair(U_611,U_612),U_616)
| ~ in(ordered_pair(U_612,U_611),U_616)
| ~ in(U_611,U_617)
| ~ in(U_612,U_617)
| ~ is_antisymmetric_in(U_616,U_617)
| ~ sP187(U_612,U_618,U_616,U_611,U_617) ),
inference(clausify,[status(thm)],[f_120_6]) ).
cnf(f_120_9,plain,
( is_antisymmetric_in(U_616,U_618)
| sP186(U_618,U_616)
| ~ sP187(U_612,U_618,U_616,U_611,U_617) ),
inference(clausify,[status(thm)],[f_120_6]) ).
cnf(f_120_10,plain,
( in(sK103(U_616,U_618),U_618)
| ~ sP186(U_618,U_616) ),
inference(clausify,[status(thm)],[f_120_6]) ).
cnf(f_120_11,plain,
( in(sK104(U_616,U_618),U_618)
| ~ sP186(U_618,U_616) ),
inference(clausify,[status(thm)],[f_120_6]) ).
cnf(f_120_12,plain,
( in(ordered_pair(sK103(U_616,U_618),sK104(U_616,U_618)),U_616)
| ~ sP186(U_618,U_616) ),
inference(clausify,[status(thm)],[f_120_6]) ).
cnf(f_120_13,plain,
( in(ordered_pair(sK104(U_616,U_618),sK103(U_616,U_618)),U_616)
| ~ sP186(U_618,U_616) ),
inference(clausify,[status(thm)],[f_120_6]) ).
cnf(f_120_14,plain,
( sK103(U_616,U_618) != sK104(U_616,U_618)
| ~ sP186(U_618,U_616) ),
inference(clausify,[status(thm)],[f_120_6]) ).
fof(f_121_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_121_2,plain,
! [U_619] : cast_to_subset(U_619) = U_619,
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_619] : cast_to_subset(U_619) = U_619,
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
cast_to_subset(U_619) = U_619,
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_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_122_2,plain,
! [U_627,U_626] :
( ( U_626 = union(U_627)
| ? [U_625] :
( ( ~ in(U_625,U_626)
& ? [U_624] :
( in(U_624,U_627)
& in(U_625,U_624) ) )
| ( ! [U_623] :
( ~ in(U_623,U_627)
| ~ in(U_625,U_623) )
& in(U_625,U_626) ) ) )
& ( ! [U_622] :
( ( in(U_622,U_626)
| ! [U_621] :
( ~ in(U_621,U_627)
| ~ in(U_622,U_621) ) )
& ( ? [U_620] :
( in(U_620,U_627)
& in(U_622,U_620) )
| ~ in(U_622,U_626) ) )
| U_626 != union(U_627) ) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_635,U_633] :
( U_633 = union(U_635)
| ? [U_631] :
( ~ in(U_631,U_633)
& ? [U_624] :
( in(U_624,U_635)
& in(U_631,U_624) ) )
| ? [U_630] :
( ! [U_623] :
( ~ in(U_623,U_635)
| ~ in(U_630,U_623) )
& in(U_630,U_633) ) )
& ! [U_634,U_632] :
( ( ! [U_629] :
( in(U_629,U_632)
| ! [U_621] :
( ~ in(U_621,U_634)
| ~ in(U_629,U_621) ) )
& ! [U_628] :
( ? [U_620] :
( in(U_620,U_634)
& in(U_628,U_620) )
| ~ in(U_628,U_632) ) )
| U_632 != union(U_634) ) ),
inference(miniscope,[status(thm)],[f_122_2]) ).
fof(f_122_4,plain,
( ! [U_635,U_633] :
( U_633 = union(U_635)
| ? [U_631] :
( ~ in(U_631,U_633)
& ? [U_624] :
( in(U_624,U_635)
& in(U_631,U_624) ) )
| ? [U_630] :
( ! [U_623] :
( ~ in(U_623,U_635)
| ~ in(U_630,U_623) )
& in(U_630,U_633) ) )
& ! [U_634,U_632] :
( ( ! [U_629] :
( in(U_629,U_632)
| ! [U_621] :
( ~ in(U_621,U_634)
| ~ in(U_629,U_621) ) )
& ! [U_628] :
( ( in(sK105(U_634,U_632,U_628),U_634)
& in(U_628,sK105(U_634,U_632,U_628)) )
| ~ in(U_628,U_632) ) )
| U_632 != union(U_634) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_620,sK105(U_634,U_632,U_628))],[f_122_3]) ).
fof(f_122_5,plain,
( ! [U_635,U_633] :
( U_633 = union(U_635)
| ? [U_631] :
( ~ in(U_631,U_633)
& ? [U_624] :
( in(U_624,U_635)
& in(U_631,U_624) ) )
| ( ! [U_623] :
( ~ in(U_623,U_635)
| ~ in(sK106(U_635,U_633),U_623) )
& in(sK106(U_635,U_633),U_633) ) )
& ! [U_634,U_632] :
( ( ! [U_629] :
( in(U_629,U_632)
| ! [U_621] :
( ~ in(U_621,U_634)
| ~ in(U_629,U_621) ) )
& ! [U_628] :
( ( in(sK105(U_634,U_632,U_628),U_634)
& in(U_628,sK105(U_634,U_632,U_628)) )
| ~ in(U_628,U_632) ) )
| U_632 != union(U_634) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_630,sK106(U_635,U_633))],[f_122_4]) ).
fof(f_122_6,plain,
( ! [U_635,U_633] :
( U_633 = union(U_635)
| ( ~ in(sK107(U_635,U_633),U_633)
& ? [U_624] :
( in(U_624,U_635)
& in(sK107(U_635,U_633),U_624) ) )
| ( ! [U_623] :
( ~ in(U_623,U_635)
| ~ in(sK106(U_635,U_633),U_623) )
& in(sK106(U_635,U_633),U_633) ) )
& ! [U_634,U_632] :
( ( ! [U_629] :
( in(U_629,U_632)
| ! [U_621] :
( ~ in(U_621,U_634)
| ~ in(U_629,U_621) ) )
& ! [U_628] :
( ( in(sK105(U_634,U_632,U_628),U_634)
& in(U_628,sK105(U_634,U_632,U_628)) )
| ~ in(U_628,U_632) ) )
| U_632 != union(U_634) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_631,sK107(U_635,U_633))],[f_122_5]) ).
fof(f_122_7,plain,
( ! [U_635,U_633] :
( U_633 = union(U_635)
| ( ~ in(sK107(U_635,U_633),U_633)
& in(sK108(U_635,U_633),U_635)
& in(sK107(U_635,U_633),sK108(U_635,U_633)) )
| ( ! [U_623] :
( ~ in(U_623,U_635)
| ~ in(sK106(U_635,U_633),U_623) )
& in(sK106(U_635,U_633),U_633) ) )
& ! [U_634,U_632] :
( ( ! [U_629] :
( in(U_629,U_632)
| ! [U_621] :
( ~ in(U_621,U_634)
| ~ in(U_629,U_621) ) )
& ! [U_628] :
( ( in(sK105(U_634,U_632,U_628),U_634)
& in(U_628,sK105(U_634,U_632,U_628)) )
| ~ in(U_628,U_632) ) )
| U_632 != union(U_634) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_624,sK108(U_635,U_633))],[f_122_6]) ).
fof(f_122_8,plain,
( ! [U_635,U_633] :
( ~ in(sK107(U_635,U_633),U_633)
| ~ sP191(U_635,U_633) )
& ! [U_635,U_633] :
( in(sK108(U_635,U_633),U_635)
| ~ sP191(U_635,U_633) )
& ! [U_635,U_633] :
( in(sK107(U_635,U_633),sK108(U_635,U_633))
| ~ sP191(U_635,U_633) )
& ! [U_635,U_633,U_623] :
( ~ in(U_623,U_635)
| ~ in(sK106(U_635,U_633),U_623)
| ~ sP190(U_635,U_633,U_623) )
& ! [U_635,U_633,U_623] :
( in(sK106(U_635,U_633),U_633)
| ~ sP190(U_635,U_633,U_623) )
& ! [U_628,U_632,U_634] :
( in(sK105(U_634,U_632,U_628),U_634)
| ~ sP188(U_628,U_632,U_634) )
& ! [U_628,U_632,U_634] :
( in(U_628,sK105(U_634,U_632,U_628))
| ~ sP188(U_628,U_632,U_634) )
& ! [U_621,U_629,U_628,U_632,U_634] :
( in(U_629,U_632)
| ~ in(U_621,U_634)
| ~ in(U_629,U_621)
| ~ sP189(U_621,U_629,U_628,U_632,U_634) )
& ! [U_621,U_629,U_628,U_632,U_634] :
( sP188(U_628,U_632,U_634)
| ~ in(U_628,U_632)
| ~ sP189(U_621,U_629,U_628,U_632,U_634) )
& ! [U_635,U_633,U_623] :
( U_633 = union(U_635)
| sP191(U_635,U_633)
| sP190(U_635,U_633,U_623) )
& ! [U_621,U_629,U_628,U_632,U_634] :
( sP189(U_621,U_629,U_628,U_632,U_634)
| U_632 != union(U_634) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188,sP189,sP190,sP191])],[f_122_7]) ).
cnf(f_122_9,plain,
( sP189(U_621,U_629,U_628,U_632,U_634)
| U_632 != union(U_634) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_10,plain,
( U_633 = union(U_635)
| sP191(U_635,U_633)
| sP190(U_635,U_633,U_623) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_11,plain,
( sP188(U_628,U_632,U_634)
| ~ in(U_628,U_632)
| ~ sP189(U_621,U_629,U_628,U_632,U_634) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_12,plain,
( in(U_629,U_632)
| ~ in(U_621,U_634)
| ~ in(U_629,U_621)
| ~ sP189(U_621,U_629,U_628,U_632,U_634) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_13,plain,
( in(U_628,sK105(U_634,U_632,U_628))
| ~ sP188(U_628,U_632,U_634) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_14,plain,
( in(sK105(U_634,U_632,U_628),U_634)
| ~ sP188(U_628,U_632,U_634) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_15,plain,
( in(sK106(U_635,U_633),U_633)
| ~ sP190(U_635,U_633,U_623) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_16,plain,
( ~ in(U_623,U_635)
| ~ in(sK106(U_635,U_633),U_623)
| ~ sP190(U_635,U_633,U_623) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_17,plain,
( in(sK107(U_635,U_633),sK108(U_635,U_633))
| ~ sP191(U_635,U_633) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_18,plain,
( in(sK108(U_635,U_633),U_635)
| ~ sP191(U_635,U_633) ),
inference(clausify,[status(thm)],[f_122_8]) ).
cnf(f_122_19,plain,
( ~ in(sK107(U_635,U_633),U_633)
| ~ sP191(U_635,U_633) ),
inference(clausify,[status(thm)],[f_122_8]) ).
fof(f_123_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_123_2,plain,
! [U_636] :
( ( ( well_ordering(U_636)
| ~ well_founded_relation(U_636)
| ~ connected(U_636)
| ~ antisymmetric(U_636)
| ~ transitive(U_636)
| ~ reflexive(U_636) )
& ( ( well_founded_relation(U_636)
& connected(U_636)
& antisymmetric(U_636)
& transitive(U_636)
& reflexive(U_636) )
| ~ well_ordering(U_636) ) )
| ~ relation(U_636) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_636] :
( well_founded_relation(U_636)
| ~ sP192(U_636) )
& ! [U_636] :
( connected(U_636)
| ~ sP192(U_636) )
& ! [U_636] :
( antisymmetric(U_636)
| ~ sP192(U_636) )
& ! [U_636] :
( transitive(U_636)
| ~ sP192(U_636) )
& ! [U_636] :
( reflexive(U_636)
| ~ sP192(U_636) )
& ! [U_636] :
( well_ordering(U_636)
| ~ well_founded_relation(U_636)
| ~ connected(U_636)
| ~ antisymmetric(U_636)
| ~ transitive(U_636)
| ~ reflexive(U_636)
| ~ sP193(U_636) )
& ! [U_636] :
( sP192(U_636)
| ~ well_ordering(U_636)
| ~ sP193(U_636) )
& ! [U_636] :
( sP193(U_636)
| ~ relation(U_636) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192,sP193])],[f_123_2]) ).
cnf(f_123_4,plain,
( sP193(U_636)
| ~ relation(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_5,plain,
( sP192(U_636)
| ~ well_ordering(U_636)
| ~ sP193(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_6,plain,
( well_ordering(U_636)
| ~ well_founded_relation(U_636)
| ~ connected(U_636)
| ~ antisymmetric(U_636)
| ~ transitive(U_636)
| ~ reflexive(U_636)
| ~ sP193(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_7,plain,
( reflexive(U_636)
| ~ sP192(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_8,plain,
( transitive(U_636)
| ~ sP192(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_9,plain,
( antisymmetric(U_636)
| ~ sP192(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_10,plain,
( connected(U_636)
| ~ sP192(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_11,plain,
( well_founded_relation(U_636)
| ~ sP192(U_636) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_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_124_2,plain,
! [U_640,U_639] :
( ( equipotent(U_640,U_639)
| ! [U_638] :
( relation_rng(U_638) != U_639
| relation_dom(U_638) != U_640
| ~ one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ) )
& ( ? [U_637] :
( relation_rng(U_637) = U_639
& relation_dom(U_637) = U_640
& one_to_one(U_637)
& function(U_637)
& relation(U_637) )
| ~ equipotent(U_640,U_639) ) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
( ! [U_644,U_642] :
( equipotent(U_644,U_642)
| ! [U_638] :
( relation_rng(U_638) != U_642
| relation_dom(U_638) != U_644
| ~ one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ) )
& ! [U_643,U_641] :
( ? [U_637] :
( relation_rng(U_637) = U_641
& relation_dom(U_637) = U_643
& one_to_one(U_637)
& function(U_637)
& relation(U_637) )
| ~ equipotent(U_643,U_641) ) ),
inference(miniscope,[status(thm)],[f_124_2]) ).
fof(f_124_4,plain,
( ! [U_644,U_642] :
( equipotent(U_644,U_642)
| ! [U_638] :
( relation_rng(U_638) != U_642
| relation_dom(U_638) != U_644
| ~ one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ) )
& ! [U_643,U_641] :
( ( relation_rng(sK109(U_643,U_641)) = U_641
& relation_dom(sK109(U_643,U_641)) = U_643
& one_to_one(sK109(U_643,U_641))
& function(sK109(U_643,U_641))
& relation(sK109(U_643,U_641)) )
| ~ equipotent(U_643,U_641) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_637,sK109(U_643,U_641))],[f_124_3]) ).
fof(f_124_5,plain,
( ! [U_641,U_643] :
( relation_rng(sK109(U_643,U_641)) = U_641
| ~ sP194(U_641,U_643) )
& ! [U_641,U_643] :
( relation_dom(sK109(U_643,U_641)) = U_643
| ~ sP194(U_641,U_643) )
& ! [U_641,U_643] :
( one_to_one(sK109(U_643,U_641))
| ~ sP194(U_641,U_643) )
& ! [U_641,U_643] :
( function(sK109(U_643,U_641))
| ~ sP194(U_641,U_643) )
& ! [U_641,U_643] :
( relation(sK109(U_643,U_641))
| ~ sP194(U_641,U_643) )
& ! [U_638,U_642,U_644] :
( equipotent(U_644,U_642)
| relation_rng(U_638) != U_642
| relation_dom(U_638) != U_644
| ~ one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) )
& ! [U_641,U_643] :
( sP194(U_641,U_643)
| ~ equipotent(U_643,U_641) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194])],[f_124_4]) ).
cnf(f_124_6,plain,
( sP194(U_641,U_643)
| ~ equipotent(U_643,U_641) ),
inference(clausify,[status(thm)],[f_124_5]) ).
cnf(f_124_7,plain,
( equipotent(U_644,U_642)
| relation_rng(U_638) != U_642
| relation_dom(U_638) != U_644
| ~ one_to_one(U_638)
| ~ function(U_638)
| ~ relation(U_638) ),
inference(clausify,[status(thm)],[f_124_5]) ).
cnf(f_124_8,plain,
( relation(sK109(U_643,U_641))
| ~ sP194(U_641,U_643) ),
inference(clausify,[status(thm)],[f_124_5]) ).
cnf(f_124_9,plain,
( function(sK109(U_643,U_641))
| ~ sP194(U_641,U_643) ),
inference(clausify,[status(thm)],[f_124_5]) ).
cnf(f_124_10,plain,
( one_to_one(sK109(U_643,U_641))
| ~ sP194(U_641,U_643) ),
inference(clausify,[status(thm)],[f_124_5]) ).
cnf(f_124_11,plain,
( relation_dom(sK109(U_643,U_641)) = U_643
| ~ sP194(U_641,U_643) ),
inference(clausify,[status(thm)],[f_124_5]) ).
cnf(f_124_12,plain,
( relation_rng(sK109(U_643,U_641)) = U_641
| ~ sP194(U_641,U_643) ),
inference(clausify,[status(thm)],[f_124_5]) ).
fof(f_125_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_125_2,plain,
! [U_649,U_648,U_647] :
( ( U_647 = set_difference(U_649,U_648)
| ? [U_646] :
( ( ~ in(U_646,U_647)
& ~ in(U_646,U_648)
& in(U_646,U_649) )
| ( ( in(U_646,U_648)
| ~ in(U_646,U_649) )
& in(U_646,U_647) ) ) )
& ( ! [U_645] :
( ( in(U_645,U_647)
| in(U_645,U_648)
| ~ in(U_645,U_649) )
& ( ( ~ in(U_645,U_648)
& in(U_645,U_649) )
| ~ in(U_645,U_647) ) )
| U_647 != set_difference(U_649,U_648) ) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_659,U_657,U_655] :
( U_655 = set_difference(U_659,U_657)
| ? [U_653] :
( ~ in(U_653,U_655)
& ~ in(U_653,U_657)
& in(U_653,U_659) )
| ? [U_652] :
( ( in(U_652,U_657)
| ~ in(U_652,U_659) )
& in(U_652,U_655) ) )
& ! [U_658,U_656,U_654] :
( ( ! [U_651] :
( in(U_651,U_654)
| in(U_651,U_656)
| ~ in(U_651,U_658) )
& ! [U_650] :
( ( ~ in(U_650,U_656)
& in(U_650,U_658) )
| ~ in(U_650,U_654) ) )
| U_654 != set_difference(U_658,U_656) ) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
fof(f_125_4,plain,
( ! [U_659,U_657,U_655] :
( U_655 = set_difference(U_659,U_657)
| ? [U_653] :
( ~ in(U_653,U_655)
& ~ in(U_653,U_657)
& in(U_653,U_659) )
| ( ( in(sK110(U_659,U_657,U_655),U_657)
| ~ in(sK110(U_659,U_657,U_655),U_659) )
& in(sK110(U_659,U_657,U_655),U_655) ) )
& ! [U_658,U_656,U_654] :
( ( ! [U_651] :
( in(U_651,U_654)
| in(U_651,U_656)
| ~ in(U_651,U_658) )
& ! [U_650] :
( ( ~ in(U_650,U_656)
& in(U_650,U_658) )
| ~ in(U_650,U_654) ) )
| U_654 != set_difference(U_658,U_656) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_652,sK110(U_659,U_657,U_655))],[f_125_3]) ).
fof(f_125_5,plain,
( ! [U_659,U_657,U_655] :
( U_655 = set_difference(U_659,U_657)
| ( ~ in(sK111(U_659,U_657,U_655),U_655)
& ~ in(sK111(U_659,U_657,U_655),U_657)
& in(sK111(U_659,U_657,U_655),U_659) )
| ( ( in(sK110(U_659,U_657,U_655),U_657)
| ~ in(sK110(U_659,U_657,U_655),U_659) )
& in(sK110(U_659,U_657,U_655),U_655) ) )
& ! [U_658,U_656,U_654] :
( ( ! [U_651] :
( in(U_651,U_654)
| in(U_651,U_656)
| ~ in(U_651,U_658) )
& ! [U_650] :
( ( ~ in(U_650,U_656)
& in(U_650,U_658) )
| ~ in(U_650,U_654) ) )
| U_654 != set_difference(U_658,U_656) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_653,sK111(U_659,U_657,U_655))],[f_125_4]) ).
fof(f_125_6,plain,
( ! [U_659,U_655,U_657] :
( ~ in(sK111(U_659,U_657,U_655),U_655)
| ~ sP198(U_659,U_655,U_657) )
& ! [U_659,U_655,U_657] :
( ~ in(sK111(U_659,U_657,U_655),U_657)
| ~ sP198(U_659,U_655,U_657) )
& ! [U_659,U_655,U_657] :
( in(sK111(U_659,U_657,U_655),U_659)
| ~ sP198(U_659,U_655,U_657) )
& ! [U_659,U_655,U_657] :
( in(sK110(U_659,U_657,U_655),U_657)
| ~ in(sK110(U_659,U_657,U_655),U_659)
| ~ sP197(U_659,U_655,U_657) )
& ! [U_659,U_655,U_657] :
( in(sK110(U_659,U_657,U_655),U_655)
| ~ sP197(U_659,U_655,U_657) )
& ! [U_650,U_658,U_656] :
( ~ in(U_650,U_656)
| ~ sP195(U_650,U_658,U_656) )
& ! [U_650,U_658,U_656] :
( in(U_650,U_658)
| ~ sP195(U_650,U_658,U_656) )
& ! [U_654,U_651,U_650,U_658,U_656] :
( in(U_651,U_654)
| in(U_651,U_656)
| ~ in(U_651,U_658)
| ~ sP196(U_654,U_651,U_650,U_658,U_656) )
& ! [U_654,U_651,U_650,U_658,U_656] :
( sP195(U_650,U_658,U_656)
| ~ in(U_650,U_654)
| ~ sP196(U_654,U_651,U_650,U_658,U_656) )
& ! [U_659,U_655,U_657] :
( U_655 = set_difference(U_659,U_657)
| sP198(U_659,U_655,U_657)
| sP197(U_659,U_655,U_657) )
& ! [U_654,U_651,U_650,U_658,U_656] :
( sP196(U_654,U_651,U_650,U_658,U_656)
| U_654 != set_difference(U_658,U_656) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195,sP196,sP197,sP198])],[f_125_5]) ).
cnf(f_125_7,plain,
( sP196(U_654,U_651,U_650,U_658,U_656)
| U_654 != set_difference(U_658,U_656) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_8,plain,
( U_655 = set_difference(U_659,U_657)
| sP198(U_659,U_655,U_657)
| sP197(U_659,U_655,U_657) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_9,plain,
( sP195(U_650,U_658,U_656)
| ~ in(U_650,U_654)
| ~ sP196(U_654,U_651,U_650,U_658,U_656) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_10,plain,
( in(U_651,U_654)
| in(U_651,U_656)
| ~ in(U_651,U_658)
| ~ sP196(U_654,U_651,U_650,U_658,U_656) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_11,plain,
( in(U_650,U_658)
| ~ sP195(U_650,U_658,U_656) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_12,plain,
( ~ in(U_650,U_656)
| ~ sP195(U_650,U_658,U_656) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_13,plain,
( in(sK110(U_659,U_657,U_655),U_655)
| ~ sP197(U_659,U_655,U_657) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_14,plain,
( in(sK110(U_659,U_657,U_655),U_657)
| ~ in(sK110(U_659,U_657,U_655),U_659)
| ~ sP197(U_659,U_655,U_657) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_15,plain,
( in(sK111(U_659,U_657,U_655),U_659)
| ~ sP198(U_659,U_655,U_657) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_16,plain,
( ~ in(sK111(U_659,U_657,U_655),U_657)
| ~ sP198(U_659,U_655,U_657) ),
inference(clausify,[status(thm)],[f_125_6]) ).
cnf(f_125_17,plain,
( ~ in(sK111(U_659,U_657,U_655),U_655)
| ~ sP198(U_659,U_655,U_657) ),
inference(clausify,[status(thm)],[f_125_6]) ).
fof(f_126_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_126_2,plain,
! [U_667] :
( ! [U_666] :
( ( U_666 = relation_rng(U_667)
| ? [U_665] :
( ( ~ in(U_665,U_666)
& ? [U_664] :
( U_665 = apply(U_667,U_664)
& in(U_664,relation_dom(U_667)) ) )
| ( ! [U_663] :
( U_665 != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667)) )
& in(U_665,U_666) ) ) )
& ( ! [U_662] :
( ( in(U_662,U_666)
| ! [U_661] :
( U_662 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667)) ) )
& ( ? [U_660] :
( U_662 = apply(U_667,U_660)
& in(U_660,relation_dom(U_667)) )
| ~ in(U_662,U_666) ) )
| U_666 != relation_rng(U_667) ) )
| ~ function(U_667)
| ~ relation(U_667) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_667] :
( ( ! [U_673] :
( U_673 = relation_rng(U_667)
| ? [U_671] :
( ~ in(U_671,U_673)
& ? [U_664] :
( U_671 = apply(U_667,U_664)
& in(U_664,relation_dom(U_667)) ) )
| ? [U_670] :
( ! [U_663] :
( U_670 != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667)) )
& in(U_670,U_673) ) )
& ! [U_672] :
( ( ! [U_669] :
( in(U_669,U_672)
| ! [U_661] :
( U_669 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667)) ) )
& ! [U_668] :
( ? [U_660] :
( U_668 = apply(U_667,U_660)
& in(U_660,relation_dom(U_667)) )
| ~ in(U_668,U_672) ) )
| U_672 != relation_rng(U_667) ) )
| ~ function(U_667)
| ~ relation(U_667) ),
inference(miniscope,[status(thm)],[f_126_2]) ).
fof(f_126_4,plain,
! [U_667] :
( ( ! [U_673] :
( U_673 = relation_rng(U_667)
| ? [U_671] :
( ~ in(U_671,U_673)
& ? [U_664] :
( U_671 = apply(U_667,U_664)
& in(U_664,relation_dom(U_667)) ) )
| ? [U_670] :
( ! [U_663] :
( U_670 != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667)) )
& in(U_670,U_673) ) )
& ! [U_672] :
( ( ! [U_669] :
( in(U_669,U_672)
| ! [U_661] :
( U_669 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667)) ) )
& ! [U_668] :
( ( U_668 = apply(U_667,sK112(U_667,U_672,U_668))
& in(sK112(U_667,U_672,U_668),relation_dom(U_667)) )
| ~ in(U_668,U_672) ) )
| U_672 != relation_rng(U_667) ) )
| ~ function(U_667)
| ~ relation(U_667) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_660,sK112(U_667,U_672,U_668))],[f_126_3]) ).
fof(f_126_5,plain,
! [U_667] :
( ( ! [U_673] :
( U_673 = relation_rng(U_667)
| ? [U_671] :
( ~ in(U_671,U_673)
& ? [U_664] :
( U_671 = apply(U_667,U_664)
& in(U_664,relation_dom(U_667)) ) )
| ( ! [U_663] :
( sK113(U_667,U_673) != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667)) )
& in(sK113(U_667,U_673),U_673) ) )
& ! [U_672] :
( ( ! [U_669] :
( in(U_669,U_672)
| ! [U_661] :
( U_669 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667)) ) )
& ! [U_668] :
( ( U_668 = apply(U_667,sK112(U_667,U_672,U_668))
& in(sK112(U_667,U_672,U_668),relation_dom(U_667)) )
| ~ in(U_668,U_672) ) )
| U_672 != relation_rng(U_667) ) )
| ~ function(U_667)
| ~ relation(U_667) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_670,sK113(U_667,U_673))],[f_126_4]) ).
fof(f_126_6,plain,
! [U_667] :
( ( ! [U_673] :
( U_673 = relation_rng(U_667)
| ( ~ in(sK114(U_667,U_673),U_673)
& ? [U_664] :
( sK114(U_667,U_673) = apply(U_667,U_664)
& in(U_664,relation_dom(U_667)) ) )
| ( ! [U_663] :
( sK113(U_667,U_673) != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667)) )
& in(sK113(U_667,U_673),U_673) ) )
& ! [U_672] :
( ( ! [U_669] :
( in(U_669,U_672)
| ! [U_661] :
( U_669 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667)) ) )
& ! [U_668] :
( ( U_668 = apply(U_667,sK112(U_667,U_672,U_668))
& in(sK112(U_667,U_672,U_668),relation_dom(U_667)) )
| ~ in(U_668,U_672) ) )
| U_672 != relation_rng(U_667) ) )
| ~ function(U_667)
| ~ relation(U_667) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_671,sK114(U_667,U_673))],[f_126_5]) ).
fof(f_126_7,plain,
! [U_667] :
( ( ! [U_673] :
( U_673 = relation_rng(U_667)
| ( ~ in(sK114(U_667,U_673),U_673)
& sK114(U_667,U_673) = apply(U_667,sK115(U_667,U_673))
& in(sK115(U_667,U_673),relation_dom(U_667)) )
| ( ! [U_663] :
( sK113(U_667,U_673) != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667)) )
& in(sK113(U_667,U_673),U_673) ) )
& ! [U_672] :
( ( ! [U_669] :
( in(U_669,U_672)
| ! [U_661] :
( U_669 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667)) ) )
& ! [U_668] :
( ( U_668 = apply(U_667,sK112(U_667,U_672,U_668))
& in(sK112(U_667,U_672,U_668),relation_dom(U_667)) )
| ~ in(U_668,U_672) ) )
| U_672 != relation_rng(U_667) ) )
| ~ function(U_667)
| ~ relation(U_667) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_664,sK115(U_667,U_673))],[f_126_6]) ).
fof(f_126_8,plain,
( ! [U_673,U_667] :
( ~ in(sK114(U_667,U_673),U_673)
| ~ sP202(U_673,U_667) )
& ! [U_673,U_667] :
( sK114(U_667,U_673) = apply(U_667,sK115(U_667,U_673))
| ~ sP202(U_673,U_667) )
& ! [U_673,U_667] :
( in(sK115(U_667,U_673),relation_dom(U_667))
| ~ sP202(U_673,U_667) )
& ! [U_673,U_663,U_667] :
( sK113(U_667,U_673) != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667))
| ~ sP201(U_673,U_663,U_667) )
& ! [U_673,U_663,U_667] :
( in(sK113(U_667,U_673),U_673)
| ~ sP201(U_673,U_663,U_667) )
& ! [U_668,U_672,U_667] :
( U_668 = apply(U_667,sK112(U_667,U_672,U_668))
| ~ sP199(U_668,U_672,U_667) )
& ! [U_668,U_672,U_667] :
( in(sK112(U_667,U_672,U_668),relation_dom(U_667))
| ~ sP199(U_668,U_672,U_667) )
& ! [U_669,U_668,U_672,U_661,U_667] :
( in(U_669,U_672)
| U_669 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667))
| ~ sP200(U_669,U_668,U_672,U_661,U_667) )
& ! [U_669,U_668,U_672,U_661,U_667] :
( sP199(U_668,U_672,U_667)
| ~ in(U_668,U_672)
| ~ sP200(U_669,U_668,U_672,U_661,U_667) )
& ! [U_669,U_668,U_672,U_673,U_663,U_661,U_667] :
( U_673 = relation_rng(U_667)
| sP202(U_673,U_667)
| sP201(U_673,U_663,U_667)
| ~ sP203(U_669,U_668,U_672,U_673,U_663,U_661,U_667) )
& ! [U_669,U_668,U_672,U_673,U_663,U_661,U_667] :
( sP200(U_669,U_668,U_672,U_661,U_667)
| U_672 != relation_rng(U_667)
| ~ sP203(U_669,U_668,U_672,U_673,U_663,U_661,U_667) )
& ! [U_669,U_668,U_672,U_673,U_663,U_661,U_667] :
( sP203(U_669,U_668,U_672,U_673,U_663,U_661,U_667)
| ~ function(U_667)
| ~ relation(U_667) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199,sP200,sP201,sP202,sP203])],[f_126_7]) ).
cnf(f_126_9,plain,
( sP203(U_669,U_668,U_672,U_673,U_663,U_661,U_667)
| ~ function(U_667)
| ~ relation(U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_10,plain,
( sP200(U_669,U_668,U_672,U_661,U_667)
| U_672 != relation_rng(U_667)
| ~ sP203(U_669,U_668,U_672,U_673,U_663,U_661,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_11,plain,
( U_673 = relation_rng(U_667)
| sP202(U_673,U_667)
| sP201(U_673,U_663,U_667)
| ~ sP203(U_669,U_668,U_672,U_673,U_663,U_661,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_12,plain,
( sP199(U_668,U_672,U_667)
| ~ in(U_668,U_672)
| ~ sP200(U_669,U_668,U_672,U_661,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_13,plain,
( in(U_669,U_672)
| U_669 != apply(U_667,U_661)
| ~ in(U_661,relation_dom(U_667))
| ~ sP200(U_669,U_668,U_672,U_661,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_14,plain,
( in(sK112(U_667,U_672,U_668),relation_dom(U_667))
| ~ sP199(U_668,U_672,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_15,plain,
( U_668 = apply(U_667,sK112(U_667,U_672,U_668))
| ~ sP199(U_668,U_672,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_16,plain,
( in(sK113(U_667,U_673),U_673)
| ~ sP201(U_673,U_663,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_17,plain,
( sK113(U_667,U_673) != apply(U_667,U_663)
| ~ in(U_663,relation_dom(U_667))
| ~ sP201(U_673,U_663,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_18,plain,
( in(sK115(U_667,U_673),relation_dom(U_667))
| ~ sP202(U_673,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_19,plain,
( sK114(U_667,U_673) = apply(U_667,sK115(U_667,U_673))
| ~ sP202(U_673,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
cnf(f_126_20,plain,
( ~ in(sK114(U_667,U_673),U_673)
| ~ sP202(U_673,U_667) ),
inference(clausify,[status(thm)],[f_126_8]) ).
fof(f_127_1,plain,
! [A] :
( ( ( transitive_relstr(A)
| ~ is_transitive_in(the_InternalRel(A),the_carrier(A)) )
& ( is_transitive_in(the_InternalRel(A),the_carrier(A))
| ~ transitive_relstr(A) ) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d5_orders_2]) ).
fof(f_127_2,plain,
! [U_674] :
( ( ( transitive_relstr(U_674)
| ~ is_transitive_in(the_InternalRel(U_674),the_carrier(U_674)) )
& ( is_transitive_in(the_InternalRel(U_674),the_carrier(U_674))
| ~ transitive_relstr(U_674) ) )
| ~ rel_str(U_674) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( ! [U_674] :
( transitive_relstr(U_674)
| ~ is_transitive_in(the_InternalRel(U_674),the_carrier(U_674))
| ~ sP204(U_674) )
& ! [U_674] :
( is_transitive_in(the_InternalRel(U_674),the_carrier(U_674))
| ~ transitive_relstr(U_674)
| ~ sP204(U_674) )
& ! [U_674] :
( sP204(U_674)
| ~ rel_str(U_674) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_127_2]) ).
cnf(f_127_4,plain,
( sP204(U_674)
| ~ rel_str(U_674) ),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_127_5,plain,
( is_transitive_in(the_InternalRel(U_674),the_carrier(U_674))
| ~ transitive_relstr(U_674)
| ~ sP204(U_674) ),
inference(clausify,[status(thm)],[f_127_3]) ).
cnf(f_127_6,plain,
( transitive_relstr(U_674)
| ~ is_transitive_in(the_InternalRel(U_674),the_carrier(U_674))
| ~ sP204(U_674) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [A] :
( ( A = omega
| ? [B] :
( ~ subset(A,B)
& being_limit_ordinal(B)
& in(empty_set,B)
& ordinal(B) )
| ~ ordinal(A)
| ~ being_limit_ordinal(A)
| ~ in(empty_set,A) )
& ( ( ! [B] :
( subset(A,B)
| ~ being_limit_ordinal(B)
| ~ in(empty_set,B)
| ~ ordinal(B) )
& ordinal(A)
& being_limit_ordinal(A)
& in(empty_set,A) )
| A != omega ) ),
inference(fof_nnf,[status(thm)],[d5_ordinal2]) ).
fof(f_128_2,plain,
! [U_677] :
( ( U_677 = omega
| ? [U_676] :
( ~ subset(U_677,U_676)
& being_limit_ordinal(U_676)
& in(empty_set,U_676)
& ordinal(U_676) )
| ~ ordinal(U_677)
| ~ being_limit_ordinal(U_677)
| ~ in(empty_set,U_677) )
& ( ( ! [U_675] :
( subset(U_677,U_675)
| ~ being_limit_ordinal(U_675)
| ~ in(empty_set,U_675)
| ~ ordinal(U_675) )
& ordinal(U_677)
& being_limit_ordinal(U_677)
& in(empty_set,U_677) )
| U_677 != omega ) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_679] :
( U_679 = omega
| ? [U_676] :
( ~ subset(U_679,U_676)
& being_limit_ordinal(U_676)
& in(empty_set,U_676)
& ordinal(U_676) )
| ~ ordinal(U_679)
| ~ being_limit_ordinal(U_679)
| ~ in(empty_set,U_679) )
& ! [U_678] :
( ( ! [U_675] :
( subset(U_678,U_675)
| ~ being_limit_ordinal(U_675)
| ~ in(empty_set,U_675)
| ~ ordinal(U_675) )
& ordinal(U_678)
& being_limit_ordinal(U_678)
& in(empty_set,U_678) )
| U_678 != omega ) ),
inference(miniscope,[status(thm)],[f_128_2]) ).
fof(f_128_4,plain,
( ! [U_679] :
( U_679 = omega
| ( ~ subset(U_679,sK116(U_679))
& being_limit_ordinal(sK116(U_679))
& in(empty_set,sK116(U_679))
& ordinal(sK116(U_679)) )
| ~ ordinal(U_679)
| ~ being_limit_ordinal(U_679)
| ~ in(empty_set,U_679) )
& ! [U_678] :
( ( ! [U_675] :
( subset(U_678,U_675)
| ~ being_limit_ordinal(U_675)
| ~ in(empty_set,U_675)
| ~ ordinal(U_675) )
& ordinal(U_678)
& being_limit_ordinal(U_678)
& in(empty_set,U_678) )
| U_678 != omega ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_676,sK116(U_679))],[f_128_3]) ).
fof(f_128_5,plain,
( ! [U_679] :
( ~ subset(U_679,sK116(U_679))
| ~ sP206(U_679) )
& ! [U_679] :
( being_limit_ordinal(sK116(U_679))
| ~ sP206(U_679) )
& ! [U_679] :
( in(empty_set,sK116(U_679))
| ~ sP206(U_679) )
& ! [U_679] :
( ordinal(sK116(U_679))
| ~ sP206(U_679) )
& ! [U_675,U_678] :
( subset(U_678,U_675)
| ~ being_limit_ordinal(U_675)
| ~ in(empty_set,U_675)
| ~ ordinal(U_675)
| ~ sP205(U_675,U_678) )
& ! [U_675,U_678] :
( ordinal(U_678)
| ~ sP205(U_675,U_678) )
& ! [U_675,U_678] :
( being_limit_ordinal(U_678)
| ~ sP205(U_675,U_678) )
& ! [U_675,U_678] :
( in(empty_set,U_678)
| ~ sP205(U_675,U_678) )
& ! [U_679] :
( U_679 = omega
| sP206(U_679)
| ~ ordinal(U_679)
| ~ being_limit_ordinal(U_679)
| ~ in(empty_set,U_679) )
& ! [U_675,U_678] :
( sP205(U_675,U_678)
| U_678 != omega ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205,sP206])],[f_128_4]) ).
cnf(f_128_6,plain,
( sP205(U_675,U_678)
| U_678 != omega ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_7,plain,
( U_679 = omega
| sP206(U_679)
| ~ ordinal(U_679)
| ~ being_limit_ordinal(U_679)
| ~ in(empty_set,U_679) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_8,plain,
( in(empty_set,U_678)
| ~ sP205(U_675,U_678) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_9,plain,
( being_limit_ordinal(U_678)
| ~ sP205(U_675,U_678) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_10,plain,
( ordinal(U_678)
| ~ sP205(U_675,U_678) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_11,plain,
( subset(U_678,U_675)
| ~ being_limit_ordinal(U_675)
| ~ in(empty_set,U_675)
| ~ ordinal(U_675)
| ~ sP205(U_675,U_678) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_12,plain,
( ordinal(sK116(U_679))
| ~ sP206(U_679) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_13,plain,
( in(empty_set,sK116(U_679))
| ~ sP206(U_679) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_14,plain,
( being_limit_ordinal(sK116(U_679))
| ~ sP206(U_679) ),
inference(clausify,[status(thm)],[f_128_5]) ).
cnf(f_128_15,plain,
( ~ subset(U_679,sK116(U_679))
| ~ sP206(U_679) ),
inference(clausify,[status(thm)],[f_128_5]) ).
fof(f_129_1,plain,
! [A] :
( ! [B] :
( ( ( open_subset(B,A)
| ~ in(B,the_topology(A)) )
& ( in(B,the_topology(A))
| ~ open_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d5_pre_topc]) ).
fof(f_129_2,plain,
! [U_681] :
( ! [U_680] :
( ( ( open_subset(U_680,U_681)
| ~ in(U_680,the_topology(U_681)) )
& ( in(U_680,the_topology(U_681))
| ~ open_subset(U_680,U_681) ) )
| ~ element(U_680,powerset(the_carrier(U_681))) )
| ~ top_str(U_681) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_680,U_681] :
( open_subset(U_680,U_681)
| ~ in(U_680,the_topology(U_681))
| ~ sP207(U_680,U_681) )
& ! [U_680,U_681] :
( in(U_680,the_topology(U_681))
| ~ open_subset(U_680,U_681)
| ~ sP207(U_680,U_681) )
& ! [U_680,U_681] :
( sP207(U_680,U_681)
| ~ element(U_680,powerset(the_carrier(U_681)))
| ~ top_str(U_681) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_129_2]) ).
cnf(f_129_4,plain,
( sP207(U_680,U_681)
| ~ element(U_680,powerset(the_carrier(U_681)))
| ~ top_str(U_681) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_5,plain,
( in(U_680,the_topology(U_681))
| ~ open_subset(U_680,U_681)
| ~ sP207(U_680,U_681) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_6,plain,
( open_subset(U_680,U_681)
| ~ in(U_680,the_topology(U_681))
| ~ sP207(U_680,U_681) ),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_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_130_2,plain,
! [U_689] :
( ! [U_688] :
( ( U_688 = relation_rng(U_689)
| ? [U_687] :
( ( ~ in(U_687,U_688)
& ? [U_686] : in(ordered_pair(U_686,U_687),U_689) )
| ( ! [U_685] : ~ in(ordered_pair(U_685,U_687),U_689)
& in(U_687,U_688) ) ) )
& ( ! [U_684] :
( ( in(U_684,U_688)
| ! [U_683] : ~ in(ordered_pair(U_683,U_684),U_689) )
& ( ? [U_682] : in(ordered_pair(U_682,U_684),U_689)
| ~ in(U_684,U_688) ) )
| U_688 != relation_rng(U_689) ) )
| ~ relation(U_689) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_689] :
( ( ! [U_695] :
( U_695 = relation_rng(U_689)
| ? [U_693] :
( ~ in(U_693,U_695)
& ? [U_686] : in(ordered_pair(U_686,U_693),U_689) )
| ? [U_692] :
( ! [U_685] : ~ in(ordered_pair(U_685,U_692),U_689)
& in(U_692,U_695) ) )
& ! [U_694] :
( ( ! [U_691] :
( in(U_691,U_694)
| ! [U_683] : ~ in(ordered_pair(U_683,U_691),U_689) )
& ! [U_690] :
( ? [U_682] : in(ordered_pair(U_682,U_690),U_689)
| ~ in(U_690,U_694) ) )
| U_694 != relation_rng(U_689) ) )
| ~ relation(U_689) ),
inference(miniscope,[status(thm)],[f_130_2]) ).
fof(f_130_4,plain,
! [U_689] :
( ( ! [U_695] :
( U_695 = relation_rng(U_689)
| ? [U_693] :
( ~ in(U_693,U_695)
& ? [U_686] : in(ordered_pair(U_686,U_693),U_689) )
| ? [U_692] :
( ! [U_685] : ~ in(ordered_pair(U_685,U_692),U_689)
& in(U_692,U_695) ) )
& ! [U_694] :
( ( ! [U_691] :
( in(U_691,U_694)
| ! [U_683] : ~ in(ordered_pair(U_683,U_691),U_689) )
& ! [U_690] :
( in(ordered_pair(sK117(U_689,U_694,U_690),U_690),U_689)
| ~ in(U_690,U_694) ) )
| U_694 != relation_rng(U_689) ) )
| ~ relation(U_689) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_682,sK117(U_689,U_694,U_690))],[f_130_3]) ).
fof(f_130_5,plain,
! [U_689] :
( ( ! [U_695] :
( U_695 = relation_rng(U_689)
| ? [U_693] :
( ~ in(U_693,U_695)
& ? [U_686] : in(ordered_pair(U_686,U_693),U_689) )
| ( ! [U_685] : ~ in(ordered_pair(U_685,sK118(U_689,U_695)),U_689)
& in(sK118(U_689,U_695),U_695) ) )
& ! [U_694] :
( ( ! [U_691] :
( in(U_691,U_694)
| ! [U_683] : ~ in(ordered_pair(U_683,U_691),U_689) )
& ! [U_690] :
( in(ordered_pair(sK117(U_689,U_694,U_690),U_690),U_689)
| ~ in(U_690,U_694) ) )
| U_694 != relation_rng(U_689) ) )
| ~ relation(U_689) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_692,sK118(U_689,U_695))],[f_130_4]) ).
fof(f_130_6,plain,
! [U_689] :
( ( ! [U_695] :
( U_695 = relation_rng(U_689)
| ( ~ in(sK119(U_689,U_695),U_695)
& ? [U_686] : in(ordered_pair(U_686,sK119(U_689,U_695)),U_689) )
| ( ! [U_685] : ~ in(ordered_pair(U_685,sK118(U_689,U_695)),U_689)
& in(sK118(U_689,U_695),U_695) ) )
& ! [U_694] :
( ( ! [U_691] :
( in(U_691,U_694)
| ! [U_683] : ~ in(ordered_pair(U_683,U_691),U_689) )
& ! [U_690] :
( in(ordered_pair(sK117(U_689,U_694,U_690),U_690),U_689)
| ~ in(U_690,U_694) ) )
| U_694 != relation_rng(U_689) ) )
| ~ relation(U_689) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_693,sK119(U_689,U_695))],[f_130_5]) ).
fof(f_130_7,plain,
! [U_689] :
( ( ! [U_695] :
( U_695 = relation_rng(U_689)
| ( ~ in(sK119(U_689,U_695),U_695)
& in(ordered_pair(sK120(U_689,U_695),sK119(U_689,U_695)),U_689) )
| ( ! [U_685] : ~ in(ordered_pair(U_685,sK118(U_689,U_695)),U_689)
& in(sK118(U_689,U_695),U_695) ) )
& ! [U_694] :
( ( ! [U_691] :
( in(U_691,U_694)
| ! [U_683] : ~ in(ordered_pair(U_683,U_691),U_689) )
& ! [U_690] :
( in(ordered_pair(sK117(U_689,U_694,U_690),U_690),U_689)
| ~ in(U_690,U_694) ) )
| U_694 != relation_rng(U_689) ) )
| ~ relation(U_689) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_686,sK120(U_689,U_695))],[f_130_6]) ).
fof(f_130_8,plain,
( ! [U_695,U_689] :
( ~ in(sK119(U_689,U_695),U_695)
| ~ sP210(U_695,U_689) )
& ! [U_695,U_689] :
( in(ordered_pair(sK120(U_689,U_695),sK119(U_689,U_695)),U_689)
| ~ sP210(U_695,U_689) )
& ! [U_695,U_689,U_685] :
( ~ in(ordered_pair(U_685,sK118(U_689,U_695)),U_689)
| ~ sP209(U_695,U_689,U_685) )
& ! [U_695,U_689,U_685] :
( in(sK118(U_689,U_695),U_695)
| ~ sP209(U_695,U_689,U_685) )
& ! [U_683,U_689,U_694,U_690,U_691] :
( in(U_691,U_694)
| ~ in(ordered_pair(U_683,U_691),U_689)
| ~ sP208(U_683,U_689,U_694,U_690,U_691) )
& ! [U_683,U_689,U_694,U_690,U_691] :
( in(ordered_pair(sK117(U_689,U_694,U_690),U_690),U_689)
| ~ in(U_690,U_694)
| ~ sP208(U_683,U_689,U_694,U_690,U_691) )
& ! [U_695,U_683,U_689,U_685,U_694,U_690,U_691] :
( U_695 = relation_rng(U_689)
| sP210(U_695,U_689)
| sP209(U_695,U_689,U_685)
| ~ sP211(U_695,U_683,U_689,U_685,U_694,U_690,U_691) )
& ! [U_695,U_683,U_689,U_685,U_694,U_690,U_691] :
( sP208(U_683,U_689,U_694,U_690,U_691)
| U_694 != relation_rng(U_689)
| ~ sP211(U_695,U_683,U_689,U_685,U_694,U_690,U_691) )
& ! [U_695,U_683,U_689,U_685,U_694,U_690,U_691] :
( sP211(U_695,U_683,U_689,U_685,U_694,U_690,U_691)
| ~ relation(U_689) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208,sP209,sP210,sP211])],[f_130_7]) ).
cnf(f_130_9,plain,
( sP211(U_695,U_683,U_689,U_685,U_694,U_690,U_691)
| ~ relation(U_689) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_10,plain,
( sP208(U_683,U_689,U_694,U_690,U_691)
| U_694 != relation_rng(U_689)
| ~ sP211(U_695,U_683,U_689,U_685,U_694,U_690,U_691) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_11,plain,
( U_695 = relation_rng(U_689)
| sP210(U_695,U_689)
| sP209(U_695,U_689,U_685)
| ~ sP211(U_695,U_683,U_689,U_685,U_694,U_690,U_691) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_12,plain,
( in(ordered_pair(sK117(U_689,U_694,U_690),U_690),U_689)
| ~ in(U_690,U_694)
| ~ sP208(U_683,U_689,U_694,U_690,U_691) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_13,plain,
( in(U_691,U_694)
| ~ in(ordered_pair(U_683,U_691),U_689)
| ~ sP208(U_683,U_689,U_694,U_690,U_691) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_14,plain,
( in(sK118(U_689,U_695),U_695)
| ~ sP209(U_695,U_689,U_685) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_15,plain,
( ~ in(ordered_pair(U_685,sK118(U_689,U_695)),U_689)
| ~ sP209(U_695,U_689,U_685) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_16,plain,
( in(ordered_pair(sK120(U_689,U_695),sK119(U_689,U_695)),U_689)
| ~ sP210(U_695,U_689) ),
inference(clausify,[status(thm)],[f_130_8]) ).
cnf(f_130_17,plain,
( ~ in(sK119(U_689,U_695),U_695)
| ~ sP210(U_695,U_689) ),
inference(clausify,[status(thm)],[f_130_8]) ).
fof(f_131_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_131_2,plain,
! [U_697,U_696] :
( subset_complement(U_697,U_696) = set_difference(U_697,U_696)
| ~ element(U_696,powerset(U_697)) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_697,U_696] :
( subset_complement(U_697,U_696) = set_difference(U_697,U_696)
| ~ element(U_696,powerset(U_697)) ),
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
( subset_complement(U_697,U_696) = set_difference(U_697,U_696)
| ~ element(U_696,powerset(U_697)) ),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_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_132_2,plain,
! [U_699,U_698] : ordered_pair(U_699,U_698) = unordered_pair(unordered_pair(U_699,U_698),singleton(U_699)),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_698,U_699] : ordered_pair(U_699,U_698) = unordered_pair(unordered_pair(U_699,U_698),singleton(U_699)),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
ordered_pair(U_699,U_698) = unordered_pair(unordered_pair(U_699,U_698),singleton(U_699)),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_701] :
( ! [U_700] :
( ( well_orders(U_701,U_700)
| ~ is_well_founded_in(U_701,U_700)
| ~ is_connected_in(U_701,U_700)
| ~ is_antisymmetric_in(U_701,U_700)
| ~ is_transitive_in(U_701,U_700)
| ~ is_reflexive_in(U_701,U_700) )
& ( ( is_well_founded_in(U_701,U_700)
& is_connected_in(U_701,U_700)
& is_antisymmetric_in(U_701,U_700)
& is_transitive_in(U_701,U_700)
& is_reflexive_in(U_701,U_700) )
| ~ well_orders(U_701,U_700) ) )
| ~ relation(U_701) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_701] :
( ( ! [U_703] :
( well_orders(U_701,U_703)
| ~ is_well_founded_in(U_701,U_703)
| ~ is_connected_in(U_701,U_703)
| ~ is_antisymmetric_in(U_701,U_703)
| ~ is_transitive_in(U_701,U_703)
| ~ is_reflexive_in(U_701,U_703) )
& ! [U_702] :
( ( is_well_founded_in(U_701,U_702)
& is_connected_in(U_701,U_702)
& is_antisymmetric_in(U_701,U_702)
& is_transitive_in(U_701,U_702)
& is_reflexive_in(U_701,U_702) )
| ~ well_orders(U_701,U_702) ) )
| ~ relation(U_701) ),
inference(miniscope,[status(thm)],[f_133_2]) ).
fof(f_133_4,plain,
( ! [U_701,U_702] :
( is_well_founded_in(U_701,U_702)
| ~ sP212(U_701,U_702) )
& ! [U_701,U_702] :
( is_connected_in(U_701,U_702)
| ~ sP212(U_701,U_702) )
& ! [U_701,U_702] :
( is_antisymmetric_in(U_701,U_702)
| ~ sP212(U_701,U_702) )
& ! [U_701,U_702] :
( is_transitive_in(U_701,U_702)
| ~ sP212(U_701,U_702) )
& ! [U_701,U_702] :
( is_reflexive_in(U_701,U_702)
| ~ sP212(U_701,U_702) )
& ! [U_703,U_701,U_702] :
( well_orders(U_701,U_703)
| ~ is_well_founded_in(U_701,U_703)
| ~ is_connected_in(U_701,U_703)
| ~ is_antisymmetric_in(U_701,U_703)
| ~ is_transitive_in(U_701,U_703)
| ~ is_reflexive_in(U_701,U_703)
| ~ sP213(U_703,U_701,U_702) )
& ! [U_703,U_701,U_702] :
( sP212(U_701,U_702)
| ~ well_orders(U_701,U_702)
| ~ sP213(U_703,U_701,U_702) )
& ! [U_703,U_701,U_702] :
( sP213(U_703,U_701,U_702)
| ~ relation(U_701) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212,sP213])],[f_133_3]) ).
cnf(f_133_5,plain,
( sP213(U_703,U_701,U_702)
| ~ relation(U_701) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_6,plain,
( sP212(U_701,U_702)
| ~ well_orders(U_701,U_702)
| ~ sP213(U_703,U_701,U_702) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_7,plain,
( well_orders(U_701,U_703)
| ~ is_well_founded_in(U_701,U_703)
| ~ is_connected_in(U_701,U_703)
| ~ is_antisymmetric_in(U_701,U_703)
| ~ is_transitive_in(U_701,U_703)
| ~ is_reflexive_in(U_701,U_703)
| ~ sP213(U_703,U_701,U_702) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_8,plain,
( is_reflexive_in(U_701,U_702)
| ~ sP212(U_701,U_702) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_9,plain,
( is_transitive_in(U_701,U_702)
| ~ sP212(U_701,U_702) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_10,plain,
( is_antisymmetric_in(U_701,U_702)
| ~ sP212(U_701,U_702) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_11,plain,
( is_connected_in(U_701,U_702)
| ~ sP212(U_701,U_702) ),
inference(clausify,[status(thm)],[f_133_4]) ).
cnf(f_133_12,plain,
( is_well_founded_in(U_701,U_702)
| ~ sP212(U_701,U_702) ),
inference(clausify,[status(thm)],[f_133_4]) ).
fof(f_134_1,plain,
! [A] :
( ( ( antisymmetric_relstr(A)
| ~ is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) )
& ( is_antisymmetric_in(the_InternalRel(A),the_carrier(A))
| ~ antisymmetric_relstr(A) ) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d6_orders_2]) ).
fof(f_134_2,plain,
! [U_704] :
( ( ( antisymmetric_relstr(U_704)
| ~ is_antisymmetric_in(the_InternalRel(U_704),the_carrier(U_704)) )
& ( is_antisymmetric_in(the_InternalRel(U_704),the_carrier(U_704))
| ~ antisymmetric_relstr(U_704) ) )
| ~ rel_str(U_704) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
( ! [U_704] :
( antisymmetric_relstr(U_704)
| ~ is_antisymmetric_in(the_InternalRel(U_704),the_carrier(U_704))
| ~ sP214(U_704) )
& ! [U_704] :
( is_antisymmetric_in(the_InternalRel(U_704),the_carrier(U_704))
| ~ antisymmetric_relstr(U_704)
| ~ sP214(U_704) )
& ! [U_704] :
( sP214(U_704)
| ~ rel_str(U_704) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_134_2]) ).
cnf(f_134_4,plain,
( sP214(U_704)
| ~ rel_str(U_704) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_5,plain,
( is_antisymmetric_in(the_InternalRel(U_704),the_carrier(U_704))
| ~ antisymmetric_relstr(U_704)
| ~ sP214(U_704) ),
inference(clausify,[status(thm)],[f_134_3]) ).
cnf(f_134_6,plain,
( antisymmetric_relstr(U_704)
| ~ is_antisymmetric_in(the_InternalRel(U_704),the_carrier(U_704))
| ~ sP214(U_704) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_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_135_2,plain,
! [U_705] :
( ( being_limit_ordinal(U_705)
| U_705 != union(U_705) )
& ( U_705 = union(U_705)
| ~ being_limit_ordinal(U_705) ) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ! [U_707] :
( being_limit_ordinal(U_707)
| U_707 != union(U_707) )
& ! [U_706] :
( U_706 = union(U_706)
| ~ being_limit_ordinal(U_706) ) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
fof(f_135_4,plain,
( ! [U_707] :
( being_limit_ordinal(U_707)
| U_707 != union(U_707) )
& ! [U_706] :
( U_706 = union(U_706)
| ~ being_limit_ordinal(U_706) ) ),
inference(definitional_conversion,[status(esa)],[f_135_3]) ).
cnf(f_135_5,plain,
( U_706 = union(U_706)
| ~ being_limit_ordinal(U_706) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_6,plain,
( being_limit_ordinal(U_707)
| U_707 != union(U_707) ),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_1,plain,
! [A] :
( ! [B] :
( ( ( closed_subset(B,A)
| ~ open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) )
& ( open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A)
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[d6_pre_topc]) ).
fof(f_136_2,plain,
! [U_709] :
( ! [U_708] :
( ( ( closed_subset(U_708,U_709)
| ~ open_subset(subset_difference(the_carrier(U_709),cast_as_carrier_subset(U_709),U_708),U_709) )
& ( open_subset(subset_difference(the_carrier(U_709),cast_as_carrier_subset(U_709),U_708),U_709)
| ~ closed_subset(U_708,U_709) ) )
| ~ element(U_708,powerset(the_carrier(U_709))) )
| ~ top_str(U_709) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_709,U_708] :
( closed_subset(U_708,U_709)
| ~ open_subset(subset_difference(the_carrier(U_709),cast_as_carrier_subset(U_709),U_708),U_709)
| ~ sP215(U_709,U_708) )
& ! [U_709,U_708] :
( open_subset(subset_difference(the_carrier(U_709),cast_as_carrier_subset(U_709),U_708),U_709)
| ~ closed_subset(U_708,U_709)
| ~ sP215(U_709,U_708) )
& ! [U_709,U_708] :
( sP215(U_709,U_708)
| ~ element(U_708,powerset(the_carrier(U_709)))
| ~ top_str(U_709) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_136_2]) ).
cnf(f_136_4,plain,
( sP215(U_709,U_708)
| ~ element(U_708,powerset(the_carrier(U_709)))
| ~ top_str(U_709) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_5,plain,
( open_subset(subset_difference(the_carrier(U_709),cast_as_carrier_subset(U_709),U_708),U_709)
| ~ closed_subset(U_708,U_709)
| ~ sP215(U_709,U_708) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_6,plain,
( closed_subset(U_708,U_709)
| ~ open_subset(subset_difference(the_carrier(U_709),cast_as_carrier_subset(U_709),U_708),U_709)
| ~ sP215(U_709,U_708) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_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_137_2,plain,
! [U_710] :
( relation_field(U_710) = set_union2(relation_dom(U_710),relation_rng(U_710))
| ~ relation(U_710) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_710] :
( relation_field(U_710) = set_union2(relation_dom(U_710),relation_rng(U_710))
| ~ relation(U_710) ),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
( relation_field(U_710) = set_union2(relation_dom(U_710),relation_rng(U_710))
| ~ relation(U_710) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_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_138_2,plain,
! [U_716] :
( ! [U_715] :
( ( is_connected_in(U_716,U_715)
| ? [U_714,U_713] :
( ~ in(ordered_pair(U_713,U_714),U_716)
& ~ in(ordered_pair(U_714,U_713),U_716)
& U_714 != U_713
& in(U_713,U_715)
& in(U_714,U_715) ) )
& ( ! [U_712,U_711] :
( in(ordered_pair(U_711,U_712),U_716)
| in(ordered_pair(U_712,U_711),U_716)
| U_712 = U_711
| ~ in(U_711,U_715)
| ~ in(U_712,U_715) )
| ~ is_connected_in(U_716,U_715) ) )
| ~ relation(U_716) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_716] :
( ( ! [U_718] :
( is_connected_in(U_716,U_718)
| ? [U_714] :
( ? [U_713] :
( ~ in(ordered_pair(U_713,U_714),U_716)
& ~ in(ordered_pair(U_714,U_713),U_716)
& U_714 != U_713
& in(U_713,U_718) )
& in(U_714,U_718) ) )
& ! [U_717] :
( ! [U_712] :
( ! [U_711] :
( in(ordered_pair(U_711,U_712),U_716)
| in(ordered_pair(U_712,U_711),U_716)
| U_712 = U_711
| ~ in(U_711,U_717) )
| ~ in(U_712,U_717) )
| ~ is_connected_in(U_716,U_717) ) )
| ~ relation(U_716) ),
inference(miniscope,[status(thm)],[f_138_2]) ).
fof(f_138_4,plain,
! [U_716] :
( ( ! [U_718] :
( is_connected_in(U_716,U_718)
| ( ? [U_713] :
( ~ in(ordered_pair(U_713,sK121(U_716,U_718)),U_716)
& ~ in(ordered_pair(sK121(U_716,U_718),U_713),U_716)
& sK121(U_716,U_718) != U_713
& in(U_713,U_718) )
& in(sK121(U_716,U_718),U_718) ) )
& ! [U_717] :
( ! [U_712] :
( ! [U_711] :
( in(ordered_pair(U_711,U_712),U_716)
| in(ordered_pair(U_712,U_711),U_716)
| U_712 = U_711
| ~ in(U_711,U_717) )
| ~ in(U_712,U_717) )
| ~ is_connected_in(U_716,U_717) ) )
| ~ relation(U_716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_714,sK121(U_716,U_718))],[f_138_3]) ).
fof(f_138_5,plain,
! [U_716] :
( ( ! [U_718] :
( is_connected_in(U_716,U_718)
| ( ~ in(ordered_pair(sK122(U_716,U_718),sK121(U_716,U_718)),U_716)
& ~ in(ordered_pair(sK121(U_716,U_718),sK122(U_716,U_718)),U_716)
& sK121(U_716,U_718) != sK122(U_716,U_718)
& in(sK122(U_716,U_718),U_718)
& in(sK121(U_716,U_718),U_718) ) )
& ! [U_717] :
( ! [U_712] :
( ! [U_711] :
( in(ordered_pair(U_711,U_712),U_716)
| in(ordered_pair(U_712,U_711),U_716)
| U_712 = U_711
| ~ in(U_711,U_717) )
| ~ in(U_712,U_717) )
| ~ is_connected_in(U_716,U_717) ) )
| ~ relation(U_716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_713,sK122(U_716,U_718))],[f_138_4]) ).
fof(f_138_6,plain,
( ! [U_716,U_718] :
( ~ in(ordered_pair(sK122(U_716,U_718),sK121(U_716,U_718)),U_716)
| ~ sP216(U_716,U_718) )
& ! [U_716,U_718] :
( ~ in(ordered_pair(sK121(U_716,U_718),sK122(U_716,U_718)),U_716)
| ~ sP216(U_716,U_718) )
& ! [U_716,U_718] :
( sK121(U_716,U_718) != sK122(U_716,U_718)
| ~ sP216(U_716,U_718) )
& ! [U_716,U_718] :
( in(sK122(U_716,U_718),U_718)
| ~ sP216(U_716,U_718) )
& ! [U_716,U_718] :
( in(sK121(U_716,U_718),U_718)
| ~ sP216(U_716,U_718) )
& ! [U_716,U_712,U_717,U_718,U_711] :
( is_connected_in(U_716,U_718)
| sP216(U_716,U_718)
| ~ sP217(U_716,U_712,U_717,U_718,U_711) )
& ! [U_716,U_712,U_717,U_718,U_711] :
( in(ordered_pair(U_711,U_712),U_716)
| in(ordered_pair(U_712,U_711),U_716)
| U_712 = U_711
| ~ in(U_711,U_717)
| ~ in(U_712,U_717)
| ~ is_connected_in(U_716,U_717)
| ~ sP217(U_716,U_712,U_717,U_718,U_711) )
& ! [U_716,U_712,U_717,U_718,U_711] :
( sP217(U_716,U_712,U_717,U_718,U_711)
| ~ relation(U_716) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216,sP217])],[f_138_5]) ).
cnf(f_138_7,plain,
( sP217(U_716,U_712,U_717,U_718,U_711)
| ~ relation(U_716) ),
inference(clausify,[status(thm)],[f_138_6]) ).
cnf(f_138_8,plain,
( in(ordered_pair(U_711,U_712),U_716)
| in(ordered_pair(U_712,U_711),U_716)
| U_712 = U_711
| ~ in(U_711,U_717)
| ~ in(U_712,U_717)
| ~ is_connected_in(U_716,U_717)
| ~ sP217(U_716,U_712,U_717,U_718,U_711) ),
inference(clausify,[status(thm)],[f_138_6]) ).
cnf(f_138_9,plain,
( is_connected_in(U_716,U_718)
| sP216(U_716,U_718)
| ~ sP217(U_716,U_712,U_717,U_718,U_711) ),
inference(clausify,[status(thm)],[f_138_6]) ).
cnf(f_138_10,plain,
( in(sK121(U_716,U_718),U_718)
| ~ sP216(U_716,U_718) ),
inference(clausify,[status(thm)],[f_138_6]) ).
cnf(f_138_11,plain,
( in(sK122(U_716,U_718),U_718)
| ~ sP216(U_716,U_718) ),
inference(clausify,[status(thm)],[f_138_6]) ).
cnf(f_138_12,plain,
( sK121(U_716,U_718) != sK122(U_716,U_718)
| ~ sP216(U_716,U_718) ),
inference(clausify,[status(thm)],[f_138_6]) ).
cnf(f_138_13,plain,
( ~ in(ordered_pair(sK121(U_716,U_718),sK122(U_716,U_718)),U_716)
| ~ sP216(U_716,U_718) ),
inference(clausify,[status(thm)],[f_138_6]) ).
cnf(f_138_14,plain,
( ~ in(ordered_pair(sK122(U_716,U_718),sK121(U_716,U_718)),U_716)
| ~ sP216(U_716,U_718) ),
inference(clausify,[status(thm)],[f_138_6]) ).
fof(f_139_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_139_2,plain,
! [U_720] :
( ! [U_719] : relation_restriction(U_720,U_719) = set_intersection2(U_720,cartesian_product2(U_719,U_719))
| ~ relation(U_720) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_719,U_720] :
( relation_restriction(U_720,U_719) = set_intersection2(U_720,cartesian_product2(U_719,U_719))
| ~ relation(U_720) ),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
( relation_restriction(U_720,U_719) = set_intersection2(U_720,cartesian_product2(U_719,U_719))
| ~ relation(U_720) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_726] :
( ! [U_725] :
( ( ( U_725 = relation_inverse(U_726)
| ? [U_724,U_723] :
( ( ~ in(ordered_pair(U_724,U_723),U_725)
& in(ordered_pair(U_723,U_724),U_726) )
| ( ~ in(ordered_pair(U_723,U_724),U_726)
& in(ordered_pair(U_724,U_723),U_725) ) ) )
& ( ! [U_722,U_721] :
( ( in(ordered_pair(U_722,U_721),U_725)
| ~ in(ordered_pair(U_721,U_722),U_726) )
& ( in(ordered_pair(U_721,U_722),U_726)
| ~ in(ordered_pair(U_722,U_721),U_725) ) )
| U_725 != relation_inverse(U_726) ) )
| ~ relation(U_725) )
| ~ relation(U_726) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_726] :
( ! [U_725] :
( ( ( U_725 = relation_inverse(U_726)
| ? [U_734,U_732] :
( ~ in(ordered_pair(U_734,U_732),U_725)
& in(ordered_pair(U_732,U_734),U_726) )
| ? [U_733,U_731] :
( ~ in(ordered_pair(U_731,U_733),U_726)
& in(ordered_pair(U_733,U_731),U_725) ) )
& ( ( ! [U_730,U_728] :
( in(ordered_pair(U_730,U_728),U_725)
| ~ in(ordered_pair(U_728,U_730),U_726) )
& ! [U_729,U_727] :
( in(ordered_pair(U_727,U_729),U_726)
| ~ in(ordered_pair(U_729,U_727),U_725) ) )
| U_725 != relation_inverse(U_726) ) )
| ~ relation(U_725) )
| ~ relation(U_726) ),
inference(miniscope,[status(thm)],[f_140_2]) ).
fof(f_140_4,plain,
! [U_726] :
( ! [U_725] :
( ( ( U_725 = relation_inverse(U_726)
| ? [U_734,U_732] :
( ~ in(ordered_pair(U_734,U_732),U_725)
& in(ordered_pair(U_732,U_734),U_726) )
| ? [U_731] :
( ~ in(ordered_pair(U_731,sK123(U_726,U_725)),U_726)
& in(ordered_pair(sK123(U_726,U_725),U_731),U_725) ) )
& ( ( ! [U_730,U_728] :
( in(ordered_pair(U_730,U_728),U_725)
| ~ in(ordered_pair(U_728,U_730),U_726) )
& ! [U_729,U_727] :
( in(ordered_pair(U_727,U_729),U_726)
| ~ in(ordered_pair(U_729,U_727),U_725) ) )
| U_725 != relation_inverse(U_726) ) )
| ~ relation(U_725) )
| ~ relation(U_726) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_733,sK123(U_726,U_725))],[f_140_3]) ).
fof(f_140_5,plain,
! [U_726] :
( ! [U_725] :
( ( ( U_725 = relation_inverse(U_726)
| ? [U_734,U_732] :
( ~ in(ordered_pair(U_734,U_732),U_725)
& in(ordered_pair(U_732,U_734),U_726) )
| ( ~ in(ordered_pair(sK124(U_726,U_725),sK123(U_726,U_725)),U_726)
& in(ordered_pair(sK123(U_726,U_725),sK124(U_726,U_725)),U_725) ) )
& ( ( ! [U_730,U_728] :
( in(ordered_pair(U_730,U_728),U_725)
| ~ in(ordered_pair(U_728,U_730),U_726) )
& ! [U_729,U_727] :
( in(ordered_pair(U_727,U_729),U_726)
| ~ in(ordered_pair(U_729,U_727),U_725) ) )
| U_725 != relation_inverse(U_726) ) )
| ~ relation(U_725) )
| ~ relation(U_726) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_731,sK124(U_726,U_725))],[f_140_4]) ).
fof(f_140_6,plain,
! [U_726] :
( ! [U_725] :
( ( ( U_725 = relation_inverse(U_726)
| ? [U_732] :
( ~ in(ordered_pair(sK125(U_726,U_725),U_732),U_725)
& in(ordered_pair(U_732,sK125(U_726,U_725)),U_726) )
| ( ~ in(ordered_pair(sK124(U_726,U_725),sK123(U_726,U_725)),U_726)
& in(ordered_pair(sK123(U_726,U_725),sK124(U_726,U_725)),U_725) ) )
& ( ( ! [U_730,U_728] :
( in(ordered_pair(U_730,U_728),U_725)
| ~ in(ordered_pair(U_728,U_730),U_726) )
& ! [U_729,U_727] :
( in(ordered_pair(U_727,U_729),U_726)
| ~ in(ordered_pair(U_729,U_727),U_725) ) )
| U_725 != relation_inverse(U_726) ) )
| ~ relation(U_725) )
| ~ relation(U_726) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_734,sK125(U_726,U_725))],[f_140_5]) ).
fof(f_140_7,plain,
! [U_726] :
( ! [U_725] :
( ( ( U_725 = relation_inverse(U_726)
| ( ~ in(ordered_pair(sK125(U_726,U_725),sK126(U_726,U_725)),U_725)
& in(ordered_pair(sK126(U_726,U_725),sK125(U_726,U_725)),U_726) )
| ( ~ in(ordered_pair(sK124(U_726,U_725),sK123(U_726,U_725)),U_726)
& in(ordered_pair(sK123(U_726,U_725),sK124(U_726,U_725)),U_725) ) )
& ( ( ! [U_730,U_728] :
( in(ordered_pair(U_730,U_728),U_725)
| ~ in(ordered_pair(U_728,U_730),U_726) )
& ! [U_729,U_727] :
( in(ordered_pair(U_727,U_729),U_726)
| ~ in(ordered_pair(U_729,U_727),U_725) ) )
| U_725 != relation_inverse(U_726) ) )
| ~ relation(U_725) )
| ~ relation(U_726) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_732,sK126(U_726,U_725))],[f_140_6]) ).
fof(f_140_8,plain,
( ! [U_726,U_725] :
( ~ in(ordered_pair(sK125(U_726,U_725),sK126(U_726,U_725)),U_725)
| ~ sP220(U_726,U_725) )
& ! [U_726,U_725] :
( in(ordered_pair(sK126(U_726,U_725),sK125(U_726,U_725)),U_726)
| ~ sP220(U_726,U_725) )
& ! [U_726,U_725] :
( ~ in(ordered_pair(sK124(U_726,U_725),sK123(U_726,U_725)),U_726)
| ~ sP219(U_726,U_725) )
& ! [U_726,U_725] :
( in(ordered_pair(sK123(U_726,U_725),sK124(U_726,U_725)),U_725)
| ~ sP219(U_726,U_725) )
& ! [U_730,U_727,U_729,U_726,U_728,U_725] :
( in(ordered_pair(U_730,U_728),U_725)
| ~ in(ordered_pair(U_728,U_730),U_726)
| ~ sP218(U_730,U_727,U_729,U_726,U_728,U_725) )
& ! [U_730,U_727,U_729,U_726,U_728,U_725] :
( in(ordered_pair(U_727,U_729),U_726)
| ~ in(ordered_pair(U_729,U_727),U_725)
| ~ sP218(U_730,U_727,U_729,U_726,U_728,U_725) )
& ! [U_730,U_727,U_729,U_726,U_728,U_725] :
( U_725 = relation_inverse(U_726)
| sP220(U_726,U_725)
| sP219(U_726,U_725)
| ~ sP221(U_730,U_727,U_729,U_726,U_728,U_725) )
& ! [U_730,U_727,U_729,U_726,U_728,U_725] :
( sP218(U_730,U_727,U_729,U_726,U_728,U_725)
| U_725 != relation_inverse(U_726)
| ~ sP221(U_730,U_727,U_729,U_726,U_728,U_725) )
& ! [U_730,U_727,U_729,U_726,U_728,U_725] :
( sP221(U_730,U_727,U_729,U_726,U_728,U_725)
| ~ relation(U_725)
| ~ relation(U_726) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218,sP219,sP220,sP221])],[f_140_7]) ).
cnf(f_140_9,plain,
( sP221(U_730,U_727,U_729,U_726,U_728,U_725)
| ~ relation(U_725)
| ~ relation(U_726) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_10,plain,
( sP218(U_730,U_727,U_729,U_726,U_728,U_725)
| U_725 != relation_inverse(U_726)
| ~ sP221(U_730,U_727,U_729,U_726,U_728,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_11,plain,
( U_725 = relation_inverse(U_726)
| sP220(U_726,U_725)
| sP219(U_726,U_725)
| ~ sP221(U_730,U_727,U_729,U_726,U_728,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_12,plain,
( in(ordered_pair(U_727,U_729),U_726)
| ~ in(ordered_pair(U_729,U_727),U_725)
| ~ sP218(U_730,U_727,U_729,U_726,U_728,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_13,plain,
( in(ordered_pair(U_730,U_728),U_725)
| ~ in(ordered_pair(U_728,U_730),U_726)
| ~ sP218(U_730,U_727,U_729,U_726,U_728,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_14,plain,
( in(ordered_pair(sK123(U_726,U_725),sK124(U_726,U_725)),U_725)
| ~ sP219(U_726,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_15,plain,
( ~ in(ordered_pair(sK124(U_726,U_725),sK123(U_726,U_725)),U_726)
| ~ sP219(U_726,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_16,plain,
( in(ordered_pair(sK126(U_726,U_725),sK125(U_726,U_725)),U_726)
| ~ sP220(U_726,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
cnf(f_140_17,plain,
( ~ in(ordered_pair(sK125(U_726,U_725),sK126(U_726,U_725)),U_725)
| ~ sP220(U_726,U_725) ),
inference(clausify,[status(thm)],[f_140_8]) ).
fof(f_141_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_141_2,plain,
! [U_741] :
( ! [U_740] :
( ! [U_739] :
( ( ( relation_isomorphism(U_741,U_740,U_739)
| ? [U_738,U_737] :
( ( ~ in(ordered_pair(U_738,U_737),U_741)
& in(ordered_pair(apply(U_739,U_738),apply(U_739,U_737)),U_740)
& in(U_737,relation_field(U_741))
& in(U_738,relation_field(U_741)) )
| ( ( ~ in(ordered_pair(apply(U_739,U_738),apply(U_739,U_737)),U_740)
| ~ in(U_737,relation_field(U_741))
| ~ in(U_738,relation_field(U_741)) )
& in(ordered_pair(U_738,U_737),U_741) ) )
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741) )
& ( ( ! [U_736,U_735] :
( ( in(ordered_pair(U_736,U_735),U_741)
| ~ in(ordered_pair(apply(U_739,U_736),apply(U_739,U_735)),U_740)
| ~ in(U_735,relation_field(U_741))
| ~ in(U_736,relation_field(U_741)) )
& ( ( in(ordered_pair(apply(U_739,U_736),apply(U_739,U_735)),U_740)
& in(U_735,relation_field(U_741))
& in(U_736,relation_field(U_741)) )
| ~ in(ordered_pair(U_736,U_735),U_741) ) )
& one_to_one(U_739)
& relation_rng(U_739) = relation_field(U_740)
& relation_dom(U_739) = relation_field(U_741) )
| ~ relation_isomorphism(U_741,U_740,U_739) ) )
| ~ function(U_739)
| ~ relation(U_739) )
| ~ relation(U_740) )
| ~ relation(U_741) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
! [U_741] :
( ! [U_740] :
( ! [U_739] :
( ( ( relation_isomorphism(U_741,U_740,U_739)
| ? [U_749,U_747] :
( ~ in(ordered_pair(U_749,U_747),U_741)
& in(ordered_pair(apply(U_739,U_749),apply(U_739,U_747)),U_740)
& in(U_747,relation_field(U_741))
& in(U_749,relation_field(U_741)) )
| ? [U_748,U_746] :
( ( ~ in(ordered_pair(apply(U_739,U_748),apply(U_739,U_746)),U_740)
| ~ in(U_746,relation_field(U_741))
| ~ in(U_748,relation_field(U_741)) )
& in(ordered_pair(U_748,U_746),U_741) )
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741) )
& ( ( ! [U_745,U_743] :
( in(ordered_pair(U_745,U_743),U_741)
| ~ in(ordered_pair(apply(U_739,U_745),apply(U_739,U_743)),U_740)
| ~ in(U_743,relation_field(U_741))
| ~ in(U_745,relation_field(U_741)) )
& ! [U_744,U_742] :
( ( in(ordered_pair(apply(U_739,U_744),apply(U_739,U_742)),U_740)
& in(U_742,relation_field(U_741))
& in(U_744,relation_field(U_741)) )
| ~ in(ordered_pair(U_744,U_742),U_741) )
& one_to_one(U_739)
& relation_rng(U_739) = relation_field(U_740)
& relation_dom(U_739) = relation_field(U_741) )
| ~ relation_isomorphism(U_741,U_740,U_739) ) )
| ~ function(U_739)
| ~ relation(U_739) )
| ~ relation(U_740) )
| ~ relation(U_741) ),
inference(miniscope,[status(thm)],[f_141_2]) ).
fof(f_141_4,plain,
! [U_741] :
( ! [U_740] :
( ! [U_739] :
( ( ( relation_isomorphism(U_741,U_740,U_739)
| ? [U_749,U_747] :
( ~ in(ordered_pair(U_749,U_747),U_741)
& in(ordered_pair(apply(U_739,U_749),apply(U_739,U_747)),U_740)
& in(U_747,relation_field(U_741))
& in(U_749,relation_field(U_741)) )
| ? [U_746] :
( ( ~ in(ordered_pair(apply(U_739,sK127(U_741,U_740,U_739)),apply(U_739,U_746)),U_740)
| ~ in(U_746,relation_field(U_741))
| ~ in(sK127(U_741,U_740,U_739),relation_field(U_741)) )
& in(ordered_pair(sK127(U_741,U_740,U_739),U_746),U_741) )
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741) )
& ( ( ! [U_745,U_743] :
( in(ordered_pair(U_745,U_743),U_741)
| ~ in(ordered_pair(apply(U_739,U_745),apply(U_739,U_743)),U_740)
| ~ in(U_743,relation_field(U_741))
| ~ in(U_745,relation_field(U_741)) )
& ! [U_744,U_742] :
( ( in(ordered_pair(apply(U_739,U_744),apply(U_739,U_742)),U_740)
& in(U_742,relation_field(U_741))
& in(U_744,relation_field(U_741)) )
| ~ in(ordered_pair(U_744,U_742),U_741) )
& one_to_one(U_739)
& relation_rng(U_739) = relation_field(U_740)
& relation_dom(U_739) = relation_field(U_741) )
| ~ relation_isomorphism(U_741,U_740,U_739) ) )
| ~ function(U_739)
| ~ relation(U_739) )
| ~ relation(U_740) )
| ~ relation(U_741) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_748,sK127(U_741,U_740,U_739))],[f_141_3]) ).
fof(f_141_5,plain,
! [U_741] :
( ! [U_740] :
( ! [U_739] :
( ( ( relation_isomorphism(U_741,U_740,U_739)
| ? [U_749,U_747] :
( ~ in(ordered_pair(U_749,U_747),U_741)
& in(ordered_pair(apply(U_739,U_749),apply(U_739,U_747)),U_740)
& in(U_747,relation_field(U_741))
& in(U_749,relation_field(U_741)) )
| ( ( ~ in(ordered_pair(apply(U_739,sK127(U_741,U_740,U_739)),apply(U_739,sK128(U_741,U_740,U_739))),U_740)
| ~ in(sK128(U_741,U_740,U_739),relation_field(U_741))
| ~ in(sK127(U_741,U_740,U_739),relation_field(U_741)) )
& in(ordered_pair(sK127(U_741,U_740,U_739),sK128(U_741,U_740,U_739)),U_741) )
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741) )
& ( ( ! [U_745,U_743] :
( in(ordered_pair(U_745,U_743),U_741)
| ~ in(ordered_pair(apply(U_739,U_745),apply(U_739,U_743)),U_740)
| ~ in(U_743,relation_field(U_741))
| ~ in(U_745,relation_field(U_741)) )
& ! [U_744,U_742] :
( ( in(ordered_pair(apply(U_739,U_744),apply(U_739,U_742)),U_740)
& in(U_742,relation_field(U_741))
& in(U_744,relation_field(U_741)) )
| ~ in(ordered_pair(U_744,U_742),U_741) )
& one_to_one(U_739)
& relation_rng(U_739) = relation_field(U_740)
& relation_dom(U_739) = relation_field(U_741) )
| ~ relation_isomorphism(U_741,U_740,U_739) ) )
| ~ function(U_739)
| ~ relation(U_739) )
| ~ relation(U_740) )
| ~ relation(U_741) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_746,sK128(U_741,U_740,U_739))],[f_141_4]) ).
fof(f_141_6,plain,
! [U_741] :
( ! [U_740] :
( ! [U_739] :
( ( ( relation_isomorphism(U_741,U_740,U_739)
| ? [U_747] :
( ~ in(ordered_pair(sK129(U_741,U_740,U_739),U_747),U_741)
& in(ordered_pair(apply(U_739,sK129(U_741,U_740,U_739)),apply(U_739,U_747)),U_740)
& in(U_747,relation_field(U_741))
& in(sK129(U_741,U_740,U_739),relation_field(U_741)) )
| ( ( ~ in(ordered_pair(apply(U_739,sK127(U_741,U_740,U_739)),apply(U_739,sK128(U_741,U_740,U_739))),U_740)
| ~ in(sK128(U_741,U_740,U_739),relation_field(U_741))
| ~ in(sK127(U_741,U_740,U_739),relation_field(U_741)) )
& in(ordered_pair(sK127(U_741,U_740,U_739),sK128(U_741,U_740,U_739)),U_741) )
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741) )
& ( ( ! [U_745,U_743] :
( in(ordered_pair(U_745,U_743),U_741)
| ~ in(ordered_pair(apply(U_739,U_745),apply(U_739,U_743)),U_740)
| ~ in(U_743,relation_field(U_741))
| ~ in(U_745,relation_field(U_741)) )
& ! [U_744,U_742] :
( ( in(ordered_pair(apply(U_739,U_744),apply(U_739,U_742)),U_740)
& in(U_742,relation_field(U_741))
& in(U_744,relation_field(U_741)) )
| ~ in(ordered_pair(U_744,U_742),U_741) )
& one_to_one(U_739)
& relation_rng(U_739) = relation_field(U_740)
& relation_dom(U_739) = relation_field(U_741) )
| ~ relation_isomorphism(U_741,U_740,U_739) ) )
| ~ function(U_739)
| ~ relation(U_739) )
| ~ relation(U_740) )
| ~ relation(U_741) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_749,sK129(U_741,U_740,U_739))],[f_141_5]) ).
fof(f_141_7,plain,
! [U_741] :
( ! [U_740] :
( ! [U_739] :
( ( ( relation_isomorphism(U_741,U_740,U_739)
| ( ~ in(ordered_pair(sK129(U_741,U_740,U_739),sK130(U_741,U_740,U_739)),U_741)
& in(ordered_pair(apply(U_739,sK129(U_741,U_740,U_739)),apply(U_739,sK130(U_741,U_740,U_739))),U_740)
& in(sK130(U_741,U_740,U_739),relation_field(U_741))
& in(sK129(U_741,U_740,U_739),relation_field(U_741)) )
| ( ( ~ in(ordered_pair(apply(U_739,sK127(U_741,U_740,U_739)),apply(U_739,sK128(U_741,U_740,U_739))),U_740)
| ~ in(sK128(U_741,U_740,U_739),relation_field(U_741))
| ~ in(sK127(U_741,U_740,U_739),relation_field(U_741)) )
& in(ordered_pair(sK127(U_741,U_740,U_739),sK128(U_741,U_740,U_739)),U_741) )
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741) )
& ( ( ! [U_745,U_743] :
( in(ordered_pair(U_745,U_743),U_741)
| ~ in(ordered_pair(apply(U_739,U_745),apply(U_739,U_743)),U_740)
| ~ in(U_743,relation_field(U_741))
| ~ in(U_745,relation_field(U_741)) )
& ! [U_744,U_742] :
( ( in(ordered_pair(apply(U_739,U_744),apply(U_739,U_742)),U_740)
& in(U_742,relation_field(U_741))
& in(U_744,relation_field(U_741)) )
| ~ in(ordered_pair(U_744,U_742),U_741) )
& one_to_one(U_739)
& relation_rng(U_739) = relation_field(U_740)
& relation_dom(U_739) = relation_field(U_741) )
| ~ relation_isomorphism(U_741,U_740,U_739) ) )
| ~ function(U_739)
| ~ relation(U_739) )
| ~ relation(U_740) )
| ~ relation(U_741) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_747,sK130(U_741,U_740,U_739))],[f_141_6]) ).
fof(f_141_8,plain,
( ! [U_739,U_741,U_740] :
( ~ in(ordered_pair(sK129(U_741,U_740,U_739),sK130(U_741,U_740,U_739)),U_741)
| ~ sP225(U_739,U_741,U_740) )
& ! [U_739,U_741,U_740] :
( in(ordered_pair(apply(U_739,sK129(U_741,U_740,U_739)),apply(U_739,sK130(U_741,U_740,U_739))),U_740)
| ~ sP225(U_739,U_741,U_740) )
& ! [U_739,U_741,U_740] :
( in(sK130(U_741,U_740,U_739),relation_field(U_741))
| ~ sP225(U_739,U_741,U_740) )
& ! [U_739,U_741,U_740] :
( in(sK129(U_741,U_740,U_739),relation_field(U_741))
| ~ sP225(U_739,U_741,U_740) )
& ! [U_739,U_741,U_740] :
( ~ in(ordered_pair(apply(U_739,sK127(U_741,U_740,U_739)),apply(U_739,sK128(U_741,U_740,U_739))),U_740)
| ~ in(sK128(U_741,U_740,U_739),relation_field(U_741))
| ~ in(sK127(U_741,U_740,U_739),relation_field(U_741))
| ~ sP224(U_739,U_741,U_740) )
& ! [U_739,U_741,U_740] :
( in(ordered_pair(sK127(U_741,U_740,U_739),sK128(U_741,U_740,U_739)),U_741)
| ~ sP224(U_739,U_741,U_740) )
& ! [U_739,U_741,U_742,U_744,U_740] :
( in(ordered_pair(apply(U_739,U_744),apply(U_739,U_742)),U_740)
| ~ sP222(U_739,U_741,U_742,U_744,U_740) )
& ! [U_739,U_741,U_742,U_744,U_740] :
( in(U_742,relation_field(U_741))
| ~ sP222(U_739,U_741,U_742,U_744,U_740) )
& ! [U_739,U_741,U_742,U_744,U_740] :
( in(U_744,relation_field(U_741))
| ~ sP222(U_739,U_741,U_742,U_744,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( in(ordered_pair(U_745,U_743),U_741)
| ~ in(ordered_pair(apply(U_739,U_745),apply(U_739,U_743)),U_740)
| ~ in(U_743,relation_field(U_741))
| ~ in(U_745,relation_field(U_741))
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( sP222(U_739,U_741,U_742,U_744,U_740)
| ~ in(ordered_pair(U_744,U_742),U_741)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( one_to_one(U_739)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( relation_rng(U_739) = relation_field(U_740)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( relation_dom(U_739) = relation_field(U_741)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( relation_isomorphism(U_741,U_740,U_739)
| sP225(U_739,U_741,U_740)
| sP224(U_739,U_741,U_740)
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741)
| ~ sP226(U_739,U_741,U_742,U_743,U_744,U_745,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740)
| ~ relation_isomorphism(U_741,U_740,U_739)
| ~ sP226(U_739,U_741,U_742,U_743,U_744,U_745,U_740) )
& ! [U_739,U_741,U_742,U_743,U_744,U_745,U_740] :
( sP226(U_739,U_741,U_742,U_743,U_744,U_745,U_740)
| ~ function(U_739)
| ~ relation(U_739)
| ~ relation(U_740)
| ~ relation(U_741) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222,sP223,sP224,sP225,sP226])],[f_141_7]) ).
cnf(f_141_9,plain,
( sP226(U_739,U_741,U_742,U_743,U_744,U_745,U_740)
| ~ function(U_739)
| ~ relation(U_739)
| ~ relation(U_740)
| ~ relation(U_741) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_10,plain,
( sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740)
| ~ relation_isomorphism(U_741,U_740,U_739)
| ~ sP226(U_739,U_741,U_742,U_743,U_744,U_745,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_11,plain,
( relation_isomorphism(U_741,U_740,U_739)
| sP225(U_739,U_741,U_740)
| sP224(U_739,U_741,U_740)
| ~ one_to_one(U_739)
| relation_rng(U_739) != relation_field(U_740)
| relation_dom(U_739) != relation_field(U_741)
| ~ sP226(U_739,U_741,U_742,U_743,U_744,U_745,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_12,plain,
( relation_dom(U_739) = relation_field(U_741)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_13,plain,
( relation_rng(U_739) = relation_field(U_740)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_14,plain,
( one_to_one(U_739)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_15,plain,
( sP222(U_739,U_741,U_742,U_744,U_740)
| ~ in(ordered_pair(U_744,U_742),U_741)
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_16,plain,
( in(ordered_pair(U_745,U_743),U_741)
| ~ in(ordered_pair(apply(U_739,U_745),apply(U_739,U_743)),U_740)
| ~ in(U_743,relation_field(U_741))
| ~ in(U_745,relation_field(U_741))
| ~ sP223(U_739,U_741,U_742,U_743,U_744,U_745,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_17,plain,
( in(U_744,relation_field(U_741))
| ~ sP222(U_739,U_741,U_742,U_744,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_18,plain,
( in(U_742,relation_field(U_741))
| ~ sP222(U_739,U_741,U_742,U_744,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_19,plain,
( in(ordered_pair(apply(U_739,U_744),apply(U_739,U_742)),U_740)
| ~ sP222(U_739,U_741,U_742,U_744,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_20,plain,
( in(ordered_pair(sK127(U_741,U_740,U_739),sK128(U_741,U_740,U_739)),U_741)
| ~ sP224(U_739,U_741,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_21,plain,
( ~ in(ordered_pair(apply(U_739,sK127(U_741,U_740,U_739)),apply(U_739,sK128(U_741,U_740,U_739))),U_740)
| ~ in(sK128(U_741,U_740,U_739),relation_field(U_741))
| ~ in(sK127(U_741,U_740,U_739),relation_field(U_741))
| ~ sP224(U_739,U_741,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_22,plain,
( in(sK129(U_741,U_740,U_739),relation_field(U_741))
| ~ sP225(U_739,U_741,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_23,plain,
( in(sK130(U_741,U_740,U_739),relation_field(U_741))
| ~ sP225(U_739,U_741,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_24,plain,
( in(ordered_pair(apply(U_739,sK129(U_741,U_740,U_739)),apply(U_739,sK130(U_741,U_740,U_739))),U_740)
| ~ sP225(U_739,U_741,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
cnf(f_141_25,plain,
( ~ in(ordered_pair(sK129(U_741,U_740,U_739),sK130(U_741,U_740,U_739)),U_741)
| ~ sP225(U_739,U_741,U_740) ),
inference(clausify,[status(thm)],[f_141_8]) ).
fof(f_142_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_142_2,plain,
! [U_751,U_750] :
( ( disjoint(U_751,U_750)
| set_intersection2(U_751,U_750) != empty_set )
& ( set_intersection2(U_751,U_750) = empty_set
| ~ disjoint(U_751,U_750) ) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_755,U_753] :
( disjoint(U_755,U_753)
| set_intersection2(U_755,U_753) != empty_set )
& ! [U_754,U_752] :
( set_intersection2(U_754,U_752) = empty_set
| ~ disjoint(U_754,U_752) ) ),
inference(miniscope,[status(thm)],[f_142_2]) ).
fof(f_142_4,plain,
( ! [U_755,U_753] :
( disjoint(U_755,U_753)
| set_intersection2(U_755,U_753) != empty_set )
& ! [U_752,U_754] :
( set_intersection2(U_754,U_752) = empty_set
| ~ disjoint(U_754,U_752) ) ),
inference(definitional_conversion,[status(esa)],[f_142_3]) ).
cnf(f_142_5,plain,
( set_intersection2(U_754,U_752) = empty_set
| ~ disjoint(U_754,U_752) ),
inference(clausify,[status(thm)],[f_142_4]) ).
cnf(f_142_6,plain,
( disjoint(U_755,U_753)
| set_intersection2(U_755,U_753) != empty_set ),
inference(clausify,[status(thm)],[f_142_4]) ).
fof(f_143_1,plain,
! [A] :
( relation_of_lattice(A) = a_1_0_filter_1(A)
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d8_filter_1]) ).
fof(f_143_2,plain,
! [U_756] :
( relation_of_lattice(U_756) = a_1_0_filter_1(U_756)
| ~ latt_str(U_756)
| ~ lattice(U_756)
| empty_carrier(U_756) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_756] :
( relation_of_lattice(U_756) = a_1_0_filter_1(U_756)
| ~ latt_str(U_756)
| ~ lattice(U_756)
| empty_carrier(U_756) ),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
( relation_of_lattice(U_756) = a_1_0_filter_1(U_756)
| ~ latt_str(U_756)
| ~ lattice(U_756)
| empty_carrier(U_756) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_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_144_2,plain,
! [U_761] :
( ( ( one_to_one(U_761)
| ? [U_760,U_759] :
( U_760 != U_759
& apply(U_761,U_760) = apply(U_761,U_759)
& in(U_759,relation_dom(U_761))
& in(U_760,relation_dom(U_761)) ) )
& ( ! [U_758,U_757] :
( U_758 = U_757
| apply(U_761,U_758) != apply(U_761,U_757)
| ~ in(U_757,relation_dom(U_761))
| ~ in(U_758,relation_dom(U_761)) )
| ~ one_to_one(U_761) ) )
| ~ function(U_761)
| ~ relation(U_761) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_761] :
( ( ( one_to_one(U_761)
| ? [U_759] :
( sK131(U_761) != U_759
& apply(U_761,sK131(U_761)) = apply(U_761,U_759)
& in(U_759,relation_dom(U_761))
& in(sK131(U_761),relation_dom(U_761)) ) )
& ( ! [U_758,U_757] :
( U_758 = U_757
| apply(U_761,U_758) != apply(U_761,U_757)
| ~ in(U_757,relation_dom(U_761))
| ~ in(U_758,relation_dom(U_761)) )
| ~ one_to_one(U_761) ) )
| ~ function(U_761)
| ~ relation(U_761) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_760,sK131(U_761))],[f_144_2]) ).
fof(f_144_4,plain,
! [U_761] :
( ( ( one_to_one(U_761)
| ( sK131(U_761) != sK132(U_761)
& apply(U_761,sK131(U_761)) = apply(U_761,sK132(U_761))
& in(sK132(U_761),relation_dom(U_761))
& in(sK131(U_761),relation_dom(U_761)) ) )
& ( ! [U_758,U_757] :
( U_758 = U_757
| apply(U_761,U_758) != apply(U_761,U_757)
| ~ in(U_757,relation_dom(U_761))
| ~ in(U_758,relation_dom(U_761)) )
| ~ one_to_one(U_761) ) )
| ~ function(U_761)
| ~ relation(U_761) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_759,sK132(U_761))],[f_144_3]) ).
fof(f_144_5,plain,
( ! [U_761] :
( sK131(U_761) != sK132(U_761)
| ~ sP227(U_761) )
& ! [U_761] :
( apply(U_761,sK131(U_761)) = apply(U_761,sK132(U_761))
| ~ sP227(U_761) )
& ! [U_761] :
( in(sK132(U_761),relation_dom(U_761))
| ~ sP227(U_761) )
& ! [U_761] :
( in(sK131(U_761),relation_dom(U_761))
| ~ sP227(U_761) )
& ! [U_757,U_758,U_761] :
( one_to_one(U_761)
| sP227(U_761)
| ~ sP228(U_757,U_758,U_761) )
& ! [U_757,U_758,U_761] :
( U_758 = U_757
| apply(U_761,U_758) != apply(U_761,U_757)
| ~ in(U_757,relation_dom(U_761))
| ~ in(U_758,relation_dom(U_761))
| ~ one_to_one(U_761)
| ~ sP228(U_757,U_758,U_761) )
& ! [U_757,U_758,U_761] :
( sP228(U_757,U_758,U_761)
| ~ function(U_761)
| ~ relation(U_761) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227,sP228])],[f_144_4]) ).
cnf(f_144_6,plain,
( sP228(U_757,U_758,U_761)
| ~ function(U_761)
| ~ relation(U_761) ),
inference(clausify,[status(thm)],[f_144_5]) ).
cnf(f_144_7,plain,
( U_758 = U_757
| apply(U_761,U_758) != apply(U_761,U_757)
| ~ in(U_757,relation_dom(U_761))
| ~ in(U_758,relation_dom(U_761))
| ~ one_to_one(U_761)
| ~ sP228(U_757,U_758,U_761) ),
inference(clausify,[status(thm)],[f_144_5]) ).
cnf(f_144_8,plain,
( one_to_one(U_761)
| sP227(U_761)
| ~ sP228(U_757,U_758,U_761) ),
inference(clausify,[status(thm)],[f_144_5]) ).
cnf(f_144_9,plain,
( in(sK131(U_761),relation_dom(U_761))
| ~ sP227(U_761) ),
inference(clausify,[status(thm)],[f_144_5]) ).
cnf(f_144_10,plain,
( in(sK132(U_761),relation_dom(U_761))
| ~ sP227(U_761) ),
inference(clausify,[status(thm)],[f_144_5]) ).
cnf(f_144_11,plain,
( apply(U_761,sK131(U_761)) = apply(U_761,sK132(U_761))
| ~ sP227(U_761) ),
inference(clausify,[status(thm)],[f_144_5]) ).
cnf(f_144_12,plain,
( sK131(U_761) != sK132(U_761)
| ~ sP227(U_761) ),
inference(clausify,[status(thm)],[f_144_5]) ).
fof(f_145_1,plain,
! [A] :
( ! [B,C] :
( ( ( relstr_element_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) ) )
& ( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d8_lattice3]) ).
fof(f_145_2,plain,
! [U_766] :
( ! [U_765,U_764] :
( ( ( relstr_element_smaller(U_766,U_765,U_764)
| ? [U_763] :
( ~ related(U_766,U_764,U_763)
& in(U_763,U_765)
& element(U_763,the_carrier(U_766)) ) )
& ( ! [U_762] :
( related(U_766,U_764,U_762)
| ~ in(U_762,U_765)
| ~ element(U_762,the_carrier(U_766)) )
| ~ relstr_element_smaller(U_766,U_765,U_764) ) )
| ~ element(U_764,the_carrier(U_766)) )
| ~ rel_str(U_766) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_766] :
( ! [U_765,U_764] :
( ( ( relstr_element_smaller(U_766,U_765,U_764)
| ( ~ related(U_766,U_764,sK133(U_766,U_765,U_764))
& in(sK133(U_766,U_765,U_764),U_765)
& element(sK133(U_766,U_765,U_764),the_carrier(U_766)) ) )
& ( ! [U_762] :
( related(U_766,U_764,U_762)
| ~ in(U_762,U_765)
| ~ element(U_762,the_carrier(U_766)) )
| ~ relstr_element_smaller(U_766,U_765,U_764) ) )
| ~ element(U_764,the_carrier(U_766)) )
| ~ rel_str(U_766) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_763,sK133(U_766,U_765,U_764))],[f_145_2]) ).
fof(f_145_4,plain,
( ! [U_765,U_766,U_764] :
( ~ related(U_766,U_764,sK133(U_766,U_765,U_764))
| ~ sP229(U_765,U_766,U_764) )
& ! [U_765,U_766,U_764] :
( in(sK133(U_766,U_765,U_764),U_765)
| ~ sP229(U_765,U_766,U_764) )
& ! [U_765,U_766,U_764] :
( element(sK133(U_766,U_765,U_764),the_carrier(U_766))
| ~ sP229(U_765,U_766,U_764) )
& ! [U_765,U_762,U_766,U_764] :
( relstr_element_smaller(U_766,U_765,U_764)
| sP229(U_765,U_766,U_764)
| ~ sP230(U_765,U_762,U_766,U_764) )
& ! [U_765,U_762,U_766,U_764] :
( related(U_766,U_764,U_762)
| ~ in(U_762,U_765)
| ~ element(U_762,the_carrier(U_766))
| ~ relstr_element_smaller(U_766,U_765,U_764)
| ~ sP230(U_765,U_762,U_766,U_764) )
& ! [U_765,U_762,U_766,U_764] :
( sP230(U_765,U_762,U_766,U_764)
| ~ element(U_764,the_carrier(U_766))
| ~ rel_str(U_766) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229,sP230])],[f_145_3]) ).
cnf(f_145_5,plain,
( sP230(U_765,U_762,U_766,U_764)
| ~ element(U_764,the_carrier(U_766))
| ~ rel_str(U_766) ),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_6,plain,
( related(U_766,U_764,U_762)
| ~ in(U_762,U_765)
| ~ element(U_762,the_carrier(U_766))
| ~ relstr_element_smaller(U_766,U_765,U_764)
| ~ sP230(U_765,U_762,U_766,U_764) ),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_7,plain,
( relstr_element_smaller(U_766,U_765,U_764)
| sP229(U_765,U_766,U_764)
| ~ sP230(U_765,U_762,U_766,U_764) ),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_8,plain,
( element(sK133(U_766,U_765,U_764),the_carrier(U_766))
| ~ sP229(U_765,U_766,U_764) ),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_9,plain,
( in(sK133(U_766,U_765,U_764),U_765)
| ~ sP229(U_765,U_766,U_764) ),
inference(clausify,[status(thm)],[f_145_4]) ).
cnf(f_145_10,plain,
( ~ related(U_766,U_764,sK133(U_766,U_765,U_764))
| ~ sP229(U_765,U_766,U_764) ),
inference(clausify,[status(thm)],[f_145_4]) ).
fof(f_146_1,plain,
! [A] :
( ( ( meet_absorbing(A)
| ? [B] :
( ? [C] :
( join(A,meet(A,B,C),C) != C
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) ) )
& ( ! [B] :
( ! [C] :
( join(A,meet(A,B,C),C) = C
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ meet_absorbing(A) ) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d8_lattices]) ).
fof(f_146_2,plain,
! [U_771] :
( ( ( meet_absorbing(U_771)
| ? [U_770] :
( ? [U_769] :
( join(U_771,meet(U_771,U_770,U_769),U_769) != U_769
& element(U_769,the_carrier(U_771)) )
& element(U_770,the_carrier(U_771)) ) )
& ( ! [U_768] :
( ! [U_767] :
( join(U_771,meet(U_771,U_768,U_767),U_767) = U_767
| ~ element(U_767,the_carrier(U_771)) )
| ~ element(U_768,the_carrier(U_771)) )
| ~ meet_absorbing(U_771) ) )
| ~ latt_str(U_771)
| empty_carrier(U_771) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_771] :
( ( ( meet_absorbing(U_771)
| ( ? [U_769] :
( join(U_771,meet(U_771,sK134(U_771),U_769),U_769) != U_769
& element(U_769,the_carrier(U_771)) )
& element(sK134(U_771),the_carrier(U_771)) ) )
& ( ! [U_768] :
( ! [U_767] :
( join(U_771,meet(U_771,U_768,U_767),U_767) = U_767
| ~ element(U_767,the_carrier(U_771)) )
| ~ element(U_768,the_carrier(U_771)) )
| ~ meet_absorbing(U_771) ) )
| ~ latt_str(U_771)
| empty_carrier(U_771) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_770,sK134(U_771))],[f_146_2]) ).
fof(f_146_4,plain,
! [U_771] :
( ( ( meet_absorbing(U_771)
| ( join(U_771,meet(U_771,sK134(U_771),sK135(U_771)),sK135(U_771)) != sK135(U_771)
& element(sK135(U_771),the_carrier(U_771))
& element(sK134(U_771),the_carrier(U_771)) ) )
& ( ! [U_768] :
( ! [U_767] :
( join(U_771,meet(U_771,U_768,U_767),U_767) = U_767
| ~ element(U_767,the_carrier(U_771)) )
| ~ element(U_768,the_carrier(U_771)) )
| ~ meet_absorbing(U_771) ) )
| ~ latt_str(U_771)
| empty_carrier(U_771) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_769,sK135(U_771))],[f_146_3]) ).
fof(f_146_5,plain,
( ! [U_771] :
( join(U_771,meet(U_771,sK134(U_771),sK135(U_771)),sK135(U_771)) != sK135(U_771)
| ~ sP231(U_771) )
& ! [U_771] :
( element(sK135(U_771),the_carrier(U_771))
| ~ sP231(U_771) )
& ! [U_771] :
( element(sK134(U_771),the_carrier(U_771))
| ~ sP231(U_771) )
& ! [U_771,U_768,U_767] :
( meet_absorbing(U_771)
| sP231(U_771)
| ~ sP232(U_771,U_768,U_767) )
& ! [U_771,U_768,U_767] :
( join(U_771,meet(U_771,U_768,U_767),U_767) = U_767
| ~ element(U_767,the_carrier(U_771))
| ~ element(U_768,the_carrier(U_771))
| ~ meet_absorbing(U_771)
| ~ sP232(U_771,U_768,U_767) )
& ! [U_771,U_768,U_767] :
( sP232(U_771,U_768,U_767)
| ~ latt_str(U_771)
| empty_carrier(U_771) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231,sP232])],[f_146_4]) ).
cnf(f_146_6,plain,
( sP232(U_771,U_768,U_767)
| ~ latt_str(U_771)
| empty_carrier(U_771) ),
inference(clausify,[status(thm)],[f_146_5]) ).
cnf(f_146_7,plain,
( join(U_771,meet(U_771,U_768,U_767),U_767) = U_767
| ~ element(U_767,the_carrier(U_771))
| ~ element(U_768,the_carrier(U_771))
| ~ meet_absorbing(U_771)
| ~ sP232(U_771,U_768,U_767) ),
inference(clausify,[status(thm)],[f_146_5]) ).
cnf(f_146_8,plain,
( meet_absorbing(U_771)
| sP231(U_771)
| ~ sP232(U_771,U_768,U_767) ),
inference(clausify,[status(thm)],[f_146_5]) ).
cnf(f_146_9,plain,
( element(sK134(U_771),the_carrier(U_771))
| ~ sP231(U_771) ),
inference(clausify,[status(thm)],[f_146_5]) ).
cnf(f_146_10,plain,
( element(sK135(U_771),the_carrier(U_771))
| ~ sP231(U_771) ),
inference(clausify,[status(thm)],[f_146_5]) ).
cnf(f_146_11,plain,
( join(U_771,meet(U_771,sK134(U_771),sK135(U_771)),sK135(U_771)) != sK135(U_771)
| ~ sP231(U_771) ),
inference(clausify,[status(thm)],[f_146_5]) ).
fof(f_147_1,plain,
! [A] :
( ! [B] :
( ( ( is_a_cover_of_carrier(A,B)
| cast_as_carrier_subset(A) != union_of_subsets(the_carrier(A),B) )
& ( cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B)
| ~ is_a_cover_of_carrier(A,B) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d8_pre_topc]) ).
fof(f_147_2,plain,
! [U_773] :
( ! [U_772] :
( ( ( is_a_cover_of_carrier(U_773,U_772)
| cast_as_carrier_subset(U_773) != union_of_subsets(the_carrier(U_773),U_772) )
& ( cast_as_carrier_subset(U_773) = union_of_subsets(the_carrier(U_773),U_772)
| ~ is_a_cover_of_carrier(U_773,U_772) ) )
| ~ element(U_772,powerset(powerset(the_carrier(U_773)))) )
| ~ one_sorted_str(U_773) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
( ! [U_773,U_772] :
( is_a_cover_of_carrier(U_773,U_772)
| cast_as_carrier_subset(U_773) != union_of_subsets(the_carrier(U_773),U_772)
| ~ sP233(U_773,U_772) )
& ! [U_773,U_772] :
( cast_as_carrier_subset(U_773) = union_of_subsets(the_carrier(U_773),U_772)
| ~ is_a_cover_of_carrier(U_773,U_772)
| ~ sP233(U_773,U_772) )
& ! [U_773,U_772] :
( sP233(U_773,U_772)
| ~ element(U_772,powerset(powerset(the_carrier(U_773))))
| ~ one_sorted_str(U_773) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_147_2]) ).
cnf(f_147_4,plain,
( sP233(U_773,U_772)
| ~ element(U_772,powerset(powerset(the_carrier(U_773))))
| ~ one_sorted_str(U_773) ),
inference(clausify,[status(thm)],[f_147_3]) ).
cnf(f_147_5,plain,
( cast_as_carrier_subset(U_773) = union_of_subsets(the_carrier(U_773),U_772)
| ~ is_a_cover_of_carrier(U_773,U_772)
| ~ sP233(U_773,U_772) ),
inference(clausify,[status(thm)],[f_147_3]) ).
cnf(f_147_6,plain,
( is_a_cover_of_carrier(U_773,U_772)
| cast_as_carrier_subset(U_773) != union_of_subsets(the_carrier(U_773),U_772)
| ~ sP233(U_773,U_772) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_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_148_2,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ? [U_781,U_780] :
( ( ~ in(ordered_pair(U_781,U_780),U_782)
& ? [U_779] :
( in(ordered_pair(U_779,U_780),U_783)
& in(ordered_pair(U_781,U_779),U_784) ) )
| ( ! [U_778] :
( ~ in(ordered_pair(U_778,U_780),U_783)
| ~ in(ordered_pair(U_781,U_778),U_784) )
& in(ordered_pair(U_781,U_780),U_782) ) ) )
& ( ! [U_777,U_776] :
( ( in(ordered_pair(U_777,U_776),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_776),U_783)
| ~ in(ordered_pair(U_777,U_775),U_784) ) )
& ( ? [U_774] :
( in(ordered_pair(U_774,U_776),U_783)
& in(ordered_pair(U_777,U_774),U_784) )
| ~ in(ordered_pair(U_777,U_776),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ? [U_792,U_790] :
( ~ in(ordered_pair(U_792,U_790),U_782)
& ? [U_779] :
( in(ordered_pair(U_779,U_790),U_783)
& in(ordered_pair(U_792,U_779),U_784) ) )
| ? [U_791,U_789] :
( ! [U_778] :
( ~ in(ordered_pair(U_778,U_789),U_783)
| ~ in(ordered_pair(U_791,U_778),U_784) )
& in(ordered_pair(U_791,U_789),U_782) ) )
& ( ( ! [U_788,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784) ) )
& ! [U_787,U_785] :
( ? [U_774] :
( in(ordered_pair(U_774,U_785),U_783)
& in(ordered_pair(U_787,U_774),U_784) )
| ~ in(ordered_pair(U_787,U_785),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(miniscope,[status(thm)],[f_148_2]) ).
fof(f_148_4,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ? [U_792,U_790] :
( ~ in(ordered_pair(U_792,U_790),U_782)
& ? [U_779] :
( in(ordered_pair(U_779,U_790),U_783)
& in(ordered_pair(U_792,U_779),U_784) ) )
| ? [U_791,U_789] :
( ! [U_778] :
( ~ in(ordered_pair(U_778,U_789),U_783)
| ~ in(ordered_pair(U_791,U_778),U_784) )
& in(ordered_pair(U_791,U_789),U_782) ) )
& ( ( ! [U_788,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784) ) )
& ! [U_787,U_785] :
( ( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
& in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784) )
| ~ in(ordered_pair(U_787,U_785),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_774,sK136(U_784,U_783,U_782,U_787,U_785))],[f_148_3]) ).
fof(f_148_5,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ? [U_792,U_790] :
( ~ in(ordered_pair(U_792,U_790),U_782)
& ? [U_779] :
( in(ordered_pair(U_779,U_790),U_783)
& in(ordered_pair(U_792,U_779),U_784) ) )
| ? [U_789] :
( ! [U_778] :
( ~ in(ordered_pair(U_778,U_789),U_783)
| ~ in(ordered_pair(sK137(U_784,U_783,U_782),U_778),U_784) )
& in(ordered_pair(sK137(U_784,U_783,U_782),U_789),U_782) ) )
& ( ( ! [U_788,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784) ) )
& ! [U_787,U_785] :
( ( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
& in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784) )
| ~ in(ordered_pair(U_787,U_785),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_791,sK137(U_784,U_783,U_782))],[f_148_4]) ).
fof(f_148_6,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ? [U_792,U_790] :
( ~ in(ordered_pair(U_792,U_790),U_782)
& ? [U_779] :
( in(ordered_pair(U_779,U_790),U_783)
& in(ordered_pair(U_792,U_779),U_784) ) )
| ( ! [U_778] :
( ~ in(ordered_pair(U_778,sK138(U_784,U_783,U_782)),U_783)
| ~ in(ordered_pair(sK137(U_784,U_783,U_782),U_778),U_784) )
& in(ordered_pair(sK137(U_784,U_783,U_782),sK138(U_784,U_783,U_782)),U_782) ) )
& ( ( ! [U_788,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784) ) )
& ! [U_787,U_785] :
( ( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
& in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784) )
| ~ in(ordered_pair(U_787,U_785),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_789,sK138(U_784,U_783,U_782))],[f_148_5]) ).
fof(f_148_7,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ? [U_790] :
( ~ in(ordered_pair(sK139(U_784,U_783,U_782),U_790),U_782)
& ? [U_779] :
( in(ordered_pair(U_779,U_790),U_783)
& in(ordered_pair(sK139(U_784,U_783,U_782),U_779),U_784) ) )
| ( ! [U_778] :
( ~ in(ordered_pair(U_778,sK138(U_784,U_783,U_782)),U_783)
| ~ in(ordered_pair(sK137(U_784,U_783,U_782),U_778),U_784) )
& in(ordered_pair(sK137(U_784,U_783,U_782),sK138(U_784,U_783,U_782)),U_782) ) )
& ( ( ! [U_788,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784) ) )
& ! [U_787,U_785] :
( ( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
& in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784) )
| ~ in(ordered_pair(U_787,U_785),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_792,sK139(U_784,U_783,U_782))],[f_148_6]) ).
fof(f_148_8,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ( ~ in(ordered_pair(sK139(U_784,U_783,U_782),sK140(U_784,U_783,U_782)),U_782)
& ? [U_779] :
( in(ordered_pair(U_779,sK140(U_784,U_783,U_782)),U_783)
& in(ordered_pair(sK139(U_784,U_783,U_782),U_779),U_784) ) )
| ( ! [U_778] :
( ~ in(ordered_pair(U_778,sK138(U_784,U_783,U_782)),U_783)
| ~ in(ordered_pair(sK137(U_784,U_783,U_782),U_778),U_784) )
& in(ordered_pair(sK137(U_784,U_783,U_782),sK138(U_784,U_783,U_782)),U_782) ) )
& ( ( ! [U_788,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784) ) )
& ! [U_787,U_785] :
( ( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
& in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784) )
| ~ in(ordered_pair(U_787,U_785),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_790,sK140(U_784,U_783,U_782))],[f_148_7]) ).
fof(f_148_9,plain,
! [U_784] :
( ! [U_783] :
( ! [U_782] :
( ( ( U_782 = relation_composition(U_784,U_783)
| ( ~ in(ordered_pair(sK139(U_784,U_783,U_782),sK140(U_784,U_783,U_782)),U_782)
& in(ordered_pair(sK141(U_784,U_783,U_782),sK140(U_784,U_783,U_782)),U_783)
& in(ordered_pair(sK139(U_784,U_783,U_782),sK141(U_784,U_783,U_782)),U_784) )
| ( ! [U_778] :
( ~ in(ordered_pair(U_778,sK138(U_784,U_783,U_782)),U_783)
| ~ in(ordered_pair(sK137(U_784,U_783,U_782),U_778),U_784) )
& in(ordered_pair(sK137(U_784,U_783,U_782),sK138(U_784,U_783,U_782)),U_782) ) )
& ( ( ! [U_788,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ! [U_775] :
( ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784) ) )
& ! [U_787,U_785] :
( ( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
& in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784) )
| ~ in(ordered_pair(U_787,U_785),U_782) ) )
| U_782 != relation_composition(U_784,U_783) ) )
| ~ relation(U_782) )
| ~ relation(U_783) )
| ~ relation(U_784) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_779,sK141(U_784,U_783,U_782))],[f_148_8]) ).
fof(f_148_10,plain,
( ! [U_782,U_783,U_784] :
( ~ in(ordered_pair(sK139(U_784,U_783,U_782),sK140(U_784,U_783,U_782)),U_782)
| ~ sP237(U_782,U_783,U_784) )
& ! [U_782,U_783,U_784] :
( in(ordered_pair(sK141(U_784,U_783,U_782),sK140(U_784,U_783,U_782)),U_783)
| ~ sP237(U_782,U_783,U_784) )
& ! [U_782,U_783,U_784] :
( in(ordered_pair(sK139(U_784,U_783,U_782),sK141(U_784,U_783,U_782)),U_784)
| ~ sP237(U_782,U_783,U_784) )
& ! [U_778,U_782,U_783,U_784] :
( ~ in(ordered_pair(U_778,sK138(U_784,U_783,U_782)),U_783)
| ~ in(ordered_pair(sK137(U_784,U_783,U_782),U_778),U_784)
| ~ sP236(U_778,U_782,U_783,U_784) )
& ! [U_778,U_782,U_783,U_784] :
( in(ordered_pair(sK137(U_784,U_783,U_782),sK138(U_784,U_783,U_782)),U_782)
| ~ sP236(U_778,U_782,U_783,U_784) )
& ! [U_782,U_783,U_784,U_785,U_787] :
( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
| ~ sP234(U_782,U_783,U_784,U_785,U_787) )
& ! [U_782,U_783,U_784,U_785,U_787] :
( in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784)
| ~ sP234(U_782,U_783,U_784,U_785,U_787) )
& ! [U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786] :
( in(ordered_pair(U_788,U_786),U_782)
| ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784)
| ~ sP235(U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) )
& ! [U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786] :
( sP234(U_782,U_783,U_784,U_785,U_787)
| ~ in(ordered_pair(U_787,U_785),U_782)
| ~ sP235(U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) )
& ! [U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786] :
( U_782 = relation_composition(U_784,U_783)
| sP237(U_782,U_783,U_784)
| sP236(U_778,U_782,U_783,U_784)
| ~ sP238(U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) )
& ! [U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786] :
( sP235(U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786)
| U_782 != relation_composition(U_784,U_783)
| ~ sP238(U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) )
& ! [U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786] :
( sP238(U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786)
| ~ relation(U_782)
| ~ relation(U_783)
| ~ relation(U_784) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234,sP235,sP236,sP237,sP238])],[f_148_9]) ).
cnf(f_148_11,plain,
( sP238(U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786)
| ~ relation(U_782)
| ~ relation(U_783)
| ~ relation(U_784) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_12,plain,
( sP235(U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786)
| U_782 != relation_composition(U_784,U_783)
| ~ sP238(U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_13,plain,
( U_782 = relation_composition(U_784,U_783)
| sP237(U_782,U_783,U_784)
| sP236(U_778,U_782,U_783,U_784)
| ~ sP238(U_778,U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_14,plain,
( sP234(U_782,U_783,U_784,U_785,U_787)
| ~ in(ordered_pair(U_787,U_785),U_782)
| ~ sP235(U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_15,plain,
( in(ordered_pair(U_788,U_786),U_782)
| ~ in(ordered_pair(U_775,U_786),U_783)
| ~ in(ordered_pair(U_788,U_775),U_784)
| ~ sP235(U_782,U_783,U_784,U_785,U_787,U_788,U_775,U_786) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_16,plain,
( in(ordered_pair(U_787,sK136(U_784,U_783,U_782,U_787,U_785)),U_784)
| ~ sP234(U_782,U_783,U_784,U_785,U_787) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_17,plain,
( in(ordered_pair(sK136(U_784,U_783,U_782,U_787,U_785),U_785),U_783)
| ~ sP234(U_782,U_783,U_784,U_785,U_787) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_18,plain,
( in(ordered_pair(sK137(U_784,U_783,U_782),sK138(U_784,U_783,U_782)),U_782)
| ~ sP236(U_778,U_782,U_783,U_784) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_19,plain,
( ~ in(ordered_pair(U_778,sK138(U_784,U_783,U_782)),U_783)
| ~ in(ordered_pair(sK137(U_784,U_783,U_782),U_778),U_784)
| ~ sP236(U_778,U_782,U_783,U_784) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_20,plain,
( in(ordered_pair(sK139(U_784,U_783,U_782),sK141(U_784,U_783,U_782)),U_784)
| ~ sP237(U_782,U_783,U_784) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_21,plain,
( in(ordered_pair(sK141(U_784,U_783,U_782),sK140(U_784,U_783,U_782)),U_783)
| ~ sP237(U_782,U_783,U_784) ),
inference(clausify,[status(thm)],[f_148_10]) ).
cnf(f_148_22,plain,
( ~ in(ordered_pair(sK139(U_784,U_783,U_782),sK140(U_784,U_783,U_782)),U_782)
| ~ sP237(U_782,U_783,U_784) ),
inference(clausify,[status(thm)],[f_148_10]) ).
fof(f_149_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_149_2,plain,
! [U_800] :
( ! [U_799] :
( ( is_transitive_in(U_800,U_799)
| ? [U_798,U_797,U_796] :
( ~ in(ordered_pair(U_798,U_796),U_800)
& in(ordered_pair(U_797,U_796),U_800)
& in(ordered_pair(U_798,U_797),U_800)
& in(U_796,U_799)
& in(U_797,U_799)
& in(U_798,U_799) ) )
& ( ! [U_795,U_794,U_793] :
( in(ordered_pair(U_795,U_793),U_800)
| ~ in(ordered_pair(U_794,U_793),U_800)
| ~ in(ordered_pair(U_795,U_794),U_800)
| ~ in(U_793,U_799)
| ~ in(U_794,U_799)
| ~ in(U_795,U_799) )
| ~ is_transitive_in(U_800,U_799) ) )
| ~ relation(U_800) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_800] :
( ( ! [U_802] :
( is_transitive_in(U_800,U_802)
| ? [U_798,U_797,U_796] :
( ~ in(ordered_pair(U_798,U_796),U_800)
& in(ordered_pair(U_797,U_796),U_800)
& in(ordered_pair(U_798,U_797),U_800)
& in(U_796,U_802)
& in(U_797,U_802)
& in(U_798,U_802) ) )
& ! [U_801] :
( ! [U_795,U_794,U_793] :
( in(ordered_pair(U_795,U_793),U_800)
| ~ in(ordered_pair(U_794,U_793),U_800)
| ~ in(ordered_pair(U_795,U_794),U_800)
| ~ in(U_793,U_801)
| ~ in(U_794,U_801)
| ~ in(U_795,U_801) )
| ~ is_transitive_in(U_800,U_801) ) )
| ~ relation(U_800) ),
inference(miniscope,[status(thm)],[f_149_2]) ).
fof(f_149_4,plain,
! [U_800] :
( ( ! [U_802] :
( is_transitive_in(U_800,U_802)
| ? [U_797,U_796] :
( ~ in(ordered_pair(sK142(U_800,U_802),U_796),U_800)
& in(ordered_pair(U_797,U_796),U_800)
& in(ordered_pair(sK142(U_800,U_802),U_797),U_800)
& in(U_796,U_802)
& in(U_797,U_802)
& in(sK142(U_800,U_802),U_802) ) )
& ! [U_801] :
( ! [U_795,U_794,U_793] :
( in(ordered_pair(U_795,U_793),U_800)
| ~ in(ordered_pair(U_794,U_793),U_800)
| ~ in(ordered_pair(U_795,U_794),U_800)
| ~ in(U_793,U_801)
| ~ in(U_794,U_801)
| ~ in(U_795,U_801) )
| ~ is_transitive_in(U_800,U_801) ) )
| ~ relation(U_800) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_798,sK142(U_800,U_802))],[f_149_3]) ).
fof(f_149_5,plain,
! [U_800] :
( ( ! [U_802] :
( is_transitive_in(U_800,U_802)
| ? [U_796] :
( ~ in(ordered_pair(sK142(U_800,U_802),U_796),U_800)
& in(ordered_pair(sK143(U_800,U_802),U_796),U_800)
& in(ordered_pair(sK142(U_800,U_802),sK143(U_800,U_802)),U_800)
& in(U_796,U_802)
& in(sK143(U_800,U_802),U_802)
& in(sK142(U_800,U_802),U_802) ) )
& ! [U_801] :
( ! [U_795,U_794,U_793] :
( in(ordered_pair(U_795,U_793),U_800)
| ~ in(ordered_pair(U_794,U_793),U_800)
| ~ in(ordered_pair(U_795,U_794),U_800)
| ~ in(U_793,U_801)
| ~ in(U_794,U_801)
| ~ in(U_795,U_801) )
| ~ is_transitive_in(U_800,U_801) ) )
| ~ relation(U_800) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_797,sK143(U_800,U_802))],[f_149_4]) ).
fof(f_149_6,plain,
! [U_800] :
( ( ! [U_802] :
( is_transitive_in(U_800,U_802)
| ( ~ in(ordered_pair(sK142(U_800,U_802),sK144(U_800,U_802)),U_800)
& in(ordered_pair(sK143(U_800,U_802),sK144(U_800,U_802)),U_800)
& in(ordered_pair(sK142(U_800,U_802),sK143(U_800,U_802)),U_800)
& in(sK144(U_800,U_802),U_802)
& in(sK143(U_800,U_802),U_802)
& in(sK142(U_800,U_802),U_802) ) )
& ! [U_801] :
( ! [U_795,U_794,U_793] :
( in(ordered_pair(U_795,U_793),U_800)
| ~ in(ordered_pair(U_794,U_793),U_800)
| ~ in(ordered_pair(U_795,U_794),U_800)
| ~ in(U_793,U_801)
| ~ in(U_794,U_801)
| ~ in(U_795,U_801) )
| ~ is_transitive_in(U_800,U_801) ) )
| ~ relation(U_800) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_796,sK144(U_800,U_802))],[f_149_5]) ).
fof(f_149_7,plain,
( ! [U_802,U_800] :
( ~ in(ordered_pair(sK142(U_800,U_802),sK144(U_800,U_802)),U_800)
| ~ sP239(U_802,U_800) )
& ! [U_802,U_800] :
( in(ordered_pair(sK143(U_800,U_802),sK144(U_800,U_802)),U_800)
| ~ sP239(U_802,U_800) )
& ! [U_802,U_800] :
( in(ordered_pair(sK142(U_800,U_802),sK143(U_800,U_802)),U_800)
| ~ sP239(U_802,U_800) )
& ! [U_802,U_800] :
( in(sK144(U_800,U_802),U_802)
| ~ sP239(U_802,U_800) )
& ! [U_802,U_800] :
( in(sK143(U_800,U_802),U_802)
| ~ sP239(U_802,U_800) )
& ! [U_802,U_800] :
( in(sK142(U_800,U_802),U_802)
| ~ sP239(U_802,U_800) )
& ! [U_801,U_802,U_794,U_795,U_793,U_800] :
( is_transitive_in(U_800,U_802)
| sP239(U_802,U_800)
| ~ sP240(U_801,U_802,U_794,U_795,U_793,U_800) )
& ! [U_801,U_802,U_794,U_795,U_793,U_800] :
( in(ordered_pair(U_795,U_793),U_800)
| ~ in(ordered_pair(U_794,U_793),U_800)
| ~ in(ordered_pair(U_795,U_794),U_800)
| ~ in(U_793,U_801)
| ~ in(U_794,U_801)
| ~ in(U_795,U_801)
| ~ is_transitive_in(U_800,U_801)
| ~ sP240(U_801,U_802,U_794,U_795,U_793,U_800) )
& ! [U_801,U_802,U_794,U_795,U_793,U_800] :
( sP240(U_801,U_802,U_794,U_795,U_793,U_800)
| ~ relation(U_800) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239,sP240])],[f_149_6]) ).
cnf(f_149_8,plain,
( sP240(U_801,U_802,U_794,U_795,U_793,U_800)
| ~ relation(U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_9,plain,
( in(ordered_pair(U_795,U_793),U_800)
| ~ in(ordered_pair(U_794,U_793),U_800)
| ~ in(ordered_pair(U_795,U_794),U_800)
| ~ in(U_793,U_801)
| ~ in(U_794,U_801)
| ~ in(U_795,U_801)
| ~ is_transitive_in(U_800,U_801)
| ~ sP240(U_801,U_802,U_794,U_795,U_793,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_10,plain,
( is_transitive_in(U_800,U_802)
| sP239(U_802,U_800)
| ~ sP240(U_801,U_802,U_794,U_795,U_793,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_11,plain,
( in(sK142(U_800,U_802),U_802)
| ~ sP239(U_802,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_12,plain,
( in(sK143(U_800,U_802),U_802)
| ~ sP239(U_802,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_13,plain,
( in(sK144(U_800,U_802),U_802)
| ~ sP239(U_802,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_14,plain,
( in(ordered_pair(sK142(U_800,U_802),sK143(U_800,U_802)),U_800)
| ~ sP239(U_802,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_15,plain,
( in(ordered_pair(sK143(U_800,U_802),sK144(U_800,U_802)),U_800)
| ~ sP239(U_802,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
cnf(f_149_16,plain,
( ~ in(ordered_pair(sK142(U_800,U_802),sK144(U_800,U_802)),U_800)
| ~ sP239(U_802,U_800) ),
inference(clausify,[status(thm)],[f_149_7]) ).
fof(f_150_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_150_2,plain,
! [U_807,U_806] :
( ! [U_805] :
( ( ( U_805 = complements_of_subsets(U_807,U_806)
| ? [U_804] :
( ( ( ~ in(U_804,U_805)
& in(subset_complement(U_807,U_804),U_806) )
| ( ~ in(subset_complement(U_807,U_804),U_806)
& in(U_804,U_805) ) )
& element(U_804,powerset(U_807)) ) )
& ( ! [U_803] :
( ( ( in(U_803,U_805)
| ~ in(subset_complement(U_807,U_803),U_806) )
& ( in(subset_complement(U_807,U_803),U_806)
| ~ in(U_803,U_805) ) )
| ~ element(U_803,powerset(U_807)) )
| U_805 != complements_of_subsets(U_807,U_806) ) )
| ~ element(U_805,powerset(powerset(U_807))) )
| ~ element(U_806,powerset(powerset(U_807))) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_807,U_806] :
( ! [U_805] :
( ( ( U_805 = complements_of_subsets(U_807,U_806)
| ( ( ( ~ in(sK145(U_807,U_806,U_805),U_805)
& in(subset_complement(U_807,sK145(U_807,U_806,U_805)),U_806) )
| ( ~ in(subset_complement(U_807,sK145(U_807,U_806,U_805)),U_806)
& in(sK145(U_807,U_806,U_805),U_805) ) )
& element(sK145(U_807,U_806,U_805),powerset(U_807)) ) )
& ( ! [U_803] :
( ( ( in(U_803,U_805)
| ~ in(subset_complement(U_807,U_803),U_806) )
& ( in(subset_complement(U_807,U_803),U_806)
| ~ in(U_803,U_805) ) )
| ~ element(U_803,powerset(U_807)) )
| U_805 != complements_of_subsets(U_807,U_806) ) )
| ~ element(U_805,powerset(powerset(U_807))) )
| ~ element(U_806,powerset(powerset(U_807))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_804,sK145(U_807,U_806,U_805))],[f_150_2]) ).
fof(f_150_4,plain,
( ! [U_806,U_807,U_805] :
( ~ in(sK145(U_807,U_806,U_805),U_805)
| ~ sP243(U_806,U_807,U_805) )
& ! [U_806,U_807,U_805] :
( in(subset_complement(U_807,sK145(U_807,U_806,U_805)),U_806)
| ~ sP243(U_806,U_807,U_805) )
& ! [U_806,U_807,U_805] :
( ~ in(subset_complement(U_807,sK145(U_807,U_806,U_805)),U_806)
| ~ sP242(U_806,U_807,U_805) )
& ! [U_806,U_807,U_805] :
( in(sK145(U_807,U_806,U_805),U_805)
| ~ sP242(U_806,U_807,U_805) )
& ! [U_806,U_807,U_805] :
( sP243(U_806,U_807,U_805)
| sP242(U_806,U_807,U_805)
| ~ sP244(U_806,U_807,U_805) )
& ! [U_806,U_807,U_805] :
( element(sK145(U_807,U_806,U_805),powerset(U_807))
| ~ sP244(U_806,U_807,U_805) )
& ! [U_806,U_803,U_807,U_805] :
( in(U_803,U_805)
| ~ in(subset_complement(U_807,U_803),U_806)
| ~ sP241(U_806,U_803,U_807,U_805) )
& ! [U_806,U_803,U_807,U_805] :
( in(subset_complement(U_807,U_803),U_806)
| ~ in(U_803,U_805)
| ~ sP241(U_806,U_803,U_807,U_805) )
& ! [U_806,U_803,U_807,U_805] :
( U_805 = complements_of_subsets(U_807,U_806)
| sP244(U_806,U_807,U_805)
| ~ sP245(U_806,U_803,U_807,U_805) )
& ! [U_806,U_803,U_807,U_805] :
( sP241(U_806,U_803,U_807,U_805)
| ~ element(U_803,powerset(U_807))
| U_805 != complements_of_subsets(U_807,U_806)
| ~ sP245(U_806,U_803,U_807,U_805) )
& ! [U_806,U_803,U_807,U_805] :
( sP245(U_806,U_803,U_807,U_805)
| ~ element(U_805,powerset(powerset(U_807)))
| ~ element(U_806,powerset(powerset(U_807))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241,sP242,sP243,sP244,sP245])],[f_150_3]) ).
cnf(f_150_5,plain,
( sP245(U_806,U_803,U_807,U_805)
| ~ element(U_805,powerset(powerset(U_807)))
| ~ element(U_806,powerset(powerset(U_807))) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_6,plain,
( sP241(U_806,U_803,U_807,U_805)
| ~ element(U_803,powerset(U_807))
| U_805 != complements_of_subsets(U_807,U_806)
| ~ sP245(U_806,U_803,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_7,plain,
( U_805 = complements_of_subsets(U_807,U_806)
| sP244(U_806,U_807,U_805)
| ~ sP245(U_806,U_803,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_8,plain,
( in(subset_complement(U_807,U_803),U_806)
| ~ in(U_803,U_805)
| ~ sP241(U_806,U_803,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_9,plain,
( in(U_803,U_805)
| ~ in(subset_complement(U_807,U_803),U_806)
| ~ sP241(U_806,U_803,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_10,plain,
( element(sK145(U_807,U_806,U_805),powerset(U_807))
| ~ sP244(U_806,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_11,plain,
( sP243(U_806,U_807,U_805)
| sP242(U_806,U_807,U_805)
| ~ sP244(U_806,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_12,plain,
( in(sK145(U_807,U_806,U_805),U_805)
| ~ sP242(U_806,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_13,plain,
( ~ in(subset_complement(U_807,sK145(U_807,U_806,U_805)),U_806)
| ~ sP242(U_806,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_14,plain,
( in(subset_complement(U_807,sK145(U_807,U_806,U_805)),U_806)
| ~ sP243(U_806,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
cnf(f_150_15,plain,
( ~ in(sK145(U_807,U_806,U_805),U_805)
| ~ sP243(U_806,U_807,U_805) ),
inference(clausify,[status(thm)],[f_150_4]) ).
fof(f_151_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_151_2,plain,
! [U_809,U_808] :
( ( proper_subset(U_809,U_808)
| U_809 = U_808
| ~ subset(U_809,U_808) )
& ( ( U_809 != U_808
& subset(U_809,U_808) )
| ~ proper_subset(U_809,U_808) ) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
( ! [U_813,U_811] :
( proper_subset(U_813,U_811)
| U_813 = U_811
| ~ subset(U_813,U_811) )
& ! [U_812,U_810] :
( ( U_812 != U_810
& subset(U_812,U_810) )
| ~ proper_subset(U_812,U_810) ) ),
inference(miniscope,[status(thm)],[f_151_2]) ).
fof(f_151_4,plain,
( ! [U_810,U_812] :
( U_812 != U_810
| ~ sP246(U_810,U_812) )
& ! [U_810,U_812] :
( subset(U_812,U_810)
| ~ sP246(U_810,U_812) )
& ! [U_811,U_813] :
( proper_subset(U_813,U_811)
| U_813 = U_811
| ~ subset(U_813,U_811) )
& ! [U_810,U_812] :
( sP246(U_810,U_812)
| ~ proper_subset(U_812,U_810) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246])],[f_151_3]) ).
cnf(f_151_5,plain,
( sP246(U_810,U_812)
| ~ proper_subset(U_812,U_810) ),
inference(clausify,[status(thm)],[f_151_4]) ).
cnf(f_151_6,plain,
( proper_subset(U_813,U_811)
| U_813 = U_811
| ~ subset(U_813,U_811) ),
inference(clausify,[status(thm)],[f_151_4]) ).
cnf(f_151_7,plain,
( subset(U_812,U_810)
| ~ sP246(U_810,U_812) ),
inference(clausify,[status(thm)],[f_151_4]) ).
cnf(f_151_8,plain,
( U_812 != U_810
| ~ sP246(U_810,U_812) ),
inference(clausify,[status(thm)],[f_151_4]) ).
fof(f_152_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_152_2,plain,
! [U_814] :
( function_inverse(U_814) = relation_inverse(U_814)
| ~ one_to_one(U_814)
| ~ function(U_814)
| ~ relation(U_814) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_814] :
( function_inverse(U_814) = relation_inverse(U_814)
| ~ one_to_one(U_814)
| ~ function(U_814)
| ~ relation(U_814) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( function_inverse(U_814) = relation_inverse(U_814)
| ~ one_to_one(U_814)
| ~ function(U_814)
| ~ relation(U_814) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [A] :
( ! [B,C] :
( ( ( relstr_set_smaller(A,B,C)
| ? [D] :
( ~ related(A,D,C)
& in(D,B)
& element(D,the_carrier(A)) ) )
& ( ! [D] :
( related(A,D,C)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d9_lattice3]) ).
fof(f_153_2,plain,
! [U_819] :
( ! [U_818,U_817] :
( ( ( relstr_set_smaller(U_819,U_818,U_817)
| ? [U_816] :
( ~ related(U_819,U_816,U_817)
& in(U_816,U_818)
& element(U_816,the_carrier(U_819)) ) )
& ( ! [U_815] :
( related(U_819,U_815,U_817)
| ~ in(U_815,U_818)
| ~ element(U_815,the_carrier(U_819)) )
| ~ relstr_set_smaller(U_819,U_818,U_817) ) )
| ~ element(U_817,the_carrier(U_819)) )
| ~ rel_str(U_819) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_819] :
( ! [U_818,U_817] :
( ( ( relstr_set_smaller(U_819,U_818,U_817)
| ( ~ related(U_819,sK146(U_819,U_818,U_817),U_817)
& in(sK146(U_819,U_818,U_817),U_818)
& element(sK146(U_819,U_818,U_817),the_carrier(U_819)) ) )
& ( ! [U_815] :
( related(U_819,U_815,U_817)
| ~ in(U_815,U_818)
| ~ element(U_815,the_carrier(U_819)) )
| ~ relstr_set_smaller(U_819,U_818,U_817) ) )
| ~ element(U_817,the_carrier(U_819)) )
| ~ rel_str(U_819) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_816,sK146(U_819,U_818,U_817))],[f_153_2]) ).
fof(f_153_4,plain,
( ! [U_818,U_817,U_819] :
( ~ related(U_819,sK146(U_819,U_818,U_817),U_817)
| ~ sP247(U_818,U_817,U_819) )
& ! [U_818,U_817,U_819] :
( in(sK146(U_819,U_818,U_817),U_818)
| ~ sP247(U_818,U_817,U_819) )
& ! [U_818,U_817,U_819] :
( element(sK146(U_819,U_818,U_817),the_carrier(U_819))
| ~ sP247(U_818,U_817,U_819) )
& ! [U_818,U_815,U_817,U_819] :
( relstr_set_smaller(U_819,U_818,U_817)
| sP247(U_818,U_817,U_819)
| ~ sP248(U_818,U_815,U_817,U_819) )
& ! [U_818,U_815,U_817,U_819] :
( related(U_819,U_815,U_817)
| ~ in(U_815,U_818)
| ~ element(U_815,the_carrier(U_819))
| ~ relstr_set_smaller(U_819,U_818,U_817)
| ~ sP248(U_818,U_815,U_817,U_819) )
& ! [U_818,U_815,U_817,U_819] :
( sP248(U_818,U_815,U_817,U_819)
| ~ element(U_817,the_carrier(U_819))
| ~ rel_str(U_819) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247,sP248])],[f_153_3]) ).
cnf(f_153_5,plain,
( sP248(U_818,U_815,U_817,U_819)
| ~ element(U_817,the_carrier(U_819))
| ~ rel_str(U_819) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_6,plain,
( related(U_819,U_815,U_817)
| ~ in(U_815,U_818)
| ~ element(U_815,the_carrier(U_819))
| ~ relstr_set_smaller(U_819,U_818,U_817)
| ~ sP248(U_818,U_815,U_817,U_819) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_7,plain,
( relstr_set_smaller(U_819,U_818,U_817)
| sP247(U_818,U_817,U_819)
| ~ sP248(U_818,U_815,U_817,U_819) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_8,plain,
( element(sK146(U_819,U_818,U_817),the_carrier(U_819))
| ~ sP247(U_818,U_817,U_819) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_9,plain,
( in(sK146(U_819,U_818,U_817),U_818)
| ~ sP247(U_818,U_817,U_819) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_10,plain,
( ~ related(U_819,sK146(U_819,U_818,U_817),U_817)
| ~ sP247(U_818,U_817,U_819) ),
inference(clausify,[status(thm)],[f_153_4]) ).
fof(f_154_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( related(A,B,C)
| ~ in(ordered_pair(B,C),the_InternalRel(A)) )
& ( in(ordered_pair(B,C),the_InternalRel(A))
| ~ related(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d9_orders_2]) ).
fof(f_154_2,plain,
! [U_822] :
( ! [U_821] :
( ! [U_820] :
( ( ( related(U_822,U_821,U_820)
| ~ in(ordered_pair(U_821,U_820),the_InternalRel(U_822)) )
& ( in(ordered_pair(U_821,U_820),the_InternalRel(U_822))
| ~ related(U_822,U_821,U_820) ) )
| ~ element(U_820,the_carrier(U_822)) )
| ~ element(U_821,the_carrier(U_822)) )
| ~ rel_str(U_822) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
( ! [U_820,U_821,U_822] :
( related(U_822,U_821,U_820)
| ~ in(ordered_pair(U_821,U_820),the_InternalRel(U_822))
| ~ sP249(U_820,U_821,U_822) )
& ! [U_820,U_821,U_822] :
( in(ordered_pair(U_821,U_820),the_InternalRel(U_822))
| ~ related(U_822,U_821,U_820)
| ~ sP249(U_820,U_821,U_822) )
& ! [U_820,U_821,U_822] :
( sP249(U_820,U_821,U_822)
| ~ element(U_820,the_carrier(U_822))
| ~ element(U_821,the_carrier(U_822))
| ~ rel_str(U_822) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249])],[f_154_2]) ).
cnf(f_154_4,plain,
( sP249(U_820,U_821,U_822)
| ~ element(U_820,the_carrier(U_822))
| ~ element(U_821,the_carrier(U_822))
| ~ rel_str(U_822) ),
inference(clausify,[status(thm)],[f_154_3]) ).
cnf(f_154_5,plain,
( in(ordered_pair(U_821,U_820),the_InternalRel(U_822))
| ~ related(U_822,U_821,U_820)
| ~ sP249(U_820,U_821,U_822) ),
inference(clausify,[status(thm)],[f_154_3]) ).
cnf(f_154_6,plain,
( related(U_822,U_821,U_820)
| ~ in(ordered_pair(U_821,U_820),the_InternalRel(U_822))
| ~ sP249(U_820,U_821,U_822) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_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_155_2,plain,
! [U_823] :
( ( ( reflexive(U_823)
| ~ is_reflexive_in(U_823,relation_field(U_823)) )
& ( is_reflexive_in(U_823,relation_field(U_823))
| ~ reflexive(U_823) ) )
| ~ relation(U_823) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
( ! [U_823] :
( reflexive(U_823)
| ~ is_reflexive_in(U_823,relation_field(U_823))
| ~ sP250(U_823) )
& ! [U_823] :
( is_reflexive_in(U_823,relation_field(U_823))
| ~ reflexive(U_823)
| ~ sP250(U_823) )
& ! [U_823] :
( sP250(U_823)
| ~ relation(U_823) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP250])],[f_155_2]) ).
cnf(f_155_4,plain,
( sP250(U_823)
| ~ relation(U_823) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_5,plain,
( is_reflexive_in(U_823,relation_field(U_823))
| ~ reflexive(U_823)
| ~ sP250(U_823) ),
inference(clausify,[status(thm)],[f_155_3]) ).
cnf(f_155_6,plain,
( reflexive(U_823)
| ~ is_reflexive_in(U_823,relation_field(U_823))
| ~ sP250(U_823) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [A,B] :
( ( rel_str(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[dt_g1_orders_2]) ).
fof(f_156_2,plain,
! [U_825,U_824] :
( ( rel_str(rel_str_of(U_825,U_824))
& strict_rel_str(rel_str_of(U_825,U_824)) )
| ~ relation_of2(U_824,U_825,U_825) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
( ! [U_825,U_824] :
( rel_str(rel_str_of(U_825,U_824))
| ~ sP251(U_825,U_824) )
& ! [U_825,U_824] :
( strict_rel_str(rel_str_of(U_825,U_824))
| ~ sP251(U_825,U_824) )
& ! [U_825,U_824] :
( sP251(U_825,U_824)
| ~ relation_of2(U_824,U_825,U_825) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251])],[f_156_2]) ).
cnf(f_156_4,plain,
( sP251(U_825,U_824)
| ~ relation_of2(U_824,U_825,U_825) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_5,plain,
( strict_rel_str(rel_str_of(U_825,U_824))
| ~ sP251(U_825,U_824) ),
inference(clausify,[status(thm)],[f_156_3]) ).
cnf(f_156_6,plain,
( rel_str(rel_str_of(U_825,U_824))
| ~ sP251(U_825,U_824) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
! [A,B,C] :
( ( latt_str(latt_str_of(A,B,C))
& strict_latt_str(latt_str_of(A,B,C)) )
| ~ relation_of2(C,cartesian_product2(A,A),A)
| ~ quasi_total(C,cartesian_product2(A,A),A)
| ~ function(C)
| ~ relation_of2(B,cartesian_product2(A,A),A)
| ~ quasi_total(B,cartesian_product2(A,A),A)
| ~ function(B) ),
inference(fof_nnf,[status(thm)],[dt_g3_lattices]) ).
fof(f_157_2,plain,
! [U_828,U_827,U_826] :
( ( latt_str(latt_str_of(U_828,U_827,U_826))
& strict_latt_str(latt_str_of(U_828,U_827,U_826)) )
| ~ relation_of2(U_826,cartesian_product2(U_828,U_828),U_828)
| ~ quasi_total(U_826,cartesian_product2(U_828,U_828),U_828)
| ~ function(U_826)
| ~ relation_of2(U_827,cartesian_product2(U_828,U_828),U_828)
| ~ quasi_total(U_827,cartesian_product2(U_828,U_828),U_828)
| ~ function(U_827) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_826,U_828,U_827] :
( latt_str(latt_str_of(U_828,U_827,U_826))
| ~ sP252(U_826,U_828,U_827) )
& ! [U_826,U_828,U_827] :
( strict_latt_str(latt_str_of(U_828,U_827,U_826))
| ~ sP252(U_826,U_828,U_827) )
& ! [U_826,U_828,U_827] :
( sP252(U_826,U_828,U_827)
| ~ relation_of2(U_826,cartesian_product2(U_828,U_828),U_828)
| ~ quasi_total(U_826,cartesian_product2(U_828,U_828),U_828)
| ~ function(U_826)
| ~ relation_of2(U_827,cartesian_product2(U_828,U_828),U_828)
| ~ quasi_total(U_827,cartesian_product2(U_828,U_828),U_828)
| ~ function(U_827) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_157_2]) ).
cnf(f_157_4,plain,
( sP252(U_826,U_828,U_827)
| ~ relation_of2(U_826,cartesian_product2(U_828,U_828),U_828)
| ~ quasi_total(U_826,cartesian_product2(U_828,U_828),U_828)
| ~ function(U_826)
| ~ relation_of2(U_827,cartesian_product2(U_828,U_828),U_828)
| ~ quasi_total(U_827,cartesian_product2(U_828,U_828),U_828)
| ~ function(U_827) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( strict_latt_str(latt_str_of(U_828,U_827,U_826))
| ~ sP252(U_826,U_828,U_827) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( latt_str(latt_str_of(U_828,U_827,U_826))
| ~ sP252(U_826,U_828,U_827) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [A,B,C,D] :
( element(k10_filter_1(A,B,C,D),the_carrier(k8_filter_1(A,B)))
| ~ element(D,the_carrier(B))
| ~ element(C,the_carrier(A))
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B)
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k10_filter_1]) ).
fof(f_158_2,plain,
! [U_832,U_831,U_830,U_829] :
( element(k10_filter_1(U_832,U_831,U_830,U_829),the_carrier(k8_filter_1(U_832,U_831)))
| ~ element(U_829,the_carrier(U_831))
| ~ element(U_830,the_carrier(U_832))
| ~ latt_str(U_831)
| ~ lattice(U_831)
| empty_carrier(U_831)
| ~ latt_str(U_832)
| ~ lattice(U_832)
| empty_carrier(U_832) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_829,U_830,U_831,U_832] :
( element(k10_filter_1(U_832,U_831,U_830,U_829),the_carrier(k8_filter_1(U_832,U_831)))
| ~ element(U_829,the_carrier(U_831))
| ~ element(U_830,the_carrier(U_832))
| ~ latt_str(U_831)
| ~ lattice(U_831)
| empty_carrier(U_831)
| ~ latt_str(U_832)
| ~ lattice(U_832)
| empty_carrier(U_832) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( element(k10_filter_1(U_832,U_831,U_830,U_829),the_carrier(k8_filter_1(U_832,U_831)))
| ~ element(U_829,the_carrier(U_831))
| ~ element(U_830,the_carrier(U_832))
| ~ latt_str(U_831)
| ~ lattice(U_831)
| empty_carrier(U_831)
| ~ latt_str(U_832)
| ~ lattice(U_832)
| empty_carrier(U_832) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
fof(f_159_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_159_1]) ).
cnf(f_159_3,plain,
$true,
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [A,B] :
( element(join_of_latt_set(A,B),the_carrier(A))
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k15_lattice3]) ).
fof(f_160_2,plain,
! [U_834,U_833] :
( element(join_of_latt_set(U_834,U_833),the_carrier(U_834))
| ~ latt_str(U_834)
| empty_carrier(U_834) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_834] :
( ! [U_833] : element(join_of_latt_set(U_834,U_833),the_carrier(U_834))
| ~ latt_str(U_834)
| empty_carrier(U_834) ),
inference(miniscope,[status(thm)],[f_160_2]) ).
fof(f_160_4,plain,
! [U_833,U_834] :
( element(join_of_latt_set(U_834,U_833),the_carrier(U_834))
| ~ latt_str(U_834)
| empty_carrier(U_834) ),
inference(definitional_conversion,[status(esa)],[f_160_3]) ).
cnf(f_160_5,plain,
( element(join_of_latt_set(U_834,U_833),the_carrier(U_834))
| ~ latt_str(U_834)
| empty_carrier(U_834) ),
inference(clausify,[status(thm)],[f_160_4]) ).
fof(f_161_1,plain,
! [A,B] :
( element(meet_of_latt_set(A,B),the_carrier(A))
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k16_lattice3]) ).
fof(f_161_2,plain,
! [U_836,U_835] :
( element(meet_of_latt_set(U_836,U_835),the_carrier(U_836))
| ~ latt_str(U_836)
| empty_carrier(U_836) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_836] :
( ! [U_835] : element(meet_of_latt_set(U_836,U_835),the_carrier(U_836))
| ~ latt_str(U_836)
| empty_carrier(U_836) ),
inference(miniscope,[status(thm)],[f_161_2]) ).
fof(f_161_4,plain,
! [U_836,U_835] :
( element(meet_of_latt_set(U_836,U_835),the_carrier(U_836))
| ~ latt_str(U_836)
| empty_carrier(U_836) ),
inference(definitional_conversion,[status(esa)],[f_161_3]) ).
cnf(f_161_5,plain,
( element(meet_of_latt_set(U_836,U_835),the_carrier(U_836))
| ~ latt_str(U_836)
| empty_carrier(U_836) ),
inference(clausify,[status(thm)],[f_161_4]) ).
fof(f_162_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_binop_1]) ).
fof(f_162_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_162_1]) ).
cnf(f_162_3,plain,
$true,
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [A,B,C,D] :
( element(ordered_pair_as_product_element(A,B,C,D),cartesian_product2(A,B))
| ~ element(D,B)
| ~ element(C,A)
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_domain_1]) ).
fof(f_163_2,plain,
! [U_840,U_839,U_838,U_837] :
( element(ordered_pair_as_product_element(U_840,U_839,U_838,U_837),cartesian_product2(U_840,U_839))
| ~ element(U_837,U_839)
| ~ element(U_838,U_840)
| empty(U_839)
| empty(U_840) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_839,U_840,U_838,U_837] :
( element(ordered_pair_as_product_element(U_840,U_839,U_838,U_837),cartesian_product2(U_840,U_839))
| ~ element(U_837,U_839)
| ~ element(U_838,U_840)
| empty(U_839)
| empty(U_840) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( element(ordered_pair_as_product_element(U_840,U_839,U_838,U_837),cartesian_product2(U_840,U_839))
| ~ element(U_837,U_839)
| ~ element(U_838,U_840)
| empty(U_839)
| empty(U_840) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_enumset1]) ).
fof(f_164_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_164_1]) ).
cnf(f_164_3,plain,
$true,
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
fof(f_165_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_165_1]) ).
cnf(f_165_3,plain,
$true,
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_1,plain,
! [A] :
( latt_str(boole_lattice(A))
& strict_latt_str(boole_lattice(A)) ),
inference(fof_nnf,[status(thm)],[dt_k1_lattice3]) ).
fof(f_166_2,plain,
! [U_841] :
( latt_str(boole_lattice(U_841))
& strict_latt_str(boole_lattice(U_841)) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
( ! [U_843] : latt_str(boole_lattice(U_843))
& ! [U_842] : strict_latt_str(boole_lattice(U_842)) ),
inference(miniscope,[status(thm)],[f_166_2]) ).
fof(f_166_4,plain,
( ! [U_843] : latt_str(boole_lattice(U_843))
& ! [U_842] : strict_latt_str(boole_lattice(U_842)) ),
inference(definitional_conversion,[status(esa)],[f_166_3]) ).
cnf(f_166_5,plain,
strict_latt_str(boole_lattice(U_842)),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_6,plain,
latt_str(boole_lattice(U_843)),
inference(clausify,[status(thm)],[f_166_4]) ).
fof(f_167_1,plain,
! [A,B,C] :
( element(join(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_lattices]) ).
fof(f_167_2,plain,
! [U_846,U_845,U_844] :
( element(join(U_846,U_845,U_844),the_carrier(U_846))
| ~ element(U_844,the_carrier(U_846))
| ~ element(U_845,the_carrier(U_846))
| ~ join_semilatt_str(U_846)
| empty_carrier(U_846) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_844,U_845,U_846] :
( element(join(U_846,U_845,U_844),the_carrier(U_846))
| ~ element(U_844,the_carrier(U_846))
| ~ element(U_845,the_carrier(U_846))
| ~ join_semilatt_str(U_846)
| empty_carrier(U_846) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( element(join(U_846,U_845,U_844),the_carrier(U_846))
| ~ element(U_844,the_carrier(U_846))
| ~ element(U_845,the_carrier(U_846))
| ~ join_semilatt_str(U_846)
| empty_carrier(U_846) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_mcart_1]) ).
fof(f_168_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_168_1]) ).
cnf(f_168_3,plain,
$true,
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
fof(f_169_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_169_1]) ).
cnf(f_169_3,plain,
$true,
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_1,plain,
! [A] : element(k1_pcomps_1(A),powerset(powerset(A))),
inference(fof_nnf,[status(thm)],[dt_k1_pcomps_1]) ).
fof(f_170_2,plain,
! [U_847] : element(k1_pcomps_1(U_847),powerset(powerset(U_847))),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_847] : element(k1_pcomps_1(U_847),powerset(powerset(U_847))),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
element(k1_pcomps_1(U_847),powerset(powerset(U_847))),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
! [A] :
( element(empty_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_pre_topc]) ).
fof(f_171_2,plain,
! [U_848] :
( element(empty_carrier_subset(U_848),powerset(the_carrier(U_848)))
| ~ one_sorted_str(U_848) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_848] :
( element(empty_carrier_subset(U_848),powerset(the_carrier(U_848)))
| ~ one_sorted_str(U_848) ),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
( element(empty_carrier_subset(U_848),powerset(the_carrier(U_848)))
| ~ one_sorted_str(U_848) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_172_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_172_1]) ).
cnf(f_172_3,plain,
$true,
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
fof(f_173_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_173_1]) ).
cnf(f_173_3,plain,
$true,
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_174_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_174_1]) ).
cnf(f_174_3,plain,
$true,
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_1,plain,
! [A,B] :
( element(interior(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_tops_1]) ).
fof(f_175_2,plain,
! [U_850,U_849] :
( element(interior(U_850,U_849),powerset(the_carrier(U_850)))
| ~ element(U_849,powerset(the_carrier(U_850)))
| ~ top_str(U_850) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_849,U_850] :
( element(interior(U_850,U_849),powerset(the_carrier(U_850)))
| ~ element(U_849,powerset(the_carrier(U_850)))
| ~ top_str(U_850) ),
inference(definitional_conversion,[status(esa)],[f_175_2]) ).
cnf(f_175_4,plain,
( element(interior(U_850,U_849),powerset(the_carrier(U_850)))
| ~ element(U_849,powerset(the_carrier(U_850)))
| ~ top_str(U_850) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_wellord1]) ).
fof(f_176_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_176_1]) ).
cnf(f_176_3,plain,
$true,
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_1,plain,
! [A] : relation(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k1_wellord2]) ).
fof(f_177_2,plain,
! [U_851] : relation(inclusion_relation(U_851)),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_851] : relation(inclusion_relation(U_851)),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
relation(inclusion_relation(U_851)),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_178_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_178_1]) ).
cnf(f_178_3,plain,
$true,
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_179_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_179_1]) ).
cnf(f_179_3,plain,
$true,
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [A,B,C,D,E,F] :
( element(apply_binary_as_element(A,B,C,D,E,F),C)
| ~ element(F,B)
| ~ element(E,A)
| ~ relation_of2(D,cartesian_product2(A,B),C)
| ~ quasi_total(D,cartesian_product2(A,B),C)
| ~ function(D)
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_binop_1]) ).
fof(f_180_2,plain,
! [U_857,U_856,U_855,U_854,U_853,U_852] :
( element(apply_binary_as_element(U_857,U_856,U_855,U_854,U_853,U_852),U_855)
| ~ element(U_852,U_856)
| ~ element(U_853,U_857)
| ~ relation_of2(U_854,cartesian_product2(U_857,U_856),U_855)
| ~ quasi_total(U_854,cartesian_product2(U_857,U_856),U_855)
| ~ function(U_854)
| empty(U_856)
| empty(U_857) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_852,U_853,U_854,U_855,U_856,U_857] :
( element(apply_binary_as_element(U_857,U_856,U_855,U_854,U_853,U_852),U_855)
| ~ element(U_852,U_856)
| ~ element(U_853,U_857)
| ~ relation_of2(U_854,cartesian_product2(U_857,U_856),U_855)
| ~ quasi_total(U_854,cartesian_product2(U_857,U_856),U_855)
| ~ function(U_854)
| empty(U_856)
| empty(U_857) ),
inference(definitional_conversion,[status(esa)],[f_180_2]) ).
cnf(f_180_4,plain,
( element(apply_binary_as_element(U_857,U_856,U_855,U_854,U_853,U_852),U_855)
| ~ element(U_852,U_856)
| ~ element(U_853,U_857)
| ~ relation_of2(U_854,cartesian_product2(U_857,U_856),U_855)
| ~ quasi_total(U_854,cartesian_product2(U_857,U_856),U_855)
| ~ function(U_854)
| empty(U_856)
| empty(U_857) ),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_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_181_2,plain,
! [U_858] :
( ( function(function_inverse(U_858))
& relation(function_inverse(U_858)) )
| ~ function(U_858)
| ~ relation(U_858) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_858] :
( function(function_inverse(U_858))
| ~ sP253(U_858) )
& ! [U_858] :
( relation(function_inverse(U_858))
| ~ sP253(U_858) )
& ! [U_858] :
( sP253(U_858)
| ~ function(U_858)
| ~ relation(U_858) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253])],[f_181_2]) ).
cnf(f_181_4,plain,
( sP253(U_858)
| ~ function(U_858)
| ~ relation(U_858) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
( relation(function_inverse(U_858))
| ~ sP253(U_858) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_6,plain,
( function(function_inverse(U_858))
| ~ sP253(U_858) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [A] :
( ( relation_of2_as_subset(k2_lattice3(A),the_carrier(A),the_carrier(A))
& v1_partfun1(k2_lattice3(A),the_carrier(A),the_carrier(A))
& transitive(k2_lattice3(A))
& antisymmetric(k2_lattice3(A))
& reflexive(k2_lattice3(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_lattice3]) ).
fof(f_182_2,plain,
! [U_859] :
( ( relation_of2_as_subset(k2_lattice3(U_859),the_carrier(U_859),the_carrier(U_859))
& v1_partfun1(k2_lattice3(U_859),the_carrier(U_859),the_carrier(U_859))
& transitive(k2_lattice3(U_859))
& antisymmetric(k2_lattice3(U_859))
& reflexive(k2_lattice3(U_859)) )
| ~ latt_str(U_859)
| ~ lattice(U_859)
| empty_carrier(U_859) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( ! [U_859] :
( relation_of2_as_subset(k2_lattice3(U_859),the_carrier(U_859),the_carrier(U_859))
| ~ sP254(U_859) )
& ! [U_859] :
( v1_partfun1(k2_lattice3(U_859),the_carrier(U_859),the_carrier(U_859))
| ~ sP254(U_859) )
& ! [U_859] :
( transitive(k2_lattice3(U_859))
| ~ sP254(U_859) )
& ! [U_859] :
( antisymmetric(k2_lattice3(U_859))
| ~ sP254(U_859) )
& ! [U_859] :
( reflexive(k2_lattice3(U_859))
| ~ sP254(U_859) )
& ! [U_859] :
( sP254(U_859)
| ~ latt_str(U_859)
| ~ lattice(U_859)
| empty_carrier(U_859) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_182_2]) ).
cnf(f_182_4,plain,
( sP254(U_859)
| ~ latt_str(U_859)
| ~ lattice(U_859)
| empty_carrier(U_859) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_5,plain,
( reflexive(k2_lattice3(U_859))
| ~ sP254(U_859) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_6,plain,
( antisymmetric(k2_lattice3(U_859))
| ~ sP254(U_859) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_7,plain,
( transitive(k2_lattice3(U_859))
| ~ sP254(U_859) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_8,plain,
( v1_partfun1(k2_lattice3(U_859),the_carrier(U_859),the_carrier(U_859))
| ~ sP254(U_859) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_9,plain,
( relation_of2_as_subset(k2_lattice3(U_859),the_carrier(U_859),the_carrier(U_859))
| ~ sP254(U_859) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [A,B,C] :
( element(meet(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_lattices]) ).
fof(f_183_2,plain,
! [U_862,U_861,U_860] :
( element(meet(U_862,U_861,U_860),the_carrier(U_862))
| ~ element(U_860,the_carrier(U_862))
| ~ element(U_861,the_carrier(U_862))
| ~ meet_semilatt_str(U_862)
| empty_carrier(U_862) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_861,U_862,U_860] :
( element(meet(U_862,U_861,U_860),the_carrier(U_862))
| ~ element(U_860,the_carrier(U_862))
| ~ element(U_861,the_carrier(U_862))
| ~ meet_semilatt_str(U_862)
| empty_carrier(U_862) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( element(meet(U_862,U_861,U_860),the_carrier(U_862))
| ~ element(U_860,the_carrier(U_862))
| ~ element(U_861,the_carrier(U_862))
| ~ meet_semilatt_str(U_862)
| empty_carrier(U_862) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_mcart_1]) ).
fof(f_184_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_184_1]) ).
cnf(f_184_3,plain,
$true,
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_pre_topc]) ).
fof(f_185_2,plain,
! [U_863] :
( element(cast_as_carrier_subset(U_863),powerset(the_carrier(U_863)))
| ~ one_sorted_str(U_863) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_863] :
( element(cast_as_carrier_subset(U_863),powerset(the_carrier(U_863)))
| ~ one_sorted_str(U_863) ),
inference(definitional_conversion,[status(esa)],[f_185_2]) ).
cnf(f_185_4,plain,
( element(cast_as_carrier_subset(U_863),powerset(the_carrier(U_863)))
| ~ one_sorted_str(U_863) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
fof(f_186_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_186_1]) ).
cnf(f_186_3,plain,
$true,
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_187_2,plain,
! [U_864] : element(cast_to_subset(U_864),powerset(U_864)),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_864] : element(cast_to_subset(U_864),powerset(U_864)),
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
element(cast_to_subset(U_864),powerset(U_864)),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_188_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_188_1]) ).
cnf(f_188_3,plain,
$true,
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_189_2,plain,
! [U_866,U_865] :
( relation(relation_restriction(U_866,U_865))
| ~ relation(U_866) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_866] :
( ! [U_865] : relation(relation_restriction(U_866,U_865))
| ~ relation(U_866) ),
inference(miniscope,[status(thm)],[f_189_2]) ).
fof(f_189_4,plain,
! [U_865,U_866] :
( relation(relation_restriction(U_866,U_865))
| ~ relation(U_866) ),
inference(definitional_conversion,[status(esa)],[f_189_3]) ).
cnf(f_189_5,plain,
( relation(relation_restriction(U_866,U_865))
| ~ relation(U_866) ),
inference(clausify,[status(thm)],[f_189_4]) ).
fof(f_190_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_190_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_190_1]) ).
cnf(f_190_3,plain,
$true,
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_191_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_191_1]) ).
cnf(f_191_3,plain,
$true,
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [A] :
( ( rel_str(poset_of_lattice(A))
& antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_lattice3]) ).
fof(f_192_2,plain,
! [U_867] :
( ( rel_str(poset_of_lattice(U_867))
& antisymmetric_relstr(poset_of_lattice(U_867))
& transitive_relstr(poset_of_lattice(U_867))
& reflexive_relstr(poset_of_lattice(U_867))
& strict_rel_str(poset_of_lattice(U_867)) )
| ~ latt_str(U_867)
| ~ lattice(U_867)
| empty_carrier(U_867) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
( ! [U_867] :
( rel_str(poset_of_lattice(U_867))
| ~ sP255(U_867) )
& ! [U_867] :
( antisymmetric_relstr(poset_of_lattice(U_867))
| ~ sP255(U_867) )
& ! [U_867] :
( transitive_relstr(poset_of_lattice(U_867))
| ~ sP255(U_867) )
& ! [U_867] :
( reflexive_relstr(poset_of_lattice(U_867))
| ~ sP255(U_867) )
& ! [U_867] :
( strict_rel_str(poset_of_lattice(U_867))
| ~ sP255(U_867) )
& ! [U_867] :
( sP255(U_867)
| ~ latt_str(U_867)
| ~ lattice(U_867)
| empty_carrier(U_867) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255])],[f_192_2]) ).
cnf(f_192_4,plain,
( sP255(U_867)
| ~ latt_str(U_867)
| ~ lattice(U_867)
| empty_carrier(U_867) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
( strict_rel_str(poset_of_lattice(U_867))
| ~ sP255(U_867) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_6,plain,
( reflexive_relstr(poset_of_lattice(U_867))
| ~ sP255(U_867) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_7,plain,
( transitive_relstr(poset_of_lattice(U_867))
| ~ sP255(U_867) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_8,plain,
( antisymmetric_relstr(poset_of_lattice(U_867))
| ~ sP255(U_867) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_9,plain,
( rel_str(poset_of_lattice(U_867))
| ~ sP255(U_867) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [A,B,C] :
( element(join_commut(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_lattices]) ).
fof(f_193_2,plain,
! [U_870,U_869,U_868] :
( element(join_commut(U_870,U_869,U_868),the_carrier(U_870))
| ~ element(U_868,the_carrier(U_870))
| ~ element(U_869,the_carrier(U_870))
| ~ join_semilatt_str(U_870)
| ~ join_commutative(U_870)
| empty_carrier(U_870) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_868,U_870,U_869] :
( element(join_commut(U_870,U_869,U_868),the_carrier(U_870))
| ~ element(U_868,the_carrier(U_870))
| ~ element(U_869,the_carrier(U_870))
| ~ join_semilatt_str(U_870)
| ~ join_commutative(U_870)
| empty_carrier(U_870) ),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
( element(join_commut(U_870,U_869,U_868),the_carrier(U_870))
| ~ element(U_868,the_carrier(U_870))
| ~ element(U_869,the_carrier(U_870))
| ~ join_semilatt_str(U_870)
| ~ join_commutative(U_870)
| empty_carrier(U_870) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_194_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_194_1]) ).
cnf(f_194_3,plain,
$true,
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_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_195_2,plain,
! [U_872,U_871] :
( element(subset_complement(U_872,U_871),powerset(U_872))
| ~ element(U_871,powerset(U_872)) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_872,U_871] :
( element(subset_complement(U_872,U_871),powerset(U_872))
| ~ element(U_871,powerset(U_872)) ),
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
( element(subset_complement(U_872,U_871),powerset(U_872))
| ~ element(U_871,powerset(U_872)) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_196_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_196_1]) ).
cnf(f_196_3,plain,
$true,
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_197_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_197_1]) ).
cnf(f_197_3,plain,
$true,
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [A,B] :
( element(cast_to_el_of_LattPOSet(A,B),the_carrier(poset_of_lattice(A)))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_lattice3]) ).
fof(f_198_2,plain,
! [U_874,U_873] :
( element(cast_to_el_of_LattPOSet(U_874,U_873),the_carrier(poset_of_lattice(U_874)))
| ~ element(U_873,the_carrier(U_874))
| ~ latt_str(U_874)
| ~ lattice(U_874)
| empty_carrier(U_874) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_873,U_874] :
( element(cast_to_el_of_LattPOSet(U_874,U_873),the_carrier(poset_of_lattice(U_874)))
| ~ element(U_873,the_carrier(U_874))
| ~ latt_str(U_874)
| ~ lattice(U_874)
| empty_carrier(U_874) ),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
( element(cast_to_el_of_LattPOSet(U_874,U_873),the_carrier(poset_of_lattice(U_874)))
| ~ element(U_873,the_carrier(U_874))
| ~ latt_str(U_874)
| ~ lattice(U_874)
| empty_carrier(U_874) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [A,B,C] :
( element(meet_commut(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_lattices]) ).
fof(f_199_2,plain,
! [U_877,U_876,U_875] :
( element(meet_commut(U_877,U_876,U_875),the_carrier(U_877))
| ~ element(U_875,the_carrier(U_877))
| ~ element(U_876,the_carrier(U_877))
| ~ meet_semilatt_str(U_877)
| ~ meet_commutative(U_877)
| empty_carrier(U_877) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_875,U_876,U_877] :
( element(meet_commut(U_877,U_876,U_875),the_carrier(U_877))
| ~ element(U_875,the_carrier(U_877))
| ~ element(U_876,the_carrier(U_877))
| ~ meet_semilatt_str(U_877)
| ~ meet_commutative(U_877)
| empty_carrier(U_877) ),
inference(definitional_conversion,[status(esa)],[f_199_2]) ).
cnf(f_199_4,plain,
( element(meet_commut(U_877,U_876,U_875),the_carrier(U_877))
| ~ element(U_875,the_carrier(U_877))
| ~ element(U_876,the_carrier(U_877))
| ~ meet_semilatt_str(U_877)
| ~ meet_commutative(U_877)
| empty_carrier(U_877) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,plain,
! [A] :
( relation(relation_inverse(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k4_relat_1]) ).
fof(f_200_2,plain,
! [U_878] :
( relation(relation_inverse(U_878))
| ~ relation(U_878) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_878] :
( relation(relation_inverse(U_878))
| ~ relation(U_878) ),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
( relation(relation_inverse(U_878))
| ~ relation(U_878) ),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_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_201_2,plain,
! [U_881,U_880,U_879] :
( element(relation_dom_as_subset(U_881,U_880,U_879),powerset(U_881))
| ~ relation_of2(U_879,U_881,U_880) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_879,U_880,U_881] :
( element(relation_dom_as_subset(U_881,U_880,U_879),powerset(U_881))
| ~ relation_of2(U_879,U_881,U_880) ),
inference(definitional_conversion,[status(esa)],[f_201_2]) ).
cnf(f_201_4,plain,
( element(relation_dom_as_subset(U_881,U_880,U_879),powerset(U_881))
| ~ relation_of2(U_879,U_881,U_880) ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_1,plain,
! [A,B,C] :
( element(subset_union2(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k4_subset_1]) ).
fof(f_202_2,plain,
! [U_884,U_883,U_882] :
( element(subset_union2(U_884,U_883,U_882),powerset(U_884))
| ~ element(U_882,powerset(U_884))
| ~ element(U_883,powerset(U_884)) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_882,U_883,U_884] :
( element(subset_union2(U_884,U_883,U_882),powerset(U_884))
| ~ element(U_882,powerset(U_884))
| ~ element(U_883,powerset(U_884)) ),
inference(definitional_conversion,[status(esa)],[f_202_2]) ).
cnf(f_202_4,plain,
( element(subset_union2(U_884,U_883,U_882),powerset(U_884))
| ~ element(U_882,powerset(U_884))
| ~ element(U_883,powerset(U_884)) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_203_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_203_1]) ).
cnf(f_203_3,plain,
$true,
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
fof(f_204_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_204_1]) ).
cnf(f_204_3,plain,
$true,
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [A,B] :
( element(cast_to_el_of_lattice(A,B),the_carrier(A))
| ~ element(B,the_carrier(poset_of_lattice(A)))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_lattice3]) ).
fof(f_205_2,plain,
! [U_886,U_885] :
( element(cast_to_el_of_lattice(U_886,U_885),the_carrier(U_886))
| ~ element(U_885,the_carrier(poset_of_lattice(U_886)))
| ~ latt_str(U_886)
| ~ lattice(U_886)
| empty_carrier(U_886) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_885,U_886] :
( element(cast_to_el_of_lattice(U_886,U_885),the_carrier(U_886))
| ~ element(U_885,the_carrier(poset_of_lattice(U_886)))
| ~ latt_str(U_886)
| ~ lattice(U_886)
| empty_carrier(U_886) ),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
( element(cast_to_el_of_lattice(U_886,U_885),the_carrier(U_886))
| ~ element(U_885,the_carrier(poset_of_lattice(U_886)))
| ~ latt_str(U_886)
| ~ lattice(U_886)
| empty_carrier(U_886) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_1,plain,
! [A] :
( element(bottom_of_semilattstr(A),the_carrier(A))
| ~ meet_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_lattices]) ).
fof(f_206_2,plain,
! [U_887] :
( element(bottom_of_semilattstr(U_887),the_carrier(U_887))
| ~ meet_semilatt_str(U_887)
| empty_carrier(U_887) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_887] :
( element(bottom_of_semilattstr(U_887),the_carrier(U_887))
| ~ meet_semilatt_str(U_887)
| empty_carrier(U_887) ),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
( element(bottom_of_semilattstr(U_887),the_carrier(U_887))
| ~ meet_semilatt_str(U_887)
| empty_carrier(U_887) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k5_ordinal2]) ).
fof(f_207_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_207_1]) ).
cnf(f_207_3,plain,
$true,
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_208_2,plain,
! [U_889,U_888] :
( relation(relation_composition(U_889,U_888))
| ~ relation(U_888)
| ~ relation(U_889) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_889,U_888] :
( relation(relation_composition(U_889,U_888))
| ~ relation(U_888)
| ~ relation(U_889) ),
inference(definitional_conversion,[status(esa)],[f_208_2]) ).
cnf(f_208_4,plain,
( relation(relation_composition(U_889,U_888))
| ~ relation(U_888)
| ~ relation(U_889) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_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_209_2,plain,
! [U_892,U_891,U_890] :
( element(relation_rng_as_subset(U_892,U_891,U_890),powerset(U_891))
| ~ relation_of2(U_890,U_892,U_891) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_892,U_890,U_891] :
( element(relation_rng_as_subset(U_892,U_891,U_890),powerset(U_891))
| ~ relation_of2(U_890,U_892,U_891) ),
inference(definitional_conversion,[status(esa)],[f_209_2]) ).
cnf(f_209_4,plain,
( element(relation_rng_as_subset(U_892,U_891,U_890),powerset(U_891))
| ~ relation_of2(U_890,U_892,U_891) ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_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_210_2,plain,
! [U_894,U_893] :
( element(union_of_subsets(U_894,U_893),powerset(U_894))
| ~ element(U_893,powerset(powerset(U_894))) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_893,U_894] :
( element(union_of_subsets(U_894,U_893),powerset(U_894))
| ~ element(U_893,powerset(powerset(U_894))) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( element(union_of_subsets(U_894,U_893),powerset(U_894))
| ~ element(U_893,powerset(powerset(U_894))) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [A,B,C] :
( element(subset_intersection2(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k5_subset_1]) ).
fof(f_211_2,plain,
! [U_897,U_896,U_895] :
( element(subset_intersection2(U_897,U_896,U_895),powerset(U_897))
| ~ element(U_895,powerset(U_897))
| ~ element(U_896,powerset(U_897)) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_896,U_895,U_897] :
( element(subset_intersection2(U_897,U_896,U_895),powerset(U_897))
| ~ element(U_895,powerset(U_897))
| ~ element(U_896,powerset(U_897)) ),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
( element(subset_intersection2(U_897,U_896,U_895),powerset(U_897))
| ~ element(U_895,powerset(U_897))
| ~ element(U_896,powerset(U_897)) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_1,plain,
! [A] :
( relation_of2_as_subset(identity_as_relation_of(A),A,A)
& v1_partfun1(identity_as_relation_of(A),A,A) ),
inference(fof_nnf,[status(thm)],[dt_k6_partfun1]) ).
fof(f_212_2,plain,
! [U_898] :
( relation_of2_as_subset(identity_as_relation_of(U_898),U_898,U_898)
& v1_partfun1(identity_as_relation_of(U_898),U_898,U_898) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
( ! [U_900] : relation_of2_as_subset(identity_as_relation_of(U_900),U_900,U_900)
& ! [U_899] : v1_partfun1(identity_as_relation_of(U_899),U_899,U_899) ),
inference(miniscope,[status(thm)],[f_212_2]) ).
fof(f_212_4,plain,
( ! [U_900] : relation_of2_as_subset(identity_as_relation_of(U_900),U_900,U_900)
& ! [U_899] : v1_partfun1(identity_as_relation_of(U_899),U_899,U_899) ),
inference(definitional_conversion,[status(esa)],[f_212_3]) ).
cnf(f_212_5,plain,
v1_partfun1(identity_as_relation_of(U_899),U_899,U_899),
inference(clausify,[status(thm)],[f_212_4]) ).
cnf(f_212_6,plain,
relation_of2_as_subset(identity_as_relation_of(U_900),U_900,U_900),
inference(clausify,[status(thm)],[f_212_4]) ).
fof(f_213_1,plain,
! [A,B] :
( element(topstr_closure(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k6_pre_topc]) ).
fof(f_213_2,plain,
! [U_902,U_901] :
( element(topstr_closure(U_902,U_901),powerset(the_carrier(U_902)))
| ~ element(U_901,powerset(the_carrier(U_902)))
| ~ top_str(U_902) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_901,U_902] :
( element(topstr_closure(U_902,U_901),powerset(the_carrier(U_902)))
| ~ element(U_901,powerset(the_carrier(U_902)))
| ~ top_str(U_902) ),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
( element(topstr_closure(U_902,U_901),powerset(the_carrier(U_902)))
| ~ element(U_901,powerset(the_carrier(U_902)))
| ~ top_str(U_902) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_214_2,plain,
! [U_903] : relation(identity_relation(U_903)),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_903] : relation(identity_relation(U_903)),
inference(definitional_conversion,[status(esa)],[f_214_2]) ).
cnf(f_214_4,plain,
relation(identity_relation(U_903)),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_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_215_2,plain,
! [U_905,U_904] :
( element(meet_of_subsets(U_905,U_904),powerset(U_905))
| ~ element(U_904,powerset(powerset(U_905))) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_904,U_905] :
( element(meet_of_subsets(U_905,U_904),powerset(U_905))
| ~ element(U_904,powerset(powerset(U_905))) ),
inference(definitional_conversion,[status(esa)],[f_215_2]) ).
cnf(f_215_4,plain,
( element(meet_of_subsets(U_905,U_904),powerset(U_905))
| ~ element(U_904,powerset(powerset(U_905))) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_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_216_2,plain,
! [U_908,U_907,U_906] :
( element(subset_difference(U_908,U_907,U_906),powerset(U_908))
| ~ element(U_906,powerset(U_908))
| ~ element(U_907,powerset(U_908)) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_907,U_906,U_908] :
( element(subset_difference(U_908,U_907,U_906),powerset(U_908))
| ~ element(U_906,powerset(U_908))
| ~ element(U_907,powerset(U_908)) ),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
( element(subset_difference(U_908,U_907,U_906),powerset(U_908))
| ~ element(U_906,powerset(U_908))
| ~ element(U_907,powerset(U_908)) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [A] :
( ( relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A))
& quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A))
& function(identity_on_carrier(A)) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_grcat_1]) ).
fof(f_217_2,plain,
! [U_909] :
( ( relation_of2_as_subset(identity_on_carrier(U_909),the_carrier(U_909),the_carrier(U_909))
& quasi_total(identity_on_carrier(U_909),the_carrier(U_909),the_carrier(U_909))
& function(identity_on_carrier(U_909)) )
| ~ one_sorted_str(U_909) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
( ! [U_909] :
( relation_of2_as_subset(identity_on_carrier(U_909),the_carrier(U_909),the_carrier(U_909))
| ~ sP256(U_909) )
& ! [U_909] :
( quasi_total(identity_on_carrier(U_909),the_carrier(U_909),the_carrier(U_909))
| ~ sP256(U_909) )
& ! [U_909] :
( function(identity_on_carrier(U_909))
| ~ sP256(U_909) )
& ! [U_909] :
( sP256(U_909)
| ~ one_sorted_str(U_909) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256])],[f_217_2]) ).
cnf(f_217_4,plain,
( sP256(U_909)
| ~ one_sorted_str(U_909) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_5,plain,
( function(identity_on_carrier(U_909))
| ~ sP256(U_909) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_6,plain,
( quasi_total(identity_on_carrier(U_909),the_carrier(U_909),the_carrier(U_909))
| ~ sP256(U_909) ),
inference(clausify,[status(thm)],[f_217_3]) ).
cnf(f_217_7,plain,
( relation_of2_as_subset(identity_on_carrier(U_909),the_carrier(U_909),the_carrier(U_909))
| ~ sP256(U_909) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_218_2,plain,
! [U_911,U_910] :
( relation(relation_dom_restriction(U_911,U_910))
| ~ relation(U_911) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_911] :
( ! [U_910] : relation(relation_dom_restriction(U_911,U_910))
| ~ relation(U_911) ),
inference(miniscope,[status(thm)],[f_218_2]) ).
fof(f_218_4,plain,
! [U_911,U_910] :
( relation(relation_dom_restriction(U_911,U_910))
| ~ relation(U_911) ),
inference(definitional_conversion,[status(esa)],[f_218_3]) ).
cnf(f_218_5,plain,
( relation(relation_dom_restriction(U_911,U_910))
| ~ relation(U_911) ),
inference(clausify,[status(thm)],[f_218_4]) ).
fof(f_219_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_219_2,plain,
! [U_913,U_912] :
( element(complements_of_subsets(U_913,U_912),powerset(powerset(U_913)))
| ~ element(U_912,powerset(powerset(U_913))) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_912,U_913] :
( element(complements_of_subsets(U_913,U_912),powerset(powerset(U_913)))
| ~ element(U_912,powerset(powerset(U_913))) ),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
( element(complements_of_subsets(U_913,U_912),powerset(powerset(U_913)))
| ~ element(U_912,powerset(powerset(U_913))) ),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_1,plain,
! [A,B] :
( ( latt_str(k8_filter_1(A,B))
& strict_latt_str(k8_filter_1(A,B)) )
| ~ latt_str(B)
| empty_carrier(B)
| ~ latt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k8_filter_1]) ).
fof(f_220_2,plain,
! [U_915,U_914] :
( ( latt_str(k8_filter_1(U_915,U_914))
& strict_latt_str(k8_filter_1(U_915,U_914)) )
| ~ latt_str(U_914)
| empty_carrier(U_914)
| ~ latt_str(U_915)
| empty_carrier(U_915) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
( ! [U_914,U_915] :
( latt_str(k8_filter_1(U_915,U_914))
| ~ sP257(U_914,U_915) )
& ! [U_914,U_915] :
( strict_latt_str(k8_filter_1(U_915,U_914))
| ~ sP257(U_914,U_915) )
& ! [U_914,U_915] :
( sP257(U_914,U_915)
| ~ latt_str(U_914)
| empty_carrier(U_914)
| ~ latt_str(U_915)
| empty_carrier(U_915) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257])],[f_220_2]) ).
cnf(f_220_4,plain,
( sP257(U_914,U_915)
| ~ latt_str(U_914)
| empty_carrier(U_914)
| ~ latt_str(U_915)
| empty_carrier(U_915) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_5,plain,
( strict_latt_str(k8_filter_1(U_915,U_914))
| ~ sP257(U_914,U_915) ),
inference(clausify,[status(thm)],[f_220_3]) ).
cnf(f_220_6,plain,
( latt_str(k8_filter_1(U_915,U_914))
| ~ sP257(U_914,U_915) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [A,B,C,D] :
( element(apply_as_element(A,B,C,D),B)
| ~ element(D,A)
| ~ relation_of2(C,A,B)
| ~ quasi_total(C,A,B)
| ~ function(C)
| empty(A) ),
inference(fof_nnf,[status(thm)],[dt_k8_funct_2]) ).
fof(f_221_2,plain,
! [U_919,U_918,U_917,U_916] :
( element(apply_as_element(U_919,U_918,U_917,U_916),U_918)
| ~ element(U_916,U_919)
| ~ relation_of2(U_917,U_919,U_918)
| ~ quasi_total(U_917,U_919,U_918)
| ~ function(U_917)
| empty(U_919) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_918,U_916,U_917,U_919] :
( element(apply_as_element(U_919,U_918,U_917,U_916),U_918)
| ~ element(U_916,U_919)
| ~ relation_of2(U_917,U_919,U_918)
| ~ quasi_total(U_917,U_919,U_918)
| ~ function(U_917)
| empty(U_919) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( element(apply_as_element(U_919,U_918,U_917,U_916),U_918)
| ~ element(U_916,U_919)
| ~ relation_of2(U_917,U_919,U_918)
| ~ quasi_total(U_917,U_919,U_918)
| ~ function(U_917)
| empty(U_919) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_222_2,plain,
! [U_921,U_920] :
( relation(relation_rng_restriction(U_921,U_920))
| ~ relation(U_920) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_920,U_921] :
( relation(relation_rng_restriction(U_921,U_920))
| ~ relation(U_920) ),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
( relation(relation_rng_restriction(U_921,U_920))
| ~ relation(U_920) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [A] :
( relation(relation_of_lattice(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k9_filter_1]) ).
fof(f_223_2,plain,
! [U_922] :
( relation(relation_of_lattice(U_922))
| ~ latt_str(U_922)
| ~ lattice(U_922)
| empty_carrier(U_922) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_922] :
( relation(relation_of_lattice(U_922))
| ~ latt_str(U_922)
| ~ lattice(U_922)
| empty_carrier(U_922) ),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
( relation(relation_of_lattice(U_922))
| ~ latt_str(U_922)
| ~ lattice(U_922)
| empty_carrier(U_922) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
fof(f_224_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_224_1]) ).
cnf(f_224_3,plain,
$true,
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [A] :
( one_sorted_str(A)
| ~ meet_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_lattices]) ).
fof(f_225_2,plain,
! [U_923] :
( one_sorted_str(U_923)
| ~ meet_semilatt_str(U_923) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_923] :
( one_sorted_str(U_923)
| ~ meet_semilatt_str(U_923) ),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
( one_sorted_str(U_923)
| ~ meet_semilatt_str(U_923) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_226_2,plain,
! [U_924] :
( one_sorted_str(U_924)
| ~ rel_str(U_924) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_924] :
( one_sorted_str(U_924)
| ~ rel_str(U_924) ),
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
( one_sorted_str(U_924)
| ~ rel_str(U_924) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [A] :
( one_sorted_str(A)
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_pre_topc]) ).
fof(f_227_2,plain,
! [U_925] :
( one_sorted_str(U_925)
| ~ top_str(U_925) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_925] :
( one_sorted_str(U_925)
| ~ top_str(U_925) ),
inference(definitional_conversion,[status(esa)],[f_227_2]) ).
cnf(f_227_4,plain,
( one_sorted_str(U_925)
| ~ top_str(U_925) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_228_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_228_1]) ).
cnf(f_228_3,plain,
$true,
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_1,plain,
! [A] :
( one_sorted_str(A)
| ~ join_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_229_2,plain,
! [U_926] :
( one_sorted_str(U_926)
| ~ join_semilatt_str(U_926) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_926] :
( one_sorted_str(U_926)
| ~ join_semilatt_str(U_926) ),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
( one_sorted_str(U_926)
| ~ join_semilatt_str(U_926) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [A] :
( ( join_semilatt_str(A)
& meet_semilatt_str(A) )
| ~ latt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l3_lattices]) ).
fof(f_230_2,plain,
! [U_927] :
( ( join_semilatt_str(U_927)
& meet_semilatt_str(U_927) )
| ~ latt_str(U_927) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
( ! [U_927] :
( join_semilatt_str(U_927)
| ~ sP258(U_927) )
& ! [U_927] :
( meet_semilatt_str(U_927)
| ~ sP258(U_927) )
& ! [U_927] :
( sP258(U_927)
| ~ latt_str(U_927) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_230_2]) ).
cnf(f_230_4,plain,
( sP258(U_927)
| ~ latt_str(U_927) ),
inference(clausify,[status(thm)],[f_230_3]) ).
cnf(f_230_5,plain,
( meet_semilatt_str(U_927)
| ~ sP258(U_927) ),
inference(clausify,[status(thm)],[f_230_3]) ).
cnf(f_230_6,plain,
( join_semilatt_str(U_927)
| ~ sP258(U_927) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [A,B] :
( ! [C] :
( element(C,powerset(the_carrier(A)))
| ~ point_neighbourhood(C,A,B) )
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_m1_connsp_2]) ).
fof(f_231_2,plain,
! [U_930,U_929] :
( ! [U_928] :
( element(U_928,powerset(the_carrier(U_930)))
| ~ point_neighbourhood(U_928,U_930,U_929) )
| ~ element(U_929,the_carrier(U_930))
| ~ top_str(U_930)
| ~ topological_space(U_930)
| empty_carrier(U_930) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_928,U_930,U_929] :
( element(U_928,powerset(the_carrier(U_930)))
| ~ point_neighbourhood(U_928,U_930,U_929)
| ~ element(U_929,the_carrier(U_930))
| ~ top_str(U_930)
| ~ topological_space(U_930)
| empty_carrier(U_930) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( element(U_928,powerset(the_carrier(U_930)))
| ~ point_neighbourhood(U_928,U_930,U_929)
| ~ element(U_929,the_carrier(U_930))
| ~ top_str(U_930)
| ~ topological_space(U_930)
| empty_carrier(U_930) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_232_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_232_1]) ).
cnf(f_232_3,plain,
$true,
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_233_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_233_1]) ).
cnf(f_233_3,plain,
$true,
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_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_234_2,plain,
! [U_933,U_932,U_931] :
( element(U_931,powerset(cartesian_product2(U_933,U_932)))
| ~ relation_of2_as_subset(U_931,U_933,U_932) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_931,U_933,U_932] :
( element(U_931,powerset(cartesian_product2(U_933,U_932)))
| ~ relation_of2_as_subset(U_931,U_933,U_932) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( element(U_931,powerset(cartesian_product2(U_933,U_932)))
| ~ relation_of2_as_subset(U_931,U_933,U_932) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [A] :
( ( relation_of2_as_subset(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_meet(A)) )
| ~ meet_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_lattices]) ).
fof(f_235_2,plain,
! [U_934] :
( ( relation_of2_as_subset(the_L_meet(U_934),cartesian_product2(the_carrier(U_934),the_carrier(U_934)),the_carrier(U_934))
& quasi_total(the_L_meet(U_934),cartesian_product2(the_carrier(U_934),the_carrier(U_934)),the_carrier(U_934))
& function(the_L_meet(U_934)) )
| ~ meet_semilatt_str(U_934) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
( ! [U_934] :
( relation_of2_as_subset(the_L_meet(U_934),cartesian_product2(the_carrier(U_934),the_carrier(U_934)),the_carrier(U_934))
| ~ sP259(U_934) )
& ! [U_934] :
( quasi_total(the_L_meet(U_934),cartesian_product2(the_carrier(U_934),the_carrier(U_934)),the_carrier(U_934))
| ~ sP259(U_934) )
& ! [U_934] :
( function(the_L_meet(U_934))
| ~ sP259(U_934) )
& ! [U_934] :
( sP259(U_934)
| ~ meet_semilatt_str(U_934) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_235_2]) ).
cnf(f_235_4,plain,
( sP259(U_934)
| ~ meet_semilatt_str(U_934) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_5,plain,
( function(the_L_meet(U_934))
| ~ sP259(U_934) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_6,plain,
( quasi_total(the_L_meet(U_934),cartesian_product2(the_carrier(U_934),the_carrier(U_934)),the_carrier(U_934))
| ~ sP259(U_934) ),
inference(clausify,[status(thm)],[f_235_3]) ).
cnf(f_235_7,plain,
( relation_of2_as_subset(the_L_meet(U_934),cartesian_product2(the_carrier(U_934),the_carrier(U_934)),the_carrier(U_934))
| ~ sP259(U_934) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [A] :
( relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_orders_2]) ).
fof(f_236_2,plain,
! [U_935] :
( relation_of2_as_subset(the_InternalRel(U_935),the_carrier(U_935),the_carrier(U_935))
| ~ rel_str(U_935) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_935] :
( relation_of2_as_subset(the_InternalRel(U_935),the_carrier(U_935),the_carrier(U_935))
| ~ rel_str(U_935) ),
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
( relation_of2_as_subset(the_InternalRel(U_935),the_carrier(U_935),the_carrier(U_935))
| ~ rel_str(U_935) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [A] :
( element(the_topology(A),powerset(powerset(the_carrier(A))))
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u1_pre_topc]) ).
fof(f_237_2,plain,
! [U_936] :
( element(the_topology(U_936),powerset(powerset(the_carrier(U_936))))
| ~ top_str(U_936) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_936] :
( element(the_topology(U_936),powerset(powerset(the_carrier(U_936))))
| ~ top_str(U_936) ),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
( element(the_topology(U_936),powerset(powerset(the_carrier(U_936))))
| ~ top_str(U_936) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_238_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_238_1]) ).
cnf(f_238_3,plain,
$true,
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_1,plain,
! [A] :
( ( relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A)) )
| ~ join_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u2_lattices]) ).
fof(f_239_2,plain,
! [U_937] :
( ( relation_of2_as_subset(the_L_join(U_937),cartesian_product2(the_carrier(U_937),the_carrier(U_937)),the_carrier(U_937))
& quasi_total(the_L_join(U_937),cartesian_product2(the_carrier(U_937),the_carrier(U_937)),the_carrier(U_937))
& function(the_L_join(U_937)) )
| ~ join_semilatt_str(U_937) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
( ! [U_937] :
( relation_of2_as_subset(the_L_join(U_937),cartesian_product2(the_carrier(U_937),the_carrier(U_937)),the_carrier(U_937))
| ~ sP260(U_937) )
& ! [U_937] :
( quasi_total(the_L_join(U_937),cartesian_product2(the_carrier(U_937),the_carrier(U_937)),the_carrier(U_937))
| ~ sP260(U_937) )
& ! [U_937] :
( function(the_L_join(U_937))
| ~ sP260(U_937) )
& ! [U_937] :
( sP260(U_937)
| ~ join_semilatt_str(U_937) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260])],[f_239_2]) ).
cnf(f_239_4,plain,
( sP260(U_937)
| ~ join_semilatt_str(U_937) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_5,plain,
( function(the_L_join(U_937))
| ~ sP260(U_937) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_6,plain,
( quasi_total(the_L_join(U_937),cartesian_product2(the_carrier(U_937),the_carrier(U_937)),the_carrier(U_937))
| ~ sP260(U_937) ),
inference(clausify,[status(thm)],[f_239_3]) ).
cnf(f_239_7,plain,
( relation_of2_as_subset(the_L_join(U_937),cartesian_product2(the_carrier(U_937),the_carrier(U_937)),the_carrier(U_937))
| ~ sP260(U_937) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
? [A] : meet_semilatt_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_lattices]) ).
fof(f_240_2,plain,
? [U_938] : meet_semilatt_str(U_938),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
meet_semilatt_str(sK147),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_938,sK147)],[f_240_2]) ).
fof(f_240_4,plain,
meet_semilatt_str(sK147),
inference(definitional_conversion,[status(esa)],[f_240_3]) ).
cnf(f_240_5,plain,
meet_semilatt_str(sK147),
inference(clausify,[status(thm)],[f_240_4]) ).
fof(f_241_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_241_2,plain,
? [U_939] : rel_str(U_939),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
rel_str(sK148),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_939,sK148)],[f_241_2]) ).
fof(f_241_4,plain,
rel_str(sK148),
inference(definitional_conversion,[status(esa)],[f_241_3]) ).
cnf(f_241_5,plain,
rel_str(sK148),
inference(clausify,[status(thm)],[f_241_4]) ).
fof(f_242_1,plain,
? [A] : top_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_pre_topc]) ).
fof(f_242_2,plain,
? [U_940] : top_str(U_940),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
top_str(sK149),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_940,sK149)],[f_242_2]) ).
fof(f_242_4,plain,
top_str(sK149),
inference(definitional_conversion,[status(esa)],[f_242_3]) ).
cnf(f_242_5,plain,
top_str(sK149),
inference(clausify,[status(thm)],[f_242_4]) ).
fof(f_243_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_243_2,plain,
? [U_941] : one_sorted_str(U_941),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
one_sorted_str(sK150),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_941,sK150)],[f_243_2]) ).
fof(f_243_4,plain,
one_sorted_str(sK150),
inference(definitional_conversion,[status(esa)],[f_243_3]) ).
cnf(f_243_5,plain,
one_sorted_str(sK150),
inference(clausify,[status(thm)],[f_243_4]) ).
fof(f_244_1,plain,
? [A] : join_semilatt_str(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_244_2,plain,
? [U_942] : join_semilatt_str(U_942),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
join_semilatt_str(sK151),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_942,sK151)],[f_244_2]) ).
fof(f_244_4,plain,
join_semilatt_str(sK151),
inference(definitional_conversion,[status(esa)],[f_244_3]) ).
cnf(f_244_5,plain,
join_semilatt_str(sK151),
inference(clausify,[status(thm)],[f_244_4]) ).
fof(f_245_1,plain,
? [A] : latt_str(A),
inference(fof_nnf,[status(thm)],[existence_l3_lattices]) ).
fof(f_245_2,plain,
? [U_943] : latt_str(U_943),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
latt_str(sK152),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_943,sK152)],[f_245_2]) ).
fof(f_245_4,plain,
latt_str(sK152),
inference(definitional_conversion,[status(esa)],[f_245_3]) ).
cnf(f_245_5,plain,
latt_str(sK152),
inference(clausify,[status(thm)],[f_245_4]) ).
fof(f_246_1,plain,
! [A,B] :
( ? [C] : point_neighbourhood(C,A,B)
| ~ element(B,the_carrier(A))
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[existence_m1_connsp_2]) ).
fof(f_246_2,plain,
! [U_946,U_945] :
( ? [U_944] : point_neighbourhood(U_944,U_946,U_945)
| ~ element(U_945,the_carrier(U_946))
| ~ top_str(U_946)
| ~ topological_space(U_946)
| empty_carrier(U_946) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_946,U_945] :
( point_neighbourhood(sK153(U_946,U_945),U_946,U_945)
| ~ element(U_945,the_carrier(U_946))
| ~ top_str(U_946)
| ~ topological_space(U_946)
| empty_carrier(U_946) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_944,sK153(U_946,U_945))],[f_246_2]) ).
fof(f_246_4,plain,
! [U_945,U_946] :
( point_neighbourhood(sK153(U_946,U_945),U_946,U_945)
| ~ element(U_945,the_carrier(U_946))
| ~ top_str(U_946)
| ~ topological_space(U_946)
| empty_carrier(U_946) ),
inference(definitional_conversion,[status(esa)],[f_246_3]) ).
cnf(f_246_5,plain,
( point_neighbourhood(sK153(U_946,U_945),U_946,U_945)
| ~ element(U_945,the_carrier(U_946))
| ~ top_str(U_946)
| ~ topological_space(U_946)
| empty_carrier(U_946) ),
inference(clausify,[status(thm)],[f_246_4]) ).
fof(f_247_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_247_2,plain,
! [U_949,U_948] :
? [U_947] : relation_of2(U_947,U_949,U_948),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_949,U_948] : relation_of2(sK154(U_949,U_948),U_949,U_948),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_947,sK154(U_949,U_948))],[f_247_2]) ).
fof(f_247_4,plain,
! [U_948,U_949] : relation_of2(sK154(U_949,U_948),U_949,U_948),
inference(definitional_conversion,[status(esa)],[f_247_3]) ).
cnf(f_247_5,plain,
relation_of2(sK154(U_949,U_948),U_949,U_948),
inference(clausify,[status(thm)],[f_247_4]) ).
fof(f_248_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_248_2,plain,
! [U_951] :
? [U_950] : element(U_950,U_951),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_951] : element(sK155(U_951),U_951),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_950,sK155(U_951))],[f_248_2]) ).
fof(f_248_4,plain,
! [U_951] : element(sK155(U_951),U_951),
inference(definitional_conversion,[status(esa)],[f_248_3]) ).
cnf(f_248_5,plain,
element(sK155(U_951),U_951),
inference(clausify,[status(thm)],[f_248_4]) ).
fof(f_249_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_249_2,plain,
! [U_954,U_953] :
? [U_952] : relation_of2_as_subset(U_952,U_954,U_953),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_954,U_953] : relation_of2_as_subset(sK156(U_954,U_953),U_954,U_953),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_952,sK156(U_954,U_953))],[f_249_2]) ).
fof(f_249_4,plain,
! [U_953,U_954] : relation_of2_as_subset(sK156(U_954,U_953),U_954,U_953),
inference(definitional_conversion,[status(esa)],[f_249_3]) ).
cnf(f_249_5,plain,
relation_of2_as_subset(sK156(U_954,U_953),U_954,U_953),
inference(clausify,[status(thm)],[f_249_4]) ).
fof(f_250_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(B) ),
inference(fof_nnf,[status(thm)],[fc10_finset_1]) ).
fof(f_250_2,plain,
! [U_956,U_955] :
( finite(set_intersection2(U_956,U_955))
| ~ finite(U_955) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_955,U_956] :
( finite(set_intersection2(U_956,U_955))
| ~ finite(U_955) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( finite(set_intersection2(U_956,U_955))
| ~ finite(U_955) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_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_251_2,plain,
! [U_958,U_957] :
( ( relation(relation_composition(U_957,U_958))
& empty(relation_composition(U_957,U_958)) )
| ~ relation(U_957)
| ~ empty(U_958) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_957,U_958] :
( relation(relation_composition(U_957,U_958))
| ~ sP261(U_957,U_958) )
& ! [U_957,U_958] :
( empty(relation_composition(U_957,U_958))
| ~ sP261(U_957,U_958) )
& ! [U_957,U_958] :
( sP261(U_957,U_958)
| ~ relation(U_957)
| ~ empty(U_958) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261])],[f_251_2]) ).
cnf(f_251_4,plain,
( sP261(U_957,U_958)
| ~ relation(U_957)
| ~ empty(U_958) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
( empty(relation_composition(U_957,U_958))
| ~ sP261(U_957,U_958) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_6,plain,
( relation(relation_composition(U_957,U_958))
| ~ sP261(U_957,U_958) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc11_finset_1]) ).
fof(f_252_2,plain,
! [U_960,U_959] :
( finite(set_intersection2(U_960,U_959))
| ~ finite(U_960) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_960] :
( ! [U_959] : finite(set_intersection2(U_960,U_959))
| ~ finite(U_960) ),
inference(miniscope,[status(thm)],[f_252_2]) ).
fof(f_252_4,plain,
! [U_960,U_959] :
( finite(set_intersection2(U_960,U_959))
| ~ finite(U_960) ),
inference(definitional_conversion,[status(esa)],[f_252_3]) ).
cnf(f_252_5,plain,
( finite(set_intersection2(U_960,U_959))
| ~ finite(U_960) ),
inference(clausify,[status(thm)],[f_252_4]) ).
fof(f_253_1,plain,
! [A] :
( ( relation(relation_inverse(A))
& empty(relation_inverse(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc11_relat_1]) ).
fof(f_253_2,plain,
! [U_961] :
( ( relation(relation_inverse(U_961))
& empty(relation_inverse(U_961)) )
| ~ empty(U_961) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_961] :
( relation(relation_inverse(U_961))
| ~ sP262(U_961) )
& ! [U_961] :
( empty(relation_inverse(U_961))
| ~ sP262(U_961) )
& ! [U_961] :
( sP262(U_961)
| ~ empty(U_961) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262])],[f_253_2]) ).
cnf(f_253_4,plain,
( sP262(U_961)
| ~ empty(U_961) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
( empty(relation_inverse(U_961))
| ~ sP262(U_961) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_6,plain,
( relation(relation_inverse(U_961))
| ~ sP262(U_961) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc12_finset_1]) ).
fof(f_254_2,plain,
! [U_963,U_962] :
( finite(set_difference(U_963,U_962))
| ~ finite(U_963) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_963] :
( ! [U_962] : finite(set_difference(U_963,U_962))
| ~ finite(U_963) ),
inference(miniscope,[status(thm)],[f_254_2]) ).
fof(f_254_4,plain,
! [U_963,U_962] :
( finite(set_difference(U_963,U_962))
| ~ finite(U_963) ),
inference(definitional_conversion,[status(esa)],[f_254_3]) ).
cnf(f_254_5,plain,
( finite(set_difference(U_963,U_962))
| ~ finite(U_963) ),
inference(clausify,[status(thm)],[f_254_4]) ).
fof(f_255_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_255_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_255_1]) ).
cnf(f_255_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_255_2]) ).
cnf(f_255_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_255_2]) ).
cnf(f_255_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_1,plain,
! [A,B] :
( finite(relation_image(A,B))
| ~ finite(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc13_finset_1]) ).
fof(f_256_2,plain,
! [U_965,U_964] :
( finite(relation_image(U_965,U_964))
| ~ finite(U_964)
| ~ function(U_965)
| ~ relation(U_965) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_964,U_965] :
( finite(relation_image(U_965,U_964))
| ~ finite(U_964)
| ~ function(U_965)
| ~ relation(U_965) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( finite(relation_image(U_965,U_964))
| ~ finite(U_964)
| ~ function(U_965)
| ~ relation(U_965) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_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_257_2,plain,
! [U_967,U_966] :
( ( relation_empty_yielding(relation_dom_restriction(U_967,U_966))
& relation(relation_dom_restriction(U_967,U_966)) )
| ~ relation_empty_yielding(U_967)
| ~ relation(U_967) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_967] :
( ( ! [U_969] : relation_empty_yielding(relation_dom_restriction(U_967,U_969))
& ! [U_968] : relation(relation_dom_restriction(U_967,U_968)) )
| ~ relation_empty_yielding(U_967)
| ~ relation(U_967) ),
inference(miniscope,[status(thm)],[f_257_2]) ).
fof(f_257_4,plain,
( ! [U_967,U_969,U_968] :
( relation_empty_yielding(relation_dom_restriction(U_967,U_969))
| ~ sP263(U_967,U_969,U_968) )
& ! [U_967,U_969,U_968] :
( relation(relation_dom_restriction(U_967,U_968))
| ~ sP263(U_967,U_969,U_968) )
& ! [U_967,U_969,U_968] :
( sP263(U_967,U_969,U_968)
| ~ relation_empty_yielding(U_967)
| ~ relation(U_967) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263])],[f_257_3]) ).
cnf(f_257_5,plain,
( sP263(U_967,U_969,U_968)
| ~ relation_empty_yielding(U_967)
| ~ relation(U_967) ),
inference(clausify,[status(thm)],[f_257_4]) ).
cnf(f_257_6,plain,
( relation(relation_dom_restriction(U_967,U_968))
| ~ sP263(U_967,U_969,U_968) ),
inference(clausify,[status(thm)],[f_257_4]) ).
cnf(f_257_7,plain,
( relation_empty_yielding(relation_dom_restriction(U_967,U_969))
| ~ sP263(U_967,U_969,U_968) ),
inference(clausify,[status(thm)],[f_257_4]) ).
fof(f_258_1,plain,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
inference(fof_nnf,[status(thm)],[fc1_finset_1]) ).
fof(f_258_2,plain,
! [U_970] :
( finite(singleton(U_970))
& ~ empty(singleton(U_970)) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_972] : finite(singleton(U_972))
& ! [U_971] : ~ empty(singleton(U_971)) ),
inference(miniscope,[status(thm)],[f_258_2]) ).
fof(f_258_4,plain,
( ! [U_972] : finite(singleton(U_972))
& ! [U_971] : ~ empty(singleton(U_971)) ),
inference(definitional_conversion,[status(esa)],[f_258_3]) ).
cnf(f_258_5,plain,
~ empty(singleton(U_971)),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_6,plain,
finite(singleton(U_972)),
inference(clausify,[status(thm)],[f_258_4]) ).
fof(f_259_1,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(fof_nnf,[status(thm)],[fc1_finsub_1]) ).
fof(f_259_2,plain,
! [U_973] :
( preboolean(powerset(U_973))
& diff_closed(powerset(U_973))
& cup_closed(powerset(U_973))
& ~ empty(powerset(U_973)) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
( ! [U_977] : preboolean(powerset(U_977))
& ! [U_976] : diff_closed(powerset(U_976))
& ! [U_975] : cup_closed(powerset(U_975))
& ! [U_974] : ~ empty(powerset(U_974)) ),
inference(miniscope,[status(thm)],[f_259_2]) ).
fof(f_259_4,plain,
( ! [U_977] : preboolean(powerset(U_977))
& ! [U_976] : diff_closed(powerset(U_976))
& ! [U_975] : cup_closed(powerset(U_975))
& ! [U_974] : ~ empty(powerset(U_974)) ),
inference(definitional_conversion,[status(esa)],[f_259_3]) ).
cnf(f_259_5,plain,
~ empty(powerset(U_974)),
inference(clausify,[status(thm)],[f_259_4]) ).
cnf(f_259_6,plain,
cup_closed(powerset(U_975)),
inference(clausify,[status(thm)],[f_259_4]) ).
cnf(f_259_7,plain,
diff_closed(powerset(U_976)),
inference(clausify,[status(thm)],[f_259_4]) ).
cnf(f_259_8,plain,
preboolean(powerset(U_977)),
inference(clausify,[status(thm)],[f_259_4]) ).
fof(f_260_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_260_2,plain,
! [U_979,U_978] :
( ( function(relation_composition(U_979,U_978))
& relation(relation_composition(U_979,U_978)) )
| ~ function(U_978)
| ~ relation(U_978)
| ~ function(U_979)
| ~ relation(U_979) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_979,U_978] :
( function(relation_composition(U_979,U_978))
| ~ sP264(U_979,U_978) )
& ! [U_979,U_978] :
( relation(relation_composition(U_979,U_978))
| ~ sP264(U_979,U_978) )
& ! [U_979,U_978] :
( sP264(U_979,U_978)
| ~ function(U_978)
| ~ relation(U_978)
| ~ function(U_979)
| ~ relation(U_979) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264])],[f_260_2]) ).
cnf(f_260_4,plain,
( sP264(U_979,U_978)
| ~ function(U_978)
| ~ relation(U_978)
| ~ function(U_979)
| ~ relation(U_979) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_5,plain,
( relation(relation_composition(U_979,U_978))
| ~ sP264(U_979,U_978) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_6,plain,
( function(relation_composition(U_979,U_978))
| ~ sP264(U_979,U_978) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [A] :
( strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(fof_nnf,[status(thm)],[fc1_lattice3]) ).
fof(f_261_2,plain,
! [U_980] :
( strict_latt_str(boole_lattice(U_980))
& ~ empty_carrier(boole_lattice(U_980)) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( ! [U_982] : strict_latt_str(boole_lattice(U_982))
& ! [U_981] : ~ empty_carrier(boole_lattice(U_981)) ),
inference(miniscope,[status(thm)],[f_261_2]) ).
fof(f_261_4,plain,
( ! [U_982] : strict_latt_str(boole_lattice(U_982))
& ! [U_981] : ~ empty_carrier(boole_lattice(U_981)) ),
inference(definitional_conversion,[status(esa)],[f_261_3]) ).
cnf(f_261_5,plain,
~ empty_carrier(boole_lattice(U_981)),
inference(clausify,[status(thm)],[f_261_4]) ).
cnf(f_261_6,plain,
strict_latt_str(boole_lattice(U_982)),
inference(clausify,[status(thm)],[f_261_4]) ).
fof(f_262_1,plain,
! [A,B] :
( ( strict_rel_str(rel_str_of(A,B))
& ~ empty_carrier(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc1_orders_2]) ).
fof(f_262_2,plain,
! [U_984,U_983] :
( ( strict_rel_str(rel_str_of(U_984,U_983))
& ~ empty_carrier(rel_str_of(U_984,U_983)) )
| ~ relation_of2(U_983,U_984,U_984)
| empty(U_984) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
( ! [U_983,U_984] :
( strict_rel_str(rel_str_of(U_984,U_983))
| ~ sP265(U_983,U_984) )
& ! [U_983,U_984] :
( ~ empty_carrier(rel_str_of(U_984,U_983))
| ~ sP265(U_983,U_984) )
& ! [U_983,U_984] :
( sP265(U_983,U_984)
| ~ relation_of2(U_983,U_984,U_984)
| empty(U_984) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265])],[f_262_2]) ).
cnf(f_262_4,plain,
( sP265(U_983,U_984)
| ~ relation_of2(U_983,U_984,U_984)
| empty(U_984) ),
inference(clausify,[status(thm)],[f_262_3]) ).
cnf(f_262_5,plain,
( ~ empty_carrier(rel_str_of(U_984,U_983))
| ~ sP265(U_983,U_984) ),
inference(clausify,[status(thm)],[f_262_3]) ).
cnf(f_262_6,plain,
( strict_rel_str(rel_str_of(U_984,U_983))
| ~ sP265(U_983,U_984) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_263_2,plain,
! [U_985] : ~ empty(succ(U_985)),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_985] : ~ empty(succ(U_985)),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
~ empty(succ(U_985)),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
inference(fof_nnf,[status(thm)],[fc1_ordinal2]) ).
fof(f_264_2,plain,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
inference(definitional_conversion,[status(esa)],[f_264_1]) ).
cnf(f_264_3,plain,
epsilon_transitive(omega),
inference(clausify,[status(thm)],[f_264_2]) ).
cnf(f_264_4,plain,
epsilon_connected(omega),
inference(clausify,[status(thm)],[f_264_2]) ).
cnf(f_264_5,plain,
ordinal(omega),
inference(clausify,[status(thm)],[f_264_2]) ).
cnf(f_264_6,plain,
~ empty(omega),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [A] :
( ( v5_membered(empty_carrier_subset(A))
& v4_membered(empty_carrier_subset(A))
& v3_membered(empty_carrier_subset(A))
& v2_membered(empty_carrier_subset(A))
& v1_membered(empty_carrier_subset(A))
& empty(empty_carrier_subset(A)) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[fc1_pre_topc]) ).
fof(f_265_2,plain,
! [U_986] :
( ( v5_membered(empty_carrier_subset(U_986))
& v4_membered(empty_carrier_subset(U_986))
& v3_membered(empty_carrier_subset(U_986))
& v2_membered(empty_carrier_subset(U_986))
& v1_membered(empty_carrier_subset(U_986))
& empty(empty_carrier_subset(U_986)) )
| ~ one_sorted_str(U_986) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
( ! [U_986] :
( v5_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) )
& ! [U_986] :
( v4_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) )
& ! [U_986] :
( v3_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) )
& ! [U_986] :
( v2_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) )
& ! [U_986] :
( v1_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) )
& ! [U_986] :
( empty(empty_carrier_subset(U_986))
| ~ sP266(U_986) )
& ! [U_986] :
( sP266(U_986)
| ~ one_sorted_str(U_986) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266])],[f_265_2]) ).
cnf(f_265_4,plain,
( sP266(U_986)
| ~ one_sorted_str(U_986) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_5,plain,
( empty(empty_carrier_subset(U_986))
| ~ sP266(U_986) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_6,plain,
( v1_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_7,plain,
( v2_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_8,plain,
( v3_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_9,plain,
( v4_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_10,plain,
( v5_membered(empty_carrier_subset(U_986))
| ~ sP266(U_986) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_266_2,plain,
! [U_988,U_987] :
( relation(set_intersection2(U_988,U_987))
| ~ relation(U_987)
| ~ relation(U_988) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_987,U_988] :
( relation(set_intersection2(U_988,U_987))
| ~ relation(U_987)
| ~ relation(U_988) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( relation(set_intersection2(U_988,U_987))
| ~ relation(U_987)
| ~ relation(U_988) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_267_2,plain,
! [U_989] :
( ~ empty(the_carrier(U_989))
| ~ one_sorted_str(U_989)
| empty_carrier(U_989) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_989] :
( ~ empty(the_carrier(U_989))
| ~ one_sorted_str(U_989)
| empty_carrier(U_989) ),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
( ~ empty(the_carrier(U_989))
| ~ one_sorted_str(U_989)
| empty_carrier(U_989) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_268_2,plain,
! [U_990] : ~ empty(powerset(U_990)),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_990] : ~ empty(powerset(U_990)),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
~ empty(powerset(U_990)),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_269_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_269_1]) ).
cnf(f_269_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_270_2,plain,
! [U_992,U_991] : ~ empty(ordered_pair(U_992,U_991)),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_991,U_992] : ~ empty(ordered_pair(U_992,U_991)),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
~ empty(ordered_pair(U_992,U_991)),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [A,B] :
( v1_membered(set_intersection2(A,B))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc27_membered]) ).
fof(f_271_2,plain,
! [U_994,U_993] :
( v1_membered(set_intersection2(U_994,U_993))
| ~ v1_membered(U_994) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_994] :
( ! [U_993] : v1_membered(set_intersection2(U_994,U_993))
| ~ v1_membered(U_994) ),
inference(miniscope,[status(thm)],[f_271_2]) ).
fof(f_271_4,plain,
! [U_993,U_994] :
( v1_membered(set_intersection2(U_994,U_993))
| ~ v1_membered(U_994) ),
inference(definitional_conversion,[status(esa)],[f_271_3]) ).
cnf(f_271_5,plain,
( v1_membered(set_intersection2(U_994,U_993))
| ~ v1_membered(U_994) ),
inference(clausify,[status(thm)],[f_271_4]) ).
fof(f_272_1,plain,
! [A,B] :
( v1_membered(set_intersection2(B,A))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc28_membered]) ).
fof(f_272_2,plain,
! [U_996,U_995] :
( v1_membered(set_intersection2(U_995,U_996))
| ~ v1_membered(U_996) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_996] :
( ! [U_995] : v1_membered(set_intersection2(U_995,U_996))
| ~ v1_membered(U_996) ),
inference(miniscope,[status(thm)],[f_272_2]) ).
fof(f_272_4,plain,
! [U_995,U_996] :
( v1_membered(set_intersection2(U_995,U_996))
| ~ v1_membered(U_996) ),
inference(definitional_conversion,[status(esa)],[f_272_3]) ).
cnf(f_272_5,plain,
( v1_membered(set_intersection2(U_995,U_996))
| ~ v1_membered(U_996) ),
inference(clausify,[status(thm)],[f_272_4]) ).
fof(f_273_1,plain,
! [A,B] :
( ( v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[fc29_membered]) ).
fof(f_273_2,plain,
! [U_998,U_997] :
( ( v2_membered(set_intersection2(U_998,U_997))
& v1_membered(set_intersection2(U_998,U_997)) )
| ~ v2_membered(U_998) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_998] :
( ( ! [U_1000] : v2_membered(set_intersection2(U_998,U_1000))
& ! [U_999] : v1_membered(set_intersection2(U_998,U_999)) )
| ~ v2_membered(U_998) ),
inference(miniscope,[status(thm)],[f_273_2]) ).
fof(f_273_4,plain,
( ! [U_998,U_999,U_1000] :
( v2_membered(set_intersection2(U_998,U_1000))
| ~ sP267(U_998,U_999,U_1000) )
& ! [U_998,U_999,U_1000] :
( v1_membered(set_intersection2(U_998,U_999))
| ~ sP267(U_998,U_999,U_1000) )
& ! [U_998,U_999,U_1000] :
( sP267(U_998,U_999,U_1000)
| ~ v2_membered(U_998) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_273_3]) ).
cnf(f_273_5,plain,
( sP267(U_998,U_999,U_1000)
| ~ v2_membered(U_998) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_6,plain,
( v1_membered(set_intersection2(U_998,U_999))
| ~ sP267(U_998,U_999,U_1000) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_7,plain,
( v2_membered(set_intersection2(U_998,U_1000))
| ~ sP267(U_998,U_999,U_1000) ),
inference(clausify,[status(thm)],[f_273_4]) ).
fof(f_274_1,plain,
! [A] :
( ( natural(succ(A))
& ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ natural(A)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc2_arytm_3]) ).
fof(f_274_2,plain,
! [U_1001] :
( ( natural(succ(U_1001))
& ordinal(succ(U_1001))
& epsilon_connected(succ(U_1001))
& epsilon_transitive(succ(U_1001))
& ~ empty(succ(U_1001)) )
| ~ natural(U_1001)
| ~ ordinal(U_1001) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
( ! [U_1001] :
( natural(succ(U_1001))
| ~ sP268(U_1001) )
& ! [U_1001] :
( ordinal(succ(U_1001))
| ~ sP268(U_1001) )
& ! [U_1001] :
( epsilon_connected(succ(U_1001))
| ~ sP268(U_1001) )
& ! [U_1001] :
( epsilon_transitive(succ(U_1001))
| ~ sP268(U_1001) )
& ! [U_1001] :
( ~ empty(succ(U_1001))
| ~ sP268(U_1001) )
& ! [U_1001] :
( sP268(U_1001)
| ~ natural(U_1001)
| ~ ordinal(U_1001) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268])],[f_274_2]) ).
cnf(f_274_4,plain,
( sP268(U_1001)
| ~ natural(U_1001)
| ~ ordinal(U_1001) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( ~ empty(succ(U_1001))
| ~ sP268(U_1001) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_6,plain,
( epsilon_transitive(succ(U_1001))
| ~ sP268(U_1001) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_7,plain,
( epsilon_connected(succ(U_1001))
| ~ sP268(U_1001) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_8,plain,
( ordinal(succ(U_1001))
| ~ sP268(U_1001) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_9,plain,
( natural(succ(U_1001))
| ~ sP268(U_1001) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_funct_1]) ).
fof(f_275_2,plain,
! [U_1002] :
( function(identity_relation(U_1002))
& relation(identity_relation(U_1002)) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_1004] : function(identity_relation(U_1004))
& ! [U_1003] : relation(identity_relation(U_1003)) ),
inference(miniscope,[status(thm)],[f_275_2]) ).
fof(f_275_4,plain,
( ! [U_1004] : function(identity_relation(U_1004))
& ! [U_1003] : relation(identity_relation(U_1003)) ),
inference(definitional_conversion,[status(esa)],[f_275_3]) ).
cnf(f_275_5,plain,
relation(identity_relation(U_1003)),
inference(clausify,[status(thm)],[f_275_4]) ).
cnf(f_275_6,plain,
function(identity_relation(U_1004)),
inference(clausify,[status(thm)],[f_275_4]) ).
fof(f_276_1,plain,
! [A] :
( ( v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v1_binop_1(the_L_join(A),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A))
& relation(the_L_join(A)) )
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc2_lattice2]) ).
fof(f_276_2,plain,
! [U_1005] :
( ( v1_partfun1(the_L_join(U_1005),cartesian_product2(the_carrier(U_1005),the_carrier(U_1005)),the_carrier(U_1005))
& v1_binop_1(the_L_join(U_1005),the_carrier(U_1005))
& quasi_total(the_L_join(U_1005),cartesian_product2(the_carrier(U_1005),the_carrier(U_1005)),the_carrier(U_1005))
& function(the_L_join(U_1005))
& relation(the_L_join(U_1005)) )
| ~ join_semilatt_str(U_1005)
| ~ join_commutative(U_1005)
| empty_carrier(U_1005) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
( ! [U_1005] :
( v1_partfun1(the_L_join(U_1005),cartesian_product2(the_carrier(U_1005),the_carrier(U_1005)),the_carrier(U_1005))
| ~ sP269(U_1005) )
& ! [U_1005] :
( v1_binop_1(the_L_join(U_1005),the_carrier(U_1005))
| ~ sP269(U_1005) )
& ! [U_1005] :
( quasi_total(the_L_join(U_1005),cartesian_product2(the_carrier(U_1005),the_carrier(U_1005)),the_carrier(U_1005))
| ~ sP269(U_1005) )
& ! [U_1005] :
( function(the_L_join(U_1005))
| ~ sP269(U_1005) )
& ! [U_1005] :
( relation(the_L_join(U_1005))
| ~ sP269(U_1005) )
& ! [U_1005] :
( sP269(U_1005)
| ~ join_semilatt_str(U_1005)
| ~ join_commutative(U_1005)
| empty_carrier(U_1005) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269])],[f_276_2]) ).
cnf(f_276_4,plain,
( sP269(U_1005)
| ~ join_semilatt_str(U_1005)
| ~ join_commutative(U_1005)
| empty_carrier(U_1005) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_5,plain,
( relation(the_L_join(U_1005))
| ~ sP269(U_1005) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_6,plain,
( function(the_L_join(U_1005))
| ~ sP269(U_1005) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_7,plain,
( quasi_total(the_L_join(U_1005),cartesian_product2(the_carrier(U_1005),the_carrier(U_1005)),the_carrier(U_1005))
| ~ sP269(U_1005) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_8,plain,
( v1_binop_1(the_L_join(U_1005),the_carrier(U_1005))
| ~ sP269(U_1005) ),
inference(clausify,[status(thm)],[f_276_3]) ).
cnf(f_276_9,plain,
( v1_partfun1(the_L_join(U_1005),cartesian_product2(the_carrier(U_1005),the_carrier(U_1005)),the_carrier(U_1005))
| ~ sP269(U_1005) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [A] :
( lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(fof_nnf,[status(thm)],[fc2_lattice3]) ).
fof(f_277_2,plain,
! [U_1006] :
( lattice(boole_lattice(U_1006))
& join_absorbing(boole_lattice(U_1006))
& meet_absorbing(boole_lattice(U_1006))
& meet_associative(boole_lattice(U_1006))
& meet_commutative(boole_lattice(U_1006))
& join_associative(boole_lattice(U_1006))
& join_commutative(boole_lattice(U_1006))
& strict_latt_str(boole_lattice(U_1006))
& ~ empty_carrier(boole_lattice(U_1006)) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
( ! [U_1015] : lattice(boole_lattice(U_1015))
& ! [U_1014] : join_absorbing(boole_lattice(U_1014))
& ! [U_1013] : meet_absorbing(boole_lattice(U_1013))
& ! [U_1012] : meet_associative(boole_lattice(U_1012))
& ! [U_1011] : meet_commutative(boole_lattice(U_1011))
& ! [U_1010] : join_associative(boole_lattice(U_1010))
& ! [U_1009] : join_commutative(boole_lattice(U_1009))
& ! [U_1008] : strict_latt_str(boole_lattice(U_1008))
& ! [U_1007] : ~ empty_carrier(boole_lattice(U_1007)) ),
inference(miniscope,[status(thm)],[f_277_2]) ).
fof(f_277_4,plain,
( ! [U_1015] : lattice(boole_lattice(U_1015))
& ! [U_1014] : join_absorbing(boole_lattice(U_1014))
& ! [U_1013] : meet_absorbing(boole_lattice(U_1013))
& ! [U_1012] : meet_associative(boole_lattice(U_1012))
& ! [U_1011] : meet_commutative(boole_lattice(U_1011))
& ! [U_1010] : join_associative(boole_lattice(U_1010))
& ! [U_1009] : join_commutative(boole_lattice(U_1009))
& ! [U_1008] : strict_latt_str(boole_lattice(U_1008))
& ! [U_1007] : ~ empty_carrier(boole_lattice(U_1007)) ),
inference(definitional_conversion,[status(esa)],[f_277_3]) ).
cnf(f_277_5,plain,
~ empty_carrier(boole_lattice(U_1007)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_6,plain,
strict_latt_str(boole_lattice(U_1008)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_7,plain,
join_commutative(boole_lattice(U_1009)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_8,plain,
join_associative(boole_lattice(U_1010)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_9,plain,
meet_commutative(boole_lattice(U_1011)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_10,plain,
meet_associative(boole_lattice(U_1012)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_11,plain,
meet_absorbing(boole_lattice(U_1013)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_12,plain,
join_absorbing(boole_lattice(U_1014)),
inference(clausify,[status(thm)],[f_277_4]) ).
cnf(f_277_13,plain,
lattice(boole_lattice(U_1015)),
inference(clausify,[status(thm)],[f_277_4]) ).
fof(f_278_1,plain,
! [A] :
( ( v1_partfun1(the_InternalRel(A),the_carrier(A),the_carrier(A))
& transitive(the_InternalRel(A))
& antisymmetric(the_InternalRel(A))
& reflexive(the_InternalRel(A))
& relation(the_InternalRel(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A)
| ~ transitive_relstr(A)
| ~ reflexive_relstr(A) ),
inference(fof_nnf,[status(thm)],[fc2_orders_2]) ).
fof(f_278_2,plain,
! [U_1016] :
( ( v1_partfun1(the_InternalRel(U_1016),the_carrier(U_1016),the_carrier(U_1016))
& transitive(the_InternalRel(U_1016))
& antisymmetric(the_InternalRel(U_1016))
& reflexive(the_InternalRel(U_1016))
& relation(the_InternalRel(U_1016)) )
| ~ rel_str(U_1016)
| ~ antisymmetric_relstr(U_1016)
| ~ transitive_relstr(U_1016)
| ~ reflexive_relstr(U_1016) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
( ! [U_1016] :
( v1_partfun1(the_InternalRel(U_1016),the_carrier(U_1016),the_carrier(U_1016))
| ~ sP270(U_1016) )
& ! [U_1016] :
( transitive(the_InternalRel(U_1016))
| ~ sP270(U_1016) )
& ! [U_1016] :
( antisymmetric(the_InternalRel(U_1016))
| ~ sP270(U_1016) )
& ! [U_1016] :
( reflexive(the_InternalRel(U_1016))
| ~ sP270(U_1016) )
& ! [U_1016] :
( relation(the_InternalRel(U_1016))
| ~ sP270(U_1016) )
& ! [U_1016] :
( sP270(U_1016)
| ~ rel_str(U_1016)
| ~ antisymmetric_relstr(U_1016)
| ~ transitive_relstr(U_1016)
| ~ reflexive_relstr(U_1016) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP270])],[f_278_2]) ).
cnf(f_278_4,plain,
( sP270(U_1016)
| ~ rel_str(U_1016)
| ~ antisymmetric_relstr(U_1016)
| ~ transitive_relstr(U_1016)
| ~ reflexive_relstr(U_1016) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_5,plain,
( relation(the_InternalRel(U_1016))
| ~ sP270(U_1016) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_6,plain,
( reflexive(the_InternalRel(U_1016))
| ~ sP270(U_1016) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_7,plain,
( antisymmetric(the_InternalRel(U_1016))
| ~ sP270(U_1016) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_8,plain,
( transitive(the_InternalRel(U_1016))
| ~ sP270(U_1016) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_9,plain,
( v1_partfun1(the_InternalRel(U_1016),the_carrier(U_1016),the_carrier(U_1016))
| ~ sP270(U_1016) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_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_279_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_279_1]) ).
cnf(f_279_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
cnf(f_279_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
cnf(f_279_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
cnf(f_279_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
cnf(f_279_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
cnf(f_279_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
cnf(f_279_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
cnf(f_279_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_1,plain,
! [A] :
( transitive(identity_relation(A))
& antisymmetric(identity_relation(A))
& symmetric(identity_relation(A))
& reflexive(identity_relation(A))
& function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(fof_nnf,[status(thm)],[fc2_partfun1]) ).
fof(f_280_2,plain,
! [U_1017] :
( transitive(identity_relation(U_1017))
& antisymmetric(identity_relation(U_1017))
& symmetric(identity_relation(U_1017))
& reflexive(identity_relation(U_1017))
& function(identity_relation(U_1017))
& relation(identity_relation(U_1017)) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
( ! [U_1023] : transitive(identity_relation(U_1023))
& ! [U_1022] : antisymmetric(identity_relation(U_1022))
& ! [U_1021] : symmetric(identity_relation(U_1021))
& ! [U_1020] : reflexive(identity_relation(U_1020))
& ! [U_1019] : function(identity_relation(U_1019))
& ! [U_1018] : relation(identity_relation(U_1018)) ),
inference(miniscope,[status(thm)],[f_280_2]) ).
fof(f_280_4,plain,
( ! [U_1023] : transitive(identity_relation(U_1023))
& ! [U_1022] : antisymmetric(identity_relation(U_1022))
& ! [U_1021] : symmetric(identity_relation(U_1021))
& ! [U_1020] : reflexive(identity_relation(U_1020))
& ! [U_1019] : function(identity_relation(U_1019))
& ! [U_1018] : relation(identity_relation(U_1018)) ),
inference(definitional_conversion,[status(esa)],[f_280_3]) ).
cnf(f_280_5,plain,
relation(identity_relation(U_1018)),
inference(clausify,[status(thm)],[f_280_4]) ).
cnf(f_280_6,plain,
function(identity_relation(U_1019)),
inference(clausify,[status(thm)],[f_280_4]) ).
cnf(f_280_7,plain,
reflexive(identity_relation(U_1020)),
inference(clausify,[status(thm)],[f_280_4]) ).
cnf(f_280_8,plain,
symmetric(identity_relation(U_1021)),
inference(clausify,[status(thm)],[f_280_4]) ).
cnf(f_280_9,plain,
antisymmetric(identity_relation(U_1022)),
inference(clausify,[status(thm)],[f_280_4]) ).
cnf(f_280_10,plain,
transitive(identity_relation(U_1023)),
inference(clausify,[status(thm)],[f_280_4]) ).
fof(f_281_1,plain,
! [A] :
( ~ empty(cast_as_carrier_subset(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc2_pre_topc]) ).
fof(f_281_2,plain,
! [U_1024] :
( ~ empty(cast_as_carrier_subset(U_1024))
| ~ one_sorted_str(U_1024)
| empty_carrier(U_1024) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_1024] :
( ~ empty(cast_as_carrier_subset(U_1024))
| ~ one_sorted_str(U_1024)
| empty_carrier(U_1024) ),
inference(definitional_conversion,[status(esa)],[f_281_2]) ).
cnf(f_281_4,plain,
( ~ empty(cast_as_carrier_subset(U_1024))
| ~ one_sorted_str(U_1024)
| empty_carrier(U_1024) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_282_2,plain,
! [U_1026,U_1025] :
( relation(set_union2(U_1026,U_1025))
| ~ relation(U_1025)
| ~ relation(U_1026) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_1025,U_1026] :
( relation(set_union2(U_1026,U_1025))
| ~ relation(U_1025)
| ~ relation(U_1026) ),
inference(definitional_conversion,[status(esa)],[f_282_2]) ).
cnf(f_282_4,plain,
( relation(set_union2(U_1026,U_1025))
| ~ relation(U_1025)
| ~ relation(U_1026) ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_283_2,plain,
! [U_1027] : ~ empty(singleton(U_1027)),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1027] : ~ empty(singleton(U_1027)),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
~ empty(singleton(U_1027)),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_1,plain,
! [A,B] :
( closed_subset(topstr_closure(A,B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc2_tops_1]) ).
fof(f_284_2,plain,
! [U_1029,U_1028] :
( closed_subset(topstr_closure(U_1029,U_1028),U_1029)
| ~ element(U_1028,powerset(the_carrier(U_1029)))
| ~ top_str(U_1029)
| ~ topological_space(U_1029) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_1028,U_1029] :
( closed_subset(topstr_closure(U_1029,U_1028),U_1029)
| ~ element(U_1028,powerset(the_carrier(U_1029)))
| ~ top_str(U_1029)
| ~ topological_space(U_1029) ),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
( closed_subset(topstr_closure(U_1029,U_1028),U_1029)
| ~ element(U_1028,powerset(the_carrier(U_1029)))
| ~ top_str(U_1029)
| ~ topological_space(U_1029) ),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_285_2,plain,
! [U_1031,U_1030] :
( ~ empty(set_union2(U_1031,U_1030))
| empty(U_1031) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_1031] :
( ! [U_1030] : ~ empty(set_union2(U_1031,U_1030))
| empty(U_1031) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
fof(f_285_4,plain,
! [U_1031,U_1030] :
( ~ empty(set_union2(U_1031,U_1030))
| empty(U_1031) ),
inference(definitional_conversion,[status(esa)],[f_285_3]) ).
cnf(f_285_5,plain,
( ~ empty(set_union2(U_1031,U_1030))
| empty(U_1031) ),
inference(clausify,[status(thm)],[f_285_4]) ).
fof(f_286_1,plain,
! [A,B] :
( ( v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[fc30_membered]) ).
fof(f_286_2,plain,
! [U_1033,U_1032] :
( ( v2_membered(set_intersection2(U_1032,U_1033))
& v1_membered(set_intersection2(U_1032,U_1033)) )
| ~ v2_membered(U_1033) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1033] :
( ( ! [U_1035] : v2_membered(set_intersection2(U_1035,U_1033))
& ! [U_1034] : v1_membered(set_intersection2(U_1034,U_1033)) )
| ~ v2_membered(U_1033) ),
inference(miniscope,[status(thm)],[f_286_2]) ).
fof(f_286_4,plain,
( ! [U_1033,U_1034,U_1035] :
( v2_membered(set_intersection2(U_1035,U_1033))
| ~ sP271(U_1033,U_1034,U_1035) )
& ! [U_1033,U_1034,U_1035] :
( v1_membered(set_intersection2(U_1034,U_1033))
| ~ sP271(U_1033,U_1034,U_1035) )
& ! [U_1033,U_1034,U_1035] :
( sP271(U_1033,U_1034,U_1035)
| ~ v2_membered(U_1033) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271])],[f_286_3]) ).
cnf(f_286_5,plain,
( sP271(U_1033,U_1034,U_1035)
| ~ v2_membered(U_1033) ),
inference(clausify,[status(thm)],[f_286_4]) ).
cnf(f_286_6,plain,
( v1_membered(set_intersection2(U_1034,U_1033))
| ~ sP271(U_1033,U_1034,U_1035) ),
inference(clausify,[status(thm)],[f_286_4]) ).
cnf(f_286_7,plain,
( v2_membered(set_intersection2(U_1035,U_1033))
| ~ sP271(U_1033,U_1034,U_1035) ),
inference(clausify,[status(thm)],[f_286_4]) ).
fof(f_287_1,plain,
! [A,B] :
( ( v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[fc31_membered]) ).
fof(f_287_2,plain,
! [U_1037,U_1036] :
( ( v3_membered(set_intersection2(U_1037,U_1036))
& v2_membered(set_intersection2(U_1037,U_1036))
& v1_membered(set_intersection2(U_1037,U_1036)) )
| ~ v3_membered(U_1037) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_1037] :
( ( ! [U_1040] : v3_membered(set_intersection2(U_1037,U_1040))
& ! [U_1039] : v2_membered(set_intersection2(U_1037,U_1039))
& ! [U_1038] : v1_membered(set_intersection2(U_1037,U_1038)) )
| ~ v3_membered(U_1037) ),
inference(miniscope,[status(thm)],[f_287_2]) ).
fof(f_287_4,plain,
( ! [U_1037,U_1038,U_1039,U_1040] :
( v3_membered(set_intersection2(U_1037,U_1040))
| ~ sP272(U_1037,U_1038,U_1039,U_1040) )
& ! [U_1037,U_1038,U_1039,U_1040] :
( v2_membered(set_intersection2(U_1037,U_1039))
| ~ sP272(U_1037,U_1038,U_1039,U_1040) )
& ! [U_1037,U_1038,U_1039,U_1040] :
( v1_membered(set_intersection2(U_1037,U_1038))
| ~ sP272(U_1037,U_1038,U_1039,U_1040) )
& ! [U_1037,U_1038,U_1039,U_1040] :
( sP272(U_1037,U_1038,U_1039,U_1040)
| ~ v3_membered(U_1037) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP272])],[f_287_3]) ).
cnf(f_287_5,plain,
( sP272(U_1037,U_1038,U_1039,U_1040)
| ~ v3_membered(U_1037) ),
inference(clausify,[status(thm)],[f_287_4]) ).
cnf(f_287_6,plain,
( v1_membered(set_intersection2(U_1037,U_1038))
| ~ sP272(U_1037,U_1038,U_1039,U_1040) ),
inference(clausify,[status(thm)],[f_287_4]) ).
cnf(f_287_7,plain,
( v2_membered(set_intersection2(U_1037,U_1039))
| ~ sP272(U_1037,U_1038,U_1039,U_1040) ),
inference(clausify,[status(thm)],[f_287_4]) ).
cnf(f_287_8,plain,
( v3_membered(set_intersection2(U_1037,U_1040))
| ~ sP272(U_1037,U_1038,U_1039,U_1040) ),
inference(clausify,[status(thm)],[f_287_4]) ).
fof(f_288_1,plain,
! [A,B] :
( ( v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[fc32_membered]) ).
fof(f_288_2,plain,
! [U_1042,U_1041] :
( ( v3_membered(set_intersection2(U_1041,U_1042))
& v2_membered(set_intersection2(U_1041,U_1042))
& v1_membered(set_intersection2(U_1041,U_1042)) )
| ~ v3_membered(U_1042) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1042] :
( ( ! [U_1045] : v3_membered(set_intersection2(U_1045,U_1042))
& ! [U_1044] : v2_membered(set_intersection2(U_1044,U_1042))
& ! [U_1043] : v1_membered(set_intersection2(U_1043,U_1042)) )
| ~ v3_membered(U_1042) ),
inference(miniscope,[status(thm)],[f_288_2]) ).
fof(f_288_4,plain,
( ! [U_1042,U_1044,U_1043,U_1045] :
( v3_membered(set_intersection2(U_1045,U_1042))
| ~ sP273(U_1042,U_1044,U_1043,U_1045) )
& ! [U_1042,U_1044,U_1043,U_1045] :
( v2_membered(set_intersection2(U_1044,U_1042))
| ~ sP273(U_1042,U_1044,U_1043,U_1045) )
& ! [U_1042,U_1044,U_1043,U_1045] :
( v1_membered(set_intersection2(U_1043,U_1042))
| ~ sP273(U_1042,U_1044,U_1043,U_1045) )
& ! [U_1042,U_1044,U_1043,U_1045] :
( sP273(U_1042,U_1044,U_1043,U_1045)
| ~ v3_membered(U_1042) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273])],[f_288_3]) ).
cnf(f_288_5,plain,
( sP273(U_1042,U_1044,U_1043,U_1045)
| ~ v3_membered(U_1042) ),
inference(clausify,[status(thm)],[f_288_4]) ).
cnf(f_288_6,plain,
( v1_membered(set_intersection2(U_1043,U_1042))
| ~ sP273(U_1042,U_1044,U_1043,U_1045) ),
inference(clausify,[status(thm)],[f_288_4]) ).
cnf(f_288_7,plain,
( v2_membered(set_intersection2(U_1044,U_1042))
| ~ sP273(U_1042,U_1044,U_1043,U_1045) ),
inference(clausify,[status(thm)],[f_288_4]) ).
cnf(f_288_8,plain,
( v3_membered(set_intersection2(U_1045,U_1042))
| ~ sP273(U_1042,U_1044,U_1043,U_1045) ),
inference(clausify,[status(thm)],[f_288_4]) ).
fof(f_289_1,plain,
! [A,B] :
( ( v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[fc33_membered]) ).
fof(f_289_2,plain,
! [U_1047,U_1046] :
( ( v4_membered(set_intersection2(U_1047,U_1046))
& v3_membered(set_intersection2(U_1047,U_1046))
& v2_membered(set_intersection2(U_1047,U_1046))
& v1_membered(set_intersection2(U_1047,U_1046)) )
| ~ v4_membered(U_1047) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_1047] :
( ( ! [U_1051] : v4_membered(set_intersection2(U_1047,U_1051))
& ! [U_1050] : v3_membered(set_intersection2(U_1047,U_1050))
& ! [U_1049] : v2_membered(set_intersection2(U_1047,U_1049))
& ! [U_1048] : v1_membered(set_intersection2(U_1047,U_1048)) )
| ~ v4_membered(U_1047) ),
inference(miniscope,[status(thm)],[f_289_2]) ).
fof(f_289_4,plain,
( ! [U_1050,U_1051,U_1049,U_1047,U_1048] :
( v4_membered(set_intersection2(U_1047,U_1051))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) )
& ! [U_1050,U_1051,U_1049,U_1047,U_1048] :
( v3_membered(set_intersection2(U_1047,U_1050))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) )
& ! [U_1050,U_1051,U_1049,U_1047,U_1048] :
( v2_membered(set_intersection2(U_1047,U_1049))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) )
& ! [U_1050,U_1051,U_1049,U_1047,U_1048] :
( v1_membered(set_intersection2(U_1047,U_1048))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) )
& ! [U_1050,U_1051,U_1049,U_1047,U_1048] :
( sP274(U_1050,U_1051,U_1049,U_1047,U_1048)
| ~ v4_membered(U_1047) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274])],[f_289_3]) ).
cnf(f_289_5,plain,
( sP274(U_1050,U_1051,U_1049,U_1047,U_1048)
| ~ v4_membered(U_1047) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_6,plain,
( v1_membered(set_intersection2(U_1047,U_1048))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_7,plain,
( v2_membered(set_intersection2(U_1047,U_1049))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_8,plain,
( v3_membered(set_intersection2(U_1047,U_1050))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) ),
inference(clausify,[status(thm)],[f_289_4]) ).
cnf(f_289_9,plain,
( v4_membered(set_intersection2(U_1047,U_1051))
| ~ sP274(U_1050,U_1051,U_1049,U_1047,U_1048) ),
inference(clausify,[status(thm)],[f_289_4]) ).
fof(f_290_1,plain,
! [A,B] :
( ( v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[fc34_membered]) ).
fof(f_290_2,plain,
! [U_1053,U_1052] :
( ( v4_membered(set_intersection2(U_1052,U_1053))
& v3_membered(set_intersection2(U_1052,U_1053))
& v2_membered(set_intersection2(U_1052,U_1053))
& v1_membered(set_intersection2(U_1052,U_1053)) )
| ~ v4_membered(U_1053) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_1053] :
( ( ! [U_1057] : v4_membered(set_intersection2(U_1057,U_1053))
& ! [U_1056] : v3_membered(set_intersection2(U_1056,U_1053))
& ! [U_1055] : v2_membered(set_intersection2(U_1055,U_1053))
& ! [U_1054] : v1_membered(set_intersection2(U_1054,U_1053)) )
| ~ v4_membered(U_1053) ),
inference(miniscope,[status(thm)],[f_290_2]) ).
fof(f_290_4,plain,
( ! [U_1053,U_1055,U_1054,U_1056,U_1057] :
( v4_membered(set_intersection2(U_1057,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) )
& ! [U_1053,U_1055,U_1054,U_1056,U_1057] :
( v3_membered(set_intersection2(U_1056,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) )
& ! [U_1053,U_1055,U_1054,U_1056,U_1057] :
( v2_membered(set_intersection2(U_1055,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) )
& ! [U_1053,U_1055,U_1054,U_1056,U_1057] :
( v1_membered(set_intersection2(U_1054,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) )
& ! [U_1053,U_1055,U_1054,U_1056,U_1057] :
( sP275(U_1053,U_1055,U_1054,U_1056,U_1057)
| ~ v4_membered(U_1053) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275])],[f_290_3]) ).
cnf(f_290_5,plain,
( sP275(U_1053,U_1055,U_1054,U_1056,U_1057)
| ~ v4_membered(U_1053) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_6,plain,
( v1_membered(set_intersection2(U_1054,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_7,plain,
( v2_membered(set_intersection2(U_1055,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_8,plain,
( v3_membered(set_intersection2(U_1056,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) ),
inference(clausify,[status(thm)],[f_290_4]) ).
cnf(f_290_9,plain,
( v4_membered(set_intersection2(U_1057,U_1053))
| ~ sP275(U_1053,U_1055,U_1054,U_1056,U_1057) ),
inference(clausify,[status(thm)],[f_290_4]) ).
fof(f_291_1,plain,
! [A,B] :
( ( v5_membered(set_intersection2(A,B))
& v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[fc35_membered]) ).
fof(f_291_2,plain,
! [U_1059,U_1058] :
( ( v5_membered(set_intersection2(U_1059,U_1058))
& v4_membered(set_intersection2(U_1059,U_1058))
& v3_membered(set_intersection2(U_1059,U_1058))
& v2_membered(set_intersection2(U_1059,U_1058))
& v1_membered(set_intersection2(U_1059,U_1058)) )
| ~ v5_membered(U_1059) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_1059] :
( ( ! [U_1064] : v5_membered(set_intersection2(U_1059,U_1064))
& ! [U_1063] : v4_membered(set_intersection2(U_1059,U_1063))
& ! [U_1062] : v3_membered(set_intersection2(U_1059,U_1062))
& ! [U_1061] : v2_membered(set_intersection2(U_1059,U_1061))
& ! [U_1060] : v1_membered(set_intersection2(U_1059,U_1060)) )
| ~ v5_membered(U_1059) ),
inference(miniscope,[status(thm)],[f_291_2]) ).
fof(f_291_4,plain,
( ! [U_1059,U_1061,U_1060,U_1062,U_1063,U_1064] :
( v5_membered(set_intersection2(U_1059,U_1064))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) )
& ! [U_1059,U_1061,U_1060,U_1062,U_1063,U_1064] :
( v4_membered(set_intersection2(U_1059,U_1063))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) )
& ! [U_1059,U_1061,U_1060,U_1062,U_1063,U_1064] :
( v3_membered(set_intersection2(U_1059,U_1062))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) )
& ! [U_1059,U_1061,U_1060,U_1062,U_1063,U_1064] :
( v2_membered(set_intersection2(U_1059,U_1061))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) )
& ! [U_1059,U_1061,U_1060,U_1062,U_1063,U_1064] :
( v1_membered(set_intersection2(U_1059,U_1060))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) )
& ! [U_1059,U_1061,U_1060,U_1062,U_1063,U_1064] :
( sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064)
| ~ v5_membered(U_1059) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_291_3]) ).
cnf(f_291_5,plain,
( sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064)
| ~ v5_membered(U_1059) ),
inference(clausify,[status(thm)],[f_291_4]) ).
cnf(f_291_6,plain,
( v1_membered(set_intersection2(U_1059,U_1060))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_291_4]) ).
cnf(f_291_7,plain,
( v2_membered(set_intersection2(U_1059,U_1061))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_291_4]) ).
cnf(f_291_8,plain,
( v3_membered(set_intersection2(U_1059,U_1062))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_291_4]) ).
cnf(f_291_9,plain,
( v4_membered(set_intersection2(U_1059,U_1063))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_291_4]) ).
cnf(f_291_10,plain,
( v5_membered(set_intersection2(U_1059,U_1064))
| ~ sP276(U_1059,U_1061,U_1060,U_1062,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_291_4]) ).
fof(f_292_1,plain,
! [A,B] :
( ( v5_membered(set_intersection2(B,A))
& v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[fc36_membered]) ).
fof(f_292_2,plain,
! [U_1066,U_1065] :
( ( v5_membered(set_intersection2(U_1065,U_1066))
& v4_membered(set_intersection2(U_1065,U_1066))
& v3_membered(set_intersection2(U_1065,U_1066))
& v2_membered(set_intersection2(U_1065,U_1066))
& v1_membered(set_intersection2(U_1065,U_1066)) )
| ~ v5_membered(U_1066) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1066] :
( ( ! [U_1071] : v5_membered(set_intersection2(U_1071,U_1066))
& ! [U_1070] : v4_membered(set_intersection2(U_1070,U_1066))
& ! [U_1069] : v3_membered(set_intersection2(U_1069,U_1066))
& ! [U_1068] : v2_membered(set_intersection2(U_1068,U_1066))
& ! [U_1067] : v1_membered(set_intersection2(U_1067,U_1066)) )
| ~ v5_membered(U_1066) ),
inference(miniscope,[status(thm)],[f_292_2]) ).
fof(f_292_4,plain,
( ! [U_1067,U_1068,U_1066,U_1069,U_1070,U_1071] :
( v5_membered(set_intersection2(U_1071,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) )
& ! [U_1067,U_1068,U_1066,U_1069,U_1070,U_1071] :
( v4_membered(set_intersection2(U_1070,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) )
& ! [U_1067,U_1068,U_1066,U_1069,U_1070,U_1071] :
( v3_membered(set_intersection2(U_1069,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) )
& ! [U_1067,U_1068,U_1066,U_1069,U_1070,U_1071] :
( v2_membered(set_intersection2(U_1068,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) )
& ! [U_1067,U_1068,U_1066,U_1069,U_1070,U_1071] :
( v1_membered(set_intersection2(U_1067,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) )
& ! [U_1067,U_1068,U_1066,U_1069,U_1070,U_1071] :
( sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071)
| ~ v5_membered(U_1066) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277])],[f_292_3]) ).
cnf(f_292_5,plain,
( sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071)
| ~ v5_membered(U_1066) ),
inference(clausify,[status(thm)],[f_292_4]) ).
cnf(f_292_6,plain,
( v1_membered(set_intersection2(U_1067,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) ),
inference(clausify,[status(thm)],[f_292_4]) ).
cnf(f_292_7,plain,
( v2_membered(set_intersection2(U_1068,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) ),
inference(clausify,[status(thm)],[f_292_4]) ).
cnf(f_292_8,plain,
( v3_membered(set_intersection2(U_1069,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) ),
inference(clausify,[status(thm)],[f_292_4]) ).
cnf(f_292_9,plain,
( v4_membered(set_intersection2(U_1070,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) ),
inference(clausify,[status(thm)],[f_292_4]) ).
cnf(f_292_10,plain,
( v5_membered(set_intersection2(U_1071,U_1066))
| ~ sP277(U_1067,U_1068,U_1066,U_1069,U_1070,U_1071) ),
inference(clausify,[status(thm)],[f_292_4]) ).
fof(f_293_1,plain,
! [A,B] :
( v1_membered(set_difference(A,B))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc37_membered]) ).
fof(f_293_2,plain,
! [U_1073,U_1072] :
( v1_membered(set_difference(U_1073,U_1072))
| ~ v1_membered(U_1073) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_1073] :
( ! [U_1072] : v1_membered(set_difference(U_1073,U_1072))
| ~ v1_membered(U_1073) ),
inference(miniscope,[status(thm)],[f_293_2]) ).
fof(f_293_4,plain,
! [U_1072,U_1073] :
( v1_membered(set_difference(U_1073,U_1072))
| ~ v1_membered(U_1073) ),
inference(definitional_conversion,[status(esa)],[f_293_3]) ).
cnf(f_293_5,plain,
( v1_membered(set_difference(U_1073,U_1072))
| ~ v1_membered(U_1073) ),
inference(clausify,[status(thm)],[f_293_4]) ).
fof(f_294_1,plain,
! [A,B] :
( ( v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[fc38_membered]) ).
fof(f_294_2,plain,
! [U_1075,U_1074] :
( ( v2_membered(set_difference(U_1075,U_1074))
& v1_membered(set_difference(U_1075,U_1074)) )
| ~ v2_membered(U_1075) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_1075] :
( ( ! [U_1077] : v2_membered(set_difference(U_1075,U_1077))
& ! [U_1076] : v1_membered(set_difference(U_1075,U_1076)) )
| ~ v2_membered(U_1075) ),
inference(miniscope,[status(thm)],[f_294_2]) ).
fof(f_294_4,plain,
( ! [U_1075,U_1076,U_1077] :
( v2_membered(set_difference(U_1075,U_1077))
| ~ sP278(U_1075,U_1076,U_1077) )
& ! [U_1075,U_1076,U_1077] :
( v1_membered(set_difference(U_1075,U_1076))
| ~ sP278(U_1075,U_1076,U_1077) )
& ! [U_1075,U_1076,U_1077] :
( sP278(U_1075,U_1076,U_1077)
| ~ v2_membered(U_1075) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP278])],[f_294_3]) ).
cnf(f_294_5,plain,
( sP278(U_1075,U_1076,U_1077)
| ~ v2_membered(U_1075) ),
inference(clausify,[status(thm)],[f_294_4]) ).
cnf(f_294_6,plain,
( v1_membered(set_difference(U_1075,U_1076))
| ~ sP278(U_1075,U_1076,U_1077) ),
inference(clausify,[status(thm)],[f_294_4]) ).
cnf(f_294_7,plain,
( v2_membered(set_difference(U_1075,U_1077))
| ~ sP278(U_1075,U_1076,U_1077) ),
inference(clausify,[status(thm)],[f_294_4]) ).
fof(f_295_1,plain,
! [A,B] :
( ( v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[fc39_membered]) ).
fof(f_295_2,plain,
! [U_1079,U_1078] :
( ( v3_membered(set_difference(U_1079,U_1078))
& v2_membered(set_difference(U_1079,U_1078))
& v1_membered(set_difference(U_1079,U_1078)) )
| ~ v3_membered(U_1079) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1079] :
( ( ! [U_1082] : v3_membered(set_difference(U_1079,U_1082))
& ! [U_1081] : v2_membered(set_difference(U_1079,U_1081))
& ! [U_1080] : v1_membered(set_difference(U_1079,U_1080)) )
| ~ v3_membered(U_1079) ),
inference(miniscope,[status(thm)],[f_295_2]) ).
fof(f_295_4,plain,
( ! [U_1080,U_1081,U_1082,U_1079] :
( v3_membered(set_difference(U_1079,U_1082))
| ~ sP279(U_1080,U_1081,U_1082,U_1079) )
& ! [U_1080,U_1081,U_1082,U_1079] :
( v2_membered(set_difference(U_1079,U_1081))
| ~ sP279(U_1080,U_1081,U_1082,U_1079) )
& ! [U_1080,U_1081,U_1082,U_1079] :
( v1_membered(set_difference(U_1079,U_1080))
| ~ sP279(U_1080,U_1081,U_1082,U_1079) )
& ! [U_1080,U_1081,U_1082,U_1079] :
( sP279(U_1080,U_1081,U_1082,U_1079)
| ~ v3_membered(U_1079) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279])],[f_295_3]) ).
cnf(f_295_5,plain,
( sP279(U_1080,U_1081,U_1082,U_1079)
| ~ v3_membered(U_1079) ),
inference(clausify,[status(thm)],[f_295_4]) ).
cnf(f_295_6,plain,
( v1_membered(set_difference(U_1079,U_1080))
| ~ sP279(U_1080,U_1081,U_1082,U_1079) ),
inference(clausify,[status(thm)],[f_295_4]) ).
cnf(f_295_7,plain,
( v2_membered(set_difference(U_1079,U_1081))
| ~ sP279(U_1080,U_1081,U_1082,U_1079) ),
inference(clausify,[status(thm)],[f_295_4]) ).
cnf(f_295_8,plain,
( v3_membered(set_difference(U_1079,U_1082))
| ~ sP279(U_1080,U_1081,U_1082,U_1079) ),
inference(clausify,[status(thm)],[f_295_4]) ).
fof(f_296_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_296_2,plain,
! [U_1083] :
( ( function(relation_inverse(U_1083))
& relation(relation_inverse(U_1083)) )
| ~ one_to_one(U_1083)
| ~ function(U_1083)
| ~ relation(U_1083) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
( ! [U_1083] :
( function(relation_inverse(U_1083))
| ~ sP280(U_1083) )
& ! [U_1083] :
( relation(relation_inverse(U_1083))
| ~ sP280(U_1083) )
& ! [U_1083] :
( sP280(U_1083)
| ~ one_to_one(U_1083)
| ~ function(U_1083)
| ~ relation(U_1083) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_296_2]) ).
cnf(f_296_4,plain,
( sP280(U_1083)
| ~ one_to_one(U_1083)
| ~ function(U_1083)
| ~ relation(U_1083) ),
inference(clausify,[status(thm)],[f_296_3]) ).
cnf(f_296_5,plain,
( relation(relation_inverse(U_1083))
| ~ sP280(U_1083) ),
inference(clausify,[status(thm)],[f_296_3]) ).
cnf(f_296_6,plain,
( function(relation_inverse(U_1083))
| ~ sP280(U_1083) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [A] :
( ( v1_partfun1(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v2_binop_1(the_L_join(A),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A))
& relation(the_L_join(A)) )
| ~ join_semilatt_str(A)
| ~ join_associative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc3_lattice2]) ).
fof(f_297_2,plain,
! [U_1084] :
( ( v1_partfun1(the_L_join(U_1084),cartesian_product2(the_carrier(U_1084),the_carrier(U_1084)),the_carrier(U_1084))
& v2_binop_1(the_L_join(U_1084),the_carrier(U_1084))
& quasi_total(the_L_join(U_1084),cartesian_product2(the_carrier(U_1084),the_carrier(U_1084)),the_carrier(U_1084))
& function(the_L_join(U_1084))
& relation(the_L_join(U_1084)) )
| ~ join_semilatt_str(U_1084)
| ~ join_associative(U_1084)
| empty_carrier(U_1084) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
( ! [U_1084] :
( v1_partfun1(the_L_join(U_1084),cartesian_product2(the_carrier(U_1084),the_carrier(U_1084)),the_carrier(U_1084))
| ~ sP281(U_1084) )
& ! [U_1084] :
( v2_binop_1(the_L_join(U_1084),the_carrier(U_1084))
| ~ sP281(U_1084) )
& ! [U_1084] :
( quasi_total(the_L_join(U_1084),cartesian_product2(the_carrier(U_1084),the_carrier(U_1084)),the_carrier(U_1084))
| ~ sP281(U_1084) )
& ! [U_1084] :
( function(the_L_join(U_1084))
| ~ sP281(U_1084) )
& ! [U_1084] :
( relation(the_L_join(U_1084))
| ~ sP281(U_1084) )
& ! [U_1084] :
( sP281(U_1084)
| ~ join_semilatt_str(U_1084)
| ~ join_associative(U_1084)
| empty_carrier(U_1084) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_297_2]) ).
cnf(f_297_4,plain,
( sP281(U_1084)
| ~ join_semilatt_str(U_1084)
| ~ join_associative(U_1084)
| empty_carrier(U_1084) ),
inference(clausify,[status(thm)],[f_297_3]) ).
cnf(f_297_5,plain,
( relation(the_L_join(U_1084))
| ~ sP281(U_1084) ),
inference(clausify,[status(thm)],[f_297_3]) ).
cnf(f_297_6,plain,
( function(the_L_join(U_1084))
| ~ sP281(U_1084) ),
inference(clausify,[status(thm)],[f_297_3]) ).
cnf(f_297_7,plain,
( quasi_total(the_L_join(U_1084),cartesian_product2(the_carrier(U_1084),the_carrier(U_1084)),the_carrier(U_1084))
| ~ sP281(U_1084) ),
inference(clausify,[status(thm)],[f_297_3]) ).
cnf(f_297_8,plain,
( v2_binop_1(the_L_join(U_1084),the_carrier(U_1084))
| ~ sP281(U_1084) ),
inference(clausify,[status(thm)],[f_297_3]) ).
cnf(f_297_9,plain,
( v1_partfun1(the_L_join(U_1084),cartesian_product2(the_carrier(U_1084),the_carrier(U_1084)),the_carrier(U_1084))
| ~ sP281(U_1084) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [A,B,C] :
( ( strict_latt_str(latt_str_of(A,B,C))
& ~ empty_carrier(latt_str_of(A,B,C)) )
| ~ relation_of2(C,cartesian_product2(A,A),A)
| ~ quasi_total(C,cartesian_product2(A,A),A)
| ~ function(C)
| ~ relation_of2(B,cartesian_product2(A,A),A)
| ~ quasi_total(B,cartesian_product2(A,A),A)
| ~ function(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_lattices]) ).
fof(f_298_2,plain,
! [U_1087,U_1086,U_1085] :
( ( strict_latt_str(latt_str_of(U_1087,U_1086,U_1085))
& ~ empty_carrier(latt_str_of(U_1087,U_1086,U_1085)) )
| ~ relation_of2(U_1085,cartesian_product2(U_1087,U_1087),U_1087)
| ~ quasi_total(U_1085,cartesian_product2(U_1087,U_1087),U_1087)
| ~ function(U_1085)
| ~ relation_of2(U_1086,cartesian_product2(U_1087,U_1087),U_1087)
| ~ quasi_total(U_1086,cartesian_product2(U_1087,U_1087),U_1087)
| ~ function(U_1086)
| empty(U_1087) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
( ! [U_1086,U_1085,U_1087] :
( strict_latt_str(latt_str_of(U_1087,U_1086,U_1085))
| ~ sP282(U_1086,U_1085,U_1087) )
& ! [U_1086,U_1085,U_1087] :
( ~ empty_carrier(latt_str_of(U_1087,U_1086,U_1085))
| ~ sP282(U_1086,U_1085,U_1087) )
& ! [U_1086,U_1085,U_1087] :
( sP282(U_1086,U_1085,U_1087)
| ~ relation_of2(U_1085,cartesian_product2(U_1087,U_1087),U_1087)
| ~ quasi_total(U_1085,cartesian_product2(U_1087,U_1087),U_1087)
| ~ function(U_1085)
| ~ relation_of2(U_1086,cartesian_product2(U_1087,U_1087),U_1087)
| ~ quasi_total(U_1086,cartesian_product2(U_1087,U_1087),U_1087)
| ~ function(U_1086)
| empty(U_1087) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282])],[f_298_2]) ).
cnf(f_298_4,plain,
( sP282(U_1086,U_1085,U_1087)
| ~ relation_of2(U_1085,cartesian_product2(U_1087,U_1087),U_1087)
| ~ quasi_total(U_1085,cartesian_product2(U_1087,U_1087),U_1087)
| ~ function(U_1085)
| ~ relation_of2(U_1086,cartesian_product2(U_1087,U_1087),U_1087)
| ~ quasi_total(U_1086,cartesian_product2(U_1087,U_1087),U_1087)
| ~ function(U_1086)
| empty(U_1087) ),
inference(clausify,[status(thm)],[f_298_3]) ).
cnf(f_298_5,plain,
( ~ empty_carrier(latt_str_of(U_1087,U_1086,U_1085))
| ~ sP282(U_1086,U_1085,U_1087) ),
inference(clausify,[status(thm)],[f_298_3]) ).
cnf(f_298_6,plain,
( strict_latt_str(latt_str_of(U_1087,U_1086,U_1085))
| ~ sP282(U_1086,U_1085,U_1087) ),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_1,plain,
! [A,B] :
( ( antisymmetric_relstr(rel_str_of(A,B))
& transitive_relstr(rel_str_of(A,B))
& reflexive_relstr(rel_str_of(A,B))
& strict_rel_str(rel_str_of(A,B)) )
| ~ relation_of2(B,A,A)
| ~ v1_partfun1(B,A,A)
| ~ transitive(B)
| ~ antisymmetric(B)
| ~ reflexive(B) ),
inference(fof_nnf,[status(thm)],[fc3_orders_2]) ).
fof(f_299_2,plain,
! [U_1089,U_1088] :
( ( antisymmetric_relstr(rel_str_of(U_1089,U_1088))
& transitive_relstr(rel_str_of(U_1089,U_1088))
& reflexive_relstr(rel_str_of(U_1089,U_1088))
& strict_rel_str(rel_str_of(U_1089,U_1088)) )
| ~ relation_of2(U_1088,U_1089,U_1089)
| ~ v1_partfun1(U_1088,U_1089,U_1089)
| ~ transitive(U_1088)
| ~ antisymmetric(U_1088)
| ~ reflexive(U_1088) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
( ! [U_1089,U_1088] :
( antisymmetric_relstr(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) )
& ! [U_1089,U_1088] :
( transitive_relstr(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) )
& ! [U_1089,U_1088] :
( reflexive_relstr(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) )
& ! [U_1089,U_1088] :
( strict_rel_str(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) )
& ! [U_1089,U_1088] :
( sP283(U_1089,U_1088)
| ~ relation_of2(U_1088,U_1089,U_1089)
| ~ v1_partfun1(U_1088,U_1089,U_1089)
| ~ transitive(U_1088)
| ~ antisymmetric(U_1088)
| ~ reflexive(U_1088) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_299_2]) ).
cnf(f_299_4,plain,
( sP283(U_1089,U_1088)
| ~ relation_of2(U_1088,U_1089,U_1089)
| ~ v1_partfun1(U_1088,U_1089,U_1089)
| ~ transitive(U_1088)
| ~ antisymmetric(U_1088)
| ~ reflexive(U_1088) ),
inference(clausify,[status(thm)],[f_299_3]) ).
cnf(f_299_5,plain,
( strict_rel_str(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) ),
inference(clausify,[status(thm)],[f_299_3]) ).
cnf(f_299_6,plain,
( reflexive_relstr(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) ),
inference(clausify,[status(thm)],[f_299_3]) ).
cnf(f_299_7,plain,
( transitive_relstr(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) ),
inference(clausify,[status(thm)],[f_299_3]) ).
cnf(f_299_8,plain,
( antisymmetric_relstr(rel_str_of(U_1089,U_1088))
| ~ sP283(U_1089,U_1088) ),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_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_300_2,plain,
! [U_1090] :
( ( ordinal(succ(U_1090))
& epsilon_connected(succ(U_1090))
& epsilon_transitive(succ(U_1090))
& ~ empty(succ(U_1090)) )
| ~ ordinal(U_1090) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
( ! [U_1090] :
( ordinal(succ(U_1090))
| ~ sP284(U_1090) )
& ! [U_1090] :
( epsilon_connected(succ(U_1090))
| ~ sP284(U_1090) )
& ! [U_1090] :
( epsilon_transitive(succ(U_1090))
| ~ sP284(U_1090) )
& ! [U_1090] :
( ~ empty(succ(U_1090))
| ~ sP284(U_1090) )
& ! [U_1090] :
( sP284(U_1090)
| ~ ordinal(U_1090) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_300_2]) ).
cnf(f_300_4,plain,
( sP284(U_1090)
| ~ ordinal(U_1090) ),
inference(clausify,[status(thm)],[f_300_3]) ).
cnf(f_300_5,plain,
( ~ empty(succ(U_1090))
| ~ sP284(U_1090) ),
inference(clausify,[status(thm)],[f_300_3]) ).
cnf(f_300_6,plain,
( epsilon_transitive(succ(U_1090))
| ~ sP284(U_1090) ),
inference(clausify,[status(thm)],[f_300_3]) ).
cnf(f_300_7,plain,
( epsilon_connected(succ(U_1090))
| ~ sP284(U_1090) ),
inference(clausify,[status(thm)],[f_300_3]) ).
cnf(f_300_8,plain,
( ordinal(succ(U_1090))
| ~ sP284(U_1090) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_1,plain,
! [A,B] :
( relation(set_difference(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc3_relat_1]) ).
fof(f_301_2,plain,
! [U_1092,U_1091] :
( relation(set_difference(U_1092,U_1091))
| ~ relation(U_1091)
| ~ relation(U_1092) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_1091,U_1092] :
( relation(set_difference(U_1092,U_1091))
| ~ relation(U_1091)
| ~ relation(U_1092) ),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
( relation(set_difference(U_1092,U_1091))
| ~ relation(U_1091)
| ~ relation(U_1092) ),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_302_2,plain,
! [U_1094,U_1093] : ~ empty(unordered_pair(U_1094,U_1093)),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_1093,U_1094] : ~ empty(unordered_pair(U_1094,U_1093)),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
~ empty(unordered_pair(U_1094,U_1093)),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_1,plain,
! [A,B] :
( open_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ closed_subset(B,A)
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc3_tops_1]) ).
fof(f_303_2,plain,
! [U_1096,U_1095] :
( open_subset(subset_complement(the_carrier(U_1096),U_1095),U_1096)
| ~ element(U_1095,powerset(the_carrier(U_1096)))
| ~ closed_subset(U_1095,U_1096)
| ~ top_str(U_1096)
| ~ topological_space(U_1096) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_1095,U_1096] :
( open_subset(subset_complement(the_carrier(U_1096),U_1095),U_1096)
| ~ element(U_1095,powerset(the_carrier(U_1096)))
| ~ closed_subset(U_1095,U_1096)
| ~ top_str(U_1096)
| ~ topological_space(U_1096) ),
inference(definitional_conversion,[status(esa)],[f_303_2]) ).
cnf(f_303_4,plain,
( open_subset(subset_complement(the_carrier(U_1096),U_1095),U_1096)
| ~ element(U_1095,powerset(the_carrier(U_1096)))
| ~ closed_subset(U_1095,U_1096)
| ~ top_str(U_1096)
| ~ topological_space(U_1096) ),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_304_2,plain,
! [U_1098,U_1097] :
( ~ empty(set_union2(U_1097,U_1098))
| empty(U_1098) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1098] :
( ! [U_1097] : ~ empty(set_union2(U_1097,U_1098))
| empty(U_1098) ),
inference(miniscope,[status(thm)],[f_304_2]) ).
fof(f_304_4,plain,
! [U_1097,U_1098] :
( ~ empty(set_union2(U_1097,U_1098))
| empty(U_1098) ),
inference(definitional_conversion,[status(esa)],[f_304_3]) ).
cnf(f_304_5,plain,
( ~ empty(set_union2(U_1097,U_1098))
| empty(U_1098) ),
inference(clausify,[status(thm)],[f_304_4]) ).
fof(f_305_1,plain,
! [A,B] :
( ( v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[fc40_membered]) ).
fof(f_305_2,plain,
! [U_1100,U_1099] :
( ( v4_membered(set_difference(U_1100,U_1099))
& v3_membered(set_difference(U_1100,U_1099))
& v2_membered(set_difference(U_1100,U_1099))
& v1_membered(set_difference(U_1100,U_1099)) )
| ~ v4_membered(U_1100) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_1100] :
( ( ! [U_1104] : v4_membered(set_difference(U_1100,U_1104))
& ! [U_1103] : v3_membered(set_difference(U_1100,U_1103))
& ! [U_1102] : v2_membered(set_difference(U_1100,U_1102))
& ! [U_1101] : v1_membered(set_difference(U_1100,U_1101)) )
| ~ v4_membered(U_1100) ),
inference(miniscope,[status(thm)],[f_305_2]) ).
fof(f_305_4,plain,
( ! [U_1100,U_1101,U_1102,U_1103,U_1104] :
( v4_membered(set_difference(U_1100,U_1104))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) )
& ! [U_1100,U_1101,U_1102,U_1103,U_1104] :
( v3_membered(set_difference(U_1100,U_1103))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) )
& ! [U_1100,U_1101,U_1102,U_1103,U_1104] :
( v2_membered(set_difference(U_1100,U_1102))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) )
& ! [U_1100,U_1101,U_1102,U_1103,U_1104] :
( v1_membered(set_difference(U_1100,U_1101))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) )
& ! [U_1100,U_1101,U_1102,U_1103,U_1104] :
( sP285(U_1100,U_1101,U_1102,U_1103,U_1104)
| ~ v4_membered(U_1100) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285])],[f_305_3]) ).
cnf(f_305_5,plain,
( sP285(U_1100,U_1101,U_1102,U_1103,U_1104)
| ~ v4_membered(U_1100) ),
inference(clausify,[status(thm)],[f_305_4]) ).
cnf(f_305_6,plain,
( v1_membered(set_difference(U_1100,U_1101))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) ),
inference(clausify,[status(thm)],[f_305_4]) ).
cnf(f_305_7,plain,
( v2_membered(set_difference(U_1100,U_1102))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) ),
inference(clausify,[status(thm)],[f_305_4]) ).
cnf(f_305_8,plain,
( v3_membered(set_difference(U_1100,U_1103))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) ),
inference(clausify,[status(thm)],[f_305_4]) ).
cnf(f_305_9,plain,
( v4_membered(set_difference(U_1100,U_1104))
| ~ sP285(U_1100,U_1101,U_1102,U_1103,U_1104) ),
inference(clausify,[status(thm)],[f_305_4]) ).
fof(f_306_1,plain,
! [A,B] :
( ( v5_membered(set_difference(A,B))
& v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[fc41_membered]) ).
fof(f_306_2,plain,
! [U_1106,U_1105] :
( ( v5_membered(set_difference(U_1106,U_1105))
& v4_membered(set_difference(U_1106,U_1105))
& v3_membered(set_difference(U_1106,U_1105))
& v2_membered(set_difference(U_1106,U_1105))
& v1_membered(set_difference(U_1106,U_1105)) )
| ~ v5_membered(U_1106) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_1106] :
( ( ! [U_1111] : v5_membered(set_difference(U_1106,U_1111))
& ! [U_1110] : v4_membered(set_difference(U_1106,U_1110))
& ! [U_1109] : v3_membered(set_difference(U_1106,U_1109))
& ! [U_1108] : v2_membered(set_difference(U_1106,U_1108))
& ! [U_1107] : v1_membered(set_difference(U_1106,U_1107)) )
| ~ v5_membered(U_1106) ),
inference(miniscope,[status(thm)],[f_306_2]) ).
fof(f_306_4,plain,
( ! [U_1107,U_1106,U_1108,U_1109,U_1110,U_1111] :
( v5_membered(set_difference(U_1106,U_1111))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) )
& ! [U_1107,U_1106,U_1108,U_1109,U_1110,U_1111] :
( v4_membered(set_difference(U_1106,U_1110))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) )
& ! [U_1107,U_1106,U_1108,U_1109,U_1110,U_1111] :
( v3_membered(set_difference(U_1106,U_1109))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) )
& ! [U_1107,U_1106,U_1108,U_1109,U_1110,U_1111] :
( v2_membered(set_difference(U_1106,U_1108))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) )
& ! [U_1107,U_1106,U_1108,U_1109,U_1110,U_1111] :
( v1_membered(set_difference(U_1106,U_1107))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) )
& ! [U_1107,U_1106,U_1108,U_1109,U_1110,U_1111] :
( sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111)
| ~ v5_membered(U_1106) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_306_3]) ).
cnf(f_306_5,plain,
( sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111)
| ~ v5_membered(U_1106) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_6,plain,
( v1_membered(set_difference(U_1106,U_1107))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_7,plain,
( v2_membered(set_difference(U_1106,U_1108))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_8,plain,
( v3_membered(set_difference(U_1106,U_1109))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_9,plain,
( v4_membered(set_difference(U_1106,U_1110))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) ),
inference(clausify,[status(thm)],[f_306_4]) ).
cnf(f_306_10,plain,
( v5_membered(set_difference(U_1106,U_1111))
| ~ sP286(U_1107,U_1106,U_1108,U_1109,U_1110,U_1111) ),
inference(clausify,[status(thm)],[f_306_4]) ).
fof(f_307_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_307_2,plain,
! [U_1113,U_1112] :
( ( function(relation_dom_restriction(U_1113,U_1112))
& relation(relation_dom_restriction(U_1113,U_1112)) )
| ~ function(U_1113)
| ~ relation(U_1113) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_1113] :
( ( ! [U_1115] : function(relation_dom_restriction(U_1113,U_1115))
& ! [U_1114] : relation(relation_dom_restriction(U_1113,U_1114)) )
| ~ function(U_1113)
| ~ relation(U_1113) ),
inference(miniscope,[status(thm)],[f_307_2]) ).
fof(f_307_4,plain,
( ! [U_1113,U_1115,U_1114] :
( function(relation_dom_restriction(U_1113,U_1115))
| ~ sP287(U_1113,U_1115,U_1114) )
& ! [U_1113,U_1115,U_1114] :
( relation(relation_dom_restriction(U_1113,U_1114))
| ~ sP287(U_1113,U_1115,U_1114) )
& ! [U_1113,U_1115,U_1114] :
( sP287(U_1113,U_1115,U_1114)
| ~ function(U_1113)
| ~ relation(U_1113) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287])],[f_307_3]) ).
cnf(f_307_5,plain,
( sP287(U_1113,U_1115,U_1114)
| ~ function(U_1113)
| ~ relation(U_1113) ),
inference(clausify,[status(thm)],[f_307_4]) ).
cnf(f_307_6,plain,
( relation(relation_dom_restriction(U_1113,U_1114))
| ~ sP287(U_1113,U_1115,U_1114) ),
inference(clausify,[status(thm)],[f_307_4]) ).
cnf(f_307_7,plain,
( function(relation_dom_restriction(U_1113,U_1115))
| ~ sP287(U_1113,U_1115,U_1114) ),
inference(clausify,[status(thm)],[f_307_4]) ).
fof(f_308_1,plain,
! [A] :
( ( v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v1_binop_1(the_L_meet(A),the_carrier(A))
& quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_meet(A))
& relation(the_L_meet(A)) )
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc4_lattice2]) ).
fof(f_308_2,plain,
! [U_1116] :
( ( v1_partfun1(the_L_meet(U_1116),cartesian_product2(the_carrier(U_1116),the_carrier(U_1116)),the_carrier(U_1116))
& v1_binop_1(the_L_meet(U_1116),the_carrier(U_1116))
& quasi_total(the_L_meet(U_1116),cartesian_product2(the_carrier(U_1116),the_carrier(U_1116)),the_carrier(U_1116))
& function(the_L_meet(U_1116))
& relation(the_L_meet(U_1116)) )
| ~ meet_semilatt_str(U_1116)
| ~ meet_commutative(U_1116)
| empty_carrier(U_1116) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
( ! [U_1116] :
( v1_partfun1(the_L_meet(U_1116),cartesian_product2(the_carrier(U_1116),the_carrier(U_1116)),the_carrier(U_1116))
| ~ sP288(U_1116) )
& ! [U_1116] :
( v1_binop_1(the_L_meet(U_1116),the_carrier(U_1116))
| ~ sP288(U_1116) )
& ! [U_1116] :
( quasi_total(the_L_meet(U_1116),cartesian_product2(the_carrier(U_1116),the_carrier(U_1116)),the_carrier(U_1116))
| ~ sP288(U_1116) )
& ! [U_1116] :
( function(the_L_meet(U_1116))
| ~ sP288(U_1116) )
& ! [U_1116] :
( relation(the_L_meet(U_1116))
| ~ sP288(U_1116) )
& ! [U_1116] :
( sP288(U_1116)
| ~ meet_semilatt_str(U_1116)
| ~ meet_commutative(U_1116)
| empty_carrier(U_1116) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_308_2]) ).
cnf(f_308_4,plain,
( sP288(U_1116)
| ~ meet_semilatt_str(U_1116)
| ~ meet_commutative(U_1116)
| empty_carrier(U_1116) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_5,plain,
( relation(the_L_meet(U_1116))
| ~ sP288(U_1116) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_6,plain,
( function(the_L_meet(U_1116))
| ~ sP288(U_1116) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_7,plain,
( quasi_total(the_L_meet(U_1116),cartesian_product2(the_carrier(U_1116),the_carrier(U_1116)),the_carrier(U_1116))
| ~ sP288(U_1116) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_8,plain,
( v1_binop_1(the_L_meet(U_1116),the_carrier(U_1116))
| ~ sP288(U_1116) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_9,plain,
( v1_partfun1(the_L_meet(U_1116),cartesian_product2(the_carrier(U_1116),the_carrier(U_1116)),the_carrier(U_1116))
| ~ sP288(U_1116) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_1,plain,
! [A] :
( ( antisymmetric_relstr(poset_of_lattice(A))
& transitive_relstr(poset_of_lattice(A))
& reflexive_relstr(poset_of_lattice(A))
& strict_rel_str(poset_of_lattice(A))
& ~ empty_carrier(poset_of_lattice(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc4_lattice3]) ).
fof(f_309_2,plain,
! [U_1117] :
( ( antisymmetric_relstr(poset_of_lattice(U_1117))
& transitive_relstr(poset_of_lattice(U_1117))
& reflexive_relstr(poset_of_lattice(U_1117))
& strict_rel_str(poset_of_lattice(U_1117))
& ~ empty_carrier(poset_of_lattice(U_1117)) )
| ~ latt_str(U_1117)
| ~ lattice(U_1117)
| empty_carrier(U_1117) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
( ! [U_1117] :
( antisymmetric_relstr(poset_of_lattice(U_1117))
| ~ sP289(U_1117) )
& ! [U_1117] :
( transitive_relstr(poset_of_lattice(U_1117))
| ~ sP289(U_1117) )
& ! [U_1117] :
( reflexive_relstr(poset_of_lattice(U_1117))
| ~ sP289(U_1117) )
& ! [U_1117] :
( strict_rel_str(poset_of_lattice(U_1117))
| ~ sP289(U_1117) )
& ! [U_1117] :
( ~ empty_carrier(poset_of_lattice(U_1117))
| ~ sP289(U_1117) )
& ! [U_1117] :
( sP289(U_1117)
| ~ latt_str(U_1117)
| ~ lattice(U_1117)
| empty_carrier(U_1117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289])],[f_309_2]) ).
cnf(f_309_4,plain,
( sP289(U_1117)
| ~ latt_str(U_1117)
| ~ lattice(U_1117)
| empty_carrier(U_1117) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_5,plain,
( ~ empty_carrier(poset_of_lattice(U_1117))
| ~ sP289(U_1117) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_6,plain,
( strict_rel_str(poset_of_lattice(U_1117))
| ~ sP289(U_1117) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_7,plain,
( reflexive_relstr(poset_of_lattice(U_1117))
| ~ sP289(U_1117) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_8,plain,
( transitive_relstr(poset_of_lattice(U_1117))
| ~ sP289(U_1117) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_9,plain,
( antisymmetric_relstr(poset_of_lattice(U_1117))
| ~ sP289(U_1117) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_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_310_2,plain,
! [U_1118] :
( ( ordinal(union(U_1118))
& epsilon_connected(union(U_1118))
& epsilon_transitive(union(U_1118)) )
| ~ ordinal(U_1118) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
( ! [U_1118] :
( ordinal(union(U_1118))
| ~ sP290(U_1118) )
& ! [U_1118] :
( epsilon_connected(union(U_1118))
| ~ sP290(U_1118) )
& ! [U_1118] :
( epsilon_transitive(union(U_1118))
| ~ sP290(U_1118) )
& ! [U_1118] :
( sP290(U_1118)
| ~ ordinal(U_1118) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290])],[f_310_2]) ).
cnf(f_310_4,plain,
( sP290(U_1118)
| ~ ordinal(U_1118) ),
inference(clausify,[status(thm)],[f_310_3]) ).
cnf(f_310_5,plain,
( epsilon_transitive(union(U_1118))
| ~ sP290(U_1118) ),
inference(clausify,[status(thm)],[f_310_3]) ).
cnf(f_310_6,plain,
( epsilon_connected(union(U_1118))
| ~ sP290(U_1118) ),
inference(clausify,[status(thm)],[f_310_3]) ).
cnf(f_310_7,plain,
( ordinal(union(U_1118))
| ~ sP290(U_1118) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_311_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_311_1]) ).
cnf(f_311_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_311_2]) ).
cnf(f_311_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
! [A,B] :
( ~ empty(cartesian_product2(A,B))
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc4_subset_1]) ).
fof(f_312_2,plain,
! [U_1120,U_1119] :
( ~ empty(cartesian_product2(U_1120,U_1119))
| empty(U_1119)
| empty(U_1120) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_1120,U_1119] :
( ~ empty(cartesian_product2(U_1120,U_1119))
| empty(U_1119)
| empty(U_1120) ),
inference(definitional_conversion,[status(esa)],[f_312_2]) ).
cnf(f_312_4,plain,
( ~ empty(cartesian_product2(U_1120,U_1119))
| empty(U_1119)
| empty(U_1120) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [A,B] :
( closed_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ open_subset(B,A)
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc4_tops_1]) ).
fof(f_313_2,plain,
! [U_1122,U_1121] :
( closed_subset(subset_complement(the_carrier(U_1122),U_1121),U_1122)
| ~ element(U_1121,powerset(the_carrier(U_1122)))
| ~ open_subset(U_1121,U_1122)
| ~ top_str(U_1122)
| ~ topological_space(U_1122) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_1121,U_1122] :
( closed_subset(subset_complement(the_carrier(U_1122),U_1121),U_1122)
| ~ element(U_1121,powerset(the_carrier(U_1122)))
| ~ open_subset(U_1121,U_1122)
| ~ top_str(U_1122)
| ~ topological_space(U_1122) ),
inference(definitional_conversion,[status(esa)],[f_313_2]) ).
cnf(f_313_4,plain,
( closed_subset(subset_complement(the_carrier(U_1122),U_1121),U_1122)
| ~ element(U_1121,powerset(the_carrier(U_1122)))
| ~ open_subset(U_1121,U_1122)
| ~ top_str(U_1122)
| ~ topological_space(U_1122) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_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_314_2,plain,
! [U_1124,U_1123] :
( ( function(relation_rng_restriction(U_1124,U_1123))
& relation(relation_rng_restriction(U_1124,U_1123)) )
| ~ function(U_1123)
| ~ relation(U_1123) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
( ! [U_1124,U_1123] :
( function(relation_rng_restriction(U_1124,U_1123))
| ~ sP291(U_1124,U_1123) )
& ! [U_1124,U_1123] :
( relation(relation_rng_restriction(U_1124,U_1123))
| ~ sP291(U_1124,U_1123) )
& ! [U_1124,U_1123] :
( sP291(U_1124,U_1123)
| ~ function(U_1123)
| ~ relation(U_1123) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291])],[f_314_2]) ).
cnf(f_314_4,plain,
( sP291(U_1124,U_1123)
| ~ function(U_1123)
| ~ relation(U_1123) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_5,plain,
( relation(relation_rng_restriction(U_1124,U_1123))
| ~ sP291(U_1124,U_1123) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_6,plain,
( function(relation_rng_restriction(U_1124,U_1123))
| ~ sP291(U_1124,U_1123) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [A] :
( ( v1_partfun1(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& v2_binop_1(the_L_meet(A),the_carrier(A))
& quasi_total(the_L_meet(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_meet(A))
& relation(the_L_meet(A)) )
| ~ meet_semilatt_str(A)
| ~ meet_associative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc5_lattice2]) ).
fof(f_315_2,plain,
! [U_1125] :
( ( v1_partfun1(the_L_meet(U_1125),cartesian_product2(the_carrier(U_1125),the_carrier(U_1125)),the_carrier(U_1125))
& v2_binop_1(the_L_meet(U_1125),the_carrier(U_1125))
& quasi_total(the_L_meet(U_1125),cartesian_product2(the_carrier(U_1125),the_carrier(U_1125)),the_carrier(U_1125))
& function(the_L_meet(U_1125))
& relation(the_L_meet(U_1125)) )
| ~ meet_semilatt_str(U_1125)
| ~ meet_associative(U_1125)
| empty_carrier(U_1125) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
( ! [U_1125] :
( v1_partfun1(the_L_meet(U_1125),cartesian_product2(the_carrier(U_1125),the_carrier(U_1125)),the_carrier(U_1125))
| ~ sP292(U_1125) )
& ! [U_1125] :
( v2_binop_1(the_L_meet(U_1125),the_carrier(U_1125))
| ~ sP292(U_1125) )
& ! [U_1125] :
( quasi_total(the_L_meet(U_1125),cartesian_product2(the_carrier(U_1125),the_carrier(U_1125)),the_carrier(U_1125))
| ~ sP292(U_1125) )
& ! [U_1125] :
( function(the_L_meet(U_1125))
| ~ sP292(U_1125) )
& ! [U_1125] :
( relation(the_L_meet(U_1125))
| ~ sP292(U_1125) )
& ! [U_1125] :
( sP292(U_1125)
| ~ meet_semilatt_str(U_1125)
| ~ meet_associative(U_1125)
| empty_carrier(U_1125) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP292])],[f_315_2]) ).
cnf(f_315_4,plain,
( sP292(U_1125)
| ~ meet_semilatt_str(U_1125)
| ~ meet_associative(U_1125)
| empty_carrier(U_1125) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_5,plain,
( relation(the_L_meet(U_1125))
| ~ sP292(U_1125) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_6,plain,
( function(the_L_meet(U_1125))
| ~ sP292(U_1125) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_7,plain,
( quasi_total(the_L_meet(U_1125),cartesian_product2(the_carrier(U_1125),the_carrier(U_1125)),the_carrier(U_1125))
| ~ sP292(U_1125) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_8,plain,
( v2_binop_1(the_L_meet(U_1125),the_carrier(U_1125))
| ~ sP292(U_1125) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_9,plain,
( v1_partfun1(the_L_meet(U_1125),cartesian_product2(the_carrier(U_1125),the_carrier(U_1125)),the_carrier(U_1125))
| ~ sP292(U_1125) ),
inference(clausify,[status(thm)],[f_315_3]) ).
fof(f_316_1,plain,
! [A] :
( closed_subset(cast_as_carrier_subset(A),A)
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc5_pre_topc]) ).
fof(f_316_2,plain,
! [U_1126] :
( closed_subset(cast_as_carrier_subset(U_1126),U_1126)
| ~ top_str(U_1126)
| ~ topological_space(U_1126) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
! [U_1126] :
( closed_subset(cast_as_carrier_subset(U_1126),U_1126)
| ~ top_str(U_1126)
| ~ topological_space(U_1126) ),
inference(definitional_conversion,[status(esa)],[f_316_2]) ).
cnf(f_316_4,plain,
( closed_subset(cast_as_carrier_subset(U_1126),U_1126)
| ~ top_str(U_1126)
| ~ topological_space(U_1126) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_317_2,plain,
! [U_1127] :
( ~ empty(relation_dom(U_1127))
| ~ relation(U_1127)
| empty(U_1127) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_1127] :
( ~ empty(relation_dom(U_1127))
| ~ relation(U_1127)
| empty(U_1127) ),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_4,plain,
( ~ empty(relation_dom(U_1127))
| ~ relation(U_1127)
| empty(U_1127) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_1,plain,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc6_membered]) ).
fof(f_318_2,plain,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_318_1]) ).
cnf(f_318_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_318_2]) ).
cnf(f_318_4,plain,
v1_membered(empty_set),
inference(clausify,[status(thm)],[f_318_2]) ).
cnf(f_318_5,plain,
v2_membered(empty_set),
inference(clausify,[status(thm)],[f_318_2]) ).
cnf(f_318_6,plain,
v3_membered(empty_set),
inference(clausify,[status(thm)],[f_318_2]) ).
cnf(f_318_7,plain,
v4_membered(empty_set),
inference(clausify,[status(thm)],[f_318_2]) ).
cnf(f_318_8,plain,
v5_membered(empty_set),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_319_2,plain,
! [U_1128] :
( ~ empty(relation_rng(U_1128))
| ~ relation(U_1128)
| empty(U_1128) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_1128] :
( ~ empty(relation_rng(U_1128))
| ~ relation(U_1128)
| empty(U_1128) ),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
( ~ empty(relation_rng(U_1128))
| ~ relation(U_1128)
| empty(U_1128) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [A,B] :
( open_subset(interior(A,B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc6_tops_1]) ).
fof(f_320_2,plain,
! [U_1130,U_1129] :
( open_subset(interior(U_1130,U_1129),U_1130)
| ~ element(U_1129,powerset(the_carrier(U_1130)))
| ~ top_str(U_1130)
| ~ topological_space(U_1130) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1129,U_1130] :
( open_subset(interior(U_1130,U_1129),U_1130)
| ~ element(U_1129,powerset(the_carrier(U_1130)))
| ~ top_str(U_1130)
| ~ topological_space(U_1130) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( open_subset(interior(U_1130,U_1129),U_1130)
| ~ element(U_1129,powerset(the_carrier(U_1130)))
| ~ top_str(U_1130)
| ~ topological_space(U_1130) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_321_2,plain,
! [U_1131] :
( ( relation(relation_dom(U_1131))
& empty(relation_dom(U_1131)) )
| ~ empty(U_1131) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
( ! [U_1131] :
( relation(relation_dom(U_1131))
| ~ sP293(U_1131) )
& ! [U_1131] :
( empty(relation_dom(U_1131))
| ~ sP293(U_1131) )
& ! [U_1131] :
( sP293(U_1131)
| ~ empty(U_1131) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_321_2]) ).
cnf(f_321_4,plain,
( sP293(U_1131)
| ~ empty(U_1131) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_5,plain,
( empty(relation_dom(U_1131))
| ~ sP293(U_1131) ),
inference(clausify,[status(thm)],[f_321_3]) ).
cnf(f_321_6,plain,
( relation(relation_dom(U_1131))
| ~ sP293(U_1131) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_322_2,plain,
! [U_1132] :
( ( relation(relation_rng(U_1132))
& empty(relation_rng(U_1132)) )
| ~ empty(U_1132) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
( ! [U_1132] :
( relation(relation_rng(U_1132))
| ~ sP294(U_1132) )
& ! [U_1132] :
( empty(relation_rng(U_1132))
| ~ sP294(U_1132) )
& ! [U_1132] :
( sP294(U_1132)
| ~ empty(U_1132) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_322_2]) ).
cnf(f_322_4,plain,
( sP294(U_1132)
| ~ empty(U_1132) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_5,plain,
( empty(relation_rng(U_1132))
| ~ sP294(U_1132) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_6,plain,
( relation(relation_rng(U_1132))
| ~ sP294(U_1132) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_1,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc9_finset_1]) ).
fof(f_323_2,plain,
! [U_1134,U_1133] :
( finite(set_union2(U_1134,U_1133))
| ~ finite(U_1133)
| ~ finite(U_1134) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
! [U_1133,U_1134] :
( finite(set_union2(U_1134,U_1133))
| ~ finite(U_1133)
| ~ finite(U_1134) ),
inference(definitional_conversion,[status(esa)],[f_323_2]) ).
cnf(f_323_4,plain,
( finite(set_union2(U_1134,U_1133))
| ~ finite(U_1133)
| ~ finite(U_1134) ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_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_324_2,plain,
! [U_1136,U_1135] :
( ( relation(relation_composition(U_1136,U_1135))
& empty(relation_composition(U_1136,U_1135)) )
| ~ relation(U_1135)
| ~ empty(U_1136) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
( ! [U_1136,U_1135] :
( relation(relation_composition(U_1136,U_1135))
| ~ sP295(U_1136,U_1135) )
& ! [U_1136,U_1135] :
( empty(relation_composition(U_1136,U_1135))
| ~ sP295(U_1136,U_1135) )
& ! [U_1136,U_1135] :
( sP295(U_1136,U_1135)
| ~ relation(U_1135)
| ~ empty(U_1136) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_324_2]) ).
cnf(f_324_4,plain,
( sP295(U_1136,U_1135)
| ~ relation(U_1135)
| ~ empty(U_1136) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_5,plain,
( empty(relation_composition(U_1136,U_1135))
| ~ sP295(U_1136,U_1135) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_6,plain,
( relation(relation_composition(U_1136,U_1135))
| ~ sP295(U_1136,U_1135) ),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_1,plain,
! [A,B] :
( ( ( in(A,a_1_0_filter_1(B))
| ! [C,D] :
( ~ below_refl(B,C,D)
| A != ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
| ~ element(D,the_carrier(B))
| ~ element(C,the_carrier(B)) ) )
& ( ? [C,D] :
( below_refl(B,C,D)
& A = ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
& element(D,the_carrier(B))
& element(C,the_carrier(B)) )
| ~ in(A,a_1_0_filter_1(B)) ) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[fraenkel_a_1_0_filter_1]) ).
fof(f_325_2,plain,
! [U_1142,U_1141] :
( ( ( in(U_1142,a_1_0_filter_1(U_1141))
| ! [U_1140,U_1139] :
( ~ below_refl(U_1141,U_1140,U_1139)
| U_1142 != ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1140,U_1139)
| ~ element(U_1139,the_carrier(U_1141))
| ~ element(U_1140,the_carrier(U_1141)) ) )
& ( ? [U_1138,U_1137] :
( below_refl(U_1141,U_1138,U_1137)
& U_1142 = ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1138,U_1137)
& element(U_1137,the_carrier(U_1141))
& element(U_1138,the_carrier(U_1141)) )
| ~ in(U_1142,a_1_0_filter_1(U_1141)) ) )
| ~ latt_str(U_1141)
| ~ lattice(U_1141)
| empty_carrier(U_1141) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1142,U_1141] :
( ( ( in(U_1142,a_1_0_filter_1(U_1141))
| ! [U_1140] :
( ! [U_1139] :
( ~ below_refl(U_1141,U_1140,U_1139)
| U_1142 != ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1140,U_1139)
| ~ element(U_1139,the_carrier(U_1141)) )
| ~ element(U_1140,the_carrier(U_1141)) ) )
& ( ? [U_1138] :
( ? [U_1137] :
( below_refl(U_1141,U_1138,U_1137)
& U_1142 = ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1138,U_1137)
& element(U_1137,the_carrier(U_1141)) )
& element(U_1138,the_carrier(U_1141)) )
| ~ in(U_1142,a_1_0_filter_1(U_1141)) ) )
| ~ latt_str(U_1141)
| ~ lattice(U_1141)
| empty_carrier(U_1141) ),
inference(miniscope,[status(thm)],[f_325_2]) ).
fof(f_325_4,plain,
! [U_1142,U_1141] :
( ( ( in(U_1142,a_1_0_filter_1(U_1141))
| ! [U_1140] :
( ! [U_1139] :
( ~ below_refl(U_1141,U_1140,U_1139)
| U_1142 != ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1140,U_1139)
| ~ element(U_1139,the_carrier(U_1141)) )
| ~ element(U_1140,the_carrier(U_1141)) ) )
& ( ( ? [U_1137] :
( below_refl(U_1141,sK157(U_1142,U_1141),U_1137)
& U_1142 = ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),sK157(U_1142,U_1141),U_1137)
& element(U_1137,the_carrier(U_1141)) )
& element(sK157(U_1142,U_1141),the_carrier(U_1141)) )
| ~ in(U_1142,a_1_0_filter_1(U_1141)) ) )
| ~ latt_str(U_1141)
| ~ lattice(U_1141)
| empty_carrier(U_1141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_1138,sK157(U_1142,U_1141))],[f_325_3]) ).
fof(f_325_5,plain,
! [U_1142,U_1141] :
( ( ( in(U_1142,a_1_0_filter_1(U_1141))
| ! [U_1140] :
( ! [U_1139] :
( ~ below_refl(U_1141,U_1140,U_1139)
| U_1142 != ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1140,U_1139)
| ~ element(U_1139,the_carrier(U_1141)) )
| ~ element(U_1140,the_carrier(U_1141)) ) )
& ( ( below_refl(U_1141,sK157(U_1142,U_1141),sK158(U_1142,U_1141))
& U_1142 = ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),sK157(U_1142,U_1141),sK158(U_1142,U_1141))
& element(sK158(U_1142,U_1141),the_carrier(U_1141))
& element(sK157(U_1142,U_1141),the_carrier(U_1141)) )
| ~ in(U_1142,a_1_0_filter_1(U_1141)) ) )
| ~ latt_str(U_1141)
| ~ lattice(U_1141)
| empty_carrier(U_1141) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_1137,sK158(U_1142,U_1141))],[f_325_4]) ).
fof(f_325_6,plain,
( ! [U_1141,U_1142] :
( below_refl(U_1141,sK157(U_1142,U_1141),sK158(U_1142,U_1141))
| ~ sP296(U_1141,U_1142) )
& ! [U_1141,U_1142] :
( U_1142 = ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),sK157(U_1142,U_1141),sK158(U_1142,U_1141))
| ~ sP296(U_1141,U_1142) )
& ! [U_1141,U_1142] :
( element(sK158(U_1142,U_1141),the_carrier(U_1141))
| ~ sP296(U_1141,U_1142) )
& ! [U_1141,U_1142] :
( element(sK157(U_1142,U_1141),the_carrier(U_1141))
| ~ sP296(U_1141,U_1142) )
& ! [U_1139,U_1140,U_1141,U_1142] :
( in(U_1142,a_1_0_filter_1(U_1141))
| ~ below_refl(U_1141,U_1140,U_1139)
| U_1142 != ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1140,U_1139)
| ~ element(U_1139,the_carrier(U_1141))
| ~ element(U_1140,the_carrier(U_1141))
| ~ sP297(U_1139,U_1140,U_1141,U_1142) )
& ! [U_1139,U_1140,U_1141,U_1142] :
( sP296(U_1141,U_1142)
| ~ in(U_1142,a_1_0_filter_1(U_1141))
| ~ sP297(U_1139,U_1140,U_1141,U_1142) )
& ! [U_1139,U_1140,U_1141,U_1142] :
( sP297(U_1139,U_1140,U_1141,U_1142)
| ~ latt_str(U_1141)
| ~ lattice(U_1141)
| empty_carrier(U_1141) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296,sP297])],[f_325_5]) ).
cnf(f_325_7,plain,
( sP297(U_1139,U_1140,U_1141,U_1142)
| ~ latt_str(U_1141)
| ~ lattice(U_1141)
| empty_carrier(U_1141) ),
inference(clausify,[status(thm)],[f_325_6]) ).
cnf(f_325_8,plain,
( sP296(U_1141,U_1142)
| ~ in(U_1142,a_1_0_filter_1(U_1141))
| ~ sP297(U_1139,U_1140,U_1141,U_1142) ),
inference(clausify,[status(thm)],[f_325_6]) ).
cnf(f_325_9,plain,
( in(U_1142,a_1_0_filter_1(U_1141))
| ~ below_refl(U_1141,U_1140,U_1139)
| U_1142 != ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),U_1140,U_1139)
| ~ element(U_1139,the_carrier(U_1141))
| ~ element(U_1140,the_carrier(U_1141))
| ~ sP297(U_1139,U_1140,U_1141,U_1142) ),
inference(clausify,[status(thm)],[f_325_6]) ).
cnf(f_325_10,plain,
( element(sK157(U_1142,U_1141),the_carrier(U_1141))
| ~ sP296(U_1141,U_1142) ),
inference(clausify,[status(thm)],[f_325_6]) ).
cnf(f_325_11,plain,
( element(sK158(U_1142,U_1141),the_carrier(U_1141))
| ~ sP296(U_1141,U_1142) ),
inference(clausify,[status(thm)],[f_325_6]) ).
cnf(f_325_12,plain,
( U_1142 = ordered_pair_as_product_element(the_carrier(U_1141),the_carrier(U_1141),sK157(U_1142,U_1141),sK158(U_1142,U_1141))
| ~ sP296(U_1141,U_1142) ),
inference(clausify,[status(thm)],[f_325_6]) ).
cnf(f_325_13,plain,
( below_refl(U_1141,sK157(U_1142,U_1141),sK158(U_1142,U_1141))
| ~ sP296(U_1141,U_1142) ),
inference(clausify,[status(thm)],[f_325_6]) ).
fof(f_326_1,plain,
! [A,B,C] :
( ( ( in(A,a_2_2_lattice3(B,C))
| ! [D] :
( ~ latt_set_smaller(B,D,C)
| A != D
| ~ element(D,the_carrier(B)) ) )
& ( ? [D] :
( latt_set_smaller(B,D,C)
& A = D
& element(D,the_carrier(B)) )
| ~ in(A,a_2_2_lattice3(B,C)) ) )
| ~ latt_str(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[fraenkel_a_2_2_lattice3]) ).
fof(f_326_2,plain,
! [U_1147,U_1146,U_1145] :
( ( ( in(U_1147,a_2_2_lattice3(U_1146,U_1145))
| ! [U_1144] :
( ~ latt_set_smaller(U_1146,U_1144,U_1145)
| U_1147 != U_1144
| ~ element(U_1144,the_carrier(U_1146)) ) )
& ( ? [U_1143] :
( latt_set_smaller(U_1146,U_1143,U_1145)
& U_1147 = U_1143
& element(U_1143,the_carrier(U_1146)) )
| ~ in(U_1147,a_2_2_lattice3(U_1146,U_1145)) ) )
| ~ latt_str(U_1146)
| empty_carrier(U_1146) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1147,U_1146] :
( ( ! [U_1149] :
( in(U_1147,a_2_2_lattice3(U_1146,U_1149))
| ! [U_1144] :
( ~ latt_set_smaller(U_1146,U_1144,U_1149)
| U_1147 != U_1144
| ~ element(U_1144,the_carrier(U_1146)) ) )
& ! [U_1148] :
( ? [U_1143] :
( latt_set_smaller(U_1146,U_1143,U_1148)
& U_1147 = U_1143
& element(U_1143,the_carrier(U_1146)) )
| ~ in(U_1147,a_2_2_lattice3(U_1146,U_1148)) ) )
| ~ latt_str(U_1146)
| empty_carrier(U_1146) ),
inference(miniscope,[status(thm)],[f_326_2]) ).
fof(f_326_4,plain,
! [U_1147,U_1146] :
( ( ! [U_1149] :
( in(U_1147,a_2_2_lattice3(U_1146,U_1149))
| ! [U_1144] :
( ~ latt_set_smaller(U_1146,U_1144,U_1149)
| U_1147 != U_1144
| ~ element(U_1144,the_carrier(U_1146)) ) )
& ! [U_1148] :
( ( latt_set_smaller(U_1146,sK159(U_1147,U_1146,U_1148),U_1148)
& U_1147 = sK159(U_1147,U_1146,U_1148)
& element(sK159(U_1147,U_1146,U_1148),the_carrier(U_1146)) )
| ~ in(U_1147,a_2_2_lattice3(U_1146,U_1148)) ) )
| ~ latt_str(U_1146)
| empty_carrier(U_1146) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_1143,sK159(U_1147,U_1146,U_1148))],[f_326_3]) ).
fof(f_326_5,plain,
( ! [U_1146,U_1147,U_1148] :
( latt_set_smaller(U_1146,sK159(U_1147,U_1146,U_1148),U_1148)
| ~ sP298(U_1146,U_1147,U_1148) )
& ! [U_1146,U_1147,U_1148] :
( U_1147 = sK159(U_1147,U_1146,U_1148)
| ~ sP298(U_1146,U_1147,U_1148) )
& ! [U_1146,U_1147,U_1148] :
( element(sK159(U_1147,U_1146,U_1148),the_carrier(U_1146))
| ~ sP298(U_1146,U_1147,U_1148) )
& ! [U_1146,U_1147,U_1144,U_1149,U_1148] :
( in(U_1147,a_2_2_lattice3(U_1146,U_1149))
| ~ latt_set_smaller(U_1146,U_1144,U_1149)
| U_1147 != U_1144
| ~ element(U_1144,the_carrier(U_1146))
| ~ sP299(U_1146,U_1147,U_1144,U_1149,U_1148) )
& ! [U_1146,U_1147,U_1144,U_1149,U_1148] :
( sP298(U_1146,U_1147,U_1148)
| ~ in(U_1147,a_2_2_lattice3(U_1146,U_1148))
| ~ sP299(U_1146,U_1147,U_1144,U_1149,U_1148) )
& ! [U_1146,U_1147,U_1144,U_1149,U_1148] :
( sP299(U_1146,U_1147,U_1144,U_1149,U_1148)
| ~ latt_str(U_1146)
| empty_carrier(U_1146) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298,sP299])],[f_326_4]) ).
cnf(f_326_6,plain,
( sP299(U_1146,U_1147,U_1144,U_1149,U_1148)
| ~ latt_str(U_1146)
| empty_carrier(U_1146) ),
inference(clausify,[status(thm)],[f_326_5]) ).
cnf(f_326_7,plain,
( sP298(U_1146,U_1147,U_1148)
| ~ in(U_1147,a_2_2_lattice3(U_1146,U_1148))
| ~ sP299(U_1146,U_1147,U_1144,U_1149,U_1148) ),
inference(clausify,[status(thm)],[f_326_5]) ).
cnf(f_326_8,plain,
( in(U_1147,a_2_2_lattice3(U_1146,U_1149))
| ~ latt_set_smaller(U_1146,U_1144,U_1149)
| U_1147 != U_1144
| ~ element(U_1144,the_carrier(U_1146))
| ~ sP299(U_1146,U_1147,U_1144,U_1149,U_1148) ),
inference(clausify,[status(thm)],[f_326_5]) ).
cnf(f_326_9,plain,
( element(sK159(U_1147,U_1146,U_1148),the_carrier(U_1146))
| ~ sP298(U_1146,U_1147,U_1148) ),
inference(clausify,[status(thm)],[f_326_5]) ).
cnf(f_326_10,plain,
( U_1147 = sK159(U_1147,U_1146,U_1148)
| ~ sP298(U_1146,U_1147,U_1148) ),
inference(clausify,[status(thm)],[f_326_5]) ).
cnf(f_326_11,plain,
( latt_set_smaller(U_1146,sK159(U_1147,U_1146,U_1148),U_1148)
| ~ sP298(U_1146,U_1147,U_1148) ),
inference(clausify,[status(thm)],[f_326_5]) ).
fof(f_327_1,plain,
! [A,B,C] :
( ( ( in(A,a_2_3_lattice3(B,C))
| ! [D] :
( ~ latt_set_smaller(B,D,C)
| A != D
| ~ element(D,the_carrier(B)) ) )
& ( ? [D] :
( latt_set_smaller(B,D,C)
& A = D
& element(D,the_carrier(B)) )
| ~ in(A,a_2_3_lattice3(B,C)) ) )
| ~ latt_str(B)
| ~ complete_latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[fraenkel_a_2_3_lattice3]) ).
fof(f_327_2,plain,
! [U_1154,U_1153,U_1152] :
( ( ( in(U_1154,a_2_3_lattice3(U_1153,U_1152))
| ! [U_1151] :
( ~ latt_set_smaller(U_1153,U_1151,U_1152)
| U_1154 != U_1151
| ~ element(U_1151,the_carrier(U_1153)) ) )
& ( ? [U_1150] :
( latt_set_smaller(U_1153,U_1150,U_1152)
& U_1154 = U_1150
& element(U_1150,the_carrier(U_1153)) )
| ~ in(U_1154,a_2_3_lattice3(U_1153,U_1152)) ) )
| ~ latt_str(U_1153)
| ~ complete_latt_str(U_1153)
| ~ lattice(U_1153)
| empty_carrier(U_1153) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1154,U_1153] :
( ( ! [U_1156] :
( in(U_1154,a_2_3_lattice3(U_1153,U_1156))
| ! [U_1151] :
( ~ latt_set_smaller(U_1153,U_1151,U_1156)
| U_1154 != U_1151
| ~ element(U_1151,the_carrier(U_1153)) ) )
& ! [U_1155] :
( ? [U_1150] :
( latt_set_smaller(U_1153,U_1150,U_1155)
& U_1154 = U_1150
& element(U_1150,the_carrier(U_1153)) )
| ~ in(U_1154,a_2_3_lattice3(U_1153,U_1155)) ) )
| ~ latt_str(U_1153)
| ~ complete_latt_str(U_1153)
| ~ lattice(U_1153)
| empty_carrier(U_1153) ),
inference(miniscope,[status(thm)],[f_327_2]) ).
fof(f_327_4,plain,
! [U_1154,U_1153] :
( ( ! [U_1156] :
( in(U_1154,a_2_3_lattice3(U_1153,U_1156))
| ! [U_1151] :
( ~ latt_set_smaller(U_1153,U_1151,U_1156)
| U_1154 != U_1151
| ~ element(U_1151,the_carrier(U_1153)) ) )
& ! [U_1155] :
( ( latt_set_smaller(U_1153,sK160(U_1154,U_1153,U_1155),U_1155)
& U_1154 = sK160(U_1154,U_1153,U_1155)
& element(sK160(U_1154,U_1153,U_1155),the_carrier(U_1153)) )
| ~ in(U_1154,a_2_3_lattice3(U_1153,U_1155)) ) )
| ~ latt_str(U_1153)
| ~ complete_latt_str(U_1153)
| ~ lattice(U_1153)
| empty_carrier(U_1153) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_1150,sK160(U_1154,U_1153,U_1155))],[f_327_3]) ).
fof(f_327_5,plain,
( ! [U_1154,U_1155,U_1153] :
( latt_set_smaller(U_1153,sK160(U_1154,U_1153,U_1155),U_1155)
| ~ sP300(U_1154,U_1155,U_1153) )
& ! [U_1154,U_1155,U_1153] :
( U_1154 = sK160(U_1154,U_1153,U_1155)
| ~ sP300(U_1154,U_1155,U_1153) )
& ! [U_1154,U_1155,U_1153] :
( element(sK160(U_1154,U_1153,U_1155),the_carrier(U_1153))
| ~ sP300(U_1154,U_1155,U_1153) )
& ! [U_1154,U_1155,U_1151,U_1153,U_1156] :
( in(U_1154,a_2_3_lattice3(U_1153,U_1156))
| ~ latt_set_smaller(U_1153,U_1151,U_1156)
| U_1154 != U_1151
| ~ element(U_1151,the_carrier(U_1153))
| ~ sP301(U_1154,U_1155,U_1151,U_1153,U_1156) )
& ! [U_1154,U_1155,U_1151,U_1153,U_1156] :
( sP300(U_1154,U_1155,U_1153)
| ~ in(U_1154,a_2_3_lattice3(U_1153,U_1155))
| ~ sP301(U_1154,U_1155,U_1151,U_1153,U_1156) )
& ! [U_1154,U_1155,U_1151,U_1153,U_1156] :
( sP301(U_1154,U_1155,U_1151,U_1153,U_1156)
| ~ latt_str(U_1153)
| ~ complete_latt_str(U_1153)
| ~ lattice(U_1153)
| empty_carrier(U_1153) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP300,sP301])],[f_327_4]) ).
cnf(f_327_6,plain,
( sP301(U_1154,U_1155,U_1151,U_1153,U_1156)
| ~ latt_str(U_1153)
| ~ complete_latt_str(U_1153)
| ~ lattice(U_1153)
| empty_carrier(U_1153) ),
inference(clausify,[status(thm)],[f_327_5]) ).
cnf(f_327_7,plain,
( sP300(U_1154,U_1155,U_1153)
| ~ in(U_1154,a_2_3_lattice3(U_1153,U_1155))
| ~ sP301(U_1154,U_1155,U_1151,U_1153,U_1156) ),
inference(clausify,[status(thm)],[f_327_5]) ).
cnf(f_327_8,plain,
( in(U_1154,a_2_3_lattice3(U_1153,U_1156))
| ~ latt_set_smaller(U_1153,U_1151,U_1156)
| U_1154 != U_1151
| ~ element(U_1151,the_carrier(U_1153))
| ~ sP301(U_1154,U_1155,U_1151,U_1153,U_1156) ),
inference(clausify,[status(thm)],[f_327_5]) ).
cnf(f_327_9,plain,
( element(sK160(U_1154,U_1153,U_1155),the_carrier(U_1153))
| ~ sP300(U_1154,U_1155,U_1153) ),
inference(clausify,[status(thm)],[f_327_5]) ).
cnf(f_327_10,plain,
( U_1154 = sK160(U_1154,U_1153,U_1155)
| ~ sP300(U_1154,U_1155,U_1153) ),
inference(clausify,[status(thm)],[f_327_5]) ).
cnf(f_327_11,plain,
( latt_set_smaller(U_1153,sK160(U_1154,U_1153,U_1155),U_1155)
| ~ sP300(U_1154,U_1155,U_1153) ),
inference(clausify,[status(thm)],[f_327_5]) ).
fof(f_328_1,plain,
! [A,B] :
( ! [C,D] :
( ( B = D
& A = C )
| rel_str_of(A,B) != rel_str_of(C,D) )
| ~ relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[free_g1_orders_2]) ).
fof(f_328_2,plain,
! [U_1160,U_1159] :
( ! [U_1158,U_1157] :
( ( U_1159 = U_1157
& U_1160 = U_1158 )
| rel_str_of(U_1160,U_1159) != rel_str_of(U_1158,U_1157) )
| ~ relation_of2(U_1159,U_1160,U_1160) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
( ! [U_1160,U_1159,U_1158,U_1157] :
( U_1159 = U_1157
| ~ sP302(U_1160,U_1159,U_1158,U_1157) )
& ! [U_1160,U_1159,U_1158,U_1157] :
( U_1160 = U_1158
| ~ sP302(U_1160,U_1159,U_1158,U_1157) )
& ! [U_1160,U_1159,U_1158,U_1157] :
( sP302(U_1160,U_1159,U_1158,U_1157)
| rel_str_of(U_1160,U_1159) != rel_str_of(U_1158,U_1157)
| ~ relation_of2(U_1159,U_1160,U_1160) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302])],[f_328_2]) ).
cnf(f_328_4,plain,
( sP302(U_1160,U_1159,U_1158,U_1157)
| rel_str_of(U_1160,U_1159) != rel_str_of(U_1158,U_1157)
| ~ relation_of2(U_1159,U_1160,U_1160) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_5,plain,
( U_1160 = U_1158
| ~ sP302(U_1160,U_1159,U_1158,U_1157) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_6,plain,
( U_1159 = U_1157
| ~ sP302(U_1160,U_1159,U_1158,U_1157) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_1,plain,
! [A,B,C] :
( ! [D,E,F] :
( ( C = F
& B = E
& A = D )
| latt_str_of(A,B,C) != latt_str_of(D,E,F) )
| ~ relation_of2(C,cartesian_product2(A,A),A)
| ~ quasi_total(C,cartesian_product2(A,A),A)
| ~ function(C)
| ~ relation_of2(B,cartesian_product2(A,A),A)
| ~ quasi_total(B,cartesian_product2(A,A),A)
| ~ function(B) ),
inference(fof_nnf,[status(thm)],[free_g3_lattices]) ).
fof(f_329_2,plain,
! [U_1166,U_1165,U_1164] :
( ! [U_1163,U_1162,U_1161] :
( ( U_1164 = U_1161
& U_1165 = U_1162
& U_1166 = U_1163 )
| latt_str_of(U_1166,U_1165,U_1164) != latt_str_of(U_1163,U_1162,U_1161) )
| ~ relation_of2(U_1164,cartesian_product2(U_1166,U_1166),U_1166)
| ~ quasi_total(U_1164,cartesian_product2(U_1166,U_1166),U_1166)
| ~ function(U_1164)
| ~ relation_of2(U_1165,cartesian_product2(U_1166,U_1166),U_1166)
| ~ quasi_total(U_1165,cartesian_product2(U_1166,U_1166),U_1166)
| ~ function(U_1165) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
( ! [U_1163,U_1164,U_1166,U_1162,U_1165,U_1161] :
( U_1164 = U_1161
| ~ sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161) )
& ! [U_1163,U_1164,U_1166,U_1162,U_1165,U_1161] :
( U_1165 = U_1162
| ~ sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161) )
& ! [U_1163,U_1164,U_1166,U_1162,U_1165,U_1161] :
( U_1166 = U_1163
| ~ sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161) )
& ! [U_1163,U_1164,U_1166,U_1162,U_1165,U_1161] :
( sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161)
| latt_str_of(U_1166,U_1165,U_1164) != latt_str_of(U_1163,U_1162,U_1161)
| ~ relation_of2(U_1164,cartesian_product2(U_1166,U_1166),U_1166)
| ~ quasi_total(U_1164,cartesian_product2(U_1166,U_1166),U_1166)
| ~ function(U_1164)
| ~ relation_of2(U_1165,cartesian_product2(U_1166,U_1166),U_1166)
| ~ quasi_total(U_1165,cartesian_product2(U_1166,U_1166),U_1166)
| ~ function(U_1165) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP303])],[f_329_2]) ).
cnf(f_329_4,plain,
( sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161)
| latt_str_of(U_1166,U_1165,U_1164) != latt_str_of(U_1163,U_1162,U_1161)
| ~ relation_of2(U_1164,cartesian_product2(U_1166,U_1166),U_1166)
| ~ quasi_total(U_1164,cartesian_product2(U_1166,U_1166),U_1166)
| ~ function(U_1164)
| ~ relation_of2(U_1165,cartesian_product2(U_1166,U_1166),U_1166)
| ~ quasi_total(U_1165,cartesian_product2(U_1166,U_1166),U_1166)
| ~ function(U_1165) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_5,plain,
( U_1166 = U_1163
| ~ sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_6,plain,
( U_1165 = U_1162
| ~ sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_7,plain,
( U_1164 = U_1161
| ~ sP303(U_1163,U_1164,U_1166,U_1162,U_1165,U_1161) ),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_330_2,plain,
! [U_1168,U_1167] : set_union2(U_1168,U_1168) = U_1168,
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_1168] : set_union2(U_1168,U_1168) = U_1168,
inference(miniscope,[status(thm)],[f_330_2]) ).
fof(f_330_4,plain,
! [U_1168] : set_union2(U_1168,U_1168) = U_1168,
inference(definitional_conversion,[status(esa)],[f_330_3]) ).
cnf(f_330_5,plain,
set_union2(U_1168,U_1168) = U_1168,
inference(clausify,[status(thm)],[f_330_4]) ).
fof(f_331_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_331_2,plain,
! [U_1170,U_1169] : set_intersection2(U_1170,U_1170) = U_1170,
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1170] : set_intersection2(U_1170,U_1170) = U_1170,
inference(miniscope,[status(thm)],[f_331_2]) ).
fof(f_331_4,plain,
! [U_1170] : set_intersection2(U_1170,U_1170) = U_1170,
inference(definitional_conversion,[status(esa)],[f_331_3]) ).
cnf(f_331_5,plain,
set_intersection2(U_1170,U_1170) = U_1170,
inference(clausify,[status(thm)],[f_331_4]) ).
fof(f_332_1,plain,
! [A,B,C] :
( subset_union2(A,B,B) = B
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[idempotence_k4_subset_1]) ).
fof(f_332_2,plain,
! [U_1173,U_1172,U_1171] :
( subset_union2(U_1173,U_1172,U_1172) = U_1172
| ~ element(U_1171,powerset(U_1173))
| ~ element(U_1172,powerset(U_1173)) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_1173,U_1172] :
( ! [U_1171] : ~ element(U_1171,powerset(U_1173))
| ~ element(U_1172,powerset(U_1173))
| subset_union2(U_1173,U_1172,U_1172) = U_1172 ),
inference(miniscope,[status(thm)],[f_332_2]) ).
fof(f_332_4,plain,
! [U_1171,U_1172,U_1173] :
( ~ element(U_1171,powerset(U_1173))
| ~ element(U_1172,powerset(U_1173))
| subset_union2(U_1173,U_1172,U_1172) = U_1172 ),
inference(definitional_conversion,[status(esa)],[f_332_3]) ).
cnf(f_332_5,plain,
( ~ element(U_1171,powerset(U_1173))
| ~ element(U_1172,powerset(U_1173))
| subset_union2(U_1173,U_1172,U_1172) = U_1172 ),
inference(clausify,[status(thm)],[f_332_4]) ).
fof(f_333_1,plain,
! [A,B,C] :
( subset_intersection2(A,B,B) = B
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[idempotence_k5_subset_1]) ).
fof(f_333_2,plain,
! [U_1176,U_1175,U_1174] :
( subset_intersection2(U_1176,U_1175,U_1175) = U_1175
| ~ element(U_1174,powerset(U_1176))
| ~ element(U_1175,powerset(U_1176)) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_1176,U_1175] :
( ! [U_1174] : ~ element(U_1174,powerset(U_1176))
| ~ element(U_1175,powerset(U_1176))
| subset_intersection2(U_1176,U_1175,U_1175) = U_1175 ),
inference(miniscope,[status(thm)],[f_333_2]) ).
fof(f_333_4,plain,
! [U_1176,U_1175,U_1174] :
( ~ element(U_1174,powerset(U_1176))
| ~ element(U_1175,powerset(U_1176))
| subset_intersection2(U_1176,U_1175,U_1175) = U_1175 ),
inference(definitional_conversion,[status(esa)],[f_333_3]) ).
cnf(f_333_5,plain,
( ~ element(U_1174,powerset(U_1176))
| ~ element(U_1175,powerset(U_1176))
| subset_intersection2(U_1176,U_1175,U_1175) = U_1175 ),
inference(clausify,[status(thm)],[f_333_4]) ).
fof(f_334_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_334_2,plain,
! [U_1178,U_1177] :
( subset_complement(U_1178,subset_complement(U_1178,U_1177)) = U_1177
| ~ element(U_1177,powerset(U_1178)) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1178,U_1177] :
( subset_complement(U_1178,subset_complement(U_1178,U_1177)) = U_1177
| ~ element(U_1177,powerset(U_1178)) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( subset_complement(U_1178,subset_complement(U_1178,U_1177)) = U_1177
| ~ element(U_1177,powerset(U_1178)) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_1,plain,
! [A] :
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1]) ).
fof(f_335_2,plain,
! [U_1179] :
( relation_inverse(relation_inverse(U_1179)) = U_1179
| ~ relation(U_1179) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_1179] :
( relation_inverse(relation_inverse(U_1179)) = U_1179
| ~ relation(U_1179) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( relation_inverse(relation_inverse(U_1179)) = U_1179
| ~ relation(U_1179) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_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_336_2,plain,
! [U_1181,U_1180] :
( complements_of_subsets(U_1181,complements_of_subsets(U_1181,U_1180)) = U_1180
| ~ element(U_1180,powerset(powerset(U_1181))) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_1180,U_1181] :
( complements_of_subsets(U_1181,complements_of_subsets(U_1181,U_1180)) = U_1180
| ~ element(U_1180,powerset(powerset(U_1181))) ),
inference(definitional_conversion,[status(esa)],[f_336_2]) ).
cnf(f_336_4,plain,
( complements_of_subsets(U_1181,complements_of_subsets(U_1181,U_1180)) = U_1180
| ~ element(U_1180,powerset(powerset(U_1181))) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_337_2,plain,
! [U_1183,U_1182] : ~ proper_subset(U_1183,U_1183),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_1183] : ~ proper_subset(U_1183,U_1183),
inference(miniscope,[status(thm)],[f_337_2]) ).
fof(f_337_4,plain,
! [U_1183] : ~ proper_subset(U_1183,U_1183),
inference(definitional_conversion,[status(esa)],[f_337_3]) ).
cnf(f_337_5,plain,
~ proper_subset(U_1183,U_1183),
inference(clausify,[status(thm)],[f_337_4]) ).
fof(f_338_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_338_2,plain,
! [U_1186] :
( ( ( reflexive(U_1186)
| ? [U_1185] :
( ~ in(ordered_pair(U_1185,U_1185),U_1186)
& in(U_1185,relation_field(U_1186)) ) )
& ( ! [U_1184] :
( in(ordered_pair(U_1184,U_1184),U_1186)
| ~ in(U_1184,relation_field(U_1186)) )
| ~ reflexive(U_1186) ) )
| ~ relation(U_1186) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1186] :
( ( ( reflexive(U_1186)
| ( ~ in(ordered_pair(sK161(U_1186),sK161(U_1186)),U_1186)
& in(sK161(U_1186),relation_field(U_1186)) ) )
& ( ! [U_1184] :
( in(ordered_pair(U_1184,U_1184),U_1186)
| ~ in(U_1184,relation_field(U_1186)) )
| ~ reflexive(U_1186) ) )
| ~ relation(U_1186) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_1185,sK161(U_1186))],[f_338_2]) ).
fof(f_338_4,plain,
( ! [U_1186] :
( ~ in(ordered_pair(sK161(U_1186),sK161(U_1186)),U_1186)
| ~ sP304(U_1186) )
& ! [U_1186] :
( in(sK161(U_1186),relation_field(U_1186))
| ~ sP304(U_1186) )
& ! [U_1184,U_1186] :
( reflexive(U_1186)
| sP304(U_1186)
| ~ sP305(U_1184,U_1186) )
& ! [U_1184,U_1186] :
( in(ordered_pair(U_1184,U_1184),U_1186)
| ~ in(U_1184,relation_field(U_1186))
| ~ reflexive(U_1186)
| ~ sP305(U_1184,U_1186) )
& ! [U_1184,U_1186] :
( sP305(U_1184,U_1186)
| ~ relation(U_1186) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP304,sP305])],[f_338_3]) ).
cnf(f_338_5,plain,
( sP305(U_1184,U_1186)
| ~ relation(U_1186) ),
inference(clausify,[status(thm)],[f_338_4]) ).
cnf(f_338_6,plain,
( in(ordered_pair(U_1184,U_1184),U_1186)
| ~ in(U_1184,relation_field(U_1186))
| ~ reflexive(U_1186)
| ~ sP305(U_1184,U_1186) ),
inference(clausify,[status(thm)],[f_338_4]) ).
cnf(f_338_7,plain,
( reflexive(U_1186)
| sP304(U_1186)
| ~ sP305(U_1184,U_1186) ),
inference(clausify,[status(thm)],[f_338_4]) ).
cnf(f_338_8,plain,
( in(sK161(U_1186),relation_field(U_1186))
| ~ sP304(U_1186) ),
inference(clausify,[status(thm)],[f_338_4]) ).
cnf(f_338_9,plain,
( ~ in(ordered_pair(sK161(U_1186),sK161(U_1186)),U_1186)
| ~ sP304(U_1186) ),
inference(clausify,[status(thm)],[f_338_4]) ).
fof(f_339_1,plain,
! [A] : singleton(A) != empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1]) ).
fof(f_339_2,plain,
! [U_1187] : singleton(U_1187) != empty_set,
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_1187] : singleton(U_1187) != empty_set,
inference(definitional_conversion,[status(esa)],[f_339_2]) ).
cnf(f_339_4,plain,
singleton(U_1187) != empty_set,
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l23_zfmisc_1]) ).
fof(f_340_2,plain,
! [U_1189,U_1188] :
( set_union2(singleton(U_1189),U_1188) = U_1188
| ~ in(U_1189,U_1188) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
! [U_1189,U_1188] :
( set_union2(singleton(U_1189),U_1188) = U_1188
| ~ in(U_1189,U_1188) ),
inference(definitional_conversion,[status(esa)],[f_340_2]) ).
cnf(f_340_4,plain,
( set_union2(singleton(U_1189),U_1188) = U_1188
| ~ in(U_1189,U_1188) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_1,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1]) ).
fof(f_341_2,plain,
! [U_1191,U_1190] :
( ~ in(U_1191,U_1190)
| ~ disjoint(singleton(U_1191),U_1190) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1191,U_1190] :
( ~ in(U_1191,U_1190)
| ~ disjoint(singleton(U_1191),U_1190) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
( ~ in(U_1191,U_1190)
| ~ disjoint(singleton(U_1191),U_1190) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_1,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(fof_nnf,[status(thm)],[l28_zfmisc_1]) ).
fof(f_342_2,plain,
! [U_1193,U_1192] :
( disjoint(singleton(U_1193),U_1192)
| in(U_1193,U_1192) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_1193,U_1192] :
( disjoint(singleton(U_1193),U_1192)
| in(U_1193,U_1192) ),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,plain,
( disjoint(singleton(U_1193),U_1192)
| in(U_1193,U_1192) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_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_343_2,plain,
! [U_1195,U_1194] :
( subset(relation_dom(relation_rng_restriction(U_1195,U_1194)),relation_dom(U_1194))
| ~ relation(U_1194) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_1194,U_1195] :
( subset(relation_dom(relation_rng_restriction(U_1195,U_1194)),relation_dom(U_1194))
| ~ relation(U_1194) ),
inference(definitional_conversion,[status(esa)],[f_343_2]) ).
cnf(f_343_4,plain,
( subset(relation_dom(relation_rng_restriction(U_1195,U_1194)),relation_dom(U_1194))
| ~ relation(U_1194) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_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_344_2,plain,
! [U_1202] :
( ( ( transitive(U_1202)
| ? [U_1201,U_1200,U_1199] :
( ~ in(ordered_pair(U_1201,U_1199),U_1202)
& in(ordered_pair(U_1200,U_1199),U_1202)
& in(ordered_pair(U_1201,U_1200),U_1202) ) )
& ( ! [U_1198,U_1197,U_1196] :
( in(ordered_pair(U_1198,U_1196),U_1202)
| ~ in(ordered_pair(U_1197,U_1196),U_1202)
| ~ in(ordered_pair(U_1198,U_1197),U_1202) )
| ~ transitive(U_1202) ) )
| ~ relation(U_1202) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_1202] :
( ( ( transitive(U_1202)
| ? [U_1200,U_1199] :
( ~ in(ordered_pair(sK162(U_1202),U_1199),U_1202)
& in(ordered_pair(U_1200,U_1199),U_1202)
& in(ordered_pair(sK162(U_1202),U_1200),U_1202) ) )
& ( ! [U_1198,U_1197,U_1196] :
( in(ordered_pair(U_1198,U_1196),U_1202)
| ~ in(ordered_pair(U_1197,U_1196),U_1202)
| ~ in(ordered_pair(U_1198,U_1197),U_1202) )
| ~ transitive(U_1202) ) )
| ~ relation(U_1202) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_1201,sK162(U_1202))],[f_344_2]) ).
fof(f_344_4,plain,
! [U_1202] :
( ( ( transitive(U_1202)
| ? [U_1199] :
( ~ in(ordered_pair(sK162(U_1202),U_1199),U_1202)
& in(ordered_pair(sK163(U_1202),U_1199),U_1202)
& in(ordered_pair(sK162(U_1202),sK163(U_1202)),U_1202) ) )
& ( ! [U_1198,U_1197,U_1196] :
( in(ordered_pair(U_1198,U_1196),U_1202)
| ~ in(ordered_pair(U_1197,U_1196),U_1202)
| ~ in(ordered_pair(U_1198,U_1197),U_1202) )
| ~ transitive(U_1202) ) )
| ~ relation(U_1202) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_1200,sK163(U_1202))],[f_344_3]) ).
fof(f_344_5,plain,
! [U_1202] :
( ( ( transitive(U_1202)
| ( ~ in(ordered_pair(sK162(U_1202),sK164(U_1202)),U_1202)
& in(ordered_pair(sK163(U_1202),sK164(U_1202)),U_1202)
& in(ordered_pair(sK162(U_1202),sK163(U_1202)),U_1202) ) )
& ( ! [U_1198,U_1197,U_1196] :
( in(ordered_pair(U_1198,U_1196),U_1202)
| ~ in(ordered_pair(U_1197,U_1196),U_1202)
| ~ in(ordered_pair(U_1198,U_1197),U_1202) )
| ~ transitive(U_1202) ) )
| ~ relation(U_1202) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_1199,sK164(U_1202))],[f_344_4]) ).
fof(f_344_6,plain,
( ! [U_1202] :
( ~ in(ordered_pair(sK162(U_1202),sK164(U_1202)),U_1202)
| ~ sP306(U_1202) )
& ! [U_1202] :
( in(ordered_pair(sK163(U_1202),sK164(U_1202)),U_1202)
| ~ sP306(U_1202) )
& ! [U_1202] :
( in(ordered_pair(sK162(U_1202),sK163(U_1202)),U_1202)
| ~ sP306(U_1202) )
& ! [U_1196,U_1197,U_1198,U_1202] :
( transitive(U_1202)
| sP306(U_1202)
| ~ sP307(U_1196,U_1197,U_1198,U_1202) )
& ! [U_1196,U_1197,U_1198,U_1202] :
( in(ordered_pair(U_1198,U_1196),U_1202)
| ~ in(ordered_pair(U_1197,U_1196),U_1202)
| ~ in(ordered_pair(U_1198,U_1197),U_1202)
| ~ transitive(U_1202)
| ~ sP307(U_1196,U_1197,U_1198,U_1202) )
& ! [U_1196,U_1197,U_1198,U_1202] :
( sP307(U_1196,U_1197,U_1198,U_1202)
| ~ relation(U_1202) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306,sP307])],[f_344_5]) ).
cnf(f_344_7,plain,
( sP307(U_1196,U_1197,U_1198,U_1202)
| ~ relation(U_1202) ),
inference(clausify,[status(thm)],[f_344_6]) ).
cnf(f_344_8,plain,
( in(ordered_pair(U_1198,U_1196),U_1202)
| ~ in(ordered_pair(U_1197,U_1196),U_1202)
| ~ in(ordered_pair(U_1198,U_1197),U_1202)
| ~ transitive(U_1202)
| ~ sP307(U_1196,U_1197,U_1198,U_1202) ),
inference(clausify,[status(thm)],[f_344_6]) ).
cnf(f_344_9,plain,
( transitive(U_1202)
| sP306(U_1202)
| ~ sP307(U_1196,U_1197,U_1198,U_1202) ),
inference(clausify,[status(thm)],[f_344_6]) ).
cnf(f_344_10,plain,
( in(ordered_pair(sK162(U_1202),sK163(U_1202)),U_1202)
| ~ sP306(U_1202) ),
inference(clausify,[status(thm)],[f_344_6]) ).
cnf(f_344_11,plain,
( in(ordered_pair(sK163(U_1202),sK164(U_1202)),U_1202)
| ~ sP306(U_1202) ),
inference(clausify,[status(thm)],[f_344_6]) ).
cnf(f_344_12,plain,
( ~ in(ordered_pair(sK162(U_1202),sK164(U_1202)),U_1202)
| ~ sP306(U_1202) ),
inference(clausify,[status(thm)],[f_344_6]) ).
fof(f_345_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_345_2,plain,
! [U_1204,U_1203] :
( ( subset(singleton(U_1204),U_1203)
| ~ in(U_1204,U_1203) )
& ( in(U_1204,U_1203)
| ~ subset(singleton(U_1204),U_1203) ) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
( ! [U_1208,U_1206] :
( subset(singleton(U_1208),U_1206)
| ~ in(U_1208,U_1206) )
& ! [U_1207,U_1205] :
( in(U_1207,U_1205)
| ~ subset(singleton(U_1207),U_1205) ) ),
inference(miniscope,[status(thm)],[f_345_2]) ).
fof(f_345_4,plain,
( ! [U_1208,U_1206] :
( subset(singleton(U_1208),U_1206)
| ~ in(U_1208,U_1206) )
& ! [U_1205,U_1207] :
( in(U_1207,U_1205)
| ~ subset(singleton(U_1207),U_1205) ) ),
inference(definitional_conversion,[status(esa)],[f_345_3]) ).
cnf(f_345_5,plain,
( in(U_1207,U_1205)
| ~ subset(singleton(U_1207),U_1205) ),
inference(clausify,[status(thm)],[f_345_4]) ).
cnf(f_345_6,plain,
( subset(singleton(U_1208),U_1206)
| ~ in(U_1208,U_1206) ),
inference(clausify,[status(thm)],[f_345_4]) ).
fof(f_346_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_346_2,plain,
! [U_1211,U_1210] :
( ? [U_1209] :
( well_orders(U_1209,U_1211)
& relation(U_1209) )
| ~ equipotent(U_1211,relation_field(U_1210))
| ~ well_ordering(U_1210)
| ~ relation(U_1210) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_1211,U_1210] :
( ( well_orders(sK165(U_1211,U_1210),U_1211)
& relation(sK165(U_1211,U_1210)) )
| ~ equipotent(U_1211,relation_field(U_1210))
| ~ well_ordering(U_1210)
| ~ relation(U_1210) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_1209,sK165(U_1211,U_1210))],[f_346_2]) ).
fof(f_346_4,plain,
( ! [U_1211,U_1210] :
( well_orders(sK165(U_1211,U_1210),U_1211)
| ~ sP308(U_1211,U_1210) )
& ! [U_1211,U_1210] :
( relation(sK165(U_1211,U_1210))
| ~ sP308(U_1211,U_1210) )
& ! [U_1211,U_1210] :
( sP308(U_1211,U_1210)
| ~ equipotent(U_1211,relation_field(U_1210))
| ~ well_ordering(U_1210)
| ~ relation(U_1210) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308])],[f_346_3]) ).
cnf(f_346_5,plain,
( sP308(U_1211,U_1210)
| ~ equipotent(U_1211,relation_field(U_1210))
| ~ well_ordering(U_1210)
| ~ relation(U_1210) ),
inference(clausify,[status(thm)],[f_346_4]) ).
cnf(f_346_6,plain,
( relation(sK165(U_1211,U_1210))
| ~ sP308(U_1211,U_1210) ),
inference(clausify,[status(thm)],[f_346_4]) ).
cnf(f_346_7,plain,
( well_orders(sK165(U_1211,U_1210),U_1211)
| ~ sP308(U_1211,U_1210) ),
inference(clausify,[status(thm)],[f_346_4]) ).
fof(f_347_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_347_2,plain,
! [U_1213,U_1212] :
( ( set_difference(U_1213,U_1212) = empty_set
| ~ subset(U_1213,U_1212) )
& ( subset(U_1213,U_1212)
| set_difference(U_1213,U_1212) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
( ! [U_1217,U_1215] :
( set_difference(U_1217,U_1215) = empty_set
| ~ subset(U_1217,U_1215) )
& ! [U_1216,U_1214] :
( subset(U_1216,U_1214)
| set_difference(U_1216,U_1214) != empty_set ) ),
inference(miniscope,[status(thm)],[f_347_2]) ).
fof(f_347_4,plain,
( ! [U_1215,U_1217] :
( set_difference(U_1217,U_1215) = empty_set
| ~ subset(U_1217,U_1215) )
& ! [U_1214,U_1216] :
( subset(U_1216,U_1214)
| set_difference(U_1216,U_1214) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_347_3]) ).
cnf(f_347_5,plain,
( subset(U_1216,U_1214)
| set_difference(U_1216,U_1214) != empty_set ),
inference(clausify,[status(thm)],[f_347_4]) ).
cnf(f_347_6,plain,
( set_difference(U_1217,U_1215) = empty_set
| ~ subset(U_1217,U_1215) ),
inference(clausify,[status(thm)],[f_347_4]) ).
fof(f_348_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_348_2,plain,
! [U_1220,U_1219] :
( ! [U_1218] :
( in(U_1218,U_1220)
| ~ in(U_1218,U_1219) )
| ~ element(U_1219,powerset(U_1220)) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
! [U_1218,U_1220,U_1219] :
( in(U_1218,U_1220)
| ~ in(U_1218,U_1219)
| ~ element(U_1219,powerset(U_1220)) ),
inference(definitional_conversion,[status(esa)],[f_348_2]) ).
cnf(f_348_4,plain,
( in(U_1218,U_1220)
| ~ in(U_1218,U_1219)
| ~ element(U_1219,powerset(U_1220)) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_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_349_2,plain,
! [U_1225] :
( ( ( antisymmetric(U_1225)
| ? [U_1224,U_1223] :
( U_1224 != U_1223
& in(ordered_pair(U_1223,U_1224),U_1225)
& in(ordered_pair(U_1224,U_1223),U_1225) ) )
& ( ! [U_1222,U_1221] :
( U_1222 = U_1221
| ~ in(ordered_pair(U_1221,U_1222),U_1225)
| ~ in(ordered_pair(U_1222,U_1221),U_1225) )
| ~ antisymmetric(U_1225) ) )
| ~ relation(U_1225) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_1225] :
( ( ( antisymmetric(U_1225)
| ? [U_1223] :
( sK166(U_1225) != U_1223
& in(ordered_pair(U_1223,sK166(U_1225)),U_1225)
& in(ordered_pair(sK166(U_1225),U_1223),U_1225) ) )
& ( ! [U_1222,U_1221] :
( U_1222 = U_1221
| ~ in(ordered_pair(U_1221,U_1222),U_1225)
| ~ in(ordered_pair(U_1222,U_1221),U_1225) )
| ~ antisymmetric(U_1225) ) )
| ~ relation(U_1225) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_1224,sK166(U_1225))],[f_349_2]) ).
fof(f_349_4,plain,
! [U_1225] :
( ( ( antisymmetric(U_1225)
| ( sK166(U_1225) != sK167(U_1225)
& in(ordered_pair(sK167(U_1225),sK166(U_1225)),U_1225)
& in(ordered_pair(sK166(U_1225),sK167(U_1225)),U_1225) ) )
& ( ! [U_1222,U_1221] :
( U_1222 = U_1221
| ~ in(ordered_pair(U_1221,U_1222),U_1225)
| ~ in(ordered_pair(U_1222,U_1221),U_1225) )
| ~ antisymmetric(U_1225) ) )
| ~ relation(U_1225) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_1223,sK167(U_1225))],[f_349_3]) ).
fof(f_349_5,plain,
( ! [U_1225] :
( sK166(U_1225) != sK167(U_1225)
| ~ sP309(U_1225) )
& ! [U_1225] :
( in(ordered_pair(sK167(U_1225),sK166(U_1225)),U_1225)
| ~ sP309(U_1225) )
& ! [U_1225] :
( in(ordered_pair(sK166(U_1225),sK167(U_1225)),U_1225)
| ~ sP309(U_1225) )
& ! [U_1221,U_1222,U_1225] :
( antisymmetric(U_1225)
| sP309(U_1225)
| ~ sP310(U_1221,U_1222,U_1225) )
& ! [U_1221,U_1222,U_1225] :
( U_1222 = U_1221
| ~ in(ordered_pair(U_1221,U_1222),U_1225)
| ~ in(ordered_pair(U_1222,U_1221),U_1225)
| ~ antisymmetric(U_1225)
| ~ sP310(U_1221,U_1222,U_1225) )
& ! [U_1221,U_1222,U_1225] :
( sP310(U_1221,U_1222,U_1225)
| ~ relation(U_1225) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309,sP310])],[f_349_4]) ).
cnf(f_349_6,plain,
( sP310(U_1221,U_1222,U_1225)
| ~ relation(U_1225) ),
inference(clausify,[status(thm)],[f_349_5]) ).
cnf(f_349_7,plain,
( U_1222 = U_1221
| ~ in(ordered_pair(U_1221,U_1222),U_1225)
| ~ in(ordered_pair(U_1222,U_1221),U_1225)
| ~ antisymmetric(U_1225)
| ~ sP310(U_1221,U_1222,U_1225) ),
inference(clausify,[status(thm)],[f_349_5]) ).
cnf(f_349_8,plain,
( antisymmetric(U_1225)
| sP309(U_1225)
| ~ sP310(U_1221,U_1222,U_1225) ),
inference(clausify,[status(thm)],[f_349_5]) ).
cnf(f_349_9,plain,
( in(ordered_pair(sK166(U_1225),sK167(U_1225)),U_1225)
| ~ sP309(U_1225) ),
inference(clausify,[status(thm)],[f_349_5]) ).
cnf(f_349_10,plain,
( in(ordered_pair(sK167(U_1225),sK166(U_1225)),U_1225)
| ~ sP309(U_1225) ),
inference(clausify,[status(thm)],[f_349_5]) ).
cnf(f_349_11,plain,
( sK166(U_1225) != sK167(U_1225)
| ~ sP309(U_1225) ),
inference(clausify,[status(thm)],[f_349_5]) ).
fof(f_350_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_350_2,plain,
! [U_1228,U_1227,U_1226] :
( subset(U_1228,set_difference(U_1227,singleton(U_1226)))
| in(U_1226,U_1228)
| ~ subset(U_1228,U_1227) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1228,U_1227] :
( ! [U_1226] :
( subset(U_1228,set_difference(U_1227,singleton(U_1226)))
| in(U_1226,U_1228) )
| ~ subset(U_1228,U_1227) ),
inference(miniscope,[status(thm)],[f_350_2]) ).
fof(f_350_4,plain,
! [U_1226,U_1227,U_1228] :
( subset(U_1228,set_difference(U_1227,singleton(U_1226)))
| in(U_1226,U_1228)
| ~ subset(U_1228,U_1227) ),
inference(definitional_conversion,[status(esa)],[f_350_3]) ).
cnf(f_350_5,plain,
( subset(U_1228,set_difference(U_1227,singleton(U_1226)))
| in(U_1226,U_1228)
| ~ subset(U_1228,U_1227) ),
inference(clausify,[status(thm)],[f_350_4]) ).
fof(f_351_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( in(C,subset_complement(the_carrier(A),B))
| in(C,B) )
& ( ~ in(C,B)
| ~ in(C,subset_complement(the_carrier(A),B)) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[l40_tops_1]) ).
fof(f_351_2,plain,
! [U_1231] :
( ! [U_1230] :
( ! [U_1229] :
( ( ( in(U_1229,subset_complement(the_carrier(U_1231),U_1230))
| in(U_1229,U_1230) )
& ( ~ in(U_1229,U_1230)
| ~ in(U_1229,subset_complement(the_carrier(U_1231),U_1230)) ) )
| ~ element(U_1229,the_carrier(U_1231)) )
| ~ element(U_1230,powerset(the_carrier(U_1231))) )
| ~ one_sorted_str(U_1231)
| empty_carrier(U_1231) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
( ! [U_1231,U_1229,U_1230] :
( in(U_1229,subset_complement(the_carrier(U_1231),U_1230))
| in(U_1229,U_1230)
| ~ sP311(U_1231,U_1229,U_1230) )
& ! [U_1231,U_1229,U_1230] :
( ~ in(U_1229,U_1230)
| ~ in(U_1229,subset_complement(the_carrier(U_1231),U_1230))
| ~ sP311(U_1231,U_1229,U_1230) )
& ! [U_1231,U_1229,U_1230] :
( sP311(U_1231,U_1229,U_1230)
| ~ element(U_1229,the_carrier(U_1231))
| ~ element(U_1230,powerset(the_carrier(U_1231)))
| ~ one_sorted_str(U_1231)
| empty_carrier(U_1231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP311])],[f_351_2]) ).
cnf(f_351_4,plain,
( sP311(U_1231,U_1229,U_1230)
| ~ element(U_1229,the_carrier(U_1231))
| ~ element(U_1230,powerset(the_carrier(U_1231)))
| ~ one_sorted_str(U_1231)
| empty_carrier(U_1231) ),
inference(clausify,[status(thm)],[f_351_3]) ).
cnf(f_351_5,plain,
( ~ in(U_1229,U_1230)
| ~ in(U_1229,subset_complement(the_carrier(U_1231),U_1230))
| ~ sP311(U_1231,U_1229,U_1230) ),
inference(clausify,[status(thm)],[f_351_3]) ).
cnf(f_351_6,plain,
( in(U_1229,subset_complement(the_carrier(U_1231),U_1230))
| in(U_1229,U_1230)
| ~ sP311(U_1231,U_1229,U_1230) ),
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_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_352_2,plain,
! [U_1236] :
( ( ( connected(U_1236)
| ? [U_1235,U_1234] :
( ~ in(ordered_pair(U_1234,U_1235),U_1236)
& ~ in(ordered_pair(U_1235,U_1234),U_1236)
& U_1235 != U_1234
& in(U_1234,relation_field(U_1236))
& in(U_1235,relation_field(U_1236)) ) )
& ( ! [U_1233,U_1232] :
( in(ordered_pair(U_1232,U_1233),U_1236)
| in(ordered_pair(U_1233,U_1232),U_1236)
| U_1233 = U_1232
| ~ in(U_1232,relation_field(U_1236))
| ~ in(U_1233,relation_field(U_1236)) )
| ~ connected(U_1236) ) )
| ~ relation(U_1236) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
! [U_1236] :
( ( ( connected(U_1236)
| ? [U_1235] :
( ? [U_1234] :
( ~ in(ordered_pair(U_1234,U_1235),U_1236)
& ~ in(ordered_pair(U_1235,U_1234),U_1236)
& U_1235 != U_1234
& in(U_1234,relation_field(U_1236)) )
& in(U_1235,relation_field(U_1236)) ) )
& ( ! [U_1233] :
( ! [U_1232] :
( in(ordered_pair(U_1232,U_1233),U_1236)
| in(ordered_pair(U_1233,U_1232),U_1236)
| U_1233 = U_1232
| ~ in(U_1232,relation_field(U_1236)) )
| ~ in(U_1233,relation_field(U_1236)) )
| ~ connected(U_1236) ) )
| ~ relation(U_1236) ),
inference(miniscope,[status(thm)],[f_352_2]) ).
fof(f_352_4,plain,
! [U_1236] :
( ( ( connected(U_1236)
| ( ? [U_1234] :
( ~ in(ordered_pair(U_1234,sK168(U_1236)),U_1236)
& ~ in(ordered_pair(sK168(U_1236),U_1234),U_1236)
& sK168(U_1236) != U_1234
& in(U_1234,relation_field(U_1236)) )
& in(sK168(U_1236),relation_field(U_1236)) ) )
& ( ! [U_1233] :
( ! [U_1232] :
( in(ordered_pair(U_1232,U_1233),U_1236)
| in(ordered_pair(U_1233,U_1232),U_1236)
| U_1233 = U_1232
| ~ in(U_1232,relation_field(U_1236)) )
| ~ in(U_1233,relation_field(U_1236)) )
| ~ connected(U_1236) ) )
| ~ relation(U_1236) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_1235,sK168(U_1236))],[f_352_3]) ).
fof(f_352_5,plain,
! [U_1236] :
( ( ( connected(U_1236)
| ( ~ in(ordered_pair(sK169(U_1236),sK168(U_1236)),U_1236)
& ~ in(ordered_pair(sK168(U_1236),sK169(U_1236)),U_1236)
& sK168(U_1236) != sK169(U_1236)
& in(sK169(U_1236),relation_field(U_1236))
& in(sK168(U_1236),relation_field(U_1236)) ) )
& ( ! [U_1233] :
( ! [U_1232] :
( in(ordered_pair(U_1232,U_1233),U_1236)
| in(ordered_pair(U_1233,U_1232),U_1236)
| U_1233 = U_1232
| ~ in(U_1232,relation_field(U_1236)) )
| ~ in(U_1233,relation_field(U_1236)) )
| ~ connected(U_1236) ) )
| ~ relation(U_1236) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_1234,sK169(U_1236))],[f_352_4]) ).
fof(f_352_6,plain,
( ! [U_1236] :
( ~ in(ordered_pair(sK169(U_1236),sK168(U_1236)),U_1236)
| ~ sP312(U_1236) )
& ! [U_1236] :
( ~ in(ordered_pair(sK168(U_1236),sK169(U_1236)),U_1236)
| ~ sP312(U_1236) )
& ! [U_1236] :
( sK168(U_1236) != sK169(U_1236)
| ~ sP312(U_1236) )
& ! [U_1236] :
( in(sK169(U_1236),relation_field(U_1236))
| ~ sP312(U_1236) )
& ! [U_1236] :
( in(sK168(U_1236),relation_field(U_1236))
| ~ sP312(U_1236) )
& ! [U_1232,U_1236,U_1233] :
( connected(U_1236)
| sP312(U_1236)
| ~ sP313(U_1232,U_1236,U_1233) )
& ! [U_1232,U_1236,U_1233] :
( in(ordered_pair(U_1232,U_1233),U_1236)
| in(ordered_pair(U_1233,U_1232),U_1236)
| U_1233 = U_1232
| ~ in(U_1232,relation_field(U_1236))
| ~ in(U_1233,relation_field(U_1236))
| ~ connected(U_1236)
| ~ sP313(U_1232,U_1236,U_1233) )
& ! [U_1232,U_1236,U_1233] :
( sP313(U_1232,U_1236,U_1233)
| ~ relation(U_1236) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312,sP313])],[f_352_5]) ).
cnf(f_352_7,plain,
( sP313(U_1232,U_1236,U_1233)
| ~ relation(U_1236) ),
inference(clausify,[status(thm)],[f_352_6]) ).
cnf(f_352_8,plain,
( in(ordered_pair(U_1232,U_1233),U_1236)
| in(ordered_pair(U_1233,U_1232),U_1236)
| U_1233 = U_1232
| ~ in(U_1232,relation_field(U_1236))
| ~ in(U_1233,relation_field(U_1236))
| ~ connected(U_1236)
| ~ sP313(U_1232,U_1236,U_1233) ),
inference(clausify,[status(thm)],[f_352_6]) ).
cnf(f_352_9,plain,
( connected(U_1236)
| sP312(U_1236)
| ~ sP313(U_1232,U_1236,U_1233) ),
inference(clausify,[status(thm)],[f_352_6]) ).
cnf(f_352_10,plain,
( in(sK168(U_1236),relation_field(U_1236))
| ~ sP312(U_1236) ),
inference(clausify,[status(thm)],[f_352_6]) ).
cnf(f_352_11,plain,
( in(sK169(U_1236),relation_field(U_1236))
| ~ sP312(U_1236) ),
inference(clausify,[status(thm)],[f_352_6]) ).
cnf(f_352_12,plain,
( sK168(U_1236) != sK169(U_1236)
| ~ sP312(U_1236) ),
inference(clausify,[status(thm)],[f_352_6]) ).
cnf(f_352_13,plain,
( ~ in(ordered_pair(sK168(U_1236),sK169(U_1236)),U_1236)
| ~ sP312(U_1236) ),
inference(clausify,[status(thm)],[f_352_6]) ).
cnf(f_352_14,plain,
( ~ in(ordered_pair(sK169(U_1236),sK168(U_1236)),U_1236)
| ~ sP312(U_1236) ),
inference(clausify,[status(thm)],[f_352_6]) ).
fof(f_353_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_353_2,plain,
! [U_1238,U_1237] :
( ( subset(U_1238,singleton(U_1237))
| ( U_1238 != singleton(U_1237)
& U_1238 != empty_set ) )
& ( U_1238 = singleton(U_1237)
| U_1238 = empty_set
| ~ subset(U_1238,singleton(U_1237)) ) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
( ! [U_1242,U_1240] :
( subset(U_1242,singleton(U_1240))
| ( U_1242 != singleton(U_1240)
& U_1242 != empty_set ) )
& ! [U_1241,U_1239] :
( U_1241 = singleton(U_1239)
| U_1241 = empty_set
| ~ subset(U_1241,singleton(U_1239)) ) ),
inference(miniscope,[status(thm)],[f_353_2]) ).
fof(f_353_4,plain,
( ! [U_1242,U_1240] :
( U_1242 != singleton(U_1240)
| ~ sP314(U_1242,U_1240) )
& ! [U_1242,U_1240] :
( U_1242 != empty_set
| ~ sP314(U_1242,U_1240) )
& ! [U_1242,U_1240] :
( subset(U_1242,singleton(U_1240))
| sP314(U_1242,U_1240) )
& ! [U_1241,U_1239] :
( U_1241 = singleton(U_1239)
| U_1241 = empty_set
| ~ subset(U_1241,singleton(U_1239)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP314])],[f_353_3]) ).
cnf(f_353_5,plain,
( U_1241 = singleton(U_1239)
| U_1241 = empty_set
| ~ subset(U_1241,singleton(U_1239)) ),
inference(clausify,[status(thm)],[f_353_4]) ).
cnf(f_353_6,plain,
( subset(U_1242,singleton(U_1240))
| sP314(U_1242,U_1240) ),
inference(clausify,[status(thm)],[f_353_4]) ).
cnf(f_353_7,plain,
( U_1242 != empty_set
| ~ sP314(U_1242,U_1240) ),
inference(clausify,[status(thm)],[f_353_4]) ).
cnf(f_353_8,plain,
( U_1242 != singleton(U_1240)
| ~ sP314(U_1242,U_1240) ),
inference(clausify,[status(thm)],[f_353_4]) ).
fof(f_354_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_354_2,plain,
! [U_1244,U_1243] :
( subset(U_1244,union(U_1243))
| ~ in(U_1244,U_1243) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_1244,U_1243] :
( subset(U_1244,union(U_1243))
| ~ in(U_1244,U_1243) ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( subset(U_1244,union(U_1243))
| ~ in(U_1244,U_1243) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_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_355_2,plain,
! [U_1248,U_1247,U_1246,U_1245] :
( ( in(ordered_pair(U_1248,U_1247),cartesian_product2(U_1246,U_1245))
| ~ in(U_1247,U_1245)
| ~ in(U_1248,U_1246) )
& ( ( in(U_1247,U_1245)
& in(U_1248,U_1246) )
| ~ in(ordered_pair(U_1248,U_1247),cartesian_product2(U_1246,U_1245)) ) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
( ! [U_1256,U_1254,U_1252,U_1250] :
( in(ordered_pair(U_1256,U_1254),cartesian_product2(U_1252,U_1250))
| ~ in(U_1254,U_1250)
| ~ in(U_1256,U_1252) )
& ! [U_1255,U_1253,U_1251,U_1249] :
( ( in(U_1253,U_1249)
& in(U_1255,U_1251) )
| ~ in(ordered_pair(U_1255,U_1253),cartesian_product2(U_1251,U_1249)) ) ),
inference(miniscope,[status(thm)],[f_355_2]) ).
fof(f_355_4,plain,
( ! [U_1251,U_1255,U_1249,U_1253] :
( in(U_1253,U_1249)
| ~ sP315(U_1251,U_1255,U_1249,U_1253) )
& ! [U_1251,U_1255,U_1249,U_1253] :
( in(U_1255,U_1251)
| ~ sP315(U_1251,U_1255,U_1249,U_1253) )
& ! [U_1254,U_1250,U_1252,U_1256] :
( in(ordered_pair(U_1256,U_1254),cartesian_product2(U_1252,U_1250))
| ~ in(U_1254,U_1250)
| ~ in(U_1256,U_1252) )
& ! [U_1251,U_1255,U_1249,U_1253] :
( sP315(U_1251,U_1255,U_1249,U_1253)
| ~ in(ordered_pair(U_1255,U_1253),cartesian_product2(U_1251,U_1249)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP315])],[f_355_3]) ).
cnf(f_355_5,plain,
( sP315(U_1251,U_1255,U_1249,U_1253)
| ~ in(ordered_pair(U_1255,U_1253),cartesian_product2(U_1251,U_1249)) ),
inference(clausify,[status(thm)],[f_355_4]) ).
cnf(f_355_6,plain,
( in(ordered_pair(U_1256,U_1254),cartesian_product2(U_1252,U_1250))
| ~ in(U_1254,U_1250)
| ~ in(U_1256,U_1252) ),
inference(clausify,[status(thm)],[f_355_4]) ).
cnf(f_355_7,plain,
( in(U_1255,U_1251)
| ~ sP315(U_1251,U_1255,U_1249,U_1253) ),
inference(clausify,[status(thm)],[f_355_4]) ).
cnf(f_355_8,plain,
( in(U_1253,U_1249)
| ~ sP315(U_1251,U_1255,U_1249,U_1253) ),
inference(clausify,[status(thm)],[f_355_4]) ).
fof(f_356_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_356_2,plain,
! [U_1259,U_1258] :
( element(U_1259,powerset(U_1258))
| ? [U_1257] :
( ~ in(U_1257,U_1258)
& in(U_1257,U_1259) ) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
! [U_1259,U_1258] :
( element(U_1259,powerset(U_1258))
| ( ~ in(sK170(U_1259,U_1258),U_1258)
& in(sK170(U_1259,U_1258),U_1259) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_1257,sK170(U_1259,U_1258))],[f_356_2]) ).
fof(f_356_4,plain,
( ! [U_1258,U_1259] :
( ~ in(sK170(U_1259,U_1258),U_1258)
| ~ sP316(U_1258,U_1259) )
& ! [U_1258,U_1259] :
( in(sK170(U_1259,U_1258),U_1259)
| ~ sP316(U_1258,U_1259) )
& ! [U_1258,U_1259] :
( element(U_1259,powerset(U_1258))
| sP316(U_1258,U_1259) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP316])],[f_356_3]) ).
cnf(f_356_5,plain,
( element(U_1259,powerset(U_1258))
| sP316(U_1258,U_1259) ),
inference(clausify,[status(thm)],[f_356_4]) ).
cnf(f_356_6,plain,
( in(sK170(U_1259,U_1258),U_1259)
| ~ sP316(U_1258,U_1259) ),
inference(clausify,[status(thm)],[f_356_4]) ).
cnf(f_356_7,plain,
( ~ in(sK170(U_1259,U_1258),U_1258)
| ~ sP316(U_1258,U_1259) ),
inference(clausify,[status(thm)],[f_356_4]) ).
fof(f_357_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_357_2,plain,
! [U_1262,U_1261,U_1260] :
( ( ( in(U_1261,relation_dom(relation_dom_restriction(U_1260,U_1262)))
| ~ in(U_1261,U_1262)
| ~ in(U_1261,relation_dom(U_1260)) )
& ( ( in(U_1261,U_1262)
& in(U_1261,relation_dom(U_1260)) )
| ~ in(U_1261,relation_dom(relation_dom_restriction(U_1260,U_1262))) ) )
| ~ function(U_1260)
| ~ relation(U_1260) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
( ! [U_1261,U_1260,U_1262] :
( in(U_1261,U_1262)
| ~ sP317(U_1261,U_1260,U_1262) )
& ! [U_1261,U_1260,U_1262] :
( in(U_1261,relation_dom(U_1260))
| ~ sP317(U_1261,U_1260,U_1262) )
& ! [U_1261,U_1260,U_1262] :
( in(U_1261,relation_dom(relation_dom_restriction(U_1260,U_1262)))
| ~ in(U_1261,U_1262)
| ~ in(U_1261,relation_dom(U_1260))
| ~ sP318(U_1261,U_1260,U_1262) )
& ! [U_1261,U_1260,U_1262] :
( sP317(U_1261,U_1260,U_1262)
| ~ in(U_1261,relation_dom(relation_dom_restriction(U_1260,U_1262)))
| ~ sP318(U_1261,U_1260,U_1262) )
& ! [U_1261,U_1260,U_1262] :
( sP318(U_1261,U_1260,U_1262)
| ~ function(U_1260)
| ~ relation(U_1260) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP317,sP318])],[f_357_2]) ).
cnf(f_357_4,plain,
( sP318(U_1261,U_1260,U_1262)
| ~ function(U_1260)
| ~ relation(U_1260) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_5,plain,
( sP317(U_1261,U_1260,U_1262)
| ~ in(U_1261,relation_dom(relation_dom_restriction(U_1260,U_1262)))
| ~ sP318(U_1261,U_1260,U_1262) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_6,plain,
( in(U_1261,relation_dom(relation_dom_restriction(U_1260,U_1262)))
| ~ in(U_1261,U_1262)
| ~ in(U_1261,relation_dom(U_1260))
| ~ sP318(U_1261,U_1260,U_1262) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_7,plain,
( in(U_1261,relation_dom(U_1260))
| ~ sP317(U_1261,U_1260,U_1262) ),
inference(clausify,[status(thm)],[f_357_3]) ).
cnf(f_357_8,plain,
( in(U_1261,U_1262)
| ~ sP317(U_1261,U_1260,U_1262) ),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_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_358_2,plain,
? [U_1263] :
( natural(U_1263)
& ordinal(U_1263)
& epsilon_connected(U_1263)
& epsilon_transitive(U_1263)
& ~ empty(U_1263) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
( natural(sK171)
& ordinal(sK171)
& epsilon_connected(sK171)
& epsilon_transitive(sK171)
& ~ empty(sK171) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_1263,sK171)],[f_358_2]) ).
fof(f_358_4,plain,
( natural(sK171)
& ordinal(sK171)
& epsilon_connected(sK171)
& epsilon_transitive(sK171)
& ~ empty(sK171) ),
inference(definitional_conversion,[status(esa)],[f_358_3]) ).
cnf(f_358_5,plain,
~ empty(sK171),
inference(clausify,[status(thm)],[f_358_4]) ).
cnf(f_358_6,plain,
epsilon_transitive(sK171),
inference(clausify,[status(thm)],[f_358_4]) ).
cnf(f_358_7,plain,
epsilon_connected(sK171),
inference(clausify,[status(thm)],[f_358_4]) ).
cnf(f_358_8,plain,
ordinal(sK171),
inference(clausify,[status(thm)],[f_358_4]) ).
cnf(f_358_9,plain,
natural(sK171),
inference(clausify,[status(thm)],[f_358_4]) ).
fof(f_359_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_359_2,plain,
? [U_1264] :
( finite(U_1264)
& ~ empty(U_1264) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
( finite(sK172)
& ~ empty(sK172) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_1264,sK172)],[f_359_2]) ).
fof(f_359_4,plain,
( finite(sK172)
& ~ empty(sK172) ),
inference(definitional_conversion,[status(esa)],[f_359_3]) ).
cnf(f_359_5,plain,
~ empty(sK172),
inference(clausify,[status(thm)],[f_359_4]) ).
cnf(f_359_6,plain,
finite(sK172),
inference(clausify,[status(thm)],[f_359_4]) ).
fof(f_360_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_360_2,plain,
? [U_1265] :
( function(U_1265)
& relation(U_1265) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
( function(sK173)
& relation(sK173) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_1265,sK173)],[f_360_2]) ).
fof(f_360_4,plain,
( function(sK173)
& relation(sK173) ),
inference(definitional_conversion,[status(esa)],[f_360_3]) ).
cnf(f_360_5,plain,
relation(sK173),
inference(clausify,[status(thm)],[f_360_4]) ).
cnf(f_360_6,plain,
function(sK173),
inference(clausify,[status(thm)],[f_360_4]) ).
fof(f_361_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_361_2,plain,
! [U_1268,U_1267] :
? [U_1266] :
( quasi_total(U_1266,U_1268,U_1267)
& function(U_1266)
& relation(U_1266)
& relation_of2(U_1266,U_1268,U_1267) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_1268,U_1267] :
( quasi_total(sK174(U_1268,U_1267),U_1268,U_1267)
& function(sK174(U_1268,U_1267))
& relation(sK174(U_1268,U_1267))
& relation_of2(sK174(U_1268,U_1267),U_1268,U_1267) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_1266,sK174(U_1268,U_1267))],[f_361_2]) ).
fof(f_361_4,plain,
( ! [U_1268,U_1267] : quasi_total(sK174(U_1268,U_1267),U_1268,U_1267)
& ! [U_1268,U_1267] : function(sK174(U_1268,U_1267))
& ! [U_1268,U_1267] : relation(sK174(U_1268,U_1267))
& ! [U_1268,U_1267] : relation_of2(sK174(U_1268,U_1267),U_1268,U_1267) ),
inference(definitional_conversion,[status(esa)],[f_361_3]) ).
cnf(f_361_5,plain,
relation_of2(sK174(U_1268,U_1267),U_1268,U_1267),
inference(clausify,[status(thm)],[f_361_4]) ).
cnf(f_361_6,plain,
relation(sK174(U_1268,U_1267)),
inference(clausify,[status(thm)],[f_361_4]) ).
cnf(f_361_7,plain,
function(sK174(U_1268,U_1267)),
inference(clausify,[status(thm)],[f_361_4]) ).
cnf(f_361_8,plain,
quasi_total(sK174(U_1268,U_1267),U_1268,U_1267),
inference(clausify,[status(thm)],[f_361_4]) ).
fof(f_362_1,plain,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_membered]) ).
fof(f_362_2,plain,
? [U_1269] :
( v5_membered(U_1269)
& v4_membered(U_1269)
& v3_membered(U_1269)
& v2_membered(U_1269)
& v1_membered(U_1269)
& ~ empty(U_1269) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
( v5_membered(sK175)
& v4_membered(sK175)
& v3_membered(sK175)
& v2_membered(sK175)
& v1_membered(sK175)
& ~ empty(sK175) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_1269,sK175)],[f_362_2]) ).
fof(f_362_4,plain,
( v5_membered(sK175)
& v4_membered(sK175)
& v3_membered(sK175)
& v2_membered(sK175)
& v1_membered(sK175)
& ~ empty(sK175) ),
inference(definitional_conversion,[status(esa)],[f_362_3]) ).
cnf(f_362_5,plain,
~ empty(sK175),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_6,plain,
v1_membered(sK175),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_7,plain,
v2_membered(sK175),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_8,plain,
v3_membered(sK175),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_9,plain,
v4_membered(sK175),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_10,plain,
v5_membered(sK175),
inference(clausify,[status(thm)],[f_362_4]) ).
fof(f_363_1,plain,
? [A] :
( strict_rel_str(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc1_orders_2]) ).
fof(f_363_2,plain,
? [U_1270] :
( strict_rel_str(U_1270)
& rel_str(U_1270) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
( strict_rel_str(sK176)
& rel_str(sK176) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_1270,sK176)],[f_363_2]) ).
fof(f_363_4,plain,
( strict_rel_str(sK176)
& rel_str(sK176) ),
inference(definitional_conversion,[status(esa)],[f_363_3]) ).
cnf(f_363_5,plain,
rel_str(sK176),
inference(clausify,[status(thm)],[f_363_4]) ).
cnf(f_363_6,plain,
strict_rel_str(sK176),
inference(clausify,[status(thm)],[f_363_4]) ).
fof(f_364_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_364_2,plain,
? [U_1271] :
( ordinal(U_1271)
& epsilon_connected(U_1271)
& epsilon_transitive(U_1271) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
( ordinal(sK177)
& epsilon_connected(sK177)
& epsilon_transitive(sK177) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_1271,sK177)],[f_364_2]) ).
fof(f_364_4,plain,
( ordinal(sK177)
& epsilon_connected(sK177)
& epsilon_transitive(sK177) ),
inference(definitional_conversion,[status(esa)],[f_364_3]) ).
cnf(f_364_5,plain,
epsilon_transitive(sK177),
inference(clausify,[status(thm)],[f_364_4]) ).
cnf(f_364_6,plain,
epsilon_connected(sK177),
inference(clausify,[status(thm)],[f_364_4]) ).
cnf(f_364_7,plain,
ordinal(sK177),
inference(clausify,[status(thm)],[f_364_4]) ).
fof(f_365_1,plain,
? [A] :
( being_limit_ordinal(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal2]) ).
fof(f_365_2,plain,
? [U_1272] :
( being_limit_ordinal(U_1272)
& ordinal(U_1272)
& epsilon_connected(U_1272)
& epsilon_transitive(U_1272) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
( being_limit_ordinal(sK178)
& ordinal(sK178)
& epsilon_connected(sK178)
& epsilon_transitive(sK178) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_1272,sK178)],[f_365_2]) ).
fof(f_365_4,plain,
( being_limit_ordinal(sK178)
& ordinal(sK178)
& epsilon_connected(sK178)
& epsilon_transitive(sK178) ),
inference(definitional_conversion,[status(esa)],[f_365_3]) ).
cnf(f_365_5,plain,
epsilon_transitive(sK178),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_6,plain,
epsilon_connected(sK178),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_7,plain,
ordinal(sK178),
inference(clausify,[status(thm)],[f_365_4]) ).
cnf(f_365_8,plain,
being_limit_ordinal(sK178),
inference(clausify,[status(thm)],[f_365_4]) ).
fof(f_366_1,plain,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_partfun1]) ).
fof(f_366_2,plain,
? [U_1273] :
( empty(U_1273)
& one_to_one(U_1273)
& function(U_1273)
& relation(U_1273) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
( empty(sK179)
& one_to_one(sK179)
& function(sK179)
& relation(sK179) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_1273,sK179)],[f_366_2]) ).
fof(f_366_4,plain,
( empty(sK179)
& one_to_one(sK179)
& function(sK179)
& relation(sK179) ),
inference(definitional_conversion,[status(esa)],[f_366_3]) ).
cnf(f_366_5,plain,
relation(sK179),
inference(clausify,[status(thm)],[f_366_4]) ).
cnf(f_366_6,plain,
function(sK179),
inference(clausify,[status(thm)],[f_366_4]) ).
cnf(f_366_7,plain,
one_to_one(sK179),
inference(clausify,[status(thm)],[f_366_4]) ).
cnf(f_366_8,plain,
empty(sK179),
inference(clausify,[status(thm)],[f_366_4]) ).
fof(f_367_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_367_2,plain,
? [U_1274] :
( relation(U_1274)
& empty(U_1274) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
( relation(sK180)
& empty(sK180) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_1274,sK180)],[f_367_2]) ).
fof(f_367_4,plain,
( relation(sK180)
& empty(sK180) ),
inference(definitional_conversion,[status(esa)],[f_367_3]) ).
cnf(f_367_5,plain,
empty(sK180),
inference(clausify,[status(thm)],[f_367_4]) ).
cnf(f_367_6,plain,
relation(sK180),
inference(clausify,[status(thm)],[f_367_4]) ).
fof(f_368_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_368_2,plain,
! [U_1276] :
( ? [U_1275] :
( ~ empty(U_1275)
& element(U_1275,powerset(U_1276)) )
| empty(U_1276) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_1276] :
( ( ~ empty(sK181(U_1276))
& element(sK181(U_1276),powerset(U_1276)) )
| empty(U_1276) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_1275,sK181(U_1276))],[f_368_2]) ).
fof(f_368_4,plain,
( ! [U_1276] :
( ~ empty(sK181(U_1276))
| ~ sP319(U_1276) )
& ! [U_1276] :
( element(sK181(U_1276),powerset(U_1276))
| ~ sP319(U_1276) )
& ! [U_1276] :
( sP319(U_1276)
| empty(U_1276) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP319])],[f_368_3]) ).
cnf(f_368_5,plain,
( sP319(U_1276)
| empty(U_1276) ),
inference(clausify,[status(thm)],[f_368_4]) ).
cnf(f_368_6,plain,
( element(sK181(U_1276),powerset(U_1276))
| ~ sP319(U_1276) ),
inference(clausify,[status(thm)],[f_368_4]) ).
cnf(f_368_7,plain,
( ~ empty(sK181(U_1276))
| ~ sP319(U_1276) ),
inference(clausify,[status(thm)],[f_368_4]) ).
fof(f_369_1,plain,
! [A] :
( ? [B] :
( open_subset(B,A)
& element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[rc1_tops_1]) ).
fof(f_369_2,plain,
! [U_1278] :
( ? [U_1277] :
( open_subset(U_1277,U_1278)
& element(U_1277,powerset(the_carrier(U_1278))) )
| ~ top_str(U_1278)
| ~ topological_space(U_1278) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
! [U_1278] :
( ( open_subset(sK182(U_1278),U_1278)
& element(sK182(U_1278),powerset(the_carrier(U_1278))) )
| ~ top_str(U_1278)
| ~ topological_space(U_1278) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_1277,sK182(U_1278))],[f_369_2]) ).
fof(f_369_4,plain,
( ! [U_1278] :
( open_subset(sK182(U_1278),U_1278)
| ~ sP320(U_1278) )
& ! [U_1278] :
( element(sK182(U_1278),powerset(the_carrier(U_1278)))
| ~ sP320(U_1278) )
& ! [U_1278] :
( sP320(U_1278)
| ~ top_str(U_1278)
| ~ topological_space(U_1278) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP320])],[f_369_3]) ).
cnf(f_369_5,plain,
( sP320(U_1278)
| ~ top_str(U_1278)
| ~ topological_space(U_1278) ),
inference(clausify,[status(thm)],[f_369_4]) ).
cnf(f_369_6,plain,
( element(sK182(U_1278),powerset(the_carrier(U_1278)))
| ~ sP320(U_1278) ),
inference(clausify,[status(thm)],[f_369_4]) ).
cnf(f_369_7,plain,
( open_subset(sK182(U_1278),U_1278)
| ~ sP320(U_1278) ),
inference(clausify,[status(thm)],[f_369_4]) ).
fof(f_370_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_370_2,plain,
? [U_1279] : empty(U_1279),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
empty(sK183),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_1279,sK183)],[f_370_2]) ).
fof(f_370_4,plain,
empty(sK183),
inference(definitional_conversion,[status(esa)],[f_370_3]) ).
cnf(f_370_5,plain,
empty(sK183),
inference(clausify,[status(thm)],[f_370_4]) ).
fof(f_371_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_371_2,plain,
! [U_1281] :
? [U_1280] :
( finite(U_1280)
& natural(U_1280)
& ordinal(U_1280)
& epsilon_connected(U_1280)
& epsilon_transitive(U_1280)
& one_to_one(U_1280)
& function(U_1280)
& relation(U_1280)
& empty(U_1280)
& element(U_1280,powerset(U_1281)) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
! [U_1281] :
( finite(sK184(U_1281))
& natural(sK184(U_1281))
& ordinal(sK184(U_1281))
& epsilon_connected(sK184(U_1281))
& epsilon_transitive(sK184(U_1281))
& one_to_one(sK184(U_1281))
& function(sK184(U_1281))
& relation(sK184(U_1281))
& empty(sK184(U_1281))
& element(sK184(U_1281),powerset(U_1281)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_1280,sK184(U_1281))],[f_371_2]) ).
fof(f_371_4,plain,
( ! [U_1281] : finite(sK184(U_1281))
& ! [U_1281] : natural(sK184(U_1281))
& ! [U_1281] : ordinal(sK184(U_1281))
& ! [U_1281] : epsilon_connected(sK184(U_1281))
& ! [U_1281] : epsilon_transitive(sK184(U_1281))
& ! [U_1281] : one_to_one(sK184(U_1281))
& ! [U_1281] : function(sK184(U_1281))
& ! [U_1281] : relation(sK184(U_1281))
& ! [U_1281] : empty(sK184(U_1281))
& ! [U_1281] : element(sK184(U_1281),powerset(U_1281)) ),
inference(definitional_conversion,[status(esa)],[f_371_3]) ).
cnf(f_371_5,plain,
element(sK184(U_1281),powerset(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_6,plain,
empty(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_7,plain,
relation(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_8,plain,
function(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_9,plain,
one_to_one(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_10,plain,
epsilon_transitive(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_11,plain,
epsilon_connected(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_12,plain,
ordinal(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_13,plain,
natural(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_14,plain,
finite(sK184(U_1281)),
inference(clausify,[status(thm)],[f_371_4]) ).
fof(f_372_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_372_2,plain,
? [U_1282] :
( function(U_1282)
& empty(U_1282)
& relation(U_1282) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
( function(sK185)
& empty(sK185)
& relation(sK185) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_1282,sK185)],[f_372_2]) ).
fof(f_372_4,plain,
( function(sK185)
& empty(sK185)
& relation(sK185) ),
inference(definitional_conversion,[status(esa)],[f_372_3]) ).
cnf(f_372_5,plain,
relation(sK185),
inference(clausify,[status(thm)],[f_372_4]) ).
cnf(f_372_6,plain,
empty(sK185),
inference(clausify,[status(thm)],[f_372_4]) ).
cnf(f_372_7,plain,
function(sK185),
inference(clausify,[status(thm)],[f_372_4]) ).
fof(f_373_1,plain,
! [A] :
? [B] :
( bijective(B,A,A)
& onto(B,A,A)
& quasi_total(B,A,A)
& one_to_one(B)
& function(B)
& relation(B)
& relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_2]) ).
fof(f_373_2,plain,
! [U_1284] :
? [U_1283] :
( bijective(U_1283,U_1284,U_1284)
& onto(U_1283,U_1284,U_1284)
& quasi_total(U_1283,U_1284,U_1284)
& one_to_one(U_1283)
& function(U_1283)
& relation(U_1283)
& relation_of2(U_1283,U_1284,U_1284) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
! [U_1284] :
( bijective(sK186(U_1284),U_1284,U_1284)
& onto(sK186(U_1284),U_1284,U_1284)
& quasi_total(sK186(U_1284),U_1284,U_1284)
& one_to_one(sK186(U_1284))
& function(sK186(U_1284))
& relation(sK186(U_1284))
& relation_of2(sK186(U_1284),U_1284,U_1284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_1283,sK186(U_1284))],[f_373_2]) ).
fof(f_373_4,plain,
( ! [U_1284] : bijective(sK186(U_1284),U_1284,U_1284)
& ! [U_1284] : onto(sK186(U_1284),U_1284,U_1284)
& ! [U_1284] : quasi_total(sK186(U_1284),U_1284,U_1284)
& ! [U_1284] : one_to_one(sK186(U_1284))
& ! [U_1284] : function(sK186(U_1284))
& ! [U_1284] : relation(sK186(U_1284))
& ! [U_1284] : relation_of2(sK186(U_1284),U_1284,U_1284) ),
inference(definitional_conversion,[status(esa)],[f_373_3]) ).
cnf(f_373_5,plain,
relation_of2(sK186(U_1284),U_1284,U_1284),
inference(clausify,[status(thm)],[f_373_4]) ).
cnf(f_373_6,plain,
relation(sK186(U_1284)),
inference(clausify,[status(thm)],[f_373_4]) ).
cnf(f_373_7,plain,
function(sK186(U_1284)),
inference(clausify,[status(thm)],[f_373_4]) ).
cnf(f_373_8,plain,
one_to_one(sK186(U_1284)),
inference(clausify,[status(thm)],[f_373_4]) ).
cnf(f_373_9,plain,
quasi_total(sK186(U_1284),U_1284,U_1284),
inference(clausify,[status(thm)],[f_373_4]) ).
cnf(f_373_10,plain,
onto(sK186(U_1284),U_1284,U_1284),
inference(clausify,[status(thm)],[f_373_4]) ).
cnf(f_373_11,plain,
bijective(sK186(U_1284),U_1284,U_1284),
inference(clausify,[status(thm)],[f_373_4]) ).
fof(f_374_1,plain,
? [A] :
( antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[rc2_orders_2]) ).
fof(f_374_2,plain,
? [U_1285] :
( antisymmetric_relstr(U_1285)
& transitive_relstr(U_1285)
& reflexive_relstr(U_1285)
& strict_rel_str(U_1285)
& ~ empty_carrier(U_1285)
& rel_str(U_1285) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
( antisymmetric_relstr(sK187)
& transitive_relstr(sK187)
& reflexive_relstr(sK187)
& strict_rel_str(sK187)
& ~ empty_carrier(sK187)
& rel_str(sK187) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_1285,sK187)],[f_374_2]) ).
fof(f_374_4,plain,
( antisymmetric_relstr(sK187)
& transitive_relstr(sK187)
& reflexive_relstr(sK187)
& strict_rel_str(sK187)
& ~ empty_carrier(sK187)
& rel_str(sK187) ),
inference(definitional_conversion,[status(esa)],[f_374_3]) ).
cnf(f_374_5,plain,
rel_str(sK187),
inference(clausify,[status(thm)],[f_374_4]) ).
cnf(f_374_6,plain,
~ empty_carrier(sK187),
inference(clausify,[status(thm)],[f_374_4]) ).
cnf(f_374_7,plain,
strict_rel_str(sK187),
inference(clausify,[status(thm)],[f_374_4]) ).
cnf(f_374_8,plain,
reflexive_relstr(sK187),
inference(clausify,[status(thm)],[f_374_4]) ).
cnf(f_374_9,plain,
transitive_relstr(sK187),
inference(clausify,[status(thm)],[f_374_4]) ).
cnf(f_374_10,plain,
antisymmetric_relstr(sK187),
inference(clausify,[status(thm)],[f_374_4]) ).
fof(f_375_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_375_2,plain,
? [U_1286] :
( ordinal(U_1286)
& epsilon_connected(U_1286)
& epsilon_transitive(U_1286)
& empty(U_1286)
& one_to_one(U_1286)
& function(U_1286)
& relation(U_1286) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
( ordinal(sK188)
& epsilon_connected(sK188)
& epsilon_transitive(sK188)
& empty(sK188)
& one_to_one(sK188)
& function(sK188)
& relation(sK188) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_1286,sK188)],[f_375_2]) ).
fof(f_375_4,plain,
( ordinal(sK188)
& epsilon_connected(sK188)
& epsilon_transitive(sK188)
& empty(sK188)
& one_to_one(sK188)
& function(sK188)
& relation(sK188) ),
inference(definitional_conversion,[status(esa)],[f_375_3]) ).
cnf(f_375_5,plain,
relation(sK188),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_6,plain,
function(sK188),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_7,plain,
one_to_one(sK188),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_8,plain,
empty(sK188),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_9,plain,
epsilon_transitive(sK188),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_10,plain,
epsilon_connected(sK188),
inference(clausify,[status(thm)],[f_375_4]) ).
cnf(f_375_11,plain,
ordinal(sK188),
inference(clausify,[status(thm)],[f_375_4]) ).
fof(f_376_1,plain,
! [A,B] :
? [C] :
( function(C)
& relation(C)
& relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[rc2_partfun1]) ).
fof(f_376_2,plain,
! [U_1289,U_1288] :
? [U_1287] :
( function(U_1287)
& relation(U_1287)
& relation_of2(U_1287,U_1289,U_1288) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
! [U_1289,U_1288] :
( function(sK189(U_1289,U_1288))
& relation(sK189(U_1289,U_1288))
& relation_of2(sK189(U_1289,U_1288),U_1289,U_1288) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_1287,sK189(U_1289,U_1288))],[f_376_2]) ).
fof(f_376_4,plain,
( ! [U_1289,U_1288] : function(sK189(U_1289,U_1288))
& ! [U_1289,U_1288] : relation(sK189(U_1289,U_1288))
& ! [U_1289,U_1288] : relation_of2(sK189(U_1289,U_1288),U_1289,U_1288) ),
inference(definitional_conversion,[status(esa)],[f_376_3]) ).
cnf(f_376_5,plain,
relation_of2(sK189(U_1289,U_1288),U_1289,U_1288),
inference(clausify,[status(thm)],[f_376_4]) ).
cnf(f_376_6,plain,
relation(sK189(U_1289,U_1288)),
inference(clausify,[status(thm)],[f_376_4]) ).
cnf(f_376_7,plain,
function(sK189(U_1289,U_1288)),
inference(clausify,[status(thm)],[f_376_4]) ).
fof(f_377_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_377_2,plain,
? [U_1290] :
( relation(U_1290)
& ~ empty(U_1290) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
( relation(sK190)
& ~ empty(sK190) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_1290,sK190)],[f_377_2]) ).
fof(f_377_4,plain,
( relation(sK190)
& ~ empty(sK190) ),
inference(definitional_conversion,[status(esa)],[f_377_3]) ).
cnf(f_377_5,plain,
~ empty(sK190),
inference(clausify,[status(thm)],[f_377_4]) ).
cnf(f_377_6,plain,
relation(sK190),
inference(clausify,[status(thm)],[f_377_4]) ).
fof(f_378_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_378_2,plain,
! [U_1292] :
? [U_1291] :
( empty(U_1291)
& element(U_1291,powerset(U_1292)) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_1292] :
( empty(sK191(U_1292))
& element(sK191(U_1292),powerset(U_1292)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_1291,sK191(U_1292))],[f_378_2]) ).
fof(f_378_4,plain,
( ! [U_1292] : empty(sK191(U_1292))
& ! [U_1292] : element(sK191(U_1292),powerset(U_1292)) ),
inference(definitional_conversion,[status(esa)],[f_378_3]) ).
cnf(f_378_5,plain,
element(sK191(U_1292),powerset(U_1292)),
inference(clausify,[status(thm)],[f_378_4]) ).
cnf(f_378_6,plain,
empty(sK191(U_1292)),
inference(clausify,[status(thm)],[f_378_4]) ).
fof(f_379_1,plain,
! [A] :
? [B] :
( ~ proper_element(B,powerset(A))
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_tex_2]) ).
fof(f_379_2,plain,
! [U_1294] :
? [U_1293] :
( ~ proper_element(U_1293,powerset(U_1294))
& element(U_1293,powerset(U_1294)) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1294] :
( ~ proper_element(sK192(U_1294),powerset(U_1294))
& element(sK192(U_1294),powerset(U_1294)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_1293,sK192(U_1294))],[f_379_2]) ).
fof(f_379_4,plain,
( ! [U_1294] : ~ proper_element(sK192(U_1294),powerset(U_1294))
& ! [U_1294] : element(sK192(U_1294),powerset(U_1294)) ),
inference(definitional_conversion,[status(esa)],[f_379_3]) ).
cnf(f_379_5,plain,
element(sK192(U_1294),powerset(U_1294)),
inference(clausify,[status(thm)],[f_379_4]) ).
cnf(f_379_6,plain,
~ proper_element(sK192(U_1294),powerset(U_1294)),
inference(clausify,[status(thm)],[f_379_4]) ).
fof(f_380_1,plain,
! [A] :
( ? [B] :
( closed_subset(B,A)
& open_subset(B,A)
& element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[rc2_tops_1]) ).
fof(f_380_2,plain,
! [U_1296] :
( ? [U_1295] :
( closed_subset(U_1295,U_1296)
& open_subset(U_1295,U_1296)
& element(U_1295,powerset(the_carrier(U_1296))) )
| ~ top_str(U_1296)
| ~ topological_space(U_1296) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
! [U_1296] :
( ( closed_subset(sK193(U_1296),U_1296)
& open_subset(sK193(U_1296),U_1296)
& element(sK193(U_1296),powerset(the_carrier(U_1296))) )
| ~ top_str(U_1296)
| ~ topological_space(U_1296) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_1295,sK193(U_1296))],[f_380_2]) ).
fof(f_380_4,plain,
( ! [U_1296] :
( closed_subset(sK193(U_1296),U_1296)
| ~ sP321(U_1296) )
& ! [U_1296] :
( open_subset(sK193(U_1296),U_1296)
| ~ sP321(U_1296) )
& ! [U_1296] :
( element(sK193(U_1296),powerset(the_carrier(U_1296)))
| ~ sP321(U_1296) )
& ! [U_1296] :
( sP321(U_1296)
| ~ top_str(U_1296)
| ~ topological_space(U_1296) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP321])],[f_380_3]) ).
cnf(f_380_5,plain,
( sP321(U_1296)
| ~ top_str(U_1296)
| ~ topological_space(U_1296) ),
inference(clausify,[status(thm)],[f_380_4]) ).
cnf(f_380_6,plain,
( element(sK193(U_1296),powerset(the_carrier(U_1296)))
| ~ sP321(U_1296) ),
inference(clausify,[status(thm)],[f_380_4]) ).
cnf(f_380_7,plain,
( open_subset(sK193(U_1296),U_1296)
| ~ sP321(U_1296) ),
inference(clausify,[status(thm)],[f_380_4]) ).
cnf(f_380_8,plain,
( closed_subset(sK193(U_1296),U_1296)
| ~ sP321(U_1296) ),
inference(clausify,[status(thm)],[f_380_4]) ).
fof(f_381_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_381_2,plain,
? [U_1297] : ~ empty(U_1297),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
~ empty(sK194),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_1297,sK194)],[f_381_2]) ).
fof(f_381_4,plain,
~ empty(sK194),
inference(definitional_conversion,[status(esa)],[f_381_3]) ).
cnf(f_381_5,plain,
~ empty(sK194),
inference(clausify,[status(thm)],[f_381_4]) ).
fof(f_382_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_382_2,plain,
! [U_1299] :
( ? [U_1298] :
( finite(U_1298)
& ~ empty(U_1298)
& element(U_1298,powerset(U_1299)) )
| empty(U_1299) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_1299] :
( ( finite(sK195(U_1299))
& ~ empty(sK195(U_1299))
& element(sK195(U_1299),powerset(U_1299)) )
| empty(U_1299) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_1298,sK195(U_1299))],[f_382_2]) ).
fof(f_382_4,plain,
( ! [U_1299] :
( finite(sK195(U_1299))
| ~ sP322(U_1299) )
& ! [U_1299] :
( ~ empty(sK195(U_1299))
| ~ sP322(U_1299) )
& ! [U_1299] :
( element(sK195(U_1299),powerset(U_1299))
| ~ sP322(U_1299) )
& ! [U_1299] :
( sP322(U_1299)
| empty(U_1299) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP322])],[f_382_3]) ).
cnf(f_382_5,plain,
( sP322(U_1299)
| empty(U_1299) ),
inference(clausify,[status(thm)],[f_382_4]) ).
cnf(f_382_6,plain,
( element(sK195(U_1299),powerset(U_1299))
| ~ sP322(U_1299) ),
inference(clausify,[status(thm)],[f_382_4]) ).
cnf(f_382_7,plain,
( ~ empty(sK195(U_1299))
| ~ sP322(U_1299) ),
inference(clausify,[status(thm)],[f_382_4]) ).
cnf(f_382_8,plain,
( finite(sK195(U_1299))
| ~ sP322(U_1299) ),
inference(clausify,[status(thm)],[f_382_4]) ).
fof(f_383_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_383_2,plain,
? [U_1300] :
( one_to_one(U_1300)
& function(U_1300)
& relation(U_1300) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
( one_to_one(sK196)
& function(sK196)
& relation(sK196) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_1300,sK196)],[f_383_2]) ).
fof(f_383_4,plain,
( one_to_one(sK196)
& function(sK196)
& relation(sK196) ),
inference(definitional_conversion,[status(esa)],[f_383_3]) ).
cnf(f_383_5,plain,
relation(sK196),
inference(clausify,[status(thm)],[f_383_4]) ).
cnf(f_383_6,plain,
function(sK196),
inference(clausify,[status(thm)],[f_383_4]) ).
cnf(f_383_7,plain,
one_to_one(sK196),
inference(clausify,[status(thm)],[f_383_4]) ).
fof(f_384_1,plain,
? [A] :
( strict_latt_str(A)
& latt_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_lattices]) ).
fof(f_384_2,plain,
? [U_1301] :
( strict_latt_str(U_1301)
& latt_str(U_1301) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
( strict_latt_str(sK197)
& latt_str(sK197) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_1301,sK197)],[f_384_2]) ).
fof(f_384_4,plain,
( strict_latt_str(sK197)
& latt_str(sK197) ),
inference(definitional_conversion,[status(esa)],[f_384_3]) ).
cnf(f_384_5,plain,
latt_str(sK197),
inference(clausify,[status(thm)],[f_384_4]) ).
cnf(f_384_6,plain,
strict_latt_str(sK197),
inference(clausify,[status(thm)],[f_384_4]) ).
fof(f_385_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_385_2,plain,
? [U_1302] :
( ordinal(U_1302)
& epsilon_connected(U_1302)
& epsilon_transitive(U_1302)
& ~ empty(U_1302) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
( ordinal(sK198)
& epsilon_connected(sK198)
& epsilon_transitive(sK198)
& ~ empty(sK198) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_1302,sK198)],[f_385_2]) ).
fof(f_385_4,plain,
( ordinal(sK198)
& epsilon_connected(sK198)
& epsilon_transitive(sK198)
& ~ empty(sK198) ),
inference(definitional_conversion,[status(esa)],[f_385_3]) ).
cnf(f_385_5,plain,
~ empty(sK198),
inference(clausify,[status(thm)],[f_385_4]) ).
cnf(f_385_6,plain,
epsilon_transitive(sK198),
inference(clausify,[status(thm)],[f_385_4]) ).
cnf(f_385_7,plain,
epsilon_connected(sK198),
inference(clausify,[status(thm)],[f_385_4]) ).
cnf(f_385_8,plain,
ordinal(sK198),
inference(clausify,[status(thm)],[f_385_4]) ).
fof(f_386_1,plain,
! [A] :
? [B] :
( v1_partfun1(B,A,A)
& transitive(B)
& antisymmetric(B)
& symmetric(B)
& reflexive(B)
& relation(B)
& relation_of2(B,A,A) ),
inference(fof_nnf,[status(thm)],[rc3_partfun1]) ).
fof(f_386_2,plain,
! [U_1304] :
? [U_1303] :
( v1_partfun1(U_1303,U_1304,U_1304)
& transitive(U_1303)
& antisymmetric(U_1303)
& symmetric(U_1303)
& reflexive(U_1303)
& relation(U_1303)
& relation_of2(U_1303,U_1304,U_1304) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
! [U_1304] :
( v1_partfun1(sK199(U_1304),U_1304,U_1304)
& transitive(sK199(U_1304))
& antisymmetric(sK199(U_1304))
& symmetric(sK199(U_1304))
& reflexive(sK199(U_1304))
& relation(sK199(U_1304))
& relation_of2(sK199(U_1304),U_1304,U_1304) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_1303,sK199(U_1304))],[f_386_2]) ).
fof(f_386_4,plain,
( ! [U_1304] : v1_partfun1(sK199(U_1304),U_1304,U_1304)
& ! [U_1304] : transitive(sK199(U_1304))
& ! [U_1304] : antisymmetric(sK199(U_1304))
& ! [U_1304] : symmetric(sK199(U_1304))
& ! [U_1304] : reflexive(sK199(U_1304))
& ! [U_1304] : relation(sK199(U_1304))
& ! [U_1304] : relation_of2(sK199(U_1304),U_1304,U_1304) ),
inference(definitional_conversion,[status(esa)],[f_386_3]) ).
cnf(f_386_5,plain,
relation_of2(sK199(U_1304),U_1304,U_1304),
inference(clausify,[status(thm)],[f_386_4]) ).
cnf(f_386_6,plain,
relation(sK199(U_1304)),
inference(clausify,[status(thm)],[f_386_4]) ).
cnf(f_386_7,plain,
reflexive(sK199(U_1304)),
inference(clausify,[status(thm)],[f_386_4]) ).
cnf(f_386_8,plain,
symmetric(sK199(U_1304)),
inference(clausify,[status(thm)],[f_386_4]) ).
cnf(f_386_9,plain,
antisymmetric(sK199(U_1304)),
inference(clausify,[status(thm)],[f_386_4]) ).
cnf(f_386_10,plain,
transitive(sK199(U_1304)),
inference(clausify,[status(thm)],[f_386_4]) ).
cnf(f_386_11,plain,
v1_partfun1(sK199(U_1304),U_1304,U_1304),
inference(clausify,[status(thm)],[f_386_4]) ).
fof(f_387_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_387_2,plain,
? [U_1305] :
( relation_empty_yielding(U_1305)
& relation(U_1305) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
( relation_empty_yielding(sK200)
& relation(sK200) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_1305,sK200)],[f_387_2]) ).
fof(f_387_4,plain,
( relation_empty_yielding(sK200)
& relation(sK200) ),
inference(definitional_conversion,[status(esa)],[f_387_3]) ).
cnf(f_387_5,plain,
relation(sK200),
inference(clausify,[status(thm)],[f_387_4]) ).
cnf(f_387_6,plain,
relation_empty_yielding(sK200),
inference(clausify,[status(thm)],[f_387_4]) ).
fof(f_388_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_388_2,plain,
? [U_1306] :
( ~ empty_carrier(U_1306)
& one_sorted_str(U_1306) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
( ~ empty_carrier(sK201)
& one_sorted_str(sK201) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_1306,sK201)],[f_388_2]) ).
fof(f_388_4,plain,
( ~ empty_carrier(sK201)
& one_sorted_str(sK201) ),
inference(definitional_conversion,[status(esa)],[f_388_3]) ).
cnf(f_388_5,plain,
one_sorted_str(sK201),
inference(clausify,[status(thm)],[f_388_4]) ).
cnf(f_388_6,plain,
~ empty_carrier(sK201),
inference(clausify,[status(thm)],[f_388_4]) ).
fof(f_389_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc4_finset_1]) ).
fof(f_389_2,plain,
! [U_1308] :
( ? [U_1307] :
( finite(U_1307)
& ~ empty(U_1307)
& element(U_1307,powerset(U_1308)) )
| empty(U_1308) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
! [U_1308] :
( ( finite(sK202(U_1308))
& ~ empty(sK202(U_1308))
& element(sK202(U_1308),powerset(U_1308)) )
| empty(U_1308) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_1307,sK202(U_1308))],[f_389_2]) ).
fof(f_389_4,plain,
( ! [U_1308] :
( finite(sK202(U_1308))
| ~ sP323(U_1308) )
& ! [U_1308] :
( ~ empty(sK202(U_1308))
| ~ sP323(U_1308) )
& ! [U_1308] :
( element(sK202(U_1308),powerset(U_1308))
| ~ sP323(U_1308) )
& ! [U_1308] :
( sP323(U_1308)
| empty(U_1308) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323])],[f_389_3]) ).
cnf(f_389_5,plain,
( sP323(U_1308)
| empty(U_1308) ),
inference(clausify,[status(thm)],[f_389_4]) ).
cnf(f_389_6,plain,
( element(sK202(U_1308),powerset(U_1308))
| ~ sP323(U_1308) ),
inference(clausify,[status(thm)],[f_389_4]) ).
cnf(f_389_7,plain,
( ~ empty(sK202(U_1308))
| ~ sP323(U_1308) ),
inference(clausify,[status(thm)],[f_389_4]) ).
cnf(f_389_8,plain,
( finite(sK202(U_1308))
| ~ sP323(U_1308) ),
inference(clausify,[status(thm)],[f_389_4]) ).
fof(f_390_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_390_2,plain,
? [U_1309] :
( function(U_1309)
& relation_empty_yielding(U_1309)
& relation(U_1309) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
( function(sK203)
& relation_empty_yielding(sK203)
& relation(sK203) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_1309,sK203)],[f_390_2]) ).
fof(f_390_4,plain,
( function(sK203)
& relation_empty_yielding(sK203)
& relation(sK203) ),
inference(definitional_conversion,[status(esa)],[f_390_3]) ).
cnf(f_390_5,plain,
relation(sK203),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_6,plain,
relation_empty_yielding(sK203),
inference(clausify,[status(thm)],[f_390_4]) ).
cnf(f_390_7,plain,
function(sK203),
inference(clausify,[status(thm)],[f_390_4]) ).
fof(f_391_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_391_2,plain,
! [U_1311] :
( ? [U_1310] :
( ~ empty(U_1310)
& element(U_1310,powerset(the_carrier(U_1311))) )
| ~ one_sorted_str(U_1311)
| empty_carrier(U_1311) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_1311] :
( ( ~ empty(sK204(U_1311))
& element(sK204(U_1311),powerset(the_carrier(U_1311))) )
| ~ one_sorted_str(U_1311)
| empty_carrier(U_1311) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_1310,sK204(U_1311))],[f_391_2]) ).
fof(f_391_4,plain,
( ! [U_1311] :
( ~ empty(sK204(U_1311))
| ~ sP324(U_1311) )
& ! [U_1311] :
( element(sK204(U_1311),powerset(the_carrier(U_1311)))
| ~ sP324(U_1311) )
& ! [U_1311] :
( sP324(U_1311)
| ~ one_sorted_str(U_1311)
| empty_carrier(U_1311) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP324])],[f_391_3]) ).
cnf(f_391_5,plain,
( sP324(U_1311)
| ~ one_sorted_str(U_1311)
| empty_carrier(U_1311) ),
inference(clausify,[status(thm)],[f_391_4]) ).
cnf(f_391_6,plain,
( element(sK204(U_1311),powerset(the_carrier(U_1311)))
| ~ sP324(U_1311) ),
inference(clausify,[status(thm)],[f_391_4]) ).
cnf(f_391_7,plain,
( ~ empty(sK204(U_1311))
| ~ sP324(U_1311) ),
inference(clausify,[status(thm)],[f_391_4]) ).
fof(f_392_1,plain,
? [A] :
( strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(fof_nnf,[status(thm)],[rc6_lattices]) ).
fof(f_392_2,plain,
? [U_1312] :
( strict_latt_str(U_1312)
& ~ empty_carrier(U_1312)
& latt_str(U_1312) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
( strict_latt_str(sK205)
& ~ empty_carrier(sK205)
& latt_str(sK205) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_1312,sK205)],[f_392_2]) ).
fof(f_392_4,plain,
( strict_latt_str(sK205)
& ~ empty_carrier(sK205)
& latt_str(sK205) ),
inference(definitional_conversion,[status(esa)],[f_392_3]) ).
cnf(f_392_5,plain,
latt_str(sK205),
inference(clausify,[status(thm)],[f_392_4]) ).
cnf(f_392_6,plain,
~ empty_carrier(sK205),
inference(clausify,[status(thm)],[f_392_4]) ).
cnf(f_392_7,plain,
strict_latt_str(sK205),
inference(clausify,[status(thm)],[f_392_4]) ).
fof(f_393_1,plain,
! [A] :
( ? [B] :
( closed_subset(B,A)
& element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[rc6_pre_topc]) ).
fof(f_393_2,plain,
! [U_1314] :
( ? [U_1313] :
( closed_subset(U_1313,U_1314)
& element(U_1313,powerset(the_carrier(U_1314))) )
| ~ top_str(U_1314)
| ~ topological_space(U_1314) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
! [U_1314] :
( ( closed_subset(sK206(U_1314),U_1314)
& element(sK206(U_1314),powerset(the_carrier(U_1314))) )
| ~ top_str(U_1314)
| ~ topological_space(U_1314) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_1313,sK206(U_1314))],[f_393_2]) ).
fof(f_393_4,plain,
( ! [U_1314] :
( closed_subset(sK206(U_1314),U_1314)
| ~ sP325(U_1314) )
& ! [U_1314] :
( element(sK206(U_1314),powerset(the_carrier(U_1314)))
| ~ sP325(U_1314) )
& ! [U_1314] :
( sP325(U_1314)
| ~ top_str(U_1314)
| ~ topological_space(U_1314) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP325])],[f_393_3]) ).
cnf(f_393_5,plain,
( sP325(U_1314)
| ~ top_str(U_1314)
| ~ topological_space(U_1314) ),
inference(clausify,[status(thm)],[f_393_4]) ).
cnf(f_393_6,plain,
( element(sK206(U_1314),powerset(the_carrier(U_1314)))
| ~ sP325(U_1314) ),
inference(clausify,[status(thm)],[f_393_4]) ).
cnf(f_393_7,plain,
( closed_subset(sK206(U_1314),U_1314)
| ~ sP325(U_1314) ),
inference(clausify,[status(thm)],[f_393_4]) ).
fof(f_394_1,plain,
! [A] :
( ? [B] :
( closed_subset(B,A)
& ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc7_pre_topc]) ).
fof(f_394_2,plain,
! [U_1316] :
( ? [U_1315] :
( closed_subset(U_1315,U_1316)
& ~ empty(U_1315)
& element(U_1315,powerset(the_carrier(U_1316))) )
| ~ top_str(U_1316)
| ~ topological_space(U_1316)
| empty_carrier(U_1316) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1316] :
( ( closed_subset(sK207(U_1316),U_1316)
& ~ empty(sK207(U_1316))
& element(sK207(U_1316),powerset(the_carrier(U_1316))) )
| ~ top_str(U_1316)
| ~ topological_space(U_1316)
| empty_carrier(U_1316) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_1315,sK207(U_1316))],[f_394_2]) ).
fof(f_394_4,plain,
( ! [U_1316] :
( closed_subset(sK207(U_1316),U_1316)
| ~ sP326(U_1316) )
& ! [U_1316] :
( ~ empty(sK207(U_1316))
| ~ sP326(U_1316) )
& ! [U_1316] :
( element(sK207(U_1316),powerset(the_carrier(U_1316)))
| ~ sP326(U_1316) )
& ! [U_1316] :
( sP326(U_1316)
| ~ top_str(U_1316)
| ~ topological_space(U_1316)
| empty_carrier(U_1316) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP326])],[f_394_3]) ).
cnf(f_394_5,plain,
( sP326(U_1316)
| ~ top_str(U_1316)
| ~ topological_space(U_1316)
| empty_carrier(U_1316) ),
inference(clausify,[status(thm)],[f_394_4]) ).
cnf(f_394_6,plain,
( element(sK207(U_1316),powerset(the_carrier(U_1316)))
| ~ sP326(U_1316) ),
inference(clausify,[status(thm)],[f_394_4]) ).
cnf(f_394_7,plain,
( ~ empty(sK207(U_1316))
| ~ sP326(U_1316) ),
inference(clausify,[status(thm)],[f_394_4]) ).
cnf(f_394_8,plain,
( closed_subset(sK207(U_1316),U_1316)
| ~ sP326(U_1316) ),
inference(clausify,[status(thm)],[f_394_4]) ).
fof(f_395_1,plain,
? [A] :
( lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(fof_nnf,[status(thm)],[rc9_lattices]) ).
fof(f_395_2,plain,
? [U_1317] :
( lattice(U_1317)
& join_absorbing(U_1317)
& meet_absorbing(U_1317)
& meet_associative(U_1317)
& meet_commutative(U_1317)
& join_associative(U_1317)
& join_commutative(U_1317)
& strict_latt_str(U_1317)
& ~ empty_carrier(U_1317)
& latt_str(U_1317) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
( lattice(sK208)
& join_absorbing(sK208)
& meet_absorbing(sK208)
& meet_associative(sK208)
& meet_commutative(sK208)
& join_associative(sK208)
& join_commutative(sK208)
& strict_latt_str(sK208)
& ~ empty_carrier(sK208)
& latt_str(sK208) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_1317,sK208)],[f_395_2]) ).
fof(f_395_4,plain,
( lattice(sK208)
& join_absorbing(sK208)
& meet_absorbing(sK208)
& meet_associative(sK208)
& meet_commutative(sK208)
& join_associative(sK208)
& join_commutative(sK208)
& strict_latt_str(sK208)
& ~ empty_carrier(sK208)
& latt_str(sK208) ),
inference(definitional_conversion,[status(esa)],[f_395_3]) ).
cnf(f_395_5,plain,
latt_str(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_6,plain,
~ empty_carrier(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_7,plain,
strict_latt_str(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_8,plain,
join_commutative(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_9,plain,
join_associative(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_10,plain,
meet_commutative(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_11,plain,
meet_associative(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_12,plain,
meet_absorbing(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_13,plain,
join_absorbing(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
cnf(f_395_14,plain,
lattice(sK208),
inference(clausify,[status(thm)],[f_395_4]) ).
fof(f_396_1,plain,
! [A,B,C,D] :
( k10_filter_1(A,B,C,D) = ordered_pair(C,D)
| ~ element(D,the_carrier(B))
| ~ element(C,the_carrier(A))
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B)
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k10_filter_1]) ).
fof(f_396_2,plain,
! [U_1321,U_1320,U_1319,U_1318] :
( k10_filter_1(U_1321,U_1320,U_1319,U_1318) = ordered_pair(U_1319,U_1318)
| ~ element(U_1318,the_carrier(U_1320))
| ~ element(U_1319,the_carrier(U_1321))
| ~ latt_str(U_1320)
| ~ lattice(U_1320)
| empty_carrier(U_1320)
| ~ latt_str(U_1321)
| ~ lattice(U_1321)
| empty_carrier(U_1321) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
! [U_1319,U_1318,U_1320,U_1321] :
( k10_filter_1(U_1321,U_1320,U_1319,U_1318) = ordered_pair(U_1319,U_1318)
| ~ element(U_1318,the_carrier(U_1320))
| ~ element(U_1319,the_carrier(U_1321))
| ~ latt_str(U_1320)
| ~ lattice(U_1320)
| empty_carrier(U_1320)
| ~ latt_str(U_1321)
| ~ lattice(U_1321)
| empty_carrier(U_1321) ),
inference(definitional_conversion,[status(esa)],[f_396_2]) ).
cnf(f_396_4,plain,
( k10_filter_1(U_1321,U_1320,U_1319,U_1318) = ordered_pair(U_1319,U_1318)
| ~ element(U_1318,the_carrier(U_1320))
| ~ element(U_1319,the_carrier(U_1321))
| ~ latt_str(U_1320)
| ~ lattice(U_1320)
| empty_carrier(U_1320)
| ~ latt_str(U_1321)
| ~ lattice(U_1321)
| empty_carrier(U_1321) ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [A,B,C,D] :
( ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D)
| ~ element(D,B)
| ~ element(C,A)
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k1_domain_1]) ).
fof(f_397_2,plain,
! [U_1325,U_1324,U_1323,U_1322] :
( ordered_pair_as_product_element(U_1325,U_1324,U_1323,U_1322) = ordered_pair(U_1323,U_1322)
| ~ element(U_1322,U_1324)
| ~ element(U_1323,U_1325)
| empty(U_1324)
| empty(U_1325) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
! [U_1323,U_1324,U_1322,U_1325] :
( ordered_pair_as_product_element(U_1325,U_1324,U_1323,U_1322) = ordered_pair(U_1323,U_1322)
| ~ element(U_1322,U_1324)
| ~ element(U_1323,U_1325)
| empty(U_1324)
| empty(U_1325) ),
inference(definitional_conversion,[status(esa)],[f_397_2]) ).
cnf(f_397_4,plain,
( ordered_pair_as_product_element(U_1325,U_1324,U_1323,U_1322) = ordered_pair(U_1323,U_1322)
| ~ element(U_1322,U_1324)
| ~ element(U_1323,U_1325)
| empty(U_1324)
| empty(U_1325) ),
inference(clausify,[status(thm)],[f_397_3]) ).
fof(f_398_1,plain,
! [A] : k1_pcomps_1(A) = powerset(A),
inference(fof_nnf,[status(thm)],[redefinition_k1_pcomps_1]) ).
fof(f_398_2,plain,
! [U_1326] : k1_pcomps_1(U_1326) = powerset(U_1326),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
! [U_1326] : k1_pcomps_1(U_1326) = powerset(U_1326),
inference(definitional_conversion,[status(esa)],[f_398_2]) ).
cnf(f_398_4,plain,
k1_pcomps_1(U_1326) = powerset(U_1326),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [A,B,C,D,E,F] :
( apply_binary_as_element(A,B,C,D,E,F) = apply_binary(D,E,F)
| ~ element(F,B)
| ~ element(E,A)
| ~ relation_of2(D,cartesian_product2(A,B),C)
| ~ quasi_total(D,cartesian_product2(A,B),C)
| ~ function(D)
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k2_binop_1]) ).
fof(f_399_2,plain,
! [U_1332,U_1331,U_1330,U_1329,U_1328,U_1327] :
( apply_binary_as_element(U_1332,U_1331,U_1330,U_1329,U_1328,U_1327) = apply_binary(U_1329,U_1328,U_1327)
| ~ element(U_1327,U_1331)
| ~ element(U_1328,U_1332)
| ~ relation_of2(U_1329,cartesian_product2(U_1332,U_1331),U_1330)
| ~ quasi_total(U_1329,cartesian_product2(U_1332,U_1331),U_1330)
| ~ function(U_1329)
| empty(U_1331)
| empty(U_1332) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_1327,U_1329,U_1330,U_1331,U_1328,U_1332] :
( apply_binary_as_element(U_1332,U_1331,U_1330,U_1329,U_1328,U_1327) = apply_binary(U_1329,U_1328,U_1327)
| ~ element(U_1327,U_1331)
| ~ element(U_1328,U_1332)
| ~ relation_of2(U_1329,cartesian_product2(U_1332,U_1331),U_1330)
| ~ quasi_total(U_1329,cartesian_product2(U_1332,U_1331),U_1330)
| ~ function(U_1329)
| empty(U_1331)
| empty(U_1332) ),
inference(definitional_conversion,[status(esa)],[f_399_2]) ).
cnf(f_399_4,plain,
( apply_binary_as_element(U_1332,U_1331,U_1330,U_1329,U_1328,U_1327) = apply_binary(U_1329,U_1328,U_1327)
| ~ element(U_1327,U_1331)
| ~ element(U_1328,U_1332)
| ~ relation_of2(U_1329,cartesian_product2(U_1332,U_1331),U_1330)
| ~ quasi_total(U_1329,cartesian_product2(U_1332,U_1331),U_1330)
| ~ function(U_1329)
| empty(U_1331)
| empty(U_1332) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
! [A] :
( k2_lattice3(A) = relation_of_lattice(A)
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k2_lattice3]) ).
fof(f_400_2,plain,
! [U_1333] :
( k2_lattice3(U_1333) = relation_of_lattice(U_1333)
| ~ latt_str(U_1333)
| ~ lattice(U_1333)
| empty_carrier(U_1333) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
! [U_1333] :
( k2_lattice3(U_1333) = relation_of_lattice(U_1333)
| ~ latt_str(U_1333)
| ~ lattice(U_1333)
| empty_carrier(U_1333) ),
inference(definitional_conversion,[status(esa)],[f_400_2]) ).
cnf(f_400_4,plain,
( k2_lattice3(U_1333) = relation_of_lattice(U_1333)
| ~ latt_str(U_1333)
| ~ lattice(U_1333)
| empty_carrier(U_1333) ),
inference(clausify,[status(thm)],[f_400_3]) ).
fof(f_401_1,plain,
! [A,B,C] :
( join_commut(A,B,C) = join(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k3_lattices]) ).
fof(f_401_2,plain,
! [U_1336,U_1335,U_1334] :
( join_commut(U_1336,U_1335,U_1334) = join(U_1336,U_1335,U_1334)
| ~ element(U_1334,the_carrier(U_1336))
| ~ element(U_1335,the_carrier(U_1336))
| ~ join_semilatt_str(U_1336)
| ~ join_commutative(U_1336)
| empty_carrier(U_1336) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
! [U_1334,U_1335,U_1336] :
( join_commut(U_1336,U_1335,U_1334) = join(U_1336,U_1335,U_1334)
| ~ element(U_1334,the_carrier(U_1336))
| ~ element(U_1335,the_carrier(U_1336))
| ~ join_semilatt_str(U_1336)
| ~ join_commutative(U_1336)
| empty_carrier(U_1336) ),
inference(definitional_conversion,[status(esa)],[f_401_2]) ).
cnf(f_401_4,plain,
( join_commut(U_1336,U_1335,U_1334) = join(U_1336,U_1335,U_1334)
| ~ element(U_1334,the_carrier(U_1336))
| ~ element(U_1335,the_carrier(U_1336))
| ~ join_semilatt_str(U_1336)
| ~ join_commutative(U_1336)
| empty_carrier(U_1336) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_1,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k4_lattices]) ).
fof(f_402_2,plain,
! [U_1339,U_1338,U_1337] :
( meet_commut(U_1339,U_1338,U_1337) = meet(U_1339,U_1338,U_1337)
| ~ element(U_1337,the_carrier(U_1339))
| ~ element(U_1338,the_carrier(U_1339))
| ~ meet_semilatt_str(U_1339)
| ~ meet_commutative(U_1339)
| empty_carrier(U_1339) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
! [U_1338,U_1337,U_1339] :
( meet_commut(U_1339,U_1338,U_1337) = meet(U_1339,U_1338,U_1337)
| ~ element(U_1337,the_carrier(U_1339))
| ~ element(U_1338,the_carrier(U_1339))
| ~ meet_semilatt_str(U_1339)
| ~ meet_commutative(U_1339)
| empty_carrier(U_1339) ),
inference(definitional_conversion,[status(esa)],[f_402_2]) ).
cnf(f_402_4,plain,
( meet_commut(U_1339,U_1338,U_1337) = meet(U_1339,U_1338,U_1337)
| ~ element(U_1337,the_carrier(U_1339))
| ~ element(U_1338,the_carrier(U_1339))
| ~ meet_semilatt_str(U_1339)
| ~ meet_commutative(U_1339)
| empty_carrier(U_1339) ),
inference(clausify,[status(thm)],[f_402_3]) ).
fof(f_403_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_403_2,plain,
! [U_1342,U_1341,U_1340] :
( relation_dom_as_subset(U_1342,U_1341,U_1340) = relation_dom(U_1340)
| ~ relation_of2(U_1340,U_1342,U_1341) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
! [U_1341,U_1340,U_1342] :
( relation_dom_as_subset(U_1342,U_1341,U_1340) = relation_dom(U_1340)
| ~ relation_of2(U_1340,U_1342,U_1341) ),
inference(definitional_conversion,[status(esa)],[f_403_2]) ).
cnf(f_403_4,plain,
( relation_dom_as_subset(U_1342,U_1341,U_1340) = relation_dom(U_1340)
| ~ relation_of2(U_1340,U_1342,U_1341) ),
inference(clausify,[status(thm)],[f_403_3]) ).
fof(f_404_1,plain,
! [A,B,C] :
( subset_union2(A,B,C) = set_union2(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1]) ).
fof(f_404_2,plain,
! [U_1345,U_1344,U_1343] :
( subset_union2(U_1345,U_1344,U_1343) = set_union2(U_1344,U_1343)
| ~ element(U_1343,powerset(U_1345))
| ~ element(U_1344,powerset(U_1345)) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
! [U_1344,U_1345,U_1343] :
( subset_union2(U_1345,U_1344,U_1343) = set_union2(U_1344,U_1343)
| ~ element(U_1343,powerset(U_1345))
| ~ element(U_1344,powerset(U_1345)) ),
inference(definitional_conversion,[status(esa)],[f_404_2]) ).
cnf(f_404_4,plain,
( subset_union2(U_1345,U_1344,U_1343) = set_union2(U_1344,U_1343)
| ~ element(U_1343,powerset(U_1345))
| ~ element(U_1344,powerset(U_1345)) ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_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_405_2,plain,
! [U_1348,U_1347,U_1346] :
( relation_rng_as_subset(U_1348,U_1347,U_1346) = relation_rng(U_1346)
| ~ relation_of2(U_1346,U_1348,U_1347) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
! [U_1347,U_1346,U_1348] :
( relation_rng_as_subset(U_1348,U_1347,U_1346) = relation_rng(U_1346)
| ~ relation_of2(U_1346,U_1348,U_1347) ),
inference(definitional_conversion,[status(esa)],[f_405_2]) ).
cnf(f_405_4,plain,
( relation_rng_as_subset(U_1348,U_1347,U_1346) = relation_rng(U_1346)
| ~ relation_of2(U_1346,U_1348,U_1347) ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_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_406_2,plain,
! [U_1350,U_1349] :
( union_of_subsets(U_1350,U_1349) = union(U_1349)
| ~ element(U_1349,powerset(powerset(U_1350))) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
fof(f_406_3,plain,
! [U_1349,U_1350] :
( union_of_subsets(U_1350,U_1349) = union(U_1349)
| ~ element(U_1349,powerset(powerset(U_1350))) ),
inference(definitional_conversion,[status(esa)],[f_406_2]) ).
cnf(f_406_4,plain,
( union_of_subsets(U_1350,U_1349) = union(U_1349)
| ~ element(U_1349,powerset(powerset(U_1350))) ),
inference(clausify,[status(thm)],[f_406_3]) ).
fof(f_407_1,plain,
! [A,B,C] :
( subset_intersection2(A,B,C) = set_intersection2(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1]) ).
fof(f_407_2,plain,
! [U_1353,U_1352,U_1351] :
( subset_intersection2(U_1353,U_1352,U_1351) = set_intersection2(U_1352,U_1351)
| ~ element(U_1351,powerset(U_1353))
| ~ element(U_1352,powerset(U_1353)) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_1351,U_1352,U_1353] :
( subset_intersection2(U_1353,U_1352,U_1351) = set_intersection2(U_1352,U_1351)
| ~ element(U_1351,powerset(U_1353))
| ~ element(U_1352,powerset(U_1353)) ),
inference(definitional_conversion,[status(esa)],[f_407_2]) ).
cnf(f_407_4,plain,
( subset_intersection2(U_1353,U_1352,U_1351) = set_intersection2(U_1352,U_1351)
| ~ element(U_1351,powerset(U_1353))
| ~ element(U_1352,powerset(U_1353)) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
! [A] : identity_as_relation_of(A) = identity_relation(A),
inference(fof_nnf,[status(thm)],[redefinition_k6_partfun1]) ).
fof(f_408_2,plain,
! [U_1354] : identity_as_relation_of(U_1354) = identity_relation(U_1354),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
! [U_1354] : identity_as_relation_of(U_1354) = identity_relation(U_1354),
inference(definitional_conversion,[status(esa)],[f_408_2]) ).
cnf(f_408_4,plain,
identity_as_relation_of(U_1354) = identity_relation(U_1354),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_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_409_2,plain,
! [U_1356,U_1355] :
( meet_of_subsets(U_1356,U_1355) = set_meet(U_1355)
| ~ element(U_1355,powerset(powerset(U_1356))) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
! [U_1355,U_1356] :
( meet_of_subsets(U_1356,U_1355) = set_meet(U_1355)
| ~ element(U_1355,powerset(powerset(U_1356))) ),
inference(definitional_conversion,[status(esa)],[f_409_2]) ).
cnf(f_409_4,plain,
( meet_of_subsets(U_1356,U_1355) = set_meet(U_1355)
| ~ element(U_1355,powerset(powerset(U_1356))) ),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_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_410_2,plain,
! [U_1359,U_1358,U_1357] :
( subset_difference(U_1359,U_1358,U_1357) = set_difference(U_1358,U_1357)
| ~ element(U_1357,powerset(U_1359))
| ~ element(U_1358,powerset(U_1359)) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
! [U_1357,U_1358,U_1359] :
( subset_difference(U_1359,U_1358,U_1357) = set_difference(U_1358,U_1357)
| ~ element(U_1357,powerset(U_1359))
| ~ element(U_1358,powerset(U_1359)) ),
inference(definitional_conversion,[status(esa)],[f_410_2]) ).
cnf(f_410_4,plain,
( subset_difference(U_1359,U_1358,U_1357) = set_difference(U_1358,U_1357)
| ~ element(U_1357,powerset(U_1359))
| ~ element(U_1358,powerset(U_1359)) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [A,B,C,D] :
( apply_as_element(A,B,C,D) = apply(C,D)
| ~ element(D,A)
| ~ relation_of2(C,A,B)
| ~ quasi_total(C,A,B)
| ~ function(C)
| empty(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k8_funct_2]) ).
fof(f_411_2,plain,
! [U_1363,U_1362,U_1361,U_1360] :
( apply_as_element(U_1363,U_1362,U_1361,U_1360) = apply(U_1361,U_1360)
| ~ element(U_1360,U_1363)
| ~ relation_of2(U_1361,U_1363,U_1362)
| ~ quasi_total(U_1361,U_1363,U_1362)
| ~ function(U_1361)
| empty(U_1363) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
fof(f_411_3,plain,
! [U_1361,U_1360,U_1362,U_1363] :
( apply_as_element(U_1363,U_1362,U_1361,U_1360) = apply(U_1361,U_1360)
| ~ element(U_1360,U_1363)
| ~ relation_of2(U_1361,U_1363,U_1362)
| ~ quasi_total(U_1361,U_1363,U_1362)
| ~ function(U_1361)
| empty(U_1363) ),
inference(definitional_conversion,[status(esa)],[f_411_2]) ).
cnf(f_411_4,plain,
( apply_as_element(U_1363,U_1362,U_1361,U_1360) = apply(U_1361,U_1360)
| ~ element(U_1360,U_1363)
| ~ relation_of2(U_1361,U_1363,U_1362)
| ~ quasi_total(U_1361,U_1363,U_1362)
| ~ function(U_1361)
| empty(U_1363) ),
inference(clausify,[status(thm)],[f_411_3]) ).
fof(f_412_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_412_2,plain,
! [U_1366,U_1365,U_1364] :
( ( relation_of2_as_subset(U_1364,U_1366,U_1365)
| ~ relation_of2(U_1364,U_1366,U_1365) )
& ( relation_of2(U_1364,U_1366,U_1365)
| ~ relation_of2_as_subset(U_1364,U_1366,U_1365) ) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
( ! [U_1372,U_1370,U_1368] :
( relation_of2_as_subset(U_1368,U_1372,U_1370)
| ~ relation_of2(U_1368,U_1372,U_1370) )
& ! [U_1371,U_1369,U_1367] :
( relation_of2(U_1367,U_1371,U_1369)
| ~ relation_of2_as_subset(U_1367,U_1371,U_1369) ) ),
inference(miniscope,[status(thm)],[f_412_2]) ).
fof(f_412_4,plain,
( ! [U_1368,U_1370,U_1372] :
( relation_of2_as_subset(U_1368,U_1372,U_1370)
| ~ relation_of2(U_1368,U_1372,U_1370) )
& ! [U_1367,U_1371,U_1369] :
( relation_of2(U_1367,U_1371,U_1369)
| ~ relation_of2_as_subset(U_1367,U_1371,U_1369) ) ),
inference(definitional_conversion,[status(esa)],[f_412_3]) ).
cnf(f_412_5,plain,
( relation_of2(U_1367,U_1371,U_1369)
| ~ relation_of2_as_subset(U_1367,U_1371,U_1369) ),
inference(clausify,[status(thm)],[f_412_4]) ).
cnf(f_412_6,plain,
( relation_of2_as_subset(U_1368,U_1372,U_1370)
| ~ relation_of2(U_1368,U_1372,U_1370) ),
inference(clausify,[status(thm)],[f_412_4]) ).
fof(f_413_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_413_2,plain,
! [U_1374,U_1373] :
( ( ( ordinal_subset(U_1374,U_1373)
| ~ subset(U_1374,U_1373) )
& ( subset(U_1374,U_1373)
| ~ ordinal_subset(U_1374,U_1373) ) )
| ~ ordinal(U_1373)
| ~ ordinal(U_1374) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
( ! [U_1374,U_1373] :
( ordinal_subset(U_1374,U_1373)
| ~ subset(U_1374,U_1373)
| ~ sP327(U_1374,U_1373) )
& ! [U_1374,U_1373] :
( subset(U_1374,U_1373)
| ~ ordinal_subset(U_1374,U_1373)
| ~ sP327(U_1374,U_1373) )
& ! [U_1374,U_1373] :
( sP327(U_1374,U_1373)
| ~ ordinal(U_1373)
| ~ ordinal(U_1374) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP327])],[f_413_2]) ).
cnf(f_413_4,plain,
( sP327(U_1374,U_1373)
| ~ ordinal(U_1373)
| ~ ordinal(U_1374) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_5,plain,
( subset(U_1374,U_1373)
| ~ ordinal_subset(U_1374,U_1373)
| ~ sP327(U_1374,U_1373) ),
inference(clausify,[status(thm)],[f_413_3]) ).
cnf(f_413_6,plain,
( ordinal_subset(U_1374,U_1373)
| ~ subset(U_1374,U_1373)
| ~ sP327(U_1374,U_1373) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_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_414_2,plain,
! [U_1376,U_1375] :
( ( equipotent(U_1376,U_1375)
| ~ are_equipotent(U_1376,U_1375) )
& ( are_equipotent(U_1376,U_1375)
| ~ equipotent(U_1376,U_1375) ) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
( ! [U_1380,U_1378] :
( equipotent(U_1380,U_1378)
| ~ are_equipotent(U_1380,U_1378) )
& ! [U_1379,U_1377] :
( are_equipotent(U_1379,U_1377)
| ~ equipotent(U_1379,U_1377) ) ),
inference(miniscope,[status(thm)],[f_414_2]) ).
fof(f_414_4,plain,
( ! [U_1378,U_1380] :
( equipotent(U_1380,U_1378)
| ~ are_equipotent(U_1380,U_1378) )
& ! [U_1379,U_1377] :
( are_equipotent(U_1379,U_1377)
| ~ equipotent(U_1379,U_1377) ) ),
inference(definitional_conversion,[status(esa)],[f_414_3]) ).
cnf(f_414_5,plain,
( are_equipotent(U_1379,U_1377)
| ~ equipotent(U_1379,U_1377) ),
inference(clausify,[status(thm)],[f_414_4]) ).
cnf(f_414_6,plain,
( equipotent(U_1380,U_1378)
| ~ are_equipotent(U_1380,U_1378) ),
inference(clausify,[status(thm)],[f_414_4]) ).
fof(f_415_1,plain,
! [A,B,C] :
( ( ( below_refl(A,B,C)
| ~ below(A,B,C) )
& ( below(A,B,C)
| ~ below_refl(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r3_lattices]) ).
fof(f_415_2,plain,
! [U_1383,U_1382,U_1381] :
( ( ( below_refl(U_1383,U_1382,U_1381)
| ~ below(U_1383,U_1382,U_1381) )
& ( below(U_1383,U_1382,U_1381)
| ~ below_refl(U_1383,U_1382,U_1381) ) )
| ~ element(U_1381,the_carrier(U_1383))
| ~ element(U_1382,the_carrier(U_1383))
| ~ latt_str(U_1383)
| ~ join_absorbing(U_1383)
| ~ meet_absorbing(U_1383)
| ~ meet_commutative(U_1383)
| empty_carrier(U_1383) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
( ! [U_1383,U_1382,U_1381] :
( below_refl(U_1383,U_1382,U_1381)
| ~ below(U_1383,U_1382,U_1381)
| ~ sP328(U_1383,U_1382,U_1381) )
& ! [U_1383,U_1382,U_1381] :
( below(U_1383,U_1382,U_1381)
| ~ below_refl(U_1383,U_1382,U_1381)
| ~ sP328(U_1383,U_1382,U_1381) )
& ! [U_1383,U_1382,U_1381] :
( sP328(U_1383,U_1382,U_1381)
| ~ element(U_1381,the_carrier(U_1383))
| ~ element(U_1382,the_carrier(U_1383))
| ~ latt_str(U_1383)
| ~ join_absorbing(U_1383)
| ~ meet_absorbing(U_1383)
| ~ meet_commutative(U_1383)
| empty_carrier(U_1383) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP328])],[f_415_2]) ).
cnf(f_415_4,plain,
( sP328(U_1383,U_1382,U_1381)
| ~ element(U_1381,the_carrier(U_1383))
| ~ element(U_1382,the_carrier(U_1383))
| ~ latt_str(U_1383)
| ~ join_absorbing(U_1383)
| ~ meet_absorbing(U_1383)
| ~ meet_commutative(U_1383)
| empty_carrier(U_1383) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_5,plain,
( below(U_1383,U_1382,U_1381)
| ~ below_refl(U_1383,U_1382,U_1381)
| ~ sP328(U_1383,U_1382,U_1381) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_6,plain,
( below_refl(U_1383,U_1382,U_1381)
| ~ below(U_1383,U_1382,U_1381)
| ~ sP328(U_1383,U_1382,U_1381) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_1,plain,
! [A,B,C] :
( ( ( related_reflexive(A,B,C)
| ~ related(A,B,C) )
& ( related(A,B,C)
| ~ related_reflexive(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r3_orders_2]) ).
fof(f_416_2,plain,
! [U_1386,U_1385,U_1384] :
( ( ( related_reflexive(U_1386,U_1385,U_1384)
| ~ related(U_1386,U_1385,U_1384) )
& ( related(U_1386,U_1385,U_1384)
| ~ related_reflexive(U_1386,U_1385,U_1384) ) )
| ~ element(U_1384,the_carrier(U_1386))
| ~ element(U_1385,the_carrier(U_1386))
| ~ rel_str(U_1386)
| ~ reflexive_relstr(U_1386)
| empty_carrier(U_1386) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
( ! [U_1384,U_1386,U_1385] :
( related_reflexive(U_1386,U_1385,U_1384)
| ~ related(U_1386,U_1385,U_1384)
| ~ sP329(U_1384,U_1386,U_1385) )
& ! [U_1384,U_1386,U_1385] :
( related(U_1386,U_1385,U_1384)
| ~ related_reflexive(U_1386,U_1385,U_1384)
| ~ sP329(U_1384,U_1386,U_1385) )
& ! [U_1384,U_1386,U_1385] :
( sP329(U_1384,U_1386,U_1385)
| ~ element(U_1384,the_carrier(U_1386))
| ~ element(U_1385,the_carrier(U_1386))
| ~ rel_str(U_1386)
| ~ reflexive_relstr(U_1386)
| empty_carrier(U_1386) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP329])],[f_416_2]) ).
cnf(f_416_4,plain,
( sP329(U_1384,U_1386,U_1385)
| ~ element(U_1384,the_carrier(U_1386))
| ~ element(U_1385,the_carrier(U_1386))
| ~ rel_str(U_1386)
| ~ reflexive_relstr(U_1386)
| empty_carrier(U_1386) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_5,plain,
( related(U_1386,U_1385,U_1384)
| ~ related_reflexive(U_1386,U_1385,U_1384)
| ~ sP329(U_1384,U_1386,U_1385) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_6,plain,
( related_reflexive(U_1386,U_1385,U_1384)
| ~ related(U_1386,U_1385,U_1384)
| ~ sP329(U_1384,U_1386,U_1385) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_417_2,plain,
! [U_1388,U_1387] :
( ordinal_subset(U_1388,U_1388)
| ~ ordinal(U_1387)
| ~ ordinal(U_1388) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
! [U_1388] :
( ! [U_1387] : ~ ordinal(U_1387)
| ~ ordinal(U_1388)
| ordinal_subset(U_1388,U_1388) ),
inference(miniscope,[status(thm)],[f_417_2]) ).
fof(f_417_4,plain,
! [U_1388,U_1387] :
( ~ ordinal(U_1387)
| ~ ordinal(U_1388)
| ordinal_subset(U_1388,U_1388) ),
inference(definitional_conversion,[status(esa)],[f_417_3]) ).
cnf(f_417_5,plain,
( ~ ordinal(U_1387)
| ~ ordinal(U_1388)
| ordinal_subset(U_1388,U_1388) ),
inference(clausify,[status(thm)],[f_417_4]) ).
fof(f_418_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_418_2,plain,
! [U_1390,U_1389] : subset(U_1390,U_1390),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
! [U_1390] : subset(U_1390,U_1390),
inference(miniscope,[status(thm)],[f_418_2]) ).
fof(f_418_4,plain,
! [U_1390] : subset(U_1390,U_1390),
inference(definitional_conversion,[status(esa)],[f_418_3]) ).
cnf(f_418_5,plain,
subset(U_1390,U_1390),
inference(clausify,[status(thm)],[f_418_4]) ).
fof(f_419_1,plain,
! [A,B] : equipotent(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r2_wellord2]) ).
fof(f_419_2,plain,
! [U_1392,U_1391] : equipotent(U_1392,U_1392),
inference(variable_rename,[status(thm)],[f_419_1]) ).
fof(f_419_3,plain,
! [U_1392] : equipotent(U_1392,U_1392),
inference(miniscope,[status(thm)],[f_419_2]) ).
fof(f_419_4,plain,
! [U_1392] : equipotent(U_1392,U_1392),
inference(definitional_conversion,[status(esa)],[f_419_3]) ).
cnf(f_419_5,plain,
equipotent(U_1392,U_1392),
inference(clausify,[status(thm)],[f_419_4]) ).
fof(f_420_1,plain,
! [A,B,C] :
( below_refl(A,B,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r3_lattices]) ).
fof(f_420_2,plain,
! [U_1395,U_1394,U_1393] :
( below_refl(U_1395,U_1394,U_1394)
| ~ element(U_1393,the_carrier(U_1395))
| ~ element(U_1394,the_carrier(U_1395))
| ~ latt_str(U_1395)
| ~ join_absorbing(U_1395)
| ~ meet_absorbing(U_1395)
| ~ meet_commutative(U_1395)
| empty_carrier(U_1395) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
! [U_1395,U_1394] :
( ! [U_1393] : ~ element(U_1393,the_carrier(U_1395))
| ~ element(U_1394,the_carrier(U_1395))
| ~ latt_str(U_1395)
| ~ join_absorbing(U_1395)
| ~ meet_absorbing(U_1395)
| ~ meet_commutative(U_1395)
| empty_carrier(U_1395)
| below_refl(U_1395,U_1394,U_1394) ),
inference(miniscope,[status(thm)],[f_420_2]) ).
fof(f_420_4,plain,
! [U_1393,U_1394,U_1395] :
( ~ element(U_1393,the_carrier(U_1395))
| ~ element(U_1394,the_carrier(U_1395))
| ~ latt_str(U_1395)
| ~ join_absorbing(U_1395)
| ~ meet_absorbing(U_1395)
| ~ meet_commutative(U_1395)
| empty_carrier(U_1395)
| below_refl(U_1395,U_1394,U_1394) ),
inference(definitional_conversion,[status(esa)],[f_420_3]) ).
cnf(f_420_5,plain,
( ~ element(U_1393,the_carrier(U_1395))
| ~ element(U_1394,the_carrier(U_1395))
| ~ latt_str(U_1395)
| ~ join_absorbing(U_1395)
| ~ meet_absorbing(U_1395)
| ~ meet_commutative(U_1395)
| empty_carrier(U_1395)
| below_refl(U_1395,U_1394,U_1394) ),
inference(clausify,[status(thm)],[f_420_4]) ).
fof(f_421_1,plain,
! [A,B,C] :
( related_reflexive(A,B,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ rel_str(A)
| ~ reflexive_relstr(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r3_orders_2]) ).
fof(f_421_2,plain,
! [U_1398,U_1397,U_1396] :
( related_reflexive(U_1398,U_1397,U_1397)
| ~ element(U_1396,the_carrier(U_1398))
| ~ element(U_1397,the_carrier(U_1398))
| ~ rel_str(U_1398)
| ~ reflexive_relstr(U_1398)
| empty_carrier(U_1398) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
! [U_1398,U_1397] :
( ! [U_1396] : ~ element(U_1396,the_carrier(U_1398))
| ~ element(U_1397,the_carrier(U_1398))
| ~ rel_str(U_1398)
| ~ reflexive_relstr(U_1398)
| empty_carrier(U_1398)
| related_reflexive(U_1398,U_1397,U_1397) ),
inference(miniscope,[status(thm)],[f_421_2]) ).
fof(f_421_4,plain,
! [U_1398,U_1396,U_1397] :
( ~ element(U_1396,the_carrier(U_1398))
| ~ element(U_1397,the_carrier(U_1398))
| ~ rel_str(U_1398)
| ~ reflexive_relstr(U_1398)
| empty_carrier(U_1398)
| related_reflexive(U_1398,U_1397,U_1397) ),
inference(definitional_conversion,[status(esa)],[f_421_3]) ).
cnf(f_421_5,plain,
( ~ element(U_1396,the_carrier(U_1398))
| ~ element(U_1397,the_carrier(U_1398))
| ~ rel_str(U_1398)
| ~ reflexive_relstr(U_1398)
| empty_carrier(U_1398)
| related_reflexive(U_1398,U_1397,U_1397) ),
inference(clausify,[status(thm)],[f_421_4]) ).
fof(f_422_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_422_2,plain,
! [U_1414,U_1413] :
( ? [U_1412] :
( ! [U_1411,U_1410] :
( ( in(ordered_pair(U_1411,U_1410),U_1412)
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1410,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1410,U_1409)
| U_1411 != U_1409 )
| ~ in(U_1411,U_1414)
| ~ in(U_1411,U_1414) )
& ( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1410,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1410,U_1407)
& U_1411 = U_1407 )
& in(U_1411,U_1414)
& in(U_1411,U_1414) )
| ~ in(ordered_pair(U_1411,U_1410),U_1412) ) )
& function(U_1412)
& relation(U_1412) )
| ? [U_1405,U_1404,U_1403] :
( U_1404 != U_1403
& ? [U_1402] :
( ! [U_1401] :
( in(ordered_pair(U_1403,U_1401),U_1413)
| ~ in(U_1401,U_1402) )
& in(U_1403,U_1402)
& U_1405 = U_1402 )
& in(U_1405,U_1414)
& ? [U_1400] :
( ! [U_1399] :
( in(ordered_pair(U_1404,U_1399),U_1413)
| ~ in(U_1399,U_1400) )
& in(U_1404,U_1400)
& U_1405 = U_1400 )
& in(U_1405,U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
! [U_1414,U_1413] :
( ? [U_1412] :
( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),U_1412)
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1415,U_1407)
& U_1417 = U_1407 )
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),U_1412) )
& function(U_1412)
& relation(U_1412) )
| ? [U_1405,U_1404,U_1403] :
( U_1404 != U_1403
& ? [U_1402] :
( ! [U_1401] :
( in(ordered_pair(U_1403,U_1401),U_1413)
| ~ in(U_1401,U_1402) )
& in(U_1403,U_1402)
& U_1405 = U_1402 )
& in(U_1405,U_1414)
& ? [U_1400] :
( ! [U_1399] :
( in(ordered_pair(U_1404,U_1399),U_1413)
| ~ in(U_1399,U_1400) )
& in(U_1404,U_1400)
& U_1405 = U_1400 )
& in(U_1405,U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(miniscope,[status(thm)],[f_422_2]) ).
fof(f_422_4,plain,
! [U_1414,U_1413] :
( ? [U_1412] :
( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),U_1412)
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1415,U_1407)
& U_1417 = U_1407 )
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),U_1412) )
& function(U_1412)
& relation(U_1412) )
| ? [U_1404,U_1403] :
( U_1404 != U_1403
& ? [U_1402] :
( ! [U_1401] :
( in(ordered_pair(U_1403,U_1401),U_1413)
| ~ in(U_1401,U_1402) )
& in(U_1403,U_1402)
& sK209(U_1414,U_1413) = U_1402 )
& in(sK209(U_1414,U_1413),U_1414)
& ? [U_1400] :
( ! [U_1399] :
( in(ordered_pair(U_1404,U_1399),U_1413)
| ~ in(U_1399,U_1400) )
& in(U_1404,U_1400)
& sK209(U_1414,U_1413) = U_1400 )
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_1405,sK209(U_1414,U_1413))],[f_422_3]) ).
fof(f_422_5,plain,
! [U_1414,U_1413] :
( ? [U_1412] :
( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),U_1412)
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1415,U_1407)
& U_1417 = U_1407 )
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),U_1412) )
& function(U_1412)
& relation(U_1412) )
| ? [U_1403] :
( sK210(U_1414,U_1413) != U_1403
& ? [U_1402] :
( ! [U_1401] :
( in(ordered_pair(U_1403,U_1401),U_1413)
| ~ in(U_1401,U_1402) )
& in(U_1403,U_1402)
& sK209(U_1414,U_1413) = U_1402 )
& in(sK209(U_1414,U_1413),U_1414)
& ? [U_1400] :
( ! [U_1399] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,U_1400) )
& in(sK210(U_1414,U_1413),U_1400)
& sK209(U_1414,U_1413) = U_1400 )
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_1404,sK210(U_1414,U_1413))],[f_422_4]) ).
fof(f_422_6,plain,
! [U_1414,U_1413] :
( ? [U_1412] :
( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),U_1412)
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1415,U_1407)
& U_1417 = U_1407 )
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),U_1412) )
& function(U_1412)
& relation(U_1412) )
| ( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
& ? [U_1402] :
( ! [U_1401] :
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,U_1402) )
& in(sK211(U_1414,U_1413),U_1402)
& sK209(U_1414,U_1413) = U_1402 )
& in(sK209(U_1414,U_1413),U_1414)
& ? [U_1400] :
( ! [U_1399] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,U_1400) )
& in(sK210(U_1414,U_1413),U_1400)
& sK209(U_1414,U_1413) = U_1400 )
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_1403,sK211(U_1414,U_1413))],[f_422_5]) ).
fof(f_422_7,plain,
! [U_1414,U_1413] :
( ? [U_1412] :
( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),U_1412)
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1415,U_1407)
& U_1417 = U_1407 )
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),U_1412) )
& function(U_1412)
& relation(U_1412) )
| ( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
& ? [U_1402] :
( ! [U_1401] :
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,U_1402) )
& in(sK211(U_1414,U_1413),U_1402)
& sK209(U_1414,U_1413) = U_1402 )
& in(sK209(U_1414,U_1413),U_1414)
& ! [U_1399] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,sK212(U_1414,U_1413)) )
& in(sK210(U_1414,U_1413),sK212(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK212(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_1400,sK212(U_1414,U_1413))],[f_422_6]) ).
fof(f_422_8,plain,
! [U_1414,U_1413] :
( ? [U_1412] :
( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),U_1412)
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1415,U_1407)
& U_1417 = U_1407 )
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),U_1412) )
& function(U_1412)
& relation(U_1412) )
| ( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
& ! [U_1401] :
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,sK213(U_1414,U_1413)) )
& in(sK211(U_1414,U_1413),sK213(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK213(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414)
& ! [U_1399] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,sK212(U_1414,U_1413)) )
& in(sK210(U_1414,U_1413),sK212(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK212(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_1402,sK213(U_1414,U_1413))],[f_422_7]) ).
fof(f_422_9,plain,
! [U_1414,U_1413] :
( ( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),sK214(U_1414,U_1413))
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ? [U_1407] :
( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,U_1407) )
& in(U_1415,U_1407)
& U_1417 = U_1407 )
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),sK214(U_1414,U_1413)) )
& function(sK214(U_1414,U_1413))
& relation(sK214(U_1414,U_1413)) )
| ( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
& ! [U_1401] :
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,sK213(U_1414,U_1413)) )
& in(sK211(U_1414,U_1413),sK213(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK213(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414)
& ! [U_1399] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,sK212(U_1414,U_1413)) )
& in(sK210(U_1414,U_1413),sK212(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK212(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_1412,sK214(U_1414,U_1413))],[f_422_8]) ).
fof(f_422_10,plain,
! [U_1414,U_1413] :
( ( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),sK214(U_1414,U_1413))
| ! [U_1409] :
( ? [U_1408] :
( ~ in(ordered_pair(U_1416,U_1408),U_1413)
& in(U_1408,U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,sK215(U_1414,U_1413,U_1417,U_1415)) )
& in(U_1415,sK215(U_1414,U_1413,U_1417,U_1415))
& U_1417 = sK215(U_1414,U_1413,U_1417,U_1415)
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),sK214(U_1414,U_1413)) )
& function(sK214(U_1414,U_1413))
& relation(sK214(U_1414,U_1413)) )
| ( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
& ! [U_1401] :
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,sK213(U_1414,U_1413)) )
& in(sK211(U_1414,U_1413),sK213(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK213(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414)
& ! [U_1399] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,sK212(U_1414,U_1413)) )
& in(sK210(U_1414,U_1413),sK212(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK212(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_1407,sK215(U_1414,U_1413,U_1417,U_1415))],[f_422_9]) ).
fof(f_422_11,plain,
! [U_1414,U_1413] :
( ( ! [U_1418,U_1416] :
( in(ordered_pair(U_1418,U_1416),sK214(U_1414,U_1413))
| ! [U_1409] :
( ( ~ in(ordered_pair(U_1416,sK216(U_1414,U_1413,U_1418,U_1416,U_1409)),U_1413)
& in(sK216(U_1414,U_1413,U_1418,U_1416,U_1409),U_1409) )
| ~ in(U_1416,U_1409)
| U_1418 != U_1409 )
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414) )
& ! [U_1417,U_1415] :
( ( ! [U_1406] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,sK215(U_1414,U_1413,U_1417,U_1415)) )
& in(U_1415,sK215(U_1414,U_1413,U_1417,U_1415))
& U_1417 = sK215(U_1414,U_1413,U_1417,U_1415)
& in(U_1417,U_1414)
& in(U_1417,U_1414) )
| ~ in(ordered_pair(U_1417,U_1415),sK214(U_1414,U_1413)) )
& function(sK214(U_1414,U_1413))
& relation(sK214(U_1414,U_1413)) )
| ( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
& ! [U_1401] :
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,sK213(U_1414,U_1413)) )
& in(sK211(U_1414,U_1413),sK213(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK213(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414)
& ! [U_1399] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,sK212(U_1414,U_1413)) )
& in(sK210(U_1414,U_1413),sK212(U_1414,U_1413))
& sK209(U_1414,U_1413) = sK212(U_1414,U_1413)
& in(sK209(U_1414,U_1413),U_1414) )
| ~ relation(U_1413)
| empty(U_1414) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_1408,sK216(U_1414,U_1413,U_1418,U_1416,U_1409))],[f_422_10]) ).
fof(f_422_12,plain,
( ! [U_1418,U_1409,U_1413,U_1414,U_1416] :
( ~ in(ordered_pair(U_1416,sK216(U_1414,U_1413,U_1418,U_1416,U_1409)),U_1413)
| ~ sP332(U_1418,U_1409,U_1413,U_1414,U_1416) )
& ! [U_1418,U_1409,U_1413,U_1414,U_1416] :
( in(sK216(U_1414,U_1413,U_1418,U_1416,U_1409),U_1409)
| ~ sP332(U_1418,U_1409,U_1413,U_1414,U_1416) )
& ! [U_1415,U_1417,U_1406,U_1413,U_1414] :
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,sK215(U_1414,U_1413,U_1417,U_1415))
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) )
& ! [U_1415,U_1417,U_1406,U_1413,U_1414] :
( in(U_1415,sK215(U_1414,U_1413,U_1417,U_1415))
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) )
& ! [U_1415,U_1417,U_1406,U_1413,U_1414] :
( U_1417 = sK215(U_1414,U_1413,U_1417,U_1415)
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) )
& ! [U_1415,U_1417,U_1406,U_1413,U_1414] :
( in(U_1417,U_1414)
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) )
& ! [U_1415,U_1417,U_1406,U_1413,U_1414] :
( in(U_1417,U_1414)
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) )
& ! [U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416] :
( in(ordered_pair(U_1418,U_1416),sK214(U_1414,U_1413))
| sP332(U_1418,U_1409,U_1413,U_1414,U_1416)
| ~ in(U_1416,U_1409)
| U_1418 != U_1409
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414)
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) )
& ! [U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416] :
( sP331(U_1415,U_1417,U_1406,U_1413,U_1414)
| ~ in(ordered_pair(U_1417,U_1415),sK214(U_1414,U_1413))
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) )
& ! [U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416] :
( function(sK214(U_1414,U_1413))
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) )
& ! [U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416] :
( relation(sK214(U_1414,U_1413))
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,sK213(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( in(sK211(U_1414,U_1413),sK213(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( sK209(U_1414,U_1413) = sK213(U_1414,U_1413)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( in(sK209(U_1414,U_1413),U_1414)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,sK212(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( in(sK210(U_1414,U_1413),sK212(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( sK209(U_1414,U_1413) = sK212(U_1414,U_1413)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1401,U_1413,U_1414] :
( in(sK209(U_1414,U_1413),U_1414)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) )
& ! [U_1399,U_1415,U_1418,U_1417,U_1401,U_1406,U_1409,U_1413,U_1414,U_1416] :
( sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416)
| sP330(U_1399,U_1401,U_1413,U_1414)
| ~ relation(U_1413)
| empty(U_1414) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP330,sP331,sP332,sP333])],[f_422_11]) ).
cnf(f_422_13,plain,
( sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416)
| sP330(U_1399,U_1401,U_1413,U_1414)
| ~ relation(U_1413)
| empty(U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_14,plain,
( in(sK209(U_1414,U_1413),U_1414)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_15,plain,
( sK209(U_1414,U_1413) = sK212(U_1414,U_1413)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_16,plain,
( in(sK210(U_1414,U_1413),sK212(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_17,plain,
( in(ordered_pair(sK210(U_1414,U_1413),U_1399),U_1413)
| ~ in(U_1399,sK212(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_18,plain,
( in(sK209(U_1414,U_1413),U_1414)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_19,plain,
( sK209(U_1414,U_1413) = sK213(U_1414,U_1413)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_20,plain,
( in(sK211(U_1414,U_1413),sK213(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_21,plain,
( in(ordered_pair(sK211(U_1414,U_1413),U_1401),U_1413)
| ~ in(U_1401,sK213(U_1414,U_1413))
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_22,plain,
( sK210(U_1414,U_1413) != sK211(U_1414,U_1413)
| ~ sP330(U_1399,U_1401,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_23,plain,
( relation(sK214(U_1414,U_1413))
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_24,plain,
( function(sK214(U_1414,U_1413))
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_25,plain,
( sP331(U_1415,U_1417,U_1406,U_1413,U_1414)
| ~ in(ordered_pair(U_1417,U_1415),sK214(U_1414,U_1413))
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_26,plain,
( in(ordered_pair(U_1418,U_1416),sK214(U_1414,U_1413))
| sP332(U_1418,U_1409,U_1413,U_1414,U_1416)
| ~ in(U_1416,U_1409)
| U_1418 != U_1409
| ~ in(U_1418,U_1414)
| ~ in(U_1418,U_1414)
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_27,plain,
( in(U_1417,U_1414)
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_28,plain,
( in(U_1417,U_1414)
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_29,plain,
( U_1417 = sK215(U_1414,U_1413,U_1417,U_1415)
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_30,plain,
( in(U_1415,sK215(U_1414,U_1413,U_1417,U_1415))
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_31,plain,
( in(ordered_pair(U_1415,U_1406),U_1413)
| ~ in(U_1406,sK215(U_1414,U_1413,U_1417,U_1415))
| ~ sP331(U_1415,U_1417,U_1406,U_1413,U_1414) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_32,plain,
( in(sK216(U_1414,U_1413,U_1418,U_1416,U_1409),U_1409)
| ~ sP332(U_1418,U_1409,U_1413,U_1414,U_1416) ),
inference(clausify,[status(thm)],[f_422_12]) ).
cnf(f_422_33,plain,
( ~ in(ordered_pair(U_1416,sK216(U_1414,U_1413,U_1418,U_1416,U_1409)),U_1413)
| ~ sP332(U_1418,U_1409,U_1413,U_1414,U_1416) ),
inference(clausify,[status(thm)],[f_422_12]) ).
fof(f_423_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_423_2,plain,
! [U_1425] :
( ? [U_1424] :
( ! [U_1423,U_1422] :
( ( in(ordered_pair(U_1423,U_1422),U_1424)
| U_1422 != singleton(U_1423)
| ~ in(U_1423,U_1425)
| ~ in(U_1423,U_1425) )
& ( ( U_1422 = singleton(U_1423)
& in(U_1423,U_1425)
& in(U_1423,U_1425) )
| ~ in(ordered_pair(U_1423,U_1422),U_1424) ) )
& function(U_1424)
& relation(U_1424) )
| ? [U_1421,U_1420,U_1419] :
( U_1420 != U_1419
& U_1419 = singleton(U_1421)
& in(U_1421,U_1425)
& U_1420 = singleton(U_1421)
& in(U_1421,U_1425) ) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
! [U_1425] :
( ? [U_1424] :
( ! [U_1429,U_1427] :
( in(ordered_pair(U_1429,U_1427),U_1424)
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ in(U_1429,U_1425) )
& ! [U_1428,U_1426] :
( ( U_1426 = singleton(U_1428)
& in(U_1428,U_1425)
& in(U_1428,U_1425) )
| ~ in(ordered_pair(U_1428,U_1426),U_1424) )
& function(U_1424)
& relation(U_1424) )
| ? [U_1421,U_1420,U_1419] :
( U_1420 != U_1419
& U_1419 = singleton(U_1421)
& in(U_1421,U_1425)
& U_1420 = singleton(U_1421)
& in(U_1421,U_1425) ) ),
inference(miniscope,[status(thm)],[f_423_2]) ).
fof(f_423_4,plain,
! [U_1425] :
( ? [U_1424] :
( ! [U_1429,U_1427] :
( in(ordered_pair(U_1429,U_1427),U_1424)
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ in(U_1429,U_1425) )
& ! [U_1428,U_1426] :
( ( U_1426 = singleton(U_1428)
& in(U_1428,U_1425)
& in(U_1428,U_1425) )
| ~ in(ordered_pair(U_1428,U_1426),U_1424) )
& function(U_1424)
& relation(U_1424) )
| ? [U_1420,U_1419] :
( U_1420 != U_1419
& U_1419 = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425)
& U_1420 = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_1421,sK217(U_1425))],[f_423_3]) ).
fof(f_423_5,plain,
! [U_1425] :
( ? [U_1424] :
( ! [U_1429,U_1427] :
( in(ordered_pair(U_1429,U_1427),U_1424)
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ in(U_1429,U_1425) )
& ! [U_1428,U_1426] :
( ( U_1426 = singleton(U_1428)
& in(U_1428,U_1425)
& in(U_1428,U_1425) )
| ~ in(ordered_pair(U_1428,U_1426),U_1424) )
& function(U_1424)
& relation(U_1424) )
| ? [U_1419] :
( sK218(U_1425) != U_1419
& U_1419 = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425)
& sK218(U_1425) = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_1420,sK218(U_1425))],[f_423_4]) ).
fof(f_423_6,plain,
! [U_1425] :
( ? [U_1424] :
( ! [U_1429,U_1427] :
( in(ordered_pair(U_1429,U_1427),U_1424)
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ in(U_1429,U_1425) )
& ! [U_1428,U_1426] :
( ( U_1426 = singleton(U_1428)
& in(U_1428,U_1425)
& in(U_1428,U_1425) )
| ~ in(ordered_pair(U_1428,U_1426),U_1424) )
& function(U_1424)
& relation(U_1424) )
| ( sK218(U_1425) != sK219(U_1425)
& sK219(U_1425) = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425)
& sK218(U_1425) = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_1419,sK219(U_1425))],[f_423_5]) ).
fof(f_423_7,plain,
! [U_1425] :
( ( ! [U_1429,U_1427] :
( in(ordered_pair(U_1429,U_1427),sK220(U_1425))
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ in(U_1429,U_1425) )
& ! [U_1428,U_1426] :
( ( U_1426 = singleton(U_1428)
& in(U_1428,U_1425)
& in(U_1428,U_1425) )
| ~ in(ordered_pair(U_1428,U_1426),sK220(U_1425)) )
& function(sK220(U_1425))
& relation(sK220(U_1425)) )
| ( sK218(U_1425) != sK219(U_1425)
& sK219(U_1425) = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425)
& sK218(U_1425) = singleton(sK217(U_1425))
& in(sK217(U_1425),U_1425) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_1424,sK220(U_1425))],[f_423_6]) ).
fof(f_423_8,plain,
( ! [U_1428,U_1425,U_1426] :
( U_1426 = singleton(U_1428)
| ~ sP335(U_1428,U_1425,U_1426) )
& ! [U_1428,U_1425,U_1426] :
( in(U_1428,U_1425)
| ~ sP335(U_1428,U_1425,U_1426) )
& ! [U_1428,U_1425,U_1426] :
( in(U_1428,U_1425)
| ~ sP335(U_1428,U_1425,U_1426) )
& ! [U_1428,U_1425,U_1427,U_1426,U_1429] :
( in(ordered_pair(U_1429,U_1427),sK220(U_1425))
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ in(U_1429,U_1425)
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) )
& ! [U_1428,U_1425,U_1427,U_1426,U_1429] :
( sP335(U_1428,U_1425,U_1426)
| ~ in(ordered_pair(U_1428,U_1426),sK220(U_1425))
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) )
& ! [U_1428,U_1425,U_1427,U_1426,U_1429] :
( function(sK220(U_1425))
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) )
& ! [U_1428,U_1425,U_1427,U_1426,U_1429] :
( relation(sK220(U_1425))
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) )
& ! [U_1425] :
( sK218(U_1425) != sK219(U_1425)
| ~ sP334(U_1425) )
& ! [U_1425] :
( sK219(U_1425) = singleton(sK217(U_1425))
| ~ sP334(U_1425) )
& ! [U_1425] :
( in(sK217(U_1425),U_1425)
| ~ sP334(U_1425) )
& ! [U_1425] :
( sK218(U_1425) = singleton(sK217(U_1425))
| ~ sP334(U_1425) )
& ! [U_1425] :
( in(sK217(U_1425),U_1425)
| ~ sP334(U_1425) )
& ! [U_1428,U_1425,U_1427,U_1426,U_1429] :
( sP336(U_1428,U_1425,U_1427,U_1426,U_1429)
| sP334(U_1425) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP334,sP335,sP336])],[f_423_7]) ).
cnf(f_423_9,plain,
( sP336(U_1428,U_1425,U_1427,U_1426,U_1429)
| sP334(U_1425) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_10,plain,
( in(sK217(U_1425),U_1425)
| ~ sP334(U_1425) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_11,plain,
( sK218(U_1425) = singleton(sK217(U_1425))
| ~ sP334(U_1425) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_12,plain,
( in(sK217(U_1425),U_1425)
| ~ sP334(U_1425) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_13,plain,
( sK219(U_1425) = singleton(sK217(U_1425))
| ~ sP334(U_1425) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_14,plain,
( sK218(U_1425) != sK219(U_1425)
| ~ sP334(U_1425) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_15,plain,
( relation(sK220(U_1425))
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_16,plain,
( function(sK220(U_1425))
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_17,plain,
( sP335(U_1428,U_1425,U_1426)
| ~ in(ordered_pair(U_1428,U_1426),sK220(U_1425))
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_18,plain,
( in(ordered_pair(U_1429,U_1427),sK220(U_1425))
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ in(U_1429,U_1425)
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_19,plain,
( in(U_1428,U_1425)
| ~ sP335(U_1428,U_1425,U_1426) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_20,plain,
( in(U_1428,U_1425)
| ~ sP335(U_1428,U_1425,U_1426) ),
inference(clausify,[status(thm)],[f_423_8]) ).
cnf(f_423_21,plain,
( U_1426 = singleton(U_1428)
| ~ sP335(U_1428,U_1425,U_1426) ),
inference(clausify,[status(thm)],[f_423_8]) ).
fof(f_424_1,plain,
! [A,B] :
( ? [C] :
( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ? [H] :
( E != subset_complement(the_carrier(A),H)
& H = D
& element(H,powerset(the_carrier(A))) )
| ~ in(D,complements_of_subsets(the_carrier(A),B))
| ~ in(D,complements_of_subsets(the_carrier(A),B)) )
& ( ( ! [H] :
( E = subset_complement(the_carrier(A),H)
| H != D
| ~ element(H,powerset(the_carrier(A))) )
& in(D,complements_of_subsets(the_carrier(A),B))
& in(D,complements_of_subsets(the_carrier(A),B)) )
| ~ in(ordered_pair(D,E),C) ) )
& function(C)
& relation(C) )
| ? [C,D,E] :
( D != E
& ! [G] :
( E = subset_complement(the_carrier(A),G)
| G != C
| ~ element(G,powerset(the_carrier(A))) )
& in(C,complements_of_subsets(the_carrier(A),B))
& ! [F] :
( D = subset_complement(the_carrier(A),F)
| F != C
| ~ element(F,powerset(the_carrier(A))) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_funct_1__e4_7_1__tops_2__1]) ).
fof(f_424_2,plain,
! [U_1441,U_1440] :
( ? [U_1439] :
( ! [U_1438,U_1437] :
( ( in(ordered_pair(U_1438,U_1437),U_1439)
| ? [U_1436] :
( U_1437 != subset_complement(the_carrier(U_1441),U_1436)
& U_1436 = U_1438
& element(U_1436,powerset(the_carrier(U_1441))) )
| ~ in(U_1438,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1438,complements_of_subsets(the_carrier(U_1441),U_1440)) )
& ( ( ! [U_1435] :
( U_1437 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1438
| ~ element(U_1435,powerset(the_carrier(U_1441))) )
& in(U_1438,complements_of_subsets(the_carrier(U_1441),U_1440))
& in(U_1438,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ in(ordered_pair(U_1438,U_1437),U_1439) ) )
& function(U_1439)
& relation(U_1439) )
| ? [U_1434,U_1433,U_1432] :
( U_1433 != U_1432
& ! [U_1431] :
( U_1432 = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != U_1434
| ~ element(U_1431,powerset(the_carrier(U_1441))) )
& in(U_1434,complements_of_subsets(the_carrier(U_1441),U_1440))
& ! [U_1430] :
( U_1433 = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != U_1434
| ~ element(U_1430,powerset(the_carrier(U_1441))) )
& in(U_1434,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
! [U_1441,U_1440] :
( ? [U_1439] :
( ! [U_1445,U_1443] :
( in(ordered_pair(U_1445,U_1443),U_1439)
| ? [U_1436] :
( U_1443 != subset_complement(the_carrier(U_1441),U_1436)
& U_1436 = U_1445
& element(U_1436,powerset(the_carrier(U_1441))) )
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440)) )
& ! [U_1444,U_1442] :
( ( ! [U_1435] :
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441))) )
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ in(ordered_pair(U_1444,U_1442),U_1439) )
& function(U_1439)
& relation(U_1439) )
| ? [U_1434,U_1433,U_1432] :
( U_1433 != U_1432
& ! [U_1431] :
( U_1432 = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != U_1434
| ~ element(U_1431,powerset(the_carrier(U_1441))) )
& in(U_1434,complements_of_subsets(the_carrier(U_1441),U_1440))
& ! [U_1430] :
( U_1433 = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != U_1434
| ~ element(U_1430,powerset(the_carrier(U_1441))) )
& in(U_1434,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(miniscope,[status(thm)],[f_424_2]) ).
fof(f_424_4,plain,
! [U_1441,U_1440] :
( ? [U_1439] :
( ! [U_1445,U_1443] :
( in(ordered_pair(U_1445,U_1443),U_1439)
| ? [U_1436] :
( U_1443 != subset_complement(the_carrier(U_1441),U_1436)
& U_1436 = U_1445
& element(U_1436,powerset(the_carrier(U_1441))) )
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440)) )
& ! [U_1444,U_1442] :
( ( ! [U_1435] :
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441))) )
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ in(ordered_pair(U_1444,U_1442),U_1439) )
& function(U_1439)
& relation(U_1439) )
| ? [U_1433,U_1432] :
( U_1433 != U_1432
& ! [U_1431] :
( U_1432 = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != sK221(U_1441,U_1440)
| ~ element(U_1431,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
& ! [U_1430] :
( U_1433 = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != sK221(U_1441,U_1440)
| ~ element(U_1430,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_1434,sK221(U_1441,U_1440))],[f_424_3]) ).
fof(f_424_5,plain,
! [U_1441,U_1440] :
( ? [U_1439] :
( ! [U_1445,U_1443] :
( in(ordered_pair(U_1445,U_1443),U_1439)
| ? [U_1436] :
( U_1443 != subset_complement(the_carrier(U_1441),U_1436)
& U_1436 = U_1445
& element(U_1436,powerset(the_carrier(U_1441))) )
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440)) )
& ! [U_1444,U_1442] :
( ( ! [U_1435] :
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441))) )
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ in(ordered_pair(U_1444,U_1442),U_1439) )
& function(U_1439)
& relation(U_1439) )
| ? [U_1432] :
( sK222(U_1441,U_1440) != U_1432
& ! [U_1431] :
( U_1432 = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != sK221(U_1441,U_1440)
| ~ element(U_1431,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
& ! [U_1430] :
( sK222(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != sK221(U_1441,U_1440)
| ~ element(U_1430,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_1433,sK222(U_1441,U_1440))],[f_424_4]) ).
fof(f_424_6,plain,
! [U_1441,U_1440] :
( ? [U_1439] :
( ! [U_1445,U_1443] :
( in(ordered_pair(U_1445,U_1443),U_1439)
| ? [U_1436] :
( U_1443 != subset_complement(the_carrier(U_1441),U_1436)
& U_1436 = U_1445
& element(U_1436,powerset(the_carrier(U_1441))) )
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440)) )
& ! [U_1444,U_1442] :
( ( ! [U_1435] :
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441))) )
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ in(ordered_pair(U_1444,U_1442),U_1439) )
& function(U_1439)
& relation(U_1439) )
| ( sK222(U_1441,U_1440) != sK223(U_1441,U_1440)
& ! [U_1431] :
( sK223(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != sK221(U_1441,U_1440)
| ~ element(U_1431,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
& ! [U_1430] :
( sK222(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != sK221(U_1441,U_1440)
| ~ element(U_1430,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_1432,sK223(U_1441,U_1440))],[f_424_5]) ).
fof(f_424_7,plain,
! [U_1441,U_1440] :
( ( ! [U_1445,U_1443] :
( in(ordered_pair(U_1445,U_1443),sK224(U_1441,U_1440))
| ? [U_1436] :
( U_1443 != subset_complement(the_carrier(U_1441),U_1436)
& U_1436 = U_1445
& element(U_1436,powerset(the_carrier(U_1441))) )
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440)) )
& ! [U_1444,U_1442] :
( ( ! [U_1435] :
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441))) )
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ in(ordered_pair(U_1444,U_1442),sK224(U_1441,U_1440)) )
& function(sK224(U_1441,U_1440))
& relation(sK224(U_1441,U_1440)) )
| ( sK222(U_1441,U_1440) != sK223(U_1441,U_1440)
& ! [U_1431] :
( sK223(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != sK221(U_1441,U_1440)
| ~ element(U_1431,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
& ! [U_1430] :
( sK222(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != sK221(U_1441,U_1440)
| ~ element(U_1430,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_1439,sK224(U_1441,U_1440))],[f_424_6]) ).
fof(f_424_8,plain,
! [U_1441,U_1440] :
( ( ! [U_1445,U_1443] :
( in(ordered_pair(U_1445,U_1443),sK224(U_1441,U_1440))
| ( U_1443 != subset_complement(the_carrier(U_1441),sK225(U_1441,U_1440,U_1445,U_1443))
& sK225(U_1441,U_1440,U_1445,U_1443) = U_1445
& element(sK225(U_1441,U_1440,U_1445,U_1443),powerset(the_carrier(U_1441))) )
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440)) )
& ! [U_1444,U_1442] :
( ( ! [U_1435] :
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441))) )
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
& in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ in(ordered_pair(U_1444,U_1442),sK224(U_1441,U_1440)) )
& function(sK224(U_1441,U_1440))
& relation(sK224(U_1441,U_1440)) )
| ( sK222(U_1441,U_1440) != sK223(U_1441,U_1440)
& ! [U_1431] :
( sK223(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != sK221(U_1441,U_1440)
| ~ element(U_1431,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
& ! [U_1430] :
( sK222(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != sK221(U_1441,U_1440)
| ~ element(U_1430,powerset(the_carrier(U_1441))) )
& in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440)) )
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_1436,sK225(U_1441,U_1440,U_1445,U_1443))],[f_424_7]) ).
fof(f_424_9,plain,
( ! [U_1443,U_1441,U_1440,U_1445] :
( U_1443 != subset_complement(the_carrier(U_1441),sK225(U_1441,U_1440,U_1445,U_1443))
| ~ sP339(U_1443,U_1441,U_1440,U_1445) )
& ! [U_1443,U_1441,U_1440,U_1445] :
( sK225(U_1441,U_1440,U_1445,U_1443) = U_1445
| ~ sP339(U_1443,U_1441,U_1440,U_1445) )
& ! [U_1443,U_1441,U_1440,U_1445] :
( element(sK225(U_1441,U_1440,U_1445,U_1443),powerset(the_carrier(U_1441)))
| ~ sP339(U_1443,U_1441,U_1440,U_1445) )
& ! [U_1441,U_1435,U_1442,U_1444,U_1440] :
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441)))
| ~ sP338(U_1441,U_1435,U_1442,U_1444,U_1440) )
& ! [U_1441,U_1435,U_1442,U_1444,U_1440] :
( in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP338(U_1441,U_1435,U_1442,U_1444,U_1440) )
& ! [U_1441,U_1435,U_1442,U_1444,U_1440] :
( in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP338(U_1441,U_1435,U_1442,U_1444,U_1440) )
& ! [U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445] :
( in(ordered_pair(U_1445,U_1443),sK224(U_1441,U_1440))
| sP339(U_1443,U_1441,U_1440,U_1445)
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) )
& ! [U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445] :
( sP338(U_1441,U_1435,U_1442,U_1444,U_1440)
| ~ in(ordered_pair(U_1444,U_1442),sK224(U_1441,U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) )
& ! [U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445] :
( function(sK224(U_1441,U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) )
& ! [U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445] :
( relation(sK224(U_1441,U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) )
& ! [U_1441,U_1431,U_1430,U_1440] :
( sK222(U_1441,U_1440) != sK223(U_1441,U_1440)
| ~ sP337(U_1441,U_1431,U_1430,U_1440) )
& ! [U_1441,U_1431,U_1430,U_1440] :
( sK223(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != sK221(U_1441,U_1440)
| ~ element(U_1431,powerset(the_carrier(U_1441)))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) )
& ! [U_1441,U_1431,U_1430,U_1440] :
( in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) )
& ! [U_1441,U_1431,U_1430,U_1440] :
( sK222(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != sK221(U_1441,U_1440)
| ~ element(U_1430,powerset(the_carrier(U_1441)))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) )
& ! [U_1441,U_1431,U_1430,U_1440] :
( in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) )
& ! [U_1443,U_1441,U_1435,U_1442,U_1431,U_1430,U_1444,U_1440,U_1445] :
( sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445)
| sP337(U_1441,U_1431,U_1430,U_1440)
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP337,sP338,sP339,sP340])],[f_424_8]) ).
cnf(f_424_10,plain,
( sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445)
| sP337(U_1441,U_1431,U_1430,U_1440)
| ~ element(U_1440,powerset(powerset(the_carrier(U_1441))))
| ~ one_sorted_str(U_1441) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_11,plain,
( in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_12,plain,
( sK222(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1430)
| U_1430 != sK221(U_1441,U_1440)
| ~ element(U_1430,powerset(the_carrier(U_1441)))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_13,plain,
( in(sK221(U_1441,U_1440),complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_14,plain,
( sK223(U_1441,U_1440) = subset_complement(the_carrier(U_1441),U_1431)
| U_1431 != sK221(U_1441,U_1440)
| ~ element(U_1431,powerset(the_carrier(U_1441)))
| ~ sP337(U_1441,U_1431,U_1430,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_15,plain,
( sK222(U_1441,U_1440) != sK223(U_1441,U_1440)
| ~ sP337(U_1441,U_1431,U_1430,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_16,plain,
( relation(sK224(U_1441,U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_17,plain,
( function(sK224(U_1441,U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_18,plain,
( sP338(U_1441,U_1435,U_1442,U_1444,U_1440)
| ~ in(ordered_pair(U_1444,U_1442),sK224(U_1441,U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_19,plain,
( in(ordered_pair(U_1445,U_1443),sK224(U_1441,U_1440))
| sP339(U_1443,U_1441,U_1440,U_1445)
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_20,plain,
( in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP338(U_1441,U_1435,U_1442,U_1444,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_21,plain,
( in(U_1444,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP338(U_1441,U_1435,U_1442,U_1444,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_22,plain,
( U_1442 = subset_complement(the_carrier(U_1441),U_1435)
| U_1435 != U_1444
| ~ element(U_1435,powerset(the_carrier(U_1441)))
| ~ sP338(U_1441,U_1435,U_1442,U_1444,U_1440) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_23,plain,
( element(sK225(U_1441,U_1440,U_1445,U_1443),powerset(the_carrier(U_1441)))
| ~ sP339(U_1443,U_1441,U_1440,U_1445) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_24,plain,
( sK225(U_1441,U_1440,U_1445,U_1443) = U_1445
| ~ sP339(U_1443,U_1441,U_1440,U_1445) ),
inference(clausify,[status(thm)],[f_424_9]) ).
cnf(f_424_25,plain,
( U_1443 != subset_complement(the_carrier(U_1441),sK225(U_1441,U_1440,U_1445,U_1443))
| ~ sP339(U_1443,U_1441,U_1440,U_1445) ),
inference(clausify,[status(thm)],[f_424_9]) ).
fof(f_425_1,plain,
! [A,B] :
( ? [C] :
( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ? [H] :
( E != subset_complement(the_carrier(A),H)
& H = D
& element(H,powerset(the_carrier(A))) )
| ~ in(D,B)
| ~ in(D,B) )
& ( ( ! [H] :
( E = subset_complement(the_carrier(A),H)
| H != D
| ~ element(H,powerset(the_carrier(A))) )
& in(D,B)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
& function(C)
& relation(C) )
| ? [C,D,E] :
( D != E
& ! [G] :
( E = subset_complement(the_carrier(A),G)
| G != C
| ~ element(G,powerset(the_carrier(A))) )
& in(C,B)
& ! [F] :
( D = subset_complement(the_carrier(A),F)
| F != C
| ~ element(F,powerset(the_carrier(A))) )
& in(C,B) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_funct_1__e4_7_2__tops_2__1]) ).
fof(f_425_2,plain,
! [U_1457,U_1456] :
( ? [U_1455] :
( ! [U_1454,U_1453] :
( ( in(ordered_pair(U_1454,U_1453),U_1455)
| ? [U_1452] :
( U_1453 != subset_complement(the_carrier(U_1457),U_1452)
& U_1452 = U_1454
& element(U_1452,powerset(the_carrier(U_1457))) )
| ~ in(U_1454,U_1456)
| ~ in(U_1454,U_1456) )
& ( ( ! [U_1451] :
( U_1453 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1454
| ~ element(U_1451,powerset(the_carrier(U_1457))) )
& in(U_1454,U_1456)
& in(U_1454,U_1456) )
| ~ in(ordered_pair(U_1454,U_1453),U_1455) ) )
& function(U_1455)
& relation(U_1455) )
| ? [U_1450,U_1449,U_1448] :
( U_1449 != U_1448
& ! [U_1447] :
( U_1448 = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != U_1450
| ~ element(U_1447,powerset(the_carrier(U_1457))) )
& in(U_1450,U_1456)
& ! [U_1446] :
( U_1449 = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != U_1450
| ~ element(U_1446,powerset(the_carrier(U_1457))) )
& in(U_1450,U_1456) )
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
! [U_1457,U_1456] :
( ? [U_1455] :
( ! [U_1461,U_1459] :
( in(ordered_pair(U_1461,U_1459),U_1455)
| ? [U_1452] :
( U_1459 != subset_complement(the_carrier(U_1457),U_1452)
& U_1452 = U_1461
& element(U_1452,powerset(the_carrier(U_1457))) )
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456) )
& ! [U_1460,U_1458] :
( ( ! [U_1451] :
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457))) )
& in(U_1460,U_1456)
& in(U_1460,U_1456) )
| ~ in(ordered_pair(U_1460,U_1458),U_1455) )
& function(U_1455)
& relation(U_1455) )
| ? [U_1450,U_1449,U_1448] :
( U_1449 != U_1448
& ! [U_1447] :
( U_1448 = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != U_1450
| ~ element(U_1447,powerset(the_carrier(U_1457))) )
& in(U_1450,U_1456)
& ! [U_1446] :
( U_1449 = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != U_1450
| ~ element(U_1446,powerset(the_carrier(U_1457))) )
& in(U_1450,U_1456) )
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(miniscope,[status(thm)],[f_425_2]) ).
fof(f_425_4,plain,
! [U_1457,U_1456] :
( ? [U_1455] :
( ! [U_1461,U_1459] :
( in(ordered_pair(U_1461,U_1459),U_1455)
| ? [U_1452] :
( U_1459 != subset_complement(the_carrier(U_1457),U_1452)
& U_1452 = U_1461
& element(U_1452,powerset(the_carrier(U_1457))) )
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456) )
& ! [U_1460,U_1458] :
( ( ! [U_1451] :
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457))) )
& in(U_1460,U_1456)
& in(U_1460,U_1456) )
| ~ in(ordered_pair(U_1460,U_1458),U_1455) )
& function(U_1455)
& relation(U_1455) )
| ? [U_1449,U_1448] :
( U_1449 != U_1448
& ! [U_1447] :
( U_1448 = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != sK226(U_1457,U_1456)
| ~ element(U_1447,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456)
& ! [U_1446] :
( U_1449 = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != sK226(U_1457,U_1456)
| ~ element(U_1446,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456) )
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_1450,sK226(U_1457,U_1456))],[f_425_3]) ).
fof(f_425_5,plain,
! [U_1457,U_1456] :
( ? [U_1455] :
( ! [U_1461,U_1459] :
( in(ordered_pair(U_1461,U_1459),U_1455)
| ? [U_1452] :
( U_1459 != subset_complement(the_carrier(U_1457),U_1452)
& U_1452 = U_1461
& element(U_1452,powerset(the_carrier(U_1457))) )
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456) )
& ! [U_1460,U_1458] :
( ( ! [U_1451] :
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457))) )
& in(U_1460,U_1456)
& in(U_1460,U_1456) )
| ~ in(ordered_pair(U_1460,U_1458),U_1455) )
& function(U_1455)
& relation(U_1455) )
| ? [U_1448] :
( sK227(U_1457,U_1456) != U_1448
& ! [U_1447] :
( U_1448 = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != sK226(U_1457,U_1456)
| ~ element(U_1447,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456)
& ! [U_1446] :
( sK227(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != sK226(U_1457,U_1456)
| ~ element(U_1446,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456) )
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_1449,sK227(U_1457,U_1456))],[f_425_4]) ).
fof(f_425_6,plain,
! [U_1457,U_1456] :
( ? [U_1455] :
( ! [U_1461,U_1459] :
( in(ordered_pair(U_1461,U_1459),U_1455)
| ? [U_1452] :
( U_1459 != subset_complement(the_carrier(U_1457),U_1452)
& U_1452 = U_1461
& element(U_1452,powerset(the_carrier(U_1457))) )
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456) )
& ! [U_1460,U_1458] :
( ( ! [U_1451] :
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457))) )
& in(U_1460,U_1456)
& in(U_1460,U_1456) )
| ~ in(ordered_pair(U_1460,U_1458),U_1455) )
& function(U_1455)
& relation(U_1455) )
| ( sK227(U_1457,U_1456) != sK228(U_1457,U_1456)
& ! [U_1447] :
( sK228(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != sK226(U_1457,U_1456)
| ~ element(U_1447,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456)
& ! [U_1446] :
( sK227(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != sK226(U_1457,U_1456)
| ~ element(U_1446,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456) )
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_1448,sK228(U_1457,U_1456))],[f_425_5]) ).
fof(f_425_7,plain,
! [U_1457,U_1456] :
( ( ! [U_1461,U_1459] :
( in(ordered_pair(U_1461,U_1459),sK229(U_1457,U_1456))
| ? [U_1452] :
( U_1459 != subset_complement(the_carrier(U_1457),U_1452)
& U_1452 = U_1461
& element(U_1452,powerset(the_carrier(U_1457))) )
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456) )
& ! [U_1460,U_1458] :
( ( ! [U_1451] :
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457))) )
& in(U_1460,U_1456)
& in(U_1460,U_1456) )
| ~ in(ordered_pair(U_1460,U_1458),sK229(U_1457,U_1456)) )
& function(sK229(U_1457,U_1456))
& relation(sK229(U_1457,U_1456)) )
| ( sK227(U_1457,U_1456) != sK228(U_1457,U_1456)
& ! [U_1447] :
( sK228(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != sK226(U_1457,U_1456)
| ~ element(U_1447,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456)
& ! [U_1446] :
( sK227(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != sK226(U_1457,U_1456)
| ~ element(U_1446,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456) )
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_1455,sK229(U_1457,U_1456))],[f_425_6]) ).
fof(f_425_8,plain,
! [U_1457,U_1456] :
( ( ! [U_1461,U_1459] :
( in(ordered_pair(U_1461,U_1459),sK229(U_1457,U_1456))
| ( U_1459 != subset_complement(the_carrier(U_1457),sK230(U_1457,U_1456,U_1461,U_1459))
& sK230(U_1457,U_1456,U_1461,U_1459) = U_1461
& element(sK230(U_1457,U_1456,U_1461,U_1459),powerset(the_carrier(U_1457))) )
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456) )
& ! [U_1460,U_1458] :
( ( ! [U_1451] :
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457))) )
& in(U_1460,U_1456)
& in(U_1460,U_1456) )
| ~ in(ordered_pair(U_1460,U_1458),sK229(U_1457,U_1456)) )
& function(sK229(U_1457,U_1456))
& relation(sK229(U_1457,U_1456)) )
| ( sK227(U_1457,U_1456) != sK228(U_1457,U_1456)
& ! [U_1447] :
( sK228(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != sK226(U_1457,U_1456)
| ~ element(U_1447,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456)
& ! [U_1446] :
( sK227(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != sK226(U_1457,U_1456)
| ~ element(U_1446,powerset(the_carrier(U_1457))) )
& in(sK226(U_1457,U_1456),U_1456) )
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_1452,sK230(U_1457,U_1456,U_1461,U_1459))],[f_425_7]) ).
fof(f_425_9,plain,
( ! [U_1457,U_1456,U_1459,U_1461] :
( U_1459 != subset_complement(the_carrier(U_1457),sK230(U_1457,U_1456,U_1461,U_1459))
| ~ sP343(U_1457,U_1456,U_1459,U_1461) )
& ! [U_1457,U_1456,U_1459,U_1461] :
( sK230(U_1457,U_1456,U_1461,U_1459) = U_1461
| ~ sP343(U_1457,U_1456,U_1459,U_1461) )
& ! [U_1457,U_1456,U_1459,U_1461] :
( element(sK230(U_1457,U_1456,U_1461,U_1459),powerset(the_carrier(U_1457)))
| ~ sP343(U_1457,U_1456,U_1459,U_1461) )
& ! [U_1457,U_1460,U_1451,U_1456,U_1458] :
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457)))
| ~ sP342(U_1457,U_1460,U_1451,U_1456,U_1458) )
& ! [U_1457,U_1460,U_1451,U_1456,U_1458] :
( in(U_1460,U_1456)
| ~ sP342(U_1457,U_1460,U_1451,U_1456,U_1458) )
& ! [U_1457,U_1460,U_1451,U_1456,U_1458] :
( in(U_1460,U_1456)
| ~ sP342(U_1457,U_1460,U_1451,U_1456,U_1458) )
& ! [U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461] :
( in(ordered_pair(U_1461,U_1459),sK229(U_1457,U_1456))
| sP343(U_1457,U_1456,U_1459,U_1461)
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456)
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) )
& ! [U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461] :
( sP342(U_1457,U_1460,U_1451,U_1456,U_1458)
| ~ in(ordered_pair(U_1460,U_1458),sK229(U_1457,U_1456))
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) )
& ! [U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461] :
( function(sK229(U_1457,U_1456))
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) )
& ! [U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461] :
( relation(sK229(U_1457,U_1456))
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) )
& ! [U_1457,U_1446,U_1456,U_1447] :
( sK227(U_1457,U_1456) != sK228(U_1457,U_1456)
| ~ sP341(U_1457,U_1446,U_1456,U_1447) )
& ! [U_1457,U_1446,U_1456,U_1447] :
( sK228(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != sK226(U_1457,U_1456)
| ~ element(U_1447,powerset(the_carrier(U_1457)))
| ~ sP341(U_1457,U_1446,U_1456,U_1447) )
& ! [U_1457,U_1446,U_1456,U_1447] :
( in(sK226(U_1457,U_1456),U_1456)
| ~ sP341(U_1457,U_1446,U_1456,U_1447) )
& ! [U_1457,U_1446,U_1456,U_1447] :
( sK227(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != sK226(U_1457,U_1456)
| ~ element(U_1446,powerset(the_carrier(U_1457)))
| ~ sP341(U_1457,U_1446,U_1456,U_1447) )
& ! [U_1457,U_1446,U_1456,U_1447] :
( in(sK226(U_1457,U_1456),U_1456)
| ~ sP341(U_1457,U_1446,U_1456,U_1447) )
& ! [U_1457,U_1446,U_1460,U_1451,U_1456,U_1447,U_1459,U_1458,U_1461] :
( sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461)
| sP341(U_1457,U_1446,U_1456,U_1447)
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP341,sP342,sP343,sP344])],[f_425_8]) ).
cnf(f_425_10,plain,
( sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461)
| sP341(U_1457,U_1446,U_1456,U_1447)
| ~ element(U_1456,powerset(powerset(the_carrier(U_1457))))
| ~ one_sorted_str(U_1457) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_11,plain,
( in(sK226(U_1457,U_1456),U_1456)
| ~ sP341(U_1457,U_1446,U_1456,U_1447) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_12,plain,
( sK227(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1446)
| U_1446 != sK226(U_1457,U_1456)
| ~ element(U_1446,powerset(the_carrier(U_1457)))
| ~ sP341(U_1457,U_1446,U_1456,U_1447) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_13,plain,
( in(sK226(U_1457,U_1456),U_1456)
| ~ sP341(U_1457,U_1446,U_1456,U_1447) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_14,plain,
( sK228(U_1457,U_1456) = subset_complement(the_carrier(U_1457),U_1447)
| U_1447 != sK226(U_1457,U_1456)
| ~ element(U_1447,powerset(the_carrier(U_1457)))
| ~ sP341(U_1457,U_1446,U_1456,U_1447) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_15,plain,
( sK227(U_1457,U_1456) != sK228(U_1457,U_1456)
| ~ sP341(U_1457,U_1446,U_1456,U_1447) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_16,plain,
( relation(sK229(U_1457,U_1456))
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_17,plain,
( function(sK229(U_1457,U_1456))
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_18,plain,
( sP342(U_1457,U_1460,U_1451,U_1456,U_1458)
| ~ in(ordered_pair(U_1460,U_1458),sK229(U_1457,U_1456))
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_19,plain,
( in(ordered_pair(U_1461,U_1459),sK229(U_1457,U_1456))
| sP343(U_1457,U_1456,U_1459,U_1461)
| ~ in(U_1461,U_1456)
| ~ in(U_1461,U_1456)
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_20,plain,
( in(U_1460,U_1456)
| ~ sP342(U_1457,U_1460,U_1451,U_1456,U_1458) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_21,plain,
( in(U_1460,U_1456)
| ~ sP342(U_1457,U_1460,U_1451,U_1456,U_1458) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_22,plain,
( U_1458 = subset_complement(the_carrier(U_1457),U_1451)
| U_1451 != U_1460
| ~ element(U_1451,powerset(the_carrier(U_1457)))
| ~ sP342(U_1457,U_1460,U_1451,U_1456,U_1458) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_23,plain,
( element(sK230(U_1457,U_1456,U_1461,U_1459),powerset(the_carrier(U_1457)))
| ~ sP343(U_1457,U_1456,U_1459,U_1461) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_24,plain,
( sK230(U_1457,U_1456,U_1461,U_1459) = U_1461
| ~ sP343(U_1457,U_1456,U_1459,U_1461) ),
inference(clausify,[status(thm)],[f_425_9]) ).
cnf(f_425_25,plain,
( U_1459 != subset_complement(the_carrier(U_1457),sK230(U_1457,U_1456,U_1461,U_1459))
| ~ sP343(U_1457,U_1456,U_1459,U_1461) ),
inference(clausify,[status(thm)],[f_425_9]) ).
fof(f_426_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_426_2,plain,
! [U_1465] :
( ? [U_1464] :
( ! [U_1463] :
( ordinal_subset(U_1464,U_1463)
| ~ in(U_1463,U_1465)
| ~ ordinal(U_1463) )
& in(U_1464,U_1465)
& ordinal(U_1464) )
| ! [U_1462] :
( ~ in(U_1462,U_1465)
| ~ ordinal(U_1462) ) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
! [U_1465] :
( ( ! [U_1463] :
( ordinal_subset(sK231(U_1465),U_1463)
| ~ in(U_1463,U_1465)
| ~ ordinal(U_1463) )
& in(sK231(U_1465),U_1465)
& ordinal(sK231(U_1465)) )
| ! [U_1462] :
( ~ in(U_1462,U_1465)
| ~ ordinal(U_1462) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_1464,sK231(U_1465))],[f_426_2]) ).
fof(f_426_4,plain,
( ! [U_1465,U_1463] :
( ordinal_subset(sK231(U_1465),U_1463)
| ~ in(U_1463,U_1465)
| ~ ordinal(U_1463)
| ~ sP345(U_1465,U_1463) )
& ! [U_1465,U_1463] :
( in(sK231(U_1465),U_1465)
| ~ sP345(U_1465,U_1463) )
& ! [U_1465,U_1463] :
( ordinal(sK231(U_1465))
| ~ sP345(U_1465,U_1463) )
& ! [U_1465,U_1462,U_1463] :
( sP345(U_1465,U_1463)
| ~ in(U_1462,U_1465)
| ~ ordinal(U_1462) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP345])],[f_426_3]) ).
cnf(f_426_5,plain,
( sP345(U_1465,U_1463)
| ~ in(U_1462,U_1465)
| ~ ordinal(U_1462) ),
inference(clausify,[status(thm)],[f_426_4]) ).
cnf(f_426_6,plain,
( ordinal(sK231(U_1465))
| ~ sP345(U_1465,U_1463) ),
inference(clausify,[status(thm)],[f_426_4]) ).
cnf(f_426_7,plain,
( in(sK231(U_1465),U_1465)
| ~ sP345(U_1465,U_1463) ),
inference(clausify,[status(thm)],[f_426_4]) ).
cnf(f_426_8,plain,
( ordinal_subset(sK231(U_1465),U_1463)
| ~ in(U_1463,U_1465)
| ~ ordinal(U_1463)
| ~ sP345(U_1465,U_1463) ),
inference(clausify,[status(thm)],[f_426_4]) ).
fof(f_427_1,plain,
( ! [D] :
( ! [R] :
( ? [S] :
( ! [T] :
( T = S
| ~ subset(S,T)
| ~ in(T,R) )
& in(S,R) )
| R = empty_set
| ~ element(R,powerset(powerset(D))) )
| ~ in(D,omega)
| ~ ordinal(D) )
| ? [D] :
( ? [O] :
( ! [P] :
( ? [Q] :
( Q != P
& subset(P,Q)
& in(Q,O) )
| ~ in(P,O) )
& O != empty_set
& element(O,powerset(powerset(D))) )
& in(D,omega)
& D != empty_set
& ! [K] :
( ! [L] :
( ? [M] :
( ! [N] :
( N = M
| ~ subset(M,N)
| ~ in(N,L) )
& in(M,L) )
| L = empty_set
| ~ element(L,powerset(powerset(K))) )
| ~ in(K,omega)
| ~ in(K,D)
| ~ ordinal(K) )
& being_limit_ordinal(D)
& ordinal(D) )
| ? [D] :
( ? [H] :
( ! [I] :
( ? [J] :
( J != I
& subset(I,J)
& in(J,H) )
| ~ in(I,H) )
& H != empty_set
& element(H,powerset(powerset(succ(D)))) )
& in(succ(D),omega)
& ( ! [E] :
( ? [F] :
( ! [G] :
( G = F
| ~ subset(F,G)
| ~ in(G,E) )
& in(F,E) )
| E = empty_set
| ~ element(E,powerset(powerset(D))) )
| ~ in(D,omega) )
& ordinal(D) )
| ( ? [A] :
( ! [B] :
( ? [C] :
( C != B
& subset(B,C)
& in(C,A) )
| ~ in(B,A) )
& A != empty_set
& element(A,powerset(powerset(empty_set))) )
& in(empty_set,omega) ) ),
inference(fof_nnf,[status(thm)],[s1_ordinal2__e18_27__finset_1]) ).
fof(f_427_2,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ? [U_1483] :
( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(U_1483))) )
& in(U_1483,omega)
& U_1483 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,U_1483)
| ~ ordinal(U_1479) )
& being_limit_ordinal(U_1483)
& ordinal(U_1483) )
| ? [U_1475] :
( ? [U_1474] :
( ! [U_1473] :
( ? [U_1472] :
( U_1472 != U_1473
& subset(U_1473,U_1472)
& in(U_1472,U_1474) )
| ~ in(U_1473,U_1474) )
& U_1474 != empty_set
& element(U_1474,powerset(powerset(succ(U_1475)))) )
& in(succ(U_1475),omega)
& ( ! [U_1471] :
( ? [U_1470] :
( ! [U_1469] :
( U_1469 = U_1470
| ~ subset(U_1470,U_1469)
| ~ in(U_1469,U_1471) )
& in(U_1470,U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(U_1475))) )
| ~ in(U_1475,omega) )
& ordinal(U_1475) )
| ( ? [U_1468] :
( ! [U_1467] :
( ? [U_1466] :
( U_1466 != U_1467
& subset(U_1467,U_1466)
& in(U_1466,U_1468) )
| ~ in(U_1467,U_1468) )
& U_1468 != empty_set
& element(U_1468,powerset(powerset(empty_set))) )
& in(empty_set,omega) ) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ? [U_1483] :
( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(U_1483))) )
& in(U_1483,omega)
& U_1483 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,U_1483)
| ~ ordinal(U_1479) )
& being_limit_ordinal(U_1483)
& ordinal(U_1483) )
| ? [U_1475] :
( ? [U_1474] :
( ! [U_1473] :
( ? [U_1472] :
( U_1472 != U_1473
& subset(U_1473,U_1472)
& in(U_1472,U_1474) )
| ~ in(U_1473,U_1474) )
& U_1474 != empty_set
& element(U_1474,powerset(powerset(succ(U_1475)))) )
& in(succ(U_1475),omega)
& ( ! [U_1471] :
( ? [U_1470] :
( ! [U_1469] :
( U_1469 = U_1470
| ~ subset(U_1470,U_1469)
| ~ in(U_1469,U_1471) )
& in(U_1470,U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(U_1475))) )
| ~ in(U_1475,omega) )
& ordinal(U_1475) )
| ( ! [U_1467] :
( ? [U_1466] :
( U_1466 != U_1467
& subset(U_1467,U_1466)
& in(U_1466,sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_1468,sK232)],[f_427_2]) ).
fof(f_427_4,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ? [U_1483] :
( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(U_1483))) )
& in(U_1483,omega)
& U_1483 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,U_1483)
| ~ ordinal(U_1479) )
& being_limit_ordinal(U_1483)
& ordinal(U_1483) )
| ? [U_1475] :
( ? [U_1474] :
( ! [U_1473] :
( ? [U_1472] :
( U_1472 != U_1473
& subset(U_1473,U_1472)
& in(U_1472,U_1474) )
| ~ in(U_1473,U_1474) )
& U_1474 != empty_set
& element(U_1474,powerset(powerset(succ(U_1475)))) )
& in(succ(U_1475),omega)
& ( ! [U_1471] :
( ? [U_1470] :
( ! [U_1469] :
( U_1469 = U_1470
| ~ subset(U_1470,U_1469)
| ~ in(U_1469,U_1471) )
& in(U_1470,U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(U_1475))) )
| ~ in(U_1475,omega) )
& ordinal(U_1475) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_1466,sK233(U_1467))],[f_427_3]) ).
fof(f_427_5,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ? [U_1483] :
( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(U_1483))) )
& in(U_1483,omega)
& U_1483 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,U_1483)
| ~ ordinal(U_1479) )
& being_limit_ordinal(U_1483)
& ordinal(U_1483) )
| ( ? [U_1474] :
( ! [U_1473] :
( ? [U_1472] :
( U_1472 != U_1473
& subset(U_1473,U_1472)
& in(U_1472,U_1474) )
| ~ in(U_1473,U_1474) )
& U_1474 != empty_set
& element(U_1474,powerset(powerset(succ(sK234)))) )
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ? [U_1470] :
( ! [U_1469] :
( U_1469 = U_1470
| ~ subset(U_1470,U_1469)
| ~ in(U_1469,U_1471) )
& in(U_1470,U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_1475,sK234)],[f_427_4]) ).
fof(f_427_6,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ? [U_1483] :
( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(U_1483))) )
& in(U_1483,omega)
& U_1483 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,U_1483)
| ~ ordinal(U_1479) )
& being_limit_ordinal(U_1483)
& ordinal(U_1483) )
| ( ? [U_1474] :
( ! [U_1473] :
( ? [U_1472] :
( U_1472 != U_1473
& subset(U_1473,U_1472)
& in(U_1472,U_1474) )
| ~ in(U_1473,U_1474) )
& U_1474 != empty_set
& element(U_1474,powerset(powerset(succ(sK234)))) )
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_1470,sK235(U_1471))],[f_427_5]) ).
fof(f_427_7,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ? [U_1483] :
( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(U_1483))) )
& in(U_1483,omega)
& U_1483 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,U_1483)
| ~ ordinal(U_1479) )
& being_limit_ordinal(U_1483)
& ordinal(U_1483) )
| ( ! [U_1473] :
( ? [U_1472] :
( U_1472 != U_1473
& subset(U_1473,U_1472)
& in(U_1472,sK236) )
| ~ in(U_1473,sK236) )
& sK236 != empty_set
& element(sK236,powerset(powerset(succ(sK234))))
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_1474,sK236)],[f_427_6]) ).
fof(f_427_8,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ? [U_1483] :
( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(U_1483))) )
& in(U_1483,omega)
& U_1483 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,U_1483)
| ~ ordinal(U_1479) )
& being_limit_ordinal(U_1483)
& ordinal(U_1483) )
| ( ! [U_1473] :
( ( sK237(U_1473) != U_1473
& subset(U_1473,sK237(U_1473))
& in(sK237(U_1473),sK236) )
| ~ in(U_1473,sK236) )
& sK236 != empty_set
& element(sK236,powerset(powerset(succ(sK234))))
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_1472,sK237(U_1473))],[f_427_7]) ).
fof(f_427_9,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(sK238))) )
& in(sK238,omega)
& sK238 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ? [U_1477] :
( ! [U_1476] :
( U_1476 = U_1477
| ~ subset(U_1477,U_1476)
| ~ in(U_1476,U_1478) )
& in(U_1477,U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,sK238)
| ~ ordinal(U_1479) )
& being_limit_ordinal(sK238)
& ordinal(sK238) )
| ( ! [U_1473] :
( ( sK237(U_1473) != U_1473
& subset(U_1473,sK237(U_1473))
& in(sK237(U_1473),sK236) )
| ~ in(U_1473,sK236) )
& sK236 != empty_set
& element(sK236,powerset(powerset(succ(sK234))))
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_1483,sK238)],[f_427_8]) ).
fof(f_427_10,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ( ? [U_1482] :
( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,U_1482) )
| ~ in(U_1481,U_1482) )
& U_1482 != empty_set
& element(U_1482,powerset(powerset(sK238))) )
& in(sK238,omega)
& sK238 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ( ! [U_1476] :
( U_1476 = sK239(U_1479,U_1478)
| ~ subset(sK239(U_1479,U_1478),U_1476)
| ~ in(U_1476,U_1478) )
& in(sK239(U_1479,U_1478),U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,sK238)
| ~ ordinal(U_1479) )
& being_limit_ordinal(sK238)
& ordinal(sK238) )
| ( ! [U_1473] :
( ( sK237(U_1473) != U_1473
& subset(U_1473,sK237(U_1473))
& in(sK237(U_1473),sK236) )
| ~ in(U_1473,sK236) )
& sK236 != empty_set
& element(sK236,powerset(powerset(succ(sK234))))
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_1477,sK239(U_1479,U_1478))],[f_427_9]) ).
fof(f_427_11,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ( ! [U_1481] :
( ? [U_1480] :
( U_1480 != U_1481
& subset(U_1481,U_1480)
& in(U_1480,sK240) )
| ~ in(U_1481,sK240) )
& sK240 != empty_set
& element(sK240,powerset(powerset(sK238)))
& in(sK238,omega)
& sK238 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ( ! [U_1476] :
( U_1476 = sK239(U_1479,U_1478)
| ~ subset(sK239(U_1479,U_1478),U_1476)
| ~ in(U_1476,U_1478) )
& in(sK239(U_1479,U_1478),U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,sK238)
| ~ ordinal(U_1479) )
& being_limit_ordinal(sK238)
& ordinal(sK238) )
| ( ! [U_1473] :
( ( sK237(U_1473) != U_1473
& subset(U_1473,sK237(U_1473))
& in(sK237(U_1473),sK236) )
| ~ in(U_1473,sK236) )
& sK236 != empty_set
& element(sK236,powerset(powerset(succ(sK234))))
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_1482,sK240)],[f_427_10]) ).
fof(f_427_12,plain,
( ! [U_1487] :
( ! [U_1486] :
( ? [U_1485] :
( ! [U_1484] :
( U_1484 = U_1485
| ~ subset(U_1485,U_1484)
| ~ in(U_1484,U_1486) )
& in(U_1485,U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ( ! [U_1481] :
( ( sK241(U_1481) != U_1481
& subset(U_1481,sK241(U_1481))
& in(sK241(U_1481),sK240) )
| ~ in(U_1481,sK240) )
& sK240 != empty_set
& element(sK240,powerset(powerset(sK238)))
& in(sK238,omega)
& sK238 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ( ! [U_1476] :
( U_1476 = sK239(U_1479,U_1478)
| ~ subset(sK239(U_1479,U_1478),U_1476)
| ~ in(U_1476,U_1478) )
& in(sK239(U_1479,U_1478),U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,sK238)
| ~ ordinal(U_1479) )
& being_limit_ordinal(sK238)
& ordinal(sK238) )
| ( ! [U_1473] :
( ( sK237(U_1473) != U_1473
& subset(U_1473,sK237(U_1473))
& in(sK237(U_1473),sK236) )
| ~ in(U_1473,sK236) )
& sK236 != empty_set
& element(sK236,powerset(powerset(succ(sK234))))
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_1480,sK241(U_1481))],[f_427_11]) ).
fof(f_427_13,plain,
( ! [U_1487] :
( ! [U_1486] :
( ( ! [U_1484] :
( U_1484 = sK242(U_1487,U_1486)
| ~ subset(sK242(U_1487,U_1486),U_1484)
| ~ in(U_1484,U_1486) )
& in(sK242(U_1487,U_1486),U_1486) )
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487))) )
| ~ in(U_1487,omega)
| ~ ordinal(U_1487) )
| ( ! [U_1481] :
( ( sK241(U_1481) != U_1481
& subset(U_1481,sK241(U_1481))
& in(sK241(U_1481),sK240) )
| ~ in(U_1481,sK240) )
& sK240 != empty_set
& element(sK240,powerset(powerset(sK238)))
& in(sK238,omega)
& sK238 != empty_set
& ! [U_1479] :
( ! [U_1478] :
( ( ! [U_1476] :
( U_1476 = sK239(U_1479,U_1478)
| ~ subset(sK239(U_1479,U_1478),U_1476)
| ~ in(U_1476,U_1478) )
& in(sK239(U_1479,U_1478),U_1478) )
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479))) )
| ~ in(U_1479,omega)
| ~ in(U_1479,sK238)
| ~ ordinal(U_1479) )
& being_limit_ordinal(sK238)
& ordinal(sK238) )
| ( ! [U_1473] :
( ( sK237(U_1473) != U_1473
& subset(U_1473,sK237(U_1473))
& in(sK237(U_1473),sK236) )
| ~ in(U_1473,sK236) )
& sK236 != empty_set
& element(sK236,powerset(powerset(succ(sK234))))
& in(succ(sK234),omega)
& ( ! [U_1471] :
( ( ! [U_1469] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471) )
& in(sK235(U_1471),U_1471) )
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234))) )
| ~ in(sK234,omega) )
& ordinal(sK234) )
| ( ! [U_1467] :
( ( sK233(U_1467) != U_1467
& subset(U_1467,sK233(U_1467))
& in(sK233(U_1467),sK232) )
| ~ in(U_1467,sK232) )
& sK232 != empty_set
& element(sK232,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_1485,sK242(U_1487,U_1486))],[f_427_12]) ).
fof(f_427_14,plain,
( ! [U_1484,U_1486,U_1487] :
( U_1484 = sK242(U_1487,U_1486)
| ~ subset(sK242(U_1487,U_1486),U_1484)
| ~ in(U_1484,U_1486)
| ~ sP354(U_1484,U_1486,U_1487) )
& ! [U_1484,U_1486,U_1487] :
( in(sK242(U_1487,U_1486),U_1486)
| ~ sP354(U_1484,U_1486,U_1487) )
& ! [U_1481] :
( sK241(U_1481) != U_1481
| ~ sP352(U_1481) )
& ! [U_1481] :
( subset(U_1481,sK241(U_1481))
| ~ sP352(U_1481) )
& ! [U_1481] :
( in(sK241(U_1481),sK240)
| ~ sP352(U_1481) )
& ! [U_1476,U_1478,U_1479] :
( U_1476 = sK239(U_1479,U_1478)
| ~ subset(sK239(U_1479,U_1478),U_1476)
| ~ in(U_1476,U_1478)
| ~ sP351(U_1476,U_1478,U_1479) )
& ! [U_1476,U_1478,U_1479] :
( in(sK239(U_1479,U_1478),U_1478)
| ~ sP351(U_1476,U_1478,U_1479) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( sP352(U_1481)
| ~ in(U_1481,sK240)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( sK240 != empty_set
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( element(sK240,powerset(powerset(sK238)))
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( in(sK238,omega)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( sK238 != empty_set
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( sP351(U_1476,U_1478,U_1479)
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479)))
| ~ in(U_1479,omega)
| ~ in(U_1479,sK238)
| ~ ordinal(U_1479)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( being_limit_ordinal(sK238)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1476,U_1478,U_1479,U_1481] :
( ordinal(sK238)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) )
& ! [U_1473] :
( sK237(U_1473) != U_1473
| ~ sP349(U_1473) )
& ! [U_1473] :
( subset(U_1473,sK237(U_1473))
| ~ sP349(U_1473) )
& ! [U_1473] :
( in(sK237(U_1473),sK236)
| ~ sP349(U_1473) )
& ! [U_1469,U_1471] :
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471)
| ~ sP348(U_1469,U_1471) )
& ! [U_1469,U_1471] :
( in(sK235(U_1471),U_1471)
| ~ sP348(U_1469,U_1471) )
& ! [U_1469,U_1471,U_1473] :
( sP349(U_1473)
| ~ in(U_1473,sK236)
| ~ sP350(U_1469,U_1471,U_1473) )
& ! [U_1469,U_1471,U_1473] :
( sK236 != empty_set
| ~ sP350(U_1469,U_1471,U_1473) )
& ! [U_1469,U_1471,U_1473] :
( element(sK236,powerset(powerset(succ(sK234))))
| ~ sP350(U_1469,U_1471,U_1473) )
& ! [U_1469,U_1471,U_1473] :
( in(succ(sK234),omega)
| ~ sP350(U_1469,U_1471,U_1473) )
& ! [U_1469,U_1471,U_1473] :
( sP348(U_1469,U_1471)
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234)))
| ~ in(sK234,omega)
| ~ sP350(U_1469,U_1471,U_1473) )
& ! [U_1469,U_1471,U_1473] :
( ordinal(sK234)
| ~ sP350(U_1469,U_1471,U_1473) )
& ! [U_1467] :
( sK233(U_1467) != U_1467
| ~ sP346(U_1467) )
& ! [U_1467] :
( subset(U_1467,sK233(U_1467))
| ~ sP346(U_1467) )
& ! [U_1467] :
( in(sK233(U_1467),sK232)
| ~ sP346(U_1467) )
& ! [U_1467] :
( sP346(U_1467)
| ~ in(U_1467,sK232)
| ~ sP347(U_1467) )
& ! [U_1467] :
( sK232 != empty_set
| ~ sP347(U_1467) )
& ! [U_1467] :
( element(sK232,powerset(powerset(empty_set)))
| ~ sP347(U_1467) )
& ! [U_1467] :
( in(empty_set,omega)
| ~ sP347(U_1467) )
& ! [U_1476,U_1467,U_1469,U_1478,U_1471,U_1479,U_1473,U_1484,U_1486,U_1487,U_1481] :
( sP354(U_1484,U_1486,U_1487)
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487)))
| ~ in(U_1487,omega)
| ~ ordinal(U_1487)
| sP353(U_1476,U_1478,U_1479,U_1481)
| sP350(U_1469,U_1471,U_1473)
| sP347(U_1467) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP346,sP347,sP348,sP349,sP350,sP351,sP352,sP353,sP354])],[f_427_13]) ).
cnf(f_427_15,plain,
( sP354(U_1484,U_1486,U_1487)
| U_1486 = empty_set
| ~ element(U_1486,powerset(powerset(U_1487)))
| ~ in(U_1487,omega)
| ~ ordinal(U_1487)
| sP353(U_1476,U_1478,U_1479,U_1481)
| sP350(U_1469,U_1471,U_1473)
| sP347(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_16,plain,
( in(empty_set,omega)
| ~ sP347(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_17,plain,
( element(sK232,powerset(powerset(empty_set)))
| ~ sP347(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_18,plain,
( sK232 != empty_set
| ~ sP347(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_19,plain,
( sP346(U_1467)
| ~ in(U_1467,sK232)
| ~ sP347(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_20,plain,
( in(sK233(U_1467),sK232)
| ~ sP346(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_21,plain,
( subset(U_1467,sK233(U_1467))
| ~ sP346(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_22,plain,
( sK233(U_1467) != U_1467
| ~ sP346(U_1467) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_23,plain,
( ordinal(sK234)
| ~ sP350(U_1469,U_1471,U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_24,plain,
( sP348(U_1469,U_1471)
| U_1471 = empty_set
| ~ element(U_1471,powerset(powerset(sK234)))
| ~ in(sK234,omega)
| ~ sP350(U_1469,U_1471,U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_25,plain,
( in(succ(sK234),omega)
| ~ sP350(U_1469,U_1471,U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_26,plain,
( element(sK236,powerset(powerset(succ(sK234))))
| ~ sP350(U_1469,U_1471,U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_27,plain,
( sK236 != empty_set
| ~ sP350(U_1469,U_1471,U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_28,plain,
( sP349(U_1473)
| ~ in(U_1473,sK236)
| ~ sP350(U_1469,U_1471,U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_29,plain,
( in(sK235(U_1471),U_1471)
| ~ sP348(U_1469,U_1471) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_30,plain,
( U_1469 = sK235(U_1471)
| ~ subset(sK235(U_1471),U_1469)
| ~ in(U_1469,U_1471)
| ~ sP348(U_1469,U_1471) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_31,plain,
( in(sK237(U_1473),sK236)
| ~ sP349(U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_32,plain,
( subset(U_1473,sK237(U_1473))
| ~ sP349(U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_33,plain,
( sK237(U_1473) != U_1473
| ~ sP349(U_1473) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_34,plain,
( ordinal(sK238)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_35,plain,
( being_limit_ordinal(sK238)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_36,plain,
( sP351(U_1476,U_1478,U_1479)
| U_1478 = empty_set
| ~ element(U_1478,powerset(powerset(U_1479)))
| ~ in(U_1479,omega)
| ~ in(U_1479,sK238)
| ~ ordinal(U_1479)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_37,plain,
( sK238 != empty_set
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_38,plain,
( in(sK238,omega)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_39,plain,
( element(sK240,powerset(powerset(sK238)))
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_40,plain,
( sK240 != empty_set
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_41,plain,
( sP352(U_1481)
| ~ in(U_1481,sK240)
| ~ sP353(U_1476,U_1478,U_1479,U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_42,plain,
( in(sK239(U_1479,U_1478),U_1478)
| ~ sP351(U_1476,U_1478,U_1479) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_43,plain,
( U_1476 = sK239(U_1479,U_1478)
| ~ subset(sK239(U_1479,U_1478),U_1476)
| ~ in(U_1476,U_1478)
| ~ sP351(U_1476,U_1478,U_1479) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_44,plain,
( in(sK241(U_1481),sK240)
| ~ sP352(U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_45,plain,
( subset(U_1481,sK241(U_1481))
| ~ sP352(U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_46,plain,
( sK241(U_1481) != U_1481
| ~ sP352(U_1481) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_47,plain,
( in(sK242(U_1487,U_1486),U_1486)
| ~ sP354(U_1484,U_1486,U_1487) ),
inference(clausify,[status(thm)],[f_427_14]) ).
cnf(f_427_48,plain,
( U_1484 = sK242(U_1487,U_1486)
| ~ subset(sK242(U_1487,U_1486),U_1484)
| ~ in(U_1484,U_1486)
| ~ sP354(U_1484,U_1486,U_1487) ),
inference(clausify,[status(thm)],[f_427_14]) ).
fof(f_428_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_428_2,plain,
! [U_1493,U_1492,U_1491] :
( ? [U_1490] :
( ! [U_1489,U_1488] :
( ( in(ordered_pair(U_1489,U_1488),U_1490)
| ~ in(ordered_pair(apply(U_1491,U_1489),apply(U_1491,U_1488)),U_1492)
| ~ in(U_1488,U_1493)
| ~ in(U_1489,U_1493) )
& ( ( in(ordered_pair(apply(U_1491,U_1489),apply(U_1491,U_1488)),U_1492)
& in(U_1488,U_1493)
& in(U_1489,U_1493) )
| ~ in(ordered_pair(U_1489,U_1488),U_1490) ) )
& relation(U_1490) )
| ~ function(U_1491)
| ~ relation(U_1491)
| ~ relation(U_1492) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_1493,U_1492,U_1491] :
( ? [U_1490] :
( ! [U_1497,U_1495] :
( in(ordered_pair(U_1497,U_1495),U_1490)
| ~ in(ordered_pair(apply(U_1491,U_1497),apply(U_1491,U_1495)),U_1492)
| ~ in(U_1495,U_1493)
| ~ in(U_1497,U_1493) )
& ! [U_1496,U_1494] :
( ( in(ordered_pair(apply(U_1491,U_1496),apply(U_1491,U_1494)),U_1492)
& in(U_1494,U_1493)
& in(U_1496,U_1493) )
| ~ in(ordered_pair(U_1496,U_1494),U_1490) )
& relation(U_1490) )
| ~ function(U_1491)
| ~ relation(U_1491)
| ~ relation(U_1492) ),
inference(miniscope,[status(thm)],[f_428_2]) ).
fof(f_428_4,plain,
! [U_1493,U_1492,U_1491] :
( ( ! [U_1497,U_1495] :
( in(ordered_pair(U_1497,U_1495),sK243(U_1493,U_1492,U_1491))
| ~ in(ordered_pair(apply(U_1491,U_1497),apply(U_1491,U_1495)),U_1492)
| ~ in(U_1495,U_1493)
| ~ in(U_1497,U_1493) )
& ! [U_1496,U_1494] :
( ( in(ordered_pair(apply(U_1491,U_1496),apply(U_1491,U_1494)),U_1492)
& in(U_1494,U_1493)
& in(U_1496,U_1493) )
| ~ in(ordered_pair(U_1496,U_1494),sK243(U_1493,U_1492,U_1491)) )
& relation(sK243(U_1493,U_1492,U_1491)) )
| ~ function(U_1491)
| ~ relation(U_1491)
| ~ relation(U_1492) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_1490,sK243(U_1493,U_1492,U_1491))],[f_428_3]) ).
fof(f_428_5,plain,
( ! [U_1492,U_1496,U_1494,U_1493,U_1491] :
( in(ordered_pair(apply(U_1491,U_1496),apply(U_1491,U_1494)),U_1492)
| ~ sP355(U_1492,U_1496,U_1494,U_1493,U_1491) )
& ! [U_1492,U_1496,U_1494,U_1493,U_1491] :
( in(U_1494,U_1493)
| ~ sP355(U_1492,U_1496,U_1494,U_1493,U_1491) )
& ! [U_1492,U_1496,U_1494,U_1493,U_1491] :
( in(U_1496,U_1493)
| ~ sP355(U_1492,U_1496,U_1494,U_1493,U_1491) )
& ! [U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491] :
( in(ordered_pair(U_1497,U_1495),sK243(U_1493,U_1492,U_1491))
| ~ in(ordered_pair(apply(U_1491,U_1497),apply(U_1491,U_1495)),U_1492)
| ~ in(U_1495,U_1493)
| ~ in(U_1497,U_1493)
| ~ sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491) )
& ! [U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491] :
( sP355(U_1492,U_1496,U_1494,U_1493,U_1491)
| ~ in(ordered_pair(U_1496,U_1494),sK243(U_1493,U_1492,U_1491))
| ~ sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491) )
& ! [U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491] :
( relation(sK243(U_1493,U_1492,U_1491))
| ~ sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491) )
& ! [U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491] :
( sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491)
| ~ function(U_1491)
| ~ relation(U_1491)
| ~ relation(U_1492) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP355,sP356])],[f_428_4]) ).
cnf(f_428_6,plain,
( sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491)
| ~ function(U_1491)
| ~ relation(U_1491)
| ~ relation(U_1492) ),
inference(clausify,[status(thm)],[f_428_5]) ).
cnf(f_428_7,plain,
( relation(sK243(U_1493,U_1492,U_1491))
| ~ sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491) ),
inference(clausify,[status(thm)],[f_428_5]) ).
cnf(f_428_8,plain,
( sP355(U_1492,U_1496,U_1494,U_1493,U_1491)
| ~ in(ordered_pair(U_1496,U_1494),sK243(U_1493,U_1492,U_1491))
| ~ sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491) ),
inference(clausify,[status(thm)],[f_428_5]) ).
cnf(f_428_9,plain,
( in(ordered_pair(U_1497,U_1495),sK243(U_1493,U_1492,U_1491))
| ~ in(ordered_pair(apply(U_1491,U_1497),apply(U_1491,U_1495)),U_1492)
| ~ in(U_1495,U_1493)
| ~ in(U_1497,U_1493)
| ~ sP356(U_1492,U_1495,U_1496,U_1494,U_1493,U_1497,U_1491) ),
inference(clausify,[status(thm)],[f_428_5]) ).
cnf(f_428_10,plain,
( in(U_1496,U_1493)
| ~ sP355(U_1492,U_1496,U_1494,U_1493,U_1491) ),
inference(clausify,[status(thm)],[f_428_5]) ).
cnf(f_428_11,plain,
( in(U_1494,U_1493)
| ~ sP355(U_1492,U_1496,U_1494,U_1493,U_1491) ),
inference(clausify,[status(thm)],[f_428_5]) ).
cnf(f_428_12,plain,
( in(ordered_pair(apply(U_1491,U_1496),apply(U_1491,U_1494)),U_1492)
| ~ sP355(U_1492,U_1496,U_1494,U_1493,U_1491) ),
inference(clausify,[status(thm)],[f_428_5]) ).
fof(f_429_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_429_2,plain,
! [U_1514,U_1513] :
( ? [U_1512] :
! [U_1511] :
( ( in(U_1511,U_1512)
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1511,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1511,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1511,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1511,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1511,U_1512) ) )
| ? [U_1504,U_1503,U_1502] :
( U_1503 != U_1502
& ? [U_1501] :
( ! [U_1500] :
( in(ordered_pair(U_1502,U_1500),U_1513)
| ~ in(U_1500,U_1501) )
& in(U_1502,U_1501)
& U_1504 = U_1501 )
& in(U_1504,U_1514)
& ? [U_1499] :
( ! [U_1498] :
( in(ordered_pair(U_1503,U_1498),U_1513)
| ~ in(U_1498,U_1499) )
& in(U_1503,U_1499)
& U_1504 = U_1499 )
& in(U_1504,U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_1514,U_1513] :
( ? [U_1512] :
( ! [U_1516] :
( in(U_1516,U_1512)
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1515,U_1512) ) )
| ? [U_1504,U_1503,U_1502] :
( U_1503 != U_1502
& ? [U_1501] :
( ! [U_1500] :
( in(ordered_pair(U_1502,U_1500),U_1513)
| ~ in(U_1500,U_1501) )
& in(U_1502,U_1501)
& U_1504 = U_1501 )
& in(U_1504,U_1514)
& ? [U_1499] :
( ! [U_1498] :
( in(ordered_pair(U_1503,U_1498),U_1513)
| ~ in(U_1498,U_1499) )
& in(U_1503,U_1499)
& U_1504 = U_1499 )
& in(U_1504,U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(miniscope,[status(thm)],[f_429_2]) ).
fof(f_429_4,plain,
! [U_1514,U_1513] :
( ? [U_1512] :
( ! [U_1516] :
( in(U_1516,U_1512)
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1515,U_1512) ) )
| ? [U_1503,U_1502] :
( U_1503 != U_1502
& ? [U_1501] :
( ! [U_1500] :
( in(ordered_pair(U_1502,U_1500),U_1513)
| ~ in(U_1500,U_1501) )
& in(U_1502,U_1501)
& sK244(U_1514,U_1513) = U_1501 )
& in(sK244(U_1514,U_1513),U_1514)
& ? [U_1499] :
( ! [U_1498] :
( in(ordered_pair(U_1503,U_1498),U_1513)
| ~ in(U_1498,U_1499) )
& in(U_1503,U_1499)
& sK244(U_1514,U_1513) = U_1499 )
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_1504,sK244(U_1514,U_1513))],[f_429_3]) ).
fof(f_429_5,plain,
! [U_1514,U_1513] :
( ? [U_1512] :
( ! [U_1516] :
( in(U_1516,U_1512)
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1515,U_1512) ) )
| ? [U_1502] :
( sK245(U_1514,U_1513) != U_1502
& ? [U_1501] :
( ! [U_1500] :
( in(ordered_pair(U_1502,U_1500),U_1513)
| ~ in(U_1500,U_1501) )
& in(U_1502,U_1501)
& sK244(U_1514,U_1513) = U_1501 )
& in(sK244(U_1514,U_1513),U_1514)
& ? [U_1499] :
( ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,U_1499) )
& in(sK245(U_1514,U_1513),U_1499)
& sK244(U_1514,U_1513) = U_1499 )
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_1503,sK245(U_1514,U_1513))],[f_429_4]) ).
fof(f_429_6,plain,
! [U_1514,U_1513] :
( ? [U_1512] :
( ! [U_1516] :
( in(U_1516,U_1512)
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1515,U_1512) ) )
| ( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
& ? [U_1501] :
( ! [U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,U_1501) )
& in(sK246(U_1514,U_1513),U_1501)
& sK244(U_1514,U_1513) = U_1501 )
& in(sK244(U_1514,U_1513),U_1514)
& ? [U_1499] :
( ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,U_1499) )
& in(sK245(U_1514,U_1513),U_1499)
& sK244(U_1514,U_1513) = U_1499 )
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_1502,sK246(U_1514,U_1513))],[f_429_5]) ).
fof(f_429_7,plain,
! [U_1514,U_1513] :
( ? [U_1512] :
( ! [U_1516] :
( in(U_1516,U_1512)
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1515,U_1512) ) )
| ( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
& ? [U_1501] :
( ! [U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,U_1501) )
& in(sK246(U_1514,U_1513),U_1501)
& sK244(U_1514,U_1513) = U_1501 )
& in(sK244(U_1514,U_1513),U_1514)
& ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513)) )
& in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_1499,sK247(U_1514,U_1513))],[f_429_6]) ).
fof(f_429_8,plain,
! [U_1514,U_1513] :
( ? [U_1512] :
( ! [U_1516] :
( in(U_1516,U_1512)
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1515,U_1512) ) )
| ( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
& ! [U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,sK248(U_1514,U_1513)) )
& in(sK246(U_1514,U_1513),sK248(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK248(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514)
& ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513)) )
& in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_1501,sK248(U_1514,U_1513))],[f_429_7]) ).
fof(f_429_9,plain,
! [U_1514,U_1513] :
( ( ! [U_1516] :
( in(U_1516,sK249(U_1514,U_1513))
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ? [U_1507] :
( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& U_1507 = U_1506 )
& in(U_1507,U_1514)
& in(U_1507,U_1514) )
| ~ in(U_1515,sK249(U_1514,U_1513)) ) )
| ( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
& ! [U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,sK248(U_1514,U_1513)) )
& in(sK246(U_1514,U_1513),sK248(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK248(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514)
& ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513)) )
& in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_1512,sK249(U_1514,U_1513))],[f_429_8]) ).
fof(f_429_10,plain,
! [U_1514,U_1513] :
( ( ! [U_1516] :
( in(U_1516,sK249(U_1514,U_1513))
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ( ? [U_1506] :
( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,U_1506) )
& in(U_1515,U_1506)
& sK250(U_1514,U_1513,U_1515) = U_1506 )
& in(sK250(U_1514,U_1513,U_1515),U_1514)
& in(sK250(U_1514,U_1513,U_1515),U_1514) )
| ~ in(U_1515,sK249(U_1514,U_1513)) ) )
| ( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
& ! [U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,sK248(U_1514,U_1513)) )
& in(sK246(U_1514,U_1513),sK248(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK248(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514)
& ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513)) )
& in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_1507,sK250(U_1514,U_1513,U_1515))],[f_429_9]) ).
fof(f_429_11,plain,
! [U_1514,U_1513] :
( ( ! [U_1516] :
( in(U_1516,sK249(U_1514,U_1513))
| ! [U_1510] :
( ! [U_1509] :
( ? [U_1508] :
( ~ in(ordered_pair(U_1516,U_1508),U_1513)
& in(U_1508,U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,sK251(U_1514,U_1513,U_1515)) )
& in(U_1515,sK251(U_1514,U_1513,U_1515))
& sK250(U_1514,U_1513,U_1515) = sK251(U_1514,U_1513,U_1515)
& in(sK250(U_1514,U_1513,U_1515),U_1514)
& in(sK250(U_1514,U_1513,U_1515),U_1514) )
| ~ in(U_1515,sK249(U_1514,U_1513)) ) )
| ( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
& ! [U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,sK248(U_1514,U_1513)) )
& in(sK246(U_1514,U_1513),sK248(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK248(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514)
& ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513)) )
& in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_1506,sK251(U_1514,U_1513,U_1515))],[f_429_10]) ).
fof(f_429_12,plain,
! [U_1514,U_1513] :
( ( ! [U_1516] :
( in(U_1516,sK249(U_1514,U_1513))
| ! [U_1510] :
( ! [U_1509] :
( ( ~ in(ordered_pair(U_1516,sK252(U_1514,U_1513,U_1516,U_1510,U_1509)),U_1513)
& in(sK252(U_1514,U_1513,U_1516,U_1510,U_1509),U_1509) )
| ~ in(U_1516,U_1509)
| U_1510 != U_1509 )
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514) ) )
& ! [U_1515] :
( ( ! [U_1505] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,sK251(U_1514,U_1513,U_1515)) )
& in(U_1515,sK251(U_1514,U_1513,U_1515))
& sK250(U_1514,U_1513,U_1515) = sK251(U_1514,U_1513,U_1515)
& in(sK250(U_1514,U_1513,U_1515),U_1514)
& in(sK250(U_1514,U_1513,U_1515),U_1514) )
| ~ in(U_1515,sK249(U_1514,U_1513)) ) )
| ( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
& ! [U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,sK248(U_1514,U_1513)) )
& in(sK246(U_1514,U_1513),sK248(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK248(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514)
& ! [U_1498] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513)) )
& in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
& sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
& in(sK244(U_1514,U_1513),U_1514) )
| ~ relation(U_1513)
| empty(U_1514) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_1508,sK252(U_1514,U_1513,U_1516,U_1510,U_1509))],[f_429_11]) ).
fof(f_429_13,plain,
( ! [U_1510,U_1514,U_1509,U_1516,U_1513] :
( ~ in(ordered_pair(U_1516,sK252(U_1514,U_1513,U_1516,U_1510,U_1509)),U_1513)
| ~ sP359(U_1510,U_1514,U_1509,U_1516,U_1513) )
& ! [U_1510,U_1514,U_1509,U_1516,U_1513] :
( in(sK252(U_1514,U_1513,U_1516,U_1510,U_1509),U_1509)
| ~ sP359(U_1510,U_1514,U_1509,U_1516,U_1513) )
& ! [U_1505,U_1515,U_1514,U_1513] :
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,sK251(U_1514,U_1513,U_1515))
| ~ sP358(U_1505,U_1515,U_1514,U_1513) )
& ! [U_1505,U_1515,U_1514,U_1513] :
( in(U_1515,sK251(U_1514,U_1513,U_1515))
| ~ sP358(U_1505,U_1515,U_1514,U_1513) )
& ! [U_1505,U_1515,U_1514,U_1513] :
( sK250(U_1514,U_1513,U_1515) = sK251(U_1514,U_1513,U_1515)
| ~ sP358(U_1505,U_1515,U_1514,U_1513) )
& ! [U_1505,U_1515,U_1514,U_1513] :
( in(sK250(U_1514,U_1513,U_1515),U_1514)
| ~ sP358(U_1505,U_1515,U_1514,U_1513) )
& ! [U_1505,U_1515,U_1514,U_1513] :
( in(sK250(U_1514,U_1513,U_1515),U_1514)
| ~ sP358(U_1505,U_1515,U_1514,U_1513) )
& ! [U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513] :
( in(U_1516,sK249(U_1514,U_1513))
| sP359(U_1510,U_1514,U_1509,U_1516,U_1513)
| ~ in(U_1516,U_1509)
| U_1510 != U_1509
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514)
| ~ sP360(U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513) )
& ! [U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513] :
( sP358(U_1505,U_1515,U_1514,U_1513)
| ~ in(U_1515,sK249(U_1514,U_1513))
| ~ sP360(U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,sK248(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( in(sK246(U_1514,U_1513),sK248(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( sK244(U_1514,U_1513) = sK248(U_1514,U_1513)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( in(sK244(U_1514,U_1513),U_1514)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1514,U_1513,U_1498,U_1500] :
( in(sK244(U_1514,U_1513),U_1514)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) )
& ! [U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513,U_1498,U_1500] :
( sP360(U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513)
| sP357(U_1514,U_1513,U_1498,U_1500)
| ~ relation(U_1513)
| empty(U_1514) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP357,sP358,sP359,sP360])],[f_429_12]) ).
cnf(f_429_14,plain,
( sP360(U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513)
| sP357(U_1514,U_1513,U_1498,U_1500)
| ~ relation(U_1513)
| empty(U_1514) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_15,plain,
( in(sK244(U_1514,U_1513),U_1514)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_16,plain,
( sK244(U_1514,U_1513) = sK247(U_1514,U_1513)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_17,plain,
( in(sK245(U_1514,U_1513),sK247(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_18,plain,
( in(ordered_pair(sK245(U_1514,U_1513),U_1498),U_1513)
| ~ in(U_1498,sK247(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_19,plain,
( in(sK244(U_1514,U_1513),U_1514)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_20,plain,
( sK244(U_1514,U_1513) = sK248(U_1514,U_1513)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_21,plain,
( in(sK246(U_1514,U_1513),sK248(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_22,plain,
( in(ordered_pair(sK246(U_1514,U_1513),U_1500),U_1513)
| ~ in(U_1500,sK248(U_1514,U_1513))
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_23,plain,
( sK245(U_1514,U_1513) != sK246(U_1514,U_1513)
| ~ sP357(U_1514,U_1513,U_1498,U_1500) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_24,plain,
( sP358(U_1505,U_1515,U_1514,U_1513)
| ~ in(U_1515,sK249(U_1514,U_1513))
| ~ sP360(U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_25,plain,
( in(U_1516,sK249(U_1514,U_1513))
| sP359(U_1510,U_1514,U_1509,U_1516,U_1513)
| ~ in(U_1516,U_1509)
| U_1510 != U_1509
| ~ in(U_1510,U_1514)
| ~ in(U_1510,U_1514)
| ~ sP360(U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_26,plain,
( in(sK250(U_1514,U_1513,U_1515),U_1514)
| ~ sP358(U_1505,U_1515,U_1514,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_27,plain,
( in(sK250(U_1514,U_1513,U_1515),U_1514)
| ~ sP358(U_1505,U_1515,U_1514,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_28,plain,
( sK250(U_1514,U_1513,U_1515) = sK251(U_1514,U_1513,U_1515)
| ~ sP358(U_1505,U_1515,U_1514,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_29,plain,
( in(U_1515,sK251(U_1514,U_1513,U_1515))
| ~ sP358(U_1505,U_1515,U_1514,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_30,plain,
( in(ordered_pair(U_1515,U_1505),U_1513)
| ~ in(U_1505,sK251(U_1514,U_1513,U_1515))
| ~ sP358(U_1505,U_1515,U_1514,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_31,plain,
( in(sK252(U_1514,U_1513,U_1516,U_1510,U_1509),U_1509)
| ~ sP359(U_1510,U_1514,U_1509,U_1516,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
cnf(f_429_32,plain,
( ~ in(ordered_pair(U_1516,sK252(U_1514,U_1513,U_1516,U_1510,U_1509)),U_1513)
| ~ sP359(U_1510,U_1514,U_1509,U_1516,U_1513) ),
inference(clausify,[status(thm)],[f_429_13]) ).
fof(f_430_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_430_2,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
( ? [U_1539] :
! [U_1538] :
( ( in(U_1538,U_1539)
| ! [U_1537] :
( ! [U_1536,U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ~ in(U_1536,U_1542)
| ordered_pair(U_1536,U_1535) != U_1538 )
| U_1537 != U_1538
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) ) )
& ( ? [U_1532] :
( ? [U_1531,U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& in(U_1531,U_1542)
& ordered_pair(U_1531,U_1530) = U_1538 )
& U_1532 = U_1538
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
| ~ in(U_1538,U_1539) ) )
| ? [U_1527,U_1526,U_1525] :
( U_1526 != U_1525
& ? [U_1524,U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& in(U_1524,U_1542)
& ordered_pair(U_1524,U_1523) = U_1525 )
& U_1527 = U_1525
& ? [U_1520,U_1519] :
( ? [U_1518] :
( ! [U_1517] :
( in(ordered_pair(U_1519,U_1517),U_1541)
| ~ in(U_1517,U_1518) )
& in(U_1519,U_1518)
& U_1520 = U_1518 )
& in(U_1520,U_1542)
& ordered_pair(U_1520,U_1519) = U_1526 )
& U_1527 = U_1526 ) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ? [U_1527,U_1526,U_1525] :
( U_1526 != U_1525
& ? [U_1524] :
( ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& ordered_pair(U_1524,U_1523) = U_1525 )
& in(U_1524,U_1542) )
& U_1527 = U_1525
& ? [U_1520] :
( ? [U_1519] :
( ? [U_1518] :
( ! [U_1517] :
( in(ordered_pair(U_1519,U_1517),U_1541)
| ~ in(U_1517,U_1518) )
& in(U_1519,U_1518)
& U_1520 = U_1518 )
& ordered_pair(U_1520,U_1519) = U_1526 )
& in(U_1520,U_1542) )
& U_1527 = U_1526 )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(miniscope,[status(thm)],[f_430_2]) ).
fof(f_430_4,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ? [U_1526,U_1525] :
( U_1526 != U_1525
& ? [U_1524] :
( ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& ordered_pair(U_1524,U_1523) = U_1525 )
& in(U_1524,U_1542) )
& sK253(U_1542,U_1541) = U_1525
& ? [U_1520] :
( ? [U_1519] :
( ? [U_1518] :
( ! [U_1517] :
( in(ordered_pair(U_1519,U_1517),U_1541)
| ~ in(U_1517,U_1518) )
& in(U_1519,U_1518)
& U_1520 = U_1518 )
& ordered_pair(U_1520,U_1519) = U_1526 )
& in(U_1520,U_1542) )
& sK253(U_1542,U_1541) = U_1526 )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_1527,sK253(U_1542,U_1541))],[f_430_3]) ).
fof(f_430_5,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ? [U_1525] :
( sK254(U_1542,U_1541) != U_1525
& ? [U_1524] :
( ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& ordered_pair(U_1524,U_1523) = U_1525 )
& in(U_1524,U_1542) )
& sK253(U_1542,U_1541) = U_1525
& ? [U_1520] :
( ? [U_1519] :
( ? [U_1518] :
( ! [U_1517] :
( in(ordered_pair(U_1519,U_1517),U_1541)
| ~ in(U_1517,U_1518) )
& in(U_1519,U_1518)
& U_1520 = U_1518 )
& ordered_pair(U_1520,U_1519) = sK254(U_1542,U_1541) )
& in(U_1520,U_1542) )
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_1526,sK254(U_1542,U_1541))],[f_430_4]) ).
fof(f_430_6,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ? [U_1524] :
( ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& ordered_pair(U_1524,U_1523) = sK255(U_1542,U_1541) )
& in(U_1524,U_1542) )
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ? [U_1520] :
( ? [U_1519] :
( ? [U_1518] :
( ! [U_1517] :
( in(ordered_pair(U_1519,U_1517),U_1541)
| ~ in(U_1517,U_1518) )
& in(U_1519,U_1518)
& U_1520 = U_1518 )
& ordered_pair(U_1520,U_1519) = sK254(U_1542,U_1541) )
& in(U_1520,U_1542) )
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_1525,sK255(U_1542,U_1541))],[f_430_5]) ).
fof(f_430_7,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ? [U_1524] :
( ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& ordered_pair(U_1524,U_1523) = sK255(U_1542,U_1541) )
& in(U_1524,U_1542) )
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ? [U_1519] :
( ? [U_1518] :
( ! [U_1517] :
( in(ordered_pair(U_1519,U_1517),U_1541)
| ~ in(U_1517,U_1518) )
& in(U_1519,U_1518)
& sK256(U_1542,U_1541) = U_1518 )
& ordered_pair(sK256(U_1542,U_1541),U_1519) = sK254(U_1542,U_1541) )
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_1520,sK256(U_1542,U_1541))],[f_430_6]) ).
fof(f_430_8,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ? [U_1524] :
( ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& ordered_pair(U_1524,U_1523) = sK255(U_1542,U_1541) )
& in(U_1524,U_1542) )
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ? [U_1518] :
( ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,U_1518) )
& in(sK257(U_1542,U_1541),U_1518)
& sK256(U_1542,U_1541) = U_1518 )
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_1519,sK257(U_1542,U_1541))],[f_430_7]) ).
fof(f_430_9,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ? [U_1524] :
( ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& U_1524 = U_1522 )
& ordered_pair(U_1524,U_1523) = sK255(U_1542,U_1541) )
& in(U_1524,U_1542) )
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_1518,sK258(U_1542,U_1541))],[f_430_8]) ).
fof(f_430_10,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ? [U_1523] :
( ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(U_1523,U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(U_1523,U_1522)
& sK259(U_1542,U_1541) = U_1522 )
& ordered_pair(sK259(U_1542,U_1541),U_1523) = sK255(U_1542,U_1541) )
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_1524,sK259(U_1542,U_1541))],[f_430_9]) ).
fof(f_430_11,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ? [U_1522] :
( ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,U_1522) )
& in(sK260(U_1542,U_1541),U_1522)
& sK259(U_1542,U_1541) = U_1522 )
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_1523,sK260(U_1542,U_1541))],[f_430_10]) ).
fof(f_430_12,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
? [U_1539] :
( ! [U_1544] :
( in(U_1544,U_1539)
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,U_1539) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541)) )
& in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
& sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_1522,sK261(U_1542,U_1541))],[f_430_11]) ).
fof(f_430_13,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
( ! [U_1544] :
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1531] :
( ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& U_1531 = U_1529 )
& ordered_pair(U_1531,U_1530) = U_1543 )
& in(U_1531,U_1542) ) )
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540)) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541)) )
& in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
& sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_1539,sK262(U_1542,U_1541,U_1540))],[f_430_12]) ).
fof(f_430_14,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
( ! [U_1544] :
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1530] :
( ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(U_1530,U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(U_1530,U_1529)
& sK263(U_1542,U_1541,U_1540,U_1543) = U_1529 )
& ordered_pair(sK263(U_1542,U_1541,U_1540,U_1543),U_1530) = U_1543 )
& in(sK263(U_1542,U_1541,U_1540,U_1543),U_1542) )
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540)) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541)) )
& in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
& sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_1531,sK263(U_1542,U_1541,U_1540,U_1543))],[f_430_13]) ).
fof(f_430_15,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
( ! [U_1544] :
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ? [U_1529] :
( ! [U_1528] :
( in(ordered_pair(sK264(U_1542,U_1541,U_1540,U_1543),U_1528),U_1541)
| ~ in(U_1528,U_1529) )
& in(sK264(U_1542,U_1541,U_1540,U_1543),U_1529)
& sK263(U_1542,U_1541,U_1540,U_1543) = U_1529 )
& ordered_pair(sK263(U_1542,U_1541,U_1540,U_1543),sK264(U_1542,U_1541,U_1540,U_1543)) = U_1543
& in(sK263(U_1542,U_1541,U_1540,U_1543),U_1542) )
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540)) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541)) )
& in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
& sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_1530,sK264(U_1542,U_1541,U_1540,U_1543))],[f_430_14]) ).
fof(f_430_16,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
( ! [U_1544] :
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( ? [U_1532] :
( U_1532 = U_1543
& in(U_1532,cartesian_product2(U_1542,U_1540)) )
& ! [U_1528] :
( in(ordered_pair(sK264(U_1542,U_1541,U_1540,U_1543),U_1528),U_1541)
| ~ in(U_1528,sK265(U_1542,U_1541,U_1540,U_1543)) )
& in(sK264(U_1542,U_1541,U_1540,U_1543),sK265(U_1542,U_1541,U_1540,U_1543))
& sK263(U_1542,U_1541,U_1540,U_1543) = sK265(U_1542,U_1541,U_1540,U_1543)
& ordered_pair(sK263(U_1542,U_1541,U_1540,U_1543),sK264(U_1542,U_1541,U_1540,U_1543)) = U_1543
& in(sK263(U_1542,U_1541,U_1540,U_1543),U_1542) )
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540)) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541)) )
& in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
& sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_1529,sK265(U_1542,U_1541,U_1540,U_1543))],[f_430_15]) ).
fof(f_430_17,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
( ! [U_1544] :
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ? [U_1533] :
( ~ in(ordered_pair(U_1535,U_1533),U_1541)
& in(U_1533,U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( sK266(U_1542,U_1541,U_1540,U_1543) = U_1543
& in(sK266(U_1542,U_1541,U_1540,U_1543),cartesian_product2(U_1542,U_1540))
& ! [U_1528] :
( in(ordered_pair(sK264(U_1542,U_1541,U_1540,U_1543),U_1528),U_1541)
| ~ in(U_1528,sK265(U_1542,U_1541,U_1540,U_1543)) )
& in(sK264(U_1542,U_1541,U_1540,U_1543),sK265(U_1542,U_1541,U_1540,U_1543))
& sK263(U_1542,U_1541,U_1540,U_1543) = sK265(U_1542,U_1541,U_1540,U_1543)
& ordered_pair(sK263(U_1542,U_1541,U_1540,U_1543),sK264(U_1542,U_1541,U_1540,U_1543)) = U_1543
& in(sK263(U_1542,U_1541,U_1540,U_1543),U_1542) )
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540)) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541)) )
& in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
& sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_1532,sK266(U_1542,U_1541,U_1540,U_1543))],[f_430_16]) ).
fof(f_430_18,plain,
! [U_1542,U_1541] :
( ! [U_1540] :
( ! [U_1544] :
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| ! [U_1537] :
( U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540)) )
| ! [U_1536] :
( ! [U_1535] :
( ! [U_1534] :
( ( ~ in(ordered_pair(U_1535,sK267(U_1542,U_1541,U_1540,U_1544,U_1536,U_1535,U_1534)),U_1541)
& in(sK267(U_1542,U_1541,U_1540,U_1544,U_1536,U_1535,U_1534),U_1534) )
| ~ in(U_1535,U_1534)
| U_1536 != U_1534 )
| ordered_pair(U_1536,U_1535) != U_1544 )
| ~ in(U_1536,U_1542) ) )
& ! [U_1543] :
( ( sK266(U_1542,U_1541,U_1540,U_1543) = U_1543
& in(sK266(U_1542,U_1541,U_1540,U_1543),cartesian_product2(U_1542,U_1540))
& ! [U_1528] :
( in(ordered_pair(sK264(U_1542,U_1541,U_1540,U_1543),U_1528),U_1541)
| ~ in(U_1528,sK265(U_1542,U_1541,U_1540,U_1543)) )
& in(sK264(U_1542,U_1541,U_1540,U_1543),sK265(U_1542,U_1541,U_1540,U_1543))
& sK263(U_1542,U_1541,U_1540,U_1543) = sK265(U_1542,U_1541,U_1540,U_1543)
& ordered_pair(sK263(U_1542,U_1541,U_1540,U_1543),sK264(U_1542,U_1541,U_1540,U_1543)) = U_1543
& in(sK263(U_1542,U_1541,U_1540,U_1543),U_1542) )
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540)) ) )
| ( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
& ! [U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541)) )
& in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
& sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
& ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
& in(sK259(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
& ! [U_1517] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541)) )
& in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
& sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
& ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
& in(sK256(U_1542,U_1541),U_1542)
& sK253(U_1542,U_1541) = sK254(U_1542,U_1541) )
| ~ relation(U_1541)
| empty(U_1542) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_1533,sK267(U_1542,U_1541,U_1540,U_1544,U_1536,U_1535,U_1534))],[f_430_17]) ).
fof(f_430_19,plain,
( ! [U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544] :
( ~ in(ordered_pair(U_1535,sK267(U_1542,U_1541,U_1540,U_1544,U_1536,U_1535,U_1534)),U_1541)
| ~ sP363(U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544) )
& ! [U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544] :
( in(sK267(U_1542,U_1541,U_1540,U_1544,U_1536,U_1535,U_1534),U_1534)
| ~ sP363(U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544) )
& ! [U_1528,U_1541,U_1540,U_1543,U_1542] :
( sK266(U_1542,U_1541,U_1540,U_1543) = U_1543
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) )
& ! [U_1528,U_1541,U_1540,U_1543,U_1542] :
( in(sK266(U_1542,U_1541,U_1540,U_1543),cartesian_product2(U_1542,U_1540))
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) )
& ! [U_1528,U_1541,U_1540,U_1543,U_1542] :
( in(ordered_pair(sK264(U_1542,U_1541,U_1540,U_1543),U_1528),U_1541)
| ~ in(U_1528,sK265(U_1542,U_1541,U_1540,U_1543))
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) )
& ! [U_1528,U_1541,U_1540,U_1543,U_1542] :
( in(sK264(U_1542,U_1541,U_1540,U_1543),sK265(U_1542,U_1541,U_1540,U_1543))
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) )
& ! [U_1528,U_1541,U_1540,U_1543,U_1542] :
( sK263(U_1542,U_1541,U_1540,U_1543) = sK265(U_1542,U_1541,U_1540,U_1543)
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) )
& ! [U_1528,U_1541,U_1540,U_1543,U_1542] :
( ordered_pair(sK263(U_1542,U_1541,U_1540,U_1543),sK264(U_1542,U_1541,U_1540,U_1543)) = U_1543
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) )
& ! [U_1528,U_1541,U_1540,U_1543,U_1542] :
( in(sK263(U_1542,U_1541,U_1540,U_1543),U_1542)
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) )
& ! [U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544] :
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540))
| sP363(U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544)
| ~ in(U_1535,U_1534)
| U_1536 != U_1534
| ordered_pair(U_1536,U_1535) != U_1544
| ~ in(U_1536,U_1542)
| ~ sP364(U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544) )
& ! [U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544] :
( sP362(U_1528,U_1541,U_1540,U_1543,U_1542)
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540))
| ~ sP364(U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( in(sK259(U_1542,U_1541),U_1542)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( in(sK256(U_1542,U_1541),U_1542)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1541,U_1517,U_1542,U_1521] :
( sK253(U_1542,U_1541) = sK254(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) )
& ! [U_1528,U_1535,U_1537,U_1541,U_1517,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544,U_1521] :
( sP364(U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544)
| sP361(U_1541,U_1517,U_1542,U_1521)
| ~ relation(U_1541)
| empty(U_1542) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP361,sP362,sP363,sP364])],[f_430_18]) ).
cnf(f_430_20,plain,
( sP364(U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544)
| sP361(U_1541,U_1517,U_1542,U_1521)
| ~ relation(U_1541)
| empty(U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_21,plain,
( sK253(U_1542,U_1541) = sK254(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_22,plain,
( in(sK256(U_1542,U_1541),U_1542)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_23,plain,
( ordered_pair(sK256(U_1542,U_1541),sK257(U_1542,U_1541)) = sK254(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_24,plain,
( sK256(U_1542,U_1541) = sK258(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_25,plain,
( in(sK257(U_1542,U_1541),sK258(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_26,plain,
( in(ordered_pair(sK257(U_1542,U_1541),U_1517),U_1541)
| ~ in(U_1517,sK258(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_27,plain,
( sK253(U_1542,U_1541) = sK255(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_28,plain,
( in(sK259(U_1542,U_1541),U_1542)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_29,plain,
( ordered_pair(sK259(U_1542,U_1541),sK260(U_1542,U_1541)) = sK255(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_30,plain,
( sK259(U_1542,U_1541) = sK261(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_31,plain,
( in(sK260(U_1542,U_1541),sK261(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_32,plain,
( in(ordered_pair(sK260(U_1542,U_1541),U_1521),U_1541)
| ~ in(U_1521,sK261(U_1542,U_1541))
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_33,plain,
( sK254(U_1542,U_1541) != sK255(U_1542,U_1541)
| ~ sP361(U_1541,U_1517,U_1542,U_1521) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_34,plain,
( sP362(U_1528,U_1541,U_1540,U_1543,U_1542)
| ~ in(U_1543,sK262(U_1542,U_1541,U_1540))
| ~ sP364(U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_35,plain,
( in(U_1544,sK262(U_1542,U_1541,U_1540))
| U_1537 != U_1544
| ~ in(U_1537,cartesian_product2(U_1542,U_1540))
| sP363(U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544)
| ~ in(U_1535,U_1534)
| U_1536 != U_1534
| ordered_pair(U_1536,U_1535) != U_1544
| ~ in(U_1536,U_1542)
| ~ sP364(U_1528,U_1535,U_1537,U_1541,U_1540,U_1543,U_1534,U_1542,U_1536,U_1544) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_36,plain,
( in(sK263(U_1542,U_1541,U_1540,U_1543),U_1542)
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_37,plain,
( ordered_pair(sK263(U_1542,U_1541,U_1540,U_1543),sK264(U_1542,U_1541,U_1540,U_1543)) = U_1543
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_38,plain,
( sK263(U_1542,U_1541,U_1540,U_1543) = sK265(U_1542,U_1541,U_1540,U_1543)
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_39,plain,
( in(sK264(U_1542,U_1541,U_1540,U_1543),sK265(U_1542,U_1541,U_1540,U_1543))
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_40,plain,
( in(ordered_pair(sK264(U_1542,U_1541,U_1540,U_1543),U_1528),U_1541)
| ~ in(U_1528,sK265(U_1542,U_1541,U_1540,U_1543))
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_41,plain,
( in(sK266(U_1542,U_1541,U_1540,U_1543),cartesian_product2(U_1542,U_1540))
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_42,plain,
( sK266(U_1542,U_1541,U_1540,U_1543) = U_1543
| ~ sP362(U_1528,U_1541,U_1540,U_1543,U_1542) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_43,plain,
( in(sK267(U_1542,U_1541,U_1540,U_1544,U_1536,U_1535,U_1534),U_1534)
| ~ sP363(U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544) ),
inference(clausify,[status(thm)],[f_430_19]) ).
cnf(f_430_44,plain,
( ~ in(ordered_pair(U_1535,sK267(U_1542,U_1541,U_1540,U_1544,U_1536,U_1535,U_1534)),U_1541)
| ~ sP363(U_1535,U_1541,U_1540,U_1534,U_1542,U_1536,U_1544) ),
inference(clausify,[status(thm)],[f_430_19]) ).
fof(f_431_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_431_2,plain,
! [U_1552] :
( ? [U_1551] :
! [U_1550] :
( ( in(U_1550,U_1551)
| ! [U_1549] :
( U_1550 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552) ) )
& ( ? [U_1548] :
( U_1550 = singleton(U_1548)
& in(U_1548,U_1552)
& in(U_1548,U_1552) )
| ~ in(U_1550,U_1551) ) )
| ? [U_1547,U_1546,U_1545] :
( U_1546 != U_1545
& U_1545 = singleton(U_1547)
& in(U_1547,U_1552)
& U_1546 = singleton(U_1547)
& in(U_1547,U_1552) ) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
! [U_1552] :
( ? [U_1551] :
( ! [U_1554] :
( in(U_1554,U_1551)
| ! [U_1549] :
( U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552) ) )
& ! [U_1553] :
( ? [U_1548] :
( U_1553 = singleton(U_1548)
& in(U_1548,U_1552)
& in(U_1548,U_1552) )
| ~ in(U_1553,U_1551) ) )
| ? [U_1547,U_1546,U_1545] :
( U_1546 != U_1545
& U_1545 = singleton(U_1547)
& in(U_1547,U_1552)
& U_1546 = singleton(U_1547)
& in(U_1547,U_1552) ) ),
inference(miniscope,[status(thm)],[f_431_2]) ).
fof(f_431_4,plain,
! [U_1552] :
( ? [U_1551] :
( ! [U_1554] :
( in(U_1554,U_1551)
| ! [U_1549] :
( U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552) ) )
& ! [U_1553] :
( ? [U_1548] :
( U_1553 = singleton(U_1548)
& in(U_1548,U_1552)
& in(U_1548,U_1552) )
| ~ in(U_1553,U_1551) ) )
| ? [U_1546,U_1545] :
( U_1546 != U_1545
& U_1545 = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552)
& U_1546 = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_1547,sK268(U_1552))],[f_431_3]) ).
fof(f_431_5,plain,
! [U_1552] :
( ? [U_1551] :
( ! [U_1554] :
( in(U_1554,U_1551)
| ! [U_1549] :
( U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552) ) )
& ! [U_1553] :
( ? [U_1548] :
( U_1553 = singleton(U_1548)
& in(U_1548,U_1552)
& in(U_1548,U_1552) )
| ~ in(U_1553,U_1551) ) )
| ? [U_1545] :
( sK269(U_1552) != U_1545
& U_1545 = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552)
& sK269(U_1552) = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_1546,sK269(U_1552))],[f_431_4]) ).
fof(f_431_6,plain,
! [U_1552] :
( ? [U_1551] :
( ! [U_1554] :
( in(U_1554,U_1551)
| ! [U_1549] :
( U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552) ) )
& ! [U_1553] :
( ? [U_1548] :
( U_1553 = singleton(U_1548)
& in(U_1548,U_1552)
& in(U_1548,U_1552) )
| ~ in(U_1553,U_1551) ) )
| ( sK269(U_1552) != sK270(U_1552)
& sK270(U_1552) = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552)
& sK269(U_1552) = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_1545,sK270(U_1552))],[f_431_5]) ).
fof(f_431_7,plain,
! [U_1552] :
( ( ! [U_1554] :
( in(U_1554,sK271(U_1552))
| ! [U_1549] :
( U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552) ) )
& ! [U_1553] :
( ? [U_1548] :
( U_1553 = singleton(U_1548)
& in(U_1548,U_1552)
& in(U_1548,U_1552) )
| ~ in(U_1553,sK271(U_1552)) ) )
| ( sK269(U_1552) != sK270(U_1552)
& sK270(U_1552) = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552)
& sK269(U_1552) = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_1551,sK271(U_1552))],[f_431_6]) ).
fof(f_431_8,plain,
! [U_1552] :
( ( ! [U_1554] :
( in(U_1554,sK271(U_1552))
| ! [U_1549] :
( U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552) ) )
& ! [U_1553] :
( ( U_1553 = singleton(sK272(U_1552,U_1553))
& in(sK272(U_1552,U_1553),U_1552)
& in(sK272(U_1552,U_1553),U_1552) )
| ~ in(U_1553,sK271(U_1552)) ) )
| ( sK269(U_1552) != sK270(U_1552)
& sK270(U_1552) = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552)
& sK269(U_1552) = singleton(sK268(U_1552))
& in(sK268(U_1552),U_1552) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_1548,sK272(U_1552,U_1553))],[f_431_7]) ).
fof(f_431_9,plain,
( ! [U_1552,U_1553] :
( U_1553 = singleton(sK272(U_1552,U_1553))
| ~ sP366(U_1552,U_1553) )
& ! [U_1552,U_1553] :
( in(sK272(U_1552,U_1553),U_1552)
| ~ sP366(U_1552,U_1553) )
& ! [U_1552,U_1553] :
( in(sK272(U_1552,U_1553),U_1552)
| ~ sP366(U_1552,U_1553) )
& ! [U_1549,U_1554,U_1552,U_1553] :
( in(U_1554,sK271(U_1552))
| U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552)
| ~ sP367(U_1549,U_1554,U_1552,U_1553) )
& ! [U_1549,U_1554,U_1552,U_1553] :
( sP366(U_1552,U_1553)
| ~ in(U_1553,sK271(U_1552))
| ~ sP367(U_1549,U_1554,U_1552,U_1553) )
& ! [U_1552] :
( sK269(U_1552) != sK270(U_1552)
| ~ sP365(U_1552) )
& ! [U_1552] :
( sK270(U_1552) = singleton(sK268(U_1552))
| ~ sP365(U_1552) )
& ! [U_1552] :
( in(sK268(U_1552),U_1552)
| ~ sP365(U_1552) )
& ! [U_1552] :
( sK269(U_1552) = singleton(sK268(U_1552))
| ~ sP365(U_1552) )
& ! [U_1552] :
( in(sK268(U_1552),U_1552)
| ~ sP365(U_1552) )
& ! [U_1549,U_1554,U_1552,U_1553] :
( sP367(U_1549,U_1554,U_1552,U_1553)
| sP365(U_1552) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP365,sP366,sP367])],[f_431_8]) ).
cnf(f_431_10,plain,
( sP367(U_1549,U_1554,U_1552,U_1553)
| sP365(U_1552) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_11,plain,
( in(sK268(U_1552),U_1552)
| ~ sP365(U_1552) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_12,plain,
( sK269(U_1552) = singleton(sK268(U_1552))
| ~ sP365(U_1552) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_13,plain,
( in(sK268(U_1552),U_1552)
| ~ sP365(U_1552) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_14,plain,
( sK270(U_1552) = singleton(sK268(U_1552))
| ~ sP365(U_1552) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_15,plain,
( sK269(U_1552) != sK270(U_1552)
| ~ sP365(U_1552) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_16,plain,
( sP366(U_1552,U_1553)
| ~ in(U_1553,sK271(U_1552))
| ~ sP367(U_1549,U_1554,U_1552,U_1553) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_17,plain,
( in(U_1554,sK271(U_1552))
| U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ in(U_1549,U_1552)
| ~ sP367(U_1549,U_1554,U_1552,U_1553) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_18,plain,
( in(sK272(U_1552,U_1553),U_1552)
| ~ sP366(U_1552,U_1553) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_19,plain,
( in(sK272(U_1552,U_1553),U_1552)
| ~ sP366(U_1552,U_1553) ),
inference(clausify,[status(thm)],[f_431_9]) ).
cnf(f_431_20,plain,
( U_1553 = singleton(sK272(U_1552,U_1553))
| ~ sP366(U_1552,U_1553) ),
inference(clausify,[status(thm)],[f_431_9]) ).
fof(f_432_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_432_2,plain,
! [U_1571,U_1570] :
( ? [U_1569] :
! [U_1568] :
( ( in(U_1568,U_1569)
| ! [U_1567] :
( ! [U_1566,U_1565] :
( U_1565 != singleton(U_1566)
| ~ in(U_1566,U_1571)
| ordered_pair(U_1566,U_1565) != U_1568 )
| U_1567 != U_1568
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) ) )
& ( ? [U_1564] :
( ? [U_1563,U_1562] :
( U_1562 = singleton(U_1563)
& in(U_1563,U_1571)
& ordered_pair(U_1563,U_1562) = U_1568 )
& U_1564 = U_1568
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
| ~ in(U_1568,U_1569) ) )
| ? [U_1561,U_1560,U_1559] :
( U_1560 != U_1559
& ? [U_1558,U_1557] :
( U_1557 = singleton(U_1558)
& in(U_1558,U_1571)
& ordered_pair(U_1558,U_1557) = U_1559 )
& U_1561 = U_1559
& ? [U_1556,U_1555] :
( U_1555 = singleton(U_1556)
& in(U_1556,U_1571)
& ordered_pair(U_1556,U_1555) = U_1560 )
& U_1561 = U_1560 ) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ? [U_1561,U_1560,U_1559] :
( U_1560 != U_1559
& ? [U_1558] :
( ? [U_1557] :
( U_1557 = singleton(U_1558)
& ordered_pair(U_1558,U_1557) = U_1559 )
& in(U_1558,U_1571) )
& U_1561 = U_1559
& ? [U_1556] :
( ? [U_1555] :
( U_1555 = singleton(U_1556)
& ordered_pair(U_1556,U_1555) = U_1560 )
& in(U_1556,U_1571) )
& U_1561 = U_1560 ) ),
inference(miniscope,[status(thm)],[f_432_2]) ).
fof(f_432_4,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ? [U_1560,U_1559] :
( U_1560 != U_1559
& ? [U_1558] :
( ? [U_1557] :
( U_1557 = singleton(U_1558)
& ordered_pair(U_1558,U_1557) = U_1559 )
& in(U_1558,U_1571) )
& sK273(U_1571) = U_1559
& ? [U_1556] :
( ? [U_1555] :
( U_1555 = singleton(U_1556)
& ordered_pair(U_1556,U_1555) = U_1560 )
& in(U_1556,U_1571) )
& sK273(U_1571) = U_1560 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_1561,sK273(U_1571))],[f_432_3]) ).
fof(f_432_5,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ? [U_1559] :
( sK274(U_1571) != U_1559
& ? [U_1558] :
( ? [U_1557] :
( U_1557 = singleton(U_1558)
& ordered_pair(U_1558,U_1557) = U_1559 )
& in(U_1558,U_1571) )
& sK273(U_1571) = U_1559
& ? [U_1556] :
( ? [U_1555] :
( U_1555 = singleton(U_1556)
& ordered_pair(U_1556,U_1555) = sK274(U_1571) )
& in(U_1556,U_1571) )
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_1560,sK274(U_1571))],[f_432_4]) ).
fof(f_432_6,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ( sK274(U_1571) != sK275(U_1571)
& ? [U_1558] :
( ? [U_1557] :
( U_1557 = singleton(U_1558)
& ordered_pair(U_1558,U_1557) = sK275(U_1571) )
& in(U_1558,U_1571) )
& sK273(U_1571) = sK275(U_1571)
& ? [U_1556] :
( ? [U_1555] :
( U_1555 = singleton(U_1556)
& ordered_pair(U_1556,U_1555) = sK274(U_1571) )
& in(U_1556,U_1571) )
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_1559,sK275(U_1571))],[f_432_5]) ).
fof(f_432_7,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ( sK274(U_1571) != sK275(U_1571)
& ? [U_1558] :
( ? [U_1557] :
( U_1557 = singleton(U_1558)
& ordered_pair(U_1558,U_1557) = sK275(U_1571) )
& in(U_1558,U_1571) )
& sK273(U_1571) = sK275(U_1571)
& ? [U_1555] :
( U_1555 = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),U_1555) = sK274(U_1571) )
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_1556,sK276(U_1571))],[f_432_6]) ).
fof(f_432_8,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ( sK274(U_1571) != sK275(U_1571)
& ? [U_1558] :
( ? [U_1557] :
( U_1557 = singleton(U_1558)
& ordered_pair(U_1558,U_1557) = sK275(U_1571) )
& in(U_1558,U_1571) )
& sK273(U_1571) = sK275(U_1571)
& sK277(U_1571) = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_1555,sK277(U_1571))],[f_432_7]) ).
fof(f_432_9,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ( sK274(U_1571) != sK275(U_1571)
& ? [U_1557] :
( U_1557 = singleton(sK278(U_1571))
& ordered_pair(sK278(U_1571),U_1557) = sK275(U_1571) )
& in(sK278(U_1571),U_1571)
& sK273(U_1571) = sK275(U_1571)
& sK277(U_1571) = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_1558,sK278(U_1571))],[f_432_8]) ).
fof(f_432_10,plain,
! [U_1571] :
( ! [U_1570] :
? [U_1569] :
( ! [U_1573] :
( in(U_1573,U_1569)
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,U_1569) ) )
| ( sK274(U_1571) != sK275(U_1571)
& sK279(U_1571) = singleton(sK278(U_1571))
& ordered_pair(sK278(U_1571),sK279(U_1571)) = sK275(U_1571)
& in(sK278(U_1571),U_1571)
& sK273(U_1571) = sK275(U_1571)
& sK277(U_1571) = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_1557,sK279(U_1571))],[f_432_9]) ).
fof(f_432_11,plain,
! [U_1571] :
( ! [U_1570] :
( ! [U_1573] :
( in(U_1573,sK280(U_1571,U_1570))
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1563] :
( ? [U_1562] :
( U_1562 = singleton(U_1563)
& ordered_pair(U_1563,U_1562) = U_1572 )
& in(U_1563,U_1571) ) )
| ~ in(U_1572,sK280(U_1571,U_1570)) ) )
| ( sK274(U_1571) != sK275(U_1571)
& sK279(U_1571) = singleton(sK278(U_1571))
& ordered_pair(sK278(U_1571),sK279(U_1571)) = sK275(U_1571)
& in(sK278(U_1571),U_1571)
& sK273(U_1571) = sK275(U_1571)
& sK277(U_1571) = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_1569,sK280(U_1571,U_1570))],[f_432_10]) ).
fof(f_432_12,plain,
! [U_1571] :
( ! [U_1570] :
( ! [U_1573] :
( in(U_1573,sK280(U_1571,U_1570))
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& ? [U_1562] :
( U_1562 = singleton(sK281(U_1571,U_1570,U_1572))
& ordered_pair(sK281(U_1571,U_1570,U_1572),U_1562) = U_1572 )
& in(sK281(U_1571,U_1570,U_1572),U_1571) )
| ~ in(U_1572,sK280(U_1571,U_1570)) ) )
| ( sK274(U_1571) != sK275(U_1571)
& sK279(U_1571) = singleton(sK278(U_1571))
& ordered_pair(sK278(U_1571),sK279(U_1571)) = sK275(U_1571)
& in(sK278(U_1571),U_1571)
& sK273(U_1571) = sK275(U_1571)
& sK277(U_1571) = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_1563,sK281(U_1571,U_1570,U_1572))],[f_432_11]) ).
fof(f_432_13,plain,
! [U_1571] :
( ! [U_1570] :
( ! [U_1573] :
( in(U_1573,sK280(U_1571,U_1570))
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( ? [U_1564] :
( U_1564 = U_1572
& in(U_1564,cartesian_product2(U_1571,U_1570)) )
& sK282(U_1571,U_1570,U_1572) = singleton(sK281(U_1571,U_1570,U_1572))
& ordered_pair(sK281(U_1571,U_1570,U_1572),sK282(U_1571,U_1570,U_1572)) = U_1572
& in(sK281(U_1571,U_1570,U_1572),U_1571) )
| ~ in(U_1572,sK280(U_1571,U_1570)) ) )
| ( sK274(U_1571) != sK275(U_1571)
& sK279(U_1571) = singleton(sK278(U_1571))
& ordered_pair(sK278(U_1571),sK279(U_1571)) = sK275(U_1571)
& in(sK278(U_1571),U_1571)
& sK273(U_1571) = sK275(U_1571)
& sK277(U_1571) = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_1562,sK282(U_1571,U_1570,U_1572))],[f_432_12]) ).
fof(f_432_14,plain,
! [U_1571] :
( ! [U_1570] :
( ! [U_1573] :
( in(U_1573,sK280(U_1571,U_1570))
| ! [U_1567] :
( U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570)) )
| ! [U_1566] :
( ! [U_1565] :
( U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573 )
| ~ in(U_1566,U_1571) ) )
& ! [U_1572] :
( ( sK283(U_1571,U_1570,U_1572) = U_1572
& in(sK283(U_1571,U_1570,U_1572),cartesian_product2(U_1571,U_1570))
& sK282(U_1571,U_1570,U_1572) = singleton(sK281(U_1571,U_1570,U_1572))
& ordered_pair(sK281(U_1571,U_1570,U_1572),sK282(U_1571,U_1570,U_1572)) = U_1572
& in(sK281(U_1571,U_1570,U_1572),U_1571) )
| ~ in(U_1572,sK280(U_1571,U_1570)) ) )
| ( sK274(U_1571) != sK275(U_1571)
& sK279(U_1571) = singleton(sK278(U_1571))
& ordered_pair(sK278(U_1571),sK279(U_1571)) = sK275(U_1571)
& in(sK278(U_1571),U_1571)
& sK273(U_1571) = sK275(U_1571)
& sK277(U_1571) = singleton(sK276(U_1571))
& ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
& in(sK276(U_1571),U_1571)
& sK273(U_1571) = sK274(U_1571) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_1564,sK283(U_1571,U_1570,U_1572))],[f_432_13]) ).
fof(f_432_15,plain,
( ! [U_1570,U_1572,U_1571] :
( sK283(U_1571,U_1570,U_1572) = U_1572
| ~ sP369(U_1570,U_1572,U_1571) )
& ! [U_1570,U_1572,U_1571] :
( in(sK283(U_1571,U_1570,U_1572),cartesian_product2(U_1571,U_1570))
| ~ sP369(U_1570,U_1572,U_1571) )
& ! [U_1570,U_1572,U_1571] :
( sK282(U_1571,U_1570,U_1572) = singleton(sK281(U_1571,U_1570,U_1572))
| ~ sP369(U_1570,U_1572,U_1571) )
& ! [U_1570,U_1572,U_1571] :
( ordered_pair(sK281(U_1571,U_1570,U_1572),sK282(U_1571,U_1570,U_1572)) = U_1572
| ~ sP369(U_1570,U_1572,U_1571) )
& ! [U_1570,U_1572,U_1571] :
( in(sK281(U_1571,U_1570,U_1572),U_1571)
| ~ sP369(U_1570,U_1572,U_1571) )
& ! [U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571] :
( in(U_1573,sK280(U_1571,U_1570))
| U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570))
| U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573
| ~ in(U_1566,U_1571)
| ~ sP370(U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571) )
& ! [U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571] :
( sP369(U_1570,U_1572,U_1571)
| ~ in(U_1572,sK280(U_1571,U_1570))
| ~ sP370(U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571) )
& ! [U_1571] :
( sK274(U_1571) != sK275(U_1571)
| ~ sP368(U_1571) )
& ! [U_1571] :
( sK279(U_1571) = singleton(sK278(U_1571))
| ~ sP368(U_1571) )
& ! [U_1571] :
( ordered_pair(sK278(U_1571),sK279(U_1571)) = sK275(U_1571)
| ~ sP368(U_1571) )
& ! [U_1571] :
( in(sK278(U_1571),U_1571)
| ~ sP368(U_1571) )
& ! [U_1571] :
( sK273(U_1571) = sK275(U_1571)
| ~ sP368(U_1571) )
& ! [U_1571] :
( sK277(U_1571) = singleton(sK276(U_1571))
| ~ sP368(U_1571) )
& ! [U_1571] :
( ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
| ~ sP368(U_1571) )
& ! [U_1571] :
( in(sK276(U_1571),U_1571)
| ~ sP368(U_1571) )
& ! [U_1571] :
( sK273(U_1571) = sK274(U_1571)
| ~ sP368(U_1571) )
& ! [U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571] :
( sP370(U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571)
| sP368(U_1571) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP368,sP369,sP370])],[f_432_14]) ).
cnf(f_432_16,plain,
( sP370(U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571)
| sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_17,plain,
( sK273(U_1571) = sK274(U_1571)
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_18,plain,
( in(sK276(U_1571),U_1571)
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_19,plain,
( ordered_pair(sK276(U_1571),sK277(U_1571)) = sK274(U_1571)
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_20,plain,
( sK277(U_1571) = singleton(sK276(U_1571))
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_21,plain,
( sK273(U_1571) = sK275(U_1571)
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_22,plain,
( in(sK278(U_1571),U_1571)
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_23,plain,
( ordered_pair(sK278(U_1571),sK279(U_1571)) = sK275(U_1571)
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_24,plain,
( sK279(U_1571) = singleton(sK278(U_1571))
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_25,plain,
( sK274(U_1571) != sK275(U_1571)
| ~ sP368(U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_26,plain,
( sP369(U_1570,U_1572,U_1571)
| ~ in(U_1572,sK280(U_1571,U_1570))
| ~ sP370(U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_27,plain,
( in(U_1573,sK280(U_1571,U_1570))
| U_1567 != U_1573
| ~ in(U_1567,cartesian_product2(U_1571,U_1570))
| U_1565 != singleton(U_1566)
| ordered_pair(U_1566,U_1565) != U_1573
| ~ in(U_1566,U_1571)
| ~ sP370(U_1570,U_1572,U_1573,U_1567,U_1566,U_1565,U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_28,plain,
( in(sK281(U_1571,U_1570,U_1572),U_1571)
| ~ sP369(U_1570,U_1572,U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_29,plain,
( ordered_pair(sK281(U_1571,U_1570,U_1572),sK282(U_1571,U_1570,U_1572)) = U_1572
| ~ sP369(U_1570,U_1572,U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_30,plain,
( sK282(U_1571,U_1570,U_1572) = singleton(sK281(U_1571,U_1570,U_1572))
| ~ sP369(U_1570,U_1572,U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_31,plain,
( in(sK283(U_1571,U_1570,U_1572),cartesian_product2(U_1571,U_1570))
| ~ sP369(U_1570,U_1572,U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
cnf(f_432_32,plain,
( sK283(U_1571,U_1570,U_1572) = U_1572
| ~ sP369(U_1570,U_1572,U_1571) ),
inference(clausify,[status(thm)],[f_432_15]) ).
fof(f_433_1,plain,
! [A] :
( ? [B] :
! [C] :
( ( in(C,B)
| ! [D] :
( ! [M] :
( ( ? [N] :
( ! [O] :
( ? [P] :
( P != O
& subset(O,P)
& in(P,N) )
| ~ in(O,N) )
& N != empty_set
& element(N,powerset(powerset(M))) )
& in(M,omega) )
| C != M
| ~ ordinal(M) )
| D != C
| ~ in(D,succ(A)) ) )
& ( ? [D] :
( ? [M] :
( ( ! [N] :
( ? [O] :
( ! [P] :
( P = O
| ~ subset(O,P)
| ~ in(P,N) )
& in(O,N) )
| N = empty_set
| ~ element(N,powerset(powerset(M))) )
| ~ in(M,omega) )
& C = M
& ordinal(M) )
& D = C
& in(D,succ(A)) )
| ~ in(C,B) ) )
| ? [B,C,D] :
( C != D
& ? [I] :
( ( ! [J] :
( ? [K] :
( ! [L] :
( L = K
| ~ subset(K,L)
| ~ in(L,J) )
& in(K,J) )
| J = empty_set
| ~ element(J,powerset(powerset(I))) )
| ~ in(I,omega) )
& D = I
& ordinal(I) )
& B = D
& ? [E] :
( ( ! [F] :
( ? [G] :
( ! [H] :
( H = G
| ~ subset(G,H)
| ~ in(H,F) )
& in(G,F) )
| F = empty_set
| ~ element(F,powerset(powerset(E))) )
| ~ in(E,omega) )
& C = E
& ordinal(E) )
& B = C )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e18_27__finset_1__1]) ).
fof(f_433_2,plain,
! [U_1597] :
( ? [U_1596] :
! [U_1595] :
( ( in(U_1595,U_1596)
| ! [U_1594] :
( ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1595 != U_1593
| ~ ordinal(U_1593) )
| U_1594 != U_1595
| ~ in(U_1594,succ(U_1597)) ) )
& ( ? [U_1589] :
( ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1595 = U_1588
& ordinal(U_1588) )
& U_1589 = U_1595
& in(U_1589,succ(U_1597)) )
| ~ in(U_1595,U_1596) ) )
| ? [U_1584,U_1583,U_1582] :
( U_1583 != U_1582
& ? [U_1581] :
( ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(U_1581))) )
| ~ in(U_1581,omega) )
& U_1582 = U_1581
& ordinal(U_1581) )
& U_1584 = U_1582
& ? [U_1577] :
( ( ! [U_1576] :
( ? [U_1575] :
( ! [U_1574] :
( U_1574 = U_1575
| ~ subset(U_1575,U_1574)
| ~ in(U_1574,U_1576) )
& in(U_1575,U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(U_1577))) )
| ~ in(U_1577,omega) )
& U_1583 = U_1577
& ordinal(U_1577) )
& U_1584 = U_1583 )
| ~ ordinal(U_1597) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ? [U_1584,U_1583,U_1582] :
( U_1583 != U_1582
& ? [U_1581] :
( ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(U_1581))) )
| ~ in(U_1581,omega) )
& U_1582 = U_1581
& ordinal(U_1581) )
& U_1584 = U_1582
& ? [U_1577] :
( ( ! [U_1576] :
( ? [U_1575] :
( ! [U_1574] :
( U_1574 = U_1575
| ~ subset(U_1575,U_1574)
| ~ in(U_1574,U_1576) )
& in(U_1575,U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(U_1577))) )
| ~ in(U_1577,omega) )
& U_1583 = U_1577
& ordinal(U_1577) )
& U_1584 = U_1583 )
| ~ ordinal(U_1597) ),
inference(miniscope,[status(thm)],[f_433_2]) ).
fof(f_433_4,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ? [U_1583,U_1582] :
( U_1583 != U_1582
& ? [U_1581] :
( ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(U_1581))) )
| ~ in(U_1581,omega) )
& U_1582 = U_1581
& ordinal(U_1581) )
& sK284(U_1597) = U_1582
& ? [U_1577] :
( ( ! [U_1576] :
( ? [U_1575] :
( ! [U_1574] :
( U_1574 = U_1575
| ~ subset(U_1575,U_1574)
| ~ in(U_1574,U_1576) )
& in(U_1575,U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(U_1577))) )
| ~ in(U_1577,omega) )
& U_1583 = U_1577
& ordinal(U_1577) )
& sK284(U_1597) = U_1583 )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_1584,sK284(U_1597))],[f_433_3]) ).
fof(f_433_5,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ? [U_1582] :
( sK285(U_1597) != U_1582
& ? [U_1581] :
( ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(U_1581))) )
| ~ in(U_1581,omega) )
& U_1582 = U_1581
& ordinal(U_1581) )
& sK284(U_1597) = U_1582
& ? [U_1577] :
( ( ! [U_1576] :
( ? [U_1575] :
( ! [U_1574] :
( U_1574 = U_1575
| ~ subset(U_1575,U_1574)
| ~ in(U_1574,U_1576) )
& in(U_1575,U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(U_1577))) )
| ~ in(U_1577,omega) )
& sK285(U_1597) = U_1577
& ordinal(U_1577) )
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_1583,sK285(U_1597))],[f_433_4]) ).
fof(f_433_6,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ? [U_1581] :
( ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(U_1581))) )
| ~ in(U_1581,omega) )
& sK286(U_1597) = U_1581
& ordinal(U_1581) )
& sK284(U_1597) = sK286(U_1597)
& ? [U_1577] :
( ( ! [U_1576] :
( ? [U_1575] :
( ! [U_1574] :
( U_1574 = U_1575
| ~ subset(U_1575,U_1574)
| ~ in(U_1574,U_1576) )
& in(U_1575,U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(U_1577))) )
| ~ in(U_1577,omega) )
& sK285(U_1597) = U_1577
& ordinal(U_1577) )
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_1582,sK286(U_1597))],[f_433_5]) ).
fof(f_433_7,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ? [U_1581] :
( ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(U_1581))) )
| ~ in(U_1581,omega) )
& sK286(U_1597) = U_1581
& ordinal(U_1581) )
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ? [U_1575] :
( ! [U_1574] :
( U_1574 = U_1575
| ~ subset(U_1575,U_1574)
| ~ in(U_1574,U_1576) )
& in(U_1575,U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_1577,sK287(U_1597))],[f_433_6]) ).
fof(f_433_8,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ? [U_1581] :
( ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(U_1581))) )
| ~ in(U_1581,omega) )
& sK286(U_1597) = U_1581
& ordinal(U_1581) )
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_1575,sK288(U_1597,U_1576))],[f_433_7]) ).
fof(f_433_9,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ? [U_1579] :
( ! [U_1578] :
( U_1578 = U_1579
| ~ subset(U_1579,U_1578)
| ~ in(U_1578,U_1580) )
& in(U_1579,U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_1581,sK289(U_1597))],[f_433_8]) ).
fof(f_433_10,plain,
! [U_1597] :
( ? [U_1596] :
( ! [U_1599] :
( in(U_1599,U_1596)
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,U_1596) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ( ! [U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580) )
& in(sK290(U_1597,U_1580),U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_1579,sK290(U_1597,U_1580))],[f_433_9]) ).
fof(f_433_11,plain,
! [U_1597] :
( ( ! [U_1599] :
( in(U_1599,sK291(U_1597))
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ? [U_1588] :
( ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(U_1588))) )
| ~ in(U_1588,omega) )
& U_1598 = U_1588
& ordinal(U_1588) ) )
| ~ in(U_1598,sK291(U_1597)) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ( ! [U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580) )
& in(sK290(U_1597,U_1580),U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_1596,sK291(U_1597))],[f_433_10]) ).
fof(f_433_12,plain,
! [U_1597] :
( ( ! [U_1599] :
( in(U_1599,sK291(U_1597))
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ( ! [U_1587] :
( ? [U_1586] :
( ! [U_1585] :
( U_1585 = U_1586
| ~ subset(U_1586,U_1585)
| ~ in(U_1585,U_1587) )
& in(U_1586,U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(sK292(U_1597,U_1598)))) )
| ~ in(sK292(U_1597,U_1598),omega) )
& U_1598 = sK292(U_1597,U_1598)
& ordinal(sK292(U_1597,U_1598)) )
| ~ in(U_1598,sK291(U_1597)) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ( ! [U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580) )
& in(sK290(U_1597,U_1580),U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_1588,sK292(U_1597,U_1598))],[f_433_11]) ).
fof(f_433_13,plain,
! [U_1597] :
( ( ! [U_1599] :
( in(U_1599,sK291(U_1597))
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( ? [U_1589] :
( U_1589 = U_1598
& in(U_1589,succ(U_1597)) )
& ( ! [U_1587] :
( ( ! [U_1585] :
( U_1585 = sK293(U_1597,U_1598,U_1587)
| ~ subset(sK293(U_1597,U_1598,U_1587),U_1585)
| ~ in(U_1585,U_1587) )
& in(sK293(U_1597,U_1598,U_1587),U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(sK292(U_1597,U_1598)))) )
| ~ in(sK292(U_1597,U_1598),omega) )
& U_1598 = sK292(U_1597,U_1598)
& ordinal(sK292(U_1597,U_1598)) )
| ~ in(U_1598,sK291(U_1597)) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ( ! [U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580) )
& in(sK290(U_1597,U_1580),U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_1586,sK293(U_1597,U_1598,U_1587))],[f_433_12]) ).
fof(f_433_14,plain,
! [U_1597] :
( ( ! [U_1599] :
( in(U_1599,sK291(U_1597))
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ? [U_1592] :
( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,U_1592) )
| ~ in(U_1591,U_1592) )
& U_1592 != empty_set
& element(U_1592,powerset(powerset(U_1593))) )
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( sK294(U_1597,U_1598) = U_1598
& in(sK294(U_1597,U_1598),succ(U_1597))
& ( ! [U_1587] :
( ( ! [U_1585] :
( U_1585 = sK293(U_1597,U_1598,U_1587)
| ~ subset(sK293(U_1597,U_1598,U_1587),U_1585)
| ~ in(U_1585,U_1587) )
& in(sK293(U_1597,U_1598,U_1587),U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(sK292(U_1597,U_1598)))) )
| ~ in(sK292(U_1597,U_1598),omega) )
& U_1598 = sK292(U_1597,U_1598)
& ordinal(sK292(U_1597,U_1598)) )
| ~ in(U_1598,sK291(U_1597)) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ( ! [U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580) )
& in(sK290(U_1597,U_1580),U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_1589,sK294(U_1597,U_1598))],[f_433_13]) ).
fof(f_433_15,plain,
! [U_1597] :
( ( ! [U_1599] :
( in(U_1599,sK291(U_1597))
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ! [U_1591] :
( ? [U_1590] :
( U_1590 != U_1591
& subset(U_1591,U_1590)
& in(U_1590,sK295(U_1597,U_1599,U_1593)) )
| ~ in(U_1591,sK295(U_1597,U_1599,U_1593)) )
& sK295(U_1597,U_1599,U_1593) != empty_set
& element(sK295(U_1597,U_1599,U_1593),powerset(powerset(U_1593)))
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( sK294(U_1597,U_1598) = U_1598
& in(sK294(U_1597,U_1598),succ(U_1597))
& ( ! [U_1587] :
( ( ! [U_1585] :
( U_1585 = sK293(U_1597,U_1598,U_1587)
| ~ subset(sK293(U_1597,U_1598,U_1587),U_1585)
| ~ in(U_1585,U_1587) )
& in(sK293(U_1597,U_1598,U_1587),U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(sK292(U_1597,U_1598)))) )
| ~ in(sK292(U_1597,U_1598),omega) )
& U_1598 = sK292(U_1597,U_1598)
& ordinal(sK292(U_1597,U_1598)) )
| ~ in(U_1598,sK291(U_1597)) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ( ! [U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580) )
& in(sK290(U_1597,U_1580),U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_1592,sK295(U_1597,U_1599,U_1593))],[f_433_14]) ).
fof(f_433_16,plain,
! [U_1597] :
( ( ! [U_1599] :
( in(U_1599,sK291(U_1597))
| ! [U_1594] :
( U_1594 != U_1599
| ~ in(U_1594,succ(U_1597)) )
| ! [U_1593] :
( ( ! [U_1591] :
( ( sK296(U_1597,U_1599,U_1593,U_1591) != U_1591
& subset(U_1591,sK296(U_1597,U_1599,U_1593,U_1591))
& in(sK296(U_1597,U_1599,U_1593,U_1591),sK295(U_1597,U_1599,U_1593)) )
| ~ in(U_1591,sK295(U_1597,U_1599,U_1593)) )
& sK295(U_1597,U_1599,U_1593) != empty_set
& element(sK295(U_1597,U_1599,U_1593),powerset(powerset(U_1593)))
& in(U_1593,omega) )
| U_1599 != U_1593
| ~ ordinal(U_1593) ) )
& ! [U_1598] :
( ( sK294(U_1597,U_1598) = U_1598
& in(sK294(U_1597,U_1598),succ(U_1597))
& ( ! [U_1587] :
( ( ! [U_1585] :
( U_1585 = sK293(U_1597,U_1598,U_1587)
| ~ subset(sK293(U_1597,U_1598,U_1587),U_1585)
| ~ in(U_1585,U_1587) )
& in(sK293(U_1597,U_1598,U_1587),U_1587) )
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(sK292(U_1597,U_1598)))) )
| ~ in(sK292(U_1597,U_1598),omega) )
& U_1598 = sK292(U_1597,U_1598)
& ordinal(sK292(U_1597,U_1598)) )
| ~ in(U_1598,sK291(U_1597)) ) )
| ( sK285(U_1597) != sK286(U_1597)
& ( ! [U_1580] :
( ( ! [U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580) )
& in(sK290(U_1597,U_1580),U_1580) )
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597)))) )
| ~ in(sK289(U_1597),omega) )
& sK286(U_1597) = sK289(U_1597)
& ordinal(sK289(U_1597))
& sK284(U_1597) = sK286(U_1597)
& ( ! [U_1576] :
( ( ! [U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576) )
& in(sK288(U_1597,U_1576),U_1576) )
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597)))) )
| ~ in(sK287(U_1597),omega) )
& sK285(U_1597) = sK287(U_1597)
& ordinal(sK287(U_1597))
& sK284(U_1597) = sK285(U_1597) )
| ~ ordinal(U_1597) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_1590,sK296(U_1597,U_1599,U_1593,U_1591))],[f_433_15]) ).
fof(f_433_17,plain,
( ! [U_1591,U_1597,U_1593,U_1599] :
( sK296(U_1597,U_1599,U_1593,U_1591) != U_1591
| ~ sP376(U_1591,U_1597,U_1593,U_1599) )
& ! [U_1591,U_1597,U_1593,U_1599] :
( subset(U_1591,sK296(U_1597,U_1599,U_1593,U_1591))
| ~ sP376(U_1591,U_1597,U_1593,U_1599) )
& ! [U_1591,U_1597,U_1593,U_1599] :
( in(sK296(U_1597,U_1599,U_1593,U_1591),sK295(U_1597,U_1599,U_1593))
| ~ sP376(U_1591,U_1597,U_1593,U_1599) )
& ! [U_1591,U_1597,U_1593,U_1599] :
( sP376(U_1591,U_1597,U_1593,U_1599)
| ~ in(U_1591,sK295(U_1597,U_1599,U_1593))
| ~ sP377(U_1591,U_1597,U_1593,U_1599) )
& ! [U_1591,U_1597,U_1593,U_1599] :
( sK295(U_1597,U_1599,U_1593) != empty_set
| ~ sP377(U_1591,U_1597,U_1593,U_1599) )
& ! [U_1591,U_1597,U_1593,U_1599] :
( element(sK295(U_1597,U_1599,U_1593),powerset(powerset(U_1593)))
| ~ sP377(U_1591,U_1597,U_1593,U_1599) )
& ! [U_1591,U_1597,U_1593,U_1599] :
( in(U_1593,omega)
| ~ sP377(U_1591,U_1597,U_1593,U_1599) )
& ! [U_1585,U_1587,U_1597,U_1598] :
( U_1585 = sK293(U_1597,U_1598,U_1587)
| ~ subset(sK293(U_1597,U_1598,U_1587),U_1585)
| ~ in(U_1585,U_1587)
| ~ sP374(U_1585,U_1587,U_1597,U_1598) )
& ! [U_1585,U_1587,U_1597,U_1598] :
( in(sK293(U_1597,U_1598,U_1587),U_1587)
| ~ sP374(U_1585,U_1587,U_1597,U_1598) )
& ! [U_1585,U_1587,U_1597,U_1598] :
( sK294(U_1597,U_1598) = U_1598
| ~ sP375(U_1585,U_1587,U_1597,U_1598) )
& ! [U_1585,U_1587,U_1597,U_1598] :
( in(sK294(U_1597,U_1598),succ(U_1597))
| ~ sP375(U_1585,U_1587,U_1597,U_1598) )
& ! [U_1585,U_1587,U_1597,U_1598] :
( sP374(U_1585,U_1587,U_1597,U_1598)
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(sK292(U_1597,U_1598))))
| ~ in(sK292(U_1597,U_1598),omega)
| ~ sP375(U_1585,U_1587,U_1597,U_1598) )
& ! [U_1585,U_1587,U_1597,U_1598] :
( U_1598 = sK292(U_1597,U_1598)
| ~ sP375(U_1585,U_1587,U_1597,U_1598) )
& ! [U_1585,U_1587,U_1597,U_1598] :
( ordinal(sK292(U_1597,U_1598))
| ~ sP375(U_1585,U_1587,U_1597,U_1598) )
& ! [U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598] :
( in(U_1599,sK291(U_1597))
| U_1594 != U_1599
| ~ in(U_1594,succ(U_1597))
| sP377(U_1591,U_1597,U_1593,U_1599)
| U_1599 != U_1593
| ~ ordinal(U_1593)
| ~ sP378(U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598) )
& ! [U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598] :
( sP375(U_1585,U_1587,U_1597,U_1598)
| ~ in(U_1598,sK291(U_1597))
| ~ sP378(U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598) )
& ! [U_1580,U_1597,U_1578] :
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580)
| ~ sP372(U_1580,U_1597,U_1578) )
& ! [U_1580,U_1597,U_1578] :
( in(sK290(U_1597,U_1580),U_1580)
| ~ sP372(U_1580,U_1597,U_1578) )
& ! [U_1576,U_1597,U_1574] :
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576)
| ~ sP371(U_1576,U_1597,U_1574) )
& ! [U_1576,U_1597,U_1574] :
( in(sK288(U_1597,U_1576),U_1576)
| ~ sP371(U_1576,U_1597,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( sK285(U_1597) != sK286(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( sP372(U_1580,U_1597,U_1578)
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597))))
| ~ in(sK289(U_1597),omega)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( sK286(U_1597) = sK289(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( ordinal(sK289(U_1597))
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( sK284(U_1597) = sK286(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( sP371(U_1576,U_1597,U_1574)
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597))))
| ~ in(sK287(U_1597),omega)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( sK285(U_1597) = sK287(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( ordinal(sK287(U_1597))
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1597,U_1578,U_1574] :
( sK284(U_1597) = sK285(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) )
& ! [U_1576,U_1580,U_1591,U_1585,U_1587,U_1594,U_1597,U_1578,U_1593,U_1574,U_1599,U_1598] :
( sP378(U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598)
| sP373(U_1576,U_1580,U_1597,U_1578,U_1574)
| ~ ordinal(U_1597) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP371,sP372,sP373,sP374,sP375,sP376,sP377,sP378])],[f_433_16]) ).
cnf(f_433_18,plain,
( sP378(U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598)
| sP373(U_1576,U_1580,U_1597,U_1578,U_1574)
| ~ ordinal(U_1597) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_19,plain,
( sK284(U_1597) = sK285(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_20,plain,
( ordinal(sK287(U_1597))
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_21,plain,
( sK285(U_1597) = sK287(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_22,plain,
( sP371(U_1576,U_1597,U_1574)
| U_1576 = empty_set
| ~ element(U_1576,powerset(powerset(sK287(U_1597))))
| ~ in(sK287(U_1597),omega)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_23,plain,
( sK284(U_1597) = sK286(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_24,plain,
( ordinal(sK289(U_1597))
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_25,plain,
( sK286(U_1597) = sK289(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_26,plain,
( sP372(U_1580,U_1597,U_1578)
| U_1580 = empty_set
| ~ element(U_1580,powerset(powerset(sK289(U_1597))))
| ~ in(sK289(U_1597),omega)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_27,plain,
( sK285(U_1597) != sK286(U_1597)
| ~ sP373(U_1576,U_1580,U_1597,U_1578,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_28,plain,
( in(sK288(U_1597,U_1576),U_1576)
| ~ sP371(U_1576,U_1597,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_29,plain,
( U_1574 = sK288(U_1597,U_1576)
| ~ subset(sK288(U_1597,U_1576),U_1574)
| ~ in(U_1574,U_1576)
| ~ sP371(U_1576,U_1597,U_1574) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_30,plain,
( in(sK290(U_1597,U_1580),U_1580)
| ~ sP372(U_1580,U_1597,U_1578) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_31,plain,
( U_1578 = sK290(U_1597,U_1580)
| ~ subset(sK290(U_1597,U_1580),U_1578)
| ~ in(U_1578,U_1580)
| ~ sP372(U_1580,U_1597,U_1578) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_32,plain,
( sP375(U_1585,U_1587,U_1597,U_1598)
| ~ in(U_1598,sK291(U_1597))
| ~ sP378(U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_33,plain,
( in(U_1599,sK291(U_1597))
| U_1594 != U_1599
| ~ in(U_1594,succ(U_1597))
| sP377(U_1591,U_1597,U_1593,U_1599)
| U_1599 != U_1593
| ~ ordinal(U_1593)
| ~ sP378(U_1591,U_1585,U_1587,U_1594,U_1597,U_1593,U_1599,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_34,plain,
( ordinal(sK292(U_1597,U_1598))
| ~ sP375(U_1585,U_1587,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_35,plain,
( U_1598 = sK292(U_1597,U_1598)
| ~ sP375(U_1585,U_1587,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_36,plain,
( sP374(U_1585,U_1587,U_1597,U_1598)
| U_1587 = empty_set
| ~ element(U_1587,powerset(powerset(sK292(U_1597,U_1598))))
| ~ in(sK292(U_1597,U_1598),omega)
| ~ sP375(U_1585,U_1587,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_37,plain,
( in(sK294(U_1597,U_1598),succ(U_1597))
| ~ sP375(U_1585,U_1587,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_38,plain,
( sK294(U_1597,U_1598) = U_1598
| ~ sP375(U_1585,U_1587,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_39,plain,
( in(sK293(U_1597,U_1598,U_1587),U_1587)
| ~ sP374(U_1585,U_1587,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_40,plain,
( U_1585 = sK293(U_1597,U_1598,U_1587)
| ~ subset(sK293(U_1597,U_1598,U_1587),U_1585)
| ~ in(U_1585,U_1587)
| ~ sP374(U_1585,U_1587,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_41,plain,
( in(U_1593,omega)
| ~ sP377(U_1591,U_1597,U_1593,U_1599) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_42,plain,
( element(sK295(U_1597,U_1599,U_1593),powerset(powerset(U_1593)))
| ~ sP377(U_1591,U_1597,U_1593,U_1599) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_43,plain,
( sK295(U_1597,U_1599,U_1593) != empty_set
| ~ sP377(U_1591,U_1597,U_1593,U_1599) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_44,plain,
( sP376(U_1591,U_1597,U_1593,U_1599)
| ~ in(U_1591,sK295(U_1597,U_1599,U_1593))
| ~ sP377(U_1591,U_1597,U_1593,U_1599) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_45,plain,
( in(sK296(U_1597,U_1599,U_1593,U_1591),sK295(U_1597,U_1599,U_1593))
| ~ sP376(U_1591,U_1597,U_1593,U_1599) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_46,plain,
( subset(U_1591,sK296(U_1597,U_1599,U_1593,U_1591))
| ~ sP376(U_1591,U_1597,U_1593,U_1599) ),
inference(clausify,[status(thm)],[f_433_17]) ).
cnf(f_433_47,plain,
( sK296(U_1597,U_1599,U_1593,U_1591) != U_1591
| ~ sP376(U_1591,U_1597,U_1593,U_1599) ),
inference(clausify,[status(thm)],[f_433_17]) ).
fof(f_434_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ! [H] :
( ~ subset(B,D)
| ~ closed_subset(H,A)
| H != D
| ~ element(H,powerset(the_carrier(A))) )
| E != D
| ~ in(E,powerset(the_carrier(A))) ) )
& ( ? [E] :
( ? [H] :
( subset(B,D)
& closed_subset(H,A)
& H = D
& element(H,powerset(the_carrier(A))) )
& E = D
& in(E,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ? [G] :
( subset(B,E)
& closed_subset(G,A)
& G = E
& element(G,powerset(the_carrier(A))) )
& C = E
& ? [F] :
( subset(B,D)
& closed_subset(F,A)
& F = D
& element(F,powerset(the_carrier(A))) )
& C = D )
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e1_40__pre_topc__1]) ).
fof(f_434_2,plain,
! [U_1612,U_1611] :
( ? [U_1610] :
! [U_1609] :
( ( in(U_1609,U_1610)
| ! [U_1608] :
( ! [U_1607] :
( ~ subset(U_1611,U_1609)
| ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1609
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| U_1608 != U_1609
| ~ in(U_1608,powerset(the_carrier(U_1612))) ) )
& ( ? [U_1606] :
( ? [U_1605] :
( subset(U_1611,U_1609)
& closed_subset(U_1605,U_1612)
& U_1605 = U_1609
& element(U_1605,powerset(the_carrier(U_1612))) )
& U_1606 = U_1609
& in(U_1606,powerset(the_carrier(U_1612))) )
| ~ in(U_1609,U_1610) ) )
| ? [U_1604,U_1603,U_1602] :
( U_1603 != U_1602
& ? [U_1601] :
( subset(U_1611,U_1602)
& closed_subset(U_1601,U_1612)
& U_1601 = U_1602
& element(U_1601,powerset(the_carrier(U_1612))) )
& U_1604 = U_1602
& ? [U_1600] :
( subset(U_1611,U_1603)
& closed_subset(U_1600,U_1612)
& U_1600 = U_1603
& element(U_1600,powerset(the_carrier(U_1612))) )
& U_1604 = U_1603 )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1612,U_1611] :
( ? [U_1610] :
( ! [U_1614] :
( in(U_1614,U_1610)
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& ? [U_1605] :
( closed_subset(U_1605,U_1612)
& U_1605 = U_1613
& element(U_1605,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1613) )
| ~ in(U_1613,U_1610) ) )
| ? [U_1604,U_1603,U_1602] :
( U_1603 != U_1602
& ? [U_1601] :
( closed_subset(U_1601,U_1612)
& U_1601 = U_1602
& element(U_1601,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1602)
& U_1604 = U_1602
& ? [U_1600] :
( closed_subset(U_1600,U_1612)
& U_1600 = U_1603
& element(U_1600,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1603)
& U_1604 = U_1603 )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(miniscope,[status(thm)],[f_434_2]) ).
fof(f_434_4,plain,
! [U_1612,U_1611] :
( ? [U_1610] :
( ! [U_1614] :
( in(U_1614,U_1610)
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& ? [U_1605] :
( closed_subset(U_1605,U_1612)
& U_1605 = U_1613
& element(U_1605,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1613) )
| ~ in(U_1613,U_1610) ) )
| ? [U_1603,U_1602] :
( U_1603 != U_1602
& ? [U_1601] :
( closed_subset(U_1601,U_1612)
& U_1601 = U_1602
& element(U_1601,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1602)
& sK297(U_1612,U_1611) = U_1602
& ? [U_1600] :
( closed_subset(U_1600,U_1612)
& U_1600 = U_1603
& element(U_1600,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1603)
& sK297(U_1612,U_1611) = U_1603 )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_1604,sK297(U_1612,U_1611))],[f_434_3]) ).
fof(f_434_5,plain,
! [U_1612,U_1611] :
( ? [U_1610] :
( ! [U_1614] :
( in(U_1614,U_1610)
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& ? [U_1605] :
( closed_subset(U_1605,U_1612)
& U_1605 = U_1613
& element(U_1605,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1613) )
| ~ in(U_1613,U_1610) ) )
| ? [U_1602] :
( sK298(U_1612,U_1611) != U_1602
& ? [U_1601] :
( closed_subset(U_1601,U_1612)
& U_1601 = U_1602
& element(U_1601,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1602)
& sK297(U_1612,U_1611) = U_1602
& ? [U_1600] :
( closed_subset(U_1600,U_1612)
& U_1600 = sK298(U_1612,U_1611)
& element(U_1600,powerset(the_carrier(U_1612))) )
& subset(U_1611,sK298(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK298(U_1612,U_1611) )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_1603,sK298(U_1612,U_1611))],[f_434_4]) ).
fof(f_434_6,plain,
! [U_1612,U_1611] :
( ? [U_1610] :
( ! [U_1614] :
( in(U_1614,U_1610)
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& ? [U_1605] :
( closed_subset(U_1605,U_1612)
& U_1605 = U_1613
& element(U_1605,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1613) )
| ~ in(U_1613,U_1610) ) )
| ( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
& ? [U_1601] :
( closed_subset(U_1601,U_1612)
& U_1601 = sK299(U_1612,U_1611)
& element(U_1601,powerset(the_carrier(U_1612))) )
& subset(U_1611,sK299(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
& ? [U_1600] :
( closed_subset(U_1600,U_1612)
& U_1600 = sK298(U_1612,U_1611)
& element(U_1600,powerset(the_carrier(U_1612))) )
& subset(U_1611,sK298(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK298(U_1612,U_1611) )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_1602,sK299(U_1612,U_1611))],[f_434_5]) ).
fof(f_434_7,plain,
! [U_1612,U_1611] :
( ? [U_1610] :
( ! [U_1614] :
( in(U_1614,U_1610)
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& ? [U_1605] :
( closed_subset(U_1605,U_1612)
& U_1605 = U_1613
& element(U_1605,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1613) )
| ~ in(U_1613,U_1610) ) )
| ( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
& ? [U_1601] :
( closed_subset(U_1601,U_1612)
& U_1601 = sK299(U_1612,U_1611)
& element(U_1601,powerset(the_carrier(U_1612))) )
& subset(U_1611,sK299(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
& closed_subset(sK300(U_1612,U_1611),U_1612)
& sK300(U_1612,U_1611) = sK298(U_1612,U_1611)
& element(sK300(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK298(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK298(U_1612,U_1611) )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_1600,sK300(U_1612,U_1611))],[f_434_6]) ).
fof(f_434_8,plain,
! [U_1612,U_1611] :
( ? [U_1610] :
( ! [U_1614] :
( in(U_1614,U_1610)
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& ? [U_1605] :
( closed_subset(U_1605,U_1612)
& U_1605 = U_1613
& element(U_1605,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1613) )
| ~ in(U_1613,U_1610) ) )
| ( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
& closed_subset(sK301(U_1612,U_1611),U_1612)
& sK301(U_1612,U_1611) = sK299(U_1612,U_1611)
& element(sK301(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK299(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
& closed_subset(sK300(U_1612,U_1611),U_1612)
& sK300(U_1612,U_1611) = sK298(U_1612,U_1611)
& element(sK300(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK298(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK298(U_1612,U_1611) )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_1601,sK301(U_1612,U_1611))],[f_434_7]) ).
fof(f_434_9,plain,
! [U_1612,U_1611] :
( ( ! [U_1614] :
( in(U_1614,sK302(U_1612,U_1611))
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& ? [U_1605] :
( closed_subset(U_1605,U_1612)
& U_1605 = U_1613
& element(U_1605,powerset(the_carrier(U_1612))) )
& subset(U_1611,U_1613) )
| ~ in(U_1613,sK302(U_1612,U_1611)) ) )
| ( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
& closed_subset(sK301(U_1612,U_1611),U_1612)
& sK301(U_1612,U_1611) = sK299(U_1612,U_1611)
& element(sK301(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK299(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
& closed_subset(sK300(U_1612,U_1611),U_1612)
& sK300(U_1612,U_1611) = sK298(U_1612,U_1611)
& element(sK300(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK298(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK298(U_1612,U_1611) )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_1610,sK302(U_1612,U_1611))],[f_434_8]) ).
fof(f_434_10,plain,
! [U_1612,U_1611] :
( ( ! [U_1614] :
( in(U_1614,sK302(U_1612,U_1611))
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( ? [U_1606] :
( U_1606 = U_1613
& in(U_1606,powerset(the_carrier(U_1612))) )
& closed_subset(sK303(U_1612,U_1611,U_1613),U_1612)
& sK303(U_1612,U_1611,U_1613) = U_1613
& element(sK303(U_1612,U_1611,U_1613),powerset(the_carrier(U_1612)))
& subset(U_1611,U_1613) )
| ~ in(U_1613,sK302(U_1612,U_1611)) ) )
| ( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
& closed_subset(sK301(U_1612,U_1611),U_1612)
& sK301(U_1612,U_1611) = sK299(U_1612,U_1611)
& element(sK301(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK299(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
& closed_subset(sK300(U_1612,U_1611),U_1612)
& sK300(U_1612,U_1611) = sK298(U_1612,U_1611)
& element(sK300(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK298(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK298(U_1612,U_1611) )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_1605,sK303(U_1612,U_1611,U_1613))],[f_434_9]) ).
fof(f_434_11,plain,
! [U_1612,U_1611] :
( ( ! [U_1614] :
( in(U_1614,sK302(U_1612,U_1611))
| ! [U_1608] :
( U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612))) )
| ! [U_1607] :
( ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612))) )
| ~ subset(U_1611,U_1614) )
& ! [U_1613] :
( ( sK304(U_1612,U_1611,U_1613) = U_1613
& in(sK304(U_1612,U_1611,U_1613),powerset(the_carrier(U_1612)))
& closed_subset(sK303(U_1612,U_1611,U_1613),U_1612)
& sK303(U_1612,U_1611,U_1613) = U_1613
& element(sK303(U_1612,U_1611,U_1613),powerset(the_carrier(U_1612)))
& subset(U_1611,U_1613) )
| ~ in(U_1613,sK302(U_1612,U_1611)) ) )
| ( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
& closed_subset(sK301(U_1612,U_1611),U_1612)
& sK301(U_1612,U_1611) = sK299(U_1612,U_1611)
& element(sK301(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK299(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
& closed_subset(sK300(U_1612,U_1611),U_1612)
& sK300(U_1612,U_1611) = sK298(U_1612,U_1611)
& element(sK300(U_1612,U_1611),powerset(the_carrier(U_1612)))
& subset(U_1611,sK298(U_1612,U_1611))
& sK297(U_1612,U_1611) = sK298(U_1612,U_1611) )
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_1606,sK304(U_1612,U_1611,U_1613))],[f_434_10]) ).
fof(f_434_12,plain,
( ! [U_1612,U_1611,U_1613] :
( sK304(U_1612,U_1611,U_1613) = U_1613
| ~ sP380(U_1612,U_1611,U_1613) )
& ! [U_1612,U_1611,U_1613] :
( in(sK304(U_1612,U_1611,U_1613),powerset(the_carrier(U_1612)))
| ~ sP380(U_1612,U_1611,U_1613) )
& ! [U_1612,U_1611,U_1613] :
( closed_subset(sK303(U_1612,U_1611,U_1613),U_1612)
| ~ sP380(U_1612,U_1611,U_1613) )
& ! [U_1612,U_1611,U_1613] :
( sK303(U_1612,U_1611,U_1613) = U_1613
| ~ sP380(U_1612,U_1611,U_1613) )
& ! [U_1612,U_1611,U_1613] :
( element(sK303(U_1612,U_1611,U_1613),powerset(the_carrier(U_1612)))
| ~ sP380(U_1612,U_1611,U_1613) )
& ! [U_1612,U_1611,U_1613] :
( subset(U_1611,U_1613)
| ~ sP380(U_1612,U_1611,U_1613) )
& ! [U_1612,U_1611,U_1608,U_1613,U_1614,U_1607] :
( in(U_1614,sK302(U_1612,U_1611))
| U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612)))
| ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612)))
| ~ subset(U_1611,U_1614)
| ~ sP381(U_1612,U_1611,U_1608,U_1613,U_1614,U_1607) )
& ! [U_1612,U_1611,U_1608,U_1613,U_1614,U_1607] :
( sP380(U_1612,U_1611,U_1613)
| ~ in(U_1613,sK302(U_1612,U_1611))
| ~ sP381(U_1612,U_1611,U_1608,U_1613,U_1614,U_1607) )
& ! [U_1612,U_1611] :
( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( closed_subset(sK301(U_1612,U_1611),U_1612)
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( sK301(U_1612,U_1611) = sK299(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( element(sK301(U_1612,U_1611),powerset(the_carrier(U_1612)))
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( subset(U_1611,sK299(U_1612,U_1611))
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( closed_subset(sK300(U_1612,U_1611),U_1612)
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( sK300(U_1612,U_1611) = sK298(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( element(sK300(U_1612,U_1611),powerset(the_carrier(U_1612)))
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( subset(U_1611,sK298(U_1612,U_1611))
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611] :
( sK297(U_1612,U_1611) = sK298(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) )
& ! [U_1612,U_1611,U_1608,U_1613,U_1614,U_1607] :
( sP381(U_1612,U_1611,U_1608,U_1613,U_1614,U_1607)
| sP379(U_1612,U_1611)
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP379,sP380,sP381])],[f_434_11]) ).
cnf(f_434_13,plain,
( sP381(U_1612,U_1611,U_1608,U_1613,U_1614,U_1607)
| sP379(U_1612,U_1611)
| ~ element(U_1611,powerset(the_carrier(U_1612)))
| ~ top_str(U_1612)
| ~ topological_space(U_1612) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_14,plain,
( sK297(U_1612,U_1611) = sK298(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_15,plain,
( subset(U_1611,sK298(U_1612,U_1611))
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_16,plain,
( element(sK300(U_1612,U_1611),powerset(the_carrier(U_1612)))
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_17,plain,
( sK300(U_1612,U_1611) = sK298(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_18,plain,
( closed_subset(sK300(U_1612,U_1611),U_1612)
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_19,plain,
( sK297(U_1612,U_1611) = sK299(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_20,plain,
( subset(U_1611,sK299(U_1612,U_1611))
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_21,plain,
( element(sK301(U_1612,U_1611),powerset(the_carrier(U_1612)))
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_22,plain,
( sK301(U_1612,U_1611) = sK299(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_23,plain,
( closed_subset(sK301(U_1612,U_1611),U_1612)
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_24,plain,
( sK298(U_1612,U_1611) != sK299(U_1612,U_1611)
| ~ sP379(U_1612,U_1611) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_25,plain,
( sP380(U_1612,U_1611,U_1613)
| ~ in(U_1613,sK302(U_1612,U_1611))
| ~ sP381(U_1612,U_1611,U_1608,U_1613,U_1614,U_1607) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_26,plain,
( in(U_1614,sK302(U_1612,U_1611))
| U_1608 != U_1614
| ~ in(U_1608,powerset(the_carrier(U_1612)))
| ~ closed_subset(U_1607,U_1612)
| U_1607 != U_1614
| ~ element(U_1607,powerset(the_carrier(U_1612)))
| ~ subset(U_1611,U_1614)
| ~ sP381(U_1612,U_1611,U_1608,U_1613,U_1614,U_1607) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_27,plain,
( subset(U_1611,U_1613)
| ~ sP380(U_1612,U_1611,U_1613) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_28,plain,
( element(sK303(U_1612,U_1611,U_1613),powerset(the_carrier(U_1612)))
| ~ sP380(U_1612,U_1611,U_1613) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_29,plain,
( sK303(U_1612,U_1611,U_1613) = U_1613
| ~ sP380(U_1612,U_1611,U_1613) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_30,plain,
( closed_subset(sK303(U_1612,U_1611,U_1613),U_1612)
| ~ sP380(U_1612,U_1611,U_1613) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_31,plain,
( in(sK304(U_1612,U_1611,U_1613),powerset(the_carrier(U_1612)))
| ~ sP380(U_1612,U_1611,U_1613) ),
inference(clausify,[status(thm)],[f_434_12]) ).
cnf(f_434_32,plain,
( sK304(U_1612,U_1611,U_1613) = U_1613
| ~ sP380(U_1612,U_1611,U_1613) ),
inference(clausify,[status(thm)],[f_434_12]) ).
fof(f_435_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| E != D
| ~ in(E,powerset(the_carrier(A))) ) )
& ( ? [E] :
( in(set_difference(cast_as_carrier_subset(A),D),B)
& E = D
& in(E,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& in(set_difference(cast_as_carrier_subset(A),E),B)
& C = E
& in(set_difference(cast_as_carrier_subset(A),D),B)
& C = D )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e2_37_1_1__pre_topc__1]) ).
fof(f_435_2,plain,
! [U_1623,U_1622] :
( ? [U_1621] :
! [U_1620] :
( ( in(U_1620,U_1621)
| ! [U_1619] :
( ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1620),U_1622)
| U_1619 != U_1620
| ~ in(U_1619,powerset(the_carrier(U_1623))) ) )
& ( ? [U_1618] :
( in(set_difference(cast_as_carrier_subset(U_1623),U_1620),U_1622)
& U_1618 = U_1620
& in(U_1618,powerset(the_carrier(U_1623))) )
| ~ in(U_1620,U_1621) ) )
| ? [U_1617,U_1616,U_1615] :
( U_1616 != U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),U_1615),U_1622)
& U_1617 = U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),U_1616),U_1622)
& U_1617 = U_1616 )
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
! [U_1623,U_1622] :
( ? [U_1621] :
( ! [U_1625] :
( in(U_1625,U_1621)
| ! [U_1619] :
( U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623))) )
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622) )
& ! [U_1624] :
( ( ? [U_1618] :
( U_1618 = U_1624
& in(U_1618,powerset(the_carrier(U_1623))) )
& in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622) )
| ~ in(U_1624,U_1621) ) )
| ? [U_1617,U_1616,U_1615] :
( U_1616 != U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),U_1615),U_1622)
& U_1617 = U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),U_1616),U_1622)
& U_1617 = U_1616 )
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(miniscope,[status(thm)],[f_435_2]) ).
fof(f_435_4,plain,
! [U_1623,U_1622] :
( ? [U_1621] :
( ! [U_1625] :
( in(U_1625,U_1621)
| ! [U_1619] :
( U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623))) )
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622) )
& ! [U_1624] :
( ( ? [U_1618] :
( U_1618 = U_1624
& in(U_1618,powerset(the_carrier(U_1623))) )
& in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622) )
| ~ in(U_1624,U_1621) ) )
| ? [U_1616,U_1615] :
( U_1616 != U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),U_1615),U_1622)
& sK305(U_1623,U_1622) = U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),U_1616),U_1622)
& sK305(U_1623,U_1622) = U_1616 )
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_1617,sK305(U_1623,U_1622))],[f_435_3]) ).
fof(f_435_5,plain,
! [U_1623,U_1622] :
( ? [U_1621] :
( ! [U_1625] :
( in(U_1625,U_1621)
| ! [U_1619] :
( U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623))) )
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622) )
& ! [U_1624] :
( ( ? [U_1618] :
( U_1618 = U_1624
& in(U_1618,powerset(the_carrier(U_1623))) )
& in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622) )
| ~ in(U_1624,U_1621) ) )
| ? [U_1615] :
( sK306(U_1623,U_1622) != U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),U_1615),U_1622)
& sK305(U_1623,U_1622) = U_1615
& in(set_difference(cast_as_carrier_subset(U_1623),sK306(U_1623,U_1622)),U_1622)
& sK305(U_1623,U_1622) = sK306(U_1623,U_1622) )
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_1616,sK306(U_1623,U_1622))],[f_435_4]) ).
fof(f_435_6,plain,
! [U_1623,U_1622] :
( ? [U_1621] :
( ! [U_1625] :
( in(U_1625,U_1621)
| ! [U_1619] :
( U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623))) )
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622) )
& ! [U_1624] :
( ( ? [U_1618] :
( U_1618 = U_1624
& in(U_1618,powerset(the_carrier(U_1623))) )
& in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622) )
| ~ in(U_1624,U_1621) ) )
| ( sK306(U_1623,U_1622) != sK307(U_1623,U_1622)
& in(set_difference(cast_as_carrier_subset(U_1623),sK307(U_1623,U_1622)),U_1622)
& sK305(U_1623,U_1622) = sK307(U_1623,U_1622)
& in(set_difference(cast_as_carrier_subset(U_1623),sK306(U_1623,U_1622)),U_1622)
& sK305(U_1623,U_1622) = sK306(U_1623,U_1622) )
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_1615,sK307(U_1623,U_1622))],[f_435_5]) ).
fof(f_435_7,plain,
! [U_1623,U_1622] :
( ( ! [U_1625] :
( in(U_1625,sK308(U_1623,U_1622))
| ! [U_1619] :
( U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623))) )
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622) )
& ! [U_1624] :
( ( ? [U_1618] :
( U_1618 = U_1624
& in(U_1618,powerset(the_carrier(U_1623))) )
& in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622) )
| ~ in(U_1624,sK308(U_1623,U_1622)) ) )
| ( sK306(U_1623,U_1622) != sK307(U_1623,U_1622)
& in(set_difference(cast_as_carrier_subset(U_1623),sK307(U_1623,U_1622)),U_1622)
& sK305(U_1623,U_1622) = sK307(U_1623,U_1622)
& in(set_difference(cast_as_carrier_subset(U_1623),sK306(U_1623,U_1622)),U_1622)
& sK305(U_1623,U_1622) = sK306(U_1623,U_1622) )
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_1621,sK308(U_1623,U_1622))],[f_435_6]) ).
fof(f_435_8,plain,
! [U_1623,U_1622] :
( ( ! [U_1625] :
( in(U_1625,sK308(U_1623,U_1622))
| ! [U_1619] :
( U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623))) )
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622) )
& ! [U_1624] :
( ( sK309(U_1623,U_1622,U_1624) = U_1624
& in(sK309(U_1623,U_1622,U_1624),powerset(the_carrier(U_1623)))
& in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622) )
| ~ in(U_1624,sK308(U_1623,U_1622)) ) )
| ( sK306(U_1623,U_1622) != sK307(U_1623,U_1622)
& in(set_difference(cast_as_carrier_subset(U_1623),sK307(U_1623,U_1622)),U_1622)
& sK305(U_1623,U_1622) = sK307(U_1623,U_1622)
& in(set_difference(cast_as_carrier_subset(U_1623),sK306(U_1623,U_1622)),U_1622)
& sK305(U_1623,U_1622) = sK306(U_1623,U_1622) )
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_1618,sK309(U_1623,U_1622,U_1624))],[f_435_7]) ).
fof(f_435_9,plain,
( ! [U_1624,U_1622,U_1623] :
( sK309(U_1623,U_1622,U_1624) = U_1624
| ~ sP383(U_1624,U_1622,U_1623) )
& ! [U_1624,U_1622,U_1623] :
( in(sK309(U_1623,U_1622,U_1624),powerset(the_carrier(U_1623)))
| ~ sP383(U_1624,U_1622,U_1623) )
& ! [U_1624,U_1622,U_1623] :
( in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622)
| ~ sP383(U_1624,U_1622,U_1623) )
& ! [U_1624,U_1622,U_1623,U_1625,U_1619] :
( in(U_1625,sK308(U_1623,U_1622))
| U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623)))
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622)
| ~ sP384(U_1624,U_1622,U_1623,U_1625,U_1619) )
& ! [U_1624,U_1622,U_1623,U_1625,U_1619] :
( sP383(U_1624,U_1622,U_1623)
| ~ in(U_1624,sK308(U_1623,U_1622))
| ~ sP384(U_1624,U_1622,U_1623,U_1625,U_1619) )
& ! [U_1622,U_1623] :
( sK306(U_1623,U_1622) != sK307(U_1623,U_1622)
| ~ sP382(U_1622,U_1623) )
& ! [U_1622,U_1623] :
( in(set_difference(cast_as_carrier_subset(U_1623),sK307(U_1623,U_1622)),U_1622)
| ~ sP382(U_1622,U_1623) )
& ! [U_1622,U_1623] :
( sK305(U_1623,U_1622) = sK307(U_1623,U_1622)
| ~ sP382(U_1622,U_1623) )
& ! [U_1622,U_1623] :
( in(set_difference(cast_as_carrier_subset(U_1623),sK306(U_1623,U_1622)),U_1622)
| ~ sP382(U_1622,U_1623) )
& ! [U_1622,U_1623] :
( sK305(U_1623,U_1622) = sK306(U_1623,U_1622)
| ~ sP382(U_1622,U_1623) )
& ! [U_1624,U_1622,U_1623,U_1625,U_1619] :
( sP384(U_1624,U_1622,U_1623,U_1625,U_1619)
| sP382(U_1622,U_1623)
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP382,sP383,sP384])],[f_435_8]) ).
cnf(f_435_10,plain,
( sP384(U_1624,U_1622,U_1623,U_1625,U_1619)
| sP382(U_1622,U_1623)
| ~ element(U_1622,powerset(powerset(the_carrier(U_1623))))
| ~ top_str(U_1623)
| ~ topological_space(U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_11,plain,
( sK305(U_1623,U_1622) = sK306(U_1623,U_1622)
| ~ sP382(U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_12,plain,
( in(set_difference(cast_as_carrier_subset(U_1623),sK306(U_1623,U_1622)),U_1622)
| ~ sP382(U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_13,plain,
( sK305(U_1623,U_1622) = sK307(U_1623,U_1622)
| ~ sP382(U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_14,plain,
( in(set_difference(cast_as_carrier_subset(U_1623),sK307(U_1623,U_1622)),U_1622)
| ~ sP382(U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_15,plain,
( sK306(U_1623,U_1622) != sK307(U_1623,U_1622)
| ~ sP382(U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_16,plain,
( sP383(U_1624,U_1622,U_1623)
| ~ in(U_1624,sK308(U_1623,U_1622))
| ~ sP384(U_1624,U_1622,U_1623,U_1625,U_1619) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_17,plain,
( in(U_1625,sK308(U_1623,U_1622))
| U_1619 != U_1625
| ~ in(U_1619,powerset(the_carrier(U_1623)))
| ~ in(set_difference(cast_as_carrier_subset(U_1623),U_1625),U_1622)
| ~ sP384(U_1624,U_1622,U_1623,U_1625,U_1619) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_18,plain,
( in(set_difference(cast_as_carrier_subset(U_1623),U_1624),U_1622)
| ~ sP383(U_1624,U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_19,plain,
( in(sK309(U_1623,U_1622,U_1624),powerset(the_carrier(U_1623)))
| ~ sP383(U_1624,U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
cnf(f_435_20,plain,
( sK309(U_1623,U_1622,U_1624) = U_1624
| ~ sP383(U_1624,U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_435_9]) ).
fof(f_436_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ! [H] :
( D != set_difference(H,singleton(A))
| ~ in(H,B) )
| E != D
| ~ in(E,powerset(A)) ) )
& ( ? [E] :
( ? [H] :
( D = set_difference(H,singleton(A))
& in(H,B) )
& E = D
& in(E,powerset(A)) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ? [G] :
( E = set_difference(G,singleton(A))
& in(G,B) )
& C = E
& ? [F] :
( D = set_difference(F,singleton(A))
& in(F,B) )
& C = D )
| ~ element(B,powerset(powerset(succ(A))))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e4_27_3_1__finset_1__1]) ).
fof(f_436_2,plain,
! [U_1638,U_1637] :
( ? [U_1636] :
! [U_1635] :
( ( in(U_1635,U_1636)
| ! [U_1634] :
( ! [U_1633] :
( U_1635 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) )
| U_1634 != U_1635
| ~ in(U_1634,powerset(U_1638)) ) )
& ( ? [U_1632] :
( ? [U_1631] :
( U_1635 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) )
& U_1632 = U_1635
& in(U_1632,powerset(U_1638)) )
| ~ in(U_1635,U_1636) ) )
| ? [U_1630,U_1629,U_1628] :
( U_1629 != U_1628
& ? [U_1627] :
( U_1628 = set_difference(U_1627,singleton(U_1638))
& in(U_1627,U_1637) )
& U_1630 = U_1628
& ? [U_1626] :
( U_1629 = set_difference(U_1626,singleton(U_1638))
& in(U_1626,U_1637) )
& U_1630 = U_1629 )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
! [U_1638,U_1637] :
( ? [U_1636] :
( ! [U_1640] :
( in(U_1640,U_1636)
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& ? [U_1631] :
( U_1639 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) ) )
| ~ in(U_1639,U_1636) ) )
| ? [U_1630,U_1629,U_1628] :
( U_1629 != U_1628
& ? [U_1627] :
( U_1628 = set_difference(U_1627,singleton(U_1638))
& in(U_1627,U_1637) )
& U_1630 = U_1628
& ? [U_1626] :
( U_1629 = set_difference(U_1626,singleton(U_1638))
& in(U_1626,U_1637) )
& U_1630 = U_1629 )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(miniscope,[status(thm)],[f_436_2]) ).
fof(f_436_4,plain,
! [U_1638,U_1637] :
( ? [U_1636] :
( ! [U_1640] :
( in(U_1640,U_1636)
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& ? [U_1631] :
( U_1639 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) ) )
| ~ in(U_1639,U_1636) ) )
| ? [U_1629,U_1628] :
( U_1629 != U_1628
& ? [U_1627] :
( U_1628 = set_difference(U_1627,singleton(U_1638))
& in(U_1627,U_1637) )
& sK310(U_1638,U_1637) = U_1628
& ? [U_1626] :
( U_1629 = set_difference(U_1626,singleton(U_1638))
& in(U_1626,U_1637) )
& sK310(U_1638,U_1637) = U_1629 )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_1630,sK310(U_1638,U_1637))],[f_436_3]) ).
fof(f_436_5,plain,
! [U_1638,U_1637] :
( ? [U_1636] :
( ! [U_1640] :
( in(U_1640,U_1636)
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& ? [U_1631] :
( U_1639 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) ) )
| ~ in(U_1639,U_1636) ) )
| ? [U_1628] :
( sK311(U_1638,U_1637) != U_1628
& ? [U_1627] :
( U_1628 = set_difference(U_1627,singleton(U_1638))
& in(U_1627,U_1637) )
& sK310(U_1638,U_1637) = U_1628
& ? [U_1626] :
( sK311(U_1638,U_1637) = set_difference(U_1626,singleton(U_1638))
& in(U_1626,U_1637) )
& sK310(U_1638,U_1637) = sK311(U_1638,U_1637) )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_1629,sK311(U_1638,U_1637))],[f_436_4]) ).
fof(f_436_6,plain,
! [U_1638,U_1637] :
( ? [U_1636] :
( ! [U_1640] :
( in(U_1640,U_1636)
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& ? [U_1631] :
( U_1639 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) ) )
| ~ in(U_1639,U_1636) ) )
| ( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
& ? [U_1627] :
( sK312(U_1638,U_1637) = set_difference(U_1627,singleton(U_1638))
& in(U_1627,U_1637) )
& sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
& ? [U_1626] :
( sK311(U_1638,U_1637) = set_difference(U_1626,singleton(U_1638))
& in(U_1626,U_1637) )
& sK310(U_1638,U_1637) = sK311(U_1638,U_1637) )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_1628,sK312(U_1638,U_1637))],[f_436_5]) ).
fof(f_436_7,plain,
! [U_1638,U_1637] :
( ? [U_1636] :
( ! [U_1640] :
( in(U_1640,U_1636)
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& ? [U_1631] :
( U_1639 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) ) )
| ~ in(U_1639,U_1636) ) )
| ( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
& ? [U_1627] :
( sK312(U_1638,U_1637) = set_difference(U_1627,singleton(U_1638))
& in(U_1627,U_1637) )
& sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
& sK311(U_1638,U_1637) = set_difference(sK313(U_1638,U_1637),singleton(U_1638))
& in(sK313(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK311(U_1638,U_1637) )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_1626,sK313(U_1638,U_1637))],[f_436_6]) ).
fof(f_436_8,plain,
! [U_1638,U_1637] :
( ? [U_1636] :
( ! [U_1640] :
( in(U_1640,U_1636)
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& ? [U_1631] :
( U_1639 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) ) )
| ~ in(U_1639,U_1636) ) )
| ( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
& sK312(U_1638,U_1637) = set_difference(sK314(U_1638,U_1637),singleton(U_1638))
& in(sK314(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
& sK311(U_1638,U_1637) = set_difference(sK313(U_1638,U_1637),singleton(U_1638))
& in(sK313(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK311(U_1638,U_1637) )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_1627,sK314(U_1638,U_1637))],[f_436_7]) ).
fof(f_436_9,plain,
! [U_1638,U_1637] :
( ( ! [U_1640] :
( in(U_1640,sK315(U_1638,U_1637))
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& ? [U_1631] :
( U_1639 = set_difference(U_1631,singleton(U_1638))
& in(U_1631,U_1637) ) )
| ~ in(U_1639,sK315(U_1638,U_1637)) ) )
| ( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
& sK312(U_1638,U_1637) = set_difference(sK314(U_1638,U_1637),singleton(U_1638))
& in(sK314(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
& sK311(U_1638,U_1637) = set_difference(sK313(U_1638,U_1637),singleton(U_1638))
& in(sK313(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK311(U_1638,U_1637) )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_1636,sK315(U_1638,U_1637))],[f_436_8]) ).
fof(f_436_10,plain,
! [U_1638,U_1637] :
( ( ! [U_1640] :
( in(U_1640,sK315(U_1638,U_1637))
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( ? [U_1632] :
( U_1632 = U_1639
& in(U_1632,powerset(U_1638)) )
& U_1639 = set_difference(sK316(U_1638,U_1637,U_1639),singleton(U_1638))
& in(sK316(U_1638,U_1637,U_1639),U_1637) )
| ~ in(U_1639,sK315(U_1638,U_1637)) ) )
| ( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
& sK312(U_1638,U_1637) = set_difference(sK314(U_1638,U_1637),singleton(U_1638))
& in(sK314(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
& sK311(U_1638,U_1637) = set_difference(sK313(U_1638,U_1637),singleton(U_1638))
& in(sK313(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK311(U_1638,U_1637) )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_1631,sK316(U_1638,U_1637,U_1639))],[f_436_9]) ).
fof(f_436_11,plain,
! [U_1638,U_1637] :
( ( ! [U_1640] :
( in(U_1640,sK315(U_1638,U_1637))
| ! [U_1634] :
( U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638)) )
| ! [U_1633] :
( U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637) ) )
& ! [U_1639] :
( ( sK317(U_1638,U_1637,U_1639) = U_1639
& in(sK317(U_1638,U_1637,U_1639),powerset(U_1638))
& U_1639 = set_difference(sK316(U_1638,U_1637,U_1639),singleton(U_1638))
& in(sK316(U_1638,U_1637,U_1639),U_1637) )
| ~ in(U_1639,sK315(U_1638,U_1637)) ) )
| ( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
& sK312(U_1638,U_1637) = set_difference(sK314(U_1638,U_1637),singleton(U_1638))
& in(sK314(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
& sK311(U_1638,U_1637) = set_difference(sK313(U_1638,U_1637),singleton(U_1638))
& in(sK313(U_1638,U_1637),U_1637)
& sK310(U_1638,U_1637) = sK311(U_1638,U_1637) )
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_1632,sK317(U_1638,U_1637,U_1639))],[f_436_10]) ).
fof(f_436_12,plain,
( ! [U_1639,U_1637,U_1638] :
( sK317(U_1638,U_1637,U_1639) = U_1639
| ~ sP386(U_1639,U_1637,U_1638) )
& ! [U_1639,U_1637,U_1638] :
( in(sK317(U_1638,U_1637,U_1639),powerset(U_1638))
| ~ sP386(U_1639,U_1637,U_1638) )
& ! [U_1639,U_1637,U_1638] :
( U_1639 = set_difference(sK316(U_1638,U_1637,U_1639),singleton(U_1638))
| ~ sP386(U_1639,U_1637,U_1638) )
& ! [U_1639,U_1637,U_1638] :
( in(sK316(U_1638,U_1637,U_1639),U_1637)
| ~ sP386(U_1639,U_1637,U_1638) )
& ! [U_1639,U_1640,U_1634,U_1637,U_1633,U_1638] :
( in(U_1640,sK315(U_1638,U_1637))
| U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638))
| U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637)
| ~ sP387(U_1639,U_1640,U_1634,U_1637,U_1633,U_1638) )
& ! [U_1639,U_1640,U_1634,U_1637,U_1633,U_1638] :
( sP386(U_1639,U_1637,U_1638)
| ~ in(U_1639,sK315(U_1638,U_1637))
| ~ sP387(U_1639,U_1640,U_1634,U_1637,U_1633,U_1638) )
& ! [U_1637,U_1638] :
( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
| ~ sP385(U_1637,U_1638) )
& ! [U_1637,U_1638] :
( sK312(U_1638,U_1637) = set_difference(sK314(U_1638,U_1637),singleton(U_1638))
| ~ sP385(U_1637,U_1638) )
& ! [U_1637,U_1638] :
( in(sK314(U_1638,U_1637),U_1637)
| ~ sP385(U_1637,U_1638) )
& ! [U_1637,U_1638] :
( sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
| ~ sP385(U_1637,U_1638) )
& ! [U_1637,U_1638] :
( sK311(U_1638,U_1637) = set_difference(sK313(U_1638,U_1637),singleton(U_1638))
| ~ sP385(U_1637,U_1638) )
& ! [U_1637,U_1638] :
( in(sK313(U_1638,U_1637),U_1637)
| ~ sP385(U_1637,U_1638) )
& ! [U_1637,U_1638] :
( sK310(U_1638,U_1637) = sK311(U_1638,U_1637)
| ~ sP385(U_1637,U_1638) )
& ! [U_1639,U_1640,U_1634,U_1637,U_1633,U_1638] :
( sP387(U_1639,U_1640,U_1634,U_1637,U_1633,U_1638)
| sP385(U_1637,U_1638)
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP385,sP386,sP387])],[f_436_11]) ).
cnf(f_436_13,plain,
( sP387(U_1639,U_1640,U_1634,U_1637,U_1633,U_1638)
| sP385(U_1637,U_1638)
| ~ element(U_1637,powerset(powerset(succ(U_1638))))
| ~ ordinal(U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_14,plain,
( sK310(U_1638,U_1637) = sK311(U_1638,U_1637)
| ~ sP385(U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_15,plain,
( in(sK313(U_1638,U_1637),U_1637)
| ~ sP385(U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_16,plain,
( sK311(U_1638,U_1637) = set_difference(sK313(U_1638,U_1637),singleton(U_1638))
| ~ sP385(U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_17,plain,
( sK310(U_1638,U_1637) = sK312(U_1638,U_1637)
| ~ sP385(U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_18,plain,
( in(sK314(U_1638,U_1637),U_1637)
| ~ sP385(U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_19,plain,
( sK312(U_1638,U_1637) = set_difference(sK314(U_1638,U_1637),singleton(U_1638))
| ~ sP385(U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_20,plain,
( sK311(U_1638,U_1637) != sK312(U_1638,U_1637)
| ~ sP385(U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_21,plain,
( sP386(U_1639,U_1637,U_1638)
| ~ in(U_1639,sK315(U_1638,U_1637))
| ~ sP387(U_1639,U_1640,U_1634,U_1637,U_1633,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_22,plain,
( in(U_1640,sK315(U_1638,U_1637))
| U_1634 != U_1640
| ~ in(U_1634,powerset(U_1638))
| U_1640 != set_difference(U_1633,singleton(U_1638))
| ~ in(U_1633,U_1637)
| ~ sP387(U_1639,U_1640,U_1634,U_1637,U_1633,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_23,plain,
( in(sK316(U_1638,U_1637,U_1639),U_1637)
| ~ sP386(U_1639,U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_24,plain,
( U_1639 = set_difference(sK316(U_1638,U_1637,U_1639),singleton(U_1638))
| ~ sP386(U_1639,U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_25,plain,
( in(sK317(U_1638,U_1637,U_1639),powerset(U_1638))
| ~ sP386(U_1639,U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
cnf(f_436_26,plain,
( sK317(U_1638,U_1637,U_1639) = U_1639
| ~ sP386(U_1639,U_1637,U_1638) ),
inference(clausify,[status(thm)],[f_436_12]) ).
fof(f_437_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ? [H] :
( D != subset_complement(the_carrier(A),H)
& H = E
& element(H,powerset(the_carrier(A))) )
| ~ in(E,complements_of_subsets(the_carrier(A),B))
| ~ in(E,complements_of_subsets(the_carrier(A),B)) ) )
& ( ? [E] :
( ! [H] :
( D = subset_complement(the_carrier(A),H)
| H != E
| ~ element(H,powerset(the_carrier(A))) )
& in(E,complements_of_subsets(the_carrier(A),B))
& in(E,complements_of_subsets(the_carrier(A),B)) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ! [G] :
( E = subset_complement(the_carrier(A),G)
| G != C
| ~ element(G,powerset(the_carrier(A))) )
& in(C,complements_of_subsets(the_carrier(A),B))
& ! [F] :
( D = subset_complement(the_carrier(A),F)
| F != C
| ~ element(F,powerset(the_carrier(A))) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e4_7_1__tops_2__1]) ).
fof(f_437_2,plain,
! [U_1653,U_1652] :
( ? [U_1651] :
! [U_1650] :
( ( in(U_1650,U_1651)
| ! [U_1649] :
( ? [U_1648] :
( U_1650 != subset_complement(the_carrier(U_1653),U_1648)
& U_1648 = U_1649
& element(U_1648,powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ( ? [U_1647] :
( ! [U_1646] :
( U_1650 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != U_1647
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652))
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1650,U_1651) ) )
| ? [U_1645,U_1644,U_1643] :
( U_1644 != U_1643
& ! [U_1642] :
( U_1643 = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != U_1645
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(U_1645,complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( U_1644 = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != U_1645
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(U_1645,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
! [U_1653,U_1652] :
( ? [U_1651] :
( ! [U_1655] :
( in(U_1655,U_1651)
| ! [U_1649] :
( ? [U_1648] :
( U_1655 != subset_complement(the_carrier(U_1653),U_1648)
& U_1648 = U_1649
& element(U_1648,powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ! [U_1654] :
( ? [U_1647] :
( ! [U_1646] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != U_1647
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652))
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1654,U_1651) ) )
| ? [U_1645,U_1644,U_1643] :
( U_1644 != U_1643
& ! [U_1642] :
( U_1643 = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != U_1645
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(U_1645,complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( U_1644 = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != U_1645
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(U_1645,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(miniscope,[status(thm)],[f_437_2]) ).
fof(f_437_4,plain,
! [U_1653,U_1652] :
( ? [U_1651] :
( ! [U_1655] :
( in(U_1655,U_1651)
| ! [U_1649] :
( ? [U_1648] :
( U_1655 != subset_complement(the_carrier(U_1653),U_1648)
& U_1648 = U_1649
& element(U_1648,powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ! [U_1654] :
( ? [U_1647] :
( ! [U_1646] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != U_1647
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652))
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1654,U_1651) ) )
| ? [U_1644,U_1643] :
( U_1644 != U_1643
& ! [U_1642] :
( U_1643 = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( U_1644 = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_1645,sK318(U_1653,U_1652))],[f_437_3]) ).
fof(f_437_5,plain,
! [U_1653,U_1652] :
( ? [U_1651] :
( ! [U_1655] :
( in(U_1655,U_1651)
| ! [U_1649] :
( ? [U_1648] :
( U_1655 != subset_complement(the_carrier(U_1653),U_1648)
& U_1648 = U_1649
& element(U_1648,powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ! [U_1654] :
( ? [U_1647] :
( ! [U_1646] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != U_1647
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652))
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1654,U_1651) ) )
| ? [U_1643] :
( sK319(U_1653,U_1652) != U_1643
& ! [U_1642] :
( U_1643 = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( sK319(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_1644,sK319(U_1653,U_1652))],[f_437_4]) ).
fof(f_437_6,plain,
! [U_1653,U_1652] :
( ? [U_1651] :
( ! [U_1655] :
( in(U_1655,U_1651)
| ! [U_1649] :
( ? [U_1648] :
( U_1655 != subset_complement(the_carrier(U_1653),U_1648)
& U_1648 = U_1649
& element(U_1648,powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ! [U_1654] :
( ? [U_1647] :
( ! [U_1646] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != U_1647
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652))
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1654,U_1651) ) )
| ( sK319(U_1653,U_1652) != sK320(U_1653,U_1652)
& ! [U_1642] :
( sK320(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( sK319(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_1643,sK320(U_1653,U_1652))],[f_437_5]) ).
fof(f_437_7,plain,
! [U_1653,U_1652] :
( ( ! [U_1655] :
( in(U_1655,sK321(U_1653,U_1652))
| ! [U_1649] :
( ? [U_1648] :
( U_1655 != subset_complement(the_carrier(U_1653),U_1648)
& U_1648 = U_1649
& element(U_1648,powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ! [U_1654] :
( ? [U_1647] :
( ! [U_1646] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != U_1647
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652))
& in(U_1647,complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1654,sK321(U_1653,U_1652)) ) )
| ( sK319(U_1653,U_1652) != sK320(U_1653,U_1652)
& ! [U_1642] :
( sK320(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( sK319(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_1651,sK321(U_1653,U_1652))],[f_437_6]) ).
fof(f_437_8,plain,
! [U_1653,U_1652] :
( ( ! [U_1655] :
( in(U_1655,sK321(U_1653,U_1652))
| ! [U_1649] :
( ? [U_1648] :
( U_1655 != subset_complement(the_carrier(U_1653),U_1648)
& U_1648 = U_1649
& element(U_1648,powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ! [U_1654] :
( ( ! [U_1646] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != sK322(U_1653,U_1652,U_1654)
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652))
& in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1654,sK321(U_1653,U_1652)) ) )
| ( sK319(U_1653,U_1652) != sK320(U_1653,U_1652)
& ! [U_1642] :
( sK320(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( sK319(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_1647,sK322(U_1653,U_1652,U_1654))],[f_437_7]) ).
fof(f_437_9,plain,
! [U_1653,U_1652] :
( ( ! [U_1655] :
( in(U_1655,sK321(U_1653,U_1652))
| ! [U_1649] :
( ( U_1655 != subset_complement(the_carrier(U_1653),sK323(U_1653,U_1652,U_1655,U_1649))
& sK323(U_1653,U_1652,U_1655,U_1649) = U_1649
& element(sK323(U_1653,U_1652,U_1655,U_1649),powerset(the_carrier(U_1653))) )
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652)) ) )
& ! [U_1654] :
( ( ! [U_1646] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != sK322(U_1653,U_1652,U_1654)
| ~ element(U_1646,powerset(the_carrier(U_1653))) )
& in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652))
& in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ in(U_1654,sK321(U_1653,U_1652)) ) )
| ( sK319(U_1653,U_1652) != sK320(U_1653,U_1652)
& ! [U_1642] :
( sK320(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
& ! [U_1641] :
( sK319(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653))) )
& in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652)) )
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_1648,sK323(U_1653,U_1652,U_1655,U_1649))],[f_437_8]) ).
fof(f_437_10,plain,
( ! [U_1649,U_1655,U_1652,U_1653] :
( U_1655 != subset_complement(the_carrier(U_1653),sK323(U_1653,U_1652,U_1655,U_1649))
| ~ sP390(U_1649,U_1655,U_1652,U_1653) )
& ! [U_1649,U_1655,U_1652,U_1653] :
( sK323(U_1653,U_1652,U_1655,U_1649) = U_1649
| ~ sP390(U_1649,U_1655,U_1652,U_1653) )
& ! [U_1649,U_1655,U_1652,U_1653] :
( element(sK323(U_1653,U_1652,U_1655,U_1649),powerset(the_carrier(U_1653)))
| ~ sP390(U_1649,U_1655,U_1652,U_1653) )
& ! [U_1646,U_1652,U_1654,U_1653] :
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != sK322(U_1653,U_1652,U_1654)
| ~ element(U_1646,powerset(the_carrier(U_1653)))
| ~ sP389(U_1646,U_1652,U_1654,U_1653) )
& ! [U_1646,U_1652,U_1654,U_1653] :
( in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP389(U_1646,U_1652,U_1654,U_1653) )
& ! [U_1646,U_1652,U_1654,U_1653] :
( in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP389(U_1646,U_1652,U_1654,U_1653) )
& ! [U_1646,U_1649,U_1655,U_1652,U_1654,U_1653] :
( in(U_1655,sK321(U_1653,U_1652))
| sP390(U_1649,U_1655,U_1652,U_1653)
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP391(U_1646,U_1649,U_1655,U_1652,U_1654,U_1653) )
& ! [U_1646,U_1649,U_1655,U_1652,U_1654,U_1653] :
( sP389(U_1646,U_1652,U_1654,U_1653)
| ~ in(U_1654,sK321(U_1653,U_1652))
| ~ sP391(U_1646,U_1649,U_1655,U_1652,U_1654,U_1653) )
& ! [U_1641,U_1652,U_1642,U_1653] :
( sK319(U_1653,U_1652) != sK320(U_1653,U_1652)
| ~ sP388(U_1641,U_1652,U_1642,U_1653) )
& ! [U_1641,U_1652,U_1642,U_1653] :
( sK320(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653)))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) )
& ! [U_1641,U_1652,U_1642,U_1653] :
( in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) )
& ! [U_1641,U_1652,U_1642,U_1653] :
( sK319(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653)))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) )
& ! [U_1641,U_1652,U_1642,U_1653] :
( in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) )
& ! [U_1646,U_1641,U_1649,U_1655,U_1652,U_1642,U_1654,U_1653] :
( sP391(U_1646,U_1649,U_1655,U_1652,U_1654,U_1653)
| sP388(U_1641,U_1652,U_1642,U_1653)
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP388,sP389,sP390,sP391])],[f_437_9]) ).
cnf(f_437_11,plain,
( sP391(U_1646,U_1649,U_1655,U_1652,U_1654,U_1653)
| sP388(U_1641,U_1652,U_1642,U_1653)
| ~ element(U_1652,powerset(powerset(the_carrier(U_1653))))
| ~ one_sorted_str(U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_12,plain,
( in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_13,plain,
( sK319(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1641)
| U_1641 != sK318(U_1653,U_1652)
| ~ element(U_1641,powerset(the_carrier(U_1653)))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_14,plain,
( in(sK318(U_1653,U_1652),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_15,plain,
( sK320(U_1653,U_1652) = subset_complement(the_carrier(U_1653),U_1642)
| U_1642 != sK318(U_1653,U_1652)
| ~ element(U_1642,powerset(the_carrier(U_1653)))
| ~ sP388(U_1641,U_1652,U_1642,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_16,plain,
( sK319(U_1653,U_1652) != sK320(U_1653,U_1652)
| ~ sP388(U_1641,U_1652,U_1642,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_17,plain,
( sP389(U_1646,U_1652,U_1654,U_1653)
| ~ in(U_1654,sK321(U_1653,U_1652))
| ~ sP391(U_1646,U_1649,U_1655,U_1652,U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_18,plain,
( in(U_1655,sK321(U_1653,U_1652))
| sP390(U_1649,U_1655,U_1652,U_1653)
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP391(U_1646,U_1649,U_1655,U_1652,U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_19,plain,
( in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP389(U_1646,U_1652,U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_20,plain,
( in(sK322(U_1653,U_1652,U_1654),complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP389(U_1646,U_1652,U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_21,plain,
( U_1654 = subset_complement(the_carrier(U_1653),U_1646)
| U_1646 != sK322(U_1653,U_1652,U_1654)
| ~ element(U_1646,powerset(the_carrier(U_1653)))
| ~ sP389(U_1646,U_1652,U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_22,plain,
( element(sK323(U_1653,U_1652,U_1655,U_1649),powerset(the_carrier(U_1653)))
| ~ sP390(U_1649,U_1655,U_1652,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_23,plain,
( sK323(U_1653,U_1652,U_1655,U_1649) = U_1649
| ~ sP390(U_1649,U_1655,U_1652,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
cnf(f_437_24,plain,
( U_1655 != subset_complement(the_carrier(U_1653),sK323(U_1653,U_1652,U_1655,U_1649))
| ~ sP390(U_1649,U_1655,U_1652,U_1653) ),
inference(clausify,[status(thm)],[f_437_10]) ).
fof(f_438_1,plain,
! [A,B] :
( ! [C] :
( ? [D] :
! [E] :
( ( in(E,D)
| ! [F] :
( ! [M,N] :
( ? [O] :
( N != subset_complement(the_carrier(A),O)
& O = M
& element(O,powerset(the_carrier(A))) )
| ~ in(M,complements_of_subsets(the_carrier(A),B))
| ordered_pair(M,N) != E )
| F != E
| ~ in(F,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) ) )
& ( ? [F] :
( ? [M,N] :
( ! [O] :
( N = subset_complement(the_carrier(A),O)
| O != M
| ~ element(O,powerset(the_carrier(A))) )
& in(M,complements_of_subsets(the_carrier(A),B))
& ordered_pair(M,N) = E )
& F = E
& in(F,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) )
| ~ in(E,D) ) )
| ? [D,E,F] :
( E != F
& ? [J,K] :
( ! [L] :
( K = subset_complement(the_carrier(A),L)
| L != J
| ~ element(L,powerset(the_carrier(A))) )
& in(J,complements_of_subsets(the_carrier(A),B))
& ordered_pair(J,K) = F )
& D = F
& ? [G,H] :
( ! [I] :
( H = subset_complement(the_carrier(A),I)
| I != G
| ~ element(I,powerset(the_carrier(A))) )
& in(G,complements_of_subsets(the_carrier(A),B))
& ordered_pair(G,H) = E )
& D = E ) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e4_7_1__tops_2__2]) ).
fof(f_438_2,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
( ? [U_1674] :
! [U_1673] :
( ( in(U_1673,U_1674)
| ! [U_1672] :
( ! [U_1671,U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676))
| ordered_pair(U_1671,U_1670) != U_1673 )
| U_1672 != U_1673
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) ) )
& ( ? [U_1668] :
( ? [U_1667,U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676))
& ordered_pair(U_1667,U_1666) = U_1673 )
& U_1668 = U_1673
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ~ in(U_1673,U_1674) ) )
| ? [U_1664,U_1663,U_1662] :
( U_1663 != U_1662
& ? [U_1661,U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != U_1661
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& in(U_1661,complements_of_subsets(the_carrier(U_1677),U_1676))
& ordered_pair(U_1661,U_1660) = U_1662 )
& U_1664 = U_1662
& ? [U_1658,U_1657] :
( ! [U_1656] :
( U_1657 = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != U_1658
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& in(U_1658,complements_of_subsets(the_carrier(U_1677),U_1676))
& ordered_pair(U_1658,U_1657) = U_1663 )
& U_1664 = U_1663 ) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ? [U_1664,U_1663,U_1662] :
( U_1663 != U_1662
& ? [U_1661] :
( ? [U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != U_1661
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1661,U_1660) = U_1662 )
& in(U_1661,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& U_1664 = U_1662
& ? [U_1658] :
( ? [U_1657] :
( ! [U_1656] :
( U_1657 = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != U_1658
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1658,U_1657) = U_1663 )
& in(U_1658,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& U_1664 = U_1663 )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(miniscope,[status(thm)],[f_438_2]) ).
fof(f_438_4,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ? [U_1663,U_1662] :
( U_1663 != U_1662
& ? [U_1661] :
( ? [U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != U_1661
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1661,U_1660) = U_1662 )
& in(U_1661,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = U_1662
& ? [U_1658] :
( ? [U_1657] :
( ! [U_1656] :
( U_1657 = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != U_1658
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1658,U_1657) = U_1663 )
& in(U_1658,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = U_1663 )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_1664,sK324(U_1677,U_1676))],[f_438_3]) ).
fof(f_438_5,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ? [U_1662] :
( sK325(U_1677,U_1676) != U_1662
& ? [U_1661] :
( ? [U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != U_1661
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1661,U_1660) = U_1662 )
& in(U_1661,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = U_1662
& ? [U_1658] :
( ? [U_1657] :
( ! [U_1656] :
( U_1657 = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != U_1658
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1658,U_1657) = sK325(U_1677,U_1676) )
& in(U_1658,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_1663,sK325(U_1677,U_1676))],[f_438_4]) ).
fof(f_438_6,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ? [U_1661] :
( ? [U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != U_1661
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1661,U_1660) = sK326(U_1677,U_1676) )
& in(U_1661,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ? [U_1658] :
( ? [U_1657] :
( ! [U_1656] :
( U_1657 = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != U_1658
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1658,U_1657) = sK325(U_1677,U_1676) )
& in(U_1658,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_1662,sK326(U_1677,U_1676))],[f_438_5]) ).
fof(f_438_7,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ? [U_1661] :
( ? [U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != U_1661
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1661,U_1660) = sK326(U_1677,U_1676) )
& in(U_1661,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ? [U_1657] :
( ! [U_1656] :
( U_1657 = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),U_1657) = sK325(U_1677,U_1676) )
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_1658,sK327(U_1677,U_1676))],[f_438_6]) ).
fof(f_438_8,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ? [U_1661] :
( ? [U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != U_1661
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1661,U_1660) = sK326(U_1677,U_1676) )
& in(U_1661,complements_of_subsets(the_carrier(U_1677),U_1676)) )
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_1657,sK328(U_1677,U_1676))],[f_438_7]) ).
fof(f_438_9,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ? [U_1660] :
( ! [U_1659] :
( U_1660 = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(sK329(U_1677,U_1676),U_1660) = sK326(U_1677,U_1676) )
& in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_1661,sK329(U_1677,U_1676))],[f_438_8]) ).
fof(f_438_10,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
? [U_1674] :
( ! [U_1679] :
( in(U_1679,U_1674)
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,U_1674) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ! [U_1659] :
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
& in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_1660,sK330(U_1677,U_1676))],[f_438_9]) ).
fof(f_438_11,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
( ! [U_1679] :
( in(U_1679,sK331(U_1677,U_1676,U_1675))
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1667] :
( ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != U_1667
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(U_1667,U_1666) = U_1678 )
& in(U_1667,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
| ~ in(U_1678,sK331(U_1677,U_1676,U_1675)) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ! [U_1659] :
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
& in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_1674,sK331(U_1677,U_1676,U_1675))],[f_438_10]) ).
fof(f_438_12,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
( ! [U_1679] :
( in(U_1679,sK331(U_1677,U_1676,U_1675))
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ? [U_1666] :
( ! [U_1665] :
( U_1666 = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != sK332(U_1677,U_1676,U_1675,U_1678)
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(sK332(U_1677,U_1676,U_1675,U_1678),U_1666) = U_1678 )
& in(sK332(U_1677,U_1676,U_1675,U_1678),complements_of_subsets(the_carrier(U_1677),U_1676)) )
| ~ in(U_1678,sK331(U_1677,U_1676,U_1675)) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ! [U_1659] :
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
& in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_1667,sK332(U_1677,U_1676,U_1675,U_1678))],[f_438_11]) ).
fof(f_438_13,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
( ! [U_1679] :
( in(U_1679,sK331(U_1677,U_1676,U_1675))
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( ? [U_1668] :
( U_1668 = U_1678
& in(U_1668,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
& ! [U_1665] :
( sK333(U_1677,U_1676,U_1675,U_1678) = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != sK332(U_1677,U_1676,U_1675,U_1678)
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(sK332(U_1677,U_1676,U_1675,U_1678),sK333(U_1677,U_1676,U_1675,U_1678)) = U_1678
& in(sK332(U_1677,U_1676,U_1675,U_1678),complements_of_subsets(the_carrier(U_1677),U_1676)) )
| ~ in(U_1678,sK331(U_1677,U_1676,U_1675)) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ! [U_1659] :
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
& in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_1666,sK333(U_1677,U_1676,U_1675,U_1678))],[f_438_12]) ).
fof(f_438_14,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
( ! [U_1679] :
( in(U_1679,sK331(U_1677,U_1676,U_1675))
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ? [U_1669] :
( U_1670 != subset_complement(the_carrier(U_1677),U_1669)
& U_1669 = U_1671
& element(U_1669,powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( sK334(U_1677,U_1676,U_1675,U_1678) = U_1678
& in(sK334(U_1677,U_1676,U_1675,U_1678),cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675))
& ! [U_1665] :
( sK333(U_1677,U_1676,U_1675,U_1678) = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != sK332(U_1677,U_1676,U_1675,U_1678)
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(sK332(U_1677,U_1676,U_1675,U_1678),sK333(U_1677,U_1676,U_1675,U_1678)) = U_1678
& in(sK332(U_1677,U_1676,U_1675,U_1678),complements_of_subsets(the_carrier(U_1677),U_1676)) )
| ~ in(U_1678,sK331(U_1677,U_1676,U_1675)) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ! [U_1659] :
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
& in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_1668,sK334(U_1677,U_1676,U_1675,U_1678))],[f_438_13]) ).
fof(f_438_15,plain,
! [U_1677,U_1676] :
( ! [U_1675] :
( ! [U_1679] :
( in(U_1679,sK331(U_1677,U_1676,U_1675))
| ! [U_1672] :
( U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675)) )
| ! [U_1671] :
( ! [U_1670] :
( ( U_1670 != subset_complement(the_carrier(U_1677),sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670))
& sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670) = U_1671
& element(sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670),powerset(the_carrier(U_1677))) )
| ordered_pair(U_1671,U_1670) != U_1679 )
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676)) ) )
& ! [U_1678] :
( ( sK334(U_1677,U_1676,U_1675,U_1678) = U_1678
& in(sK334(U_1677,U_1676,U_1675,U_1678),cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675))
& ! [U_1665] :
( sK333(U_1677,U_1676,U_1675,U_1678) = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != sK332(U_1677,U_1676,U_1675,U_1678)
| ~ element(U_1665,powerset(the_carrier(U_1677))) )
& ordered_pair(sK332(U_1677,U_1676,U_1675,U_1678),sK333(U_1677,U_1676,U_1675,U_1678)) = U_1678
& in(sK332(U_1677,U_1676,U_1675,U_1678),complements_of_subsets(the_carrier(U_1677),U_1676)) )
| ~ in(U_1678,sK331(U_1677,U_1676,U_1675)) ) )
| ( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
& ! [U_1659] :
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677))) )
& ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
& in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
& ! [U_1656] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677))) )
& ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
& in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
& sK324(U_1677,U_1676) = sK325(U_1677,U_1676) )
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_1669,sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670))],[f_438_14]) ).
fof(f_438_16,plain,
( ! [U_1677,U_1676,U_1679,U_1675,U_1671,U_1670] :
( U_1670 != subset_complement(the_carrier(U_1677),sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670))
| ~ sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670) )
& ! [U_1677,U_1676,U_1679,U_1675,U_1671,U_1670] :
( sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670) = U_1671
| ~ sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670) )
& ! [U_1677,U_1676,U_1679,U_1675,U_1671,U_1670] :
( element(sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670),powerset(the_carrier(U_1677)))
| ~ sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670) )
& ! [U_1677,U_1676,U_1665,U_1678,U_1675] :
( sK334(U_1677,U_1676,U_1675,U_1678) = U_1678
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) )
& ! [U_1677,U_1676,U_1665,U_1678,U_1675] :
( in(sK334(U_1677,U_1676,U_1675,U_1678),cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675))
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) )
& ! [U_1677,U_1676,U_1665,U_1678,U_1675] :
( sK333(U_1677,U_1676,U_1675,U_1678) = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != sK332(U_1677,U_1676,U_1675,U_1678)
| ~ element(U_1665,powerset(the_carrier(U_1677)))
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) )
& ! [U_1677,U_1676,U_1665,U_1678,U_1675] :
( ordered_pair(sK332(U_1677,U_1676,U_1675,U_1678),sK333(U_1677,U_1676,U_1675,U_1678)) = U_1678
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) )
& ! [U_1677,U_1676,U_1665,U_1678,U_1675] :
( in(sK332(U_1677,U_1676,U_1675,U_1678),complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) )
& ! [U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670] :
( in(U_1679,sK331(U_1677,U_1676,U_1675))
| U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675))
| sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670)
| ordered_pair(U_1671,U_1670) != U_1679
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP395(U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670) )
& ! [U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670] :
( sP393(U_1677,U_1676,U_1665,U_1678,U_1675)
| ~ in(U_1678,sK331(U_1677,U_1676,U_1675))
| ~ sP395(U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677)))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677)))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1656,U_1659,U_1676] :
( sK324(U_1677,U_1676) = sK325(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) )
& ! [U_1677,U_1672,U_1656,U_1659,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670] :
( sP395(U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670)
| sP392(U_1677,U_1656,U_1659,U_1676)
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP392,sP393,sP394,sP395])],[f_438_15]) ).
cnf(f_438_17,plain,
( sP395(U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670)
| sP392(U_1677,U_1656,U_1659,U_1676)
| ~ element(U_1676,powerset(powerset(the_carrier(U_1677))))
| ~ one_sorted_str(U_1677) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_18,plain,
( sK324(U_1677,U_1676) = sK325(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_19,plain,
( in(sK327(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_20,plain,
( ordered_pair(sK327(U_1677,U_1676),sK328(U_1677,U_1676)) = sK325(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_21,plain,
( sK328(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1656)
| U_1656 != sK327(U_1677,U_1676)
| ~ element(U_1656,powerset(the_carrier(U_1677)))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_22,plain,
( sK324(U_1677,U_1676) = sK326(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_23,plain,
( in(sK329(U_1677,U_1676),complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_24,plain,
( ordered_pair(sK329(U_1677,U_1676),sK330(U_1677,U_1676)) = sK326(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_25,plain,
( sK330(U_1677,U_1676) = subset_complement(the_carrier(U_1677),U_1659)
| U_1659 != sK329(U_1677,U_1676)
| ~ element(U_1659,powerset(the_carrier(U_1677)))
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_26,plain,
( sK325(U_1677,U_1676) != sK326(U_1677,U_1676)
| ~ sP392(U_1677,U_1656,U_1659,U_1676) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_27,plain,
( sP393(U_1677,U_1676,U_1665,U_1678,U_1675)
| ~ in(U_1678,sK331(U_1677,U_1676,U_1675))
| ~ sP395(U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_28,plain,
( in(U_1679,sK331(U_1677,U_1676,U_1675))
| U_1672 != U_1679
| ~ in(U_1672,cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675))
| sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670)
| ordered_pair(U_1671,U_1670) != U_1679
| ~ in(U_1671,complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP395(U_1677,U_1672,U_1676,U_1665,U_1679,U_1678,U_1675,U_1671,U_1670) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_29,plain,
( in(sK332(U_1677,U_1676,U_1675,U_1678),complements_of_subsets(the_carrier(U_1677),U_1676))
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_30,plain,
( ordered_pair(sK332(U_1677,U_1676,U_1675,U_1678),sK333(U_1677,U_1676,U_1675,U_1678)) = U_1678
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_31,plain,
( sK333(U_1677,U_1676,U_1675,U_1678) = subset_complement(the_carrier(U_1677),U_1665)
| U_1665 != sK332(U_1677,U_1676,U_1675,U_1678)
| ~ element(U_1665,powerset(the_carrier(U_1677)))
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_32,plain,
( in(sK334(U_1677,U_1676,U_1675,U_1678),cartesian_product2(complements_of_subsets(the_carrier(U_1677),U_1676),U_1675))
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_33,plain,
( sK334(U_1677,U_1676,U_1675,U_1678) = U_1678
| ~ sP393(U_1677,U_1676,U_1665,U_1678,U_1675) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_34,plain,
( element(sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670),powerset(the_carrier(U_1677)))
| ~ sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_35,plain,
( sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670) = U_1671
| ~ sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670) ),
inference(clausify,[status(thm)],[f_438_16]) ).
cnf(f_438_36,plain,
( U_1670 != subset_complement(the_carrier(U_1677),sK335(U_1677,U_1676,U_1675,U_1679,U_1671,U_1670))
| ~ sP394(U_1677,U_1676,U_1679,U_1675,U_1671,U_1670) ),
inference(clausify,[status(thm)],[f_438_16]) ).
fof(f_439_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ? [H] :
( D != subset_complement(the_carrier(A),H)
& H = E
& element(H,powerset(the_carrier(A))) )
| ~ in(E,B)
| ~ in(E,B) ) )
& ( ? [E] :
( ! [H] :
( D = subset_complement(the_carrier(A),H)
| H != E
| ~ element(H,powerset(the_carrier(A))) )
& in(E,B)
& in(E,B) )
| ~ in(D,C) ) )
| ? [C,D,E] :
( D != E
& ! [G] :
( E = subset_complement(the_carrier(A),G)
| G != C
| ~ element(G,powerset(the_carrier(A))) )
& in(C,B)
& ! [F] :
( D = subset_complement(the_carrier(A),F)
| F != C
| ~ element(F,powerset(the_carrier(A))) )
& in(C,B) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e4_7_2__tops_2__1]) ).
fof(f_439_2,plain,
! [U_1692,U_1691] :
( ? [U_1690] :
! [U_1689] :
( ( in(U_1689,U_1690)
| ! [U_1688] :
( ? [U_1687] :
( U_1689 != subset_complement(the_carrier(U_1692),U_1687)
& U_1687 = U_1688
& element(U_1687,powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ( ? [U_1686] :
( ! [U_1685] :
( U_1689 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != U_1686
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(U_1686,U_1691)
& in(U_1686,U_1691) )
| ~ in(U_1689,U_1690) ) )
| ? [U_1684,U_1683,U_1682] :
( U_1683 != U_1682
& ! [U_1681] :
( U_1682 = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != U_1684
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(U_1684,U_1691)
& ! [U_1680] :
( U_1683 = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != U_1684
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(U_1684,U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
! [U_1692,U_1691] :
( ? [U_1690] :
( ! [U_1694] :
( in(U_1694,U_1690)
| ! [U_1688] :
( ? [U_1687] :
( U_1694 != subset_complement(the_carrier(U_1692),U_1687)
& U_1687 = U_1688
& element(U_1687,powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ! [U_1693] :
( ? [U_1686] :
( ! [U_1685] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != U_1686
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(U_1686,U_1691)
& in(U_1686,U_1691) )
| ~ in(U_1693,U_1690) ) )
| ? [U_1684,U_1683,U_1682] :
( U_1683 != U_1682
& ! [U_1681] :
( U_1682 = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != U_1684
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(U_1684,U_1691)
& ! [U_1680] :
( U_1683 = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != U_1684
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(U_1684,U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(miniscope,[status(thm)],[f_439_2]) ).
fof(f_439_4,plain,
! [U_1692,U_1691] :
( ? [U_1690] :
( ! [U_1694] :
( in(U_1694,U_1690)
| ! [U_1688] :
( ? [U_1687] :
( U_1694 != subset_complement(the_carrier(U_1692),U_1687)
& U_1687 = U_1688
& element(U_1687,powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ! [U_1693] :
( ? [U_1686] :
( ! [U_1685] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != U_1686
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(U_1686,U_1691)
& in(U_1686,U_1691) )
| ~ in(U_1693,U_1690) ) )
| ? [U_1683,U_1682] :
( U_1683 != U_1682
& ! [U_1681] :
( U_1682 = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691)
& ! [U_1680] :
( U_1683 = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_1684,sK336(U_1692,U_1691))],[f_439_3]) ).
fof(f_439_5,plain,
! [U_1692,U_1691] :
( ? [U_1690] :
( ! [U_1694] :
( in(U_1694,U_1690)
| ! [U_1688] :
( ? [U_1687] :
( U_1694 != subset_complement(the_carrier(U_1692),U_1687)
& U_1687 = U_1688
& element(U_1687,powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ! [U_1693] :
( ? [U_1686] :
( ! [U_1685] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != U_1686
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(U_1686,U_1691)
& in(U_1686,U_1691) )
| ~ in(U_1693,U_1690) ) )
| ? [U_1682] :
( sK337(U_1692,U_1691) != U_1682
& ! [U_1681] :
( U_1682 = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691)
& ! [U_1680] :
( sK337(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_1683,sK337(U_1692,U_1691))],[f_439_4]) ).
fof(f_439_6,plain,
! [U_1692,U_1691] :
( ? [U_1690] :
( ! [U_1694] :
( in(U_1694,U_1690)
| ! [U_1688] :
( ? [U_1687] :
( U_1694 != subset_complement(the_carrier(U_1692),U_1687)
& U_1687 = U_1688
& element(U_1687,powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ! [U_1693] :
( ? [U_1686] :
( ! [U_1685] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != U_1686
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(U_1686,U_1691)
& in(U_1686,U_1691) )
| ~ in(U_1693,U_1690) ) )
| ( sK337(U_1692,U_1691) != sK338(U_1692,U_1691)
& ! [U_1681] :
( sK338(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691)
& ! [U_1680] :
( sK337(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_1682,sK338(U_1692,U_1691))],[f_439_5]) ).
fof(f_439_7,plain,
! [U_1692,U_1691] :
( ( ! [U_1694] :
( in(U_1694,sK339(U_1692,U_1691))
| ! [U_1688] :
( ? [U_1687] :
( U_1694 != subset_complement(the_carrier(U_1692),U_1687)
& U_1687 = U_1688
& element(U_1687,powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ! [U_1693] :
( ? [U_1686] :
( ! [U_1685] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != U_1686
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(U_1686,U_1691)
& in(U_1686,U_1691) )
| ~ in(U_1693,sK339(U_1692,U_1691)) ) )
| ( sK337(U_1692,U_1691) != sK338(U_1692,U_1691)
& ! [U_1681] :
( sK338(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691)
& ! [U_1680] :
( sK337(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_1690,sK339(U_1692,U_1691))],[f_439_6]) ).
fof(f_439_8,plain,
! [U_1692,U_1691] :
( ( ! [U_1694] :
( in(U_1694,sK339(U_1692,U_1691))
| ! [U_1688] :
( ? [U_1687] :
( U_1694 != subset_complement(the_carrier(U_1692),U_1687)
& U_1687 = U_1688
& element(U_1687,powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ! [U_1693] :
( ( ! [U_1685] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != sK340(U_1692,U_1691,U_1693)
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(sK340(U_1692,U_1691,U_1693),U_1691)
& in(sK340(U_1692,U_1691,U_1693),U_1691) )
| ~ in(U_1693,sK339(U_1692,U_1691)) ) )
| ( sK337(U_1692,U_1691) != sK338(U_1692,U_1691)
& ! [U_1681] :
( sK338(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691)
& ! [U_1680] :
( sK337(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_1686,sK340(U_1692,U_1691,U_1693))],[f_439_7]) ).
fof(f_439_9,plain,
! [U_1692,U_1691] :
( ( ! [U_1694] :
( in(U_1694,sK339(U_1692,U_1691))
| ! [U_1688] :
( ( U_1694 != subset_complement(the_carrier(U_1692),sK341(U_1692,U_1691,U_1694,U_1688))
& sK341(U_1692,U_1691,U_1694,U_1688) = U_1688
& element(sK341(U_1692,U_1691,U_1694,U_1688),powerset(the_carrier(U_1692))) )
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691) ) )
& ! [U_1693] :
( ( ! [U_1685] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != sK340(U_1692,U_1691,U_1693)
| ~ element(U_1685,powerset(the_carrier(U_1692))) )
& in(sK340(U_1692,U_1691,U_1693),U_1691)
& in(sK340(U_1692,U_1691,U_1693),U_1691) )
| ~ in(U_1693,sK339(U_1692,U_1691)) ) )
| ( sK337(U_1692,U_1691) != sK338(U_1692,U_1691)
& ! [U_1681] :
( sK338(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691)
& ! [U_1680] :
( sK337(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692))) )
& in(sK336(U_1692,U_1691),U_1691) )
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_1687,sK341(U_1692,U_1691,U_1694,U_1688))],[f_439_8]) ).
fof(f_439_10,plain,
( ! [U_1694,U_1691,U_1692,U_1688] :
( U_1694 != subset_complement(the_carrier(U_1692),sK341(U_1692,U_1691,U_1694,U_1688))
| ~ sP398(U_1694,U_1691,U_1692,U_1688) )
& ! [U_1694,U_1691,U_1692,U_1688] :
( sK341(U_1692,U_1691,U_1694,U_1688) = U_1688
| ~ sP398(U_1694,U_1691,U_1692,U_1688) )
& ! [U_1694,U_1691,U_1692,U_1688] :
( element(sK341(U_1692,U_1691,U_1694,U_1688),powerset(the_carrier(U_1692)))
| ~ sP398(U_1694,U_1691,U_1692,U_1688) )
& ! [U_1691,U_1692,U_1685,U_1693] :
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != sK340(U_1692,U_1691,U_1693)
| ~ element(U_1685,powerset(the_carrier(U_1692)))
| ~ sP397(U_1691,U_1692,U_1685,U_1693) )
& ! [U_1691,U_1692,U_1685,U_1693] :
( in(sK340(U_1692,U_1691,U_1693),U_1691)
| ~ sP397(U_1691,U_1692,U_1685,U_1693) )
& ! [U_1691,U_1692,U_1685,U_1693] :
( in(sK340(U_1692,U_1691,U_1693),U_1691)
| ~ sP397(U_1691,U_1692,U_1685,U_1693) )
& ! [U_1694,U_1691,U_1692,U_1685,U_1693,U_1688] :
( in(U_1694,sK339(U_1692,U_1691))
| sP398(U_1694,U_1691,U_1692,U_1688)
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691)
| ~ sP399(U_1694,U_1691,U_1692,U_1685,U_1693,U_1688) )
& ! [U_1694,U_1691,U_1692,U_1685,U_1693,U_1688] :
( sP397(U_1691,U_1692,U_1685,U_1693)
| ~ in(U_1693,sK339(U_1692,U_1691))
| ~ sP399(U_1694,U_1691,U_1692,U_1685,U_1693,U_1688) )
& ! [U_1691,U_1692,U_1680,U_1681] :
( sK337(U_1692,U_1691) != sK338(U_1692,U_1691)
| ~ sP396(U_1691,U_1692,U_1680,U_1681) )
& ! [U_1691,U_1692,U_1680,U_1681] :
( sK338(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692)))
| ~ sP396(U_1691,U_1692,U_1680,U_1681) )
& ! [U_1691,U_1692,U_1680,U_1681] :
( in(sK336(U_1692,U_1691),U_1691)
| ~ sP396(U_1691,U_1692,U_1680,U_1681) )
& ! [U_1691,U_1692,U_1680,U_1681] :
( sK337(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692)))
| ~ sP396(U_1691,U_1692,U_1680,U_1681) )
& ! [U_1691,U_1692,U_1680,U_1681] :
( in(sK336(U_1692,U_1691),U_1691)
| ~ sP396(U_1691,U_1692,U_1680,U_1681) )
& ! [U_1694,U_1691,U_1692,U_1680,U_1685,U_1681,U_1693,U_1688] :
( sP399(U_1694,U_1691,U_1692,U_1685,U_1693,U_1688)
| sP396(U_1691,U_1692,U_1680,U_1681)
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP396,sP397,sP398,sP399])],[f_439_9]) ).
cnf(f_439_11,plain,
( sP399(U_1694,U_1691,U_1692,U_1685,U_1693,U_1688)
| sP396(U_1691,U_1692,U_1680,U_1681)
| ~ element(U_1691,powerset(powerset(the_carrier(U_1692))))
| ~ one_sorted_str(U_1692) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_12,plain,
( in(sK336(U_1692,U_1691),U_1691)
| ~ sP396(U_1691,U_1692,U_1680,U_1681) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_13,plain,
( sK337(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1680)
| U_1680 != sK336(U_1692,U_1691)
| ~ element(U_1680,powerset(the_carrier(U_1692)))
| ~ sP396(U_1691,U_1692,U_1680,U_1681) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_14,plain,
( in(sK336(U_1692,U_1691),U_1691)
| ~ sP396(U_1691,U_1692,U_1680,U_1681) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_15,plain,
( sK338(U_1692,U_1691) = subset_complement(the_carrier(U_1692),U_1681)
| U_1681 != sK336(U_1692,U_1691)
| ~ element(U_1681,powerset(the_carrier(U_1692)))
| ~ sP396(U_1691,U_1692,U_1680,U_1681) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_16,plain,
( sK337(U_1692,U_1691) != sK338(U_1692,U_1691)
| ~ sP396(U_1691,U_1692,U_1680,U_1681) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_17,plain,
( sP397(U_1691,U_1692,U_1685,U_1693)
| ~ in(U_1693,sK339(U_1692,U_1691))
| ~ sP399(U_1694,U_1691,U_1692,U_1685,U_1693,U_1688) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_18,plain,
( in(U_1694,sK339(U_1692,U_1691))
| sP398(U_1694,U_1691,U_1692,U_1688)
| ~ in(U_1688,U_1691)
| ~ in(U_1688,U_1691)
| ~ sP399(U_1694,U_1691,U_1692,U_1685,U_1693,U_1688) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_19,plain,
( in(sK340(U_1692,U_1691,U_1693),U_1691)
| ~ sP397(U_1691,U_1692,U_1685,U_1693) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_20,plain,
( in(sK340(U_1692,U_1691,U_1693),U_1691)
| ~ sP397(U_1691,U_1692,U_1685,U_1693) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_21,plain,
( U_1693 = subset_complement(the_carrier(U_1692),U_1685)
| U_1685 != sK340(U_1692,U_1691,U_1693)
| ~ element(U_1685,powerset(the_carrier(U_1692)))
| ~ sP397(U_1691,U_1692,U_1685,U_1693) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_22,plain,
( element(sK341(U_1692,U_1691,U_1694,U_1688),powerset(the_carrier(U_1692)))
| ~ sP398(U_1694,U_1691,U_1692,U_1688) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_23,plain,
( sK341(U_1692,U_1691,U_1694,U_1688) = U_1688
| ~ sP398(U_1694,U_1691,U_1692,U_1688) ),
inference(clausify,[status(thm)],[f_439_10]) ).
cnf(f_439_24,plain,
( U_1694 != subset_complement(the_carrier(U_1692),sK341(U_1692,U_1691,U_1694,U_1688))
| ~ sP398(U_1694,U_1691,U_1692,U_1688) ),
inference(clausify,[status(thm)],[f_439_10]) ).
fof(f_440_1,plain,
! [A,B] :
( ! [C] :
( ? [D] :
! [E] :
( ( in(E,D)
| ! [F] :
( ! [M,N] :
( ? [O] :
( N != subset_complement(the_carrier(A),O)
& O = M
& element(O,powerset(the_carrier(A))) )
| ~ in(M,B)
| ordered_pair(M,N) != E )
| F != E
| ~ in(F,cartesian_product2(B,C)) ) )
& ( ? [F] :
( ? [M,N] :
( ! [O] :
( N = subset_complement(the_carrier(A),O)
| O != M
| ~ element(O,powerset(the_carrier(A))) )
& in(M,B)
& ordered_pair(M,N) = E )
& F = E
& in(F,cartesian_product2(B,C)) )
| ~ in(E,D) ) )
| ? [D,E,F] :
( E != F
& ? [J,K] :
( ! [L] :
( K = subset_complement(the_carrier(A),L)
| L != J
| ~ element(L,powerset(the_carrier(A))) )
& in(J,B)
& ordered_pair(J,K) = F )
& D = F
& ? [G,H] :
( ! [I] :
( H = subset_complement(the_carrier(A),I)
| I != G
| ~ element(I,powerset(the_carrier(A))) )
& in(G,B)
& ordered_pair(G,H) = E )
& D = E ) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e4_7_2__tops_2__2]) ).
fof(f_440_2,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
( ? [U_1713] :
! [U_1712] :
( ( in(U_1712,U_1713)
| ! [U_1711] :
( ! [U_1710,U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ~ in(U_1710,U_1715)
| ordered_pair(U_1710,U_1709) != U_1712 )
| U_1711 != U_1712
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) ) )
& ( ? [U_1707] :
( ? [U_1706,U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& in(U_1706,U_1715)
& ordered_pair(U_1706,U_1705) = U_1712 )
& U_1707 = U_1712
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
| ~ in(U_1712,U_1713) ) )
| ? [U_1703,U_1702,U_1701] :
( U_1702 != U_1701
& ? [U_1700,U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != U_1700
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& in(U_1700,U_1715)
& ordered_pair(U_1700,U_1699) = U_1701 )
& U_1703 = U_1701
& ? [U_1697,U_1696] :
( ! [U_1695] :
( U_1696 = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != U_1697
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& in(U_1697,U_1715)
& ordered_pair(U_1697,U_1696) = U_1702 )
& U_1703 = U_1702 ) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ? [U_1703,U_1702,U_1701] :
( U_1702 != U_1701
& ? [U_1700] :
( ? [U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != U_1700
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1700,U_1699) = U_1701 )
& in(U_1700,U_1715) )
& U_1703 = U_1701
& ? [U_1697] :
( ? [U_1696] :
( ! [U_1695] :
( U_1696 = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != U_1697
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1697,U_1696) = U_1702 )
& in(U_1697,U_1715) )
& U_1703 = U_1702 )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(miniscope,[status(thm)],[f_440_2]) ).
fof(f_440_4,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ? [U_1702,U_1701] :
( U_1702 != U_1701
& ? [U_1700] :
( ? [U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != U_1700
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1700,U_1699) = U_1701 )
& in(U_1700,U_1715) )
& sK342(U_1716,U_1715) = U_1701
& ? [U_1697] :
( ? [U_1696] :
( ! [U_1695] :
( U_1696 = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != U_1697
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1697,U_1696) = U_1702 )
& in(U_1697,U_1715) )
& sK342(U_1716,U_1715) = U_1702 )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_1703,sK342(U_1716,U_1715))],[f_440_3]) ).
fof(f_440_5,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ? [U_1701] :
( sK343(U_1716,U_1715) != U_1701
& ? [U_1700] :
( ? [U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != U_1700
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1700,U_1699) = U_1701 )
& in(U_1700,U_1715) )
& sK342(U_1716,U_1715) = U_1701
& ? [U_1697] :
( ? [U_1696] :
( ! [U_1695] :
( U_1696 = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != U_1697
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1697,U_1696) = sK343(U_1716,U_1715) )
& in(U_1697,U_1715) )
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_1702,sK343(U_1716,U_1715))],[f_440_4]) ).
fof(f_440_6,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ? [U_1700] :
( ? [U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != U_1700
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1700,U_1699) = sK344(U_1716,U_1715) )
& in(U_1700,U_1715) )
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ? [U_1697] :
( ? [U_1696] :
( ! [U_1695] :
( U_1696 = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != U_1697
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1697,U_1696) = sK343(U_1716,U_1715) )
& in(U_1697,U_1715) )
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_1701,sK344(U_1716,U_1715))],[f_440_5]) ).
fof(f_440_7,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ? [U_1700] :
( ? [U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != U_1700
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1700,U_1699) = sK344(U_1716,U_1715) )
& in(U_1700,U_1715) )
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ? [U_1696] :
( ! [U_1695] :
( U_1696 = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),U_1696) = sK343(U_1716,U_1715) )
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_1697,sK345(U_1716,U_1715))],[f_440_6]) ).
fof(f_440_8,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ? [U_1700] :
( ? [U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != U_1700
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1700,U_1699) = sK344(U_1716,U_1715) )
& in(U_1700,U_1715) )
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_1696,sK346(U_1716,U_1715))],[f_440_7]) ).
fof(f_440_9,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ? [U_1699] :
( ! [U_1698] :
( U_1699 = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(sK347(U_1716,U_1715),U_1699) = sK344(U_1716,U_1715) )
& in(sK347(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_1700,sK347(U_1716,U_1715))],[f_440_8]) ).
fof(f_440_10,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
? [U_1713] :
( ! [U_1718] :
( in(U_1718,U_1713)
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,U_1713) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ! [U_1698] :
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
& in(sK347(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_1699,sK348(U_1716,U_1715))],[f_440_9]) ).
fof(f_440_11,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
( ! [U_1718] :
( in(U_1718,sK349(U_1716,U_1715,U_1714))
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1706] :
( ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != U_1706
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(U_1706,U_1705) = U_1717 )
& in(U_1706,U_1715) ) )
| ~ in(U_1717,sK349(U_1716,U_1715,U_1714)) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ! [U_1698] :
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
& in(sK347(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_1713,sK349(U_1716,U_1715,U_1714))],[f_440_10]) ).
fof(f_440_12,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
( ! [U_1718] :
( in(U_1718,sK349(U_1716,U_1715,U_1714))
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ? [U_1705] :
( ! [U_1704] :
( U_1705 = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != sK350(U_1716,U_1715,U_1714,U_1717)
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(sK350(U_1716,U_1715,U_1714,U_1717),U_1705) = U_1717 )
& in(sK350(U_1716,U_1715,U_1714,U_1717),U_1715) )
| ~ in(U_1717,sK349(U_1716,U_1715,U_1714)) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ! [U_1698] :
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
& in(sK347(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_1706,sK350(U_1716,U_1715,U_1714,U_1717))],[f_440_11]) ).
fof(f_440_13,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
( ! [U_1718] :
( in(U_1718,sK349(U_1716,U_1715,U_1714))
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( ? [U_1707] :
( U_1707 = U_1717
& in(U_1707,cartesian_product2(U_1715,U_1714)) )
& ! [U_1704] :
( sK351(U_1716,U_1715,U_1714,U_1717) = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != sK350(U_1716,U_1715,U_1714,U_1717)
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(sK350(U_1716,U_1715,U_1714,U_1717),sK351(U_1716,U_1715,U_1714,U_1717)) = U_1717
& in(sK350(U_1716,U_1715,U_1714,U_1717),U_1715) )
| ~ in(U_1717,sK349(U_1716,U_1715,U_1714)) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ! [U_1698] :
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
& in(sK347(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_1705,sK351(U_1716,U_1715,U_1714,U_1717))],[f_440_12]) ).
fof(f_440_14,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
( ! [U_1718] :
( in(U_1718,sK349(U_1716,U_1715,U_1714))
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ? [U_1708] :
( U_1709 != subset_complement(the_carrier(U_1716),U_1708)
& U_1708 = U_1710
& element(U_1708,powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( sK352(U_1716,U_1715,U_1714,U_1717) = U_1717
& in(sK352(U_1716,U_1715,U_1714,U_1717),cartesian_product2(U_1715,U_1714))
& ! [U_1704] :
( sK351(U_1716,U_1715,U_1714,U_1717) = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != sK350(U_1716,U_1715,U_1714,U_1717)
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(sK350(U_1716,U_1715,U_1714,U_1717),sK351(U_1716,U_1715,U_1714,U_1717)) = U_1717
& in(sK350(U_1716,U_1715,U_1714,U_1717),U_1715) )
| ~ in(U_1717,sK349(U_1716,U_1715,U_1714)) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ! [U_1698] :
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
& in(sK347(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_1707,sK352(U_1716,U_1715,U_1714,U_1717))],[f_440_13]) ).
fof(f_440_15,plain,
! [U_1716,U_1715] :
( ! [U_1714] :
( ! [U_1718] :
( in(U_1718,sK349(U_1716,U_1715,U_1714))
| ! [U_1711] :
( U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714)) )
| ! [U_1710] :
( ! [U_1709] :
( ( U_1709 != subset_complement(the_carrier(U_1716),sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709))
& sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709) = U_1710
& element(sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709),powerset(the_carrier(U_1716))) )
| ordered_pair(U_1710,U_1709) != U_1718 )
| ~ in(U_1710,U_1715) ) )
& ! [U_1717] :
( ( sK352(U_1716,U_1715,U_1714,U_1717) = U_1717
& in(sK352(U_1716,U_1715,U_1714,U_1717),cartesian_product2(U_1715,U_1714))
& ! [U_1704] :
( sK351(U_1716,U_1715,U_1714,U_1717) = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != sK350(U_1716,U_1715,U_1714,U_1717)
| ~ element(U_1704,powerset(the_carrier(U_1716))) )
& ordered_pair(sK350(U_1716,U_1715,U_1714,U_1717),sK351(U_1716,U_1715,U_1714,U_1717)) = U_1717
& in(sK350(U_1716,U_1715,U_1714,U_1717),U_1715) )
| ~ in(U_1717,sK349(U_1716,U_1715,U_1714)) ) )
| ( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
& ! [U_1698] :
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716))) )
& ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
& in(sK347(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
& ! [U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716))) )
& ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
& in(sK345(U_1716,U_1715),U_1715)
& sK342(U_1716,U_1715) = sK343(U_1716,U_1715) )
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_1708,sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709))],[f_440_14]) ).
fof(f_440_16,plain,
( ! [U_1716,U_1715,U_1718,U_1714,U_1709,U_1710] :
( U_1709 != subset_complement(the_carrier(U_1716),sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709))
| ~ sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710) )
& ! [U_1716,U_1715,U_1718,U_1714,U_1709,U_1710] :
( sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709) = U_1710
| ~ sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710) )
& ! [U_1716,U_1715,U_1718,U_1714,U_1709,U_1710] :
( element(sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709),powerset(the_carrier(U_1716)))
| ~ sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710) )
& ! [U_1716,U_1704,U_1715,U_1714,U_1717] :
( sK352(U_1716,U_1715,U_1714,U_1717) = U_1717
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) )
& ! [U_1716,U_1704,U_1715,U_1714,U_1717] :
( in(sK352(U_1716,U_1715,U_1714,U_1717),cartesian_product2(U_1715,U_1714))
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) )
& ! [U_1716,U_1704,U_1715,U_1714,U_1717] :
( sK351(U_1716,U_1715,U_1714,U_1717) = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != sK350(U_1716,U_1715,U_1714,U_1717)
| ~ element(U_1704,powerset(the_carrier(U_1716)))
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) )
& ! [U_1716,U_1704,U_1715,U_1714,U_1717] :
( ordered_pair(sK350(U_1716,U_1715,U_1714,U_1717),sK351(U_1716,U_1715,U_1714,U_1717)) = U_1717
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) )
& ! [U_1716,U_1704,U_1715,U_1714,U_1717] :
( in(sK350(U_1716,U_1715,U_1714,U_1717),U_1715)
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) )
& ! [U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710] :
( in(U_1718,sK349(U_1716,U_1715,U_1714))
| U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714))
| sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710)
| ordered_pair(U_1710,U_1709) != U_1718
| ~ in(U_1710,U_1715)
| ~ sP403(U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710) )
& ! [U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710] :
( sP401(U_1716,U_1704,U_1715,U_1714,U_1717)
| ~ in(U_1717,sK349(U_1716,U_1715,U_1714))
| ~ sP403(U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716)))
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( in(sK347(U_1716,U_1715),U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716)))
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( in(sK345(U_1716,U_1715),U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1715,U_1698,U_1695] :
( sK342(U_1716,U_1715) = sK343(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) )
& ! [U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1698,U_1695,U_1709,U_1717,U_1710] :
( sP403(U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710)
| sP400(U_1716,U_1715,U_1698,U_1695)
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP400,sP401,sP402,sP403])],[f_440_15]) ).
cnf(f_440_17,plain,
( sP403(U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710)
| sP400(U_1716,U_1715,U_1698,U_1695)
| ~ element(U_1715,powerset(powerset(the_carrier(U_1716))))
| ~ one_sorted_str(U_1716) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_18,plain,
( sK342(U_1716,U_1715) = sK343(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_19,plain,
( in(sK345(U_1716,U_1715),U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_20,plain,
( ordered_pair(sK345(U_1716,U_1715),sK346(U_1716,U_1715)) = sK343(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_21,plain,
( sK346(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1695)
| U_1695 != sK345(U_1716,U_1715)
| ~ element(U_1695,powerset(the_carrier(U_1716)))
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_22,plain,
( sK342(U_1716,U_1715) = sK344(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_23,plain,
( in(sK347(U_1716,U_1715),U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_24,plain,
( ordered_pair(sK347(U_1716,U_1715),sK348(U_1716,U_1715)) = sK344(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_25,plain,
( sK348(U_1716,U_1715) = subset_complement(the_carrier(U_1716),U_1698)
| U_1698 != sK347(U_1716,U_1715)
| ~ element(U_1698,powerset(the_carrier(U_1716)))
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_26,plain,
( sK343(U_1716,U_1715) != sK344(U_1716,U_1715)
| ~ sP400(U_1716,U_1715,U_1698,U_1695) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_27,plain,
( sP401(U_1716,U_1704,U_1715,U_1714,U_1717)
| ~ in(U_1717,sK349(U_1716,U_1715,U_1714))
| ~ sP403(U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_28,plain,
( in(U_1718,sK349(U_1716,U_1715,U_1714))
| U_1711 != U_1718
| ~ in(U_1711,cartesian_product2(U_1715,U_1714))
| sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710)
| ordered_pair(U_1710,U_1709) != U_1718
| ~ in(U_1710,U_1715)
| ~ sP403(U_1716,U_1711,U_1704,U_1715,U_1718,U_1714,U_1709,U_1717,U_1710) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_29,plain,
( in(sK350(U_1716,U_1715,U_1714,U_1717),U_1715)
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_30,plain,
( ordered_pair(sK350(U_1716,U_1715,U_1714,U_1717),sK351(U_1716,U_1715,U_1714,U_1717)) = U_1717
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_31,plain,
( sK351(U_1716,U_1715,U_1714,U_1717) = subset_complement(the_carrier(U_1716),U_1704)
| U_1704 != sK350(U_1716,U_1715,U_1714,U_1717)
| ~ element(U_1704,powerset(the_carrier(U_1716)))
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_32,plain,
( in(sK352(U_1716,U_1715,U_1714,U_1717),cartesian_product2(U_1715,U_1714))
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_33,plain,
( sK352(U_1716,U_1715,U_1714,U_1717) = U_1717
| ~ sP401(U_1716,U_1704,U_1715,U_1714,U_1717) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_34,plain,
( element(sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709),powerset(the_carrier(U_1716)))
| ~ sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_35,plain,
( sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709) = U_1710
| ~ sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710) ),
inference(clausify,[status(thm)],[f_440_16]) ).
cnf(f_440_36,plain,
( U_1709 != subset_complement(the_carrier(U_1716),sK353(U_1716,U_1715,U_1714,U_1718,U_1710,U_1709))
| ~ sP402(U_1716,U_1715,U_1718,U_1714,U_1709,U_1710) ),
inference(clausify,[status(thm)],[f_440_16]) ).
fof(f_441_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_441_2,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
! [U_1732] :
( ( in(U_1732,U_1733)
| ! [U_1731] :
( ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1732 != ordered_pair(U_1730,U_1729) )
| U_1731 != U_1732
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) ) )
& ( ? [U_1728] :
( ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1732 = ordered_pair(U_1727,U_1726) )
& U_1728 = U_1732
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
| ~ in(U_1732,U_1733) ) )
| ? [U_1725,U_1724,U_1723] :
( U_1724 != U_1723
& ? [U_1722,U_1721] :
( in(ordered_pair(apply(U_1734,U_1722),apply(U_1734,U_1721)),U_1735)
& U_1723 = ordered_pair(U_1722,U_1721) )
& U_1725 = U_1723
& ? [U_1720,U_1719] :
( in(ordered_pair(apply(U_1734,U_1720),apply(U_1734,U_1719)),U_1735)
& U_1724 = ordered_pair(U_1720,U_1719) )
& U_1725 = U_1724 )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ? [U_1725,U_1724,U_1723] :
( U_1724 != U_1723
& ? [U_1722,U_1721] :
( in(ordered_pair(apply(U_1734,U_1722),apply(U_1734,U_1721)),U_1735)
& U_1723 = ordered_pair(U_1722,U_1721) )
& U_1725 = U_1723
& ? [U_1720,U_1719] :
( in(ordered_pair(apply(U_1734,U_1720),apply(U_1734,U_1719)),U_1735)
& U_1724 = ordered_pair(U_1720,U_1719) )
& U_1725 = U_1724 )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(miniscope,[status(thm)],[f_441_2]) ).
fof(f_441_4,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ? [U_1724,U_1723] :
( U_1724 != U_1723
& ? [U_1722,U_1721] :
( in(ordered_pair(apply(U_1734,U_1722),apply(U_1734,U_1721)),U_1735)
& U_1723 = ordered_pair(U_1722,U_1721) )
& sK354(U_1736,U_1735,U_1734) = U_1723
& ? [U_1720,U_1719] :
( in(ordered_pair(apply(U_1734,U_1720),apply(U_1734,U_1719)),U_1735)
& U_1724 = ordered_pair(U_1720,U_1719) )
& sK354(U_1736,U_1735,U_1734) = U_1724 )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_1725,sK354(U_1736,U_1735,U_1734))],[f_441_3]) ).
fof(f_441_5,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ? [U_1723] :
( sK355(U_1736,U_1735,U_1734) != U_1723
& ? [U_1722,U_1721] :
( in(ordered_pair(apply(U_1734,U_1722),apply(U_1734,U_1721)),U_1735)
& U_1723 = ordered_pair(U_1722,U_1721) )
& sK354(U_1736,U_1735,U_1734) = U_1723
& ? [U_1720,U_1719] :
( in(ordered_pair(apply(U_1734,U_1720),apply(U_1734,U_1719)),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(U_1720,U_1719) )
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_1724,sK355(U_1736,U_1735,U_1734))],[f_441_4]) ).
fof(f_441_6,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& ? [U_1722,U_1721] :
( in(ordered_pair(apply(U_1734,U_1722),apply(U_1734,U_1721)),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(U_1722,U_1721) )
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& ? [U_1720,U_1719] :
( in(ordered_pair(apply(U_1734,U_1720),apply(U_1734,U_1719)),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(U_1720,U_1719) )
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_1723,sK356(U_1736,U_1735,U_1734))],[f_441_5]) ).
fof(f_441_7,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& ? [U_1722,U_1721] :
( in(ordered_pair(apply(U_1734,U_1722),apply(U_1734,U_1721)),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(U_1722,U_1721) )
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& ? [U_1719] :
( in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,U_1719)),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),U_1719) )
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_1720,sK357(U_1736,U_1735,U_1734))],[f_441_6]) ).
fof(f_441_8,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& ? [U_1722,U_1721] :
( in(ordered_pair(apply(U_1734,U_1722),apply(U_1734,U_1721)),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(U_1722,U_1721) )
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_1719,sK358(U_1736,U_1735,U_1734))],[f_441_7]) ).
fof(f_441_9,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& ? [U_1721] :
( in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,U_1721)),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),U_1721) )
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_1722,sK359(U_1736,U_1735,U_1734))],[f_441_8]) ).
fof(f_441_10,plain,
! [U_1736,U_1735,U_1734] :
( ? [U_1733] :
( ! [U_1738] :
( in(U_1738,U_1733)
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,U_1733) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,sK360(U_1736,U_1735,U_1734))),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),sK360(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_1721,sK360(U_1736,U_1735,U_1734))],[f_441_9]) ).
fof(f_441_11,plain,
! [U_1736,U_1735,U_1734] :
( ( ! [U_1738] :
( in(U_1738,sK361(U_1736,U_1735,U_1734))
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1727,U_1726] :
( in(ordered_pair(apply(U_1734,U_1727),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(U_1727,U_1726) ) )
| ~ in(U_1737,sK361(U_1736,U_1735,U_1734)) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,sK360(U_1736,U_1735,U_1734))),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),sK360(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_1733,sK361(U_1736,U_1735,U_1734))],[f_441_10]) ).
fof(f_441_12,plain,
! [U_1736,U_1735,U_1734] :
( ( ! [U_1738] :
( in(U_1738,sK361(U_1736,U_1735,U_1734))
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& ? [U_1726] :
( in(ordered_pair(apply(U_1734,sK362(U_1736,U_1735,U_1734,U_1737)),apply(U_1734,U_1726)),U_1735)
& U_1737 = ordered_pair(sK362(U_1736,U_1735,U_1734,U_1737),U_1726) ) )
| ~ in(U_1737,sK361(U_1736,U_1735,U_1734)) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,sK360(U_1736,U_1735,U_1734))),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),sK360(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_1727,sK362(U_1736,U_1735,U_1734,U_1737))],[f_441_11]) ).
fof(f_441_13,plain,
! [U_1736,U_1735,U_1734] :
( ( ! [U_1738] :
( in(U_1738,sK361(U_1736,U_1735,U_1734))
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( ? [U_1728] :
( U_1728 = U_1737
& in(U_1728,cartesian_product2(U_1736,U_1736)) )
& in(ordered_pair(apply(U_1734,sK362(U_1736,U_1735,U_1734,U_1737)),apply(U_1734,sK363(U_1736,U_1735,U_1734,U_1737))),U_1735)
& U_1737 = ordered_pair(sK362(U_1736,U_1735,U_1734,U_1737),sK363(U_1736,U_1735,U_1734,U_1737)) )
| ~ in(U_1737,sK361(U_1736,U_1735,U_1734)) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,sK360(U_1736,U_1735,U_1734))),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),sK360(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_1726,sK363(U_1736,U_1735,U_1734,U_1737))],[f_441_12]) ).
fof(f_441_14,plain,
! [U_1736,U_1735,U_1734] :
( ( ! [U_1738] :
( in(U_1738,sK361(U_1736,U_1735,U_1734))
| ! [U_1731] :
( U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736)) )
| ! [U_1730,U_1729] :
( ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729) ) )
& ! [U_1737] :
( ( sK364(U_1736,U_1735,U_1734,U_1737) = U_1737
& in(sK364(U_1736,U_1735,U_1734,U_1737),cartesian_product2(U_1736,U_1736))
& in(ordered_pair(apply(U_1734,sK362(U_1736,U_1735,U_1734,U_1737)),apply(U_1734,sK363(U_1736,U_1735,U_1734,U_1737))),U_1735)
& U_1737 = ordered_pair(sK362(U_1736,U_1735,U_1734,U_1737),sK363(U_1736,U_1735,U_1734,U_1737)) )
| ~ in(U_1737,sK361(U_1736,U_1735,U_1734)) ) )
| ( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,sK360(U_1736,U_1735,U_1734))),U_1735)
& sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),sK360(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
& in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
& sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
& sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734) )
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_1728,sK364(U_1736,U_1735,U_1734,U_1737))],[f_441_13]) ).
fof(f_441_15,plain,
( ! [U_1735,U_1736,U_1737,U_1734] :
( sK364(U_1736,U_1735,U_1734,U_1737) = U_1737
| ~ sP405(U_1735,U_1736,U_1737,U_1734) )
& ! [U_1735,U_1736,U_1737,U_1734] :
( in(sK364(U_1736,U_1735,U_1734,U_1737),cartesian_product2(U_1736,U_1736))
| ~ sP405(U_1735,U_1736,U_1737,U_1734) )
& ! [U_1735,U_1736,U_1737,U_1734] :
( in(ordered_pair(apply(U_1734,sK362(U_1736,U_1735,U_1734,U_1737)),apply(U_1734,sK363(U_1736,U_1735,U_1734,U_1737))),U_1735)
| ~ sP405(U_1735,U_1736,U_1737,U_1734) )
& ! [U_1735,U_1736,U_1737,U_1734] :
( U_1737 = ordered_pair(sK362(U_1736,U_1735,U_1734,U_1737),sK363(U_1736,U_1735,U_1734,U_1737))
| ~ sP405(U_1735,U_1736,U_1737,U_1734) )
& ! [U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738] :
( in(U_1738,sK361(U_1736,U_1735,U_1734))
| U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736))
| ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729)
| ~ sP406(U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738) )
& ! [U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738] :
( sP405(U_1735,U_1736,U_1737,U_1734)
| ~ in(U_1737,sK361(U_1736,U_1735,U_1734))
| ~ sP406(U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738) )
& ! [U_1735,U_1736,U_1734] :
( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
| ~ sP404(U_1735,U_1736,U_1734) )
& ! [U_1735,U_1736,U_1734] :
( in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,sK360(U_1736,U_1735,U_1734))),U_1735)
| ~ sP404(U_1735,U_1736,U_1734) )
& ! [U_1735,U_1736,U_1734] :
( sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),sK360(U_1736,U_1735,U_1734))
| ~ sP404(U_1735,U_1736,U_1734) )
& ! [U_1735,U_1736,U_1734] :
( sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
| ~ sP404(U_1735,U_1736,U_1734) )
& ! [U_1735,U_1736,U_1734] :
( in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
| ~ sP404(U_1735,U_1736,U_1734) )
& ! [U_1735,U_1736,U_1734] :
( sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
| ~ sP404(U_1735,U_1736,U_1734) )
& ! [U_1735,U_1736,U_1734] :
( sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734)
| ~ sP404(U_1735,U_1736,U_1734) )
& ! [U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738] :
( sP406(U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738)
| sP404(U_1735,U_1736,U_1734)
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP404,sP405,sP406])],[f_441_14]) ).
cnf(f_441_16,plain,
( sP406(U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738)
| sP404(U_1735,U_1736,U_1734)
| ~ function(U_1734)
| ~ relation(U_1734)
| ~ relation(U_1735) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_17,plain,
( sK354(U_1736,U_1735,U_1734) = sK355(U_1736,U_1735,U_1734)
| ~ sP404(U_1735,U_1736,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_18,plain,
( sK355(U_1736,U_1735,U_1734) = ordered_pair(sK357(U_1736,U_1735,U_1734),sK358(U_1736,U_1735,U_1734))
| ~ sP404(U_1735,U_1736,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_19,plain,
( in(ordered_pair(apply(U_1734,sK357(U_1736,U_1735,U_1734)),apply(U_1734,sK358(U_1736,U_1735,U_1734))),U_1735)
| ~ sP404(U_1735,U_1736,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_20,plain,
( sK354(U_1736,U_1735,U_1734) = sK356(U_1736,U_1735,U_1734)
| ~ sP404(U_1735,U_1736,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_21,plain,
( sK356(U_1736,U_1735,U_1734) = ordered_pair(sK359(U_1736,U_1735,U_1734),sK360(U_1736,U_1735,U_1734))
| ~ sP404(U_1735,U_1736,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_22,plain,
( in(ordered_pair(apply(U_1734,sK359(U_1736,U_1735,U_1734)),apply(U_1734,sK360(U_1736,U_1735,U_1734))),U_1735)
| ~ sP404(U_1735,U_1736,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_23,plain,
( sK355(U_1736,U_1735,U_1734) != sK356(U_1736,U_1735,U_1734)
| ~ sP404(U_1735,U_1736,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_24,plain,
( sP405(U_1735,U_1736,U_1737,U_1734)
| ~ in(U_1737,sK361(U_1736,U_1735,U_1734))
| ~ sP406(U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_25,plain,
( in(U_1738,sK361(U_1736,U_1735,U_1734))
| U_1731 != U_1738
| ~ in(U_1731,cartesian_product2(U_1736,U_1736))
| ~ in(ordered_pair(apply(U_1734,U_1730),apply(U_1734,U_1729)),U_1735)
| U_1738 != ordered_pair(U_1730,U_1729)
| ~ sP406(U_1735,U_1736,U_1729,U_1737,U_1730,U_1731,U_1734,U_1738) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_26,plain,
( U_1737 = ordered_pair(sK362(U_1736,U_1735,U_1734,U_1737),sK363(U_1736,U_1735,U_1734,U_1737))
| ~ sP405(U_1735,U_1736,U_1737,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_27,plain,
( in(ordered_pair(apply(U_1734,sK362(U_1736,U_1735,U_1734,U_1737)),apply(U_1734,sK363(U_1736,U_1735,U_1734,U_1737))),U_1735)
| ~ sP405(U_1735,U_1736,U_1737,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_28,plain,
( in(sK364(U_1736,U_1735,U_1734,U_1737),cartesian_product2(U_1736,U_1736))
| ~ sP405(U_1735,U_1736,U_1737,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
cnf(f_441_29,plain,
( sK364(U_1736,U_1735,U_1734,U_1737) = U_1737
| ~ sP405(U_1735,U_1736,U_1737,U_1734) ),
inference(clausify,[status(thm)],[f_441_15]) ).
fof(f_442_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_442_2,plain,
! [U_1746] :
( ? [U_1745] :
! [U_1744] :
( ( in(U_1744,U_1745)
| ! [U_1743] :
( ~ ordinal(U_1744)
| U_1743 != U_1744
| ~ in(U_1743,U_1746) ) )
& ( ? [U_1742] :
( ordinal(U_1744)
& U_1742 = U_1744
& in(U_1742,U_1746) )
| ~ in(U_1744,U_1745) ) )
| ? [U_1741,U_1740,U_1739] :
( U_1740 != U_1739
& ordinal(U_1739)
& U_1741 = U_1739
& ordinal(U_1740)
& U_1741 = U_1740 ) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
( ! [U_1746] :
? [U_1745] :
( ! [U_1748] :
( in(U_1748,U_1745)
| ! [U_1743] :
( U_1743 != U_1748
| ~ in(U_1743,U_1746) )
| ~ ordinal(U_1748) )
& ! [U_1747] :
( ( ? [U_1742] :
( U_1742 = U_1747
& in(U_1742,U_1746) )
& ordinal(U_1747) )
| ~ in(U_1747,U_1745) ) )
| ? [U_1741,U_1740,U_1739] :
( U_1740 != U_1739
& ordinal(U_1739)
& U_1741 = U_1739
& ordinal(U_1740)
& U_1741 = U_1740 ) ),
inference(miniscope,[status(thm)],[f_442_2]) ).
fof(f_442_4,plain,
( ! [U_1746] :
? [U_1745] :
( ! [U_1748] :
( in(U_1748,U_1745)
| ! [U_1743] :
( U_1743 != U_1748
| ~ in(U_1743,U_1746) )
| ~ ordinal(U_1748) )
& ! [U_1747] :
( ( ? [U_1742] :
( U_1742 = U_1747
& in(U_1742,U_1746) )
& ordinal(U_1747) )
| ~ in(U_1747,U_1745) ) )
| ? [U_1740,U_1739] :
( U_1740 != U_1739
& ordinal(U_1739)
& sK365 = U_1739
& ordinal(U_1740)
& sK365 = U_1740 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_1741,sK365)],[f_442_3]) ).
fof(f_442_5,plain,
( ! [U_1746] :
? [U_1745] :
( ! [U_1748] :
( in(U_1748,U_1745)
| ! [U_1743] :
( U_1743 != U_1748
| ~ in(U_1743,U_1746) )
| ~ ordinal(U_1748) )
& ! [U_1747] :
( ( ? [U_1742] :
( U_1742 = U_1747
& in(U_1742,U_1746) )
& ordinal(U_1747) )
| ~ in(U_1747,U_1745) ) )
| ? [U_1739] :
( sK366 != U_1739
& ordinal(U_1739)
& sK365 = U_1739
& ordinal(sK366)
& sK365 = sK366 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_1740,sK366)],[f_442_4]) ).
fof(f_442_6,plain,
( ! [U_1746] :
? [U_1745] :
( ! [U_1748] :
( in(U_1748,U_1745)
| ! [U_1743] :
( U_1743 != U_1748
| ~ in(U_1743,U_1746) )
| ~ ordinal(U_1748) )
& ! [U_1747] :
( ( ? [U_1742] :
( U_1742 = U_1747
& in(U_1742,U_1746) )
& ordinal(U_1747) )
| ~ in(U_1747,U_1745) ) )
| ( sK366 != sK367
& ordinal(sK367)
& sK365 = sK367
& ordinal(sK366)
& sK365 = sK366 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_1739,sK367)],[f_442_5]) ).
fof(f_442_7,plain,
( ! [U_1746] :
( ! [U_1748] :
( in(U_1748,sK368(U_1746))
| ! [U_1743] :
( U_1743 != U_1748
| ~ in(U_1743,U_1746) )
| ~ ordinal(U_1748) )
& ! [U_1747] :
( ( ? [U_1742] :
( U_1742 = U_1747
& in(U_1742,U_1746) )
& ordinal(U_1747) )
| ~ in(U_1747,sK368(U_1746)) ) )
| ( sK366 != sK367
& ordinal(sK367)
& sK365 = sK367
& ordinal(sK366)
& sK365 = sK366 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_1745,sK368(U_1746))],[f_442_6]) ).
fof(f_442_8,plain,
( ! [U_1746] :
( ! [U_1748] :
( in(U_1748,sK368(U_1746))
| ! [U_1743] :
( U_1743 != U_1748
| ~ in(U_1743,U_1746) )
| ~ ordinal(U_1748) )
& ! [U_1747] :
( ( sK369(U_1746,U_1747) = U_1747
& in(sK369(U_1746,U_1747),U_1746)
& ordinal(U_1747) )
| ~ in(U_1747,sK368(U_1746)) ) )
| ( sK366 != sK367
& ordinal(sK367)
& sK365 = sK367
& ordinal(sK366)
& sK365 = sK366 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_1742,sK369(U_1746,U_1747))],[f_442_7]) ).
fof(f_442_9,plain,
( ! [U_1747,U_1746] :
( sK369(U_1746,U_1747) = U_1747
| ~ sP408(U_1747,U_1746) )
& ! [U_1747,U_1746] :
( in(sK369(U_1746,U_1747),U_1746)
| ~ sP408(U_1747,U_1746) )
& ! [U_1747,U_1746] :
( ordinal(U_1747)
| ~ sP408(U_1747,U_1746) )
& ! [U_1747,U_1746,U_1743,U_1748] :
( in(U_1748,sK368(U_1746))
| U_1743 != U_1748
| ~ in(U_1743,U_1746)
| ~ ordinal(U_1748)
| ~ sP409(U_1747,U_1746,U_1743,U_1748) )
& ! [U_1747,U_1746,U_1743,U_1748] :
( sP408(U_1747,U_1746)
| ~ in(U_1747,sK368(U_1746))
| ~ sP409(U_1747,U_1746,U_1743,U_1748) )
& ( sK366 != sK367
| ~ sP407 )
& ( ordinal(sK367)
| ~ sP407 )
& ( sK365 = sK367
| ~ sP407 )
& ( ordinal(sK366)
| ~ sP407 )
& ( sK365 = sK366
| ~ sP407 )
& ! [U_1747,U_1746,U_1743,U_1748] :
( sP409(U_1747,U_1746,U_1743,U_1748)
| sP407 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP407,sP408,sP409])],[f_442_8]) ).
cnf(f_442_10,plain,
( sP409(U_1747,U_1746,U_1743,U_1748)
| sP407 ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_11,plain,
( sK365 = sK366
| ~ sP407 ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_12,plain,
( ordinal(sK366)
| ~ sP407 ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_13,plain,
( sK365 = sK367
| ~ sP407 ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_14,plain,
( ordinal(sK367)
| ~ sP407 ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_15,plain,
( sK366 != sK367
| ~ sP407 ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_16,plain,
( sP408(U_1747,U_1746)
| ~ in(U_1747,sK368(U_1746))
| ~ sP409(U_1747,U_1746,U_1743,U_1748) ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_17,plain,
( in(U_1748,sK368(U_1746))
| U_1743 != U_1748
| ~ in(U_1743,U_1746)
| ~ ordinal(U_1748)
| ~ sP409(U_1747,U_1746,U_1743,U_1748) ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_18,plain,
( ordinal(U_1747)
| ~ sP408(U_1747,U_1746) ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_19,plain,
( in(sK369(U_1746,U_1747),U_1746)
| ~ sP408(U_1747,U_1746) ),
inference(clausify,[status(thm)],[f_442_9]) ).
cnf(f_442_20,plain,
( sK369(U_1746,U_1747) = U_1747
| ~ sP408(U_1747,U_1746) ),
inference(clausify,[status(thm)],[f_442_9]) ).
fof(f_443_1,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( ( in(E,D)
| ! [F] :
( ~ in(relation_image(C,E),B)
| F != E
| ~ in(F,powerset(relation_dom(C))) ) )
& ( ? [F] :
( in(relation_image(C,E),B)
& F = E
& in(F,powerset(relation_dom(C))) )
| ~ in(E,D) ) )
| ? [D,E,F] :
( E != F
& in(relation_image(C,F),B)
& D = F
& in(relation_image(C,E),B)
& D = E )
| ~ function(C)
| ~ relation(C)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[s1_tarski__e6_27__finset_1__1]) ).
fof(f_443_2,plain,
! [U_1758,U_1757,U_1756] :
( ? [U_1755] :
! [U_1754] :
( ( in(U_1754,U_1755)
| ! [U_1753] :
( ~ in(relation_image(U_1756,U_1754),U_1757)
| U_1753 != U_1754
| ~ in(U_1753,powerset(relation_dom(U_1756))) ) )
& ( ? [U_1752] :
( in(relation_image(U_1756,U_1754),U_1757)
& U_1752 = U_1754
& in(U_1752,powerset(relation_dom(U_1756))) )
| ~ in(U_1754,U_1755) ) )
| ? [U_1751,U_1750,U_1749] :
( U_1750 != U_1749
& in(relation_image(U_1756,U_1749),U_1757)
& U_1751 = U_1749
& in(relation_image(U_1756,U_1750),U_1757)
& U_1751 = U_1750 )
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
! [U_1758,U_1757,U_1756] :
( ? [U_1755] :
( ! [U_1760] :
( in(U_1760,U_1755)
| ! [U_1753] :
( U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756))) )
| ~ in(relation_image(U_1756,U_1760),U_1757) )
& ! [U_1759] :
( ( ? [U_1752] :
( U_1752 = U_1759
& in(U_1752,powerset(relation_dom(U_1756))) )
& in(relation_image(U_1756,U_1759),U_1757) )
| ~ in(U_1759,U_1755) ) )
| ? [U_1751,U_1750,U_1749] :
( U_1750 != U_1749
& in(relation_image(U_1756,U_1749),U_1757)
& U_1751 = U_1749
& in(relation_image(U_1756,U_1750),U_1757)
& U_1751 = U_1750 )
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(miniscope,[status(thm)],[f_443_2]) ).
fof(f_443_4,plain,
! [U_1758,U_1757,U_1756] :
( ? [U_1755] :
( ! [U_1760] :
( in(U_1760,U_1755)
| ! [U_1753] :
( U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756))) )
| ~ in(relation_image(U_1756,U_1760),U_1757) )
& ! [U_1759] :
( ( ? [U_1752] :
( U_1752 = U_1759
& in(U_1752,powerset(relation_dom(U_1756))) )
& in(relation_image(U_1756,U_1759),U_1757) )
| ~ in(U_1759,U_1755) ) )
| ? [U_1750,U_1749] :
( U_1750 != U_1749
& in(relation_image(U_1756,U_1749),U_1757)
& sK370(U_1758,U_1757,U_1756) = U_1749
& in(relation_image(U_1756,U_1750),U_1757)
& sK370(U_1758,U_1757,U_1756) = U_1750 )
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_1751,sK370(U_1758,U_1757,U_1756))],[f_443_3]) ).
fof(f_443_5,plain,
! [U_1758,U_1757,U_1756] :
( ? [U_1755] :
( ! [U_1760] :
( in(U_1760,U_1755)
| ! [U_1753] :
( U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756))) )
| ~ in(relation_image(U_1756,U_1760),U_1757) )
& ! [U_1759] :
( ( ? [U_1752] :
( U_1752 = U_1759
& in(U_1752,powerset(relation_dom(U_1756))) )
& in(relation_image(U_1756,U_1759),U_1757) )
| ~ in(U_1759,U_1755) ) )
| ? [U_1749] :
( sK371(U_1758,U_1757,U_1756) != U_1749
& in(relation_image(U_1756,U_1749),U_1757)
& sK370(U_1758,U_1757,U_1756) = U_1749
& in(relation_image(U_1756,sK371(U_1758,U_1757,U_1756)),U_1757)
& sK370(U_1758,U_1757,U_1756) = sK371(U_1758,U_1757,U_1756) )
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_1750,sK371(U_1758,U_1757,U_1756))],[f_443_4]) ).
fof(f_443_6,plain,
! [U_1758,U_1757,U_1756] :
( ? [U_1755] :
( ! [U_1760] :
( in(U_1760,U_1755)
| ! [U_1753] :
( U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756))) )
| ~ in(relation_image(U_1756,U_1760),U_1757) )
& ! [U_1759] :
( ( ? [U_1752] :
( U_1752 = U_1759
& in(U_1752,powerset(relation_dom(U_1756))) )
& in(relation_image(U_1756,U_1759),U_1757) )
| ~ in(U_1759,U_1755) ) )
| ( sK371(U_1758,U_1757,U_1756) != sK372(U_1758,U_1757,U_1756)
& in(relation_image(U_1756,sK372(U_1758,U_1757,U_1756)),U_1757)
& sK370(U_1758,U_1757,U_1756) = sK372(U_1758,U_1757,U_1756)
& in(relation_image(U_1756,sK371(U_1758,U_1757,U_1756)),U_1757)
& sK370(U_1758,U_1757,U_1756) = sK371(U_1758,U_1757,U_1756) )
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_1749,sK372(U_1758,U_1757,U_1756))],[f_443_5]) ).
fof(f_443_7,plain,
! [U_1758,U_1757,U_1756] :
( ( ! [U_1760] :
( in(U_1760,sK373(U_1758,U_1757,U_1756))
| ! [U_1753] :
( U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756))) )
| ~ in(relation_image(U_1756,U_1760),U_1757) )
& ! [U_1759] :
( ( ? [U_1752] :
( U_1752 = U_1759
& in(U_1752,powerset(relation_dom(U_1756))) )
& in(relation_image(U_1756,U_1759),U_1757) )
| ~ in(U_1759,sK373(U_1758,U_1757,U_1756)) ) )
| ( sK371(U_1758,U_1757,U_1756) != sK372(U_1758,U_1757,U_1756)
& in(relation_image(U_1756,sK372(U_1758,U_1757,U_1756)),U_1757)
& sK370(U_1758,U_1757,U_1756) = sK372(U_1758,U_1757,U_1756)
& in(relation_image(U_1756,sK371(U_1758,U_1757,U_1756)),U_1757)
& sK370(U_1758,U_1757,U_1756) = sK371(U_1758,U_1757,U_1756) )
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_1755,sK373(U_1758,U_1757,U_1756))],[f_443_6]) ).
fof(f_443_8,plain,
! [U_1758,U_1757,U_1756] :
( ( ! [U_1760] :
( in(U_1760,sK373(U_1758,U_1757,U_1756))
| ! [U_1753] :
( U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756))) )
| ~ in(relation_image(U_1756,U_1760),U_1757) )
& ! [U_1759] :
( ( sK374(U_1758,U_1757,U_1756,U_1759) = U_1759
& in(sK374(U_1758,U_1757,U_1756,U_1759),powerset(relation_dom(U_1756)))
& in(relation_image(U_1756,U_1759),U_1757) )
| ~ in(U_1759,sK373(U_1758,U_1757,U_1756)) ) )
| ( sK371(U_1758,U_1757,U_1756) != sK372(U_1758,U_1757,U_1756)
& in(relation_image(U_1756,sK372(U_1758,U_1757,U_1756)),U_1757)
& sK370(U_1758,U_1757,U_1756) = sK372(U_1758,U_1757,U_1756)
& in(relation_image(U_1756,sK371(U_1758,U_1757,U_1756)),U_1757)
& sK370(U_1758,U_1757,U_1756) = sK371(U_1758,U_1757,U_1756) )
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_1752,sK374(U_1758,U_1757,U_1756,U_1759))],[f_443_7]) ).
fof(f_443_9,plain,
( ! [U_1758,U_1757,U_1756,U_1759] :
( sK374(U_1758,U_1757,U_1756,U_1759) = U_1759
| ~ sP411(U_1758,U_1757,U_1756,U_1759) )
& ! [U_1758,U_1757,U_1756,U_1759] :
( in(sK374(U_1758,U_1757,U_1756,U_1759),powerset(relation_dom(U_1756)))
| ~ sP411(U_1758,U_1757,U_1756,U_1759) )
& ! [U_1758,U_1757,U_1756,U_1759] :
( in(relation_image(U_1756,U_1759),U_1757)
| ~ sP411(U_1758,U_1757,U_1756,U_1759) )
& ! [U_1760,U_1758,U_1757,U_1756,U_1759,U_1753] :
( in(U_1760,sK373(U_1758,U_1757,U_1756))
| U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756)))
| ~ in(relation_image(U_1756,U_1760),U_1757)
| ~ sP412(U_1760,U_1758,U_1757,U_1756,U_1759,U_1753) )
& ! [U_1760,U_1758,U_1757,U_1756,U_1759,U_1753] :
( sP411(U_1758,U_1757,U_1756,U_1759)
| ~ in(U_1759,sK373(U_1758,U_1757,U_1756))
| ~ sP412(U_1760,U_1758,U_1757,U_1756,U_1759,U_1753) )
& ! [U_1758,U_1757,U_1756] :
( sK371(U_1758,U_1757,U_1756) != sK372(U_1758,U_1757,U_1756)
| ~ sP410(U_1758,U_1757,U_1756) )
& ! [U_1758,U_1757,U_1756] :
( in(relation_image(U_1756,sK372(U_1758,U_1757,U_1756)),U_1757)
| ~ sP410(U_1758,U_1757,U_1756) )
& ! [U_1758,U_1757,U_1756] :
( sK370(U_1758,U_1757,U_1756) = sK372(U_1758,U_1757,U_1756)
| ~ sP410(U_1758,U_1757,U_1756) )
& ! [U_1758,U_1757,U_1756] :
( in(relation_image(U_1756,sK371(U_1758,U_1757,U_1756)),U_1757)
| ~ sP410(U_1758,U_1757,U_1756) )
& ! [U_1758,U_1757,U_1756] :
( sK370(U_1758,U_1757,U_1756) = sK371(U_1758,U_1757,U_1756)
| ~ sP410(U_1758,U_1757,U_1756) )
& ! [U_1760,U_1758,U_1757,U_1756,U_1759,U_1753] :
( sP412(U_1760,U_1758,U_1757,U_1756,U_1759,U_1753)
| sP410(U_1758,U_1757,U_1756)
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP410,sP411,sP412])],[f_443_8]) ).
cnf(f_443_10,plain,
( sP412(U_1760,U_1758,U_1757,U_1756,U_1759,U_1753)
| sP410(U_1758,U_1757,U_1756)
| ~ function(U_1756)
| ~ relation(U_1756)
| ~ element(U_1757,powerset(powerset(U_1758))) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_11,plain,
( sK370(U_1758,U_1757,U_1756) = sK371(U_1758,U_1757,U_1756)
| ~ sP410(U_1758,U_1757,U_1756) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_12,plain,
( in(relation_image(U_1756,sK371(U_1758,U_1757,U_1756)),U_1757)
| ~ sP410(U_1758,U_1757,U_1756) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_13,plain,
( sK370(U_1758,U_1757,U_1756) = sK372(U_1758,U_1757,U_1756)
| ~ sP410(U_1758,U_1757,U_1756) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_14,plain,
( in(relation_image(U_1756,sK372(U_1758,U_1757,U_1756)),U_1757)
| ~ sP410(U_1758,U_1757,U_1756) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_15,plain,
( sK371(U_1758,U_1757,U_1756) != sK372(U_1758,U_1757,U_1756)
| ~ sP410(U_1758,U_1757,U_1756) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_16,plain,
( sP411(U_1758,U_1757,U_1756,U_1759)
| ~ in(U_1759,sK373(U_1758,U_1757,U_1756))
| ~ sP412(U_1760,U_1758,U_1757,U_1756,U_1759,U_1753) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_17,plain,
( in(U_1760,sK373(U_1758,U_1757,U_1756))
| U_1753 != U_1760
| ~ in(U_1753,powerset(relation_dom(U_1756)))
| ~ in(relation_image(U_1756,U_1760),U_1757)
| ~ sP412(U_1760,U_1758,U_1757,U_1756,U_1759,U_1753) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_18,plain,
( in(relation_image(U_1756,U_1759),U_1757)
| ~ sP411(U_1758,U_1757,U_1756,U_1759) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_19,plain,
( in(sK374(U_1758,U_1757,U_1756,U_1759),powerset(relation_dom(U_1756)))
| ~ sP411(U_1758,U_1757,U_1756,U_1759) ),
inference(clausify,[status(thm)],[f_443_9]) ).
cnf(f_443_20,plain,
( sK374(U_1758,U_1757,U_1756,U_1759) = U_1759
| ~ sP411(U_1758,U_1757,U_1756,U_1759) ),
inference(clausify,[status(thm)],[f_443_9]) ).
fof(f_444_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_444_2,plain,
! [U_1773,U_1772] :
( ? [U_1771] :
! [U_1770] :
( ( in(U_1770,U_1771)
| ! [U_1769] :
( ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1770 != U_1768
| ~ ordinal(U_1768) )
| U_1769 != U_1770
| ~ in(U_1769,succ(U_1772)) ) )
& ( ? [U_1767] :
( ? [U_1766] :
( in(U_1766,U_1773)
& U_1770 = U_1766
& ordinal(U_1766) )
& U_1767 = U_1770
& in(U_1767,succ(U_1772)) )
| ~ in(U_1770,U_1771) ) )
| ? [U_1765,U_1764,U_1763] :
( U_1764 != U_1763
& ? [U_1762] :
( in(U_1762,U_1773)
& U_1763 = U_1762
& ordinal(U_1762) )
& U_1765 = U_1763
& ? [U_1761] :
( in(U_1761,U_1773)
& U_1764 = U_1761
& ordinal(U_1761) )
& U_1765 = U_1764 )
| ~ ordinal(U_1772) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
! [U_1773,U_1772] :
( ? [U_1771] :
( ! [U_1775] :
( in(U_1775,U_1771)
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& ? [U_1766] :
( in(U_1766,U_1773)
& U_1774 = U_1766
& ordinal(U_1766) ) )
| ~ in(U_1774,U_1771) ) )
| ? [U_1765,U_1764,U_1763] :
( U_1764 != U_1763
& ? [U_1762] :
( in(U_1762,U_1773)
& U_1763 = U_1762
& ordinal(U_1762) )
& U_1765 = U_1763
& ? [U_1761] :
( in(U_1761,U_1773)
& U_1764 = U_1761
& ordinal(U_1761) )
& U_1765 = U_1764 )
| ~ ordinal(U_1772) ),
inference(miniscope,[status(thm)],[f_444_2]) ).
fof(f_444_4,plain,
! [U_1773,U_1772] :
( ? [U_1771] :
( ! [U_1775] :
( in(U_1775,U_1771)
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& ? [U_1766] :
( in(U_1766,U_1773)
& U_1774 = U_1766
& ordinal(U_1766) ) )
| ~ in(U_1774,U_1771) ) )
| ? [U_1764,U_1763] :
( U_1764 != U_1763
& ? [U_1762] :
( in(U_1762,U_1773)
& U_1763 = U_1762
& ordinal(U_1762) )
& sK375(U_1773,U_1772) = U_1763
& ? [U_1761] :
( in(U_1761,U_1773)
& U_1764 = U_1761
& ordinal(U_1761) )
& sK375(U_1773,U_1772) = U_1764 )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_1765,sK375(U_1773,U_1772))],[f_444_3]) ).
fof(f_444_5,plain,
! [U_1773,U_1772] :
( ? [U_1771] :
( ! [U_1775] :
( in(U_1775,U_1771)
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& ? [U_1766] :
( in(U_1766,U_1773)
& U_1774 = U_1766
& ordinal(U_1766) ) )
| ~ in(U_1774,U_1771) ) )
| ? [U_1763] :
( sK376(U_1773,U_1772) != U_1763
& ? [U_1762] :
( in(U_1762,U_1773)
& U_1763 = U_1762
& ordinal(U_1762) )
& sK375(U_1773,U_1772) = U_1763
& ? [U_1761] :
( in(U_1761,U_1773)
& sK376(U_1773,U_1772) = U_1761
& ordinal(U_1761) )
& sK375(U_1773,U_1772) = sK376(U_1773,U_1772) )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_1764,sK376(U_1773,U_1772))],[f_444_4]) ).
fof(f_444_6,plain,
! [U_1773,U_1772] :
( ? [U_1771] :
( ! [U_1775] :
( in(U_1775,U_1771)
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& ? [U_1766] :
( in(U_1766,U_1773)
& U_1774 = U_1766
& ordinal(U_1766) ) )
| ~ in(U_1774,U_1771) ) )
| ( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
& ? [U_1762] :
( in(U_1762,U_1773)
& sK377(U_1773,U_1772) = U_1762
& ordinal(U_1762) )
& sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
& ? [U_1761] :
( in(U_1761,U_1773)
& sK376(U_1773,U_1772) = U_1761
& ordinal(U_1761) )
& sK375(U_1773,U_1772) = sK376(U_1773,U_1772) )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_1763,sK377(U_1773,U_1772))],[f_444_5]) ).
fof(f_444_7,plain,
! [U_1773,U_1772] :
( ? [U_1771] :
( ! [U_1775] :
( in(U_1775,U_1771)
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& ? [U_1766] :
( in(U_1766,U_1773)
& U_1774 = U_1766
& ordinal(U_1766) ) )
| ~ in(U_1774,U_1771) ) )
| ( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
& ? [U_1762] :
( in(U_1762,U_1773)
& sK377(U_1773,U_1772) = U_1762
& ordinal(U_1762) )
& sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
& in(sK378(U_1773,U_1772),U_1773)
& sK376(U_1773,U_1772) = sK378(U_1773,U_1772)
& ordinal(sK378(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK376(U_1773,U_1772) )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_1761,sK378(U_1773,U_1772))],[f_444_6]) ).
fof(f_444_8,plain,
! [U_1773,U_1772] :
( ? [U_1771] :
( ! [U_1775] :
( in(U_1775,U_1771)
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& ? [U_1766] :
( in(U_1766,U_1773)
& U_1774 = U_1766
& ordinal(U_1766) ) )
| ~ in(U_1774,U_1771) ) )
| ( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
& in(sK379(U_1773,U_1772),U_1773)
& sK377(U_1773,U_1772) = sK379(U_1773,U_1772)
& ordinal(sK379(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
& in(sK378(U_1773,U_1772),U_1773)
& sK376(U_1773,U_1772) = sK378(U_1773,U_1772)
& ordinal(sK378(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK376(U_1773,U_1772) )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_1762,sK379(U_1773,U_1772))],[f_444_7]) ).
fof(f_444_9,plain,
! [U_1773,U_1772] :
( ( ! [U_1775] :
( in(U_1775,sK380(U_1773,U_1772))
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& ? [U_1766] :
( in(U_1766,U_1773)
& U_1774 = U_1766
& ordinal(U_1766) ) )
| ~ in(U_1774,sK380(U_1773,U_1772)) ) )
| ( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
& in(sK379(U_1773,U_1772),U_1773)
& sK377(U_1773,U_1772) = sK379(U_1773,U_1772)
& ordinal(sK379(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
& in(sK378(U_1773,U_1772),U_1773)
& sK376(U_1773,U_1772) = sK378(U_1773,U_1772)
& ordinal(sK378(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK376(U_1773,U_1772) )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_1771,sK380(U_1773,U_1772))],[f_444_8]) ).
fof(f_444_10,plain,
! [U_1773,U_1772] :
( ( ! [U_1775] :
( in(U_1775,sK380(U_1773,U_1772))
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( ? [U_1767] :
( U_1767 = U_1774
& in(U_1767,succ(U_1772)) )
& in(sK381(U_1773,U_1772,U_1774),U_1773)
& U_1774 = sK381(U_1773,U_1772,U_1774)
& ordinal(sK381(U_1773,U_1772,U_1774)) )
| ~ in(U_1774,sK380(U_1773,U_1772)) ) )
| ( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
& in(sK379(U_1773,U_1772),U_1773)
& sK377(U_1773,U_1772) = sK379(U_1773,U_1772)
& ordinal(sK379(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
& in(sK378(U_1773,U_1772),U_1773)
& sK376(U_1773,U_1772) = sK378(U_1773,U_1772)
& ordinal(sK378(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK376(U_1773,U_1772) )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_1766,sK381(U_1773,U_1772,U_1774))],[f_444_9]) ).
fof(f_444_11,plain,
! [U_1773,U_1772] :
( ( ! [U_1775] :
( in(U_1775,sK380(U_1773,U_1772))
| ! [U_1769] :
( U_1769 != U_1775
| ~ in(U_1769,succ(U_1772)) )
| ! [U_1768] :
( ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768) ) )
& ! [U_1774] :
( ( sK382(U_1773,U_1772,U_1774) = U_1774
& in(sK382(U_1773,U_1772,U_1774),succ(U_1772))
& in(sK381(U_1773,U_1772,U_1774),U_1773)
& U_1774 = sK381(U_1773,U_1772,U_1774)
& ordinal(sK381(U_1773,U_1772,U_1774)) )
| ~ in(U_1774,sK380(U_1773,U_1772)) ) )
| ( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
& in(sK379(U_1773,U_1772),U_1773)
& sK377(U_1773,U_1772) = sK379(U_1773,U_1772)
& ordinal(sK379(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
& in(sK378(U_1773,U_1772),U_1773)
& sK376(U_1773,U_1772) = sK378(U_1773,U_1772)
& ordinal(sK378(U_1773,U_1772))
& sK375(U_1773,U_1772) = sK376(U_1773,U_1772) )
| ~ ordinal(U_1772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_1767,sK382(U_1773,U_1772,U_1774))],[f_444_10]) ).
fof(f_444_12,plain,
( ! [U_1772,U_1773,U_1774] :
( sK382(U_1773,U_1772,U_1774) = U_1774
| ~ sP414(U_1772,U_1773,U_1774) )
& ! [U_1772,U_1773,U_1774] :
( in(sK382(U_1773,U_1772,U_1774),succ(U_1772))
| ~ sP414(U_1772,U_1773,U_1774) )
& ! [U_1772,U_1773,U_1774] :
( in(sK381(U_1773,U_1772,U_1774),U_1773)
| ~ sP414(U_1772,U_1773,U_1774) )
& ! [U_1772,U_1773,U_1774] :
( U_1774 = sK381(U_1773,U_1772,U_1774)
| ~ sP414(U_1772,U_1773,U_1774) )
& ! [U_1772,U_1773,U_1774] :
( ordinal(sK381(U_1773,U_1772,U_1774))
| ~ sP414(U_1772,U_1773,U_1774) )
& ! [U_1772,U_1769,U_1773,U_1768,U_1774,U_1775] :
( in(U_1775,sK380(U_1773,U_1772))
| U_1769 != U_1775
| ~ in(U_1769,succ(U_1772))
| ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768)
| ~ sP415(U_1772,U_1769,U_1773,U_1768,U_1774,U_1775) )
& ! [U_1772,U_1769,U_1773,U_1768,U_1774,U_1775] :
( sP414(U_1772,U_1773,U_1774)
| ~ in(U_1774,sK380(U_1773,U_1772))
| ~ sP415(U_1772,U_1769,U_1773,U_1768,U_1774,U_1775) )
& ! [U_1772,U_1773] :
( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( in(sK379(U_1773,U_1772),U_1773)
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( sK377(U_1773,U_1772) = sK379(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( ordinal(sK379(U_1773,U_1772))
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( in(sK378(U_1773,U_1772),U_1773)
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( sK376(U_1773,U_1772) = sK378(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( ordinal(sK378(U_1773,U_1772))
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1773] :
( sK375(U_1773,U_1772) = sK376(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) )
& ! [U_1772,U_1769,U_1773,U_1768,U_1774,U_1775] :
( sP415(U_1772,U_1769,U_1773,U_1768,U_1774,U_1775)
| sP413(U_1772,U_1773)
| ~ ordinal(U_1772) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP413,sP414,sP415])],[f_444_11]) ).
cnf(f_444_13,plain,
( sP415(U_1772,U_1769,U_1773,U_1768,U_1774,U_1775)
| sP413(U_1772,U_1773)
| ~ ordinal(U_1772) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_14,plain,
( sK375(U_1773,U_1772) = sK376(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_15,plain,
( ordinal(sK378(U_1773,U_1772))
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_16,plain,
( sK376(U_1773,U_1772) = sK378(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_17,plain,
( in(sK378(U_1773,U_1772),U_1773)
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_18,plain,
( sK375(U_1773,U_1772) = sK377(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_19,plain,
( ordinal(sK379(U_1773,U_1772))
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_20,plain,
( sK377(U_1773,U_1772) = sK379(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_21,plain,
( in(sK379(U_1773,U_1772),U_1773)
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_22,plain,
( sK376(U_1773,U_1772) != sK377(U_1773,U_1772)
| ~ sP413(U_1772,U_1773) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_23,plain,
( sP414(U_1772,U_1773,U_1774)
| ~ in(U_1774,sK380(U_1773,U_1772))
| ~ sP415(U_1772,U_1769,U_1773,U_1768,U_1774,U_1775) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_24,plain,
( in(U_1775,sK380(U_1773,U_1772))
| U_1769 != U_1775
| ~ in(U_1769,succ(U_1772))
| ~ in(U_1768,U_1773)
| U_1775 != U_1768
| ~ ordinal(U_1768)
| ~ sP415(U_1772,U_1769,U_1773,U_1768,U_1774,U_1775) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_25,plain,
( ordinal(sK381(U_1773,U_1772,U_1774))
| ~ sP414(U_1772,U_1773,U_1774) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_26,plain,
( U_1774 = sK381(U_1773,U_1772,U_1774)
| ~ sP414(U_1772,U_1773,U_1774) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_27,plain,
( in(sK381(U_1773,U_1772,U_1774),U_1773)
| ~ sP414(U_1772,U_1773,U_1774) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_28,plain,
( in(sK382(U_1773,U_1772,U_1774),succ(U_1772))
| ~ sP414(U_1772,U_1773,U_1774) ),
inference(clausify,[status(thm)],[f_444_12]) ).
cnf(f_444_29,plain,
( sK382(U_1773,U_1772,U_1774) = U_1774
| ~ sP414(U_1772,U_1773,U_1774) ),
inference(clausify,[status(thm)],[f_444_12]) ).
fof(f_445_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_445_2,plain,
! [U_1788,U_1787] :
( ! [U_1786] :
? [U_1785] :
! [U_1784] :
( ( in(U_1784,U_1785)
| ! [U_1783,U_1782] :
( ! [U_1781] :
( ? [U_1780] :
( ~ in(ordered_pair(U_1782,U_1780),U_1787)
& in(U_1780,U_1781) )
| ~ in(U_1782,U_1781)
| U_1783 != U_1781 )
| ~ in(U_1783,U_1788)
| ordered_pair(U_1783,U_1782) != U_1784 )
| ~ in(U_1784,cartesian_product2(U_1788,U_1786)) )
& ( ( ? [U_1779,U_1778] :
( ? [U_1777] :
( ! [U_1776] :
( in(ordered_pair(U_1778,U_1776),U_1787)
| ~ in(U_1776,U_1777) )
& in(U_1778,U_1777)
& U_1779 = U_1777 )
& in(U_1779,U_1788)
& ordered_pair(U_1779,U_1778) = U_1784 )
& in(U_1784,cartesian_product2(U_1788,U_1786)) )
| ~ in(U_1784,U_1785) ) )
| ~ relation(U_1787)
| empty(U_1788) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
! [U_1788,U_1787] :
( ! [U_1786] :
? [U_1785] :
( ! [U_1790] :
( in(U_1790,U_1785)
| ! [U_1783] :
( ! [U_1782] :
( ! [U_1781] :
( ? [U_1780] :
( ~ in(ordered_pair(U_1782,U_1780),U_1787)
& in(U_1780,U_1781) )
| ~ in(U_1782,U_1781)
| U_1783 != U_1781 )
| ordered_pair(U_1783,U_1782) != U_1790 )
| ~ in(U_1783,U_1788) )
| ~ in(U_1790,cartesian_product2(U_1788,U_1786)) )
& ! [U_1789] :
( ( ? [U_1779] :
( ? [U_1778] :
( ? [U_1777] :
( ! [U_1776] :
( in(ordered_pair(U_1778,U_1776),U_1787)
| ~ in(U_1776,U_1777) )
& in(U_1778,U_1777)
& U_1779 = U_1777 )
& ordered_pair(U_1779,U_1778) = U_1789 )
& in(U_1779,U_1788) )
& in(U_1789,cartesian_product2(U_1788,U_1786)) )
| ~ in(U_1789,U_1785) ) )
| ~ relation(U_1787)
| empty(U_1788) ),
inference(miniscope,[status(thm)],[f_445_2]) ).
fof(f_445_4,plain,
! [U_1788,U_1787] :
( ! [U_1786] :
( ! [U_1790] :
( in(U_1790,sK383(U_1788,U_1787,U_1786))
| ! [U_1783] :
( ! [U_1782] :
( ! [U_1781] :
( ? [U_1780] :
( ~ in(ordered_pair(U_1782,U_1780),U_1787)
& in(U_1780,U_1781) )
| ~ in(U_1782,U_1781)
| U_1783 != U_1781 )
| ordered_pair(U_1783,U_1782) != U_1790 )
| ~ in(U_1783,U_1788) )
| ~ in(U_1790,cartesian_product2(U_1788,U_1786)) )
& ! [U_1789] :
( ( ? [U_1779] :
( ? [U_1778] :
( ? [U_1777] :
( ! [U_1776] :
( in(ordered_pair(U_1778,U_1776),U_1787)
| ~ in(U_1776,U_1777) )
& in(U_1778,U_1777)
& U_1779 = U_1777 )
& ordered_pair(U_1779,U_1778) = U_1789 )
& in(U_1779,U_1788) )
& in(U_1789,cartesian_product2(U_1788,U_1786)) )
| ~ in(U_1789,sK383(U_1788,U_1787,U_1786)) ) )
| ~ relation(U_1787)
| empty(U_1788) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_1785,sK383(U_1788,U_1787,U_1786))],[f_445_3]) ).
fof(f_445_5,plain,
! [U_1788,U_1787] :
( ! [U_1786] :
( ! [U_1790] :
( in(U_1790,sK383(U_1788,U_1787,U_1786))
| ! [U_1783] :
( ! [U_1782] :
( ! [U_1781] :
( ? [U_1780] :
( ~ in(ordered_pair(U_1782,U_1780),U_1787)
& in(U_1780,U_1781) )
| ~ in(U_1782,U_1781)
| U_1783 != U_1781 )
| ordered_pair(U_1783,U_1782) != U_1790 )
| ~ in(U_1783,U_1788) )
| ~ in(U_1790,cartesian_product2(U_1788,U_1786)) )
& ! [U_1789] :
( ( ? [U_1778] :
( ? [U_1777] :
( ! [U_1776] :
( in(ordered_pair(U_1778,U_1776),U_1787)
| ~ in(U_1776,U_1777) )
& in(U_1778,U_1777)
& sK384(U_1788,U_1787,U_1786,U_1789) = U_1777 )
& ordered_pair(sK384(U_1788,U_1787,U_1786,U_1789),U_1778) = U_1789 )
& in(sK384(U_1788,U_1787,U_1786,U_1789),U_1788)
& in(U_1789,cartesian_product2(U_1788,U_1786)) )
| ~ in(U_1789,sK383(U_1788,U_1787,U_1786)) ) )
| ~ relation(U_1787)
| empty(U_1788) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_1779,sK384(U_1788,U_1787,U_1786,U_1789))],[f_445_4]) ).
fof(f_445_6,plain,
! [U_1788,U_1787] :
( ! [U_1786] :
( ! [U_1790] :
( in(U_1790,sK383(U_1788,U_1787,U_1786))
| ! [U_1783] :
( ! [U_1782] :
( ! [U_1781] :
( ? [U_1780] :
( ~ in(ordered_pair(U_1782,U_1780),U_1787)
& in(U_1780,U_1781) )
| ~ in(U_1782,U_1781)
| U_1783 != U_1781 )
| ordered_pair(U_1783,U_1782) != U_1790 )
| ~ in(U_1783,U_1788) )
| ~ in(U_1790,cartesian_product2(U_1788,U_1786)) )
& ! [U_1789] :
( ( ? [U_1777] :
( ! [U_1776] :
( in(ordered_pair(sK385(U_1788,U_1787,U_1786,U_1789),U_1776),U_1787)
| ~ in(U_1776,U_1777) )
& in(sK385(U_1788,U_1787,U_1786,U_1789),U_1777)
& sK384(U_1788,U_1787,U_1786,U_1789) = U_1777 )
& ordered_pair(sK384(U_1788,U_1787,U_1786,U_1789),sK385(U_1788,U_1787,U_1786,U_1789)) = U_1789
& in(sK384(U_1788,U_1787,U_1786,U_1789),U_1788)
& in(U_1789,cartesian_product2(U_1788,U_1786)) )
| ~ in(U_1789,sK383(U_1788,U_1787,U_1786)) ) )
| ~ relation(U_1787)
| empty(U_1788) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_1778,sK385(U_1788,U_1787,U_1786,U_1789))],[f_445_5]) ).
fof(f_445_7,plain,
! [U_1788,U_1787] :
( ! [U_1786] :
( ! [U_1790] :
( in(U_1790,sK383(U_1788,U_1787,U_1786))
| ! [U_1783] :
( ! [U_1782] :
( ! [U_1781] :
( ? [U_1780] :
( ~ in(ordered_pair(U_1782,U_1780),U_1787)
& in(U_1780,U_1781) )
| ~ in(U_1782,U_1781)
| U_1783 != U_1781 )
| ordered_pair(U_1783,U_1782) != U_1790 )
| ~ in(U_1783,U_1788) )
| ~ in(U_1790,cartesian_product2(U_1788,U_1786)) )
& ! [U_1789] :
( ( ! [U_1776] :
( in(ordered_pair(sK385(U_1788,U_1787,U_1786,U_1789),U_1776),U_1787)
| ~ in(U_1776,sK386(U_1788,U_1787,U_1786,U_1789)) )
& in(sK385(U_1788,U_1787,U_1786,U_1789),sK386(U_1788,U_1787,U_1786,U_1789))
& sK384(U_1788,U_1787,U_1786,U_1789) = sK386(U_1788,U_1787,U_1786,U_1789)
& ordered_pair(sK384(U_1788,U_1787,U_1786,U_1789),sK385(U_1788,U_1787,U_1786,U_1789)) = U_1789
& in(sK384(U_1788,U_1787,U_1786,U_1789),U_1788)
& in(U_1789,cartesian_product2(U_1788,U_1786)) )
| ~ in(U_1789,sK383(U_1788,U_1787,U_1786)) ) )
| ~ relation(U_1787)
| empty(U_1788) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_1777,sK386(U_1788,U_1787,U_1786,U_1789))],[f_445_6]) ).
fof(f_445_8,plain,
! [U_1788,U_1787] :
( ! [U_1786] :
( ! [U_1790] :
( in(U_1790,sK383(U_1788,U_1787,U_1786))
| ! [U_1783] :
( ! [U_1782] :
( ! [U_1781] :
( ( ~ in(ordered_pair(U_1782,sK387(U_1788,U_1787,U_1786,U_1790,U_1783,U_1782,U_1781)),U_1787)
& in(sK387(U_1788,U_1787,U_1786,U_1790,U_1783,U_1782,U_1781),U_1781) )
| ~ in(U_1782,U_1781)
| U_1783 != U_1781 )
| ordered_pair(U_1783,U_1782) != U_1790 )
| ~ in(U_1783,U_1788) )
| ~ in(U_1790,cartesian_product2(U_1788,U_1786)) )
& ! [U_1789] :
( ( ! [U_1776] :
( in(ordered_pair(sK385(U_1788,U_1787,U_1786,U_1789),U_1776),U_1787)
| ~ in(U_1776,sK386(U_1788,U_1787,U_1786,U_1789)) )
& in(sK385(U_1788,U_1787,U_1786,U_1789),sK386(U_1788,U_1787,U_1786,U_1789))
& sK384(U_1788,U_1787,U_1786,U_1789) = sK386(U_1788,U_1787,U_1786,U_1789)
& ordered_pair(sK384(U_1788,U_1787,U_1786,U_1789),sK385(U_1788,U_1787,U_1786,U_1789)) = U_1789
& in(sK384(U_1788,U_1787,U_1786,U_1789),U_1788)
& in(U_1789,cartesian_product2(U_1788,U_1786)) )
| ~ in(U_1789,sK383(U_1788,U_1787,U_1786)) ) )
| ~ relation(U_1787)
| empty(U_1788) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_1780,sK387(U_1788,U_1787,U_1786,U_1790,U_1783,U_1782,U_1781))],[f_445_7]) ).
fof(f_445_9,plain,
( ! [U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788] :
( ~ in(ordered_pair(U_1782,sK387(U_1788,U_1787,U_1786,U_1790,U_1783,U_1782,U_1781)),U_1787)
| ~ sP417(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788) )
& ! [U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788] :
( in(sK387(U_1788,U_1787,U_1786,U_1790,U_1783,U_1782,U_1781),U_1781)
| ~ sP417(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788) )
& ! [U_1787,U_1786,U_1789,U_1788,U_1776] :
( in(ordered_pair(sK385(U_1788,U_1787,U_1786,U_1789),U_1776),U_1787)
| ~ in(U_1776,sK386(U_1788,U_1787,U_1786,U_1789))
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1787,U_1786,U_1789,U_1788,U_1776] :
( in(sK385(U_1788,U_1787,U_1786,U_1789),sK386(U_1788,U_1787,U_1786,U_1789))
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1787,U_1786,U_1789,U_1788,U_1776] :
( sK384(U_1788,U_1787,U_1786,U_1789) = sK386(U_1788,U_1787,U_1786,U_1789)
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1787,U_1786,U_1789,U_1788,U_1776] :
( ordered_pair(sK384(U_1788,U_1787,U_1786,U_1789),sK385(U_1788,U_1787,U_1786,U_1789)) = U_1789
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1787,U_1786,U_1789,U_1788,U_1776] :
( in(sK384(U_1788,U_1787,U_1786,U_1789),U_1788)
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1787,U_1786,U_1789,U_1788,U_1776] :
( in(U_1789,cartesian_product2(U_1788,U_1786))
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776] :
( in(U_1790,sK383(U_1788,U_1787,U_1786))
| sP417(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788)
| ~ in(U_1782,U_1781)
| U_1783 != U_1781
| ordered_pair(U_1783,U_1782) != U_1790
| ~ in(U_1783,U_1788)
| ~ in(U_1790,cartesian_product2(U_1788,U_1786))
| ~ sP418(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776] :
( sP416(U_1787,U_1786,U_1789,U_1788,U_1776)
| ~ in(U_1789,sK383(U_1788,U_1787,U_1786))
| ~ sP418(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776) )
& ! [U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776] :
( sP418(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776)
| ~ relation(U_1787)
| empty(U_1788) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP416,sP417,sP418])],[f_445_8]) ).
cnf(f_445_10,plain,
( sP418(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776)
| ~ relation(U_1787)
| empty(U_1788) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_11,plain,
( sP416(U_1787,U_1786,U_1789,U_1788,U_1776)
| ~ in(U_1789,sK383(U_1788,U_1787,U_1786))
| ~ sP418(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_12,plain,
( in(U_1790,sK383(U_1788,U_1787,U_1786))
| sP417(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788)
| ~ in(U_1782,U_1781)
| U_1783 != U_1781
| ordered_pair(U_1783,U_1782) != U_1790
| ~ in(U_1783,U_1788)
| ~ in(U_1790,cartesian_product2(U_1788,U_1786))
| ~ sP418(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_13,plain,
( in(U_1789,cartesian_product2(U_1788,U_1786))
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_14,plain,
( in(sK384(U_1788,U_1787,U_1786,U_1789),U_1788)
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_15,plain,
( ordered_pair(sK384(U_1788,U_1787,U_1786,U_1789),sK385(U_1788,U_1787,U_1786,U_1789)) = U_1789
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_16,plain,
( sK384(U_1788,U_1787,U_1786,U_1789) = sK386(U_1788,U_1787,U_1786,U_1789)
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_17,plain,
( in(sK385(U_1788,U_1787,U_1786,U_1789),sK386(U_1788,U_1787,U_1786,U_1789))
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_18,plain,
( in(ordered_pair(sK385(U_1788,U_1787,U_1786,U_1789),U_1776),U_1787)
| ~ in(U_1776,sK386(U_1788,U_1787,U_1786,U_1789))
| ~ sP416(U_1787,U_1786,U_1789,U_1788,U_1776) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_19,plain,
( in(sK387(U_1788,U_1787,U_1786,U_1790,U_1783,U_1782,U_1781),U_1781)
| ~ sP417(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788) ),
inference(clausify,[status(thm)],[f_445_9]) ).
cnf(f_445_20,plain,
( ~ in(ordered_pair(U_1782,sK387(U_1788,U_1787,U_1786,U_1790,U_1783,U_1782,U_1781)),U_1787)
| ~ sP417(U_1790,U_1781,U_1787,U_1782,U_1783,U_1786,U_1788) ),
inference(clausify,[status(thm)],[f_445_9]) ).
fof(f_446_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_446_2,plain,
! [U_1798,U_1797] :
? [U_1796] :
! [U_1795] :
( ( in(U_1795,U_1796)
| ! [U_1794,U_1793] :
( U_1793 != singleton(U_1794)
| ~ in(U_1794,U_1798)
| ordered_pair(U_1794,U_1793) != U_1795 )
| ~ in(U_1795,cartesian_product2(U_1798,U_1797)) )
& ( ( ? [U_1792,U_1791] :
( U_1791 = singleton(U_1792)
& in(U_1792,U_1798)
& ordered_pair(U_1792,U_1791) = U_1795 )
& in(U_1795,cartesian_product2(U_1798,U_1797)) )
| ~ in(U_1795,U_1796) ) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
! [U_1798,U_1797] :
? [U_1796] :
( ! [U_1800] :
( in(U_1800,U_1796)
| ! [U_1794] :
( ! [U_1793] :
( U_1793 != singleton(U_1794)
| ordered_pair(U_1794,U_1793) != U_1800 )
| ~ in(U_1794,U_1798) )
| ~ in(U_1800,cartesian_product2(U_1798,U_1797)) )
& ! [U_1799] :
( ( ? [U_1792] :
( ? [U_1791] :
( U_1791 = singleton(U_1792)
& ordered_pair(U_1792,U_1791) = U_1799 )
& in(U_1792,U_1798) )
& in(U_1799,cartesian_product2(U_1798,U_1797)) )
| ~ in(U_1799,U_1796) ) ),
inference(miniscope,[status(thm)],[f_446_2]) ).
fof(f_446_4,plain,
! [U_1798,U_1797] :
( ! [U_1800] :
( in(U_1800,sK388(U_1798,U_1797))
| ! [U_1794] :
( ! [U_1793] :
( U_1793 != singleton(U_1794)
| ordered_pair(U_1794,U_1793) != U_1800 )
| ~ in(U_1794,U_1798) )
| ~ in(U_1800,cartesian_product2(U_1798,U_1797)) )
& ! [U_1799] :
( ( ? [U_1792] :
( ? [U_1791] :
( U_1791 = singleton(U_1792)
& ordered_pair(U_1792,U_1791) = U_1799 )
& in(U_1792,U_1798) )
& in(U_1799,cartesian_product2(U_1798,U_1797)) )
| ~ in(U_1799,sK388(U_1798,U_1797)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_1796,sK388(U_1798,U_1797))],[f_446_3]) ).
fof(f_446_5,plain,
! [U_1798,U_1797] :
( ! [U_1800] :
( in(U_1800,sK388(U_1798,U_1797))
| ! [U_1794] :
( ! [U_1793] :
( U_1793 != singleton(U_1794)
| ordered_pair(U_1794,U_1793) != U_1800 )
| ~ in(U_1794,U_1798) )
| ~ in(U_1800,cartesian_product2(U_1798,U_1797)) )
& ! [U_1799] :
( ( ? [U_1791] :
( U_1791 = singleton(sK389(U_1798,U_1797,U_1799))
& ordered_pair(sK389(U_1798,U_1797,U_1799),U_1791) = U_1799 )
& in(sK389(U_1798,U_1797,U_1799),U_1798)
& in(U_1799,cartesian_product2(U_1798,U_1797)) )
| ~ in(U_1799,sK388(U_1798,U_1797)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_1792,sK389(U_1798,U_1797,U_1799))],[f_446_4]) ).
fof(f_446_6,plain,
! [U_1798,U_1797] :
( ! [U_1800] :
( in(U_1800,sK388(U_1798,U_1797))
| ! [U_1794] :
( ! [U_1793] :
( U_1793 != singleton(U_1794)
| ordered_pair(U_1794,U_1793) != U_1800 )
| ~ in(U_1794,U_1798) )
| ~ in(U_1800,cartesian_product2(U_1798,U_1797)) )
& ! [U_1799] :
( ( sK390(U_1798,U_1797,U_1799) = singleton(sK389(U_1798,U_1797,U_1799))
& ordered_pair(sK389(U_1798,U_1797,U_1799),sK390(U_1798,U_1797,U_1799)) = U_1799
& in(sK389(U_1798,U_1797,U_1799),U_1798)
& in(U_1799,cartesian_product2(U_1798,U_1797)) )
| ~ in(U_1799,sK388(U_1798,U_1797)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_1791,sK390(U_1798,U_1797,U_1799))],[f_446_5]) ).
fof(f_446_7,plain,
( ! [U_1797,U_1798,U_1799] :
( sK390(U_1798,U_1797,U_1799) = singleton(sK389(U_1798,U_1797,U_1799))
| ~ sP419(U_1797,U_1798,U_1799) )
& ! [U_1797,U_1798,U_1799] :
( ordered_pair(sK389(U_1798,U_1797,U_1799),sK390(U_1798,U_1797,U_1799)) = U_1799
| ~ sP419(U_1797,U_1798,U_1799) )
& ! [U_1797,U_1798,U_1799] :
( in(sK389(U_1798,U_1797,U_1799),U_1798)
| ~ sP419(U_1797,U_1798,U_1799) )
& ! [U_1797,U_1798,U_1799] :
( in(U_1799,cartesian_product2(U_1798,U_1797))
| ~ sP419(U_1797,U_1798,U_1799) )
& ! [U_1797,U_1800,U_1794,U_1798,U_1793] :
( in(U_1800,sK388(U_1798,U_1797))
| U_1793 != singleton(U_1794)
| ordered_pair(U_1794,U_1793) != U_1800
| ~ in(U_1794,U_1798)
| ~ in(U_1800,cartesian_product2(U_1798,U_1797)) )
& ! [U_1797,U_1798,U_1799] :
( sP419(U_1797,U_1798,U_1799)
| ~ in(U_1799,sK388(U_1798,U_1797)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP419])],[f_446_6]) ).
cnf(f_446_8,plain,
( sP419(U_1797,U_1798,U_1799)
| ~ in(U_1799,sK388(U_1798,U_1797)) ),
inference(clausify,[status(thm)],[f_446_7]) ).
cnf(f_446_9,plain,
( in(U_1800,sK388(U_1798,U_1797))
| U_1793 != singleton(U_1794)
| ordered_pair(U_1794,U_1793) != U_1800
| ~ in(U_1794,U_1798)
| ~ in(U_1800,cartesian_product2(U_1798,U_1797)) ),
inference(clausify,[status(thm)],[f_446_7]) ).
cnf(f_446_10,plain,
( in(U_1799,cartesian_product2(U_1798,U_1797))
| ~ sP419(U_1797,U_1798,U_1799) ),
inference(clausify,[status(thm)],[f_446_7]) ).
cnf(f_446_11,plain,
( in(sK389(U_1798,U_1797,U_1799),U_1798)
| ~ sP419(U_1797,U_1798,U_1799) ),
inference(clausify,[status(thm)],[f_446_7]) ).
cnf(f_446_12,plain,
( ordered_pair(sK389(U_1798,U_1797,U_1799),sK390(U_1798,U_1797,U_1799)) = U_1799
| ~ sP419(U_1797,U_1798,U_1799) ),
inference(clausify,[status(thm)],[f_446_7]) ).
cnf(f_446_13,plain,
( sK390(U_1798,U_1797,U_1799) = singleton(sK389(U_1798,U_1797,U_1799))
| ~ sP419(U_1797,U_1798,U_1799) ),
inference(clausify,[status(thm)],[f_446_7]) ).
fof(f_447_1,plain,
! [A] :
( ? [B] :
! [C] :
( ( in(C,B)
| ! [D] :
( ( ? [E] :
( ! [F] :
( ? [G] :
( G != F
& subset(F,G)
& in(G,E) )
| ~ in(F,E) )
& E != empty_set
& element(E,powerset(powerset(D))) )
& in(D,omega) )
| C != D
| ~ ordinal(D) )
| ~ in(C,succ(A)) )
& ( ( ? [D] :
( ( ! [E] :
( ? [F] :
( ! [G] :
( G = F
| ~ subset(F,G)
| ~ in(G,E) )
& in(F,E) )
| E = empty_set
| ~ element(E,powerset(powerset(D))) )
| ~ in(D,omega) )
& C = D
& ordinal(D) )
& in(C,succ(A)) )
| ~ in(C,B) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e18_27__finset_1__1]) ).
fof(f_447_2,plain,
! [U_1811] :
( ? [U_1810] :
! [U_1809] :
( ( in(U_1809,U_1810)
| ! [U_1808] :
( ( ? [U_1807] :
( ! [U_1806] :
( ? [U_1805] :
( U_1805 != U_1806
& subset(U_1806,U_1805)
& in(U_1805,U_1807) )
| ~ in(U_1806,U_1807) )
& U_1807 != empty_set
& element(U_1807,powerset(powerset(U_1808))) )
& in(U_1808,omega) )
| U_1809 != U_1808
| ~ ordinal(U_1808) )
| ~ in(U_1809,succ(U_1811)) )
& ( ( ? [U_1804] :
( ( ! [U_1803] :
( ? [U_1802] :
( ! [U_1801] :
( U_1801 = U_1802
| ~ subset(U_1802,U_1801)
| ~ in(U_1801,U_1803) )
& in(U_1802,U_1803) )
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(U_1804))) )
| ~ in(U_1804,omega) )
& U_1809 = U_1804
& ordinal(U_1804) )
& in(U_1809,succ(U_1811)) )
| ~ in(U_1809,U_1810) ) )
| ~ ordinal(U_1811) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
! [U_1811] :
( ? [U_1810] :
( ! [U_1813] :
( in(U_1813,U_1810)
| ! [U_1808] :
( ( ? [U_1807] :
( ! [U_1806] :
( ? [U_1805] :
( U_1805 != U_1806
& subset(U_1806,U_1805)
& in(U_1805,U_1807) )
| ~ in(U_1806,U_1807) )
& U_1807 != empty_set
& element(U_1807,powerset(powerset(U_1808))) )
& in(U_1808,omega) )
| U_1813 != U_1808
| ~ ordinal(U_1808) )
| ~ in(U_1813,succ(U_1811)) )
& ! [U_1812] :
( ( ? [U_1804] :
( ( ! [U_1803] :
( ? [U_1802] :
( ! [U_1801] :
( U_1801 = U_1802
| ~ subset(U_1802,U_1801)
| ~ in(U_1801,U_1803) )
& in(U_1802,U_1803) )
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(U_1804))) )
| ~ in(U_1804,omega) )
& U_1812 = U_1804
& ordinal(U_1804) )
& in(U_1812,succ(U_1811)) )
| ~ in(U_1812,U_1810) ) )
| ~ ordinal(U_1811) ),
inference(miniscope,[status(thm)],[f_447_2]) ).
fof(f_447_4,plain,
! [U_1811] :
( ( ! [U_1813] :
( in(U_1813,sK391(U_1811))
| ! [U_1808] :
( ( ? [U_1807] :
( ! [U_1806] :
( ? [U_1805] :
( U_1805 != U_1806
& subset(U_1806,U_1805)
& in(U_1805,U_1807) )
| ~ in(U_1806,U_1807) )
& U_1807 != empty_set
& element(U_1807,powerset(powerset(U_1808))) )
& in(U_1808,omega) )
| U_1813 != U_1808
| ~ ordinal(U_1808) )
| ~ in(U_1813,succ(U_1811)) )
& ! [U_1812] :
( ( ? [U_1804] :
( ( ! [U_1803] :
( ? [U_1802] :
( ! [U_1801] :
( U_1801 = U_1802
| ~ subset(U_1802,U_1801)
| ~ in(U_1801,U_1803) )
& in(U_1802,U_1803) )
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(U_1804))) )
| ~ in(U_1804,omega) )
& U_1812 = U_1804
& ordinal(U_1804) )
& in(U_1812,succ(U_1811)) )
| ~ in(U_1812,sK391(U_1811)) ) )
| ~ ordinal(U_1811) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_1810,sK391(U_1811))],[f_447_3]) ).
fof(f_447_5,plain,
! [U_1811] :
( ( ! [U_1813] :
( in(U_1813,sK391(U_1811))
| ! [U_1808] :
( ( ? [U_1807] :
( ! [U_1806] :
( ? [U_1805] :
( U_1805 != U_1806
& subset(U_1806,U_1805)
& in(U_1805,U_1807) )
| ~ in(U_1806,U_1807) )
& U_1807 != empty_set
& element(U_1807,powerset(powerset(U_1808))) )
& in(U_1808,omega) )
| U_1813 != U_1808
| ~ ordinal(U_1808) )
| ~ in(U_1813,succ(U_1811)) )
& ! [U_1812] :
( ( ( ! [U_1803] :
( ? [U_1802] :
( ! [U_1801] :
( U_1801 = U_1802
| ~ subset(U_1802,U_1801)
| ~ in(U_1801,U_1803) )
& in(U_1802,U_1803) )
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(sK392(U_1811,U_1812)))) )
| ~ in(sK392(U_1811,U_1812),omega) )
& U_1812 = sK392(U_1811,U_1812)
& ordinal(sK392(U_1811,U_1812))
& in(U_1812,succ(U_1811)) )
| ~ in(U_1812,sK391(U_1811)) ) )
| ~ ordinal(U_1811) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_1804,sK392(U_1811,U_1812))],[f_447_4]) ).
fof(f_447_6,plain,
! [U_1811] :
( ( ! [U_1813] :
( in(U_1813,sK391(U_1811))
| ! [U_1808] :
( ( ? [U_1807] :
( ! [U_1806] :
( ? [U_1805] :
( U_1805 != U_1806
& subset(U_1806,U_1805)
& in(U_1805,U_1807) )
| ~ in(U_1806,U_1807) )
& U_1807 != empty_set
& element(U_1807,powerset(powerset(U_1808))) )
& in(U_1808,omega) )
| U_1813 != U_1808
| ~ ordinal(U_1808) )
| ~ in(U_1813,succ(U_1811)) )
& ! [U_1812] :
( ( ( ! [U_1803] :
( ( ! [U_1801] :
( U_1801 = sK393(U_1811,U_1812,U_1803)
| ~ subset(sK393(U_1811,U_1812,U_1803),U_1801)
| ~ in(U_1801,U_1803) )
& in(sK393(U_1811,U_1812,U_1803),U_1803) )
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(sK392(U_1811,U_1812)))) )
| ~ in(sK392(U_1811,U_1812),omega) )
& U_1812 = sK392(U_1811,U_1812)
& ordinal(sK392(U_1811,U_1812))
& in(U_1812,succ(U_1811)) )
| ~ in(U_1812,sK391(U_1811)) ) )
| ~ ordinal(U_1811) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_1802,sK393(U_1811,U_1812,U_1803))],[f_447_5]) ).
fof(f_447_7,plain,
! [U_1811] :
( ( ! [U_1813] :
( in(U_1813,sK391(U_1811))
| ! [U_1808] :
( ( ! [U_1806] :
( ? [U_1805] :
( U_1805 != U_1806
& subset(U_1806,U_1805)
& in(U_1805,sK394(U_1811,U_1813,U_1808)) )
| ~ in(U_1806,sK394(U_1811,U_1813,U_1808)) )
& sK394(U_1811,U_1813,U_1808) != empty_set
& element(sK394(U_1811,U_1813,U_1808),powerset(powerset(U_1808)))
& in(U_1808,omega) )
| U_1813 != U_1808
| ~ ordinal(U_1808) )
| ~ in(U_1813,succ(U_1811)) )
& ! [U_1812] :
( ( ( ! [U_1803] :
( ( ! [U_1801] :
( U_1801 = sK393(U_1811,U_1812,U_1803)
| ~ subset(sK393(U_1811,U_1812,U_1803),U_1801)
| ~ in(U_1801,U_1803) )
& in(sK393(U_1811,U_1812,U_1803),U_1803) )
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(sK392(U_1811,U_1812)))) )
| ~ in(sK392(U_1811,U_1812),omega) )
& U_1812 = sK392(U_1811,U_1812)
& ordinal(sK392(U_1811,U_1812))
& in(U_1812,succ(U_1811)) )
| ~ in(U_1812,sK391(U_1811)) ) )
| ~ ordinal(U_1811) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_1807,sK394(U_1811,U_1813,U_1808))],[f_447_6]) ).
fof(f_447_8,plain,
! [U_1811] :
( ( ! [U_1813] :
( in(U_1813,sK391(U_1811))
| ! [U_1808] :
( ( ! [U_1806] :
( ( sK395(U_1811,U_1813,U_1808,U_1806) != U_1806
& subset(U_1806,sK395(U_1811,U_1813,U_1808,U_1806))
& in(sK395(U_1811,U_1813,U_1808,U_1806),sK394(U_1811,U_1813,U_1808)) )
| ~ in(U_1806,sK394(U_1811,U_1813,U_1808)) )
& sK394(U_1811,U_1813,U_1808) != empty_set
& element(sK394(U_1811,U_1813,U_1808),powerset(powerset(U_1808)))
& in(U_1808,omega) )
| U_1813 != U_1808
| ~ ordinal(U_1808) )
| ~ in(U_1813,succ(U_1811)) )
& ! [U_1812] :
( ( ( ! [U_1803] :
( ( ! [U_1801] :
( U_1801 = sK393(U_1811,U_1812,U_1803)
| ~ subset(sK393(U_1811,U_1812,U_1803),U_1801)
| ~ in(U_1801,U_1803) )
& in(sK393(U_1811,U_1812,U_1803),U_1803) )
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(sK392(U_1811,U_1812)))) )
| ~ in(sK392(U_1811,U_1812),omega) )
& U_1812 = sK392(U_1811,U_1812)
& ordinal(sK392(U_1811,U_1812))
& in(U_1812,succ(U_1811)) )
| ~ in(U_1812,sK391(U_1811)) ) )
| ~ ordinal(U_1811) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_1805,sK395(U_1811,U_1813,U_1808,U_1806))],[f_447_7]) ).
fof(f_447_9,plain,
( ! [U_1813,U_1811,U_1806,U_1808] :
( sK395(U_1811,U_1813,U_1808,U_1806) != U_1806
| ~ sP422(U_1813,U_1811,U_1806,U_1808) )
& ! [U_1813,U_1811,U_1806,U_1808] :
( subset(U_1806,sK395(U_1811,U_1813,U_1808,U_1806))
| ~ sP422(U_1813,U_1811,U_1806,U_1808) )
& ! [U_1813,U_1811,U_1806,U_1808] :
( in(sK395(U_1811,U_1813,U_1808,U_1806),sK394(U_1811,U_1813,U_1808))
| ~ sP422(U_1813,U_1811,U_1806,U_1808) )
& ! [U_1813,U_1811,U_1806,U_1808] :
( sP422(U_1813,U_1811,U_1806,U_1808)
| ~ in(U_1806,sK394(U_1811,U_1813,U_1808))
| ~ sP423(U_1813,U_1811,U_1806,U_1808) )
& ! [U_1813,U_1811,U_1806,U_1808] :
( sK394(U_1811,U_1813,U_1808) != empty_set
| ~ sP423(U_1813,U_1811,U_1806,U_1808) )
& ! [U_1813,U_1811,U_1806,U_1808] :
( element(sK394(U_1811,U_1813,U_1808),powerset(powerset(U_1808)))
| ~ sP423(U_1813,U_1811,U_1806,U_1808) )
& ! [U_1813,U_1811,U_1806,U_1808] :
( in(U_1808,omega)
| ~ sP423(U_1813,U_1811,U_1806,U_1808) )
& ! [U_1801,U_1803,U_1812,U_1811] :
( U_1801 = sK393(U_1811,U_1812,U_1803)
| ~ subset(sK393(U_1811,U_1812,U_1803),U_1801)
| ~ in(U_1801,U_1803)
| ~ sP420(U_1801,U_1803,U_1812,U_1811) )
& ! [U_1801,U_1803,U_1812,U_1811] :
( in(sK393(U_1811,U_1812,U_1803),U_1803)
| ~ sP420(U_1801,U_1803,U_1812,U_1811) )
& ! [U_1801,U_1803,U_1812,U_1811] :
( sP420(U_1801,U_1803,U_1812,U_1811)
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(sK392(U_1811,U_1812))))
| ~ in(sK392(U_1811,U_1812),omega)
| ~ sP421(U_1801,U_1803,U_1812,U_1811) )
& ! [U_1801,U_1803,U_1812,U_1811] :
( U_1812 = sK392(U_1811,U_1812)
| ~ sP421(U_1801,U_1803,U_1812,U_1811) )
& ! [U_1801,U_1803,U_1812,U_1811] :
( ordinal(sK392(U_1811,U_1812))
| ~ sP421(U_1801,U_1803,U_1812,U_1811) )
& ! [U_1801,U_1803,U_1812,U_1811] :
( in(U_1812,succ(U_1811))
| ~ sP421(U_1801,U_1803,U_1812,U_1811) )
& ! [U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808] :
( in(U_1813,sK391(U_1811))
| sP423(U_1813,U_1811,U_1806,U_1808)
| U_1813 != U_1808
| ~ ordinal(U_1808)
| ~ in(U_1813,succ(U_1811))
| ~ sP424(U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808) )
& ! [U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808] :
( sP421(U_1801,U_1803,U_1812,U_1811)
| ~ in(U_1812,sK391(U_1811))
| ~ sP424(U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808) )
& ! [U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808] :
( sP424(U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808)
| ~ ordinal(U_1811) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP420,sP421,sP422,sP423,sP424])],[f_447_8]) ).
cnf(f_447_10,plain,
( sP424(U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808)
| ~ ordinal(U_1811) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_11,plain,
( sP421(U_1801,U_1803,U_1812,U_1811)
| ~ in(U_1812,sK391(U_1811))
| ~ sP424(U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_12,plain,
( in(U_1813,sK391(U_1811))
| sP423(U_1813,U_1811,U_1806,U_1808)
| U_1813 != U_1808
| ~ ordinal(U_1808)
| ~ in(U_1813,succ(U_1811))
| ~ sP424(U_1801,U_1803,U_1812,U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_13,plain,
( in(U_1812,succ(U_1811))
| ~ sP421(U_1801,U_1803,U_1812,U_1811) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_14,plain,
( ordinal(sK392(U_1811,U_1812))
| ~ sP421(U_1801,U_1803,U_1812,U_1811) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_15,plain,
( U_1812 = sK392(U_1811,U_1812)
| ~ sP421(U_1801,U_1803,U_1812,U_1811) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_16,plain,
( sP420(U_1801,U_1803,U_1812,U_1811)
| U_1803 = empty_set
| ~ element(U_1803,powerset(powerset(sK392(U_1811,U_1812))))
| ~ in(sK392(U_1811,U_1812),omega)
| ~ sP421(U_1801,U_1803,U_1812,U_1811) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_17,plain,
( in(sK393(U_1811,U_1812,U_1803),U_1803)
| ~ sP420(U_1801,U_1803,U_1812,U_1811) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_18,plain,
( U_1801 = sK393(U_1811,U_1812,U_1803)
| ~ subset(sK393(U_1811,U_1812,U_1803),U_1801)
| ~ in(U_1801,U_1803)
| ~ sP420(U_1801,U_1803,U_1812,U_1811) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_19,plain,
( in(U_1808,omega)
| ~ sP423(U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_20,plain,
( element(sK394(U_1811,U_1813,U_1808),powerset(powerset(U_1808)))
| ~ sP423(U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_21,plain,
( sK394(U_1811,U_1813,U_1808) != empty_set
| ~ sP423(U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_22,plain,
( sP422(U_1813,U_1811,U_1806,U_1808)
| ~ in(U_1806,sK394(U_1811,U_1813,U_1808))
| ~ sP423(U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_23,plain,
( in(sK395(U_1811,U_1813,U_1808,U_1806),sK394(U_1811,U_1813,U_1808))
| ~ sP422(U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_24,plain,
( subset(U_1806,sK395(U_1811,U_1813,U_1808,U_1806))
| ~ sP422(U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
cnf(f_447_25,plain,
( sK395(U_1811,U_1813,U_1808,U_1806) != U_1806
| ~ sP422(U_1813,U_1811,U_1806,U_1808) ),
inference(clausify,[status(thm)],[f_447_9]) ).
fof(f_448_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ~ subset(B,D)
| ~ closed_subset(E,A)
| E != D
| ~ element(E,powerset(the_carrier(A))) )
| ~ in(D,powerset(the_carrier(A))) )
& ( ( ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) )
& in(D,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e1_40__pre_topc__1]) ).
fof(f_448_2,plain,
! [U_1819,U_1818] :
( ? [U_1817] :
! [U_1816] :
( ( in(U_1816,U_1817)
| ! [U_1815] :
( ~ subset(U_1818,U_1816)
| ~ closed_subset(U_1815,U_1819)
| U_1815 != U_1816
| ~ element(U_1815,powerset(the_carrier(U_1819))) )
| ~ in(U_1816,powerset(the_carrier(U_1819))) )
& ( ( ? [U_1814] :
( subset(U_1818,U_1816)
& closed_subset(U_1814,U_1819)
& U_1814 = U_1816
& element(U_1814,powerset(the_carrier(U_1819))) )
& in(U_1816,powerset(the_carrier(U_1819))) )
| ~ in(U_1816,U_1817) ) )
| ~ element(U_1818,powerset(the_carrier(U_1819)))
| ~ top_str(U_1819)
| ~ topological_space(U_1819) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
! [U_1819,U_1818] :
( ? [U_1817] :
( ! [U_1821] :
( in(U_1821,U_1817)
| ! [U_1815] :
( ~ closed_subset(U_1815,U_1819)
| U_1815 != U_1821
| ~ element(U_1815,powerset(the_carrier(U_1819))) )
| ~ subset(U_1818,U_1821)
| ~ in(U_1821,powerset(the_carrier(U_1819))) )
& ! [U_1820] :
( ( ? [U_1814] :
( closed_subset(U_1814,U_1819)
& U_1814 = U_1820
& element(U_1814,powerset(the_carrier(U_1819))) )
& subset(U_1818,U_1820)
& in(U_1820,powerset(the_carrier(U_1819))) )
| ~ in(U_1820,U_1817) ) )
| ~ element(U_1818,powerset(the_carrier(U_1819)))
| ~ top_str(U_1819)
| ~ topological_space(U_1819) ),
inference(miniscope,[status(thm)],[f_448_2]) ).
fof(f_448_4,plain,
! [U_1819,U_1818] :
( ( ! [U_1821] :
( in(U_1821,sK396(U_1819,U_1818))
| ! [U_1815] :
( ~ closed_subset(U_1815,U_1819)
| U_1815 != U_1821
| ~ element(U_1815,powerset(the_carrier(U_1819))) )
| ~ subset(U_1818,U_1821)
| ~ in(U_1821,powerset(the_carrier(U_1819))) )
& ! [U_1820] :
( ( ? [U_1814] :
( closed_subset(U_1814,U_1819)
& U_1814 = U_1820
& element(U_1814,powerset(the_carrier(U_1819))) )
& subset(U_1818,U_1820)
& in(U_1820,powerset(the_carrier(U_1819))) )
| ~ in(U_1820,sK396(U_1819,U_1818)) ) )
| ~ element(U_1818,powerset(the_carrier(U_1819)))
| ~ top_str(U_1819)
| ~ topological_space(U_1819) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_1817,sK396(U_1819,U_1818))],[f_448_3]) ).
fof(f_448_5,plain,
! [U_1819,U_1818] :
( ( ! [U_1821] :
( in(U_1821,sK396(U_1819,U_1818))
| ! [U_1815] :
( ~ closed_subset(U_1815,U_1819)
| U_1815 != U_1821
| ~ element(U_1815,powerset(the_carrier(U_1819))) )
| ~ subset(U_1818,U_1821)
| ~ in(U_1821,powerset(the_carrier(U_1819))) )
& ! [U_1820] :
( ( closed_subset(sK397(U_1819,U_1818,U_1820),U_1819)
& sK397(U_1819,U_1818,U_1820) = U_1820
& element(sK397(U_1819,U_1818,U_1820),powerset(the_carrier(U_1819)))
& subset(U_1818,U_1820)
& in(U_1820,powerset(the_carrier(U_1819))) )
| ~ in(U_1820,sK396(U_1819,U_1818)) ) )
| ~ element(U_1818,powerset(the_carrier(U_1819)))
| ~ top_str(U_1819)
| ~ topological_space(U_1819) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_1814,sK397(U_1819,U_1818,U_1820))],[f_448_4]) ).
fof(f_448_6,plain,
( ! [U_1820,U_1819,U_1818] :
( closed_subset(sK397(U_1819,U_1818,U_1820),U_1819)
| ~ sP425(U_1820,U_1819,U_1818) )
& ! [U_1820,U_1819,U_1818] :
( sK397(U_1819,U_1818,U_1820) = U_1820
| ~ sP425(U_1820,U_1819,U_1818) )
& ! [U_1820,U_1819,U_1818] :
( element(sK397(U_1819,U_1818,U_1820),powerset(the_carrier(U_1819)))
| ~ sP425(U_1820,U_1819,U_1818) )
& ! [U_1820,U_1819,U_1818] :
( subset(U_1818,U_1820)
| ~ sP425(U_1820,U_1819,U_1818) )
& ! [U_1820,U_1819,U_1818] :
( in(U_1820,powerset(the_carrier(U_1819)))
| ~ sP425(U_1820,U_1819,U_1818) )
& ! [U_1820,U_1819,U_1818,U_1815,U_1821] :
( in(U_1821,sK396(U_1819,U_1818))
| ~ closed_subset(U_1815,U_1819)
| U_1815 != U_1821
| ~ element(U_1815,powerset(the_carrier(U_1819)))
| ~ subset(U_1818,U_1821)
| ~ in(U_1821,powerset(the_carrier(U_1819)))
| ~ sP426(U_1820,U_1819,U_1818,U_1815,U_1821) )
& ! [U_1820,U_1819,U_1818,U_1815,U_1821] :
( sP425(U_1820,U_1819,U_1818)
| ~ in(U_1820,sK396(U_1819,U_1818))
| ~ sP426(U_1820,U_1819,U_1818,U_1815,U_1821) )
& ! [U_1820,U_1819,U_1818,U_1815,U_1821] :
( sP426(U_1820,U_1819,U_1818,U_1815,U_1821)
| ~ element(U_1818,powerset(the_carrier(U_1819)))
| ~ top_str(U_1819)
| ~ topological_space(U_1819) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP425,sP426])],[f_448_5]) ).
cnf(f_448_7,plain,
( sP426(U_1820,U_1819,U_1818,U_1815,U_1821)
| ~ element(U_1818,powerset(the_carrier(U_1819)))
| ~ top_str(U_1819)
| ~ topological_space(U_1819) ),
inference(clausify,[status(thm)],[f_448_6]) ).
cnf(f_448_8,plain,
( sP425(U_1820,U_1819,U_1818)
| ~ in(U_1820,sK396(U_1819,U_1818))
| ~ sP426(U_1820,U_1819,U_1818,U_1815,U_1821) ),
inference(clausify,[status(thm)],[f_448_6]) ).
cnf(f_448_9,plain,
( in(U_1821,sK396(U_1819,U_1818))
| ~ closed_subset(U_1815,U_1819)
| U_1815 != U_1821
| ~ element(U_1815,powerset(the_carrier(U_1819)))
| ~ subset(U_1818,U_1821)
| ~ in(U_1821,powerset(the_carrier(U_1819)))
| ~ sP426(U_1820,U_1819,U_1818,U_1815,U_1821) ),
inference(clausify,[status(thm)],[f_448_6]) ).
cnf(f_448_10,plain,
( in(U_1820,powerset(the_carrier(U_1819)))
| ~ sP425(U_1820,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_448_6]) ).
cnf(f_448_11,plain,
( subset(U_1818,U_1820)
| ~ sP425(U_1820,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_448_6]) ).
cnf(f_448_12,plain,
( element(sK397(U_1819,U_1818,U_1820),powerset(the_carrier(U_1819)))
| ~ sP425(U_1820,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_448_6]) ).
cnf(f_448_13,plain,
( sK397(U_1819,U_1818,U_1820) = U_1820
| ~ sP425(U_1820,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_448_6]) ).
cnf(f_448_14,plain,
( closed_subset(sK397(U_1819,U_1818,U_1820),U_1819)
| ~ sP425(U_1820,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_448_6]) ).
fof(f_449_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| ~ in(D,powerset(the_carrier(A))) )
& ( ( in(set_difference(cast_as_carrier_subset(A),D),B)
& in(D,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e2_37_1_1__pre_topc__1]) ).
fof(f_449_2,plain,
! [U_1825,U_1824] :
( ? [U_1823] :
! [U_1822] :
( ( in(U_1822,U_1823)
| ~ in(set_difference(cast_as_carrier_subset(U_1825),U_1822),U_1824)
| ~ in(U_1822,powerset(the_carrier(U_1825))) )
& ( ( in(set_difference(cast_as_carrier_subset(U_1825),U_1822),U_1824)
& in(U_1822,powerset(the_carrier(U_1825))) )
| ~ in(U_1822,U_1823) ) )
| ~ element(U_1824,powerset(powerset(the_carrier(U_1825))))
| ~ top_str(U_1825)
| ~ topological_space(U_1825) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
! [U_1825,U_1824] :
( ? [U_1823] :
( ! [U_1827] :
( in(U_1827,U_1823)
| ~ in(set_difference(cast_as_carrier_subset(U_1825),U_1827),U_1824)
| ~ in(U_1827,powerset(the_carrier(U_1825))) )
& ! [U_1826] :
( ( in(set_difference(cast_as_carrier_subset(U_1825),U_1826),U_1824)
& in(U_1826,powerset(the_carrier(U_1825))) )
| ~ in(U_1826,U_1823) ) )
| ~ element(U_1824,powerset(powerset(the_carrier(U_1825))))
| ~ top_str(U_1825)
| ~ topological_space(U_1825) ),
inference(miniscope,[status(thm)],[f_449_2]) ).
fof(f_449_4,plain,
! [U_1825,U_1824] :
( ( ! [U_1827] :
( in(U_1827,sK398(U_1825,U_1824))
| ~ in(set_difference(cast_as_carrier_subset(U_1825),U_1827),U_1824)
| ~ in(U_1827,powerset(the_carrier(U_1825))) )
& ! [U_1826] :
( ( in(set_difference(cast_as_carrier_subset(U_1825),U_1826),U_1824)
& in(U_1826,powerset(the_carrier(U_1825))) )
| ~ in(U_1826,sK398(U_1825,U_1824)) ) )
| ~ element(U_1824,powerset(powerset(the_carrier(U_1825))))
| ~ top_str(U_1825)
| ~ topological_space(U_1825) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_1823,sK398(U_1825,U_1824))],[f_449_3]) ).
fof(f_449_5,plain,
( ! [U_1825,U_1824,U_1826] :
( in(set_difference(cast_as_carrier_subset(U_1825),U_1826),U_1824)
| ~ sP427(U_1825,U_1824,U_1826) )
& ! [U_1825,U_1824,U_1826] :
( in(U_1826,powerset(the_carrier(U_1825)))
| ~ sP427(U_1825,U_1824,U_1826) )
& ! [U_1825,U_1824,U_1826,U_1827] :
( in(U_1827,sK398(U_1825,U_1824))
| ~ in(set_difference(cast_as_carrier_subset(U_1825),U_1827),U_1824)
| ~ in(U_1827,powerset(the_carrier(U_1825)))
| ~ sP428(U_1825,U_1824,U_1826,U_1827) )
& ! [U_1825,U_1824,U_1826,U_1827] :
( sP427(U_1825,U_1824,U_1826)
| ~ in(U_1826,sK398(U_1825,U_1824))
| ~ sP428(U_1825,U_1824,U_1826,U_1827) )
& ! [U_1825,U_1824,U_1826,U_1827] :
( sP428(U_1825,U_1824,U_1826,U_1827)
| ~ element(U_1824,powerset(powerset(the_carrier(U_1825))))
| ~ top_str(U_1825)
| ~ topological_space(U_1825) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP427,sP428])],[f_449_4]) ).
cnf(f_449_6,plain,
( sP428(U_1825,U_1824,U_1826,U_1827)
| ~ element(U_1824,powerset(powerset(the_carrier(U_1825))))
| ~ top_str(U_1825)
| ~ topological_space(U_1825) ),
inference(clausify,[status(thm)],[f_449_5]) ).
cnf(f_449_7,plain,
( sP427(U_1825,U_1824,U_1826)
| ~ in(U_1826,sK398(U_1825,U_1824))
| ~ sP428(U_1825,U_1824,U_1826,U_1827) ),
inference(clausify,[status(thm)],[f_449_5]) ).
cnf(f_449_8,plain,
( in(U_1827,sK398(U_1825,U_1824))
| ~ in(set_difference(cast_as_carrier_subset(U_1825),U_1827),U_1824)
| ~ in(U_1827,powerset(the_carrier(U_1825)))
| ~ sP428(U_1825,U_1824,U_1826,U_1827) ),
inference(clausify,[status(thm)],[f_449_5]) ).
cnf(f_449_9,plain,
( in(U_1826,powerset(the_carrier(U_1825)))
| ~ sP427(U_1825,U_1824,U_1826) ),
inference(clausify,[status(thm)],[f_449_5]) ).
cnf(f_449_10,plain,
( in(set_difference(cast_as_carrier_subset(U_1825),U_1826),U_1824)
| ~ sP427(U_1825,U_1824,U_1826) ),
inference(clausify,[status(thm)],[f_449_5]) ).
fof(f_450_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( D != set_difference(E,singleton(A))
| ~ in(E,B) )
| ~ in(D,powerset(A)) )
& ( ( ? [E] :
( D = set_difference(E,singleton(A))
& in(E,B) )
& in(D,powerset(A)) )
| ~ in(D,C) ) )
| ~ element(B,powerset(powerset(succ(A))))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e4_27_3_1__finset_1]) ).
fof(f_450_2,plain,
! [U_1833,U_1832] :
( ? [U_1831] :
! [U_1830] :
( ( in(U_1830,U_1831)
| ! [U_1829] :
( U_1830 != set_difference(U_1829,singleton(U_1833))
| ~ in(U_1829,U_1832) )
| ~ in(U_1830,powerset(U_1833)) )
& ( ( ? [U_1828] :
( U_1830 = set_difference(U_1828,singleton(U_1833))
& in(U_1828,U_1832) )
& in(U_1830,powerset(U_1833)) )
| ~ in(U_1830,U_1831) ) )
| ~ element(U_1832,powerset(powerset(succ(U_1833))))
| ~ ordinal(U_1833) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
! [U_1833,U_1832] :
( ? [U_1831] :
( ! [U_1835] :
( in(U_1835,U_1831)
| ! [U_1829] :
( U_1835 != set_difference(U_1829,singleton(U_1833))
| ~ in(U_1829,U_1832) )
| ~ in(U_1835,powerset(U_1833)) )
& ! [U_1834] :
( ( ? [U_1828] :
( U_1834 = set_difference(U_1828,singleton(U_1833))
& in(U_1828,U_1832) )
& in(U_1834,powerset(U_1833)) )
| ~ in(U_1834,U_1831) ) )
| ~ element(U_1832,powerset(powerset(succ(U_1833))))
| ~ ordinal(U_1833) ),
inference(miniscope,[status(thm)],[f_450_2]) ).
fof(f_450_4,plain,
! [U_1833,U_1832] :
( ( ! [U_1835] :
( in(U_1835,sK399(U_1833,U_1832))
| ! [U_1829] :
( U_1835 != set_difference(U_1829,singleton(U_1833))
| ~ in(U_1829,U_1832) )
| ~ in(U_1835,powerset(U_1833)) )
& ! [U_1834] :
( ( ? [U_1828] :
( U_1834 = set_difference(U_1828,singleton(U_1833))
& in(U_1828,U_1832) )
& in(U_1834,powerset(U_1833)) )
| ~ in(U_1834,sK399(U_1833,U_1832)) ) )
| ~ element(U_1832,powerset(powerset(succ(U_1833))))
| ~ ordinal(U_1833) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_1831,sK399(U_1833,U_1832))],[f_450_3]) ).
fof(f_450_5,plain,
! [U_1833,U_1832] :
( ( ! [U_1835] :
( in(U_1835,sK399(U_1833,U_1832))
| ! [U_1829] :
( U_1835 != set_difference(U_1829,singleton(U_1833))
| ~ in(U_1829,U_1832) )
| ~ in(U_1835,powerset(U_1833)) )
& ! [U_1834] :
( ( U_1834 = set_difference(sK400(U_1833,U_1832,U_1834),singleton(U_1833))
& in(sK400(U_1833,U_1832,U_1834),U_1832)
& in(U_1834,powerset(U_1833)) )
| ~ in(U_1834,sK399(U_1833,U_1832)) ) )
| ~ element(U_1832,powerset(powerset(succ(U_1833))))
| ~ ordinal(U_1833) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_1828,sK400(U_1833,U_1832,U_1834))],[f_450_4]) ).
fof(f_450_6,plain,
( ! [U_1834,U_1832,U_1833] :
( U_1834 = set_difference(sK400(U_1833,U_1832,U_1834),singleton(U_1833))
| ~ sP429(U_1834,U_1832,U_1833) )
& ! [U_1834,U_1832,U_1833] :
( in(sK400(U_1833,U_1832,U_1834),U_1832)
| ~ sP429(U_1834,U_1832,U_1833) )
& ! [U_1834,U_1832,U_1833] :
( in(U_1834,powerset(U_1833))
| ~ sP429(U_1834,U_1832,U_1833) )
& ! [U_1829,U_1834,U_1835,U_1832,U_1833] :
( in(U_1835,sK399(U_1833,U_1832))
| U_1835 != set_difference(U_1829,singleton(U_1833))
| ~ in(U_1829,U_1832)
| ~ in(U_1835,powerset(U_1833))
| ~ sP430(U_1829,U_1834,U_1835,U_1832,U_1833) )
& ! [U_1829,U_1834,U_1835,U_1832,U_1833] :
( sP429(U_1834,U_1832,U_1833)
| ~ in(U_1834,sK399(U_1833,U_1832))
| ~ sP430(U_1829,U_1834,U_1835,U_1832,U_1833) )
& ! [U_1829,U_1834,U_1835,U_1832,U_1833] :
( sP430(U_1829,U_1834,U_1835,U_1832,U_1833)
| ~ element(U_1832,powerset(powerset(succ(U_1833))))
| ~ ordinal(U_1833) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP429,sP430])],[f_450_5]) ).
cnf(f_450_7,plain,
( sP430(U_1829,U_1834,U_1835,U_1832,U_1833)
| ~ element(U_1832,powerset(powerset(succ(U_1833))))
| ~ ordinal(U_1833) ),
inference(clausify,[status(thm)],[f_450_6]) ).
cnf(f_450_8,plain,
( sP429(U_1834,U_1832,U_1833)
| ~ in(U_1834,sK399(U_1833,U_1832))
| ~ sP430(U_1829,U_1834,U_1835,U_1832,U_1833) ),
inference(clausify,[status(thm)],[f_450_6]) ).
cnf(f_450_9,plain,
( in(U_1835,sK399(U_1833,U_1832))
| U_1835 != set_difference(U_1829,singleton(U_1833))
| ~ in(U_1829,U_1832)
| ~ in(U_1835,powerset(U_1833))
| ~ sP430(U_1829,U_1834,U_1835,U_1832,U_1833) ),
inference(clausify,[status(thm)],[f_450_6]) ).
cnf(f_450_10,plain,
( in(U_1834,powerset(U_1833))
| ~ sP429(U_1834,U_1832,U_1833) ),
inference(clausify,[status(thm)],[f_450_6]) ).
cnf(f_450_11,plain,
( in(sK400(U_1833,U_1832,U_1834),U_1832)
| ~ sP429(U_1834,U_1832,U_1833) ),
inference(clausify,[status(thm)],[f_450_6]) ).
cnf(f_450_12,plain,
( U_1834 = set_difference(sK400(U_1833,U_1832,U_1834),singleton(U_1833))
| ~ sP429(U_1834,U_1832,U_1833) ),
inference(clausify,[status(thm)],[f_450_6]) ).
fof(f_451_1,plain,
! [A,B] :
( ! [C] :
? [D] :
! [E] :
( ( in(E,D)
| ! [F,G] :
( ? [H] :
( G != subset_complement(the_carrier(A),H)
& H = F
& element(H,powerset(the_carrier(A))) )
| ~ in(F,complements_of_subsets(the_carrier(A),B))
| ordered_pair(F,G) != E )
| ~ in(E,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) )
& ( ( ? [F,G] :
( ! [H] :
( G = subset_complement(the_carrier(A),H)
| H != F
| ~ element(H,powerset(the_carrier(A))) )
& in(F,complements_of_subsets(the_carrier(A),B))
& ordered_pair(F,G) = E )
& in(E,cartesian_product2(complements_of_subsets(the_carrier(A),B),C)) )
| ~ in(E,D) ) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e4_7_1__tops_2__1]) ).
fof(f_451_2,plain,
! [U_1846,U_1845] :
( ! [U_1844] :
? [U_1843] :
! [U_1842] :
( ( in(U_1842,U_1843)
| ! [U_1841,U_1840] :
( ? [U_1839] :
( U_1840 != subset_complement(the_carrier(U_1846),U_1839)
& U_1839 = U_1841
& element(U_1839,powerset(the_carrier(U_1846))) )
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845))
| ordered_pair(U_1841,U_1840) != U_1842 )
| ~ in(U_1842,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
& ( ( ? [U_1838,U_1837] :
( ! [U_1836] :
( U_1837 = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != U_1838
| ~ element(U_1836,powerset(the_carrier(U_1846))) )
& in(U_1838,complements_of_subsets(the_carrier(U_1846),U_1845))
& ordered_pair(U_1838,U_1837) = U_1842 )
& in(U_1842,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
| ~ in(U_1842,U_1843) ) )
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
! [U_1846,U_1845] :
( ! [U_1844] :
? [U_1843] :
( ! [U_1848] :
( in(U_1848,U_1843)
| ! [U_1841] :
( ! [U_1840] :
( ? [U_1839] :
( U_1840 != subset_complement(the_carrier(U_1846),U_1839)
& U_1839 = U_1841
& element(U_1839,powerset(the_carrier(U_1846))) )
| ordered_pair(U_1841,U_1840) != U_1848 )
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845)) )
| ~ in(U_1848,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
& ! [U_1847] :
( ( ? [U_1838] :
( ? [U_1837] :
( ! [U_1836] :
( U_1837 = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != U_1838
| ~ element(U_1836,powerset(the_carrier(U_1846))) )
& ordered_pair(U_1838,U_1837) = U_1847 )
& in(U_1838,complements_of_subsets(the_carrier(U_1846),U_1845)) )
& in(U_1847,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
| ~ in(U_1847,U_1843) ) )
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ),
inference(miniscope,[status(thm)],[f_451_2]) ).
fof(f_451_4,plain,
! [U_1846,U_1845] :
( ! [U_1844] :
( ! [U_1848] :
( in(U_1848,sK401(U_1846,U_1845,U_1844))
| ! [U_1841] :
( ! [U_1840] :
( ? [U_1839] :
( U_1840 != subset_complement(the_carrier(U_1846),U_1839)
& U_1839 = U_1841
& element(U_1839,powerset(the_carrier(U_1846))) )
| ordered_pair(U_1841,U_1840) != U_1848 )
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845)) )
| ~ in(U_1848,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
& ! [U_1847] :
( ( ? [U_1838] :
( ? [U_1837] :
( ! [U_1836] :
( U_1837 = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != U_1838
| ~ element(U_1836,powerset(the_carrier(U_1846))) )
& ordered_pair(U_1838,U_1837) = U_1847 )
& in(U_1838,complements_of_subsets(the_carrier(U_1846),U_1845)) )
& in(U_1847,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
| ~ in(U_1847,sK401(U_1846,U_1845,U_1844)) ) )
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_1843,sK401(U_1846,U_1845,U_1844))],[f_451_3]) ).
fof(f_451_5,plain,
! [U_1846,U_1845] :
( ! [U_1844] :
( ! [U_1848] :
( in(U_1848,sK401(U_1846,U_1845,U_1844))
| ! [U_1841] :
( ! [U_1840] :
( ? [U_1839] :
( U_1840 != subset_complement(the_carrier(U_1846),U_1839)
& U_1839 = U_1841
& element(U_1839,powerset(the_carrier(U_1846))) )
| ordered_pair(U_1841,U_1840) != U_1848 )
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845)) )
| ~ in(U_1848,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
& ! [U_1847] :
( ( ? [U_1837] :
( ! [U_1836] :
( U_1837 = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != sK402(U_1846,U_1845,U_1844,U_1847)
| ~ element(U_1836,powerset(the_carrier(U_1846))) )
& ordered_pair(sK402(U_1846,U_1845,U_1844,U_1847),U_1837) = U_1847 )
& in(sK402(U_1846,U_1845,U_1844,U_1847),complements_of_subsets(the_carrier(U_1846),U_1845))
& in(U_1847,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
| ~ in(U_1847,sK401(U_1846,U_1845,U_1844)) ) )
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_1838,sK402(U_1846,U_1845,U_1844,U_1847))],[f_451_4]) ).
fof(f_451_6,plain,
! [U_1846,U_1845] :
( ! [U_1844] :
( ! [U_1848] :
( in(U_1848,sK401(U_1846,U_1845,U_1844))
| ! [U_1841] :
( ! [U_1840] :
( ? [U_1839] :
( U_1840 != subset_complement(the_carrier(U_1846),U_1839)
& U_1839 = U_1841
& element(U_1839,powerset(the_carrier(U_1846))) )
| ordered_pair(U_1841,U_1840) != U_1848 )
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845)) )
| ~ in(U_1848,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
& ! [U_1847] :
( ( ! [U_1836] :
( sK403(U_1846,U_1845,U_1844,U_1847) = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != sK402(U_1846,U_1845,U_1844,U_1847)
| ~ element(U_1836,powerset(the_carrier(U_1846))) )
& ordered_pair(sK402(U_1846,U_1845,U_1844,U_1847),sK403(U_1846,U_1845,U_1844,U_1847)) = U_1847
& in(sK402(U_1846,U_1845,U_1844,U_1847),complements_of_subsets(the_carrier(U_1846),U_1845))
& in(U_1847,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
| ~ in(U_1847,sK401(U_1846,U_1845,U_1844)) ) )
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_1837,sK403(U_1846,U_1845,U_1844,U_1847))],[f_451_5]) ).
fof(f_451_7,plain,
! [U_1846,U_1845] :
( ! [U_1844] :
( ! [U_1848] :
( in(U_1848,sK401(U_1846,U_1845,U_1844))
| ! [U_1841] :
( ! [U_1840] :
( ( U_1840 != subset_complement(the_carrier(U_1846),sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840))
& sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840) = U_1841
& element(sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840),powerset(the_carrier(U_1846))) )
| ordered_pair(U_1841,U_1840) != U_1848 )
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845)) )
| ~ in(U_1848,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
& ! [U_1847] :
( ( ! [U_1836] :
( sK403(U_1846,U_1845,U_1844,U_1847) = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != sK402(U_1846,U_1845,U_1844,U_1847)
| ~ element(U_1836,powerset(the_carrier(U_1846))) )
& ordered_pair(sK402(U_1846,U_1845,U_1844,U_1847),sK403(U_1846,U_1845,U_1844,U_1847)) = U_1847
& in(sK402(U_1846,U_1845,U_1844,U_1847),complements_of_subsets(the_carrier(U_1846),U_1845))
& in(U_1847,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844)) )
| ~ in(U_1847,sK401(U_1846,U_1845,U_1844)) ) )
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_1839,sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840))],[f_451_6]) ).
fof(f_451_8,plain,
( ! [U_1845,U_1844,U_1841,U_1848,U_1840,U_1846] :
( U_1840 != subset_complement(the_carrier(U_1846),sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840))
| ~ sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846) )
& ! [U_1845,U_1844,U_1841,U_1848,U_1840,U_1846] :
( sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840) = U_1841
| ~ sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846) )
& ! [U_1845,U_1844,U_1841,U_1848,U_1840,U_1846] :
( element(sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840),powerset(the_carrier(U_1846)))
| ~ sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846) )
& ! [U_1836,U_1845,U_1844,U_1847,U_1846] :
( sK403(U_1846,U_1845,U_1844,U_1847) = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != sK402(U_1846,U_1845,U_1844,U_1847)
| ~ element(U_1836,powerset(the_carrier(U_1846)))
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) )
& ! [U_1836,U_1845,U_1844,U_1847,U_1846] :
( ordered_pair(sK402(U_1846,U_1845,U_1844,U_1847),sK403(U_1846,U_1845,U_1844,U_1847)) = U_1847
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) )
& ! [U_1836,U_1845,U_1844,U_1847,U_1846] :
( in(sK402(U_1846,U_1845,U_1844,U_1847),complements_of_subsets(the_carrier(U_1846),U_1845))
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) )
& ! [U_1836,U_1845,U_1844,U_1847,U_1846] :
( in(U_1847,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844))
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) )
& ! [U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846] :
( in(U_1848,sK401(U_1846,U_1845,U_1844))
| sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846)
| ordered_pair(U_1841,U_1840) != U_1848
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845))
| ~ in(U_1848,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844))
| ~ sP433(U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846) )
& ! [U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846] :
( sP431(U_1836,U_1845,U_1844,U_1847,U_1846)
| ~ in(U_1847,sK401(U_1846,U_1845,U_1844))
| ~ sP433(U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846) )
& ! [U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846] :
( sP433(U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846)
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP431,sP432,sP433])],[f_451_7]) ).
cnf(f_451_9,plain,
( sP433(U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846)
| ~ element(U_1845,powerset(powerset(the_carrier(U_1846))))
| ~ one_sorted_str(U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_10,plain,
( sP431(U_1836,U_1845,U_1844,U_1847,U_1846)
| ~ in(U_1847,sK401(U_1846,U_1845,U_1844))
| ~ sP433(U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_11,plain,
( in(U_1848,sK401(U_1846,U_1845,U_1844))
| sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846)
| ordered_pair(U_1841,U_1840) != U_1848
| ~ in(U_1841,complements_of_subsets(the_carrier(U_1846),U_1845))
| ~ in(U_1848,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844))
| ~ sP433(U_1836,U_1845,U_1844,U_1841,U_1848,U_1847,U_1840,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_12,plain,
( in(U_1847,cartesian_product2(complements_of_subsets(the_carrier(U_1846),U_1845),U_1844))
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_13,plain,
( in(sK402(U_1846,U_1845,U_1844,U_1847),complements_of_subsets(the_carrier(U_1846),U_1845))
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_14,plain,
( ordered_pair(sK402(U_1846,U_1845,U_1844,U_1847),sK403(U_1846,U_1845,U_1844,U_1847)) = U_1847
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_15,plain,
( sK403(U_1846,U_1845,U_1844,U_1847) = subset_complement(the_carrier(U_1846),U_1836)
| U_1836 != sK402(U_1846,U_1845,U_1844,U_1847)
| ~ element(U_1836,powerset(the_carrier(U_1846)))
| ~ sP431(U_1836,U_1845,U_1844,U_1847,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_16,plain,
( element(sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840),powerset(the_carrier(U_1846)))
| ~ sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_17,plain,
( sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840) = U_1841
| ~ sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
cnf(f_451_18,plain,
( U_1840 != subset_complement(the_carrier(U_1846),sK404(U_1846,U_1845,U_1844,U_1848,U_1841,U_1840))
| ~ sP432(U_1845,U_1844,U_1841,U_1848,U_1840,U_1846) ),
inference(clausify,[status(thm)],[f_451_8]) ).
fof(f_452_1,plain,
! [A,B] :
( ! [C] :
? [D] :
! [E] :
( ( in(E,D)
| ! [F,G] :
( ? [H] :
( G != subset_complement(the_carrier(A),H)
& H = F
& element(H,powerset(the_carrier(A))) )
| ~ in(F,B)
| ordered_pair(F,G) != E )
| ~ in(E,cartesian_product2(B,C)) )
& ( ( ? [F,G] :
( ! [H] :
( G = subset_complement(the_carrier(A),H)
| H != F
| ~ element(H,powerset(the_carrier(A))) )
& in(F,B)
& ordered_pair(F,G) = E )
& in(E,cartesian_product2(B,C)) )
| ~ in(E,D) ) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e4_7_2__tops_2__1]) ).
fof(f_452_2,plain,
! [U_1859,U_1858] :
( ! [U_1857] :
? [U_1856] :
! [U_1855] :
( ( in(U_1855,U_1856)
| ! [U_1854,U_1853] :
( ? [U_1852] :
( U_1853 != subset_complement(the_carrier(U_1859),U_1852)
& U_1852 = U_1854
& element(U_1852,powerset(the_carrier(U_1859))) )
| ~ in(U_1854,U_1858)
| ordered_pair(U_1854,U_1853) != U_1855 )
| ~ in(U_1855,cartesian_product2(U_1858,U_1857)) )
& ( ( ? [U_1851,U_1850] :
( ! [U_1849] :
( U_1850 = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != U_1851
| ~ element(U_1849,powerset(the_carrier(U_1859))) )
& in(U_1851,U_1858)
& ordered_pair(U_1851,U_1850) = U_1855 )
& in(U_1855,cartesian_product2(U_1858,U_1857)) )
| ~ in(U_1855,U_1856) ) )
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
! [U_1859,U_1858] :
( ! [U_1857] :
? [U_1856] :
( ! [U_1861] :
( in(U_1861,U_1856)
| ! [U_1854] :
( ! [U_1853] :
( ? [U_1852] :
( U_1853 != subset_complement(the_carrier(U_1859),U_1852)
& U_1852 = U_1854
& element(U_1852,powerset(the_carrier(U_1859))) )
| ordered_pair(U_1854,U_1853) != U_1861 )
| ~ in(U_1854,U_1858) )
| ~ in(U_1861,cartesian_product2(U_1858,U_1857)) )
& ! [U_1860] :
( ( ? [U_1851] :
( ? [U_1850] :
( ! [U_1849] :
( U_1850 = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != U_1851
| ~ element(U_1849,powerset(the_carrier(U_1859))) )
& ordered_pair(U_1851,U_1850) = U_1860 )
& in(U_1851,U_1858) )
& in(U_1860,cartesian_product2(U_1858,U_1857)) )
| ~ in(U_1860,U_1856) ) )
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ),
inference(miniscope,[status(thm)],[f_452_2]) ).
fof(f_452_4,plain,
! [U_1859,U_1858] :
( ! [U_1857] :
( ! [U_1861] :
( in(U_1861,sK405(U_1859,U_1858,U_1857))
| ! [U_1854] :
( ! [U_1853] :
( ? [U_1852] :
( U_1853 != subset_complement(the_carrier(U_1859),U_1852)
& U_1852 = U_1854
& element(U_1852,powerset(the_carrier(U_1859))) )
| ordered_pair(U_1854,U_1853) != U_1861 )
| ~ in(U_1854,U_1858) )
| ~ in(U_1861,cartesian_product2(U_1858,U_1857)) )
& ! [U_1860] :
( ( ? [U_1851] :
( ? [U_1850] :
( ! [U_1849] :
( U_1850 = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != U_1851
| ~ element(U_1849,powerset(the_carrier(U_1859))) )
& ordered_pair(U_1851,U_1850) = U_1860 )
& in(U_1851,U_1858) )
& in(U_1860,cartesian_product2(U_1858,U_1857)) )
| ~ in(U_1860,sK405(U_1859,U_1858,U_1857)) ) )
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_1856,sK405(U_1859,U_1858,U_1857))],[f_452_3]) ).
fof(f_452_5,plain,
! [U_1859,U_1858] :
( ! [U_1857] :
( ! [U_1861] :
( in(U_1861,sK405(U_1859,U_1858,U_1857))
| ! [U_1854] :
( ! [U_1853] :
( ? [U_1852] :
( U_1853 != subset_complement(the_carrier(U_1859),U_1852)
& U_1852 = U_1854
& element(U_1852,powerset(the_carrier(U_1859))) )
| ordered_pair(U_1854,U_1853) != U_1861 )
| ~ in(U_1854,U_1858) )
| ~ in(U_1861,cartesian_product2(U_1858,U_1857)) )
& ! [U_1860] :
( ( ? [U_1850] :
( ! [U_1849] :
( U_1850 = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != sK406(U_1859,U_1858,U_1857,U_1860)
| ~ element(U_1849,powerset(the_carrier(U_1859))) )
& ordered_pair(sK406(U_1859,U_1858,U_1857,U_1860),U_1850) = U_1860 )
& in(sK406(U_1859,U_1858,U_1857,U_1860),U_1858)
& in(U_1860,cartesian_product2(U_1858,U_1857)) )
| ~ in(U_1860,sK405(U_1859,U_1858,U_1857)) ) )
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_1851,sK406(U_1859,U_1858,U_1857,U_1860))],[f_452_4]) ).
fof(f_452_6,plain,
! [U_1859,U_1858] :
( ! [U_1857] :
( ! [U_1861] :
( in(U_1861,sK405(U_1859,U_1858,U_1857))
| ! [U_1854] :
( ! [U_1853] :
( ? [U_1852] :
( U_1853 != subset_complement(the_carrier(U_1859),U_1852)
& U_1852 = U_1854
& element(U_1852,powerset(the_carrier(U_1859))) )
| ordered_pair(U_1854,U_1853) != U_1861 )
| ~ in(U_1854,U_1858) )
| ~ in(U_1861,cartesian_product2(U_1858,U_1857)) )
& ! [U_1860] :
( ( ! [U_1849] :
( sK407(U_1859,U_1858,U_1857,U_1860) = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != sK406(U_1859,U_1858,U_1857,U_1860)
| ~ element(U_1849,powerset(the_carrier(U_1859))) )
& ordered_pair(sK406(U_1859,U_1858,U_1857,U_1860),sK407(U_1859,U_1858,U_1857,U_1860)) = U_1860
& in(sK406(U_1859,U_1858,U_1857,U_1860),U_1858)
& in(U_1860,cartesian_product2(U_1858,U_1857)) )
| ~ in(U_1860,sK405(U_1859,U_1858,U_1857)) ) )
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_1850,sK407(U_1859,U_1858,U_1857,U_1860))],[f_452_5]) ).
fof(f_452_7,plain,
! [U_1859,U_1858] :
( ! [U_1857] :
( ! [U_1861] :
( in(U_1861,sK405(U_1859,U_1858,U_1857))
| ! [U_1854] :
( ! [U_1853] :
( ( U_1853 != subset_complement(the_carrier(U_1859),sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853))
& sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853) = U_1854
& element(sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853),powerset(the_carrier(U_1859))) )
| ordered_pair(U_1854,U_1853) != U_1861 )
| ~ in(U_1854,U_1858) )
| ~ in(U_1861,cartesian_product2(U_1858,U_1857)) )
& ! [U_1860] :
( ( ! [U_1849] :
( sK407(U_1859,U_1858,U_1857,U_1860) = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != sK406(U_1859,U_1858,U_1857,U_1860)
| ~ element(U_1849,powerset(the_carrier(U_1859))) )
& ordered_pair(sK406(U_1859,U_1858,U_1857,U_1860),sK407(U_1859,U_1858,U_1857,U_1860)) = U_1860
& in(sK406(U_1859,U_1858,U_1857,U_1860),U_1858)
& in(U_1860,cartesian_product2(U_1858,U_1857)) )
| ~ in(U_1860,sK405(U_1859,U_1858,U_1857)) ) )
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_1852,sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853))],[f_452_6]) ).
fof(f_452_8,plain,
( ! [U_1857,U_1854,U_1853,U_1858,U_1861,U_1859] :
( U_1853 != subset_complement(the_carrier(U_1859),sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853))
| ~ sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859) )
& ! [U_1857,U_1854,U_1853,U_1858,U_1861,U_1859] :
( sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853) = U_1854
| ~ sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859) )
& ! [U_1857,U_1854,U_1853,U_1858,U_1861,U_1859] :
( element(sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853),powerset(the_carrier(U_1859)))
| ~ sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859) )
& ! [U_1857,U_1858,U_1849,U_1859,U_1860] :
( sK407(U_1859,U_1858,U_1857,U_1860) = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != sK406(U_1859,U_1858,U_1857,U_1860)
| ~ element(U_1849,powerset(the_carrier(U_1859)))
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) )
& ! [U_1857,U_1858,U_1849,U_1859,U_1860] :
( ordered_pair(sK406(U_1859,U_1858,U_1857,U_1860),sK407(U_1859,U_1858,U_1857,U_1860)) = U_1860
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) )
& ! [U_1857,U_1858,U_1849,U_1859,U_1860] :
( in(sK406(U_1859,U_1858,U_1857,U_1860),U_1858)
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) )
& ! [U_1857,U_1858,U_1849,U_1859,U_1860] :
( in(U_1860,cartesian_product2(U_1858,U_1857))
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) )
& ! [U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860] :
( in(U_1861,sK405(U_1859,U_1858,U_1857))
| sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859)
| ordered_pair(U_1854,U_1853) != U_1861
| ~ in(U_1854,U_1858)
| ~ in(U_1861,cartesian_product2(U_1858,U_1857))
| ~ sP436(U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860) )
& ! [U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860] :
( sP434(U_1857,U_1858,U_1849,U_1859,U_1860)
| ~ in(U_1860,sK405(U_1859,U_1858,U_1857))
| ~ sP436(U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860) )
& ! [U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860] :
( sP436(U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860)
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP434,sP435,sP436])],[f_452_7]) ).
cnf(f_452_9,plain,
( sP436(U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860)
| ~ element(U_1858,powerset(powerset(the_carrier(U_1859))))
| ~ one_sorted_str(U_1859) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_10,plain,
( sP434(U_1857,U_1858,U_1849,U_1859,U_1860)
| ~ in(U_1860,sK405(U_1859,U_1858,U_1857))
| ~ sP436(U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_11,plain,
( in(U_1861,sK405(U_1859,U_1858,U_1857))
| sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859)
| ordered_pair(U_1854,U_1853) != U_1861
| ~ in(U_1854,U_1858)
| ~ in(U_1861,cartesian_product2(U_1858,U_1857))
| ~ sP436(U_1857,U_1854,U_1853,U_1858,U_1861,U_1849,U_1859,U_1860) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_12,plain,
( in(U_1860,cartesian_product2(U_1858,U_1857))
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_13,plain,
( in(sK406(U_1859,U_1858,U_1857,U_1860),U_1858)
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_14,plain,
( ordered_pair(sK406(U_1859,U_1858,U_1857,U_1860),sK407(U_1859,U_1858,U_1857,U_1860)) = U_1860
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_15,plain,
( sK407(U_1859,U_1858,U_1857,U_1860) = subset_complement(the_carrier(U_1859),U_1849)
| U_1849 != sK406(U_1859,U_1858,U_1857,U_1860)
| ~ element(U_1849,powerset(the_carrier(U_1859)))
| ~ sP434(U_1857,U_1858,U_1849,U_1859,U_1860) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_16,plain,
( element(sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853),powerset(the_carrier(U_1859)))
| ~ sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_17,plain,
( sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853) = U_1854
| ~ sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859) ),
inference(clausify,[status(thm)],[f_452_8]) ).
cnf(f_452_18,plain,
( U_1853 != subset_complement(the_carrier(U_1859),sK408(U_1859,U_1858,U_1857,U_1861,U_1854,U_1853))
| ~ sP435(U_1857,U_1854,U_1853,U_1858,U_1861,U_1859) ),
inference(clausify,[status(thm)],[f_452_8]) ).
fof(f_453_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_453_2,plain,
! [U_1870,U_1869,U_1868] :
( ? [U_1867] :
! [U_1866] :
( ( in(U_1866,U_1867)
| ! [U_1865,U_1864] :
( ~ in(ordered_pair(apply(U_1868,U_1865),apply(U_1868,U_1864)),U_1869)
| U_1866 != ordered_pair(U_1865,U_1864) )
| ~ in(U_1866,cartesian_product2(U_1870,U_1870)) )
& ( ( ? [U_1863,U_1862] :
( in(ordered_pair(apply(U_1868,U_1863),apply(U_1868,U_1862)),U_1869)
& U_1866 = ordered_pair(U_1863,U_1862) )
& in(U_1866,cartesian_product2(U_1870,U_1870)) )
| ~ in(U_1866,U_1867) ) )
| ~ function(U_1868)
| ~ relation(U_1868)
| ~ relation(U_1869) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
! [U_1870,U_1869,U_1868] :
( ? [U_1867] :
( ! [U_1872] :
( in(U_1872,U_1867)
| ! [U_1865,U_1864] :
( ~ in(ordered_pair(apply(U_1868,U_1865),apply(U_1868,U_1864)),U_1869)
| U_1872 != ordered_pair(U_1865,U_1864) )
| ~ in(U_1872,cartesian_product2(U_1870,U_1870)) )
& ! [U_1871] :
( ( ? [U_1863,U_1862] :
( in(ordered_pair(apply(U_1868,U_1863),apply(U_1868,U_1862)),U_1869)
& U_1871 = ordered_pair(U_1863,U_1862) )
& in(U_1871,cartesian_product2(U_1870,U_1870)) )
| ~ in(U_1871,U_1867) ) )
| ~ function(U_1868)
| ~ relation(U_1868)
| ~ relation(U_1869) ),
inference(miniscope,[status(thm)],[f_453_2]) ).
fof(f_453_4,plain,
! [U_1870,U_1869,U_1868] :
( ( ! [U_1872] :
( in(U_1872,sK409(U_1870,U_1869,U_1868))
| ! [U_1865,U_1864] :
( ~ in(ordered_pair(apply(U_1868,U_1865),apply(U_1868,U_1864)),U_1869)
| U_1872 != ordered_pair(U_1865,U_1864) )
| ~ in(U_1872,cartesian_product2(U_1870,U_1870)) )
& ! [U_1871] :
( ( ? [U_1863,U_1862] :
( in(ordered_pair(apply(U_1868,U_1863),apply(U_1868,U_1862)),U_1869)
& U_1871 = ordered_pair(U_1863,U_1862) )
& in(U_1871,cartesian_product2(U_1870,U_1870)) )
| ~ in(U_1871,sK409(U_1870,U_1869,U_1868)) ) )
| ~ function(U_1868)
| ~ relation(U_1868)
| ~ relation(U_1869) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_1867,sK409(U_1870,U_1869,U_1868))],[f_453_3]) ).
fof(f_453_5,plain,
! [U_1870,U_1869,U_1868] :
( ( ! [U_1872] :
( in(U_1872,sK409(U_1870,U_1869,U_1868))
| ! [U_1865,U_1864] :
( ~ in(ordered_pair(apply(U_1868,U_1865),apply(U_1868,U_1864)),U_1869)
| U_1872 != ordered_pair(U_1865,U_1864) )
| ~ in(U_1872,cartesian_product2(U_1870,U_1870)) )
& ! [U_1871] :
( ( ? [U_1862] :
( in(ordered_pair(apply(U_1868,sK410(U_1870,U_1869,U_1868,U_1871)),apply(U_1868,U_1862)),U_1869)
& U_1871 = ordered_pair(sK410(U_1870,U_1869,U_1868,U_1871),U_1862) )
& in(U_1871,cartesian_product2(U_1870,U_1870)) )
| ~ in(U_1871,sK409(U_1870,U_1869,U_1868)) ) )
| ~ function(U_1868)
| ~ relation(U_1868)
| ~ relation(U_1869) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_1863,sK410(U_1870,U_1869,U_1868,U_1871))],[f_453_4]) ).
fof(f_453_6,plain,
! [U_1870,U_1869,U_1868] :
( ( ! [U_1872] :
( in(U_1872,sK409(U_1870,U_1869,U_1868))
| ! [U_1865,U_1864] :
( ~ in(ordered_pair(apply(U_1868,U_1865),apply(U_1868,U_1864)),U_1869)
| U_1872 != ordered_pair(U_1865,U_1864) )
| ~ in(U_1872,cartesian_product2(U_1870,U_1870)) )
& ! [U_1871] :
( ( in(ordered_pair(apply(U_1868,sK410(U_1870,U_1869,U_1868,U_1871)),apply(U_1868,sK411(U_1870,U_1869,U_1868,U_1871))),U_1869)
& U_1871 = ordered_pair(sK410(U_1870,U_1869,U_1868,U_1871),sK411(U_1870,U_1869,U_1868,U_1871))
& in(U_1871,cartesian_product2(U_1870,U_1870)) )
| ~ in(U_1871,sK409(U_1870,U_1869,U_1868)) ) )
| ~ function(U_1868)
| ~ relation(U_1868)
| ~ relation(U_1869) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_1862,sK411(U_1870,U_1869,U_1868,U_1871))],[f_453_5]) ).
fof(f_453_7,plain,
( ! [U_1870,U_1871,U_1868,U_1869] :
( in(ordered_pair(apply(U_1868,sK410(U_1870,U_1869,U_1868,U_1871)),apply(U_1868,sK411(U_1870,U_1869,U_1868,U_1871))),U_1869)
| ~ sP437(U_1870,U_1871,U_1868,U_1869) )
& ! [U_1870,U_1871,U_1868,U_1869] :
( U_1871 = ordered_pair(sK410(U_1870,U_1869,U_1868,U_1871),sK411(U_1870,U_1869,U_1868,U_1871))
| ~ sP437(U_1870,U_1871,U_1868,U_1869) )
& ! [U_1870,U_1871,U_1868,U_1869] :
( in(U_1871,cartesian_product2(U_1870,U_1870))
| ~ sP437(U_1870,U_1871,U_1868,U_1869) )
& ! [U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865] :
( in(U_1872,sK409(U_1870,U_1869,U_1868))
| ~ in(ordered_pair(apply(U_1868,U_1865),apply(U_1868,U_1864)),U_1869)
| U_1872 != ordered_pair(U_1865,U_1864)
| ~ in(U_1872,cartesian_product2(U_1870,U_1870))
| ~ sP438(U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865) )
& ! [U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865] :
( sP437(U_1870,U_1871,U_1868,U_1869)
| ~ in(U_1871,sK409(U_1870,U_1869,U_1868))
| ~ sP438(U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865) )
& ! [U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865] :
( sP438(U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865)
| ~ function(U_1868)
| ~ relation(U_1868)
| ~ relation(U_1869) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP437,sP438])],[f_453_6]) ).
cnf(f_453_8,plain,
( sP438(U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865)
| ~ function(U_1868)
| ~ relation(U_1868)
| ~ relation(U_1869) ),
inference(clausify,[status(thm)],[f_453_7]) ).
cnf(f_453_9,plain,
( sP437(U_1870,U_1871,U_1868,U_1869)
| ~ in(U_1871,sK409(U_1870,U_1869,U_1868))
| ~ sP438(U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865) ),
inference(clausify,[status(thm)],[f_453_7]) ).
cnf(f_453_10,plain,
( in(U_1872,sK409(U_1870,U_1869,U_1868))
| ~ in(ordered_pair(apply(U_1868,U_1865),apply(U_1868,U_1864)),U_1869)
| U_1872 != ordered_pair(U_1865,U_1864)
| ~ in(U_1872,cartesian_product2(U_1870,U_1870))
| ~ sP438(U_1870,U_1872,U_1864,U_1871,U_1868,U_1869,U_1865) ),
inference(clausify,[status(thm)],[f_453_7]) ).
cnf(f_453_11,plain,
( in(U_1871,cartesian_product2(U_1870,U_1870))
| ~ sP437(U_1870,U_1871,U_1868,U_1869) ),
inference(clausify,[status(thm)],[f_453_7]) ).
cnf(f_453_12,plain,
( U_1871 = ordered_pair(sK410(U_1870,U_1869,U_1868,U_1871),sK411(U_1870,U_1869,U_1868,U_1871))
| ~ sP437(U_1870,U_1871,U_1868,U_1869) ),
inference(clausify,[status(thm)],[f_453_7]) ).
cnf(f_453_13,plain,
( in(ordered_pair(apply(U_1868,sK410(U_1870,U_1869,U_1868,U_1871)),apply(U_1868,sK411(U_1870,U_1869,U_1868,U_1871))),U_1869)
| ~ sP437(U_1870,U_1871,U_1868,U_1869) ),
inference(clausify,[status(thm)],[f_453_7]) ).
fof(f_454_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_454_2,plain,
! [U_1875] :
? [U_1874] :
! [U_1873] :
( ( in(U_1873,U_1874)
| ~ ordinal(U_1873)
| ~ in(U_1873,U_1875) )
& ( ( ordinal(U_1873)
& in(U_1873,U_1875) )
| ~ in(U_1873,U_1874) ) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
! [U_1875] :
? [U_1874] :
( ! [U_1877] :
( in(U_1877,U_1874)
| ~ ordinal(U_1877)
| ~ in(U_1877,U_1875) )
& ! [U_1876] :
( ( ordinal(U_1876)
& in(U_1876,U_1875) )
| ~ in(U_1876,U_1874) ) ),
inference(miniscope,[status(thm)],[f_454_2]) ).
fof(f_454_4,plain,
! [U_1875] :
( ! [U_1877] :
( in(U_1877,sK412(U_1875))
| ~ ordinal(U_1877)
| ~ in(U_1877,U_1875) )
& ! [U_1876] :
( ( ordinal(U_1876)
& in(U_1876,U_1875) )
| ~ in(U_1876,sK412(U_1875)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_1874,sK412(U_1875))],[f_454_3]) ).
fof(f_454_5,plain,
( ! [U_1875,U_1876] :
( ordinal(U_1876)
| ~ sP439(U_1875,U_1876) )
& ! [U_1875,U_1876] :
( in(U_1876,U_1875)
| ~ sP439(U_1875,U_1876) )
& ! [U_1875,U_1877] :
( in(U_1877,sK412(U_1875))
| ~ ordinal(U_1877)
| ~ in(U_1877,U_1875) )
& ! [U_1875,U_1876] :
( sP439(U_1875,U_1876)
| ~ in(U_1876,sK412(U_1875)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP439])],[f_454_4]) ).
cnf(f_454_6,plain,
( sP439(U_1875,U_1876)
| ~ in(U_1876,sK412(U_1875)) ),
inference(clausify,[status(thm)],[f_454_5]) ).
cnf(f_454_7,plain,
( in(U_1877,sK412(U_1875))
| ~ ordinal(U_1877)
| ~ in(U_1877,U_1875) ),
inference(clausify,[status(thm)],[f_454_5]) ).
cnf(f_454_8,plain,
( in(U_1876,U_1875)
| ~ sP439(U_1875,U_1876) ),
inference(clausify,[status(thm)],[f_454_5]) ).
cnf(f_454_9,plain,
( ordinal(U_1876)
| ~ sP439(U_1875,U_1876) ),
inference(clausify,[status(thm)],[f_454_5]) ).
fof(f_455_1,plain,
! [A,B,C] :
( ? [D] :
! [E] :
( ( in(E,D)
| ~ in(relation_image(C,E),B)
| ~ in(E,powerset(relation_dom(C))) )
& ( ( in(relation_image(C,E),B)
& in(E,powerset(relation_dom(C))) )
| ~ in(E,D) ) )
| ~ function(C)
| ~ relation(C)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e6_27__finset_1]) ).
fof(f_455_2,plain,
! [U_1882,U_1881,U_1880] :
( ? [U_1879] :
! [U_1878] :
( ( in(U_1878,U_1879)
| ~ in(relation_image(U_1880,U_1878),U_1881)
| ~ in(U_1878,powerset(relation_dom(U_1880))) )
& ( ( in(relation_image(U_1880,U_1878),U_1881)
& in(U_1878,powerset(relation_dom(U_1880))) )
| ~ in(U_1878,U_1879) ) )
| ~ function(U_1880)
| ~ relation(U_1880)
| ~ element(U_1881,powerset(powerset(U_1882))) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
! [U_1882,U_1881,U_1880] :
( ? [U_1879] :
( ! [U_1884] :
( in(U_1884,U_1879)
| ~ in(relation_image(U_1880,U_1884),U_1881)
| ~ in(U_1884,powerset(relation_dom(U_1880))) )
& ! [U_1883] :
( ( in(relation_image(U_1880,U_1883),U_1881)
& in(U_1883,powerset(relation_dom(U_1880))) )
| ~ in(U_1883,U_1879) ) )
| ~ function(U_1880)
| ~ relation(U_1880)
| ~ element(U_1881,powerset(powerset(U_1882))) ),
inference(miniscope,[status(thm)],[f_455_2]) ).
fof(f_455_4,plain,
! [U_1882,U_1881,U_1880] :
( ( ! [U_1884] :
( in(U_1884,sK413(U_1882,U_1881,U_1880))
| ~ in(relation_image(U_1880,U_1884),U_1881)
| ~ in(U_1884,powerset(relation_dom(U_1880))) )
& ! [U_1883] :
( ( in(relation_image(U_1880,U_1883),U_1881)
& in(U_1883,powerset(relation_dom(U_1880))) )
| ~ in(U_1883,sK413(U_1882,U_1881,U_1880)) ) )
| ~ function(U_1880)
| ~ relation(U_1880)
| ~ element(U_1881,powerset(powerset(U_1882))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_1879,sK413(U_1882,U_1881,U_1880))],[f_455_3]) ).
fof(f_455_5,plain,
( ! [U_1880,U_1881,U_1883] :
( in(relation_image(U_1880,U_1883),U_1881)
| ~ sP440(U_1880,U_1881,U_1883) )
& ! [U_1880,U_1881,U_1883] :
( in(U_1883,powerset(relation_dom(U_1880)))
| ~ sP440(U_1880,U_1881,U_1883) )
& ! [U_1882,U_1880,U_1881,U_1884,U_1883] :
( in(U_1884,sK413(U_1882,U_1881,U_1880))
| ~ in(relation_image(U_1880,U_1884),U_1881)
| ~ in(U_1884,powerset(relation_dom(U_1880)))
| ~ sP441(U_1882,U_1880,U_1881,U_1884,U_1883) )
& ! [U_1882,U_1880,U_1881,U_1884,U_1883] :
( sP440(U_1880,U_1881,U_1883)
| ~ in(U_1883,sK413(U_1882,U_1881,U_1880))
| ~ sP441(U_1882,U_1880,U_1881,U_1884,U_1883) )
& ! [U_1882,U_1880,U_1881,U_1884,U_1883] :
( sP441(U_1882,U_1880,U_1881,U_1884,U_1883)
| ~ function(U_1880)
| ~ relation(U_1880)
| ~ element(U_1881,powerset(powerset(U_1882))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP440,sP441])],[f_455_4]) ).
cnf(f_455_6,plain,
( sP441(U_1882,U_1880,U_1881,U_1884,U_1883)
| ~ function(U_1880)
| ~ relation(U_1880)
| ~ element(U_1881,powerset(powerset(U_1882))) ),
inference(clausify,[status(thm)],[f_455_5]) ).
cnf(f_455_7,plain,
( sP440(U_1880,U_1881,U_1883)
| ~ in(U_1883,sK413(U_1882,U_1881,U_1880))
| ~ sP441(U_1882,U_1880,U_1881,U_1884,U_1883) ),
inference(clausify,[status(thm)],[f_455_5]) ).
cnf(f_455_8,plain,
( in(U_1884,sK413(U_1882,U_1881,U_1880))
| ~ in(relation_image(U_1880,U_1884),U_1881)
| ~ in(U_1884,powerset(relation_dom(U_1880)))
| ~ sP441(U_1882,U_1880,U_1881,U_1884,U_1883) ),
inference(clausify,[status(thm)],[f_455_5]) ).
cnf(f_455_9,plain,
( in(U_1883,powerset(relation_dom(U_1880)))
| ~ sP440(U_1880,U_1881,U_1883) ),
inference(clausify,[status(thm)],[f_455_5]) ).
cnf(f_455_10,plain,
( in(relation_image(U_1880,U_1883),U_1881)
| ~ sP440(U_1880,U_1881,U_1883) ),
inference(clausify,[status(thm)],[f_455_5]) ).
fof(f_456_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_456_2,plain,
! [U_1890,U_1889] :
( ? [U_1888] :
! [U_1887] :
( ( in(U_1887,U_1888)
| ! [U_1886] :
( ~ in(U_1886,U_1890)
| U_1887 != U_1886
| ~ ordinal(U_1886) )
| ~ in(U_1887,succ(U_1889)) )
& ( ( ? [U_1885] :
( in(U_1885,U_1890)
& U_1887 = U_1885
& ordinal(U_1885) )
& in(U_1887,succ(U_1889)) )
| ~ in(U_1887,U_1888) ) )
| ~ ordinal(U_1889) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
! [U_1890,U_1889] :
( ? [U_1888] :
( ! [U_1892] :
( in(U_1892,U_1888)
| ! [U_1886] :
( ~ in(U_1886,U_1890)
| U_1892 != U_1886
| ~ ordinal(U_1886) )
| ~ in(U_1892,succ(U_1889)) )
& ! [U_1891] :
( ( ? [U_1885] :
( in(U_1885,U_1890)
& U_1891 = U_1885
& ordinal(U_1885) )
& in(U_1891,succ(U_1889)) )
| ~ in(U_1891,U_1888) ) )
| ~ ordinal(U_1889) ),
inference(miniscope,[status(thm)],[f_456_2]) ).
fof(f_456_4,plain,
! [U_1890,U_1889] :
( ( ! [U_1892] :
( in(U_1892,sK414(U_1890,U_1889))
| ! [U_1886] :
( ~ in(U_1886,U_1890)
| U_1892 != U_1886
| ~ ordinal(U_1886) )
| ~ in(U_1892,succ(U_1889)) )
& ! [U_1891] :
( ( ? [U_1885] :
( in(U_1885,U_1890)
& U_1891 = U_1885
& ordinal(U_1885) )
& in(U_1891,succ(U_1889)) )
| ~ in(U_1891,sK414(U_1890,U_1889)) ) )
| ~ ordinal(U_1889) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_1888,sK414(U_1890,U_1889))],[f_456_3]) ).
fof(f_456_5,plain,
! [U_1890,U_1889] :
( ( ! [U_1892] :
( in(U_1892,sK414(U_1890,U_1889))
| ! [U_1886] :
( ~ in(U_1886,U_1890)
| U_1892 != U_1886
| ~ ordinal(U_1886) )
| ~ in(U_1892,succ(U_1889)) )
& ! [U_1891] :
( ( in(sK415(U_1890,U_1889,U_1891),U_1890)
& U_1891 = sK415(U_1890,U_1889,U_1891)
& ordinal(sK415(U_1890,U_1889,U_1891))
& in(U_1891,succ(U_1889)) )
| ~ in(U_1891,sK414(U_1890,U_1889)) ) )
| ~ ordinal(U_1889) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_1885,sK415(U_1890,U_1889,U_1891))],[f_456_4]) ).
fof(f_456_6,plain,
( ! [U_1891,U_1890,U_1889] :
( in(sK415(U_1890,U_1889,U_1891),U_1890)
| ~ sP442(U_1891,U_1890,U_1889) )
& ! [U_1891,U_1890,U_1889] :
( U_1891 = sK415(U_1890,U_1889,U_1891)
| ~ sP442(U_1891,U_1890,U_1889) )
& ! [U_1891,U_1890,U_1889] :
( ordinal(sK415(U_1890,U_1889,U_1891))
| ~ sP442(U_1891,U_1890,U_1889) )
& ! [U_1891,U_1890,U_1889] :
( in(U_1891,succ(U_1889))
| ~ sP442(U_1891,U_1890,U_1889) )
& ! [U_1891,U_1892,U_1890,U_1889,U_1886] :
( in(U_1892,sK414(U_1890,U_1889))
| ~ in(U_1886,U_1890)
| U_1892 != U_1886
| ~ ordinal(U_1886)
| ~ in(U_1892,succ(U_1889))
| ~ sP443(U_1891,U_1892,U_1890,U_1889,U_1886) )
& ! [U_1891,U_1892,U_1890,U_1889,U_1886] :
( sP442(U_1891,U_1890,U_1889)
| ~ in(U_1891,sK414(U_1890,U_1889))
| ~ sP443(U_1891,U_1892,U_1890,U_1889,U_1886) )
& ! [U_1891,U_1892,U_1890,U_1889,U_1886] :
( sP443(U_1891,U_1892,U_1890,U_1889,U_1886)
| ~ ordinal(U_1889) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP442,sP443])],[f_456_5]) ).
cnf(f_456_7,plain,
( sP443(U_1891,U_1892,U_1890,U_1889,U_1886)
| ~ ordinal(U_1889) ),
inference(clausify,[status(thm)],[f_456_6]) ).
cnf(f_456_8,plain,
( sP442(U_1891,U_1890,U_1889)
| ~ in(U_1891,sK414(U_1890,U_1889))
| ~ sP443(U_1891,U_1892,U_1890,U_1889,U_1886) ),
inference(clausify,[status(thm)],[f_456_6]) ).
cnf(f_456_9,plain,
( in(U_1892,sK414(U_1890,U_1889))
| ~ in(U_1886,U_1890)
| U_1892 != U_1886
| ~ ordinal(U_1886)
| ~ in(U_1892,succ(U_1889))
| ~ sP443(U_1891,U_1892,U_1890,U_1889,U_1886) ),
inference(clausify,[status(thm)],[f_456_6]) ).
cnf(f_456_10,plain,
( in(U_1891,succ(U_1889))
| ~ sP442(U_1891,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_456_6]) ).
cnf(f_456_11,plain,
( ordinal(sK415(U_1890,U_1889,U_1891))
| ~ sP442(U_1891,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_456_6]) ).
cnf(f_456_12,plain,
( U_1891 = sK415(U_1890,U_1889,U_1891)
| ~ sP442(U_1891,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_456_6]) ).
cnf(f_456_13,plain,
( in(sK415(U_1890,U_1889,U_1891),U_1890)
| ~ sP442(U_1891,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_456_6]) ).
fof(f_457_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_457_2,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ? [U_1903] :
( ! [U_1902,U_1901] :
( ? [U_1900] :
( ~ in(ordered_pair(U_1902,U_1900),U_1908)
& in(U_1900,U_1901) )
| ~ in(U_1902,U_1901)
| U_1903 != U_1901 )
& in(U_1903,U_1909) )
| ? [U_1899,U_1898,U_1897] :
( U_1898 != U_1897
& ? [U_1896] :
( ! [U_1895] :
( in(ordered_pair(U_1897,U_1895),U_1908)
| ~ in(U_1895,U_1896) )
& in(U_1897,U_1896)
& U_1899 = U_1896 )
& ? [U_1894] :
( ! [U_1893] :
( in(ordered_pair(U_1898,U_1893),U_1908)
| ~ in(U_1893,U_1894) )
& in(U_1898,U_1894)
& U_1899 = U_1894 )
& in(U_1899,U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ? [U_1903] :
( ! [U_1902,U_1901] :
( ? [U_1900] :
( ~ in(ordered_pair(U_1902,U_1900),U_1908)
& in(U_1900,U_1901) )
| ~ in(U_1902,U_1901)
| U_1903 != U_1901 )
& in(U_1903,U_1909) )
| ? [U_1898,U_1897] :
( U_1898 != U_1897
& ? [U_1896] :
( ! [U_1895] :
( in(ordered_pair(U_1897,U_1895),U_1908)
| ~ in(U_1895,U_1896) )
& in(U_1897,U_1896)
& sK416(U_1909,U_1908) = U_1896 )
& ? [U_1894] :
( ! [U_1893] :
( in(ordered_pair(U_1898,U_1893),U_1908)
| ~ in(U_1893,U_1894) )
& in(U_1898,U_1894)
& sK416(U_1909,U_1908) = U_1894 )
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_1899,sK416(U_1909,U_1908))],[f_457_2]) ).
fof(f_457_4,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ? [U_1903] :
( ! [U_1902,U_1901] :
( ? [U_1900] :
( ~ in(ordered_pair(U_1902,U_1900),U_1908)
& in(U_1900,U_1901) )
| ~ in(U_1902,U_1901)
| U_1903 != U_1901 )
& in(U_1903,U_1909) )
| ? [U_1897] :
( sK417(U_1909,U_1908) != U_1897
& ? [U_1896] :
( ! [U_1895] :
( in(ordered_pair(U_1897,U_1895),U_1908)
| ~ in(U_1895,U_1896) )
& in(U_1897,U_1896)
& sK416(U_1909,U_1908) = U_1896 )
& ? [U_1894] :
( ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,U_1894) )
& in(sK417(U_1909,U_1908),U_1894)
& sK416(U_1909,U_1908) = U_1894 )
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_1898,sK417(U_1909,U_1908))],[f_457_3]) ).
fof(f_457_5,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ? [U_1903] :
( ! [U_1902,U_1901] :
( ? [U_1900] :
( ~ in(ordered_pair(U_1902,U_1900),U_1908)
& in(U_1900,U_1901) )
| ~ in(U_1902,U_1901)
| U_1903 != U_1901 )
& in(U_1903,U_1909) )
| ( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
& ? [U_1896] :
( ! [U_1895] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,U_1896) )
& in(sK418(U_1909,U_1908),U_1896)
& sK416(U_1909,U_1908) = U_1896 )
& ? [U_1894] :
( ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,U_1894) )
& in(sK417(U_1909,U_1908),U_1894)
& sK416(U_1909,U_1908) = U_1894 )
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_1897,sK418(U_1909,U_1908))],[f_457_4]) ).
fof(f_457_6,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ? [U_1903] :
( ! [U_1902,U_1901] :
( ? [U_1900] :
( ~ in(ordered_pair(U_1902,U_1900),U_1908)
& in(U_1900,U_1901) )
| ~ in(U_1902,U_1901)
| U_1903 != U_1901 )
& in(U_1903,U_1909) )
| ( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
& ? [U_1896] :
( ! [U_1895] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,U_1896) )
& in(sK418(U_1909,U_1908),U_1896)
& sK416(U_1909,U_1908) = U_1896 )
& ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908)) )
& in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_1894,sK419(U_1909,U_1908))],[f_457_5]) ).
fof(f_457_7,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ? [U_1903] :
( ! [U_1902,U_1901] :
( ? [U_1900] :
( ~ in(ordered_pair(U_1902,U_1900),U_1908)
& in(U_1900,U_1901) )
| ~ in(U_1902,U_1901)
| U_1903 != U_1901 )
& in(U_1903,U_1909) )
| ( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
& ! [U_1895] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,sK420(U_1909,U_1908)) )
& in(sK418(U_1909,U_1908),sK420(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK420(U_1909,U_1908)
& ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908)) )
& in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_1896,sK420(U_1909,U_1908))],[f_457_6]) ).
fof(f_457_8,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ( ! [U_1902,U_1901] :
( ? [U_1900] :
( ~ in(ordered_pair(U_1902,U_1900),U_1908)
& in(U_1900,U_1901) )
| ~ in(U_1902,U_1901)
| sK421(U_1909,U_1908) != U_1901 )
& in(sK421(U_1909,U_1908),U_1909) )
| ( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
& ! [U_1895] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,sK420(U_1909,U_1908)) )
& in(sK418(U_1909,U_1908),sK420(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK420(U_1909,U_1908)
& ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908)) )
& in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_1903,sK421(U_1909,U_1908))],[f_457_7]) ).
fof(f_457_9,plain,
! [U_1909,U_1908] :
( ? [U_1907] :
( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(U_1907,U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(U_1907,U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(U_1907) = U_1909
& function(U_1907)
& relation(U_1907) )
| ( ! [U_1902,U_1901] :
( ( ~ in(ordered_pair(U_1902,sK422(U_1909,U_1908,U_1902,U_1901)),U_1908)
& in(sK422(U_1909,U_1908,U_1902,U_1901),U_1901) )
| ~ in(U_1902,U_1901)
| sK421(U_1909,U_1908) != U_1901 )
& in(sK421(U_1909,U_1908),U_1909) )
| ( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
& ! [U_1895] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,sK420(U_1909,U_1908)) )
& in(sK418(U_1909,U_1908),sK420(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK420(U_1909,U_1908)
& ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908)) )
& in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_1900,sK422(U_1909,U_1908,U_1902,U_1901))],[f_457_8]) ).
fof(f_457_10,plain,
! [U_1909,U_1908] :
( ( ! [U_1906] :
( ? [U_1905] :
( ! [U_1904] :
( in(ordered_pair(apply(sK423(U_1909,U_1908),U_1906),U_1904),U_1908)
| ~ in(U_1904,U_1905) )
& in(apply(sK423(U_1909,U_1908),U_1906),U_1905)
& U_1906 = U_1905 )
| ~ in(U_1906,U_1909) )
& relation_dom(sK423(U_1909,U_1908)) = U_1909
& function(sK423(U_1909,U_1908))
& relation(sK423(U_1909,U_1908)) )
| ( ! [U_1902,U_1901] :
( ( ~ in(ordered_pair(U_1902,sK422(U_1909,U_1908,U_1902,U_1901)),U_1908)
& in(sK422(U_1909,U_1908,U_1902,U_1901),U_1901) )
| ~ in(U_1902,U_1901)
| sK421(U_1909,U_1908) != U_1901 )
& in(sK421(U_1909,U_1908),U_1909) )
| ( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
& ! [U_1895] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,sK420(U_1909,U_1908)) )
& in(sK418(U_1909,U_1908),sK420(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK420(U_1909,U_1908)
& ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908)) )
& in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_1907,sK423(U_1909,U_1908))],[f_457_9]) ).
fof(f_457_11,plain,
! [U_1909,U_1908] :
( ( ! [U_1906] :
( ( ! [U_1904] :
( in(ordered_pair(apply(sK423(U_1909,U_1908),U_1906),U_1904),U_1908)
| ~ in(U_1904,sK424(U_1909,U_1908,U_1906)) )
& in(apply(sK423(U_1909,U_1908),U_1906),sK424(U_1909,U_1908,U_1906))
& U_1906 = sK424(U_1909,U_1908,U_1906) )
| ~ in(U_1906,U_1909) )
& relation_dom(sK423(U_1909,U_1908)) = U_1909
& function(sK423(U_1909,U_1908))
& relation(sK423(U_1909,U_1908)) )
| ( ! [U_1902,U_1901] :
( ( ~ in(ordered_pair(U_1902,sK422(U_1909,U_1908,U_1902,U_1901)),U_1908)
& in(sK422(U_1909,U_1908,U_1902,U_1901),U_1901) )
| ~ in(U_1902,U_1901)
| sK421(U_1909,U_1908) != U_1901 )
& in(sK421(U_1909,U_1908),U_1909) )
| ( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
& ! [U_1895] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,sK420(U_1909,U_1908)) )
& in(sK418(U_1909,U_1908),sK420(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK420(U_1909,U_1908)
& ! [U_1893] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908)) )
& in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
& sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
& in(sK416(U_1909,U_1908),U_1909) )
| ~ relation(U_1908)
| empty(U_1909) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_1905,sK424(U_1909,U_1908,U_1906))],[f_457_10]) ).
fof(f_457_12,plain,
( ! [U_1904,U_1906,U_1908,U_1909] :
( in(ordered_pair(apply(sK423(U_1909,U_1908),U_1906),U_1904),U_1908)
| ~ in(U_1904,sK424(U_1909,U_1908,U_1906))
| ~ sP447(U_1904,U_1906,U_1908,U_1909) )
& ! [U_1904,U_1906,U_1908,U_1909] :
( in(apply(sK423(U_1909,U_1908),U_1906),sK424(U_1909,U_1908,U_1906))
| ~ sP447(U_1904,U_1906,U_1908,U_1909) )
& ! [U_1904,U_1906,U_1908,U_1909] :
( U_1906 = sK424(U_1909,U_1908,U_1906)
| ~ sP447(U_1904,U_1906,U_1908,U_1909) )
& ! [U_1904,U_1906,U_1908,U_1909] :
( sP447(U_1904,U_1906,U_1908,U_1909)
| ~ in(U_1906,U_1909)
| ~ sP448(U_1904,U_1906,U_1908,U_1909) )
& ! [U_1904,U_1906,U_1908,U_1909] :
( relation_dom(sK423(U_1909,U_1908)) = U_1909
| ~ sP448(U_1904,U_1906,U_1908,U_1909) )
& ! [U_1904,U_1906,U_1908,U_1909] :
( function(sK423(U_1909,U_1908))
| ~ sP448(U_1904,U_1906,U_1908,U_1909) )
& ! [U_1904,U_1906,U_1908,U_1909] :
( relation(sK423(U_1909,U_1908))
| ~ sP448(U_1904,U_1906,U_1908,U_1909) )
& ! [U_1901,U_1902,U_1908,U_1909] :
( ~ in(ordered_pair(U_1902,sK422(U_1909,U_1908,U_1902,U_1901)),U_1908)
| ~ sP445(U_1901,U_1902,U_1908,U_1909) )
& ! [U_1901,U_1902,U_1908,U_1909] :
( in(sK422(U_1909,U_1908,U_1902,U_1901),U_1901)
| ~ sP445(U_1901,U_1902,U_1908,U_1909) )
& ! [U_1901,U_1902,U_1908,U_1909] :
( sP445(U_1901,U_1902,U_1908,U_1909)
| ~ in(U_1902,U_1901)
| sK421(U_1909,U_1908) != U_1901
| ~ sP446(U_1901,U_1902,U_1908,U_1909) )
& ! [U_1901,U_1902,U_1908,U_1909] :
( in(sK421(U_1909,U_1908),U_1909)
| ~ sP446(U_1901,U_1902,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,sK420(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( in(sK418(U_1909,U_1908),sK420(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( sK416(U_1909,U_1908) = sK420(U_1909,U_1908)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1893,U_1895,U_1908,U_1909] :
( in(sK416(U_1909,U_1908),U_1909)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) )
& ! [U_1904,U_1893,U_1901,U_1902,U_1895,U_1906,U_1908,U_1909] :
( sP448(U_1904,U_1906,U_1908,U_1909)
| sP446(U_1901,U_1902,U_1908,U_1909)
| sP444(U_1893,U_1895,U_1908,U_1909)
| ~ relation(U_1908)
| empty(U_1909) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP444,sP445,sP446,sP447,sP448])],[f_457_11]) ).
cnf(f_457_13,plain,
( sP448(U_1904,U_1906,U_1908,U_1909)
| sP446(U_1901,U_1902,U_1908,U_1909)
| sP444(U_1893,U_1895,U_1908,U_1909)
| ~ relation(U_1908)
| empty(U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_14,plain,
( in(sK416(U_1909,U_1908),U_1909)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_15,plain,
( sK416(U_1909,U_1908) = sK419(U_1909,U_1908)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_16,plain,
( in(sK417(U_1909,U_1908),sK419(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_17,plain,
( in(ordered_pair(sK417(U_1909,U_1908),U_1893),U_1908)
| ~ in(U_1893,sK419(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_18,plain,
( sK416(U_1909,U_1908) = sK420(U_1909,U_1908)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_19,plain,
( in(sK418(U_1909,U_1908),sK420(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_20,plain,
( in(ordered_pair(sK418(U_1909,U_1908),U_1895),U_1908)
| ~ in(U_1895,sK420(U_1909,U_1908))
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_21,plain,
( sK417(U_1909,U_1908) != sK418(U_1909,U_1908)
| ~ sP444(U_1893,U_1895,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_22,plain,
( in(sK421(U_1909,U_1908),U_1909)
| ~ sP446(U_1901,U_1902,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_23,plain,
( sP445(U_1901,U_1902,U_1908,U_1909)
| ~ in(U_1902,U_1901)
| sK421(U_1909,U_1908) != U_1901
| ~ sP446(U_1901,U_1902,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_24,plain,
( in(sK422(U_1909,U_1908,U_1902,U_1901),U_1901)
| ~ sP445(U_1901,U_1902,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_25,plain,
( ~ in(ordered_pair(U_1902,sK422(U_1909,U_1908,U_1902,U_1901)),U_1908)
| ~ sP445(U_1901,U_1902,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_26,plain,
( relation(sK423(U_1909,U_1908))
| ~ sP448(U_1904,U_1906,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_27,plain,
( function(sK423(U_1909,U_1908))
| ~ sP448(U_1904,U_1906,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_28,plain,
( relation_dom(sK423(U_1909,U_1908)) = U_1909
| ~ sP448(U_1904,U_1906,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_29,plain,
( sP447(U_1904,U_1906,U_1908,U_1909)
| ~ in(U_1906,U_1909)
| ~ sP448(U_1904,U_1906,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_30,plain,
( U_1906 = sK424(U_1909,U_1908,U_1906)
| ~ sP447(U_1904,U_1906,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_31,plain,
( in(apply(sK423(U_1909,U_1908),U_1906),sK424(U_1909,U_1908,U_1906))
| ~ sP447(U_1904,U_1906,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
cnf(f_457_32,plain,
( in(ordered_pair(apply(sK423(U_1909,U_1908),U_1906),U_1904),U_1908)
| ~ in(U_1904,sK424(U_1909,U_1908,U_1906))
| ~ sP447(U_1904,U_1906,U_1908,U_1909) ),
inference(clausify,[status(thm)],[f_457_12]) ).
fof(f_458_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_458_2,plain,
! [U_1917] :
( ? [U_1916] :
( ! [U_1915] :
( apply(U_1916,U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917) )
& relation_dom(U_1916) = U_1917
& function(U_1916)
& relation(U_1916) )
| ? [U_1914] :
( ! [U_1913] : U_1913 != singleton(U_1914)
& in(U_1914,U_1917) )
| ? [U_1912,U_1911,U_1910] :
( U_1911 != U_1910
& U_1910 = singleton(U_1912)
& U_1911 = singleton(U_1912)
& in(U_1912,U_1917) ) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
! [U_1917] :
( ? [U_1916] :
( ! [U_1915] :
( apply(U_1916,U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917) )
& relation_dom(U_1916) = U_1917
& function(U_1916)
& relation(U_1916) )
| ? [U_1914] :
( ! [U_1913] : U_1913 != singleton(U_1914)
& in(U_1914,U_1917) )
| ? [U_1911,U_1910] :
( U_1911 != U_1910
& U_1910 = singleton(sK425(U_1917))
& U_1911 = singleton(sK425(U_1917))
& in(sK425(U_1917),U_1917) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_1912,sK425(U_1917))],[f_458_2]) ).
fof(f_458_4,plain,
! [U_1917] :
( ? [U_1916] :
( ! [U_1915] :
( apply(U_1916,U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917) )
& relation_dom(U_1916) = U_1917
& function(U_1916)
& relation(U_1916) )
| ? [U_1914] :
( ! [U_1913] : U_1913 != singleton(U_1914)
& in(U_1914,U_1917) )
| ? [U_1910] :
( sK426(U_1917) != U_1910
& U_1910 = singleton(sK425(U_1917))
& sK426(U_1917) = singleton(sK425(U_1917))
& in(sK425(U_1917),U_1917) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_1911,sK426(U_1917))],[f_458_3]) ).
fof(f_458_5,plain,
! [U_1917] :
( ? [U_1916] :
( ! [U_1915] :
( apply(U_1916,U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917) )
& relation_dom(U_1916) = U_1917
& function(U_1916)
& relation(U_1916) )
| ? [U_1914] :
( ! [U_1913] : U_1913 != singleton(U_1914)
& in(U_1914,U_1917) )
| ( sK426(U_1917) != sK427(U_1917)
& sK427(U_1917) = singleton(sK425(U_1917))
& sK426(U_1917) = singleton(sK425(U_1917))
& in(sK425(U_1917),U_1917) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK427]),skolemize(U_1910,sK427(U_1917))],[f_458_4]) ).
fof(f_458_6,plain,
! [U_1917] :
( ? [U_1916] :
( ! [U_1915] :
( apply(U_1916,U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917) )
& relation_dom(U_1916) = U_1917
& function(U_1916)
& relation(U_1916) )
| ( ! [U_1913] : U_1913 != singleton(sK428(U_1917))
& in(sK428(U_1917),U_1917) )
| ( sK426(U_1917) != sK427(U_1917)
& sK427(U_1917) = singleton(sK425(U_1917))
& sK426(U_1917) = singleton(sK425(U_1917))
& in(sK425(U_1917),U_1917) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_1914,sK428(U_1917))],[f_458_5]) ).
fof(f_458_7,plain,
! [U_1917] :
( ( ! [U_1915] :
( apply(sK429(U_1917),U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917) )
& relation_dom(sK429(U_1917)) = U_1917
& function(sK429(U_1917))
& relation(sK429(U_1917)) )
| ( ! [U_1913] : U_1913 != singleton(sK428(U_1917))
& in(sK428(U_1917),U_1917) )
| ( sK426(U_1917) != sK427(U_1917)
& sK427(U_1917) = singleton(sK425(U_1917))
& sK426(U_1917) = singleton(sK425(U_1917))
& in(sK425(U_1917),U_1917) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_1916,sK429(U_1917))],[f_458_6]) ).
fof(f_458_8,plain,
( ! [U_1915,U_1917] :
( apply(sK429(U_1917),U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917)
| ~ sP451(U_1915,U_1917) )
& ! [U_1915,U_1917] :
( relation_dom(sK429(U_1917)) = U_1917
| ~ sP451(U_1915,U_1917) )
& ! [U_1915,U_1917] :
( function(sK429(U_1917))
| ~ sP451(U_1915,U_1917) )
& ! [U_1915,U_1917] :
( relation(sK429(U_1917))
| ~ sP451(U_1915,U_1917) )
& ! [U_1917,U_1913] :
( U_1913 != singleton(sK428(U_1917))
| ~ sP450(U_1917,U_1913) )
& ! [U_1917,U_1913] :
( in(sK428(U_1917),U_1917)
| ~ sP450(U_1917,U_1913) )
& ! [U_1917] :
( sK426(U_1917) != sK427(U_1917)
| ~ sP449(U_1917) )
& ! [U_1917] :
( sK427(U_1917) = singleton(sK425(U_1917))
| ~ sP449(U_1917) )
& ! [U_1917] :
( sK426(U_1917) = singleton(sK425(U_1917))
| ~ sP449(U_1917) )
& ! [U_1917] :
( in(sK425(U_1917),U_1917)
| ~ sP449(U_1917) )
& ! [U_1915,U_1917,U_1913] :
( sP451(U_1915,U_1917)
| sP450(U_1917,U_1913)
| sP449(U_1917) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP449,sP450,sP451])],[f_458_7]) ).
cnf(f_458_9,plain,
( sP451(U_1915,U_1917)
| sP450(U_1917,U_1913)
| sP449(U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_10,plain,
( in(sK425(U_1917),U_1917)
| ~ sP449(U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_11,plain,
( sK426(U_1917) = singleton(sK425(U_1917))
| ~ sP449(U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_12,plain,
( sK427(U_1917) = singleton(sK425(U_1917))
| ~ sP449(U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_13,plain,
( sK426(U_1917) != sK427(U_1917)
| ~ sP449(U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_14,plain,
( in(sK428(U_1917),U_1917)
| ~ sP450(U_1917,U_1913) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_15,plain,
( U_1913 != singleton(sK428(U_1917))
| ~ sP450(U_1917,U_1913) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_16,plain,
( relation(sK429(U_1917))
| ~ sP451(U_1915,U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_17,plain,
( function(sK429(U_1917))
| ~ sP451(U_1915,U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_18,plain,
( relation_dom(sK429(U_1917)) = U_1917
| ~ sP451(U_1915,U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
cnf(f_458_19,plain,
( apply(sK429(U_1917),U_1915) = singleton(U_1915)
| ~ in(U_1915,U_1917)
| ~ sP451(U_1915,U_1917) ),
inference(clausify,[status(thm)],[f_458_8]) ).
fof(f_459_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ! [I] :
( apply(C,D) = subset_complement(the_carrier(A),I)
| I != D
| ~ element(I,powerset(the_carrier(A))) )
| ~ in(D,complements_of_subsets(the_carrier(A),B)) )
& relation_dom(C) = complements_of_subsets(the_carrier(A),B)
& function(C)
& relation(C) )
| ? [C] :
( ! [D] :
? [H] :
( D != subset_complement(the_carrier(A),H)
& H = C
& element(H,powerset(the_carrier(A))) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
| ? [C,D,E] :
( D != E
& ! [G] :
( E = subset_complement(the_carrier(A),G)
| G != C
| ~ element(G,powerset(the_carrier(A))) )
& ! [F] :
( D = subset_complement(the_carrier(A),F)
| F != C
| ~ element(F,powerset(the_carrier(A))) )
& in(C,complements_of_subsets(the_carrier(A),B)) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s2_funct_1__e4_7_1__tops_2]) ).
fof(f_459_2,plain,
! [U_1930,U_1929] :
( ? [U_1928] :
( ! [U_1927] :
( ! [U_1926] :
( apply(U_1928,U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930))) )
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929)) )
& relation_dom(U_1928) = complements_of_subsets(the_carrier(U_1930),U_1929)
& function(U_1928)
& relation(U_1928) )
| ? [U_1925] :
( ! [U_1924] :
? [U_1923] :
( U_1924 != subset_complement(the_carrier(U_1930),U_1923)
& U_1923 = U_1925
& element(U_1923,powerset(the_carrier(U_1930))) )
& in(U_1925,complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ? [U_1922,U_1921,U_1920] :
( U_1921 != U_1920
& ! [U_1919] :
( U_1920 = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != U_1922
| ~ element(U_1919,powerset(the_carrier(U_1930))) )
& ! [U_1918] :
( U_1921 = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != U_1922
| ~ element(U_1918,powerset(the_carrier(U_1930))) )
& in(U_1922,complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
! [U_1930,U_1929] :
( ? [U_1928] :
( ! [U_1927] :
( ! [U_1926] :
( apply(U_1928,U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930))) )
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929)) )
& relation_dom(U_1928) = complements_of_subsets(the_carrier(U_1930),U_1929)
& function(U_1928)
& relation(U_1928) )
| ? [U_1925] :
( ! [U_1924] :
? [U_1923] :
( U_1924 != subset_complement(the_carrier(U_1930),U_1923)
& U_1923 = U_1925
& element(U_1923,powerset(the_carrier(U_1930))) )
& in(U_1925,complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ? [U_1921,U_1920] :
( U_1921 != U_1920
& ! [U_1919] :
( U_1920 = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930))) )
& ! [U_1918] :
( U_1921 = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930))) )
& in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_1922,sK430(U_1930,U_1929))],[f_459_2]) ).
fof(f_459_4,plain,
! [U_1930,U_1929] :
( ? [U_1928] :
( ! [U_1927] :
( ! [U_1926] :
( apply(U_1928,U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930))) )
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929)) )
& relation_dom(U_1928) = complements_of_subsets(the_carrier(U_1930),U_1929)
& function(U_1928)
& relation(U_1928) )
| ? [U_1925] :
( ! [U_1924] :
? [U_1923] :
( U_1924 != subset_complement(the_carrier(U_1930),U_1923)
& U_1923 = U_1925
& element(U_1923,powerset(the_carrier(U_1930))) )
& in(U_1925,complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ? [U_1920] :
( sK431(U_1930,U_1929) != U_1920
& ! [U_1919] :
( U_1920 = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930))) )
& ! [U_1918] :
( sK431(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930))) )
& in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_1921,sK431(U_1930,U_1929))],[f_459_3]) ).
fof(f_459_5,plain,
! [U_1930,U_1929] :
( ? [U_1928] :
( ! [U_1927] :
( ! [U_1926] :
( apply(U_1928,U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930))) )
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929)) )
& relation_dom(U_1928) = complements_of_subsets(the_carrier(U_1930),U_1929)
& function(U_1928)
& relation(U_1928) )
| ? [U_1925] :
( ! [U_1924] :
? [U_1923] :
( U_1924 != subset_complement(the_carrier(U_1930),U_1923)
& U_1923 = U_1925
& element(U_1923,powerset(the_carrier(U_1930))) )
& in(U_1925,complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ( sK431(U_1930,U_1929) != sK432(U_1930,U_1929)
& ! [U_1919] :
( sK432(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930))) )
& ! [U_1918] :
( sK431(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930))) )
& in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_1920,sK432(U_1930,U_1929))],[f_459_4]) ).
fof(f_459_6,plain,
! [U_1930,U_1929] :
( ? [U_1928] :
( ! [U_1927] :
( ! [U_1926] :
( apply(U_1928,U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930))) )
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929)) )
& relation_dom(U_1928) = complements_of_subsets(the_carrier(U_1930),U_1929)
& function(U_1928)
& relation(U_1928) )
| ( ! [U_1924] :
? [U_1923] :
( U_1924 != subset_complement(the_carrier(U_1930),U_1923)
& U_1923 = sK433(U_1930,U_1929)
& element(U_1923,powerset(the_carrier(U_1930))) )
& in(sK433(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ( sK431(U_1930,U_1929) != sK432(U_1930,U_1929)
& ! [U_1919] :
( sK432(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930))) )
& ! [U_1918] :
( sK431(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930))) )
& in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_1925,sK433(U_1930,U_1929))],[f_459_5]) ).
fof(f_459_7,plain,
! [U_1930,U_1929] :
( ? [U_1928] :
( ! [U_1927] :
( ! [U_1926] :
( apply(U_1928,U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930))) )
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929)) )
& relation_dom(U_1928) = complements_of_subsets(the_carrier(U_1930),U_1929)
& function(U_1928)
& relation(U_1928) )
| ( ! [U_1924] :
( U_1924 != subset_complement(the_carrier(U_1930),sK434(U_1930,U_1929,U_1924))
& sK434(U_1930,U_1929,U_1924) = sK433(U_1930,U_1929)
& element(sK434(U_1930,U_1929,U_1924),powerset(the_carrier(U_1930))) )
& in(sK433(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ( sK431(U_1930,U_1929) != sK432(U_1930,U_1929)
& ! [U_1919] :
( sK432(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930))) )
& ! [U_1918] :
( sK431(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930))) )
& in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_1923,sK434(U_1930,U_1929,U_1924))],[f_459_6]) ).
fof(f_459_8,plain,
! [U_1930,U_1929] :
( ( ! [U_1927] :
( ! [U_1926] :
( apply(sK435(U_1930,U_1929),U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930))) )
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929)) )
& relation_dom(sK435(U_1930,U_1929)) = complements_of_subsets(the_carrier(U_1930),U_1929)
& function(sK435(U_1930,U_1929))
& relation(sK435(U_1930,U_1929)) )
| ( ! [U_1924] :
( U_1924 != subset_complement(the_carrier(U_1930),sK434(U_1930,U_1929,U_1924))
& sK434(U_1930,U_1929,U_1924) = sK433(U_1930,U_1929)
& element(sK434(U_1930,U_1929,U_1924),powerset(the_carrier(U_1930))) )
& in(sK433(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ( sK431(U_1930,U_1929) != sK432(U_1930,U_1929)
& ! [U_1919] :
( sK432(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930))) )
& ! [U_1918] :
( sK431(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930))) )
& in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929)) )
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_1928,sK435(U_1930,U_1929))],[f_459_7]) ).
fof(f_459_9,plain,
( ! [U_1930,U_1926,U_1927,U_1929] :
( apply(sK435(U_1930,U_1929),U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930)))
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929))
| ~ sP454(U_1930,U_1926,U_1927,U_1929) )
& ! [U_1930,U_1926,U_1927,U_1929] :
( relation_dom(sK435(U_1930,U_1929)) = complements_of_subsets(the_carrier(U_1930),U_1929)
| ~ sP454(U_1930,U_1926,U_1927,U_1929) )
& ! [U_1930,U_1926,U_1927,U_1929] :
( function(sK435(U_1930,U_1929))
| ~ sP454(U_1930,U_1926,U_1927,U_1929) )
& ! [U_1930,U_1926,U_1927,U_1929] :
( relation(sK435(U_1930,U_1929))
| ~ sP454(U_1930,U_1926,U_1927,U_1929) )
& ! [U_1930,U_1929,U_1924] :
( U_1924 != subset_complement(the_carrier(U_1930),sK434(U_1930,U_1929,U_1924))
| ~ sP453(U_1930,U_1929,U_1924) )
& ! [U_1930,U_1929,U_1924] :
( sK434(U_1930,U_1929,U_1924) = sK433(U_1930,U_1929)
| ~ sP453(U_1930,U_1929,U_1924) )
& ! [U_1930,U_1929,U_1924] :
( element(sK434(U_1930,U_1929,U_1924),powerset(the_carrier(U_1930)))
| ~ sP453(U_1930,U_1929,U_1924) )
& ! [U_1930,U_1929,U_1924] :
( in(sK433(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929))
| ~ sP453(U_1930,U_1929,U_1924) )
& ! [U_1930,U_1919,U_1929,U_1918] :
( sK431(U_1930,U_1929) != sK432(U_1930,U_1929)
| ~ sP452(U_1930,U_1919,U_1929,U_1918) )
& ! [U_1930,U_1919,U_1929,U_1918] :
( sK432(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930)))
| ~ sP452(U_1930,U_1919,U_1929,U_1918) )
& ! [U_1930,U_1919,U_1929,U_1918] :
( sK431(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930)))
| ~ sP452(U_1930,U_1919,U_1929,U_1918) )
& ! [U_1930,U_1919,U_1929,U_1918] :
( in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929))
| ~ sP452(U_1930,U_1919,U_1929,U_1918) )
& ! [U_1930,U_1926,U_1927,U_1919,U_1929,U_1918,U_1924] :
( sP454(U_1930,U_1926,U_1927,U_1929)
| sP453(U_1930,U_1929,U_1924)
| sP452(U_1930,U_1919,U_1929,U_1918)
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP452,sP453,sP454])],[f_459_8]) ).
cnf(f_459_10,plain,
( sP454(U_1930,U_1926,U_1927,U_1929)
| sP453(U_1930,U_1929,U_1924)
| sP452(U_1930,U_1919,U_1929,U_1918)
| ~ element(U_1929,powerset(powerset(the_carrier(U_1930))))
| ~ one_sorted_str(U_1930) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_11,plain,
( in(sK430(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929))
| ~ sP452(U_1930,U_1919,U_1929,U_1918) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_12,plain,
( sK431(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1918)
| U_1918 != sK430(U_1930,U_1929)
| ~ element(U_1918,powerset(the_carrier(U_1930)))
| ~ sP452(U_1930,U_1919,U_1929,U_1918) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_13,plain,
( sK432(U_1930,U_1929) = subset_complement(the_carrier(U_1930),U_1919)
| U_1919 != sK430(U_1930,U_1929)
| ~ element(U_1919,powerset(the_carrier(U_1930)))
| ~ sP452(U_1930,U_1919,U_1929,U_1918) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_14,plain,
( sK431(U_1930,U_1929) != sK432(U_1930,U_1929)
| ~ sP452(U_1930,U_1919,U_1929,U_1918) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_15,plain,
( in(sK433(U_1930,U_1929),complements_of_subsets(the_carrier(U_1930),U_1929))
| ~ sP453(U_1930,U_1929,U_1924) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_16,plain,
( element(sK434(U_1930,U_1929,U_1924),powerset(the_carrier(U_1930)))
| ~ sP453(U_1930,U_1929,U_1924) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_17,plain,
( sK434(U_1930,U_1929,U_1924) = sK433(U_1930,U_1929)
| ~ sP453(U_1930,U_1929,U_1924) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_18,plain,
( U_1924 != subset_complement(the_carrier(U_1930),sK434(U_1930,U_1929,U_1924))
| ~ sP453(U_1930,U_1929,U_1924) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_19,plain,
( relation(sK435(U_1930,U_1929))
| ~ sP454(U_1930,U_1926,U_1927,U_1929) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_20,plain,
( function(sK435(U_1930,U_1929))
| ~ sP454(U_1930,U_1926,U_1927,U_1929) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_21,plain,
( relation_dom(sK435(U_1930,U_1929)) = complements_of_subsets(the_carrier(U_1930),U_1929)
| ~ sP454(U_1930,U_1926,U_1927,U_1929) ),
inference(clausify,[status(thm)],[f_459_9]) ).
cnf(f_459_22,plain,
( apply(sK435(U_1930,U_1929),U_1927) = subset_complement(the_carrier(U_1930),U_1926)
| U_1926 != U_1927
| ~ element(U_1926,powerset(the_carrier(U_1930)))
| ~ in(U_1927,complements_of_subsets(the_carrier(U_1930),U_1929))
| ~ sP454(U_1930,U_1926,U_1927,U_1929) ),
inference(clausify,[status(thm)],[f_459_9]) ).
fof(f_460_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ! [I] :
( apply(C,D) = subset_complement(the_carrier(A),I)
| I != D
| ~ element(I,powerset(the_carrier(A))) )
| ~ in(D,B) )
& relation_dom(C) = B
& function(C)
& relation(C) )
| ? [C] :
( ! [D] :
? [H] :
( D != subset_complement(the_carrier(A),H)
& H = C
& element(H,powerset(the_carrier(A))) )
& in(C,B) )
| ? [C,D,E] :
( D != E
& ! [G] :
( E = subset_complement(the_carrier(A),G)
| G != C
| ~ element(G,powerset(the_carrier(A))) )
& ! [F] :
( D = subset_complement(the_carrier(A),F)
| F != C
| ~ element(F,powerset(the_carrier(A))) )
& in(C,B) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[s2_funct_1__e4_7_2__tops_2]) ).
fof(f_460_2,plain,
! [U_1943,U_1942] :
( ? [U_1941] :
( ! [U_1940] :
( ! [U_1939] :
( apply(U_1941,U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943))) )
| ~ in(U_1940,U_1942) )
& relation_dom(U_1941) = U_1942
& function(U_1941)
& relation(U_1941) )
| ? [U_1938] :
( ! [U_1937] :
? [U_1936] :
( U_1937 != subset_complement(the_carrier(U_1943),U_1936)
& U_1936 = U_1938
& element(U_1936,powerset(the_carrier(U_1943))) )
& in(U_1938,U_1942) )
| ? [U_1935,U_1934,U_1933] :
( U_1934 != U_1933
& ! [U_1932] :
( U_1933 = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != U_1935
| ~ element(U_1932,powerset(the_carrier(U_1943))) )
& ! [U_1931] :
( U_1934 = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != U_1935
| ~ element(U_1931,powerset(the_carrier(U_1943))) )
& in(U_1935,U_1942) )
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
! [U_1943,U_1942] :
( ? [U_1941] :
( ! [U_1940] :
( ! [U_1939] :
( apply(U_1941,U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943))) )
| ~ in(U_1940,U_1942) )
& relation_dom(U_1941) = U_1942
& function(U_1941)
& relation(U_1941) )
| ? [U_1938] :
( ! [U_1937] :
? [U_1936] :
( U_1937 != subset_complement(the_carrier(U_1943),U_1936)
& U_1936 = U_1938
& element(U_1936,powerset(the_carrier(U_1943))) )
& in(U_1938,U_1942) )
| ? [U_1934,U_1933] :
( U_1934 != U_1933
& ! [U_1932] :
( U_1933 = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943))) )
& ! [U_1931] :
( U_1934 = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943))) )
& in(sK436(U_1943,U_1942),U_1942) )
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_1935,sK436(U_1943,U_1942))],[f_460_2]) ).
fof(f_460_4,plain,
! [U_1943,U_1942] :
( ? [U_1941] :
( ! [U_1940] :
( ! [U_1939] :
( apply(U_1941,U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943))) )
| ~ in(U_1940,U_1942) )
& relation_dom(U_1941) = U_1942
& function(U_1941)
& relation(U_1941) )
| ? [U_1938] :
( ! [U_1937] :
? [U_1936] :
( U_1937 != subset_complement(the_carrier(U_1943),U_1936)
& U_1936 = U_1938
& element(U_1936,powerset(the_carrier(U_1943))) )
& in(U_1938,U_1942) )
| ? [U_1933] :
( sK437(U_1943,U_1942) != U_1933
& ! [U_1932] :
( U_1933 = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943))) )
& ! [U_1931] :
( sK437(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943))) )
& in(sK436(U_1943,U_1942),U_1942) )
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_1934,sK437(U_1943,U_1942))],[f_460_3]) ).
fof(f_460_5,plain,
! [U_1943,U_1942] :
( ? [U_1941] :
( ! [U_1940] :
( ! [U_1939] :
( apply(U_1941,U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943))) )
| ~ in(U_1940,U_1942) )
& relation_dom(U_1941) = U_1942
& function(U_1941)
& relation(U_1941) )
| ? [U_1938] :
( ! [U_1937] :
? [U_1936] :
( U_1937 != subset_complement(the_carrier(U_1943),U_1936)
& U_1936 = U_1938
& element(U_1936,powerset(the_carrier(U_1943))) )
& in(U_1938,U_1942) )
| ( sK437(U_1943,U_1942) != sK438(U_1943,U_1942)
& ! [U_1932] :
( sK438(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943))) )
& ! [U_1931] :
( sK437(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943))) )
& in(sK436(U_1943,U_1942),U_1942) )
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_1933,sK438(U_1943,U_1942))],[f_460_4]) ).
fof(f_460_6,plain,
! [U_1943,U_1942] :
( ? [U_1941] :
( ! [U_1940] :
( ! [U_1939] :
( apply(U_1941,U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943))) )
| ~ in(U_1940,U_1942) )
& relation_dom(U_1941) = U_1942
& function(U_1941)
& relation(U_1941) )
| ( ! [U_1937] :
? [U_1936] :
( U_1937 != subset_complement(the_carrier(U_1943),U_1936)
& U_1936 = sK439(U_1943,U_1942)
& element(U_1936,powerset(the_carrier(U_1943))) )
& in(sK439(U_1943,U_1942),U_1942) )
| ( sK437(U_1943,U_1942) != sK438(U_1943,U_1942)
& ! [U_1932] :
( sK438(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943))) )
& ! [U_1931] :
( sK437(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943))) )
& in(sK436(U_1943,U_1942),U_1942) )
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_1938,sK439(U_1943,U_1942))],[f_460_5]) ).
fof(f_460_7,plain,
! [U_1943,U_1942] :
( ? [U_1941] :
( ! [U_1940] :
( ! [U_1939] :
( apply(U_1941,U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943))) )
| ~ in(U_1940,U_1942) )
& relation_dom(U_1941) = U_1942
& function(U_1941)
& relation(U_1941) )
| ( ! [U_1937] :
( U_1937 != subset_complement(the_carrier(U_1943),sK440(U_1943,U_1942,U_1937))
& sK440(U_1943,U_1942,U_1937) = sK439(U_1943,U_1942)
& element(sK440(U_1943,U_1942,U_1937),powerset(the_carrier(U_1943))) )
& in(sK439(U_1943,U_1942),U_1942) )
| ( sK437(U_1943,U_1942) != sK438(U_1943,U_1942)
& ! [U_1932] :
( sK438(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943))) )
& ! [U_1931] :
( sK437(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943))) )
& in(sK436(U_1943,U_1942),U_1942) )
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_1936,sK440(U_1943,U_1942,U_1937))],[f_460_6]) ).
fof(f_460_8,plain,
! [U_1943,U_1942] :
( ( ! [U_1940] :
( ! [U_1939] :
( apply(sK441(U_1943,U_1942),U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943))) )
| ~ in(U_1940,U_1942) )
& relation_dom(sK441(U_1943,U_1942)) = U_1942
& function(sK441(U_1943,U_1942))
& relation(sK441(U_1943,U_1942)) )
| ( ! [U_1937] :
( U_1937 != subset_complement(the_carrier(U_1943),sK440(U_1943,U_1942,U_1937))
& sK440(U_1943,U_1942,U_1937) = sK439(U_1943,U_1942)
& element(sK440(U_1943,U_1942,U_1937),powerset(the_carrier(U_1943))) )
& in(sK439(U_1943,U_1942),U_1942) )
| ( sK437(U_1943,U_1942) != sK438(U_1943,U_1942)
& ! [U_1932] :
( sK438(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943))) )
& ! [U_1931] :
( sK437(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943))) )
& in(sK436(U_1943,U_1942),U_1942) )
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_1941,sK441(U_1943,U_1942))],[f_460_7]) ).
fof(f_460_9,plain,
( ! [U_1942,U_1940,U_1943,U_1939] :
( apply(sK441(U_1943,U_1942),U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943)))
| ~ in(U_1940,U_1942)
| ~ sP457(U_1942,U_1940,U_1943,U_1939) )
& ! [U_1942,U_1940,U_1943,U_1939] :
( relation_dom(sK441(U_1943,U_1942)) = U_1942
| ~ sP457(U_1942,U_1940,U_1943,U_1939) )
& ! [U_1942,U_1940,U_1943,U_1939] :
( function(sK441(U_1943,U_1942))
| ~ sP457(U_1942,U_1940,U_1943,U_1939) )
& ! [U_1942,U_1940,U_1943,U_1939] :
( relation(sK441(U_1943,U_1942))
| ~ sP457(U_1942,U_1940,U_1943,U_1939) )
& ! [U_1942,U_1943,U_1937] :
( U_1937 != subset_complement(the_carrier(U_1943),sK440(U_1943,U_1942,U_1937))
| ~ sP456(U_1942,U_1943,U_1937) )
& ! [U_1942,U_1943,U_1937] :
( sK440(U_1943,U_1942,U_1937) = sK439(U_1943,U_1942)
| ~ sP456(U_1942,U_1943,U_1937) )
& ! [U_1942,U_1943,U_1937] :
( element(sK440(U_1943,U_1942,U_1937),powerset(the_carrier(U_1943)))
| ~ sP456(U_1942,U_1943,U_1937) )
& ! [U_1942,U_1943,U_1937] :
( in(sK439(U_1943,U_1942),U_1942)
| ~ sP456(U_1942,U_1943,U_1937) )
& ! [U_1942,U_1943,U_1932,U_1931] :
( sK437(U_1943,U_1942) != sK438(U_1943,U_1942)
| ~ sP455(U_1942,U_1943,U_1932,U_1931) )
& ! [U_1942,U_1943,U_1932,U_1931] :
( sK438(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943)))
| ~ sP455(U_1942,U_1943,U_1932,U_1931) )
& ! [U_1942,U_1943,U_1932,U_1931] :
( sK437(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943)))
| ~ sP455(U_1942,U_1943,U_1932,U_1931) )
& ! [U_1942,U_1943,U_1932,U_1931] :
( in(sK436(U_1943,U_1942),U_1942)
| ~ sP455(U_1942,U_1943,U_1932,U_1931) )
& ! [U_1942,U_1940,U_1943,U_1937,U_1939,U_1932,U_1931] :
( sP457(U_1942,U_1940,U_1943,U_1939)
| sP456(U_1942,U_1943,U_1937)
| sP455(U_1942,U_1943,U_1932,U_1931)
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP455,sP456,sP457])],[f_460_8]) ).
cnf(f_460_10,plain,
( sP457(U_1942,U_1940,U_1943,U_1939)
| sP456(U_1942,U_1943,U_1937)
| sP455(U_1942,U_1943,U_1932,U_1931)
| ~ element(U_1942,powerset(powerset(the_carrier(U_1943))))
| ~ one_sorted_str(U_1943) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_11,plain,
( in(sK436(U_1943,U_1942),U_1942)
| ~ sP455(U_1942,U_1943,U_1932,U_1931) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_12,plain,
( sK437(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1931)
| U_1931 != sK436(U_1943,U_1942)
| ~ element(U_1931,powerset(the_carrier(U_1943)))
| ~ sP455(U_1942,U_1943,U_1932,U_1931) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_13,plain,
( sK438(U_1943,U_1942) = subset_complement(the_carrier(U_1943),U_1932)
| U_1932 != sK436(U_1943,U_1942)
| ~ element(U_1932,powerset(the_carrier(U_1943)))
| ~ sP455(U_1942,U_1943,U_1932,U_1931) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_14,plain,
( sK437(U_1943,U_1942) != sK438(U_1943,U_1942)
| ~ sP455(U_1942,U_1943,U_1932,U_1931) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_15,plain,
( in(sK439(U_1943,U_1942),U_1942)
| ~ sP456(U_1942,U_1943,U_1937) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_16,plain,
( element(sK440(U_1943,U_1942,U_1937),powerset(the_carrier(U_1943)))
| ~ sP456(U_1942,U_1943,U_1937) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_17,plain,
( sK440(U_1943,U_1942,U_1937) = sK439(U_1943,U_1942)
| ~ sP456(U_1942,U_1943,U_1937) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_18,plain,
( U_1937 != subset_complement(the_carrier(U_1943),sK440(U_1943,U_1942,U_1937))
| ~ sP456(U_1942,U_1943,U_1937) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_19,plain,
( relation(sK441(U_1943,U_1942))
| ~ sP457(U_1942,U_1940,U_1943,U_1939) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_20,plain,
( function(sK441(U_1943,U_1942))
| ~ sP457(U_1942,U_1940,U_1943,U_1939) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_21,plain,
( relation_dom(sK441(U_1943,U_1942)) = U_1942
| ~ sP457(U_1942,U_1940,U_1943,U_1939) ),
inference(clausify,[status(thm)],[f_460_9]) ).
cnf(f_460_22,plain,
( apply(sK441(U_1943,U_1942),U_1940) = subset_complement(the_carrier(U_1943),U_1939)
| U_1939 != U_1940
| ~ element(U_1939,powerset(the_carrier(U_1943)))
| ~ in(U_1940,U_1942)
| ~ sP457(U_1942,U_1940,U_1943,U_1939) ),
inference(clausify,[status(thm)],[f_460_9]) ).
fof(f_461_1,plain,
( ! [A] :
( ! [I] :
( ? [J] :
( ! [K] :
( K = J
| ~ subset(J,K)
| ~ in(K,I) )
& in(J,I) )
| I = empty_set
| ~ element(I,powerset(powerset(A))) )
| ~ in(A,omega)
| ~ ordinal(A) )
| ? [A] :
( ? [F] :
( ! [G] :
( ? [H] :
( H != G
& subset(G,H)
& in(H,F) )
| ~ in(G,F) )
& F != empty_set
& element(F,powerset(powerset(A))) )
& in(A,omega)
& ! [B] :
( ! [C] :
( ? [D] :
( ! [E] :
( E = D
| ~ subset(D,E)
| ~ in(E,C) )
& in(D,C) )
| C = empty_set
| ~ element(C,powerset(powerset(B))) )
| ~ in(B,omega)
| ~ in(B,A)
| ~ ordinal(B) )
& ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[s2_ordinal1__e18_27__finset_1__1]) ).
fof(f_461_2,plain,
( ! [U_1955] :
( ! [U_1954] :
( ? [U_1953] :
( ! [U_1952] :
( U_1952 = U_1953
| ~ subset(U_1953,U_1952)
| ~ in(U_1952,U_1954) )
& in(U_1953,U_1954) )
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955))) )
| ~ in(U_1955,omega)
| ~ ordinal(U_1955) )
| ? [U_1951] :
( ? [U_1950] :
( ! [U_1949] :
( ? [U_1948] :
( U_1948 != U_1949
& subset(U_1949,U_1948)
& in(U_1948,U_1950) )
| ~ in(U_1949,U_1950) )
& U_1950 != empty_set
& element(U_1950,powerset(powerset(U_1951))) )
& in(U_1951,omega)
& ! [U_1947] :
( ! [U_1946] :
( ? [U_1945] :
( ! [U_1944] :
( U_1944 = U_1945
| ~ subset(U_1945,U_1944)
| ~ in(U_1944,U_1946) )
& in(U_1945,U_1946) )
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947))) )
| ~ in(U_1947,omega)
| ~ in(U_1947,U_1951)
| ~ ordinal(U_1947) )
& ordinal(U_1951) ) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
( ! [U_1955] :
( ! [U_1954] :
( ? [U_1953] :
( ! [U_1952] :
( U_1952 = U_1953
| ~ subset(U_1953,U_1952)
| ~ in(U_1952,U_1954) )
& in(U_1953,U_1954) )
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955))) )
| ~ in(U_1955,omega)
| ~ ordinal(U_1955) )
| ( ? [U_1950] :
( ! [U_1949] :
( ? [U_1948] :
( U_1948 != U_1949
& subset(U_1949,U_1948)
& in(U_1948,U_1950) )
| ~ in(U_1949,U_1950) )
& U_1950 != empty_set
& element(U_1950,powerset(powerset(sK442))) )
& in(sK442,omega)
& ! [U_1947] :
( ! [U_1946] :
( ? [U_1945] :
( ! [U_1944] :
( U_1944 = U_1945
| ~ subset(U_1945,U_1944)
| ~ in(U_1944,U_1946) )
& in(U_1945,U_1946) )
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947))) )
| ~ in(U_1947,omega)
| ~ in(U_1947,sK442)
| ~ ordinal(U_1947) )
& ordinal(sK442) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_1951,sK442)],[f_461_2]) ).
fof(f_461_4,plain,
( ! [U_1955] :
( ! [U_1954] :
( ? [U_1953] :
( ! [U_1952] :
( U_1952 = U_1953
| ~ subset(U_1953,U_1952)
| ~ in(U_1952,U_1954) )
& in(U_1953,U_1954) )
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955))) )
| ~ in(U_1955,omega)
| ~ ordinal(U_1955) )
| ( ? [U_1950] :
( ! [U_1949] :
( ? [U_1948] :
( U_1948 != U_1949
& subset(U_1949,U_1948)
& in(U_1948,U_1950) )
| ~ in(U_1949,U_1950) )
& U_1950 != empty_set
& element(U_1950,powerset(powerset(sK442))) )
& in(sK442,omega)
& ! [U_1947] :
( ! [U_1946] :
( ( ! [U_1944] :
( U_1944 = sK443(U_1947,U_1946)
| ~ subset(sK443(U_1947,U_1946),U_1944)
| ~ in(U_1944,U_1946) )
& in(sK443(U_1947,U_1946),U_1946) )
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947))) )
| ~ in(U_1947,omega)
| ~ in(U_1947,sK442)
| ~ ordinal(U_1947) )
& ordinal(sK442) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_1945,sK443(U_1947,U_1946))],[f_461_3]) ).
fof(f_461_5,plain,
( ! [U_1955] :
( ! [U_1954] :
( ? [U_1953] :
( ! [U_1952] :
( U_1952 = U_1953
| ~ subset(U_1953,U_1952)
| ~ in(U_1952,U_1954) )
& in(U_1953,U_1954) )
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955))) )
| ~ in(U_1955,omega)
| ~ ordinal(U_1955) )
| ( ! [U_1949] :
( ? [U_1948] :
( U_1948 != U_1949
& subset(U_1949,U_1948)
& in(U_1948,sK444) )
| ~ in(U_1949,sK444) )
& sK444 != empty_set
& element(sK444,powerset(powerset(sK442)))
& in(sK442,omega)
& ! [U_1947] :
( ! [U_1946] :
( ( ! [U_1944] :
( U_1944 = sK443(U_1947,U_1946)
| ~ subset(sK443(U_1947,U_1946),U_1944)
| ~ in(U_1944,U_1946) )
& in(sK443(U_1947,U_1946),U_1946) )
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947))) )
| ~ in(U_1947,omega)
| ~ in(U_1947,sK442)
| ~ ordinal(U_1947) )
& ordinal(sK442) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_1950,sK444)],[f_461_4]) ).
fof(f_461_6,plain,
( ! [U_1955] :
( ! [U_1954] :
( ? [U_1953] :
( ! [U_1952] :
( U_1952 = U_1953
| ~ subset(U_1953,U_1952)
| ~ in(U_1952,U_1954) )
& in(U_1953,U_1954) )
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955))) )
| ~ in(U_1955,omega)
| ~ ordinal(U_1955) )
| ( ! [U_1949] :
( ( sK445(U_1949) != U_1949
& subset(U_1949,sK445(U_1949))
& in(sK445(U_1949),sK444) )
| ~ in(U_1949,sK444) )
& sK444 != empty_set
& element(sK444,powerset(powerset(sK442)))
& in(sK442,omega)
& ! [U_1947] :
( ! [U_1946] :
( ( ! [U_1944] :
( U_1944 = sK443(U_1947,U_1946)
| ~ subset(sK443(U_1947,U_1946),U_1944)
| ~ in(U_1944,U_1946) )
& in(sK443(U_1947,U_1946),U_1946) )
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947))) )
| ~ in(U_1947,omega)
| ~ in(U_1947,sK442)
| ~ ordinal(U_1947) )
& ordinal(sK442) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_1948,sK445(U_1949))],[f_461_5]) ).
fof(f_461_7,plain,
( ! [U_1955] :
( ! [U_1954] :
( ( ! [U_1952] :
( U_1952 = sK446(U_1955,U_1954)
| ~ subset(sK446(U_1955,U_1954),U_1952)
| ~ in(U_1952,U_1954) )
& in(sK446(U_1955,U_1954),U_1954) )
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955))) )
| ~ in(U_1955,omega)
| ~ ordinal(U_1955) )
| ( ! [U_1949] :
( ( sK445(U_1949) != U_1949
& subset(U_1949,sK445(U_1949))
& in(sK445(U_1949),sK444) )
| ~ in(U_1949,sK444) )
& sK444 != empty_set
& element(sK444,powerset(powerset(sK442)))
& in(sK442,omega)
& ! [U_1947] :
( ! [U_1946] :
( ( ! [U_1944] :
( U_1944 = sK443(U_1947,U_1946)
| ~ subset(sK443(U_1947,U_1946),U_1944)
| ~ in(U_1944,U_1946) )
& in(sK443(U_1947,U_1946),U_1946) )
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947))) )
| ~ in(U_1947,omega)
| ~ in(U_1947,sK442)
| ~ ordinal(U_1947) )
& ordinal(sK442) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK446]),skolemize(U_1953,sK446(U_1955,U_1954))],[f_461_6]) ).
fof(f_461_8,plain,
( ! [U_1952,U_1955,U_1954] :
( U_1952 = sK446(U_1955,U_1954)
| ~ subset(sK446(U_1955,U_1954),U_1952)
| ~ in(U_1952,U_1954)
| ~ sP461(U_1952,U_1955,U_1954) )
& ! [U_1952,U_1955,U_1954] :
( in(sK446(U_1955,U_1954),U_1954)
| ~ sP461(U_1952,U_1955,U_1954) )
& ! [U_1949] :
( sK445(U_1949) != U_1949
| ~ sP459(U_1949) )
& ! [U_1949] :
( subset(U_1949,sK445(U_1949))
| ~ sP459(U_1949) )
& ! [U_1949] :
( in(sK445(U_1949),sK444)
| ~ sP459(U_1949) )
& ! [U_1947,U_1944,U_1946] :
( U_1944 = sK443(U_1947,U_1946)
| ~ subset(sK443(U_1947,U_1946),U_1944)
| ~ in(U_1944,U_1946)
| ~ sP458(U_1947,U_1944,U_1946) )
& ! [U_1947,U_1944,U_1946] :
( in(sK443(U_1947,U_1946),U_1946)
| ~ sP458(U_1947,U_1944,U_1946) )
& ! [U_1949,U_1947,U_1944,U_1946] :
( sP459(U_1949)
| ~ in(U_1949,sK444)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) )
& ! [U_1949,U_1947,U_1944,U_1946] :
( sK444 != empty_set
| ~ sP460(U_1949,U_1947,U_1944,U_1946) )
& ! [U_1949,U_1947,U_1944,U_1946] :
( element(sK444,powerset(powerset(sK442)))
| ~ sP460(U_1949,U_1947,U_1944,U_1946) )
& ! [U_1949,U_1947,U_1944,U_1946] :
( in(sK442,omega)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) )
& ! [U_1949,U_1947,U_1944,U_1946] :
( sP458(U_1947,U_1944,U_1946)
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947)))
| ~ in(U_1947,omega)
| ~ in(U_1947,sK442)
| ~ ordinal(U_1947)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) )
& ! [U_1949,U_1947,U_1944,U_1946] :
( ordinal(sK442)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) )
& ! [U_1949,U_1952,U_1947,U_1955,U_1944,U_1946,U_1954] :
( sP461(U_1952,U_1955,U_1954)
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955)))
| ~ in(U_1955,omega)
| ~ ordinal(U_1955)
| sP460(U_1949,U_1947,U_1944,U_1946) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP458,sP459,sP460,sP461])],[f_461_7]) ).
cnf(f_461_9,plain,
( sP461(U_1952,U_1955,U_1954)
| U_1954 = empty_set
| ~ element(U_1954,powerset(powerset(U_1955)))
| ~ in(U_1955,omega)
| ~ ordinal(U_1955)
| sP460(U_1949,U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_10,plain,
( ordinal(sK442)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_11,plain,
( sP458(U_1947,U_1944,U_1946)
| U_1946 = empty_set
| ~ element(U_1946,powerset(powerset(U_1947)))
| ~ in(U_1947,omega)
| ~ in(U_1947,sK442)
| ~ ordinal(U_1947)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_12,plain,
( in(sK442,omega)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_13,plain,
( element(sK444,powerset(powerset(sK442)))
| ~ sP460(U_1949,U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_14,plain,
( sK444 != empty_set
| ~ sP460(U_1949,U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_15,plain,
( sP459(U_1949)
| ~ in(U_1949,sK444)
| ~ sP460(U_1949,U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_16,plain,
( in(sK443(U_1947,U_1946),U_1946)
| ~ sP458(U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_17,plain,
( U_1944 = sK443(U_1947,U_1946)
| ~ subset(sK443(U_1947,U_1946),U_1944)
| ~ in(U_1944,U_1946)
| ~ sP458(U_1947,U_1944,U_1946) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_18,plain,
( in(sK445(U_1949),sK444)
| ~ sP459(U_1949) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_19,plain,
( subset(U_1949,sK445(U_1949))
| ~ sP459(U_1949) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_20,plain,
( sK445(U_1949) != U_1949
| ~ sP459(U_1949) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_21,plain,
( in(sK446(U_1955,U_1954),U_1954)
| ~ sP461(U_1952,U_1955,U_1954) ),
inference(clausify,[status(thm)],[f_461_8]) ).
cnf(f_461_22,plain,
( U_1952 = sK446(U_1955,U_1954)
| ~ subset(sK446(U_1955,U_1954),U_1952)
| ~ in(U_1952,U_1954)
| ~ sP461(U_1952,U_1955,U_1954) ),
inference(clausify,[status(thm)],[f_461_8]) ).
fof(f_462_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_462_2,plain,
! [U_1958] :
? [U_1957] :
( ! [U_1956] :
( apply(U_1957,U_1956) = singleton(U_1956)
| ~ in(U_1956,U_1958) )
& relation_dom(U_1957) = U_1958
& function(U_1957)
& relation(U_1957) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_1958] :
( ! [U_1956] :
( apply(sK447(U_1958),U_1956) = singleton(U_1956)
| ~ in(U_1956,U_1958) )
& relation_dom(sK447(U_1958)) = U_1958
& function(sK447(U_1958))
& relation(sK447(U_1958)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_1957,sK447(U_1958))],[f_462_2]) ).
fof(f_462_4,plain,
( ! [U_1958,U_1956] :
( apply(sK447(U_1958),U_1956) = singleton(U_1956)
| ~ in(U_1956,U_1958) )
& ! [U_1958] : relation_dom(sK447(U_1958)) = U_1958
& ! [U_1958] : function(sK447(U_1958))
& ! [U_1958] : relation(sK447(U_1958)) ),
inference(definitional_conversion,[status(esa)],[f_462_3]) ).
cnf(f_462_5,plain,
relation(sK447(U_1958)),
inference(clausify,[status(thm)],[f_462_4]) ).
cnf(f_462_6,plain,
function(sK447(U_1958)),
inference(clausify,[status(thm)],[f_462_4]) ).
cnf(f_462_7,plain,
relation_dom(sK447(U_1958)) = U_1958,
inference(clausify,[status(thm)],[f_462_4]) ).
cnf(f_462_8,plain,
( apply(sK447(U_1958),U_1956) = singleton(U_1956)
| ~ in(U_1956,U_1958) ),
inference(clausify,[status(thm)],[f_462_4]) ).
fof(f_463_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ( ( in(D,C)
| ! [E] :
( ~ subset(B,D)
| ~ closed_subset(E,A)
| E != D
| ~ element(E,powerset(the_carrier(A))) ) )
& ( ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ~ element(D,powerset(the_carrier(A))) )
& element(C,powerset(powerset(the_carrier(A)))) )
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s3_subset_1__e1_40__pre_topc]) ).
fof(f_463_2,plain,
! [U_1964,U_1963] :
( ? [U_1962] :
( ! [U_1961] :
( ( ( in(U_1961,U_1962)
| ! [U_1960] :
( ~ subset(U_1963,U_1961)
| ~ closed_subset(U_1960,U_1964)
| U_1960 != U_1961
| ~ element(U_1960,powerset(the_carrier(U_1964))) ) )
& ( ? [U_1959] :
( subset(U_1963,U_1961)
& closed_subset(U_1959,U_1964)
& U_1959 = U_1961
& element(U_1959,powerset(the_carrier(U_1964))) )
| ~ in(U_1961,U_1962) ) )
| ~ element(U_1961,powerset(the_carrier(U_1964))) )
& element(U_1962,powerset(powerset(the_carrier(U_1964)))) )
| ~ element(U_1963,powerset(the_carrier(U_1964)))
| ~ top_str(U_1964)
| ~ topological_space(U_1964) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
! [U_1964,U_1963] :
( ? [U_1962] :
( ! [U_1961] :
( ( ( in(U_1961,U_1962)
| ! [U_1960] :
( ~ closed_subset(U_1960,U_1964)
| U_1960 != U_1961
| ~ element(U_1960,powerset(the_carrier(U_1964))) )
| ~ subset(U_1963,U_1961) )
& ( ( ? [U_1959] :
( closed_subset(U_1959,U_1964)
& U_1959 = U_1961
& element(U_1959,powerset(the_carrier(U_1964))) )
& subset(U_1963,U_1961) )
| ~ in(U_1961,U_1962) ) )
| ~ element(U_1961,powerset(the_carrier(U_1964))) )
& element(U_1962,powerset(powerset(the_carrier(U_1964)))) )
| ~ element(U_1963,powerset(the_carrier(U_1964)))
| ~ top_str(U_1964)
| ~ topological_space(U_1964) ),
inference(miniscope,[status(thm)],[f_463_2]) ).
fof(f_463_4,plain,
! [U_1964,U_1963] :
( ( ! [U_1961] :
( ( ( in(U_1961,sK448(U_1964,U_1963))
| ! [U_1960] :
( ~ closed_subset(U_1960,U_1964)
| U_1960 != U_1961
| ~ element(U_1960,powerset(the_carrier(U_1964))) )
| ~ subset(U_1963,U_1961) )
& ( ( ? [U_1959] :
( closed_subset(U_1959,U_1964)
& U_1959 = U_1961
& element(U_1959,powerset(the_carrier(U_1964))) )
& subset(U_1963,U_1961) )
| ~ in(U_1961,sK448(U_1964,U_1963)) ) )
| ~ element(U_1961,powerset(the_carrier(U_1964))) )
& element(sK448(U_1964,U_1963),powerset(powerset(the_carrier(U_1964)))) )
| ~ element(U_1963,powerset(the_carrier(U_1964)))
| ~ top_str(U_1964)
| ~ topological_space(U_1964) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_1962,sK448(U_1964,U_1963))],[f_463_3]) ).
fof(f_463_5,plain,
! [U_1964,U_1963] :
( ( ! [U_1961] :
( ( ( in(U_1961,sK448(U_1964,U_1963))
| ! [U_1960] :
( ~ closed_subset(U_1960,U_1964)
| U_1960 != U_1961
| ~ element(U_1960,powerset(the_carrier(U_1964))) )
| ~ subset(U_1963,U_1961) )
& ( ( closed_subset(sK449(U_1964,U_1963,U_1961),U_1964)
& sK449(U_1964,U_1963,U_1961) = U_1961
& element(sK449(U_1964,U_1963,U_1961),powerset(the_carrier(U_1964)))
& subset(U_1963,U_1961) )
| ~ in(U_1961,sK448(U_1964,U_1963)) ) )
| ~ element(U_1961,powerset(the_carrier(U_1964))) )
& element(sK448(U_1964,U_1963),powerset(powerset(the_carrier(U_1964)))) )
| ~ element(U_1963,powerset(the_carrier(U_1964)))
| ~ top_str(U_1964)
| ~ topological_space(U_1964) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_1959,sK449(U_1964,U_1963,U_1961))],[f_463_4]) ).
fof(f_463_6,plain,
( ! [U_1961,U_1963,U_1964] :
( closed_subset(sK449(U_1964,U_1963,U_1961),U_1964)
| ~ sP462(U_1961,U_1963,U_1964) )
& ! [U_1961,U_1963,U_1964] :
( sK449(U_1964,U_1963,U_1961) = U_1961
| ~ sP462(U_1961,U_1963,U_1964) )
& ! [U_1961,U_1963,U_1964] :
( element(sK449(U_1964,U_1963,U_1961),powerset(the_carrier(U_1964)))
| ~ sP462(U_1961,U_1963,U_1964) )
& ! [U_1961,U_1963,U_1964] :
( subset(U_1963,U_1961)
| ~ sP462(U_1961,U_1963,U_1964) )
& ! [U_1961,U_1960,U_1963,U_1964] :
( in(U_1961,sK448(U_1964,U_1963))
| ~ closed_subset(U_1960,U_1964)
| U_1960 != U_1961
| ~ element(U_1960,powerset(the_carrier(U_1964)))
| ~ subset(U_1963,U_1961)
| ~ sP463(U_1961,U_1960,U_1963,U_1964) )
& ! [U_1961,U_1960,U_1963,U_1964] :
( sP462(U_1961,U_1963,U_1964)
| ~ in(U_1961,sK448(U_1964,U_1963))
| ~ sP463(U_1961,U_1960,U_1963,U_1964) )
& ! [U_1961,U_1960,U_1963,U_1964] :
( sP463(U_1961,U_1960,U_1963,U_1964)
| ~ element(U_1961,powerset(the_carrier(U_1964)))
| ~ sP464(U_1961,U_1960,U_1963,U_1964) )
& ! [U_1961,U_1960,U_1963,U_1964] :
( element(sK448(U_1964,U_1963),powerset(powerset(the_carrier(U_1964))))
| ~ sP464(U_1961,U_1960,U_1963,U_1964) )
& ! [U_1961,U_1960,U_1963,U_1964] :
( sP464(U_1961,U_1960,U_1963,U_1964)
| ~ element(U_1963,powerset(the_carrier(U_1964)))
| ~ top_str(U_1964)
| ~ topological_space(U_1964) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP462,sP463,sP464])],[f_463_5]) ).
cnf(f_463_7,plain,
( sP464(U_1961,U_1960,U_1963,U_1964)
| ~ element(U_1963,powerset(the_carrier(U_1964)))
| ~ top_str(U_1964)
| ~ topological_space(U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_8,plain,
( element(sK448(U_1964,U_1963),powerset(powerset(the_carrier(U_1964))))
| ~ sP464(U_1961,U_1960,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_9,plain,
( sP463(U_1961,U_1960,U_1963,U_1964)
| ~ element(U_1961,powerset(the_carrier(U_1964)))
| ~ sP464(U_1961,U_1960,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_10,plain,
( sP462(U_1961,U_1963,U_1964)
| ~ in(U_1961,sK448(U_1964,U_1963))
| ~ sP463(U_1961,U_1960,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_11,plain,
( in(U_1961,sK448(U_1964,U_1963))
| ~ closed_subset(U_1960,U_1964)
| U_1960 != U_1961
| ~ element(U_1960,powerset(the_carrier(U_1964)))
| ~ subset(U_1963,U_1961)
| ~ sP463(U_1961,U_1960,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_12,plain,
( subset(U_1963,U_1961)
| ~ sP462(U_1961,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_13,plain,
( element(sK449(U_1964,U_1963,U_1961),powerset(the_carrier(U_1964)))
| ~ sP462(U_1961,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_14,plain,
( sK449(U_1964,U_1963,U_1961) = U_1961
| ~ sP462(U_1961,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
cnf(f_463_15,plain,
( closed_subset(sK449(U_1964,U_1963,U_1961),U_1964)
| ~ sP462(U_1961,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_463_6]) ).
fof(f_464_1,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ( ( in(D,C)
| ~ in(set_difference(cast_as_carrier_subset(A),D),B) )
& ( in(set_difference(cast_as_carrier_subset(A),D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(the_carrier(A))) )
& element(C,powerset(powerset(the_carrier(A)))) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s3_subset_1__e2_37_1_1__pre_topc]) ).
fof(f_464_2,plain,
! [U_1968,U_1967] :
( ? [U_1966] :
( ! [U_1965] :
( ( ( in(U_1965,U_1966)
| ~ in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967) )
& ( in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967)
| ~ in(U_1965,U_1966) ) )
| ~ element(U_1965,powerset(the_carrier(U_1968))) )
& element(U_1966,powerset(powerset(the_carrier(U_1968)))) )
| ~ element(U_1967,powerset(powerset(the_carrier(U_1968))))
| ~ top_str(U_1968)
| ~ topological_space(U_1968) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
! [U_1968,U_1967] :
( ( ! [U_1965] :
( ( ( in(U_1965,sK450(U_1968,U_1967))
| ~ in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967) )
& ( in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967)
| ~ in(U_1965,sK450(U_1968,U_1967)) ) )
| ~ element(U_1965,powerset(the_carrier(U_1968))) )
& element(sK450(U_1968,U_1967),powerset(powerset(the_carrier(U_1968)))) )
| ~ element(U_1967,powerset(powerset(the_carrier(U_1968))))
| ~ top_str(U_1968)
| ~ topological_space(U_1968) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_1966,sK450(U_1968,U_1967))],[f_464_2]) ).
fof(f_464_4,plain,
( ! [U_1967,U_1965,U_1968] :
( in(U_1965,sK450(U_1968,U_1967))
| ~ in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967)
| ~ sP465(U_1967,U_1965,U_1968) )
& ! [U_1967,U_1965,U_1968] :
( in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967)
| ~ in(U_1965,sK450(U_1968,U_1967))
| ~ sP465(U_1967,U_1965,U_1968) )
& ! [U_1967,U_1965,U_1968] :
( sP465(U_1967,U_1965,U_1968)
| ~ element(U_1965,powerset(the_carrier(U_1968)))
| ~ sP466(U_1967,U_1965,U_1968) )
& ! [U_1967,U_1965,U_1968] :
( element(sK450(U_1968,U_1967),powerset(powerset(the_carrier(U_1968))))
| ~ sP466(U_1967,U_1965,U_1968) )
& ! [U_1967,U_1965,U_1968] :
( sP466(U_1967,U_1965,U_1968)
| ~ element(U_1967,powerset(powerset(the_carrier(U_1968))))
| ~ top_str(U_1968)
| ~ topological_space(U_1968) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP465,sP466])],[f_464_3]) ).
cnf(f_464_5,plain,
( sP466(U_1967,U_1965,U_1968)
| ~ element(U_1967,powerset(powerset(the_carrier(U_1968))))
| ~ top_str(U_1968)
| ~ topological_space(U_1968) ),
inference(clausify,[status(thm)],[f_464_4]) ).
cnf(f_464_6,plain,
( element(sK450(U_1968,U_1967),powerset(powerset(the_carrier(U_1968))))
| ~ sP466(U_1967,U_1965,U_1968) ),
inference(clausify,[status(thm)],[f_464_4]) ).
cnf(f_464_7,plain,
( sP465(U_1967,U_1965,U_1968)
| ~ element(U_1965,powerset(the_carrier(U_1968)))
| ~ sP466(U_1967,U_1965,U_1968) ),
inference(clausify,[status(thm)],[f_464_4]) ).
cnf(f_464_8,plain,
( in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967)
| ~ in(U_1965,sK450(U_1968,U_1967))
| ~ sP465(U_1967,U_1965,U_1968) ),
inference(clausify,[status(thm)],[f_464_4]) ).
cnf(f_464_9,plain,
( in(U_1965,sK450(U_1968,U_1967))
| ~ in(set_difference(cast_as_carrier_subset(U_1968),U_1965),U_1967)
| ~ sP465(U_1967,U_1965,U_1968) ),
inference(clausify,[status(thm)],[f_464_4]) ).
fof(f_465_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_465_2,plain,
! [U_1970,U_1969] :
( disjoint(U_1969,U_1970)
| ~ disjoint(U_1970,U_1969) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
! [U_1970,U_1969] :
( disjoint(U_1969,U_1970)
| ~ disjoint(U_1970,U_1969) ),
inference(definitional_conversion,[status(esa)],[f_465_2]) ).
cnf(f_465_4,plain,
( disjoint(U_1969,U_1970)
| ~ disjoint(U_1970,U_1969) ),
inference(clausify,[status(thm)],[f_465_3]) ).
fof(f_466_1,plain,
! [A,B] :
( equipotent(B,A)
| ~ equipotent(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r2_wellord2]) ).
fof(f_466_2,plain,
! [U_1972,U_1971] :
( equipotent(U_1971,U_1972)
| ~ equipotent(U_1972,U_1971) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
! [U_1972,U_1971] :
( equipotent(U_1971,U_1972)
| ~ equipotent(U_1972,U_1971) ),
inference(definitional_conversion,[status(esa)],[f_466_2]) ).
cnf(f_466_4,plain,
( equipotent(U_1971,U_1972)
| ~ equipotent(U_1972,U_1971) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_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_467_2,plain,
! [U_1976,U_1975,U_1974,U_1973] :
( ( in(ordered_pair(U_1976,U_1975),cartesian_product2(U_1974,U_1973))
| ~ in(U_1975,U_1973)
| ~ in(U_1976,U_1974) )
& ( ( in(U_1975,U_1973)
& in(U_1976,U_1974) )
| ~ in(ordered_pair(U_1976,U_1975),cartesian_product2(U_1974,U_1973)) ) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
( ! [U_1984,U_1982,U_1980,U_1978] :
( in(ordered_pair(U_1984,U_1982),cartesian_product2(U_1980,U_1978))
| ~ in(U_1982,U_1978)
| ~ in(U_1984,U_1980) )
& ! [U_1983,U_1981,U_1979,U_1977] :
( ( in(U_1981,U_1977)
& in(U_1983,U_1979) )
| ~ in(ordered_pair(U_1983,U_1981),cartesian_product2(U_1979,U_1977)) ) ),
inference(miniscope,[status(thm)],[f_467_2]) ).
fof(f_467_4,plain,
( ! [U_1977,U_1983,U_1981,U_1979] :
( in(U_1981,U_1977)
| ~ sP467(U_1977,U_1983,U_1981,U_1979) )
& ! [U_1977,U_1983,U_1981,U_1979] :
( in(U_1983,U_1979)
| ~ sP467(U_1977,U_1983,U_1981,U_1979) )
& ! [U_1978,U_1982,U_1980,U_1984] :
( in(ordered_pair(U_1984,U_1982),cartesian_product2(U_1980,U_1978))
| ~ in(U_1982,U_1978)
| ~ in(U_1984,U_1980) )
& ! [U_1977,U_1983,U_1981,U_1979] :
( sP467(U_1977,U_1983,U_1981,U_1979)
| ~ in(ordered_pair(U_1983,U_1981),cartesian_product2(U_1979,U_1977)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP467])],[f_467_3]) ).
cnf(f_467_5,plain,
( sP467(U_1977,U_1983,U_1981,U_1979)
| ~ in(ordered_pair(U_1983,U_1981),cartesian_product2(U_1979,U_1977)) ),
inference(clausify,[status(thm)],[f_467_4]) ).
cnf(f_467_6,plain,
( in(ordered_pair(U_1984,U_1982),cartesian_product2(U_1980,U_1978))
| ~ in(U_1982,U_1978)
| ~ in(U_1984,U_1980) ),
inference(clausify,[status(thm)],[f_467_4]) ).
cnf(f_467_7,plain,
( in(U_1983,U_1979)
| ~ sP467(U_1977,U_1983,U_1981,U_1979) ),
inference(clausify,[status(thm)],[f_467_4]) ).
cnf(f_467_8,plain,
( in(U_1981,U_1977)
| ~ sP467(U_1977,U_1983,U_1981,U_1979) ),
inference(clausify,[status(thm)],[f_467_4]) ).
fof(f_468_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_468_2,plain,
! [U_1985] : in(U_1985,succ(U_1985)),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
! [U_1985] : in(U_1985,succ(U_1985)),
inference(definitional_conversion,[status(esa)],[f_468_2]) ).
cnf(f_468_4,plain,
in(U_1985,succ(U_1985)),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_1,plain,
! [A,B] :
( ( ( B != empty_set
| complements_of_subsets(A,B) = empty_set )
& ( complements_of_subsets(A,B) != empty_set
| B = empty_set ) )
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t10_tops_2]) ).
fof(f_469_2,plain,
! [U_1987,U_1986] :
( ( ( U_1986 != empty_set
| complements_of_subsets(U_1987,U_1986) = empty_set )
& ( complements_of_subsets(U_1987,U_1986) != empty_set
| U_1986 = empty_set ) )
| ~ element(U_1986,powerset(powerset(U_1987))) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
( ! [U_1986,U_1987] :
( U_1986 != empty_set
| complements_of_subsets(U_1987,U_1986) = empty_set
| ~ sP468(U_1986,U_1987) )
& ! [U_1986,U_1987] :
( complements_of_subsets(U_1987,U_1986) != empty_set
| U_1986 = empty_set
| ~ sP468(U_1986,U_1987) )
& ! [U_1986,U_1987] :
( sP468(U_1986,U_1987)
| ~ element(U_1986,powerset(powerset(U_1987))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP468])],[f_469_2]) ).
cnf(f_469_4,plain,
( sP468(U_1986,U_1987)
| ~ element(U_1986,powerset(powerset(U_1987))) ),
inference(clausify,[status(thm)],[f_469_3]) ).
cnf(f_469_5,plain,
( complements_of_subsets(U_1987,U_1986) != empty_set
| U_1986 = empty_set
| ~ sP468(U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_469_3]) ).
cnf(f_469_6,plain,
( U_1986 != empty_set
| complements_of_subsets(U_1987,U_1986) = empty_set
| ~ sP468(U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_469_3]) ).
fof(f_470_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_470_2,plain,
! [U_1991,U_1990,U_1989,U_1988] :
( U_1991 = U_1988
| U_1991 = U_1989
| unordered_pair(U_1991,U_1990) != unordered_pair(U_1989,U_1988) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
! [U_1991,U_1990,U_1989] :
( ! [U_1988] :
( U_1991 = U_1988
| unordered_pair(U_1991,U_1990) != unordered_pair(U_1989,U_1988) )
| U_1991 = U_1989 ),
inference(miniscope,[status(thm)],[f_470_2]) ).
fof(f_470_4,plain,
! [U_1990,U_1988,U_1991,U_1989] :
( U_1991 = U_1988
| unordered_pair(U_1991,U_1990) != unordered_pair(U_1989,U_1988)
| U_1991 = U_1989 ),
inference(definitional_conversion,[status(esa)],[f_470_3]) ).
cnf(f_470_5,plain,
( U_1991 = U_1988
| unordered_pair(U_1991,U_1990) != unordered_pair(U_1989,U_1988)
| U_1991 = U_1989 ),
inference(clausify,[status(thm)],[f_470_4]) ).
fof(f_471_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_471_2,plain,
! [U_1994,U_1993,U_1992] :
( ( ( in(U_1994,relation_rng(relation_rng_restriction(U_1993,U_1992)))
| ~ in(U_1994,relation_rng(U_1992))
| ~ in(U_1994,U_1993) )
& ( ( in(U_1994,relation_rng(U_1992))
& in(U_1994,U_1993) )
| ~ in(U_1994,relation_rng(relation_rng_restriction(U_1993,U_1992))) ) )
| ~ relation(U_1992) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
( ! [U_1992,U_1993,U_1994] :
( in(U_1994,relation_rng(U_1992))
| ~ sP469(U_1992,U_1993,U_1994) )
& ! [U_1992,U_1993,U_1994] :
( in(U_1994,U_1993)
| ~ sP469(U_1992,U_1993,U_1994) )
& ! [U_1992,U_1993,U_1994] :
( in(U_1994,relation_rng(relation_rng_restriction(U_1993,U_1992)))
| ~ in(U_1994,relation_rng(U_1992))
| ~ in(U_1994,U_1993)
| ~ sP470(U_1992,U_1993,U_1994) )
& ! [U_1992,U_1993,U_1994] :
( sP469(U_1992,U_1993,U_1994)
| ~ in(U_1994,relation_rng(relation_rng_restriction(U_1993,U_1992)))
| ~ sP470(U_1992,U_1993,U_1994) )
& ! [U_1992,U_1993,U_1994] :
( sP470(U_1992,U_1993,U_1994)
| ~ relation(U_1992) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP469,sP470])],[f_471_2]) ).
cnf(f_471_4,plain,
( sP470(U_1992,U_1993,U_1994)
| ~ relation(U_1992) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_5,plain,
( sP469(U_1992,U_1993,U_1994)
| ~ in(U_1994,relation_rng(relation_rng_restriction(U_1993,U_1992)))
| ~ sP470(U_1992,U_1993,U_1994) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_6,plain,
( in(U_1994,relation_rng(relation_rng_restriction(U_1993,U_1992)))
| ~ in(U_1994,relation_rng(U_1992))
| ~ in(U_1994,U_1993)
| ~ sP470(U_1992,U_1993,U_1994) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_7,plain,
( in(U_1994,U_1993)
| ~ sP469(U_1992,U_1993,U_1994) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_8,plain,
( in(U_1994,relation_rng(U_1992))
| ~ sP469(U_1992,U_1993,U_1994) ),
inference(clausify,[status(thm)],[f_471_3]) ).
fof(f_472_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_472_2,plain,
! [U_1996,U_1995] :
( subset(relation_rng(relation_rng_restriction(U_1996,U_1995)),U_1996)
| ~ relation(U_1995) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
! [U_1996,U_1995] :
( subset(relation_rng(relation_rng_restriction(U_1996,U_1995)),U_1996)
| ~ relation(U_1995) ),
inference(definitional_conversion,[status(esa)],[f_472_2]) ).
cnf(f_472_4,plain,
( subset(relation_rng(relation_rng_restriction(U_1996,U_1995)),U_1996)
| ~ relation(U_1995) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_1,plain,
! [A,B] :
( subset(relation_rng_restriction(A,B),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1]) ).
fof(f_473_2,plain,
! [U_1998,U_1997] :
( subset(relation_rng_restriction(U_1998,U_1997),U_1997)
| ~ relation(U_1997) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_1998,U_1997] :
( subset(relation_rng_restriction(U_1998,U_1997),U_1997)
| ~ relation(U_1997) ),
inference(definitional_conversion,[status(esa)],[f_473_2]) ).
cnf(f_473_4,plain,
( subset(relation_rng_restriction(U_1998,U_1997),U_1997)
| ~ relation(U_1997) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_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_474_2,plain,
! [U_2000,U_1999] :
( subset(relation_rng(relation_rng_restriction(U_2000,U_1999)),relation_rng(U_1999))
| ~ relation(U_1999) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
! [U_2000,U_1999] :
( subset(relation_rng(relation_rng_restriction(U_2000,U_1999)),relation_rng(U_1999))
| ~ relation(U_1999) ),
inference(definitional_conversion,[status(esa)],[f_474_2]) ).
cnf(f_474_4,plain,
( subset(relation_rng(relation_rng_restriction(U_2000,U_1999)),relation_rng(U_1999))
| ~ relation(U_1999) ),
inference(clausify,[status(thm)],[f_474_3]) ).
fof(f_475_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_475_2,plain,
! [U_2003,U_2002,U_2001] :
( ( subset(cartesian_product2(U_2001,U_2003),cartesian_product2(U_2001,U_2002))
& subset(cartesian_product2(U_2003,U_2001),cartesian_product2(U_2002,U_2001)) )
| ~ subset(U_2003,U_2002) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
! [U_2003,U_2002] :
( ( ! [U_2005] : subset(cartesian_product2(U_2005,U_2003),cartesian_product2(U_2005,U_2002))
& ! [U_2004] : subset(cartesian_product2(U_2003,U_2004),cartesian_product2(U_2002,U_2004)) )
| ~ subset(U_2003,U_2002) ),
inference(miniscope,[status(thm)],[f_475_2]) ).
fof(f_475_4,plain,
( ! [U_2002,U_2003,U_2004,U_2005] :
( subset(cartesian_product2(U_2005,U_2003),cartesian_product2(U_2005,U_2002))
| ~ sP471(U_2002,U_2003,U_2004,U_2005) )
& ! [U_2002,U_2003,U_2004,U_2005] :
( subset(cartesian_product2(U_2003,U_2004),cartesian_product2(U_2002,U_2004))
| ~ sP471(U_2002,U_2003,U_2004,U_2005) )
& ! [U_2002,U_2003,U_2004,U_2005] :
( sP471(U_2002,U_2003,U_2004,U_2005)
| ~ subset(U_2003,U_2002) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP471])],[f_475_3]) ).
cnf(f_475_5,plain,
( sP471(U_2002,U_2003,U_2004,U_2005)
| ~ subset(U_2003,U_2002) ),
inference(clausify,[status(thm)],[f_475_4]) ).
cnf(f_475_6,plain,
( subset(cartesian_product2(U_2003,U_2004),cartesian_product2(U_2002,U_2004))
| ~ sP471(U_2002,U_2003,U_2004,U_2005) ),
inference(clausify,[status(thm)],[f_475_4]) ).
cnf(f_475_7,plain,
( subset(cartesian_product2(U_2005,U_2003),cartesian_product2(U_2005,U_2002))
| ~ sP471(U_2002,U_2003,U_2004,U_2005) ),
inference(clausify,[status(thm)],[f_475_4]) ).
fof(f_476_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_476_2,plain,
! [U_2007,U_2006] :
( relation_rng(relation_rng_restriction(U_2007,U_2006)) = set_intersection2(relation_rng(U_2006),U_2007)
| ~ relation(U_2006) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_2006,U_2007] :
( relation_rng(relation_rng_restriction(U_2007,U_2006)) = set_intersection2(relation_rng(U_2006),U_2007)
| ~ relation(U_2006) ),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
( relation_rng(relation_rng_restriction(U_2007,U_2006)) = set_intersection2(relation_rng(U_2006),U_2007)
| ~ relation(U_2006) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_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_477_2,plain,
! [U_2011,U_2010,U_2009,U_2008] :
( subset(cartesian_product2(U_2011,U_2009),cartesian_product2(U_2010,U_2008))
| ~ subset(U_2009,U_2008)
| ~ subset(U_2011,U_2010) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
! [U_2008,U_2009,U_2010,U_2011] :
( subset(cartesian_product2(U_2011,U_2009),cartesian_product2(U_2010,U_2008))
| ~ subset(U_2009,U_2008)
| ~ subset(U_2011,U_2010) ),
inference(definitional_conversion,[status(esa)],[f_477_2]) ).
cnf(f_477_4,plain,
( subset(cartesian_product2(U_2011,U_2009),cartesian_product2(U_2010,U_2008))
| ~ subset(U_2009,U_2008)
| ~ subset(U_2011,U_2010) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [A,B] :
( meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t11_tops_2]) ).
fof(f_478_2,plain,
! [U_2013,U_2012] :
( meet_of_subsets(U_2013,complements_of_subsets(U_2013,U_2012)) = subset_complement(U_2013,union_of_subsets(U_2013,U_2012))
| U_2012 = empty_set
| ~ element(U_2012,powerset(powerset(U_2013))) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_2013,U_2012] :
( meet_of_subsets(U_2013,complements_of_subsets(U_2013,U_2012)) = subset_complement(U_2013,union_of_subsets(U_2013,U_2012))
| U_2012 = empty_set
| ~ element(U_2012,powerset(powerset(U_2013))) ),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
( meet_of_subsets(U_2013,complements_of_subsets(U_2013,U_2012)) = subset_complement(U_2013,union_of_subsets(U_2013,U_2012))
| U_2012 = empty_set
| ~ element(U_2012,powerset(powerset(U_2013))) ),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t12_pre_topc]) ).
fof(f_479_2,plain,
! [U_2014] :
( cast_as_carrier_subset(U_2014) = the_carrier(U_2014)
| ~ one_sorted_str(U_2014) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
! [U_2014] :
( cast_as_carrier_subset(U_2014) = the_carrier(U_2014)
| ~ one_sorted_str(U_2014) ),
inference(definitional_conversion,[status(esa)],[f_479_2]) ).
cnf(f_479_4,plain,
( cast_as_carrier_subset(U_2014) = the_carrier(U_2014)
| ~ one_sorted_str(U_2014) ),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_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_480_2,plain,
! [U_2017,U_2016,U_2015] :
( ( subset(relation_rng(U_2015),U_2016)
& subset(relation_dom(U_2015),U_2017) )
| ~ relation_of2_as_subset(U_2015,U_2017,U_2016) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
( ! [U_2015,U_2016,U_2017] :
( subset(relation_rng(U_2015),U_2016)
| ~ sP472(U_2015,U_2016,U_2017) )
& ! [U_2015,U_2016,U_2017] :
( subset(relation_dom(U_2015),U_2017)
| ~ sP472(U_2015,U_2016,U_2017) )
& ! [U_2015,U_2016,U_2017] :
( sP472(U_2015,U_2016,U_2017)
| ~ relation_of2_as_subset(U_2015,U_2017,U_2016) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP472])],[f_480_2]) ).
cnf(f_480_4,plain,
( sP472(U_2015,U_2016,U_2017)
| ~ relation_of2_as_subset(U_2015,U_2017,U_2016) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_5,plain,
( subset(relation_dom(U_2015),U_2017)
| ~ sP472(U_2015,U_2016,U_2017) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_6,plain,
( subset(relation_rng(U_2015),U_2016)
| ~ sP472(U_2015,U_2016,U_2017) ),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_1,plain,
! [A,B] :
( union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t12_tops_2]) ).
fof(f_481_2,plain,
! [U_2019,U_2018] :
( union_of_subsets(U_2019,complements_of_subsets(U_2019,U_2018)) = subset_complement(U_2019,meet_of_subsets(U_2019,U_2018))
| U_2018 = empty_set
| ~ element(U_2018,powerset(powerset(U_2019))) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
! [U_2018,U_2019] :
( union_of_subsets(U_2019,complements_of_subsets(U_2019,U_2018)) = subset_complement(U_2019,meet_of_subsets(U_2019,U_2018))
| U_2018 = empty_set
| ~ element(U_2018,powerset(powerset(U_2019))) ),
inference(definitional_conversion,[status(esa)],[f_481_2]) ).
cnf(f_481_4,plain,
( union_of_subsets(U_2019,complements_of_subsets(U_2019,U_2018)) = subset_complement(U_2019,meet_of_subsets(U_2019,U_2018))
| U_2018 = empty_set
| ~ element(U_2018,powerset(powerset(U_2019))) ),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_482_2,plain,
! [U_2021,U_2020] :
( set_union2(U_2021,U_2020) = U_2020
| ~ subset(U_2021,U_2020) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
! [U_2021,U_2020] :
( set_union2(U_2021,U_2020) = U_2020
| ~ subset(U_2021,U_2020) ),
inference(definitional_conversion,[status(esa)],[f_482_2]) ).
cnf(f_482_4,plain,
( set_union2(U_2021,U_2020) = U_2020
| ~ subset(U_2021,U_2020) ),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_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_483_2,plain,
! [U_2027] :
? [U_2026] :
( ! [U_2025] :
( in(U_2025,U_2026)
| are_equipotent(U_2025,U_2026)
| ~ subset(U_2025,U_2026) )
& ! [U_2024] :
( in(powerset(U_2024),U_2026)
| ~ in(U_2024,U_2026) )
& ! [U_2023,U_2022] :
( in(U_2022,U_2026)
| ~ subset(U_2022,U_2023)
| ~ in(U_2023,U_2026) )
& in(U_2027,U_2026) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
! [U_2027] :
( ! [U_2025] :
( in(U_2025,sK451(U_2027))
| are_equipotent(U_2025,sK451(U_2027))
| ~ subset(U_2025,sK451(U_2027)) )
& ! [U_2024] :
( in(powerset(U_2024),sK451(U_2027))
| ~ in(U_2024,sK451(U_2027)) )
& ! [U_2023,U_2022] :
( in(U_2022,sK451(U_2027))
| ~ subset(U_2022,U_2023)
| ~ in(U_2023,sK451(U_2027)) )
& in(U_2027,sK451(U_2027)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_2026,sK451(U_2027))],[f_483_2]) ).
fof(f_483_4,plain,
( ! [U_2025,U_2027] :
( in(U_2025,sK451(U_2027))
| are_equipotent(U_2025,sK451(U_2027))
| ~ subset(U_2025,sK451(U_2027)) )
& ! [U_2024,U_2027] :
( in(powerset(U_2024),sK451(U_2027))
| ~ in(U_2024,sK451(U_2027)) )
& ! [U_2023,U_2022,U_2027] :
( in(U_2022,sK451(U_2027))
| ~ subset(U_2022,U_2023)
| ~ in(U_2023,sK451(U_2027)) )
& ! [U_2027] : in(U_2027,sK451(U_2027)) ),
inference(definitional_conversion,[status(esa)],[f_483_3]) ).
cnf(f_483_5,plain,
in(U_2027,sK451(U_2027)),
inference(clausify,[status(thm)],[f_483_4]) ).
cnf(f_483_6,plain,
( in(U_2022,sK451(U_2027))
| ~ subset(U_2022,U_2023)
| ~ in(U_2023,sK451(U_2027)) ),
inference(clausify,[status(thm)],[f_483_4]) ).
cnf(f_483_7,plain,
( in(powerset(U_2024),sK451(U_2027))
| ~ in(U_2024,sK451(U_2027)) ),
inference(clausify,[status(thm)],[f_483_4]) ).
cnf(f_483_8,plain,
( in(U_2025,sK451(U_2027))
| are_equipotent(U_2025,sK451(U_2027))
| ~ subset(U_2025,sK451(U_2027)) ),
inference(clausify,[status(thm)],[f_483_4]) ).
fof(f_484_1,plain,
! [A] :
( ( ( compact_top_space(A)
| ? [B] :
( meet_of_subsets(the_carrier(A),B) = empty_set
& closed_subsets(B,A)
& centered(B)
& element(B,powerset(powerset(the_carrier(A)))) ) )
& ( ! [B] :
( meet_of_subsets(the_carrier(A),B) != empty_set
| ~ closed_subsets(B,A)
| ~ centered(B)
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ compact_top_space(A) ) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t13_compts_1]) ).
fof(f_484_2,plain,
! [U_2030] :
( ( ( compact_top_space(U_2030)
| ? [U_2029] :
( meet_of_subsets(the_carrier(U_2030),U_2029) = empty_set
& closed_subsets(U_2029,U_2030)
& centered(U_2029)
& element(U_2029,powerset(powerset(the_carrier(U_2030)))) ) )
& ( ! [U_2028] :
( meet_of_subsets(the_carrier(U_2030),U_2028) != empty_set
| ~ closed_subsets(U_2028,U_2030)
| ~ centered(U_2028)
| ~ element(U_2028,powerset(powerset(the_carrier(U_2030)))) )
| ~ compact_top_space(U_2030) ) )
| ~ top_str(U_2030)
| ~ topological_space(U_2030)
| empty_carrier(U_2030) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
! [U_2030] :
( ( ( compact_top_space(U_2030)
| ( meet_of_subsets(the_carrier(U_2030),sK452(U_2030)) = empty_set
& closed_subsets(sK452(U_2030),U_2030)
& centered(sK452(U_2030))
& element(sK452(U_2030),powerset(powerset(the_carrier(U_2030)))) ) )
& ( ! [U_2028] :
( meet_of_subsets(the_carrier(U_2030),U_2028) != empty_set
| ~ closed_subsets(U_2028,U_2030)
| ~ centered(U_2028)
| ~ element(U_2028,powerset(powerset(the_carrier(U_2030)))) )
| ~ compact_top_space(U_2030) ) )
| ~ top_str(U_2030)
| ~ topological_space(U_2030)
| empty_carrier(U_2030) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_2029,sK452(U_2030))],[f_484_2]) ).
fof(f_484_4,plain,
( ! [U_2030] :
( meet_of_subsets(the_carrier(U_2030),sK452(U_2030)) = empty_set
| ~ sP473(U_2030) )
& ! [U_2030] :
( closed_subsets(sK452(U_2030),U_2030)
| ~ sP473(U_2030) )
& ! [U_2030] :
( centered(sK452(U_2030))
| ~ sP473(U_2030) )
& ! [U_2030] :
( element(sK452(U_2030),powerset(powerset(the_carrier(U_2030))))
| ~ sP473(U_2030) )
& ! [U_2030,U_2028] :
( compact_top_space(U_2030)
| sP473(U_2030)
| ~ sP474(U_2030,U_2028) )
& ! [U_2030,U_2028] :
( meet_of_subsets(the_carrier(U_2030),U_2028) != empty_set
| ~ closed_subsets(U_2028,U_2030)
| ~ centered(U_2028)
| ~ element(U_2028,powerset(powerset(the_carrier(U_2030))))
| ~ compact_top_space(U_2030)
| ~ sP474(U_2030,U_2028) )
& ! [U_2030,U_2028] :
( sP474(U_2030,U_2028)
| ~ top_str(U_2030)
| ~ topological_space(U_2030)
| empty_carrier(U_2030) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP473,sP474])],[f_484_3]) ).
cnf(f_484_5,plain,
( sP474(U_2030,U_2028)
| ~ top_str(U_2030)
| ~ topological_space(U_2030)
| empty_carrier(U_2030) ),
inference(clausify,[status(thm)],[f_484_4]) ).
cnf(f_484_6,plain,
( meet_of_subsets(the_carrier(U_2030),U_2028) != empty_set
| ~ closed_subsets(U_2028,U_2030)
| ~ centered(U_2028)
| ~ element(U_2028,powerset(powerset(the_carrier(U_2030))))
| ~ compact_top_space(U_2030)
| ~ sP474(U_2030,U_2028) ),
inference(clausify,[status(thm)],[f_484_4]) ).
cnf(f_484_7,plain,
( compact_top_space(U_2030)
| sP473(U_2030)
| ~ sP474(U_2030,U_2028) ),
inference(clausify,[status(thm)],[f_484_4]) ).
cnf(f_484_8,plain,
( element(sK452(U_2030),powerset(powerset(the_carrier(U_2030))))
| ~ sP473(U_2030) ),
inference(clausify,[status(thm)],[f_484_4]) ).
cnf(f_484_9,plain,
( centered(sK452(U_2030))
| ~ sP473(U_2030) ),
inference(clausify,[status(thm)],[f_484_4]) ).
cnf(f_484_10,plain,
( closed_subsets(sK452(U_2030),U_2030)
| ~ sP473(U_2030) ),
inference(clausify,[status(thm)],[f_484_4]) ).
cnf(f_484_11,plain,
( meet_of_subsets(the_carrier(U_2030),sK452(U_2030)) = empty_set
| ~ sP473(U_2030) ),
inference(clausify,[status(thm)],[f_484_4]) ).
fof(f_485_1,plain,
! [A,B] :
( finite(A)
| ~ finite(B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t13_finset_1]) ).
fof(f_485_2,plain,
! [U_2032,U_2031] :
( finite(U_2032)
| ~ finite(U_2031)
| ~ subset(U_2032,U_2031) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
fof(f_485_3,plain,
! [U_2032] :
( ! [U_2031] :
( ~ finite(U_2031)
| ~ subset(U_2032,U_2031) )
| finite(U_2032) ),
inference(miniscope,[status(thm)],[f_485_2]) ).
fof(f_485_4,plain,
! [U_2032,U_2031] :
( ~ finite(U_2031)
| ~ subset(U_2032,U_2031)
| finite(U_2032) ),
inference(definitional_conversion,[status(esa)],[f_485_3]) ).
cnf(f_485_5,plain,
( ~ finite(U_2031)
| ~ subset(U_2032,U_2031)
| finite(U_2032) ),
inference(clausify,[status(thm)],[f_485_4]) ).
fof(f_486_1,plain,
! [A] :
( ! [B] :
( ( ( finite(complements_of_subsets(the_carrier(A),B))
| ~ finite(B) )
& ( finite(B)
| ~ finite(complements_of_subsets(the_carrier(A),B)) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t13_tops_2]) ).
fof(f_486_2,plain,
! [U_2034] :
( ! [U_2033] :
( ( ( finite(complements_of_subsets(the_carrier(U_2034),U_2033))
| ~ finite(U_2033) )
& ( finite(U_2033)
| ~ finite(complements_of_subsets(the_carrier(U_2034),U_2033)) ) )
| ~ element(U_2033,powerset(powerset(the_carrier(U_2034)))) )
| ~ one_sorted_str(U_2034) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
( ! [U_2034,U_2033] :
( finite(complements_of_subsets(the_carrier(U_2034),U_2033))
| ~ finite(U_2033)
| ~ sP475(U_2034,U_2033) )
& ! [U_2034,U_2033] :
( finite(U_2033)
| ~ finite(complements_of_subsets(the_carrier(U_2034),U_2033))
| ~ sP475(U_2034,U_2033) )
& ! [U_2034,U_2033] :
( sP475(U_2034,U_2033)
| ~ element(U_2033,powerset(powerset(the_carrier(U_2034))))
| ~ one_sorted_str(U_2034) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP475])],[f_486_2]) ).
cnf(f_486_4,plain,
( sP475(U_2034,U_2033)
| ~ element(U_2033,powerset(powerset(the_carrier(U_2034))))
| ~ one_sorted_str(U_2034) ),
inference(clausify,[status(thm)],[f_486_3]) ).
cnf(f_486_5,plain,
( finite(U_2033)
| ~ finite(complements_of_subsets(the_carrier(U_2034),U_2033))
| ~ sP475(U_2034,U_2033) ),
inference(clausify,[status(thm)],[f_486_3]) ).
cnf(f_486_6,plain,
( finite(complements_of_subsets(the_carrier(U_2034),U_2033))
| ~ finite(U_2033)
| ~ sP475(U_2034,U_2033) ),
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_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_487_2,plain,
! [U_2037,U_2036,U_2035] :
( relation_dom_restriction(relation_rng_restriction(U_2037,U_2035),U_2036) = relation_rng_restriction(U_2037,relation_dom_restriction(U_2035,U_2036))
| ~ relation(U_2035) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
! [U_2036,U_2035,U_2037] :
( relation_dom_restriction(relation_rng_restriction(U_2037,U_2035),U_2036) = relation_rng_restriction(U_2037,relation_dom_restriction(U_2035,U_2036))
| ~ relation(U_2035) ),
inference(definitional_conversion,[status(esa)],[f_487_2]) ).
cnf(f_487_4,plain,
( relation_dom_restriction(relation_rng_restriction(U_2037,U_2035),U_2036) = relation_rng_restriction(U_2037,relation_dom_restriction(U_2035,U_2036))
| ~ relation(U_2035) ),
inference(clausify,[status(thm)],[f_487_3]) ).
fof(f_488_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_488_2,plain,
! [U_2042,U_2041,U_2040] :
( ( ( in(U_2042,relation_image(U_2040,U_2041))
| ! [U_2039] :
( ~ in(U_2039,U_2041)
| ~ in(ordered_pair(U_2039,U_2042),U_2040)
| ~ in(U_2039,relation_dom(U_2040)) ) )
& ( ? [U_2038] :
( in(U_2038,U_2041)
& in(ordered_pair(U_2038,U_2042),U_2040)
& in(U_2038,relation_dom(U_2040)) )
| ~ in(U_2042,relation_image(U_2040,U_2041)) ) )
| ~ relation(U_2040) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
! [U_2042,U_2041,U_2040] :
( ( ( in(U_2042,relation_image(U_2040,U_2041))
| ! [U_2039] :
( ~ in(U_2039,U_2041)
| ~ in(ordered_pair(U_2039,U_2042),U_2040)
| ~ in(U_2039,relation_dom(U_2040)) ) )
& ( ( in(sK453(U_2042,U_2041,U_2040),U_2041)
& in(ordered_pair(sK453(U_2042,U_2041,U_2040),U_2042),U_2040)
& in(sK453(U_2042,U_2041,U_2040),relation_dom(U_2040)) )
| ~ in(U_2042,relation_image(U_2040,U_2041)) ) )
| ~ relation(U_2040) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_2038,sK453(U_2042,U_2041,U_2040))],[f_488_2]) ).
fof(f_488_4,plain,
( ! [U_2040,U_2041,U_2042] :
( in(sK453(U_2042,U_2041,U_2040),U_2041)
| ~ sP476(U_2040,U_2041,U_2042) )
& ! [U_2040,U_2041,U_2042] :
( in(ordered_pair(sK453(U_2042,U_2041,U_2040),U_2042),U_2040)
| ~ sP476(U_2040,U_2041,U_2042) )
& ! [U_2040,U_2041,U_2042] :
( in(sK453(U_2042,U_2041,U_2040),relation_dom(U_2040))
| ~ sP476(U_2040,U_2041,U_2042) )
& ! [U_2040,U_2041,U_2039,U_2042] :
( in(U_2042,relation_image(U_2040,U_2041))
| ~ in(U_2039,U_2041)
| ~ in(ordered_pair(U_2039,U_2042),U_2040)
| ~ in(U_2039,relation_dom(U_2040))
| ~ sP477(U_2040,U_2041,U_2039,U_2042) )
& ! [U_2040,U_2041,U_2039,U_2042] :
( sP476(U_2040,U_2041,U_2042)
| ~ in(U_2042,relation_image(U_2040,U_2041))
| ~ sP477(U_2040,U_2041,U_2039,U_2042) )
& ! [U_2040,U_2041,U_2039,U_2042] :
( sP477(U_2040,U_2041,U_2039,U_2042)
| ~ relation(U_2040) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP476,sP477])],[f_488_3]) ).
cnf(f_488_5,plain,
( sP477(U_2040,U_2041,U_2039,U_2042)
| ~ relation(U_2040) ),
inference(clausify,[status(thm)],[f_488_4]) ).
cnf(f_488_6,plain,
( sP476(U_2040,U_2041,U_2042)
| ~ in(U_2042,relation_image(U_2040,U_2041))
| ~ sP477(U_2040,U_2041,U_2039,U_2042) ),
inference(clausify,[status(thm)],[f_488_4]) ).
cnf(f_488_7,plain,
( in(U_2042,relation_image(U_2040,U_2041))
| ~ in(U_2039,U_2041)
| ~ in(ordered_pair(U_2039,U_2042),U_2040)
| ~ in(U_2039,relation_dom(U_2040))
| ~ sP477(U_2040,U_2041,U_2039,U_2042) ),
inference(clausify,[status(thm)],[f_488_4]) ).
cnf(f_488_8,plain,
( in(sK453(U_2042,U_2041,U_2040),relation_dom(U_2040))
| ~ sP476(U_2040,U_2041,U_2042) ),
inference(clausify,[status(thm)],[f_488_4]) ).
cnf(f_488_9,plain,
( in(ordered_pair(sK453(U_2042,U_2041,U_2040),U_2042),U_2040)
| ~ sP476(U_2040,U_2041,U_2042) ),
inference(clausify,[status(thm)],[f_488_4]) ).
cnf(f_488_10,plain,
( in(sK453(U_2042,U_2041,U_2040),U_2041)
| ~ sP476(U_2040,U_2041,U_2042) ),
inference(clausify,[status(thm)],[f_488_4]) ).
fof(f_489_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_489_2,plain,
! [U_2044,U_2043] :
( subset(relation_image(U_2043,U_2044),relation_rng(U_2043))
| ~ relation(U_2043) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
! [U_2044,U_2043] :
( subset(relation_image(U_2043,U_2044),relation_rng(U_2043))
| ~ relation(U_2043) ),
inference(definitional_conversion,[status(esa)],[f_489_2]) ).
cnf(f_489_4,plain,
( subset(relation_image(U_2043,U_2044),relation_rng(U_2043))
| ~ relation(U_2043) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_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_490_2,plain,
! [U_2046,U_2045] :
( subset(relation_image(U_2045,relation_inverse_image(U_2045,U_2046)),U_2046)
| ~ function(U_2045)
| ~ relation(U_2045) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
! [U_2046,U_2045] :
( subset(relation_image(U_2045,relation_inverse_image(U_2045,U_2046)),U_2046)
| ~ function(U_2045)
| ~ relation(U_2045) ),
inference(definitional_conversion,[status(esa)],[f_490_2]) ).
cnf(f_490_4,plain,
( subset(relation_image(U_2045,relation_inverse_image(U_2045,U_2046)),U_2046)
| ~ function(U_2045)
| ~ relation(U_2045) ),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_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_491_2,plain,
! [U_2048,U_2047] :
( relation_image(U_2047,U_2048) = relation_image(U_2047,set_intersection2(relation_dom(U_2047),U_2048))
| ~ relation(U_2047) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
! [U_2047,U_2048] :
( relation_image(U_2047,U_2048) = relation_image(U_2047,set_intersection2(relation_dom(U_2047),U_2048))
| ~ relation(U_2047) ),
inference(definitional_conversion,[status(esa)],[f_491_2]) ).
cnf(f_491_4,plain,
( relation_image(U_2047,U_2048) = relation_image(U_2047,set_intersection2(relation_dom(U_2047),U_2048))
| ~ relation(U_2047) ),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_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_492_2,plain,
! [U_2050,U_2049] :
( subset(U_2050,relation_inverse_image(U_2049,relation_image(U_2049,U_2050)))
| ~ subset(U_2050,relation_dom(U_2049))
| ~ relation(U_2049) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
! [U_2050,U_2049] :
( subset(U_2050,relation_inverse_image(U_2049,relation_image(U_2049,U_2050)))
| ~ subset(U_2050,relation_dom(U_2049))
| ~ relation(U_2049) ),
inference(definitional_conversion,[status(esa)],[f_492_2]) ).
cnf(f_492_4,plain,
( subset(U_2050,relation_inverse_image(U_2049,relation_image(U_2049,U_2050)))
| ~ subset(U_2050,relation_dom(U_2049))
| ~ relation(U_2049) ),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t146_relat_1]) ).
fof(f_493_2,plain,
! [U_2051] :
( relation_image(U_2051,relation_dom(U_2051)) = relation_rng(U_2051)
| ~ relation(U_2051) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
! [U_2051] :
( relation_image(U_2051,relation_dom(U_2051)) = relation_rng(U_2051)
| ~ relation(U_2051) ),
inference(definitional_conversion,[status(esa)],[f_493_2]) ).
cnf(f_493_4,plain,
( relation_image(U_2051,relation_dom(U_2051)) = relation_rng(U_2051)
| ~ relation(U_2051) ),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_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_494_2,plain,
! [U_2053,U_2052] :
( relation_image(U_2052,relation_inverse_image(U_2052,U_2053)) = U_2053
| ~ subset(U_2053,relation_rng(U_2052))
| ~ function(U_2052)
| ~ relation(U_2052) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
! [U_2052,U_2053] :
( relation_image(U_2052,relation_inverse_image(U_2052,U_2053)) = U_2053
| ~ subset(U_2053,relation_rng(U_2052))
| ~ function(U_2052)
| ~ relation(U_2052) ),
inference(definitional_conversion,[status(esa)],[f_494_2]) ).
cnf(f_494_4,plain,
( relation_image(U_2052,relation_inverse_image(U_2052,U_2053)) = U_2053
| ~ subset(U_2053,relation_rng(U_2052))
| ~ function(U_2052)
| ~ relation(U_2052) ),
inference(clausify,[status(thm)],[f_494_3]) ).
fof(f_495_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_495_2,plain,
! [U_2057,U_2056,U_2055,U_2054] :
( relation_of2_as_subset(U_2054,U_2055,U_2056)
| ~ subset(relation_rng(U_2054),U_2056)
| ~ relation_of2_as_subset(U_2054,U_2055,U_2057) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
! [U_2056,U_2057,U_2054,U_2055] :
( relation_of2_as_subset(U_2054,U_2055,U_2056)
| ~ subset(relation_rng(U_2054),U_2056)
| ~ relation_of2_as_subset(U_2054,U_2055,U_2057) ),
inference(definitional_conversion,[status(esa)],[f_495_2]) ).
cnf(f_495_4,plain,
( relation_of2_as_subset(U_2054,U_2055,U_2056)
| ~ subset(relation_rng(U_2054),U_2056)
| ~ relation_of2_as_subset(U_2054,U_2055,U_2057) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_1,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[t15_finset_1]) ).
fof(f_496_2,plain,
! [U_2059,U_2058] :
( finite(set_intersection2(U_2059,U_2058))
| ~ finite(U_2059) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
! [U_2059] :
( ! [U_2058] : finite(set_intersection2(U_2059,U_2058))
| ~ finite(U_2059) ),
inference(miniscope,[status(thm)],[f_496_2]) ).
fof(f_496_4,plain,
! [U_2058,U_2059] :
( finite(set_intersection2(U_2059,U_2058))
| ~ finite(U_2059) ),
inference(definitional_conversion,[status(esa)],[f_496_3]) ).
cnf(f_496_5,plain,
( finite(set_intersection2(U_2059,U_2058))
| ~ finite(U_2059) ),
inference(clausify,[status(thm)],[f_496_4]) ).
fof(f_497_1,plain,
! [A] :
( ! [B] :
( subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B
| ~ element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t15_pre_topc]) ).
fof(f_497_2,plain,
! [U_2061] :
( ! [U_2060] :
( subset_intersection2(the_carrier(U_2061),U_2060,cast_as_carrier_subset(U_2061)) = U_2060
| ~ element(U_2060,powerset(the_carrier(U_2061))) )
| ~ one_sorted_str(U_2061) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
! [U_2061,U_2060] :
( subset_intersection2(the_carrier(U_2061),U_2060,cast_as_carrier_subset(U_2061)) = U_2060
| ~ element(U_2060,powerset(the_carrier(U_2061)))
| ~ one_sorted_str(U_2061) ),
inference(definitional_conversion,[status(esa)],[f_497_2]) ).
cnf(f_497_4,plain,
( subset_intersection2(the_carrier(U_2061),U_2060,cast_as_carrier_subset(U_2061)) = U_2060
| ~ element(U_2060,powerset(the_carrier(U_2061)))
| ~ one_sorted_str(U_2061) ),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_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_498_2,plain,
! [U_2063] :
( ! [U_2062] :
( relation_rng(relation_composition(U_2063,U_2062)) = relation_image(U_2062,relation_rng(U_2063))
| ~ relation(U_2062) )
| ~ relation(U_2063) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
! [U_2062,U_2063] :
( relation_rng(relation_composition(U_2063,U_2062)) = relation_image(U_2062,relation_rng(U_2063))
| ~ relation(U_2062)
| ~ relation(U_2063) ),
inference(definitional_conversion,[status(esa)],[f_498_2]) ).
cnf(f_498_4,plain,
( relation_rng(relation_composition(U_2063,U_2062)) = relation_image(U_2062,relation_rng(U_2063))
| ~ relation(U_2062)
| ~ relation(U_2063) ),
inference(clausify,[status(thm)],[f_498_3]) ).
fof(f_499_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_499_2,plain,
! [U_2068,U_2067,U_2066] :
( ( ( in(U_2068,relation_inverse_image(U_2066,U_2067))
| ! [U_2065] :
( ~ in(U_2065,U_2067)
| ~ in(ordered_pair(U_2068,U_2065),U_2066)
| ~ in(U_2065,relation_rng(U_2066)) ) )
& ( ? [U_2064] :
( in(U_2064,U_2067)
& in(ordered_pair(U_2068,U_2064),U_2066)
& in(U_2064,relation_rng(U_2066)) )
| ~ in(U_2068,relation_inverse_image(U_2066,U_2067)) ) )
| ~ relation(U_2066) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
! [U_2068,U_2067,U_2066] :
( ( ( in(U_2068,relation_inverse_image(U_2066,U_2067))
| ! [U_2065] :
( ~ in(U_2065,U_2067)
| ~ in(ordered_pair(U_2068,U_2065),U_2066)
| ~ in(U_2065,relation_rng(U_2066)) ) )
& ( ( in(sK454(U_2068,U_2067,U_2066),U_2067)
& in(ordered_pair(U_2068,sK454(U_2068,U_2067,U_2066)),U_2066)
& in(sK454(U_2068,U_2067,U_2066),relation_rng(U_2066)) )
| ~ in(U_2068,relation_inverse_image(U_2066,U_2067)) ) )
| ~ relation(U_2066) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_2064,sK454(U_2068,U_2067,U_2066))],[f_499_2]) ).
fof(f_499_4,plain,
( ! [U_2066,U_2067,U_2068] :
( in(sK454(U_2068,U_2067,U_2066),U_2067)
| ~ sP478(U_2066,U_2067,U_2068) )
& ! [U_2066,U_2067,U_2068] :
( in(ordered_pair(U_2068,sK454(U_2068,U_2067,U_2066)),U_2066)
| ~ sP478(U_2066,U_2067,U_2068) )
& ! [U_2066,U_2067,U_2068] :
( in(sK454(U_2068,U_2067,U_2066),relation_rng(U_2066))
| ~ sP478(U_2066,U_2067,U_2068) )
& ! [U_2065,U_2066,U_2067,U_2068] :
( in(U_2068,relation_inverse_image(U_2066,U_2067))
| ~ in(U_2065,U_2067)
| ~ in(ordered_pair(U_2068,U_2065),U_2066)
| ~ in(U_2065,relation_rng(U_2066))
| ~ sP479(U_2065,U_2066,U_2067,U_2068) )
& ! [U_2065,U_2066,U_2067,U_2068] :
( sP478(U_2066,U_2067,U_2068)
| ~ in(U_2068,relation_inverse_image(U_2066,U_2067))
| ~ sP479(U_2065,U_2066,U_2067,U_2068) )
& ! [U_2065,U_2066,U_2067,U_2068] :
( sP479(U_2065,U_2066,U_2067,U_2068)
| ~ relation(U_2066) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP478,sP479])],[f_499_3]) ).
cnf(f_499_5,plain,
( sP479(U_2065,U_2066,U_2067,U_2068)
| ~ relation(U_2066) ),
inference(clausify,[status(thm)],[f_499_4]) ).
cnf(f_499_6,plain,
( sP478(U_2066,U_2067,U_2068)
| ~ in(U_2068,relation_inverse_image(U_2066,U_2067))
| ~ sP479(U_2065,U_2066,U_2067,U_2068) ),
inference(clausify,[status(thm)],[f_499_4]) ).
cnf(f_499_7,plain,
( in(U_2068,relation_inverse_image(U_2066,U_2067))
| ~ in(U_2065,U_2067)
| ~ in(ordered_pair(U_2068,U_2065),U_2066)
| ~ in(U_2065,relation_rng(U_2066))
| ~ sP479(U_2065,U_2066,U_2067,U_2068) ),
inference(clausify,[status(thm)],[f_499_4]) ).
cnf(f_499_8,plain,
( in(sK454(U_2068,U_2067,U_2066),relation_rng(U_2066))
| ~ sP478(U_2066,U_2067,U_2068) ),
inference(clausify,[status(thm)],[f_499_4]) ).
cnf(f_499_9,plain,
( in(ordered_pair(U_2068,sK454(U_2068,U_2067,U_2066)),U_2066)
| ~ sP478(U_2066,U_2067,U_2068) ),
inference(clausify,[status(thm)],[f_499_4]) ).
cnf(f_499_10,plain,
( in(sK454(U_2068,U_2067,U_2066),U_2067)
| ~ sP478(U_2066,U_2067,U_2068) ),
inference(clausify,[status(thm)],[f_499_4]) ).
fof(f_500_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_500_2,plain,
! [U_2070,U_2069] :
( subset(relation_inverse_image(U_2069,U_2070),relation_dom(U_2069))
| ~ relation(U_2069) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
! [U_2070,U_2069] :
( subset(relation_inverse_image(U_2069,U_2070),relation_dom(U_2069))
| ~ relation(U_2069) ),
inference(definitional_conversion,[status(esa)],[f_500_2]) ).
cnf(f_500_4,plain,
( subset(relation_inverse_image(U_2069,U_2070),relation_dom(U_2069))
| ~ relation(U_2069) ),
inference(clausify,[status(thm)],[f_500_3]) ).
fof(f_501_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_501_2,plain,
! [U_2074,U_2073,U_2072,U_2071] :
( relation_of2_as_subset(U_2071,U_2072,U_2073)
| ~ subset(U_2074,U_2073)
| ~ relation_of2_as_subset(U_2071,U_2072,U_2074) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
! [U_2073,U_2074,U_2072,U_2071] :
( relation_of2_as_subset(U_2071,U_2072,U_2073)
| ~ subset(U_2074,U_2073)
| ~ relation_of2_as_subset(U_2071,U_2072,U_2074) ),
inference(definitional_conversion,[status(esa)],[f_501_2]) ).
cnf(f_501_4,plain,
( relation_of2_as_subset(U_2071,U_2072,U_2073)
| ~ subset(U_2074,U_2073)
| ~ relation_of2_as_subset(U_2071,U_2072,U_2074) ),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [A] :
( ! [B] :
( ( ( closed_subsets(B,A)
| ~ open_subsets(complements_of_subsets(the_carrier(A),B),A) )
& ( open_subsets(complements_of_subsets(the_carrier(A),B),A)
| ~ closed_subsets(B,A) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t16_tops_2]) ).
fof(f_502_2,plain,
! [U_2076] :
( ! [U_2075] :
( ( ( closed_subsets(U_2075,U_2076)
| ~ open_subsets(complements_of_subsets(the_carrier(U_2076),U_2075),U_2076) )
& ( open_subsets(complements_of_subsets(the_carrier(U_2076),U_2075),U_2076)
| ~ closed_subsets(U_2075,U_2076) ) )
| ~ element(U_2075,powerset(powerset(the_carrier(U_2076)))) )
| ~ top_str(U_2076) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
( ! [U_2076,U_2075] :
( closed_subsets(U_2075,U_2076)
| ~ open_subsets(complements_of_subsets(the_carrier(U_2076),U_2075),U_2076)
| ~ sP480(U_2076,U_2075) )
& ! [U_2076,U_2075] :
( open_subsets(complements_of_subsets(the_carrier(U_2076),U_2075),U_2076)
| ~ closed_subsets(U_2075,U_2076)
| ~ sP480(U_2076,U_2075) )
& ! [U_2076,U_2075] :
( sP480(U_2076,U_2075)
| ~ element(U_2075,powerset(powerset(the_carrier(U_2076))))
| ~ top_str(U_2076) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP480])],[f_502_2]) ).
cnf(f_502_4,plain,
( sP480(U_2076,U_2075)
| ~ element(U_2075,powerset(powerset(the_carrier(U_2076))))
| ~ top_str(U_2076) ),
inference(clausify,[status(thm)],[f_502_3]) ).
cnf(f_502_5,plain,
( open_subsets(complements_of_subsets(the_carrier(U_2076),U_2075),U_2076)
| ~ closed_subsets(U_2075,U_2076)
| ~ sP480(U_2076,U_2075) ),
inference(clausify,[status(thm)],[f_502_3]) ).
cnf(f_502_6,plain,
( closed_subsets(U_2075,U_2076)
| ~ open_subsets(complements_of_subsets(the_carrier(U_2076),U_2075),U_2076)
| ~ sP480(U_2076,U_2075) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_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_503_2,plain,
! [U_2079,U_2078,U_2077] :
( ( ( in(U_2079,relation_restriction(U_2077,U_2078))
| ~ in(U_2079,cartesian_product2(U_2078,U_2078))
| ~ in(U_2079,U_2077) )
& ( ( in(U_2079,cartesian_product2(U_2078,U_2078))
& in(U_2079,U_2077) )
| ~ in(U_2079,relation_restriction(U_2077,U_2078)) ) )
| ~ relation(U_2077) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
( ! [U_2078,U_2079,U_2077] :
( in(U_2079,cartesian_product2(U_2078,U_2078))
| ~ sP481(U_2078,U_2079,U_2077) )
& ! [U_2078,U_2079,U_2077] :
( in(U_2079,U_2077)
| ~ sP481(U_2078,U_2079,U_2077) )
& ! [U_2078,U_2079,U_2077] :
( in(U_2079,relation_restriction(U_2077,U_2078))
| ~ in(U_2079,cartesian_product2(U_2078,U_2078))
| ~ in(U_2079,U_2077)
| ~ sP482(U_2078,U_2079,U_2077) )
& ! [U_2078,U_2079,U_2077] :
( sP481(U_2078,U_2079,U_2077)
| ~ in(U_2079,relation_restriction(U_2077,U_2078))
| ~ sP482(U_2078,U_2079,U_2077) )
& ! [U_2078,U_2079,U_2077] :
( sP482(U_2078,U_2079,U_2077)
| ~ relation(U_2077) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP481,sP482])],[f_503_2]) ).
cnf(f_503_4,plain,
( sP482(U_2078,U_2079,U_2077)
| ~ relation(U_2077) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_5,plain,
( sP481(U_2078,U_2079,U_2077)
| ~ in(U_2079,relation_restriction(U_2077,U_2078))
| ~ sP482(U_2078,U_2079,U_2077) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_6,plain,
( in(U_2079,relation_restriction(U_2077,U_2078))
| ~ in(U_2079,cartesian_product2(U_2078,U_2078))
| ~ in(U_2079,U_2077)
| ~ sP482(U_2078,U_2079,U_2077) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_7,plain,
( in(U_2079,U_2077)
| ~ sP481(U_2078,U_2079,U_2077) ),
inference(clausify,[status(thm)],[f_503_3]) ).
cnf(f_503_8,plain,
( in(U_2079,cartesian_product2(U_2078,U_2078))
| ~ sP481(U_2078,U_2079,U_2077) ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_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_504_2,plain,
! [U_2081,U_2080] :
( relation_inverse_image(U_2080,U_2081) != empty_set
| ~ subset(U_2081,relation_rng(U_2080))
| U_2081 = empty_set
| ~ relation(U_2080) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
! [U_2080,U_2081] :
( relation_inverse_image(U_2080,U_2081) != empty_set
| ~ subset(U_2081,relation_rng(U_2080))
| U_2081 = empty_set
| ~ relation(U_2080) ),
inference(definitional_conversion,[status(esa)],[f_504_2]) ).
cnf(f_504_4,plain,
( relation_inverse_image(U_2080,U_2081) != empty_set
| ~ subset(U_2081,relation_rng(U_2080))
| U_2081 = empty_set
| ~ relation(U_2080) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_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_505_2,plain,
! [U_2084,U_2083,U_2082] :
( subset(relation_inverse_image(U_2082,U_2084),relation_inverse_image(U_2082,U_2083))
| ~ subset(U_2084,U_2083)
| ~ relation(U_2082) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
! [U_2083,U_2082,U_2084] :
( subset(relation_inverse_image(U_2082,U_2084),relation_inverse_image(U_2082,U_2083))
| ~ subset(U_2084,U_2083)
| ~ relation(U_2082) ),
inference(definitional_conversion,[status(esa)],[f_505_2]) ).
cnf(f_505_4,plain,
( subset(relation_inverse_image(U_2082,U_2084),relation_inverse_image(U_2082,U_2083))
| ~ subset(U_2084,U_2083)
| ~ relation(U_2082) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_1,plain,
! [A,B] :
( finite(relation_image(B,A))
| ~ finite(A)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t17_finset_1]) ).
fof(f_506_2,plain,
! [U_2086,U_2085] :
( finite(relation_image(U_2085,U_2086))
| ~ finite(U_2086)
| ~ function(U_2085)
| ~ relation(U_2085) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_2086,U_2085] :
( finite(relation_image(U_2085,U_2086))
| ~ finite(U_2086)
| ~ function(U_2085)
| ~ relation(U_2085) ),
inference(definitional_conversion,[status(esa)],[f_506_2]) ).
cnf(f_506_4,plain,
( finite(relation_image(U_2085,U_2086))
| ~ finite(U_2086)
| ~ function(U_2085)
| ~ relation(U_2085) ),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_1,plain,
! [A] :
( ! [B] :
( subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)
| ~ element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t17_pre_topc]) ).
fof(f_507_2,plain,
! [U_2088] :
( ! [U_2087] :
( subset_complement(the_carrier(U_2088),U_2087) = subset_difference(the_carrier(U_2088),cast_as_carrier_subset(U_2088),U_2087)
| ~ element(U_2087,powerset(the_carrier(U_2088))) )
| ~ one_sorted_str(U_2088) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
! [U_2087,U_2088] :
( subset_complement(the_carrier(U_2088),U_2087) = subset_difference(the_carrier(U_2088),cast_as_carrier_subset(U_2088),U_2087)
| ~ element(U_2087,powerset(the_carrier(U_2088)))
| ~ one_sorted_str(U_2088) ),
inference(definitional_conversion,[status(esa)],[f_507_2]) ).
cnf(f_507_4,plain,
( subset_complement(the_carrier(U_2088),U_2087) = subset_difference(the_carrier(U_2088),cast_as_carrier_subset(U_2088),U_2087)
| ~ element(U_2087,powerset(the_carrier(U_2088)))
| ~ one_sorted_str(U_2088) ),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_1,plain,
! [A] :
( ! [B] :
( ( ( open_subsets(B,A)
| ~ closed_subsets(complements_of_subsets(the_carrier(A),B),A) )
& ( closed_subsets(complements_of_subsets(the_carrier(A),B),A)
| ~ open_subsets(B,A) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t17_tops_2]) ).
fof(f_508_2,plain,
! [U_2090] :
( ! [U_2089] :
( ( ( open_subsets(U_2089,U_2090)
| ~ closed_subsets(complements_of_subsets(the_carrier(U_2090),U_2089),U_2090) )
& ( closed_subsets(complements_of_subsets(the_carrier(U_2090),U_2089),U_2090)
| ~ open_subsets(U_2089,U_2090) ) )
| ~ element(U_2089,powerset(powerset(the_carrier(U_2090)))) )
| ~ top_str(U_2090) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
fof(f_508_3,plain,
( ! [U_2090,U_2089] :
( open_subsets(U_2089,U_2090)
| ~ closed_subsets(complements_of_subsets(the_carrier(U_2090),U_2089),U_2090)
| ~ sP483(U_2090,U_2089) )
& ! [U_2090,U_2089] :
( closed_subsets(complements_of_subsets(the_carrier(U_2090),U_2089),U_2090)
| ~ open_subsets(U_2089,U_2090)
| ~ sP483(U_2090,U_2089) )
& ! [U_2090,U_2089] :
( sP483(U_2090,U_2089)
| ~ element(U_2089,powerset(powerset(the_carrier(U_2090))))
| ~ top_str(U_2090) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP483])],[f_508_2]) ).
cnf(f_508_4,plain,
( sP483(U_2090,U_2089)
| ~ element(U_2089,powerset(powerset(the_carrier(U_2090))))
| ~ top_str(U_2090) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_5,plain,
( closed_subsets(complements_of_subsets(the_carrier(U_2090),U_2089),U_2090)
| ~ open_subsets(U_2089,U_2090)
| ~ sP483(U_2090,U_2089) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_6,plain,
( open_subsets(U_2089,U_2090)
| ~ closed_subsets(complements_of_subsets(the_carrier(U_2090),U_2089),U_2090)
| ~ sP483(U_2090,U_2089) ),
inference(clausify,[status(thm)],[f_508_3]) ).
fof(f_509_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_509_2,plain,
! [U_2092,U_2091] :
( relation_restriction(U_2091,U_2092) = relation_dom_restriction(relation_rng_restriction(U_2092,U_2091),U_2092)
| ~ relation(U_2091) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
! [U_2092,U_2091] :
( relation_restriction(U_2091,U_2092) = relation_dom_restriction(relation_rng_restriction(U_2092,U_2091),U_2092)
| ~ relation(U_2091) ),
inference(definitional_conversion,[status(esa)],[f_509_2]) ).
cnf(f_509_4,plain,
( relation_restriction(U_2091,U_2092) = relation_dom_restriction(relation_rng_restriction(U_2092,U_2091),U_2092)
| ~ relation(U_2091) ),
inference(clausify,[status(thm)],[f_509_3]) ).
fof(f_510_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_510_2,plain,
! [U_2094,U_2093] : subset(set_intersection2(U_2094,U_2093),U_2094),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
! [U_2094,U_2093] : subset(set_intersection2(U_2094,U_2093),U_2094),
inference(definitional_conversion,[status(esa)],[f_510_2]) ).
cnf(f_510_4,plain,
subset(set_intersection2(U_2094,U_2093),U_2094),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_1,plain,
! [A] :
( ! [B] :
( ? [C] :
( ! [D] :
( D = C
| ~ subset(C,D)
| ~ in(D,B) )
& in(C,B) )
| B = empty_set
| ~ element(B,powerset(powerset(A))) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[t18_finset_1]) ).
fof(f_511_2,plain,
! [U_2098] :
( ! [U_2097] :
( ? [U_2096] :
( ! [U_2095] :
( U_2095 = U_2096
| ~ subset(U_2096,U_2095)
| ~ in(U_2095,U_2097) )
& in(U_2096,U_2097) )
| U_2097 = empty_set
| ~ element(U_2097,powerset(powerset(U_2098))) )
| ~ finite(U_2098) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_2098] :
( ! [U_2097] :
( ( ! [U_2095] :
( U_2095 = sK455(U_2098,U_2097)
| ~ subset(sK455(U_2098,U_2097),U_2095)
| ~ in(U_2095,U_2097) )
& in(sK455(U_2098,U_2097),U_2097) )
| U_2097 = empty_set
| ~ element(U_2097,powerset(powerset(U_2098))) )
| ~ finite(U_2098) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_2096,sK455(U_2098,U_2097))],[f_511_2]) ).
fof(f_511_4,plain,
( ! [U_2097,U_2095,U_2098] :
( U_2095 = sK455(U_2098,U_2097)
| ~ subset(sK455(U_2098,U_2097),U_2095)
| ~ in(U_2095,U_2097)
| ~ sP484(U_2097,U_2095,U_2098) )
& ! [U_2097,U_2095,U_2098] :
( in(sK455(U_2098,U_2097),U_2097)
| ~ sP484(U_2097,U_2095,U_2098) )
& ! [U_2097,U_2095,U_2098] :
( sP484(U_2097,U_2095,U_2098)
| U_2097 = empty_set
| ~ element(U_2097,powerset(powerset(U_2098)))
| ~ finite(U_2098) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP484])],[f_511_3]) ).
cnf(f_511_5,plain,
( sP484(U_2097,U_2095,U_2098)
| U_2097 = empty_set
| ~ element(U_2097,powerset(powerset(U_2098)))
| ~ finite(U_2098) ),
inference(clausify,[status(thm)],[f_511_4]) ).
cnf(f_511_6,plain,
( in(sK455(U_2098,U_2097),U_2097)
| ~ sP484(U_2097,U_2095,U_2098) ),
inference(clausify,[status(thm)],[f_511_4]) ).
cnf(f_511_7,plain,
( U_2095 = sK455(U_2098,U_2097)
| ~ subset(sK455(U_2098,U_2097),U_2095)
| ~ in(U_2095,U_2097)
| ~ sP484(U_2097,U_2095,U_2098) ),
inference(clausify,[status(thm)],[f_511_4]) ).
fof(f_512_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_512_2,plain,
! [U_2100,U_2099] :
( relation_restriction(U_2099,U_2100) = relation_rng_restriction(U_2100,relation_dom_restriction(U_2099,U_2100))
| ~ relation(U_2099) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_2100,U_2099] :
( relation_restriction(U_2099,U_2100) = relation_rng_restriction(U_2100,relation_dom_restriction(U_2099,U_2100))
| ~ relation(U_2099) ),
inference(definitional_conversion,[status(esa)],[f_512_2]) ).
cnf(f_512_4,plain,
( relation_restriction(U_2099,U_2100) = relation_rng_restriction(U_2100,relation_dom_restriction(U_2099,U_2100))
| ~ relation(U_2099) ),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_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_513_2,plain,
! [U_2103,U_2102,U_2101] :
( ( in(U_2103,U_2102)
& in(U_2103,relation_field(U_2101)) )
| ~ in(U_2103,relation_field(relation_restriction(U_2101,U_2102)))
| ~ relation(U_2101) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
( ! [U_2103,U_2102,U_2101] :
( in(U_2103,U_2102)
| ~ sP485(U_2103,U_2102,U_2101) )
& ! [U_2103,U_2102,U_2101] :
( in(U_2103,relation_field(U_2101))
| ~ sP485(U_2103,U_2102,U_2101) )
& ! [U_2103,U_2102,U_2101] :
( sP485(U_2103,U_2102,U_2101)
| ~ in(U_2103,relation_field(relation_restriction(U_2101,U_2102)))
| ~ relation(U_2101) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP485])],[f_513_2]) ).
cnf(f_513_4,plain,
( sP485(U_2103,U_2102,U_2101)
| ~ in(U_2103,relation_field(relation_restriction(U_2101,U_2102)))
| ~ relation(U_2101) ),
inference(clausify,[status(thm)],[f_513_3]) ).
cnf(f_513_5,plain,
( in(U_2103,relation_field(U_2101))
| ~ sP485(U_2103,U_2102,U_2101) ),
inference(clausify,[status(thm)],[f_513_3]) ).
cnf(f_513_6,plain,
( in(U_2103,U_2102)
| ~ sP485(U_2103,U_2102,U_2101) ),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_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_514_2,plain,
! [U_2106,U_2105,U_2104] :
( subset(U_2106,set_intersection2(U_2105,U_2104))
| ~ subset(U_2106,U_2104)
| ~ subset(U_2106,U_2105) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_2105,U_2106,U_2104] :
( subset(U_2106,set_intersection2(U_2105,U_2104))
| ~ subset(U_2106,U_2104)
| ~ subset(U_2106,U_2105) ),
inference(definitional_conversion,[status(esa)],[f_514_2]) ).
cnf(f_514_4,plain,
( subset(U_2106,set_intersection2(U_2105,U_2104))
| ~ subset(U_2106,U_2104)
| ~ subset(U_2106,U_2105) ),
inference(clausify,[status(thm)],[f_514_3]) ).
fof(f_515_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_515_2,plain,
! [U_2107] : set_union2(U_2107,empty_set) = U_2107,
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_2107] : set_union2(U_2107,empty_set) = U_2107,
inference(definitional_conversion,[status(esa)],[f_515_2]) ).
cnf(f_515_4,plain,
set_union2(U_2107,empty_set) = U_2107,
inference(clausify,[status(thm)],[f_515_3]) ).
fof(f_516_1,plain,
! [A,B] :
( ! [C] :
( ( meet(boole_lattice(A),B,C) = set_intersection2(B,C)
& join(boole_lattice(A),B,C) = set_union2(B,C) )
| ~ element(C,the_carrier(boole_lattice(A))) )
| ~ element(B,the_carrier(boole_lattice(A))) ),
inference(fof_nnf,[status(thm)],[t1_lattice3]) ).
fof(f_516_2,plain,
! [U_2110,U_2109] :
( ! [U_2108] :
( ( meet(boole_lattice(U_2110),U_2109,U_2108) = set_intersection2(U_2109,U_2108)
& join(boole_lattice(U_2110),U_2109,U_2108) = set_union2(U_2109,U_2108) )
| ~ element(U_2108,the_carrier(boole_lattice(U_2110))) )
| ~ element(U_2109,the_carrier(boole_lattice(U_2110))) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
( ! [U_2110,U_2108,U_2109] :
( meet(boole_lattice(U_2110),U_2109,U_2108) = set_intersection2(U_2109,U_2108)
| ~ sP486(U_2110,U_2108,U_2109) )
& ! [U_2110,U_2108,U_2109] :
( join(boole_lattice(U_2110),U_2109,U_2108) = set_union2(U_2109,U_2108)
| ~ sP486(U_2110,U_2108,U_2109) )
& ! [U_2110,U_2108,U_2109] :
( sP486(U_2110,U_2108,U_2109)
| ~ element(U_2108,the_carrier(boole_lattice(U_2110)))
| ~ element(U_2109,the_carrier(boole_lattice(U_2110))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP486])],[f_516_2]) ).
cnf(f_516_4,plain,
( sP486(U_2110,U_2108,U_2109)
| ~ element(U_2108,the_carrier(boole_lattice(U_2110)))
| ~ element(U_2109,the_carrier(boole_lattice(U_2110))) ),
inference(clausify,[status(thm)],[f_516_3]) ).
cnf(f_516_5,plain,
( join(boole_lattice(U_2110),U_2109,U_2108) = set_union2(U_2109,U_2108)
| ~ sP486(U_2110,U_2108,U_2109) ),
inference(clausify,[status(thm)],[f_516_3]) ).
cnf(f_516_6,plain,
( meet(boole_lattice(U_2110),U_2109,U_2108) = set_intersection2(U_2109,U_2108)
| ~ sP486(U_2110,U_2108,U_2109) ),
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_517_2,plain,
! [U_2112,U_2111] :
( element(U_2112,U_2111)
| ~ in(U_2112,U_2111) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
! [U_2112,U_2111] :
( element(U_2112,U_2111)
| ~ in(U_2112,U_2111) ),
inference(definitional_conversion,[status(esa)],[f_517_2]) ).
cnf(f_517_4,plain,
( element(U_2112,U_2111)
| ~ in(U_2112,U_2111) ),
inference(clausify,[status(thm)],[f_517_3]) ).
fof(f_518_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_518_2,plain,
! [U_2115,U_2114,U_2113] :
( subset(U_2115,U_2113)
| ~ subset(U_2114,U_2113)
| ~ subset(U_2115,U_2114) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
! [U_2114,U_2113,U_2115] :
( subset(U_2115,U_2113)
| ~ subset(U_2114,U_2113)
| ~ subset(U_2115,U_2114) ),
inference(definitional_conversion,[status(esa)],[f_518_2]) ).
cnf(f_518_4,plain,
( subset(U_2115,U_2113)
| ~ subset(U_2114,U_2113)
| ~ subset(U_2115,U_2114) ),
inference(clausify,[status(thm)],[f_518_3]) ).
fof(f_519_1,plain,
powerset(empty_set) = singleton(empty_set),
inference(fof_nnf,[status(thm)],[t1_zfmisc_1]) ).
fof(f_519_2,plain,
powerset(empty_set) = singleton(empty_set),
inference(definitional_conversion,[status(esa)],[f_519_1]) ).
cnf(f_519_3,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[f_519_2]) ).
fof(f_520_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_520_2,plain,
! [U_2118,U_2117,U_2116] :
( ( in(U_2117,relation_rng(U_2116))
& in(U_2118,relation_dom(U_2116)) )
| ~ in(ordered_pair(U_2118,U_2117),U_2116)
| ~ relation(U_2116) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
( ! [U_2116,U_2117,U_2118] :
( in(U_2117,relation_rng(U_2116))
| ~ sP487(U_2116,U_2117,U_2118) )
& ! [U_2116,U_2117,U_2118] :
( in(U_2118,relation_dom(U_2116))
| ~ sP487(U_2116,U_2117,U_2118) )
& ! [U_2116,U_2117,U_2118] :
( sP487(U_2116,U_2117,U_2118)
| ~ in(ordered_pair(U_2118,U_2117),U_2116)
| ~ relation(U_2116) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP487])],[f_520_2]) ).
cnf(f_520_4,plain,
( sP487(U_2116,U_2117,U_2118)
| ~ in(ordered_pair(U_2118,U_2117),U_2116)
| ~ relation(U_2116) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_5,plain,
( in(U_2118,relation_dom(U_2116))
| ~ sP487(U_2116,U_2117,U_2118) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_6,plain,
( in(U_2117,relation_rng(U_2116))
| ~ sP487(U_2116,U_2117,U_2118) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_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_521_2,plain,
! [U_2120,U_2119] :
( ( subset(relation_field(relation_restriction(U_2119,U_2120)),U_2120)
& subset(relation_field(relation_restriction(U_2119,U_2120)),relation_field(U_2119)) )
| ~ relation(U_2119) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
( ! [U_2119,U_2120] :
( subset(relation_field(relation_restriction(U_2119,U_2120)),U_2120)
| ~ sP488(U_2119,U_2120) )
& ! [U_2119,U_2120] :
( subset(relation_field(relation_restriction(U_2119,U_2120)),relation_field(U_2119))
| ~ sP488(U_2119,U_2120) )
& ! [U_2119,U_2120] :
( sP488(U_2119,U_2120)
| ~ relation(U_2119) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP488])],[f_521_2]) ).
cnf(f_521_4,plain,
( sP488(U_2119,U_2120)
| ~ relation(U_2119) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_5,plain,
( subset(relation_field(relation_restriction(U_2119,U_2120)),relation_field(U_2119))
| ~ sP488(U_2119,U_2120) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_6,plain,
( subset(relation_field(relation_restriction(U_2119,U_2120)),U_2120)
| ~ sP488(U_2119,U_2120) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_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_522_2,plain,
! [U_2123,U_2122] :
( ! [U_2121] :
( ( ( in(U_2123,relation_dom(relation_composition(U_2121,U_2122)))
| ~ in(apply(U_2121,U_2123),relation_dom(U_2122))
| ~ in(U_2123,relation_dom(U_2121)) )
& ( ( in(apply(U_2121,U_2123),relation_dom(U_2122))
& in(U_2123,relation_dom(U_2121)) )
| ~ in(U_2123,relation_dom(relation_composition(U_2121,U_2122))) ) )
| ~ function(U_2121)
| ~ relation(U_2121) )
| ~ function(U_2122)
| ~ relation(U_2122) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
( ! [U_2121,U_2122,U_2123] :
( in(apply(U_2121,U_2123),relation_dom(U_2122))
| ~ sP489(U_2121,U_2122,U_2123) )
& ! [U_2121,U_2122,U_2123] :
( in(U_2123,relation_dom(U_2121))
| ~ sP489(U_2121,U_2122,U_2123) )
& ! [U_2121,U_2122,U_2123] :
( in(U_2123,relation_dom(relation_composition(U_2121,U_2122)))
| ~ in(apply(U_2121,U_2123),relation_dom(U_2122))
| ~ in(U_2123,relation_dom(U_2121))
| ~ sP490(U_2121,U_2122,U_2123) )
& ! [U_2121,U_2122,U_2123] :
( sP489(U_2121,U_2122,U_2123)
| ~ in(U_2123,relation_dom(relation_composition(U_2121,U_2122)))
| ~ sP490(U_2121,U_2122,U_2123) )
& ! [U_2121,U_2122,U_2123] :
( sP490(U_2121,U_2122,U_2123)
| ~ function(U_2121)
| ~ relation(U_2121)
| ~ function(U_2122)
| ~ relation(U_2122) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP489,sP490])],[f_522_2]) ).
cnf(f_522_4,plain,
( sP490(U_2121,U_2122,U_2123)
| ~ function(U_2121)
| ~ relation(U_2121)
| ~ function(U_2122)
| ~ relation(U_2122) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_5,plain,
( sP489(U_2121,U_2122,U_2123)
| ~ in(U_2123,relation_dom(relation_composition(U_2121,U_2122)))
| ~ sP490(U_2121,U_2122,U_2123) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_6,plain,
( in(U_2123,relation_dom(relation_composition(U_2121,U_2122)))
| ~ in(apply(U_2121,U_2123),relation_dom(U_2122))
| ~ in(U_2123,relation_dom(U_2121))
| ~ sP490(U_2121,U_2122,U_2123) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_7,plain,
( in(U_2123,relation_dom(U_2121))
| ~ sP489(U_2121,U_2122,U_2123) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_8,plain,
( in(apply(U_2121,U_2123),relation_dom(U_2122))
| ~ sP489(U_2121,U_2122,U_2123) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_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_523_2,plain,
! [U_2128,U_2127,U_2126,U_2125] :
( ! [U_2124] :
( apply(relation_composition(U_2125,U_2124),U_2126) = apply(U_2124,apply(U_2125,U_2126))
| U_2127 = empty_set
| ~ in(U_2126,U_2128)
| ~ function(U_2124)
| ~ relation(U_2124) )
| ~ relation_of2_as_subset(U_2125,U_2128,U_2127)
| ~ quasi_total(U_2125,U_2128,U_2127)
| ~ function(U_2125) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
! [U_2127,U_2126,U_2128,U_2125,U_2124] :
( apply(relation_composition(U_2125,U_2124),U_2126) = apply(U_2124,apply(U_2125,U_2126))
| U_2127 = empty_set
| ~ in(U_2126,U_2128)
| ~ function(U_2124)
| ~ relation(U_2124)
| ~ relation_of2_as_subset(U_2125,U_2128,U_2127)
| ~ quasi_total(U_2125,U_2128,U_2127)
| ~ function(U_2125) ),
inference(definitional_conversion,[status(esa)],[f_523_2]) ).
cnf(f_523_4,plain,
( apply(relation_composition(U_2125,U_2124),U_2126) = apply(U_2124,apply(U_2125,U_2126))
| U_2127 = empty_set
| ~ in(U_2126,U_2128)
| ~ function(U_2124)
| ~ relation(U_2124)
| ~ relation_of2_as_subset(U_2125,U_2128,U_2127)
| ~ quasi_total(U_2125,U_2128,U_2127)
| ~ function(U_2125) ),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_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_524_2,plain,
! [U_2130] :
( ! [U_2129] :
( in(U_2130,U_2129)
| ~ proper_subset(U_2130,U_2129)
| ~ ordinal(U_2129) )
| ~ epsilon_transitive(U_2130) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
! [U_2129,U_2130] :
( in(U_2130,U_2129)
| ~ proper_subset(U_2130,U_2129)
| ~ ordinal(U_2129)
| ~ epsilon_transitive(U_2130) ),
inference(definitional_conversion,[status(esa)],[f_524_2]) ).
cnf(f_524_4,plain,
( in(U_2130,U_2129)
| ~ proper_subset(U_2130,U_2129)
| ~ ordinal(U_2129)
| ~ epsilon_transitive(U_2130) ),
inference(clausify,[status(thm)],[f_524_3]) ).
fof(f_525_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_525_2,plain,
! [U_2131] :
( subset(U_2131,cartesian_product2(relation_dom(U_2131),relation_rng(U_2131)))
| ~ relation(U_2131) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
fof(f_525_3,plain,
! [U_2131] :
( subset(U_2131,cartesian_product2(relation_dom(U_2131),relation_rng(U_2131)))
| ~ relation(U_2131) ),
inference(definitional_conversion,[status(esa)],[f_525_2]) ).
cnf(f_525_4,plain,
( subset(U_2131,cartesian_product2(relation_dom(U_2131),relation_rng(U_2131)))
| ~ relation(U_2131) ),
inference(clausify,[status(thm)],[f_525_3]) ).
fof(f_526_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_526_2,plain,
! [U_2134,U_2133,U_2132] :
( subset(fiber(relation_restriction(U_2132,U_2134),U_2133),fiber(U_2132,U_2133))
| ~ relation(U_2132) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
! [U_2133,U_2134,U_2132] :
( subset(fiber(relation_restriction(U_2132,U_2134),U_2133),fiber(U_2132,U_2133))
| ~ relation(U_2132) ),
inference(definitional_conversion,[status(esa)],[f_526_2]) ).
cnf(f_526_4,plain,
( subset(fiber(relation_restriction(U_2132,U_2134),U_2133),fiber(U_2132,U_2133))
| ~ relation(U_2132) ),
inference(clausify,[status(thm)],[f_526_3]) ).
fof(f_527_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_527_2,plain,
! [U_2137,U_2136] :
( ! [U_2135] :
( apply(relation_composition(U_2135,U_2136),U_2137) = apply(U_2136,apply(U_2135,U_2137))
| ~ in(U_2137,relation_dom(relation_composition(U_2135,U_2136)))
| ~ function(U_2135)
| ~ relation(U_2135) )
| ~ function(U_2136)
| ~ relation(U_2136) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
fof(f_527_3,plain,
! [U_2135,U_2136,U_2137] :
( apply(relation_composition(U_2135,U_2136),U_2137) = apply(U_2136,apply(U_2135,U_2137))
| ~ in(U_2137,relation_dom(relation_composition(U_2135,U_2136)))
| ~ function(U_2135)
| ~ relation(U_2135)
| ~ function(U_2136)
| ~ relation(U_2136) ),
inference(definitional_conversion,[status(esa)],[f_527_2]) ).
cnf(f_527_4,plain,
( apply(relation_composition(U_2135,U_2136),U_2137) = apply(U_2136,apply(U_2135,U_2137))
| ~ in(U_2137,relation_dom(relation_composition(U_2135,U_2136)))
| ~ function(U_2135)
| ~ relation(U_2135)
| ~ function(U_2136)
| ~ relation(U_2136) ),
inference(clausify,[status(thm)],[f_527_3]) ).
fof(f_528_1,plain,
! [A] :
( ! [B] :
( subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B
| ~ element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t22_pre_topc]) ).
fof(f_528_2,plain,
! [U_2139] :
( ! [U_2138] :
( subset_difference(the_carrier(U_2139),cast_as_carrier_subset(U_2139),subset_difference(the_carrier(U_2139),cast_as_carrier_subset(U_2139),U_2138)) = U_2138
| ~ element(U_2138,powerset(the_carrier(U_2139))) )
| ~ one_sorted_str(U_2139) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
! [U_2139,U_2138] :
( subset_difference(the_carrier(U_2139),cast_as_carrier_subset(U_2139),subset_difference(the_carrier(U_2139),cast_as_carrier_subset(U_2139),U_2138)) = U_2138
| ~ element(U_2138,powerset(the_carrier(U_2139)))
| ~ one_sorted_str(U_2139) ),
inference(definitional_conversion,[status(esa)],[f_528_2]) ).
cnf(f_528_4,plain,
( subset_difference(the_carrier(U_2139),cast_as_carrier_subset(U_2139),subset_difference(the_carrier(U_2139),cast_as_carrier_subset(U_2139),U_2138)) = U_2138
| ~ element(U_2138,powerset(the_carrier(U_2139)))
| ~ one_sorted_str(U_2139) ),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_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_529_2,plain,
! [U_2146,U_2145,U_2144] :
( ( ( ! [U_2143] :
( ? [U_2142] : in(ordered_pair(U_2143,U_2142),U_2144)
| ~ in(U_2143,U_2145) )
| relation_dom_as_subset(U_2145,U_2146,U_2144) != U_2145 )
& ( relation_dom_as_subset(U_2145,U_2146,U_2144) = U_2145
| ? [U_2141] :
( ! [U_2140] : ~ in(ordered_pair(U_2141,U_2140),U_2144)
& in(U_2141,U_2145) ) ) )
| ~ relation_of2_as_subset(U_2144,U_2145,U_2146) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
! [U_2146,U_2145,U_2144] :
( ( ( ! [U_2143] :
( ? [U_2142] : in(ordered_pair(U_2143,U_2142),U_2144)
| ~ in(U_2143,U_2145) )
| relation_dom_as_subset(U_2145,U_2146,U_2144) != U_2145 )
& ( relation_dom_as_subset(U_2145,U_2146,U_2144) = U_2145
| ( ! [U_2140] : ~ in(ordered_pair(sK456(U_2146,U_2145,U_2144),U_2140),U_2144)
& in(sK456(U_2146,U_2145,U_2144),U_2145) ) ) )
| ~ relation_of2_as_subset(U_2144,U_2145,U_2146) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK456]),skolemize(U_2141,sK456(U_2146,U_2145,U_2144))],[f_529_2]) ).
fof(f_529_4,plain,
! [U_2146,U_2145,U_2144] :
( ( ( ! [U_2143] :
( in(ordered_pair(U_2143,sK457(U_2146,U_2145,U_2144,U_2143)),U_2144)
| ~ in(U_2143,U_2145) )
| relation_dom_as_subset(U_2145,U_2146,U_2144) != U_2145 )
& ( relation_dom_as_subset(U_2145,U_2146,U_2144) = U_2145
| ( ! [U_2140] : ~ in(ordered_pair(sK456(U_2146,U_2145,U_2144),U_2140),U_2144)
& in(sK456(U_2146,U_2145,U_2144),U_2145) ) ) )
| ~ relation_of2_as_subset(U_2144,U_2145,U_2146) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_2142,sK457(U_2146,U_2145,U_2144,U_2143))],[f_529_3]) ).
fof(f_529_5,plain,
( ! [U_2140,U_2144,U_2145,U_2146] :
( ~ in(ordered_pair(sK456(U_2146,U_2145,U_2144),U_2140),U_2144)
| ~ sP491(U_2140,U_2144,U_2145,U_2146) )
& ! [U_2140,U_2144,U_2145,U_2146] :
( in(sK456(U_2146,U_2145,U_2144),U_2145)
| ~ sP491(U_2140,U_2144,U_2145,U_2146) )
& ! [U_2140,U_2143,U_2144,U_2145,U_2146] :
( in(ordered_pair(U_2143,sK457(U_2146,U_2145,U_2144,U_2143)),U_2144)
| ~ in(U_2143,U_2145)
| relation_dom_as_subset(U_2145,U_2146,U_2144) != U_2145
| ~ sP492(U_2140,U_2143,U_2144,U_2145,U_2146) )
& ! [U_2140,U_2143,U_2144,U_2145,U_2146] :
( relation_dom_as_subset(U_2145,U_2146,U_2144) = U_2145
| sP491(U_2140,U_2144,U_2145,U_2146)
| ~ sP492(U_2140,U_2143,U_2144,U_2145,U_2146) )
& ! [U_2140,U_2143,U_2144,U_2145,U_2146] :
( sP492(U_2140,U_2143,U_2144,U_2145,U_2146)
| ~ relation_of2_as_subset(U_2144,U_2145,U_2146) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP491,sP492])],[f_529_4]) ).
cnf(f_529_6,plain,
( sP492(U_2140,U_2143,U_2144,U_2145,U_2146)
| ~ relation_of2_as_subset(U_2144,U_2145,U_2146) ),
inference(clausify,[status(thm)],[f_529_5]) ).
cnf(f_529_7,plain,
( relation_dom_as_subset(U_2145,U_2146,U_2144) = U_2145
| sP491(U_2140,U_2144,U_2145,U_2146)
| ~ sP492(U_2140,U_2143,U_2144,U_2145,U_2146) ),
inference(clausify,[status(thm)],[f_529_5]) ).
cnf(f_529_8,plain,
( in(ordered_pair(U_2143,sK457(U_2146,U_2145,U_2144,U_2143)),U_2144)
| ~ in(U_2143,U_2145)
| relation_dom_as_subset(U_2145,U_2146,U_2144) != U_2145
| ~ sP492(U_2140,U_2143,U_2144,U_2145,U_2146) ),
inference(clausify,[status(thm)],[f_529_5]) ).
cnf(f_529_9,plain,
( in(sK456(U_2146,U_2145,U_2144),U_2145)
| ~ sP491(U_2140,U_2144,U_2145,U_2146) ),
inference(clausify,[status(thm)],[f_529_5]) ).
cnf(f_529_10,plain,
( ~ in(ordered_pair(sK456(U_2146,U_2145,U_2144),U_2140),U_2144)
| ~ sP491(U_2140,U_2144,U_2145,U_2146) ),
inference(clausify,[status(thm)],[f_529_5]) ).
fof(f_530_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_530_2,plain,
! [U_2148,U_2147] :
( reflexive(relation_restriction(U_2147,U_2148))
| ~ reflexive(U_2147)
| ~ relation(U_2147) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
! [U_2147,U_2148] :
( reflexive(relation_restriction(U_2147,U_2148))
| ~ reflexive(U_2147)
| ~ relation(U_2147) ),
inference(definitional_conversion,[status(esa)],[f_530_2]) ).
cnf(f_530_4,plain,
( reflexive(relation_restriction(U_2147,U_2148))
| ~ reflexive(U_2147)
| ~ relation(U_2147) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_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_531_2,plain,
! [U_2151,U_2150] :
( ! [U_2149] :
( apply(relation_composition(U_2150,U_2149),U_2151) = apply(U_2149,apply(U_2150,U_2151))
| ~ in(U_2151,relation_dom(U_2150))
| ~ function(U_2149)
| ~ relation(U_2149) )
| ~ function(U_2150)
| ~ relation(U_2150) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
! [U_2150,U_2149,U_2151] :
( apply(relation_composition(U_2150,U_2149),U_2151) = apply(U_2149,apply(U_2150,U_2151))
| ~ in(U_2151,relation_dom(U_2150))
| ~ function(U_2149)
| ~ relation(U_2149)
| ~ function(U_2150)
| ~ relation(U_2150) ),
inference(definitional_conversion,[status(esa)],[f_531_2]) ).
cnf(f_531_4,plain,
( apply(relation_composition(U_2150,U_2149),U_2151) = apply(U_2149,apply(U_2150,U_2151))
| ~ in(U_2151,relation_dom(U_2150))
| ~ function(U_2149)
| ~ relation(U_2149)
| ~ function(U_2150)
| ~ relation(U_2150) ),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( below(A,meet_commut(A,B,C),B)
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| ~ meet_absorbing(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t23_lattices]) ).
fof(f_532_2,plain,
! [U_2154] :
( ! [U_2153] :
( ! [U_2152] :
( below(U_2154,meet_commut(U_2154,U_2153,U_2152),U_2153)
| ~ element(U_2152,the_carrier(U_2154)) )
| ~ element(U_2153,the_carrier(U_2154)) )
| ~ latt_str(U_2154)
| ~ meet_absorbing(U_2154)
| ~ meet_commutative(U_2154)
| empty_carrier(U_2154) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
! [U_2154,U_2153,U_2152] :
( below(U_2154,meet_commut(U_2154,U_2153,U_2152),U_2153)
| ~ element(U_2152,the_carrier(U_2154))
| ~ element(U_2153,the_carrier(U_2154))
| ~ latt_str(U_2154)
| ~ meet_absorbing(U_2154)
| ~ meet_commutative(U_2154)
| empty_carrier(U_2154) ),
inference(definitional_conversion,[status(esa)],[f_532_2]) ).
cnf(f_532_4,plain,
( below(U_2154,meet_commut(U_2154,U_2153,U_2152),U_2153)
| ~ element(U_2152,the_carrier(U_2154))
| ~ element(U_2153,the_carrier(U_2154))
| ~ latt_str(U_2154)
| ~ meet_absorbing(U_2154)
| ~ meet_commutative(U_2154)
| empty_carrier(U_2154) ),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_533_2,plain,
! [U_2156,U_2155] :
( ordinal(U_2156)
| ~ in(U_2156,U_2155)
| ~ ordinal(U_2155) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
! [U_2155,U_2156] :
( ordinal(U_2156)
| ~ in(U_2156,U_2155)
| ~ ordinal(U_2155) ),
inference(definitional_conversion,[status(esa)],[f_533_2]) ).
cnf(f_533_4,plain,
( ordinal(U_2156)
| ~ in(U_2156,U_2155)
| ~ ordinal(U_2155) ),
inference(clausify,[status(thm)],[f_533_3]) ).
fof(f_534_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_534_2,plain,
! [U_2163,U_2162,U_2161] :
( ( ( ! [U_2160] :
( ? [U_2159] : in(ordered_pair(U_2159,U_2160),U_2161)
| ~ in(U_2160,U_2162) )
| relation_rng_as_subset(U_2163,U_2162,U_2161) != U_2162 )
& ( relation_rng_as_subset(U_2163,U_2162,U_2161) = U_2162
| ? [U_2158] :
( ! [U_2157] : ~ in(ordered_pair(U_2157,U_2158),U_2161)
& in(U_2158,U_2162) ) ) )
| ~ relation_of2_as_subset(U_2161,U_2163,U_2162) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
! [U_2163,U_2162,U_2161] :
( ( ( ! [U_2160] :
( ? [U_2159] : in(ordered_pair(U_2159,U_2160),U_2161)
| ~ in(U_2160,U_2162) )
| relation_rng_as_subset(U_2163,U_2162,U_2161) != U_2162 )
& ( relation_rng_as_subset(U_2163,U_2162,U_2161) = U_2162
| ( ! [U_2157] : ~ in(ordered_pair(U_2157,sK458(U_2163,U_2162,U_2161)),U_2161)
& in(sK458(U_2163,U_2162,U_2161),U_2162) ) ) )
| ~ relation_of2_as_subset(U_2161,U_2163,U_2162) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_2158,sK458(U_2163,U_2162,U_2161))],[f_534_2]) ).
fof(f_534_4,plain,
! [U_2163,U_2162,U_2161] :
( ( ( ! [U_2160] :
( in(ordered_pair(sK459(U_2163,U_2162,U_2161,U_2160),U_2160),U_2161)
| ~ in(U_2160,U_2162) )
| relation_rng_as_subset(U_2163,U_2162,U_2161) != U_2162 )
& ( relation_rng_as_subset(U_2163,U_2162,U_2161) = U_2162
| ( ! [U_2157] : ~ in(ordered_pair(U_2157,sK458(U_2163,U_2162,U_2161)),U_2161)
& in(sK458(U_2163,U_2162,U_2161),U_2162) ) ) )
| ~ relation_of2_as_subset(U_2161,U_2163,U_2162) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_2159,sK459(U_2163,U_2162,U_2161,U_2160))],[f_534_3]) ).
fof(f_534_5,plain,
( ! [U_2157,U_2161,U_2162,U_2163] :
( ~ in(ordered_pair(U_2157,sK458(U_2163,U_2162,U_2161)),U_2161)
| ~ sP493(U_2157,U_2161,U_2162,U_2163) )
& ! [U_2157,U_2161,U_2162,U_2163] :
( in(sK458(U_2163,U_2162,U_2161),U_2162)
| ~ sP493(U_2157,U_2161,U_2162,U_2163) )
& ! [U_2157,U_2160,U_2161,U_2162,U_2163] :
( in(ordered_pair(sK459(U_2163,U_2162,U_2161,U_2160),U_2160),U_2161)
| ~ in(U_2160,U_2162)
| relation_rng_as_subset(U_2163,U_2162,U_2161) != U_2162
| ~ sP494(U_2157,U_2160,U_2161,U_2162,U_2163) )
& ! [U_2157,U_2160,U_2161,U_2162,U_2163] :
( relation_rng_as_subset(U_2163,U_2162,U_2161) = U_2162
| sP493(U_2157,U_2161,U_2162,U_2163)
| ~ sP494(U_2157,U_2160,U_2161,U_2162,U_2163) )
& ! [U_2157,U_2160,U_2161,U_2162,U_2163] :
( sP494(U_2157,U_2160,U_2161,U_2162,U_2163)
| ~ relation_of2_as_subset(U_2161,U_2163,U_2162) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP493,sP494])],[f_534_4]) ).
cnf(f_534_6,plain,
( sP494(U_2157,U_2160,U_2161,U_2162,U_2163)
| ~ relation_of2_as_subset(U_2161,U_2163,U_2162) ),
inference(clausify,[status(thm)],[f_534_5]) ).
cnf(f_534_7,plain,
( relation_rng_as_subset(U_2163,U_2162,U_2161) = U_2162
| sP493(U_2157,U_2161,U_2162,U_2163)
| ~ sP494(U_2157,U_2160,U_2161,U_2162,U_2163) ),
inference(clausify,[status(thm)],[f_534_5]) ).
cnf(f_534_8,plain,
( in(ordered_pair(sK459(U_2163,U_2162,U_2161,U_2160),U_2160),U_2161)
| ~ in(U_2160,U_2162)
| relation_rng_as_subset(U_2163,U_2162,U_2161) != U_2162
| ~ sP494(U_2157,U_2160,U_2161,U_2162,U_2163) ),
inference(clausify,[status(thm)],[f_534_5]) ).
cnf(f_534_9,plain,
( in(sK458(U_2163,U_2162,U_2161),U_2162)
| ~ sP493(U_2157,U_2161,U_2162,U_2163) ),
inference(clausify,[status(thm)],[f_534_5]) ).
cnf(f_534_10,plain,
( ~ in(ordered_pair(U_2157,sK458(U_2163,U_2162,U_2161)),U_2161)
| ~ sP493(U_2157,U_2161,U_2162,U_2163) ),
inference(clausify,[status(thm)],[f_534_5]) ).
fof(f_535_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_535_2,plain,
! [U_2165,U_2164] :
( connected(relation_restriction(U_2164,U_2165))
| ~ connected(U_2164)
| ~ relation(U_2164) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
fof(f_535_3,plain,
! [U_2165,U_2164] :
( connected(relation_restriction(U_2164,U_2165))
| ~ connected(U_2164)
| ~ relation(U_2164) ),
inference(definitional_conversion,[status(esa)],[f_535_2]) ).
cnf(f_535_4,plain,
( connected(relation_restriction(U_2164,U_2165))
| ~ connected(U_2164)
| ~ relation(U_2164) ),
inference(clausify,[status(thm)],[f_535_3]) ).
fof(f_536_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_536_2,plain,
! [U_2167] :
( ! [U_2166] :
( in(U_2166,U_2167)
| U_2167 = U_2166
| in(U_2167,U_2166)
| ~ ordinal(U_2166) )
| ~ ordinal(U_2167) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
fof(f_536_3,plain,
! [U_2166,U_2167] :
( in(U_2166,U_2167)
| U_2167 = U_2166
| in(U_2167,U_2166)
| ~ ordinal(U_2166)
| ~ ordinal(U_2167) ),
inference(definitional_conversion,[status(esa)],[f_536_2]) ).
cnf(f_536_4,plain,
( in(U_2166,U_2167)
| U_2167 = U_2166
| in(U_2167,U_2166)
| ~ ordinal(U_2166)
| ~ ordinal(U_2167) ),
inference(clausify,[status(thm)],[f_536_3]) ).
fof(f_537_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_537_2,plain,
! [U_2169,U_2168] :
( transitive(relation_restriction(U_2168,U_2169))
| ~ transitive(U_2168)
| ~ relation(U_2168) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
! [U_2169,U_2168] :
( transitive(relation_restriction(U_2168,U_2169))
| ~ transitive(U_2168)
| ~ relation(U_2168) ),
inference(definitional_conversion,[status(esa)],[f_537_2]) ).
cnf(f_537_4,plain,
( transitive(relation_restriction(U_2168,U_2169))
| ~ transitive(U_2168)
| ~ relation(U_2168) ),
inference(clausify,[status(thm)],[f_537_3]) ).
fof(f_538_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( B = C
| ~ related(A,C,B)
| ~ related(A,B,C)
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[t25_orders_2]) ).
fof(f_538_2,plain,
! [U_2172] :
( ! [U_2171] :
( ! [U_2170] :
( U_2171 = U_2170
| ~ related(U_2172,U_2170,U_2171)
| ~ related(U_2172,U_2171,U_2170)
| ~ element(U_2170,the_carrier(U_2172)) )
| ~ element(U_2171,the_carrier(U_2172)) )
| ~ rel_str(U_2172)
| ~ antisymmetric_relstr(U_2172) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
! [U_2170,U_2171,U_2172] :
( U_2171 = U_2170
| ~ related(U_2172,U_2170,U_2171)
| ~ related(U_2172,U_2171,U_2170)
| ~ element(U_2170,the_carrier(U_2172))
| ~ element(U_2171,the_carrier(U_2172))
| ~ rel_str(U_2172)
| ~ antisymmetric_relstr(U_2172) ),
inference(definitional_conversion,[status(esa)],[f_538_2]) ).
cnf(f_538_4,plain,
( U_2171 = U_2170
| ~ related(U_2172,U_2170,U_2171)
| ~ related(U_2172,U_2171,U_2170)
| ~ element(U_2170,the_carrier(U_2172))
| ~ element(U_2171,the_carrier(U_2172))
| ~ rel_str(U_2172)
| ~ antisymmetric_relstr(U_2172) ),
inference(clausify,[status(thm)],[f_538_3]) ).
fof(f_539_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_539_2,plain,
! [U_2174] :
( ! [U_2173] :
( ( subset(relation_rng(U_2174),relation_rng(U_2173))
& subset(relation_dom(U_2174),relation_dom(U_2173)) )
| ~ subset(U_2174,U_2173)
| ~ relation(U_2173) )
| ~ relation(U_2174) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
fof(f_539_3,plain,
( ! [U_2173,U_2174] :
( subset(relation_rng(U_2174),relation_rng(U_2173))
| ~ sP495(U_2173,U_2174) )
& ! [U_2173,U_2174] :
( subset(relation_dom(U_2174),relation_dom(U_2173))
| ~ sP495(U_2173,U_2174) )
& ! [U_2173,U_2174] :
( sP495(U_2173,U_2174)
| ~ subset(U_2174,U_2173)
| ~ relation(U_2173)
| ~ relation(U_2174) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP495])],[f_539_2]) ).
cnf(f_539_4,plain,
( sP495(U_2173,U_2174)
| ~ subset(U_2174,U_2173)
| ~ relation(U_2173)
| ~ relation(U_2174) ),
inference(clausify,[status(thm)],[f_539_3]) ).
cnf(f_539_5,plain,
( subset(relation_dom(U_2174),relation_dom(U_2173))
| ~ sP495(U_2173,U_2174) ),
inference(clausify,[status(thm)],[f_539_3]) ).
cnf(f_539_6,plain,
( subset(relation_rng(U_2174),relation_rng(U_2173))
| ~ sP495(U_2173,U_2174) ),
inference(clausify,[status(thm)],[f_539_3]) ).
fof(f_540_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_540_2,plain,
! [U_2176,U_2175] :
( antisymmetric(relation_restriction(U_2175,U_2176))
| ~ antisymmetric(U_2175)
| ~ relation(U_2175) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
fof(f_540_3,plain,
! [U_2175,U_2176] :
( antisymmetric(relation_restriction(U_2175,U_2176))
| ~ antisymmetric(U_2175)
| ~ relation(U_2175) ),
inference(definitional_conversion,[status(esa)],[f_540_2]) ).
cnf(f_540_4,plain,
( antisymmetric(relation_restriction(U_2175,U_2176))
| ~ antisymmetric(U_2175)
| ~ relation(U_2175) ),
inference(clausify,[status(thm)],[f_540_3]) ).
fof(f_541_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_541_2,plain,
! [U_2178,U_2177] :
( ( well_ordering(relation_restriction(U_2177,U_2178))
& relation_field(relation_restriction(U_2177,U_2178)) = U_2178 )
| ~ well_orders(U_2177,U_2178)
| ~ relation(U_2177) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
( ! [U_2177,U_2178] :
( well_ordering(relation_restriction(U_2177,U_2178))
| ~ sP496(U_2177,U_2178) )
& ! [U_2177,U_2178] :
( relation_field(relation_restriction(U_2177,U_2178)) = U_2178
| ~ sP496(U_2177,U_2178) )
& ! [U_2177,U_2178] :
( sP496(U_2177,U_2178)
| ~ well_orders(U_2177,U_2178)
| ~ relation(U_2177) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP496])],[f_541_2]) ).
cnf(f_541_4,plain,
( sP496(U_2177,U_2178)
| ~ well_orders(U_2177,U_2178)
| ~ relation(U_2177) ),
inference(clausify,[status(thm)],[f_541_3]) ).
cnf(f_541_5,plain,
( relation_field(relation_restriction(U_2177,U_2178)) = U_2178
| ~ sP496(U_2177,U_2178) ),
inference(clausify,[status(thm)],[f_541_3]) ).
cnf(f_541_6,plain,
( well_ordering(relation_restriction(U_2177,U_2178))
| ~ sP496(U_2177,U_2178) ),
inference(clausify,[status(thm)],[f_541_3]) ).
fof(f_542_1,plain,
! [A] :
( finite(relation_rng(A))
| ~ finite(relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t26_finset_1]) ).
fof(f_542_2,plain,
! [U_2179] :
( finite(relation_rng(U_2179))
| ~ finite(relation_dom(U_2179))
| ~ function(U_2179)
| ~ relation(U_2179) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
! [U_2179] :
( finite(relation_rng(U_2179))
| ~ finite(relation_dom(U_2179))
| ~ function(U_2179)
| ~ relation(U_2179) ),
inference(definitional_conversion,[status(esa)],[f_542_2]) ).
cnf(f_542_4,plain,
( finite(relation_rng(U_2179))
| ~ finite(relation_dom(U_2179))
| ~ function(U_2179)
| ~ relation(U_2179) ),
inference(clausify,[status(thm)],[f_542_3]) ).
fof(f_543_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( B = C
| ~ below(A,C,B)
| ~ below(A,B,C)
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t26_lattices]) ).
fof(f_543_2,plain,
! [U_2182] :
( ! [U_2181] :
( ! [U_2180] :
( U_2181 = U_2180
| ~ below(U_2182,U_2180,U_2181)
| ~ below(U_2182,U_2181,U_2180)
| ~ element(U_2180,the_carrier(U_2182)) )
| ~ element(U_2181,the_carrier(U_2182)) )
| ~ join_semilatt_str(U_2182)
| ~ join_commutative(U_2182)
| empty_carrier(U_2182) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
fof(f_543_3,plain,
! [U_2181,U_2180,U_2182] :
( U_2181 = U_2180
| ~ below(U_2182,U_2180,U_2181)
| ~ below(U_2182,U_2181,U_2180)
| ~ element(U_2180,the_carrier(U_2182))
| ~ element(U_2181,the_carrier(U_2182))
| ~ join_semilatt_str(U_2182)
| ~ join_commutative(U_2182)
| empty_carrier(U_2182) ),
inference(definitional_conversion,[status(esa)],[f_543_2]) ).
cnf(f_543_4,plain,
( U_2181 = U_2180
| ~ below(U_2182,U_2180,U_2181)
| ~ below(U_2182,U_2181,U_2180)
| ~ element(U_2180,the_carrier(U_2182))
| ~ element(U_2181,the_carrier(U_2182))
| ~ join_semilatt_str(U_2182)
| ~ join_commutative(U_2182)
| empty_carrier(U_2182) ),
inference(clausify,[status(thm)],[f_543_3]) ).
fof(f_544_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( related(A,B,D)
| ~ related(A,C,D)
| ~ related(A,B,C)
| ~ element(D,the_carrier(A)) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ transitive_relstr(A) ),
inference(fof_nnf,[status(thm)],[t26_orders_2]) ).
fof(f_544_2,plain,
! [U_2186] :
( ! [U_2185] :
( ! [U_2184] :
( ! [U_2183] :
( related(U_2186,U_2185,U_2183)
| ~ related(U_2186,U_2184,U_2183)
| ~ related(U_2186,U_2185,U_2184)
| ~ element(U_2183,the_carrier(U_2186)) )
| ~ element(U_2184,the_carrier(U_2186)) )
| ~ element(U_2185,the_carrier(U_2186)) )
| ~ rel_str(U_2186)
| ~ transitive_relstr(U_2186) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
fof(f_544_3,plain,
! [U_2186,U_2183,U_2184,U_2185] :
( related(U_2186,U_2185,U_2183)
| ~ related(U_2186,U_2184,U_2183)
| ~ related(U_2186,U_2185,U_2184)
| ~ element(U_2183,the_carrier(U_2186))
| ~ element(U_2184,the_carrier(U_2186))
| ~ element(U_2185,the_carrier(U_2186))
| ~ rel_str(U_2186)
| ~ transitive_relstr(U_2186) ),
inference(definitional_conversion,[status(esa)],[f_544_2]) ).
cnf(f_544_4,plain,
( related(U_2186,U_2185,U_2183)
| ~ related(U_2186,U_2184,U_2183)
| ~ related(U_2186,U_2185,U_2184)
| ~ element(U_2183,the_carrier(U_2186))
| ~ element(U_2184,the_carrier(U_2186))
| ~ element(U_2185,the_carrier(U_2186))
| ~ rel_str(U_2186)
| ~ transitive_relstr(U_2186) ),
inference(clausify,[status(thm)],[f_544_3]) ).
fof(f_545_1,plain,
! [A] :
? [B] :
( well_orders(B,A)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t26_wellord2]) ).
fof(f_545_2,plain,
! [U_2188] :
? [U_2187] :
( well_orders(U_2187,U_2188)
& relation(U_2187) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
fof(f_545_3,plain,
! [U_2188] :
( well_orders(sK460(U_2188),U_2188)
& relation(sK460(U_2188)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_2187,sK460(U_2188))],[f_545_2]) ).
fof(f_545_4,plain,
( ! [U_2188] : well_orders(sK460(U_2188),U_2188)
& ! [U_2188] : relation(sK460(U_2188)) ),
inference(definitional_conversion,[status(esa)],[f_545_3]) ).
cnf(f_545_5,plain,
relation(sK460(U_2188)),
inference(clausify,[status(thm)],[f_545_4]) ).
cnf(f_545_6,plain,
well_orders(sK460(U_2188),U_2188),
inference(clausify,[status(thm)],[f_545_4]) ).
fof(f_546_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_546_2,plain,
! [U_2191,U_2190,U_2189] :
( subset(set_intersection2(U_2191,U_2189),set_intersection2(U_2190,U_2189))
| ~ subset(U_2191,U_2190) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
fof(f_546_3,plain,
! [U_2191,U_2190] :
( ! [U_2189] : subset(set_intersection2(U_2191,U_2189),set_intersection2(U_2190,U_2189))
| ~ subset(U_2191,U_2190) ),
inference(miniscope,[status(thm)],[f_546_2]) ).
fof(f_546_4,plain,
! [U_2189,U_2190,U_2191] :
( subset(set_intersection2(U_2191,U_2189),set_intersection2(U_2190,U_2189))
| ~ subset(U_2191,U_2190) ),
inference(definitional_conversion,[status(esa)],[f_546_3]) ).
cnf(f_546_5,plain,
( subset(set_intersection2(U_2191,U_2189),set_intersection2(U_2190,U_2189))
| ~ subset(U_2191,U_2190) ),
inference(clausify,[status(thm)],[f_546_4]) ).
fof(f_547_1,plain,
! [A,B] :
( ! [C] :
( ( ( latt_set_smaller(B,C,A)
| ~ relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) )
& ( relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))
| ~ latt_set_smaller(B,C,A) ) )
| ~ element(C,the_carrier(B)) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[t28_lattice3]) ).
fof(f_547_2,plain,
! [U_2194,U_2193] :
( ! [U_2192] :
( ( ( latt_set_smaller(U_2193,U_2192,U_2194)
| ~ relstr_element_smaller(poset_of_lattice(U_2193),U_2194,cast_to_el_of_LattPOSet(U_2193,U_2192)) )
& ( relstr_element_smaller(poset_of_lattice(U_2193),U_2194,cast_to_el_of_LattPOSet(U_2193,U_2192))
| ~ latt_set_smaller(U_2193,U_2192,U_2194) ) )
| ~ element(U_2192,the_carrier(U_2193)) )
| ~ latt_str(U_2193)
| ~ lattice(U_2193)
| empty_carrier(U_2193) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
fof(f_547_3,plain,
( ! [U_2194,U_2192,U_2193] :
( latt_set_smaller(U_2193,U_2192,U_2194)
| ~ relstr_element_smaller(poset_of_lattice(U_2193),U_2194,cast_to_el_of_LattPOSet(U_2193,U_2192))
| ~ sP497(U_2194,U_2192,U_2193) )
& ! [U_2194,U_2192,U_2193] :
( relstr_element_smaller(poset_of_lattice(U_2193),U_2194,cast_to_el_of_LattPOSet(U_2193,U_2192))
| ~ latt_set_smaller(U_2193,U_2192,U_2194)
| ~ sP497(U_2194,U_2192,U_2193) )
& ! [U_2194,U_2192,U_2193] :
( sP497(U_2194,U_2192,U_2193)
| ~ element(U_2192,the_carrier(U_2193))
| ~ latt_str(U_2193)
| ~ lattice(U_2193)
| empty_carrier(U_2193) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP497])],[f_547_2]) ).
cnf(f_547_4,plain,
( sP497(U_2194,U_2192,U_2193)
| ~ element(U_2192,the_carrier(U_2193))
| ~ latt_str(U_2193)
| ~ lattice(U_2193)
| empty_carrier(U_2193) ),
inference(clausify,[status(thm)],[f_547_3]) ).
cnf(f_547_5,plain,
( relstr_element_smaller(poset_of_lattice(U_2193),U_2194,cast_to_el_of_LattPOSet(U_2193,U_2192))
| ~ latt_set_smaller(U_2193,U_2192,U_2194)
| ~ sP497(U_2194,U_2192,U_2193) ),
inference(clausify,[status(thm)],[f_547_3]) ).
cnf(f_547_6,plain,
( latt_set_smaller(U_2193,U_2192,U_2194)
| ~ relstr_element_smaller(poset_of_lattice(U_2193),U_2194,cast_to_el_of_LattPOSet(U_2193,U_2192))
| ~ sP497(U_2194,U_2192,U_2193) ),
inference(clausify,[status(thm)],[f_547_3]) ).
fof(f_548_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_548_2,plain,
! [U_2198] :
( ? [U_2197] :
( ! [U_2196] :
( in(apply(U_2197,U_2196),U_2196)
| ~ in(U_2196,U_2198) )
& relation_dom(U_2197) = U_2198
& function(U_2197)
& relation(U_2197) )
| ? [U_2195] :
( U_2195 = empty_set
& in(U_2195,U_2198) )
| empty(U_2198) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
! [U_2198] :
( ? [U_2197] :
( ! [U_2196] :
( in(apply(U_2197,U_2196),U_2196)
| ~ in(U_2196,U_2198) )
& relation_dom(U_2197) = U_2198
& function(U_2197)
& relation(U_2197) )
| ( sK461(U_2198) = empty_set
& in(sK461(U_2198),U_2198) )
| empty(U_2198) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_2195,sK461(U_2198))],[f_548_2]) ).
fof(f_548_4,plain,
! [U_2198] :
( ( ! [U_2196] :
( in(apply(sK462(U_2198),U_2196),U_2196)
| ~ in(U_2196,U_2198) )
& relation_dom(sK462(U_2198)) = U_2198
& function(sK462(U_2198))
& relation(sK462(U_2198)) )
| ( sK461(U_2198) = empty_set
& in(sK461(U_2198),U_2198) )
| empty(U_2198) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_2197,sK462(U_2198))],[f_548_3]) ).
fof(f_548_5,plain,
( ! [U_2196,U_2198] :
( in(apply(sK462(U_2198),U_2196),U_2196)
| ~ in(U_2196,U_2198)
| ~ sP499(U_2196,U_2198) )
& ! [U_2196,U_2198] :
( relation_dom(sK462(U_2198)) = U_2198
| ~ sP499(U_2196,U_2198) )
& ! [U_2196,U_2198] :
( function(sK462(U_2198))
| ~ sP499(U_2196,U_2198) )
& ! [U_2196,U_2198] :
( relation(sK462(U_2198))
| ~ sP499(U_2196,U_2198) )
& ! [U_2198] :
( sK461(U_2198) = empty_set
| ~ sP498(U_2198) )
& ! [U_2198] :
( in(sK461(U_2198),U_2198)
| ~ sP498(U_2198) )
& ! [U_2196,U_2198] :
( sP499(U_2196,U_2198)
| sP498(U_2198)
| empty(U_2198) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP498,sP499])],[f_548_4]) ).
cnf(f_548_6,plain,
( sP499(U_2196,U_2198)
| sP498(U_2198)
| empty(U_2198) ),
inference(clausify,[status(thm)],[f_548_5]) ).
cnf(f_548_7,plain,
( in(sK461(U_2198),U_2198)
| ~ sP498(U_2198) ),
inference(clausify,[status(thm)],[f_548_5]) ).
cnf(f_548_8,plain,
( sK461(U_2198) = empty_set
| ~ sP498(U_2198) ),
inference(clausify,[status(thm)],[f_548_5]) ).
cnf(f_548_9,plain,
( relation(sK462(U_2198))
| ~ sP499(U_2196,U_2198) ),
inference(clausify,[status(thm)],[f_548_5]) ).
cnf(f_548_10,plain,
( function(sK462(U_2198))
| ~ sP499(U_2196,U_2198) ),
inference(clausify,[status(thm)],[f_548_5]) ).
cnf(f_548_11,plain,
( relation_dom(sK462(U_2198)) = U_2198
| ~ sP499(U_2196,U_2198) ),
inference(clausify,[status(thm)],[f_548_5]) ).
cnf(f_548_12,plain,
( in(apply(sK462(U_2198),U_2196),U_2196)
| ~ in(U_2196,U_2198)
| ~ sP499(U_2196,U_2198) ),
inference(clausify,[status(thm)],[f_548_5]) ).
fof(f_549_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_549_2,plain,
! [U_2200,U_2199] :
( set_intersection2(U_2200,U_2199) = U_2200
| ~ subset(U_2200,U_2199) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
! [U_2199,U_2200] :
( set_intersection2(U_2200,U_2199) = U_2200
| ~ subset(U_2200,U_2199) ),
inference(definitional_conversion,[status(esa)],[f_549_2]) ).
cnf(f_549_4,plain,
( set_intersection2(U_2200,U_2199) = U_2200
| ~ subset(U_2200,U_2199) ),
inference(clausify,[status(thm)],[f_549_3]) ).
fof(f_550_1,plain,
! [A,B] :
( ! [C] :
( ( ( relstr_element_smaller(poset_of_lattice(B),A,C)
| ~ latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) )
& ( latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
| ~ relstr_element_smaller(poset_of_lattice(B),A,C) ) )
| ~ element(C,the_carrier(poset_of_lattice(B))) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[t29_lattice3]) ).
fof(f_550_2,plain,
! [U_2203,U_2202] :
( ! [U_2201] :
( ( ( relstr_element_smaller(poset_of_lattice(U_2202),U_2203,U_2201)
| ~ latt_set_smaller(U_2202,cast_to_el_of_lattice(U_2202,U_2201),U_2203) )
& ( latt_set_smaller(U_2202,cast_to_el_of_lattice(U_2202,U_2201),U_2203)
| ~ relstr_element_smaller(poset_of_lattice(U_2202),U_2203,U_2201) ) )
| ~ element(U_2201,the_carrier(poset_of_lattice(U_2202))) )
| ~ latt_str(U_2202)
| ~ lattice(U_2202)
| empty_carrier(U_2202) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
( ! [U_2202,U_2203,U_2201] :
( relstr_element_smaller(poset_of_lattice(U_2202),U_2203,U_2201)
| ~ latt_set_smaller(U_2202,cast_to_el_of_lattice(U_2202,U_2201),U_2203)
| ~ sP500(U_2202,U_2203,U_2201) )
& ! [U_2202,U_2203,U_2201] :
( latt_set_smaller(U_2202,cast_to_el_of_lattice(U_2202,U_2201),U_2203)
| ~ relstr_element_smaller(poset_of_lattice(U_2202),U_2203,U_2201)
| ~ sP500(U_2202,U_2203,U_2201) )
& ! [U_2202,U_2203,U_2201] :
( sP500(U_2202,U_2203,U_2201)
| ~ element(U_2201,the_carrier(poset_of_lattice(U_2202)))
| ~ latt_str(U_2202)
| ~ lattice(U_2202)
| empty_carrier(U_2202) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP500])],[f_550_2]) ).
cnf(f_550_4,plain,
( sP500(U_2202,U_2203,U_2201)
| ~ element(U_2201,the_carrier(poset_of_lattice(U_2202)))
| ~ latt_str(U_2202)
| ~ lattice(U_2202)
| empty_carrier(U_2202) ),
inference(clausify,[status(thm)],[f_550_3]) ).
cnf(f_550_5,plain,
( latt_set_smaller(U_2202,cast_to_el_of_lattice(U_2202,U_2201),U_2203)
| ~ relstr_element_smaller(poset_of_lattice(U_2202),U_2203,U_2201)
| ~ sP500(U_2202,U_2203,U_2201) ),
inference(clausify,[status(thm)],[f_550_3]) ).
cnf(f_550_6,plain,
( relstr_element_smaller(poset_of_lattice(U_2202),U_2203,U_2201)
| ~ latt_set_smaller(U_2202,cast_to_el_of_lattice(U_2202,U_2201),U_2203)
| ~ sP500(U_2202,U_2203,U_2201) ),
inference(clausify,[status(thm)],[f_550_3]) ).
fof(f_551_1,plain,
! [A] :
( ! [B] :
( ( ( closed_subset(B,A)
| ~ open_subset(subset_complement(the_carrier(A),B),A) )
& ( open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t29_tops_1]) ).
fof(f_551_2,plain,
! [U_2205] :
( ! [U_2204] :
( ( ( closed_subset(U_2204,U_2205)
| ~ open_subset(subset_complement(the_carrier(U_2205),U_2204),U_2205) )
& ( open_subset(subset_complement(the_carrier(U_2205),U_2204),U_2205)
| ~ closed_subset(U_2204,U_2205) ) )
| ~ element(U_2204,powerset(the_carrier(U_2205))) )
| ~ top_str(U_2205) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
( ! [U_2205,U_2204] :
( closed_subset(U_2204,U_2205)
| ~ open_subset(subset_complement(the_carrier(U_2205),U_2204),U_2205)
| ~ sP501(U_2205,U_2204) )
& ! [U_2205,U_2204] :
( open_subset(subset_complement(the_carrier(U_2205),U_2204),U_2205)
| ~ closed_subset(U_2204,U_2205)
| ~ sP501(U_2205,U_2204) )
& ! [U_2205,U_2204] :
( sP501(U_2205,U_2204)
| ~ element(U_2204,powerset(the_carrier(U_2205)))
| ~ top_str(U_2205) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP501])],[f_551_2]) ).
cnf(f_551_4,plain,
( sP501(U_2205,U_2204)
| ~ element(U_2204,powerset(the_carrier(U_2205)))
| ~ top_str(U_2205) ),
inference(clausify,[status(thm)],[f_551_3]) ).
cnf(f_551_5,plain,
( open_subset(subset_complement(the_carrier(U_2205),U_2204),U_2205)
| ~ closed_subset(U_2204,U_2205)
| ~ sP501(U_2205,U_2204) ),
inference(clausify,[status(thm)],[f_551_3]) ).
cnf(f_551_6,plain,
( closed_subset(U_2204,U_2205)
| ~ open_subset(subset_complement(the_carrier(U_2205),U_2204),U_2205)
| ~ sP501(U_2205,U_2204) ),
inference(clausify,[status(thm)],[f_551_3]) ).
fof(f_552_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_552_2,plain,
! [U_2206] : set_intersection2(U_2206,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
! [U_2206] : set_intersection2(U_2206,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_552_2]) ).
cnf(f_552_4,plain,
set_intersection2(U_2206,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_552_3]) ).
fof(f_553_1,plain,
! [A,B] :
( ! [C] :
( ( ( below(boole_lattice(A),B,C)
| ~ subset(B,C) )
& ( subset(B,C)
| ~ below(boole_lattice(A),B,C) ) )
| ~ element(C,the_carrier(boole_lattice(A))) )
| ~ element(B,the_carrier(boole_lattice(A))) ),
inference(fof_nnf,[status(thm)],[t2_lattice3]) ).
fof(f_553_2,plain,
! [U_2209,U_2208] :
( ! [U_2207] :
( ( ( below(boole_lattice(U_2209),U_2208,U_2207)
| ~ subset(U_2208,U_2207) )
& ( subset(U_2208,U_2207)
| ~ below(boole_lattice(U_2209),U_2208,U_2207) ) )
| ~ element(U_2207,the_carrier(boole_lattice(U_2209))) )
| ~ element(U_2208,the_carrier(boole_lattice(U_2209))) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
( ! [U_2209,U_2208,U_2207] :
( below(boole_lattice(U_2209),U_2208,U_2207)
| ~ subset(U_2208,U_2207)
| ~ sP502(U_2209,U_2208,U_2207) )
& ! [U_2209,U_2208,U_2207] :
( subset(U_2208,U_2207)
| ~ below(boole_lattice(U_2209),U_2208,U_2207)
| ~ sP502(U_2209,U_2208,U_2207) )
& ! [U_2209,U_2208,U_2207] :
( sP502(U_2209,U_2208,U_2207)
| ~ element(U_2207,the_carrier(boole_lattice(U_2209)))
| ~ element(U_2208,the_carrier(boole_lattice(U_2209))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP502])],[f_553_2]) ).
cnf(f_553_4,plain,
( sP502(U_2209,U_2208,U_2207)
| ~ element(U_2207,the_carrier(boole_lattice(U_2209)))
| ~ element(U_2208,the_carrier(boole_lattice(U_2209))) ),
inference(clausify,[status(thm)],[f_553_3]) ).
cnf(f_553_5,plain,
( subset(U_2208,U_2207)
| ~ below(boole_lattice(U_2209),U_2208,U_2207)
| ~ sP502(U_2209,U_2208,U_2207) ),
inference(clausify,[status(thm)],[f_553_3]) ).
cnf(f_553_6,plain,
( below(boole_lattice(U_2209),U_2208,U_2207)
| ~ subset(U_2208,U_2207)
| ~ sP502(U_2209,U_2208,U_2207) ),
inference(clausify,[status(thm)],[f_553_3]) ).
fof(f_554_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_554_2,plain,
! [U_2211,U_2210] :
( in(U_2211,U_2210)
| empty(U_2210)
| ~ element(U_2211,U_2210) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
! [U_2211,U_2210] :
( in(U_2211,U_2210)
| empty(U_2210)
| ~ element(U_2211,U_2210) ),
inference(definitional_conversion,[status(esa)],[f_554_2]) ).
cnf(f_554_4,plain,
( in(U_2211,U_2210)
| empty(U_2210)
| ~ element(U_2211,U_2210) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_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_555_2,plain,
! [U_2214,U_2213] :
( U_2214 = U_2213
| ? [U_2212] :
( ( ~ in(U_2212,U_2214)
& in(U_2212,U_2213) )
| ( ~ in(U_2212,U_2213)
& in(U_2212,U_2214) ) ) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
! [U_2214,U_2213] :
( U_2214 = U_2213
| ? [U_2216] :
( ~ in(U_2216,U_2214)
& in(U_2216,U_2213) )
| ? [U_2215] :
( ~ in(U_2215,U_2213)
& in(U_2215,U_2214) ) ),
inference(miniscope,[status(thm)],[f_555_2]) ).
fof(f_555_4,plain,
! [U_2214,U_2213] :
( U_2214 = U_2213
| ? [U_2216] :
( ~ in(U_2216,U_2214)
& in(U_2216,U_2213) )
| ( ~ in(sK463(U_2214,U_2213),U_2213)
& in(sK463(U_2214,U_2213),U_2214) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_2215,sK463(U_2214,U_2213))],[f_555_3]) ).
fof(f_555_5,plain,
! [U_2214,U_2213] :
( U_2214 = U_2213
| ( ~ in(sK464(U_2214,U_2213),U_2214)
& in(sK464(U_2214,U_2213),U_2213) )
| ( ~ in(sK463(U_2214,U_2213),U_2213)
& in(sK463(U_2214,U_2213),U_2214) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_2216,sK464(U_2214,U_2213))],[f_555_4]) ).
fof(f_555_6,plain,
( ! [U_2213,U_2214] :
( ~ in(sK464(U_2214,U_2213),U_2214)
| ~ sP504(U_2213,U_2214) )
& ! [U_2213,U_2214] :
( in(sK464(U_2214,U_2213),U_2213)
| ~ sP504(U_2213,U_2214) )
& ! [U_2213,U_2214] :
( ~ in(sK463(U_2214,U_2213),U_2213)
| ~ sP503(U_2213,U_2214) )
& ! [U_2213,U_2214] :
( in(sK463(U_2214,U_2213),U_2214)
| ~ sP503(U_2213,U_2214) )
& ! [U_2213,U_2214] :
( U_2214 = U_2213
| sP504(U_2213,U_2214)
| sP503(U_2213,U_2214) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP503,sP504])],[f_555_5]) ).
cnf(f_555_7,plain,
( U_2214 = U_2213
| sP504(U_2213,U_2214)
| sP503(U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_555_6]) ).
cnf(f_555_8,plain,
( in(sK463(U_2214,U_2213),U_2214)
| ~ sP503(U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_555_6]) ).
cnf(f_555_9,plain,
( ~ in(sK463(U_2214,U_2213),U_2213)
| ~ sP503(U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_555_6]) ).
cnf(f_555_10,plain,
( in(sK464(U_2214,U_2213),U_2213)
| ~ sP504(U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_555_6]) ).
cnf(f_555_11,plain,
( ~ in(sK464(U_2214,U_2213),U_2214)
| ~ sP504(U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_555_6]) ).
fof(f_556_1,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t2_wellord2]) ).
fof(f_556_2,plain,
! [U_2217] : reflexive(inclusion_relation(U_2217)),
inference(variable_rename,[status(thm)],[f_556_1]) ).
fof(f_556_3,plain,
! [U_2217] : reflexive(inclusion_relation(U_2217)),
inference(definitional_conversion,[status(esa)],[f_556_2]) ).
cnf(f_556_4,plain,
reflexive(inclusion_relation(U_2217)),
inference(clausify,[status(thm)],[f_556_3]) ).
fof(f_557_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_557_2,plain,
! [U_2218] : subset(empty_set,U_2218),
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
! [U_2218] : subset(empty_set,U_2218),
inference(definitional_conversion,[status(esa)],[f_557_2]) ).
cnf(f_557_4,plain,
subset(empty_set,U_2218),
inference(clausify,[status(thm)],[f_557_3]) ).
fof(f_558_1,plain,
! [A,B] :
( ! [C] :
( ( ( latt_element_smaller(B,C,A)
| ~ relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) )
& ( relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C))
| ~ latt_element_smaller(B,C,A) ) )
| ~ element(C,the_carrier(B)) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[t30_lattice3]) ).
fof(f_558_2,plain,
! [U_2221,U_2220] :
( ! [U_2219] :
( ( ( latt_element_smaller(U_2220,U_2219,U_2221)
| ~ relstr_set_smaller(poset_of_lattice(U_2220),U_2221,cast_to_el_of_LattPOSet(U_2220,U_2219)) )
& ( relstr_set_smaller(poset_of_lattice(U_2220),U_2221,cast_to_el_of_LattPOSet(U_2220,U_2219))
| ~ latt_element_smaller(U_2220,U_2219,U_2221) ) )
| ~ element(U_2219,the_carrier(U_2220)) )
| ~ latt_str(U_2220)
| ~ lattice(U_2220)
| empty_carrier(U_2220) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
( ! [U_2221,U_2220,U_2219] :
( latt_element_smaller(U_2220,U_2219,U_2221)
| ~ relstr_set_smaller(poset_of_lattice(U_2220),U_2221,cast_to_el_of_LattPOSet(U_2220,U_2219))
| ~ sP505(U_2221,U_2220,U_2219) )
& ! [U_2221,U_2220,U_2219] :
( relstr_set_smaller(poset_of_lattice(U_2220),U_2221,cast_to_el_of_LattPOSet(U_2220,U_2219))
| ~ latt_element_smaller(U_2220,U_2219,U_2221)
| ~ sP505(U_2221,U_2220,U_2219) )
& ! [U_2221,U_2220,U_2219] :
( sP505(U_2221,U_2220,U_2219)
| ~ element(U_2219,the_carrier(U_2220))
| ~ latt_str(U_2220)
| ~ lattice(U_2220)
| empty_carrier(U_2220) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP505])],[f_558_2]) ).
cnf(f_558_4,plain,
( sP505(U_2221,U_2220,U_2219)
| ~ element(U_2219,the_carrier(U_2220))
| ~ latt_str(U_2220)
| ~ lattice(U_2220)
| empty_carrier(U_2220) ),
inference(clausify,[status(thm)],[f_558_3]) ).
cnf(f_558_5,plain,
( relstr_set_smaller(poset_of_lattice(U_2220),U_2221,cast_to_el_of_LattPOSet(U_2220,U_2219))
| ~ latt_element_smaller(U_2220,U_2219,U_2221)
| ~ sP505(U_2221,U_2220,U_2219) ),
inference(clausify,[status(thm)],[f_558_3]) ).
cnf(f_558_6,plain,
( latt_element_smaller(U_2220,U_2219,U_2221)
| ~ relstr_set_smaller(poset_of_lattice(U_2220),U_2221,cast_to_el_of_LattPOSet(U_2220,U_2219))
| ~ sP505(U_2221,U_2220,U_2219) ),
inference(clausify,[status(thm)],[f_558_3]) ).
fof(f_559_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_559_2,plain,
! [U_2224,U_2223,U_2222] :
( ( in(U_2223,relation_field(U_2222))
& in(U_2224,relation_field(U_2222)) )
| ~ in(ordered_pair(U_2224,U_2223),U_2222)
| ~ relation(U_2222) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
( ! [U_2222,U_2224,U_2223] :
( in(U_2223,relation_field(U_2222))
| ~ sP506(U_2222,U_2224,U_2223) )
& ! [U_2222,U_2224,U_2223] :
( in(U_2224,relation_field(U_2222))
| ~ sP506(U_2222,U_2224,U_2223) )
& ! [U_2222,U_2224,U_2223] :
( sP506(U_2222,U_2224,U_2223)
| ~ in(ordered_pair(U_2224,U_2223),U_2222)
| ~ relation(U_2222) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP506])],[f_559_2]) ).
cnf(f_559_4,plain,
( sP506(U_2222,U_2224,U_2223)
| ~ in(ordered_pair(U_2224,U_2223),U_2222)
| ~ relation(U_2222) ),
inference(clausify,[status(thm)],[f_559_3]) ).
cnf(f_559_5,plain,
( in(U_2224,relation_field(U_2222))
| ~ sP506(U_2222,U_2224,U_2223) ),
inference(clausify,[status(thm)],[f_559_3]) ).
cnf(f_559_6,plain,
( in(U_2223,relation_field(U_2222))
| ~ sP506(U_2222,U_2224,U_2223) ),
inference(clausify,[status(thm)],[f_559_3]) ).
fof(f_560_1,plain,
! [A] :
( ! [B] :
( ( ( open_subset(B,A)
| ~ closed_subset(subset_complement(the_carrier(A),B),A) )
& ( closed_subset(subset_complement(the_carrier(A),B),A)
| ~ open_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t30_tops_1]) ).
fof(f_560_2,plain,
! [U_2226] :
( ! [U_2225] :
( ( ( open_subset(U_2225,U_2226)
| ~ closed_subset(subset_complement(the_carrier(U_2226),U_2225),U_2226) )
& ( closed_subset(subset_complement(the_carrier(U_2226),U_2225),U_2226)
| ~ open_subset(U_2225,U_2226) ) )
| ~ element(U_2225,powerset(the_carrier(U_2226))) )
| ~ top_str(U_2226) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
( ! [U_2226,U_2225] :
( open_subset(U_2225,U_2226)
| ~ closed_subset(subset_complement(the_carrier(U_2226),U_2225),U_2226)
| ~ sP507(U_2226,U_2225) )
& ! [U_2226,U_2225] :
( closed_subset(subset_complement(the_carrier(U_2226),U_2225),U_2226)
| ~ open_subset(U_2225,U_2226)
| ~ sP507(U_2226,U_2225) )
& ! [U_2226,U_2225] :
( sP507(U_2226,U_2225)
| ~ element(U_2225,powerset(the_carrier(U_2226)))
| ~ top_str(U_2226) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP507])],[f_560_2]) ).
cnf(f_560_4,plain,
( sP507(U_2226,U_2225)
| ~ element(U_2225,powerset(the_carrier(U_2226)))
| ~ top_str(U_2226) ),
inference(clausify,[status(thm)],[f_560_3]) ).
cnf(f_560_5,plain,
( closed_subset(subset_complement(the_carrier(U_2226),U_2225),U_2226)
| ~ open_subset(U_2225,U_2226)
| ~ sP507(U_2226,U_2225) ),
inference(clausify,[status(thm)],[f_560_3]) ).
cnf(f_560_6,plain,
( open_subset(U_2225,U_2226)
| ~ closed_subset(subset_complement(the_carrier(U_2226),U_2225),U_2226)
| ~ sP507(U_2226,U_2225) ),
inference(clausify,[status(thm)],[f_560_3]) ).
fof(f_561_1,plain,
! [A,B] :
( ! [C] :
( ( ( relstr_set_smaller(poset_of_lattice(B),A,C)
| ~ latt_element_smaller(B,cast_to_el_of_lattice(B,C),A) )
& ( latt_element_smaller(B,cast_to_el_of_lattice(B,C),A)
| ~ relstr_set_smaller(poset_of_lattice(B),A,C) ) )
| ~ element(C,the_carrier(poset_of_lattice(B))) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[t31_lattice3]) ).
fof(f_561_2,plain,
! [U_2229,U_2228] :
( ! [U_2227] :
( ( ( relstr_set_smaller(poset_of_lattice(U_2228),U_2229,U_2227)
| ~ latt_element_smaller(U_2228,cast_to_el_of_lattice(U_2228,U_2227),U_2229) )
& ( latt_element_smaller(U_2228,cast_to_el_of_lattice(U_2228,U_2227),U_2229)
| ~ relstr_set_smaller(poset_of_lattice(U_2228),U_2229,U_2227) ) )
| ~ element(U_2227,the_carrier(poset_of_lattice(U_2228))) )
| ~ latt_str(U_2228)
| ~ lattice(U_2228)
| empty_carrier(U_2228) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
( ! [U_2229,U_2227,U_2228] :
( relstr_set_smaller(poset_of_lattice(U_2228),U_2229,U_2227)
| ~ latt_element_smaller(U_2228,cast_to_el_of_lattice(U_2228,U_2227),U_2229)
| ~ sP508(U_2229,U_2227,U_2228) )
& ! [U_2229,U_2227,U_2228] :
( latt_element_smaller(U_2228,cast_to_el_of_lattice(U_2228,U_2227),U_2229)
| ~ relstr_set_smaller(poset_of_lattice(U_2228),U_2229,U_2227)
| ~ sP508(U_2229,U_2227,U_2228) )
& ! [U_2229,U_2227,U_2228] :
( sP508(U_2229,U_2227,U_2228)
| ~ element(U_2227,the_carrier(poset_of_lattice(U_2228)))
| ~ latt_str(U_2228)
| ~ lattice(U_2228)
| empty_carrier(U_2228) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP508])],[f_561_2]) ).
cnf(f_561_4,plain,
( sP508(U_2229,U_2227,U_2228)
| ~ element(U_2227,the_carrier(poset_of_lattice(U_2228)))
| ~ latt_str(U_2228)
| ~ lattice(U_2228)
| empty_carrier(U_2228) ),
inference(clausify,[status(thm)],[f_561_3]) ).
cnf(f_561_5,plain,
( latt_element_smaller(U_2228,cast_to_el_of_lattice(U_2228,U_2227),U_2229)
| ~ relstr_set_smaller(poset_of_lattice(U_2228),U_2229,U_2227)
| ~ sP508(U_2229,U_2227,U_2228) ),
inference(clausify,[status(thm)],[f_561_3]) ).
cnf(f_561_6,plain,
( relstr_set_smaller(poset_of_lattice(U_2228),U_2229,U_2227)
| ~ latt_element_smaller(U_2228,cast_to_el_of_lattice(U_2228,U_2227),U_2229)
| ~ sP508(U_2229,U_2227,U_2228) ),
inference(clausify,[status(thm)],[f_561_3]) ).
fof(f_562_1,plain,
! [A] :
( ordinal(A)
| ? [B] :
( ( ~ subset(B,A)
| ~ ordinal(B) )
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[t31_ordinal1]) ).
fof(f_562_2,plain,
! [U_2231] :
( ordinal(U_2231)
| ? [U_2230] :
( ( ~ subset(U_2230,U_2231)
| ~ ordinal(U_2230) )
& in(U_2230,U_2231) ) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
! [U_2231] :
( ordinal(U_2231)
| ( ( ~ subset(sK465(U_2231),U_2231)
| ~ ordinal(sK465(U_2231)) )
& in(sK465(U_2231),U_2231) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_2230,sK465(U_2231))],[f_562_2]) ).
fof(f_562_4,plain,
( ! [U_2231] :
( ~ subset(sK465(U_2231),U_2231)
| ~ ordinal(sK465(U_2231))
| ~ sP509(U_2231) )
& ! [U_2231] :
( in(sK465(U_2231),U_2231)
| ~ sP509(U_2231) )
& ! [U_2231] :
( ordinal(U_2231)
| sP509(U_2231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP509])],[f_562_3]) ).
cnf(f_562_5,plain,
( ordinal(U_2231)
| sP509(U_2231) ),
inference(clausify,[status(thm)],[f_562_4]) ).
cnf(f_562_6,plain,
( in(sK465(U_2231),U_2231)
| ~ sP509(U_2231) ),
inference(clausify,[status(thm)],[f_562_4]) ).
cnf(f_562_7,plain,
( ~ subset(sK465(U_2231),U_2231)
| ~ ordinal(sK465(U_2231))
| ~ sP509(U_2231) ),
inference(clausify,[status(thm)],[f_562_4]) ).
fof(f_563_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_563_2,plain,
! [U_2233,U_2232] :
( well_founded_relation(relation_restriction(U_2232,U_2233))
| ~ well_founded_relation(U_2232)
| ~ relation(U_2232) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
! [U_2232,U_2233] :
( well_founded_relation(relation_restriction(U_2232,U_2233))
| ~ well_founded_relation(U_2232)
| ~ relation(U_2232) ),
inference(definitional_conversion,[status(esa)],[f_563_2]) ).
cnf(f_563_4,plain,
( well_founded_relation(relation_restriction(U_2232,U_2233))
| ~ well_founded_relation(U_2232)
| ~ relation(U_2232) ),
inference(clausify,[status(thm)],[f_563_3]) ).
fof(f_564_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A))
| ~ below_refl(A,B,C) )
& ( below_refl(A,B,C)
| ~ in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A)) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t32_filter_1]) ).
fof(f_564_2,plain,
! [U_2236] :
( ! [U_2235] :
( ! [U_2234] :
( ( ( in(ordered_pair_as_product_element(the_carrier(U_2236),the_carrier(U_2236),U_2235,U_2234),relation_of_lattice(U_2236))
| ~ below_refl(U_2236,U_2235,U_2234) )
& ( below_refl(U_2236,U_2235,U_2234)
| ~ in(ordered_pair_as_product_element(the_carrier(U_2236),the_carrier(U_2236),U_2235,U_2234),relation_of_lattice(U_2236)) ) )
| ~ element(U_2234,the_carrier(U_2236)) )
| ~ element(U_2235,the_carrier(U_2236)) )
| ~ latt_str(U_2236)
| ~ lattice(U_2236)
| empty_carrier(U_2236) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
( ! [U_2235,U_2234,U_2236] :
( in(ordered_pair_as_product_element(the_carrier(U_2236),the_carrier(U_2236),U_2235,U_2234),relation_of_lattice(U_2236))
| ~ below_refl(U_2236,U_2235,U_2234)
| ~ sP510(U_2235,U_2234,U_2236) )
& ! [U_2235,U_2234,U_2236] :
( below_refl(U_2236,U_2235,U_2234)
| ~ in(ordered_pair_as_product_element(the_carrier(U_2236),the_carrier(U_2236),U_2235,U_2234),relation_of_lattice(U_2236))
| ~ sP510(U_2235,U_2234,U_2236) )
& ! [U_2235,U_2234,U_2236] :
( sP510(U_2235,U_2234,U_2236)
| ~ element(U_2234,the_carrier(U_2236))
| ~ element(U_2235,the_carrier(U_2236))
| ~ latt_str(U_2236)
| ~ lattice(U_2236)
| empty_carrier(U_2236) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP510])],[f_564_2]) ).
cnf(f_564_4,plain,
( sP510(U_2235,U_2234,U_2236)
| ~ element(U_2234,the_carrier(U_2236))
| ~ element(U_2235,the_carrier(U_2236))
| ~ latt_str(U_2236)
| ~ lattice(U_2236)
| empty_carrier(U_2236) ),
inference(clausify,[status(thm)],[f_564_3]) ).
cnf(f_564_5,plain,
( below_refl(U_2236,U_2235,U_2234)
| ~ in(ordered_pair_as_product_element(the_carrier(U_2236),the_carrier(U_2236),U_2235,U_2234),relation_of_lattice(U_2236))
| ~ sP510(U_2235,U_2234,U_2236) ),
inference(clausify,[status(thm)],[f_564_3]) ).
cnf(f_564_6,plain,
( in(ordered_pair_as_product_element(the_carrier(U_2236),the_carrier(U_2236),U_2235,U_2234),relation_of_lattice(U_2236))
| ~ below_refl(U_2236,U_2235,U_2234)
| ~ sP510(U_2235,U_2234,U_2236) ),
inference(clausify,[status(thm)],[f_564_3]) ).
fof(f_565_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_565_2,plain,
! [U_2240,U_2239] :
( ? [U_2238] :
( ! [U_2237] :
( ordinal_subset(U_2238,U_2237)
| ~ in(U_2237,U_2240)
| ~ ordinal(U_2237) )
& in(U_2238,U_2240)
& ordinal(U_2238) )
| U_2240 = empty_set
| ~ subset(U_2240,U_2239)
| ~ ordinal(U_2239) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
! [U_2240,U_2239] :
( ( ! [U_2237] :
( ordinal_subset(sK466(U_2240,U_2239),U_2237)
| ~ in(U_2237,U_2240)
| ~ ordinal(U_2237) )
& in(sK466(U_2240,U_2239),U_2240)
& ordinal(sK466(U_2240,U_2239)) )
| U_2240 = empty_set
| ~ subset(U_2240,U_2239)
| ~ ordinal(U_2239) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_2238,sK466(U_2240,U_2239))],[f_565_2]) ).
fof(f_565_4,plain,
( ! [U_2237,U_2240,U_2239] :
( ordinal_subset(sK466(U_2240,U_2239),U_2237)
| ~ in(U_2237,U_2240)
| ~ ordinal(U_2237)
| ~ sP511(U_2237,U_2240,U_2239) )
& ! [U_2237,U_2240,U_2239] :
( in(sK466(U_2240,U_2239),U_2240)
| ~ sP511(U_2237,U_2240,U_2239) )
& ! [U_2237,U_2240,U_2239] :
( ordinal(sK466(U_2240,U_2239))
| ~ sP511(U_2237,U_2240,U_2239) )
& ! [U_2237,U_2240,U_2239] :
( sP511(U_2237,U_2240,U_2239)
| U_2240 = empty_set
| ~ subset(U_2240,U_2239)
| ~ ordinal(U_2239) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP511])],[f_565_3]) ).
cnf(f_565_5,plain,
( sP511(U_2237,U_2240,U_2239)
| U_2240 = empty_set
| ~ subset(U_2240,U_2239)
| ~ ordinal(U_2239) ),
inference(clausify,[status(thm)],[f_565_4]) ).
cnf(f_565_6,plain,
( ordinal(sK466(U_2240,U_2239))
| ~ sP511(U_2237,U_2240,U_2239) ),
inference(clausify,[status(thm)],[f_565_4]) ).
cnf(f_565_7,plain,
( in(sK466(U_2240,U_2239),U_2240)
| ~ sP511(U_2237,U_2240,U_2239) ),
inference(clausify,[status(thm)],[f_565_4]) ).
cnf(f_565_8,plain,
( ordinal_subset(sK466(U_2240,U_2239),U_2237)
| ~ in(U_2237,U_2240)
| ~ ordinal(U_2237)
| ~ sP511(U_2237,U_2240,U_2239) ),
inference(clausify,[status(thm)],[f_565_4]) ).
fof(f_566_1,plain,
! [A,B] :
( well_ordering(relation_restriction(B,A))
| ~ well_ordering(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t32_wellord1]) ).
fof(f_566_2,plain,
! [U_2242,U_2241] :
( well_ordering(relation_restriction(U_2241,U_2242))
| ~ well_ordering(U_2241)
| ~ relation(U_2241) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
fof(f_566_3,plain,
! [U_2242,U_2241] :
( well_ordering(relation_restriction(U_2241,U_2242))
| ~ well_ordering(U_2241)
| ~ relation(U_2241) ),
inference(definitional_conversion,[status(esa)],[f_566_2]) ).
cnf(f_566_4,plain,
( well_ordering(relation_restriction(U_2241,U_2242))
| ~ well_ordering(U_2241)
| ~ relation(U_2241) ),
inference(clausify,[status(thm)],[f_566_3]) ).
fof(f_567_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_567_2,plain,
! [U_2244] :
( ! [U_2243] :
( ( ( in(U_2244,U_2243)
| ~ ordinal_subset(succ(U_2244),U_2243) )
& ( ordinal_subset(succ(U_2244),U_2243)
| ~ in(U_2244,U_2243) ) )
| ~ ordinal(U_2243) )
| ~ ordinal(U_2244) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
( ! [U_2243,U_2244] :
( in(U_2244,U_2243)
| ~ ordinal_subset(succ(U_2244),U_2243)
| ~ sP512(U_2243,U_2244) )
& ! [U_2243,U_2244] :
( ordinal_subset(succ(U_2244),U_2243)
| ~ in(U_2244,U_2243)
| ~ sP512(U_2243,U_2244) )
& ! [U_2243,U_2244] :
( sP512(U_2243,U_2244)
| ~ ordinal(U_2243)
| ~ ordinal(U_2244) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP512])],[f_567_2]) ).
cnf(f_567_4,plain,
( sP512(U_2243,U_2244)
| ~ ordinal(U_2243)
| ~ ordinal(U_2244) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_5,plain,
( ordinal_subset(succ(U_2244),U_2243)
| ~ in(U_2244,U_2243)
| ~ sP512(U_2243,U_2244) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_6,plain,
( in(U_2244,U_2243)
| ~ ordinal_subset(succ(U_2244),U_2243)
| ~ sP512(U_2243,U_2244) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_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_568_2,plain,
! [U_2247,U_2246,U_2245] :
( subset(set_difference(U_2247,U_2245),set_difference(U_2246,U_2245))
| ~ subset(U_2247,U_2246) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
! [U_2247,U_2246] :
( ! [U_2245] : subset(set_difference(U_2247,U_2245),set_difference(U_2246,U_2245))
| ~ subset(U_2247,U_2246) ),
inference(miniscope,[status(thm)],[f_568_2]) ).
fof(f_568_4,plain,
! [U_2247,U_2246,U_2245] :
( subset(set_difference(U_2247,U_2245),set_difference(U_2246,U_2245))
| ~ subset(U_2247,U_2246) ),
inference(definitional_conversion,[status(esa)],[f_568_3]) ).
cnf(f_568_5,plain,
( subset(set_difference(U_2247,U_2245),set_difference(U_2246,U_2245))
| ~ subset(U_2247,U_2246) ),
inference(clausify,[status(thm)],[f_568_4]) ).
fof(f_569_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_569_2,plain,
! [U_2251,U_2250,U_2249,U_2248] :
( ( U_2250 = U_2248
& U_2251 = U_2249 )
| ordered_pair(U_2251,U_2250) != ordered_pair(U_2249,U_2248) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
( ! [U_2249,U_2250,U_2251,U_2248] :
( U_2250 = U_2248
| ~ sP513(U_2249,U_2250,U_2251,U_2248) )
& ! [U_2249,U_2250,U_2251,U_2248] :
( U_2251 = U_2249
| ~ sP513(U_2249,U_2250,U_2251,U_2248) )
& ! [U_2249,U_2250,U_2251,U_2248] :
( sP513(U_2249,U_2250,U_2251,U_2248)
| ordered_pair(U_2251,U_2250) != ordered_pair(U_2249,U_2248) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP513])],[f_569_2]) ).
cnf(f_569_4,plain,
( sP513(U_2249,U_2250,U_2251,U_2248)
| ordered_pair(U_2251,U_2250) != ordered_pair(U_2249,U_2248) ),
inference(clausify,[status(thm)],[f_569_3]) ).
cnf(f_569_5,plain,
( U_2251 = U_2249
| ~ sP513(U_2249,U_2250,U_2251,U_2248) ),
inference(clausify,[status(thm)],[f_569_3]) ).
cnf(f_569_6,plain,
( U_2250 = U_2248
| ~ sP513(U_2249,U_2250,U_2251,U_2248) ),
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_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_570_2,plain,
! [U_2255,U_2254] :
( ( ( U_2254 = identity_relation(U_2255)
| ? [U_2253] :
( apply(U_2254,U_2253) != U_2253
& in(U_2253,U_2255) )
| relation_dom(U_2254) != U_2255 )
& ( ( ! [U_2252] :
( apply(U_2254,U_2252) = U_2252
| ~ in(U_2252,U_2255) )
& relation_dom(U_2254) = U_2255 )
| U_2254 != identity_relation(U_2255) ) )
| ~ function(U_2254)
| ~ relation(U_2254) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
! [U_2255,U_2254] :
( ( ( U_2254 = identity_relation(U_2255)
| ( apply(U_2254,sK467(U_2255,U_2254)) != sK467(U_2255,U_2254)
& in(sK467(U_2255,U_2254),U_2255) )
| relation_dom(U_2254) != U_2255 )
& ( ( ! [U_2252] :
( apply(U_2254,U_2252) = U_2252
| ~ in(U_2252,U_2255) )
& relation_dom(U_2254) = U_2255 )
| U_2254 != identity_relation(U_2255) ) )
| ~ function(U_2254)
| ~ relation(U_2254) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_2253,sK467(U_2255,U_2254))],[f_570_2]) ).
fof(f_570_4,plain,
( ! [U_2254,U_2255] :
( apply(U_2254,sK467(U_2255,U_2254)) != sK467(U_2255,U_2254)
| ~ sP515(U_2254,U_2255) )
& ! [U_2254,U_2255] :
( in(sK467(U_2255,U_2254),U_2255)
| ~ sP515(U_2254,U_2255) )
& ! [U_2254,U_2252,U_2255] :
( apply(U_2254,U_2252) = U_2252
| ~ in(U_2252,U_2255)
| ~ sP514(U_2254,U_2252,U_2255) )
& ! [U_2254,U_2252,U_2255] :
( relation_dom(U_2254) = U_2255
| ~ sP514(U_2254,U_2252,U_2255) )
& ! [U_2254,U_2252,U_2255] :
( U_2254 = identity_relation(U_2255)
| sP515(U_2254,U_2255)
| relation_dom(U_2254) != U_2255
| ~ sP516(U_2254,U_2252,U_2255) )
& ! [U_2254,U_2252,U_2255] :
( sP514(U_2254,U_2252,U_2255)
| U_2254 != identity_relation(U_2255)
| ~ sP516(U_2254,U_2252,U_2255) )
& ! [U_2254,U_2252,U_2255] :
( sP516(U_2254,U_2252,U_2255)
| ~ function(U_2254)
| ~ relation(U_2254) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP514,sP515,sP516])],[f_570_3]) ).
cnf(f_570_5,plain,
( sP516(U_2254,U_2252,U_2255)
| ~ function(U_2254)
| ~ relation(U_2254) ),
inference(clausify,[status(thm)],[f_570_4]) ).
cnf(f_570_6,plain,
( sP514(U_2254,U_2252,U_2255)
| U_2254 != identity_relation(U_2255)
| ~ sP516(U_2254,U_2252,U_2255) ),
inference(clausify,[status(thm)],[f_570_4]) ).
cnf(f_570_7,plain,
( U_2254 = identity_relation(U_2255)
| sP515(U_2254,U_2255)
| relation_dom(U_2254) != U_2255
| ~ sP516(U_2254,U_2252,U_2255) ),
inference(clausify,[status(thm)],[f_570_4]) ).
cnf(f_570_8,plain,
( relation_dom(U_2254) = U_2255
| ~ sP514(U_2254,U_2252,U_2255) ),
inference(clausify,[status(thm)],[f_570_4]) ).
cnf(f_570_9,plain,
( apply(U_2254,U_2252) = U_2252
| ~ in(U_2252,U_2255)
| ~ sP514(U_2254,U_2252,U_2255) ),
inference(clausify,[status(thm)],[f_570_4]) ).
cnf(f_570_10,plain,
( in(sK467(U_2255,U_2254),U_2255)
| ~ sP515(U_2254,U_2255) ),
inference(clausify,[status(thm)],[f_570_4]) ).
cnf(f_570_11,plain,
( apply(U_2254,sK467(U_2255,U_2254)) != sK467(U_2255,U_2254)
| ~ sP515(U_2254,U_2255) ),
inference(clausify,[status(thm)],[f_570_4]) ).
fof(f_571_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( B = meet_of_latt_set(A,C)
| ? [D] :
( ~ below_refl(A,D,B)
& latt_set_smaller(A,D,C)
& element(D,the_carrier(A)) )
| ~ latt_set_smaller(A,B,C) )
& ( ( ! [D] :
( below_refl(A,D,B)
| ~ latt_set_smaller(A,D,C)
| ~ element(D,the_carrier(A)) )
& latt_set_smaller(A,B,C) )
| B != meet_of_latt_set(A,C) ) )
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| ~ complete_latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t34_lattice3]) ).
fof(f_571_2,plain,
! [U_2260] :
( ! [U_2259] :
( ! [U_2258] :
( ( U_2259 = meet_of_latt_set(U_2260,U_2258)
| ? [U_2257] :
( ~ below_refl(U_2260,U_2257,U_2259)
& latt_set_smaller(U_2260,U_2257,U_2258)
& element(U_2257,the_carrier(U_2260)) )
| ~ latt_set_smaller(U_2260,U_2259,U_2258) )
& ( ( ! [U_2256] :
( below_refl(U_2260,U_2256,U_2259)
| ~ latt_set_smaller(U_2260,U_2256,U_2258)
| ~ element(U_2256,the_carrier(U_2260)) )
& latt_set_smaller(U_2260,U_2259,U_2258) )
| U_2259 != meet_of_latt_set(U_2260,U_2258) ) )
| ~ element(U_2259,the_carrier(U_2260)) )
| ~ latt_str(U_2260)
| ~ complete_latt_str(U_2260)
| ~ lattice(U_2260)
| empty_carrier(U_2260) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
! [U_2260] :
( ! [U_2259] :
( ( ! [U_2262] :
( U_2259 = meet_of_latt_set(U_2260,U_2262)
| ? [U_2257] :
( ~ below_refl(U_2260,U_2257,U_2259)
& latt_set_smaller(U_2260,U_2257,U_2262)
& element(U_2257,the_carrier(U_2260)) )
| ~ latt_set_smaller(U_2260,U_2259,U_2262) )
& ! [U_2261] :
( ( ! [U_2256] :
( below_refl(U_2260,U_2256,U_2259)
| ~ latt_set_smaller(U_2260,U_2256,U_2261)
| ~ element(U_2256,the_carrier(U_2260)) )
& latt_set_smaller(U_2260,U_2259,U_2261) )
| U_2259 != meet_of_latt_set(U_2260,U_2261) ) )
| ~ element(U_2259,the_carrier(U_2260)) )
| ~ latt_str(U_2260)
| ~ complete_latt_str(U_2260)
| ~ lattice(U_2260)
| empty_carrier(U_2260) ),
inference(miniscope,[status(thm)],[f_571_2]) ).
fof(f_571_4,plain,
! [U_2260] :
( ! [U_2259] :
( ( ! [U_2262] :
( U_2259 = meet_of_latt_set(U_2260,U_2262)
| ( ~ below_refl(U_2260,sK468(U_2260,U_2259,U_2262),U_2259)
& latt_set_smaller(U_2260,sK468(U_2260,U_2259,U_2262),U_2262)
& element(sK468(U_2260,U_2259,U_2262),the_carrier(U_2260)) )
| ~ latt_set_smaller(U_2260,U_2259,U_2262) )
& ! [U_2261] :
( ( ! [U_2256] :
( below_refl(U_2260,U_2256,U_2259)
| ~ latt_set_smaller(U_2260,U_2256,U_2261)
| ~ element(U_2256,the_carrier(U_2260)) )
& latt_set_smaller(U_2260,U_2259,U_2261) )
| U_2259 != meet_of_latt_set(U_2260,U_2261) ) )
| ~ element(U_2259,the_carrier(U_2260)) )
| ~ latt_str(U_2260)
| ~ complete_latt_str(U_2260)
| ~ lattice(U_2260)
| empty_carrier(U_2260) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_2257,sK468(U_2260,U_2259,U_2262))],[f_571_3]) ).
fof(f_571_5,plain,
( ! [U_2259,U_2260,U_2262] :
( ~ below_refl(U_2260,sK468(U_2260,U_2259,U_2262),U_2259)
| ~ sP518(U_2259,U_2260,U_2262) )
& ! [U_2259,U_2260,U_2262] :
( latt_set_smaller(U_2260,sK468(U_2260,U_2259,U_2262),U_2262)
| ~ sP518(U_2259,U_2260,U_2262) )
& ! [U_2259,U_2260,U_2262] :
( element(sK468(U_2260,U_2259,U_2262),the_carrier(U_2260))
| ~ sP518(U_2259,U_2260,U_2262) )
& ! [U_2259,U_2261,U_2260,U_2256] :
( below_refl(U_2260,U_2256,U_2259)
| ~ latt_set_smaller(U_2260,U_2256,U_2261)
| ~ element(U_2256,the_carrier(U_2260))
| ~ sP517(U_2259,U_2261,U_2260,U_2256) )
& ! [U_2259,U_2261,U_2260,U_2256] :
( latt_set_smaller(U_2260,U_2259,U_2261)
| ~ sP517(U_2259,U_2261,U_2260,U_2256) )
& ! [U_2259,U_2261,U_2260,U_2262,U_2256] :
( U_2259 = meet_of_latt_set(U_2260,U_2262)
| sP518(U_2259,U_2260,U_2262)
| ~ latt_set_smaller(U_2260,U_2259,U_2262)
| ~ sP519(U_2259,U_2261,U_2260,U_2262,U_2256) )
& ! [U_2259,U_2261,U_2260,U_2262,U_2256] :
( sP517(U_2259,U_2261,U_2260,U_2256)
| U_2259 != meet_of_latt_set(U_2260,U_2261)
| ~ sP519(U_2259,U_2261,U_2260,U_2262,U_2256) )
& ! [U_2259,U_2261,U_2260,U_2262,U_2256] :
( sP519(U_2259,U_2261,U_2260,U_2262,U_2256)
| ~ element(U_2259,the_carrier(U_2260))
| ~ latt_str(U_2260)
| ~ complete_latt_str(U_2260)
| ~ lattice(U_2260)
| empty_carrier(U_2260) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP517,sP518,sP519])],[f_571_4]) ).
cnf(f_571_6,plain,
( sP519(U_2259,U_2261,U_2260,U_2262,U_2256)
| ~ element(U_2259,the_carrier(U_2260))
| ~ latt_str(U_2260)
| ~ complete_latt_str(U_2260)
| ~ lattice(U_2260)
| empty_carrier(U_2260) ),
inference(clausify,[status(thm)],[f_571_5]) ).
cnf(f_571_7,plain,
( sP517(U_2259,U_2261,U_2260,U_2256)
| U_2259 != meet_of_latt_set(U_2260,U_2261)
| ~ sP519(U_2259,U_2261,U_2260,U_2262,U_2256) ),
inference(clausify,[status(thm)],[f_571_5]) ).
cnf(f_571_8,plain,
( U_2259 = meet_of_latt_set(U_2260,U_2262)
| sP518(U_2259,U_2260,U_2262)
| ~ latt_set_smaller(U_2260,U_2259,U_2262)
| ~ sP519(U_2259,U_2261,U_2260,U_2262,U_2256) ),
inference(clausify,[status(thm)],[f_571_5]) ).
cnf(f_571_9,plain,
( latt_set_smaller(U_2260,U_2259,U_2261)
| ~ sP517(U_2259,U_2261,U_2260,U_2256) ),
inference(clausify,[status(thm)],[f_571_5]) ).
cnf(f_571_10,plain,
( below_refl(U_2260,U_2256,U_2259)
| ~ latt_set_smaller(U_2260,U_2256,U_2261)
| ~ element(U_2256,the_carrier(U_2260))
| ~ sP517(U_2259,U_2261,U_2260,U_2256) ),
inference(clausify,[status(thm)],[f_571_5]) ).
cnf(f_571_11,plain,
( element(sK468(U_2260,U_2259,U_2262),the_carrier(U_2260))
| ~ sP518(U_2259,U_2260,U_2262) ),
inference(clausify,[status(thm)],[f_571_5]) ).
cnf(f_571_12,plain,
( latt_set_smaller(U_2260,sK468(U_2260,U_2259,U_2262),U_2262)
| ~ sP518(U_2259,U_2260,U_2262) ),
inference(clausify,[status(thm)],[f_571_5]) ).
cnf(f_571_13,plain,
( ~ below_refl(U_2260,sK468(U_2260,U_2259,U_2262),U_2259)
| ~ sP518(U_2259,U_2260,U_2262) ),
inference(clausify,[status(thm)],[f_571_5]) ).
fof(f_572_1,plain,
! [A,B] :
( apply(identity_relation(A),B) = B
| ~ in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1]) ).
fof(f_572_2,plain,
! [U_2264,U_2263] :
( apply(identity_relation(U_2264),U_2263) = U_2263
| ~ in(U_2263,U_2264) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
! [U_2263,U_2264] :
( apply(identity_relation(U_2264),U_2263) = U_2263
| ~ in(U_2263,U_2264) ),
inference(definitional_conversion,[status(esa)],[f_572_2]) ).
cnf(f_572_4,plain,
( apply(identity_relation(U_2264),U_2263) = U_2263
| ~ in(U_2263,U_2264) ),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_1,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1]) ).
fof(f_573_2,plain,
! [U_2266,U_2265] : subset(set_difference(U_2266,U_2265),U_2266),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
! [U_2266,U_2265] : subset(set_difference(U_2266,U_2265),U_2266),
inference(definitional_conversion,[status(esa)],[f_573_2]) ).
cnf(f_573_4,plain,
subset(set_difference(U_2266,U_2265),U_2266),
inference(clausify,[status(thm)],[f_573_3]) ).
fof(f_574_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_574_2,plain,
! [U_2267] :
( ( relation_dom(U_2267) = relation_rng(relation_inverse(U_2267))
& relation_rng(U_2267) = relation_dom(relation_inverse(U_2267)) )
| ~ relation(U_2267) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
( ! [U_2267] :
( relation_dom(U_2267) = relation_rng(relation_inverse(U_2267))
| ~ sP520(U_2267) )
& ! [U_2267] :
( relation_rng(U_2267) = relation_dom(relation_inverse(U_2267))
| ~ sP520(U_2267) )
& ! [U_2267] :
( sP520(U_2267)
| ~ relation(U_2267) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP520])],[f_574_2]) ).
cnf(f_574_4,plain,
( sP520(U_2267)
| ~ relation(U_2267) ),
inference(clausify,[status(thm)],[f_574_3]) ).
cnf(f_574_5,plain,
( relation_rng(U_2267) = relation_dom(relation_inverse(U_2267))
| ~ sP520(U_2267) ),
inference(clausify,[status(thm)],[f_574_3]) ).
cnf(f_574_6,plain,
( relation_dom(U_2267) = relation_rng(relation_inverse(U_2267))
| ~ sP520(U_2267) ),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_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_575_2,plain,
! [U_2269,U_2268] :
( ( set_difference(U_2269,U_2268) = empty_set
| ~ subset(U_2269,U_2268) )
& ( subset(U_2269,U_2268)
| set_difference(U_2269,U_2268) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
( ! [U_2273,U_2271] :
( set_difference(U_2273,U_2271) = empty_set
| ~ subset(U_2273,U_2271) )
& ! [U_2272,U_2270] :
( subset(U_2272,U_2270)
| set_difference(U_2272,U_2270) != empty_set ) ),
inference(miniscope,[status(thm)],[f_575_2]) ).
fof(f_575_4,plain,
( ! [U_2271,U_2273] :
( set_difference(U_2273,U_2271) = empty_set
| ~ subset(U_2273,U_2271) )
& ! [U_2272,U_2270] :
( subset(U_2272,U_2270)
| set_difference(U_2272,U_2270) != empty_set ) ),
inference(definitional_conversion,[status(esa)],[f_575_3]) ).
cnf(f_575_5,plain,
( subset(U_2272,U_2270)
| set_difference(U_2272,U_2270) != empty_set ),
inference(clausify,[status(thm)],[f_575_4]) ).
cnf(f_575_6,plain,
( set_difference(U_2273,U_2271) = empty_set
| ~ subset(U_2273,U_2271) ),
inference(clausify,[status(thm)],[f_575_4]) ).
fof(f_576_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_576_2,plain,
! [U_2275,U_2274] :
( ( subset(singleton(U_2275),U_2274)
| ~ in(U_2275,U_2274) )
& ( in(U_2275,U_2274)
| ~ subset(singleton(U_2275),U_2274) ) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
( ! [U_2279,U_2277] :
( subset(singleton(U_2279),U_2277)
| ~ in(U_2279,U_2277) )
& ! [U_2278,U_2276] :
( in(U_2278,U_2276)
| ~ subset(singleton(U_2278),U_2276) ) ),
inference(miniscope,[status(thm)],[f_576_2]) ).
fof(f_576_4,plain,
( ! [U_2277,U_2279] :
( subset(singleton(U_2279),U_2277)
| ~ in(U_2279,U_2277) )
& ! [U_2276,U_2278] :
( in(U_2278,U_2276)
| ~ subset(singleton(U_2278),U_2276) ) ),
inference(definitional_conversion,[status(esa)],[f_576_3]) ).
cnf(f_576_5,plain,
( in(U_2278,U_2276)
| ~ subset(singleton(U_2278),U_2276) ),
inference(clausify,[status(thm)],[f_576_4]) ).
cnf(f_576_6,plain,
( subset(singleton(U_2279),U_2277)
| ~ in(U_2279,U_2277) ),
inference(clausify,[status(thm)],[f_576_4]) ).
fof(f_577_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_577_2,plain,
! [U_2282,U_2281,U_2280] :
( ( subset(unordered_pair(U_2282,U_2281),U_2280)
| ~ in(U_2281,U_2280)
| ~ in(U_2282,U_2280) )
& ( ( in(U_2281,U_2280)
& in(U_2282,U_2280) )
| ~ subset(unordered_pair(U_2282,U_2281),U_2280) ) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
( ! [U_2288,U_2286,U_2284] :
( subset(unordered_pair(U_2288,U_2286),U_2284)
| ~ in(U_2286,U_2284)
| ~ in(U_2288,U_2284) )
& ! [U_2287,U_2285,U_2283] :
( ( in(U_2285,U_2283)
& in(U_2287,U_2283) )
| ~ subset(unordered_pair(U_2287,U_2285),U_2283) ) ),
inference(miniscope,[status(thm)],[f_577_2]) ).
fof(f_577_4,plain,
( ! [U_2287,U_2283,U_2285] :
( in(U_2285,U_2283)
| ~ sP521(U_2287,U_2283,U_2285) )
& ! [U_2287,U_2283,U_2285] :
( in(U_2287,U_2283)
| ~ sP521(U_2287,U_2283,U_2285) )
& ! [U_2286,U_2284,U_2288] :
( subset(unordered_pair(U_2288,U_2286),U_2284)
| ~ in(U_2286,U_2284)
| ~ in(U_2288,U_2284) )
& ! [U_2287,U_2283,U_2285] :
( sP521(U_2287,U_2283,U_2285)
| ~ subset(unordered_pair(U_2287,U_2285),U_2283) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP521])],[f_577_3]) ).
cnf(f_577_5,plain,
( sP521(U_2287,U_2283,U_2285)
| ~ subset(unordered_pair(U_2287,U_2285),U_2283) ),
inference(clausify,[status(thm)],[f_577_4]) ).
cnf(f_577_6,plain,
( subset(unordered_pair(U_2288,U_2286),U_2284)
| ~ in(U_2286,U_2284)
| ~ in(U_2288,U_2284) ),
inference(clausify,[status(thm)],[f_577_4]) ).
cnf(f_577_7,plain,
( in(U_2287,U_2283)
| ~ sP521(U_2287,U_2283,U_2285) ),
inference(clausify,[status(thm)],[f_577_4]) ).
cnf(f_577_8,plain,
( in(U_2285,U_2283)
| ~ sP521(U_2287,U_2283,U_2285) ),
inference(clausify,[status(thm)],[f_577_4]) ).
fof(f_578_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_578_2,plain,
! [U_2290,U_2289] :
( relation_field(relation_restriction(U_2289,U_2290)) = U_2290
| ~ subset(U_2290,relation_field(U_2289))
| ~ well_ordering(U_2289)
| ~ relation(U_2289) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
! [U_2289,U_2290] :
( relation_field(relation_restriction(U_2289,U_2290)) = U_2290
| ~ subset(U_2290,relation_field(U_2289))
| ~ well_ordering(U_2289)
| ~ relation(U_2289) ),
inference(definitional_conversion,[status(esa)],[f_578_2]) ).
cnf(f_578_4,plain,
( relation_field(relation_restriction(U_2289,U_2290)) = U_2290
| ~ subset(U_2290,relation_field(U_2289))
| ~ well_ordering(U_2289)
| ~ relation(U_2289) ),
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_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_579_2,plain,
! [U_2292,U_2291] : set_union2(U_2292,set_difference(U_2291,U_2292)) = set_union2(U_2292,U_2291),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
! [U_2292,U_2291] : set_union2(U_2292,set_difference(U_2291,U_2292)) = set_union2(U_2292,U_2291),
inference(definitional_conversion,[status(esa)],[f_579_2]) ).
cnf(f_579_4,plain,
set_union2(U_2292,set_difference(U_2291,U_2292)) = set_union2(U_2292,U_2291),
inference(clausify,[status(thm)],[f_579_3]) ).
fof(f_580_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_580_2,plain,
! [U_2294,U_2293] :
( ( subset(U_2294,singleton(U_2293))
| ( U_2294 != singleton(U_2293)
& U_2294 != empty_set ) )
& ( U_2294 = singleton(U_2293)
| U_2294 = empty_set
| ~ subset(U_2294,singleton(U_2293)) ) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
( ! [U_2298,U_2296] :
( subset(U_2298,singleton(U_2296))
| ( U_2298 != singleton(U_2296)
& U_2298 != empty_set ) )
& ! [U_2297,U_2295] :
( U_2297 = singleton(U_2295)
| U_2297 = empty_set
| ~ subset(U_2297,singleton(U_2295)) ) ),
inference(miniscope,[status(thm)],[f_580_2]) ).
fof(f_580_4,plain,
( ! [U_2296,U_2298] :
( U_2298 != singleton(U_2296)
| ~ sP522(U_2296,U_2298) )
& ! [U_2296,U_2298] :
( U_2298 != empty_set
| ~ sP522(U_2296,U_2298) )
& ! [U_2296,U_2298] :
( subset(U_2298,singleton(U_2296))
| sP522(U_2296,U_2298) )
& ! [U_2297,U_2295] :
( U_2297 = singleton(U_2295)
| U_2297 = empty_set
| ~ subset(U_2297,singleton(U_2295)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP522])],[f_580_3]) ).
cnf(f_580_5,plain,
( U_2297 = singleton(U_2295)
| U_2297 = empty_set
| ~ subset(U_2297,singleton(U_2295)) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_6,plain,
( subset(U_2298,singleton(U_2296))
| sP522(U_2296,U_2298) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_7,plain,
( U_2298 != empty_set
| ~ sP522(U_2296,U_2298) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_8,plain,
( U_2298 != singleton(U_2296)
| ~ sP522(U_2296,U_2298) ),
inference(clausify,[status(thm)],[f_580_4]) ).
fof(f_581_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_581_2,plain,
! [U_2299] : set_difference(U_2299,empty_set) = U_2299,
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
! [U_2299] : set_difference(U_2299,empty_set) = U_2299,
inference(definitional_conversion,[status(esa)],[f_581_2]) ).
cnf(f_581_4,plain,
set_difference(U_2299,empty_set) = U_2299,
inference(clausify,[status(thm)],[f_581_3]) ).
fof(f_582_1,plain,
! [A] :
( bottom_of_semilattstr(boole_lattice(A)) = empty_set
& lower_bounded_semilattstr(boole_lattice(A)) ),
inference(fof_nnf,[status(thm)],[t3_lattice3]) ).
fof(f_582_2,plain,
! [U_2300] :
( bottom_of_semilattstr(boole_lattice(U_2300)) = empty_set
& lower_bounded_semilattstr(boole_lattice(U_2300)) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
( ! [U_2302] : bottom_of_semilattstr(boole_lattice(U_2302)) = empty_set
& ! [U_2301] : lower_bounded_semilattstr(boole_lattice(U_2301)) ),
inference(miniscope,[status(thm)],[f_582_2]) ).
fof(f_582_4,plain,
( ! [U_2302] : bottom_of_semilattstr(boole_lattice(U_2302)) = empty_set
& ! [U_2301] : lower_bounded_semilattstr(boole_lattice(U_2301)) ),
inference(definitional_conversion,[status(esa)],[f_582_3]) ).
cnf(f_582_5,plain,
lower_bounded_semilattstr(boole_lattice(U_2301)),
inference(clausify,[status(thm)],[f_582_4]) ).
cnf(f_582_6,plain,
bottom_of_semilattstr(boole_lattice(U_2302)) = empty_set,
inference(clausify,[status(thm)],[f_582_4]) ).
fof(f_583_1,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t3_ordinal1]) ).
fof(f_583_2,plain,
! [U_2305,U_2304,U_2303] :
( ~ in(U_2303,U_2305)
| ~ in(U_2304,U_2303)
| ~ in(U_2305,U_2304) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
fof(f_583_3,plain,
! [U_2305,U_2304] :
( ! [U_2303] :
( ~ in(U_2303,U_2305)
| ~ in(U_2304,U_2303) )
| ~ in(U_2305,U_2304) ),
inference(miniscope,[status(thm)],[f_583_2]) ).
fof(f_583_4,plain,
! [U_2303,U_2304,U_2305] :
( ~ in(U_2303,U_2305)
| ~ in(U_2304,U_2303)
| ~ in(U_2305,U_2304) ),
inference(definitional_conversion,[status(esa)],[f_583_3]) ).
cnf(f_583_5,plain,
( ~ in(U_2303,U_2305)
| ~ in(U_2304,U_2303)
| ~ in(U_2305,U_2304) ),
inference(clausify,[status(thm)],[f_583_4]) ).
fof(f_584_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_584_2,plain,
! [U_2307,U_2306] :
( ( element(U_2307,powerset(U_2306))
| ~ subset(U_2307,U_2306) )
& ( subset(U_2307,U_2306)
| ~ element(U_2307,powerset(U_2306)) ) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
fof(f_584_3,plain,
( ! [U_2311,U_2309] :
( element(U_2311,powerset(U_2309))
| ~ subset(U_2311,U_2309) )
& ! [U_2310,U_2308] :
( subset(U_2310,U_2308)
| ~ element(U_2310,powerset(U_2308)) ) ),
inference(miniscope,[status(thm)],[f_584_2]) ).
fof(f_584_4,plain,
( ! [U_2311,U_2309] :
( element(U_2311,powerset(U_2309))
| ~ subset(U_2311,U_2309) )
& ! [U_2310,U_2308] :
( subset(U_2310,U_2308)
| ~ element(U_2310,powerset(U_2308)) ) ),
inference(definitional_conversion,[status(esa)],[f_584_3]) ).
cnf(f_584_5,plain,
( subset(U_2310,U_2308)
| ~ element(U_2310,powerset(U_2308)) ),
inference(clausify,[status(thm)],[f_584_4]) ).
cnf(f_584_6,plain,
( element(U_2311,powerset(U_2309))
| ~ subset(U_2311,U_2309) ),
inference(clausify,[status(thm)],[f_584_4]) ).
fof(f_585_1,plain,
! [A] : transitive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t3_wellord2]) ).
fof(f_585_2,plain,
! [U_2312] : transitive(inclusion_relation(U_2312)),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
! [U_2312] : transitive(inclusion_relation(U_2312)),
inference(definitional_conversion,[status(esa)],[f_585_2]) ).
cnf(f_585_4,plain,
transitive(inclusion_relation(U_2312)),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_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_586_2,plain,
! [U_2316,U_2315] :
( ( ~ disjoint(U_2316,U_2315)
| ! [U_2314] :
( ~ in(U_2314,U_2315)
| ~ in(U_2314,U_2316) ) )
& ( ? [U_2313] :
( in(U_2313,U_2315)
& in(U_2313,U_2316) )
| disjoint(U_2316,U_2315) ) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
( ! [U_2320,U_2318] :
( ~ disjoint(U_2320,U_2318)
| ! [U_2314] :
( ~ in(U_2314,U_2318)
| ~ in(U_2314,U_2320) ) )
& ! [U_2319,U_2317] :
( ? [U_2313] :
( in(U_2313,U_2317)
& in(U_2313,U_2319) )
| disjoint(U_2319,U_2317) ) ),
inference(miniscope,[status(thm)],[f_586_2]) ).
fof(f_586_4,plain,
( ! [U_2320,U_2318] :
( ~ disjoint(U_2320,U_2318)
| ! [U_2314] :
( ~ in(U_2314,U_2318)
| ~ in(U_2314,U_2320) ) )
& ! [U_2319,U_2317] :
( ( in(sK469(U_2319,U_2317),U_2317)
& in(sK469(U_2319,U_2317),U_2319) )
| disjoint(U_2319,U_2317) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_2313,sK469(U_2319,U_2317))],[f_586_3]) ).
fof(f_586_5,plain,
( ! [U_2317,U_2319] :
( in(sK469(U_2319,U_2317),U_2317)
| ~ sP523(U_2317,U_2319) )
& ! [U_2317,U_2319] :
( in(sK469(U_2319,U_2317),U_2319)
| ~ sP523(U_2317,U_2319) )
& ! [U_2314,U_2320,U_2318] :
( ~ disjoint(U_2320,U_2318)
| ~ in(U_2314,U_2318)
| ~ in(U_2314,U_2320) )
& ! [U_2317,U_2319] :
( sP523(U_2317,U_2319)
| disjoint(U_2319,U_2317) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP523])],[f_586_4]) ).
cnf(f_586_6,plain,
( sP523(U_2317,U_2319)
| disjoint(U_2319,U_2317) ),
inference(clausify,[status(thm)],[f_586_5]) ).
cnf(f_586_7,plain,
( ~ disjoint(U_2320,U_2318)
| ~ in(U_2314,U_2318)
| ~ in(U_2314,U_2320) ),
inference(clausify,[status(thm)],[f_586_5]) ).
cnf(f_586_8,plain,
( in(sK469(U_2319,U_2317),U_2319)
| ~ sP523(U_2317,U_2319) ),
inference(clausify,[status(thm)],[f_586_5]) ).
cnf(f_586_9,plain,
( in(sK469(U_2319,U_2317),U_2317)
| ~ sP523(U_2317,U_2319) ),
inference(clausify,[status(thm)],[f_586_5]) ).
fof(f_587_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_587_2,plain,
! [U_2321] :
( U_2321 = empty_set
| ~ subset(U_2321,empty_set) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
! [U_2321] :
( U_2321 = empty_set
| ~ subset(U_2321,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_587_2]) ).
cnf(f_587_4,plain,
( U_2321 = empty_set
| ~ subset(U_2321,empty_set) ),
inference(clausify,[status(thm)],[f_587_3]) ).
fof(f_588_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_588_2,plain,
! [U_2323,U_2322] : set_difference(set_union2(U_2323,U_2322),U_2322) = set_difference(U_2323,U_2322),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
! [U_2322,U_2323] : set_difference(set_union2(U_2323,U_2322),U_2322) = set_difference(U_2323,U_2322),
inference(definitional_conversion,[status(esa)],[f_588_2]) ).
cnf(f_588_4,plain,
set_difference(set_union2(U_2323,U_2322),U_2322) = set_difference(U_2323,U_2322),
inference(clausify,[status(thm)],[f_588_3]) ).
fof(f_589_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_589_2,plain,
! [U_2326] :
( ( ( being_limit_ordinal(U_2326)
| ? [U_2325] :
( ~ in(succ(U_2325),U_2326)
& in(U_2325,U_2326)
& ordinal(U_2325) ) )
& ( ! [U_2324] :
( in(succ(U_2324),U_2326)
| ~ in(U_2324,U_2326)
| ~ ordinal(U_2324) )
| ~ being_limit_ordinal(U_2326) ) )
| ~ ordinal(U_2326) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
! [U_2326] :
( ( ( being_limit_ordinal(U_2326)
| ( ~ in(succ(sK470(U_2326)),U_2326)
& in(sK470(U_2326),U_2326)
& ordinal(sK470(U_2326)) ) )
& ( ! [U_2324] :
( in(succ(U_2324),U_2326)
| ~ in(U_2324,U_2326)
| ~ ordinal(U_2324) )
| ~ being_limit_ordinal(U_2326) ) )
| ~ ordinal(U_2326) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_2325,sK470(U_2326))],[f_589_2]) ).
fof(f_589_4,plain,
( ! [U_2326] :
( ~ in(succ(sK470(U_2326)),U_2326)
| ~ sP524(U_2326) )
& ! [U_2326] :
( in(sK470(U_2326),U_2326)
| ~ sP524(U_2326) )
& ! [U_2326] :
( ordinal(sK470(U_2326))
| ~ sP524(U_2326) )
& ! [U_2324,U_2326] :
( being_limit_ordinal(U_2326)
| sP524(U_2326)
| ~ sP525(U_2324,U_2326) )
& ! [U_2324,U_2326] :
( in(succ(U_2324),U_2326)
| ~ in(U_2324,U_2326)
| ~ ordinal(U_2324)
| ~ being_limit_ordinal(U_2326)
| ~ sP525(U_2324,U_2326) )
& ! [U_2324,U_2326] :
( sP525(U_2324,U_2326)
| ~ ordinal(U_2326) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP524,sP525])],[f_589_3]) ).
cnf(f_589_5,plain,
( sP525(U_2324,U_2326)
| ~ ordinal(U_2326) ),
inference(clausify,[status(thm)],[f_589_4]) ).
cnf(f_589_6,plain,
( in(succ(U_2324),U_2326)
| ~ in(U_2324,U_2326)
| ~ ordinal(U_2324)
| ~ being_limit_ordinal(U_2326)
| ~ sP525(U_2324,U_2326) ),
inference(clausify,[status(thm)],[f_589_4]) ).
cnf(f_589_7,plain,
( being_limit_ordinal(U_2326)
| sP524(U_2326)
| ~ sP525(U_2324,U_2326) ),
inference(clausify,[status(thm)],[f_589_4]) ).
cnf(f_589_8,plain,
( ordinal(sK470(U_2326))
| ~ sP524(U_2326) ),
inference(clausify,[status(thm)],[f_589_4]) ).
cnf(f_589_9,plain,
( in(sK470(U_2326),U_2326)
| ~ sP524(U_2326) ),
inference(clausify,[status(thm)],[f_589_4]) ).
cnf(f_589_10,plain,
( ~ in(succ(sK470(U_2326)),U_2326)
| ~ sP524(U_2326) ),
inference(clausify,[status(thm)],[f_589_4]) ).
fof(f_590_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_590_2,plain,
! [U_2329] :
( ( ( ~ being_limit_ordinal(U_2329)
| ! [U_2328] :
( U_2329 != succ(U_2328)
| ~ ordinal(U_2328) ) )
& ( ? [U_2327] :
( U_2329 = succ(U_2327)
& ordinal(U_2327) )
| being_limit_ordinal(U_2329) ) )
| ~ ordinal(U_2329) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
fof(f_590_3,plain,
! [U_2329] :
( ( ( ~ being_limit_ordinal(U_2329)
| ! [U_2328] :
( U_2329 != succ(U_2328)
| ~ ordinal(U_2328) ) )
& ( ( U_2329 = succ(sK471(U_2329))
& ordinal(sK471(U_2329)) )
| being_limit_ordinal(U_2329) ) )
| ~ ordinal(U_2329) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_2327,sK471(U_2329))],[f_590_2]) ).
fof(f_590_4,plain,
( ! [U_2329] :
( U_2329 = succ(sK471(U_2329))
| ~ sP526(U_2329) )
& ! [U_2329] :
( ordinal(sK471(U_2329))
| ~ sP526(U_2329) )
& ! [U_2329,U_2328] :
( ~ being_limit_ordinal(U_2329)
| U_2329 != succ(U_2328)
| ~ ordinal(U_2328)
| ~ sP527(U_2329,U_2328) )
& ! [U_2329,U_2328] :
( sP526(U_2329)
| being_limit_ordinal(U_2329)
| ~ sP527(U_2329,U_2328) )
& ! [U_2329,U_2328] :
( sP527(U_2329,U_2328)
| ~ ordinal(U_2329) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP526,sP527])],[f_590_3]) ).
cnf(f_590_5,plain,
( sP527(U_2329,U_2328)
| ~ ordinal(U_2329) ),
inference(clausify,[status(thm)],[f_590_4]) ).
cnf(f_590_6,plain,
( sP526(U_2329)
| being_limit_ordinal(U_2329)
| ~ sP527(U_2329,U_2328) ),
inference(clausify,[status(thm)],[f_590_4]) ).
cnf(f_590_7,plain,
( ~ being_limit_ordinal(U_2329)
| U_2329 != succ(U_2328)
| ~ ordinal(U_2328)
| ~ sP527(U_2329,U_2328) ),
inference(clausify,[status(thm)],[f_590_4]) ).
cnf(f_590_8,plain,
( ordinal(sK471(U_2329))
| ~ sP526(U_2329) ),
inference(clausify,[status(thm)],[f_590_4]) ).
cnf(f_590_9,plain,
( U_2329 = succ(sK471(U_2329))
| ~ sP526(U_2329) ),
inference(clausify,[status(thm)],[f_590_4]) ).
fof(f_591_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_591_2,plain,
! [U_2332,U_2331] :
( ! [U_2330] :
( ( ( disjoint(U_2331,U_2330)
| ~ subset(U_2331,subset_complement(U_2332,U_2330)) )
& ( subset(U_2331,subset_complement(U_2332,U_2330))
| ~ disjoint(U_2331,U_2330) ) )
| ~ element(U_2330,powerset(U_2332)) )
| ~ element(U_2331,powerset(U_2332)) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
( ! [U_2330,U_2332,U_2331] :
( disjoint(U_2331,U_2330)
| ~ subset(U_2331,subset_complement(U_2332,U_2330))
| ~ sP528(U_2330,U_2332,U_2331) )
& ! [U_2330,U_2332,U_2331] :
( subset(U_2331,subset_complement(U_2332,U_2330))
| ~ disjoint(U_2331,U_2330)
| ~ sP528(U_2330,U_2332,U_2331) )
& ! [U_2330,U_2332,U_2331] :
( sP528(U_2330,U_2332,U_2331)
| ~ element(U_2330,powerset(U_2332))
| ~ element(U_2331,powerset(U_2332)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP528])],[f_591_2]) ).
cnf(f_591_4,plain,
( sP528(U_2330,U_2332,U_2331)
| ~ element(U_2330,powerset(U_2332))
| ~ element(U_2331,powerset(U_2332)) ),
inference(clausify,[status(thm)],[f_591_3]) ).
cnf(f_591_5,plain,
( subset(U_2331,subset_complement(U_2332,U_2330))
| ~ disjoint(U_2331,U_2330)
| ~ sP528(U_2330,U_2332,U_2331) ),
inference(clausify,[status(thm)],[f_591_3]) ).
cnf(f_591_6,plain,
( disjoint(U_2331,U_2330)
| ~ subset(U_2331,subset_complement(U_2332,U_2330))
| ~ sP528(U_2330,U_2332,U_2331) ),
inference(clausify,[status(thm)],[f_591_3]) ).
fof(f_592_1,plain,
! [A] :
( ! [B] :
( closed_subset(meet_of_subsets(the_carrier(A),B),A)
| ? [C] :
( ~ closed_subset(C,A)
& in(C,B)
& element(C,powerset(the_carrier(A))) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[t44_pre_topc]) ).
fof(f_592_2,plain,
! [U_2335] :
( ! [U_2334] :
( closed_subset(meet_of_subsets(the_carrier(U_2335),U_2334),U_2335)
| ? [U_2333] :
( ~ closed_subset(U_2333,U_2335)
& in(U_2333,U_2334)
& element(U_2333,powerset(the_carrier(U_2335))) )
| ~ element(U_2334,powerset(powerset(the_carrier(U_2335)))) )
| ~ top_str(U_2335)
| ~ topological_space(U_2335) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
! [U_2335] :
( ! [U_2334] :
( closed_subset(meet_of_subsets(the_carrier(U_2335),U_2334),U_2335)
| ( ~ closed_subset(sK472(U_2335,U_2334),U_2335)
& in(sK472(U_2335,U_2334),U_2334)
& element(sK472(U_2335,U_2334),powerset(the_carrier(U_2335))) )
| ~ element(U_2334,powerset(powerset(the_carrier(U_2335)))) )
| ~ top_str(U_2335)
| ~ topological_space(U_2335) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_2333,sK472(U_2335,U_2334))],[f_592_2]) ).
fof(f_592_4,plain,
( ! [U_2335,U_2334] :
( ~ closed_subset(sK472(U_2335,U_2334),U_2335)
| ~ sP529(U_2335,U_2334) )
& ! [U_2335,U_2334] :
( in(sK472(U_2335,U_2334),U_2334)
| ~ sP529(U_2335,U_2334) )
& ! [U_2335,U_2334] :
( element(sK472(U_2335,U_2334),powerset(the_carrier(U_2335)))
| ~ sP529(U_2335,U_2334) )
& ! [U_2335,U_2334] :
( closed_subset(meet_of_subsets(the_carrier(U_2335),U_2334),U_2335)
| sP529(U_2335,U_2334)
| ~ element(U_2334,powerset(powerset(the_carrier(U_2335))))
| ~ top_str(U_2335)
| ~ topological_space(U_2335) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP529])],[f_592_3]) ).
cnf(f_592_5,plain,
( closed_subset(meet_of_subsets(the_carrier(U_2335),U_2334),U_2335)
| sP529(U_2335,U_2334)
| ~ element(U_2334,powerset(powerset(the_carrier(U_2335))))
| ~ top_str(U_2335)
| ~ topological_space(U_2335) ),
inference(clausify,[status(thm)],[f_592_4]) ).
cnf(f_592_6,plain,
( element(sK472(U_2335,U_2334),powerset(the_carrier(U_2335)))
| ~ sP529(U_2335,U_2334) ),
inference(clausify,[status(thm)],[f_592_4]) ).
cnf(f_592_7,plain,
( in(sK472(U_2335,U_2334),U_2334)
| ~ sP529(U_2335,U_2334) ),
inference(clausify,[status(thm)],[f_592_4]) ).
cnf(f_592_8,plain,
( ~ closed_subset(sK472(U_2335,U_2334),U_2335)
| ~ sP529(U_2335,U_2334) ),
inference(clausify,[status(thm)],[f_592_4]) ).
fof(f_593_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_593_2,plain,
! [U_2337] :
( ! [U_2336] :
( subset(relation_dom(relation_composition(U_2337,U_2336)),relation_dom(U_2337))
| ~ relation(U_2336) )
| ~ relation(U_2337) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
! [U_2336,U_2337] :
( subset(relation_dom(relation_composition(U_2337,U_2336)),relation_dom(U_2337))
| ~ relation(U_2336)
| ~ relation(U_2337) ),
inference(definitional_conversion,[status(esa)],[f_593_2]) ).
cnf(f_593_4,plain,
( subset(relation_dom(relation_composition(U_2337,U_2336)),relation_dom(U_2337))
| ~ relation(U_2336)
| ~ relation(U_2337) ),
inference(clausify,[status(thm)],[f_593_3]) ).
fof(f_594_1,plain,
! [A] :
( ! [B] :
( subset(interior(A,B),B)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t44_tops_1]) ).
fof(f_594_2,plain,
! [U_2339] :
( ! [U_2338] :
( subset(interior(U_2339,U_2338),U_2338)
| ~ element(U_2338,powerset(the_carrier(U_2339))) )
| ~ top_str(U_2339) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
! [U_2338,U_2339] :
( subset(interior(U_2339,U_2338),U_2338)
| ~ element(U_2338,powerset(the_carrier(U_2339)))
| ~ top_str(U_2339) ),
inference(definitional_conversion,[status(esa)],[f_594_2]) ).
cnf(f_594_4,plain,
( subset(interior(U_2339,U_2338),U_2338)
| ~ element(U_2338,powerset(the_carrier(U_2339)))
| ~ top_str(U_2339) ),
inference(clausify,[status(thm)],[f_594_3]) ).
fof(f_595_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( in(C,topstr_closure(A,B))
| ? [D] :
( ~ in(C,D)
& subset(B,D)
& closed_subset(D,A)
& element(D,powerset(the_carrier(A))) ) )
& ( ! [D] :
( in(C,D)
| ~ subset(B,D)
| ~ closed_subset(D,A)
| ~ element(D,powerset(the_carrier(A))) )
| ~ in(C,topstr_closure(A,B)) ) )
| ~ in(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t45_pre_topc]) ).
fof(f_595_2,plain,
! [U_2344] :
( ! [U_2343] :
( ! [U_2342] :
( ( ( in(U_2342,topstr_closure(U_2344,U_2343))
| ? [U_2341] :
( ~ in(U_2342,U_2341)
& subset(U_2343,U_2341)
& closed_subset(U_2341,U_2344)
& element(U_2341,powerset(the_carrier(U_2344))) ) )
& ( ! [U_2340] :
( in(U_2342,U_2340)
| ~ subset(U_2343,U_2340)
| ~ closed_subset(U_2340,U_2344)
| ~ element(U_2340,powerset(the_carrier(U_2344))) )
| ~ in(U_2342,topstr_closure(U_2344,U_2343)) ) )
| ~ in(U_2342,the_carrier(U_2344)) )
| ~ element(U_2343,powerset(the_carrier(U_2344))) )
| ~ top_str(U_2344) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
fof(f_595_3,plain,
! [U_2344] :
( ! [U_2343] :
( ! [U_2342] :
( ( ( in(U_2342,topstr_closure(U_2344,U_2343))
| ( ~ in(U_2342,sK473(U_2344,U_2343,U_2342))
& subset(U_2343,sK473(U_2344,U_2343,U_2342))
& closed_subset(sK473(U_2344,U_2343,U_2342),U_2344)
& element(sK473(U_2344,U_2343,U_2342),powerset(the_carrier(U_2344))) ) )
& ( ! [U_2340] :
( in(U_2342,U_2340)
| ~ subset(U_2343,U_2340)
| ~ closed_subset(U_2340,U_2344)
| ~ element(U_2340,powerset(the_carrier(U_2344))) )
| ~ in(U_2342,topstr_closure(U_2344,U_2343)) ) )
| ~ in(U_2342,the_carrier(U_2344)) )
| ~ element(U_2343,powerset(the_carrier(U_2344))) )
| ~ top_str(U_2344) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_2341,sK473(U_2344,U_2343,U_2342))],[f_595_2]) ).
fof(f_595_4,plain,
( ! [U_2344,U_2343,U_2342] :
( ~ in(U_2342,sK473(U_2344,U_2343,U_2342))
| ~ sP530(U_2344,U_2343,U_2342) )
& ! [U_2344,U_2343,U_2342] :
( subset(U_2343,sK473(U_2344,U_2343,U_2342))
| ~ sP530(U_2344,U_2343,U_2342) )
& ! [U_2344,U_2343,U_2342] :
( closed_subset(sK473(U_2344,U_2343,U_2342),U_2344)
| ~ sP530(U_2344,U_2343,U_2342) )
& ! [U_2344,U_2343,U_2342] :
( element(sK473(U_2344,U_2343,U_2342),powerset(the_carrier(U_2344)))
| ~ sP530(U_2344,U_2343,U_2342) )
& ! [U_2344,U_2340,U_2343,U_2342] :
( in(U_2342,topstr_closure(U_2344,U_2343))
| sP530(U_2344,U_2343,U_2342)
| ~ sP531(U_2344,U_2340,U_2343,U_2342) )
& ! [U_2344,U_2340,U_2343,U_2342] :
( in(U_2342,U_2340)
| ~ subset(U_2343,U_2340)
| ~ closed_subset(U_2340,U_2344)
| ~ element(U_2340,powerset(the_carrier(U_2344)))
| ~ in(U_2342,topstr_closure(U_2344,U_2343))
| ~ sP531(U_2344,U_2340,U_2343,U_2342) )
& ! [U_2344,U_2340,U_2343,U_2342] :
( sP531(U_2344,U_2340,U_2343,U_2342)
| ~ in(U_2342,the_carrier(U_2344))
| ~ element(U_2343,powerset(the_carrier(U_2344)))
| ~ top_str(U_2344) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP530,sP531])],[f_595_3]) ).
cnf(f_595_5,plain,
( sP531(U_2344,U_2340,U_2343,U_2342)
| ~ in(U_2342,the_carrier(U_2344))
| ~ element(U_2343,powerset(the_carrier(U_2344)))
| ~ top_str(U_2344) ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_6,plain,
( in(U_2342,U_2340)
| ~ subset(U_2343,U_2340)
| ~ closed_subset(U_2340,U_2344)
| ~ element(U_2340,powerset(the_carrier(U_2344)))
| ~ in(U_2342,topstr_closure(U_2344,U_2343))
| ~ sP531(U_2344,U_2340,U_2343,U_2342) ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_7,plain,
( in(U_2342,topstr_closure(U_2344,U_2343))
| sP530(U_2344,U_2343,U_2342)
| ~ sP531(U_2344,U_2340,U_2343,U_2342) ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_8,plain,
( element(sK473(U_2344,U_2343,U_2342),powerset(the_carrier(U_2344)))
| ~ sP530(U_2344,U_2343,U_2342) ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_9,plain,
( closed_subset(sK473(U_2344,U_2343,U_2342),U_2344)
| ~ sP530(U_2344,U_2343,U_2342) ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_10,plain,
( subset(U_2343,sK473(U_2344,U_2343,U_2342))
| ~ sP530(U_2344,U_2343,U_2342) ),
inference(clausify,[status(thm)],[f_595_4]) ).
cnf(f_595_11,plain,
( ~ in(U_2342,sK473(U_2344,U_2343,U_2342))
| ~ sP530(U_2344,U_2343,U_2342) ),
inference(clausify,[status(thm)],[f_595_4]) ).
fof(f_596_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_596_2,plain,
! [U_2346] :
( ! [U_2345] :
( subset(relation_rng(relation_composition(U_2346,U_2345)),relation_rng(U_2345))
| ~ relation(U_2345) )
| ~ relation(U_2346) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
! [U_2346,U_2345] :
( subset(relation_rng(relation_composition(U_2346,U_2345)),relation_rng(U_2345))
| ~ relation(U_2345)
| ~ relation(U_2346) ),
inference(definitional_conversion,[status(esa)],[f_596_2]) ).
cnf(f_596_4,plain,
( subset(relation_rng(relation_composition(U_2346,U_2345)),relation_rng(U_2345))
| ~ relation(U_2345)
| ~ relation(U_2346) ),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_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_597_2,plain,
! [U_2348,U_2347] :
( U_2347 = set_union2(U_2348,set_difference(U_2347,U_2348))
| ~ subset(U_2348,U_2347) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
! [U_2347,U_2348] :
( U_2347 = set_union2(U_2348,set_difference(U_2347,U_2348))
| ~ subset(U_2348,U_2347) ),
inference(definitional_conversion,[status(esa)],[f_597_2]) ).
cnf(f_597_4,plain,
( U_2347 = set_union2(U_2348,set_difference(U_2347,U_2348))
| ~ subset(U_2348,U_2347) ),
inference(clausify,[status(thm)],[f_597_3]) ).
fof(f_598_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_598_2,plain,
! [U_2353,U_2352,U_2351,U_2350] :
( ! [U_2349] :
( ( in(U_2349,relation_inverse_image(U_2350,U_2351))
| ~ in(apply(U_2350,U_2349),U_2351)
| ~ in(U_2349,U_2353) )
& ( ( in(apply(U_2350,U_2349),U_2351)
& in(U_2349,U_2353) )
| ~ in(U_2349,relation_inverse_image(U_2350,U_2351)) ) )
| U_2352 = empty_set
| ~ relation_of2_as_subset(U_2350,U_2353,U_2352)
| ~ quasi_total(U_2350,U_2353,U_2352)
| ~ function(U_2350) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
fof(f_598_3,plain,
! [U_2353,U_2352,U_2351,U_2350] :
( ( ! [U_2355] :
( in(U_2355,relation_inverse_image(U_2350,U_2351))
| ~ in(apply(U_2350,U_2355),U_2351)
| ~ in(U_2355,U_2353) )
& ! [U_2354] :
( ( in(apply(U_2350,U_2354),U_2351)
& in(U_2354,U_2353) )
| ~ in(U_2354,relation_inverse_image(U_2350,U_2351)) ) )
| U_2352 = empty_set
| ~ relation_of2_as_subset(U_2350,U_2353,U_2352)
| ~ quasi_total(U_2350,U_2353,U_2352)
| ~ function(U_2350) ),
inference(miniscope,[status(thm)],[f_598_2]) ).
fof(f_598_4,plain,
( ! [U_2351,U_2350,U_2354,U_2353] :
( in(apply(U_2350,U_2354),U_2351)
| ~ sP532(U_2351,U_2350,U_2354,U_2353) )
& ! [U_2351,U_2350,U_2354,U_2353] :
( in(U_2354,U_2353)
| ~ sP532(U_2351,U_2350,U_2354,U_2353) )
& ! [U_2351,U_2350,U_2354,U_2355,U_2353] :
( in(U_2355,relation_inverse_image(U_2350,U_2351))
| ~ in(apply(U_2350,U_2355),U_2351)
| ~ in(U_2355,U_2353)
| ~ sP533(U_2351,U_2350,U_2354,U_2355,U_2353) )
& ! [U_2351,U_2350,U_2354,U_2355,U_2353] :
( sP532(U_2351,U_2350,U_2354,U_2353)
| ~ in(U_2354,relation_inverse_image(U_2350,U_2351))
| ~ sP533(U_2351,U_2350,U_2354,U_2355,U_2353) )
& ! [U_2351,U_2350,U_2352,U_2354,U_2355,U_2353] :
( sP533(U_2351,U_2350,U_2354,U_2355,U_2353)
| U_2352 = empty_set
| ~ relation_of2_as_subset(U_2350,U_2353,U_2352)
| ~ quasi_total(U_2350,U_2353,U_2352)
| ~ function(U_2350) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP532,sP533])],[f_598_3]) ).
cnf(f_598_5,plain,
( sP533(U_2351,U_2350,U_2354,U_2355,U_2353)
| U_2352 = empty_set
| ~ relation_of2_as_subset(U_2350,U_2353,U_2352)
| ~ quasi_total(U_2350,U_2353,U_2352)
| ~ function(U_2350) ),
inference(clausify,[status(thm)],[f_598_4]) ).
cnf(f_598_6,plain,
( sP532(U_2351,U_2350,U_2354,U_2353)
| ~ in(U_2354,relation_inverse_image(U_2350,U_2351))
| ~ sP533(U_2351,U_2350,U_2354,U_2355,U_2353) ),
inference(clausify,[status(thm)],[f_598_4]) ).
cnf(f_598_7,plain,
( in(U_2355,relation_inverse_image(U_2350,U_2351))
| ~ in(apply(U_2350,U_2355),U_2351)
| ~ in(U_2355,U_2353)
| ~ sP533(U_2351,U_2350,U_2354,U_2355,U_2353) ),
inference(clausify,[status(thm)],[f_598_4]) ).
cnf(f_598_8,plain,
( in(U_2354,U_2353)
| ~ sP532(U_2351,U_2350,U_2354,U_2353) ),
inference(clausify,[status(thm)],[f_598_4]) ).
cnf(f_598_9,plain,
( in(apply(U_2350,U_2354),U_2351)
| ~ sP532(U_2351,U_2350,U_2354,U_2353) ),
inference(clausify,[status(thm)],[f_598_4]) ).
fof(f_599_1,plain,
! [A] :
( ! [B] :
( ? [C] :
( topstr_closure(A,B) = meet_of_subsets(the_carrier(A),C)
& ! [D] :
( ( ( in(D,C)
| ~ subset(B,D)
| ~ closed_subset(D,A) )
& ( ( subset(B,D)
& closed_subset(D,A) )
| ~ in(D,C) ) )
| ~ element(D,powerset(the_carrier(A))) )
& element(C,powerset(powerset(the_carrier(A)))) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[t46_pre_topc]) ).
fof(f_599_2,plain,
! [U_2359] :
( ! [U_2358] :
( ? [U_2357] :
( topstr_closure(U_2359,U_2358) = meet_of_subsets(the_carrier(U_2359),U_2357)
& ! [U_2356] :
( ( ( in(U_2356,U_2357)
| ~ subset(U_2358,U_2356)
| ~ closed_subset(U_2356,U_2359) )
& ( ( subset(U_2358,U_2356)
& closed_subset(U_2356,U_2359) )
| ~ in(U_2356,U_2357) ) )
| ~ element(U_2356,powerset(the_carrier(U_2359))) )
& element(U_2357,powerset(powerset(the_carrier(U_2359)))) )
| ~ element(U_2358,powerset(the_carrier(U_2359))) )
| ~ top_str(U_2359)
| ~ topological_space(U_2359) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
fof(f_599_3,plain,
! [U_2359] :
( ! [U_2358] :
( ( topstr_closure(U_2359,U_2358) = meet_of_subsets(the_carrier(U_2359),sK474(U_2359,U_2358))
& ! [U_2356] :
( ( ( in(U_2356,sK474(U_2359,U_2358))
| ~ subset(U_2358,U_2356)
| ~ closed_subset(U_2356,U_2359) )
& ( ( subset(U_2358,U_2356)
& closed_subset(U_2356,U_2359) )
| ~ in(U_2356,sK474(U_2359,U_2358)) ) )
| ~ element(U_2356,powerset(the_carrier(U_2359))) )
& element(sK474(U_2359,U_2358),powerset(powerset(the_carrier(U_2359)))) )
| ~ element(U_2358,powerset(the_carrier(U_2359))) )
| ~ top_str(U_2359)
| ~ topological_space(U_2359) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_2357,sK474(U_2359,U_2358))],[f_599_2]) ).
fof(f_599_4,plain,
( ! [U_2359,U_2356,U_2358] :
( subset(U_2358,U_2356)
| ~ sP534(U_2359,U_2356,U_2358) )
& ! [U_2359,U_2356,U_2358] :
( closed_subset(U_2356,U_2359)
| ~ sP534(U_2359,U_2356,U_2358) )
& ! [U_2359,U_2356,U_2358] :
( in(U_2356,sK474(U_2359,U_2358))
| ~ subset(U_2358,U_2356)
| ~ closed_subset(U_2356,U_2359)
| ~ sP535(U_2359,U_2356,U_2358) )
& ! [U_2359,U_2356,U_2358] :
( sP534(U_2359,U_2356,U_2358)
| ~ in(U_2356,sK474(U_2359,U_2358))
| ~ sP535(U_2359,U_2356,U_2358) )
& ! [U_2359,U_2356,U_2358] :
( topstr_closure(U_2359,U_2358) = meet_of_subsets(the_carrier(U_2359),sK474(U_2359,U_2358))
| ~ sP536(U_2359,U_2356,U_2358) )
& ! [U_2359,U_2356,U_2358] :
( sP535(U_2359,U_2356,U_2358)
| ~ element(U_2356,powerset(the_carrier(U_2359)))
| ~ sP536(U_2359,U_2356,U_2358) )
& ! [U_2359,U_2356,U_2358] :
( element(sK474(U_2359,U_2358),powerset(powerset(the_carrier(U_2359))))
| ~ sP536(U_2359,U_2356,U_2358) )
& ! [U_2359,U_2356,U_2358] :
( sP536(U_2359,U_2356,U_2358)
| ~ element(U_2358,powerset(the_carrier(U_2359)))
| ~ top_str(U_2359)
| ~ topological_space(U_2359) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP534,sP535,sP536])],[f_599_3]) ).
cnf(f_599_5,plain,
( sP536(U_2359,U_2356,U_2358)
| ~ element(U_2358,powerset(the_carrier(U_2359)))
| ~ top_str(U_2359)
| ~ topological_space(U_2359) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_6,plain,
( element(sK474(U_2359,U_2358),powerset(powerset(the_carrier(U_2359))))
| ~ sP536(U_2359,U_2356,U_2358) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_7,plain,
( sP535(U_2359,U_2356,U_2358)
| ~ element(U_2356,powerset(the_carrier(U_2359)))
| ~ sP536(U_2359,U_2356,U_2358) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_8,plain,
( topstr_closure(U_2359,U_2358) = meet_of_subsets(the_carrier(U_2359),sK474(U_2359,U_2358))
| ~ sP536(U_2359,U_2356,U_2358) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_9,plain,
( sP534(U_2359,U_2356,U_2358)
| ~ in(U_2356,sK474(U_2359,U_2358))
| ~ sP535(U_2359,U_2356,U_2358) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_10,plain,
( in(U_2356,sK474(U_2359,U_2358))
| ~ subset(U_2358,U_2356)
| ~ closed_subset(U_2356,U_2359)
| ~ sP535(U_2359,U_2356,U_2358) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_11,plain,
( closed_subset(U_2356,U_2359)
| ~ sP534(U_2359,U_2356,U_2358) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_12,plain,
( subset(U_2358,U_2356)
| ~ sP534(U_2359,U_2356,U_2358) ),
inference(clausify,[status(thm)],[f_599_4]) ).
fof(f_600_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_600_2,plain,
! [U_2361] :
( ! [U_2360] :
( relation_dom(relation_composition(U_2361,U_2360)) = relation_dom(U_2361)
| ~ subset(relation_rng(U_2361),relation_dom(U_2360))
| ~ relation(U_2360) )
| ~ relation(U_2361) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
fof(f_600_3,plain,
! [U_2360,U_2361] :
( relation_dom(relation_composition(U_2361,U_2360)) = relation_dom(U_2361)
| ~ subset(relation_rng(U_2361),relation_dom(U_2360))
| ~ relation(U_2360)
| ~ relation(U_2361) ),
inference(definitional_conversion,[status(esa)],[f_600_2]) ).
cnf(f_600_4,plain,
( relation_dom(relation_composition(U_2361,U_2360)) = relation_dom(U_2361)
| ~ subset(relation_rng(U_2361),relation_dom(U_2360))
| ~ relation(U_2360)
| ~ relation(U_2361) ),
inference(clausify,[status(thm)],[f_600_3]) ).
fof(f_601_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_601_2,plain,
! [U_2363,U_2362] :
( complements_of_subsets(U_2363,U_2362) != empty_set
| U_2362 = empty_set
| ~ element(U_2362,powerset(powerset(U_2363))) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
! [U_2362,U_2363] :
( complements_of_subsets(U_2363,U_2362) != empty_set
| U_2362 = empty_set
| ~ element(U_2362,powerset(powerset(U_2363))) ),
inference(definitional_conversion,[status(esa)],[f_601_2]) ).
cnf(f_601_4,plain,
( complements_of_subsets(U_2363,U_2362) != empty_set
| U_2362 = empty_set
| ~ element(U_2362,powerset(powerset(U_2363))) ),
inference(clausify,[status(thm)],[f_601_3]) ).
fof(f_602_1,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t46_zfmisc_1]) ).
fof(f_602_2,plain,
! [U_2365,U_2364] :
( set_union2(singleton(U_2365),U_2364) = U_2364
| ~ in(U_2365,U_2364) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
! [U_2365,U_2364] :
( set_union2(singleton(U_2365),U_2364) = U_2364
| ~ in(U_2365,U_2364) ),
inference(definitional_conversion,[status(esa)],[f_602_2]) ).
cnf(f_602_4,plain,
( set_union2(singleton(U_2365),U_2364) = U_2364
| ~ in(U_2365,U_2364) ),
inference(clausify,[status(thm)],[f_602_3]) ).
fof(f_603_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_603_2,plain,
! [U_2367] :
( ! [U_2366] :
( relation_rng(relation_composition(U_2366,U_2367)) = relation_rng(U_2367)
| ~ subset(relation_dom(U_2367),relation_rng(U_2366))
| ~ relation(U_2366) )
| ~ relation(U_2367) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
! [U_2366,U_2367] :
( relation_rng(relation_composition(U_2366,U_2367)) = relation_rng(U_2367)
| ~ subset(relation_dom(U_2367),relation_rng(U_2366))
| ~ relation(U_2366)
| ~ relation(U_2367) ),
inference(definitional_conversion,[status(esa)],[f_603_2]) ).
cnf(f_603_4,plain,
( relation_rng(relation_composition(U_2366,U_2367)) = relation_rng(U_2367)
| ~ subset(relation_dom(U_2367),relation_rng(U_2366))
| ~ relation(U_2366)
| ~ relation(U_2367) ),
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_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_604_2,plain,
! [U_2369,U_2368] :
( subset_difference(U_2369,cast_to_subset(U_2369),union_of_subsets(U_2369,U_2368)) = meet_of_subsets(U_2369,complements_of_subsets(U_2369,U_2368))
| U_2368 = empty_set
| ~ element(U_2368,powerset(powerset(U_2369))) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
! [U_2369,U_2368] :
( subset_difference(U_2369,cast_to_subset(U_2369),union_of_subsets(U_2369,U_2368)) = meet_of_subsets(U_2369,complements_of_subsets(U_2369,U_2368))
| U_2368 = empty_set
| ~ element(U_2368,powerset(powerset(U_2369))) ),
inference(definitional_conversion,[status(esa)],[f_604_2]) ).
cnf(f_604_4,plain,
( subset_difference(U_2369,cast_to_subset(U_2369),union_of_subsets(U_2369,U_2368)) = meet_of_subsets(U_2369,complements_of_subsets(U_2369,U_2368))
| U_2368 = empty_set
| ~ element(U_2368,powerset(powerset(U_2369))) ),
inference(clausify,[status(thm)],[f_604_3]) ).
fof(f_605_1,plain,
! [A] :
( ! [B] :
( subset(B,topstr_closure(A,B))
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t48_pre_topc]) ).
fof(f_605_2,plain,
! [U_2371] :
( ! [U_2370] :
( subset(U_2370,topstr_closure(U_2371,U_2370))
| ~ element(U_2370,powerset(the_carrier(U_2371))) )
| ~ top_str(U_2371) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
fof(f_605_3,plain,
! [U_2371,U_2370] :
( subset(U_2370,topstr_closure(U_2371,U_2370))
| ~ element(U_2370,powerset(the_carrier(U_2371)))
| ~ top_str(U_2371) ),
inference(definitional_conversion,[status(esa)],[f_605_2]) ).
cnf(f_605_4,plain,
( subset(U_2370,topstr_closure(U_2371,U_2370))
| ~ element(U_2370,powerset(the_carrier(U_2371)))
| ~ top_str(U_2371) ),
inference(clausify,[status(thm)],[f_605_3]) ).
fof(f_606_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_606_2,plain,
! [U_2373,U_2372] :
( union_of_subsets(U_2373,complements_of_subsets(U_2373,U_2372)) = subset_difference(U_2373,cast_to_subset(U_2373),meet_of_subsets(U_2373,U_2372))
| U_2372 = empty_set
| ~ element(U_2372,powerset(powerset(U_2373))) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
! [U_2372,U_2373] :
( union_of_subsets(U_2373,complements_of_subsets(U_2373,U_2372)) = subset_difference(U_2373,cast_to_subset(U_2373),meet_of_subsets(U_2373,U_2372))
| U_2372 = empty_set
| ~ element(U_2372,powerset(powerset(U_2373))) ),
inference(definitional_conversion,[status(esa)],[f_606_2]) ).
cnf(f_606_4,plain,
( union_of_subsets(U_2373,complements_of_subsets(U_2373,U_2372)) = subset_difference(U_2373,cast_to_subset(U_2373),meet_of_subsets(U_2373,U_2372))
| U_2372 = empty_set
| ~ element(U_2372,powerset(powerset(U_2373))) ),
inference(clausify,[status(thm)],[f_606_3]) ).
fof(f_607_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_607_2,plain,
! [U_2375,U_2374] : set_difference(U_2375,set_difference(U_2375,U_2374)) = set_intersection2(U_2375,U_2374),
inference(variable_rename,[status(thm)],[f_607_1]) ).
fof(f_607_3,plain,
! [U_2375,U_2374] : set_difference(U_2375,set_difference(U_2375,U_2374)) = set_intersection2(U_2375,U_2374),
inference(definitional_conversion,[status(esa)],[f_607_2]) ).
cnf(f_607_4,plain,
set_difference(U_2375,set_difference(U_2375,U_2374)) = set_intersection2(U_2375,U_2374),
inference(clausify,[status(thm)],[f_607_3]) ).
fof(f_608_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_608_2,plain,
! [U_2378] :
( ! [U_2377] :
( ! [U_2376] :
( relation_isomorphism(U_2377,U_2378,function_inverse(U_2376))
| ~ relation_isomorphism(U_2378,U_2377,U_2376)
| ~ function(U_2376)
| ~ relation(U_2376) )
| ~ relation(U_2377) )
| ~ relation(U_2378) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
! [U_2376,U_2377,U_2378] :
( relation_isomorphism(U_2377,U_2378,function_inverse(U_2376))
| ~ relation_isomorphism(U_2378,U_2377,U_2376)
| ~ function(U_2376)
| ~ relation(U_2376)
| ~ relation(U_2377)
| ~ relation(U_2378) ),
inference(definitional_conversion,[status(esa)],[f_608_2]) ).
cnf(f_608_4,plain,
( relation_isomorphism(U_2377,U_2378,function_inverse(U_2376))
| ~ relation_isomorphism(U_2378,U_2377,U_2376)
| ~ function(U_2376)
| ~ relation(U_2376)
| ~ relation(U_2377)
| ~ relation(U_2378) ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_609_2,plain,
! [U_2379] : set_difference(empty_set,U_2379) = empty_set,
inference(variable_rename,[status(thm)],[f_609_1]) ).
fof(f_609_3,plain,
! [U_2379] : set_difference(empty_set,U_2379) = empty_set,
inference(definitional_conversion,[status(esa)],[f_609_2]) ).
cnf(f_609_4,plain,
set_difference(empty_set,U_2379) = empty_set,
inference(clausify,[status(thm)],[f_609_3]) ).
fof(f_610_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_610_2,plain,
! [U_2382,U_2381,U_2380] :
( element(U_2382,U_2380)
| ~ element(U_2381,powerset(U_2380))
| ~ in(U_2382,U_2381) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
fof(f_610_3,plain,
! [U_2382,U_2381,U_2380] :
( element(U_2382,U_2380)
| ~ element(U_2381,powerset(U_2380))
| ~ in(U_2382,U_2381) ),
inference(definitional_conversion,[status(esa)],[f_610_2]) ).
cnf(f_610_4,plain,
( element(U_2382,U_2380)
| ~ element(U_2381,powerset(U_2380))
| ~ in(U_2382,U_2381) ),
inference(clausify,[status(thm)],[f_610_3]) ).
fof(f_611_1,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t4_wellord2]) ).
fof(f_611_2,plain,
! [U_2383] :
( connected(inclusion_relation(U_2383))
| ~ ordinal(U_2383) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
! [U_2383] :
( connected(inclusion_relation(U_2383))
| ~ ordinal(U_2383) ),
inference(definitional_conversion,[status(esa)],[f_611_2]) ).
cnf(f_611_4,plain,
( connected(inclusion_relation(U_2383))
| ~ ordinal(U_2383) ),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_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_612_2,plain,
! [U_2387,U_2386] :
( ( ~ disjoint(U_2387,U_2386)
| ! [U_2385] : ~ in(U_2385,set_intersection2(U_2387,U_2386)) )
& ( ? [U_2384] : in(U_2384,set_intersection2(U_2387,U_2386))
| disjoint(U_2387,U_2386) ) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
( ! [U_2391,U_2389] :
( ~ disjoint(U_2391,U_2389)
| ! [U_2385] : ~ in(U_2385,set_intersection2(U_2391,U_2389)) )
& ! [U_2390,U_2388] :
( ? [U_2384] : in(U_2384,set_intersection2(U_2390,U_2388))
| disjoint(U_2390,U_2388) ) ),
inference(miniscope,[status(thm)],[f_612_2]) ).
fof(f_612_4,plain,
( ! [U_2391,U_2389] :
( ~ disjoint(U_2391,U_2389)
| ! [U_2385] : ~ in(U_2385,set_intersection2(U_2391,U_2389)) )
& ! [U_2390,U_2388] :
( in(sK475(U_2390,U_2388),set_intersection2(U_2390,U_2388))
| disjoint(U_2390,U_2388) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_2384,sK475(U_2390,U_2388))],[f_612_3]) ).
fof(f_612_5,plain,
( ! [U_2391,U_2385,U_2389] :
( ~ disjoint(U_2391,U_2389)
| ~ in(U_2385,set_intersection2(U_2391,U_2389)) )
& ! [U_2390,U_2388] :
( in(sK475(U_2390,U_2388),set_intersection2(U_2390,U_2388))
| disjoint(U_2390,U_2388) ) ),
inference(definitional_conversion,[status(esa)],[f_612_4]) ).
cnf(f_612_6,plain,
( in(sK475(U_2390,U_2388),set_intersection2(U_2390,U_2388))
| disjoint(U_2390,U_2388) ),
inference(clausify,[status(thm)],[f_612_5]) ).
cnf(f_612_7,plain,
( ~ disjoint(U_2391,U_2389)
| ~ in(U_2385,set_intersection2(U_2391,U_2389)) ),
inference(clausify,[status(thm)],[f_612_5]) ).
fof(f_613_1,plain,
! [A] :
( ( bottom_of_semilattstr(A) = join_of_latt_set(A,empty_set)
& latt_str(A)
& lower_bounded_semilattstr(A)
& lattice(A)
& ~ empty_carrier(A) )
| ~ latt_str(A)
| ~ complete_latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t50_lattice3]) ).
fof(f_613_2,plain,
! [U_2392] :
( ( bottom_of_semilattstr(U_2392) = join_of_latt_set(U_2392,empty_set)
& latt_str(U_2392)
& lower_bounded_semilattstr(U_2392)
& lattice(U_2392)
& ~ empty_carrier(U_2392) )
| ~ latt_str(U_2392)
| ~ complete_latt_str(U_2392)
| ~ lattice(U_2392)
| empty_carrier(U_2392) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
fof(f_613_3,plain,
( ! [U_2392] :
( bottom_of_semilattstr(U_2392) = join_of_latt_set(U_2392,empty_set)
| ~ sP537(U_2392) )
& ! [U_2392] :
( latt_str(U_2392)
| ~ sP537(U_2392) )
& ! [U_2392] :
( lower_bounded_semilattstr(U_2392)
| ~ sP537(U_2392) )
& ! [U_2392] :
( lattice(U_2392)
| ~ sP537(U_2392) )
& ! [U_2392] :
( ~ empty_carrier(U_2392)
| ~ sP537(U_2392) )
& ! [U_2392] :
( sP537(U_2392)
| ~ latt_str(U_2392)
| ~ complete_latt_str(U_2392)
| ~ lattice(U_2392)
| empty_carrier(U_2392) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP537])],[f_613_2]) ).
cnf(f_613_4,plain,
( sP537(U_2392)
| ~ latt_str(U_2392)
| ~ complete_latt_str(U_2392)
| ~ lattice(U_2392)
| empty_carrier(U_2392) ),
inference(clausify,[status(thm)],[f_613_3]) ).
cnf(f_613_5,plain,
( ~ empty_carrier(U_2392)
| ~ sP537(U_2392) ),
inference(clausify,[status(thm)],[f_613_3]) ).
cnf(f_613_6,plain,
( lattice(U_2392)
| ~ sP537(U_2392) ),
inference(clausify,[status(thm)],[f_613_3]) ).
cnf(f_613_7,plain,
( lower_bounded_semilattstr(U_2392)
| ~ sP537(U_2392) ),
inference(clausify,[status(thm)],[f_613_3]) ).
cnf(f_613_8,plain,
( latt_str(U_2392)
| ~ sP537(U_2392) ),
inference(clausify,[status(thm)],[f_613_3]) ).
cnf(f_613_9,plain,
( bottom_of_semilattstr(U_2392) = join_of_latt_set(U_2392,empty_set)
| ~ sP537(U_2392) ),
inference(clausify,[status(thm)],[f_613_3]) ).
fof(f_614_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_614_2,plain,
! [U_2395] :
( ! [U_2394] :
( ! [U_2393] :
( in(U_2393,subset_complement(U_2395,U_2394))
| in(U_2393,U_2394)
| ~ element(U_2393,U_2395) )
| ~ element(U_2394,powerset(U_2395)) )
| U_2395 = empty_set ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
fof(f_614_3,plain,
! [U_2394,U_2393,U_2395] :
( in(U_2393,subset_complement(U_2395,U_2394))
| in(U_2393,U_2394)
| ~ element(U_2393,U_2395)
| ~ element(U_2394,powerset(U_2395))
| U_2395 = empty_set ),
inference(definitional_conversion,[status(esa)],[f_614_2]) ).
cnf(f_614_4,plain,
( in(U_2393,subset_complement(U_2395,U_2394))
| in(U_2393,U_2394)
| ~ element(U_2393,U_2395)
| ~ element(U_2394,powerset(U_2395))
| U_2395 = empty_set ),
inference(clausify,[status(thm)],[f_614_3]) ).
fof(f_615_1,plain,
! [A] :
( ! [B] :
( open_subset(interior(A,B),A)
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[t51_tops_1]) ).
fof(f_615_2,plain,
! [U_2397] :
( ! [U_2396] :
( open_subset(interior(U_2397,U_2396),U_2397)
| ~ element(U_2396,powerset(the_carrier(U_2397))) )
| ~ top_str(U_2397)
| ~ topological_space(U_2397) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
fof(f_615_3,plain,
! [U_2396,U_2397] :
( open_subset(interior(U_2397,U_2396),U_2397)
| ~ element(U_2396,powerset(the_carrier(U_2397)))
| ~ top_str(U_2397)
| ~ topological_space(U_2397) ),
inference(definitional_conversion,[status(esa)],[f_615_2]) ).
cnf(f_615_4,plain,
( open_subset(interior(U_2397,U_2396),U_2397)
| ~ element(U_2396,powerset(the_carrier(U_2397)))
| ~ top_str(U_2397)
| ~ topological_space(U_2397) ),
inference(clausify,[status(thm)],[f_615_3]) ).
fof(f_616_1,plain,
! [A] :
( ! [B] :
( ( ( closed_subset(B,A)
| topstr_closure(A,B) != B
| ~ topological_space(A) )
& ( topstr_closure(A,B) = B
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[t52_pre_topc]) ).
fof(f_616_2,plain,
! [U_2399] :
( ! [U_2398] :
( ( ( closed_subset(U_2398,U_2399)
| topstr_closure(U_2399,U_2398) != U_2398
| ~ topological_space(U_2399) )
& ( topstr_closure(U_2399,U_2398) = U_2398
| ~ closed_subset(U_2398,U_2399) ) )
| ~ element(U_2398,powerset(the_carrier(U_2399))) )
| ~ top_str(U_2399) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
( ! [U_2399,U_2398] :
( closed_subset(U_2398,U_2399)
| topstr_closure(U_2399,U_2398) != U_2398
| ~ topological_space(U_2399)
| ~ sP538(U_2399,U_2398) )
& ! [U_2399,U_2398] :
( topstr_closure(U_2399,U_2398) = U_2398
| ~ closed_subset(U_2398,U_2399)
| ~ sP538(U_2399,U_2398) )
& ! [U_2399,U_2398] :
( sP538(U_2399,U_2398)
| ~ element(U_2398,powerset(the_carrier(U_2399)))
| ~ top_str(U_2399) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP538])],[f_616_2]) ).
cnf(f_616_4,plain,
( sP538(U_2399,U_2398)
| ~ element(U_2398,powerset(the_carrier(U_2399)))
| ~ top_str(U_2399) ),
inference(clausify,[status(thm)],[f_616_3]) ).
cnf(f_616_5,plain,
( topstr_closure(U_2399,U_2398) = U_2398
| ~ closed_subset(U_2398,U_2399)
| ~ sP538(U_2399,U_2398) ),
inference(clausify,[status(thm)],[f_616_3]) ).
cnf(f_616_6,plain,
( closed_subset(U_2398,U_2399)
| topstr_closure(U_2399,U_2398) != U_2398
| ~ topological_space(U_2399)
| ~ sP538(U_2399,U_2398) ),
inference(clausify,[status(thm)],[f_616_3]) ).
fof(f_617_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_617_2,plain,
! [U_2402] :
( ! [U_2401] :
( ! [U_2400] :
( ( ( well_founded_relation(U_2401)
| ~ well_founded_relation(U_2402) )
& ( antisymmetric(U_2401)
| ~ antisymmetric(U_2402) )
& ( connected(U_2401)
| ~ connected(U_2402) )
& ( transitive(U_2401)
| ~ transitive(U_2402) )
& ( reflexive(U_2401)
| ~ reflexive(U_2402) ) )
| ~ relation_isomorphism(U_2402,U_2401,U_2400)
| ~ function(U_2400)
| ~ relation(U_2400) )
| ~ relation(U_2401) )
| ~ relation(U_2402) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
( ! [U_2402,U_2401] :
( well_founded_relation(U_2401)
| ~ well_founded_relation(U_2402)
| ~ sP539(U_2402,U_2401) )
& ! [U_2402,U_2401] :
( antisymmetric(U_2401)
| ~ antisymmetric(U_2402)
| ~ sP539(U_2402,U_2401) )
& ! [U_2402,U_2401] :
( connected(U_2401)
| ~ connected(U_2402)
| ~ sP539(U_2402,U_2401) )
& ! [U_2402,U_2401] :
( transitive(U_2401)
| ~ transitive(U_2402)
| ~ sP539(U_2402,U_2401) )
& ! [U_2402,U_2401] :
( reflexive(U_2401)
| ~ reflexive(U_2402)
| ~ sP539(U_2402,U_2401) )
& ! [U_2402,U_2400,U_2401] :
( sP539(U_2402,U_2401)
| ~ relation_isomorphism(U_2402,U_2401,U_2400)
| ~ function(U_2400)
| ~ relation(U_2400)
| ~ relation(U_2401)
| ~ relation(U_2402) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP539])],[f_617_2]) ).
cnf(f_617_4,plain,
( sP539(U_2402,U_2401)
| ~ relation_isomorphism(U_2402,U_2401,U_2400)
| ~ function(U_2400)
| ~ relation(U_2400)
| ~ relation(U_2401)
| ~ relation(U_2402) ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_5,plain,
( reflexive(U_2401)
| ~ reflexive(U_2402)
| ~ sP539(U_2402,U_2401) ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_6,plain,
( transitive(U_2401)
| ~ transitive(U_2402)
| ~ sP539(U_2402,U_2401) ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_7,plain,
( connected(U_2401)
| ~ connected(U_2402)
| ~ sP539(U_2402,U_2401) ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_8,plain,
( antisymmetric(U_2401)
| ~ antisymmetric(U_2402)
| ~ sP539(U_2402,U_2401) ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_9,plain,
( well_founded_relation(U_2401)
| ~ well_founded_relation(U_2402)
| ~ sP539(U_2402,U_2401) ),
inference(clausify,[status(thm)],[f_617_3]) ).
fof(f_618_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_618_2,plain,
! [U_2408] :
( ! [U_2407] :
( ( ( U_2407 = function_inverse(U_2408)
| ? [U_2406,U_2405] :
( ( ( U_2405 != apply(U_2407,U_2406)
| ~ in(U_2406,relation_rng(U_2408)) )
& U_2406 = apply(U_2408,U_2405)
& in(U_2405,relation_dom(U_2408)) )
| ( ( U_2406 != apply(U_2408,U_2405)
| ~ in(U_2405,relation_dom(U_2408)) )
& U_2405 = apply(U_2407,U_2406)
& in(U_2406,relation_rng(U_2408)) ) )
| relation_dom(U_2407) != relation_rng(U_2408) )
& ( ( ! [U_2404,U_2403] :
( ( ( U_2403 = apply(U_2407,U_2404)
& in(U_2404,relation_rng(U_2408)) )
| U_2404 != apply(U_2408,U_2403)
| ~ in(U_2403,relation_dom(U_2408)) )
& ( ( U_2404 = apply(U_2408,U_2403)
& in(U_2403,relation_dom(U_2408)) )
| U_2403 != apply(U_2407,U_2404)
| ~ in(U_2404,relation_rng(U_2408)) ) )
& relation_dom(U_2407) = relation_rng(U_2408) )
| U_2407 != function_inverse(U_2408) ) )
| ~ function(U_2407)
| ~ relation(U_2407) )
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
! [U_2408] :
( ! [U_2407] :
( ( ( U_2407 = function_inverse(U_2408)
| ? [U_2416,U_2414] :
( ( U_2414 != apply(U_2407,U_2416)
| ~ in(U_2416,relation_rng(U_2408)) )
& U_2416 = apply(U_2408,U_2414)
& in(U_2414,relation_dom(U_2408)) )
| ? [U_2415,U_2413] :
( ( U_2415 != apply(U_2408,U_2413)
| ~ in(U_2413,relation_dom(U_2408)) )
& U_2413 = apply(U_2407,U_2415)
& in(U_2415,relation_rng(U_2408)) )
| relation_dom(U_2407) != relation_rng(U_2408) )
& ( ( ! [U_2412,U_2410] :
( ( U_2410 = apply(U_2407,U_2412)
& in(U_2412,relation_rng(U_2408)) )
| U_2412 != apply(U_2408,U_2410)
| ~ in(U_2410,relation_dom(U_2408)) )
& ! [U_2411,U_2409] :
( ( U_2411 = apply(U_2408,U_2409)
& in(U_2409,relation_dom(U_2408)) )
| U_2409 != apply(U_2407,U_2411)
| ~ in(U_2411,relation_rng(U_2408)) )
& relation_dom(U_2407) = relation_rng(U_2408) )
| U_2407 != function_inverse(U_2408) ) )
| ~ function(U_2407)
| ~ relation(U_2407) )
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ),
inference(miniscope,[status(thm)],[f_618_2]) ).
fof(f_618_4,plain,
! [U_2408] :
( ! [U_2407] :
( ( ( U_2407 = function_inverse(U_2408)
| ? [U_2416,U_2414] :
( ( U_2414 != apply(U_2407,U_2416)
| ~ in(U_2416,relation_rng(U_2408)) )
& U_2416 = apply(U_2408,U_2414)
& in(U_2414,relation_dom(U_2408)) )
| ? [U_2413] :
( ( sK476(U_2408,U_2407) != apply(U_2408,U_2413)
| ~ in(U_2413,relation_dom(U_2408)) )
& U_2413 = apply(U_2407,sK476(U_2408,U_2407))
& in(sK476(U_2408,U_2407),relation_rng(U_2408)) )
| relation_dom(U_2407) != relation_rng(U_2408) )
& ( ( ! [U_2412,U_2410] :
( ( U_2410 = apply(U_2407,U_2412)
& in(U_2412,relation_rng(U_2408)) )
| U_2412 != apply(U_2408,U_2410)
| ~ in(U_2410,relation_dom(U_2408)) )
& ! [U_2411,U_2409] :
( ( U_2411 = apply(U_2408,U_2409)
& in(U_2409,relation_dom(U_2408)) )
| U_2409 != apply(U_2407,U_2411)
| ~ in(U_2411,relation_rng(U_2408)) )
& relation_dom(U_2407) = relation_rng(U_2408) )
| U_2407 != function_inverse(U_2408) ) )
| ~ function(U_2407)
| ~ relation(U_2407) )
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_2415,sK476(U_2408,U_2407))],[f_618_3]) ).
fof(f_618_5,plain,
! [U_2408] :
( ! [U_2407] :
( ( ( U_2407 = function_inverse(U_2408)
| ? [U_2416,U_2414] :
( ( U_2414 != apply(U_2407,U_2416)
| ~ in(U_2416,relation_rng(U_2408)) )
& U_2416 = apply(U_2408,U_2414)
& in(U_2414,relation_dom(U_2408)) )
| ( ( sK476(U_2408,U_2407) != apply(U_2408,sK477(U_2408,U_2407))
| ~ in(sK477(U_2408,U_2407),relation_dom(U_2408)) )
& sK477(U_2408,U_2407) = apply(U_2407,sK476(U_2408,U_2407))
& in(sK476(U_2408,U_2407),relation_rng(U_2408)) )
| relation_dom(U_2407) != relation_rng(U_2408) )
& ( ( ! [U_2412,U_2410] :
( ( U_2410 = apply(U_2407,U_2412)
& in(U_2412,relation_rng(U_2408)) )
| U_2412 != apply(U_2408,U_2410)
| ~ in(U_2410,relation_dom(U_2408)) )
& ! [U_2411,U_2409] :
( ( U_2411 = apply(U_2408,U_2409)
& in(U_2409,relation_dom(U_2408)) )
| U_2409 != apply(U_2407,U_2411)
| ~ in(U_2411,relation_rng(U_2408)) )
& relation_dom(U_2407) = relation_rng(U_2408) )
| U_2407 != function_inverse(U_2408) ) )
| ~ function(U_2407)
| ~ relation(U_2407) )
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_2413,sK477(U_2408,U_2407))],[f_618_4]) ).
fof(f_618_6,plain,
! [U_2408] :
( ! [U_2407] :
( ( ( U_2407 = function_inverse(U_2408)
| ? [U_2414] :
( ( U_2414 != apply(U_2407,sK478(U_2408,U_2407))
| ~ in(sK478(U_2408,U_2407),relation_rng(U_2408)) )
& sK478(U_2408,U_2407) = apply(U_2408,U_2414)
& in(U_2414,relation_dom(U_2408)) )
| ( ( sK476(U_2408,U_2407) != apply(U_2408,sK477(U_2408,U_2407))
| ~ in(sK477(U_2408,U_2407),relation_dom(U_2408)) )
& sK477(U_2408,U_2407) = apply(U_2407,sK476(U_2408,U_2407))
& in(sK476(U_2408,U_2407),relation_rng(U_2408)) )
| relation_dom(U_2407) != relation_rng(U_2408) )
& ( ( ! [U_2412,U_2410] :
( ( U_2410 = apply(U_2407,U_2412)
& in(U_2412,relation_rng(U_2408)) )
| U_2412 != apply(U_2408,U_2410)
| ~ in(U_2410,relation_dom(U_2408)) )
& ! [U_2411,U_2409] :
( ( U_2411 = apply(U_2408,U_2409)
& in(U_2409,relation_dom(U_2408)) )
| U_2409 != apply(U_2407,U_2411)
| ~ in(U_2411,relation_rng(U_2408)) )
& relation_dom(U_2407) = relation_rng(U_2408) )
| U_2407 != function_inverse(U_2408) ) )
| ~ function(U_2407)
| ~ relation(U_2407) )
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_2416,sK478(U_2408,U_2407))],[f_618_5]) ).
fof(f_618_7,plain,
! [U_2408] :
( ! [U_2407] :
( ( ( U_2407 = function_inverse(U_2408)
| ( ( sK479(U_2408,U_2407) != apply(U_2407,sK478(U_2408,U_2407))
| ~ in(sK478(U_2408,U_2407),relation_rng(U_2408)) )
& sK478(U_2408,U_2407) = apply(U_2408,sK479(U_2408,U_2407))
& in(sK479(U_2408,U_2407),relation_dom(U_2408)) )
| ( ( sK476(U_2408,U_2407) != apply(U_2408,sK477(U_2408,U_2407))
| ~ in(sK477(U_2408,U_2407),relation_dom(U_2408)) )
& sK477(U_2408,U_2407) = apply(U_2407,sK476(U_2408,U_2407))
& in(sK476(U_2408,U_2407),relation_rng(U_2408)) )
| relation_dom(U_2407) != relation_rng(U_2408) )
& ( ( ! [U_2412,U_2410] :
( ( U_2410 = apply(U_2407,U_2412)
& in(U_2412,relation_rng(U_2408)) )
| U_2412 != apply(U_2408,U_2410)
| ~ in(U_2410,relation_dom(U_2408)) )
& ! [U_2411,U_2409] :
( ( U_2411 = apply(U_2408,U_2409)
& in(U_2409,relation_dom(U_2408)) )
| U_2409 != apply(U_2407,U_2411)
| ~ in(U_2411,relation_rng(U_2408)) )
& relation_dom(U_2407) = relation_rng(U_2408) )
| U_2407 != function_inverse(U_2408) ) )
| ~ function(U_2407)
| ~ relation(U_2407) )
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_2414,sK479(U_2408,U_2407))],[f_618_6]) ).
fof(f_618_8,plain,
( ! [U_2407,U_2408] :
( sK479(U_2408,U_2407) != apply(U_2407,sK478(U_2408,U_2407))
| ~ in(sK478(U_2408,U_2407),relation_rng(U_2408))
| ~ sP544(U_2407,U_2408) )
& ! [U_2407,U_2408] :
( sK478(U_2408,U_2407) = apply(U_2408,sK479(U_2408,U_2407))
| ~ sP544(U_2407,U_2408) )
& ! [U_2407,U_2408] :
( in(sK479(U_2408,U_2407),relation_dom(U_2408))
| ~ sP544(U_2407,U_2408) )
& ! [U_2407,U_2408] :
( sK476(U_2408,U_2407) != apply(U_2408,sK477(U_2408,U_2407))
| ~ in(sK477(U_2408,U_2407),relation_dom(U_2408))
| ~ sP543(U_2407,U_2408) )
& ! [U_2407,U_2408] :
( sK477(U_2408,U_2407) = apply(U_2407,sK476(U_2408,U_2407))
| ~ sP543(U_2407,U_2408) )
& ! [U_2407,U_2408] :
( in(sK476(U_2408,U_2407),relation_rng(U_2408))
| ~ sP543(U_2407,U_2408) )
& ! [U_2407,U_2412,U_2408,U_2410] :
( U_2410 = apply(U_2407,U_2412)
| ~ sP541(U_2407,U_2412,U_2408,U_2410) )
& ! [U_2407,U_2412,U_2408,U_2410] :
( in(U_2412,relation_rng(U_2408))
| ~ sP541(U_2407,U_2412,U_2408,U_2410) )
& ! [U_2408,U_2411,U_2409] :
( U_2411 = apply(U_2408,U_2409)
| ~ sP540(U_2408,U_2411,U_2409) )
& ! [U_2408,U_2411,U_2409] :
( in(U_2409,relation_dom(U_2408))
| ~ sP540(U_2408,U_2411,U_2409) )
& ! [U_2407,U_2412,U_2408,U_2410,U_2411,U_2409] :
( sP541(U_2407,U_2412,U_2408,U_2410)
| U_2412 != apply(U_2408,U_2410)
| ~ in(U_2410,relation_dom(U_2408))
| ~ sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) )
& ! [U_2407,U_2412,U_2408,U_2410,U_2411,U_2409] :
( sP540(U_2408,U_2411,U_2409)
| U_2409 != apply(U_2407,U_2411)
| ~ in(U_2411,relation_rng(U_2408))
| ~ sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) )
& ! [U_2407,U_2412,U_2408,U_2410,U_2411,U_2409] :
( relation_dom(U_2407) = relation_rng(U_2408)
| ~ sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) )
& ! [U_2407,U_2412,U_2408,U_2410,U_2411,U_2409] :
( U_2407 = function_inverse(U_2408)
| sP544(U_2407,U_2408)
| sP543(U_2407,U_2408)
| relation_dom(U_2407) != relation_rng(U_2408)
| ~ sP545(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) )
& ! [U_2407,U_2412,U_2408,U_2410,U_2411,U_2409] :
( sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409)
| U_2407 != function_inverse(U_2408)
| ~ sP545(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) )
& ! [U_2407,U_2412,U_2408,U_2410,U_2411,U_2409] :
( sP545(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409)
| ~ function(U_2407)
| ~ relation(U_2407)
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP540,sP541,sP542,sP543,sP544,sP545])],[f_618_7]) ).
cnf(f_618_9,plain,
( sP545(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409)
| ~ function(U_2407)
| ~ relation(U_2407)
| ~ one_to_one(U_2408)
| ~ function(U_2408)
| ~ relation(U_2408) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_10,plain,
( sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409)
| U_2407 != function_inverse(U_2408)
| ~ sP545(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_11,plain,
( U_2407 = function_inverse(U_2408)
| sP544(U_2407,U_2408)
| sP543(U_2407,U_2408)
| relation_dom(U_2407) != relation_rng(U_2408)
| ~ sP545(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_12,plain,
( relation_dom(U_2407) = relation_rng(U_2408)
| ~ sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_13,plain,
( sP540(U_2408,U_2411,U_2409)
| U_2409 != apply(U_2407,U_2411)
| ~ in(U_2411,relation_rng(U_2408))
| ~ sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_14,plain,
( sP541(U_2407,U_2412,U_2408,U_2410)
| U_2412 != apply(U_2408,U_2410)
| ~ in(U_2410,relation_dom(U_2408))
| ~ sP542(U_2407,U_2412,U_2408,U_2410,U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_15,plain,
( in(U_2409,relation_dom(U_2408))
| ~ sP540(U_2408,U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_16,plain,
( U_2411 = apply(U_2408,U_2409)
| ~ sP540(U_2408,U_2411,U_2409) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_17,plain,
( in(U_2412,relation_rng(U_2408))
| ~ sP541(U_2407,U_2412,U_2408,U_2410) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_18,plain,
( U_2410 = apply(U_2407,U_2412)
| ~ sP541(U_2407,U_2412,U_2408,U_2410) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_19,plain,
( in(sK476(U_2408,U_2407),relation_rng(U_2408))
| ~ sP543(U_2407,U_2408) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_20,plain,
( sK477(U_2408,U_2407) = apply(U_2407,sK476(U_2408,U_2407))
| ~ sP543(U_2407,U_2408) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_21,plain,
( sK476(U_2408,U_2407) != apply(U_2408,sK477(U_2408,U_2407))
| ~ in(sK477(U_2408,U_2407),relation_dom(U_2408))
| ~ sP543(U_2407,U_2408) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_22,plain,
( in(sK479(U_2408,U_2407),relation_dom(U_2408))
| ~ sP544(U_2407,U_2408) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_23,plain,
( sK478(U_2408,U_2407) = apply(U_2408,sK479(U_2408,U_2407))
| ~ sP544(U_2407,U_2408) ),
inference(clausify,[status(thm)],[f_618_8]) ).
cnf(f_618_24,plain,
( sK479(U_2408,U_2407) != apply(U_2407,sK478(U_2408,U_2407))
| ~ in(sK478(U_2408,U_2407),relation_rng(U_2408))
| ~ sP544(U_2407,U_2408) ),
inference(clausify,[status(thm)],[f_618_8]) ).
fof(f_619_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_619_2,plain,
! [U_2419,U_2418,U_2417] :
( ~ in(U_2418,U_2417)
| ~ in(U_2418,subset_complement(U_2419,U_2417))
| ~ element(U_2417,powerset(U_2419)) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
! [U_2419,U_2418,U_2417] :
( ~ in(U_2418,U_2417)
| ~ in(U_2418,subset_complement(U_2419,U_2417))
| ~ element(U_2417,powerset(U_2419)) ),
inference(definitional_conversion,[status(esa)],[f_619_2]) ).
cnf(f_619_4,plain,
( ~ in(U_2418,U_2417)
| ~ in(U_2418,subset_complement(U_2419,U_2417))
| ~ element(U_2417,powerset(U_2419)) ),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_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_620_2,plain,
! [U_2422] :
( ! [U_2421] :
( ! [U_2420] :
( well_ordering(U_2421)
| ~ relation_isomorphism(U_2422,U_2421,U_2420)
| ~ well_ordering(U_2422)
| ~ function(U_2420)
| ~ relation(U_2420) )
| ~ relation(U_2421) )
| ~ relation(U_2422) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
! [U_2421,U_2422,U_2420] :
( well_ordering(U_2421)
| ~ relation_isomorphism(U_2422,U_2421,U_2420)
| ~ well_ordering(U_2422)
| ~ function(U_2420)
| ~ relation(U_2420)
| ~ relation(U_2421)
| ~ relation(U_2422) ),
inference(definitional_conversion,[status(esa)],[f_620_2]) ).
cnf(f_620_4,plain,
( well_ordering(U_2421)
| ~ relation_isomorphism(U_2422,U_2421,U_2420)
| ~ well_ordering(U_2422)
| ~ function(U_2420)
| ~ relation(U_2420)
| ~ relation(U_2421)
| ~ relation(U_2422) ),
inference(clausify,[status(thm)],[f_620_3]) ).
fof(f_621_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_621_2,plain,
! [U_2423] :
( ( relation_dom(U_2423) = relation_rng(function_inverse(U_2423))
& relation_rng(U_2423) = relation_dom(function_inverse(U_2423)) )
| ~ one_to_one(U_2423)
| ~ function(U_2423)
| ~ relation(U_2423) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
( ! [U_2423] :
( relation_dom(U_2423) = relation_rng(function_inverse(U_2423))
| ~ sP546(U_2423) )
& ! [U_2423] :
( relation_rng(U_2423) = relation_dom(function_inverse(U_2423))
| ~ sP546(U_2423) )
& ! [U_2423] :
( sP546(U_2423)
| ~ one_to_one(U_2423)
| ~ function(U_2423)
| ~ relation(U_2423) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP546])],[f_621_2]) ).
cnf(f_621_4,plain,
( sP546(U_2423)
| ~ one_to_one(U_2423)
| ~ function(U_2423)
| ~ relation(U_2423) ),
inference(clausify,[status(thm)],[f_621_3]) ).
cnf(f_621_5,plain,
( relation_rng(U_2423) = relation_dom(function_inverse(U_2423))
| ~ sP546(U_2423) ),
inference(clausify,[status(thm)],[f_621_3]) ).
cnf(f_621_6,plain,
( relation_dom(U_2423) = relation_rng(function_inverse(U_2423))
| ~ sP546(U_2423) ),
inference(clausify,[status(thm)],[f_621_3]) ).
fof(f_622_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( ( open_subset(C,A)
| interior(A,C) != C )
& ( interior(B,D) = D
| ~ open_subset(D,B) ) )
| ~ element(D,powerset(the_carrier(B))) )
| ~ element(C,powerset(the_carrier(A))) )
| ~ top_str(B) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[t55_tops_1]) ).
fof(f_622_2,plain,
! [U_2427] :
( ! [U_2426] :
( ! [U_2425] :
( ! [U_2424] :
( ( ( open_subset(U_2425,U_2427)
| interior(U_2427,U_2425) != U_2425 )
& ( interior(U_2426,U_2424) = U_2424
| ~ open_subset(U_2424,U_2426) ) )
| ~ element(U_2424,powerset(the_carrier(U_2426))) )
| ~ element(U_2425,powerset(the_carrier(U_2427))) )
| ~ top_str(U_2426) )
| ~ top_str(U_2427)
| ~ topological_space(U_2427) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
( ! [U_2424,U_2427,U_2426,U_2425] :
( open_subset(U_2425,U_2427)
| interior(U_2427,U_2425) != U_2425
| ~ sP547(U_2424,U_2427,U_2426,U_2425) )
& ! [U_2424,U_2427,U_2426,U_2425] :
( interior(U_2426,U_2424) = U_2424
| ~ open_subset(U_2424,U_2426)
| ~ sP547(U_2424,U_2427,U_2426,U_2425) )
& ! [U_2424,U_2427,U_2426,U_2425] :
( sP547(U_2424,U_2427,U_2426,U_2425)
| ~ element(U_2424,powerset(the_carrier(U_2426)))
| ~ element(U_2425,powerset(the_carrier(U_2427)))
| ~ top_str(U_2426)
| ~ top_str(U_2427)
| ~ topological_space(U_2427) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP547])],[f_622_2]) ).
cnf(f_622_4,plain,
( sP547(U_2424,U_2427,U_2426,U_2425)
| ~ element(U_2424,powerset(the_carrier(U_2426)))
| ~ element(U_2425,powerset(the_carrier(U_2427)))
| ~ top_str(U_2426)
| ~ top_str(U_2427)
| ~ topological_space(U_2427) ),
inference(clausify,[status(thm)],[f_622_3]) ).
cnf(f_622_5,plain,
( interior(U_2426,U_2424) = U_2424
| ~ open_subset(U_2424,U_2426)
| ~ sP547(U_2424,U_2427,U_2426,U_2425) ),
inference(clausify,[status(thm)],[f_622_3]) ).
cnf(f_622_6,plain,
( open_subset(U_2425,U_2427)
| interior(U_2427,U_2425) != U_2425
| ~ sP547(U_2424,U_2427,U_2426,U_2425) ),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_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_623_2,plain,
! [U_2430] :
( U_2430 = empty_set
| ? [U_2429,U_2428] : in(ordered_pair(U_2429,U_2428),U_2430)
| ~ relation(U_2430) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
! [U_2430] :
( U_2430 = empty_set
| ? [U_2428] : in(ordered_pair(sK480(U_2430),U_2428),U_2430)
| ~ relation(U_2430) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_2429,sK480(U_2430))],[f_623_2]) ).
fof(f_623_4,plain,
! [U_2430] :
( U_2430 = empty_set
| in(ordered_pair(sK480(U_2430),sK481(U_2430)),U_2430)
| ~ relation(U_2430) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_2428,sK481(U_2430))],[f_623_3]) ).
fof(f_623_5,plain,
! [U_2430] :
( U_2430 = empty_set
| in(ordered_pair(sK480(U_2430),sK481(U_2430)),U_2430)
| ~ relation(U_2430) ),
inference(definitional_conversion,[status(esa)],[f_623_4]) ).
cnf(f_623_6,plain,
( U_2430 = empty_set
| in(ordered_pair(sK480(U_2430),sK481(U_2430)),U_2430)
| ~ relation(U_2430) ),
inference(clausify,[status(thm)],[f_623_5]) ).
fof(f_624_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_624_2,plain,
! [U_2432,U_2431] :
( ( U_2432 = apply(relation_composition(function_inverse(U_2431),U_2431),U_2432)
& U_2432 = apply(U_2431,apply(function_inverse(U_2431),U_2432)) )
| ~ in(U_2432,relation_rng(U_2431))
| ~ one_to_one(U_2431)
| ~ function(U_2431)
| ~ relation(U_2431) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
( ! [U_2431,U_2432] :
( U_2432 = apply(relation_composition(function_inverse(U_2431),U_2431),U_2432)
| ~ sP548(U_2431,U_2432) )
& ! [U_2431,U_2432] :
( U_2432 = apply(U_2431,apply(function_inverse(U_2431),U_2432))
| ~ sP548(U_2431,U_2432) )
& ! [U_2431,U_2432] :
( sP548(U_2431,U_2432)
| ~ in(U_2432,relation_rng(U_2431))
| ~ one_to_one(U_2431)
| ~ function(U_2431)
| ~ relation(U_2431) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP548])],[f_624_2]) ).
cnf(f_624_4,plain,
( sP548(U_2431,U_2432)
| ~ in(U_2432,relation_rng(U_2431))
| ~ one_to_one(U_2431)
| ~ function(U_2431)
| ~ relation(U_2431) ),
inference(clausify,[status(thm)],[f_624_3]) ).
cnf(f_624_5,plain,
( U_2432 = apply(U_2431,apply(function_inverse(U_2431),U_2432))
| ~ sP548(U_2431,U_2432) ),
inference(clausify,[status(thm)],[f_624_3]) ).
cnf(f_624_6,plain,
( U_2432 = apply(relation_composition(function_inverse(U_2431),U_2431),U_2432)
| ~ sP548(U_2431,U_2432) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( point_neighbourhood(B,A,C)
| ~ in(C,B)
| ~ open_subset(B,A)
| ~ element(C,the_carrier(A)) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t5_connsp_2]) ).
fof(f_625_2,plain,
! [U_2435] :
( ! [U_2434] :
( ! [U_2433] :
( point_neighbourhood(U_2434,U_2435,U_2433)
| ~ in(U_2433,U_2434)
| ~ open_subset(U_2434,U_2435)
| ~ element(U_2433,the_carrier(U_2435)) )
| ~ element(U_2434,powerset(the_carrier(U_2435))) )
| ~ top_str(U_2435)
| ~ topological_space(U_2435)
| empty_carrier(U_2435) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
! [U_2434,U_2433,U_2435] :
( point_neighbourhood(U_2434,U_2435,U_2433)
| ~ in(U_2433,U_2434)
| ~ open_subset(U_2434,U_2435)
| ~ element(U_2433,the_carrier(U_2435))
| ~ element(U_2434,powerset(the_carrier(U_2435)))
| ~ top_str(U_2435)
| ~ topological_space(U_2435)
| empty_carrier(U_2435) ),
inference(definitional_conversion,[status(esa)],[f_625_2]) ).
cnf(f_625_4,plain,
( point_neighbourhood(U_2434,U_2435,U_2433)
| ~ in(U_2433,U_2434)
| ~ open_subset(U_2434,U_2435)
| ~ element(U_2433,the_carrier(U_2435))
| ~ element(U_2434,powerset(the_carrier(U_2435)))
| ~ top_str(U_2435)
| ~ topological_space(U_2435)
| empty_carrier(U_2435) ),
inference(clausify,[status(thm)],[f_625_3]) ).
fof(f_626_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_626_2,plain,
! [U_2438,U_2437,U_2436] :
( ~ empty(U_2436)
| ~ element(U_2437,powerset(U_2436))
| ~ in(U_2438,U_2437) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
fof(f_626_3,plain,
! [U_2438,U_2437] :
( ! [U_2436] :
( ~ empty(U_2436)
| ~ element(U_2437,powerset(U_2436)) )
| ~ in(U_2438,U_2437) ),
inference(miniscope,[status(thm)],[f_626_2]) ).
fof(f_626_4,plain,
! [U_2437,U_2438,U_2436] :
( ~ empty(U_2436)
| ~ element(U_2437,powerset(U_2436))
| ~ in(U_2438,U_2437) ),
inference(definitional_conversion,[status(esa)],[f_626_3]) ).
cnf(f_626_5,plain,
( ~ empty(U_2436)
| ~ element(U_2437,powerset(U_2436))
| ~ in(U_2438,U_2437) ),
inference(clausify,[status(thm)],[f_626_4]) ).
fof(f_627_1,plain,
! [A,B] :
( ( ( proper_element(B,powerset(A))
| B = A )
& ( B != A
| ~ proper_element(B,powerset(A)) ) )
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t5_tex_2]) ).
fof(f_627_2,plain,
! [U_2440,U_2439] :
( ( ( proper_element(U_2439,powerset(U_2440))
| U_2439 = U_2440 )
& ( U_2439 != U_2440
| ~ proper_element(U_2439,powerset(U_2440)) ) )
| ~ element(U_2439,powerset(U_2440)) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
( ! [U_2439,U_2440] :
( proper_element(U_2439,powerset(U_2440))
| U_2439 = U_2440
| ~ sP549(U_2439,U_2440) )
& ! [U_2439,U_2440] :
( U_2439 != U_2440
| ~ proper_element(U_2439,powerset(U_2440))
| ~ sP549(U_2439,U_2440) )
& ! [U_2439,U_2440] :
( sP549(U_2439,U_2440)
| ~ element(U_2439,powerset(U_2440)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP549])],[f_627_2]) ).
cnf(f_627_4,plain,
( sP549(U_2439,U_2440)
| ~ element(U_2439,powerset(U_2440)) ),
inference(clausify,[status(thm)],[f_627_3]) ).
cnf(f_627_5,plain,
( U_2439 != U_2440
| ~ proper_element(U_2439,powerset(U_2440))
| ~ sP549(U_2439,U_2440) ),
inference(clausify,[status(thm)],[f_627_3]) ).
cnf(f_627_6,plain,
( proper_element(U_2439,powerset(U_2440))
| U_2439 = U_2440
| ~ sP549(U_2439,U_2440) ),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_1,plain,
! [A] :
( ! [B] :
( B != empty_set
| ~ is_a_cover_of_carrier(A,B)
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t5_tops_2]) ).
fof(f_628_2,plain,
! [U_2442] :
( ! [U_2441] :
( U_2441 != empty_set
| ~ is_a_cover_of_carrier(U_2442,U_2441)
| ~ element(U_2441,powerset(powerset(the_carrier(U_2442)))) )
| ~ one_sorted_str(U_2442)
| empty_carrier(U_2442) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
! [U_2442,U_2441] :
( U_2441 != empty_set
| ~ is_a_cover_of_carrier(U_2442,U_2441)
| ~ element(U_2441,powerset(powerset(the_carrier(U_2442))))
| ~ one_sorted_str(U_2442)
| empty_carrier(U_2442) ),
inference(definitional_conversion,[status(esa)],[f_628_2]) ).
cnf(f_628_4,plain,
( U_2441 != empty_set
| ~ is_a_cover_of_carrier(U_2442,U_2441)
| ~ element(U_2441,powerset(powerset(the_carrier(U_2442))))
| ~ one_sorted_str(U_2442)
| empty_carrier(U_2442) ),
inference(clausify,[status(thm)],[f_628_3]) ).
fof(f_629_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_629_2,plain,
! [U_2443] :
( ( ( well_founded_relation(U_2443)
| ~ is_well_founded_in(U_2443,relation_field(U_2443)) )
& ( is_well_founded_in(U_2443,relation_field(U_2443))
| ~ well_founded_relation(U_2443) ) )
| ~ relation(U_2443) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
fof(f_629_3,plain,
( ! [U_2443] :
( well_founded_relation(U_2443)
| ~ is_well_founded_in(U_2443,relation_field(U_2443))
| ~ sP550(U_2443) )
& ! [U_2443] :
( is_well_founded_in(U_2443,relation_field(U_2443))
| ~ well_founded_relation(U_2443)
| ~ sP550(U_2443) )
& ! [U_2443] :
( sP550(U_2443)
| ~ relation(U_2443) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP550])],[f_629_2]) ).
cnf(f_629_4,plain,
( sP550(U_2443)
| ~ relation(U_2443) ),
inference(clausify,[status(thm)],[f_629_3]) ).
cnf(f_629_5,plain,
( is_well_founded_in(U_2443,relation_field(U_2443))
| ~ well_founded_relation(U_2443)
| ~ sP550(U_2443) ),
inference(clausify,[status(thm)],[f_629_3]) ).
cnf(f_629_6,plain,
( well_founded_relation(U_2443)
| ~ is_well_founded_in(U_2443,relation_field(U_2443))
| ~ sP550(U_2443) ),
inference(clausify,[status(thm)],[f_629_3]) ).
fof(f_630_1,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[t5_wellord2]) ).
fof(f_630_2,plain,
! [U_2444] : antisymmetric(inclusion_relation(U_2444)),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
! [U_2444] : antisymmetric(inclusion_relation(U_2444)),
inference(definitional_conversion,[status(esa)],[f_630_2]) ).
cnf(f_630_4,plain,
antisymmetric(inclusion_relation(U_2444)),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_1,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(fof_nnf,[status(thm)],[t60_relat_1]) ).
fof(f_631_2,plain,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(definitional_conversion,[status(esa)],[f_631_1]) ).
cnf(f_631_3,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_631_2]) ).
cnf(f_631_4,plain,
relation_rng(empty_set) = empty_set,
inference(clausify,[status(thm)],[f_631_2]) ).
fof(f_632_1,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t60_xboole_1]) ).
fof(f_632_2,plain,
! [U_2446,U_2445] :
( ~ proper_subset(U_2445,U_2446)
| ~ subset(U_2446,U_2445) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
! [U_2445,U_2446] :
( ~ proper_subset(U_2445,U_2446)
| ~ subset(U_2446,U_2445) ),
inference(definitional_conversion,[status(esa)],[f_632_2]) ).
cnf(f_632_4,plain,
( ~ proper_subset(U_2445,U_2446)
| ~ subset(U_2446,U_2445) ),
inference(clausify,[status(thm)],[f_632_3]) ).
fof(f_633_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_633_2,plain,
! [U_2447] :
( one_to_one(function_inverse(U_2447))
| ~ one_to_one(U_2447)
| ~ function(U_2447)
| ~ relation(U_2447) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
! [U_2447] :
( one_to_one(function_inverse(U_2447))
| ~ one_to_one(U_2447)
| ~ function(U_2447)
| ~ relation(U_2447) ),
inference(definitional_conversion,[status(esa)],[f_633_2]) ).
cnf(f_633_4,plain,
( one_to_one(function_inverse(U_2447))
| ~ one_to_one(U_2447)
| ~ function(U_2447)
| ~ relation(U_2447) ),
inference(clausify,[status(thm)],[f_633_3]) ).
fof(f_634_1,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t63_xboole_1]) ).
fof(f_634_2,plain,
! [U_2450,U_2449,U_2448] :
( disjoint(U_2450,U_2448)
| ~ disjoint(U_2449,U_2448)
| ~ subset(U_2450,U_2449) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
fof(f_634_3,plain,
! [U_2450,U_2449,U_2448] :
( disjoint(U_2450,U_2448)
| ~ disjoint(U_2449,U_2448)
| ~ subset(U_2450,U_2449) ),
inference(definitional_conversion,[status(esa)],[f_634_2]) ).
cnf(f_634_4,plain,
( disjoint(U_2450,U_2448)
| ~ disjoint(U_2449,U_2448)
| ~ subset(U_2450,U_2449) ),
inference(clausify,[status(thm)],[f_634_3]) ).
fof(f_635_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_635_2,plain,
! [U_2451] :
( U_2451 = empty_set
| ( relation_rng(U_2451) != empty_set
& relation_dom(U_2451) != empty_set )
| ~ relation(U_2451) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
fof(f_635_3,plain,
( ! [U_2451] :
( relation_rng(U_2451) != empty_set
| ~ sP551(U_2451) )
& ! [U_2451] :
( relation_dom(U_2451) != empty_set
| ~ sP551(U_2451) )
& ! [U_2451] :
( U_2451 = empty_set
| sP551(U_2451)
| ~ relation(U_2451) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP551])],[f_635_2]) ).
cnf(f_635_4,plain,
( U_2451 = empty_set
| sP551(U_2451)
| ~ relation(U_2451) ),
inference(clausify,[status(thm)],[f_635_3]) ).
cnf(f_635_5,plain,
( relation_dom(U_2451) != empty_set
| ~ sP551(U_2451) ),
inference(clausify,[status(thm)],[f_635_3]) ).
cnf(f_635_6,plain,
( relation_rng(U_2451) != empty_set
| ~ sP551(U_2451) ),
inference(clausify,[status(thm)],[f_635_3]) ).
fof(f_636_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_636_2,plain,
! [U_2452] :
( ( ( relation_dom(U_2452) = empty_set
| relation_rng(U_2452) != empty_set )
& ( relation_rng(U_2452) = empty_set
| relation_dom(U_2452) != empty_set ) )
| ~ relation(U_2452) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
( ! [U_2452] :
( relation_dom(U_2452) = empty_set
| relation_rng(U_2452) != empty_set
| ~ sP552(U_2452) )
& ! [U_2452] :
( relation_rng(U_2452) = empty_set
| relation_dom(U_2452) != empty_set
| ~ sP552(U_2452) )
& ! [U_2452] :
( sP552(U_2452)
| ~ relation(U_2452) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP552])],[f_636_2]) ).
cnf(f_636_4,plain,
( sP552(U_2452)
| ~ relation(U_2452) ),
inference(clausify,[status(thm)],[f_636_3]) ).
cnf(f_636_5,plain,
( relation_rng(U_2452) = empty_set
| relation_dom(U_2452) != empty_set
| ~ sP552(U_2452) ),
inference(clausify,[status(thm)],[f_636_3]) ).
cnf(f_636_6,plain,
( relation_dom(U_2452) = empty_set
| relation_rng(U_2452) != empty_set
| ~ sP552(U_2452) ),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_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_637_2,plain,
! [U_2454,U_2453] :
( ( set_difference(U_2454,singleton(U_2453)) = U_2454
| in(U_2453,U_2454) )
& ( ~ in(U_2453,U_2454)
| set_difference(U_2454,singleton(U_2453)) != U_2454 ) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
( ! [U_2458,U_2456] :
( set_difference(U_2458,singleton(U_2456)) = U_2458
| in(U_2456,U_2458) )
& ! [U_2457,U_2455] :
( ~ in(U_2455,U_2457)
| set_difference(U_2457,singleton(U_2455)) != U_2457 ) ),
inference(miniscope,[status(thm)],[f_637_2]) ).
fof(f_637_4,plain,
( ! [U_2458,U_2456] :
( set_difference(U_2458,singleton(U_2456)) = U_2458
| in(U_2456,U_2458) )
& ! [U_2455,U_2457] :
( ~ in(U_2455,U_2457)
| set_difference(U_2457,singleton(U_2455)) != U_2457 ) ),
inference(definitional_conversion,[status(esa)],[f_637_3]) ).
cnf(f_637_5,plain,
( ~ in(U_2455,U_2457)
| set_difference(U_2457,singleton(U_2455)) != U_2457 ),
inference(clausify,[status(thm)],[f_637_4]) ).
cnf(f_637_6,plain,
( set_difference(U_2458,singleton(U_2456)) = U_2458
| in(U_2456,U_2458) ),
inference(clausify,[status(thm)],[f_637_4]) ).
fof(f_638_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_638_2,plain,
! [U_2463,U_2462] :
( ! [U_2461] :
( ( ( U_2462 = relation_dom_restriction(U_2461,U_2463)
| ? [U_2460] :
( apply(U_2462,U_2460) != apply(U_2461,U_2460)
& in(U_2460,relation_dom(U_2462)) )
| relation_dom(U_2462) != set_intersection2(relation_dom(U_2461),U_2463) )
& ( ( ! [U_2459] :
( apply(U_2462,U_2459) = apply(U_2461,U_2459)
| ~ in(U_2459,relation_dom(U_2462)) )
& relation_dom(U_2462) = set_intersection2(relation_dom(U_2461),U_2463) )
| U_2462 != relation_dom_restriction(U_2461,U_2463) ) )
| ~ function(U_2461)
| ~ relation(U_2461) )
| ~ function(U_2462)
| ~ relation(U_2462) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
! [U_2463,U_2462] :
( ! [U_2461] :
( ( ( U_2462 = relation_dom_restriction(U_2461,U_2463)
| ( apply(U_2462,sK482(U_2463,U_2462,U_2461)) != apply(U_2461,sK482(U_2463,U_2462,U_2461))
& in(sK482(U_2463,U_2462,U_2461),relation_dom(U_2462)) )
| relation_dom(U_2462) != set_intersection2(relation_dom(U_2461),U_2463) )
& ( ( ! [U_2459] :
( apply(U_2462,U_2459) = apply(U_2461,U_2459)
| ~ in(U_2459,relation_dom(U_2462)) )
& relation_dom(U_2462) = set_intersection2(relation_dom(U_2461),U_2463) )
| U_2462 != relation_dom_restriction(U_2461,U_2463) ) )
| ~ function(U_2461)
| ~ relation(U_2461) )
| ~ function(U_2462)
| ~ relation(U_2462) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_2460,sK482(U_2463,U_2462,U_2461))],[f_638_2]) ).
fof(f_638_4,plain,
( ! [U_2461,U_2462,U_2463] :
( apply(U_2462,sK482(U_2463,U_2462,U_2461)) != apply(U_2461,sK482(U_2463,U_2462,U_2461))
| ~ sP554(U_2461,U_2462,U_2463) )
& ! [U_2461,U_2462,U_2463] :
( in(sK482(U_2463,U_2462,U_2461),relation_dom(U_2462))
| ~ sP554(U_2461,U_2462,U_2463) )
& ! [U_2459,U_2461,U_2462,U_2463] :
( apply(U_2462,U_2459) = apply(U_2461,U_2459)
| ~ in(U_2459,relation_dom(U_2462))
| ~ sP553(U_2459,U_2461,U_2462,U_2463) )
& ! [U_2459,U_2461,U_2462,U_2463] :
( relation_dom(U_2462) = set_intersection2(relation_dom(U_2461),U_2463)
| ~ sP553(U_2459,U_2461,U_2462,U_2463) )
& ! [U_2459,U_2461,U_2462,U_2463] :
( U_2462 = relation_dom_restriction(U_2461,U_2463)
| sP554(U_2461,U_2462,U_2463)
| relation_dom(U_2462) != set_intersection2(relation_dom(U_2461),U_2463)
| ~ sP555(U_2459,U_2461,U_2462,U_2463) )
& ! [U_2459,U_2461,U_2462,U_2463] :
( sP553(U_2459,U_2461,U_2462,U_2463)
| U_2462 != relation_dom_restriction(U_2461,U_2463)
| ~ sP555(U_2459,U_2461,U_2462,U_2463) )
& ! [U_2459,U_2461,U_2462,U_2463] :
( sP555(U_2459,U_2461,U_2462,U_2463)
| ~ function(U_2461)
| ~ relation(U_2461)
| ~ function(U_2462)
| ~ relation(U_2462) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP553,sP554,sP555])],[f_638_3]) ).
cnf(f_638_5,plain,
( sP555(U_2459,U_2461,U_2462,U_2463)
| ~ function(U_2461)
| ~ relation(U_2461)
| ~ function(U_2462)
| ~ relation(U_2462) ),
inference(clausify,[status(thm)],[f_638_4]) ).
cnf(f_638_6,plain,
( sP553(U_2459,U_2461,U_2462,U_2463)
| U_2462 != relation_dom_restriction(U_2461,U_2463)
| ~ sP555(U_2459,U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_638_4]) ).
cnf(f_638_7,plain,
( U_2462 = relation_dom_restriction(U_2461,U_2463)
| sP554(U_2461,U_2462,U_2463)
| relation_dom(U_2462) != set_intersection2(relation_dom(U_2461),U_2463)
| ~ sP555(U_2459,U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_638_4]) ).
cnf(f_638_8,plain,
( relation_dom(U_2462) = set_intersection2(relation_dom(U_2461),U_2463)
| ~ sP553(U_2459,U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_638_4]) ).
cnf(f_638_9,plain,
( apply(U_2462,U_2459) = apply(U_2461,U_2459)
| ~ in(U_2459,relation_dom(U_2462))
| ~ sP553(U_2459,U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_638_4]) ).
cnf(f_638_10,plain,
( in(sK482(U_2463,U_2462,U_2461),relation_dom(U_2462))
| ~ sP554(U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_638_4]) ).
cnf(f_638_11,plain,
( apply(U_2462,sK482(U_2463,U_2462,U_2461)) != apply(U_2461,sK482(U_2463,U_2462,U_2461))
| ~ sP554(U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_638_4]) ).
fof(f_639_1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(fof_nnf,[status(thm)],[t69_enumset1]) ).
fof(f_639_2,plain,
! [U_2464] : unordered_pair(U_2464,U_2464) = singleton(U_2464),
inference(variable_rename,[status(thm)],[f_639_1]) ).
fof(f_639_3,plain,
! [U_2464] : unordered_pair(U_2464,U_2464) = singleton(U_2464),
inference(definitional_conversion,[status(esa)],[f_639_2]) ).
cnf(f_639_4,plain,
unordered_pair(U_2464,U_2464) = singleton(U_2464),
inference(clausify,[status(thm)],[f_639_3]) ).
fof(f_640_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_640_2,plain,
! [U_2465] :
( U_2465 = empty_set
| ~ empty(U_2465) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
! [U_2465] :
( U_2465 = empty_set
| ~ empty(U_2465) ),
inference(definitional_conversion,[status(esa)],[f_640_2]) ).
cnf(f_640_4,plain,
( U_2465 = empty_set
| ~ empty(U_2465) ),
inference(clausify,[status(thm)],[f_640_3]) ).
fof(f_641_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_641_2,plain,
! [U_2469,U_2468,U_2467,U_2466] :
( in(apply(U_2466,U_2467),relation_rng(U_2466))
| U_2468 = empty_set
| ~ in(U_2467,U_2469)
| ~ relation_of2_as_subset(U_2466,U_2469,U_2468)
| ~ quasi_total(U_2466,U_2469,U_2468)
| ~ function(U_2466) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
! [U_2469,U_2468,U_2467,U_2466] :
( in(apply(U_2466,U_2467),relation_rng(U_2466))
| U_2468 = empty_set
| ~ in(U_2467,U_2469)
| ~ relation_of2_as_subset(U_2466,U_2469,U_2468)
| ~ quasi_total(U_2466,U_2469,U_2468)
| ~ function(U_2466) ),
inference(definitional_conversion,[status(esa)],[f_641_2]) ).
cnf(f_641_4,plain,
( in(apply(U_2466,U_2467),relation_rng(U_2466))
| U_2468 = empty_set
| ~ in(U_2467,U_2469)
| ~ relation_of2_as_subset(U_2466,U_2469,U_2468)
| ~ quasi_total(U_2466,U_2469,U_2468)
| ~ function(U_2466) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_1,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t6_wellord2]) ).
fof(f_642_2,plain,
! [U_2470] :
( well_founded_relation(inclusion_relation(U_2470))
| ~ ordinal(U_2470) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
fof(f_642_3,plain,
! [U_2470] :
( well_founded_relation(inclusion_relation(U_2470))
| ~ ordinal(U_2470) ),
inference(definitional_conversion,[status(esa)],[f_642_2]) ).
cnf(f_642_4,plain,
( well_founded_relation(inclusion_relation(U_2470))
| ~ ordinal(U_2470) ),
inference(clausify,[status(thm)],[f_642_3]) ).
fof(f_643_1,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
inference(negate,[status(cth)],[t6_yellow_0]) ).
fof(f_643_2,negated_conjecture,
? [A] :
( ? [B] :
( ( ~ relstr_element_smaller(A,empty_set,B)
| ~ relstr_set_smaller(A,empty_set,B) )
& element(B,the_carrier(A)) )
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[f_643_1]) ).
fof(f_643_3,negated_conjecture,
? [U_2472] :
( ? [U_2471] :
( ( ~ relstr_element_smaller(U_2472,empty_set,U_2471)
| ~ relstr_set_smaller(U_2472,empty_set,U_2471) )
& element(U_2471,the_carrier(U_2472)) )
& rel_str(U_2472) ),
inference(variable_rename,[status(thm)],[f_643_2]) ).
fof(f_643_4,negated_conjecture,
( ? [U_2471] :
( ( ~ relstr_element_smaller(sK483,empty_set,U_2471)
| ~ relstr_set_smaller(sK483,empty_set,U_2471) )
& element(U_2471,the_carrier(sK483)) )
& rel_str(sK483) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_2472,sK483)],[f_643_3]) ).
fof(f_643_5,negated_conjecture,
( ( ~ relstr_element_smaller(sK483,empty_set,sK484)
| ~ relstr_set_smaller(sK483,empty_set,sK484) )
& element(sK484,the_carrier(sK483))
& rel_str(sK483) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_2471,sK484)],[f_643_4]) ).
fof(f_643_6,negated_conjecture,
( ( ~ relstr_element_smaller(sK483,empty_set,sK484)
| ~ relstr_set_smaller(sK483,empty_set,sK484) )
& element(sK484,the_carrier(sK483))
& rel_str(sK483) ),
inference(definitional_conversion,[status(esa)],[f_643_5]) ).
cnf(f_643_7,negated_conjecture,
rel_str(sK483),
inference(clausify,[status(thm)],[f_643_6]) ).
cnf(f_643_8,negated_conjecture,
element(sK484,the_carrier(sK483)),
inference(clausify,[status(thm)],[f_643_6]) ).
cnf(f_643_9,negated_conjecture,
( ~ relstr_element_smaller(sK483,empty_set,sK484)
| ~ relstr_set_smaller(sK483,empty_set,sK484) ),
inference(clausify,[status(thm)],[f_643_6]) ).
fof(f_644_1,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1]) ).
fof(f_644_2,plain,
! [U_2474,U_2473] :
( U_2474 = U_2473
| ~ subset(singleton(U_2474),singleton(U_2473)) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
! [U_2473,U_2474] :
( U_2474 = U_2473
| ~ subset(singleton(U_2474),singleton(U_2473)) ),
inference(definitional_conversion,[status(esa)],[f_644_2]) ).
cnf(f_644_4,plain,
( U_2474 = U_2473
| ~ subset(singleton(U_2474),singleton(U_2473)) ),
inference(clausify,[status(thm)],[f_644_3]) ).
fof(f_645_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_645_2,plain,
! [U_2477,U_2476,U_2475] :
( apply(relation_dom_restriction(U_2475,U_2477),U_2476) = apply(U_2475,U_2476)
| ~ in(U_2476,relation_dom(relation_dom_restriction(U_2475,U_2477)))
| ~ function(U_2475)
| ~ relation(U_2475) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
! [U_2475,U_2476,U_2477] :
( apply(relation_dom_restriction(U_2475,U_2477),U_2476) = apply(U_2475,U_2476)
| ~ in(U_2476,relation_dom(relation_dom_restriction(U_2475,U_2477)))
| ~ function(U_2475)
| ~ relation(U_2475) ),
inference(definitional_conversion,[status(esa)],[f_645_2]) ).
cnf(f_645_4,plain,
( apply(relation_dom_restriction(U_2475,U_2477),U_2476) = apply(U_2475,U_2476)
| ~ in(U_2476,relation_dom(relation_dom_restriction(U_2475,U_2477)))
| ~ function(U_2475)
| ~ relation(U_2475) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_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_646_2,plain,
! [U_2478] :
( relation_rng(identity_relation(U_2478)) = U_2478
& relation_dom(identity_relation(U_2478)) = U_2478 ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
( ! [U_2480] : relation_rng(identity_relation(U_2480)) = U_2480
& ! [U_2479] : relation_dom(identity_relation(U_2479)) = U_2479 ),
inference(miniscope,[status(thm)],[f_646_2]) ).
fof(f_646_4,plain,
( ! [U_2480] : relation_rng(identity_relation(U_2480)) = U_2480
& ! [U_2479] : relation_dom(identity_relation(U_2479)) = U_2479 ),
inference(definitional_conversion,[status(esa)],[f_646_3]) ).
cnf(f_646_5,plain,
relation_dom(identity_relation(U_2479)) = U_2479,
inference(clausify,[status(thm)],[f_646_4]) ).
cnf(f_646_6,plain,
relation_rng(identity_relation(U_2480)) = U_2480,
inference(clausify,[status(thm)],[f_646_4]) ).
fof(f_647_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_647_2,plain,
! [U_2483,U_2482,U_2481] :
( apply(relation_dom_restriction(U_2481,U_2483),U_2482) = apply(U_2481,U_2482)
| ~ in(U_2482,U_2483)
| ~ function(U_2481)
| ~ relation(U_2481) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
! [U_2481,U_2482,U_2483] :
( apply(relation_dom_restriction(U_2481,U_2483),U_2482) = apply(U_2481,U_2482)
| ~ in(U_2482,U_2483)
| ~ function(U_2481)
| ~ relation(U_2481) ),
inference(definitional_conversion,[status(esa)],[f_647_2]) ).
cnf(f_647_4,plain,
( apply(relation_dom_restriction(U_2481,U_2483),U_2482) = apply(U_2481,U_2482)
| ~ in(U_2482,U_2483)
| ~ function(U_2481)
| ~ relation(U_2481) ),
inference(clausify,[status(thm)],[f_647_3]) ).
fof(f_648_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_648_2,plain,
! [U_2487,U_2486,U_2485,U_2484] :
( ( ( in(ordered_pair(U_2487,U_2486),relation_composition(identity_relation(U_2485),U_2484))
| ~ in(ordered_pair(U_2487,U_2486),U_2484)
| ~ in(U_2487,U_2485) )
& ( ( in(ordered_pair(U_2487,U_2486),U_2484)
& in(U_2487,U_2485) )
| ~ in(ordered_pair(U_2487,U_2486),relation_composition(identity_relation(U_2485),U_2484)) ) )
| ~ relation(U_2484) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
fof(f_648_3,plain,
( ! [U_2484,U_2485,U_2486,U_2487] :
( in(ordered_pair(U_2487,U_2486),U_2484)
| ~ sP556(U_2484,U_2485,U_2486,U_2487) )
& ! [U_2484,U_2485,U_2486,U_2487] :
( in(U_2487,U_2485)
| ~ sP556(U_2484,U_2485,U_2486,U_2487) )
& ! [U_2484,U_2485,U_2486,U_2487] :
( in(ordered_pair(U_2487,U_2486),relation_composition(identity_relation(U_2485),U_2484))
| ~ in(ordered_pair(U_2487,U_2486),U_2484)
| ~ in(U_2487,U_2485)
| ~ sP557(U_2484,U_2485,U_2486,U_2487) )
& ! [U_2484,U_2485,U_2486,U_2487] :
( sP556(U_2484,U_2485,U_2486,U_2487)
| ~ in(ordered_pair(U_2487,U_2486),relation_composition(identity_relation(U_2485),U_2484))
| ~ sP557(U_2484,U_2485,U_2486,U_2487) )
& ! [U_2484,U_2485,U_2486,U_2487] :
( sP557(U_2484,U_2485,U_2486,U_2487)
| ~ relation(U_2484) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP556,sP557])],[f_648_2]) ).
cnf(f_648_4,plain,
( sP557(U_2484,U_2485,U_2486,U_2487)
| ~ relation(U_2484) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_5,plain,
( sP556(U_2484,U_2485,U_2486,U_2487)
| ~ in(ordered_pair(U_2487,U_2486),relation_composition(identity_relation(U_2485),U_2484))
| ~ sP557(U_2484,U_2485,U_2486,U_2487) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_6,plain,
( in(ordered_pair(U_2487,U_2486),relation_composition(identity_relation(U_2485),U_2484))
| ~ in(ordered_pair(U_2487,U_2486),U_2484)
| ~ in(U_2487,U_2485)
| ~ sP557(U_2484,U_2485,U_2486,U_2487) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_7,plain,
( in(U_2487,U_2485)
| ~ sP556(U_2484,U_2485,U_2486,U_2487) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_8,plain,
( in(ordered_pair(U_2487,U_2486),U_2484)
| ~ sP556(U_2484,U_2485,U_2486,U_2487) ),
inference(clausify,[status(thm)],[f_648_3]) ).
fof(f_649_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_649_2,plain,
! [U_2489,U_2488] :
( ~ empty(U_2488)
| ~ in(U_2489,U_2488) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
fof(f_649_3,plain,
! [U_2488,U_2489] :
( ~ empty(U_2488)
| ~ in(U_2489,U_2488) ),
inference(definitional_conversion,[status(esa)],[f_649_2]) ).
cnf(f_649_4,plain,
( ~ empty(U_2488)
| ~ in(U_2489,U_2488) ),
inference(clausify,[status(thm)],[f_649_3]) ).
fof(f_650_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( below_refl(A,B,C)
| ~ related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C)) )
& ( related_reflexive(poset_of_lattice(A),cast_to_el_of_LattPOSet(A,B),cast_to_el_of_LattPOSet(A,C))
| ~ below_refl(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t7_lattice3]) ).
fof(f_650_2,plain,
! [U_2492] :
( ! [U_2491] :
( ! [U_2490] :
( ( ( below_refl(U_2492,U_2491,U_2490)
| ~ related_reflexive(poset_of_lattice(U_2492),cast_to_el_of_LattPOSet(U_2492,U_2491),cast_to_el_of_LattPOSet(U_2492,U_2490)) )
& ( related_reflexive(poset_of_lattice(U_2492),cast_to_el_of_LattPOSet(U_2492,U_2491),cast_to_el_of_LattPOSet(U_2492,U_2490))
| ~ below_refl(U_2492,U_2491,U_2490) ) )
| ~ element(U_2490,the_carrier(U_2492)) )
| ~ element(U_2491,the_carrier(U_2492)) )
| ~ latt_str(U_2492)
| ~ lattice(U_2492)
| empty_carrier(U_2492) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
fof(f_650_3,plain,
( ! [U_2492,U_2490,U_2491] :
( below_refl(U_2492,U_2491,U_2490)
| ~ related_reflexive(poset_of_lattice(U_2492),cast_to_el_of_LattPOSet(U_2492,U_2491),cast_to_el_of_LattPOSet(U_2492,U_2490))
| ~ sP558(U_2492,U_2490,U_2491) )
& ! [U_2492,U_2490,U_2491] :
( related_reflexive(poset_of_lattice(U_2492),cast_to_el_of_LattPOSet(U_2492,U_2491),cast_to_el_of_LattPOSet(U_2492,U_2490))
| ~ below_refl(U_2492,U_2491,U_2490)
| ~ sP558(U_2492,U_2490,U_2491) )
& ! [U_2492,U_2490,U_2491] :
( sP558(U_2492,U_2490,U_2491)
| ~ element(U_2490,the_carrier(U_2492))
| ~ element(U_2491,the_carrier(U_2492))
| ~ latt_str(U_2492)
| ~ lattice(U_2492)
| empty_carrier(U_2492) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP558])],[f_650_2]) ).
cnf(f_650_4,plain,
( sP558(U_2492,U_2490,U_2491)
| ~ element(U_2490,the_carrier(U_2492))
| ~ element(U_2491,the_carrier(U_2492))
| ~ latt_str(U_2492)
| ~ lattice(U_2492)
| empty_carrier(U_2492) ),
inference(clausify,[status(thm)],[f_650_3]) ).
cnf(f_650_5,plain,
( related_reflexive(poset_of_lattice(U_2492),cast_to_el_of_LattPOSet(U_2492,U_2491),cast_to_el_of_LattPOSet(U_2492,U_2490))
| ~ below_refl(U_2492,U_2491,U_2490)
| ~ sP558(U_2492,U_2490,U_2491) ),
inference(clausify,[status(thm)],[f_650_3]) ).
cnf(f_650_6,plain,
( below_refl(U_2492,U_2491,U_2490)
| ~ related_reflexive(poset_of_lattice(U_2492),cast_to_el_of_LattPOSet(U_2492,U_2491),cast_to_el_of_LattPOSet(U_2492,U_2490))
| ~ sP558(U_2492,U_2490,U_2491) ),
inference(clausify,[status(thm)],[f_650_3]) ).
fof(f_651_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_651_2,plain,
! [U_2494,U_2493] :
( pair_second(ordered_pair(U_2494,U_2493)) = U_2493
& pair_first(ordered_pair(U_2494,U_2493)) = U_2494 ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
fof(f_651_3,plain,
( ! [U_2498,U_2496] : pair_second(ordered_pair(U_2498,U_2496)) = U_2496
& ! [U_2497,U_2495] : pair_first(ordered_pair(U_2497,U_2495)) = U_2497 ),
inference(miniscope,[status(thm)],[f_651_2]) ).
fof(f_651_4,plain,
( ! [U_2496,U_2498] : pair_second(ordered_pair(U_2498,U_2496)) = U_2496
& ! [U_2495,U_2497] : pair_first(ordered_pair(U_2497,U_2495)) = U_2497 ),
inference(definitional_conversion,[status(esa)],[f_651_3]) ).
cnf(f_651_5,plain,
pair_first(ordered_pair(U_2497,U_2495)) = U_2497,
inference(clausify,[status(thm)],[f_651_4]) ).
cnf(f_651_6,plain,
pair_second(ordered_pair(U_2498,U_2496)) = U_2496,
inference(clausify,[status(thm)],[f_651_4]) ).
fof(f_652_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_652_2,plain,
! [U_2502,U_2501] :
( ? [U_2500] :
( ! [U_2499] :
( ~ in(U_2499,U_2500)
| ~ in(U_2499,U_2501) )
& in(U_2500,U_2501) )
| ~ in(U_2502,U_2501) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
! [U_2502,U_2501] :
( ( ! [U_2499] :
( ~ in(U_2499,sK485(U_2502,U_2501))
| ~ in(U_2499,U_2501) )
& in(sK485(U_2502,U_2501),U_2501) )
| ~ in(U_2502,U_2501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_2500,sK485(U_2502,U_2501))],[f_652_2]) ).
fof(f_652_4,plain,
( ! [U_2499,U_2502,U_2501] :
( ~ in(U_2499,sK485(U_2502,U_2501))
| ~ in(U_2499,U_2501)
| ~ sP559(U_2499,U_2502,U_2501) )
& ! [U_2499,U_2502,U_2501] :
( in(sK485(U_2502,U_2501),U_2501)
| ~ sP559(U_2499,U_2502,U_2501) )
& ! [U_2499,U_2502,U_2501] :
( sP559(U_2499,U_2502,U_2501)
| ~ in(U_2502,U_2501) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP559])],[f_652_3]) ).
cnf(f_652_5,plain,
( sP559(U_2499,U_2502,U_2501)
| ~ in(U_2502,U_2501) ),
inference(clausify,[status(thm)],[f_652_4]) ).
cnf(f_652_6,plain,
( in(sK485(U_2502,U_2501),U_2501)
| ~ sP559(U_2499,U_2502,U_2501) ),
inference(clausify,[status(thm)],[f_652_4]) ).
cnf(f_652_7,plain,
( ~ in(U_2499,sK485(U_2502,U_2501))
| ~ in(U_2499,U_2501)
| ~ sP559(U_2499,U_2502,U_2501) ),
inference(clausify,[status(thm)],[f_652_4]) ).
fof(f_653_1,plain,
! [A] :
( well_ordering(inclusion_relation(A))
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t7_wellord2]) ).
fof(f_653_2,plain,
! [U_2503] :
( well_ordering(inclusion_relation(U_2503))
| ~ ordinal(U_2503) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
! [U_2503] :
( well_ordering(inclusion_relation(U_2503))
| ~ ordinal(U_2503) ),
inference(definitional_conversion,[status(esa)],[f_653_2]) ).
cnf(f_653_4,plain,
( well_ordering(inclusion_relation(U_2503))
| ~ ordinal(U_2503) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_654_2,plain,
! [U_2505,U_2504] : subset(U_2505,set_union2(U_2505,U_2504)),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
! [U_2505,U_2504] : subset(U_2505,set_union2(U_2505,U_2504)),
inference(definitional_conversion,[status(esa)],[f_654_2]) ).
cnf(f_654_4,plain,
subset(U_2505,set_union2(U_2505,U_2504)),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_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_655_2,plain,
! [U_2507,U_2506] :
( ( disjoint(U_2507,U_2506)
| set_difference(U_2507,U_2506) != U_2507 )
& ( set_difference(U_2507,U_2506) = U_2507
| ~ disjoint(U_2507,U_2506) ) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
( ! [U_2511,U_2509] :
( disjoint(U_2511,U_2509)
| set_difference(U_2511,U_2509) != U_2511 )
& ! [U_2510,U_2508] :
( set_difference(U_2510,U_2508) = U_2510
| ~ disjoint(U_2510,U_2508) ) ),
inference(miniscope,[status(thm)],[f_655_2]) ).
fof(f_655_4,plain,
( ! [U_2511,U_2509] :
( disjoint(U_2511,U_2509)
| set_difference(U_2511,U_2509) != U_2511 )
& ! [U_2510,U_2508] :
( set_difference(U_2510,U_2508) = U_2510
| ~ disjoint(U_2510,U_2508) ) ),
inference(definitional_conversion,[status(esa)],[f_655_3]) ).
cnf(f_655_5,plain,
( set_difference(U_2510,U_2508) = U_2510
| ~ disjoint(U_2510,U_2508) ),
inference(clausify,[status(thm)],[f_655_4]) ).
cnf(f_655_6,plain,
( disjoint(U_2511,U_2509)
| set_difference(U_2511,U_2509) != U_2511 ),
inference(clausify,[status(thm)],[f_655_4]) ).
fof(f_656_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_656_2,plain,
! [U_2514,U_2513,U_2512] :
( ( ( in(U_2514,relation_dom(relation_dom_restriction(U_2512,U_2513)))
| ~ in(U_2514,relation_dom(U_2512))
| ~ in(U_2514,U_2513) )
& ( ( in(U_2514,relation_dom(U_2512))
& in(U_2514,U_2513) )
| ~ in(U_2514,relation_dom(relation_dom_restriction(U_2512,U_2513))) ) )
| ~ relation(U_2512) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
( ! [U_2512,U_2513,U_2514] :
( in(U_2514,relation_dom(U_2512))
| ~ sP560(U_2512,U_2513,U_2514) )
& ! [U_2512,U_2513,U_2514] :
( in(U_2514,U_2513)
| ~ sP560(U_2512,U_2513,U_2514) )
& ! [U_2512,U_2513,U_2514] :
( in(U_2514,relation_dom(relation_dom_restriction(U_2512,U_2513)))
| ~ in(U_2514,relation_dom(U_2512))
| ~ in(U_2514,U_2513)
| ~ sP561(U_2512,U_2513,U_2514) )
& ! [U_2512,U_2513,U_2514] :
( sP560(U_2512,U_2513,U_2514)
| ~ in(U_2514,relation_dom(relation_dom_restriction(U_2512,U_2513)))
| ~ sP561(U_2512,U_2513,U_2514) )
& ! [U_2512,U_2513,U_2514] :
( sP561(U_2512,U_2513,U_2514)
| ~ relation(U_2512) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP560,sP561])],[f_656_2]) ).
cnf(f_656_4,plain,
( sP561(U_2512,U_2513,U_2514)
| ~ relation(U_2512) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_5,plain,
( sP560(U_2512,U_2513,U_2514)
| ~ in(U_2514,relation_dom(relation_dom_restriction(U_2512,U_2513)))
| ~ sP561(U_2512,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_6,plain,
( in(U_2514,relation_dom(relation_dom_restriction(U_2512,U_2513)))
| ~ in(U_2514,relation_dom(U_2512))
| ~ in(U_2514,U_2513)
| ~ sP561(U_2512,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_7,plain,
( in(U_2514,U_2513)
| ~ sP560(U_2512,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_8,plain,
( in(U_2514,relation_dom(U_2512))
| ~ sP560(U_2512,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_656_3]) ).
fof(f_657_1,plain,
! [A,B] :
( subset(relation_dom_restriction(B,A),B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1]) ).
fof(f_657_2,plain,
! [U_2516,U_2515] :
( subset(relation_dom_restriction(U_2515,U_2516),U_2515)
| ~ relation(U_2515) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
! [U_2515,U_2516] :
( subset(relation_dom_restriction(U_2515,U_2516),U_2515)
| ~ relation(U_2515) ),
inference(definitional_conversion,[status(esa)],[f_657_2]) ).
cnf(f_657_4,plain,
( subset(relation_dom_restriction(U_2515,U_2516),U_2515)
| ~ relation(U_2515) ),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_658_2,plain,
! [U_2518,U_2517] :
( ~ empty(U_2517)
| U_2518 = U_2517
| ~ empty(U_2518) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
! [U_2518] :
( ! [U_2517] :
( ~ empty(U_2517)
| U_2518 = U_2517 )
| ~ empty(U_2518) ),
inference(miniscope,[status(thm)],[f_658_2]) ).
fof(f_658_4,plain,
! [U_2517,U_2518] :
( ~ empty(U_2517)
| U_2518 = U_2517
| ~ empty(U_2518) ),
inference(definitional_conversion,[status(esa)],[f_658_3]) ).
cnf(f_658_5,plain,
( ~ empty(U_2517)
| U_2518 = U_2517
| ~ empty(U_2518) ),
inference(clausify,[status(thm)],[f_658_4]) ).
fof(f_659_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_659_2,plain,
! [U_2521,U_2520,U_2519] :
( ( ( in(ordered_pair(U_2521,U_2520),U_2519)
| U_2520 != apply(U_2519,U_2521)
| ~ in(U_2521,relation_dom(U_2519)) )
& ( ( U_2520 = apply(U_2519,U_2521)
& in(U_2521,relation_dom(U_2519)) )
| ~ in(ordered_pair(U_2521,U_2520),U_2519) ) )
| ~ function(U_2519)
| ~ relation(U_2519) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
( ! [U_2520,U_2519,U_2521] :
( U_2520 = apply(U_2519,U_2521)
| ~ sP562(U_2520,U_2519,U_2521) )
& ! [U_2520,U_2519,U_2521] :
( in(U_2521,relation_dom(U_2519))
| ~ sP562(U_2520,U_2519,U_2521) )
& ! [U_2520,U_2519,U_2521] :
( in(ordered_pair(U_2521,U_2520),U_2519)
| U_2520 != apply(U_2519,U_2521)
| ~ in(U_2521,relation_dom(U_2519))
| ~ sP563(U_2520,U_2519,U_2521) )
& ! [U_2520,U_2519,U_2521] :
( sP562(U_2520,U_2519,U_2521)
| ~ in(ordered_pair(U_2521,U_2520),U_2519)
| ~ sP563(U_2520,U_2519,U_2521) )
& ! [U_2520,U_2519,U_2521] :
( sP563(U_2520,U_2519,U_2521)
| ~ function(U_2519)
| ~ relation(U_2519) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP562,sP563])],[f_659_2]) ).
cnf(f_659_4,plain,
( sP563(U_2520,U_2519,U_2521)
| ~ function(U_2519)
| ~ relation(U_2519) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_5,plain,
( sP562(U_2520,U_2519,U_2521)
| ~ in(ordered_pair(U_2521,U_2520),U_2519)
| ~ sP563(U_2520,U_2519,U_2521) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_6,plain,
( in(ordered_pair(U_2521,U_2520),U_2519)
| U_2520 != apply(U_2519,U_2521)
| ~ in(U_2521,relation_dom(U_2519))
| ~ sP563(U_2520,U_2519,U_2521) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_7,plain,
( in(U_2521,relation_dom(U_2519))
| ~ sP562(U_2520,U_2519,U_2521) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_8,plain,
( U_2520 = apply(U_2519,U_2521)
| ~ sP562(U_2520,U_2519,U_2521) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_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_660_2,plain,
! [U_2522] :
( ( ( well_orders(U_2522,relation_field(U_2522))
| ~ well_ordering(U_2522) )
& ( well_ordering(U_2522)
| ~ well_orders(U_2522,relation_field(U_2522)) ) )
| ~ relation(U_2522) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
( ! [U_2522] :
( well_orders(U_2522,relation_field(U_2522))
| ~ well_ordering(U_2522)
| ~ sP564(U_2522) )
& ! [U_2522] :
( well_ordering(U_2522)
| ~ well_orders(U_2522,relation_field(U_2522))
| ~ sP564(U_2522) )
& ! [U_2522] :
( sP564(U_2522)
| ~ relation(U_2522) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP564])],[f_660_2]) ).
cnf(f_660_4,plain,
( sP564(U_2522)
| ~ relation(U_2522) ),
inference(clausify,[status(thm)],[f_660_3]) ).
cnf(f_660_5,plain,
( well_ordering(U_2522)
| ~ well_orders(U_2522,relation_field(U_2522))
| ~ sP564(U_2522) ),
inference(clausify,[status(thm)],[f_660_3]) ).
cnf(f_660_6,plain,
( well_orders(U_2522,relation_field(U_2522))
| ~ well_ordering(U_2522)
| ~ sP564(U_2522) ),
inference(clausify,[status(thm)],[f_660_3]) ).
fof(f_661_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_661_2,plain,
! [U_2525,U_2524,U_2523] :
( subset(set_union2(U_2525,U_2523),U_2524)
| ~ subset(U_2523,U_2524)
| ~ subset(U_2525,U_2524) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
! [U_2523,U_2525,U_2524] :
( subset(set_union2(U_2525,U_2523),U_2524)
| ~ subset(U_2523,U_2524)
| ~ subset(U_2525,U_2524) ),
inference(definitional_conversion,[status(esa)],[f_661_2]) ).
cnf(f_661_4,plain,
( subset(set_union2(U_2525,U_2523),U_2524)
| ~ subset(U_2523,U_2524)
| ~ subset(U_2525,U_2524) ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t8_zfmisc_1]) ).
fof(f_662_2,plain,
! [U_2528,U_2527,U_2526] :
( U_2528 = U_2527
| singleton(U_2528) != unordered_pair(U_2527,U_2526) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_2528,U_2527] :
( ! [U_2526] : singleton(U_2528) != unordered_pair(U_2527,U_2526)
| U_2528 = U_2527 ),
inference(miniscope,[status(thm)],[f_662_2]) ).
fof(f_662_4,plain,
! [U_2527,U_2528,U_2526] :
( singleton(U_2528) != unordered_pair(U_2527,U_2526)
| U_2528 = U_2527 ),
inference(definitional_conversion,[status(esa)],[f_662_3]) ).
cnf(f_662_5,plain,
( singleton(U_2528) != unordered_pair(U_2527,U_2526)
| U_2528 = U_2527 ),
inference(clausify,[status(thm)],[f_662_4]) ).
fof(f_663_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_663_2,plain,
! [U_2530,U_2529] :
( relation_dom(relation_dom_restriction(U_2529,U_2530)) = set_intersection2(relation_dom(U_2529),U_2530)
| ~ relation(U_2529) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
! [U_2529,U_2530] :
( relation_dom(relation_dom_restriction(U_2529,U_2530)) = set_intersection2(relation_dom(U_2529),U_2530)
| ~ relation(U_2529) ),
inference(definitional_conversion,[status(esa)],[f_663_2]) ).
cnf(f_663_4,plain,
( relation_dom(relation_dom_restriction(U_2529,U_2530)) = set_intersection2(relation_dom(U_2529),U_2530)
| ~ relation(U_2529) ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_1,plain,
! [A] :
( ! [B] :
( apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B
| ~ element(B,the_carrier(A)) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t91_tmap_1]) ).
fof(f_664_2,plain,
! [U_2532] :
( ! [U_2531] :
( apply_as_element(the_carrier(U_2532),the_carrier(U_2532),identity_on_carrier(U_2532),U_2531) = U_2531
| ~ element(U_2531,the_carrier(U_2532)) )
| ~ one_sorted_str(U_2532)
| empty_carrier(U_2532) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
! [U_2532,U_2531] :
( apply_as_element(the_carrier(U_2532),the_carrier(U_2532),identity_on_carrier(U_2532),U_2531) = U_2531
| ~ element(U_2531,the_carrier(U_2532))
| ~ one_sorted_str(U_2532)
| empty_carrier(U_2532) ),
inference(definitional_conversion,[status(esa)],[f_664_2]) ).
cnf(f_664_4,plain,
( apply_as_element(the_carrier(U_2532),the_carrier(U_2532),identity_on_carrier(U_2532),U_2531) = U_2531
| ~ element(U_2531,the_carrier(U_2532))
| ~ one_sorted_str(U_2532)
| empty_carrier(U_2532) ),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_665_2,plain,
! [U_2534,U_2533] :
( subset(U_2534,union(U_2533))
| ~ in(U_2534,U_2533) ),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
! [U_2533,U_2534] :
( subset(U_2534,union(U_2533))
| ~ in(U_2534,U_2533) ),
inference(definitional_conversion,[status(esa)],[f_665_2]) ).
cnf(f_665_4,plain,
( subset(U_2534,union(U_2533))
| ~ in(U_2534,U_2533) ),
inference(clausify,[status(thm)],[f_665_3]) ).
fof(f_666_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_666_2,plain,
! [U_2536,U_2535] :
( relation_dom_restriction(U_2535,U_2536) = relation_composition(identity_relation(U_2536),U_2535)
| ~ relation(U_2535) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
! [U_2535,U_2536] :
( relation_dom_restriction(U_2535,U_2536) = relation_composition(identity_relation(U_2536),U_2535)
| ~ relation(U_2535) ),
inference(definitional_conversion,[status(esa)],[f_666_2]) ).
cnf(f_666_4,plain,
( relation_dom_restriction(U_2535,U_2536) = relation_composition(identity_relation(U_2536),U_2535)
| ~ relation(U_2535) ),
inference(clausify,[status(thm)],[f_666_3]) ).
fof(f_667_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_667_2,plain,
! [U_2538,U_2537] :
( subset(relation_rng(relation_dom_restriction(U_2537,U_2538)),relation_rng(U_2537))
| ~ relation(U_2537) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
! [U_2537,U_2538] :
( subset(relation_rng(relation_dom_restriction(U_2537,U_2538)),relation_rng(U_2537))
| ~ relation(U_2537) ),
inference(definitional_conversion,[status(esa)],[f_667_2]) ).
cnf(f_667_4,plain,
( subset(relation_rng(relation_dom_restriction(U_2537,U_2538)),relation_rng(U_2537))
| ~ relation(U_2537) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_1,plain,
! [A] : union(powerset(A)) = A,
inference(fof_nnf,[status(thm)],[t99_zfmisc_1]) ).
fof(f_668_2,plain,
! [U_2539] : union(powerset(U_2539)) = U_2539,
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
! [U_2539] : union(powerset(U_2539)) = U_2539,
inference(definitional_conversion,[status(esa)],[f_668_2]) ).
cnf(f_668_4,plain,
union(powerset(U_2539)) = U_2539,
inference(clausify,[status(thm)],[f_668_3]) ).
fof(f_669_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_669_2,plain,
! [U_2543,U_2542,U_2541,U_2540] :
( ( relation_of2_as_subset(U_2540,U_2543,U_2541)
& quasi_total(U_2540,U_2543,U_2541)
& function(U_2540) )
| ( U_2543 != empty_set
& U_2542 = empty_set )
| ~ subset(U_2542,U_2541)
| ~ relation_of2_as_subset(U_2540,U_2543,U_2542)
| ~ quasi_total(U_2540,U_2543,U_2542)
| ~ function(U_2540) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
( ! [U_2541,U_2540,U_2543] :
( relation_of2_as_subset(U_2540,U_2543,U_2541)
| ~ sP566(U_2541,U_2540,U_2543) )
& ! [U_2541,U_2540,U_2543] :
( quasi_total(U_2540,U_2543,U_2541)
| ~ sP566(U_2541,U_2540,U_2543) )
& ! [U_2541,U_2540,U_2543] :
( function(U_2540)
| ~ sP566(U_2541,U_2540,U_2543) )
& ! [U_2542,U_2543] :
( U_2543 != empty_set
| ~ sP565(U_2542,U_2543) )
& ! [U_2542,U_2543] :
( U_2542 = empty_set
| ~ sP565(U_2542,U_2543) )
& ! [U_2541,U_2540,U_2542,U_2543] :
( sP566(U_2541,U_2540,U_2543)
| sP565(U_2542,U_2543)
| ~ subset(U_2542,U_2541)
| ~ relation_of2_as_subset(U_2540,U_2543,U_2542)
| ~ quasi_total(U_2540,U_2543,U_2542)
| ~ function(U_2540) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP565,sP566])],[f_669_2]) ).
cnf(f_669_4,plain,
( sP566(U_2541,U_2540,U_2543)
| sP565(U_2542,U_2543)
| ~ subset(U_2542,U_2541)
| ~ relation_of2_as_subset(U_2540,U_2543,U_2542)
| ~ quasi_total(U_2540,U_2543,U_2542)
| ~ function(U_2540) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_5,plain,
( U_2542 = empty_set
| ~ sP565(U_2542,U_2543) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_6,plain,
( U_2543 != empty_set
| ~ sP565(U_2542,U_2543) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_7,plain,
( function(U_2540)
| ~ sP566(U_2541,U_2540,U_2543) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_8,plain,
( quasi_total(U_2540,U_2543,U_2541)
| ~ sP566(U_2541,U_2540,U_2543) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_9,plain,
( relation_of2_as_subset(U_2540,U_2543,U_2541)
| ~ sP566(U_2541,U_2540,U_2543) ),
inference(clausify,[status(thm)],[f_669_3]) ).
fof(f_670_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_670_2,plain,
! [U_2551] :
? [U_2550] :
( ! [U_2549] :
( in(U_2549,U_2550)
| are_equipotent(U_2549,U_2550)
| ~ subset(U_2549,U_2550) )
& ! [U_2548] :
( ? [U_2547] :
( ! [U_2546] :
( in(U_2546,U_2547)
| ~ subset(U_2546,U_2548) )
& in(U_2547,U_2550) )
| ~ in(U_2548,U_2550) )
& ! [U_2545,U_2544] :
( in(U_2544,U_2550)
| ~ subset(U_2544,U_2545)
| ~ in(U_2545,U_2550) )
& in(U_2551,U_2550) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
fof(f_670_3,plain,
! [U_2551] :
( ! [U_2549] :
( in(U_2549,sK486(U_2551))
| are_equipotent(U_2549,sK486(U_2551))
| ~ subset(U_2549,sK486(U_2551)) )
& ! [U_2548] :
( ? [U_2547] :
( ! [U_2546] :
( in(U_2546,U_2547)
| ~ subset(U_2546,U_2548) )
& in(U_2547,sK486(U_2551)) )
| ~ in(U_2548,sK486(U_2551)) )
& ! [U_2545,U_2544] :
( in(U_2544,sK486(U_2551))
| ~ subset(U_2544,U_2545)
| ~ in(U_2545,sK486(U_2551)) )
& in(U_2551,sK486(U_2551)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_2550,sK486(U_2551))],[f_670_2]) ).
fof(f_670_4,plain,
! [U_2551] :
( ! [U_2549] :
( in(U_2549,sK486(U_2551))
| are_equipotent(U_2549,sK486(U_2551))
| ~ subset(U_2549,sK486(U_2551)) )
& ! [U_2548] :
( ( ! [U_2546] :
( in(U_2546,sK487(U_2551,U_2548))
| ~ subset(U_2546,U_2548) )
& in(sK487(U_2551,U_2548),sK486(U_2551)) )
| ~ in(U_2548,sK486(U_2551)) )
& ! [U_2545,U_2544] :
( in(U_2544,sK486(U_2551))
| ~ subset(U_2544,U_2545)
| ~ in(U_2545,sK486(U_2551)) )
& in(U_2551,sK486(U_2551)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_2547,sK487(U_2551,U_2548))],[f_670_3]) ).
fof(f_670_5,plain,
( ! [U_2551,U_2548,U_2546] :
( in(U_2546,sK487(U_2551,U_2548))
| ~ subset(U_2546,U_2548)
| ~ sP567(U_2551,U_2548,U_2546) )
& ! [U_2551,U_2548,U_2546] :
( in(sK487(U_2551,U_2548),sK486(U_2551))
| ~ sP567(U_2551,U_2548,U_2546) )
& ! [U_2551,U_2549] :
( in(U_2549,sK486(U_2551))
| are_equipotent(U_2549,sK486(U_2551))
| ~ subset(U_2549,sK486(U_2551)) )
& ! [U_2551,U_2548,U_2546] :
( sP567(U_2551,U_2548,U_2546)
| ~ in(U_2548,sK486(U_2551)) )
& ! [U_2551,U_2544,U_2545] :
( in(U_2544,sK486(U_2551))
| ~ subset(U_2544,U_2545)
| ~ in(U_2545,sK486(U_2551)) )
& ! [U_2551] : in(U_2551,sK486(U_2551)) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP567])],[f_670_4]) ).
cnf(f_670_6,plain,
in(U_2551,sK486(U_2551)),
inference(clausify,[status(thm)],[f_670_5]) ).
cnf(f_670_7,plain,
( in(U_2544,sK486(U_2551))
| ~ subset(U_2544,U_2545)
| ~ in(U_2545,sK486(U_2551)) ),
inference(clausify,[status(thm)],[f_670_5]) ).
cnf(f_670_8,plain,
( sP567(U_2551,U_2548,U_2546)
| ~ in(U_2548,sK486(U_2551)) ),
inference(clausify,[status(thm)],[f_670_5]) ).
cnf(f_670_9,plain,
( in(U_2549,sK486(U_2551))
| are_equipotent(U_2549,sK486(U_2551))
| ~ subset(U_2549,sK486(U_2551)) ),
inference(clausify,[status(thm)],[f_670_5]) ).
cnf(f_670_10,plain,
( in(sK487(U_2551,U_2548),sK486(U_2551))
| ~ sP567(U_2551,U_2548,U_2546) ),
inference(clausify,[status(thm)],[f_670_5]) ).
cnf(f_670_11,plain,
( in(U_2546,sK487(U_2551,U_2548))
| ~ subset(U_2546,U_2548)
| ~ sP567(U_2551,U_2548,U_2546) ),
inference(clausify,[status(thm)],[f_670_5]) ).
fof(f_671_1,plain,
! [A,B,C] :
( B = C
| singleton(A) != unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1]) ).
fof(f_671_2,plain,
! [U_2554,U_2553,U_2552] :
( U_2553 = U_2552
| singleton(U_2554) != unordered_pair(U_2553,U_2552) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
fof(f_671_3,plain,
! [U_2554,U_2552,U_2553] :
( U_2553 = U_2552
| singleton(U_2554) != unordered_pair(U_2553,U_2552) ),
inference(definitional_conversion,[status(esa)],[f_671_2]) ).
cnf(f_671_4,plain,
( U_2553 = U_2552
| singleton(U_2554) != unordered_pair(U_2553,U_2552) ),
inference(clausify,[status(thm)],[f_671_3]) ).
cnf(f_91_5_simplified,plain,
( sP133(U_409,U_406,U_408,U_410)
| ~ element(U_408,the_carrier(U_410))
| ~ latt_str(U_410)
| ~ complete_latt_str(U_410)
| ~ lattice(U_410)
| empty_carrier(U_410) ),
inference(simplify_clause,[status(thm)],[f_91_5]) ).
cnf(f_159_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_159_3]) ).
cnf(f_162_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_162_3]) ).
cnf(f_164_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_164_3]) ).
cnf(f_165_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_165_3]) ).
cnf(f_168_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_168_3]) ).
cnf(f_169_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_169_3]) ).
cnf(f_172_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_172_3]) ).
cnf(f_173_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_173_3]) ).
cnf(f_174_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_174_3]) ).
cnf(f_176_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_176_3]) ).
cnf(f_178_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_178_3]) ).
cnf(f_179_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_179_3]) ).
cnf(f_184_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_184_3]) ).
cnf(f_186_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_186_3]) ).
cnf(f_188_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_188_3]) ).
cnf(f_190_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_190_3]) ).
cnf(f_191_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_191_3]) ).
cnf(f_194_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_194_3]) ).
cnf(f_196_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_196_3]) ).
cnf(f_197_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_197_3]) ).
cnf(f_203_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_203_3]) ).
cnf(f_204_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_204_3]) ).
cnf(f_207_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_207_3]) ).
cnf(f_224_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_224_3]) ).
cnf(f_228_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_228_3]) ).
cnf(f_232_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_232_3]) ).
cnf(f_233_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_233_3]) ).
cnf(f_238_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_238_3]) ).
cnf(f_422_26_simplified,plain,
( in(ordered_pair(U_1418,U_1416),sK214(U_1414,U_1413))
| sP332(U_1418,U_1409,U_1413,U_1414,U_1416)
| ~ in(U_1416,U_1409)
| U_1418 != U_1409
| ~ in(U_1418,U_1414)
| ~ sP333(U_1415,U_1418,U_1417,U_1406,U_1409,U_1413,U_1414,U_1416) ),
inference(simplify_clause,[status(thm)],[f_422_26]) ).
cnf(f_423_18_simplified,plain,
( in(ordered_pair(U_1429,U_1427),sK220(U_1425))
| U_1427 != singleton(U_1429)
| ~ in(U_1429,U_1425)
| ~ sP336(U_1428,U_1425,U_1427,U_1426,U_1429) ),
inference(simplify_clause,[status(thm)],[f_423_18]) ).
cnf(f_424_19_simplified,plain,
( in(ordered_pair(U_1445,U_1443),sK224(U_1441,U_1440))
| sP339(U_1443,U_1441,U_1440,U_1445)
| ~ in(U_1445,complements_of_subsets(the_carrier(U_1441),U_1440))
| ~ sP340(U_1443,U_1441,U_1435,U_1442,U_1444,U_1440,U_1445) ),
inference(simplify_clause,[status(thm)],[f_424_19]) ).
cnf(f_425_19_simplified,plain,
( in(ordered_pair(U_1461,U_1459),sK229(U_1457,U_1456))
| sP343(U_1457,U_1456,U_1459,U_1461)
| ~ in(U_1461,U_1456)
| ~ sP344(U_1457,U_1460,U_1451,U_1456,U_1459,U_1458,U_1461) ),
inference(simplify_clause,[status(thm)],[f_425_19]) ).
cnf(f_429_25_simplified,plain,
( in(U_1516,sK249(U_1514,U_1513))
| sP359(U_1510,U_1514,U_1509,U_1516,U_1513)
| ~ in(U_1516,U_1509)
| U_1510 != U_1509
| ~ in(U_1510,U_1514)
| ~ sP360(U_1505,U_1515,U_1510,U_1514,U_1509,U_1516,U_1513) ),
inference(simplify_clause,[status(thm)],[f_429_25]) ).
cnf(f_431_17_simplified,plain,
( in(U_1554,sK271(U_1552))
| U_1554 != singleton(U_1549)
| ~ in(U_1549,U_1552)
| ~ sP367(U_1549,U_1554,U_1552,U_1553) ),
inference(simplify_clause,[status(thm)],[f_431_17]) ).
cnf(f_437_18_simplified,plain,
( in(U_1655,sK321(U_1653,U_1652))
| sP390(U_1649,U_1655,U_1652,U_1653)
| ~ in(U_1649,complements_of_subsets(the_carrier(U_1653),U_1652))
| ~ sP391(U_1646,U_1649,U_1655,U_1652,U_1654,U_1653) ),
inference(simplify_clause,[status(thm)],[f_437_18]) ).
cnf(f_439_18_simplified,plain,
( in(U_1694,sK339(U_1692,U_1691))
| sP398(U_1694,U_1691,U_1692,U_1688)
| ~ in(U_1688,U_1691)
| ~ sP399(U_1694,U_1691,U_1692,U_1685,U_1693,U_1688) ),
inference(simplify_clause,[status(thm)],[f_439_18]) ).
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,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( the_InternalRel(Eq_x_0) = the_InternalRel(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( rel_str_of(Eq_x_0,Eq_x_1) = rel_str_of(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,
( the_L_join(Eq_x_0) = the_L_join(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( the_L_meet(Eq_x_0) = the_L_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( latt_str_of(Eq_x_0,Eq_x_1,Eq_x_2) = latt_str_of(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_10,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,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_13,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_14,axiom,
( join_commut(Eq_x_0,Eq_x_1,Eq_x_2) = join_commut(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_15,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_16,axiom,
( meet_commut(Eq_x_0,Eq_x_1,Eq_x_2) = meet_commut(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_17,axiom,
( subset_union2(Eq_x_0,Eq_x_1,Eq_x_2) = subset_union2(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_18,axiom,
( subset_intersection2(Eq_x_0,Eq_x_1,Eq_x_2) = subset_intersection2(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,
( identity_relation(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,axiom,
( identity_on_carrier(Eq_x_0) = identity_on_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( identity_as_relation_of(Eq_x_0) = identity_as_relation_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,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_25,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,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_27,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_28,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,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_30,axiom,
( meet(Eq_x_0,Eq_x_1,Eq_x_2) = meet(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_31,axiom,
( topstr_closure(Eq_x_0,Eq_x_1) = topstr_closure(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,
( bottom_of_semilattstr(Eq_x_0) = bottom_of_semilattstr(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( apply_binary(Eq_x_0,Eq_x_1,Eq_x_2) = apply_binary(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_34,axiom,
( interior(Eq_x_0,Eq_x_1) = interior(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,
( 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_36,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,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_38,axiom,
( boole_lattice(Eq_x_0) = boole_lattice(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( join(Eq_x_0,Eq_x_1,Eq_x_2) = join(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_40,axiom,
( apply_binary_as_element(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = apply_binary_as_element(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_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_functions]) ).
cnf(equality_41,axiom,
( pair_first(Eq_x_0) = pair_first(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( the_topology(Eq_x_0) = the_topology(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,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_46,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,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_48,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_49,axiom,
( inclusion_relation(Eq_x_0) = inclusion_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( join_of_latt_set(Eq_x_0,Eq_x_1) = join_of_latt_set(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( meet_of_latt_set(Eq_x_0,Eq_x_1) = meet_of_latt_set(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( a_2_2_lattice3(Eq_x_0,Eq_x_1) = a_2_2_lattice3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( poset_of_lattice(Eq_x_0) = poset_of_lattice(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( k2_lattice3(Eq_x_0) = k2_lattice3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( pair_second(Eq_x_0) = pair_second(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( empty_carrier_subset(Eq_x_0) = empty_carrier_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( cast_to_el_of_LattPOSet(Eq_x_0,Eq_x_1) = cast_to_el_of_LattPOSet(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( cast_as_carrier_subset(Eq_x_0) = cast_as_carrier_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( cast_to_el_of_lattice(Eq_x_0,Eq_x_1) = cast_to_el_of_lattice(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,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_62,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_63,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_64,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_65,axiom,
( relation_inverse(Eq_x_0) = relation_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( relation_of_lattice(Eq_x_0) = relation_of_lattice(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( a_1_0_filter_1(Eq_x_0) = a_1_0_filter_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,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_69,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_70,axiom,
( function_inverse(Eq_x_0) = function_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( k10_filter_1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = k10_filter_1(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_72,axiom,
( k8_filter_1(Eq_x_0,Eq_x_1) = k8_filter_1(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,
( ordered_pair_as_product_element(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = ordered_pair_as_product_element(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_74,axiom,
( k1_pcomps_1(Eq_x_0) = k1_pcomps_1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,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_76,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_77,axiom,
( apply_as_element(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = apply_as_element(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_78,axiom,
( a_2_3_lattice3(Eq_x_0,Eq_x_1) = a_2_3_lattice3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( 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_80,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_81,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_82,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_83,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_84,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_85,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_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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_96,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_97,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK21(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_100,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_101,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_102,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( 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_104,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_105,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_106,axiom,
( 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_107,axiom,
( sK29(Eq_x_0,Eq_x_1,Eq_x_2) = sK29(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,
( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(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,
( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(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,
( sK32(Eq_x_0,Eq_x_1,Eq_x_2) = sK32(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_111,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_112,axiom,
( sK34(Eq_x_0,Eq_x_1,Eq_x_2) = sK34(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_113,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK35(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_114,axiom,
( sK36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK36(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_115,axiom,
( sK37(Eq_x_0) = sK37(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_116,axiom,
( sK38(Eq_x_0) = sK38(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_117,axiom,
( sK39(Eq_x_0) = sK39(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_118,axiom,
( sK40(Eq_x_0) = sK40(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_119,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_120,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_121,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_122,axiom,
( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_123,axiom,
( sK45(Eq_x_0) = sK45(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_124,axiom,
( sK46(Eq_x_0) = sK46(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_125,axiom,
( sK47(Eq_x_0) = sK47(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_126,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_127,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_128,axiom,
( sK50(Eq_x_0) = sK50(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_129,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_130,axiom,
( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(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,
( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_132,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_133,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_134,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_135,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_136,axiom,
( sK58(Eq_x_0,Eq_x_1) = sK58(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_137,axiom,
( 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_138,axiom,
( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_139,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(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,
( sK62(Eq_x_0,Eq_x_1) = sK62(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,
( sK63(Eq_x_0) = sK63(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_142,axiom,
( sK64(Eq_x_0,Eq_x_1) = sK64(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_143,axiom,
( sK65(Eq_x_0,Eq_x_1) = sK65(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_144,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_145,axiom,
( sK67(Eq_x_0) = sK67(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_146,axiom,
( sK68(Eq_x_0,Eq_x_1) = sK68(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_147,axiom,
( sK69(Eq_x_0,Eq_x_1) = sK69(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_148,axiom,
( sK70(Eq_x_0) = sK70(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_149,axiom,
( sK71(Eq_x_0,Eq_x_1) = sK71(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_150,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_151,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_152,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_153,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_154,axiom,
( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_155,axiom,
( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_156,axiom,
( sK78(Eq_x_0,Eq_x_1) = sK78(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_157,axiom,
( sK79(Eq_x_0) = sK79(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_158,axiom,
( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_159,axiom,
( sK81(Eq_x_0,Eq_x_1,Eq_x_2) = sK81(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_160,axiom,
( sK82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK82(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_161,axiom,
( sK83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK83(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_162,axiom,
( sK84(Eq_x_0,Eq_x_1,Eq_x_2) = sK84(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_163,axiom,
( 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_164,axiom,
( sK86(Eq_x_0,Eq_x_1,Eq_x_2) = sK86(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_165,axiom,
( sK87(Eq_x_0,Eq_x_1,Eq_x_2) = sK87(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_166,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_167,axiom,
( sK89(Eq_x_0) = sK89(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_168,axiom,
( sK90(Eq_x_0) = sK90(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_169,axiom,
( sK91(Eq_x_0) = sK91(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_170,axiom,
( sK92(Eq_x_0,Eq_x_1) = sK92(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_171,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_172,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_173,axiom,
( sK95(Eq_x_0,Eq_x_1,Eq_x_2) = sK95(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_174,axiom,
( sK96(Eq_x_0,Eq_x_1) = sK96(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_175,axiom,
( sK97(Eq_x_0,Eq_x_1,Eq_x_2) = sK97(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_176,axiom,
( sK98(Eq_x_0,Eq_x_1,Eq_x_2) = sK98(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_177,axiom,
( sK99(Eq_x_0,Eq_x_1,Eq_x_2) = sK99(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_178,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_179,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_180,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_181,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_182,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_183,axiom,
( sK105(Eq_x_0,Eq_x_1,Eq_x_2) = sK105(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_184,axiom,
( sK106(Eq_x_0,Eq_x_1) = sK106(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,
( sK107(Eq_x_0,Eq_x_1) = sK107(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,
( sK108(Eq_x_0,Eq_x_1) = sK108(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_187,axiom,
( sK109(Eq_x_0,Eq_x_1) = sK109(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_188,axiom,
( sK110(Eq_x_0,Eq_x_1,Eq_x_2) = sK110(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_189,axiom,
( sK111(Eq_x_0,Eq_x_1,Eq_x_2) = sK111(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_190,axiom,
( sK112(Eq_x_0,Eq_x_1,Eq_x_2) = sK112(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_191,axiom,
( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_192,axiom,
( sK114(Eq_x_0,Eq_x_1) = sK114(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_193,axiom,
( sK115(Eq_x_0,Eq_x_1) = sK115(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_194,axiom,
( sK116(Eq_x_0) = sK116(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_195,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_196,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_197,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_198,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_199,axiom,
( sK121(Eq_x_0,Eq_x_1) = sK121(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,
( 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_201,axiom,
( sK123(Eq_x_0,Eq_x_1) = sK123(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_202,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_203,axiom,
( sK125(Eq_x_0,Eq_x_1) = sK125(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_204,axiom,
( sK126(Eq_x_0,Eq_x_1) = sK126(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,
( sK127(Eq_x_0,Eq_x_1,Eq_x_2) = sK127(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_206,axiom,
( sK128(Eq_x_0,Eq_x_1,Eq_x_2) = sK128(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_207,axiom,
( sK129(Eq_x_0,Eq_x_1,Eq_x_2) = sK129(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_208,axiom,
( sK130(Eq_x_0,Eq_x_1,Eq_x_2) = sK130(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_209,axiom,
( sK131(Eq_x_0) = sK131(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_210,axiom,
( sK132(Eq_x_0) = sK132(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_211,axiom,
( sK133(Eq_x_0,Eq_x_1,Eq_x_2) = sK133(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_212,axiom,
( sK134(Eq_x_0) = sK134(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_213,axiom,
( sK135(Eq_x_0) = sK135(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_214,axiom,
( sK136(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK136(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_215,axiom,
( sK137(Eq_x_0,Eq_x_1,Eq_x_2) = sK137(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_216,axiom,
( sK138(Eq_x_0,Eq_x_1,Eq_x_2) = sK138(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_217,axiom,
( sK139(Eq_x_0,Eq_x_1,Eq_x_2) = sK139(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_218,axiom,
( sK140(Eq_x_0,Eq_x_1,Eq_x_2) = sK140(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_219,axiom,
( sK141(Eq_x_0,Eq_x_1,Eq_x_2) = sK141(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_220,axiom,
( sK142(Eq_x_0,Eq_x_1) = sK142(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_221,axiom,
( sK143(Eq_x_0,Eq_x_1) = sK143(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_222,axiom,
( sK144(Eq_x_0,Eq_x_1) = sK144(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_223,axiom,
( sK145(Eq_x_0,Eq_x_1,Eq_x_2) = sK145(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_224,axiom,
( sK146(Eq_x_0,Eq_x_1,Eq_x_2) = sK146(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_225,axiom,
( sK153(Eq_x_0,Eq_x_1) = sK153(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_226,axiom,
( sK154(Eq_x_0,Eq_x_1) = sK154(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_227,axiom,
( sK155(Eq_x_0) = sK155(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_228,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_229,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_230,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_231,axiom,
( sK159(Eq_x_0,Eq_x_1,Eq_x_2) = sK159(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_232,axiom,
( sK160(Eq_x_0,Eq_x_1,Eq_x_2) = sK160(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_233,axiom,
( sK161(Eq_x_0) = sK161(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_234,axiom,
( sK162(Eq_x_0) = sK162(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_235,axiom,
( sK163(Eq_x_0) = sK163(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_236,axiom,
( sK164(Eq_x_0) = sK164(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_237,axiom,
( sK165(Eq_x_0,Eq_x_1) = sK165(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_238,axiom,
( sK166(Eq_x_0) = sK166(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_239,axiom,
( sK167(Eq_x_0) = sK167(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_240,axiom,
( sK168(Eq_x_0) = sK168(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_241,axiom,
( sK169(Eq_x_0) = sK169(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_242,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_243,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_244,axiom,
( sK181(Eq_x_0) = sK181(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_245,axiom,
( sK182(Eq_x_0) = sK182(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_246,axiom,
( sK184(Eq_x_0) = sK184(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_247,axiom,
( sK186(Eq_x_0) = sK186(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_248,axiom,
( sK189(Eq_x_0,Eq_x_1) = sK189(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,
( sK191(Eq_x_0) = sK191(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_250,axiom,
( sK192(Eq_x_0) = sK192(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_251,axiom,
( sK193(Eq_x_0) = sK193(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_252,axiom,
( sK195(Eq_x_0) = sK195(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_253,axiom,
( sK199(Eq_x_0) = sK199(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_254,axiom,
( sK202(Eq_x_0) = sK202(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_255,axiom,
( sK204(Eq_x_0) = sK204(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_256,axiom,
( sK206(Eq_x_0) = sK206(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_257,axiom,
( sK207(Eq_x_0) = sK207(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_258,axiom,
( sK209(Eq_x_0,Eq_x_1) = sK209(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_259,axiom,
( sK210(Eq_x_0,Eq_x_1) = sK210(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_260,axiom,
( sK211(Eq_x_0,Eq_x_1) = sK211(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_261,axiom,
( sK212(Eq_x_0,Eq_x_1) = sK212(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,
( sK213(Eq_x_0,Eq_x_1) = sK213(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_263,axiom,
( sK214(Eq_x_0,Eq_x_1) = sK214(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_264,axiom,
( sK215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK215(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_265,axiom,
( sK216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK216(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_266,axiom,
( sK217(Eq_x_0) = sK217(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_267,axiom,
( sK218(Eq_x_0) = sK218(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_268,axiom,
( sK219(Eq_x_0) = sK219(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_269,axiom,
( sK220(Eq_x_0) = sK220(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_270,axiom,
( sK221(Eq_x_0,Eq_x_1) = sK221(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,
( sK222(Eq_x_0,Eq_x_1) = sK222(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,
( sK223(Eq_x_0,Eq_x_1) = sK223(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,
( sK224(Eq_x_0,Eq_x_1) = sK224(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,
( sK225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK225(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_275,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_276,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_277,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_278,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_279,axiom,
( sK230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK230(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_280,axiom,
( sK231(Eq_x_0) = sK231(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_281,axiom,
( sK233(Eq_x_0) = sK233(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_282,axiom,
( sK235(Eq_x_0) = sK235(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_283,axiom,
( sK237(Eq_x_0) = sK237(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_284,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_285,axiom,
( sK241(Eq_x_0) = sK241(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_286,axiom,
( sK242(Eq_x_0,Eq_x_1) = sK242(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_287,axiom,
( sK243(Eq_x_0,Eq_x_1,Eq_x_2) = sK243(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,
( sK244(Eq_x_0,Eq_x_1) = sK244(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_289,axiom,
( sK245(Eq_x_0,Eq_x_1) = sK245(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_290,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_291,axiom,
( sK247(Eq_x_0,Eq_x_1) = sK247(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_292,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_293,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_294,axiom,
( sK250(Eq_x_0,Eq_x_1,Eq_x_2) = sK250(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_295,axiom,
( sK251(Eq_x_0,Eq_x_1,Eq_x_2) = sK251(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_296,axiom,
( sK252(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK252(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_297,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_298,axiom,
( sK254(Eq_x_0,Eq_x_1) = sK254(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,
( 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_300,axiom,
( sK256(Eq_x_0,Eq_x_1) = sK256(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,
( sK257(Eq_x_0,Eq_x_1) = sK257(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_302,axiom,
( sK258(Eq_x_0,Eq_x_1) = sK258(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_303,axiom,
( sK259(Eq_x_0,Eq_x_1) = sK259(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,
( sK260(Eq_x_0,Eq_x_1) = sK260(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,
( sK261(Eq_x_0,Eq_x_1) = sK261(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,
( sK262(Eq_x_0,Eq_x_1,Eq_x_2) = sK262(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_307,axiom,
( sK263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK263(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_308,axiom,
( sK264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK264(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_309,axiom,
( sK265(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK265(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_310,axiom,
( sK266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK266(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_311,axiom,
( sK267(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK267(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_312,axiom,
( sK268(Eq_x_0) = sK268(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_313,axiom,
( sK269(Eq_x_0) = sK269(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_314,axiom,
( sK270(Eq_x_0) = sK270(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_315,axiom,
( sK271(Eq_x_0) = sK271(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_316,axiom,
( sK272(Eq_x_0,Eq_x_1) = sK272(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_317,axiom,
( sK273(Eq_x_0) = sK273(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_318,axiom,
( sK274(Eq_x_0) = sK274(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_319,axiom,
( sK275(Eq_x_0) = sK275(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_320,axiom,
( sK276(Eq_x_0) = sK276(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_321,axiom,
( sK277(Eq_x_0) = sK277(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_322,axiom,
( sK278(Eq_x_0) = sK278(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_323,axiom,
( sK279(Eq_x_0) = sK279(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_324,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_325,axiom,
( sK281(Eq_x_0,Eq_x_1,Eq_x_2) = sK281(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_326,axiom,
( sK282(Eq_x_0,Eq_x_1,Eq_x_2) = sK282(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_327,axiom,
( sK283(Eq_x_0,Eq_x_1,Eq_x_2) = sK283(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_328,axiom,
( sK284(Eq_x_0) = sK284(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_329,axiom,
( sK285(Eq_x_0) = sK285(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_330,axiom,
( sK286(Eq_x_0) = sK286(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_331,axiom,
( sK287(Eq_x_0) = sK287(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_332,axiom,
( sK288(Eq_x_0,Eq_x_1) = sK288(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_333,axiom,
( sK289(Eq_x_0) = sK289(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_334,axiom,
( sK290(Eq_x_0,Eq_x_1) = sK290(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_335,axiom,
( sK291(Eq_x_0) = sK291(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_336,axiom,
( sK292(Eq_x_0,Eq_x_1) = sK292(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_337,axiom,
( sK293(Eq_x_0,Eq_x_1,Eq_x_2) = sK293(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_338,axiom,
( sK294(Eq_x_0,Eq_x_1) = sK294(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_339,axiom,
( sK295(Eq_x_0,Eq_x_1,Eq_x_2) = sK295(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_340,axiom,
( sK296(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK296(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_341,axiom,
( sK297(Eq_x_0,Eq_x_1) = sK297(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_342,axiom,
( sK298(Eq_x_0,Eq_x_1) = sK298(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_343,axiom,
( sK299(Eq_x_0,Eq_x_1) = sK299(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_344,axiom,
( sK300(Eq_x_0,Eq_x_1) = sK300(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_345,axiom,
( sK301(Eq_x_0,Eq_x_1) = sK301(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_346,axiom,
( sK302(Eq_x_0,Eq_x_1) = sK302(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_347,axiom,
( sK303(Eq_x_0,Eq_x_1,Eq_x_2) = sK303(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_348,axiom,
( sK304(Eq_x_0,Eq_x_1,Eq_x_2) = sK304(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_349,axiom,
( sK305(Eq_x_0,Eq_x_1) = sK305(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_350,axiom,
( sK306(Eq_x_0,Eq_x_1) = sK306(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_351,axiom,
( sK307(Eq_x_0,Eq_x_1) = sK307(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_352,axiom,
( sK308(Eq_x_0,Eq_x_1) = sK308(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_353,axiom,
( sK309(Eq_x_0,Eq_x_1,Eq_x_2) = sK309(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_354,axiom,
( sK310(Eq_x_0,Eq_x_1) = sK310(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_355,axiom,
( sK311(Eq_x_0,Eq_x_1) = sK311(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_356,axiom,
( sK312(Eq_x_0,Eq_x_1) = sK312(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_357,axiom,
( sK313(Eq_x_0,Eq_x_1) = sK313(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_358,axiom,
( sK314(Eq_x_0,Eq_x_1) = sK314(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_359,axiom,
( sK315(Eq_x_0,Eq_x_1) = sK315(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_360,axiom,
( sK316(Eq_x_0,Eq_x_1,Eq_x_2) = sK316(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_361,axiom,
( sK317(Eq_x_0,Eq_x_1,Eq_x_2) = sK317(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_362,axiom,
( sK318(Eq_x_0,Eq_x_1) = sK318(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_363,axiom,
( sK319(Eq_x_0,Eq_x_1) = sK319(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_364,axiom,
( sK320(Eq_x_0,Eq_x_1) = sK320(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_365,axiom,
( sK321(Eq_x_0,Eq_x_1) = sK321(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_366,axiom,
( sK322(Eq_x_0,Eq_x_1,Eq_x_2) = sK322(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_367,axiom,
( sK323(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK323(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_368,axiom,
( sK324(Eq_x_0,Eq_x_1) = sK324(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_369,axiom,
( sK325(Eq_x_0,Eq_x_1) = sK325(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_370,axiom,
( sK326(Eq_x_0,Eq_x_1) = sK326(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_371,axiom,
( sK327(Eq_x_0,Eq_x_1) = sK327(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_372,axiom,
( sK328(Eq_x_0,Eq_x_1) = sK328(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_373,axiom,
( sK329(Eq_x_0,Eq_x_1) = sK329(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_374,axiom,
( sK330(Eq_x_0,Eq_x_1) = sK330(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_375,axiom,
( sK331(Eq_x_0,Eq_x_1,Eq_x_2) = sK331(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_376,axiom,
( sK332(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK332(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_377,axiom,
( sK333(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK333(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_378,axiom,
( sK334(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK334(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_379,axiom,
( sK335(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK335(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_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_functions]) ).
cnf(equality_380,axiom,
( sK336(Eq_x_0,Eq_x_1) = sK336(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_381,axiom,
( sK337(Eq_x_0,Eq_x_1) = sK337(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_382,axiom,
( sK338(Eq_x_0,Eq_x_1) = sK338(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_383,axiom,
( sK339(Eq_x_0,Eq_x_1) = sK339(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_384,axiom,
( sK340(Eq_x_0,Eq_x_1,Eq_x_2) = sK340(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_385,axiom,
( sK341(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK341(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_386,axiom,
( sK342(Eq_x_0,Eq_x_1) = sK342(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_387,axiom,
( sK343(Eq_x_0,Eq_x_1) = sK343(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_388,axiom,
( sK344(Eq_x_0,Eq_x_1) = sK344(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_389,axiom,
( sK345(Eq_x_0,Eq_x_1) = sK345(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_390,axiom,
( sK346(Eq_x_0,Eq_x_1) = sK346(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_391,axiom,
( sK347(Eq_x_0,Eq_x_1) = sK347(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_392,axiom,
( sK348(Eq_x_0,Eq_x_1) = sK348(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_393,axiom,
( sK349(Eq_x_0,Eq_x_1,Eq_x_2) = sK349(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_394,axiom,
( sK350(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK350(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_395,axiom,
( sK351(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK351(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_396,axiom,
( sK352(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK352(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_397,axiom,
( sK353(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK353(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_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_functions]) ).
cnf(equality_398,axiom,
( sK354(Eq_x_0,Eq_x_1,Eq_x_2) = sK354(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_399,axiom,
( sK355(Eq_x_0,Eq_x_1,Eq_x_2) = sK355(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_400,axiom,
( sK356(Eq_x_0,Eq_x_1,Eq_x_2) = sK356(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_401,axiom,
( sK357(Eq_x_0,Eq_x_1,Eq_x_2) = sK357(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_402,axiom,
( sK358(Eq_x_0,Eq_x_1,Eq_x_2) = sK358(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_403,axiom,
( sK359(Eq_x_0,Eq_x_1,Eq_x_2) = sK359(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_404,axiom,
( sK360(Eq_x_0,Eq_x_1,Eq_x_2) = sK360(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_405,axiom,
( sK361(Eq_x_0,Eq_x_1,Eq_x_2) = sK361(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_406,axiom,
( sK362(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK362(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_407,axiom,
( sK363(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK363(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_408,axiom,
( sK364(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK364(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_409,axiom,
( sK368(Eq_x_0) = sK368(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_410,axiom,
( sK369(Eq_x_0,Eq_x_1) = sK369(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_411,axiom,
( sK370(Eq_x_0,Eq_x_1,Eq_x_2) = sK370(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_412,axiom,
( sK371(Eq_x_0,Eq_x_1,Eq_x_2) = sK371(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_413,axiom,
( sK372(Eq_x_0,Eq_x_1,Eq_x_2) = sK372(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_414,axiom,
( sK373(Eq_x_0,Eq_x_1,Eq_x_2) = sK373(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_415,axiom,
( sK374(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK374(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_416,axiom,
( sK375(Eq_x_0,Eq_x_1) = sK375(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_417,axiom,
( sK376(Eq_x_0,Eq_x_1) = sK376(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_418,axiom,
( sK377(Eq_x_0,Eq_x_1) = sK377(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_419,axiom,
( sK378(Eq_x_0,Eq_x_1) = sK378(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_420,axiom,
( sK379(Eq_x_0,Eq_x_1) = sK379(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_421,axiom,
( sK380(Eq_x_0,Eq_x_1) = sK380(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_422,axiom,
( sK381(Eq_x_0,Eq_x_1,Eq_x_2) = sK381(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_423,axiom,
( sK382(Eq_x_0,Eq_x_1,Eq_x_2) = sK382(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_424,axiom,
( sK383(Eq_x_0,Eq_x_1,Eq_x_2) = sK383(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_425,axiom,
( sK384(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK384(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_426,axiom,
( sK385(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK385(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_427,axiom,
( sK386(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK386(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_428,axiom,
( sK387(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK387(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_429,axiom,
( sK388(Eq_x_0,Eq_x_1) = sK388(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_430,axiom,
( sK389(Eq_x_0,Eq_x_1,Eq_x_2) = sK389(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_431,axiom,
( sK390(Eq_x_0,Eq_x_1,Eq_x_2) = sK390(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_432,axiom,
( sK391(Eq_x_0) = sK391(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_433,axiom,
( sK392(Eq_x_0,Eq_x_1) = sK392(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_434,axiom,
( sK393(Eq_x_0,Eq_x_1,Eq_x_2) = sK393(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_435,axiom,
( sK394(Eq_x_0,Eq_x_1,Eq_x_2) = sK394(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_436,axiom,
( sK395(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK395(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_437,axiom,
( sK396(Eq_x_0,Eq_x_1) = sK396(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_438,axiom,
( sK397(Eq_x_0,Eq_x_1,Eq_x_2) = sK397(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_439,axiom,
( sK398(Eq_x_0,Eq_x_1) = sK398(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_440,axiom,
( sK399(Eq_x_0,Eq_x_1) = sK399(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_441,axiom,
( sK400(Eq_x_0,Eq_x_1,Eq_x_2) = sK400(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_442,axiom,
( sK401(Eq_x_0,Eq_x_1,Eq_x_2) = sK401(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_443,axiom,
( sK402(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK402(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_444,axiom,
( sK403(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK403(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_445,axiom,
( sK404(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK404(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_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_functions]) ).
cnf(equality_446,axiom,
( sK405(Eq_x_0,Eq_x_1,Eq_x_2) = sK405(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_447,axiom,
( sK406(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK406(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_448,axiom,
( sK407(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK407(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_449,axiom,
( sK408(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK408(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_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_functions]) ).
cnf(equality_450,axiom,
( sK409(Eq_x_0,Eq_x_1,Eq_x_2) = sK409(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_451,axiom,
( sK410(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK410(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_452,axiom,
( sK411(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK411(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_453,axiom,
( sK412(Eq_x_0) = sK412(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_454,axiom,
( sK413(Eq_x_0,Eq_x_1,Eq_x_2) = sK413(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_455,axiom,
( sK414(Eq_x_0,Eq_x_1) = sK414(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_456,axiom,
( sK415(Eq_x_0,Eq_x_1,Eq_x_2) = sK415(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_457,axiom,
( sK416(Eq_x_0,Eq_x_1) = sK416(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_458,axiom,
( sK417(Eq_x_0,Eq_x_1) = sK417(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_459,axiom,
( sK418(Eq_x_0,Eq_x_1) = sK418(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_460,axiom,
( sK419(Eq_x_0,Eq_x_1) = sK419(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_461,axiom,
( sK420(Eq_x_0,Eq_x_1) = sK420(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_462,axiom,
( sK421(Eq_x_0,Eq_x_1) = sK421(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_463,axiom,
( sK422(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK422(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_464,axiom,
( sK423(Eq_x_0,Eq_x_1) = sK423(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_465,axiom,
( sK424(Eq_x_0,Eq_x_1,Eq_x_2) = sK424(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_466,axiom,
( sK425(Eq_x_0) = sK425(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_467,axiom,
( sK426(Eq_x_0) = sK426(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_468,axiom,
( sK427(Eq_x_0) = sK427(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_469,axiom,
( sK428(Eq_x_0) = sK428(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_470,axiom,
( sK429(Eq_x_0) = sK429(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_471,axiom,
( sK430(Eq_x_0,Eq_x_1) = sK430(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_472,axiom,
( sK431(Eq_x_0,Eq_x_1) = sK431(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_473,axiom,
( sK432(Eq_x_0,Eq_x_1) = sK432(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_474,axiom,
( sK433(Eq_x_0,Eq_x_1) = sK433(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_475,axiom,
( sK434(Eq_x_0,Eq_x_1,Eq_x_2) = sK434(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_476,axiom,
( sK435(Eq_x_0,Eq_x_1) = sK435(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_477,axiom,
( sK436(Eq_x_0,Eq_x_1) = sK436(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_478,axiom,
( sK437(Eq_x_0,Eq_x_1) = sK437(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_479,axiom,
( sK438(Eq_x_0,Eq_x_1) = sK438(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_480,axiom,
( sK439(Eq_x_0,Eq_x_1) = sK439(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_481,axiom,
( sK440(Eq_x_0,Eq_x_1,Eq_x_2) = sK440(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_482,axiom,
( sK441(Eq_x_0,Eq_x_1) = sK441(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_483,axiom,
( sK443(Eq_x_0,Eq_x_1) = sK443(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_484,axiom,
( sK445(Eq_x_0) = sK445(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_485,axiom,
( sK446(Eq_x_0,Eq_x_1) = sK446(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_486,axiom,
( sK447(Eq_x_0) = sK447(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_487,axiom,
( sK448(Eq_x_0,Eq_x_1) = sK448(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_488,axiom,
( sK449(Eq_x_0,Eq_x_1,Eq_x_2) = sK449(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_489,axiom,
( sK450(Eq_x_0,Eq_x_1) = sK450(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_490,axiom,
( sK451(Eq_x_0) = sK451(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_491,axiom,
( sK452(Eq_x_0) = sK452(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_492,axiom,
( sK453(Eq_x_0,Eq_x_1,Eq_x_2) = sK453(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_493,axiom,
( sK454(Eq_x_0,Eq_x_1,Eq_x_2) = sK454(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_494,axiom,
( sK455(Eq_x_0,Eq_x_1) = sK455(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_495,axiom,
( sK456(Eq_x_0,Eq_x_1,Eq_x_2) = sK456(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_496,axiom,
( sK457(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK457(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_497,axiom,
( sK458(Eq_x_0,Eq_x_1,Eq_x_2) = sK458(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_498,axiom,
( sK459(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK459(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_499,axiom,
( sK460(Eq_x_0) = sK460(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_500,axiom,
( sK461(Eq_x_0) = sK461(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_501,axiom,
( sK462(Eq_x_0) = sK462(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_502,axiom,
( sK463(Eq_x_0,Eq_x_1) = sK463(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_503,axiom,
( sK464(Eq_x_0,Eq_x_1) = sK464(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_504,axiom,
( sK465(Eq_x_0) = sK465(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_505,axiom,
( sK466(Eq_x_0,Eq_x_1) = sK466(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_506,axiom,
( sK467(Eq_x_0,Eq_x_1) = sK467(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_507,axiom,
( sK468(Eq_x_0,Eq_x_1,Eq_x_2) = sK468(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_508,axiom,
( sK469(Eq_x_0,Eq_x_1) = sK469(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_509,axiom,
( sK470(Eq_x_0) = sK470(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_510,axiom,
( sK471(Eq_x_0) = sK471(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_511,axiom,
( sK472(Eq_x_0,Eq_x_1) = sK472(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_512,axiom,
( sK473(Eq_x_0,Eq_x_1,Eq_x_2) = sK473(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_513,axiom,
( sK474(Eq_x_0,Eq_x_1) = sK474(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_514,axiom,
( sK475(Eq_x_0,Eq_x_1) = sK475(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_515,axiom,
( sK476(Eq_x_0,Eq_x_1) = sK476(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_516,axiom,
( sK477(Eq_x_0,Eq_x_1) = sK477(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_517,axiom,
( sK478(Eq_x_0,Eq_x_1) = sK478(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_518,axiom,
( sK479(Eq_x_0,Eq_x_1) = sK479(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_519,axiom,
( sK480(Eq_x_0) = sK480(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_520,axiom,
( sK481(Eq_x_0) = sK481(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_521,axiom,
( sK482(Eq_x_0,Eq_x_1,Eq_x_2) = sK482(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_522,axiom,
( sK485(Eq_x_0,Eq_x_1) = sK485(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_523,axiom,
( sK486(Eq_x_0) = sK486(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_524,axiom,
( sK487(Eq_x_0,Eq_x_1) = sK487(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_525,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_526,axiom,
( strict_rel_str(Eq_y_0)
| ~ strict_rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_527,axiom,
( latt_str(Eq_y_0)
| ~ latt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_528,axiom,
( strict_latt_str(Eq_y_0)
| ~ strict_latt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_529,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_530,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_531,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_532,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_533,axiom,
( v1_xcmplx_0(Eq_y_0)
| ~ v1_xcmplx_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_534,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_535,axiom,
( v1_xreal_0(Eq_y_0)
| ~ v1_xreal_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_536,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_537,axiom,
( v1_rat_1(Eq_y_0)
| ~ v1_rat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_538,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_539,axiom,
( v1_int_1(Eq_y_0)
| ~ v1_int_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_540,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_541,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_542,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_543,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_544,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_545,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_546,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_547,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_548,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_549,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_550,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_551,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_552,axiom,
( v1_partfun1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ v1_partfun1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_553,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_554,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_555,axiom,
( lattice(Eq_y_0)
| ~ lattice(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_556,axiom,
( join_commutative(Eq_y_0)
| ~ join_commutative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_557,axiom,
( join_associative(Eq_y_0)
| ~ join_associative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_558,axiom,
( meet_commutative(Eq_y_0)
| ~ meet_commutative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_559,axiom,
( meet_associative(Eq_y_0)
| ~ meet_associative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_560,axiom,
( meet_absorbing(Eq_y_0)
| ~ meet_absorbing(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_561,axiom,
( join_absorbing(Eq_y_0)
| ~ join_absorbing(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_562,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_563,axiom,
( symmetric(Eq_y_0)
| ~ symmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_564,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_565,axiom,
( reflexive(Eq_y_0)
| ~ reflexive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_566,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_567,axiom,
( bijective(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ bijective(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( onto(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ onto(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( join_semilatt_str(Eq_y_0)
| ~ join_semilatt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_570,axiom,
( meet_semilatt_str(Eq_y_0)
| ~ meet_semilatt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_571,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_572,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_573,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_574,axiom,
( antisymmetric(Eq_y_0)
| ~ antisymmetric(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_575,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_576,axiom,
( lower_bounded_semilattstr(Eq_y_0)
| ~ lower_bounded_semilattstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_577,axiom,
( top_str(Eq_y_0)
| ~ top_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_578,axiom,
( open_subset(Eq_y_0,Eq_y_1)
| ~ open_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_579,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_580,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_581,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_582,axiom,
( latt_set_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ latt_set_smaller(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( below(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ below(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_584,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_585,axiom,
( latt_element_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ latt_element_smaller(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( topological_space(Eq_y_0)
| ~ topological_space(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_587,axiom,
( point_neighbourhood(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ point_neighbourhood(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( 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_589,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_590,axiom,
( open_subsets(Eq_y_0,Eq_y_1)
| ~ open_subsets(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_591,axiom,
( complete_latt_str(Eq_y_0)
| ~ complete_latt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_592,axiom,
( centered(Eq_y_0)
| ~ centered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_593,axiom,
( proper_element(Eq_y_0,Eq_y_1)
| ~ proper_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_594,axiom,
( closed_subsets(Eq_y_0,Eq_y_1)
| ~ closed_subsets(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_595,axiom,
( closed_subset(Eq_y_0,Eq_y_1)
| ~ closed_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_596,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_597,axiom,
( compact_top_space(Eq_y_0)
| ~ compact_top_space(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_598,axiom,
( is_a_cover_of_carrier(Eq_y_0,Eq_y_1)
| ~ is_a_cover_of_carrier(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_599,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_600,axiom,
( well_ordering(Eq_y_0)
| ~ well_ordering(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_601,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_602,axiom,
( transitive_relstr(Eq_y_0)
| ~ transitive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_603,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_604,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_605,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_606,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_607,axiom,
( relstr_element_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relstr_element_smaller(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( related(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ related(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( relstr_set_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relstr_set_smaller(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( reflexive_relstr(Eq_y_0)
| ~ reflexive_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_611,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_612,axiom,
( v1_binop_1(Eq_y_0,Eq_y_1)
| ~ v1_binop_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_613,axiom,
( v2_binop_1(Eq_y_0,Eq_y_1)
| ~ v2_binop_1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_614,axiom,
( below_refl(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ below_refl(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( 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_616,axiom,
( related_reflexive(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ related_reflexive(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_617,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_618,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_619,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_620,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_621,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_622,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_623,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_624,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_625,axiom,
( sP8(Eq_y_0)
| ~ sP8(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_626,axiom,
( sP9(Eq_y_0)
| ~ sP9(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_627,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_628,axiom,
( sP11(Eq_y_0)
| ~ sP11(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_629,axiom,
( sP12(Eq_y_0)
| ~ sP12(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_630,axiom,
( sP13(Eq_y_0)
| ~ sP13(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_631,axiom,
( sP14(Eq_y_0)
| ~ sP14(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_632,axiom,
( sP15(Eq_y_0)
| ~ sP15(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_633,axiom,
( sP16(Eq_y_0)
| ~ sP16(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_634,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_635,axiom,
( sP18(Eq_y_0)
| ~ sP18(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_636,axiom,
( sP19(Eq_y_0)
| ~ sP19(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_637,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_638,axiom,
( sP21(Eq_y_0)
| ~ sP21(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_639,axiom,
( sP22(Eq_y_0,Eq_y_1)
| ~ sP22(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,
( 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_641,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_642,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_643,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP26(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_644,axiom,
( sP27(Eq_y_0,Eq_y_1)
| ~ sP27(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,
( sP28(Eq_y_0,Eq_y_1)
| ~ sP28(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_646,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP29(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_647,axiom,
( sP30(Eq_y_0,Eq_y_1)
| ~ sP30(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_648,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP31(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_649,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP32(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_650,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_651,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP35(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_653,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP36(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_654,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP37(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,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP38(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_656,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_657,axiom,
( sP40(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)
| ~ sP40(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_658,axiom,
( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP41(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_659,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP42(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_660,axiom,
( sP43(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP45(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_663,axiom,
( sP46(Eq_y_0)
| ~ sP46(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_664,axiom,
( sP47(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2)
| 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,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP48(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_666,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_667,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_668,axiom,
( sP51(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP51(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_669,axiom,
( sP52(Eq_y_0,Eq_y_1)
| ~ sP52(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_670,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_671,axiom,
( sP54(Eq_y_0,Eq_y_1)
| ~ sP54(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,
( 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_673,axiom,
( sP56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP56(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_674,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP57(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_675,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_676,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP59(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_677,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP60(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_678,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP61(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_679,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP62(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_680,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP63(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_681,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_682,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_683,axiom,
( sP66(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)
| ~ sP66(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_684,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP67(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_685,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP68(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_686,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP69(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_687,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_688,axiom,
( sP71(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)
| ~ sP71(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_689,axiom,
( sP72(Eq_y_0)
| ~ sP72(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_690,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_691,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_692,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_693,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_694,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_695,axiom,
( sP78(Eq_y_0)
| ~ sP78(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_696,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_697,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP80(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_698,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_699,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP82(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_700,axiom,
( sP83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP83(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_701,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_702,axiom,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP85(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_703,axiom,
( sP86(Eq_y_0)
| ~ sP86(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_704,axiom,
( sP87(Eq_y_0)
| ~ sP87(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_705,axiom,
( sP88(Eq_y_0,Eq_y_1)
| ~ sP88(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_706,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_707,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_708,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_709,axiom,
( sP92(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP92(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_710,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP93(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_711,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_712,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP95(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_713,axiom,
( sP96(Eq_y_0,Eq_y_1)
| ~ sP96(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_714,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP97(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_715,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP98(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_716,axiom,
( sP99(Eq_y_0)
| ~ sP99(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_717,axiom,
( sP100(Eq_y_0)
| ~ sP100(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_718,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_719,axiom,
( sP102(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP102(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_720,axiom,
( sP103(Eq_y_0,Eq_y_1)
| ~ sP103(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_721,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP104(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_722,axiom,
( sP105(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP105(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_723,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_724,axiom,
( sP107(Eq_y_0,Eq_y_1)
| ~ sP107(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_725,axiom,
( sP108(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP108(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_726,axiom,
( sP109(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP109(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_727,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_728,axiom,
( sP111(Eq_y_0)
| ~ sP111(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_729,axiom,
( sP112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP112(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_730,axiom,
( sP113(Eq_y_0,Eq_y_1)
| ~ sP113(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_731,axiom,
( sP114(Eq_y_0,Eq_y_1)
| ~ sP114(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_732,axiom,
( sP115(Eq_y_0,Eq_y_1)
| ~ sP115(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_733,axiom,
( sP116(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_734,axiom,
( sP117(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_735,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_736,axiom,
( sP119(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_737,axiom,
( sP120(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_738,axiom,
( sP121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP121(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_739,axiom,
( sP122(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP122(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_740,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP123(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_741,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_742,axiom,
( sP125(Eq_y_0,Eq_y_1)
| ~ sP125(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_743,axiom,
( sP126(Eq_y_0,Eq_y_1)
| ~ sP126(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_744,axiom,
( sP127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP127(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_745,axiom,
( sP128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP128(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_746,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_747,axiom,
( sP130(Eq_y_0,Eq_y_1)
| ~ sP130(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_748,axiom,
( sP131(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP131(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_749,axiom,
( sP132(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_750,axiom,
( sP133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP133(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_751,axiom,
( sP134(Eq_y_0,Eq_y_1)
| ~ sP134(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_752,axiom,
( sP135(Eq_y_0)
| ~ sP135(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_753,axiom,
( sP136(Eq_y_0,Eq_y_1)
| ~ sP136(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_754,axiom,
( sP137(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP137(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_755,axiom,
( sP138(Eq_y_0)
| ~ sP138(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_756,axiom,
( sP139(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP139(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_757,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_758,axiom,
( sP141(Eq_y_0,Eq_y_1)
| ~ sP141(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_759,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_760,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_761,axiom,
( sP144(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_762,axiom,
( sP145(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP145(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_763,axiom,
( sP146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_764,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_765,axiom,
( sP148(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP148(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_766,axiom,
( sP149(Eq_y_0,Eq_y_1)
| ~ sP149(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_767,axiom,
( sP150(Eq_y_0,Eq_y_1)
| ~ sP150(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_768,axiom,
( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_769,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_770,axiom,
( sP153(Eq_y_0,Eq_y_1)
| ~ sP153(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_771,axiom,
( sP154(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_772,axiom,
( sP155(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP155(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_773,axiom,
( sP156(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP156(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_774,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_775,axiom,
( sP158(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_776,axiom,
( sP159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP159(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_777,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP160(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_778,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_779,axiom,
( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_780,axiom,
( sP163(Eq_y_0,Eq_y_1)
| ~ sP163(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_781,axiom,
( sP164(Eq_y_0,Eq_y_1)
| ~ sP164(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_782,axiom,
( sP165(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP165(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_783,axiom,
( sP166(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP166(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_784,axiom,
( sP167(Eq_y_0)
| ~ sP167(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_785,axiom,
( sP168(Eq_y_0,Eq_y_1)
| ~ sP168(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_786,axiom,
( sP169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP169(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_787,axiom,
( sP170(Eq_y_0,Eq_y_1)
| ~ sP170(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_788,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_789,axiom,
( sP172(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP172(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_790,axiom,
( sP173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP173(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_791,axiom,
( sP174(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP174(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_792,axiom,
( sP175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP175(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_793,axiom,
( sP176(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP176(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_794,axiom,
( sP177(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP177(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_795,axiom,
( sP178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP178(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_796,axiom,
( sP179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_797,axiom,
( sP180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP180(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_798,axiom,
( sP181(Eq_y_0)
| ~ sP181(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_799,axiom,
( sP182(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP182(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_800,axiom,
( sP183(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP183(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_801,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_802,axiom,
( sP185(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP185(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_803,axiom,
( sP186(Eq_y_0,Eq_y_1)
| ~ sP186(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_804,axiom,
( sP187(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP187(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_805,axiom,
( sP188(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP188(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_806,axiom,
( sP189(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP189(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_807,axiom,
( sP190(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP190(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_808,axiom,
( sP191(Eq_y_0,Eq_y_1)
| ~ sP191(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_809,axiom,
( sP192(Eq_y_0)
| ~ sP192(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_810,axiom,
( sP193(Eq_y_0)
| ~ sP193(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_811,axiom,
( sP194(Eq_y_0,Eq_y_1)
| ~ sP194(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_812,axiom,
( sP195(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP195(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_813,axiom,
( sP196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP196(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_814,axiom,
( sP197(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP197(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_815,axiom,
( sP198(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP198(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_816,axiom,
( sP199(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP199(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_817,axiom,
( sP200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP200(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_818,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_819,axiom,
( sP202(Eq_y_0,Eq_y_1)
| ~ sP202(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_820,axiom,
( sP203(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP203(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_821,axiom,
( sP204(Eq_y_0)
| ~ sP204(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_822,axiom,
( sP205(Eq_y_0,Eq_y_1)
| ~ sP205(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_823,axiom,
( sP206(Eq_y_0)
| ~ sP206(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_824,axiom,
( sP207(Eq_y_0,Eq_y_1)
| ~ sP207(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_825,axiom,
( sP208(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP208(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_826,axiom,
( sP209(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP209(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_827,axiom,
( sP210(Eq_y_0,Eq_y_1)
| ~ sP210(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_828,axiom,
( sP211(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP211(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_829,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_830,axiom,
( sP213(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP213(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_831,axiom,
( sP214(Eq_y_0)
| ~ sP214(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_832,axiom,
( sP215(Eq_y_0,Eq_y_1)
| ~ sP215(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_833,axiom,
( sP216(Eq_y_0,Eq_y_1)
| ~ sP216(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_834,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_835,axiom,
( sP218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP218(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_836,axiom,
( sP219(Eq_y_0,Eq_y_1)
| ~ sP219(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_837,axiom,
( sP220(Eq_y_0,Eq_y_1)
| ~ sP220(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_838,axiom,
( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP221(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_839,axiom,
( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP222(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_840,axiom,
( sP223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP223(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_841,axiom,
( sP224(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP224(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_842,axiom,
( sP225(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_843,axiom,
( sP226(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP226(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_844,axiom,
( sP227(Eq_y_0)
| ~ sP227(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_845,axiom,
( sP228(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_846,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_847,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_848,axiom,
( sP231(Eq_y_0)
| ~ sP231(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_849,axiom,
( sP232(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP232(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_850,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_851,axiom,
( sP234(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP234(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_852,axiom,
( sP235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP235(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_853,axiom,
( sP236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_854,axiom,
( sP237(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_855,axiom,
( sP238(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)
| ~ sP238(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_856,axiom,
( sP239(Eq_y_0,Eq_y_1)
| ~ sP239(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_857,axiom,
( sP240(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP240(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_858,axiom,
( sP241(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP241(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_859,axiom,
( sP242(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP242(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_860,axiom,
( sP243(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP243(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_861,axiom,
( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_862,axiom,
( sP245(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP245(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_863,axiom,
( sP246(Eq_y_0,Eq_y_1)
| ~ sP246(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_864,axiom,
( sP247(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP247(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_865,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_866,axiom,
( sP249(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP249(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_867,axiom,
( sP250(Eq_y_0)
| ~ sP250(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_868,axiom,
( sP251(Eq_y_0,Eq_y_1)
| ~ sP251(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_869,axiom,
( sP252(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP252(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_870,axiom,
( sP253(Eq_y_0)
| ~ sP253(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_871,axiom,
( sP254(Eq_y_0)
| ~ sP254(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_872,axiom,
( sP255(Eq_y_0)
| ~ sP255(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_873,axiom,
( sP256(Eq_y_0)
| ~ sP256(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_874,axiom,
( sP257(Eq_y_0,Eq_y_1)
| ~ sP257(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_875,axiom,
( sP258(Eq_y_0)
| ~ sP258(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_876,axiom,
( sP259(Eq_y_0)
| ~ sP259(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_877,axiom,
( sP260(Eq_y_0)
| ~ sP260(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_878,axiom,
( sP261(Eq_y_0,Eq_y_1)
| ~ sP261(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_879,axiom,
( sP262(Eq_y_0)
| ~ sP262(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_880,axiom,
( sP263(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP263(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_881,axiom,
( sP264(Eq_y_0,Eq_y_1)
| ~ sP264(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_882,axiom,
( sP265(Eq_y_0,Eq_y_1)
| ~ sP265(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_883,axiom,
( sP266(Eq_y_0)
| ~ sP266(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_884,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_885,axiom,
( sP268(Eq_y_0)
| ~ sP268(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_886,axiom,
( sP269(Eq_y_0)
| ~ sP269(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_887,axiom,
( sP270(Eq_y_0)
| ~ sP270(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_888,axiom,
( sP271(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP271(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_889,axiom,
( sP272(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP272(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_890,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_891,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_892,axiom,
( sP275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP275(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_893,axiom,
( sP276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP276(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_894,axiom,
( sP277(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP277(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_895,axiom,
( sP278(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_896,axiom,
( sP279(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP279(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_897,axiom,
( sP280(Eq_y_0)
| ~ sP280(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_898,axiom,
( sP281(Eq_y_0)
| ~ sP281(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_899,axiom,
( sP282(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP282(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_900,axiom,
( sP283(Eq_y_0,Eq_y_1)
| ~ sP283(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_901,axiom,
( sP284(Eq_y_0)
| ~ sP284(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_902,axiom,
( sP285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP285(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_903,axiom,
( sP286(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP286(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_904,axiom,
( sP287(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP287(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_905,axiom,
( sP288(Eq_y_0)
| ~ sP288(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_906,axiom,
( sP289(Eq_y_0)
| ~ sP289(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_907,axiom,
( sP290(Eq_y_0)
| ~ sP290(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_908,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_909,axiom,
( sP292(Eq_y_0)
| ~ sP292(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_910,axiom,
( sP293(Eq_y_0)
| ~ sP293(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_911,axiom,
( sP294(Eq_y_0)
| ~ sP294(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_912,axiom,
( sP295(Eq_y_0,Eq_y_1)
| ~ sP295(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_913,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_914,axiom,
( sP297(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP297(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_915,axiom,
( sP298(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP298(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_916,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_917,axiom,
( sP300(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP300(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_918,axiom,
( sP301(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP301(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_919,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_920,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_921,axiom,
( sP304(Eq_y_0)
| ~ sP304(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_922,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_923,axiom,
( sP306(Eq_y_0)
| ~ sP306(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_924,axiom,
( sP307(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP307(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_925,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_926,axiom,
( sP309(Eq_y_0)
| ~ sP309(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_927,axiom,
( sP310(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP310(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_928,axiom,
( sP311(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP311(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_929,axiom,
( sP312(Eq_y_0)
| ~ sP312(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_930,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_931,axiom,
( sP314(Eq_y_0,Eq_y_1)
| ~ sP314(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_932,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_933,axiom,
( sP316(Eq_y_0,Eq_y_1)
| ~ sP316(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_934,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_935,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_936,axiom,
( sP319(Eq_y_0)
| ~ sP319(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_937,axiom,
( sP320(Eq_y_0)
| ~ sP320(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_938,axiom,
( sP321(Eq_y_0)
| ~ sP321(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_939,axiom,
( sP322(Eq_y_0)
| ~ sP322(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_940,axiom,
( sP323(Eq_y_0)
| ~ sP323(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_941,axiom,
( sP324(Eq_y_0)
| ~ sP324(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_942,axiom,
( sP325(Eq_y_0)
| ~ sP325(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_943,axiom,
( sP326(Eq_y_0)
| ~ sP326(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_944,axiom,
( sP327(Eq_y_0,Eq_y_1)
| ~ sP327(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_945,axiom,
( sP328(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP328(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_946,axiom,
( sP329(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP329(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_947,axiom,
( sP330(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP330(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_948,axiom,
( sP331(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP331(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_949,axiom,
( sP332(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP332(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_950,axiom,
( sP333(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP333(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_951,axiom,
( sP334(Eq_y_0)
| ~ sP334(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_952,axiom,
( sP335(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP335(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_953,axiom,
( sP336(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP336(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_954,axiom,
( sP337(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP337(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_955,axiom,
( sP338(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP338(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_956,axiom,
( sP339(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP339(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_957,axiom,
( sP340(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP340(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_958,axiom,
( sP341(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP341(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_959,axiom,
( sP342(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP342(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_960,axiom,
( sP343(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP343(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_961,axiom,
( sP344(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP344(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_962,axiom,
( sP345(Eq_y_0,Eq_y_1)
| ~ sP345(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_963,axiom,
( sP346(Eq_y_0)
| ~ sP346(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_964,axiom,
( sP347(Eq_y_0)
| ~ sP347(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_965,axiom,
( sP348(Eq_y_0,Eq_y_1)
| ~ sP348(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_966,axiom,
( sP349(Eq_y_0)
| ~ sP349(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_967,axiom,
( sP350(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP350(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_968,axiom,
( sP351(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP351(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_969,axiom,
( sP352(Eq_y_0)
| ~ sP352(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_970,axiom,
( sP353(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP353(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_971,axiom,
( sP354(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP354(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_972,axiom,
( sP355(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP355(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_973,axiom,
( sP356(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP356(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_974,axiom,
( sP357(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP357(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_975,axiom,
( sP358(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP358(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_976,axiom,
( sP359(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP359(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_977,axiom,
( sP360(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP360(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_978,axiom,
( sP361(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP361(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_979,axiom,
( sP362(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP362(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_980,axiom,
( sP363(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP363(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_981,axiom,
( sP364(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)
| ~ sP364(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_982,axiom,
( sP365(Eq_y_0)
| ~ sP365(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_983,axiom,
( sP366(Eq_y_0,Eq_y_1)
| ~ sP366(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_984,axiom,
( sP367(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP367(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_985,axiom,
( sP368(Eq_y_0)
| ~ sP368(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_986,axiom,
( sP369(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP369(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_987,axiom,
( sP370(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP370(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_988,axiom,
( sP371(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP371(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_989,axiom,
( sP372(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP372(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_990,axiom,
( sP373(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP373(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_991,axiom,
( sP374(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP374(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_992,axiom,
( sP375(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP375(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_993,axiom,
( sP376(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP376(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_994,axiom,
( sP377(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP377(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_995,axiom,
( sP378(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP378(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_996,axiom,
( sP379(Eq_y_0,Eq_y_1)
| ~ sP379(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_997,axiom,
( sP380(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP380(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_998,axiom,
( sP381(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP381(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_999,axiom,
( sP382(Eq_y_0,Eq_y_1)
| ~ sP382(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1000,axiom,
( sP383(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP383(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1001,axiom,
( sP384(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP384(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_1002,axiom,
( sP385(Eq_y_0,Eq_y_1)
| ~ sP385(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1003,axiom,
( sP386(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP386(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1004,axiom,
( sP387(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP387(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_1005,axiom,
( sP388(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP388(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_1006,axiom,
( sP389(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP389(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_1007,axiom,
( sP390(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP390(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_1008,axiom,
( sP391(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP391(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_1009,axiom,
( sP392(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP392(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_1010,axiom,
( sP393(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP393(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_1011,axiom,
( sP394(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP394(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_1012,axiom,
( sP395(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)
| ~ sP395(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_1013,axiom,
( sP396(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP396(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_1014,axiom,
( sP397(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP397(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_1015,axiom,
( sP398(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP398(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_1016,axiom,
( sP399(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP399(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_1017,axiom,
( sP400(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP400(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_1018,axiom,
( sP401(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP401(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_1019,axiom,
( sP402(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP402(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_1020,axiom,
( sP403(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)
| ~ sP403(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_1021,axiom,
( sP404(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP404(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1022,axiom,
( sP405(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP405(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_1023,axiom,
( sP406(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP406(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_1024,axiom,
( sP408(Eq_y_0,Eq_y_1)
| ~ sP408(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1025,axiom,
( sP409(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP409(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_1026,axiom,
( sP410(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP410(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1027,axiom,
( sP411(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP411(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_1028,axiom,
( sP412(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP412(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_1029,axiom,
( sP413(Eq_y_0,Eq_y_1)
| ~ sP413(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1030,axiom,
( sP414(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP414(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1031,axiom,
( sP415(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP415(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_1032,axiom,
( sP416(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP416(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_1033,axiom,
( sP417(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP417(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_1034,axiom,
( sP418(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)
| ~ sP418(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_1035,axiom,
( sP419(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP419(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1036,axiom,
( sP420(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP420(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_1037,axiom,
( sP421(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP421(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_1038,axiom,
( sP422(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP422(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_1039,axiom,
( sP423(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP423(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_1040,axiom,
( sP424(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP424(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_1041,axiom,
( sP425(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP425(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1042,axiom,
( sP426(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP426(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_1043,axiom,
( sP427(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP427(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1044,axiom,
( sP428(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP428(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_1045,axiom,
( sP429(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP429(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1046,axiom,
( sP430(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP430(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_1047,axiom,
( sP431(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP431(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_1048,axiom,
( sP432(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP432(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_1049,axiom,
( sP433(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP433(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_1050,axiom,
( sP434(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP434(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_1051,axiom,
( sP435(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP435(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_1052,axiom,
( sP436(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP436(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_1053,axiom,
( sP437(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP437(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_1054,axiom,
( sP438(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP438(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_1055,axiom,
( sP439(Eq_y_0,Eq_y_1)
| ~ sP439(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1056,axiom,
( sP440(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP440(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1057,axiom,
( sP441(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP441(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_1058,axiom,
( sP442(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP442(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1059,axiom,
( sP443(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP443(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_1060,axiom,
( sP444(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP444(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_1061,axiom,
( sP445(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP445(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_1062,axiom,
( sP446(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP446(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_1063,axiom,
( sP447(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP447(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_1064,axiom,
( sP448(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP448(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_1065,axiom,
( sP449(Eq_y_0)
| ~ sP449(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1066,axiom,
( sP450(Eq_y_0,Eq_y_1)
| ~ sP450(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1067,axiom,
( sP451(Eq_y_0,Eq_y_1)
| ~ sP451(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1068,axiom,
( sP452(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP452(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_1069,axiom,
( sP453(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP453(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1070,axiom,
( sP454(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP454(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_1071,axiom,
( sP455(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP455(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_1072,axiom,
( sP456(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP456(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1073,axiom,
( sP457(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP457(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_1074,axiom,
( sP458(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP458(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1075,axiom,
( sP459(Eq_y_0)
| ~ sP459(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1076,axiom,
( sP460(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP460(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_1077,axiom,
( sP461(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP461(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1078,axiom,
( sP462(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP462(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1079,axiom,
( sP463(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP463(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_1080,axiom,
( sP464(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP464(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_1081,axiom,
( sP465(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP465(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1082,axiom,
( sP466(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP466(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1083,axiom,
( sP467(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP467(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_1084,axiom,
( sP468(Eq_y_0,Eq_y_1)
| ~ sP468(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1085,axiom,
( sP469(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP469(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1086,axiom,
( sP470(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP470(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1087,axiom,
( sP471(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP471(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_1088,axiom,
( sP472(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP472(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1089,axiom,
( sP473(Eq_y_0)
| ~ sP473(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1090,axiom,
( sP474(Eq_y_0,Eq_y_1)
| ~ sP474(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1091,axiom,
( sP475(Eq_y_0,Eq_y_1)
| ~ sP475(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1092,axiom,
( sP476(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP476(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1093,axiom,
( sP477(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP477(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_1094,axiom,
( sP478(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP478(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1095,axiom,
( sP479(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP479(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_1096,axiom,
( sP480(Eq_y_0,Eq_y_1)
| ~ sP480(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1097,axiom,
( sP481(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP481(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1098,axiom,
( sP482(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP482(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1099,axiom,
( sP483(Eq_y_0,Eq_y_1)
| ~ sP483(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1100,axiom,
( sP484(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP484(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1101,axiom,
( sP485(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP485(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1102,axiom,
( sP486(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP486(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1103,axiom,
( sP487(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP487(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1104,axiom,
( sP488(Eq_y_0,Eq_y_1)
| ~ sP488(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1105,axiom,
( sP489(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP489(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1106,axiom,
( sP490(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP490(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1107,axiom,
( sP491(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP491(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_1108,axiom,
( sP492(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP492(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_1109,axiom,
( sP493(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP493(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_1110,axiom,
( sP494(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP494(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_1111,axiom,
( sP495(Eq_y_0,Eq_y_1)
| ~ sP495(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1112,axiom,
( sP496(Eq_y_0,Eq_y_1)
| ~ sP496(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1113,axiom,
( sP497(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP497(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1114,axiom,
( sP498(Eq_y_0)
| ~ sP498(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1115,axiom,
( sP499(Eq_y_0,Eq_y_1)
| ~ sP499(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1116,axiom,
( sP500(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP500(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1117,axiom,
( sP501(Eq_y_0,Eq_y_1)
| ~ sP501(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1118,axiom,
( sP502(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP502(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1119,axiom,
( sP503(Eq_y_0,Eq_y_1)
| ~ sP503(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1120,axiom,
( sP504(Eq_y_0,Eq_y_1)
| ~ sP504(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1121,axiom,
( sP505(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP505(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1122,axiom,
( sP506(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP506(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1123,axiom,
( sP507(Eq_y_0,Eq_y_1)
| ~ sP507(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1124,axiom,
( sP508(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP508(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1125,axiom,
( sP509(Eq_y_0)
| ~ sP509(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1126,axiom,
( sP510(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP510(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1127,axiom,
( sP511(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP511(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1128,axiom,
( sP512(Eq_y_0,Eq_y_1)
| ~ sP512(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1129,axiom,
( sP513(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP513(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_1130,axiom,
( sP514(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP514(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1131,axiom,
( sP515(Eq_y_0,Eq_y_1)
| ~ sP515(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1132,axiom,
( sP516(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP516(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1133,axiom,
( sP517(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP517(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_1134,axiom,
( sP518(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP518(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1135,axiom,
( sP519(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP519(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_1136,axiom,
( sP520(Eq_y_0)
| ~ sP520(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1137,axiom,
( sP521(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP521(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1138,axiom,
( sP522(Eq_y_0,Eq_y_1)
| ~ sP522(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1139,axiom,
( sP523(Eq_y_0,Eq_y_1)
| ~ sP523(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1140,axiom,
( sP524(Eq_y_0)
| ~ sP524(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1141,axiom,
( sP525(Eq_y_0,Eq_y_1)
| ~ sP525(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1142,axiom,
( sP526(Eq_y_0)
| ~ sP526(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1143,axiom,
( sP527(Eq_y_0,Eq_y_1)
| ~ sP527(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1144,axiom,
( sP528(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP528(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1145,axiom,
( sP529(Eq_y_0,Eq_y_1)
| ~ sP529(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1146,axiom,
( sP530(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP530(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1147,axiom,
( sP531(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP531(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_1148,axiom,
( sP532(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP532(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_1149,axiom,
( sP533(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP533(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_1150,axiom,
( sP534(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP534(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1151,axiom,
( sP535(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP535(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1152,axiom,
( sP536(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP536(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1153,axiom,
( sP537(Eq_y_0)
| ~ sP537(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1154,axiom,
( sP538(Eq_y_0,Eq_y_1)
| ~ sP538(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1155,axiom,
( sP539(Eq_y_0,Eq_y_1)
| ~ sP539(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1156,axiom,
( sP540(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP540(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1157,axiom,
( sP541(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP541(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_1158,axiom,
( sP542(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP542(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_1159,axiom,
( sP543(Eq_y_0,Eq_y_1)
| ~ sP543(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1160,axiom,
( sP544(Eq_y_0,Eq_y_1)
| ~ sP544(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1161,axiom,
( sP545(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP545(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_1162,axiom,
( sP546(Eq_y_0)
| ~ sP546(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1163,axiom,
( sP547(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP547(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_1164,axiom,
( sP548(Eq_y_0,Eq_y_1)
| ~ sP548(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1165,axiom,
( sP549(Eq_y_0,Eq_y_1)
| ~ sP549(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1166,axiom,
( sP550(Eq_y_0)
| ~ sP550(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1167,axiom,
( sP551(Eq_y_0)
| ~ sP551(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1168,axiom,
( sP552(Eq_y_0)
| ~ sP552(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1169,axiom,
( sP553(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP553(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_1170,axiom,
( sP554(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP554(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1171,axiom,
( sP555(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP555(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_1172,axiom,
( sP556(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP556(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_1173,axiom,
( sP557(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP557(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_1174,axiom,
( sP558(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP558(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1175,axiom,
( sP559(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP559(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1176,axiom,
( sP560(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP560(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1177,axiom,
( sP561(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP561(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1178,axiom,
( sP562(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP562(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1179,axiom,
( sP563(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP563(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1180,axiom,
( sP564(Eq_y_0)
| ~ sP564(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1181,axiom,
( sP565(Eq_y_0,Eq_y_1)
| ~ sP565(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1182,axiom,
( sP566(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP566(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_1183,axiom,
( sP567(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP567(Eq_x_0,Eq_x_1,Eq_x_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
% 0.00/0.02 % Problem : SEU355+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 20 00:02:44 UTC 2026
% 0.02/0.36 % CPUTime :
% 249.64/250.02 % SZS status Theorem for theBenchmark
% 249.64/250.02 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------